Finite Group Databasebeta

← C3×#10594754 #13174351

Subgroups — C3×#10594754 #13174351

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×#64315C211yesmaximal, characteristic, complemented
2C3×#64314C211yesmaximal, characteristic, complemented
3C3×SD16×C3⋊D3C211yesmaximal, characteristic, complemented
4C32×#915C211yesmaximal, characteristic, complemented
5C32×#914C211yesmaximal, characteristic, complemented
6C3×#63951C211yesmaximal, characteristic, complemented
7C3×#63949C211yesmaximal, characteristic, complemented
8C3×D3×#215C211yesmaximal, characteristic, complemented
9C3×#63937C211yesmaximal, characteristic, complemented
10C3×#63933C211yesmaximal, characteristic, complemented
11C3×D3×#214C211yesmaximal, characteristic, complemented
12C3×#63810C211yesmaximal, characteristic, complemented
13C3×#63805C211yesmaximal, characteristic, complemented
14C3×#63801C211yesmaximal, characteristic, complemented
15C3×#63795C211yesmaximal, characteristic, complemented
16C3×#5778—31nomaximal
17C3×#5775—31nomaximal
18#10594754C311yesmaximal, characteristic, direct product factor
19C3×Q8×C3⋊D3C2211yescharacteristic, complemented
20C3×D4×C3⋊D3C2211yescharacteristic
21C32×#239C2211yescharacteristic, 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×#3799C2211yescharacteristic
31C3×#3798—21no—
32C3×#3798C2211yescharacteristic
33C3×#3796—21no—
34C3×#3796C2211yescharacteristic
35C3×#3796C2211yescharacteristic, complemented
36C3×#3795—21no—
37C3×#3795C2211yescharacteristic, complemented
38C3×D3×Dic6—21no—
39C3×D3×Dic6C2211yescharacteristic, complemented
40C33×SD16C2211yescharacteristic, complemented
41C3×#3755C2211yescharacteristic, complemented
42C3×#3754C2211yescharacteristic, complemented
43C3×#3744C2211yescharacteristic, complemented
44C3×C8×C3⋊D3C2211yescharacteristic, complemented
45C32×#216C2211yescharacteristic, complemented
46C32×#215C2211yescharacteristic, complemented
47C32×#214C2211yescharacteristic, complemented
48C32×#213C2211yescharacteristic, complemented
49C32×Dic12C2211yescharacteristic, complemented
50C32×D24C2211yescharacteristic, complemented
51C32×ΓL(1,𝔽25)C2211yescharacteristic, complemented
52C32×ΓL(1,𝔽25)C2211yescharacteristic, complemented
53C3×#3719C2211yescharacteristic, complemented
54C3×#3717C2211yescharacteristic, complemented
55C3×#3716C2211yescharacteristic, complemented
56C3×#3715C2211yescharacteristic, complemented
57C3×#3715C2211yescharacteristic, complemented
58C3×#3714C2211yescharacteristic, complemented
59C3×#3712C2211yescharacteristic, complemented
60C3×D3×C3⋊C8C2211yescharacteristic, complemented
61C3×D3×C3⋊C8C2211yescharacteristic, complemented
62C3×#1010—31no—
63C3×#1009—31no—
64C3×#1007—31no—
65C3×#1004—31no—
66#64315C2×C311yescharacteristic, complemented
67#64314C2×C311yescharacteristic, complemented
68C32×#137—31no—
69C32×AGL(1,ℤ/8)—31no—
70SD16×C3⋊D3C2×C311yescharacteristic, complemented
71C3×#950—31no—
72C3×#950—31no—
73C2×C3×#215—31no—
74C2×C3×#214—31no—
75C3×#919—31no—
76C3×#919—31no—
77C3×#918—31no—
78C3×#918—31no—
79C3×#915—21no—
80C3×#915—31no—
81C3×#915D311yescharacteristic, complemented
82C3×#915C2×C311yescharacteristic, complemented
83C3×#914—21no—
84C3×#914—31no—
85C3×#914D311yescharacteristic, complemented
86C3×#914C2×C311yescharacteristic, complemented
87C3×D3×SD16—31no—
88C3×D3×SD16—31no—
89C3×D3×SD16—31no—
90C3×D3×SD16—31no—
91C3×D3×SD16—61no—
92C3×#912—31no—
93C3×#912—31no—
94C3×#911—31no—
95C3×#911—31no—
96C3×#909—31no—
97C3×#908—31no—
98C3×#907—31no—
99C3×#907—31no—
100#63951C2×C311yescharacteristic, complemented
101#63949C2×C311yescharacteristic, complemented
102D3×#215C2×C311yescharacteristic, complemented
103#63937C2×C311yescharacteristic, complemented
104#63933C2×C311yescharacteristic, complemented
105D3×#214C2×C311yescharacteristic, complemented
106#63810C2×C311yescharacteristic, complemented
107#63805C2×C311yescharacteristic, complemented
108#63801C2×C311yescharacteristic, complemented
109#63795C2×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)C2311yescharacteristic
117C3×C4×C3⋊D3—21no—
118C3×C4×C3⋊D3C2311yescharacteristic
119C3×#634—21no—
120C3×#634C2311yescharacteristic
121C32×#67—21no—
122C32×#67—21no—
123C2×C32×Dic3—21no—
124C32×D12—21no—
125C32×D12C2311yescharacteristic
126C32×D12C2311yescharacteristic
127C32×C4×D3—21no—
128C32×C4×D3—21no—
129C32×C4×D3C2311yescharacteristic
130C32×C4×D3C2311yescharacteristic
131C32×Dic6—21no—
132C32×Dic6C2311yescharacteristic
133C32×Dic6C2311yescharacteristic
134C3×#627—21no—
135C3×#627D411yescharacteristic
136C3×#626—21no—
137C3×#626—21no—
138C3×#626—21no—
139C3×#626—21no—
140C3×#626D411yescharacteristic
141C3×#626D411yescharacteristic
142C3×#625—21no—
143C3×#625D411yescharacteristic
144C3×#624—21no—
145C3×D3×Dic3—21no—
146C3×D3×Dic3—21no—
147C3×D3×Dic3—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#5775—31no—
156C32×#41—31no—
157C32×#41—31no—
158C2×C32×Q8—31no—
159C2×C32×D4—31no—
160Q8×C3⋊D3C22×C311yescharacteristic, complemented
161D4×C3⋊D3C22×C311yescharacteristic
162C2×C3×#67—61no—
163C2×C3×#67—61no—
164C3×#239—21no—
165C3×#239—31no—
166C3×#239—31no—
167C3×#239—31no—
168C3×#239—61no—
169C3×#239C2×D311yescharacteristic, complemented
170C3×#239C22×C311yescharacteristic, complemented
171C3×D3×Q8—21no—
172C3×D3×Q8—31no—
173C3×D3×Q8—31no—
174C3×D3×Q8—31no—
175C3×D3×Q8—61no—
176C3×D3×Q8—61no—
177C3×D3×Q8C2×D311yescharacteristic, complemented
178C3×D3×Q8C22×C311yescharacteristic, complemented
179C3×#237—21no—
180C3×#237—31no—
181C3×#237—31no—
182C3×#237—31no—
183C3×#237—61no—
184C3×#237—61no—
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—61no—
203C3×#235—61no—
204C3×#235—61no—
205C3×#235—61no—
206C2×C3×D12—31no—
207C2×C3×D12—61no—
208C2×C3×Dic6—31no—
209C2×C3×Dic6—61no—
210#3811—21no—
211D3×#67—21no—
212C2×#626—21no—
213#3804—21no—
214D3×D12C22×C311yescharacteristic
215#3799C22×C311yescharacteristic
216#3798—21no—
217#3798C22×C311yescharacteristic
218#3796—21no—
219#3796C22×C311yescharacteristic
220#3796C22×C311yescharacteristic, complemented
221#3795—21no—
222#3795C22×C311yescharacteristic, complemented
223D3×Dic6—21no—
224D3×Dic6C22×C311yescharacteristic, complemented
225C32×Q16—31no—
226C32×Q16—31no—
227C32×SD16—21no—
228C32×SD16—21no—
229C32×SD16—21no—
230C32×SD16—31no—
231C32×SD16—31no—
232C32×SD16—41no—
233C32×SD16C2×D311yescharacteristic, complemented
234C32×SD16C2×D311yescharacteristic, complemented
235C32×SD16C22×C311yescharacteristic, complemented
236C32×D8—31no—
237C32×D8—31no—
238C32×M16—31no—
239C32×M16—31no—
240#3755C22×C311yescharacteristic, complemented
241#3754C22×C311yescharacteristic, complemented
242#3744C22×C311yescharacteristic, complemented
243C8×C3⋊D3C22×C311yescharacteristic, complemented
244C3×#216—21no—
245C3×#216—31no—
246C3×#216C2×D311yescharacteristic, complemented
247C3×#216C22×C311yescharacteristic, complemented
248C3×#215—21no—
249C3×#215—31no—
250C3×#215—31no—
251C3×#215—31no—
252C3×#215—31no—
253C3×#215—31no—
254C3×#215—61no—
255C3×#215C2×D311yescharacteristic, complemented
256C3×#215C22×C311yescharacteristic, complemented
257C3×#214—21no—
258C3×#214—31no—
259C3×#214—31no—
260C3×#214—31no—
261C3×#214—31no—
262C3×#214—31no—
263C3×#214—61no—
264C3×#214C2×D311yescharacteristic, complemented
265C3×#214C22×C311yescharacteristic, complemented
266C3×#213—21no—
267C3×#213—31no—
268C3×#213C2×D311yescharacteristic, complemented
269C3×#213C22×C311yescharacteristic, complemented
270C2×C3×C3⋊C8—31no—
271C2×C3×C3⋊C8—31no—
272C3×Dic12—21no—
273C3×Dic12—31no—
274C3×Dic12C2×D311yescharacteristic, complemented
275C3×Dic12C22×C311yescharacteristic, complemented
276C3×D24—21no—
277C3×D24—31no—
278C3×D24C2×D311yescharacteristic, complemented
279C3×D24C22×C311yescharacteristic, complemented
280C3×#204—31no—
281C3×#204—31no—
282C3×#204—31no—
283C3×#204—31no—
284C3×#204—61no—
285C3×ΓL(1,𝔽25)—21no—
286C3×ΓL(1,𝔽25)—21no—
287C3×ΓL(1,𝔽25)—31no—
288C3×ΓL(1,𝔽25)—31no—
289C3×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
290C3×ΓL(1,𝔽25)C2×D311yescharacteristic, complemented
291C3×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
292C3×ΓL(1,𝔽25)C22×C311yescharacteristic, complemented
293C3×D3×C8—31no—
294C3×D3×C8—31no—
295C3×D3×C8—31no—
296C3×D3×C8—31no—
297C3×D3×C8—61no—
298#3719C22×C311yescharacteristic, complemented
299#3717C22×C311yescharacteristic, complemented
300#3716C22×C311yescharacteristic, complemented
301#3715C22×C311yescharacteristic, complemented
302#3715C22×C311yescharacteristic, complemented
303#3714C22×C311yescharacteristic, complemented
304#3712C22×C311yescharacteristic, complemented
305D3×C3⋊C8C22×C311yescharacteristic, complemented
306D3×C3⋊C8C22×C311yescharacteristic, complemented
307C22×C33—21no—
308C2×C3×C3⋊D3—21no—
309C2×C3×C3⋊D3—81no—
310C2×C3×C3⋊D3C2×D411yescharacteristic
311C2×C32×D3—21no—
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⋊Dic3—21no—
320C3×C3⋊Dic3C2×D411yescharacteristic
321C32×Dic3—21no—
322C32×Dic3—21no—
323C32×Dic3C2×D411yescharacteristic
324C32×Dic3C2×D411yescharacteristic
325C3×2−1+4—91no—
326C3×H(5,𝔽2)—91no—
327#1010—31no—
328#1009—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)—31no—
337C3×AGL(1,ℤ/8)—31no—
338C3×AGL(1,ℤ/8)—61no—
339C3×AGL(1,ℤ/8)—91no—
340C3×AGL(1,ℤ/8)—91no—
341C3×#135—91no—
342C3×#135—91no—
343C3×#135—91no—
344C2×C3×SD16—91no—
345C2×C3×SD16—91no—
346C2×C3×SD16—91no—
347C3×#131—91no—
348#950—31no—
349#950—31no—
350C2×#215—31no—
351C2×#214—31no—
352#919—31no—
353#919—31no—
354#918—31no—
355#918—31no—
356#915—31no—
357#915C3×D311yescharacteristic, complemented
358#914—31no—
359#914C3×D311yescharacteristic, complemented
360D3×SD16—31no—
361D3×SD16—31no—
362D3×SD16—31no—
363D3×SD16—31no—
364D3×SD16—61no—
365#912—31no—
366#912—31no—
367#911—31no—
368#911—31no—
369#909—31no—
370#908—31no—
371#907—31no—
372#907—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—41no—
390C32×Q8—61no—
391C32×Q8C22×D311yescharacteristic
392C32×Q8C22×D311yescharacteristic
393C32×Q8C23×C311yescharacteristic
394C32×D4—21no—
395C32×D4—21no—
396C32×D4—21no—
397C32×D4—31no—
398C32×D4—31no—
399C32×D4—41no—
400C32×D4—61no—
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)C23×C311yescharacteristic
413C4×C3⋊D3—21no—
414C4×C3⋊D3C23×C311yescharacteristic
415#634—21no—
416#634C23×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—61no—
435C3×#67—121no—
436C2×C3×Dic3—21no—
437C2×C3×Dic3—21no—
438C2×C3×Dic3—41no—
439C2×C3×Dic3—61no—
440C2×C3×Dic3—61no—
441C2×C3×Dic3—61no—
442C2×C3×Dic3—61no—
443C3×D12—21no—
444C3×D12—21no—
445C3×D12—21no—
446C3×D12—21no—
447C3×D12—31no—
448C3×D12—31no—
449C3×D12—31no—
450C3×D12—31no—
451C3×D12—41no—
452C3×D12—61no—
453C3×D12—61no—
454C3×D12—61no—
455C3×D12—61no—
456C3×D12—61no—
457C3×D12C22×D311yescharacteristic
458C3×D12C22×D311yescharacteristic
459C3×D12C23×C311yescharacteristic
460C3×D12C23×C311yescharacteristic
461C3×C4×D3—21no—
462C3×C4×D3—21no—
463C3×C4×D3—21no—
464C3×C4×D3—21no—
465C3×C4×D3—21no—
466C3×C4×D3—21no—
467C3×C4×D3—31no—
468C3×C4×D3—31no—
469C3×C4×D3—41no—
470C3×C4×D3—41no—
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—31no—
490C3×Dic6—31no—
491C3×Dic6—31no—
492C3×Dic6—31no—
493C3×Dic6—41no—
494C3×Dic6—61no—
495C3×Dic6—61no—
496C3×Dic6—61no—
497C3×Dic6—61no—
498C3×Dic6—61no—
499C3×Dic6—121no—
500C3×Dic6C22×D311yescharacteristic
501C3×Dic6C22×D311yescharacteristic
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#626C3×D411yescharacteristic
511#626C3×D411yescharacteristic
512#625—21no—
513#625C3×D411yescharacteristic
514#624—21no—
515D3×Dic3—21no—
516D3×Dic3—21no—
517D3×Dic3—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—
543C32×D3—21no—
544C32×D3—21no—
545C32×D3—41no—
546C32×D3—41no—
547C3×#41—31no—
548C3×#41—31no—
549C3×#41—31no—
550C3×#41—31no—
551C3×#41—61no—
552C3×#41—61no—
553C3×#41—91no—
554C3×#41—91no—
555C3×#41—91no—
556C3×#41—91no—
557C3×#41—91no—
558C3×#41—181no—
559C3×#41—181no—
560C3×#41—181no—
561C3×#41—181no—
562C2×C3×Q8—31no—
563C2×C3×Q8—31no—
564C2×C3×Q8—61no—
565C2×C3×Q8—91no—
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—61no—
582#239C2×C3×D311yescharacteristic, complemented
583D3×Q8—31no—
584D3×Q8—31no—
585D3×Q8—31no—
586D3×Q8—61no—
587D3×Q8—61no—
588D3×Q8C2×C3×D311yescharacteristic, complemented
589#237—31no—
590#237—31no—
591#237—31no—
592#237—61no—
593#237—61no—
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—61no—
609#235—61no—
610#235—61no—
611#235—61no—
612C2×D12—31no—
613C2×D12—61no—
614C2×Dic6—31no—
615C2×Dic6—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—41no—
631C3×SD16—61no—
632C3×SD16—61no—
633C3×SD16—91no—
634C3×SD16—91no—
635C3×SD16—91no—
636C3×SD16—91no—
637C3×SD16—91no—
638C3×SD16—91no—
639C3×SD16—91no—
640C3×SD16D3211yescharacteristic, complemented
641C3×SD16C2×C3×D311yescharacteristic, complemented
642C3×SD16C2×C3×D311yescharacteristic, complemented
643C3×D8—31no—
644C3×D8—31no—
645C3×D8—31no—
646C3×D8—31no—
647C3×D8—61no—
648C3×D8—61no—
649C3×D8—91no—
650C3×M16—31no—
651C3×M16—31no—
652C3×M16—31no—
653C3×M16—31no—
654C3×M16—61no—
655C3×M16—61no—
656C3×M16—91no—
657C2×C3×C8—91no—
658C2×C3×C8—91no—
659C2×C3×C8—91no—
660#216—31no—
661#216C2×C3×D311yescharacteristic, complemented
662#215—31no—
663#215—31no—
664#215—31no—
665#215—31no—
666#215—31no—
667#215—61no—
668#215C2×C3×D311yescharacteristic, complemented
669#214—31no—
670#214—31no—
671#214—31no—
672#214—31no—
673#214—31no—
674#214—61no—
675#214C2×C3×D311yescharacteristic, complemented
676#213—31no—
677#213C2×C3×D311yescharacteristic, complemented
678C2×C3⋊C8—31no—
679C2×C3⋊C8—31no—
680Dic12—31no—
681Dic12C2×C3×D311yescharacteristic, complemented
682D24—31no—
683D24C2×C3×D311yescharacteristic, complemented
684#204—31no—
685#204—31no—
686#204—31no—
687#204—31no—
688#204—61no—
689ΓL(1,𝔽25)—31no—
690ΓL(1,𝔽25)—31no—
691ΓL(1,𝔽25)C2×C3×D311yescharacteristic, complemented
692ΓL(1,𝔽25)C2×C3×D311yescharacteristic, complemented
693D3×C8—31no—
694D3×C8—31no—
695D3×C8—31no—
696D3×C8—31no—
697D3×C8—61no—
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—61no—
708C22×C32—81no—
709C22×C32—241no—
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—21no—
718C2×C3×D3—21no—
719C2×C3×D3—31no—
720C2×C3×D3—31no—
721C2×C3×D3—41no—
722C2×C3×D3—41no—
723C2×C3×D3—61no—
724C2×C3×D3—61no—
725C2×C3×D3—61no—
726C2×C3×D3—81no—
727C2×C3×D3—81no—
728C2×C3×D3—82no—
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—81no—
755C32×C4C23×D311yescharacteristic
756C32×C4C23×D311yescharacteristic
757C32×C4C24×C311yescharacteristic
758C3⋊Dic3—21no—
759C3⋊Dic3C2×C3×D411yescharacteristic
760C3×Dic3—21no—
761C3×Dic3—21no—
762C3×Dic3—21no—
763C3×Dic3—21no—
764C3×Dic3—21no—
765C3×Dic3—21no—
766C3×Dic3—31no—
767C3×Dic3—31no—
768C3×Dic3—41no—
769C3×Dic3—41no—
770C3×Dic3—61no—
771C3×Dic3—61no—
772C3×Dic3—61no—
773C3×Dic3—121no—
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)—31no—
784AGL(1,ℤ/8)—91no—
785AGL(1,ℤ/8)—91no—
786#135—91no—
787#135—91no—
788#135—91no—
789C2×SD16—91no—
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—41no—
813C3×Q8—61no—
814C3×Q8—61no—
815C3×Q8—61no—
816C3×Q8—61no—
817C3×Q8—91no—
818C3×Q8—91no—
819C3×Q8—121no—
820C3×Q8—181no—
821C3×Q8—181no—
822C3×Q8C2×D3211yescharacteristic
823C3×Q8C22×C3×D311yescharacteristic
824C3×Q8C22×C3×D311yescharacteristic
825C3×D4—21no—
826C3×D4—21no—
827C3×D4—21no—
828C3×D4—31no—
829C3×D4—31no—
830C3×D4—31no—
831C3×D4—31no—
832C3×D4—41no—
833C3×D4—61no—
834C3×D4—61no—
835C3×D4—61no—
836C3×D4—61no—
837C3×D4—61no—
838C3×D4—61no—
839C3×D4—61no—
840C3×D4—61no—
841C3×D4—91no—
842C3×D4—91no—
843C3×D4—91no—
844C3×D4—91no—
845C3×D4—121no—
846C3×D4—121no—
847C3×D4—121no—
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—61no—
893#67—121no—
894C2×Dic3—21no—
895C2×Dic3—61no—
896C2×Dic3—61no—
897C2×Dic3—61no—
898C2×Dic3—61no—
899D12—21no—
900D12—31no—
901D12—31no—
902D12—31no—
903D12—31no—
904D12—61no—
905D12—61no—
906D12—61no—
907D12—61no—
908D12—61no—
909D12C22×C3×D311yescharacteristic
910D12C22×C3×D311yescharacteristic
911C4×D3—21no—
912C4×D3—21no—
913C4×D3—31no—
914C4×D3—31no—
915C4×D3—61no—
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—121no—
925C4×D3C22×C3×D311yescharacteristic
926C4×D3C22×C3×D311yescharacteristic
927Dic6—21no—
928Dic6—31no—
929Dic6—31no—
930Dic6—31no—
931Dic6—31no—
932Dic6—61no—
933Dic6—61no—
934Dic6—61no—
935Dic6—61no—
936Dic6—61no—
937Dic6—121no—
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—121no—
973C2×C32—161no—
974C2×C32C2×D3×D411yescharacteristic
975C2×C32C2×D3×D411yescharacteristic
976C2×C32C22×C3×D411yescharacteristic
977C3⋊D3—21no—
978C3⋊D3—41no—
979C3×D3—21no—
980C3×D3—21no—
981C3×D3—21no—
982C3×D3—21no—
983C3×D3—41no—
984C3×D3—41no—
985C3×D3—41no—
986C3×D3—41no—
987C3×D3—41no—
988C3×D3—41no—
989C3×D3—62no—
990C3×D3—61no—
991C3×D3—61no—
992C3×D3—81no—
993C3×D3—81no—
994C3×D3—121no—
995C3×D3—121no—
996C3×D3—241no—
997#41—31no—
998#41—31no—
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—91no—
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—91no—
1024SD16—91no—
1025SD16—91no—
1026SD16—91no—
1027SD16—91no—
1028SD16—91no—
1029SD16—91no—
1030SD16C3×D3211yescharacteristic, complemented
1031D8—31no—
1032D8—31no—
1033D8—91no—
1034M16—31no—
1035M16—31no—
1036M16—91no—
1037C2×C8—91no—
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—61no—
1055C22×C3—61no—
1056C22×C3—81no—
1057C22×C3—91no—
1058C22×C3—121no—
1059C22×C3—121no—
1060C22×C3—181no—
1061C22×C3—241no—
1062C22×C3—241no—
1063C22×C3—242no—
1064C22×C3—721no—
1065C22×C3—721no—
1066C2×D3—21no—
1067C2×D3—21no—
1068C2×D3—31no—
1069C2×D3—31no—
1070C2×D3—61no—
1071C2×D3—61no—
1072C2×D3—61no—
1073C2×D3—81no—
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—81no—
1103C3×C4—91no—
1104C3×C4—121no—
1105C3×C4—121no—
1106C3×C4—181no—
1107C3×C4C22×D3211yescharacteristic
1108C3×C4C23×C3×D311yescharacteristic
1109C3×C4C23×C3×D311yescharacteristic
1110Dic3—21no—
1111Dic3—21no—
1112Dic3—31no—
1113Dic3—31no—
1114Dic3—61no—
1115Dic3—61no—
1116Dic3—61no—
1117Dic3—121no—
1118Dic3C3×D3×D411yescharacteristic
1119Dic3C3×D3×D411yescharacteristic
1120C32—21no—
1121C32—21no—
1122C32—21no—
1123C32—41no—
1124C32#577511yescharacteristic, complemented
1125C32#577811yescharacteristic, complemented
1126C32C3×#57711yescharacteristic, complemented
1127C23—61no—
1128C23—181no—
1129C23—181no—
1130Q8—31no—
1131Q8—31no—
1132Q8—61no—
1133Q8—91no—
1134Q8—91no—
1135Q8—181no—
1136Q8—181no—
1137Q8C2×C3×D3211yescharacteristic
1138D4—31no—
1139D4—31no—
1140D4—61no—
1141D4—61no—
1142D4—61no—
1143D4—91no—
1144D4—91no—
1145D4—91no—
1146D4—91no—
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—61no—
1178C2×C3—61no—
1179C2×C3—61no—
1180C2×C3—61no—
1181C2×C3—81no—
1182C2×C3—81no—
1183C2×C3—81no—
1184C2×C3—121no—
1185C2×C3—121no—
1186C2×C3—121no—
1187C2×C3—121no—
1188C2×C3—121no—
1189C2×C3—121no—
1190C2×C3—161no—
1191C2×C3—181no—
1192C2×C3—241no—
1193C2×C3—241no—
1194C2×C3—361no—
1195C2×C3D32×D411yescharacteristic
1196C2×C3C2×C3×D3×D411yescharacteristic
1197C2×C3C2×C3×D3×D411yescharacteristic
1198D3—21no—
1199D3—21no—
1200D3—41no—
1201D3—41no—
1202D3—62no—
1203D3—61no—
1204D3—61no—
1205D3—121no—
1206D3—121no—
1207D3—241no—
1208C22—21no—
1209C22—31no—
1210C22—31no—
1211C22—61no—
1212C22—61no—
1213C22—91no—
1214C22—181no—
1215C22—241no—
1216C22—721no—
1217C22—721no—
1218C4—21no—
1219C4—31no—
1220C4—31no—
1221C4—61no—
1222C4—61no—
1223C4—91no—
1224C4—181no—
1225C4C22×C3×D3211yescharacteristic
1226C3—21no—
1227C3—21no—
1228C3—21no—
1229C3—41no—
1230C3#1059475411yescharacteristic, direct product factor
1231C3C3×#577511yescharacteristic, complemented
1232C3C3×#577811yescharacteristic, complemented
1233C2—41no—
1234C2—61no—
1235C2—61no—
1236C2—121no—
1237C2—121no—
1238C2—181no—
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×#64315C2semidirect
2. C3×#64314C2semidirect
3. C3×SD16×C3⋊D3C2semidirect
4. C32×#915C2semidirect
5. C32×#914C2semidirect
6. C3×#63951C2semidirect
7. C3×#63949C2semidirect
8. C3×D3×#215C2semidirect
9. C3×#63937C2semidirect
10. C3×#63933C2semidirect
11. C3×D3×#214C2semidirect
12. C3×#63810C2semidirect
13. C3×#63805C2semidirect
14. C3×#63801C2semidirect
15. C3×#63795C2semidirect
18. #10594754C3direct (N × H)
19. C3×Q8×C3⋊D3C22semidirect
21. C32×#239C22semidirect
22. C32×D3×Q8C22semidirect
35. C3×#3796C22semidirect
37. C3×#3795C22semidirect
39. C3×D3×Dic6C22semidirect
40. C33×SD16C22semidirect
41. C3×#3755C22semidirect
42. C3×#3754C22semidirect
43. C3×#3744C22semidirect
44. C3×C8×C3⋊D3C22semidirect
45. C32×#216C22semidirect
46. C32×#215C22semidirect
47. C32×#214C22semidirect
48. C32×#213C22semidirect
49. C32×Dic12C22semidirect
50. C32×D24C22semidirect
51. C32×ΓL(1,𝔽25)C22semidirect
52. C32×ΓL(1,𝔽25)C22semidirect
53. C3×#3719C22semidirect
54. C3×#3717C22semidirect
55. C3×#3716C22semidirect
56. C3×#3715C22semidirect
57. C3×#3715C22semidirect
58. C3×#3714C22semidirect
59. C3×#3712C22semidirect
60. C3×D3×C3⋊C8C22semidirect
61. C3×D3×C3⋊C8C22semidirect
66. #64315C2×C3semidirect
67. #64314C2×C3semidirect
70. SD16×C3⋊D3C2×C3semidirect
81. C3×#915D3semidirect
82. C3×#915C2×C3semidirect
85. C3×#914D3semidirect
86. C3×#914C2×C3semidirect
100. #63951C2×C3semidirect
101. #63949C2×C3semidirect
102. D3×#215C2×C3semidirect
103. #63937C2×C3semidirect
104. #63933C2×C3semidirect
105. D3×#214C2×C3semidirect
106. #63810C2×C3semidirect
107. #63805C2×C3semidirect
108. #63801C2×C3semidirect
109. #63795C2×C3semidirect
160. Q8×C3⋊D3C22×C3semidirect
169. C3×#239C2×D3semidirect
170. C3×#239C22×C3semidirect
177. C3×D3×Q8C2×D3semidirect
178. C3×D3×Q8C22×C3semidirect
220. #3796C22×C3semidirect
222. #3795C22×C3semidirect
224. D3×Dic6C22×C3semidirect
233. C32×SD16C2×D3semidirect
234. C32×SD16C2×D3semidirect
235. C32×SD16C22×C3semidirect
240. #3755C22×C3semidirect
241. #3754C22×C3semidirect
242. #3744C22×C3semidirect
243. C8×C3⋊D3C22×C3semidirect
246. C3×#216C2×D3semidirect
247. C3×#216C22×C3semidirect
255. C3×#215C2×D3semidirect
256. C3×#215C22×C3semidirect
264. C3×#214C2×D3semidirect
265. C3×#214C22×C3semidirect
268. C3×#213C2×D3semidirect
269. C3×#213C22×C3semidirect
274. C3×Dic12C2×D3semidirect
275. C3×Dic12C22×C3semidirect
278. C3×D24C2×D3semidirect
279. C3×D24C22×C3semidirect
289. C3×ΓL(1,𝔽25)C2×D3semidirect
290. C3×ΓL(1,𝔽25)C2×D3semidirect
291. C3×ΓL(1,𝔽25)C22×C3semidirect
292. C3×ΓL(1,𝔽25)C22×C3semidirect
298. #3719C22×C3semidirect
299. #3717C22×C3semidirect
300. #3716C22×C3semidirect
301. #3715C22×C3semidirect
302. #3715C22×C3semidirect
303. #3714C22×C3semidirect
304. #3712C22×C3semidirect
305. D3×C3⋊C8C22×C3semidirect
306. D3×C3⋊C8C22×C3semidirect
357. #915C3×D3semidirect
359. #914C3×D3semidirect
582. #239C2×C3×D3semidirect
588. D3×Q8C2×C3×D3semidirect
640. C3×SD16D32semidirect
641. C3×SD16C2×C3×D3semidirect
642. C3×SD16C2×C3×D3semidirect
661. #216C2×C3×D3semidirect
668. #215C2×C3×D3semidirect
675. #214C2×C3×D3semidirect
677. #213C2×C3×D3semidirect
681. Dic12C2×C3×D3semidirect
683. D24C2×C3×D3semidirect
691. ΓL(1,𝔽25)C2×C3×D3semidirect
692. ΓL(1,𝔽25)C2×C3×D3semidirect
793. C33#577semidirect
1030. SD16C3×D32semidirect
1124. C32#5775semidirect
1125. C32#5778semidirect
1126. C32C3×#577semidirect
1230. C3#10594754direct (N × H)
1231. C3C3×#5775semidirect
1232. C3C3×#5778semidirect

Maximal subgroups

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

subgroupindex
C3×#643152
C3×#643142
C3×SD16×C3⋊D32
C32×#9152
C32×#9142
C3×#639512
C3×#639492
C3×D3×#2152
C3×#639372
C3×#639332
C3×D3×#2142
C3×#638102
C3×#638052
C3×#638012
C3×#637952
C3×#57783
C3×#57753
#105947543