Finite Group Databasebeta

← #11819109

Subgroups — #11819109

Order 1152.

1111 conjugacy classes of subgroups.

The subgroup lattice has 827 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63918C211yesmaximal, characteristic, complemented
2C2×#63888C211yesmaximal, characteristic
3#10592369C211yesmaximal, characteristic
4C3×#4660C211yesmaximal, characteristic, complemented
5C3×#4646C211yesmaximal, characteristic, complemented
6#10591396C211yesmaximal, characteristic, complemented
7#10591367C211yesmaximal, characteristic
8#10591266C211yesmaximal, characteristic
9#10591261C211yesmaximal, characteristic, complemented
10#10591241C211yesmaximal, characteristic, complemented
11#10591235C211yesmaximal, characteristic, complemented
12#10591233C211yesmaximal, characteristic
13#10591218C211yesmaximal, characteristic, complemented
14#10591205C211yesmaximal, characteristic
15#10591205C211yesmaximal, characteristic
16#78148—31nomaximal
17#76633—31nomaximal
18C22×C3×Dic6C2211yescharacteristic
19C22×#627C2211yescharacteristic
20C22×#627C2211yescharacteristic
21C22×#624C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×Dic3⋊C4C2211yescharacteristic
29C2×C3×Dic3⋊C4C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×#3724C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33C2×Dic3⋊Dic3C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×Dic32C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39#63918—24no—
40#63888—24no—
41C32×#95C2211yescharacteristic
42#63658C2211yescharacteristic
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×#946—31no—
56C2×#896—31no—
57C2×#888—31no—
58C2×#869—31no—
59C3×#400—31no—
60C3×#391—31no—
61#5229—31no—
62#4990—31no—
63#4987—31no—
64Dic3×C4⋊C4—31no—
65#4973—31no—
66C4×(C2×D3)⋊C4—31no—
67#4673—31no—
68#4673—31no—
69#4673—31no—
70#4673—31no—
71#4670—31no—
72#4670—31no—
73#4670—31no—
74#4670—61no—
75#4667—31no—
76#4666—31no—
77#4660—31no—
78#4660—31no—
79#4660D311yescharacteristic, complemented
80#4649—31no—
81#4646—31no—
82#4646—31no—
83#4646—31no—
84#4646—31no—
85#4646D311yescharacteristic, complemented
86C23×C3⋊D3C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C22×C3×Dic3C2311yescharacteristic
96C22×C3×Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C2×C3×Dic6—22no—
102C2×C3×Dic6—22no—
103C2×C3×Dic6—22no—
104C2×#627—22no—
105C2×#627—22no—
106C2×#627—22no—
107C2×#627—22no—
108C2×#627—41no—
109C2×#627—41no—
110C2×#624—22no—
111C2×#624—22no—
112C2×#624—22no—
113#3752—22no—
114#3752—41no—
115#3752Q814yescomplemented
116C4⋊(C3⋊Dic3)—22no—
117C4×C3⋊Dic3—41no—
118C3×C4⋊Dic3—22no—
119C3×Dic3⋊C4—22no—
120C3×Dic3⋊C4—22no—
121C3×C4×Dic3—22no—
122#3724—22no—
123Dic3⋊Dic3—22no—
124Dic3⋊Dic3D414yes—
125#3722—22no—
126#3722—22no—
127#3722—41no—
128Dic32—22no—
129Dic32—41no—
130#2492—91noSylow
131C22×C3×Q8—31no—
132C22×C4×D3—31no—
133C22×C4×D3—31no—
134C22×Dic6—31no—
135C22×Dic6—31no—
136C22×Dic6—31no—
137C22×Dic6—31no—
138C22×Dic6C2×D311yescharacteristic
139C2×C3×C4⋊C4—31no—
140C2×C3×C4⋊C4—31no—
141C2×C3×C4⋊C4—31no—
142C2×C3×C42—31no—
143#946—64no—
144C2×(C2×D3)⋊C4—31no—
145C2×(C2×D3)⋊C4—31no—
146C2×(C2×D3)⋊C4—31no—
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—61no—
157C2×(C2×D3)⋊C4—61no—
158C2×(C2×D3)⋊C4—61no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—61no—
164C2×C4⋊Dic3C2×D311yescharacteristic
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—31no—
168C2×Dic3⋊C4—31no—
169C2×Dic3⋊C4C2×D311yescharacteristic
170C2×Dic3⋊C4C2×D311yescharacteristic
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3—31no—
174C2×C4×Dic3—31no—
175C2×C4×Dic3—31no—
176C2×C4×Dic3—31no—
177C2×C4×Dic3—61no—
178C2×C4×Dic3C2×D311yescharacteristic
179#896—64no—
180#888—64no—
181#869—64no—
182C3×#95—21no—
183C3×#95—31no—
184C3×#95—31no—
185C3×#95—31no—
186C3×#95—31no—
187C3×#95—31no—
188C3×#95—31no—
189C3×#95—31no—
190C3×#95C2×D311yescharacteristic
191C3×#95C2×D311yescharacteristic
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—61no—
205C3⋊#95C2×D311yescharacteristic
206C3⋊#95C2×D311yescharacteristic
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×Q812yes—
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⋊Dic3C2×D412yes—
237C2×C3⋊Dic3C2×Q812yes—
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×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×Dic3C2×D412yes—
258C2×C3×Dic3C2×D412yes—
259C2×C3×Dic3#4112yes—
260C2×C3×Dic3#4112yes—
261C2×C3×Dic3#4112yes—
262C3×Dic6—44no—
263#627—44no—
264#627—44no—
265#624—44no—
266C2×C4⋊Q8—91no—
267C2×C22⋊Q8—91no—
268#400—31no—
269#400—91no—
270#393—91no—
271#393—91no—
272#391—31no—
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—
281C23×D3—31no—
282C23×D3—31no—
283C23×D3—61no—
284C2×C3×Q8—62no—
285C2×C3×Q8—62no—
286C2×C3×Q8—62no—
287C22×C3×C4—21no—
288C22×C3×C4—21no—
289C22×C3×C4—21no—
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—31no—
297C22×C3×C4—31no—
298C22×C3×C4C22×D311yescharacteristic
299C22×C3×C4C22×D311yescharacteristic
300C22×C3×C4C22×D311yescharacteristic
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D311yescharacteristic
303C22×C3×C4C22×D311yescharacteristic
304C22×Dic3—31no—
305C22×Dic3—31no—
306C22×Dic3—31no—
307C22×Dic3—31no—
308C22×Dic3—31no—
309C22×Dic3—31no—
310C22×Dic3—61no—
311C22×Dic3—61no—
312C22×Dic3—61no—
313C22×Dic3C22×D311yescharacteristic
314C22×Dic3C22×D311yescharacteristic
315C22×Dic3C22×D311yescharacteristic
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C2×C4×D3—62no—
322C2×C4×D3—62no—
323C2×C4×D3—62no—
324C2×C4×D3—62no—
325C2×C4×D3—62no—
326C2×C4×D3—62no—
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—62no—
336C2×Dic6—62no—
337C2×Dic6—62no—
338C2×Dic6—121no—
339C2×Dic6—121no—
340C2×Dic6—121no—
341C2×Dic6—121no—
342C3×C4⋊C4—62no—
343C3×C4⋊C4—62no—
344C3×C4⋊C4—62no—
345C3×C42—62no—
346(C2×D3)⋊C4—34no—
347(C2×D3)⋊C4—34no—
348(C2×D3)⋊C4—64no—
349(C2×D3)⋊C4—62no—
350(C2×D3)⋊C4—62no—
351(C2×D3)⋊C4—62no—
352(C2×D3)⋊C4—62no—
353(C2×D3)⋊C4—62no—
354(C2×D3)⋊C4—62no—
355(C2×D3)⋊C4—122no—
356(C2×D3)⋊C4—121no—
357(C2×D3)⋊C4—121no—
358(C2×D3)⋊C4—121no—
359(C2×D3)⋊C4—121no—
360(C2×D3)⋊C4—122no—
361C4⋊Dic3—22no—
362C4⋊Dic3—34no—
363C4⋊Dic3—62no—
364C4⋊Dic3—62no—
365C4⋊Dic3—62no—
366C4⋊Dic3—122no—
367Dic3⋊C4—22no—
368Dic3⋊C4—22no—
369Dic3⋊C4—34no—
370Dic3⋊C4—62no—
371Dic3⋊C4—62no—
372Dic3⋊C4—62no—
373C4×Dic3—22no—
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—22no—
402C3×Dic3—22no—
403C3×Dic3—41no—
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—91no—
413C4⋊Q8—184no—
414C22⋊Q8—184no—
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⋊C4—91no—
422C2×C22⋊C4—91no—
423C2×C22⋊C4—91no—
424C2×C22⋊C4—91no—
425C2×C22⋊C4—91no—
426C2×C22⋊C4—91no—
427C2×C22⋊C4—91no—
428C2×C42—31no—
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—31no—
438#95—31no—
439#95—91no—
440#95—91no—
441#95—91no—
442#95—91no—
443#95—91no—
444#95—91no—
445#95D3211yescharacteristic
446C23×C3—21no—
447C23×C3C23×D311yescharacteristic
448C23×C3C23×D311yescharacteristic
449C22×D3—32no—
450C22×D3—32no—
451C22×D3—62no—
452C22×D3—61no—
453C22×D3—61no—
454C22×D3—61no—
455C22×D3—61no—
456C22×D3—61no—
457C22×D3—61no—
458C22×D3—61no—
459C22×D3—61no—
460C22×D3—61no—
461C22×D3—61no—
462C22×D3—61no—
463C22×D3—61no—
464C22×D3—121no—
465C22×D3—121no—
466C22×D3—121no—
467C22×D3—121no—
468C22×D3—121no—
469C22×D3—121no—
470C3×Q8—124no—
471C2×C3×C4—21no—
472C2×C3×C4—21no—
473C2×C3×C4—21no—
474C2×C3×C4—21no—
475C2×C3×C4—22no—
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—21no—
483C2×C3×C4—21no—
484C2×C3×C4—21no—
485C2×C3×C4—21no—
486C2×C3×C4—21no—
487C2×C3×C4—21no—
488C2×C3×C4—22no—
489C2×C3×C4—32no—
490C2×C3×C4—32no—
491C2×C3×C4—32no—
492C2×C3×C4—32no—
493C2×C3×C4—32no—
494C2×C3×C4—41no—
495C2×C3×C4—41no—
496C2×C3×C4—41no—
497C2×C3×C4—41no—
498C2×C3×C4—41no—
499C2×C3×C4—41no—
500C2×C3×C4—41no—
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×C4—61no—
515C2×C3×C4—61no—
516C2×C3×C4—61no—
517C2×C3×C4—61no—
518C2×C3×C4—61no—
519C2×C3×C4—61no—
520C2×C3×C4D3×Q812yes—
521C2×C3×C4D3×Q812yes—
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—21no—
539C2×Dic3—21no—
540C2×Dic3—21no—
541C2×Dic3—32no—
542C2×Dic3—32no—
543C2×Dic3—32no—
544C2×Dic3—32no—
545C2×Dic3—62no—
546C2×Dic3—62no—
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—61no—
558C2×Dic3—61no—
559C2×Dic3—61no—
560C2×Dic3—61no—
561C2×Dic3—121no—
562C2×Dic3—121no—
563C2×Dic3—121no—
564C2×Dic3—121no—
565C2×Dic3—121no—
566C2×Dic3—121no—
567C2×Dic3—121no—
568C2×Dic3#23512yes—
569C2×Dic3D3×D412yes—
570C2×Dic3D3×D412yes—
571C2×Dic3#23712yes—
572C2×Dic3#23912yes—
573C4×D3—124no—
574C4×D3—124no—
575Dic6—44no—
576Dic6—124no—
577Dic6—124no—
578Dic6—124no—
579Dic6—124no—
580C2×C32C2×#12411yescharacteristic
581C2×C32#53311yescharacteristic
582C2×C32#54211yescharacteristic
583C2×C32#54611yescharacteristic
584C2×C32D4×Q811yescharacteristic
585C2×C32#55411yescharacteristic
586C2×C32#55611yescharacteristic
587C3⋊D3—42no—
588C24—91no—
589C2×Q8—62no—
590C2×Q8—62no—
591C2×Q8—62no—
592C2×Q8—182no—
593C2×Q8—182no—
594C2×Q8—182no—
595C2×Q8—182no—
596C2×Q8—361no—
597C2×Q8—361no—
598C22×C4—31no—
599C22×C4—31no—
600C22×C4—31no—
601C22×C4—31no—
602C22×C4—31no—
603C22×C4—31no—
604C22×C4—31no—
605C22×C4—31no—
606C22×C4—91no—
607C22×C4—91no—
608C22×C4—91no—
609C22×C4—182no—
610C22×C4—182no—
611C22×C4—182no—
612C22×C4C2×D3211yescharacteristic
613C22×C4C2×D3211yescharacteristic
614C22×C4C2×D3211yescharacteristic
615C4⋊C4—62no—
616C4⋊C4—62no—
617C4⋊C4—62no—
618C4⋊C4—94no—
619C4⋊C4—182no—
620C4⋊C4—182no—
621C4⋊C4—182no—
622C22⋊C4—94no—
623C22⋊C4—182no—
624C22⋊C4—182no—
625C22⋊C4—182no—
626C22⋊C4—361no—
627C22⋊C4—361no—
628C42—62no—
629C42—182no—
630C42—361no—
631C42—361no—
632C22×C3—21no—
633C22×C3—21no—
634C22×C3—21no—
635C22×C3—21no—
636C22×C3—21no—
637C22×C3—21no—
638C22×C3—21no—
639C22×C3C2×#23511yescharacteristic
640C22×C3C2×D3×D411yescharacteristic
641C22×C3C2×D3×D411yescharacteristic
642C22×C3C2×#23711yescharacteristic
643C22×C3C2×D3×Q811yescharacteristic
644C22×C3C2×D3×Q811yescharacteristic
645C22×C3C2×#23911yescharacteristic
646C22×C3D3×#4111yescharacteristic
647C22×C3D3×#4111yescharacteristic
648C22×C3D3×#4111yescharacteristic
649C22×C3#100911yescharacteristic
650C22×C3#100911yescharacteristic
651C22×C3#101011yescharacteristic
652C22×C3#101011yescharacteristic
653C2×D3—62no—
654C2×D3—62no—
655C2×D3—62no—
656C2×D3—62no—
657C2×D3—62no—
658C2×D3—62no—
659C2×D3—122no—
660C2×D3—122no—
661C2×D3—122no—
662C2×D3—121no—
663C2×D3—121no—
664C2×D3—121no—
665C2×D3—121no—
666C2×D3—121no—
667C2×D3—121no—
668C2×D3—121no—
669C2×D3—121no—
670C2×D3—241no—
671C2×D3—241no—
672C2×D3—241no—
673C2×D3—241no—
674C3×C4—22no—
675C3×C4—22no—
676C3×C4—34no—
677C3×C4—42no—
678C3×C4—42no—
679C3×C4—41no—
680C3×C4—41no—
681C3×C4—41no—
682C3×C4—41no—
683C3×C4—62no—
684C3×C4—62no—
685C3×C4—81no—
686C3×C4—121no—
687C3×C4—121no—
688C3×C4—121no—
689C3×C4—121no—
690C3×C4—121no—
691Dic3—22no—
692Dic3—22no—
693Dic3—41no—
694Dic3—41no—
695Dic3—41no—
696Dic3—41no—
697Dic3—41no—
698Dic3—62no—
699Dic3—62no—
700Dic3—62no—
701Dic3—62no—
702Dic3—122no—
703Dic3—122no—
704Dic3—121no—
705Dic3—121no—
706Dic3—241no—
707Dic3#88514yes—
708C32#249211yescharacteristic, complemented, Sylow
709C23—92no—
710C23—181no—
711C23—181no—
712C23—181no—
713C23—181no—
714C23—181no—
715C23—181no—
716C23C22×D3211yescharacteristic
717Q8—124no—
718Q8—364no—
719Q8—364no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—32no—
729C2×C4—32no—
730C2×C4—32no—
731C2×C4—32no—
732C2×C4—32no—
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—61no—
748C2×C4—61no—
749C2×C4—61no—
750C2×C4—61no—
751C2×C4—61no—
752C2×C4—92no—
753C2×C4—92no—
754C2×C4—181no—
755C2×C4—181no—
756C2×C4—181no—
757C2×C4—181no—
758C2×C4—181no—
759C2×C4—181no—
760C2×C4—181no—
761C2×C4—364no—
762C2×C4#379712yes—
763C2×C3—21no—
764C2×C3—21no—
765C2×C3—21no—
766C2×C3—21no—
767C2×C3—21no—
768C2×C3—21no—
769C2×C3—21no—
770C2×C3C2×#88511yescharacteristic
771C2×C3#557911yescharacteristic
772C2×C3#558411yescharacteristic
773C2×C3#563011yescharacteristic
774C2×C3#563211yescharacteristic
775C2×C3#563211yescharacteristic
776C2×C3#565411yescharacteristic
777C2×C3D3×#12411yescharacteristic
778C2×C3#568211yescharacteristic
779C2×C3#568811yescharacteristic
780C2×C3#569011yescharacteristic
781C2×C3#570211yescharacteristic
782C2×C3#571011yescharacteristic
783C2×C3#572811yescharacteristic
784D3—122no—
785D3—122no—
786D3—242no—
787C22—182no—
788C22—182no—
789C22—182no—
790C22—361no—
791C22—361no—
792C22—361no—
793C22—361no—
794C22C2×#379711yescharacteristic
795C22D3×#23511yescharacteristic
796C22#6430811yescharacteristic
797C22#6430911yescharacteristic
798C22D32×D411yescharacteristic
799C22D3×#23711yescharacteristic
800C22D3×#23911yescharacteristic
801C4—22no—
802C4—34no—
803C4—41no—
804C4—41no—
805C4—62no—
806C4—62no—
807C4—121no—
808C4—121no—
809C4—121no—
810C4—121no—
811C4—121no—
812C4—182no—
813C4—182no—
814C4—361no—
815C3—21no—
816C3#7663311yescharacteristic, complemented
817C3#7814811yescharacteristic, complemented
818C2—362no—
819C2#1059393811yescharacteristic
820C2#1059407211yescharacteristic
821C2#1059413811yescharacteristic
822C2D3×#88511yescharacteristic
823C2#1059442111yescharacteristic
824C2#1059444811yescharacteristic
825C2#1059462011yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3⋊D3C23
hypercenter#95D32
hypocenterC32#2492
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C2×#63918C2semidirect
4. C3×#4660C2semidirect
5. C3×#4646C2semidirect
6. #10591396C2semidirect
9. #10591261C2semidirect
10. #10591241C2semidirect
11. #10591235C2semidirect
13. #10591218C2semidirect
79. #4660D3semidirect
85. #4646D3semidirect
115. #3752Q8semidirect
708. C32#2492semidirect
816. C3#76633semidirect
817. C3#78148semidirect

Maximal subgroups

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

subgroupindex
C2×#639182
C2×#638882
#105923692
C3×#46602
C3×#46462
#105913962
#105913672
#105912662
#105912612
#105912412
#105912352
#105912332
#105912182
#105912052
#781483
#766333