Finite Group Databasebeta

← #11819105

Subgroups — #11819105

Order 1152.

1177 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64105C211yesmaximal, characteristic
2C2×#63839C211yesmaximal, characteristic, complemented
3C3×#4985C211yesmaximal, characteristic, complemented
4C3×#4973C211yesmaximal, characteristic, complemented
5#10591355C211yesmaximal, characteristic
6#10591310C211yesmaximal, characteristic
7#10591289C211yesmaximal, characteristic
8#10591273C211yesmaximal, characteristic, complemented
9#10591273C211yesmaximal, characteristic, complemented
10#10591260C211yesmaximal, characteristic
11#10591259C211yesmaximal, characteristic
12#10591243C211yesmaximal, characteristic, complemented
13#10591236C211yesmaximal, characteristic, complemented
14#10591210C211yesmaximal, characteristic, complemented
15#10591205C211yesmaximal, characteristic
16#78148—31nomaximal
17#76517—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C22×C3×Dic6C2211yescharacteristic
21C22×#627C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27#64105—24no—
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×C4×Dic3C2211yescharacteristic
30C2×#3724C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×#3722C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63839—24no—
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
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×#944—31no—
56C2×#896—31no—
57C2×#896—31no—
58C2×#896—61no—
59C2×#888—31no—
60C3×#400—31no—
61C3×#391—31no—
62#5231—31no—
63#4990—31no—
64#4985D311yescharacteristic, complemented
65#4973D311yescharacteristic, complemented
66#4940—31no—
67C4×Dic3⋊C4—31no—
68#4673—31no—
69#4673—31no—
70#4673—31no—
71#4670—31no—
72#4669—31no—
73#4667—31no—
74#4667—31no—
75#4666—31no—
76#4666—31no—
77#4660—31no—
78#4658—31no—
79#4649—31no—
80#4646—31no—
81#4646—31no—
82#4646—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
93C2×C4×C3⋊D3—22no—
94C2×C4×C3⋊D3—22no—
95C2×C4×C3⋊D3—22no—
96C2×#634—22no—
97C2×#634—22no—
98C2×#634—22no—
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×Dic6—22no—
108C2×C3×Dic6—22no—
109C2×C3×Dic6—41no—
110C2×#627—22no—
111C2×#627—22no—
112C2×#627—41no—
113C32×C4⋊C4—22no—
114#3752—22no—
115#3752—22no—
116#3750—22no—
117#3750D414yes—
118C3×Dic3⋊C4—22no—
119C3×C4×Dic3—41no—
120#3724—22no—
121#3724—22no—
122Dic3⋊Dic3—22no—
123#3722—22no—
124#3722—41no—
125#3722—41no—
126#3722Q814yescomplemented
127Dic32—22no—
128Dic32—22no—
129Dic32—41no—
130#2492—91noSylow
131C22×C3×Q8—31no—
132C22×C4×D3—31no—
133C22×C4×D3—31no—
134C22×C4×D3—61no—
135C22×Dic6—31no—
136C22×Dic6—31no—
137C22×Dic6—31no—
138C22×Dic6—31no—
139C22×Dic6—61no—
140C22×Dic6C2×D311yescharacteristic
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4C2×D311yescharacteristic
144C2×C3×C4⋊C4C2×D311yescharacteristic
145C2×C3×C42—31no—
146#944—64no—
147C2×(C2×D3)⋊C4—31no—
148C2×(C2×D3)⋊C4—31no—
149C2×(C2×D3)⋊C4—31no—
150C2×(C2×D3)⋊C4—31no—
151C2×(C2×D3)⋊C4—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4—31no—
156C2×(C2×D3)⋊C4—31no—
157C2×(C2×D3)⋊C4—31no—
158C2×(C2×D3)⋊C4—31no—
159C2×(C2×D3)⋊C4—61no—
160C2×(C2×D3)⋊C4—61no—
161C2×C4⋊Dic3—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—61no—
172C2×Dic3⋊C4—61no—
173C2×Dic3⋊C4C2×D311yescharacteristic
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—31no—
179C2×C4×Dic3—31no—
180C2×C4×Dic3C2×D311yescharacteristic
181#896—64no—
182#896—64no—
183#896—68no—
184#888—64no—
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—31no—
204C3⋊#95C2×D311yescharacteristic
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
207C3⋊#95C2×D311yescharacteristic
208C3⋊#95C2×D311yescharacteristic
209C3⋊#95C2×D311yescharacteristic
210C3⋊#95C2×D311yescharacteristic
211C3⋊#95C2×D311yescharacteristic
212C3⋊#95C2×D311yescharacteristic
213C23×C32C2411yescharacteristic
214C22×C3⋊D3—21no—
215C22×C3⋊D3—21no—
216C22×C3⋊D3—21no—
217C22×C3⋊D3—21no—
218C22×C3⋊D3—21no—
219C22×C3⋊D3—21no—
220C22×C3⋊D3C2×Q812yes—
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×C4—21no—
229C2×C32×C4C2×D412yes—
230C2×C3⋊Dic3—21no—
231C2×C3⋊Dic3—21no—
232C2×C3⋊Dic3—21no—
233C2×C3⋊Dic3—21no—
234C2×C3⋊Dic3—21no—
235C2×C3⋊Dic3C2×D412yes—
236C2×C3⋊Dic3C2×D412yes—
237C2×C3⋊Dic3#4112yes—
238C2×C3⋊Dic3#4112yes—
239C4×C3⋊D3—44no—
240#634—44no—
241C2×C3×Dic3—21no—
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×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
262C2×C3×Dic3C2×Q812yes—
263C2×C3×Dic3C2×Q812yes—
264C2×C3×Dic3#4112yes—
265C3×Dic6—44no—
266#627—44no—
267C2×C4⋊Q8—91no—
268C2×C22⋊Q8—91no—
269#400—31no—
270#400—91no—
271#393—91no—
272#393—91no—
273#391—31no—
274#391—91no—
275#391—91no—
276#391—91no—
277#388—91no—
278#388—91no—
279#380—91no—
280C4×C4⋊C4—91no—
281C4×C22⋊C4—91no—
282C23×D3—31no—
283C23×D3—31no—
284C23×D3—61no—
285C2×C3×Q8—62no—
286C2×C3×Q8—62no—
287C2×C3×Q8—121no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
290C22×C3×C4—21no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4—31no—
295C22×C3×C4—31no—
296C22×C3×C4—31no—
297C22×C3×C4—31no—
298C22×C3×C4—31no—
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—61no—
312C22×Dic3—61no—
313C22×Dic3—61no—
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C2×C4×D3—62no—
323C2×C4×D3—62no—
324C2×C4×D3—62no—
325C2×C4×D3—62no—
326C2×C4×D3—62no—
327C2×C4×D3—62no—
328C2×C4×D3—64no—
329C2×C4×D3—122no—
330C2×C4×D3—122no—
331C2×Dic6—22no—
332C2×Dic6—22no—
333C2×Dic6—41no—
334C2×Dic6—62no—
335C2×Dic6—62no—
336C2×Dic6—62no—
337C2×Dic6—62no—
338C2×Dic6—62no—
339C2×Dic6—62no—
340C2×Dic6—62no—
341C2×Dic6—62no—
342C2×Dic6—62no—
343C2×Dic6—64no—
344C2×Dic6—62no—
345C2×Dic6—122no—
346C2×Dic6—122no—
347C2×Dic6—121no—
348C2×Dic6—121no—
349C3×C4⋊C4—24no—
350C3×C4⋊C4—22no—
351C3×C4⋊C4—22no—
352C3×C4⋊C4—62no—
353C3×C42—121no—
354(C2×D3)⋊C4—34no—
355(C2×D3)⋊C4—34no—
356(C2×D3)⋊C4—62no—
357(C2×D3)⋊C4—62no—
358(C2×D3)⋊C4—62no—
359(C2×D3)⋊C4—64no—
360(C2×D3)⋊C4—64no—
361(C2×D3)⋊C4—62no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—121no—
365(C2×D3)⋊C4—121no—
366(C2×D3)⋊C4—121no—
367(C2×D3)⋊C4—121no—
368C4⋊Dic3—62no—
369Dic3⋊C4—22no—
370Dic3⋊C4—34no—
371Dic3⋊C4—34no—
372Dic3⋊C4—64no—
373Dic3⋊C4—62no—
374Dic3⋊C4—62no—
375Dic3⋊C4—62no—
376Dic3⋊C4—62no—
377Dic3⋊C4—62no—
378Dic3⋊C4—62no—
379Dic3⋊C4—62no—
380Dic3⋊C4—64no—
381C4×Dic3—41no—
382C4×Dic3—62no—
383C4×Dic3—62no—
384C4×Dic3—62no—
385C4×Dic3—62no—
386C4×Dic3—121no—
387C4×Dic3—121no—
388C22×C32C22×D411yescharacteristic
389C22×C32C22×Q811yescharacteristic
390C22×C32C2×#4111yescharacteristic
391C22×C32C2×#4111yescharacteristic
392C22×C32C2×#4111yescharacteristic
393C22×C32H(5,𝔽2)11yescharacteristic
394C22×C322−1+411yescharacteristic
395C2×C3⋊D3—22no—
396C2×C3⋊D3—22no—
397C2×C3⋊D3—22no—
398C2×C3⋊D3—41no—
399C2×C3⋊D3—41no—
400C2×C3⋊D3—41no—
401C2×C3⋊D3—41no—
402C32×C4—22no—
403C32×C4—41no—
404C32×C4—41no—
405C3⋊Dic3—22no—
406C3⋊Dic3—41no—
407C3⋊Dic3#12414yes—
408C3×Dic3—22no—
409C3×Dic3—22no—
410C3×Dic3—22no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C22×Q8—31no—
417C22×Q8—91no—
418C22×Q8—91no—
419C23×C4—91no—
420C4⋊Q8—184no—
421C22⋊Q8—184no—
422C2×C4⋊C4—31no—
423C2×C4⋊C4—91no—
424C2×C4⋊C4—91no—
425C2×C4⋊C4—91no—
426C2×C4⋊C4—91no—
427C2×C4⋊C4—91no—
428C2×C4⋊C4D3211yescharacteristic
429C2×C22⋊C4—91no—
430C2×C22⋊C4—91no—
431C2×C22⋊C4—91no—
432C2×C22⋊C4—91no—
433C2×C22⋊C4—91no—
434C2×C22⋊C4—91no—
435C2×C42—31no—
436C2×C42—91no—
437C2×C42—91no—
438C2×C42—91no—
439#95—31no—
440#95—31no—
441#95—31no—
442#95—31no—
443#95—31no—
444#95—31no—
445#95—31no—
446#95—31no—
447#95—31no—
448#95—91no—
449#95—91no—
450#95—91no—
451#95—91no—
452#95—91no—
453C23×C3—21no—
454C23×C3C23×D311yescharacteristic
455C23×C3C23×D311yescharacteristic
456C22×D3—32no—
457C22×D3—32no—
458C22×D3—62no—
459C22×D3—62no—
460C22×D3—62no—
461C22×D3—61no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—61no—
465C22×D3—61no—
466C22×D3—61no—
467C22×D3—61no—
468C22×D3—61no—
469C22×D3—61no—
470C22×D3—61no—
471C22×D3—61no—
472C22×D3—61no—
473C22×D3—121no—
474C22×D3—121no—
475C22×D3—121no—
476C22×D3—121no—
477C3×Q8—124no—
478C2×C3×C4—21no—
479C2×C3×C4—21no—
480C2×C3×C4—21no—
481C2×C3×C4—21no—
482C2×C3×C4—22no—
483C2×C3×C4—22no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—21no—
489C2×C3×C4—21no—
490C2×C3×C4—21no—
491C2×C3×C4—21no—
492C2×C3×C4—21no—
493C2×C3×C4—21no—
494C2×C3×C4—21no—
495C2×C3×C4—21no—
496C2×C3×C4—22no—
497C2×C3×C4—32no—
498C2×C3×C4—32no—
499C2×C3×C4—32no—
500C2×C3×C4—41no—
501C2×C3×C4—41no—
502C2×C3×C4—41no—
503C2×C3×C4—41no—
504C2×C3×C4—41no—
505C2×C3×C4—41no—
506C2×C3×C4—61no—
507C2×C3×C4—61no—
508C2×C3×C4—61no—
509C2×C3×C4—61no—
510C2×C3×C4—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4—61no—
521C2×C3×C4—61no—
522C2×C3×C4—61no—
523C2×C3×C4—61no—
524C2×C3×C4—61no—
525C2×C3×C4—61no—
526C2×C3×C4—61no—
527C2×C3×C4D3×D412yes—
528C2×C3×C4D3×D412yes—
529C2×Dic3—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—21no—
535C2×Dic3—21no—
536C2×Dic3—21no—
537C2×Dic3—21no—
538C2×Dic3—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—21no—
542C2×Dic3—21no—
543C2×Dic3—21no—
544C2×Dic3—21no—
545C2×Dic3—21no—
546C2×Dic3—21no—
547C2×Dic3—21no—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—32no—
551C2×Dic3—32no—
552C2×Dic3—32no—
553C2×Dic3—32no—
554C2×Dic3—32no—
555C2×Dic3—32no—
556C2×Dic3—32no—
557C2×Dic3—32no—
558C2×Dic3—62no—
559C2×Dic3—62no—
560C2×Dic3—62no—
561C2×Dic3—62no—
562C2×Dic3—61no—
563C2×Dic3—61no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—62no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—61no—
571C2×Dic3—61no—
572C2×Dic3—61no—
573C2×Dic3—121no—
574C2×Dic3—121no—
575C2×Dic3—121no—
576C2×Dic3—121no—
577C2×Dic3#23512yes—
578C2×Dic3D3×Q812yes—
579C2×Dic3D3×Q812yes—
580C4×D3—124no—
581C4×D3—124no—
582C4×D3—128no—
583Dic6—44no—
584Dic6—124no—
585Dic6—124no—
586Dic6—124no—
587Dic6—124no—
588Dic6—128no—
589C2×C32C2×#12411yescharacteristic
590C2×C32#53311yescharacteristic
591C2×C32#54211yescharacteristic
592C2×C32#54611yescharacteristic
593C2×C32D4×Q811yescharacteristic
594C2×C32#55411yescharacteristic
595C2×C32#55611yescharacteristic
596C3⋊D3—42no—
597C24—91no—
598C2×Q8—62no—
599C2×Q8—62no—
600C2×Q8—121no—
601C2×Q8—182no—
602C2×Q8—182no—
603C2×Q8—182no—
604C2×Q8—182no—
605C2×Q8—182no—
606C2×Q8—361no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—31no—
611C22×C4—31no—
612C22×C4—31no—
613C22×C4—31no—
614C22×C4—31no—
615C22×C4—91no—
616C22×C4—91no—
617C22×C4—91no—
618C22×C4—182no—
619C22×C4—182no—
620C22×C4—182no—
621C22×C4C2×D3211yescharacteristic
622C22×C4C2×D3211yescharacteristic
623C22×C4C2×D3211yescharacteristic
624C4⋊C4—22no—
625C4⋊C4—62no—
626C4⋊C4—94no—
627C4⋊C4—182no—
628C4⋊C4—182no—
629C4⋊C4—182no—
630C4⋊C4—182no—
631C22⋊C4—94no—
632C22⋊C4—182no—
633C22⋊C4—182no—
634C22⋊C4—182no—
635C22⋊C4—361no—
636C22⋊C4—361no—
637C42—121no—
638C42—182no—
639C42—182no—
640C42—361no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—21no—
645C22×C3—21no—
646C22×C3—21no—
647C22×C3—21no—
648C22×C3C2×#23511yescharacteristic
649C22×C3C2×D3×D411yescharacteristic
650C22×C3C2×D3×D411yescharacteristic
651C22×C3#100411yescharacteristic
652C22×C3C2×D3×Q811yescharacteristic
653C22×C3C2×D3×Q811yescharacteristic
654C22×C3#100711yescharacteristic
655C22×C3D3×#4111yescharacteristic
656C22×C3D3×#4111yescharacteristic
657C22×C3D3×#4111yescharacteristic
658C22×C3D3×#4111yescharacteristic
659C22×C3D3×#4111yescharacteristic
660C22×C3#100911yescharacteristic
661C22×C3#101011yescharacteristic
662C2×D3—64no—
663C2×D3—62no—
664C2×D3—62no—
665C2×D3—62no—
666C2×D3—62no—
667C2×D3—62no—
668C2×D3—62no—
669C2×D3—122no—
670C2×D3—122no—
671C2×D3—122no—
672C2×D3—122no—
673C2×D3—122no—
674C2×D3—122no—
675C2×D3—121no—
676C2×D3—121no—
677C2×D3—121no—
678C2×D3—121no—
679C2×D3—121no—
680C2×D3—121no—
681C2×D3—121no—
682C2×D3—121no—
683C3×C4—22no—
684C3×C4—22no—
685C3×C4—42no—
686C3×C4—42no—
687C3×C4—42no—
688C3×C4—41no—
689C3×C4—41no—
690C3×C4—41no—
691C3×C4—41no—
692C3×C4—62no—
693C3×C4—62no—
694C3×C4—62no—
695C3×C4—121no—
696C3×C4—121no—
697C3×C4—121no—
698C3×C4—121no—
699C3×C4—121no—
700Dic3—22no—
701Dic3—22no—
702Dic3—22no—
703Dic3—34no—
704Dic3—34no—
705Dic3—41no—
706Dic3—41no—
707Dic3—41no—
708Dic3—41no—
709Dic3—41no—
710Dic3—64no—
711Dic3—62no—
712Dic3—62no—
713Dic3—122no—
714Dic3—122no—
715Dic3—121no—
716Dic3—121no—
717C32#249211yescharacteristic, complemented, Sylow
718C23—92no—
719C23—181no—
720C23—181no—
721C23—181no—
722C23—181no—
723C23—181no—
724C23—181no—
725C23C22×D3211yescharacteristic
726Q8—124no—
727Q8—364no—
728Q8—364no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—21no—
737C2×C4—32no—
738C2×C4—32no—
739C2×C4—32no—
740C2×C4—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—61no—
753C2×C4—61no—
754C2×C4—61no—
755C2×C4—61no—
756C2×C4—61no—
757C2×C4—61no—
758C2×C4—61no—
759C2×C4—61no—
760C2×C4—61no—
761C2×C4—92no—
762C2×C4—92no—
763C2×C4—92no—
764C2×C4—92no—
765C2×C4—181no—
766C2×C4—181no—
767C2×C4—181no—
768C2×C4—181no—
769C2×C4—181no—
770C2×C4—364no—
771C2×C4#381112yes—
772C2×C3—21no—
773C2×C3—21no—
774C2×C3—21no—
775C2×C3—21no—
776C2×C3—21no—
777C2×C3—21no—
778C2×C3—21no—
779C2×C3#549011yescharacteristic
780C2×C3#556811yescharacteristic
781C2×C3#557811yescharacteristic
782C2×C3#563211yescharacteristic
783C2×C3#563611yescharacteristic
784C2×C3#564011yescharacteristic
785C2×C3#565411yescharacteristic
786C2×C3D3×#12411yescharacteristic
787C2×C3D3×#12411yescharacteristic
788C2×C3#568811yescharacteristic
789C2×C3#569011yescharacteristic
790C2×C3#570211yescharacteristic
791C2×C3#571011yescharacteristic
792C2×C3#572711yescharacteristic
793D3—124no—
794D3—122no—
795D3—122no—
796C22—182no—
797C22—182no—
798C22—182no—
799C22—361no—
800C22—361no—
801C22—361no—
802C22—361no—
803C22D3×#23511yescharacteristic
804C22#6430711yescharacteristic
805C22#6431211yescharacteristic
806C22#6431211yescharacteristic
807C22#6431511yescharacteristic
808C22D32×Q811yescharacteristic
809C22C2×#381111yescharacteristic
810C4—22no—
811C4—41no—
812C4—41no—
813C4—62no—
814C4—62no—
815C4—62no—
816C4—94no—
817C4—121no—
818C4—121no—
819C4—121no—
820C4—121no—
821C4—121no—
822C4—182no—
823C4—361no—
824C3—21no—
825C3#7651711yescharacteristic, complemented
826C3#7814811yescharacteristic, complemented
827C2—362no—
828C2#1059439511yescharacteristic
829C2#1059439811yescharacteristic
830C2#1059442411yescharacteristic
831C2#1059457711yescharacteristic
832C2#1059507711yescharacteristic
833C2#1059517011yescharacteristic
834C2#1059536111yescharacteristic
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×#63839C2semidirect
3. C3×#4985C2semidirect
4. C3×#4973C2semidirect
8. #10591273C2semidirect
9. #10591273C2semidirect
12. #10591243C2semidirect
13. #10591236C2semidirect
14. #10591210C2semidirect
64. #4985D3semidirect
65. #4973D3semidirect
126. #3722Q8semidirect
717. C32#2492semidirect
825. C3#76517semidirect
826. C3#78148semidirect

Maximal subgroups

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

subgroupindex
C2×#641052
C2×#638392
C3×#49852
C3×#49732
#105913552
#105913102
#105912892
#105912732
#105912602
#105912592
#105912432
#105912362
#105912102
#105912052
#781483
#765173