Finite Group Databasebeta

← #34026389

Subgroups — #34026389

Order 18688.

1114 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22626440C212yesmaximal, complemented
2#22626122C212yesmaximal, complemented
3#22626122C212yesmaximal, complemented
4#22626120C212yesmaximal, complemented
5#22625793C211yesmaximal, characteristic
6#22625793C211yesmaximal, characteristic
7#22625791C211yesmaximal, characteristic
8#22625678C211yesmaximal, characteristic
9#22625678C211yesmaximal, characteristic
10C4×#14556649C211yesmaximal, characteristic
11C2×#17989291C211yesmaximal, characteristic
12C2×#14556649C2211yescharacteristic
13C2×#14556649C2211yescharacteristic
14C2×#14556649C2211yescharacteristic
15C2×#14556649C2211yescharacteristic
16#17989538—22no—
17#17989536—22no—
18#17989536—22no—
19#17989529C2212yes—
20#17989529C2212yes—
21#17989529C2212yes—
22C4⋊C4×#64408—22no—
23C4×C22⋊#64408C2212yes—
24C4×C22⋊#64408C2212yes—
25C4×C22⋊#64408C2212yes—
26#17989465C2212yes—
27#17989465C2212yes—
28#17989465C2212yes—
29#17989465C2212yes—
30#17989465C2212yes—
31#17989465C2212yes—
32#17989291—22no—
33#17989291—22no—
34#17989291—22no—
35#17989291—22no—
36C2×#14556589C411yescharacteristic, complemented
37C2×#14556581C411yescharacteristic, complemented
38C2×#14556581C411yescharacteristic, complemented
39C2×#14556569C2211yescharacteristic
40C2×#14556569C2211yescharacteristic
41C2×#14556568C411yescharacteristic, complemented
42C2×#14556568C411yescharacteristic, complemented
43C2×#14556567C2211yescharacteristic
44C2×#14556556C411yescharacteristic, complemented
45C2×C4×C22⋊D73C2211yescharacteristic
46C2×#14556551C2211yescharacteristic
47C2×#14556551C2211yescharacteristic
48C22×#11924007C411yescharacteristic, complemented
49C2×C4⋊C4×D73C2211yescharacteristic
50C2×C22⋊Q8×C73C411yescharacteristic, complemented
51C2×C4⋊#64408—22no—
52C2×C4⋊#64408—22no—
53C2×C4⋊#64408—22no—
54C2×C22⋊#64408C2312yes—
55C2×C22⋊#64408C2312yes—
56C2×C22⋊#64408C2312yes—
57C2×C22⋊#64408C2312yes—
58C2×C4×#64408—22no—
59C2×C4×#64408—22no—
60C2×C4×#64408—22no—
61#14556649—22no—
62#14556649—22no—
63#14556649—22no—
64#14556649Q814yescomplemented
65(C2×#64408)⋊C4—22no—
66(C2×#64408)⋊C4—22no—
67(C2×#64408)⋊C4—22no—
68(C2×#64408)⋊C4—22no—
69(C2×#64408)⋊C4—22no—
70(C2×#64408)⋊C4—22no—
71C22×Dic146C2×C411yescharacteristic
72C22×Dic146C2×C411yescharacteristic
73C22×C22⋊D73C2311yescharacteristic
74C23×Dic73C2×C411yescharacteristic
75C23×Dic73C2×C411yescharacteristic
76C22×C4×D73C2311yescharacteristic
77C22×C4×D73C2311yescharacteristic
78C22×C4×D73C2311yescharacteristic
79#14556589—22no—
80#14556589—22no—
81#14556581—22no—
82#14556581—22no—
83#14556581—22no—
84#14556581—22no—
85#14556569—22no—
86#14556569—22no—
87#14556569—22no—
88#14556569—22no—
89#14556568—22no—
90#14556568—22no—
91#14556568—22no—
92#14556568—22no—
93#14556567—22no—
94#14556567—22no—
95#14556556—21no—
96#14556556—21no—
97#14556556—21no—
98#14556556—21no—
99C4×C22⋊D73—22no—
100C4×C22⋊D73—22no—
101#14556551—22no—
102#14556551—22no—
103#14556551—22no—
104#14556551—22no—
105C2×C4⋊Dic73C2×C411yescharacteristic
106C2×C4⋊Dic73C2×C411yescharacteristic
107C2×#11924007—21no—
108C2×#11924007—21no—
109C2×#11924007—21no—
110C2×#11924007—21no—
111C2×#11924007C2×C411yescharacteristic
112C2×#11924007C2×C411yescharacteristic
113C2×#11924007C2×C411yescharacteristic
114C2×#11924007C2×C411yescharacteristic
115C2×#11924007C2×C411yescharacteristic
116C2×#11924007C2×C411yescharacteristic
117C2×#11924007C2×C411yescharacteristic
118C2×#11924007C2×C411yescharacteristic
119C2×#11924007C2×C411yescharacteristic
120C2×#11924007C2×C411yescharacteristic
121C2×#11924007C2×C411yescharacteristic
122C4⋊C4×D73D412yes—
123C4⋊C4×D73D412yes—
124C4⋊C4×D73D412yes—
125C4⋊C4×D73D412yes—
126C2×C22⋊Dic73C2×C411yescharacteristic
127C2×#11924005C2311yescharacteristic
128C2×#11924005C2311yescharacteristic
129C2×#11924005C2311yescharacteristic
130C2×C4×Dic73C2×C411yescharacteristic
131C2×C4×Dic73C2×C411yescharacteristic
132C2×C4×Dic73C2×C411yescharacteristic
133C22×Q8×C73C2×C411yescharacteristic
134C23×C4×C73C2×C411yescharacteristic
135C22⋊Q8×C73—22no—
136C22⋊Q8×C73—22no—
137C2×C4⋊C4×C73C2×C411yescharacteristic
138C2×C4⋊C4×C73C2×C411yescharacteristic
139C2×C4⋊C4×C73C2×C411yescharacteristic
140C2×C22⋊C4×C73C2×C411yescharacteristic
141C2×C22⋊C4×C73C2×C411yescharacteristic
142C22×#64408—22no—
143C22×#64408—22no—
144C22×#64408—22no—
145C22×#64408—22no—
146C4⋊#64408—44no—
147C4⋊#64408—82no—
148C4⋊#64408—82no—
149C22⋊#64408—22no—
150C22⋊#64408—22no—
151C22⋊#64408—22no—
152C22⋊#64408—22no—
153C22⋊#64408—22no—
154C22⋊#64408—22no—
155C22⋊#64408—22no—
156C22⋊#64408C2×Q814yes—
157C4×#64408—44no—
158C4×#64408—82no—
159C4×#64408—82no—
160C23×D73C2411yescharacteristic
161C2×Dic146—21no—
162C2×Dic146—21no—
163C2×Dic146—22no—
164C2×Dic146—42no—
165C2×Dic146—81no—
166C2×C22⋊D73—22no—
167C2×C22⋊D73—22no—
168C2×C22⋊D73C2×Q812yes—
169C2×C22⋊D73#4112yes—
170C22×Dic73—21no—
171C22×Dic73—21no—
172C22×Dic73—21no—
173C22×Dic73—21no—
174C22×Dic73—42no—
175C22×Dic73—81no—
176C22×Dic73C22×C411yescharacteristic
177C22×Dic73C22×C411yescharacteristic
178C22×Dic73C22×C411yescharacteristic
179C22×Dic73C22×C411yescharacteristic
180C22×Dic73C22×C411yescharacteristic
181C22×Dic73C22×C411yescharacteristic
182C22×Dic73C22×C411yescharacteristic
183C2×C4×D73—42no—
184C2×C4×D73—81no—
185C2×C4×D73—81no—
186C2×C4×D73C2×D412yes—
187C2×C4×D73C2×D412yes—
188C2×C4×D73C2×D412yes—
189C2×C4×D73C2×D412yes—
190C2×C4×D73C2×D412yes—
191C2×C4×D73C2×D412yes—
192C4⋊Dic73—22no—
193C4⋊Dic73C22⋊C412yes—
194C4⋊Dic73C22⋊C412yes—
195#11924007—21no—
196#11924007—21no—
197#11924007—22no—
198#11924007—22no—
199#11924007—22no—
200#11924007—21no—
201#11924007—21no—
202#11924007—21no—
203#11924007—21no—
204#11924007—22no—
205#11924007—21no—
206#11924007—21no—
207#11924007—22no—
208#11924007C22⋊C411yescharacteristic
209#11924007C22⋊C411yescharacteristic
210#11924007C22⋊C411yescharacteristic
211#11924007C22⋊C411yescharacteristic
212#11924007C22⋊C412yes—
213#11924007C22⋊C412yes—
214C22⋊Dic73—22no—
215#11924005—22no—
216#11924005—22no—
217#11924005—22no—
218C4×Dic73—21no—
219C4×Dic73—21no—
220C4×Dic73—21no—
221C4×Dic73—21no—
222C4×Dic73—21no—
223C4×Dic73—21no—
224C24×C73C22×C411yescharacteristic
225C2×Q8×C73—22no—
226C2×Q8×C73—81no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—81no—
230C22×C4×C73C22×C411yescharacteristic
231C22×C4×C73C22×C411yescharacteristic
232C22×C4×C73C22×C411yescharacteristic
233C22×C4×C73C22×C411yescharacteristic
234C22×C4×C73C22×C411yescharacteristic
235C22×C4×C73C22×C411yescharacteristic
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—22no—
239C4⋊C4×C73C22⋊C412yes—
240C4⋊C4×C73C22⋊C412yes—
241C22⋊C4×C73—22no—
242C22⋊C4×C73—22no—
243C23×C73—21no—
244C23×C73—21no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73C4×Q812yes—
248C23×C73C23×C411yescharacteristic
249C22×D73—41no—
250C22×D73—41no—
251C22×D73C22×D412yes—
252C22×D73C22×Q811yescharacteristic
253C22×D73C2×#4111yescharacteristic
254C22×D732−1+412yes—
255C2×#64408—24no—
256C2×#64408—42no—
257C2×#64408—42no—
258C2×#64408—42no—
259C2×#64408—42no—
260C2×#64408—42no—
261C2×#64408—42no—
262C2×#64408—42no—
263C2×#64408—42no—
264C2×#64408—42no—
265C2×#64408—42no—
266C2×#64408—42no—
267Q8×C73—82no—
268C2×C4×C73—21no—
269C2×C4×C73—21no—
270C2×C4×C73—21no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—81no—
278C2×C4×C73—81no—
279C2×C4×C73C2×C22⋊C412yes—
280C2×C4×C73C2×C22⋊C412yes—
281C2×C4×C73C2×C22⋊C411yescharacteristic
282C2×C4×C73C2×C22⋊C411yescharacteristic
283C22⋊D73—24no—
284C22⋊D73—24no—
285C2×Dic73—21no—
286C2×Dic73—21no—
287C2×Dic73—22no—
288C2×Dic73—21no—
289C2×Dic73—21no—
290C2×Dic73—21no—
291C2×Dic73—41no—
292C2×Dic73—41no—
293C2×Dic73—42no—
294C2×Dic73—42no—
295C2×Dic73—41no—
296C2×Dic73—41no—
297C2×Dic73—41no—
298C2×Dic73—81no—
299C2×Dic73—81no—
300C2×Dic73C2×C22⋊C411yescharacteristic
301C2×Dic73C2×C22⋊C411yescharacteristic
302C2×Dic73C2×C22⋊C411yescharacteristic
303C2×Dic73C2×C22⋊C412yes—
304C2×Dic73C2×C22⋊C411yescharacteristic
305C2×Dic73C4×Q812yes—
306C4×D73—24no—
307C4×D73—42no—
308C4×D73—42no—
309C4×D73—42no—
310C4×D73—42no—
311C4×D73—42no—
312Dic146—42no—
313Dic146—42no—
314Dic146—82no—
315C22×C73—21no—
316C22×C73—21no—
317C22×C73—22no—
318C22×C73—42no—
319C22×C73—42no—
320C22×C73—41no—
321C22×C73—41no—
322C22×C73C22×C22⋊C411yescharacteristic
323C22×C73C2×C4×Q811yescharacteristic
324C22×C73#51911yescharacteristic
325C2×D73—22no—
326C2×D73—22no—
327C2×D73—41no—
328C2×D73—41no—
329C2×D73—42no—
330C2×D73#54812yes—
331C2×D73D4×Q812yes—
332#64408—44no—
333#64408—82no—
334#64408—82no—
335#64408—82no—
336C4×C73—22no—
337C4×C73—21no—
338C4×C73—21no—
339C4×C73—22no—
340C4×C73—41no—
341C4×C73—41no—
342C4×C73—41no—
343Dic73—22no—
344Dic73—21no—
345Dic73—22no—
346Dic73—21no—
347Dic73—21no—
348Dic73—41no—
349Dic73—41no—
350Dic73—41no—
351Dic73#41012yes—
352#22513—731nomaximal, Sylow
353C2×C73—21no—
354C2×C73—21no—
355C2×C73—42no—
356C2×C73Q8×C22⋊C411yescharacteristic
357C2×C73C2×#41011yescharacteristic
358C2×C73#288311yescharacteristic
359D73—22no—
360D73—22no—
361C2×#554—731no—
362#2345—732no—
363#1996—732no—
364#1996—732no—
365#1996—732no—
366#1799—731no—
367#1799—731no—
368#1799—731no—
369C4×#99—731no—
370C4×#99—731no—
371C4×#99—731no—
372C73#2251311yescharacteristic, complemented, Sylow
373#554—1462no—
374#554—1462no—
375#554—1462no—
376#554—1462no—
377C2×C4⋊Q8—731no—
378C2×#125—731no—
379C2×#125—731no—
380C2×C22⋊Q8—731no—
381C2×C22⋊Q8—731no—
382C2×C22⋊Q8—731no—
383C2×C22⋊Q8—731no—
384C2×C22⋊Q8—731no—
385C2×C22⋊Q8#6440811yescharacteristic, complemented
386C2×C4×Q8—731no—
387C2×C4×D4—731no—
388C2×C4×D4—731no—
389C2×C4×D4—731no—
390C22×C4⋊C4—731no—
391C22×C4⋊C4—731no—
392C2×#99—731no—
393C2×#99—731no—
394C2×#99—731no—
395C2×#99—731no—
396#389—1462no—
397#387—1462no—
398#387—1462no—
399#380—732no—
400#380—732no—
401#380—732no—
402C4×C4⋊C4—1462no—
403C4×C22⋊C4—732no—
404C4×C22⋊C4—732no—
405C4×C22⋊C4—732no—
406#342—732no—
407#342—732no—
408#342—732no—
409#342—732no—
410#342—732no—
411#342—732no—
412C22×Q8—731no—
413C22×Q8—731no—
414C22×Q8C2×#6440811yescharacteristic
415C22×D4—731no—
416C23×C4—731no—
417C23×C4—731no—
418C23×C4—731no—
419C23×C4—731no—
420C23×C4—731no—
421C23×C4C2×#6440811yescharacteristic
422C4⋊Q8—1462no—
423C4⋊Q8—1462no—
424#125—1462no—
425#125—1462no—
426#125—1462no—
427#125—1462no—
428C22⋊Q8—22no—
429C22⋊Q8—22no—
430C22⋊Q8—1462no—
431C22⋊Q8—1462no—
432C22⋊Q8—1462no—
433C22⋊Q8—1462no—
434C22⋊Q8—1462no—
435C22⋊Q8—1462no—
436C22⋊Q8—1462no—
437C22⋊Q8—1462no—
438C22⋊Q8—1462no—
439C22⋊Q8—1462no—
440C4×Q8—1461no—
441C4×Q8—1461no—
442C4×Q8—1461no—
443C4×Q8—1461no—
444C4×D4—1462no—
445C4×D4—1462no—
446C4×D4—1462no—
447C4×D4—1462no—
448C4×D4—1462no—
449C4×D4—1462no—
450C2×C4⋊C4—731no—
451C2×C4⋊C4—731no—
452C2×C4⋊C4—731no—
453C2×C4⋊C4—732no—
454C2×C4⋊C4—732no—
455C2×C4⋊C4—732no—
456C2×C4⋊C4—732no—
457C2×C4⋊C4—731no—
458C2×C4⋊C4—731no—
459C2×C4⋊C4—731no—
460C2×C4⋊C4—731no—
461C2×C4⋊C4—731no—
462C2×C4⋊C4—731no—
463C2×C4⋊C4—731no—
464C2×C4⋊C4—731no—
465C2×C4⋊C4—731no—
466C2×C4⋊C4—731no—
467C2×C4⋊C4—1462no—
468C2×C4⋊C4—1462no—
469C2×C4⋊C4—1462no—
470C2×C4⋊C4—1461no—
471C2×C4⋊C4—1461no—
472C2×C4⋊C4—1461no—
473C2×C4⋊C4—1461no—
474C2×C4⋊C4C2×#6440811yescharacteristic
475C2×C4⋊C4C2×#6440811yescharacteristic
476C2×C4⋊C4C2×#6440811yescharacteristic
477C2×C22⋊C4—732no—
478C2×C22⋊C4—731no—
479C2×C22⋊C4—731no—
480C2×C22⋊C4—731no—
481C2×C22⋊C4—731no—
482C2×C22⋊C4—732no—
483C2×C22⋊C4—732no—
484C2×C22⋊C4—732no—
485C2×C22⋊C4C2×#6440811yescharacteristic
486C2×C22⋊C4C2×#6440811yescharacteristic
487C2×C42—731no—
488C2×C42—731no—
489C2×C42—731no—
490C2×C42—1462no—
491C2×C42—1462no—
492C2×C42—1462no—
493#99—734no—
494#99—1462no—
495#99—1462no—
496#99—1462no—
497#95—1462no—
498#95—1462no—
499#95—1462no—
500#95—1462no—
501#95—1462no—
502#95—1462no—
503C24—731no—
504C24C22×#6440811yescharacteristic
505C2×Q8—22no—
506C2×Q8—81no—
507C2×Q8—2922no—
508C2×Q8—5841no—
509C2×Q8—1461no—
510C2×Q8—1461no—
511C2×Q8—1462no—
512C2×D4—732no—
513C2×D4—732no—
514C2×D4—1462no—
515C2×D4—1462no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—81no—
519C22×C4—2922no—
520C22×C4—2922no—
521C22×C4—5841no—
522C22×C4—5841no—
523C22×C4—5841no—
524C22×C4—731no—
525C22×C4—731no—
526C22×C4—732no—
527C22×C4—732no—
528C22×C4—732no—
529C22×C4—732no—
530C22×C4—732no—
531C22×C4—731no—
532C22×C4—731no—
533C22×C4—731no—
534C22×C4—731no—
535C22×C4—731no—
536C22×C4—732no—
537C22×C4—1462no—
538C22×C4—1462no—
539C22×C4—1462no—
540C22×C4—1461no—
541C22×C4—1461no—
542C22×C4—1462no—
543C22×C4—1461no—
544C22×C4—1461no—
545C22×C4C22×#6440811yescharacteristic
546C22×C4C22×#6440811yescharacteristic
547C22×C4C22×#6440811yescharacteristic
548C22×C4C22×#6440811yescharacteristic
549C22×C4C22×#6440811yescharacteristic
550C22×C4C22×#6440811yescharacteristic
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—22no—
554C4⋊C4—2924no—
555C4⋊C4—5842no—
556C4⋊C4—5842no—
557C4⋊C4—731no—
558C4⋊C4—731no—
559C4⋊C4—731no—
560C4⋊C4—731no—
561C4⋊C4—732no—
562C4⋊C4—732no—
563C4⋊C4—732no—
564C4⋊C4—732no—
565C4⋊C4—1461no—
566C4⋊C4—1461no—
567C4⋊C4—1461no—
568C4⋊C4—1461no—
569C4⋊C4—1462no—
570C4⋊C4—1461no—
571C4⋊C4—1461no—
572C4⋊C4—1462no—
573C4⋊C4—1461no—
574C4⋊C4—1461no—
575C4⋊C4—1462no—
576C4⋊C4—1462no—
577C4⋊C4—1462no—
578C4⋊C4—1462no—
579C4⋊C4C22⋊#6440812yes—
580C4⋊C4C22⋊#6440812yes—
581C22⋊C4—22no—
582C22⋊C4—22no—
583C22⋊C4—734no—
584C22⋊C4—1462no—
585C22⋊C4—1462no—
586C22⋊C4—1462no—
587C22⋊C4—1462no—
588C22⋊C4—1462no—
589C22⋊C4—1462no—
590C22⋊C4—1462no—
591C22⋊C4—1462no—
592C22⋊C4—1462no—
593C22⋊C4—1462no—
594C22⋊C4—1462no—
595C42—2924no—
596C42—5842no—
597C42—5842no—
598C42—1461no—
599C42—1461no—
600C42—1461no—
601C42—1461no—
602C42—1461no—
603C42—1461no—
604C23—21no—
605C23—21no—
606C23—41no—
607C23—41no—
608C23—2921no—
609C23—2921no—
610C23—731no—
611C23—731no—
612C23—732no—
613C23—732no—
614C23Q8×#6440812yes—
615C23C23×#6440811yescharacteristic
616Q8—82no—
617Q8—2922no—
618Q8—2922no—
619Q8—5842no—
620D4—1464no—
621D4—1464no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—81no—
632C2×C4—81no—
633C2×C4—2922no—
634C2×C4—2922no—
635C2×C4—2922no—
636C2×C4—2922no—
637C2×C4—2922no—
638C2×C4—2922no—
639C2×C4—2922no—
640C2×C4—2922no—
641C2×C4—2922no—
642C2×C4—2921no—
643C2×C4—2921no—
644C2×C4—2921no—
645C2×C4—2922no—
646C2×C4—2922no—
647C2×C4—2922no—
648C2×C4—2922no—
649C2×C4—2922no—
650C2×C4—2922no—
651C2×C4—2922no—
652C2×C4—2922no—
653C2×C4—2922no—
654C2×C4—2921no—
655C2×C4—2921no—
656C2×C4—5841no—
657C2×C4—5841no—
658C2×C4—731no—
659C2×C4—731no—
660C2×C4—731no—
661C2×C4—731no—
662C2×C4—732no—
663C2×C4—732no—
664C2×C4—1464no—
665C2×C4—1464no—
666C2×C4—1461no—
667C2×C4—1461no—
668C2×C4—1461no—
669C2×C4—1462no—
670C2×C4—1461no—
671C2×C4—1461no—
672C2×C4C2×C22⋊#6440811yescharacteristic
673C2×C4C2×C22⋊#6440811yescharacteristic
674C2×C4C2×C22⋊#6440812yes—
675C2×C4C2×C22⋊#6440812yes—
676C22—21no—
677C22—21no—
678C22—22no—
679C22—42no—
680C22—42no—
681C22—41no—
682C22—41no—
683C22—2921no—
684C22—2921no—
685C22—2922no—
686C22—732no—
687C22—732no—
688C22—1462no—
689C22—1462no—
690C22C22×C22⋊#6440811yescharacteristic
691C22C2×Q8×#6440811yescharacteristic
692C22#1798965511yescharacteristic
693C4—22no—
694C4—21no—
695C4—21no—
696C4—22no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—2924no—
701C4—2921no—
702C4—2921no—
703C4—2921no—
704C4—5842no—
705C4—5842no—
706C4—5842no—
707C4—732no—
708C4—1462no—
709C4—1461no—
710C4—1461no—
711C4—1461no—
712C4—1462no—
713C2—21no—
714C2—21no—
715C2—42no—
716C2—1462no—
717C2—1462no—
718C2Q8×C22⋊#6440811yescharacteristic
719C2D73⋊#41011yescharacteristic
720C2#2262653011yescharacteristic
subgroupG/H
centerC22C22×C22⋊#64408
commutatorC23×C73C23×C4
FrattiniC23C23×#64408
FittingC2×C22⋊Q8×C73C4
socleC22×C73C22×C22⋊C4
prime radicalC22×C22⋊D73C23
cosocleC23×D73C24
hypercenterC2×C22⋊Q8#64408
hypocenterC73#22513
LCSG ▷ C23×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C4⋊C4 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #22626440C2semidirect
2. #22626122C2semidirect
3. #22626122C2semidirect
4. #22626120C2semidirect
36. C2×#14556589C4semidirect
37. C2×#14556581C4semidirect
38. C2×#14556581C4semidirect
41. C2×#14556568C4semidirect
42. C2×#14556568C4semidirect
44. C2×#14556556C4semidirect
48. C22×#11924007C4semidirect
50. C2×C22⋊Q8×C73C4semidirect
64. #14556649Q8semidirect
372. C73#22513semidirect
385. C2×C22⋊Q8#64408semidirect

Maximal subgroups

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

subgroupindex
#226264402
#226261222
#226261202
#226257932
#226257912
#226256782
C4×#145566492
C2×#179892912
#2251373