Finite Group Databasebeta

← #11807122

Subgroups — #11807122

Order 1152.

1085 conjugacy classes of subgroups.

The subgroup lattice has 753 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63840C211yesmaximal, characteristic
2#10592345C211yesmaximal, characteristic
3C3×#4649C211yesmaximal, characteristic
4C3×#4647C211yesmaximal, characteristic
5#10591330C211yesmaximal, characteristic
6C4×Dic3⋊Dic3C211yesmaximal, characteristic
7#10591265C211yesmaximal, characteristic
8#10591241C211yesmaximal, characteristic
9Dic3×Dic3⋊C4C211yesmaximal, characteristic
10Dic3×Dic3⋊C4C211yesmaximal, characteristic
11Dic3×Dic3⋊C4C211yesmaximal, characteristic
12#10591235C211yesmaximal, characteristic
13#10591234C211yesmaximal, characteristic
14#10591213C211yesmaximal, characteristic
15#10591191C211yesmaximal, characteristic
16#75987—31nomaximal
17#73657—31nomaximal
18C22×#634C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C2×#3750C2211yescharacteristic
21C2×C4×C3⋊Dic3C2211yescharacteristic
22C2×C3×C4⋊Dic3C2211yescharacteristic
23C2×C3×Dic3⋊C4C2211yescharacteristic
24C2×C3×Dic3⋊C4C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×Dic3⋊Dic3C2211yescharacteristic
35C2×Dic3⋊Dic3C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C2×Dic32C2211yescharacteristic
41#63840C418yescomplemented
42C32×#95C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#888—31no—
55C2×#888—31no—
56C3×#389—31no—
57C3×C4×C4⋊C4—31no—
58#4984—31no—
59#4976—31no—
60#4976—31no—
61Dic3×C4⋊C4—31no—
62Dic3×C4⋊C4—31no—
63Dic3×C4⋊C4—31no—
64Dic3×C4⋊C4—31no—
65#4973—31no—
66#4973—31no—
67#4972—31no—
68C4×C4⋊Dic3—31no—
69C4×Dic3⋊C4—31no—
70C4×Dic3⋊C4—31no—
71C4×Dic3⋊C4—31no—
72C4×Dic3⋊C4—31no—
73#4929—31no—
74#4929—31no—
75#4928—31no—
76#4649—31no—
77#4649D311yescharacteristic
78#4647—31no—
79#4647D311yescharacteristic
80#4646—31no—
81#4646—31no—
82#4646—31no—
83#4646—31no—
84#4646—61no—
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C3⋊Dic3C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C2×#634—41no—
93C2×#634—41no—
94C2×#634C2×C414yes—
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C2×#627—41no—
104C2×#627—41no—
105C2×#627C2×C414yes—
106#3750—41no—
107C4×C3⋊Dic3—41no—
108C3×C4⋊Dic3—41no—
109C3×Dic3⋊C4—22no—
110C3×Dic3⋊C4—41no—
111C3×Dic3⋊C4C2×C414yes—
112C3×Dic3⋊C4C2×C414yes—
113C3×Dic3⋊C4Q814yescomplemented
114C3×C4×Dic3—22no—
115C3×C4×Dic3—22no—
116C3×C4×Dic3—41no—
117C3×C4×Dic3—41no—
118Dic3⋊Dic3—22no—
119Dic3⋊Dic3—41no—
120Dic3⋊Dic3C2×C414yes—
121Dic3⋊Dic3C2×C414yes—
122Dic3⋊Dic3Q814yescomplemented
123Dic32—22no—
124Dic32—22no—
125Dic32—41no—
126Dic32C2×C414yes—
127#2369—91noSylow
128C22×Dic6—31no—
129C22×Dic6—31no—
130C22×Dic6—31no—
131C22×Dic6—31no—
132C22×Dic6—61no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4—31no—
138C2×C3×C4⋊C4—31no—
139C2×C3×C42—31no—
140C2×C3×C42—31no—
141C2×C3×C42—31no—
142C2×C3×C42—31no—
143C2×C4⋊Dic3—31no—
144C2×C4⋊Dic3—31no—
145C2×C4⋊Dic3—31no—
146C2×C4⋊Dic3—31no—
147C2×C4⋊Dic3—31no—
148C2×C4⋊Dic3C2×D311yescharacteristic
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4—31no—
151C2×Dic3⋊C4—31no—
152C2×Dic3⋊C4—31no—
153C2×Dic3⋊C4—31no—
154C2×Dic3⋊C4—31no—
155C2×Dic3⋊C4—31no—
156C2×Dic3⋊C4—61no—
157C2×Dic3⋊C4C2×D311yescharacteristic
158C2×Dic3⋊C4C2×D311yescharacteristic
159C2×Dic3⋊C4C2×D311yescharacteristic
160C2×Dic3⋊C4C2×D311yescharacteristic
161C2×Dic3⋊C4C2×D311yescharacteristic
162C2×C4×Dic3—31no—
163C2×C4×Dic3—31no—
164C2×C4×Dic3—31no—
165C2×C4×Dic3—31no—
166C2×C4×Dic3—31no—
167C2×C4×Dic3—31no—
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—61no—
173C2×C4×Dic3C2×D311yescharacteristic
174C2×C4×Dic3C2×D311yescharacteristic
175C2×C4×Dic3C2×D311yescharacteristic
176C2×C4×Dic3C2×D311yescharacteristic
177#888—38no—
178#888—38no—
179C3×#95—21no—
180C3×#95—31no—
181C3×#95—31no—
182C3×#95C2×D311yescharacteristic
183C3×#95C2×D311yescharacteristic
184C3⋊#95—31no—
185C3⋊#95—31no—
186C3⋊#95—31no—
187C3⋊#95—31no—
188C3⋊#95—31no—
189C3⋊#95—31no—
190C3⋊#95—31no—
191C3⋊#95—31no—
192C3⋊#95—31no—
193C3⋊#95—31no—
194C3⋊#95—31no—
195C3⋊#95—31no—
196C3⋊#95—31no—
197C3⋊#95—31no—
198C3⋊#95—31no—
199C3⋊#95—31no—
200C3⋊#95—31no—
201C3⋊#95—31no—
202C3⋊#95—61no—
203C3⋊#95—61no—
204C3⋊#95—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C23×C32C2411yescharacteristic
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C32×C4—21no—
213C2×C32×C4—21no—
214C2×C32×C4—21no—
215C2×C32×C4C22×C412yes—
216C2×C32×C4C2×Q812yes—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3C22×C412yes—
227C2×C3⋊Dic3C22×C412yes—
228C2×C3⋊Dic3C2×Q812yes—
229#634—44no—
230C2×C3×Dic3—21no—
231C2×C3×Dic3—21no—
232C2×C3×Dic3—21no—
233C2×C3×Dic3—21no—
234C2×C3×Dic3—21no—
235C2×C3×Dic3—21no—
236C2×C3×Dic3—21no—
237C2×C3×Dic3—21no—
238C2×C3×Dic3—21no—
239C2×C3×Dic3—21no—
240C2×C3×Dic3—21no—
241C2×C3×Dic3—21no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3C22×C412yes—
245C2×C3×Dic3C22×C412yes—
246C2×C3×Dic3C22×C412yes—
247C2×C3×Dic3C22×C412yes—
248C2×C3×Dic3C2×Q812yes—
249C2×C3×Dic3C2×Q812yes—
250C2×C3×Dic3C2×Q812yes—
251C2×C3×Dic3C2×Q812yes—
252C2×C3×Dic3#4112yes—
253C2×C3×Dic3#4112yes—
254#627—44no—
255C2×C4⋊Q8—91no—
256#391—91no—
257#391—91no—
258#391—91no—
259#391—91no—
260#389—31no—
261#389—91no—
262#389—91no—
263#389—91no—
264C4×C4⋊C4—31no—
265C4×C4⋊C4—91no—
266C4×C4⋊C4—91no—
267C4×C4⋊C4—91no—
268C4×C4⋊C4—91no—
269C4×C4⋊C4—91no—
270C22×C3×C4—21no—
271C22×C3×C4—21no—
272C22×C3×C4—21no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4C22×D311yescharacteristic
282C22×C3×C4C22×D311yescharacteristic
283C22×C3×C4C22×D311yescharacteristic
284C22×C3×C4C22×D311yescharacteristic
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×Dic3—31no—
288C22×Dic3—31no—
289C22×Dic3—31no—
290C22×Dic3—31no—
291C22×Dic3—31no—
292C22×Dic3—31no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—61no—
296C22×Dic3—61no—
297C22×Dic3—61no—
298C22×Dic3—61no—
299C22×Dic3C22×D311yescharacteristic
300C22×Dic3C22×D311yescharacteristic
301C22×Dic3C22×D311yescharacteristic
302C22×Dic3C22×D311yescharacteristic
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C2×Dic6—34no—
308C2×Dic6—34no—
309C2×Dic6—34no—
310C2×Dic6—34no—
311C2×Dic6—64no—
312C2×Dic6—121no—
313C2×Dic6—121no—
314C2×Dic6—121no—
315C2×Dic6—121no—
316C2×Dic6—121no—
317C2×Dic6—121no—
318C2×Dic6—121no—
319C2×Dic6—121no—
320C2×Dic6—122no—
321C2×Dic6—122no—
322C3×C4⋊C4—34no—
323C3×C4⋊C4—34no—
324C3×C4⋊C4—34no—
325C3×C4⋊C4—62no—
326C3×C4⋊C4—121no—
327C3×C4⋊C4—121no—
328C3×C42—62no—
329C3×C42—62no—
330C3×C42—121no—
331C3×C42—121no—
332C4⋊Dic3—34no—
333C4⋊Dic3—34no—
334C4⋊Dic3—34no—
335C4⋊Dic3—41no—
336C4⋊Dic3—62no—
337C4⋊Dic3—121no—
338Dic3⋊C4—22no—
339Dic3⋊C4—34no—
340Dic3⋊C4—34no—
341Dic3⋊C4—34no—
342Dic3⋊C4—41no—
343Dic3⋊C4—62no—
344Dic3⋊C4—121no—
345Dic3⋊C4—121no—
346Dic3⋊C4—121no—
347Dic3⋊C4—122no—
348Dic3⋊C4Dic614yescomplemented
349Dic3⋊C4C4×D314yes—
350Dic3⋊C4C4×D314yes—
351C4×Dic3—22no—
352C4×Dic3—22no—
353C4×Dic3—34no—
354C4×Dic3—34no—
355C4×Dic3—41no—
356C4×Dic3—41no—
357C4×Dic3—62no—
358C4×Dic3—62no—
359C4×Dic3—62no—
360C4×Dic3—62no—
361C4×Dic3—121no—
362C4×Dic3—121no—
363C4×Dic3—121no—
364C4×Dic3—121no—
365C4×Dic3—122no—
366C22×C32C23×C411yescharacteristic
367C22×C32C22×Q811yescharacteristic
368C22×C32C22×Q811yescharacteristic
369C22×C32C2×#4111yescharacteristic
370C22×C32C2×#4111yescharacteristic
371C22×C32H(5,𝔽2)11yescharacteristic
372C22×C32H(5,𝔽2)11yescharacteristic
373C32×C4—22no—
374C32×C4—22no—
375C32×C4—41no—
376C3⋊Dic3—22no—
377C3⋊Dic3—22no—
378C3⋊Dic3—22no—
379C3⋊Dic3—41no—
380C3×Dic3—22no—
381C3×Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3—22no—
384C3×Dic3—41no—
385C3×Dic3—41no—
386C3×Dic3C4×Q814yes—
387C3×Dic3C4×Q814yes—
388C22×Q8—91no—
389C22×Q8—91no—
390C4⋊Q8—98no—
391C2×C4⋊C4—31no—
392C2×C4⋊C4—31no—
393C2×C4⋊C4—31no—
394C2×C4⋊C4—31no—
395C2×C4⋊C4—31no—
396C2×C4⋊C4—31no—
397C2×C4⋊C4—91no—
398C2×C4⋊C4—91no—
399C2×C4⋊C4—91no—
400C2×C4⋊C4—91no—
401C2×C4⋊C4—91no—
402C2×C4⋊C4—91no—
403C2×C42—31no—
404C2×C42—31no—
405C2×C42—31no—
406C2×C42—31no—
407C2×C42—91no—
408C2×C42—91no—
409C2×C42—91no—
410C2×C42—91no—
411C2×C42—91no—
412#95—31no—
413#95—31no—
414#95—91no—
415#95—91no—
416#95—91no—
417#95—91no—
418#95—91no—
419#95—91no—
420#95—91no—
421#95—91no—
422#95—91no—
423#95D3211yescharacteristic
424C23×C3—21no—
425C23×C3C23×D311yescharacteristic
426C23×C3C23×D311yescharacteristic
427C2×C3×C4—21no—
428C2×C3×C4—21no—
429C2×C3×C4—21no—
430C2×C3×C4—21no—
431C2×C3×C4—21no—
432C2×C3×C4—21no—
433C2×C3×C4—21no—
434C2×C3×C4—21no—
435C2×C3×C4—21no—
436C2×C3×C4—21no—
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—22no—
442C2×C3×C4—22no—
443C2×C3×C4—32no—
444C2×C3×C4—32no—
445C2×C3×C4—32no—
446C2×C3×C4—32no—
447C2×C3×C4—32no—
448C2×C3×C4—32no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—32no—
452C2×C3×C4—32no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—41no—
458C2×C3×C4—41no—
459C2×C3×C4—41no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4C2×Dic612yes—
475C2×C3×C4C2×C4×D312yes—
476C2×C3×C4C2×C4×D312yes—
477C2×C3×C4D3×Q812yes—
478C2×Dic3—21no—
479C2×Dic3—21no—
480C2×Dic3—21no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—32no—
493C2×Dic3—32no—
494C2×Dic3—32no—
495C2×Dic3—32no—
496C2×Dic3—32no—
497C2×Dic3—32no—
498C2×Dic3—62no—
499C2×Dic3—62no—
500C2×Dic3—62no—
501C2×Dic3—62no—
502C2×Dic3—62no—
503C2×Dic3—61no—
504C2×Dic3—61no—
505C2×Dic3—61no—
506C2×Dic3—61no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—121no—
522C2×Dic3—121no—
523C2×Dic3—121no—
524C2×Dic3—121no—
525C2×Dic3—121no—
526C2×Dic3—121no—
527C2×Dic3—121no—
528C2×Dic3C2×Dic612yes—
529C2×Dic3C2×Dic612yes—
530C2×Dic3C2×C4×D312yes—
531C2×Dic3C2×C4×D312yes—
532C2×Dic3C2×C4×D312yes—
533C2×Dic3C2×C4×D312yes—
534C2×Dic3#23512yes—
535C2×Dic3#23712yes—
536C2×Dic3D3×Q812yes—
537C2×Dic3D3×Q812yes—
538Dic6—124no—
539Dic6—124no—
540Dic6—124no—
541Dic6—124no—
542Dic6—128no—
543C2×C32C2×C4×Q811yescharacteristic
544C2×C32C2×C4×Q811yescharacteristic
545C2×C32#51811yescharacteristic
546C2×C32#55411yescharacteristic
547C2×C32#55411yescharacteristic
548C2×C32#55511yescharacteristic
549C2×C32Q8211yescharacteristic
550C2×Q8—94no—
551C2×Q8—94no—
552C2×Q8—361no—
553C2×Q8—361no—
554C2×Q8—361no—
555C2×Q8—361no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—31no—
564C22×C4—91no—
565C22×C4—91no—
566C22×C4—91no—
567C22×C4—91no—
568C22×C4C2×D3211yescharacteristic
569C22×C4C2×D3211yescharacteristic
570C22×C4C2×D3211yescharacteristic
571C4⋊C4—34no—
572C4⋊C4—34no—
573C4⋊C4—34no—
574C4⋊C4—62no—
575C4⋊C4—94no—
576C4⋊C4—94no—
577C4⋊C4—94no—
578C4⋊C4—121no—
579C4⋊C4—121no—
580C4⋊C4—182no—
581C4⋊C4—361no—
582C4⋊C4—361no—
583C42—62no—
584C42—62no—
585C42—94no—
586C42—121no—
587C42—121no—
588C42—182no—
589C42—182no—
590C42—361no—
591C42—361no—
592C22×C3—21no—
593C22×C3—21no—
594C22×C3—21no—
595C22×C3—21no—
596C22×C3—21no—
597C22×C3—21no—
598C22×C3—21no—
599C22×C3C22×Dic611yescharacteristic
600C22×C3C22×C4×D311yescharacteristic
601C22×C3C22×C4×D311yescharacteristic
602C22×C3C2×#23511yescharacteristic
603C22×C3C2×#23711yescharacteristic
604C22×C3#100411yescharacteristic
605C22×C3#100411yescharacteristic
606C22×C3C2×D3×Q811yescharacteristic
607C22×C3C2×D3×Q811yescharacteristic
608C22×C3C2×D3×Q811yescharacteristic
609C22×C3D3×#4111yescharacteristic
610C22×C3D3×#4111yescharacteristic
611C22×C3#100911yescharacteristic
612C22×C3#100911yescharacteristic
613C3×C4—22no—
614C3×C4—22no—
615C3×C4—22no—
616C3×C4—22no—
617C3×C4—34no—
618C3×C4—34no—
619C3×C4—42no—
620C3×C4—42no—
621C3×C4—41no—
622C3×C4—41no—
623C3×C4—62no—
624C3×C4—62no—
625C3×C4—62no—
626C3×C4—62no—
627C3×C4—81no—
628C3×C4—121no—
629C3×C4—121no—
630Dic3—22no—
631Dic3—22no—
632Dic3—22no—
633Dic3—22no—
634Dic3—41no—
635Dic3—41no—
636Dic3—64no—
637Dic3—62no—
638Dic3—62no—
639Dic3—62no—
640Dic3—62no—
641Dic3—62no—
642Dic3—62no—
643Dic3—122no—
644Dic3—122no—
645Dic3—121no—
646Dic3—121no—
647Dic3—241no—
648Dic3C4×Dic614yes—
649Dic3#88714yes—
650C32#236911yescharacteristic, complemented, Sylow
651C23C22×D3211yescharacteristic
652Q8—364no—
653Q8—364no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—32no—
662C2×C4—32no—
663C2×C4—32no—
664C2×C4—32no—
665C2×C4—32no—
666C2×C4—32no—
667C2×C4—32no—
668C2×C4—32no—
669C2×C4—32no—
670C2×C4—32no—
671C2×C4—61no—
672C2×C4—61no—
673C2×C4—61no—
674C2×C4—61no—
675C2×C4—61no—
676C2×C4—61no—
677C2×C4—61no—
678C2×C4—61no—
679C2×C4—61no—
680C2×C4—61no—
681C2×C4—61no—
682C2×C4—61no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—92no—
686C2×C4—92no—
687C2×C4—92no—
688C2×C4—181no—
689C2×C4—181no—
690C2×C4—181no—
691C2×C4—181no—
692C2×C4—181no—
693C2×C4—181no—
694C2×C4—181no—
695C2×C4—181no—
696C2×C4—181no—
697C2×C4D3×Dic612yes—
698C2×C4C4×D3212yes—
699C2×C3—21no—
700C2×C3—21no—
701C2×C3—21no—
702C2×C3—21no—
703C2×C3—21no—
704C2×C3—21no—
705C2×C3—21no—
706C2×C3C2×C4×Dic611yescharacteristic
707C2×C3C2×#88711yescharacteristic
708C2×C3#551111yescharacteristic
709C2×C3#553211yescharacteristic
710C2×C3#553911yescharacteristic
711C2×C3#554511yescharacteristic
712C2×C3#554511yescharacteristic
713C2×C3Q8×Dic611yescharacteristic
714C2×C3C4×D3×Q811yescharacteristic
715C2×C3C4×D3×Q811yescharacteristic
716C2×C3#561611yescharacteristic
717C2×C3#563511yescharacteristic
718C2×C3#569011yescharacteristic
719C2×C3#572211yescharacteristic
720C22C2×D3×Dic611yescharacteristic
721C22C2×C4×D3211yescharacteristic
722C22D3×#23511yescharacteristic
723C22D3×#23711yescharacteristic
724C22#6431411yescharacteristic
725C22#6431411yescharacteristic
726C22D32×Q811yescharacteristic
727C4—22no—
728C4—22no—
729C4—34no—
730C4—34no—
731C4—41no—
732C4—62no—
733C4—62no—
734C4—62no—
735C4—62no—
736C4—121no—
737C4—121no—
738C4—182no—
739C4—182no—
740C4—182no—
741C4—361no—
742C3—21no—
743C3#7365711yescharacteristic, complemented
744C3#7598711yescharacteristic, complemented
745C2C4×D3×Dic611yescharacteristic
746C2#1059410411yescharacteristic
747C2#1059413311yescharacteristic
748C2#1059425611yescharacteristic
749C2#1059431211yescharacteristic
750C2D3×#88711yescharacteristic
751C2#1059453811yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, prime radical, cosocleC23×C32C24
hypercenter#95D32
hypocenterC32#2369
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
41. #63840C4semidirect
113. C3×Dic3⋊C4Q8semidirect
122. Dic3⋊Dic3Q8semidirect
348. Dic3⋊C4Dic6semidirect
650. C32#2369semidirect
743. C3#73657semidirect
744. C3#75987semidirect

Maximal subgroups

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

subgroupindex
C2×#638402
#105923452
C3×#46492
C3×#46472
#105913302
C4×Dic3⋊Dic32
#105912652
#105912412
Dic3×Dic3⋊C42
#105912352
#105912342
#105912132
#105911912
#759873
#736573