Finite Group Databasebeta

← #11819106

Subgroups — #11819106

Order 1152.

1109 conjugacy classes of subgroups.

The subgroup lattice has 817 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#896C211yesmaximal, characteristic
2C2×#63840C211yesmaximal, characteristic, complemented
3#10592672C211yesmaximal, characteristic, complemented
4C3×#4985C211yesmaximal, characteristic, complemented
5#10591322C211yesmaximal, characteristic
6#10591295C211yesmaximal, characteristic
7#10591293C211yesmaximal, characteristic
8#10591284C211yesmaximal, characteristic
9#10591283C211yesmaximal, characteristic
10#10591261C211yesmaximal, characteristic, complemented
11#10591261C211yesmaximal, characteristic, complemented
12#10591241C211yesmaximal, characteristic, complemented
13#10591237C211yesmaximal, characteristic
14#10591235C211yesmaximal, characteristic, complemented
15#10591196C211yesmaximal, characteristic, complemented
16#82773—31nomaximal
17#78148—31nomaximal
18C22×#634C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C4×C3⋊Dic3C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2211yescharacteristic
25C2×C3×(C2×D3)⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×Dic3⋊C4C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C3×#896—24no—
30C2×Dic3⋊Dic3C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×(C2×D3)⋊Dic3C2211yescharacteristic
34C2×(C2×D3)⋊Dic3C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63840—24no—
41#63658C2211yescharacteristic
42#63658C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×C3×C22⋊Q8—31no—
56C2×#896D311yescharacteristic
57C2×#888—31no—
58C2×#888—31no—
59C3×#400—31no—
60#5229—31no—
61#5229—31no—
62#5212—31no—
63C4×#217—31no—
64#4990—31no—
65#4985—31no—
66#4985D311yescharacteristic, complemented
67Dic3×C4⋊C4—31no—
68#4973—31no—
69#4973—31no—
70#4973—31no—
71#4973—61no—
72#4947—31no—
73#4947—31no—
74#4945—31no—
75#4945—31no—
76#4673—31no—
77#4673—31no—
78#4670—31no—
79#4667—31no—
80#4666—31no—
81#4660—31no—
82#4649—31no—
83#4646—31no—
84#4646—31no—
85#4646—31no—
86C23×C3×D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C2×#634—22no—
95C2×#634—22no—
96C2×#634—41no—
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×Dic6—22no—
108C2×C3×Dic6—22no—
109C2×C3×Dic6—22no—
110C2×#627—22no—
111C2×#627—22no—
112C2×#627—41no—
113C32×C4⋊C4—22no—
114C4×C3⋊Dic3—41no—
115C3×(C2×D3)⋊C4—22no—
116C3×(C2×D3)⋊C4—22no—
117C3×Dic3⋊C4—22no—
118C3×Dic3⋊C4—22no—
119C3×Dic3⋊C4D414yes—
120Dic3⋊Dic3—22no—
121Dic3⋊Dic3—22no—
122Dic3⋊Dic3—22no—
123(C2×D3)⋊Dic3—22no—
124(C2×D3)⋊Dic3—41no—
125(C2×D3)⋊Dic3—41no—
126(C2×D3)⋊Dic3Q814yescomplemented
127Dic32—22no—
128Dic32—22no—
129Dic32—41no—
130#2492—91noSylow
131C22×C3×Q8—31no—
132C23×C3×C4—31no—
133C22×C4×D3C2×D311yescharacteristic
134C22×Dic6—31no—
135C22×Dic6—31no—
136C22×Dic6—31no—
137C22×Dic6—31no—
138C22×Dic6—61no—
139C22×Dic6C2×D311yescharacteristic
140C3×C22⋊Q8—64no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4—31no—
144C2×C3×C4⋊C4—31no—
145C2×C3×C4⋊C4C2×D311yescharacteristic
146C2×C3×C4⋊C4C2×D311yescharacteristic
147C2×C3×C22⋊C4—31no—
148C2×C3×C22⋊C4—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×#217—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4C2×D311yescharacteristic
158C2×(C2×D3)⋊C4C2×D311yescharacteristic
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4C2×D311yescharacteristic
166C2×Dic3⋊C4C2×D311yescharacteristic
167C2×Dic3⋊C4C2×D311yescharacteristic
168C2×C4×Dic3—31no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—61no—
177#896—24no—
178#888—64no—
179#888—64no—
180C3×#95—31no—
181C3×#95—31no—
182C3×#95—31no—
183C3×#95—31no—
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—31no—
203C3⋊#95—61no—
204C3⋊#95—61no—
205C3⋊#95—61no—
206C3⋊#95—61no—
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C23×C32C2411yescharacteristic
213C22×C3×D3—21no—
214C22×C3×D3—21no—
215C22×C3×D3—21no—
216C22×C3×D3—21no—
217C22×C3×D3—21no—
218C22×C3×D3—21no—
219C22×C3×D3C2×Q812yes—
220C2×C32×C4—21no—
221C2×C32×C4—21no—
222C2×C32×C4—21no—
223C2×C32×C4—21no—
224C2×C32×C4—21no—
225C2×C32×C4—21no—
226C2×C32×C4—21no—
227C2×C32×C4—21no—
228C2×C32×C4C2×D412yes—
229C2×C3⋊Dic3—21no—
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⋊Dic3C2×Q812yes—
240C2×C3⋊Dic3#4112yes—
241#634—44no—
242C2×C3×Dic3—21no—
243C2×C3×Dic3—21no—
244C2×C3×Dic3—21no—
245C2×C3×Dic3—21no—
246C2×C3×Dic3—21no—
247C2×C3×Dic3—21no—
248C2×C3×Dic3—21no—
249C2×C3×Dic3—21no—
250C2×C3×Dic3—21no—
251C2×C3×Dic3—21no—
252C2×C3×Dic3—21no—
253C2×C3×Dic3—21no—
254C2×C3×Dic3—21no—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3C2×D412yes—
259C2×C3×Dic3C2×D412yes—
260C2×C3×Dic3C2×Q812yes—
261C2×C3×Dic3#4112yes—
262C2×C3×Dic3#4112yes—
263C3×C4×D3—44no—
264C3×Dic6—44no—
265#627—44no—
266C2×C4⋊Q8—91no—
267C2×C22⋊Q8—31no—
268#400—31no—
269#400—91no—
270#393—91no—
271#393—91no—
272#391—91no—
273#391—91no—
274#391—91no—
275#391—91no—
276#388—91no—
277#388—91no—
278#380—91no—
279C4×C4⋊C4—91no—
280C4×C22⋊C4—91no—
281C24×C3—31no—
282C23×D3C22×D311yescharacteristic
283C2×C3×Q8—62no—
284C2×C3×Q8—62no—
285C2×C3×Q8—62no—
286C22×C3×C4—21no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—62no—
297C22×C3×C4—62no—
298C22×C3×C4—62no—
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C22×D311yescharacteristic
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—31no—
311C22×Dic3—31no—
312C22×Dic3—31no—
313C22×Dic3—61no—
314C22×Dic3—61no—
315C22×Dic3—61no—
316C22×Dic3—61no—
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C2×C4×D3—22no—
325C2×C4×D3—22no—
326C2×C4×D3—22no—
327C2×Dic6—22no—
328C2×Dic6—22no—
329C2×Dic6—22no—
330C2×Dic6—62no—
331C2×Dic6—62no—
332C2×Dic6—62no—
333C2×Dic6—62no—
334C2×Dic6—62no—
335C2×Dic6—64no—
336C2×Dic6—62no—
337C2×Dic6—62no—
338C2×Dic6—62no—
339C2×Dic6—122no—
340C2×Dic6—121no—
341C2×Dic6—121no—
342C2×Dic6—121no—
343C2×Dic6—121no—
344C2×Dic6—122no—
345C3×C4⋊C4—22no—
346C3×C4⋊C4—22no—
347C3×C4⋊C4—34no—
348C3×C4⋊C4—42no—
349C3×C4⋊C4—62no—
350C3×C4⋊C4—62no—
351C3×C22⋊C4—62no—
352C3×C22⋊C4—62no—
353#217—34no—
354#217—62no—
355#217—121no—
356#217—121no—
357(C2×D3)⋊C4—22no—
358(C2×D3)⋊C4—22no—
359(C2×D3)⋊C4—34no—
360(C2×D3)⋊C4—62no—
361(C2×D3)⋊C4—121no—
362(C2×D3)⋊C4—121no—
363C4⋊Dic3—62no—
364C4⋊Dic3—62no—
365C4⋊Dic3—62no—
366Dic3⋊C4—22no—
367Dic3⋊C4—22no—
368Dic3⋊C4—62no—
369Dic3⋊C4—62no—
370Dic3⋊C4—62no—
371Dic3⋊C4#6714yes—
372C4×Dic3—62no—
373C4×Dic3—62no—
374C4×Dic3—62no—
375C4×Dic3—62no—
376C4×Dic3—121no—
377C4×Dic3—121no—
378C4×Dic3—121no—
379C4×Dic3—121no—
380C4×Dic3—122no—
381C22×C32C22×D411yescharacteristic
382C22×C32C22×Q811yescharacteristic
383C22×C32C2×#4111yescharacteristic
384C22×C32C2×#4111yescharacteristic
385C22×C32C2×#4111yescharacteristic
386C22×C32H(5,𝔽2)11yescharacteristic
387C22×C322−1+411yescharacteristic
388C2×C3×D3—22no—
389C2×C3×D3—22no—
390C2×C3×D3—22no—
391C2×C3×D3—41no—
392C2×C3×D3—41no—
393C2×C3×D3—41no—
394C2×C3×D3—41no—
395C32×C4—22no—
396C32×C4—41no—
397C32×C4—41no—
398C3⋊Dic3—22no—
399C3⋊Dic3—22no—
400C3⋊Dic3—41no—
401C3⋊Dic3—41no—
402C3×Dic3—22no—
403C3×Dic3—22no—
404C3×Dic3—41no—
405C3×Dic3—41no—
406C3×Dic3—41no—
407C3×Dic3—41no—
408C3×Dic3#12414yes—
409C22×Q8—31no—
410C22×Q8—91no—
411C22×Q8—91no—
412C23×C4—31no—
413C4⋊Q8—184no—
414C22⋊Q8—64no—
415C2×C4⋊C4—31no—
416C2×C4⋊C4—31no—
417C2×C4⋊C4—31no—
418C2×C4⋊C4—91no—
419C2×C4⋊C4—91no—
420C2×C4⋊C4—91no—
421C2×C4⋊C4D3211yescharacteristic
422C2×C22⋊C4—31no—
423C2×C22⋊C4—31no—
424C2×C22⋊C4—91no—
425C2×C22⋊C4—91no—
426C2×C22⋊C4—91no—
427C2×C22⋊C4—91no—
428C2×C42—91no—
429C2×C42—91no—
430C2×C42—91no—
431C2×C42—91no—
432#95—31no—
433#95—31no—
434#95—31no—
435#95—31no—
436#95—31no—
437#95—91no—
438#95—91no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95—91no—
443#95—91no—
444#95—91no—
445#95—91no—
446C23×C3—21no—
447C23×C3—32no—
448C23×C3—61no—
449C23×C3—61no—
450C23×C3—61no—
451C23×C3—61no—
452C23×C3—61no—
453C23×C3—61no—
454C23×C3C23×D311yescharacteristic
455C23×C3C23×D311yescharacteristic
456C22×D3—21no—
457C22×D3—21no—
458C22×D3—21no—
459C22×D3—21no—
460C22×D3—21no—
461C22×D3—21no—
462C22×D3D3×Q812yes—
463C3×Q8—124no—
464C2×C3×C4—22no—
465C2×C3×C4—22no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—21no—
476C2×C3×C4—21no—
477C2×C3×C4—21no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—22no—
483C2×C3×C4—32no—
484C2×C3×C4—32no—
485C2×C3×C4—32no—
486C2×C3×C4—32no—
487C2×C3×C4—32no—
488C2×C3×C4—41no—
489C2×C3×C4—41no—
490C2×C3×C4—41no—
491C2×C3×C4—41no—
492C2×C3×C4—41no—
493C2×C3×C4—41no—
494C2×C3×C4—61no—
495C2×C3×C4—61no—
496C2×C3×C4—61no—
497C2×C3×C4—61no—
498C2×C3×C4—61no—
499C2×C3×C4—61no—
500C2×C3×C4—61no—
501C2×C3×C4—61no—
502C2×C3×C4—61no—
503C2×C3×C4—61no—
504C2×C3×C4—61no—
505C2×C3×C4—61no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—124no—
511C2×C3×C4D3×D412yes—
512C2×C3×C4C2×#6712yes—
513C2×Dic3—21no—
514C2×Dic3—21no—
515C2×Dic3—21no—
516C2×Dic3—21no—
517C2×Dic3—21no—
518C2×Dic3—21no—
519C2×Dic3—21no—
520C2×Dic3—21no—
521C2×Dic3—21no—
522C2×Dic3—21no—
523C2×Dic3—21no—
524C2×Dic3—21no—
525C2×Dic3—21no—
526C2×Dic3—21no—
527C2×Dic3—21no—
528C2×Dic3—21no—
529C2×Dic3—32no—
530C2×Dic3—32no—
531C2×Dic3—32no—
532C2×Dic3—32no—
533C2×Dic3—62no—
534C2×Dic3—62no—
535C2×Dic3—61no—
536C2×Dic3—61no—
537C2×Dic3—61no—
538C2×Dic3—61no—
539C2×Dic3—61no—
540C2×Dic3—61no—
541C2×Dic3—61no—
542C2×Dic3—61no—
543C2×Dic3—62no—
544C2×Dic3—62no—
545C2×Dic3—61no—
546C2×Dic3—61no—
547C2×Dic3—61no—
548C2×Dic3—61no—
549C2×Dic3—61no—
550C2×Dic3—61no—
551C2×Dic3—61no—
552C2×Dic3—61no—
553C2×Dic3—61no—
554C2×Dic3—61no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—121no—
558C2×Dic3—121no—
559C2×Dic3—121no—
560C2×Dic3—121no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3#23712yes—
566C2×Dic3#23712yes—
567C2×Dic3D3×Q812yes—
568C2×Dic3C2×#6712yes—
569C2×Dic3C2×#6712yes—
570C4×D3—44no—
571Dic6—44no—
572Dic6—124no—
573Dic6—124no—
574Dic6—124no—
575Dic6—124no—
576Dic6—128no—
577C2×C32C2×#12411yescharacteristic
578C2×C32#53311yescharacteristic
579C2×C32#54211yescharacteristic
580C2×C32#54611yescharacteristic
581C2×C32D4×Q811yescharacteristic
582C2×C32#55411yescharacteristic
583C2×C32#55611yescharacteristic
584C3×D3—42no—
585C24—31no—
586C2×Q8—62no—
587C2×Q8—62no—
588C2×Q8—62no—
589C2×Q8—182no—
590C2×Q8—182no—
591C2×Q8—182no—
592C2×Q8—182no—
593C2×Q8—361no—
594C2×Q8—361no—
595C22×C4—31no—
596C22×C4—31no—
597C22×C4—31no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—62no—
603C22×C4—62no—
604C22×C4—62no—
605C22×C4—91no—
606C22×C4—91no—
607C22×C4—91no—
608C22×C4—91no—
609C22×C4C2×D3211yescharacteristic
610C22×C4C2×D3211yescharacteristic
611C22×C4C2×D3211yescharacteristic
612C4⋊C4—22no—
613C4⋊C4—34no—
614C4⋊C4—62no—
615C4⋊C4—62no—
616C4⋊C4—182no—
617C4⋊C4—182no—
618C4⋊C4—182no—
619C22⋊C4—62no—
620C22⋊C4—62no—
621C22⋊C4—94no—
622C22⋊C4—182no—
623C22⋊C4—361no—
624C22⋊C4—361no—
625C42—182no—
626C42—182no—
627C42—361no—
628C42—361no—
629C22×C3—21no—
630C22×C3—21no—
631C22×C3—21no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—62no—
637C22×C3—62no—
638C22×C3—62no—
639C22×C3—121no—
640C22×C3—121no—
641C22×C3—121no—
642C22×C3—121no—
643C22×C3C2×D3×D411yescharacteristic
644C22×C3C2×#23711yescharacteristic
645C22×C3C2×#23711yescharacteristic
646C22×C3C2×D3×Q811yescharacteristic
647C22×C3C2×D3×Q811yescharacteristic
648C22×C3#100711yescharacteristic
649C22×C3D3×#4111yescharacteristic
650C22×C3D3×#4111yescharacteristic
651C22×C3D3×#4111yescharacteristic
652C22×C3D3×#4111yescharacteristic
653C22×C3#100911yescharacteristic
654C22×C3#100911yescharacteristic
655C22×C3#101011yescharacteristic
656C22×C3C22×#6711yescharacteristic
657C2×D3—22no—
658C2×D3—22no—
659C2×D3—22no—
660C2×D3—41no—
661C2×D3—41no—
662C2×D3—41no—
663C2×D3—41no—
664C3×C4—24no—
665C3×C4—22no—
666C3×C4—22no—
667C3×C4—34no—
668C3×C4—41no—
669C3×C4—41no—
670C3×C4—41no—
671C3×C4—41no—
672C3×C4—62no—
673C3×C4—62no—
674C3×C4—81no—
675C3×C4—81no—
676C3×C4—121no—
677C3×C4—121no—
678C3×C4—121no—
679C3×C4—121no—
680Dic3—22no—
681Dic3—22no—
682Dic3—41no—
683Dic3—41no—
684Dic3—41no—
685Dic3—41no—
686Dic3—62no—
687Dic3—62no—
688Dic3—62no—
689Dic3—62no—
690Dic3—122no—
691Dic3—122no—
692Dic3—122no—
693Dic3—122no—
694Dic3—121no—
695Dic3—121no—
696Dic3—121no—
697Dic3—121no—
698Dic3#93614yes—
699C32#249211yescharacteristic, complemented, Sylow
700C23—32no—
701C23—61no—
702C23—61no—
703C23—61no—
704C23—61no—
705C23—61no—
706C23—61no—
707C23C22×D3211yescharacteristic
708Q8—124no—
709Q8—364no—
710Q8—364no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—32no—
720C2×C4—32no—
721C2×C4—32no—
722C2×C4—32no—
723C2×C4—32no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—61no—
732C2×C4—61no—
733C2×C4—61no—
734C2×C4—61no—
735C2×C4—61no—
736C2×C4—61no—
737C2×C4—61no—
738C2×C4—61no—
739C2×C4—61no—
740C2×C4—92no—
741C2×C4—92no—
742C2×C4—124no—
743C2×C4—181no—
744C2×C4—181no—
745C2×C4—181no—
746C2×C4—181no—
747C2×C4—181no—
748C2×C4—181no—
749C2×C4—181no—
750C2×C4—181no—
751C2×C4—181no—
752C2×C4—181no—
753C2×C4D3×#6712yes—
754C2×C3—21no—
755C2×C3—21no—
756C2×C3—21no—
757C2×C3—21no—
758C2×C3—21no—
759C2×C3—21no—
760C2×C3—21no—
761C2×C3—122no—
762C2×C3#562211yescharacteristic
763C2×C3#563211yescharacteristic
764C2×C3#563511yescharacteristic
765C2×C3#564111yescharacteristic
766C2×C3#564311yescharacteristic
767C2×C3#565411yescharacteristic
768C2×C3D3×#12411yescharacteristic
769C2×C3#568811yescharacteristic
770C2×C3#569011yescharacteristic
771C2×C3#570211yescharacteristic
772C2×C3#571011yescharacteristic
773C2×C3C2×#93611yescharacteristic
774C2×C3Q8×#6711yescharacteristic
775C2×C3#582911yescharacteristic
776D3—42no—
777C22—62no—
778C22—62no—
779C22—62no—
780C22—121no—
781C22—121no—
782C22—121no—
783C22—121no—
784C22#6430611yescharacteristic
785C22#6430811yescharacteristic
786C22D3×#23711yescharacteristic
787C22D3×#23711yescharacteristic
788C22#6431511yescharacteristic
789C22D32×Q811yescharacteristic
790C22C2×D3×#6711yescharacteristic
791C4—22no—
792C4—34no—
793C4—41no—
794C4—41no—
795C4—62no—
796C4—62no—
797C4—121no—
798C4—121no—
799C4—121no—
800C4—121no—
801C4—182no—
802C4—182no—
803C4—361no—
804C4—361no—
805C3—21no—
806C3#7814811yescharacteristic, complemented
807C3#8277311yescharacteristic, complemented
808C2—122no—
809C2#1059438811yescharacteristic
810C2#1059439611yescharacteristic
811C2#1059445111yescharacteristic
812C2#1059455411yescharacteristic
813C2#1059506811yescharacteristic
814C2D3×#93611yescharacteristic
815C2#1059540011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC23×C3×D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63840C2semidirect
3. #10592672C2semidirect
4. C3×#4985C2semidirect
10. #10591261C2semidirect
11. #10591261C2semidirect
12. #10591241C2semidirect
14. #10591235C2semidirect
15. #10591196C2semidirect
66. #4985D3semidirect
126. (C2×D3)⋊Dic3Q8semidirect
699. C32#2492semidirect
806. C3#78148semidirect
807. C3#82773semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8962
C2×#638402
#105926722
C3×#49852
#105913222
#105912952
#105912932
#105912842
#105912832
#105912612
#105912412
#105912372
#105912352
#105911962
#827733
#781483