Finite Group Databasebeta

← #11819193

Subgroups — #11819193

Order 1152.

989 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592642C211yesmaximal, characteristic
2C3×#4946C211yesmaximal, characteristic
3C3×Dic3×C22⋊C4C211yesmaximal, characteristic
4#10591716C211yesmaximal, characteristic
5#10591697C211yesmaximal, characteristic
6C2×#63579C211yesmaximal, characteristic
7#10591693C211yesmaximal, characteristic
8#10591341C211yesmaximal, characteristic, complemented
9#10591331C211yesmaximal, characteristic, complemented
10#10591228C211yesmaximal, characteristic, complemented
11#10591223C211yesmaximal, characteristic, complemented
12#10591211C211yesmaximal, characteristic, complemented
13#10591201C211yesmaximal, characteristic, complemented
14#10591199C211yesmaximal, characteristic, complemented
15#10591193C211yesmaximal, characteristic, complemented
16#74459—31nomaximal
17#73509—31nomaximal
18C23×C3⋊Dic3C2211yescharacteristic
19C23×C3×Dic3C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C2×C32×C22⋊C4C2211yescharacteristic
22C2×#3757C2211yescharacteristic
23C2×C3×#217C2211yescharacteristic
24C2×C3×#217C2211yescharacteristic
25C2×C3×Dic3⋊C4C2211yescharacteristic
26C2×C3×Dic3⋊C4C2211yescharacteristic
27C2×C3×C4×Dic3C2211yescharacteristic
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×#3724C2211yescharacteristic
30C2×#3724C2211yescharacteristic
31C2×Dic3⋊Dic3C2211yescharacteristic
32C2×Dic3⋊Dic3C2211yescharacteristic
33#63658C2211yescharacteristic
34#63658C2211yescharacteristic
35#63658C2211yescharacteristic
36#63658C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38C3×C3⋊#95C2211yescharacteristic
39C3×C3⋊#95C2211yescharacteristic
40C3×C3⋊#95C2211yescharacteristic
41#63579C2211yescharacteristic
42#63579C2211yescharacteristic
43#63579C2211yescharacteristic
44#63579C2211yescharacteristic
45#63579C2211yescharacteristic
46#63579C2211yescharacteristic
47#63579C2211yescharacteristic
48#63579C2211yescharacteristic
49#63579C2211yescharacteristic
50#63579C2211yescharacteristic
51#63579C2211yescharacteristic
52#63579C2211yescharacteristic
53C3×#385—31no—
54C3×C4×C22⋊C4—31no—
55#5212—31no—
56#5210—31no—
57C2×C3⋊#95—31no—
58C2×C3⋊#95—31no—
59#4986—31no—
60#4985—31no—
61#4980—31no—
62#4978—31no—
63#4946—31no—
64#4946D311yescharacteristic
65#4943—31no—
66#4943—31no—
67#4943—31no—
68#4943—31no—
69#4943—61no—
70#4942—31no—
71Dic3×C22⋊C4D311yescharacteristic
72#4937—31no—
73#4933—31no—
74#4933—31no—
75#4933—31no—
76C3⋊#401—31no—
77C3⋊#401—31no—
78#4660—31no—
79#4658—31no—
80#4658—31no—
81#4658—31no—
82#4654—31no—
83#4651—31no—
84C24×C32C2311yescharacteristic
85C22×C32×C4C2311yescharacteristic
86C22×C32×C4C2311yescharacteristic
87C22×C3⋊Dic3—22no—
88C22×C3⋊Dic3—22no—
89C22×C3⋊Dic3—22no—
90C22×C3⋊Dic3C2311yescharacteristic
91C22×C3⋊Dic3C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3×Dic3—22no—
95C22×C3×Dic3—22no—
96C22×C3×Dic3—22no—
97C22×C3×Dic3—22no—
98C22×C3×Dic3—41no—
99C22×C3×Dic3—41no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C32×C22⋊C4—22no—
109#3757—22no—
110C3×#217—22no—
111C3×#217—22no—
112C3×Dic3⋊C4—22no—
113C3×Dic3⋊C4—41no—
114C3×C4×Dic3—22no—
115C3×C4×Dic3—41no—
116#3724—22no—
117#3724—41no—
118Dic3⋊Dic3—22no—
119Dic3⋊Dic3—41no—
120#2493—91noSylow
121C23×C3×C4—31no—
122C23×C3×C4—31no—
123C23×Dic3—31no—
124C23×Dic3—31no—
125C23×Dic3—61no—
126C23×Dic3C2×D311yescharacteristic
127C23×Dic3C2×D311yescharacteristic
128C2×C3×C4⋊C4—31no—
129C2×C3×C4⋊C4—31no—
130C2×C3×C22⋊C4—21no—
131C2×C3×C22⋊C4—31no—
132C2×C3×C22⋊C4—31no—
133C2×C3×C22⋊C4C2×D311yescharacteristic
134C2×C3×C22⋊C4C2×D311yescharacteristic
135C2×C3×C42—31no—
136C2×C3×C42—31no—
137C2×#217—31no—
138C2×#217—31no—
139C2×#217—61no—
140C2×#217C2×D311yescharacteristic
141C2×#217C2×D311yescharacteristic
142C2×C4⋊Dic3—31no—
143C2×C4⋊Dic3—31no—
144C2×Dic3⋊C4—31no—
145C2×Dic3⋊C4—31no—
146C2×Dic3⋊C4—31no—
147C2×Dic3⋊C4—31no—
148C2×Dic3⋊C4—31no—
149C2×Dic3⋊C4—31no—
150C2×Dic3⋊C4C2×D311yescharacteristic
151C2×Dic3⋊C4C2×D311yescharacteristic
152C2×C4×Dic3C2×D311yescharacteristic
153C2×C4×Dic3C2×D311yescharacteristic
154C3×#95—31no—
155C3×#95—31no—
156C3×#95—31no—
157C3×#95—31no—
158C3⋊#95—31no—
159C3⋊#95—31no—
160C3⋊#95—31no—
161C3⋊#95—31no—
162C3⋊#95—31no—
163C3⋊#95—31no—
164C3⋊#95—31no—
165C3⋊#95—31no—
166C3⋊#95—31no—
167C3⋊#95—31no—
168C3⋊#95—31no—
169C3⋊#95—31no—
170C3⋊#95—31no—
171C3⋊#95—31no—
172C3⋊#95—31no—
173C3⋊#95—31no—
174C3⋊#95—31no—
175C3⋊#95—31no—
176C3⋊#95—31no—
177C3⋊#95—31no—
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—61no—
191C3⋊#95—61no—
192C3⋊#95—61no—
193C3⋊#95—61no—
194C3⋊#95C2×D311yescharacteristic
195C3⋊#95C2×D311yescharacteristic
196C3⋊#95C2×D311yescharacteristic
197C3⋊#95C2×D311yescharacteristic
198C23×C32—21no—
199C23×C32—21no—
200C23×C32—21no—
201C23×C32—21no—
202C23×C32#4112yes—
203C23×C32#4112yes—
204C23×C32#4112yes—
205C23×C32C2411yescharacteristic
206C2×C32×C4—21no—
207C2×C32×C4—21no—
208C2×C32×C4—21no—
209C2×C32×C4—21no—
210C2×C32×C4—21no—
211C2×C32×C4—21no—
212C2×C3⋊Dic3—21no—
213C2×C3⋊Dic3—21no—
214C2×C3⋊Dic3—21no—
215C2×C3⋊Dic3—21no—
216C2×C3⋊Dic3—21no—
217C2×C3⋊Dic3—21no—
218C2×C3⋊Dic3—21no—
219C2×C3⋊Dic3—21no—
220C2×C3⋊Dic3—21no—
221C2×C3⋊Dic3—21no—
222C2×C3⋊Dic3—21no—
223C2×C3⋊Dic3—21no—
224C2×C3⋊Dic3—44no—
225C2×C3×Dic3—21no—
226C2×C3×Dic3—21no—
227C2×C3×Dic3—21no—
228C2×C3×Dic3—21no—
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×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—44no—
248C2×C3×Dic3—44no—
249C2×C3×Dic3#4112yes—
250C2×C3×Dic3#4112yes—
251#401—91no—
252#400—91no—
253#400—91no—
254#400—91no—
255#387—91no—
256#387—91no—
257#387—91no—
258#385—31no—
259#385—91no—
260#383—91no—
261#381—91no—
262#381—91no—
263#380—91no—
264C4×C22⋊C4—31no—
265C2×#95—91no—
266C24×C3—21no—
267C24×C3C22×D311yescharacteristic
268C24×C3C22×D311yescharacteristic
269C22×C3×C4—21no—
270C22×C3×C4—21no—
271C22×C3×C4—31no—
272C22×C3×C4—31no—
273C22×C3×C4—31no—
274C22×C3×C4—31no—
275C22×C3×C4—31no—
276C22×C3×C4—31no—
277C22×C3×C4—31no—
278C22×C3×C4—31no—
279C22×C3×C4—62no—
280C22×C3×C4—62no—
281C22×C3×C4—62no—
282C22×C3×C4—62no—
283C22×C3×C4—121no—
284C22×C3×C4—121no—
285C22×C3×C4C22×D311yescharacteristic
286C22×C3×C4C22×D311yescharacteristic
287C22×C3×C4C22×D311yescharacteristic
288C22×C3×C4C22×D311yescharacteristic
289C22×Dic3—22no—
290C22×Dic3—22no—
291C22×Dic3—22no—
292C22×Dic3—22no—
293C22×Dic3—31no—
294C22×Dic3—31no—
295C22×Dic3—31no—
296C22×Dic3—31no—
297C22×Dic3—31no—
298C22×Dic3—31no—
299C22×Dic3—31no—
300C22×Dic3—31no—
301C22×Dic3—41no—
302C22×Dic3—41no—
303C22×Dic3—61no—
304C22×Dic3—61no—
305C22×Dic3—61no—
306C22×Dic3—61no—
307C22×Dic3—64no—
308C22×Dic3—62no—
309C22×Dic3—62no—
310C22×Dic3—62no—
311C22×Dic3—62no—
312C22×Dic3—62no—
313C22×Dic3—62no—
314C22×Dic3—122no—
315C22×Dic3—122no—
316C22×Dic3C22×D311yescharacteristic
317C22×Dic3C22×D311yescharacteristic
318C22×Dic3C22×D311yescharacteristic
319C22×Dic3C22×D311yescharacteristic
320C22×Dic3C22×D311yescharacteristic
321C22×Dic3C22×D311yescharacteristic
322C22×Dic3C22×D311yescharacteristic
323C22×Dic3C22×D311yescharacteristic
324C3×C4⋊C4—62no—
325C3×C4⋊C4—121no—
326C3×C22⋊C4—22no—
327C3×C22⋊C4—22no—
328C3×C22⋊C4—42no—
329C3×C22⋊C4—62no—
330C3×C22⋊C4—62no—
331C3×C42—62no—
332C3×C42—121no—
333#217—22no—
334#217—22no—
335#217—62no—
336#217—62no—
337#217—122no—
338C4⋊Dic3—62no—
339C4⋊Dic3—121no—
340Dic3⋊C4—22no—
341Dic3⋊C4—41no—
342Dic3⋊C4—62no—
343Dic3⋊C4—62no—
344Dic3⋊C4—62no—
345Dic3⋊C4—121no—
346Dic3⋊C4—121no—
347Dic3⋊C4—121no—
348C4×Dic3—22no—
349C4×Dic3—41no—
350C22×C32—22no—
351C22×C32—22no—
352C22×C32—22no—
353C22×C32—22no—
354C22×C32—22no—
355C22×C32—22no—
356C22×C32#12614yes—
357C22×C32C2×#4111yescharacteristic
358C22×C32C2×#4111yescharacteristic
359C22×C32C2×#4111yescharacteristic
360C22×C32C2×#4111yescharacteristic
361C22×C32C2×#4111yescharacteristic
362C22×C32H(5,𝔽2)11yescharacteristic
363C22×C322−1+411yescharacteristic
364C32×C4—41no—
365C32×C4—41no—
366C3⋊Dic3—41no—
367C3⋊Dic3—41no—
368C3⋊Dic3—41no—
369C3⋊Dic3—41no—
370C3×Dic3—22no—
371C3×Dic3—22no—
372C3×Dic3—41no—
373C3×Dic3—41no—
374C3×Dic3—41no—
375C3×Dic3—41no—
376C3×Dic3—41no—
377C3×Dic3—41no—
378C23×C4—31no—
379C23×C4—31no—
380C23×C4—91no—
381C2×C4⋊C4—31no—
382C2×C4⋊C4—31no—
383C2×C4⋊C4—91no—
384C2×C4⋊C4—91no—
385C2×C4⋊C4—91no—
386C2×C4⋊C4—91no—
387C2×C22⋊C4—31no—
388C2×C22⋊C4—31no—
389C2×C22⋊C4—91no—
390C2×C22⋊C4D3211yescharacteristic
391C2×C42—31no—
392C2×C42—31no—
393#95—31no—
394#95—31no—
395#95—31no—
396#95—31no—
397#95—91no—
398#95—91no—
399#95—91no—
400#95—91no—
401#95—91no—
402#95—91no—
403#95—91no—
404#95—91no—
405#95—91no—
406#95—91no—
407#95—91no—
408#95—91no—
409#95—91no—
410#95—91no—
411#95—91no—
412#95—91no—
413C23×C3—21no—
414C23×C3—21no—
415C23×C3—21no—
416C23×C3—21no—
417C23×C3—21no—
418C23×C3—21no—
419C23×C3—21no—
420C23×C3—21no—
421C23×C3—21no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—41no—
426C23×C3—41no—
427C23×C3—41no—
428C23×C3—41no—
429C23×C3#23512yes—
430C23×C3#23512yes—
431C23×C3#23512yes—
432C23×C3#23512yes—
433C23×C3#23712yes—
434C23×C3#23912yes—
435C23×C3C23×D311yescharacteristic
436C23×C3C23×D311yescharacteristic
437C2×C3×C4—21no—
438C2×C3×C4—21no—
439C2×C3×C4—21no—
440C2×C3×C4—21no—
441C2×C3×C4—21no—
442C2×C3×C4—21no—
443C2×C3×C4—21no—
444C2×C3×C4—21no—
445C2×C3×C4—21no—
446C2×C3×C4—21no—
447C2×C3×C4—21no—
448C2×C3×C4—21no—
449C2×C3×C4—32no—
450C2×C3×C4—32no—
451C2×C3×C4—41no—
452C2×C3×C4—41no—
453C2×C3×C4—41no—
454C2×C3×C4—41no—
455C2×C3×C4—41no—
456C2×C3×C4—41no—
457C2×C3×C4—61no—
458C2×C3×C4—61no—
459C2×C3×C4—61no—
460C2×C3×C4—61no—
461C2×C3×C4—61no—
462C2×C3×C4—61no—
463C2×C3×C4—61no—
464C2×C3×C4—61no—
465C2×C3×C4—61no—
466C2×C3×C4—61no—
467C2×C3×C4—61no—
468C2×C3×C4—61no—
469C2×C3×C4—61no—
470C2×C3×C4—61no—
471C2×C3×C4—61no—
472C2×C3×C4—61no—
473C2×C3×C4—61no—
474C2×C3×C4—61no—
475C2×C3×C4—61no—
476C2×C3×C4—61no—
477C2×C3×C4—61no—
478C2×C3×C4—61no—
479C2×C3×C4—124no—
480C2×C3×C4—124no—
481C2×Dic3—21no—
482C2×Dic3—21no—
483C2×Dic3—21no—
484C2×Dic3—21no—
485C2×Dic3—21no—
486C2×Dic3—21no—
487C2×Dic3—21no—
488C2×Dic3—21no—
489C2×Dic3—21no—
490C2×Dic3—21no—
491C2×Dic3—21no—
492C2×Dic3—21no—
493C2×Dic3—21no—
494C2×Dic3—21no—
495C2×Dic3—21no—
496C2×Dic3—21no—
497C2×Dic3—21no—
498C2×Dic3—21no—
499C2×Dic3—21no—
500C2×Dic3—21no—
501C2×Dic3—21no—
502C2×Dic3—21no—
503C2×Dic3—44no—
504C2×Dic3—44no—
505C2×Dic3—62no—
506C2×Dic3—62no—
507C2×Dic3—61no—
508C2×Dic3—61no—
509C2×Dic3—61no—
510C2×Dic3—61no—
511C2×Dic3—61no—
512C2×Dic3—61no—
513C2×Dic3—61no—
514C2×Dic3—61no—
515C2×Dic3—61no—
516C2×Dic3—61no—
517C2×Dic3—61no—
518C2×Dic3—61no—
519C2×Dic3—61no—
520C2×Dic3—61no—
521C2×Dic3—61no—
522C2×Dic3—61no—
523C2×Dic3—61no—
524C2×Dic3—61no—
525C2×Dic3—61no—
526C2×Dic3—61no—
527C2×Dic3—61no—
528C2×Dic3—61no—
529C2×Dic3—61no—
530C2×Dic3—61no—
531C2×Dic3—121no—
532C2×Dic3—121no—
533C2×Dic3—121no—
534C2×Dic3—121no—
535C2×Dic3—121no—
536C2×Dic3—121no—
537C2×Dic3—121no—
538C2×Dic3—121no—
539C2×Dic3—121no—
540C2×Dic3—121no—
541C2×Dic3—128no—
542C2×Dic3—124no—
543C2×Dic3—124no—
544C2×Dic3#23712yes—
545C2×Dic3#23712yes—
546C2×C32—24no—
547C2×C32C2×#12611yescharacteristic
548C2×C32#52911yescharacteristic
549C2×C32#53911yescharacteristic
550C2×C32#55111yescharacteristic
551C2×C32#55111yescharacteristic
552C2×C32#55211yescharacteristic
553C2×C32#55211yescharacteristic
554C24C2×D3211yescharacteristic
555C22×C4—31no—
556C22×C4—31no—
557C22×C4—31no—
558C22×C4—31no—
559C22×C4—31no—
560C22×C4—31no—
561C22×C4—31no—
562C22×C4—31no—
563C22×C4—62no—
564C22×C4—62no—
565C22×C4—62no—
566C22×C4—62no—
567C22×C4—91no—
568C22×C4—91no—
569C22×C4—91no—
570C22×C4—91no—
571C22×C4—121no—
572C22×C4—121no—
573C22×C4—182no—
574C22×C4—182no—
575C22×C4—182no—
576C22×C4C2×D3211yescharacteristic
577C22×C4C2×D3211yescharacteristic
578C4⋊C4—62no—
579C4⋊C4—121no—
580C4⋊C4—182no—
581C4⋊C4—182no—
582C4⋊C4—361no—
583C4⋊C4—361no—
584C22⋊C4—22no—
585C22⋊C4—62no—
586C22⋊C4—62no—
587C22⋊C4—182no—
588C42—62no—
589C42—121no—
590C22×C3—22no—
591C22×C3—22no—
592C22×C3—22no—
593C22×C3—22no—
594C22×C3—22no—
595C22×C3—22no—
596C22×C3—22no—
597C22×C3—22no—
598C22×C3—22no—
599C22×C3—22no—
600C22×C3—22no—
601C22×C3—22no—
602C22×C3—21no—
603C22×C3—21no—
604C22×C3—21no—
605C22×C3—21no—
606C22×C3—21no—
607C22×C3—21no—
608C22×C3—21no—
609C22×C3—24no—
610C22×C3—42no—
611C22×C3—42no—
612C22×C3—42no—
613C22×C3—42no—
614C22×C3—42no—
615C22×C3—42no—
616C22×C3#87614yes—
617C22×C3#89814yes—
618C22×C3C2×#23511yescharacteristic
619C22×C3C2×#23511yescharacteristic
620C22×C3C2×#23511yescharacteristic
621C22×C3C2×#23511yescharacteristic
622C22×C3C2×#23711yescharacteristic
623C22×C3C2×#23711yescharacteristic
624C22×C3C2×#23711yescharacteristic
625C22×C3#100411yescharacteristic
626C22×C3#100411yescharacteristic
627C22×C3C2×#23911yescharacteristic
628C22×C3D3×#4111yescharacteristic
629C22×C3D3×#4111yescharacteristic
630C22×C3#101011yescharacteristic
631C22×C3#101011yescharacteristic
632C3×C4—41no—
633C3×C4—41no—
634C3×C4—41no—
635C3×C4—41no—
636C3×C4—62no—
637C3×C4—62no—
638C3×C4—81no—
639C3×C4—81no—
640C3×C4—121no—
641C3×C4—121no—
642C3×C4—121no—
643C3×C4—121no—
644C3×C4—121no—
645C3×C4—121no—
646Dic3—22no—
647Dic3—22no—
648Dic3—41no—
649Dic3—41no—
650Dic3—41no—
651Dic3—41no—
652Dic3—41no—
653Dic3—41no—
654Dic3—122no—
655Dic3—122no—
656Dic3—121no—
657Dic3—121no—
658Dic3—121no—
659Dic3—121no—
660Dic3—121no—
661Dic3—121no—
662Dic3—121no—
663Dic3—121no—
664Dic3—241no—
665Dic3—241no—
666C32#249311yescharacteristic, complemented, Sylow
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23#379812yes—
672C23#379912yes—
673C23#380412yes—
674C23C22×D3211yescharacteristic
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—32no—
682C2×C4—32no—
683C2×C4—61no—
684C2×C4—61no—
685C2×C4—61no—
686C2×C4—61no—
687C2×C4—61no—
688C2×C4—61no—
689C2×C4—61no—
690C2×C4—61no—
691C2×C4—61no—
692C2×C4—61no—
693C2×C4—61no—
694C2×C4—61no—
695C2×C4—61no—
696C2×C4—61no—
697C2×C4—61no—
698C2×C4—61no—
699C2×C4—61no—
700C2×C4—61no—
701C2×C4—61no—
702C2×C4—61no—
703C2×C4—61no—
704C2×C4—61no—
705C2×C4—124no—
706C2×C4—124no—
707C2×C4—181no—
708C2×C4—181no—
709C2×C4—181no—
710C2×C4—181no—
711C2×C4—181no—
712C2×C4—181no—
713C2×C4—181no—
714C2×C4—181no—
715C2×C4—181no—
716C2×C4—181no—
717C2×C4—181no—
718C2×C4—181no—
719C2×C4—364no—
720C2×C3—24no—
721C2×C3—24no—
722C2×C3—21no—
723C2×C3—21no—
724C2×C3—21no—
725C2×C3—21no—
726C2×C3—21no—
727C2×C3—21no—
728C2×C3—21no—
729C2×C3—44no—
730C2×C3C2×#87611yescharacteristic
731C2×C3#549511yescharacteristic
732C2×C3C2×#89811yescharacteristic
733C2×C3#553111yescharacteristic
734C2×C3#553811yescharacteristic
735C2×C3#554111yescharacteristic
736C2×C3#554111yescharacteristic
737C2×C3#555611yescharacteristic
738C2×C3#555611yescharacteristic
739C2×C3#556411yescharacteristic
740C2×C3#558711yescharacteristic
741C2×C3#562411yescharacteristic
742C2×C3#564511yescharacteristic
743C2×C3#565011yescharacteristic
744C22—22no—
745C22—22no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22#6386814yes—
751C22C2×#379811yescharacteristic
752C22C2×#379911yescharacteristic
753C22#6430911yescharacteristic
754C22D3×#23711yescharacteristic
755C22D3×#23711yescharacteristic
756C22#6431311yescharacteristic
757C22C2×#380411yescharacteristic
758C4—41no—
759C4—41no—
760C4—62no—
761C4—62no—
762C4—121no—
763C4—121no—
764C4—121no—
765C4—121no—
766C4—121no—
767C4—121no—
768C4—361no—
769C4—361no—
770C4—361no—
771C4—361no—
772C3—21no—
773C3#7350911yescharacteristic, complemented
774C3#7445911yescharacteristic, complemented
775C2—24no—
776C2#1059403911yescharacteristic
777C2#1059420911yescharacteristic
778C2#1059421611yescharacteristic
779C2#1059424111yescharacteristic
780C2C2×#6386811yescharacteristic
781C2#1059511711yescharacteristic
782C2#1059517511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC24×C32C23
hypercenterC2×C22⋊C4D32
hypocenterC32#2493
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
8. #10591341C2semidirect
9. #10591331C2semidirect
10. #10591228C2semidirect
11. #10591223C2semidirect
12. #10591211C2semidirect
13. #10591201C2semidirect
14. #10591199C2semidirect
15. #10591193C2semidirect
666. C32#2493semidirect
773. C3#73509semidirect
774. C3#74459semidirect

Maximal subgroups

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

subgroupindex
#105926422
C3×#49462
C3×Dic3×C22⋊C42
#105917162
#105916972
C2×#635792
#105916932
#105913412
#105913312
#105912282
#105912232
#105912112
#105912012
#105911992
#105911932
#744593
#735093