Finite Group Databasebeta

← #11819113

Subgroups — #11819113

Order 1152.

1161 conjugacy classes of subgroups.

The subgroup lattice has 825 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64097C211yesmaximal, characteristic, complemented
2C2×#63899C211yesmaximal, characteristic
3C3×#4990C211yesmaximal, characteristic
4C3×#4986C211yesmaximal, characteristic, complemented
5#10591396C211yesmaximal, characteristic, complemented
6#10591369C211yesmaximal, characteristic
7#10591368C211yesmaximal, characteristic
8#10591322C211yesmaximal, characteristic
9#10591322C211yesmaximal, characteristic
10#10591316C211yesmaximal, characteristic
11#10591273C211yesmaximal, characteristic, complemented
12#10591243C211yesmaximal, characteristic, complemented
13#10591236C211yesmaximal, characteristic, complemented
14#10591218C211yesmaximal, characteristic, complemented
15#10591213C211yesmaximal, characteristic, complemented
16#78148—31nomaximal
17#75547—31nomaximal
18C22×#634C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C2×C32×C4⋊C4C2211yescharacteristic
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25C2×#3750C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27#64097—24no—
28C2×C3×(C2×D3)⋊C4C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×C4⋊Dic3C2211yescharacteristic
32C2×C3×C4×Dic3C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×(C2×D3)⋊Dic3C2211yescharacteristic
36C2×(C2×D3)⋊Dic3C2211yescharacteristic
37C2×(C2×D3)⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40#63899—24no—
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55C2×#896—31no—
56C2×#888—31no—
57C2×#888—31no—
58C2×#888—61no—
59C2×#878—31no—
60C3×#400—31no—
61C3×#388—31no—
62#4990D311yescharacteristic
63#4986D311yescharacteristic, complemented
64#4973—31no—
65#4951—31no—
66#4947—31no—
67#4947—31no—
68#4942—31no—
69Dic3×C22⋊C4—31no—
70C4×Dic3⋊C4—31no—
71#4929—31no—
72#4673—31no—
73#4673—31no—
74#4670—31no—
75#4667—31no—
76#4666—31no—
77#4660—31no—
78#4660—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
93C22×C3⋊Dic3C2311yescharacteristic
94C2×#634—22no—
95C2×#634—22no—
96C2×#634—22no—
97C2×#634—22no—
98C2×#634—41no—
99C2×#634—41no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×#627—22no—
108C2×#627—22no—
109C2×#627—22no—
110C2×D3×Dic3—22no—
111C2×D3×Dic3—22no—
112C2×D3×Dic3—22no—
113C32×C4⋊C4—22no—
114C4⋊(C3⋊Dic3)—22no—
115#3750—22no—
116#3750D414yes—
117C4×C3⋊Dic3—22no—
118C3×(C2×D3)⋊C4—22no—
119C3×(C2×D3)⋊C4—41no—
120C3×(C2×D3)⋊C4Q814yescomplemented
121C3×C4⋊Dic3—22no—
122C3×C4×Dic3—41no—
123#3724—22no—
124#3724—22no—
125(C2×D3)⋊Dic3—22no—
126(C2×D3)⋊Dic3—22no—
127(C2×D3)⋊Dic3—41no—
128Dic32—22no—
129Dic32—41no—
130#2492—91noSylow
131C23×Dic3—31no—
132C22×C4×D3—31no—
133C22×Dic6—31no—
134C22×Dic6—31no—
135C22×Dic6—31no—
136C22×Dic6—31no—
137C22×Dic6—31no—
138C22×Dic6—31no—
139C22×Dic6—61no—
140C22×Dic6—61no—
141C2×C3×C4⋊C4—21no—
142C2×C3×C4⋊C4—31no—
143C2×C3×C4⋊C4C2×D311yescharacteristic
144C2×C3×C4⋊C4C2×D311yescharacteristic
145C2×C3×C22⋊C4—31no—
146C2×C3×C22⋊C4—31no—
147C2×C3×C22⋊C4—31no—
148C2×C3×C42—31no—
149C2×#217—31no—
150C2×#217—31no—
151C2×#217—31no—
152C2×(C2×D3)⋊C4—31no—
153C2×(C2×D3)⋊C4—31no—
154C2×(C2×D3)⋊C4—31no—
155C2×(C2×D3)⋊C4C2×D311yescharacteristic
156C2×(C2×D3)⋊C4C2×D311yescharacteristic
157C2×(C2×D3)⋊C4C2×D311yescharacteristic
158C2×C4⋊Dic3—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—61no—
161C2×C4⋊Dic3C2×D311yescharacteristic
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—61no—
171C2×Dic3⋊C4—61no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—31no—
178C2×C4×Dic3—61no—
179C2×C4×Dic3C2×D311yescharacteristic
180#896—64no—
181#888—64no—
182#888—64no—
183#888—68no—
184#878—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⋊#95—31no—
205C3⋊#95—31no—
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×C4C2×D412yes—
229C2×C32×C4C2×Q812yes—
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⋊Dic3C2×D412yes—
238C2×C3⋊Dic3C2×D412yes—
239C2×C3⋊Dic3#4112yes—
240C2×C3⋊Dic3#4112yes—
241C2×C3⋊Dic3#4112yes—
242#634—44no—
243#634—44no—
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×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3C2×Q812yes—
265#627—44no—
266D3×Dic3—44no—
267C2×C4⋊Q8—91no—
268C2×C22⋊Q8—91no—
269#400—31no—
270#400—91no—
271#393—91no—
272#393—91no—
273#391—91no—
274#391—91no—
275#391—91no—
276#391—91no—
277#388—31no—
278#388—91no—
279#380—91no—
280C4×C4⋊C4—91no—
281C4×C22⋊C4—91no—
282C24×C3—31no—
283C23×D3C22×D311yescharacteristic
284C22×C3×C4—21no—
285C22×C3×C4—21no—
286C22×C3×C4—21no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—31no—
290C22×C3×C4—31no—
291C22×C3×C4—31no—
292C22×C3×C4—31no—
293C22×C3×C4—31no—
294C22×C3×C4C22×D311yescharacteristic
295C22×C3×C4C22×D311yescharacteristic
296C22×C3×C4C22×D311yescharacteristic
297C22×C3×C4C22×D311yescharacteristic
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×Dic3—31no—
301C22×Dic3—31no—
302C22×Dic3—31no—
303C22×Dic3—31no—
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—61no—
309C22×Dic3—61no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—62no—
313C22×Dic3—62no—
314C22×Dic3—62no—
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×Dic6—62no—
326C2×Dic6—62no—
327C2×Dic6—62no—
328C2×Dic6—62no—
329C2×Dic6—62no—
330C2×Dic6—62no—
331C2×Dic6—62no—
332C2×Dic6—62no—
333C2×Dic6—62no—
334C2×Dic6—62no—
335C2×Dic6—62no—
336C2×Dic6—62no—
337C2×Dic6—64no—
338C2×Dic6—64no—
339C2×Dic6—62no—
340C2×Dic6—62no—
341C2×Dic6—122no—
342C2×Dic6—122no—
343C2×Dic6—121no—
344C2×Dic6—121no—
345C2×Dic6—121no—
346C2×Dic6—121no—
347C2×Dic6—122no—
348C2×Dic6—122no—
349C3×C4⋊C4—24no—
350C3×C4⋊C4—22no—
351C3×C4⋊C4—22no—
352C3×C4⋊C4—62no—
353C3×C22⋊C4—34no—
354C3×C22⋊C4—62no—
355C3×C22⋊C4—121no—
356C3×C42—121no—
357#217—62no—
358#217—62no—
359#217—121no—
360(C2×D3)⋊C4—22no—
361(C2×D3)⋊C4—41no—
362(C2×D3)⋊C4—62no—
363(C2×D3)⋊C4—62no—
364(C2×D3)⋊C4—121no—
365(C2×D3)⋊C4Dic614yescomplemented
366C4⋊Dic3—22no—
367C4⋊Dic3—62no—
368C4⋊Dic3—62no—
369C4⋊Dic3—64no—
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—64no—
380C4×Dic3—41no—
381C4×Dic3—62no—
382C4×Dic3—62no—
383C4×Dic3—62no—
384C4×Dic3—62no—
385C4×Dic3—64no—
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—22no—
404C32×C4—41no—
405C3⋊Dic3—22no—
406C3⋊Dic3—22no—
407C3⋊Dic3—41no—
408C3⋊Dic3#12414yes—
409C3×Dic3—22no—
410C3×Dic3—41no—
411C3×Dic3—41no—
412C3×Dic3—41no—
413C3×Dic3—41no—
414C3×Dic3—41no—
415C3×Dic3—41no—
416C22×Q8—91no—
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—31no—
430C2×C22⋊C4—31no—
431C2×C22⋊C4—31no—
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—91no—
447#95—91no—
448#95—91no—
449#95—91no—
450#95—91no—
451#95—91no—
452#95—91no—
453C23×C3—21no—
454C23×C3—32no—
455C23×C3—61no—
456C23×C3—61no—
457C23×C3—61no—
458C23×C3—61no—
459C23×C3—61no—
460C23×C3—61no—
461C23×C3C23×D311yescharacteristic
462C23×C3C23×D311yescharacteristic
463C22×D3—21no—
464C22×D3—21no—
465C22×D3—21no—
466C22×D3—21no—
467C22×D3—21no—
468C22×D3—21no—
469C22×D3C2×Dic612yes—
470C2×C3×C4—22no—
471C2×C3×C4—22no—
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—22no—
481C2×C3×C4—21no—
482C2×C3×C4—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—22no—
488C2×C3×C4—22no—
489C2×C3×C4—32no—
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—61no—
511C2×C3×C4—61no—
512C2×C3×C4—61no—
513C2×C3×C4—61no—
514C2×C3×C4C2×Dic612yes—
515C2×C3×C4D3×D412yes—
516C2×C3×C4D3×D412yes—
517C2×C3×C4D3×Q812yes—
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—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—32no—
539C2×Dic3—32no—
540C2×Dic3—32no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—32no—
546C2×Dic3—32no—
547C2×Dic3—32no—
548C2×Dic3—62no—
549C2×Dic3—62no—
550C2×Dic3—62no—
551C2×Dic3—62no—
552C2×Dic3—62no—
553C2×Dic3—62no—
554C2×Dic3—62no—
555C2×Dic3—61no—
556C2×Dic3—61no—
557C2×Dic3—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—61no—
562C2×Dic3—61no—
563C2×Dic3—62no—
564C2×Dic3—61no—
565C2×Dic3—61no—
566C2×Dic3—61no—
567C2×Dic3—61no—
568C2×Dic3—61no—
569C2×Dic3—61no—
570C2×Dic3—121no—
571C2×Dic3—121no—
572C2×Dic3—121no—
573C2×Dic3—121no—
574C2×Dic3—124no—
575C2×Dic3C2×Dic612yes—
576C4×D3—124no—
577Dic6—124no—
578Dic6—124no—
579Dic6—124no—
580Dic6—124no—
581Dic6—124no—
582Dic6—124no—
583Dic6—128no—
584Dic6—128no—
585C2×C32C2×#12411yescharacteristic
586C2×C32#53311yescharacteristic
587C2×C32#54211yescharacteristic
588C2×C32#54611yescharacteristic
589C2×C32D4×Q811yescharacteristic
590C2×C32#55411yescharacteristic
591C2×C32#55611yescharacteristic
592C3×D3—42no—
593C24—31no—
594C2×Q8—182no—
595C2×Q8—182no—
596C2×Q8—182no—
597C2×Q8—182no—
598C2×Q8—182no—
599C2×Q8—182no—
600C2×Q8—182no—
601C2×Q8—361no—
602C2×Q8—361no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—31no—
607C22×C4—31no—
608C22×C4—31no—
609C22×C4—31no—
610C22×C4—91no—
611C22×C4—91no—
612C22×C4—91no—
613C22×C4—91no—
614C22×C4—182no—
615C22×C4—182no—
616C22×C4—182no—
617C22×C4C2×D3211yescharacteristic
618C22×C4C2×D3211yescharacteristic
619C22×C4C2×D3211yescharacteristic
620C4⋊C4—22no—
621C4⋊C4—62no—
622C4⋊C4—94no—
623C4⋊C4—182no—
624C4⋊C4—182no—
625C4⋊C4—182no—
626C4⋊C4—182no—
627C22⋊C4—34no—
628C22⋊C4—62no—
629C22⋊C4—121no—
630C22⋊C4—182no—
631C22⋊C4—182no—
632C22⋊C4—361no—
633C42—121no—
634C42—182no—
635C42—182no—
636C42—361no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3—21no—
640C22×C3—21no—
641C22×C3—21no—
642C22×C3—21no—
643C22×C3—21no—
644C22×C3—62no—
645C22×C3—62no—
646C22×C3—62no—
647C22×C3—121no—
648C22×C3—121no—
649C22×C3—121no—
650C22×C3—121no—
651C22×C3C22×Dic611yescharacteristic
652C22×C3C2×D3×D411yescharacteristic
653C22×C3C2×D3×D411yescharacteristic
654C22×C3#100411yescharacteristic
655C22×C3C2×D3×Q811yescharacteristic
656C22×C3D3×#4111yescharacteristic
657C22×C3D3×#4111yescharacteristic
658C22×C3D3×#4111yescharacteristic
659C22×C3D3×#4111yescharacteristic
660C22×C3D3×#4111yescharacteristic
661C22×C3D3×#4111yescharacteristic
662C22×C3#100911yescharacteristic
663C22×C3#101011yescharacteristic
664C22×C3#101011yescharacteristic
665C2×D3—22no—
666C2×D3—22no—
667C2×D3—22no—
668C2×D3—41no—
669C2×D3—41no—
670C2×D3—41no—
671C2×D3—41no—
672C3×C4—24no—
673C3×C4—22no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—22no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—62no—
682C3×C4—121no—
683C3×C4—121no—
684C3×C4—121no—
685C3×C4—121no—
686C3×C4—121no—
687C3×C4—121no—
688Dic3—22no—
689Dic3—34no—
690Dic3—34no—
691Dic3—41no—
692Dic3—41no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697Dic3—64no—
698Dic3—64no—
699Dic3—62no—
700Dic3—62no—
701Dic3—62no—
702Dic3—62no—
703Dic3—122no—
704Dic3—122no—
705Dic3—121no—
706Dic3—121no—
707C32#249211yescharacteristic, complemented, Sylow
708C23—32no—
709C23—61no—
710C23—61no—
711C23—61no—
712C23—61no—
713C23—61no—
714C23—61no—
715C23C22×D3211yescharacteristic
716Q8—364no—
717Q8—364no—
718Q8—364no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—32no—
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—61no—
741C2×C4—61no—
742C2×C4—61no—
743C2×C4—61no—
744C2×C4—61no—
745C2×C4—61no—
746C2×C4—61no—
747C2×C4—92no—
748C2×C4—92no—
749C2×C4—92no—
750C2×C4—92no—
751C2×C4—92no—
752C2×C4—181no—
753C2×C4—181no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—181no—
759C2×C4—364no—
760C2×C4D3×Dic612yes—
761C2×C4#381112yes—
762C2×C3—21no—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—122no—
770C2×C3#551711yescharacteristic
771C2×C3D4×Dic611yescharacteristic
772C2×C3#553911yescharacteristic
773C2×C3#561011yescharacteristic
774C2×C3#563211yescharacteristic
775C2×C3#565411yescharacteristic
776C2×C3#566211yescharacteristic
777C2×C3D3×#12411yescharacteristic
778C2×C3D3×#12411yescharacteristic
779C2×C3#568811yescharacteristic
780C2×C3#569011yescharacteristic
781C2×C3#570211yescharacteristic
782C2×C3#570211yescharacteristic
783C2×C3#571011yescharacteristic
784D3—42no—
785C22—62no—
786C22—62no—
787C22—62no—
788C22—121no—
789C22—121no—
790C22—121no—
791C22—121no—
792C22C2×D3×Dic611yescharacteristic
793C22#6429811yescharacteristic
794C22#6431211yescharacteristic
795C22#6431411yescharacteristic
796C22#6431911yescharacteristic
797C22#6431911yescharacteristic
798C22C2×#381111yescharacteristic
799C4—22no—
800C4—22no—
801C4—41no—
802C4—62no—
803C4—94no—
804C4—121no—
805C4—121no—
806C4—121no—
807C4—121no—
808C4—121no—
809C4—121no—
810C4—182no—
811C4—182no—
812C4—361no—
813C3—21no—
814C3#7554711yescharacteristic, complemented
815C3#7814811yescharacteristic, complemented
816C2—122no—
817C2#1059447711yescharacteristic
818C2#1059448011yescharacteristic
819C2#1059448511yescharacteristic
820C2#1059448711yescharacteristic
821C2#1059491511yescharacteristic
822C2#1059516311yescharacteristic
823C2#1059543211yescharacteristic
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
1. C2×#64097C2semidirect
4. C3×#4986C2semidirect
5. #10591396C2semidirect
11. #10591273C2semidirect
12. #10591243C2semidirect
13. #10591236C2semidirect
14. #10591218C2semidirect
15. #10591213C2semidirect
63. #4986D3semidirect
120. C3×(C2×D3)⋊C4Q8semidirect
365. (C2×D3)⋊C4Dic6semidirect
707. C32#2492semidirect
814. C3#75547semidirect
815. C3#78148semidirect

Maximal subgroups

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

subgroupindex
C2×#640972
C2×#638992
C3×#49902
C3×#49862
#105913962
#105913692
#105913682
#105913222
#105913162
#105912732
#105912432
#105912362
#105912182
#105912132
#781483
#755473