Finite Group Databasebeta

← C3×#10594755 #13174352

Subgroups — C3×#10594755 #13174352

Order 1728.

1290 conjugacy classes of subgroups.

The subgroup lattice has 1286 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64320C211yesmaximal, characteristic, complemented
2C3×#64314C211yesmaximal, characteristic, complemented
3C3×#64123C211yesmaximal, characteristic, complemented
4C32×#916C211yesmaximal, characteristic, complemented
5C32×#914C211yesmaximal, characteristic, complemented
6C3×#63950C211yesmaximal, characteristic, complemented
7C3×#63949C211yesmaximal, characteristic, complemented
8C3×#63939C211yesmaximal, characteristic, complemented
9C3×#63926C211yesmaximal, characteristic, complemented
10C3×#63925C211yesmaximal, characteristic, complemented
11C3×D3×#213C211yesmaximal, characteristic, complemented
12C3×#63804C211yesmaximal, characteristic, complemented
13C3×#63798C211yesmaximal, characteristic, complemented
14C3×#63794C211yesmaximal, characteristic, complemented
15C3×D3×D24C211yesmaximal, characteristic, complemented
16C3×#5774—31nomaximal
17C3×#5769—31nomaximal
18#10594755C311yesmaximal, characteristic, direct product factor
19C3×#3832C2211yescharacteristic, complemented
20C3×D4×C3⋊D3C2211yescharacteristic, complemented
21C32×#239C2211yescharacteristic, complemented
22C32×#239C2211yescharacteristic, complemented
23C32×#237C2211yescharacteristic, complemented
24C32×D3×D4C2211yescharacteristic, complemented
25C3×#3811—21no—
26C3×D3×#67—21no—
27C2×C3×#626—21no—
28C3×#3804—21no—
29C3×#3802—21no—
30C3×#3802C2211yescharacteristic, complemented
31C3×D3×D12—21no—
32C3×D3×D12—21no—
33C3×D3×D12C2211yescharacteristic, complemented
34C3×D3×D12C2211yescharacteristic, complemented
35C3×D3×D12C2211yescharacteristic, complemented
36C3×#3799C2211yescharacteristic, complemented
37C3×#3798—21no—
38C3×#3798C2211yescharacteristic
39C3×#3796C2211yescharacteristic, complemented
40C33×SD16C2211yescharacteristic, complemented
41C3×#3755C2211yescharacteristic, complemented
42C3×#3753C2211yescharacteristic, complemented
43C3×#3745C2211yescharacteristic, complemented
44C3×#3743C2211yescharacteristic, complemented
45C32×#216C2211yescharacteristic, complemented
46C32×#215C2211yescharacteristic, complemented
47C32×#213C2211yescharacteristic, complemented
48C32×#213C2211yescharacteristic, complemented
49C32×D24C2211yescharacteristic, complemented
50C32×#204C2211yescharacteristic, complemented
51C32×ΓL(1,𝔽25)C2211yescharacteristic, complemented
52C32×D3×C8C2211yescharacteristic, complemented
53C3×#3717C2211yescharacteristic, complemented
54C3×#3715C2211yescharacteristic, complemented
55C3×#3714C2211yescharacteristic, complemented
56C3×#3714C2211yescharacteristic, complemented
57C3×#3714C2211yescharacteristic, complemented
58C3×#3713C2211yescharacteristic, complemented
59C3×#3711C2211yescharacteristic, complemented
60C3×#3710C2211yescharacteristic, complemented
61C3×D3×C3⋊C8C2211yescharacteristic, complemented
62C3×#1009—31no—
63C3×#1009—31no—
64C3×#1009—31no—
65C3×#1004—31no—
66#64320C2×C311yescharacteristic, complemented
67#64314C2×C311yescharacteristic, complemented
68C32×AGL(1,ℤ/8)—31no—
69C32×#135—31no—
70#64123C2×C311yescharacteristic, complemented
71C3×#950—31no—
72C3×#949—31no—
73C3×#949—31no—
74C2×C3×#213—31no—
75C3×#919—31no—
76C3×#919—31no—
77C3×#916—21no—
78C3×#916—31no—
79C3×#916D311yescharacteristic, complemented
80C3×#916C2×C311yescharacteristic, complemented
81C3×#914—21no—
82C3×#914—31no—
83C3×#914—31no—
84C3×#914—31no—
85C3×#914—31no—
86C3×#914—31no—
87C3×#914—61no—
88C3×#914D311yescharacteristic, complemented
89C3×#914C2×C311yescharacteristic, complemented
90C3×#911—31no—
91C3×#911—31no—
92C3×D3×D8—31no—
93C3×D3×D8—31no—
94C3×D3×D8—31no—
95C3×D3×D8—31no—
96C3×#908—31no—
97C3×#907—31no—
98C2×C3×D24—31no—
99C3×#901—31no—
100#63950C2×C311yescharacteristic, complemented
101#63949C2×C311yescharacteristic, complemented
102#63939C2×C311yescharacteristic, complemented
103#63926C2×C311yescharacteristic, complemented
104#63925C2×C311yescharacteristic, complemented
105D3×#213C2×C311yescharacteristic, complemented
106#63804C2×C311yescharacteristic, complemented
107#63798C2×C311yescharacteristic, complemented
108#63794C2×C311yescharacteristic, complemented
109D3×D24C2×C311yescharacteristic, complemented
110C22×C3×C3⋊D3—21no—
111C22×C32×D3—21no—
112C2×C3×D32—21no—
113C2×C3×D32—21no—
114C2×C3×D32—21no—
115C2×C3×D32—21no—
116C33×Q8C2311yescharacteristic
117C33×D4C2311yescharacteristic
118C3×#638—21no—
119C3×C4⋊(C3⋊D3)—21no—
120C3×C4⋊(C3⋊D3)C2311yescharacteristic
121C3×C4⋊(C3⋊D3)C2311yescharacteristic
122C3×C4×C3⋊D3—21no—
123C3×C4×C3⋊D3C2311yescharacteristic
124C32×#67—21no—
125C32×#67—21no—
126C2×C32×Dic3—21no—
127C32×D12—21no—
128C32×D12—21no—
129C32×D12C2311yescharacteristic
130C32×D12C2311yescharacteristic
131C32×D12C2311yescharacteristic
132C32×C4×D3—21no—
133C32×C4×D3—21no—
134C32×C4×D3C2311yescharacteristic
135C32×C4×D3C2311yescharacteristic
136C32×Dic6C2311yescharacteristic
137C3×#627D411yescharacteristic
138C3×#626—21no—
139C3×#626—21no—
140C3×#626—21no—
141C3×#626—21no—
142C3×#626—21no—
143C3×#626D411yescharacteristic
144C3×#626D411yescharacteristic
145C3×#625—21no—
146C3×#625D411yescharacteristic
147C3×#624—21no—
148C3×D3×Dic3—21no—
149C33×C8C2311yescharacteristic
150C3×C3⋊(C3⋊C8)C2311yescharacteristic
151C32×C3⋊C8C2311yescharacteristic
152C32×C3⋊C8C2311yescharacteristic
153C3×#576—91no—
154#5774—31no—
155#5769—31no—
156C32×#41—31no—
157C32×#41—31no—
158C32×#41—31no—
159C2×C32×D4—31no—
160#3832C22×C311yescharacteristic, complemented
161D4×C3⋊D3C22×C311yescharacteristic, complemented
162C2×C3×#67—61no—
163C2×C3×#67—61no—
164C3×#239—21no—
165C3×#239—21no—
166C3×#239—31no—
167C3×#239—31no—
168C3×#239—31no—
169C3×#239—31no—
170C3×#239—61no—
171C3×#239C2×D311yescharacteristic, complemented
172C3×#239C2×D311yescharacteristic, complemented
173C3×#239C22×C311yescharacteristic, complemented
174C3×#239C22×C311yescharacteristic, complemented
175C3×#237—21no—
176C3×#237—31no—
177C3×#237—61no—
178C3×#237C2×D311yescharacteristic, complemented
179C3×#237C22×C311yescharacteristic, complemented
180C3×D3×D4—21no—
181C3×D3×D4—31no—
182C3×D3×D4—31no—
183C3×D3×D4—31no—
184C3×D3×D4—31no—
185C3×D3×D4—31no—
186C3×D3×D4—31no—
187C3×D3×D4—31no—
188C3×D3×D4—61no—
189C3×D3×D4—61no—
190C3×D3×D4—61no—
191C3×D3×D4—61no—
192C3×D3×D4—61no—
193C3×D3×D4—61no—
194C3×D3×D4—61no—
195C3×D3×D4—61no—
196C3×D3×D4C2×D311yescharacteristic, complemented
197C3×D3×D4C22×C311yescharacteristic, complemented
198C3×#235—31no—
199C3×#235—31no—
200C3×#235—31no—
201C3×#235—61no—
202C3×#235—61no—
203C3×#235—61no—
204C2×C3×D12—31no—
205C2×C3×D12—31no—
206C2×C3×D12—31no—
207C2×C3×D12—61no—
208C2×C3×D12—61no—
209C2×C3×D12—61no—
210#3811—21no—
211D3×#67—21no—
212C2×#626—21no—
213#3804—21no—
214#3802—21no—
215#3802C22×C311yescharacteristic, complemented
216D3×D12—21no—
217D3×D12—21no—
218D3×D12C22×C311yescharacteristic, complemented
219D3×D12C22×C311yescharacteristic, complemented
220D3×D12C22×C311yescharacteristic, complemented
221#3799C22×C311yescharacteristic, complemented
222#3798—21no—
223#3798C22×C311yescharacteristic
224#3796C22×C311yescharacteristic, complemented
225C32×Q16—31no—
226C32×SD16—21no—
227C32×SD16—21no—
228C32×SD16—21no—
229C32×SD16—31no—
230C32×SD16—31no—
231C32×SD16—41no—
232C32×SD16C2×D311yescharacteristic, complemented
233C32×SD16C2×D311yescharacteristic, complemented
234C32×SD16C22×C311yescharacteristic, complemented
235C32×D8—31no—
236C32×D8—31no—
237C32×D8—31no—
238C32×M16—31no—
239C2×C32×C8—31no—
240#3755C22×C311yescharacteristic, complemented
241#3753C22×C311yescharacteristic, complemented
242#3745C22×C311yescharacteristic, complemented
243#3743C22×C311yescharacteristic, complemented
244C3×#216—21no—
245C3×#216C2×D311yescharacteristic, complemented
246C3×#216C22×C311yescharacteristic, complemented
247C3×#215—21no—
248C3×#215—31no—
249C3×#215—31no—
250C3×#215—31no—
251C3×#215—31no—
252C3×#215—61no—
253C3×#215C2×D311yescharacteristic, complemented
254C3×#215C22×C311yescharacteristic, complemented
255C3×#214—31no—
256C3×#213—21no—
257C3×#213—21no—
258C3×#213—31no—
259C3×#213—31no—
260C3×#213—31no—
261C3×#213—31no—
262C3×#213—31no—
263C3×#213—31no—
264C3×#213—31no—
265C3×#213—61no—
266C3×#213C2×D311yescharacteristic, complemented
267C3×#213C2×D311yescharacteristic, complemented
268C3×#213C22×C311yescharacteristic, complemented
269C3×#213C22×C311yescharacteristic, complemented
270C3×#208—31no—
271C2×C3×C3⋊C8—31no—
272C3×D24—21no—
273C3×D24—31no—
274C3×D24—31no—
275C3×D24—31no—
276C3×D24—31no—
277C3×D24—31no—
278C3×D24—61no—
279C3×D24C2×D311yescharacteristic, complemented
280C3×D24C22×C311yescharacteristic, complemented
281C3×#204—21no—
282C3×#204—31no—
283C3×#204C2×D311yescharacteristic, complemented
284C3×#204C22×C311yescharacteristic, complemented
285C3×ΓL(1,𝔽25)—21no—
286C3×ΓL(1,𝔽25)—31no—
287C3×ΓL(1,𝔽25)—31no—
288C3×ΓL(1,𝔽25)—31no—
289C3×ΓL(1,𝔽25)—61no—
290C3×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
291C3×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
292C3×D3×C8—21no—
293C3×D3×C8—31no—
294C3×D3×C8—31no—
295C3×D3×C8—31no—
296C3×D3×C8C2×D311yescharacteristic, complemented
297C3×D3×C8C22×C311yescharacteristic, complemented
298#3717C22×C311yescharacteristic, complemented
299#3715C22×C311yescharacteristic, complemented
300#3714C22×C311yescharacteristic, complemented
301#3714C22×C311yescharacteristic, complemented
302#3714C22×C311yescharacteristic, complemented
303#3713C22×C311yescharacteristic, complemented
304#3711C22×C311yescharacteristic, complemented
305#3710C22×C311yescharacteristic, complemented
306D3×C3⋊C8C22×C311yescharacteristic, complemented
307C22×C33—21no—
308C2×C3×C3⋊D3—21no—
309C2×C3×C3⋊D3—21no—
310C2×C3×C3⋊D3—81no—
311C2×C3×C3⋊D3C2×D411yescharacteristic
312C2×C32×D3—21no—
313C2×C32×D3—21no—
314C2×C32×D3—21no—
315C2×C32×D3—81no—
316C2×C32×D3C2×D411yescharacteristic
317C2×C32×D3C2×D411yescharacteristic
318C3×D32—81no—
319C3×D32—81no—
320C3×D32—81no—
321C3×D32—81no—
322C33×C4—21no—
323C33×C4C2411yescharacteristic
324C3×C3⋊Dic3C2×D411yescharacteristic
325C32×Dic3—21no—
326C32×Dic3C2×D411yescharacteristic
327C32×Dic3C2×D411yescharacteristic
328C3×H(5,𝔽2)—91no—
329C3×H(5,𝔽2)—91no—
330#1009—31no—
331#1009—31no—
332#1009—31no—
333#1004—31no—
334C3×AGL(1,ℤ/8)—31no—
335C3×AGL(1,ℤ/8)—31no—
336C3×AGL(1,ℤ/8)—61no—
337C3×AGL(1,ℤ/8)—91no—
338C3×AGL(1,ℤ/8)—91no—
339C3×AGL(1,ℤ/8)—91no—
340C3×AGL(1,ℤ/8)—91no—
341C3×AGL(1,ℤ/8)—91no—
342C3×#135—31no—
343C3×#135—31no—
344C3×#135—61no—
345C3×#135—91no—
346C3×#135—91no—
347C2×C3×D8—91no—
348C2×C3×D8—91no—
349C2×C3×D8—91no—
350C3×#131—91no—
351#950—31no—
352#949—31no—
353#949—31no—
354C2×#213—31no—
355#919—31no—
356#919—31no—
357#916—31no—
358#916C3×D311yescharacteristic, complemented
359#914—31no—
360#914—31no—
361#914—31no—
362#914—31no—
363#914—31no—
364#914—61no—
365#914C3×D311yescharacteristic, complemented
366#911—31no—
367#911—31no—
368D3×D8—31no—
369D3×D8—31no—
370D3×D8—31no—
371D3×D8—31no—
372#908—31no—
373#907—31no—
374C2×D24—31no—
375#901—31no—
376C23×C32—61no—
377C22×C3⋊D3—21no—
378C22×C3×D3—21no—
379C22×C3×D3—21no—
380C22×C3×D3—41no—
381C22×C3×D3—61no—
382C22×C3×D3—61no—
383C22×C3×D3—61no—
384C22×C3×D3—61no—
385C22×C3×D3—61no—
386C22×C3×D3—61no—
387C22×C3×D3—61no—
388C22×C3×D3—61no—
389C22×C3×D3—61no—
390C22×C3×D3—61no—
391C22×C3×D3—121no—
392C2×D32—21no—
393C2×D32—21no—
394C2×D32—21no—
395C2×D32—21no—
396C32×Q8—21no—
397C32×Q8—21no—
398C32×Q8—21no—
399C32×Q8—31no—
400C32×Q8—41no—
401C32×Q8C22×D311yescharacteristic
402C32×Q8C22×D311yescharacteristic
403C32×Q8C23×C311yescharacteristic
404C32×D4—21no—
405C32×D4—21no—
406C32×D4—21no—
407C32×D4—31no—
408C32×D4—31no—
409C32×D4—31no—
410C32×D4—41no—
411C32×D4—61no—
412C32×D4—61no—
413C32×D4—61no—
414C32×D4—61no—
415C32×D4C22×D311yescharacteristic
416C32×D4C22×D311yescharacteristic
417C32×D4C23×C311yescharacteristic
418C2×C32×C4—31no—
419C2×C32×C4—31no—
420C2×C32×C4—61no—
421C2×C32×C4—61no—
422C2×C32×C4—61no—
423#638—21no—
424C4⋊(C3⋊D3)—21no—
425C4⋊(C3⋊D3)C23×C311yescharacteristic
426C4⋊(C3⋊D3)C23×C311yescharacteristic
427C4×C3⋊D3—21no—
428C4×C3⋊D3C23×C311yescharacteristic
429C3×#67—21no—
430C3×#67—21no—
431C3×#67—21no—
432C3×#67—21no—
433C3×#67—31no—
434C3×#67—31no—
435C3×#67—31no—
436C3×#67—31no—
437C3×#67—41no—
438C3×#67—41no—
439C3×#67—61no—
440C3×#67—61no—
441C3×#67—61no—
442C3×#67—61no—
443C3×#67—61no—
444C3×#67—61no—
445C3×#67—61no—
446C3×#67—61no—
447C3×#67—61no—
448C3×#67—121no—
449C2×C3×Dic3—21no—
450C2×C3×Dic3—21no—
451C2×C3×Dic3—41no—
452C2×C3×Dic3—61no—
453C3×D12—21no—
454C3×D12—21no—
455C3×D12—21no—
456C3×D12—21no—
457C3×D12—21no—
458C3×D12—21no—
459C3×D12—21no—
460C3×D12—31no—
461C3×D12—31no—
462C3×D12—31no—
463C3×D12—31no—
464C3×D12—31no—
465C3×D12—31no—
466C3×D12—41no—
467C3×D12—41no—
468C3×D12—61no—
469C3×D12—61no—
470C3×D12—61no—
471C3×D12—61no—
472C3×D12—61no—
473C3×D12—61no—
474C3×D12—61no—
475C3×D12—61no—
476C3×D12—61no—
477C3×D12—121no—
478C3×D12C22×D311yescharacteristic
479C3×D12C22×D311yescharacteristic
480C3×D12C22×D311yescharacteristic
481C3×D12C23×C311yescharacteristic
482C3×D12C23×C311yescharacteristic
483C3×D12C23×C311yescharacteristic
484C3×C4×D3—21no—
485C3×C4×D3—21no—
486C3×C4×D3—21no—
487C3×C4×D3—21no—
488C3×C4×D3—21no—
489C3×C4×D3—21no—
490C3×C4×D3—31no—
491C3×C4×D3—31no—
492C3×C4×D3—41no—
493C3×C4×D3—41no—
494C3×C4×D3—61no—
495C3×C4×D3—61no—
496C3×C4×D3—61no—
497C3×C4×D3—61no—
498C3×C4×D3—61no—
499C3×C4×D3—61no—
500C3×C4×D3—121no—
501C3×C4×D3C22×D311yescharacteristic
502C3×C4×D3C22×D311yescharacteristic
503C3×C4×D3C23×C311yescharacteristic
504C3×C4×D3C23×C311yescharacteristic
505C3×Dic6—21no—
506C3×Dic6—31no—
507C3×Dic6—31no—
508C3×Dic6C22×D311yescharacteristic
509C3×Dic6C23×C311yescharacteristic
510#627C3×D411yescharacteristic
511#626—21no—
512#626—21no—
513#626—21no—
514#626—21no—
515#626—21no—
516#626C3×D411yescharacteristic
517#626C3×D411yescharacteristic
518#625—21no—
519#625C3×D411yescharacteristic
520#624—21no—
521D3×Dic3—21no—
522C32×C8—21no—
523C32×C8—21no—
524C32×C8—21no—
525C32×C8—31no—
526C32×C8—31no—
527C32×C8—41no—
528C32×C8C22×D311yescharacteristic
529C32×C8C22×D311yescharacteristic
530C32×C8C23×C311yescharacteristic
531C3⋊(C3⋊C8)C23×C311yescharacteristic
532C3×C3⋊C8—21no—
533C3×C3⋊C8—21no—
534C3×C3⋊C8—31no—
535C3×C3⋊C8—31no—
536C3×C3⋊C8—61no—
537C3×C3⋊C8C22×D311yescharacteristic
538C3×C3⋊C8C22×D311yescharacteristic
539C3×C3⋊C8C23×C311yescharacteristic
540C3×C3⋊C8C23×C311yescharacteristic
541#576—91noSylow
542C2×C33—41no—
543C2×C33C22×D411yescharacteristic
544C3×C3⋊D3—21no—
545C3×C3⋊D3—41no—
546C3×C3⋊D3—41no—
547C32×D3—21no—
548C32×D3—21no—
549C32×D3—41no—
550C32×D3—41no—
551C32×D3—41no—
552C3×#41—31no—
553C3×#41—31no—
554C3×#41—31no—
555C3×#41—31no—
556C3×#41—31no—
557C3×#41—31no—
558C3×#41—61no—
559C3×#41—61no—
560C3×#41—61no—
561C3×#41—91no—
562C3×#41—91no—
563C3×#41—91no—
564C3×#41—91no—
565C3×#41—181no—
566C3×#41—181no—
567C2×C3×D4—31no—
568C2×C3×D4—31no—
569C2×C3×D4—61no—
570C2×C3×D4—91no—
571C2×C3×D4—91no—
572C2×C3×D4—91no—
573C2×C3×D4—91no—
574C2×C3×D4—91no—
575C2×C3×D4—181no—
576C2×C3×D4—181no—
577C2×C3×D4—181no—
578C2×C3×D4—181no—
579C2×C3×D4—181no—
580C2×C3×D4—181no—
581C2×#67—61no—
582C2×#67—61no—
583#239—31no—
584#239—31no—
585#239—31no—
586#239—31no—
587#239—61no—
588#239C2×C3×D311yescharacteristic, complemented
589#239C2×C3×D311yescharacteristic, complemented
590#237—31no—
591#237—61no—
592#237C2×C3×D311yescharacteristic, complemented
593D3×D4—31no—
594D3×D4—31no—
595D3×D4—31no—
596D3×D4—31no—
597D3×D4—31no—
598D3×D4—31no—
599D3×D4—31no—
600D3×D4—61no—
601D3×D4—61no—
602D3×D4—61no—
603D3×D4—61no—
604D3×D4—61no—
605D3×D4—61no—
606D3×D4—61no—
607D3×D4—61no—
608D3×D4C2×C3×D311yescharacteristic, complemented
609#235—31no—
610#235—31no—
611#235—31no—
612#235—61no—
613#235—61no—
614#235—61no—
615C2×D12—31no—
616C2×D12—31no—
617C2×D12—31no—
618C2×D12—61no—
619C2×D12—61no—
620C2×D12—61no—
621C3×Q16—31no—
622C3×Q16—31no—
623C3×Q16—61no—
624C3×SD16—21no—
625C3×SD16—21no—
626C3×SD16—21no—
627C3×SD16—31no—
628C3×SD16—31no—
629C3×SD16—31no—
630C3×SD16—31no—
631C3×SD16—41no—
632C3×SD16—61no—
633C3×SD16—61no—
634C3×SD16—91no—
635C3×SD16—91no—
636C3×SD16—91no—
637C3×SD16D3211yescharacteristic, complemented
638C3×SD16C2×C3×D311yescharacteristic, complemented
639C3×SD16C2×C3×D311yescharacteristic, complemented
640C3×D8—31no—
641C3×D8—31no—
642C3×D8—31no—
643C3×D8—31no—
644C3×D8—31no—
645C3×D8—31no—
646C3×D8—61no—
647C3×D8—61no—
648C3×D8—61no—
649C3×D8—91no—
650C3×D8—91no—
651C3×D8—91no—
652C3×D8—91no—
653C3×D8—91no—
654C3×D8—91no—
655C3×M16—31no—
656C3×M16—31no—
657C3×M16—61no—
658C3×M16—91no—
659C3×M16—91no—
660C2×C3×C8—31no—
661C2×C3×C8—31no—
662C2×C3×C8—61no—
663C2×C3×C8—91no—
664C2×C3×C8—91no—
665#216C2×C3×D311yescharacteristic, complemented
666#215—31no—
667#215—31no—
668#215—31no—
669#215—31no—
670#215—61no—
671#215C2×C3×D311yescharacteristic, complemented
672#214—31no—
673#213—31no—
674#213—31no—
675#213—31no—
676#213—31no—
677#213—31no—
678#213—31no—
679#213—31no—
680#213—61no—
681#213C2×C3×D311yescharacteristic, complemented
682#213C2×C3×D311yescharacteristic, complemented
683#208—31no—
684C2×C3⋊C8—31no—
685D24—31no—
686D24—31no—
687D24—31no—
688D24—31no—
689D24—31no—
690D24—61no—
691D24C2×C3×D311yescharacteristic, complemented
692#204—31no—
693#204C2×C3×D311yescharacteristic, complemented
694ΓL(1,𝔽25)—31no—
695ΓL(1,𝔽25)—31no—
696ΓL(1,𝔽25)—31no—
697ΓL(1,𝔽25)—61no—
698ΓL(1,𝔽25)C2×C3×D311yescharacteristic, complemented
699D3×C8—31no—
700D3×C8—31no—
701D3×C8—31no—
702D3×C8C2×C3×D311yescharacteristic, complemented
703C22×C32—21no—
704C22×C32—21no—
705C22×C32—21no—
706C22×C32—31no—
707C22×C32—31no—
708C22×C32—41no—
709C22×C32—41no—
710C22×C32—41no—
711C22×C32—61no—
712C22×C32—61no—
713C22×C32—61no—
714C22×C32—81no—
715C22×C32—241no—
716C2×C3⋊D3—21no—
717C2×C3⋊D3—21no—
718C2×C3⋊D3—81no—
719C2×C3⋊D3C2×C3×D411yescharacteristic
720C2×C3×D3—21no—
721C2×C3×D3—21no—
722C2×C3×D3—21no—
723C2×C3×D3—21no—
724C2×C3×D3—21no—
725C2×C3×D3—21no—
726C2×C3×D3—21no—
727C2×C3×D3—21no—
728C2×C3×D3—31no—
729C2×C3×D3—31no—
730C2×C3×D3—41no—
731C2×C3×D3—41no—
732C2×C3×D3—41no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—61no—
738C2×C3×D3—81no—
739C2×C3×D3—81no—
740C2×C3×D3—82no—
741C2×C3×D3—121no—
742C2×C3×D3—121no—
743C2×C3×D3—241no—
744C2×C3×D3—241no—
745C2×C3×D3—241no—
746C2×C3×D3—241no—
747C2×C3×D3—241no—
748C2×C3×D3—241no—
749C2×C3×D3—241no—
750C2×C3×D3—241no—
751C2×C3×D3—241no—
752C2×C3×D3—241no—
753C2×C3×D3—242no—
754C2×C3×D3D3×D411yescharacteristic
755C2×C3×D3D3×D411yescharacteristic
756C2×C3×D3C2×C3×D411yescharacteristic
757C2×C3×D3C2×C3×D411yescharacteristic
758D32—81no—
759D32—81no—
760D32—81no—
761D32—81no—
762C32×C4—21no—
763C32×C4—21no—
764C32×C4—21no—
765C32×C4—21no—
766C32×C4—21no—
767C32×C4—21no—
768C32×C4—31no—
769C32×C4—31no—
770C32×C4—41no—
771C32×C4—41no—
772C32×C4—41no—
773C32×C4—41no—
774C32×C4—61no—
775C32×C4—81no—
776C32×C4C23×D311yescharacteristic
777C32×C4C23×D311yescharacteristic
778C32×C4C24×C311yescharacteristic
779C3⋊Dic3C2×C3×D411yescharacteristic
780C3×Dic3—21no—
781C3×Dic3—21no—
782C3×Dic3—21no—
783C3×Dic3—21no—
784C3×Dic3—31no—
785C3×Dic3—31no—
786C3×Dic3—41no—
787C3×Dic3—61no—
788C3×Dic3D3×D411yescharacteristic
789C3×Dic3D3×D411yescharacteristic
790C3×Dic3C2×C3×D411yescharacteristic
791C3×Dic3C2×C3×D411yescharacteristic
792H(5,𝔽2)—91no—
793H(5,𝔽2)—91no—
794AGL(1,ℤ/8)—31no—
795AGL(1,ℤ/8)—91no—
796AGL(1,ℤ/8)—91no—
797AGL(1,ℤ/8)—91no—
798AGL(1,ℤ/8)—91no—
799AGL(1,ℤ/8)—91no—
800#135—31no—
801#135—91no—
802#135—91no—
803C2×D8—91no—
804C2×D8—91no—
805C2×D8—91no—
806#131—91no—
807C33#57611yescharacteristic, complemented, Sylow
808C23×C3—61no—
809C23×C3—61no—
810C23×C3—121no—
811C23×C3—181no—
812C23×C3—181no—
813C23×C3—181no—
814C23×C3—181no—
815C23×C3—181no—
816C22×D3—21no—
817C22×D3—61no—
818C22×D3—61no—
819C22×D3—61no—
820C22×D3—61no—
821C22×D3—61no—
822C22×D3—61no—
823C22×D3—61no—
824C22×D3—61no—
825C22×D3—61no—
826C22×D3—61no—
827C22×D3—121no—
828C3×Q8—21no—
829C3×Q8—21no—
830C3×Q8—21no—
831C3×Q8—31no—
832C3×Q8—31no—
833C3×Q8—41no—
834C3×Q8—61no—
835C3×Q8—91no—
836C3×Q8C2×D3211yescharacteristic
837C3×Q8C22×C3×D311yescharacteristic
838C3×Q8C22×C3×D311yescharacteristic
839C3×D4—21no—
840C3×D4—21no—
841C3×D4—21no—
842C3×D4—31no—
843C3×D4—31no—
844C3×D4—31no—
845C3×D4—31no—
846C3×D4—31no—
847C3×D4—31no—
848C3×D4—41no—
849C3×D4—61no—
850C3×D4—61no—
851C3×D4—61no—
852C3×D4—61no—
853C3×D4—61no—
854C3×D4—61no—
855C3×D4—61no—
856C3×D4—61no—
857C3×D4—61no—
858C3×D4—61no—
859C3×D4—61no—
860C3×D4—91no—
861C3×D4—91no—
862C3×D4—91no—
863C3×D4—91no—
864C3×D4—91no—
865C3×D4—121no—
866C3×D4—121no—
867C3×D4—121no—
868C3×D4—121no—
869C3×D4—181no—
870C3×D4—181no—
871C3×D4—181no—
872C3×D4—181no—
873C3×D4—181no—
874C3×D4—181no—
875C3×D4—181no—
876C3×D4—181no—
877C3×D4C2×D3211yescharacteristic
878C3×D4C22×C3×D311yescharacteristic
879C3×D4C22×C3×D311yescharacteristic
880C2×C3×C4—31no—
881C2×C3×C4—31no—
882C2×C3×C4—31no—
883C2×C3×C4—31no—
884C2×C3×C4—61no—
885C2×C3×C4—61no—
886C2×C3×C4—61no—
887C2×C3×C4—61no—
888C2×C3×C4—61no—
889C2×C3×C4—61no—
890C2×C3×C4—61no—
891C2×C3×C4—61no—
892C2×C3×C4—91no—
893C2×C3×C4—121no—
894C2×C3×C4—121no—
895C2×C3×C4—121no—
896C2×C3×C4—181no—
897C2×C3×C4—181no—
898C2×C3×C4—181no—
899#67—21no—
900#67—21no—
901#67—31no—
902#67—31no—
903#67—31no—
904#67—31no—
905#67—61no—
906#67—61no—
907#67—61no—
908#67—61no—
909#67—61no—
910#67—61no—
911#67—61no—
912#67—61no—
913#67—61no—
914#67—121no—
915C2×Dic3—21no—
916C2×Dic3—61no—
917D12—21no—
918D12—21no—
919D12—31no—
920D12—31no—
921D12—31no—
922D12—31no—
923D12—31no—
924D12—31no—
925D12—61no—
926D12—61no—
927D12—61no—
928D12—61no—
929D12—61no—
930D12—61no—
931D12—61no—
932D12—61no—
933D12—61no—
934D12—121no—
935D12C22×C3×D311yescharacteristic
936D12C22×C3×D311yescharacteristic
937D12C22×C3×D311yescharacteristic
938C4×D3—21no—
939C4×D3—21no—
940C4×D3—31no—
941C4×D3—31no—
942C4×D3—61no—
943C4×D3—61no—
944C4×D3—61no—
945C4×D3—61no—
946C4×D3—61no—
947C4×D3—61no—
948C4×D3—121no—
949C4×D3C22×C3×D311yescharacteristic
950C4×D3C22×C3×D311yescharacteristic
951Dic6—31no—
952Dic6—31no—
953Dic6C22×C3×D311yescharacteristic
954C3×C8—21no—
955C3×C8—21no—
956C3×C8—21no—
957C3×C8—31no—
958C3×C8—31no—
959C3×C8—31no—
960C3×C8—31no—
961C3×C8—41no—
962C3×C8—61no—
963C3×C8—61no—
964C3×C8—91no—
965C3×C8C2×D3211yescharacteristic
966C3×C8C22×C3×D311yescharacteristic
967C3×C8C22×C3×D311yescharacteristic
968C3⋊C8—31no—
969C3⋊C8—31no—
970C3⋊C8—61no—
971C3⋊C8C22×C3×D311yescharacteristic
972C3⋊C8C22×C3×D311yescharacteristic
973C2×C32—21no—
974C2×C32—21no—
975C2×C32—21no—
976C2×C32—41no—
977C2×C32—41no—
978C2×C32—41no—
979C2×C32—41no—
980C2×C32—61no—
981C2×C32—61no—
982C2×C32—81no—
983C2×C32—81no—
984C2×C32—81no—
985C2×C32—121no—
986C2×C32—121no—
987C2×C32—121no—
988C2×C32—161no—
989C2×C32C2×D3×D411yescharacteristic
990C2×C32C2×D3×D411yescharacteristic
991C2×C32C22×C3×D411yescharacteristic
992C3⋊D3—21no—
993C3⋊D3—41no—
994C3⋊D3—41no—
995C3×D3—21no—
996C3×D3—21no—
997C3×D3—21no—
998C3×D3—21no—
999C3×D3—41no—
1000C3×D3—41no—
1001C3×D3—41no—
1002C3×D3—41no—
1003C3×D3—41no—
1004C3×D3—41no—
1005C3×D3—41no—
1006C3×D3—41no—
1007C3×D3—61no—
1008C3×D3—61no—
1009C3×D3—81no—
1010C3×D3—81no—
1011C3×D3—81no—
1012C3×D3—121no—
1013C3×D3—121no—
1014C3×D3—121no—
1015C3×D3—121no—
1016C3×D3—121no—
1017C3×D3—241no—
1018C3×D3—241no—
1019#41—31no—
1020#41—31no—
1021#41—31no—
1022#41—91no—
1023#41—91no—
1024#41—91no—
1025#41—91no—
1026#41—181no—
1027#41—181no—
1028C2×D4—31no—
1029C2×D4—91no—
1030C2×D4—91no—
1031C2×D4—91no—
1032C2×D4—91no—
1033C2×D4—91no—
1034C2×D4—181no—
1035C2×D4—181no—
1036C2×D4—181no—
1037C2×D4—181no—
1038C2×D4—181no—
1039C2×D4—181no—
1040Q16—31no—
1041SD16—31no—
1042SD16—31no—
1043SD16—91no—
1044SD16—91no—
1045SD16—91no—
1046SD16C3×D3211yescharacteristic, complemented
1047D8—31no—
1048D8—31no—
1049D8—31no—
1050D8—91no—
1051D8—91no—
1052D8—91no—
1053D8—91no—
1054D8—91no—
1055D8—91no—
1056M16—31no—
1057M16—91no—
1058M16—91no—
1059C2×C8—31no—
1060C2×C8—91no—
1061C2×C8—91no—
1062C22×C3—21no—
1063C22×C3—21no—
1064C22×C3—21no—
1065C22×C3—31no—
1066C22×C3—31no—
1067C22×C3—31no—
1068C22×C3—31no—
1069C22×C3—41no—
1070C22×C3—41no—
1071C22×C3—41no—
1072C22×C3—61no—
1073C22×C3—61no—
1074C22×C3—61no—
1075C22×C3—61no—
1076C22×C3—61no—
1077C22×C3—61no—
1078C22×C3—61no—
1079C22×C3—61no—
1080C22×C3—81no—
1081C22×C3—91no—
1082C22×C3—121no—
1083C22×C3—121no—
1084C22×C3—121no—
1085C22×C3—181no—
1086C22×C3—181no—
1087C22×C3—241no—
1088C22×C3—241no—
1089C22×C3—242no—
1090C22×C3—721no—
1091C22×C3—721no—
1092C22×C3—721no—
1093C22×C3—721no—
1094C22×C3—721no—
1095C2×D3—21no—
1096C2×D3—21no—
1097C2×D3—21no—
1098C2×D3—31no—
1099C2×D3—31no—
1100C2×D3—61no—
1101C2×D3—61no—
1102C2×D3—61no—
1103C2×D3—61no—
1104C2×D3—61no—
1105C2×D3—81no—
1106C2×D3—121no—
1107C2×D3—121no—
1108C2×D3—241no—
1109C2×D3—241no—
1110C2×D3—241no—
1111C2×D3—241no—
1112C2×D3—241no—
1113C2×D3—241no—
1114C2×D3—241no—
1115C2×D3—241no—
1116C2×D3—241no—
1117C2×D3—241no—
1118C2×D3—242no—
1119C2×D3C3×D3×D411yescharacteristic
1120C2×D3C3×D3×D411yescharacteristic
1121C3×C4—21no—
1122C3×C4—21no—
1123C3×C4—21no—
1124C3×C4—21no—
1125C3×C4—21no—
1126C3×C4—21no—
1127C3×C4—31no—
1128C3×C4—31no—
1129C3×C4—31no—
1130C3×C4—31no—
1131C3×C4—41no—
1132C3×C4—41no—
1133C3×C4—41no—
1134C3×C4—41no—
1135C3×C4—61no—
1136C3×C4—61no—
1137C3×C4—61no—
1138C3×C4—61no—
1139C3×C4—81no—
1140C3×C4—91no—
1141C3×C4—121no—
1142C3×C4C22×D3211yescharacteristic
1143C3×C4C23×C3×D311yescharacteristic
1144C3×C4C23×C3×D311yescharacteristic
1145Dic3—21no—
1146Dic3—31no—
1147Dic3—31no—
1148Dic3—61no—
1149Dic3C3×D3×D411yescharacteristic
1150Dic3C3×D3×D411yescharacteristic
1151C32—21no—
1152C32—21no—
1153C32—21no—
1154C32—41no—
1155C32#576911yescharacteristic, complemented
1156C32#577411yescharacteristic, complemented
1157C32C3×#57611yescharacteristic, complemented
1158C23—61no—
1159C23—181no—
1160C23—181no—
1161C23—181no—
1162C23—181no—
1163C23—181no—
1164Q8—31no—
1165Q8—91no—
1166Q8C2×C3×D3211yescharacteristic
1167D4—31no—
1168D4—31no—
1169D4—31no—
1170D4—61no—
1171D4—61no—
1172D4—61no—
1173D4—61no—
1174D4—91no—
1175D4—91no—
1176D4—91no—
1177D4—91no—
1178D4—91no—
1179D4—181no—
1180D4—181no—
1181D4—181no—
1182D4—181no—
1183D4—181no—
1184D4—181no—
1185D4—181no—
1186D4—181no—
1187D4C2×C3×D3211yescharacteristic
1188C2×C4—31no—
1189C2×C4—31no—
1190C2×C4—61no—
1191C2×C4—61no—
1192C2×C4—61no—
1193C2×C4—91no—
1194C2×C4—181no—
1195C2×C4—181no—
1196C2×C4—181no—
1197C8—31no—
1198C8—31no—
1199C8—91no—
1200C8C2×C3×D3211yescharacteristic
1201C2×C3—21no—
1202C2×C3—21no—
1203C2×C3—21no—
1204C2×C3—41no—
1205C2×C3—41no—
1206C2×C3—41no—
1207C2×C3—41no—
1208C2×C3—61no—
1209C2×C3—61no—
1210C2×C3—61no—
1211C2×C3—61no—
1212C2×C3—81no—
1213C2×C3—81no—
1214C2×C3—81no—
1215C2×C3—121no—
1216C2×C3—121no—
1217C2×C3—121no—
1218C2×C3—121no—
1219C2×C3—121no—
1220C2×C3—121no—
1221C2×C3—121no—
1222C2×C3—121no—
1223C2×C3—161no—
1224C2×C3—181no—
1225C2×C3—241no—
1226C2×C3—241no—
1227C2×C3—241no—
1228C2×C3—361no—
1229C2×C3—361no—
1230C2×C3D32×D411yescharacteristic
1231C2×C3C2×C3×D3×D411yescharacteristic
1232C2×C3C2×C3×D3×D411yescharacteristic
1233D3—21no—
1234D3—21no—
1235D3—41no—
1236D3—41no—
1237D3—41no—
1238D3—61no—
1239D3—61no—
1240D3—121no—
1241D3—121no—
1242D3—121no—
1243D3—121no—
1244D3—121no—
1245D3—241no—
1246D3—241no—
1247C22—21no—
1248C22—31no—
1249C22—31no—
1250C22—61no—
1251C22—61no—
1252C22—61no—
1253C22—91no—
1254C22—181no—
1255C22—181no—
1256C22—241no—
1257C22—721no—
1258C22—721no—
1259C22—721no—
1260C22—721no—
1261C22—721no—
1262C4—21no—
1263C4—31no—
1264C4—31no—
1265C4—61no—
1266C4—91no—
1267C4C22×C3×D3211yescharacteristic
1268C3—21no—
1269C3—21no—
1270C3—21no—
1271C3—41no—
1272C3#1059475511yescharacteristic, direct product factor
1273C3C3×#576911yescharacteristic, complemented
1274C3C3×#577411yescharacteristic, complemented
1275C2—41no—
1276C2—61no—
1277C2—61no—
1278C2—121no—
1279C2—121no—
1280C2—121no—
1281C2—181no—
1282C2—361no—
1283C2—361no—
1284C2C3×D32×D411yescharacteristic
subgroupG/H
centerC2×C3D32×D4
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×SD16C22
socleC2×C33C22×D4
hypercenterC3×SD16D32
hypocenterC32C3×#576
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C3 ◁ C3×C4 ◁ C3×SD16

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C3×#64320C2semidirect
2. C3×#64314C2semidirect
3. C3×#64123C2semidirect
4. C32×#916C2semidirect
5. C32×#914C2semidirect
6. C3×#63950C2semidirect
7. C3×#63949C2semidirect
8. C3×#63939C2semidirect
9. C3×#63926C2semidirect
10. C3×#63925C2semidirect
11. C3×D3×#213C2semidirect
12. C3×#63804C2semidirect
13. C3×#63798C2semidirect
14. C3×#63794C2semidirect
15. C3×D3×D24C2semidirect
18. #10594755C3direct (N × H)
19. C3×#3832C22semidirect
20. C3×D4×C3⋊D3C22semidirect
21. C32×#239C22semidirect
22. C32×#239C22semidirect
23. C32×#237C22semidirect
24. C32×D3×D4C22semidirect
30. C3×#3802C22semidirect
33. C3×D3×D12C22semidirect
34. C3×D3×D12C22semidirect
35. C3×D3×D12C22semidirect
36. C3×#3799C22semidirect
39. C3×#3796C22semidirect
40. C33×SD16C22semidirect
41. C3×#3755C22semidirect
42. C3×#3753C22semidirect
43. C3×#3745C22semidirect
44. C3×#3743C22semidirect
45. C32×#216C22semidirect
46. C32×#215C22semidirect
47. C32×#213C22semidirect
48. C32×#213C22semidirect
49. C32×D24C22semidirect
50. C32×#204C22semidirect
51. C32×ΓL(1,𝔽25)C22semidirect
52. C32×D3×C8C22semidirect
53. C3×#3717C22semidirect
54. C3×#3715C22semidirect
55. C3×#3714C22semidirect
56. C3×#3714C22semidirect
57. C3×#3714C22semidirect
58. C3×#3713C22semidirect
59. C3×#3711C22semidirect
60. C3×#3710C22semidirect
61. C3×D3×C3⋊C8C22semidirect
66. #64320C2×C3semidirect
67. #64314C2×C3semidirect
70. #64123C2×C3semidirect
79. C3×#916D3semidirect
80. C3×#916C2×C3semidirect
88. C3×#914D3semidirect
89. C3×#914C2×C3semidirect
100. #63950C2×C3semidirect
101. #63949C2×C3semidirect
102. #63939C2×C3semidirect
103. #63926C2×C3semidirect
104. #63925C2×C3semidirect
105. D3×#213C2×C3semidirect
106. #63804C2×C3semidirect
107. #63798C2×C3semidirect
108. #63794C2×C3semidirect
109. D3×D24C2×C3semidirect
160. #3832C22×C3semidirect
161. D4×C3⋊D3C22×C3semidirect
171. C3×#239C2×D3semidirect
172. C3×#239C2×D3semidirect
173. C3×#239C22×C3semidirect
174. C3×#239C22×C3semidirect
178. C3×#237C2×D3semidirect
179. C3×#237C22×C3semidirect
196. C3×D3×D4C2×D3semidirect
197. C3×D3×D4C22×C3semidirect
215. #3802C22×C3semidirect
218. D3×D12C22×C3semidirect
219. D3×D12C22×C3semidirect
220. D3×D12C22×C3semidirect
221. #3799C22×C3semidirect
224. #3796C22×C3semidirect
232. C32×SD16C2×D3semidirect
233. C32×SD16C2×D3semidirect
234. C32×SD16C22×C3semidirect
240. #3755C22×C3semidirect
241. #3753C22×C3semidirect
242. #3745C22×C3semidirect
243. #3743C22×C3semidirect
245. C3×#216C2×D3semidirect
246. C3×#216C22×C3semidirect
253. C3×#215C2×D3semidirect
254. C3×#215C22×C3semidirect
266. C3×#213C2×D3semidirect
267. C3×#213C2×D3semidirect
268. C3×#213C22×C3semidirect
269. C3×#213C22×C3semidirect
279. C3×D24C2×D3semidirect
280. C3×D24C22×C3semidirect
283. C3×#204C2×D3semidirect
284. C3×#204C22×C3semidirect
290. C3×ΓL(1,𝔽25)C2×D3semidirect
291. C3×ΓL(1,𝔽25)C22×C3semidirect
296. C3×D3×C8C2×D3semidirect
297. C3×D3×C8C22×C3semidirect
298. #3717C22×C3semidirect
299. #3715C22×C3semidirect
300. #3714C22×C3semidirect
301. #3714C22×C3semidirect
302. #3714C22×C3semidirect
303. #3713C22×C3semidirect
304. #3711C22×C3semidirect
305. #3710C22×C3semidirect
306. D3×C3⋊C8C22×C3semidirect
358. #916C3×D3semidirect
365. #914C3×D3semidirect
588. #239C2×C3×D3semidirect
589. #239C2×C3×D3semidirect
592. #237C2×C3×D3semidirect
608. D3×D4C2×C3×D3semidirect
637. C3×SD16D32semidirect
638. C3×SD16C2×C3×D3semidirect
639. C3×SD16C2×C3×D3semidirect
665. #216C2×C3×D3semidirect
671. #215C2×C3×D3semidirect
681. #213C2×C3×D3semidirect
682. #213C2×C3×D3semidirect
691. D24C2×C3×D3semidirect
693. #204C2×C3×D3semidirect
698. ΓL(1,𝔽25)C2×C3×D3semidirect
702. D3×C8C2×C3×D3semidirect
807. C33#576semidirect
1046. SD16C3×D32semidirect
1155. C32#5769semidirect
1156. C32#5774semidirect
1157. C32C3×#576semidirect
1272. C3#10594755direct (N × H)
1273. C3C3×#5769semidirect
1274. C3C3×#5774semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C3×#643202
C3×#643142
C3×#641232
C32×#9162
C32×#9142
C3×#639502
C3×#639492
C3×#639392
C3×#639262
C3×#639252
C3×D3×#2132
C3×#638042
C3×#637982
C3×#637942
C3×D3×D242
C3×#57743
C3×#57693
#105947553