Finite Group Databasebeta

← #11807865

Subgroups — #11807865

Order 1152.

1089 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64105C211yesmaximal, characteristic
2C3×#4984C211yesmaximal, characteristic, complemented
3C3×#4980C211yesmaximal, characteristic, complemented
4#10591325C211yesmaximal, characteristic
5#10591273C211yesmaximal, characteristic, complemented
6#10591266C211yesmaximal, characteristic
7#10591266C211yesmaximal, characteristic
8#10591264C211yesmaximal, characteristic, complemented
9#10591263C211yesmaximal, characteristic, complemented
10#10591263C211yesmaximal, characteristic, complemented
11#10591219C211yesmaximal, characteristic
12#10591213C211yesmaximal, characteristic, complemented
13#10591202C211yesmaximal, characteristic
14#10591202C211yesmaximal, characteristic
15#10591197C211yesmaximal, characteristic, complemented
16#75992—31nomaximal
17#74976—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×#634C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×#3752C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3750C2211yescharacteristic
24C2×#3750C2211yescharacteristic
25#64105C418yescomplemented
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C2×C3×C4⋊Dic3C2211yescharacteristic
28C2×C3×C4⋊Dic3C2211yescharacteristic
29C2×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×C4×Dic3C2211yescharacteristic
31C2×C3×C4×Dic3C2211yescharacteristic
32C2×#3724C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3722C2211yescharacteristic
35C2×#3722C2211yescharacteristic
36C2×#3722C2211yescharacteristic
37C2×#3722C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41C3×C3⋊#95C2211yescharacteristic
42C3×C3⋊#95C2211yescharacteristic
43C3×C3⋊#95C2211yescharacteristic
44C3×C3⋊#95C2211yescharacteristic
45C3×C3⋊#95C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54C2×#896—31no—
55C2×#896—31no—
56C2×#896—61no—
57C3×#389—31no—
58C3×#387—31no—
59#4990—31no—
60#4990—31no—
61#4987—31no—
62#4987—31no—
63#4984D311yescharacteristic, complemented
64#4980D311yescharacteristic, complemented
65#4978—31no—
66#4978—31no—
67#4976—31no—
68#4973—31no—
69#4940—31no—
70#4940—31no—
71#4933—31no—
72#4929—31no—
73#4670—31no—
74#4670—31no—
75#4669—31no—
76#4669—31no—
77#4664—31no—
78#4664—31no—
79#4655—31no—
80#4655—31no—
81#4652—31no—
82#4647—31no—
83#4646—31no—
84#4646—31no—
85C23×C3⋊D3C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C32×C4C2311yescharacteristic
88C22×C32×C4C2311yescharacteristic
89C22×C3⋊Dic3C2311yescharacteristic
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C2×C4×C3⋊D3—41no—
93C2×C4×C3⋊D3—41no—
94C2×C4×C3⋊D3C2×C414yes—
95C2×#634—41no—
96C2×#634—41no—
97C2×#634C2×C414yes—
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C32×C4⋊C4C2×C414yes—
107#3752C2×C414yes—
108#3752C2×C414yes—
109#3750C2×C414yes—
110#3750C2×C414yes—
111C3×C4⋊Dic3—41no—
112C3×C4⋊Dic3—41no—
113C3×C4⋊Dic3—41no—
114C3×C4⋊Dic3—41no—
115C3×C4×Dic3—41no—
116C3×C4×Dic3—41no—
117#3724—41no—
118#3724—41no—
119#3722—41no—
120#3722—41no—
121#3722—41no—
122#3722—41no—
123Dic32—41no—
124Dic32—41no—
125#2378—91noSylow
126C22×C4×D3—31no—
127C22×C4×D3—31no—
128C22×C4×D3—61no—
129C22×Dic6—31no—
130C22×Dic6—31no—
131C22×Dic6—61no—
132C2×C3×C4⋊C4—21no—
133C2×C3×C4⋊C4—31no—
134C2×C3×C4⋊C4—31no—
135C2×C3×C4⋊C4—31no—
136C2×C3×C4⋊C4—31no—
137C2×C3×C4⋊C4C2×D311yescharacteristic
138C2×C3×C4⋊C4C2×D311yescharacteristic
139C2×C3×C42—31no—
140C2×C3×C42—31no—
141C2×(C2×D3)⋊C4—31no—
142C2×(C2×D3)⋊C4—31no—
143C2×(C2×D3)⋊C4—31no—
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—61no—
154C2×(C2×D3)⋊C4—61no—
155C2×C4⋊Dic3C2×D311yescharacteristic
156C2×C4⋊Dic3C2×D311yescharacteristic
157C2×C4⋊Dic3C2×D311yescharacteristic
158C2×C4⋊Dic3C2×D311yescharacteristic
159C2×Dic3⋊C4—31no—
160C2×Dic3⋊C4—31no—
161C2×Dic3⋊C4—31no—
162C2×Dic3⋊C4—31no—
163C2×Dic3⋊C4—31no—
164C2×Dic3⋊C4—31no—
165C2×Dic3⋊C4—31no—
166C2×Dic3⋊C4—31no—
167C2×Dic3⋊C4—61no—
168C2×Dic3⋊C4—61no—
169C2×C4×Dic3—31no—
170C2×C4×Dic3—31no—
171C2×C4×Dic3—31no—
172C2×C4×Dic3—31no—
173C2×C4×Dic3C2×D311yescharacteristic
174C2×C4×Dic3C2×D311yescharacteristic
175#896—38no—
176#896—38no—
177#896—68no—
178C3×#95—31no—
179C3×#95—31no—
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⋊#95C2×D311yescharacteristic
201C3⋊#95C2×D311yescharacteristic
202C3⋊#95C2×D311yescharacteristic
203C3⋊#95C2×D311yescharacteristic
204C3⋊#95C2×D311yescharacteristic
205C3⋊#95C2×D311yescharacteristic
206C23×C32C2411yescharacteristic
207C22×C3⋊D3—21no—
208C22×C3⋊D3—21no—
209C22×C3⋊D3—21no—
210C22×C3⋊D3—21no—
211C22×C3⋊D3—21no—
212C22×C3⋊D3—21no—
213C22×C3⋊D3C22×C412yes—
214C2×C32×C4—21no—
215C2×C32×C4—21no—
216C2×C32×C4—21no—
217C2×C32×C4—21no—
218C2×C32×C4—21no—
219C2×C32×C4—21no—
220C2×C32×C4C22×C412yes—
221C2×C32×C4C22×C412yes—
222C2×C32×C4C22×C412yes—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—21no—
225C2×C3⋊Dic3—21no—
226C2×C3⋊Dic3—21no—
227C2×C3⋊Dic3—21no—
228C2×C3⋊Dic3—21no—
229C2×C3⋊Dic3C22×C412yes—
230C2×C3⋊Dic3C22×C412yes—
231C2×C3⋊Dic3C22×C412yes—
232C4×C3⋊D3—44no—
233#634—44no—
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×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×C22⋊Q8—91no—
259#391—91no—
260#391—91no—
261#389—31no—
262#389—91no—
263#388—91no—
264#388—91no—
265#388—91no—
266#388—91no—
267#387—31no—
268#387—91no—
269#387—91no—
270#387—91no—
271#381—91no—
272#380—91no—
273C23×D3—31no—
274C23×D3—31no—
275C23×D3—61no—
276C22×C3×C4—21no—
277C22×C3×C4—21no—
278C22×C3×C4—21no—
279C22×C3×C4—31no—
280C22×C3×C4—31no—
281C22×C3×C4—31no—
282C22×C3×C4—31no—
283C22×C3×C4—31no—
284C22×C3×C4—31no—
285C22×C3×C4—31no—
286C22×C3×C4—31no—
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×C3×C4C22×D311yescharacteristic
290C22×C3×C4C22×D311yescharacteristic
291C22×C3×C4C22×D311yescharacteristic
292C22×C3×C4C22×D311yescharacteristic
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—61no—
300C22×Dic3—61no—
301C22×Dic3—61no—
302C22×Dic3C22×D311yescharacteristic
303C22×Dic3C22×D311yescharacteristic
304C22×Dic3C22×D311yescharacteristic
305C22×Dic3C22×D311yescharacteristic
306C22×Dic3C22×D311yescharacteristic
307C22×Dic3C22×D311yescharacteristic
308C22×Dic3C22×D311yescharacteristic
309C22×Dic3C22×D311yescharacteristic
310C2×C4×D3—34no—
311C2×C4×D3—34no—
312C2×C4×D3—64no—
313C2×C4×D3—121no—
314C2×C4×D3—121no—
315C2×C4×D3—121no—
316C2×C4×D3—121no—
317C2×C4×D3—122no—
318C2×C4×D3—122no—
319C2×Dic6—34no—
320C2×Dic6—34no—
321C2×Dic6—64no—
322C2×Dic6—121no—
323C2×Dic6—121no—
324C2×Dic6—121no—
325C2×Dic6—121no—
326C2×Dic6—122no—
327C2×Dic6—122no—
328C3×C4⋊C4—24no—
329C3×C4⋊C4—121no—
330C3×C4⋊C4—121no—
331C3×C4⋊C4—121no—
332C3×C4⋊C4—121no—
333C3×C4⋊C4C4×D314yes—
334C3×C4⋊C4C4×D314yes—
335C3×C42—121no—
336C3×C42—121no—
337(C2×D3)⋊C4—34no—
338(C2×D3)⋊C4—34no—
339(C2×D3)⋊C4—34no—
340(C2×D3)⋊C4—34no—
341(C2×D3)⋊C4—64no—
342(C2×D3)⋊C4—64no—
343(C2×D3)⋊C4—121no—
344(C2×D3)⋊C4—121no—
345(C2×D3)⋊C4—121no—
346(C2×D3)⋊C4—121no—
347(C2×D3)⋊C4—121no—
348(C2×D3)⋊C4—121no—
349(C2×D3)⋊C4—121no—
350(C2×D3)⋊C4—121no—
351C4⋊Dic3—41no—
352C4⋊Dic3—41no—
353C4⋊Dic3—41no—
354C4⋊Dic3—41no—
355Dic3⋊C4—34no—
356Dic3⋊C4—34no—
357Dic3⋊C4—34no—
358Dic3⋊C4—34no—
359Dic3⋊C4—64no—
360Dic3⋊C4—64no—
361Dic3⋊C4—121no—
362Dic3⋊C4—121no—
363Dic3⋊C4—121no—
364Dic3⋊C4—121no—
365C4×Dic3—41no—
366C4×Dic3—41no—
367C4×Dic3—121no—
368C4×Dic3—121no—
369C4×Dic3—121no—
370C4×Dic3—121no—
371C22×C32C23×C411yescharacteristic
372C22×C32H(5,𝔽2)11yescharacteristic
373C22×C32H(5,𝔽2)11yescharacteristic
374C22×C32H(5,𝔽2)11yescharacteristic
375C22×C322−1+411yescharacteristic
376C22×C322−1+411yescharacteristic
377C22×C322−1+411yescharacteristic
378C2×C3⋊D3—22no—
379C2×C3⋊D3—22no—
380C2×C3⋊D3—22no—
381C2×C3⋊D3—41no—
382C2×C3⋊D3—41no—
383C2×C3⋊D3—41no—
384C2×C3⋊D3—41no—
385C32×C4—22no—
386C32×C4—22no—
387C32×C4—22no—
388C3⋊Dic3—22no—
389C3⋊Dic3—22no—
390C3⋊Dic3—22no—
391C3×Dic3—41no—
392C3×Dic3—41no—
393C3×Dic3—41no—
394C3×Dic3—41no—
395C3×Dic3—41no—
396C3×Dic3—41no—
397C3×Dic3—41no—
398C3×Dic3—41no—
399C22×Q8—91no—
400C23×C4—91no—
401C22⋊Q8—98no—
402C2×C4⋊C4—31no—
403C2×C4⋊C4—31no—
404C2×C4⋊C4—31no—
405C2×C4⋊C4—31no—
406C2×C4⋊C4—91no—
407C2×C4⋊C4—91no—
408C2×C4⋊C4—91no—
409C2×C4⋊C4—91no—
410C2×C4⋊C4D3211yescharacteristic
411C2×C22⋊C4—91no—
412C2×C22⋊C4—91no—
413C2×C22⋊C4—91no—
414C2×C22⋊C4—91no—
415C2×C22⋊C4—91no—
416C2×C22⋊C4—91no—
417C2×C42—31no—
418C2×C42—31no—
419C2×C42—91no—
420C2×C42—91no—
421#95—31no—
422#95—31no—
423#95—31no—
424#95—31no—
425#95—31no—
426#95—31no—
427#95—91no—
428#95—91no—
429#95—91no—
430#95—91no—
431#95—91no—
432#95—91no—
433#95—91no—
434#95—91no—
435C23×C3—21no—
436C23×C3C23×D311yescharacteristic
437C23×C3C23×D311yescharacteristic
438C22×D3—32no—
439C22×D3—32no—
440C22×D3—62no—
441C22×D3—62no—
442C22×D3—62no—
443C22×D3—61no—
444C22×D3—61no—
445C22×D3—61no—
446C22×D3—61no—
447C22×D3—61no—
448C22×D3—61no—
449C22×D3—61no—
450C22×D3—61no—
451C22×D3—61no—
452C22×D3—61no—
453C22×D3—61no—
454C22×D3—61no—
455C22×D3—121no—
456C22×D3—121no—
457C22×D3—121no—
458C22×D3—121no—
459C2×C3×C4—21no—
460C2×C3×C4—21no—
461C2×C3×C4—21no—
462C2×C3×C4—21no—
463C2×C3×C4—21no—
464C2×C3×C4—21no—
465C2×C3×C4—21no—
466C2×C3×C4—21no—
467C2×C3×C4—21no—
468C2×C3×C4—21no—
469C2×C3×C4—21no—
470C2×C3×C4—21no—
471C2×C3×C4—22no—
472C2×C3×C4—22no—
473C2×C3×C4—22no—
474C2×C3×C4—41no—
475C2×C3×C4—41no—
476C2×C3×C4—41no—
477C2×C3×C4—41no—
478C2×C3×C4—41no—
479C2×C3×C4—41no—
480C2×C3×C4—61no—
481C2×C3×C4—61no—
482C2×C3×C4—61no—
483C2×C3×C4—61no—
484C2×C3×C4—61no—
485C2×C3×C4—61no—
486C2×C3×C4—61no—
487C2×C3×C4—61no—
488C2×C3×C4—61no—
489C2×C3×C4—61no—
490C2×C3×C4—61no—
491C2×C3×C4—61no—
492C2×C3×C4—61no—
493C2×C3×C4—61no—
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×C4C2×C4×D312yes—
505C2×C3×C4C2×C4×D312yes—
506C2×C3×C4C2×C4×D312yes—
507C2×C3×C4C2×C4×D312yes—
508C2×C3×C4C2×C4×D312yes—
509C2×C3×C4C2×C4×D312yes—
510C2×Dic3—21no—
511C2×Dic3—21no—
512C2×Dic3—21no—
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—21no—
530C2×Dic3—21no—
531C2×Dic3—21no—
532C2×Dic3—21no—
533C2×Dic3—21no—
534C2×Dic3—32no—
535C2×Dic3—32no—
536C2×Dic3—32no—
537C2×Dic3—32no—
538C2×Dic3—32no—
539C2×Dic3—32no—
540C2×Dic3—62no—
541C2×Dic3—62no—
542C2×Dic3—62no—
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—
561C4×D3—124no—
562C4×D3—124no—
563C4×D3—128no—
564Dic6—124no—
565Dic6—124no—
566Dic6—128no—
567C2×C32#51811yescharacteristic
568C2×C32#51911yescharacteristic
569C2×C32#52011yescharacteristic
570C2×C32#56211yescharacteristic
571C2×C32#56211yescharacteristic
572C2×C32#56311yescharacteristic
573C2×C32#56311yescharacteristic
574C3⋊D3—42no—
575C24—91no—
576C2×Q8—94no—
577C2×Q8—361no—
578C2×Q8—361no—
579C22×C4—31no—
580C22×C4—31no—
581C22×C4—31no—
582C22×C4—31no—
583C22×C4—31no—
584C22×C4—31no—
585C22×C4—31no—
586C22×C4—31no—
587C22×C4—91no—
588C22×C4—91no—
589C22×C4—91no—
590C22×C4—94no—
591C22×C4—361no—
592C22×C4—361no—
593C22×C4C2×D3211yescharacteristic
594C22×C4C2×D3211yescharacteristic
595C22×C4C2×D3211yescharacteristic
596C4⋊C4—94no—
597C4⋊C4—94no—
598C4⋊C4—121no—
599C4⋊C4—121no—
600C4⋊C4—121no—
601C4⋊C4—121no—
602C4⋊C4—361no—
603C4⋊C4—361no—
604C4⋊C4#62414yes—
605C22⋊C4—94no—
606C22⋊C4—94no—
607C22⋊C4—361no—
608C22⋊C4—361no—
609C22⋊C4—361no—
610C22⋊C4—361no—
611C42—121no—
612C42—121no—
613C42—361no—
614C42—361no—
615C22×C3—21no—
616C22×C3—21no—
617C22×C3—21no—
618C22×C3—21no—
619C22×C3—21no—
620C22×C3—21no—
621C22×C3—21no—
622C22×C3C22×C4×D311yescharacteristic
623C22×C3C22×C4×D311yescharacteristic
624C22×C3#100411yescharacteristic
625C22×C3#100411yescharacteristic
626C22×C3#100411yescharacteristic
627C22×C3#100711yescharacteristic
628C22×C3#100711yescharacteristic
629C22×C3#100711yescharacteristic
630C22×C3#100911yescharacteristic
631C22×C3#100911yescharacteristic
632C22×C3#100911yescharacteristic
633C22×C3#101011yescharacteristic
634C22×C3#101011yescharacteristic
635C22×C3#101011yescharacteristic
636C2×D3—64no—
637C2×D3—62no—
638C2×D3—62no—
639C2×D3—62no—
640C2×D3—62no—
641C2×D3—62no—
642C2×D3—62no—
643C2×D3—122no—
644C2×D3—122no—
645C2×D3—122no—
646C2×D3—122no—
647C2×D3—122no—
648C2×D3—122no—
649C2×D3—121no—
650C2×D3—121no—
651C2×D3—121no—
652C2×D3—121no—
653C2×D3—121no—
654C2×D3—121no—
655C2×D3—121no—
656C2×D3—121no—
657C3×C4—22no—
658C3×C4—22no—
659C3×C4—22no—
660C3×C4—22no—
661C3×C4—22no—
662C3×C4—22no—
663C3×C4—42no—
664C3×C4—42no—
665C3×C4—42no—
666C3×C4—121no—
667C3×C4—121no—
668C3×C4—121no—
669C3×C4—121no—
670C3×C4—121no—
671C3×C4—121no—
672C3×C4—121no—
673C3×C4—121no—
674Dic3—41no—
675Dic3—41no—
676Dic3—41no—
677Dic3—41no—
678Dic3—41no—
679Dic3—41no—
680Dic3—41no—
681Dic3—41no—
682Dic3—64no—
683Dic3—62no—
684Dic3—62no—
685Dic3—62no—
686Dic3—62no—
687Dic3—62no—
688Dic3—62no—
689Dic3—122no—
690Dic3—122no—
691C32#237811yescharacteristic, complemented, Sylow
692C23—92no—
693C23—181no—
694C23—181no—
695C23—181no—
696C23—181no—
697C23—181no—
698C23—181no—
699C23C22×D3211yescharacteristic
700Q8—364no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—61no—
708C2×C4—61no—
709C2×C4—61no—
710C2×C4—61no—
711C2×C4—61no—
712C2×C4—61no—
713C2×C4—61no—
714C2×C4—61no—
715C2×C4—61no—
716C2×C4—61no—
717C2×C4—61no—
718C2×C4—61no—
719C2×C4—61no—
720C2×C4—61no—
721C2×C4—61no—
722C2×C4—61no—
723C2×C4—61no—
724C2×C4—61no—
725C2×C4—61no—
726C2×C4—61no—
727C2×C4—61no—
728C2×C4—61no—
729C2×C4—61no—
730C2×C4—61no—
731C2×C4—92no—
732C2×C4—92no—
733C2×C4—92no—
734C2×C4—181no—
735C2×C4—181no—
736C2×C4—181no—
737C2×C4—181no—
738C2×C4—181no—
739C2×C4—181no—
740C2×C4—364no—
741C2×C4C2×#62412yes—
742C2×C4C2×#62412yes—
743C2×C4C2×#62412yes—
744C2×C3—21no—
745C2×C3—21no—
746C2×C3—21no—
747C2×C3—21no—
748C2×C3—21no—
749C2×C3—21no—
750C2×C3—21no—
751C2×C3#550411yescharacteristic
752C2×C3#552311yescharacteristic
753C2×C3#554511yescharacteristic
754C2×C3#554511yescharacteristic
755C2×C3#557211yescharacteristic
756C2×C3#557211yescharacteristic
757C2×C3#562111yescharacteristic
758C2×C3#564611yescharacteristic
759C2×C3#564711yescharacteristic
760C2×C3#566711yescharacteristic
761C2×C3#569911yescharacteristic
762C2×C3#570011yescharacteristic
763C2×C3#571211yescharacteristic
764C2×C3#573511yescharacteristic
765D3—124no—
766D3—122no—
767D3—122no—
768C22—182no—
769C22—182no—
770C22—182no—
771C22—361no—
772C22—361no—
773C22—361no—
774C22—361no—
775C22#6429711yescharacteristic
776C22#6430711yescharacteristic
777C22#6431411yescharacteristic
778C22#6431411yescharacteristic
779C22#6431511yescharacteristic
780C22#6431511yescharacteristic
781C22C22×#62411yescharacteristic
782C4—22no—
783C4—22no—
784C4—22no—
785C4—121no—
786C4—121no—
787C4—121no—
788C4—121no—
789C4—121no—
790C4—121no—
791C4—121no—
792C4—121no—
793C4—182no—
794C4—182no—
795C4—182no—
796C3—21no—
797C3#7497611yescharacteristic, complemented
798C3#7599211yescharacteristic, complemented
799C2—362no—
800C2#1059433911yescharacteristic
801C2#1059449311yescharacteristic
802C2#1059450311yescharacteristic
803C2#1059458511yescharacteristic
804C2#1059499011yescharacteristic
805C2#1059522311yescharacteristic
806C2#1059533911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenterC2×C4⋊C4D32
hypocenterC32#2378
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C3×#4984C2semidirect
3. C3×#4980C2semidirect
5. #10591273C2semidirect
8. #10591264C2semidirect
9. #10591263C2semidirect
10. #10591263C2semidirect
12. #10591213C2semidirect
15. #10591197C2semidirect
25. #64105C4semidirect
63. #4984D3semidirect
64. #4980D3semidirect
691. C32#2378semidirect
797. C3#74976semidirect
798. C3#75992semidirect

Maximal subgroups

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

subgroupindex
C2×#641052
C3×#49842
C3×#49802
#105913252
#105912732
#105912662
#105912642
#105912632
#105912192
#105912132
#105912022
#105911972
#759923
#749763