Finite Group Databasebeta

← C3×#10594751 #13174348

Subgroups — C3×#10594751 #13174348

Order 1728.

1248 conjugacy classes of subgroups.

The subgroup lattice has 1242 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#64316C211yesmaximal, characteristic, complemented
2C3×#64314C211yesmaximal, characteristic, complemented
3C3×#64123C211yesmaximal, characteristic, complemented
4C32×#915C211yesmaximal, characteristic, complemented
5C32×D3×SD16C211yesmaximal, characteristic, complemented
6C3×#63950C211yesmaximal, characteristic, complemented
7C3×#63948C211yesmaximal, characteristic, complemented
8C3×D3×#215C211yesmaximal, characteristic, complemented
9C3×#63935C211yesmaximal, characteristic, complemented
10C3×#63934C211yesmaximal, characteristic, complemented
11C3×#63930C211yesmaximal, characteristic, complemented
12C3×#63811C211yesmaximal, characteristic, complemented
13C3×#63808C211yesmaximal, characteristic, complemented
14C3×#63804C211yesmaximal, characteristic, complemented
15C3×#63794C211yesmaximal, characteristic, complemented
16C3×#5778—31nomaximal
17C3×#5762—31nomaximal
18#10594751C311yesmaximal, characteristic, direct product factor
19C3×#3832C2211yescharacteristic, complemented
20C3×D4×C3⋊D3C2211yescharacteristic
21C32×D3×Q8C2211yescharacteristic, complemented
22C32×D3×Q8C2211yescharacteristic, complemented
23C32×#237C2211yescharacteristic
24C32×D3×D4C2211yescharacteristic
25C3×#3811—21no—
26C3×D3×#67—21no—
27C2×C3×#626—21no—
28C3×#3804—21no—
29C3×D3×D12C2211yescharacteristic
30C3×#3799—21no—
31C3×#3799—21no—
32C3×#3799C2211yescharacteristic
33C3×#3799C2211yescharacteristic, complemented
34C3×#3799C2211yescharacteristic, complemented
35C3×#3798—21no—
36C3×#3798C2211yescharacteristic
37C3×#3797—21no—
38C3×#3797C2211yescharacteristic, complemented
39C3×#3796C2211yescharacteristic
40C33×SD16C2211yescharacteristic, complemented
41C3×#3755C2211yescharacteristic, complemented
42C3×#3753C2211yescharacteristic, complemented
43C3×#3745C2211yescharacteristic, complemented
44C3×#3743C2211yescharacteristic, complemented
45C32×#216C2211yescharacteristic, complemented
46C32×#215C2211yescharacteristic, complemented
47C32×#214C2211yescharacteristic, complemented
48C32×#214C2211yescharacteristic, complemented
49C32×Dic12C2211yescharacteristic, complemented
50C32×#204C2211yescharacteristic, complemented
51C32×ΓL(1,𝔽25)C2211yescharacteristic, complemented
52C32×D3×C8C2211yescharacteristic, complemented
53C3×#3718C2211yescharacteristic, complemented
54C3×#3717C2211yescharacteristic, complemented
55C3×#3717C2211yescharacteristic, complemented
56C3×#3717C2211yescharacteristic, complemented
57C3×#3715C2211yescharacteristic, complemented
58C3×#3714C2211yescharacteristic, complemented
59C3×#3711C2211yescharacteristic, complemented
60C3×#3710C2211yescharacteristic, complemented
61C3×D3×C3⋊C8C2211yescharacteristic, complemented
62C3×#1009—31no—
63C3×#1007—31no—
64C3×#1007—31no—
65C3×#1004—31no—
66#64316C2×C311yescharacteristic, complemented
67#64314C2×C311yescharacteristic, complemented
68C32×#137—31no—
69C2×C32×SD16—31no—
70#64123C2×C311yescharacteristic, complemented
71C3×#950—31no—
72C3×#942—31no—
73C2×C3×#215—31no—
74C3×#932—31no—
75C3×#919—31no—
76C3×#919—31no—
77C3×#918—31no—
78C3×#918—31no—
79C3×#916—31no—
80C3×#916—31no—
81C3×#915—21no—
82C3×#915—31no—
83C3×#915D311yescharacteristic, complemented
84C3×#915C2×C311yescharacteristic, complemented
85C3×#914—31no—
86C3×#914—31no—
87C3×#914—31no—
88C3×#914—31no—
89C3×#914—61no—
90C3×D3×SD16—21no—
91C3×D3×SD16—31no—
92C3×D3×SD16—31no—
93C3×D3×SD16—31no—
94C3×D3×SD16D311yescharacteristic, complemented
95C3×D3×SD16C2×C311yescharacteristic, complemented
96C3×#908—31no—
97C3×#907—31no—
98C3×#904—31no—
99C3×#901—31no—
100#63950C2×C311yescharacteristic, complemented
101#63948C2×C311yescharacteristic, complemented
102D3×#215C2×C311yescharacteristic, complemented
103#63935C2×C311yescharacteristic, complemented
104#63934C2×C311yescharacteristic, complemented
105#63930C2×C311yescharacteristic, complemented
106#63811C2×C311yescharacteristic, complemented
107#63808C2×C311yescharacteristic, complemented
108#63804C2×C311yescharacteristic, complemented
109#63794C2×C311yescharacteristic, complemented
110C22×C3×C3⋊D3—21no—
111C22×C32×D3—21no—
112C2×C3×D32—21no—
113C33×Q8C2311yescharacteristic
114C33×D4C2311yescharacteristic
115C3×#638—21no—
116C3×C4⋊(C3⋊D3)—21no—
117C3×C4⋊(C3⋊D3)C2311yescharacteristic
118C3×C4⋊(C3⋊D3)C2311yescharacteristic
119C3×C4×C3⋊D3—21no—
120C3×C4×C3⋊D3C2311yescharacteristic
121C32×#67—21no—
122C32×#67—21no—
123C2×C32×Dic3—21no—
124C32×D12C2311yescharacteristic
125C32×C4×D3—21no—
126C32×C4×D3—21no—
127C32×C4×D3C2311yescharacteristic
128C32×C4×D3C2311yescharacteristic
129C32×Dic6—21no—
130C32×Dic6—21no—
131C32×Dic6C2311yescharacteristic
132C32×Dic6C2311yescharacteristic
133C32×Dic6C2311yescharacteristic
134C3×#627—21no—
135C3×#627D411yescharacteristic
136C3×#626—21no—
137C3×#626—21no—
138C3×#626—21no—
139C3×#626—21no—
140C3×#626—21no—
141C3×#626D411yescharacteristic
142C3×#626D411yescharacteristic
143C3×#625D411yescharacteristic
144C3×#624—21no—
145C3×#624—21no—
146C3×#624—21no—
147C3×#624—21no—
148C3×D3×Dic3—21no—
149C33×C8C2311yescharacteristic
150C3×C3⋊(C3⋊C8)C2311yescharacteristic
151C32×C3⋊C8C2311yescharacteristic
152C32×C3⋊C8C2311yescharacteristic
153C3×#577—91no—
154#5778—31no—
155#5762—31no—
156C32×#41—31no—
157C2×C32×Q8—31no—
158C2×C32×Q8—31no—
159C2×C32×D4—31no—
160#3832C22×C311yescharacteristic, complemented
161D4×C3⋊D3C22×C311yescharacteristic
162C2×C3×#67—61no—
163C2×C3×#67—61no—
164C3×#239—31no—
165C3×#239—31no—
166C3×#239—31no—
167C3×#239—31no—
168C3×#239—31no—
169C3×#239—31no—
170C3×#239—61no—
171C3×#239—61no—
172C3×#239—61no—
173C3×D3×Q8—21no—
174C3×D3×Q8—21no—
175C3×D3×Q8—31no—
176C3×D3×Q8—31no—
177C3×D3×Q8—61no—
178C3×D3×Q8—61no—
179C3×D3×Q8C2×D311yescharacteristic, complemented
180C3×D3×Q8C2×D311yescharacteristic, complemented
181C3×D3×Q8C22×C311yescharacteristic, complemented
182C3×D3×Q8C22×C311yescharacteristic, complemented
183C3×#237—21no—
184C3×#237—31no—
185C3×#237—61no—
186C3×#237C2×D311yescharacteristic
187C3×#237C22×C311yescharacteristic
188C3×D3×D4—21no—
189C3×D3×D4—31no—
190C3×D3×D4—31no—
191C3×D3×D4—31no—
192C3×D3×D4—61no—
193C3×D3×D4—61no—
194C3×D3×D4—61no—
195C3×D3×D4—61no—
196C3×D3×D4C2×D311yescharacteristic
197C3×D3×D4C22×C311yescharacteristic
198C3×#235—31no—
199C3×#235—31no—
200C3×#235—31no—
201C3×#235—31no—
202C3×#235—31no—
203C3×#235—61no—
204C3×#235—61no—
205C3×#235—61no—
206C3×#235—61no—
207C3×#235—61no—
208C2×C3×D12—31no—
209C2×C3×D12—61no—
210#3811—21no—
211D3×#67—21no—
212C2×#626—21no—
213#3804—21no—
214D3×D12C22×C311yescharacteristic
215#3799—21no—
216#3799—21no—
217#3799C22×C311yescharacteristic
218#3799C22×C311yescharacteristic, complemented
219#3799C22×C311yescharacteristic, complemented
220#3798—21no—
221#3798C22×C311yescharacteristic
222#3797—21no—
223#3797C22×C311yescharacteristic, complemented
224#3796C22×C311yescharacteristic
225C32×Q16—31no—
226C32×Q16—31no—
227C32×SD16—21no—
228C32×SD16—21no—
229C32×SD16—21no—
230C32×SD16—31no—
231C32×SD16—31no—
232C32×SD16—31no—
233C32×SD16—31no—
234C32×SD16—41no—
235C32×SD16C2×D311yescharacteristic, complemented
236C32×SD16C2×D311yescharacteristic, complemented
237C32×SD16C22×C311yescharacteristic, complemented
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×#216—31no—
246C3×#216—31no—
247C3×#216C2×D311yescharacteristic, complemented
248C3×#216C22×C311yescharacteristic, complemented
249C3×#215—21no—
250C3×#215—31no—
251C3×#215—31no—
252C3×#215—31no—
253C3×#215—31no—
254C3×#215—31no—
255C3×#215—31no—
256C3×#215—61no—
257C3×#215C2×D311yescharacteristic, complemented
258C3×#215C22×C311yescharacteristic, complemented
259C3×#214—21no—
260C3×#214—21no—
261C3×#214—31no—
262C3×#214C2×D311yescharacteristic, complemented
263C3×#214C2×D311yescharacteristic, complemented
264C3×#214C22×C311yescharacteristic, complemented
265C3×#214C22×C311yescharacteristic, complemented
266C3×#213—31no—
267C3×#213—31no—
268C3×#213—31no—
269C3×#213—61no—
270C3×#208—31no—
271C2×C3×C3⋊C8—31no—
272C3×Dic12—21no—
273C3×Dic12C2×D311yescharacteristic, complemented
274C3×Dic12C22×C311yescharacteristic, complemented
275C3×D24—31no—
276C3×D24—31no—
277C3×D24—31no—
278C3×D24—61no—
279C3×#204—21no—
280C3×#204—31no—
281C3×#204—31no—
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#3718C22×C311yescharacteristic, complemented
299#3717C22×C311yescharacteristic, complemented
300#3717C22×C311yescharacteristic, complemented
301#3717C22×C311yescharacteristic, complemented
302#3715C22×C311yescharacteristic, complemented
303#3714C22×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—81no—
314C2×C32×D3C2×D411yescharacteristic
315C2×C32×D3C2×D411yescharacteristic
316C3×D32—81no—
317C33×C4—21no—
318C33×C4C2411yescharacteristic
319C3×C3⋊Dic3C2×D411yescharacteristic
320C32×Dic3—21no—
321C32×Dic3—21no—
322C32×Dic3—21no—
323C32×Dic3C2×D411yescharacteristic
324C32×Dic3C2×D411yescharacteristic
325C3×2−1+4—91no—
326C3×H(5,𝔽2)—91no—
327#1009—31no—
328#1007—31no—
329#1007—31no—
330#1004—31no—
331C3×#137—31no—
332C3×#137—31no—
333C3×#137—61no—
334C3×#137—91no—
335C3×#137—91no—
336C3×AGL(1,ℤ/8)—91no—
337C3×AGL(1,ℤ/8)—91no—
338C3×AGL(1,ℤ/8)—91no—
339C3×#135—91no—
340C3×#135—91no—
341C3×#135—91no—
342C2×C3×SD16—31no—
343C2×C3×SD16—31no—
344C2×C3×SD16—61no—
345C2×C3×SD16—91no—
346C2×C3×SD16—91no—
347C3×#131—91no—
348#950—31no—
349#942—31no—
350C2×#215—31no—
351#932—31no—
352#919—31no—
353#919—31no—
354#918—31no—
355#918—31no—
356#916—31no—
357#916—31no—
358#915—31no—
359#915C3×D311yescharacteristic, complemented
360#914—31no—
361#914—31no—
362#914—31no—
363#914—31no—
364#914—61no—
365D3×SD16—31no—
366D3×SD16—31no—
367D3×SD16—31no—
368D3×SD16C3×D311yescharacteristic, complemented
369#908—31no—
370#907—31no—
371#904—31no—
372#901—31no—
373C23×C32—61no—
374C22×C3⋊D3—21no—
375C22×C3×D3—21no—
376C22×C3×D3—21no—
377C22×C3×D3—41no—
378C22×C3×D3—61no—
379C22×C3×D3—61no—
380C22×C3×D3—61no—
381C22×C3×D3—61no—
382C22×C3×D3—121no—
383C2×D32—21no—
384C32×Q8—21no—
385C32×Q8—21no—
386C32×Q8—21no—
387C32×Q8—31no—
388C32×Q8—31no—
389C32×Q8—31no—
390C32×Q8—41no—
391C32×Q8—61no—
392C32×Q8—61no—
393C32×Q8C22×D311yescharacteristic
394C32×Q8C22×D311yescharacteristic
395C32×Q8C23×C311yescharacteristic
396C32×D4—21no—
397C32×D4—21no—
398C32×D4—21no—
399C32×D4—31no—
400C32×D4—41no—
401C32×D4—61no—
402C32×D4—61no—
403C32×D4C22×D311yescharacteristic
404C32×D4C22×D311yescharacteristic
405C32×D4C23×C311yescharacteristic
406C2×C32×C4—31no—
407C2×C32×C4—31no—
408C2×C32×C4—61no—
409C2×C32×C4—61no—
410C2×C32×C4—61no—
411#638—21no—
412C4⋊(C3⋊D3)—21no—
413C4⋊(C3⋊D3)C23×C311yescharacteristic
414C4⋊(C3⋊D3)C23×C311yescharacteristic
415C4×C3⋊D3—21no—
416C4×C3⋊D3C23×C311yescharacteristic
417C3×#67—21no—
418C3×#67—21no—
419C3×#67—21no—
420C3×#67—21no—
421C3×#67—31no—
422C3×#67—31no—
423C3×#67—31no—
424C3×#67—31no—
425C3×#67—41no—
426C3×#67—41no—
427C3×#67—61no—
428C3×#67—61no—
429C3×#67—61no—
430C3×#67—61no—
431C3×#67—61no—
432C3×#67—61no—
433C3×#67—61no—
434C3×#67—121no—
435C2×C3×Dic3—21no—
436C2×C3×Dic3—21no—
437C2×C3×Dic3—41no—
438C2×C3×Dic3—61no—
439C3×D12—21no—
440C3×D12—31no—
441C3×D12—31no—
442C3×D12—31no—
443C3×D12—31no—
444C3×D12—31no—
445C3×D12—31no—
446C3×D12—61no—
447C3×D12—61no—
448C3×D12—61no—
449C3×D12—61no—
450C3×D12—61no—
451C3×D12—61no—
452C3×D12—61no—
453C3×D12—61no—
454C3×D12—61no—
455C3×D12—121no—
456C3×D12C22×D311yescharacteristic
457C3×D12C23×C311yescharacteristic
458C3×C4×D3—21no—
459C3×C4×D3—21no—
460C3×C4×D3—21no—
461C3×C4×D3—21no—
462C3×C4×D3—21no—
463C3×C4×D3—21no—
464C3×C4×D3—31no—
465C3×C4×D3—31no—
466C3×C4×D3—41no—
467C3×C4×D3—41no—
468C3×C4×D3—61no—
469C3×C4×D3—61no—
470C3×C4×D3—61no—
471C3×C4×D3—61no—
472C3×C4×D3—61no—
473C3×C4×D3—61no—
474C3×C4×D3—61no—
475C3×C4×D3—61no—
476C3×C4×D3—61no—
477C3×C4×D3—61no—
478C3×C4×D3—61no—
479C3×C4×D3—61no—
480C3×C4×D3—121no—
481C3×C4×D3C22×D311yescharacteristic
482C3×C4×D3C22×D311yescharacteristic
483C3×C4×D3C23×C311yescharacteristic
484C3×C4×D3C23×C311yescharacteristic
485C3×Dic6—21no—
486C3×Dic6—21no—
487C3×Dic6—21no—
488C3×Dic6—21no—
489C3×Dic6—21no—
490C3×Dic6—21no—
491C3×Dic6—21no—
492C3×Dic6—31no—
493C3×Dic6—31no—
494C3×Dic6—41no—
495C3×Dic6—41no—
496C3×Dic6—61no—
497C3×Dic6—61no—
498C3×Dic6C22×D311yescharacteristic
499C3×Dic6C22×D311yescharacteristic
500C3×Dic6C22×D311yescharacteristic
501C3×Dic6C23×C311yescharacteristic
502C3×Dic6C23×C311yescharacteristic
503C3×Dic6C23×C311yescharacteristic
504#627—21no—
505#627C3×D411yescharacteristic
506#626—21no—
507#626—21no—
508#626—21no—
509#626—21no—
510#626—21no—
511#626C3×D411yescharacteristic
512#626C3×D411yescharacteristic
513#625C3×D411yescharacteristic
514#624—21no—
515#624—21no—
516#624—21no—
517#624—21no—
518D3×Dic3—21no—
519C32×C8—21no—
520C32×C8—21no—
521C32×C8—21no—
522C32×C8—31no—
523C32×C8—31no—
524C32×C8—41no—
525C32×C8C22×D311yescharacteristic
526C32×C8C22×D311yescharacteristic
527C32×C8C23×C311yescharacteristic
528C3⋊(C3⋊C8)C23×C311yescharacteristic
529C3×C3⋊C8—21no—
530C3×C3⋊C8—21no—
531C3×C3⋊C8—31no—
532C3×C3⋊C8—31no—
533C3×C3⋊C8—61no—
534C3×C3⋊C8C22×D311yescharacteristic
535C3×C3⋊C8C22×D311yescharacteristic
536C3×C3⋊C8C23×C311yescharacteristic
537C3×C3⋊C8C23×C311yescharacteristic
538#577—91noSylow
539C2×C33—41no—
540C2×C33C22×D411yescharacteristic
541C3×C3⋊D3—21no—
542C3×C3⋊D3—41no—
543C3×C3⋊D3—41no—
544C32×D3—21no—
545C32×D3—21no—
546C32×D3—41no—
547C3×#41—31no—
548C3×#41—31no—
549C3×#41—61no—
550C3×#41—91no—
551C3×#41—91no—
552C3×#41—91no—
553C3×#41—91no—
554C3×#41—91no—
555C3×#41—91no—
556C3×#41—181no—
557C3×#41—181no—
558C3×#41—181no—
559C3×#41—181no—
560C2×C3×Q8—31no—
561C2×C3×Q8—31no—
562C2×C3×Q8—31no—
563C2×C3×Q8—31no—
564C2×C3×Q8—61no—
565C2×C3×Q8—61no—
566C2×C3×Q8—91no—
567C2×C3×Q8—181no—
568C2×C3×D4—31no—
569C2×C3×D4—31no—
570C2×C3×D4—61no—
571C2×C3×D4—91no—
572C2×C3×D4—91no—
573C2×C3×D4—181no—
574C2×C3×D4—181no—
575C2×C3×D4—181no—
576C2×#67—61no—
577C2×#67—61no—
578#239—31no—
579#239—31no—
580#239—31no—
581#239—31no—
582#239—31no—
583#239—31no—
584#239—61no—
585#239—61no—
586#239—61no—
587D3×Q8—31no—
588D3×Q8—31no—
589D3×Q8—61no—
590D3×Q8—61no—
591D3×Q8C2×C3×D311yescharacteristic, complemented
592D3×Q8C2×C3×D311yescharacteristic, complemented
593#237—31no—
594#237—61no—
595#237C2×C3×D311yescharacteristic
596D3×D4—31no—
597D3×D4—31no—
598D3×D4—31no—
599D3×D4—61no—
600D3×D4—61no—
601D3×D4—61no—
602D3×D4—61no—
603D3×D4C2×C3×D311yescharacteristic
604#235—31no—
605#235—31no—
606#235—31no—
607#235—31no—
608#235—31no—
609#235—61no—
610#235—61no—
611#235—61no—
612#235—61no—
613#235—61no—
614C2×D12—31no—
615C2×D12—61no—
616C3×Q16—31no—
617C3×Q16—31no—
618C3×Q16—31no—
619C3×Q16—31no—
620C3×Q16—61no—
621C3×Q16—61no—
622C3×Q16—91no—
623C3×SD16—21no—
624C3×SD16—21no—
625C3×SD16—21no—
626C3×SD16—31no—
627C3×SD16—31no—
628C3×SD16—31no—
629C3×SD16—31no—
630C3×SD16—31no—
631C3×SD16—31no—
632C3×SD16—31no—
633C3×SD16—31no—
634C3×SD16—41no—
635C3×SD16—61no—
636C3×SD16—61no—
637C3×SD16—61no—
638C3×SD16—61no—
639C3×SD16—91no—
640C3×SD16—91no—
641C3×SD16—91no—
642C3×SD16—91no—
643C3×SD16—91no—
644C3×SD16D3211yescharacteristic, complemented
645C3×SD16C2×C3×D311yescharacteristic, complemented
646C3×SD16C2×C3×D311yescharacteristic, complemented
647C3×D8—91no—
648C3×D8—91no—
649C3×D8—91no—
650C3×M16—31no—
651C3×M16—31no—
652C3×M16—61no—
653C3×M16—91no—
654C3×M16—91no—
655C2×C3×C8—31no—
656C2×C3×C8—31no—
657C2×C3×C8—61no—
658C2×C3×C8—91no—
659C2×C3×C8—91no—
660#216—31no—
661#216—31no—
662#216C2×C3×D311yescharacteristic, complemented
663#215—31no—
664#215—31no—
665#215—31no—
666#215—31no—
667#215—31no—
668#215—31no—
669#215—61no—
670#215C2×C3×D311yescharacteristic, complemented
671#214—31no—
672#214C2×C3×D311yescharacteristic, complemented
673#214C2×C3×D311yescharacteristic, complemented
674#213—31no—
675#213—31no—
676#213—31no—
677#213—61no—
678#208—31no—
679C2×C3⋊C8—31no—
680Dic12C2×C3×D311yescharacteristic, complemented
681D24—31no—
682D24—31no—
683D24—31no—
684D24—61no—
685#204—31no—
686#204—31no—
687#204—31no—
688#204C2×C3×D311yescharacteristic, complemented
689ΓL(1,𝔽25)—31no—
690ΓL(1,𝔽25)—31no—
691ΓL(1,𝔽25)—31no—
692ΓL(1,𝔽25)—61no—
693ΓL(1,𝔽25)C2×C3×D311yescharacteristic, complemented
694D3×C8—31no—
695D3×C8—31no—
696D3×C8—31no—
697D3×C8C2×C3×D311yescharacteristic, complemented
698C22×C32—21no—
699C22×C32—21no—
700C22×C32—21no—
701C22×C32—31no—
702C22×C32—31no—
703C22×C32—41no—
704C22×C32—41no—
705C22×C32—41no—
706C22×C32—61no—
707C22×C32—81no—
708C22×C32—241no—
709C2×C3⋊D3—21no—
710C2×C3⋊D3—21no—
711C2×C3⋊D3—81no—
712C2×C3⋊D3C2×C3×D411yescharacteristic
713C2×C3×D3—21no—
714C2×C3×D3—21no—
715C2×C3×D3—21no—
716C2×C3×D3—21no—
717C2×C3×D3—31no—
718C2×C3×D3—31no—
719C2×C3×D3—41no—
720C2×C3×D3—61no—
721C2×C3×D3—61no—
722C2×C3×D3—61no—
723C2×C3×D3—61no—
724C2×C3×D3—61no—
725C2×C3×D3—81no—
726C2×C3×D3—81no—
727C2×C3×D3—82no—
728C2×C3×D3—121no—
729C2×C3×D3—121no—
730C2×C3×D3—241no—
731C2×C3×D3—241no—
732C2×C3×D3—241no—
733C2×C3×D3—241no—
734C2×C3×D3—242no—
735C2×C3×D3D3×D411yescharacteristic
736C2×C3×D3D3×D411yescharacteristic
737C2×C3×D3C2×C3×D411yescharacteristic
738C2×C3×D3C2×C3×D411yescharacteristic
739D32—81no—
740C32×C4—21no—
741C32×C4—21no—
742C32×C4—21no—
743C32×C4—21no—
744C32×C4—21no—
745C32×C4—21no—
746C32×C4—31no—
747C32×C4—31no—
748C32×C4—41no—
749C32×C4—41no—
750C32×C4—41no—
751C32×C4—41no—
752C32×C4—61no—
753C32×C4—61no—
754C32×C4—61no—
755C32×C4—81no—
756C32×C4C23×D311yescharacteristic
757C32×C4C23×D311yescharacteristic
758C32×C4C24×C311yescharacteristic
759C3⋊Dic3C2×C3×D411yescharacteristic
760C3×Dic3—21no—
761C3×Dic3—21no—
762C3×Dic3—21no—
763C3×Dic3—21no—
764C3×Dic3—21no—
765C3×Dic3—21no—
766C3×Dic3—21no—
767C3×Dic3—21no—
768C3×Dic3—31no—
769C3×Dic3—31no—
770C3×Dic3—41no—
771C3×Dic3—41no—
772C3×Dic3—41no—
773C3×Dic3—61no—
774C3×Dic3D3×D411yescharacteristic
775C3×Dic3D3×D411yescharacteristic
776C3×Dic3C2×C3×D411yescharacteristic
777C3×Dic3C2×C3×D411yescharacteristic
7782−1+4—91no—
779H(5,𝔽2)—91no—
780#137—31no—
781#137—91no—
782#137—91no—
783AGL(1,ℤ/8)—91no—
784AGL(1,ℤ/8)—91no—
785AGL(1,ℤ/8)—91no—
786#135—91no—
787#135—91no—
788#135—91no—
789C2×SD16—31no—
790C2×SD16—91no—
791C2×SD16—91no—
792#131—91no—
793C33#57711yescharacteristic, complemented, Sylow
794C23×C3—61no—
795C23×C3—61no—
796C23×C3—121no—
797C23×C3—181no—
798C23×C3—181no—
799C22×D3—21no—
800C22×D3—61no—
801C22×D3—61no—
802C22×D3—61no—
803C22×D3—61no—
804C22×D3—121no—
805C3×Q8—21no—
806C3×Q8—21no—
807C3×Q8—21no—
808C3×Q8—31no—
809C3×Q8—31no—
810C3×Q8—31no—
811C3×Q8—31no—
812C3×Q8—31no—
813C3×Q8—31no—
814C3×Q8—41no—
815C3×Q8—61no—
816C3×Q8—61no—
817C3×Q8—61no—
818C3×Q8—61no—
819C3×Q8—61no—
820C3×Q8—61no—
821C3×Q8—61no—
822C3×Q8—91no—
823C3×Q8—121no—
824C3×Q8—121no—
825C3×Q8—181no—
826C3×Q8C2×D3211yescharacteristic
827C3×Q8C22×C3×D311yescharacteristic
828C3×Q8C22×C3×D311yescharacteristic
829C3×D4—21no—
830C3×D4—21no—
831C3×D4—21no—
832C3×D4—31no—
833C3×D4—31no—
834C3×D4—41no—
835C3×D4—61no—
836C3×D4—61no—
837C3×D4—61no—
838C3×D4—61no—
839C3×D4—61no—
840C3×D4—91no—
841C3×D4—91no—
842C3×D4—91no—
843C3×D4—91no—
844C3×D4—91no—
845C3×D4—121no—
846C3×D4—121no—
847C3×D4—181no—
848C3×D4—181no—
849C3×D4—181no—
850C3×D4—181no—
851C3×D4—181no—
852C3×D4—181no—
853C3×D4—181no—
854C3×D4C2×D3211yescharacteristic
855C3×D4C22×C3×D311yescharacteristic
856C3×D4C22×C3×D311yescharacteristic
857C2×C3×C4—31no—
858C2×C3×C4—31no—
859C2×C3×C4—31no—
860C2×C3×C4—31no—
861C2×C3×C4—61no—
862C2×C3×C4—61no—
863C2×C3×C4—61no—
864C2×C3×C4—61no—
865C2×C3×C4—61no—
866C2×C3×C4—61no—
867C2×C3×C4—61no—
868C2×C3×C4—61no—
869C2×C3×C4—91no—
870C2×C3×C4—121no—
871C2×C3×C4—121no—
872C2×C3×C4—121no—
873C2×C3×C4—181no—
874C2×C3×C4—181no—
875C2×C3×C4—181no—
876C2×C3×C4—181no—
877C2×C3×C4—181no—
878C2×C3×C4—181no—
879#67—21no—
880#67—21no—
881#67—31no—
882#67—31no—
883#67—31no—
884#67—31no—
885#67—61no—
886#67—61no—
887#67—61no—
888#67—61no—
889#67—61no—
890#67—61no—
891#67—61no—
892#67—121no—
893C2×Dic3—21no—
894C2×Dic3—61no—
895D12—31no—
896D12—31no—
897D12—31no—
898D12—31no—
899D12—31no—
900D12—31no—
901D12—61no—
902D12—61no—
903D12—61no—
904D12—61no—
905D12—61no—
906D12—61no—
907D12—61no—
908D12—61no—
909D12—61no—
910D12—121no—
911D12C22×C3×D311yescharacteristic
912C4×D3—21no—
913C4×D3—21no—
914C4×D3—31no—
915C4×D3—31no—
916C4×D3—61no—
917C4×D3—61no—
918C4×D3—61no—
919C4×D3—61no—
920C4×D3—61no—
921C4×D3—61no—
922C4×D3—61no—
923C4×D3—61no—
924C4×D3—61no—
925C4×D3—61no—
926C4×D3—61no—
927C4×D3—61no—
928C4×D3—121no—
929C4×D3C22×C3×D311yescharacteristic
930C4×D3C22×C3×D311yescharacteristic
931Dic6—21no—
932Dic6—21no—
933Dic6—31no—
934Dic6—31no—
935Dic6—61no—
936Dic6—61no—
937Dic6C22×C3×D311yescharacteristic
938Dic6C22×C3×D311yescharacteristic
939Dic6C22×C3×D311yescharacteristic
940C3×C8—21no—
941C3×C8—21no—
942C3×C8—21no—
943C3×C8—31no—
944C3×C8—31no—
945C3×C8—31no—
946C3×C8—31no—
947C3×C8—41no—
948C3×C8—61no—
949C3×C8—61no—
950C3×C8—91no—
951C3×C8C2×D3211yescharacteristic
952C3×C8C22×C3×D311yescharacteristic
953C3×C8C22×C3×D311yescharacteristic
954C3⋊C8—31no—
955C3⋊C8—31no—
956C3⋊C8—61no—
957C3⋊C8C22×C3×D311yescharacteristic
958C3⋊C8C22×C3×D311yescharacteristic
959C2×C32—21no—
960C2×C32—21no—
961C2×C32—21no—
962C2×C32—41no—
963C2×C32—41no—
964C2×C32—41no—
965C2×C32—41no—
966C2×C32—61no—
967C2×C32—61no—
968C2×C32—81no—
969C2×C32—81no—
970C2×C32—81no—
971C2×C32—121no—
972C2×C32—161no—
973C2×C32C2×D3×D411yescharacteristic
974C2×C32C2×D3×D411yescharacteristic
975C2×C32C22×C3×D411yescharacteristic
976C3⋊D3—21no—
977C3⋊D3—41no—
978C3⋊D3—41no—
979C3×D3—22no—
980C3×D3—21no—
981C3×D3—21no—
982C3×D3—21no—
983C3×D3—21no—
984C3×D3—41no—
985C3×D3—41no—
986C3×D3—41no—
987C3×D3—61no—
988C3×D3—61no—
989C3×D3—81no—
990C3×D3—121no—
991C3×D3—121no—
992C3×D3—121no—
993C3×D3—121no—
994C3×D3—121no—
995C3×D3—241no—
996C3×D3—241no—
997#41—31no—
998#41—91no—
999#41—91no—
1000#41—91no—
1001#41—91no—
1002#41—91no—
1003#41—91no—
1004#41—181no—
1005#41—181no—
1006#41—181no—
1007#41—181no—
1008C2×Q8—31no—
1009C2×Q8—31no—
1010C2×Q8—91no—
1011C2×Q8—181no—
1012C2×D4—31no—
1013C2×D4—91no—
1014C2×D4—91no—
1015C2×D4—181no—
1016C2×D4—181no—
1017C2×D4—181no—
1018Q16—31no—
1019Q16—31no—
1020Q16—91no—
1021SD16—31no—
1022SD16—31no—
1023SD16—31no—
1024SD16—31no—
1025SD16—91no—
1026SD16—91no—
1027SD16—91no—
1028SD16—91no—
1029SD16—91no—
1030SD16C3×D3211yescharacteristic, complemented
1031D8—91no—
1032D8—91no—
1033D8—91no—
1034M16—31no—
1035M16—91no—
1036M16—91no—
1037C2×C8—31no—
1038C2×C8—91no—
1039C2×C8—91no—
1040C22×C3—21no—
1041C22×C3—21no—
1042C22×C3—21no—
1043C22×C3—31no—
1044C22×C3—31no—
1045C22×C3—31no—
1046C22×C3—31no—
1047C22×C3—41no—
1048C22×C3—41no—
1049C22×C3—41no—
1050C22×C3—61no—
1051C22×C3—61no—
1052C22×C3—61no—
1053C22×C3—61no—
1054C22×C3—81no—
1055C22×C3—91no—
1056C22×C3—121no—
1057C22×C3—181no—
1058C22×C3—181no—
1059C22×C3—241no—
1060C22×C3—241no—
1061C22×C3—242no—
1062C22×C3—721no—
1063C22×C3—721no—
1064C2×D3—21no—
1065C2×D3—31no—
1066C2×D3—31no—
1067C2×D3—61no—
1068C2×D3—61no—
1069C2×D3—61no—
1070C2×D3—61no—
1071C2×D3—61no—
1072C2×D3—81no—
1073C2×D3—121no—
1074C2×D3—121no—
1075C2×D3—241no—
1076C2×D3—241no—
1077C2×D3—241no—
1078C2×D3—241no—
1079C2×D3—242no—
1080C2×D3C3×D3×D411yescharacteristic
1081C2×D3C3×D3×D411yescharacteristic
1082C3×C4—21no—
1083C3×C4—21no—
1084C3×C4—21no—
1085C3×C4—21no—
1086C3×C4—21no—
1087C3×C4—21no—
1088C3×C4—31no—
1089C3×C4—31no—
1090C3×C4—31no—
1091C3×C4—31no—
1092C3×C4—41no—
1093C3×C4—41no—
1094C3×C4—41no—
1095C3×C4—41no—
1096C3×C4—61no—
1097C3×C4—61no—
1098C3×C4—61no—
1099C3×C4—61no—
1100C3×C4—61no—
1101C3×C4—61no—
1102C3×C4—61no—
1103C3×C4—61no—
1104C3×C4—81no—
1105C3×C4—91no—
1106C3×C4—121no—
1107C3×C4—121no—
1108C3×C4—121no—
1109C3×C4C22×D3211yescharacteristic
1110C3×C4C23×C3×D311yescharacteristic
1111C3×C4C23×C3×D311yescharacteristic
1112Dic3—21no—
1113Dic3—21no—
1114Dic3—21no—
1115Dic3—31no—
1116Dic3—31no—
1117Dic3—61no—
1118Dic3C3×D3×D411yescharacteristic
1119Dic3C3×D3×D411yescharacteristic
1120C32—21no—
1121C32—21no—
1122C32—21no—
1123C32—41no—
1124C32#576211yescharacteristic, complemented
1125C32#577811yescharacteristic, complemented
1126C32C3×#57711yescharacteristic, complemented
1127C23—61no—
1128C23—181no—
1129C23—181no—
1130Q8—31no—
1131Q8—31no—
1132Q8—31no—
1133Q8—61no—
1134Q8—61no—
1135Q8—91no—
1136Q8—181no—
1137Q8C2×C3×D3211yescharacteristic
1138D4—31no—
1139D4—61no—
1140D4—61no—
1141D4—91no—
1142D4—91no—
1143D4—91no—
1144D4—91no—
1145D4—91no—
1146D4—181no—
1147D4—181no—
1148D4—181no—
1149D4—181no—
1150D4—181no—
1151D4—181no—
1152D4—181no—
1153D4C2×C3×D3211yescharacteristic
1154C2×C4—31no—
1155C2×C4—31no—
1156C2×C4—61no—
1157C2×C4—61no—
1158C2×C4—61no—
1159C2×C4—91no—
1160C2×C4—181no—
1161C2×C4—181no—
1162C2×C4—181no—
1163C2×C4—181no—
1164C2×C4—181no—
1165C2×C4—181no—
1166C8—31no—
1167C8—31no—
1168C8—91no—
1169C8C2×C3×D3211yescharacteristic
1170C2×C3—21no—
1171C2×C3—21no—
1172C2×C3—21no—
1173C2×C3—41no—
1174C2×C3—41no—
1175C2×C3—41no—
1176C2×C3—41no—
1177C2×C3—62no—
1178C2×C3—61no—
1179C2×C3—61no—
1180C2×C3—61no—
1181C2×C3—61no—
1182C2×C3—81no—
1183C2×C3—81no—
1184C2×C3—81no—
1185C2×C3—121no—
1186C2×C3—121no—
1187C2×C3—121no—
1188C2×C3—161no—
1189C2×C3—181no—
1190C2×C3—241no—
1191C2×C3—361no—
1192C2×C3—361no—
1193C2×C3D32×D411yescharacteristic
1194C2×C3C2×C3×D3×D411yescharacteristic
1195C2×C3C2×C3×D3×D411yescharacteristic
1196D3—21no—
1197D3—21no—
1198D3—41no—
1199D3—61no—
1200D3—61no—
1201D3—121no—
1202D3—121no—
1203D3—121no—
1204D3—121no—
1205D3—121no—
1206D3—241no—
1207D3—241no—
1208C22—21no—
1209C22—31no—
1210C22—31no—
1211C22—61no—
1212C22—91no—
1213C22—181no—
1214C22—181no—
1215C22—241no—
1216C22—721no—
1217C22—721no—
1218C4—21no—
1219C4—31no—
1220C4—31no—
1221C4—61no—
1222C4—61no—
1223C4—61no—
1224C4—91no—
1225C4C22×C3×D3211yescharacteristic
1226C3—21no—
1227C3—21no—
1228C3—21no—
1229C3—41no—
1230C3#1059475111yescharacteristic, direct product factor
1231C3C3×#576211yescharacteristic, complemented
1232C3C3×#577811yescharacteristic, complemented
1233C2—41no—
1234C2—61no—
1235C2—61no—
1236C2—121no—
1237C2—181no—
1238C2—361no—
1239C2—361no—
1240C2C3×D32×D411yescharacteristic
subgroupG/H
centerC2×C3D32×D4
commutator, cosocleC32×C4C24×C3
FrattiniC4C22×C3×D32
FittingC33×SD16C22
socleC2×C33C22×D4
hypercenterC3×SD16D32
hypocenterC32C3×#577
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×#64316C2semidirect
2. C3×#64314C2semidirect
3. C3×#64123C2semidirect
4. C32×#915C2semidirect
5. C32×D3×SD16C2semidirect
6. C3×#63950C2semidirect
7. C3×#63948C2semidirect
8. C3×D3×#215C2semidirect
9. C3×#63935C2semidirect
10. C3×#63934C2semidirect
11. C3×#63930C2semidirect
12. C3×#63811C2semidirect
13. C3×#63808C2semidirect
14. C3×#63804C2semidirect
15. C3×#63794C2semidirect
18. #10594751C3direct (N × H)
19. C3×#3832C22semidirect
21. C32×D3×Q8C22semidirect
22. C32×D3×Q8C22semidirect
33. C3×#3799C22semidirect
34. C3×#3799C22semidirect
38. C3×#3797C22semidirect
40. C33×SD16C22semidirect
41. C3×#3755C22semidirect
42. C3×#3753C22semidirect
43. C3×#3745C22semidirect
44. C3×#3743C22semidirect
45. C32×#216C22semidirect
46. C32×#215C22semidirect
47. C32×#214C22semidirect
48. C32×#214C22semidirect
49. C32×Dic12C22semidirect
50. C32×#204C22semidirect
51. C32×ΓL(1,𝔽25)C22semidirect
52. C32×D3×C8C22semidirect
53. C3×#3718C22semidirect
54. C3×#3717C22semidirect
55. C3×#3717C22semidirect
56. C3×#3717C22semidirect
57. C3×#3715C22semidirect
58. C3×#3714C22semidirect
59. C3×#3711C22semidirect
60. C3×#3710C22semidirect
61. C3×D3×C3⋊C8C22semidirect
66. #64316C2×C3semidirect
67. #64314C2×C3semidirect
70. #64123C2×C3semidirect
83. C3×#915D3semidirect
84. C3×#915C2×C3semidirect
94. C3×D3×SD16D3semidirect
95. C3×D3×SD16C2×C3semidirect
100. #63950C2×C3semidirect
101. #63948C2×C3semidirect
102. D3×#215C2×C3semidirect
103. #63935C2×C3semidirect
104. #63934C2×C3semidirect
105. #63930C2×C3semidirect
106. #63811C2×C3semidirect
107. #63808C2×C3semidirect
108. #63804C2×C3semidirect
109. #63794C2×C3semidirect
160. #3832C22×C3semidirect
179. C3×D3×Q8C2×D3semidirect
180. C3×D3×Q8C2×D3semidirect
181. C3×D3×Q8C22×C3semidirect
182. C3×D3×Q8C22×C3semidirect
218. #3799C22×C3semidirect
219. #3799C22×C3semidirect
223. #3797C22×C3semidirect
235. C32×SD16C2×D3semidirect
236. C32×SD16C2×D3semidirect
237. C32×SD16C22×C3semidirect
240. #3755C22×C3semidirect
241. #3753C22×C3semidirect
242. #3745C22×C3semidirect
243. #3743C22×C3semidirect
247. C3×#216C2×D3semidirect
248. C3×#216C22×C3semidirect
257. C3×#215C2×D3semidirect
258. C3×#215C22×C3semidirect
262. C3×#214C2×D3semidirect
263. C3×#214C2×D3semidirect
264. C3×#214C22×C3semidirect
265. C3×#214C22×C3semidirect
273. C3×Dic12C2×D3semidirect
274. C3×Dic12C22×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. #3718C22×C3semidirect
299. #3717C22×C3semidirect
300. #3717C22×C3semidirect
301. #3717C22×C3semidirect
302. #3715C22×C3semidirect
303. #3714C22×C3semidirect
304. #3711C22×C3semidirect
305. #3710C22×C3semidirect
306. D3×C3⋊C8C22×C3semidirect
359. #915C3×D3semidirect
368. D3×SD16C3×D3semidirect
591. D3×Q8C2×C3×D3semidirect
592. D3×Q8C2×C3×D3semidirect
644. C3×SD16D32semidirect
645. C3×SD16C2×C3×D3semidirect
646. C3×SD16C2×C3×D3semidirect
662. #216C2×C3×D3semidirect
670. #215C2×C3×D3semidirect
672. #214C2×C3×D3semidirect
673. #214C2×C3×D3semidirect
680. Dic12C2×C3×D3semidirect
688. #204C2×C3×D3semidirect
693. ΓL(1,𝔽25)C2×C3×D3semidirect
697. D3×C8C2×C3×D3semidirect
793. C33#577semidirect
1030. SD16C3×D32semidirect
1124. C32#5762semidirect
1125. C32#5778semidirect
1126. C32C3×#577semidirect
1230. C3#10594751direct (N × H)
1231. C3C3×#5762semidirect
1232. C3C3×#5778semidirect

Maximal subgroups

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

subgroupindex
C3×#643162
C3×#643142
C3×#641232
C32×#9152
C32×D3×SD162
C3×#639502
C3×#639482
C3×D3×#2152
C3×#639352
C3×#639342
C3×#639302
C3×#638112
C3×#638082
C3×#638042
C3×#637942
C3×#57783
C3×#57623
#105947513