Finite Group Databasebeta

← #33052989

Subgroups — #33052989

Order 18688.

1010 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623541C211yesmaximal, characteristic
2#22618575C211yesmaximal, characteristic, complemented
3#22608399C211yesmaximal, characteristic, complemented
4#22608394C211yesmaximal, characteristic, complemented
5#22608389C211yesmaximal, characteristic, complemented
6#22608373C211yesmaximal, characteristic, complemented
7#22608363C211yesmaximal, characteristic, complemented
8#22608355C211yesmaximal, characteristic, complemented
9#22608342C211yesmaximal, characteristic, complemented
10#22608337C211yesmaximal, characteristic, complemented
11#22608329C211yesmaximal, characteristic, complemented
12#22608321C211yesmaximal, characteristic, complemented
13#22608316C211yesmaximal, characteristic, complemented
14C2×#17988314C211yesmaximal, characteristic, complemented
15C73×#2990C211yesmaximal, characteristic, complemented
16#17989322C411yescharacteristic
17#17989297C411yescharacteristic
18#17989294C411yescharacteristic
19#17989283C411yescharacteristic
20#17989283C411yescharacteristic
21#17989281—21no—
22#17989261—21no—
23#17989261—21no—
24#17989233C411yescharacteristic
25#17989233C411yescharacteristic
26#17989225—21no—
27D4×D292C411yescharacteristic
28#17989137C2211yescharacteristic
29#17989124—21no—
30#17989121C2211yescharacteristic
31#17989121C2211yescharacteristic
32#17989096—21no—
33#17989096—21no—
34C4×#11924028C2211yescharacteristic
35C2×C4×D292C2211yescharacteristic
36C2×C4×D292C2211yescharacteristic
37C4×D4×D73—21no—
38#17988648—21no—
39#17988648—21no—
40#17988640C2211yescharacteristic, complemented
41#17988640C2211yescharacteristic, complemented
42#17988640C2211yescharacteristic, complemented
43#17988640C2211yescharacteristic, complemented
44#17988614—21no—
45#17988554—21no—
46C4×#11924012C2211yescharacteristic, complemented
47C2×C4×#10596831C2211yescharacteristic, complemented
48#17988317C2211yescharacteristic, complemented
49#17988317C2211yescharacteristic, complemented
50#17988317C2211yescharacteristic, complemented
51#17988317C2211yescharacteristic, complemented
52#17988314C2211yescharacteristic
53#17988314C2211yescharacteristic
54#17988314C2211yescharacteristic
55#17988314C2211yescharacteristic
56#17988314C2211yescharacteristic, complemented
57#17988314C2211yescharacteristic, complemented
58#17988314C2211yescharacteristic, complemented
59#17988314C2211yescharacteristic, complemented
60#17988314C2211yescharacteristic, complemented
61#17988314C2211yescharacteristic, complemented
62#17988314C2211yescharacteristic, complemented
63#17988314C2211yescharacteristic, complemented
64C4×#41×C73C2211yescharacteristic
65#446×C73—21no—
66#435×C73—21no—
67#435×C73—21no—
68C8×D4×C73—21no—
69#432×C73C2211yescharacteristic, complemented
70#432×C73C2211yescharacteristic, complemented
71#431×C73C2211yescharacteristic, complemented
72#423×C73C2211yescharacteristic, complemented
73C2×C4⋊C8×C73C2211yescharacteristic, complemented
74C2×C4⋊C8×C73C2211yescharacteristic, complemented
75C2×#11924028—21no—
76C2×#11924028C2×C411yescharacteristic
77C22×D292C2×C411yescharacteristic
78C22×D292C2×C411yescharacteristic
79C2×D4×D73—21no—
80C22×C4×D73—21no—
81C22×C4×D73—21no—
82C2×#11924012—21no—
83C22×#10596831—21no—
84#14556591C2×C411yescharacteristic
85#14556588C2×C411yescharacteristic
86#14556586—21no—
87#14556586—21no—
88#14556585—21no—
89#14556585—21no—
90#14556583C2×C411yescharacteristic
91#14556583C2×C411yescharacteristic
92#14556582—21no—
93#14556580—21no—
94#14556579—21no—
95#14556579C2×C411yescharacteristic
96#14556579C2×C411yescharacteristic
97#14556576—21no—
98#14556576—21no—
99#14556576—21no—
100#14556576—21no—
101#14556574—21no—
102#14556574—21no—
103#14556573—21no—
104#14556573—21no—
105#14556570C2×C411yescharacteristic
106#14556570C2×C411yescharacteristic
107#14556569—21no—
108#14556569—21no—
109#14556568—21no—
110#14556568—21no—
111#14556567—21no—
112#14556566—21no—
113#14556565—21no—
114#14556565C2×C411yescharacteristic
115#14556565C2×C411yescharacteristic
116#14556565C2×C411yescharacteristic
117#14556565C2×C411yescharacteristic
118#14556564—21no—
119#14556564—21no—
120#14556563—21no—
121#14556563—21no—
122#14556561—21no—
123#14556561—21no—
124#14556559—21no—
125#14556559—21no—
126C4×Dic146C2×C411yescharacteristic
127C4×Dic146C2311yescharacteristic
128C4×D292—21no—
129C4×D292—21no—
130C4×D292—21no—
131C4×D292—21no—
132C4×D292—21no—
133C4×D292C2×C411yescharacteristic
134C4×D292C2×C411yescharacteristic
135C4×D292C2×C411yescharacteristic
136C4×D292C2×C411yescharacteristic
137C4×D292C2×C411yescharacteristic
138C4×D292C2311yescharacteristic
139C4×D292C2311yescharacteristic
140C4×D292C2311yescharacteristic
141D4×Dic73—21no—
142#14556553—21no—
143C4×C22⋊D73—21no—
144C4×C22⋊D73—21no—
145C4×C22⋊D73—21no—
146C4×C22⋊D73—21no—
147#14556551—21no—
148#14556551—21no—
149#14556550C2×C411yescharacteristic
150#14556548—21no—
151#14556548—21no—
152#14556548—21no—
153C2×C4⋊Dic73C2×C411yescharacteristic
154C2×C4⋊Dic73C2×C411yescharacteristic
155C4⋊C4×D73—21no—
156C2×#11924005—21no—
157C2×#11924005—21no—
158C22⋊C4×D73—21no—
159C22⋊C4×D73—21no—
160C42×D73—21no—
161C4⋊#10596831—21no—
162C4⋊#10596831—21no—
163C4⋊#10596831—21no—
164C4⋊#10596831—21no—
165C22⋊#10596831—21no—
166C22⋊#10596831—21no—
167C22⋊#10596831—21no—
168C22⋊#10596831—21no—
169#14556502—21no—
170C4×#10596831—21no—
171C4×#10596831C2311yescharacteristic
172C4×#10596831C2311yescharacteristic
173C4×#10596831C2311yescharacteristic
174C4×#10596831C2311yescharacteristic
175C2×#41×C73D411yescharacteristic
176C2×M16×C73—21no—
177C22×C8×C73—21no—
178C22×C8×C73—21no—
179C4×Q8×C73C2×C411yescharacteristic
180C4×Q8×C73D411yescharacteristic
181C4×D4×C73C2×C411yescharacteristic
182C4×D4×C73C2×C411yescharacteristic
183C4×D4×C73C2×C411yescharacteristic
184C4×D4×C73D411yescharacteristic
185C4×D4×C73D411yescharacteristic
186C4×D4×C73D411yescharacteristic
187#117×C73D411yescharacteristic
188#117×C73D411yescharacteristic
189#117×C73D411yescharacteristic
190C2×C42×C73C2311yescharacteristic
191C2×C42×C73C2311yescharacteristic
192C2×C42×C73C2311yescharacteristic
193C4⋊C8×C73—21no—
194C4⋊C8×C73—21no—
195C4⋊C8×C73—21no—
196C4⋊C8×C73C2311yescharacteristic
197C4⋊C8×C73C2311yescharacteristic
198C4⋊C8×C73C2311yescharacteristic
199C4⋊C8×C73C2311yescharacteristic
200C22⋊C8×C73—21no—
201C22⋊C8×C73—21no—
202C22⋊C8×C73—21no—
203#97×C73—21no—
204#97×C73—21no—
205C4×C8×C73—21no—
206C23×D73—21no—
207C23×D73—21no—
208#11924028—22no—
209#11924028—41no—
210#11924028—81no—
211#11924028—81no—
212C2×Dic146—21no—
213C2×Dic146C22×C411yescharacteristic
214C2×D292—22no—
215C2×D292—22no—
216C2×D292—21no—
217C2×D292—21no—
218C2×D292—21no—
219C2×D292—21no—
220C2×D292—41no—
221C2×D292—41no—
222C2×D292C22×C411yescharacteristic
223C2×D292C22×C411yescharacteristic
224C2×D292C22×C411yescharacteristic
225C2×C22⋊D73—21no—
226C2×C22⋊D73—21no—
227C2×C22⋊D73—21no—
228C2×C22⋊D73—21no—
229C2×C22⋊D73—21no—
230D4×D73—44no—
231C22×Dic73—21no—
232C22×Dic73—21no—
233C2×C4×D73—21no—
234C2×C4×D73—21no—
235C2×C4×D73—21no—
236C2×C4×D73—21no—
237C2×C4×D73—21no—
238C2×C4×D73—21no—
239C2×C4×D73—21no—
240C2×C4×D73—21no—
241C2×C4×D73—21no—
242C2×C4×D73—81no—
243C2×C4×D73—81no—
244C2×C4×D73—81no—
245C2×C4×D73—81no—
246#11924012—42no—
247C2×#10596831—21no—
248C2×#10596831—21no—
249C2×#10596831—21no—
250C2×#10596831—21no—
251C2×#10596831—42no—
252C4⋊Dic73—21no—
253C4⋊Dic73—21no—
254C4⋊Dic73—21no—
255C4⋊Dic73C22×C411yescharacteristic
256C4⋊Dic73C22×C411yescharacteristic
257C4⋊Dic73C22×C411yescharacteristic
258C4⋊Dic73C22×C411yescharacteristic
259#11924007—21no—
260#11924007—21no—
261#11924007—21no—
262#11924007—21no—
263#11924007—21no—
264#11924007—21no—
265#11924007—21no—
266#11924007—21no—
267C22⋊Dic73—21no—
268C22⋊Dic73—21no—
269C22⋊Dic73—21no—
270#11924005—21no—
271#11924005—21no—
272#11924005—21no—
273#11924005—21no—
274#11924005—21no—
275#11924005—21no—
276#11924005—21no—
277#11924005—21no—
278#11924005—21no—
279#11924005—21no—
280#11924005—21no—
281#11924005—21no—
282#11924005—21no—
283#11924005—21no—
284#11924005—21no—
285#11924005—21no—
286C4×Dic73—21no—
287C4×Dic73—21no—
288C4×Dic73—21no—
289#41×C73—42no—
290C2×Q8×C73C22⋊C411yescharacteristic
291C2×D4×C73C22⋊C411yescharacteristic
292C2×D4×C73C22⋊C411yescharacteristic
293C2×D4×C73C22⋊C411yescharacteristic
294C22×C4×C73C22×C411yescharacteristic
295C22×C4×C73C22×C411yescharacteristic
296C22×C4×C73C22×C411yescharacteristic
297C22×C4×C73C2×D411yescharacteristic
298C22×C4×C73C2×D411yescharacteristic
299C22×C4×C73C2×D411yescharacteristic
300C22×C4×C73C2×D411yescharacteristic
301C22×C4×C73C2×D411yescharacteristic
302C22×C4×C73C2×D411yescharacteristic
303M16×C73—81no—
304C2×C8×C73—21no—
305C2×C8×C73—21no—
306C2×C8×C73—21no—
307C2×C8×C73—21no—
308C2×C8×C73—81no—
309C2×C8×C73—81no—
310C4⋊C4×C73C22⋊C411yescharacteristic
311C4⋊C4×C73C22⋊C411yescharacteristic
312C4⋊C4×C73C22⋊C411yescharacteristic
313C4⋊C4×C73C22⋊C411yescharacteristic
314C4⋊C4×C73C22⋊C411yescharacteristic
315C4⋊C4×C73C22⋊C411yescharacteristic
316C22⋊C4×C73C22⋊C411yescharacteristic
317C22⋊C4×C73C22⋊C411yescharacteristic
318C22⋊C4×C73C22⋊C411yescharacteristic
319C22⋊C4×C73C22⋊C411yescharacteristic
320C22⋊C4×C73C22⋊C411yescharacteristic
321C22⋊C4×C73C22⋊C411yescharacteristic
322C42×C73C22×C411yescharacteristic
323C42×C73C22×C411yescharacteristic
324C42×C73C22×C411yescharacteristic
325C42×C73C2×D411yescharacteristic
326C42×C73C2×D411yescharacteristic
327C42×C73C2×D411yescharacteristic
328C42×C73C2×D411yescharacteristic
329C42×C73C2×D411yescharacteristic
330C42×C73C2×D411yescharacteristic
331C42×C73C2411yescharacteristic
332C23×C73C2×C22⋊C411yescharacteristic
333C23×C73C2×C22⋊C411yescharacteristic
334C23×C73C2×C22⋊C411yescharacteristic
335C22×D73—21no—
336C22×D73—21no—
337C22×D73—21no—
338C22×D73—42no—
339C22×D73—42no—
340C22×D73—42no—
341C22×D73—42no—
342C22×D73—81no—
343C22×D73—81no—
344Q8×C73—41no—
345D4×C73—22no—
346D4×C73—22no—
347D4×C73—41no—
348C2×C4×C73—22no—
349C2×C4×C73—21no—
350C2×C4×C73—21no—
351C2×C4×C73—21no—
352C2×C4×C73—21no—
353C2×C4×C73—21no—
354C2×C4×C73—21no—
355C2×C4×C73—21no—
356C2×C4×C73—21no—
357C2×C4×C73—21no—
358C2×C4×C73—21no—
359C2×C4×C73—21no—
360C2×C4×C73—21no—
361C2×C4×C73—41no—
362C2×C4×C73—41no—
363C2×C4×C73C2×C22⋊C411yescharacteristic
364C2×C4×C73C2×C22⋊C411yescharacteristic
365C2×C4×C73C2×C22⋊C411yescharacteristic
366C2×C4×C73C2×C22⋊C411yescharacteristic
367C2×C4×C73C2×C22⋊C411yescharacteristic
368C2×C4×C73C2×C22⋊C411yescharacteristic
369C2×C4×C73C2×C22⋊C411yescharacteristic
370C2×C4×C73C2×C22⋊C411yescharacteristic
371C2×C4×C73C2×C22⋊C411yescharacteristic
372C2×C4×C73C23×C411yescharacteristic
373C2×C4×C73C22×D411yescharacteristic
374C2×C4×C73C22×D411yescharacteristic
375C22⋊D73—42no—
376C22⋊D73—42no—
377C22⋊D73—42no—
378C22⋊D73—81no—
379C22⋊D73—81no—
380C2×Dic73—21no—
381C2×Dic73—21no—
382C2×Dic73—21no—
383C2×Dic73—21no—
384C2×Dic73—21no—
385C2×Dic73—81no—
386C2×Dic73—81no—
387D292—21no—
388D292—21no—
389D292—21no—
390D292—21no—
391D292—21no—
392D292—42no—
393D292—42no—
394D292—42no—
395D292—81no—
396D292#13112yes—
397C4×D73—42no—
398C4×D73—42no—
399C4×D73—41no—
400C4×D73—41no—
401C4×D73—41no—
402C4×D73—41no—
403C4×D73—41no—
404C4×D73—41no—
405C4×D73—81no—
406C4×D73—81no—
407C4×D73—81no—
408C4×D73—81no—
409Dic146—21no—
410Dic146—21no—
411Dic146—81no—
412C8×C73—41no—
413C8×C73—41no—
414C8×C73—41no—
415C8×C73—41no—
416#10596831—41no—
417#10596831—41no—
418#10596831—41no—
419#10596831—41no—
420C22×C73—21no—
421C22×C73—21no—
422C22×C73—21no—
423C22×C73—21no—
424C22×C73—21no—
425C22×C73—21no—
426C22×C73—21no—
427C22×C73—21no—
428C22×C73#42112yes—
429C22×C73C22×C22⋊C411yescharacteristic
430C2×D73—22no—
431C2×D73—41no—
432C2×D73—41no—
433C2×D73—41no—
434C2×D73—41no—
435C2×D73—41no—
436C2×D73—41no—
437C2×D73—41no—
438C2×D73—41no—
439C2×D73—84no—
440C2×D73—84no—
441C4×C73—21no—
442C4×C73—21no—
443C4×C73—21no—
444C4×C73—21no—
445C4×C73—21no—
446C4×C73—21no—
447C4×C73—21no—
448C4×C73—21no—
449C4×C73—21no—
450C4×C73—21no—
451C4×C73C2×#13111yescharacteristic
452C4×C73#56811yescharacteristic
453C4×C73#57611yescharacteristic
454C4×C73#57711yescharacteristic
455Dic73—41no—
456Dic73—41no—
457Dic73—41no—
458Dic73—41no—
459Dic73—41no—
460#17521—731nomaximal, Sylow
461C2×C73—22no—
462C2×C73—41no—
463C2×C73—41no—
464C2×C73#288011yescharacteristic
465C2×C73#289711yescharacteristic
466C2×C73C2×#42111yescharacteristic
467D73—42no—
468D73—81no—
469D73—81no—
470#3481—731no—
471#2990D7311yescharacteristic, complemented
472#2922—731no—
473#1496—731no—
474#1495—731no—
475#1494—731no—
476#1490—731no—
477#1488—731no—
478#1486—731no—
479#1483—731no—
480#1482—731no—
481#1480—731no—
482#1478—731no—
483#1477—731no—
484C2×D4⋊C8—731no—
485C73#1752111yescharacteristic, complemented, Sylow
486#559—731no—
487#554—731no—
488#554—731no—
489#553—731no—
490#553—731no—
491#553—1461no—
492#551—1461no—
493#551—1461no—
494#546—731no—
495#546—731no—
496#546—1461no—
497D42—731no—
498#532—731no—
499#529—731no—
500#529—731no—
501#529—1461no—
502#525—1461no—
503#525—1461no—
504C4×#41—731no—
505C4×#41C2×D7311yescharacteristic
506C2×C4×D4—731no—
507C2×C4×D4—731no—
508C2×C4×D4—1461no—
509#446—21no—
510#435—21no—
511#435—21no—
512C8×D4—21no—
513#433—1461no—
514#433—1461no—
515#432C2×D7311yescharacteristic, complemented
516#432C2×D7311yescharacteristic, complemented
517#431—731no—
518#431—731no—
519#431—731no—
520#431—731no—
521#431C2×D7311yescharacteristic, complemented
522#424—1461no—
523#423C2×D7311yescharacteristic, complemented
524C2×C4⋊C8C2×D7311yescharacteristic, complemented
525C2×C4⋊C8C2×D7311yescharacteristic, complemented
526#408—1461no—
527C4×M16—731no—
528C2×C4×C8—731no—
529Q8⋊C8—731no—
530Q8⋊C8—731no—
531Q8⋊C8—731no—
532Q8⋊C8—731no—
533D4⋊C8—731no—
534D4⋊C8—731no—
535D4⋊C8—731no—
536D4⋊C8—731no—
537D4⋊C8—731no—
538D4⋊C8—731no—
539D4⋊C8—731no—
540D4⋊C8—731no—
541D4⋊C8—731no—
542D4⋊C8—731no—
543D4⋊C8—731no—
544D4⋊C8—731no—
545C2×#41—731no—
546C2×#41—1461no—
547C2×#41D29211yescharacteristic
548C22×D4—731no—
549C22×D4—731no—
550C22×D4—1461no—
551C23×C4—1461no—
552C23×C4—1461no—
553C2×M16—21no—
554C2×M16—1461no—
555C22×C8—21no—
556C22×C8—21no—
557C22×C8—1461no—
558C4⋊Q8—731no—
559#127—731no—
560#126—1461no—
561#126—1461no—
562#126—1461no—
563#126—1461no—
564#125—731no—
565#125—731no—
566#125—1461no—
567#124—731no—
568#124—731no—
569#124—1461no—
570#124—1461no—
571#123—1461no—
572#123—1461no—
573#123—1461no—
574#123—1461no—
575#123—1461no—
576#123—1461no—
577#123—1461no—
578#123—1461no—
579C22⋊Q8—731no—
580C22⋊Q8—731no—
581C22⋊Q8—1461no—
582C22⋊Q8—1461no—
583C22⋊Q8—1461no—
584C22⋊Q8—1461no—
585C22⋊Q8—1461no—
586#121—731no—
587#121—731no—
588#121—731no—
589#121—731no—
590#121—1461no—
591#121—1461no—
592#121—1461no—
593#121—1461no—
594#121—1461no—
595#121—1461no—
596#120—1461no—
597#120—1461no—
598#120—1461no—
599#120—1461no—
600C4×Q8—731no—
601C4×Q8—731no—
602C4×Q8C4×D7311yescharacteristic
603C4×Q8C22⋊D7311yescharacteristic
604C4×D4—731no—
605C4×D4—731no—
606C4×D4—731no—
607C4×D4—731no—
608C4×D4—731no—
609C4×D4—731no—
610C4×D4—731no—
611C4×D4—731no—
612C4×D4—1461no—
613C4×D4—1461no—
614C4×D4—1461no—
615C4×D4—1461no—
616C4×D4—1461no—
617C4×D4—1461no—
618C4×D4—1461no—
619C4×D4—1461no—
620C4×D4—1461no—
621C4×D4—1461no—
622C4×D4—1461no—
623C4×D4—1461no—
624C4×D4—1461no—
625C4×D4C4×D7311yescharacteristic
626C4×D4C4×D7311yescharacteristic
627C4×D4C4×D7311yescharacteristic
628C4×D4C22⋊D7311yescharacteristic
629C4×D4C22⋊D7311yescharacteristic
630C4×D4C22⋊D7311yescharacteristic
631#117—731no—
632#117—1461no—
633#117—1461no—
634#117—1461no—
635#117D29211yescharacteristic
636#117D29211yescharacteristic
637#117D29211yescharacteristic
638C2×C4⋊C4—731no—
639C2×C4⋊C4—731no—
640C2×C4⋊C4—1461no—
641C2×C22⋊C4—1461no—
642C2×C22⋊C4—1461no—
643C2×C22⋊C4—1461no—
644C2×C22⋊C4—1461no—
645C2×C42—1461no—
646C2×C42C22×D7311yescharacteristic
647C2×C42C22×D7311yescharacteristic
648C2×C42C22×D7311yescharacteristic
649C4⋊C8—21no—
650C4⋊C8—21no—
651C4⋊C8—21no—
652C4⋊C8—1461no—
653C4⋊C8—1461no—
654C4⋊C8—1461no—
655C4⋊C8—1461no—
656C4⋊C8C22×D7311yescharacteristic
657C4⋊C8C22×D7311yescharacteristic
658C4⋊C8C22×D7311yescharacteristic
659C4⋊C8C22×D7311yescharacteristic
660C22⋊C8—21no—
661C22⋊C8—21no—
662C22⋊C8—21no—
663C22⋊C8—1461no—
664C22⋊C8—1461no—
665C22⋊C8—1461no—
666C22⋊C8—1461no—
667#97—21no—
668#97—21no—
669#97—1461no—
670C4×C8—21no—
671C4×C8—731no—
672C4×C8—731no—
673C4×C8—731no—
674C4×C8—731no—
675C4×C8—1461no—
676C24—1461no—
677C24—1461no—
678#41—42no—
679#41—2921no—
680#41—5841no—
681#41—5841no—
682#41—1462no—
683C2×Q8—731no—
684C2×Q8—1461no—
685C2×Q8#1192400511yescharacteristic
686C2×D4—2921no—
687C2×D4—2921no—
688C2×D4—2924no—
689C2×D4—731no—
690C2×D4—731no—
691C2×D4—731no—
692C2×D4—1462no—
693C2×D4—1462no—
694C2×D4—1461no—
695C2×D4—1461no—
696C2×D4—1461no—
697C2×D4—1461no—
698C2×D4—1461no—
699C2×D4—1461no—
700C2×D4—1461no—
701C2×D4—1461no—
702C2×D4—1461no—
703C2×D4#1192400511yescharacteristic
704C2×D4#1192400511yescharacteristic
705C2×D4#1192400511yescharacteristic
706C22×C4—5841no—
707C22×C4—5841no—
708C22×C4—5841no—
709C22×C4—5841no—
710C22×C4—1461no—
711C22×C4—1461no—
712C22×C4—1461no—
713C22×C4—1461no—
714C22×C4—1461no—
715C22×C4—1461no—
716C22×C4—1461no—
717C22×C4—1461no—
718C22×C4—1461no—
719C22×C4—1461no—
720C22×C4—1461no—
721C22×C4C2×C4×D7311yescharacteristic
722C22×C4C2×C4×D7311yescharacteristic
723C22×C4C2×C4×D7311yescharacteristic
724C22×C4C2×C22⋊D7311yescharacteristic
725C22×C4C2×C22⋊D7311yescharacteristic
726C22×C4C2×C22⋊D7311yescharacteristic
727C22×C4C2×D29211yescharacteristic
728C22×C4C2×D29211yescharacteristic
729C22×C4C2×D29211yescharacteristic
730M16—81no—
731M16—2922no—
732C2×C8—21no—
733C2×C8—21no—
734C2×C8—21no—
735C2×C8—21no—
736C2×C8—81no—
737C2×C8—81no—
738C2×C8—2922no—
739C2×C8—1461no—
740C2×C8—1461no—
741C2×C8—1461no—
742C2×C8—1461no—
743C4⋊C4—731no—
744C4⋊C4—731no—
745C4⋊C4—731no—
746C4⋊C4—731no—
747C4⋊C4—1461no—
748C4⋊C4—1461no—
749C4⋊C4—1461no—
750C4⋊C4—1461no—
751C4⋊C4—1461no—
752C4⋊C4—1461no—
753C4⋊C4—1461no—
754C4⋊C4—1461no—
755C4⋊C4—1461no—
756C4⋊C4—1461no—
757C4⋊C4—1461no—
758C4⋊C4#1192400511yescharacteristic
759C4⋊C4#1192400511yescharacteristic
760C4⋊C4#1192400511yescharacteristic
761C4⋊C4#1192400511yescharacteristic
762C4⋊C4#1192400511yescharacteristic
763C4⋊C4#1192400511yescharacteristic
764C22⋊C4—1461no—
765C22⋊C4—1461no—
766C22⋊C4—1461no—
767C22⋊C4—1461no—
768C22⋊C4—1461no—
769C22⋊C4—1461no—
770C22⋊C4—1461no—
771C22⋊C4—1461no—
772C22⋊C4—1461no—
773C22⋊C4—1461no—
774C22⋊C4—1461no—
775C22⋊C4—1461no—
776C22⋊C4—1461no—
777C22⋊C4—1461no—
778C22⋊C4—1461no—
779C22⋊C4—1461no—
780C22⋊C4—1461no—
781C22⋊C4—1461no—
782C22⋊C4—1461no—
783C22⋊C4#1192400511yescharacteristic
784C22⋊C4#1192400511yescharacteristic
785C22⋊C4#1192400511yescharacteristic
786C22⋊C4#1192400511yescharacteristic
787C22⋊C4#1192400511yescharacteristic
788C22⋊C4#1192400511yescharacteristic
789C42—1461no—
790C42—1461no—
791C42—1461no—
792C42C2×C4×D7311yescharacteristic
793C42C2×C4×D7311yescharacteristic
794C42C2×C4×D7311yescharacteristic
795C42C2×C22⋊D7311yescharacteristic
796C42C2×C22⋊D7311yescharacteristic
797C42C2×C22⋊D7311yescharacteristic
798C42C2×D29211yescharacteristic
799C42C2×D29211yescharacteristic
800C42C2×D29211yescharacteristic
801C42C23×D7311yescharacteristic
802C23—2922no—
803C23—2922no—
804C23—2922no—
805C23—2922no—
806C23—5841no—
807C23—5841no—
808C23—1461no—
809C23—1461no—
810C23—1461no—
811C23C2×#1192400511yescharacteristic
812C23C2×#1192400511yescharacteristic
813C23C2×#1192400511yescharacteristic
814Q8—41no—
815Q8—5841no—
816Q8—1461no—
817Q8—1461no—
818D4—22no—
819D4—22no—
820D4—41no—
821D4—2922no—
822D4—2922no—
823D4—2922no—
824D4—2922no—
825D4—2922no—
826D4—2922no—
827D4—5841no—
828D4—5841no—
829D4—5841no—
830D4—732no—
831D4—1461no—
832D4—1461no—
833D4—1461no—
834D4—1461no—
835D4—1461no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—2922no—
852C2×C4—2922no—
853C2×C4—2921no—
854C2×C4—2921no—
855C2×C4—2921no—
856C2×C4—2921no—
857C2×C4—2921no—
858C2×C4—2921no—
859C2×C4—5841no—
860C2×C4—5841no—
861C2×C4—5841no—
862C2×C4—5841no—
863C2×C4—5841no—
864C2×C4—5841no—
865C2×C4—1461no—
866C2×C4—1461no—
867C2×C4—1461no—
868C2×C4—1461no—
869C2×C4—1461no—
870C2×C4C2×#1192400511yescharacteristic
871C2×C4C2×#1192400511yescharacteristic
872C2×C4C2×#1192400511yescharacteristic
873C2×C4C2×#1192400511yescharacteristic
874C2×C4C2×#1192400511yescharacteristic
875C2×C4C2×#1192400511yescharacteristic
876C2×C4C2×#1192400511yescharacteristic
877C2×C4C2×#1192400511yescharacteristic
878C2×C4C2×#1192400511yescharacteristic
879C2×C4C22×C4×D7311yescharacteristic
880C2×C4C22×C22⋊D7311yescharacteristic
881C2×C4C22×D29211yescharacteristic
882C8—41no—
883C8—41no—
884C8—41no—
885C8—41no—
886C8—2921no—
887C8—2921no—
888C8—2921no—
889C8—2921no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—21no—
894C22—21no—
895C22—21no—
896C22—21no—
897C22—21no—
898C22—2921no—
899C22—2921no—
900C22—2921no—
901C22—2921no—
902C22—2921no—
903C22—2921no—
904C22—2921no—
905C22—2921no—
906C22—5844no—
907C22—5844no—
908C22—1462no—
909C22#1798860312yes—
910C22C22×#1192400511yescharacteristic
911C4—21no—
912C4—21no—
913C4—21no—
914C4—21no—
915C4—21no—
916C4—21no—
917C4—21no—
918C4—21no—
919C4—21no—
920C4—21no—
921C4—2921no—
922C4—2921no—
923C4—2921no—
924C4—2921no—
925C4—2921no—
926C4#131×D7311yescharacteristic
927C4#1798935211yescharacteristic
928C4#1798939011yescharacteristic
929C4#1798939511yescharacteristic
930C2—22no—
931C2—41no—
932C2—41no—
933C2—2922no—
934C2—5841no—
935C2—5841no—
936C2#2261837811yescharacteristic
937C2#2261845411yescharacteristic
938C2C2×#1798860311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2990C2
socleC22×C73C22×C22⋊C4
prime radical#22623541C2
cosocleC42×C73C24
hypercenter#2990D73
hypocenterC73#17521
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C4×#41 ◁ #2990

Complements

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

NH ≅ G/Ntype
2. #22618575C2semidirect
3. #22608399C2semidirect
4. #22608394C2semidirect
5. #22608389C2semidirect
6. #22608373C2semidirect
7. #22608363C2semidirect
8. #22608355C2semidirect
9. #22608342C2semidirect
10. #22608337C2semidirect
11. #22608329C2semidirect
12. #22608321C2semidirect
13. #22608316C2semidirect
14. C2×#17988314C2semidirect
15. C73×#2990C2semidirect
40. #17988640C22semidirect
41. #17988640C22semidirect
42. #17988640C22semidirect
43. #17988640C22semidirect
46. C4×#11924012C22semidirect
47. C2×C4×#10596831C22semidirect
48. #17988317C22semidirect
49. #17988317C22semidirect
50. #17988317C22semidirect
51. #17988317C22semidirect
56. #17988314C22semidirect
57. #17988314C22semidirect
58. #17988314C22semidirect
59. #17988314C22semidirect
60. #17988314C22semidirect
61. #17988314C22semidirect
62. #17988314C22semidirect
63. #17988314C22semidirect
69. #432×C73C22semidirect
70. #432×C73C22semidirect
71. #431×C73C22semidirect
72. #423×C73C22semidirect
73. C2×C4⋊C8×C73C22semidirect
74. C2×C4⋊C8×C73C22semidirect
471. #2990D73semidirect
485. C73#17521semidirect
515. #432C2×D73semidirect
516. #432C2×D73semidirect
521. #431C2×D73semidirect
523. #423C2×D73semidirect
524. C2×C4⋊C8C2×D73semidirect
525. C2×C4⋊C8C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226235412
#226185752
#226083992
#226083942
#226083892
#226083732
#226083632
#226083552
#226083422
#226083372
#226083292
#226083212
#226083162
C2×#179883142
C73×#29902
#1752173