Finite Group Databasebeta

← #33958600

Subgroups — #33958600

Order 18688.

1682 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623827C211yesmaximal, characteristic
2#22621229C214yesmaximal, complemented
3#22621214C214yesmaximal, complemented
4#22621171C212yesmaximal, complemented
5#22621171C212yesmaximal, complemented
6#22621161C212yesmaximal, complemented
7#22621152C212yesmaximal, complemented
8#22620473C211yesmaximal, characteristic, complemented
9#22620453C211yesmaximal, characteristic, complemented
10#22620320C211yesmaximal, characteristic, complemented
11C2×#17988949C211yesmaximal, characteristic, complemented
12#22619900C212yesmaximal, complemented
13#22619889C212yesmaximal
14#22619767C212yesmaximal, complemented
15#22619756C212yesmaximal, complemented
16#22618582C211yesmaximal, characteristic, complemented
17C73×#3503C211yesmaximal, characteristic, complemented
18#17989320—21no—
19#17989320—21no—
20#17989309—21no—
21#17989309—21no—
22#17989266—22no—
23#17989266—22no—
24#17989208C2212yes—
25#17989208C2212yes—
26#17989158C2211yescharacteristic
27#17989151C2211yescharacteristic
28#17989144C2211yescharacteristic
29#17989121C2212yes—
30#17989121C2212yes—
31C2×#14556579C2211yescharacteristic
32#17989064C2211yescharacteristic
33#17989061C2211yescharacteristic
34#17988997C2212yescomplemented
35#17988997C2212yescomplemented
36#17988993C2211yescharacteristic, complemented
37#17988993C2211yescharacteristic, complemented
38#17988993C2211yescharacteristic, complemented
39#17988993C2211yescharacteristic, complemented
40#17988993C2212yescomplemented
41#17988993C2212yescomplemented
42#17988990C2212yescomplemented
43#17988983C2212yescomplemented
44#17988949C2214yes—
45#17988949C2212yes—
46#17988949C2212yes—
47#17988949C2212yes—
48#17988949C2212yes—
49#17988944C2214yes—
50#17988928C2214yescomplemented
51#17988928C2214yescomplemented
52#17988922C2214yescomplemented
53#17988917C2214yescomplemented
54#17988911C2214yes—
55#17988911C2214yes—
56#17988905C2214yes—
57#17988900C2214yes—
58#17988891C2214yescomplemented
59#17988891C2214yescomplemented
60#17988884C2214yes—
61#17988884C2214yes—
62#17988879C2214yescomplemented
63#17988874C2214yes—
64#17988869C2214yescomplemented
65#17988864C2214yes—
66#17988648C2214yescomplemented
67#17988644C2212yescomplemented
68#17988644C2212yescomplemented
69#17988627C2212yes—
70#17988627C2212yes—
71#17988623C2212yes—
72#17988623C2212yes—
73#17988614C2212yes—
74#17988595C2212yes—
75#17988591C2212yes—
76C2×#14556514C2212yes—
77C2×#14556511C2212yes—
78#17988554C2212yes—
79C4×#11924012C2211yescharacteristic
80C2×#14556502C2211yescharacteristic
81Q82×C73—21no—
82#557×C73—21no—
83#554×C73—22no—
84#554×C73—21no—
85D4×Q8×C73—22no—
86D4×Q8×C73—21no—
87#544×C73C2212yes—
88#544×C73C2214yescomplemented
89#533×C73C2211yescharacteristic
90#533×C73C2212yescomplemented
91C2×C4⋊Q8×C73C2211yescharacteristic
92C2×C4⋊Q8×C73C2212yescomplemented
93#520×C73C2212yes—
94C4×#41×C73C2211yescharacteristic
95C22×Dic146C2311yescharacteristic
96C22×D292C2311yescharacteristic
97C2×#11924012C2312yes—
98C22×#10596831C2312yes—
99#14556591C2311yescharacteristic
100#14556591C2311yescharacteristic
101#14556589—21no—
102#14556587—21no—
103#14556586—22no—
104#14556586—22no—
105#14556585—22no—
106#14556585—22no—
107#14556583C2311yescharacteristic
108#14556583C2311yescharacteristic
109#14556580—21no—
110#14556579—21no—
111#14556579—21no—
112#14556579C2312yes—
113#14556579C2312yes—
114#14556578—21no—
115#14556577—22no—
116#14556577—22no—
117#14556574—22no—
118#14556574—22no—
119#14556573—22no—
120#14556573—22no—
121#14556572—22no—
122#14556570—21no—
123#14556570—21no—
124#14556570C2312yes—
125#14556570C2312yes—
126#14556569—22no—
127#14556569—22no—
128#14556565C2312yes—
129#14556565C2312yes—
130#14556559—22no—
131C4×Dic146—21no—
132C4×Dic146—21no—
133C4×Dic146C2312yes—
134C4×Dic146C2312yes—
135#14556556—21no—
136#14556556—21no—
137C4×D292C2312yes—
138C4×D292C2312yes—
139#14556553—21no—
140#14556553—21no—
141C4×C22⋊D73—22no—
142C4×C22⋊D73—22no—
143#14556550C2311yescharacteristic
144#14556550C2311yescharacteristic
145#14556548—22no—
146#14556548—22no—
147#14556547—22no—
148C2×#11924005—21no—
149C2×#11924005—21no—
150C22⋊C4×D73—22no—
151#14556524C2312yes—
152#14556524C2314yes—
153#14556524C2312yes—
154#14556524C2312yes—
155#14556524C2312yes—
156#14556524C2314yes—
157#14556522C2312yes—
158#14556522C2314yes—
159#14556522C2312yes—
160#14556522C2314yes—
161#14556522C2312yes—
162#14556522C2312yes—
163C4⋊#10596831C2314yes—
164C4⋊#10596831C2314yes—
165#14556514C2314yes—
166#14556514C2314yes—
167#14556514C2314yes—
168#14556514C2314yes—
169#14556511C2314yes—
170#14556511C2314yes—
171#14556511C2314yes—
172#14556511C2314yes—
173C22⋊#10596831C2314yes—
174C22⋊#10596831C2314yes—
175#14556502C2311yescharacteristic
176#14556502C2311yescharacteristic
177#14556502C2312yes—
178#14556502C2312yes—
179C4×#10596831C2312yes—
180C2×#41×C73C2311yescharacteristic
181C22×Q8×C73—21no—
182C22×Q8×C73—22no—
183C4⋊Q8×C73—22no—
184C4⋊Q8×C73—24no—
185C4⋊Q8×C73—21no—
186C4⋊Q8×C73—21no—
187C4⋊Q8×C73—22no—
188C4⋊Q8×C73—22no—
189C4⋊Q8×C73C2314yes—
190C4⋊Q8×C73C2312yes—
191C4⋊Q8×C73C2312yes—
192C4⋊Q8×C73C2311yescharacteristic
193C4⋊Q8×C73C2311yescharacteristic
194#125×C73—22no—
195#125×C73—24no—
196#125×C73C2314yes—
197#125×C73C2312yes—
198C22⋊Q8×C73—21no—
199C22⋊Q8×C73—21no—
200C22⋊Q8×C73—22no—
201C22⋊Q8×C73—22no—
202C22⋊Q8×C73—24no—
203C22⋊Q8×C73—24no—
204C22⋊Q8×C73—24no—
205C4×Q8×C73—22no—
206C4×Q8×C73—21no—
207C4×Q8×C73—21no—
208C4×Q8×C73—22no—
209C4×Q8×C73—22no—
210C4×Q8×C73D411yescharacteristic
211C4×Q8×C73D411yescharacteristic
212C4×D4×C73—24no—
213C4×D4×C73—22no—
214C4×D4×C73D412yes—
215C4×D4×C73D412yes—
216C4×D4×C73D411yescharacteristic
217C4×D4×C73D411yescharacteristic
218#117×C73C2312yes—
219#117×C73C2314yes—
220#117×C73C2311yescharacteristic
221#117×C73C2312yes—
222C2×C4⋊C4×C73—21no—
223C2×C4⋊C4×C73—22no—
224C2×C4⋊C4×C73C2312yes—
225C2×C4⋊C4×C73C2314yes—
226C2×C42×C73C2312yes—
227C2×C42×C73C2311yescharacteristic
228C23×D73—21no—
229C2×Dic146—24no—
230C2×Dic146—21no—
231C2×Dic146—21no—
232C2×Dic146—21no—
233C2×Dic146C2412yes—
234C2×D292—24no—
235C2×D292—21no—
236C2×D292C2412yes—
237C2×C22⋊D73—22no—
238C2×C22⋊D73—22no—
239C22×Dic73—21no—
240C2×C4×D73—22no—
241C2×C4×D73—22no—
242#11924012—24no—
243C2×#10596831—24no—
244C2×#10596831C2414yes—
245C2×#10596831C2412yes—
246C2×#10596831C2412yes—
247C4⋊Dic73—21no—
248C4⋊Dic73—21no—
249C4⋊Dic73C2411yescharacteristic
250C4⋊Dic73C2411yescharacteristic
251C4⋊Dic73C2411yescharacteristic
252C4⋊Dic73C2411yescharacteristic
253#11924007—22no—
254#11924007—22no—
255#11924007—21no—
256#11924007—21no—
257#11924007—22no—
258#11924007—22no—
259#11924007—21no—
260#11924007—21no—
261C22⋊Dic73—21no—
262C22⋊Dic73—21no—
263C22⋊Dic73—22no—
264C22⋊Dic73—22no—
265#11924005—22no—
266#11924005—22no—
267#11924005—22no—
268#11924005—22no—
269#11924005—22no—
270#11924005—22no—
271#11924005—22no—
272#11924005—22no—
273C4×Dic73—22no—
274C4×Dic73—22no—
275C4×Dic73—21no—
276C4×Dic73—21no—
277#41×C73—24no—
278C2×Q8×C73—21no—
279C2×Q8×C73—21no—
280C2×Q8×C73—22no—
281C2×Q8×C73—24no—
282C2×Q8×C73—22no—
283C2×Q8×C73—82no—
284C2×Q8×C73—84no—
285C2×Q8×C73C2×D411yescharacteristic
286C2×D4×C73C2×D412yes—
287C2×D4×C73C2×D411yescharacteristic
288C22×C4×C73—24no—
289C22×C4×C73—22no—
290C22×C4×C73C2×D411yescharacteristic
291C22×C4×C73C2×D412yes—
292C22×C4×C73C2×D411yescharacteristic
293C22×C4×C73C2×D412yes—
294C22×C4×C73C2412yes—
295C22×C4×C73C2411yescharacteristic
296C4⋊C4×C73—22no—
297C4⋊C4×C73—21no—
298C4⋊C4×C73—24no—
299C4⋊C4×C73—22no—
300C4⋊C4×C73—24no—
301C4⋊C4×C73—22no—
302C4⋊C4×C73—21no—
303C4⋊C4×C73—24no—
304C4⋊C4×C73—22no—
305C4⋊C4×C73—24no—
306C4⋊C4×C73—22no—
307C4⋊C4×C73C2×D411yescharacteristic
308C4⋊C4×C73C2×D412yes—
309C4⋊C4×C73C2×D411yescharacteristic
310C4⋊C4×C73C2×D412yes—
311C4⋊C4×C73C2414yes—
312C4⋊C4×C73C2412yes—
313C4⋊C4×C73C2412yes—
314C22⋊C4×C73—24no—
315C22⋊C4×C73—22no—
316C22⋊C4×C73C2×D412yes—
317C22⋊C4×C73C2×D412yes—
318C22⋊C4×C73C2×D412yes—
319C42×C73—24no—
320C42×C73—22no—
321C42×C73C2×D412yes—
322C42×C73C2×D412yes—
323C42×C73C2×D411yescharacteristic
324C42×C73C2×D411yescharacteristic
325C42×C73C2411yescharacteristic
326C42×C73C2411yescharacteristic
327C42×C73C2412yes—
328C23×C73C22×D412yes—
329C23×C73C22×D411yescharacteristic
330C22×D73—22no—
331C22×D73—42no—
332C22×D73—81no—
333C22×D73—81no—
334Q8×C73—22no—
335Q8×C73—42no—
336Q8×C73—42no—
337Q8×C73—44no—
338Q8×C73—82no—
339Q8×C73—84no—
340D4×C73—24no—
341D4×C73—22no—
342C2×C4×C73—24no—
343C2×C4×C73—22no—
344C2×C4×C73—24no—
345C2×C4×C73—22no—
346C2×C4×C73—41no—
347C2×C4×C73—42no—
348C2×C4×C73—41no—
349C2×C4×C73—42no—
350C2×C4×C73—82no—
351C2×C4×C73—84no—
352C2×C4×C73C22×D412yes—
353C2×C4×C73C22×D411yescharacteristic
354C2×C4×C73C22×D411yescharacteristic
355C2×C4×C73C22×D412yes—
356C2×C4×C73C22×D411yescharacteristic
357C2×C4×C73C22×D412yes—
358C2×C4×C73C22×D411yescharacteristic
359C2×C4×C73C22×D411yescharacteristic
360C2×C4×C732−1+414yes—
361C2×C4×C73C2511yescharacteristic
362C22⋊D73—82no—
363C22⋊D73—82no—
364C2×Dic73—21no—
365C2×Dic73—21no—
366C2×Dic73—22no—
367C2×Dic73—21no—
368C2×Dic73—21no—
369C2×Dic73—42no—
370D292—24no—
371D292—42no—
372C4×D73—82no—
373C4×D73—82no—
374Dic146—24no—
375Dic146—42no—
376Dic146—81no—
377Dic146—81no—
378#10596831—22no—
379#10596831—22no—
380#10596831—24no—
381C22×C73—21no—
382C22×C73—21no—
383C22×C73—22no—
384C22×C73—22no—
385C22×C73—22no—
386C22×C73#53612yes—
387C22×C73C23×D411yescharacteristic
388C2×D73—42no—
389C2×D73—42no—
390C2×D73—42no—
391C2×D73—162no—
392C4×C73—21no—
393C4×C73—22no—
394C4×C73—21no—
395C4×C73—21no—
396C4×C73—22no—
397C4×C73—21no—
398C4×C73—22no—
399C4×C73—44no—
400C4×C73—42no—
401C4×C73—42no—
402C4×C73#53612yes—
403C4×C73C2×2−1+412yes—
404Dic73—41no—
405Dic73—41no—
406Dic73—41no—
407Dic73—41no—
408Dic73—42no—
409#60885—731nomaximal, Sylow
410C2×C73—22no—
411C2×C73—42no—
412C2×C73C2×#53611yescharacteristic
413C2×C73#358511yescharacteristic
414C2×C73#358611yescharacteristic
415D73—82no—
416#3510—731no—
417#3503D7311yescharacteristic, complemented
418#3244—734no—
419#3243—734no—
420#3240—732no—
421#3240—732no—
422#3239—732no—
423#3238—732no—
424#3165—731no—
425#3162—731no—
426#3140—731no—
427C2×#489—731no—
428#3097—732no—
429#3096—732no—
430#3082—732no—
431#3081—732no—
432#2923—731no—
433C73#6088511yescharacteristic, complemented, Sylow
434#559—1461no—
435#559—1461no—
436Q82—21no—
437#557—21no—
438#556—1461no—
439#556—1461no—
440#554—22no—
441#554—21no—
442#551—1462no—
443#551—1462no—
444D4×Q8—22no—
445D4×Q8—21no—
446#544C2×D7312yes—
447#544C2×D7314yescomplemented
448#542—732no—
449#542—732no—
450#536—731no—
451#535—731no—
452#533—731no—
453#533C2×D7311yescharacteristic
454#533C2×D7312yescomplemented
455C2×C4⋊Q8C2×D7311yescharacteristic
456C2×C4⋊Q8C2×D7312yescomplemented
457#529—732no—
458#529—732no—
459C2×#124—731no—
460#520C2×D7312yes—
461#519—731no—
462#518—731no—
463C4×#41C2×D7311yescharacteristic
464#501—731no—
465#501—731no—
466#501—731no—
467#501—731no—
468#501—732no—
469#501—732no—
470#501—732no—
471#501—732no—
472#500—732no—
473#498—732no—
474#489—732no—
475#489—732no—
476#489—734no—
477#489—732no—
478#489—732no—
479#488—734no—
480#485—734no—
481#485—734no—
482#484—734no—
483#483—734no—
484#482—734no—
485#482—734no—
486#481—734no—
487#480—734no—
488#479—734no—
489#479—734no—
490#478—734no—
491#478—734no—
492#477—734no—
493#476—734no—
494#475—734no—
495#474—734no—
496#433—734no—
497#432—732no—
498#432—732no—
499#428—732no—
500#428—732no—
501#427—732no—
502#427—732no—
503#424—732no—
504#419—732no—
505#418—732no—
506C2×#103—732no—
507C2×#102—732no—
508#408—732no—
509C4×M16—731no—
510C2×#97—731no—
511C2×#41C22×D7311yescharacteristic
512C22×Q8—21no—
513C22×Q8—22no—
514C22×Q8—731no—
515C22×D4—731no—
516C2×M16—732no—
517C22×C8—732no—
518C4⋊Q8—22no—
519C4⋊Q8—24no—
520C4⋊Q8—21no—
521C4⋊Q8—21no—
522C4⋊Q8—22no—
523C4⋊Q8—22no—
524C4⋊Q8—731no—
525C4⋊Q8—731no—
526C4⋊Q8—1461no—
527C4⋊Q8C22×D7312yes—
528C4⋊Q8C22×D7312yes—
529C4⋊Q8C22×D7311yescharacteristic
530C4⋊Q8C22×D7314yes—
531C4⋊Q8C22×D7311yescharacteristic
532#127—1461no—
533#126—1462no—
534#126—1462no—
535#126—1462no—
536#126—1462no—
537#125—22no—
538#125—24no—
539#125—731no—
540#125—731no—
541#125C22×D7312yes—
542#125C22×D7314yes—
543#124—732no—
544#124—732no—
545#124—1461no—
546#124—1461no—
547#124—1462no—
548#124—1462no—
549#124—1461no—
550#124—1461no—
551#123—1462no—
552#123—1462no—
553#123—1462no—
554#123—1462no—
555#123—1462no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—22no—
559C22⋊Q8—22no—
560C22⋊Q8—24no—
561C22⋊Q8—24no—
562C22⋊Q8—24no—
563C22⋊Q8—732no—
564C22⋊Q8—732no—
565C22⋊Q8—1461no—
566C22⋊Q8—1461no—
567C22⋊Q8—1462no—
568C22⋊Q8—1462no—
569#121—732no—
570#121—732no—
571#120—1462no—
572C4×Q8—22no—
573C4×Q8—21no—
574C4×Q8—21no—
575C4×Q8—22no—
576C4×Q8—22no—
577C4×Q8—732no—
578C4×Q8—732no—
579C4×Q8—1461no—
580C4×Q8—1461no—
581C4×Q8—1461no—
582C4×Q8—1461no—
583C4×Q8C22⋊D7311yescharacteristic
584C4×Q8C22⋊D7311yescharacteristic
585C4×D4—24no—
586C4×D4—22no—
587C4×D4—732no—
588C4×D4—732no—
589C4×D4—1462no—
590C4×D4—1462no—
591C4×D4—1461no—
592C4×D4—1461no—
593C4×D4C22⋊D7312yes—
594C4×D4C22⋊D7311yescharacteristic
595C4×D4C22⋊D7312yes—
596C4×D4C22⋊D7311yescharacteristic
597#117—731no—
598#117—731no—
599#117—1462no—
600#117—1462no—
601#117—1462no—
602#117C22×D7312yes—
603#117C22×D7314yes—
604#117C22×D7311yescharacteristic
605#117C22×D7312yes—
606C2×C4⋊C4—21no—
607C2×C4⋊C4—22no—
608C2×C4⋊C4C22×D7312yes—
609C2×C4⋊C4C22×D7314yes—
610C2×C22⋊C4—1461no—
611C2×C22⋊C4—1461no—
612C2×C22⋊C4—1462no—
613C2×C42C22×D7311yescharacteristic
614C2×C42C22×D7312yes—
615#107—732no—
616#107—732no—
617#107—732no—
618#107—732no—
619#107—734no—
620#107—734no—
621#106—732no—
622#106—732no—
623#106—732no—
624#106—732no—
625#106—734no—
626#106—734no—
627C4⋊C8—734no—
628C4⋊C8—734no—
629#103—734no—
630#103—734no—
631#103—734no—
632#103—734no—
633#102—734no—
634#102—734no—
635#102—734no—
636#102—734no—
637C22⋊C8—734no—
638C22⋊C8—734no—
639#97—731no—
640#97—731no—
641#97—732no—
642#97—732no—
643C4×C8—732no—
644C24—1461no—
645#41—24no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—22no—
649C2×Q8—24no—
650C2×Q8—22no—
651C2×Q8—82no—
652C2×Q8—84no—
653C2×Q8—732no—
654C2×Q8—1464no—
655C2×Q8—1461no—
656C2×Q8—1461no—
657C2×Q8—1461no—
658C2×Q8C2×C22⋊D7311yescharacteristic
659C2×D4—732no—
660C2×D4—1462no—
661C2×D4—1462no—
662C2×D4—1461no—
663C2×D4—1464no—
664C2×D4C2×C22⋊D7312yes—
665C2×D4C2×C22⋊D7311yescharacteristic
666C22×C4—24no—
667C22×C4—22no—
668C22×C4—1461no—
669C22×C4—1462no—
670C22×C4—1462no—
671C22×C4C2×C22⋊D7311yescharacteristic
672C22×C4C2×C22⋊D7311yescharacteristic
673C22×C4C2×C22⋊D7312yes—
674C22×C4C2×C22⋊D7312yes—
675C22×C4C23×D7312yes—
676C22×C4C23×D7311yescharacteristic
677M16—1464no—
678C2×C8—734no—
679C2×C8—732no—
680C2×C8—732no—
681C2×C8—1464no—
682C4⋊C4—22no—
683C4⋊C4—21no—
684C4⋊C4—24no—
685C4⋊C4—22no—
686C4⋊C4—24no—
687C4⋊C4—22no—
688C4⋊C4—21no—
689C4⋊C4—24no—
690C4⋊C4—22no—
691C4⋊C4—24no—
692C4⋊C4—22no—
693C4⋊C4—731no—
694C4⋊C4—731no—
695C4⋊C4—731no—
696C4⋊C4—731no—
697C4⋊C4—1461no—
698C4⋊C4—1461no—
699C4⋊C4—1462no—
700C4⋊C4—1462no—
701C4⋊C4—1462no—
702C4⋊C4—1462no—
703C4⋊C4—1461no—
704C4⋊C4—1461no—
705C4⋊C4—1461no—
706C4⋊C4—1461no—
707C4⋊C4C2×C22⋊D7311yescharacteristic
708C4⋊C4C2×C22⋊D7311yescharacteristic
709C4⋊C4C2×C22⋊D7312yes—
710C4⋊C4C2×C22⋊D7312yes—
711C4⋊C4C23×D7314yes—
712C4⋊C4C23×D7312yes—
713C4⋊C4C23×D7312yes—
714C22⋊C4—24no—
715C22⋊C4—22no—
716C22⋊C4—1461no—
717C22⋊C4—1461no—
718C22⋊C4—1462no—
719C22⋊C4—1462no—
720C22⋊C4—1462no—
721C22⋊C4—1462no—
722C22⋊C4—1462no—
723C22⋊C4—1462no—
724C22⋊C4—1462no—
725C22⋊C4—1462no—
726C22⋊C4—1462no—
727C22⋊C4—1462no—
728C22⋊C4C2×C22⋊D7312yes—
729C22⋊C4C2×C22⋊D7312yes—
730C22⋊C4C2×C22⋊D7312yes—
731C42—24no—
732C42—22no—
733C42—1461no—
734C42—1461no—
735C42—1462no—
736C42—1462no—
737C42C2×C22⋊D7312yes—
738C42C2×C22⋊D7312yes—
739C42C2×C22⋊D7311yescharacteristic
740C42C2×C22⋊D7311yescharacteristic
741C42C23×D7311yescharacteristic
742C42C23×D7311yescharacteristic
743C42C23×D7312yes—
744C23—2922no—
745C23—5841no—
746C23—5841no—
747C23—1462no—
748C23C22×C22⋊D7312yes—
749C23C22×C22⋊D7311yescharacteristic
750Q8—22no—
751Q8—42no—
752Q8—44no—
753Q8—42no—
754Q8—84no—
755Q8—82no—
756Q8—2922no—
757Q8—5841no—
758Q8—5841no—
759Q8—1464no—
760D4—24no—
761D4—22no—
762D4—2922no—
763D4—5842no—
764D4—5842no—
765D4—1464no—
766C2×C4—24no—
767C2×C4—22no—
768C2×C4—24no—
769C2×C4—22no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—42no—
773C2×C4—41no—
774C2×C4—82no—
775C2×C4—84no—
776C2×C4—2922no—
777C2×C4—5842no—
778C2×C4—5842no—
779C2×C4—1461no—
780C2×C4—1461no—
781C2×C4—1462no—
782C2×C4—1461no—
783C2×C4—1461no—
784C2×C4C22×C22⋊D7312yes—
785C2×C4C22×C22⋊D7312yes—
786C2×C4C22×C22⋊D7312yes—
787C2×C4C22×C22⋊D7311yescharacteristic
788C2×C4C22×C22⋊D7311yescharacteristic
789C2×C4C22×C22⋊D7311yescharacteristic
790C2×C4C22×C22⋊D7311yescharacteristic
791C2×C4C22×C22⋊D7311yescharacteristic
792C2×C4#1455663914yes—
793C2×C4C24×D7311yescharacteristic
794C8—1462no—
795C8—1462no—
796C8—1464no—
797C22—21no—
798C22—21no—
799C22—22no—
800C22—22no—
801C22—22no—
802C22—2922no—
803C22—2922no—
804C22—2922no—
805C22—11682no—
806C22#1798916112yes—
807C22C23×C22⋊D7311yescharacteristic
808C4—22no—
809C4—21no—
810C4—22no—
811C4—21no—
812C4—21no—
813C4—22no—
814C4—21no—
815C4—44no—
816C4—42no—
817C4—42no—
818C4—2922no—
819C4—2921no—
820C4—2921no—
821C4—2921no—
822C4—2921no—
823C4#1798916112yes—
824C4C2×#1455663912yes—
825C2—22no—
826C2—42no—
827C2—5842no—
828C2C2×#1798916111yescharacteristic
829C2#2262471111yescharacteristic
830C2#2262471811yescharacteristic
subgroupG/H
centerC22C23×C22⋊D73
commutator, cosocleC2×C4×C73C25
FrattiniC2×C4C24×D73
FittingC73×#3503C2
socleC22×C73C23×D4
prime radical#17989151C22
hypercenter#3503D73
hypocenterC73#60885
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×#41 ◁ #3503

Complements

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

NH ≅ G/Ntype
2. #22621229C2semidirect
3. #22621214C2semidirect
4. #22621171C2semidirect
5. #22621171C2semidirect
6. #22621161C2semidirect
7. #22621152C2semidirect
8. #22620473C2semidirect
9. #22620453C2semidirect
10. #22620320C2semidirect
11. C2×#17988949C2semidirect
12. #22619900C2semidirect
14. #22619767C2semidirect
15. #22619756C2semidirect
16. #22618582C2semidirect
17. C73×#3503C2semidirect
34. #17988997C22semidirect
35. #17988997C22semidirect
36. #17988993C22semidirect
37. #17988993C22semidirect
38. #17988993C22semidirect
39. #17988993C22semidirect
40. #17988993C22semidirect
41. #17988993C22semidirect
42. #17988990C22semidirect
43. #17988983C22semidirect
50. #17988928C22semidirect
51. #17988928C22semidirect
52. #17988922C22semidirect
53. #17988917C22semidirect
58. #17988891C22semidirect
59. #17988891C22semidirect
62. #17988879C22semidirect
64. #17988869C22semidirect
66. #17988648C22semidirect
67. #17988644C22semidirect
68. #17988644C22semidirect
88. #544×C73C22semidirect
90. #533×C73C22semidirect
92. C2×C4⋊Q8×C73C22semidirect
417. #3503D73semidirect
433. C73#60885semidirect
447. #544C2×D73semidirect
454. #533C2×D73semidirect
456. C2×C4⋊Q8C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226238272
#226212292
#226212142
#226211712
#226211612
#226211522
#226204732
#226204532
#226203202
C2×#179889492
#226199002
#226198892
#226197672
#226197562
#226185822
C73×#35032
#6088573