Finite Group Databasebeta

← #33054206

Subgroups — #33054206

Order 18688.

902 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623827C211yesmaximal, characteristic
2#22618945C211yesmaximal, characteristic, complemented
3#22608563C211yesmaximal, characteristic, complemented
4#22608560C211yesmaximal, characteristic, complemented
5#22608554C211yesmaximal, characteristic, complemented
6#22608552C211yesmaximal, characteristic, complemented
7#22608549C211yesmaximal, characteristic, complemented
8#22608547C211yesmaximal, characteristic, complemented
9#22608545C211yesmaximal, characteristic, complemented
10#22608539C211yesmaximal, characteristic, complemented
11#22608536C211yesmaximal, characteristic, complemented
12#22608520C211yesmaximal, characteristic, complemented
13#22608517C211yesmaximal, characteristic, complemented
14C2×#17988326C211yesmaximal, characteristic, complemented
15C73×#2970C211yesmaximal, characteristic, complemented
16#17989320—21no—
17#17989320—21no—
18#17989309—21no—
19#17989309—21no—
20#17989266—21no—
21#17989266—21no—
22#17989266—21no—
23#17989266—21no—
24#17989208C411yescharacteristic
25#17989208C411yescharacteristic
26#17989208C411yescharacteristic
27#17989208C411yescharacteristic
28#17989158C411yescharacteristic
29#17989151C411yescharacteristic
30#17989144C2211yescharacteristic
31#17989121C2211yescharacteristic
32#17989121C2211yescharacteristic
33#17989121C2211yescharacteristic
34#17989121C2211yescharacteristic
35C2×#14556579C2211yescharacteristic
36#17989064C411yescharacteristic
37#17989061C411yescharacteristic
38#17988718—21no—
39#17988659—21no—
40#17988659—21no—
41D4×#10596831—21no—
42#17988644C2211yescharacteristic
43#17988644C2211yescharacteristic, complemented
44#17988644C2211yescharacteristic, complemented
45C4×#11924012C2211yescharacteristic, complemented
46C2×#14556502C2211yescharacteristic
47C2×#14556502C2211yescharacteristic, complemented
48#17988328C2211yescharacteristic, complemented
49#17988328C2211yescharacteristic, complemented
50#17988328C2211yescharacteristic, complemented
51#17988328C2211yescharacteristic, complemented
52#17988328C2211yescharacteristic, complemented
53#17988328C2211yescharacteristic, complemented
54#17988328C2211yescharacteristic, complemented
55#17988328C2211yescharacteristic, complemented
56#17988326C2211yescharacteristic
57#17988326C2211yescharacteristic
58#17988326C2211yescharacteristic
59#17988326C2211yescharacteristic
60#17988326C2211yescharacteristic
61#17988326C2211yescharacteristic
62#17988326C2211yescharacteristic
63#17988326C2211yescharacteristic
64C4×#41×C73C2211yescharacteristic
65#446×C73—21no—
66#435×C73—21no—
67#435×C73—21no—
68C8×D4×C73—21no—
69#432×C73C2211yescharacteristic
70#432×C73C2211yescharacteristic, complemented
71#432×C73C2211yescharacteristic, complemented
72C4×M16×C73C2211yescharacteristic, complemented
73C2×#97×C73C2211yescharacteristic
74C2×#97×C73C2211yescharacteristic, complemented
75C22×Dic146C2×C411yescharacteristic
76C22×D292C2×C411yescharacteristic
77C2×#11924012—21no—
78C22×#10596831—21no—
79C22×#10596831—21no—
80#14556591C2×C411yescharacteristic
81#14556591C2×C411yescharacteristic
82#14556589—21no—
83#14556587—21no—
84#14556586—21no—
85#14556586—21no—
86#14556586—21no—
87#14556586—21no—
88#14556585—21no—
89#14556585—21no—
90#14556585—21no—
91#14556585—21no—
92#14556583C2311yescharacteristic
93#14556583C2311yescharacteristic
94#14556580—21no—
95#14556579—21no—
96#14556579—21no—
97#14556579C2×C411yescharacteristic
98#14556579C2×C411yescharacteristic
99#14556579C2311yescharacteristic
100#14556579C2311yescharacteristic
101#14556578—21no—
102#14556577—21no—
103#14556577—21no—
104#14556577—21no—
105#14556577—21no—
106#14556574—21no—
107#14556574—21no—
108#14556574—21no—
109#14556574—21no—
110#14556573—21no—
111#14556573—21no—
112#14556573—21no—
113#14556573—21no—
114#14556572—21no—
115#14556572—21no—
116#14556570—21no—
117#14556570—21no—
118#14556570C2×C411yescharacteristic
119#14556570C2×C411yescharacteristic
120#14556570C2×C411yescharacteristic
121#14556570C2×C411yescharacteristic
122#14556569—21no—
123#14556569—21no—
124#14556569—21no—
125#14556569—21no—
126#14556565C2×C411yescharacteristic
127#14556565C2×C411yescharacteristic
128#14556565C2×C411yescharacteristic
129#14556565C2×C411yescharacteristic
130#14556559—21no—
131#14556559—21no—
132C4×Dic146—21no—
133C4×Dic146—21no—
134C4×Dic146C2×C411yescharacteristic
135C4×Dic146C2×C411yescharacteristic
136C4×Dic146C2×C411yescharacteristic
137C4×Dic146C2×C411yescharacteristic
138#14556556—21no—
139#14556556—21no—
140C4×D292C2×C411yescharacteristic
141C4×D292C2×C411yescharacteristic
142C4×D292C2×C411yescharacteristic
143C4×D292C2×C411yescharacteristic
144#14556553—21no—
145#14556553—21no—
146C4×C22⋊D73—21no—
147C4×C22⋊D73—21no—
148C4×C22⋊D73—21no—
149C4×C22⋊D73—21no—
150#14556550C2×C411yescharacteristic
151#14556550C2×C411yescharacteristic
152#14556548—21no—
153#14556548—21no—
154#14556548—21no—
155#14556548—21no—
156#14556547—21no—
157#14556547—21no—
158C2×#11924005—21no—
159C2×#11924005—21no—
160C22⋊C4×D73—21no—
161C22⋊C4×D73—21no—
162C4⋊#10596831—21no—
163C4⋊#10596831—21no—
164C4⋊#10596831—21no—
165C22⋊#10596831—21no—
166C22⋊#10596831—21no—
167C22⋊#10596831—21no—
168#14556502—21no—
169#14556502—21no—
170#14556502C2311yescharacteristic
171#14556502C2311yescharacteristic
172#14556502C2311yescharacteristic
173#14556502C2311yescharacteristic
174C4×#10596831—21no—
175C2×#41×C73C2×C411yescharacteristic
176C2×M16×C73—21no—
177C22×C8×C73—21no—
178C22×C8×C73—21no—
179C4×Q8×C73D411yescharacteristic
180C4×Q8×C73D411yescharacteristic
181C4×D4×C73D411yescharacteristic
182C4×D4×C73D411yescharacteristic
183C4×D4×C73D411yescharacteristic
184C4×D4×C73D411yescharacteristic
185C4×D4×C73D411yescharacteristic
186C4×D4×C73D411yescharacteristic
187#117×C73C2×C411yescharacteristic
188#117×C73C2×C411yescharacteristic
189#117×C73C2×C411yescharacteristic
190C2×C42×C73C2311yescharacteristic
191C2×C42×C73C2311yescharacteristic
192C2×C42×C73C2311yescharacteristic
193C4⋊C8×C73—21no—
194C4⋊C8×C73—21no—
195C4⋊C8×C73—21no—
196C22⋊C8×C73—21no—
197C22⋊C8×C73—21no—
198C22⋊C8×C73—21no—
199#97×C73—21no—
200#97×C73—21no—
201#97×C73C2311yescharacteristic
202#97×C73C2311yescharacteristic
203#97×C73C2311yescharacteristic
204#97×C73C2311yescharacteristic
205C4×C8×C73—21no—
206C23×D73—21no—
207C2×Dic146—21no—
208C2×Dic146—21no—
209C2×Dic146—21no—
210C2×Dic146—42no—
211C2×Dic146C22×C411yescharacteristic
212C2×Dic146C22×C411yescharacteristic
213C2×D292—21no—
214C2×D292—42no—
215C2×D292C22×C411yescharacteristic
216C2×D292C22×C411yescharacteristic
217C2×C22⋊D73—21no—
218C2×C22⋊D73—21no—
219C2×C22⋊D73—21no—
220C2×C22⋊D73—21no—
221C22×Dic73—21no—
222C2×C4×D73—21no—
223C2×C4×D73—21no—
224C2×C4×D73—21no—
225C2×C4×D73—21no—
226#11924012—42no—
227C2×#10596831—21no—
228C2×#10596831—21no—
229C2×#10596831—21no—
230C2×#10596831—21no—
231C2×#10596831—42no—
232C2×#10596831—42no—
233C4⋊Dic73—21no—
234C4⋊Dic73—21no—
235C4⋊Dic73C22×C411yescharacteristic
236C4⋊Dic73C22×C411yescharacteristic
237C4⋊Dic73C22×C411yescharacteristic
238C4⋊Dic73C22×C411yescharacteristic
239#11924007—21no—
240#11924007—21no—
241#11924007—21no—
242#11924007—21no—
243#11924007—21no—
244#11924007—21no—
245#11924007—21no—
246#11924007—21no—
247#11924007—21no—
248#11924007—21no—
249#11924007—21no—
250#11924007—21no—
251C22⋊Dic73—21no—
252C22⋊Dic73—21no—
253C22⋊Dic73—21no—
254C22⋊Dic73—21no—
255C22⋊Dic73—21no—
256C22⋊Dic73—21no—
257#11924005—21no—
258#11924005—21no—
259#11924005—21no—
260#11924005—21no—
261#11924005—21no—
262#11924005—21no—
263#11924005—21no—
264#11924005—21no—
265#11924005—21no—
266#11924005—21no—
267#11924005—21no—
268#11924005—21no—
269#11924005—21no—
270#11924005—21no—
271#11924005—21no—
272#11924005—21no—
273C4×Dic73—21no—
274C4×Dic73—21no—
275C4×Dic73—21no—
276C4×Dic73—21no—
277C4×Dic73—21no—
278C4×Dic73—21no—
279#41×C73—42no—
280C2×Q8×C73C22⋊C411yescharacteristic
281C2×D4×C73C22⋊C411yescharacteristic
282C2×D4×C73C22⋊C411yescharacteristic
283C2×D4×C73C22⋊C411yescharacteristic
284C22×C4×C73C22×C411yescharacteristic
285C22×C4×C73C22×C411yescharacteristic
286C22×C4×C73C22×C411yescharacteristic
287C22×C4×C73C2×D411yescharacteristic
288C22×C4×C73C2×D411yescharacteristic
289C22×C4×C73C2×D411yescharacteristic
290C22×C4×C73C2×D411yescharacteristic
291C22×C4×C73C2×D411yescharacteristic
292C22×C4×C73C2×D411yescharacteristic
293M16×C73—42no—
294C2×C8×C73—21no—
295C2×C8×C73—21no—
296C2×C8×C73—21no—
297C2×C8×C73—21no—
298C2×C8×C73—42no—
299C2×C8×C73—42no—
300C4⋊C4×C73C22⋊C411yescharacteristic
301C4⋊C4×C73C22⋊C411yescharacteristic
302C4⋊C4×C73C22⋊C411yescharacteristic
303C4⋊C4×C73C22⋊C411yescharacteristic
304C4⋊C4×C73C22⋊C411yescharacteristic
305C4⋊C4×C73C22⋊C411yescharacteristic
306C22⋊C4×C73C22⋊C411yescharacteristic
307C22⋊C4×C73C22⋊C411yescharacteristic
308C22⋊C4×C73C22⋊C411yescharacteristic
309C22⋊C4×C73C22⋊C411yescharacteristic
310C22⋊C4×C73C22⋊C411yescharacteristic
311C22⋊C4×C73C22⋊C411yescharacteristic
312C42×C73C22×C411yescharacteristic
313C42×C73C22×C411yescharacteristic
314C42×C73C22×C411yescharacteristic
315C42×C73C2×D411yescharacteristic
316C42×C73C2×D411yescharacteristic
317C42×C73C2×D411yescharacteristic
318C42×C73C2×D411yescharacteristic
319C42×C73C2×D411yescharacteristic
320C42×C73C2×D411yescharacteristic
321C42×C73C2411yescharacteristic
322C23×C73C2×C22⋊C411yescharacteristic
323C23×C73C2×C22⋊C411yescharacteristic
324C23×C73C2×C22⋊C411yescharacteristic
325C22×D73—21no—
326C22×D73—21no—
327C22×D73—42no—
328C22×D73—81no—
329C22×D73—81no—
330Q8×C73—41no—
331D4×C73—22no—
332D4×C73—22no—
333D4×C73—41no—
334C2×C4×C73—22no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—41no—
339C2×C4×C73—41no—
340C2×C4×C73—41no—
341C2×C4×C73—41no—
342C2×C4×C73—41no—
343C2×C4×C73C2×C22⋊C411yescharacteristic
344C2×C4×C73C2×C22⋊C411yescharacteristic
345C2×C4×C73C2×C22⋊C411yescharacteristic
346C2×C4×C73C2×C22⋊C411yescharacteristic
347C2×C4×C73C2×C22⋊C411yescharacteristic
348C2×C4×C73C2×C22⋊C411yescharacteristic
349C2×C4×C73C2×C22⋊C411yescharacteristic
350C2×C4×C73C2×C22⋊C411yescharacteristic
351C2×C4×C73C2×C22⋊C411yescharacteristic
352C2×C4×C73C23×C411yescharacteristic
353C2×C4×C73C22×D411yescharacteristic
354C2×C4×C73C22×D411yescharacteristic
355C22⋊D73—81no—
356C22⋊D73—81no—
357C22⋊D73—81no—
358C22⋊D73—81no—
359C2×Dic73—21no—
360C2×Dic73—21no—
361C2×Dic73—21no—
362C2×Dic73—21no—
363C2×Dic73—21no—
364C2×Dic73—21no—
365C2×Dic73—42no—
366D292—41no—
367D292—41no—
368D292—42no—
369C4×D73—81no—
370C4×D73—81no—
371C4×D73—81no—
372C4×D73—81no—
373Dic146—42no—
374Dic146—41no—
375Dic146—41no—
376Dic146—81no—
377Dic146—81no—
378C8×C73—22no—
379C8×C73—41no—
380C8×C73—41no—
381C8×C73—41no—
382#10596831—22no—
383#10596831—41no—
384#10596831—41no—
385#10596831—41no—
386C22×C73—21no—
387C22×C73—21no—
388C22×C73—21no—
389C22×C73—21no—
390C22×C73—21no—
391C22×C73—21no—
392C22×C73—21no—
393C22×C73—21no—
394C22×C73#41312yes—
395C22×C73C22×C22⋊C411yescharacteristic
396C2×D73—41no—
397C2×D73—41no—
398C2×D73—41no—
399C2×D73—41no—
400C2×D73—41no—
401C2×D73—41no—
402C2×D73—162no—
403C4×C73—21no—
404C4×C73—21no—
405C4×C73—21no—
406C4×C73—21no—
407C4×C73—21no—
408C4×C73—21no—
409C4×C73—21no—
410C4×C73—21no—
411C4×C73—21no—
412C4×C73—21no—
413C4×C73—21no—
414C4×C73—21no—
415Dic73—41no—
416Dic73—41no—
417Dic73—41no—
418Dic73—41no—
419Dic73—41no—
420Dic73—41no—
421#17686—731nomaximal, Sylow
422C2×C73—22no—
423C2×C73—41no—
424C2×C73—41no—
425C2×C73C2×#41311yescharacteristic
426C2×C73#290111yescharacteristic
427C2×C73#290111yescharacteristic
428D73—81no—
429D73—81no—
430#3510—731no—
431#2970—731no—
432#2970D7311yescharacteristic, complemented
433#1535—731no—
434#1535—731no—
435#1533—731no—
436#1532—731no—
437#1532—731no—
438#1531—731no—
439#1531—731no—
440#1529—731no—
441#1529—731no—
442#1524—731no—
443#1524—731no—
444C2×#329—731no—
445C73#1768611yescharacteristic, complemented, Sylow
446#559—1461no—
447#559—1461no—
448#556—1461no—
449#556—1461no—
450#551—1461no—
451#551—1461no—
452#551—1461no—
453#551—1461no—
454#542—731no—
455#542—731no—
456#542—731no—
457#542—731no—
458#536—731no—
459#535—731no—
460#533—731no—
461#529—731no—
462#529—731no—
463#529—731no—
464#529—731no—
465C2×#124—731no—
466#519—731no—
467#518—731no—
468C4×#41C2×D7311yescharacteristic
469#446—21no—
470#446—1461no—
471#435—21no—
472#435—21no—
473#435—1461no—
474#435—1461no—
475C8×D4—21no—
476C8×D4—1461no—
477#432—731no—
478#432—731no—
479#432—731no—
480#432C2×D7311yescharacteristic
481#432C2×D7311yescharacteristic, complemented
482#432C2×D7311yescharacteristic, complemented
483C4×M16—731no—
484C4×M16C2×D7311yescharacteristic, complemented
485C2×#97—731no—
486C2×#97—731no—
487C2×#97C2×D7311yescharacteristic
488C2×#97C2×D7311yescharacteristic, complemented
489#330—731no—
490#330—731no—
491#330—731no—
492#330—731no—
493#330—731no—
494#330—731no—
495#330—731no—
496#330—731no—
497#329—731no—
498#329—731no—
499#329—731no—
500#329—731no—
501#329—731no—
502#329—731no—
503#329—731no—
504#329—731no—
505C2×#41C4×D7311yescharacteristic
506C22×Q8—731no—
507C22×D4—731no—
508C2×M16—21no—
509C2×M16—1461no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—1461no—
513C22×C8—1461no—
514C4⋊Q8—731no—
515C4⋊Q8—731no—
516C4⋊Q8—1461no—
517#127—1461no—
518#126—1461no—
519#126—1461no—
520#126—1461no—
521#126—1461no—
522#126—1461no—
523#126—1461no—
524#126—1461no—
525#126—1461no—
526#125—731no—
527#125—731no—
528#124—731no—
529#124—731no—
530#124—731no—
531#124—731no—
532#124—1461no—
533#124—1461no—
534#124—1461no—
535#124—1461no—
536#124—1461no—
537#124—1461no—
538#124—1461no—
539#124—1461no—
540#123—1461no—
541#123—1461no—
542#123—1461no—
543#123—1461no—
544#123—1461no—
545#123—1461no—
546#123—1461no—
547#123—1461no—
548#123—1461no—
549#123—1461no—
550C22⋊Q8—731no—
551C22⋊Q8—731no—
552C22⋊Q8—731no—
553C22⋊Q8—731no—
554C22⋊Q8—1461no—
555C22⋊Q8—1461no—
556C22⋊Q8—1461no—
557C22⋊Q8—1461no—
558C22⋊Q8—1461no—
559C22⋊Q8—1461no—
560#121—731no—
561#121—731no—
562#121—731no—
563#121—731no—
564#120—1461no—
565#120—1461no—
566C4×Q8—731no—
567C4×Q8—731no—
568C4×Q8—731no—
569C4×Q8—731no—
570C4×Q8—1461no—
571C4×Q8—1461no—
572C4×Q8—1461no—
573C4×Q8—1461no—
574C4×Q8D29211yescharacteristic
575C4×Q8C22⋊D7311yescharacteristic
576C4×D4—731no—
577C4×D4—731no—
578C4×D4—731no—
579C4×D4—731no—
580C4×D4—1461no—
581C4×D4—1461no—
582C4×D4—1461no—
583C4×D4—1461no—
584C4×D4—1461no—
585C4×D4—1461no—
586C4×D4D29211yescharacteristic
587C4×D4D29211yescharacteristic
588C4×D4D29211yescharacteristic
589C4×D4C22⋊D7311yescharacteristic
590C4×D4C22⋊D7311yescharacteristic
591C4×D4C22⋊D7311yescharacteristic
592#117—731no—
593#117—731no—
594#117—1461no—
595#117—1461no—
596#117—1461no—
597#117—1461no—
598#117—1461no—
599#117—1461no—
600#117C4×D7311yescharacteristic
601#117C4×D7311yescharacteristic
602#117C4×D7311yescharacteristic
603C2×C22⋊C4—1461no—
604C2×C22⋊C4—1461no—
605C2×C22⋊C4—1461no—
606C2×C22⋊C4—1461no—
607C2×C42C22×D7311yescharacteristic
608C2×C42C22×D7311yescharacteristic
609C2×C42C22×D7311yescharacteristic
610C4⋊C8—21no—
611C4⋊C8—21no—
612C4⋊C8—21no—
613C4⋊C8—1461no—
614C4⋊C8—1461no—
615C4⋊C8—1461no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—1461no—
620C22⋊C8—1461no—
621C22⋊C8—1461no—
622#97—21no—
623#97—21no—
624#97—731no—
625#97—731no—
626#97—731no—
627#97—731no—
628#97—1461no—
629#97—1461no—
630#97C22×D7311yescharacteristic
631#97C22×D7311yescharacteristic
632#97C22×D7311yescharacteristic
633#97C22×D7311yescharacteristic
634C4×C8—21no—
635C4×C8—1461no—
636C24—1461no—
637#41—42no—
638C2×Q8—2922no—
639C2×Q8—731no—
640C2×Q8—731no—
641C2×Q8—1461no—
642C2×Q8—1461no—
643C2×Q8—1461no—
644C2×Q8#1192400511yescharacteristic
645C2×D4—2922no—
646C2×D4—731no—
647C2×D4—731no—
648C2×D4—1461no—
649C2×D4—1461no—
650C2×D4—1461no—
651C2×D4—1461no—
652C2×D4—1461no—
653C2×D4#1192400511yescharacteristic
654C2×D4#1192400511yescharacteristic
655C2×D4#1192400511yescharacteristic
656C22×C4—1461no—
657C22×C4—1461no—
658C22×C4—1461no—
659C22×C4—1461no—
660C22×C4—1461no—
661C22×C4C2×C4×D7311yescharacteristic
662C22×C4C2×C4×D7311yescharacteristic
663C22×C4C2×C4×D7311yescharacteristic
664C22×C4C2×C22⋊D7311yescharacteristic
665C22×C4C2×C22⋊D7311yescharacteristic
666C22×C4C2×C22⋊D7311yescharacteristic
667C22×C4C2×D29211yescharacteristic
668C22×C4C2×D29211yescharacteristic
669C22×C4C2×D29211yescharacteristic
670M16—42no—
671M16—2922no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—42no—
677C2×C8—42no—
678C2×C8—2922no—
679C2×C8—2922no—
680C2×C8—1461no—
681C2×C8—1461no—
682C2×C8—1461no—
683C2×C8—1461no—
684C4⋊C4—731no—
685C4⋊C4—731no—
686C4⋊C4—731no—
687C4⋊C4—731no—
688C4⋊C4—1461no—
689C4⋊C4—1461no—
690C4⋊C4—1461no—
691C4⋊C4—1461no—
692C4⋊C4—1461no—
693C4⋊C4—1461no—
694C4⋊C4—1461no—
695C4⋊C4—1461no—
696C4⋊C4—1461no—
697C4⋊C4—1461no—
698C4⋊C4—1461no—
699C4⋊C4—1461no—
700C4⋊C4—1461no—
701C4⋊C4—1461no—
702C4⋊C4#1192400511yescharacteristic
703C4⋊C4#1192400511yescharacteristic
704C4⋊C4#1192400511yescharacteristic
705C4⋊C4#1192400511yescharacteristic
706C4⋊C4#1192400511yescharacteristic
707C4⋊C4#1192400511yescharacteristic
708C22⋊C4—1461no—
709C22⋊C4—1461no—
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⋊C4—1461no—
722C22⋊C4—1461no—
723C22⋊C4—1461no—
724C22⋊C4—1461no—
725C22⋊C4—1461no—
726C22⋊C4—1461no—
727C22⋊C4—1461no—
728C22⋊C4—1461no—
729C22⋊C4—1461no—
730C22⋊C4#1192400511yescharacteristic
731C22⋊C4#1192400511yescharacteristic
732C22⋊C4#1192400511yescharacteristic
733C22⋊C4#1192400511yescharacteristic
734C22⋊C4#1192400511yescharacteristic
735C22⋊C4#1192400511yescharacteristic
736C42—1461no—
737C42—1461no—
738C42—1461no—
739C42—1461no—
740C42—1461no—
741C42—1461no—
742C42C2×C4×D7311yescharacteristic
743C42C2×C4×D7311yescharacteristic
744C42C2×C4×D7311yescharacteristic
745C42C2×C22⋊D7311yescharacteristic
746C42C2×C22⋊D7311yescharacteristic
747C42C2×C22⋊D7311yescharacteristic
748C42C2×D29211yescharacteristic
749C42C2×D29211yescharacteristic
750C42C2×D29211yescharacteristic
751C42C23×D7311yescharacteristic
752C23—2922no—
753C23—5841no—
754C23—5841no—
755C23—1461no—
756C23—1461no—
757C23C2×#1192400511yescharacteristic
758C23C2×#1192400511yescharacteristic
759C23C2×#1192400511yescharacteristic
760Q8—41no—
761Q8—2921no—
762Q8—2921no—
763Q8—2922no—
764Q8—5841no—
765Q8—5841no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—2921no—
770D4—2921no—
771D4—2922no—
772D4—5841no—
773D4—5841no—
774D4—5841no—
775D4—5841no—
776C2×C4—22no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—2922no—
786C2×C4—5841no—
787C2×C4—5841no—
788C2×C4—5841no—
789C2×C4—5841no—
790C2×C4—1461no—
791C2×C4—1461no—
792C2×C4—1461no—
793C2×C4—1461no—
794C2×C4—1461no—
795C2×C4—1461no—
796C2×C4C2×#1192400511yescharacteristic
797C2×C4C2×#1192400511yescharacteristic
798C2×C4C2×#1192400511yescharacteristic
799C2×C4C2×#1192400511yescharacteristic
800C2×C4C2×#1192400511yescharacteristic
801C2×C4C2×#1192400511yescharacteristic
802C2×C4C2×#1192400511yescharacteristic
803C2×C4C2×#1192400511yescharacteristic
804C2×C4C2×#1192400511yescharacteristic
805C2×C4C22×C4×D7311yescharacteristic
806C2×C4C22×C22⋊D7311yescharacteristic
807C2×C4C22×D29211yescharacteristic
808C8—22no—
809C8—41no—
810C8—41no—
811C8—41no—
812C8—2921no—
813C8—2921no—
814C8—2921no—
815C8—1462no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—2921no—
825C22—2921no—
826C22—2921no—
827C22—2921no—
828C22—2921no—
829C22—2921no—
830C22—11682no—
831C22#1798856912yes—
832C22C22×#1192400511yescharacteristic
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—2921no—
846C4—2921no—
847C4—2921no—
848C4—2921no—
849C4—2921no—
850C4—2921no—
851C2—22no—
852C2—41no—
853C2—41no—
854C2—5841no—
855C2—5841no—
856C2C2×#1798856911yescharacteristic
857C2#2261847611yescharacteristic
858C2#2261847911yescharacteristic
subgroupG/H
centerC22C22×#11924005
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2970C2
socleC22×C73C22×C22⋊C4
prime radical#17989151C4
cosocleC42×C73C24
hypercenter#2970D73
hypocenterC73#17686
LCSG ▷ C2×C4×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #22618945C2semidirect
3. #22608563C2semidirect
4. #22608560C2semidirect
5. #22608554C2semidirect
6. #22608552C2semidirect
7. #22608549C2semidirect
8. #22608547C2semidirect
9. #22608545C2semidirect
10. #22608539C2semidirect
11. #22608536C2semidirect
12. #22608520C2semidirect
13. #22608517C2semidirect
14. C2×#17988326C2semidirect
15. C73×#2970C2semidirect
43. #17988644C22semidirect
44. #17988644C22semidirect
45. C4×#11924012C22semidirect
47. C2×#14556502C22semidirect
48. #17988328C22semidirect
49. #17988328C22semidirect
50. #17988328C22semidirect
51. #17988328C22semidirect
52. #17988328C22semidirect
53. #17988328C22semidirect
54. #17988328C22semidirect
55. #17988328C22semidirect
70. #432×C73C22semidirect
71. #432×C73C22semidirect
72. C4×M16×C73C22semidirect
74. C2×#97×C73C22semidirect
432. #2970D73semidirect
445. C73#17686semidirect
481. #432C2×D73semidirect
482. #432C2×D73semidirect
484. C4×M16C2×D73semidirect
488. C2×#97C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226238272
#226189452
#226085632
#226085602
#226085542
#226085522
#226085492
#226085472
#226085452
#226085392
#226085362
#226085202
#226085172
C2×#179883262
C73×#29702
#1768673