Finite Group Databasebeta

← #10804111

Subgroups — #10804111

Order 768.

1502 conjugacy classes of subgroups.

The subgroup lattice has 978 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#5547C211yesmaximal, characteristic
2C2×#5129C211yesmaximal, characteristic, complemented
3C2×#4727C211yesmaximal, characteristic, complemented
4C3×#1870C211yesmaximal, characteristic, complemented
5#71996C211yesmaximal, characteristic, complemented
6#71610C211yesmaximal, characteristic, complemented
7#69958C211yesmaximal, characteristic, complemented
8#69957C211yesmaximal, characteristic, complemented
9#69955C211yesmaximal, characteristic, complemented
10#69955C211yesmaximal, characteristic, complemented
11#69952C211yesmaximal, characteristic, complemented
12#68669C211yesmaximal, characteristic, complemented
13#68668C211yesmaximal, characteristic, complemented
14#68665C211yesmaximal, characteristic, complemented
15#68665C211yesmaximal, characteristic, complemented
16#21744—31nomaximal, Sylow
17C22×#235C2211yescharacteristic
18C23×C4×D3C2211yescharacteristic
19C22×C3×M16C2211yescharacteristic, complemented
20C2×C3×C4×D4C2211yescharacteristic
21C2×#939C411yescharacteristic
22C2×#937C411yescharacteristic
23C2×C4×#67C2211yescharacteristic
24C2×C4×#67C2211yescharacteristic
25C23×C3⋊C8C2211yescharacteristic, complemented
26C22×ΓL(1,𝔽25)C2211yescharacteristic, complemented
27C22×D3×C8C2211yescharacteristic, complemented
28#5547—24no—
29#5547—24no—
30C2×#896C411yescharacteristic
31C2×#894C411yescharacteristic
32C2×#884C411yescharacteristic
33C2×#883C411yescharacteristic
34C2×#882C411yescharacteristic
35C2×#878C411yescharacteristic
36C2×C4×D12C2211yescharacteristic
37C2×#872C2211yescharacteristic
38C2×C3×C22⋊C8C2211yescharacteristic
39C2×C3×C22⋊C8C2211yescharacteristic
40C2×C3×C22⋊C8C2211yescharacteristic, complemented
41C2×#830C2211yescharacteristic
42C2×#830C2211yescharacteristic
43C2×#830C2211yescharacteristic, complemented
44#5129—24no—
45C2×(C2×D3)⋊C8C2211yescharacteristic
46C2×(C2×D3)⋊C8C2211yescharacteristic
47C2×(C2×D3)⋊C8C2211yescharacteristic
48C2×(C2×D3)⋊C8C2211yescharacteristic
49C2×(C2×D3)⋊C8C2211yescharacteristic
50C2×(C2×D3)⋊C8C2211yescharacteristic
51C2×(C2×D3)⋊C8C2211yescharacteristic
52C2×(C2×D3)⋊C8C2211yescharacteristic
53C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
54C2×(C2×D3)⋊C8C2211yescharacteristic, complemented
55#4727—24no—
56C3×#336C2211yescharacteristic, complemented
57C3×#336C2211yescharacteristic, complemented
58#4550C2211yescharacteristic, complemented
59#4550C2211yescharacteristic, complemented
60#4550C2211yescharacteristic, complemented
61#4550C2211yescharacteristic, complemented
62#4524C2211yescharacteristic, complemented
63#4524C2211yescharacteristic, complemented
64C2×#525—31no—
65C2×#408—31no—
66C2×#408—31no—
67#1870—31no—
68#1870—31no—
69#1870—31no—
70#1870D311yescharacteristic, complemented
71#1869—31no—
72#1869—31no—
73#1869—31no—
74#1869—31no—
75#1818—31no—
76#1818—31no—
77#1779—31no—
78#1779—31no—
79C24×D3C2×C411yescharacteristic
80C22×C3×D4C2×C411yescharacteristic
81C23×C3×C4C2311yescharacteristic
82C23×C3×C4C2311yescharacteristic
83C22×#67C2×C411yescharacteristic
84C22×#67C2×C411yescharacteristic
85C22×#67C2×C411yescharacteristic
86C22×#67C2×C411yescharacteristic
87C23×Dic3C2×C411yescharacteristic
88C2×#235—41no—
89C2×#235—41no—
90C2×#235—41no—
91C2×#235—41no—
92C2×#235D414yes—
93C2×#235D414yes—
94C22×D12C2×C411yescharacteristic
95C22×D12C2×C411yescharacteristic
96C22×C4×D3—22no—
97C22×C4×D3—22no—
98C22×C4×D3—41no—
99C22×C4×D3—41no—
100C22×C4×D3—41no—
101C22×C4×D3—41no—
102C22×C4×D3C2×C411yescharacteristic
103C22×C4×D3C2×C411yescharacteristic
104C22×C4×D3C2311yescharacteristic
105C22×C4×D3C2311yescharacteristic
106C22×C4×D3C2311yescharacteristic
107C22×Dic6C2×C411yescharacteristic
108C2×C3×M16—22no—
109C2×C3×M16—41no—
110C2×C3×M16—41no—
111C22×C3×C8C2311yescharacteristic
112C22×C3×C8C2311yescharacteristic
113C22×C3×C8C2311yescharacteristic
114C22×C3×C8C2311yescharacteristic
115C3×C4×D4—22no—
116C3×C4×D4—22no—
117C2×C3×C4⋊C4C2×C411yescharacteristic
118C2×C3×C22⋊C4C2×C411yescharacteristic
119C2×C3×C22⋊C4C2×C411yescharacteristic
120C2×C3×C42C2311yescharacteristic
121C2×#217C2×C411yescharacteristic
122C2×#217C2×C411yescharacteristic
123#939—24no—
124#937—24no—
125C4×#67—22no—
126C4×#67—22no—
127C4×#67—22no—
128C4×#67—22no—
129C2×(C2×D3)⋊C4C2×C411yescharacteristic
130C2×(C2×D3)⋊C4C2×C411yescharacteristic
131C2×(C2×D3)⋊C4C2×C411yescharacteristic
132C2×(C2×D3)⋊C4C2×C411yescharacteristic
133C2×(C2×D3)⋊C4C2×C411yescharacteristic
134C2×(C2×D3)⋊C4C2×C411yescharacteristic
135C2×C4⋊Dic3C2×C411yescharacteristic
136C2×Dic3⋊C4C2×C411yescharacteristic
137C2×Dic3⋊C4C2×C411yescharacteristic
138C2×Dic3⋊C4C2×C411yescharacteristic
139C2×Dic3⋊C4C2×C411yescharacteristic
140C2×C4×Dic3C2311yescharacteristic
141C22×C3⋊C8—22no—
142C22×C3⋊C8—41no—
143C22×C3⋊C8—41no—
144C22×C3⋊C8C2311yescharacteristic
145C22×C3⋊C8C2311yescharacteristic
146C22×C3⋊C8C2311yescharacteristic
147C22×C3⋊C8C2311yescharacteristic
148C2×ΓL(1,𝔽25)—22no—
149C2×ΓL(1,𝔽25)—41no—
150C2×ΓL(1,𝔽25)—41no—
151C2×D3×C8—22no—
152C2×D3×C8—41no—
153C2×D3×C8—41no—
154#896—24no—
155#894—24no—
156#884—24no—
157#883—24no—
158#882—24no—
159#878—24no—
160C4×D12—22no—
161C4×D12—22no—
162#872—22no—
163#872—22no—
164C3×C22⋊C8—22no—
165C3×C22⋊C8—41no—
166C3×C22⋊C8—41no—
167#830—22no—
168#830—41no—
169#830—41no—
170(C2×D3)⋊C8—22no—
171(C2×D3)⋊C8—22no—
172(C2×D3)⋊C8—22no—
173(C2×D3)⋊C8—22no—
174(C2×D3)⋊C8—22no—
175(C2×D3)⋊C8—22no—
176(C2×D3)⋊C8—41no—
177(C2×D3)⋊C8—41no—
178(C2×D3)⋊C8—41no—
179(C2×D3)⋊C8—41no—
180C22×#41—31no—
181C24×C4—31no—
182C22×M16—31no—
183C22×M16C2×D311yescharacteristic, complemented
184C23×C8—31no—
185C23×C8—31no—
186#525—64no—
187#525—64no—
188C2×#123—31no—
189C2×#123—31no—
190C2×C22⋊Q8—31no—
191C2×C22⋊Q8—31no—
192C2×#121—31no—
193C2×#121—31no—
194C2×#120—31no—
195C2×#120—31no—
196C2×C4×D4—31no—
197C2×C4×D4—31no—
198C2×C4×D4—31no—
199C2×C4×D4C2×D311yescharacteristic
200C2×#117—31no—
201#408—64no—
202#408—64no—
203C2×C22⋊C8—31no—
204C2×C22⋊C8—31no—
205C2×C22⋊C8—31no—
206C2×C22⋊C8—31no—
207C2×C22⋊C8—31no—
208C2×C22⋊C8—31no—
209C2×C22⋊C8—31no—
210C2×C22⋊C8—31no—
211C2×C22⋊C8—31no—
212C2×C22⋊C8—31no—
213C2×C22⋊C8—31no—
214C2×C22⋊C8—31no—
215C2×C22⋊C8—31no—
216C2×C22⋊C8C2×D311yescharacteristic
217C2×C22⋊C8C2×D311yescharacteristic
218C2×C22⋊C8C2×D311yescharacteristic, complemented
219#336—31no—
220#336—31no—
221#336—31no—
222#336—31no—
223#336—31no—
224#336—31no—
225#336C2×D311yescharacteristic, complemented
226#336C2×D311yescharacteristic, complemented
227C24×C3C22×C411yescharacteristic
228C24×C3C22×C411yescharacteristic
229C23×D3—22no—
230C23×D3—22no—
231C23×D3—22no—
232C23×D3—41no—
233C23×D3—41no—
234C23×D3—41no—
235C23×D3—41no—
236C23×D3C22×C411yescharacteristic
237C23×D3C22×C411yescharacteristic
238C23×D3C22×C411yescharacteristic
239C2×C3×D4—22no—
240C2×C3×D4—22no—
241C2×C3×D4—41no—
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—21no—
248C22×C3×C4—21no—
249C22×C3×C4—21no—
250C22×C3×C4—21no—
251C22×C3×C4—21no—
252C22×C3×C4C22×C411yescharacteristic
253C22×C3×C4C22×C411yescharacteristic
254C22×C3×C4C22×C411yescharacteristic
255C22×C3×C4C22×C411yescharacteristic
256C22×C3×C4C2×D412yes—
257C22×C3×C4C2×D412yes—
258C22×C3×C4C2411yescharacteristic
259C2×#67—22no—
260C2×#67—22no—
261C2×#67—22no—
262C2×#67—22no—
263C2×#67—41no—
264C2×#67—41no—
265C2×#67—41no—
266C2×#67—41no—
267C2×#67—41no—
268C2×#67—41no—
269C2×#67C22⋊C414yes—
270C2×#67C22⋊C414yes—
271C22×Dic3—22no—
272C22×Dic3—41no—
273C22×Dic3—41no—
274C22×Dic3C22×C411yescharacteristic
275C22×Dic3C22×C411yescharacteristic
276C22×Dic3C22×C411yescharacteristic
277C22×Dic3C22×C411yescharacteristic
278C22×Dic3C22×C411yescharacteristic
279#235—44no—
280#235—44no—
281#235—44no—
282#235—44no—
283C2×D12—22no—
284C2×D12—22no—
285C2×D12—41no—
286C2×D12—41no—
287C2×D12—41no—
288C2×D12C22⋊C414yes—
289C2×C4×D3—21no—
290C2×C4×D3—21no—
291C2×C4×D3—21no—
292C2×C4×D3—21no—
293C2×C4×D3—21no—
294C2×C4×D3—21no—
295C2×C4×D3—21no—
296C2×C4×D3—21no—
297C2×C4×D3—22no—
298C2×C4×D3—21no—
299C2×C4×D3—21no—
300C2×C4×D3—21no—
301C2×C4×D3—21no—
302C2×C4×D3—21no—
303C2×C4×D3—21no—
304C2×C4×D3—22no—
305C2×C4×D3—44no—
306C2×C4×D3—44no—
307C2×C4×D3—44no—
308C2×C4×D3—44no—
309C2×C4×D3—41no—
310C2×C4×D3—41no—
311C2×C4×D3—41no—
312C2×C4×D3—41no—
313C2×C4×D3C2×D412yes—
314C2×C4×D3C2×D412yes—
315C2×C4×D3C2×D412yes—
316C2×C4×D3C2×D412yes—
317C2×Dic6—41no—
318C2×Dic6—41no—
319C2×Dic6C22⋊C414yes—
320C3×M16—44no—
321C2×C3×C8—21no—
322C2×C3×C8—21no—
323C2×C3×C8—21no—
324C2×C3×C8—21no—
325C2×C3×C8—21no—
326C2×C3×C8—21no—
327C2×C3×C8—21no—
328C2×C3×C8—21no—
329C2×C3×C8—21no—
330C2×C3×C8—21no—
331C2×C3×C8—21no—
332C2×C3×C8—21no—
333C3×C4⋊C4—22no—
334C3×C22⋊C4—22no—
335C3×C22⋊C4—22no—
336C3×C42—21no—
337C3×C42—21no—
338#217—22no—
339#217—22no—
340(C2×D3)⋊C4—22no—
341(C2×D3)⋊C4—22no—
342(C2×D3)⋊C4—22no—
343(C2×D3)⋊C4—22no—
344(C2×D3)⋊C4—22no—
345(C2×D3)⋊C4—22no—
346C4⋊Dic3—22no—
347Dic3⋊C4—22no—
348Dic3⋊C4—22no—
349Dic3⋊C4—22no—
350Dic3⋊C4—22no—
351C4×Dic3—21no—
352C4×Dic3—21no—
353C2×C3⋊C8—21no—
354C2×C3⋊C8—21no—
355C2×C3⋊C8—21no—
356C2×C3⋊C8—21no—
357C2×C3⋊C8—21no—
358C2×C3⋊C8—21no—
359C2×C3⋊C8—21no—
360C2×C3⋊C8—21no—
361C2×C3⋊C8—21no—
362C2×C3⋊C8—21no—
363C2×C3⋊C8—21no—
364C2×C3⋊C8—21no—
365C2×C3⋊C8—44no—
366ΓL(1,𝔽25)—44no—
367D3×C8—44no—
368C25—31no—
369C2×#41—34no—
370C2×#41—34no—
371C2×#41—121no—
372C2×#41—121no—
373C2×#41—121no—
374C2×#41—121no—
375C22×Q8—31no—
376C22×D4—31no—
377C22×D4—31no—
378C22×D4—31no—
379C22×D4—31no—
380C22×D4—31no—
381C22×D4—31no—
382C22×D4C4×D311yescharacteristic
383C23×C4—31no—
384C23×C4—31no—
385C23×C4—31no—
386C23×C4—31no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—62no—
390C23×C4—62no—
391C23×C4—121no—
392C23×C4—121no—
393C23×C4—121no—
394C23×C4—121no—
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C2×M16—22no—
398C2×M16—41no—
399C2×M16—41no—
400C2×M16—62no—
401C2×M16—121no—
402C2×M16—121no—
403C22×C8—31no—
404C22×C8—31no—
405C22×C8—31no—
406C22×C8—31no—
407C22×C8—62no—
408C22×C8—62no—
409C22×C8—121no—
410C22×C8—121no—
411C22×C8—121no—
412C22×C8—121no—
413C22×C8C22×D311yescharacteristic
414C22×C8C22×D311yescharacteristic
415C22×C8C22×D311yescharacteristic
416C22×C8C22×D311yescharacteristic
417#123—64no—
418#123—64no—
419C22⋊Q8—64no—
420C22⋊Q8—64no—
421#121—64no—
422#121—64no—
423#120—64no—
424#120—64no—
425C4×D4—22no—
426C4×D4—22no—
427C4×D4—62no—
428C4×D4—62no—
429C4×D4—62no—
430C4×D4—62no—
431C4×D4—62no—
432C4×D4—62no—
433#117—62no—
434#117—62no—
435C2×C4⋊C4—31no—
436C2×C4⋊C4—31no—
437C2×C4⋊C4—31no—
438C2×C4⋊C4—31no—
439C2×C4⋊C4—31no—
440C2×C4⋊C4C4×D311yescharacteristic
441C2×C22⋊C4—31no—
442C2×C22⋊C4—31no—
443C2×C22⋊C4—31no—
444C2×C22⋊C4—31no—
445C2×C22⋊C4—31no—
446C2×C22⋊C4—31no—
447C2×C22⋊C4—31no—
448C2×C22⋊C4—31no—
449C2×C22⋊C4C4×D311yescharacteristic
450C2×C22⋊C4C4×D311yescharacteristic
451C2×C42—31no—
452C2×C42C22×D311yescharacteristic
453C22⋊C8—22no—
454C22⋊C8—41no—
455C22⋊C8—41no—
456C22⋊C8—62no—
457C22⋊C8—62no—
458C22⋊C8—62no—
459C22⋊C8—62no—
460C22⋊C8—62no—
461C22⋊C8—62no—
462C22⋊C8—62no—
463C22⋊C8—121no—
464C22⋊C8—121no—
465C22⋊C8—121no—
466C22⋊C8—121no—
467C22⋊C8—121no—
468C22⋊C8—121no—
469C23×C3—21no—
470C23×C3—21no—
471C23×C3—21no—
472C23×C3—21no—
473C23×C3—21no—
474C23×C3—21no—
475C23×C3—21no—
476C23×C3—21no—
477C23×C3—21no—
478C23×C3—21no—
479C23×C3—21no—
480C23×C3—21no—
481C23×C3C2×C22⋊C412yes—
482C23×C3#13112yes—
483C23×C3C23×C411yescharacteristic
484C22×D3—21no—
485C22×D3—21no—
486C22×D3—21no—
487C22×D3—21no—
488C22×D3—21no—
489C22×D3—21no—
490C22×D3—21no—
491C22×D3—21no—
492C22×D3—21no—
493C22×D3—21no—
494C22×D3—21no—
495C22×D3—21no—
496C22×D3—21no—
497C22×D3—21no—
498C22×D3—21no—
499C22×D3—21no—
500C22×D3—21no—
501C22×D3—21no—
502C22×D3—44no—
503C22×D3—44no—
504C22×D3—44no—
505C22×D3—44no—
506C22×D3—44no—
507C22×D3—44no—
508C22×D3—44no—
509C22×D3C2×C22⋊C412yes—
510C22×D3C2×C22⋊C412yes—
511C22×D3#13112yes—
512C3×D4—44no—
513C2×C3×C4—21no—
514C2×C3×C4—21no—
515C2×C3×C4—22no—
516C2×C3×C4—22no—
517C2×C3×C4—22no—
518C2×C3×C4—22no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—41no—
529C2×C3×C4—41no—
530C2×C3×C4—41no—
531C2×C3×C4—41no—
532C2×C3×C4C2×C22⋊C412yes—
533C2×C3×C4C22×D411yescharacteristic
534C2×C3×C4C22×D411yescharacteristic
535C2×C3×C4H(5,𝔽2)11yescharacteristic
536C2×C3×C4H(5,𝔽2)11yescharacteristic
537C2×C3×C4H(5,𝔽2)11yescharacteristic
538C2×C3×C4H(5,𝔽2)11yescharacteristic
539#67—44no—
540#67—44no—
541#67—44no—
542#67—44no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—44no—
557C2×Dic3C2×C22⋊C412yes—
558C2×Dic3C2×C22⋊C412yes—
559D12—44no—
560D12—44no—
561C4×D3—22no—
562C4×D3—22no—
563C4×D3—22no—
564C4×D3—22no—
565C4×D3—22no—
566C4×D3—22no—
567C4×D3—22no—
568C4×D3—22no—
569C4×D3—44no—
570C4×D3—44no—
571C4×D3—41no—
572C4×D3—41no—
573C4×D3—41no—
574C4×D3—41no—
575Dic6—44no—
576C3×C8—41no—
577C3×C8—41no—
578C3×C8—41no—
579C3×C8—41no—
580C3⋊C8—41no—
581C3⋊C8—41no—
582C3⋊C8—41no—
583C3⋊C8—41no—
584C24—31no—
585C24—31no—
586C24—31no—
587C24—62no—
588C24—62no—
589C24—62no—
590C24—121no—
591C24—121no—
592C24—121no—
593C24—121no—
594C24C2×C4×D311yescharacteristic
595C24C2×C4×D311yescharacteristic
596#41—124no—
597#41—124no—
598#41—124no—
599#41—124no—
600C2×Q8—34no—
601C2×Q8—121no—
602C2×Q8—121no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—34no—
606C2×D4—34no—
607C2×D4—34no—
608C2×D4—41no—
609C2×D4—62no—
610C2×D4—62no—
611C2×D4—62no—
612C2×D4—62no—
613C2×D4—62no—
614C2×D4—62no—
615C2×D4—121no—
616C2×D4—121no—
617C2×D4—121no—
618C2×D4—121no—
619C2×D4—121no—
620C2×D4—121no—
621C2×D4—121no—
622C2×D4—121no—
623C2×D4—121no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—31no—
635C22×C4—31no—
636C22×C4—32no—
637C22×C4—32no—
638C22×C4—32no—
639C22×C4—32no—
640C22×C4—31no—
641C22×C4—31no—
642C22×C4—31no—
643C22×C4—62no—
644C22×C4—62no—
645C22×C4—62no—
646C22×C4—61no—
647C22×C4—61no—
648C22×C4—61no—
649C22×C4—61no—
650C22×C4—61no—
651C22×C4—61no—
652C22×C4—61no—
653C22×C4—61no—
654C22×C4—61no—
655C22×C4—61no—
656C22×C4—61no—
657C22×C4—61no—
658C22×C4—61no—
659C22×C4—61no—
660C22×C4—121no—
661C22×C4—121no—
662C22×C4—121no—
663C22×C4—121no—
664C22×C4—124no—
665C22×C4—124no—
666C22×C4—124no—
667C22×C4—124no—
668C22×C4—121no—
669C22×C4—121no—
670C22×C4C2×C4×D311yescharacteristic
671C22×C4C2×C4×D311yescharacteristic
672C22×C4C2×C4×D311yescharacteristic
673C22×C4C2×C4×D311yescharacteristic
674C22×C4D3×D412yes—
675C22×C4D3×D412yes—
676C22×C4C23×D311yescharacteristic
677M16—44no—
678M16—124no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—61no—
692C2×C8—61no—
693C2×C8—61no—
694C2×C8—61no—
695C2×C8—61no—
696C2×C8—61no—
697C2×C8—61no—
698C2×C8—61no—
699C2×C8—61no—
700C2×C8—61no—
701C2×C8—61no—
702C2×C8—61no—
703C2×C8—124no—
704C2×C8—124no—
705C4⋊C4—22no—
706C4⋊C4—62no—
707C4⋊C4—62no—
708C4⋊C4—62no—
709C4⋊C4—62no—
710C4⋊C4—62no—
711C22⋊C4—22no—
712C22⋊C4—22no—
713C22⋊C4—62no—
714C22⋊C4—62no—
715C22⋊C4—62no—
716C22⋊C4—62no—
717C22⋊C4—62no—
718C22⋊C4—62no—
719C22⋊C4—62no—
720C22⋊C4—62no—
721C42—21no—
722C42—21no—
723C42—61no—
724C42—61no—
725C22×C3—22no—
726C22×C3—22no—
727C22×C3—22no—
728C22×C3—22no—
729C22×C3—22no—
730C22×C3—22no—
731C22×C3—41no—
732C22×C3—41no—
733C22×C3—41no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3C22×C22⋊C411yescharacteristic
740C22×C3#51811yescharacteristic
741C22×C3#51811yescharacteristic
742C22×C3C2×#13111yescharacteristic
743C22×C3C2×#13111yescharacteristic
744C22×C3#56811yescharacteristic
745C22×C3#56811yescharacteristic
746C2×D3—22no—
747C2×D3—22no—
748C2×D3—22no—
749C2×D3—22no—
750C2×D3—22no—
751C2×D3—22no—
752C2×D3—22no—
753C2×D3—22no—
754C2×D3—22no—
755C2×D3—416no—
756C2×D3—41no—
757C2×D3—41no—
758C2×D3—41no—
759C2×D3—41no—
760C2×D3—41no—
761C2×D3—41no—
762C2×D3—41no—
763C2×D3—41no—
764C2×D3—41no—
765C2×D3—41no—
766C2×D3—41no—
767C2×D3—41no—
768C3×C4—22no—
769C3×C4—41no—
770C3×C4—41no—
771C3×C4—41no—
772C3×C4#53411yescharacteristic
773C3×C4#53411yescharacteristic
774C3×C4#53411yescharacteristic
775C3×C4#53411yescharacteristic
776Dic3—22no—
777Dic3—22no—
778Dic3—41no—
779Dic3—41no—
780Dic3—41no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—32no—
794C23—32no—
795C23—32no—
796C23—61no—
797C23—61no—
798C23—61no—
799C23—61no—
800C23—61no—
801C23—61no—
802C23—61no—
803C23—61no—
804C23—61no—
805C23—61no—
806C23—61no—
807C23—61no—
808C23—61no—
809C23—61no—
810C23—61no—
811C23—61no—
812C23—61no—
813C23—61no—
814C23—124no—
815C23—124no—
816C23—124no—
817C23—124no—
818C23—124no—
819C23—124no—
820C23—124no—
821C23D3×C22⋊C412yes—
822C23#90712yes—
823C23C22×C4×D311yescharacteristic
824Q8—124no—
825D4—44no—
826D4—124no—
827D4—124no—
828D4—124no—
829D4—124no—
830D4—124no—
831D4—124no—
832C2×C4—21no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—32no—
848C2×C4—32no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—61no—
854C2×C4—61no—
855C2×C4—61no—
856C2×C4—61no—
857C2×C4—62no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—61no—
866C2×C4—61no—
867C2×C4—61no—
868C2×C4—61no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—124no—
875C2×C4—124no—
876C2×C4—124no—
877C2×C4—121no—
878C2×C4—121no—
879C2×C4—121no—
880C2×C4—121no—
881C2×C4D3×C22⋊C412yes—
882C2×C4C2×D3×D411yescharacteristic
883C2×C4C2×D3×D411yescharacteristic
884C2×C4#100411yescharacteristic
885C2×C4#100411yescharacteristic
886C2×C4#100911yescharacteristic
887C2×C4#100911yescharacteristic
888C8—41no—
889C8—41no—
890C8—41no—
891C8—41no—
892C8—121no—
893C8—121no—
894C8—121no—
895C8—121no—
896C2×C3—42no—
897C2×C3—42no—
898C2×C3#230811yescharacteristic
899C2×C3#288011yescharacteristic
900C2×C3#288011yescharacteristic
901C2×C3#297611yescharacteristic
902C2×C3#297611yescharacteristic
903C2×C3#297711yescharacteristic
904C2×C3#297811yescharacteristic
905D3—42no—
906D3—42no—
907D3—42no—
908C22—22no—
909C22—22no—
910C22—22no—
911C22—22no—
912C22—22no—
913C22—22no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—62no—
923C22—62no—
924C22—62no—
925C22—62no—
926C22—62no—
927C22—62no—
928C22—62no—
929C22—62no—
930C22—62no—
931C22—1216no—
932C22—121no—
933C22—121no—
934C22—121no—
935C22—121no—
936C22—121no—
937C22—121no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22C2×D3×C22⋊C411yescharacteristic
945C22#554511yescharacteristic
946C22#554511yescharacteristic
947C22C2×#90711yescharacteristic
948C22#574511yescharacteristic
949C22D3×#13111yescharacteristic
950C22#575011yescharacteristic
951C4—22no—
952C4—41no—
953C4—41no—
954C4—41no—
955C4—62no—
956C4—62no—
957C4—121no—
958C4—121no—
959C4—121no—
960C4#558911yescharacteristic
961C4#560511yescharacteristic
962C4#560511yescharacteristic
963C4#565311yescharacteristic
964C3#2174411yescharacteristic, complemented, Sylow
965C2—42no—
966C2—42no—
967C2—122no—
968C2—122no—
969C2—122no—
970C2#7487411yescharacteristic
971C2#7863111yescharacteristic
972C2#7866311yescharacteristic
973C2#7948711yescharacteristic
974C2#7948911yescharacteristic
975C2#7954411yescharacteristic
976C2#7954511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D3
commutator, socleC23×C3C23×C4
FittingC3×#1870C2
prime radicalC2×#5547C2
cosocleC22×C3×C4C24
hypercenter#1870D3
hypocenterC3#21744
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C22×C4 ◁ #1870

Complements

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

NH ≅ G/Ntype
2. C2×#5129C2semidirect
3. C2×#4727C2semidirect
4. C3×#1870C2semidirect
5. #71996C2semidirect
6. #71610C2semidirect
7. #69958C2semidirect
8. #69957C2semidirect
9. #69955C2semidirect
10. #69955C2semidirect
11. #69952C2semidirect
12. #68669C2semidirect
13. #68668C2semidirect
14. #68665C2semidirect
15. #68665C2semidirect
19. C22×C3×M16C22semidirect
25. C23×C3⋊C8C22semidirect
26. C22×ΓL(1,𝔽25)C22semidirect
27. C22×D3×C8C22semidirect
40. C2×C3×C22⋊C8C22semidirect
43. C2×#830C22semidirect
53. C2×(C2×D3)⋊C8C22semidirect
54. C2×(C2×D3)⋊C8C22semidirect
56. C3×#336C22semidirect
57. C3×#336C22semidirect
58. #4550C22semidirect
59. #4550C22semidirect
60. #4550C22semidirect
61. #4550C22semidirect
62. #4524C22semidirect
63. #4524C22semidirect
70. #1870D3semidirect
183. C22×M16C2×D3semidirect
218. C2×C22⋊C8C2×D3semidirect
225. #336C2×D3semidirect
226. #336C2×D3semidirect
964. C3#21744semidirect

Maximal subgroups

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

subgroupindex
C2×#55472
C2×#51292
C2×#47272
C3×#18702
#719962
#716102
#699582
#699572
#699552
#699522
#686692
#686682
#686652
#217443