Finite Group Databasebeta

← #33054133

Subgroups — #33054133

Order 18688.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22623892C211yesmaximal, characteristic
2#22618582C211yesmaximal, characteristic, complemented
3#22608565C211yesmaximal, characteristic, complemented
4#22608563C211yesmaximal, characteristic, complemented
5#22608560C211yesmaximal, characteristic, complemented
6#22608554C211yesmaximal, characteristic, complemented
7#22608552C211yesmaximal, characteristic, complemented
8#22608549C211yesmaximal, characteristic, complemented
9#22608541C211yesmaximal, characteristic, complemented
10#22608536C211yesmaximal, characteristic, complemented
11#22608530C211yesmaximal, characteristic, complemented
12#22608528C211yesmaximal, characteristic, complemented
13#22608517C211yesmaximal, characteristic, complemented
14C2×#17988326C211yesmaximal, characteristic, complemented
15C73×#2970C211yesmaximal, characteristic, complemented
16#17989322C411yescharacteristic
17#17989310C411yescharacteristic
18#17989300—21no—
19#17989261—21no—
20#17989261—21no—
21D4×Dic146C411yescharacteristic
22#17989246C411yescharacteristic
23#17989246C411yescharacteristic
24#17989233C411yescharacteristic
25#17989233C411yescharacteristic
26#17989225—21no—
27D4×D292C411yescharacteristic
28#17989209—21no—
29#17989170—21no—
30#17989170—21no—
31#17989137C2211yescharacteristic
32#17989121C2211yescharacteristic
33#17989121C2211yescharacteristic
34#17989121C2211yescharacteristic
35C2×#14556579C2211yescharacteristic
36C2×#14556579C2211yescharacteristic
37#17989059—21no—
38#17988648—21no—
39#17988648—21no—
40#17988644C2211yescharacteristic, complemented
41#17988644C2211yescharacteristic, complemented
42#17988644C2211yescharacteristic, complemented
43#17988644C2211yescharacteristic, complemented
44#17988614—21no—
45#17988554—21no—
46C4×#11924012C2211yescharacteristic, complemented
47C2×#14556502C2211yescharacteristic, complemented
48#17988328C2211yescharacteristic, complemented
49#17988328C2211yescharacteristic, complemented
50#17988328C2211yescharacteristic, complemented
51#17988328C2211yescharacteristic, complemented
52#17988326C2211yescharacteristic
53#17988326C2211yescharacteristic
54#17988326C2211yescharacteristic
55#17988326C2211yescharacteristic
56#17988326C2211yescharacteristic, complemented
57#17988326C2211yescharacteristic, complemented
58#17988326C2211yescharacteristic, complemented
59#17988326C2211yescharacteristic, complemented
60#17988326C2211yescharacteristic, complemented
61#17988326C2211yescharacteristic, complemented
62#17988326C2211yescharacteristic, complemented
63#17988326C2211yescharacteristic, 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#432×C73C2211yescharacteristic, complemented
72C4×M16×C73C2211yescharacteristic, complemented
73C2×#97×C73C2211yescharacteristic, complemented
74C2×#97×C73C2211yescharacteristic, complemented
75C2×#11924028C2×C411yescharacteristic
76C2×#11924028C2×C411yescharacteristic
77C22×Dic146C2×C411yescharacteristic
78C22×Dic146C2×C411yescharacteristic
79C22×D292C2×C411yescharacteristic
80C22×D292C2×C411yescharacteristic
81C2×D4×D73—21no—
82C2×#11924012—21no—
83C22×#10596831—21no—
84#14556591C2×C411yescharacteristic
85#14556590—21no—
86#14556588C2×C411yescharacteristic
87#14556586—21no—
88#14556586—21no—
89#14556585—21no—
90#14556585—21no—
91#14556585—21no—
92#14556583C2311yescharacteristic
93#14556580—21no—
94#14556579—21no—
95#14556579—21no—
96#14556579—21no—
97#14556579—21no—
98#14556579C2×C411yescharacteristic
99#14556579C2×C411yescharacteristic
100#14556579C2×C411yescharacteristic
101#14556579C2×C411yescharacteristic
102#14556579C2311yescharacteristic
103#14556579C2311yescharacteristic
104#14556579C2311yescharacteristic
105#14556577—21no—
106#14556577—21no—
107#14556576—21no—
108#14556576—21no—
109#14556576—21no—
110#14556576—21no—
111#14556574—21no—
112#14556574—21no—
113#14556574—21no—
114#14556570C2×C411yescharacteristic
115#14556570C2×C411yescharacteristic
116#14556570C2×C411yescharacteristic
117#14556569—21no—
118#14556569—21no—
119#14556568—21no—
120#14556568—21no—
121#14556567—21no—
122#14556566—21no—
123#14556565—21no—
124#14556565—21no—
125#14556565C2×C411yescharacteristic
126#14556565C2×C411yescharacteristic
127#14556565C2×C411yescharacteristic
128#14556564—21no—
129#14556564—21no—
130#14556563—21no—
131#14556563—21no—
132#14556561—21no—
133#14556561—21no—
134#14556559—21no—
135#14556559—21no—
136C4×Dic146C2×C411yescharacteristic
137C4×Dic146C2×C411yescharacteristic
138C4×Dic146C2×C411yescharacteristic
139C4×D292—21no—
140C4×D292—21no—
141C4×D292C2×C411yescharacteristic
142C4×D292C2×C411yescharacteristic
143C4×D292C2×C411yescharacteristic
144D4×Dic73—21no—
145#14556553—21no—
146C4×C22⋊D73—21no—
147C4×C22⋊D73—21no—
148C4×C22⋊D73—21no—
149#14556551—21no—
150#14556551—21no—
151#14556549—21no—
152#14556548—21no—
153#14556548—21no—
154#14556548—21no—
155C2×#11924005—21no—
156C2×#11924005—21no—
157C2×#11924005—21no—
158C2×#11924005—21no—
159C22⋊C4×D73—21no—
160C22⋊C4×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—
170#14556502C2311yescharacteristic
171#14556502C2311yescharacteristic
172#14556502C2311yescharacteristic
173#14556502C2311yescharacteristic
174C4×#10596831—21no—
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—
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—
207C23×D73—21no—
208#11924028—81no—
209#11924028—81no—
210C2×Dic146—21no—
211C2×Dic146—21no—
212C2×Dic146—81no—
213C2×Dic146—81no—
214C2×Dic146C22×C411yescharacteristic
215C2×Dic146C22×C411yescharacteristic
216C2×Dic146C22×C411yescharacteristic
217C2×D292—21no—
218C2×D292—21no—
219C2×D292—21no—
220C2×D292—21no—
221C2×D292—81no—
222C2×D292—81no—
223C2×D292C22×C411yescharacteristic
224C2×D292C22×C411yescharacteristic
225C2×D292C22×C411yescharacteristic
226C2×C22⋊D73—21no—
227C2×C22⋊D73—21no—
228C2×C22⋊D73—21no—
229C2×C22⋊D73—21no—
230C2×C22⋊D73—21no—
231D4×D73—44no—
232C22×Dic73—21no—
233C22×Dic73—21no—
234C2×C4×D73—21no—
235C2×C4×D73—21no—
236C2×C4×D73—21no—
237C2×C4×D73—21no—
238C2×C4×D73—21no—
239#11924012—42no—
240C2×#10596831—21no—
241C2×#10596831—21no—
242C2×#10596831—21no—
243C2×#10596831—21no—
244C2×#10596831—42no—
245C4⋊Dic73—21no—
246C4⋊Dic73—21no—
247C4⋊Dic73C22×C411yescharacteristic
248C4⋊Dic73C22×C411yescharacteristic
249#11924007—21no—
250#11924007—21no—
251#11924007—21no—
252#11924007—21no—
253#11924007—21no—
254#11924007—21no—
255#11924007—21no—
256#11924007—21no—
257C22⋊Dic73—21no—
258C22⋊Dic73—21no—
259C22⋊Dic73—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—
273#11924005—21no—
274#11924005—21no—
275#11924005—21no—
276#11924005—21no—
277#11924005—21no—
278#11924005—21no—
279#11924005—21no—
280C4×Dic73—21no—
281C4×Dic73—21no—
282C4×Dic73—21no—
283#41×C73—42no—
284C2×Q8×C73C22⋊C411yescharacteristic
285C2×D4×C73C22⋊C411yescharacteristic
286C2×D4×C73C22⋊C411yescharacteristic
287C2×D4×C73C22⋊C411yescharacteristic
288C22×C4×C73C22×C411yescharacteristic
289C22×C4×C73C22×C411yescharacteristic
290C22×C4×C73C22×C411yescharacteristic
291C22×C4×C73C2×D411yescharacteristic
292C22×C4×C73C2×D411yescharacteristic
293C22×C4×C73C2×D411yescharacteristic
294C22×C4×C73C2×D411yescharacteristic
295C22×C4×C73C2×D411yescharacteristic
296C22×C4×C73C2×D411yescharacteristic
297M16×C73—42no—
298C2×C8×C73—21no—
299C2×C8×C73—21no—
300C2×C8×C73—21no—
301C2×C8×C73—21no—
302C2×C8×C73—42no—
303C2×C8×C73—42no—
304C4⋊C4×C73C22⋊C411yescharacteristic
305C4⋊C4×C73C22⋊C411yescharacteristic
306C4⋊C4×C73C22⋊C411yescharacteristic
307C4⋊C4×C73C22⋊C411yescharacteristic
308C4⋊C4×C73C22⋊C411yescharacteristic
309C4⋊C4×C73C22⋊C411yescharacteristic
310C22⋊C4×C73C22⋊C411yescharacteristic
311C22⋊C4×C73C22⋊C411yescharacteristic
312C22⋊C4×C73C22⋊C411yescharacteristic
313C22⋊C4×C73C22⋊C411yescharacteristic
314C22⋊C4×C73C22⋊C411yescharacteristic
315C22⋊C4×C73C22⋊C411yescharacteristic
316C42×C73C22×C411yescharacteristic
317C42×C73C22×C411yescharacteristic
318C42×C73C22×C411yescharacteristic
319C42×C73C2×D411yescharacteristic
320C42×C73C2×D411yescharacteristic
321C42×C73C2×D411yescharacteristic
322C42×C73C2×D411yescharacteristic
323C42×C73C2×D411yescharacteristic
324C42×C73C2×D411yescharacteristic
325C42×C73C2411yescharacteristic
326C23×C73C2×C22⋊C411yescharacteristic
327C23×C73C2×C22⋊C411yescharacteristic
328C23×C73C2×C22⋊C411yescharacteristic
329C22×D73—21no—
330C22×D73—21no—
331C22×D73—21no—
332C22×D73—42no—
333C22×D73—42no—
334C22×D73—81no—
335C22×D73—81no—
336C22×D73—81no—
337C22×D73—81no—
338Q8×C73—41no—
339D4×C73—22no—
340D4×C73—22no—
341D4×C73—41no—
342C2×C4×C73—22no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73C2×C22⋊C411yescharacteristic
352C2×C4×C73C2×C22⋊C411yescharacteristic
353C2×C4×C73C2×C22⋊C411yescharacteristic
354C2×C4×C73C2×C22⋊C411yescharacteristic
355C2×C4×C73C2×C22⋊C411yescharacteristic
356C2×C4×C73C2×C22⋊C411yescharacteristic
357C2×C4×C73C2×C22⋊C411yescharacteristic
358C2×C4×C73C2×C22⋊C411yescharacteristic
359C2×C4×C73C2×C22⋊C411yescharacteristic
360C2×C4×C73C23×C411yescharacteristic
361C2×C4×C73C22×D411yescharacteristic
362C2×C4×C73C22×D411yescharacteristic
363C22⋊D73—42no—
364C22⋊D73—42no—
365C22⋊D73—81no—
366C22⋊D73—81no—
367C22⋊D73—81no—
368C2×Dic73—21no—
369C2×Dic73—21no—
370C2×Dic73—21no—
371C2×Dic73—21no—
372C2×Dic73—21no—
373C2×Dic73—81no—
374C2×Dic73—81no—
375D292—41no—
376D292—41no—
377D292—41no—
378D292—42no—
379D292—81no—
380D292—81no—
381D292—81no—
382C4×D73—42no—
383C4×D73—81no—
384C4×D73—81no—
385C4×D73—81no—
386C4×D73—81no—
387Dic146—41no—
388Dic146—41no—
389Dic146—41no—
390Dic146—81no—
391Dic146—81no—
392C8×C73—22no—
393C8×C73—41no—
394C8×C73—41no—
395C8×C73—41no—
396#10596831—41no—
397#10596831—41no—
398#10596831—41no—
399#10596831—41no—
400C22×C73—21no—
401C22×C73—21no—
402C22×C73—21no—
403C22×C73—21no—
404C22×C73—21no—
405C22×C73—21no—
406C22×C73—21no—
407C22×C73—21no—
408C22×C73#42112yes—
409C22×C73C22×C22⋊C411yescharacteristic
410C2×D73—41no—
411C2×D73—41no—
412C2×D73—41no—
413C2×D73—41no—
414C2×D73—41no—
415C2×D73—41no—
416C2×D73—41no—
417C2×D73—41no—
418C2×D73—41no—
419C2×D73—162no—
420C2×D73—162no—
421C4×C73—21no—
422C4×C73—21no—
423C4×C73—21no—
424C4×C73—21no—
425C4×C73—21no—
426C4×C73—21no—
427C4×C73—21no—
428C4×C73—21no—
429C4×C73—21no—
430C4×C73—21no—
431C4×C73—21no—
432C4×C73—21no—
433Dic73—41no—
434Dic73—41no—
435Dic73—41no—
436Dic73—41no—
437Dic73—41no—
438#17679—731nomaximal, Sylow
439C2×C73—22no—
440C2×C73—41no—
441C2×C73—41no—
442C2×C73#288811yescharacteristic
443C2×C73C2×#42111yescharacteristic
444C2×C73#290111yescharacteristic
445D73—81no—
446D73—81no—
447D73—81no—
448#3514—731no—
449#2970D7311yescharacteristic, complemented
450#2923—731no—
451#1536—731no—
452#1535—731no—
453#1535—731no—
454#1533—731no—
455#1532—731no—
456#1532—731no—
457#1530—731no—
458#1529—731no—
459#1527—731no—
460#1527—731no—
461#1524—731no—
462C2×#329—731no—
463C73#1767911yescharacteristic, complemented, Sylow
464#559—731no—
465#556—731no—
466#555—1461no—
467#551—1461no—
468#551—1461no—
469D4×Q8—731no—
470#548—731no—
471#548—731no—
472#546—731no—
473#546—731no—
474#546—1461no—
475D42—731no—
476#542—1461no—
477#538—1461no—
478#538—1461no—
479#532—731no—
480#529—731no—
481#529—731no—
482#529—731no—
483C2×#124—731no—
484C2×#124—731no—
485#518—1461no—
486C4×#41C2×D7311yescharacteristic
487#446—21no—
488#435—21no—
489#435—21no—
490C8×D4—21no—
491#433—1461no—
492#433—1461no—
493#432—731no—
494#432—731no—
495#432—731no—
496#432—731no—
497#432C2×D7311yescharacteristic, complemented
498#432C2×D7311yescharacteristic, complemented
499#432C2×D7311yescharacteristic, complemented
500#424—1461no—
501#408—1461no—
502C4×M16—731no—
503C4×M16C2×D7311yescharacteristic, complemented
504C2×#97—731no—
505C2×#97C2×D7311yescharacteristic, complemented
506C2×#97C2×D7311yescharacteristic, complemented
507#330—731no—
508#330—731no—
509#330—731no—
510#330—731no—
511#329—731no—
512#329—731no—
513#329—731no—
514#329—731no—
515#329—731no—
516#329—731no—
517#329—731no—
518#329—731no—
519#329—731no—
520#329—731no—
521#329—731no—
522#329—731no—
523C2×#41—731no—
524C2×#41—731no—
525C2×#41D29211yescharacteristic
526C22×Q8—731no—
527C22×Q8—731no—
528C22×D4—731no—
529C22×D4—731no—
530C22×D4—1461no—
531C2×M16—21no—
532C2×M16—1461no—
533C22×C8—21no—
534C22×C8—21no—
535C22×C8—1461no—
536C4⋊Q8—731no—
537C4⋊Q8—1461no—
538#127—731no—
539#126—1461no—
540#126—1461no—
541#126—1461no—
542#126—1461no—
543#126—1461no—
544#125—731no—
545#124—731no—
546#124—731no—
547#124—731no—
548#124—731no—
549#124—731no—
550#124—731no—
551#124—731no—
552#124—1461no—
553#124—1461no—
554#124—1461no—
555#124—1461no—
556#124—1461no—
557#124—1461no—
558#124—1461no—
559#123—1461no—
560#123—1461no—
561#123—1461no—
562#123—1461no—
563#123—1461no—
564#123—1461no—
565#123—1461no—
566C22⋊Q8—731no—
567C22⋊Q8—731no—
568C22⋊Q8—731no—
569C22⋊Q8—1461no—
570C22⋊Q8—1461no—
571C22⋊Q8—1461no—
572C22⋊Q8—1461no—
573C22⋊Q8—1461no—
574#121—731no—
575#121—731no—
576#121—731no—
577#121—1461no—
578#121—1461no—
579#121—1461no—
580#121—1461no—
581#121—1461no—
582#121—1461no—
583#121—1461no—
584#120—1461no—
585#120—1461no—
586#120—1461no—
587#120—1461no—
588C4×Q8—731no—
589C4×Q8—731no—
590C4×Q8—731no—
591C4×Q8C4×D7311yescharacteristic
592C4×Q8C22⋊D7311yescharacteristic
593C4×D4—731no—
594C4×D4—731no—
595C4×D4—731no—
596C4×D4—1461no—
597C4×D4—1461no—
598C4×D4—1461no—
599C4×D4—1461no—
600C4×D4—1461no—
601C4×D4—1461no—
602C4×D4—1461no—
603C4×D4—1461no—
604C4×D4—1461no—
605C4×D4C4×D7311yescharacteristic
606C4×D4C4×D7311yescharacteristic
607C4×D4C4×D7311yescharacteristic
608C4×D4C22⋊D7311yescharacteristic
609C4×D4C22⋊D7311yescharacteristic
610C4×D4C22⋊D7311yescharacteristic
611#117—1461no—
612#117—1461no—
613#117—1461no—
614#117—1461no—
615#117D29211yescharacteristic
616#117D29211yescharacteristic
617#117D29211yescharacteristic
618C2×C22⋊C4—1461no—
619C2×C22⋊C4—1461no—
620C2×C22⋊C4—1461no—
621C2×C22⋊C4—1461no—
622C2×C22⋊C4—1461no—
623C2×C22⋊C4—1461no—
624C2×C42C22×D7311yescharacteristic
625C2×C42C22×D7311yescharacteristic
626C2×C42C22×D7311yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630C4⋊C8—1461no—
631C4⋊C8—1461no—
632C4⋊C8—1461no—
633C4⋊C8—1461no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C22⋊C8—21no—
637C22⋊C8—1461no—
638C22⋊C8—1461no—
639C22⋊C8—1461no—
640C22⋊C8—1461no—
641#97—21no—
642#97—21no—
643#97—731no—
644#97—731no—
645#97—731no—
646#97—731no—
647#97—1461no—
648#97C22×D7311yescharacteristic
649#97C22×D7311yescharacteristic
650#97C22×D7311yescharacteristic
651#97C22×D7311yescharacteristic
652C4×C8—21no—
653C4×C8—1461no—
654C24—1461no—
655C24—1461no—
656#41—42no—
657#41—5841no—
658#41—5841no—
659C2×Q8—5841no—
660C2×Q8—5841no—
661C2×Q8—731no—
662C2×Q8—731no—
663C2×Q8—731no—
664C2×Q8—1461no—
665C2×Q8—1461no—
666C2×Q8#1192400511yescharacteristic
667C2×D4—2924no—
668C2×D4—5841no—
669C2×D4—5841no—
670C2×D4—731no—
671C2×D4—731no—
672C2×D4—731no—
673C2×D4—1461no—
674C2×D4—1461no—
675C2×D4—1461no—
676C2×D4—1461no—
677C2×D4—1461no—
678C2×D4—1461no—
679C2×D4—1461no—
680C2×D4—1461no—
681C2×D4—1461no—
682C2×D4#1192400511yescharacteristic
683C2×D4#1192400511yescharacteristic
684C2×D4#1192400511yescharacteristic
685C22×C4—1461no—
686C22×C4—1461no—
687C22×C4—1461no—
688C22×C4—1461no—
689C22×C4—1461no—
690C22×C4—1461no—
691C22×C4—1461no—
692C22×C4C2×C4×D7311yescharacteristic
693C22×C4C2×C4×D7311yescharacteristic
694C22×C4C2×C4×D7311yescharacteristic
695C22×C4C2×C22⋊D7311yescharacteristic
696C22×C4C2×C22⋊D7311yescharacteristic
697C22×C4C2×C22⋊D7311yescharacteristic
698C22×C4C2×D29211yescharacteristic
699C22×C4C2×D29211yescharacteristic
700C22×C4C2×D29211yescharacteristic
701M16—42no—
702M16—2922no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—42no—
708C2×C8—42no—
709C2×C8—2922no—
710C2×C8—1461no—
711C2×C8—1461no—
712C2×C8—1461no—
713C2×C8—1461no—
714C4⋊C4—731no—
715C4⋊C4—731no—
716C4⋊C4—1461no—
717C4⋊C4—1461no—
718C4⋊C4—1461no—
719C4⋊C4—1461no—
720C4⋊C4—1461no—
721C4⋊C4—1461no—
722C4⋊C4—1461no—
723C4⋊C4—1461no—
724C4⋊C4—1461no—
725C4⋊C4—1461no—
726C4⋊C4#1192400511yescharacteristic
727C4⋊C4#1192400511yescharacteristic
728C4⋊C4#1192400511yescharacteristic
729C4⋊C4#1192400511yescharacteristic
730C4⋊C4#1192400511yescharacteristic
731C4⋊C4#1192400511yescharacteristic
732C22⋊C4—1461no—
733C22⋊C4—1461no—
734C22⋊C4—1461no—
735C22⋊C4—1461no—
736C22⋊C4—1461no—
737C22⋊C4—1461no—
738C22⋊C4—1461no—
739C22⋊C4—1461no—
740C22⋊C4—1461no—
741C22⋊C4—1461no—
742C22⋊C4—1461no—
743C22⋊C4—1461no—
744C22⋊C4—1461no—
745C22⋊C4—1461no—
746C22⋊C4—1461no—
747C22⋊C4—1461no—
748C22⋊C4—1461no—
749C22⋊C4—1461no—
750C22⋊C4—1461no—
751C22⋊C4—1461no—
752C22⋊C4—1461no—
753C22⋊C4—1461no—
754C22⋊C4—1461no—
755C22⋊C4#1192400511yescharacteristic
756C22⋊C4#1192400511yescharacteristic
757C22⋊C4#1192400511yescharacteristic
758C22⋊C4#1192400511yescharacteristic
759C22⋊C4#1192400511yescharacteristic
760C22⋊C4#1192400511yescharacteristic
761C42—1461no—
762C42—1461no—
763C42—1461no—
764C42C2×C4×D7311yescharacteristic
765C42C2×C4×D7311yescharacteristic
766C42C2×C4×D7311yescharacteristic
767C42C2×C22⋊D7311yescharacteristic
768C42C2×C22⋊D7311yescharacteristic
769C42C2×C22⋊D7311yescharacteristic
770C42C2×D29211yescharacteristic
771C42C2×D29211yescharacteristic
772C42C2×D29211yescharacteristic
773C42C23×D7311yescharacteristic
774C23—2922no—
775C23—2922no—
776C23—5841no—
777C23—5841no—
778C23—5841no—
779C23—5841no—
780C23—1461no—
781C23—1461no—
782C23—1461no—
783C23C2×#1192400511yescharacteristic
784C23C2×#1192400511yescharacteristic
785C23C2×#1192400511yescharacteristic
786Q8—41no—
787Q8—2921no—
788Q8—2921no—
789Q8—2921no—
790Q8—5841no—
791Q8—5841no—
792D4—22no—
793D4—22no—
794D4—41no—
795D4—2921no—
796D4—2921no—
797D4—2921no—
798D4—2922no—
799D4—2922no—
800D4—2922no—
801D4—5841no—
802D4—5841no—
803D4—5841no—
804D4—5841no—
805D4—5841no—
806D4—5841no—
807C2×C4—22no—
808C2×C4—41no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—41no—
813C2×C4—41no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—2922no—
817C2×C4—5841no—
818C2×C4—5841no—
819C2×C4—5841no—
820C2×C4—5841no—
821C2×C4—5841no—
822C2×C4—5841no—
823C2×C4—1461no—
824C2×C4—1461no—
825C2×C4—1461no—
826C2×C4—1461no—
827C2×C4—1461no—
828C2×C4C2×#1192400511yescharacteristic
829C2×C4C2×#1192400511yescharacteristic
830C2×C4C2×#1192400511yescharacteristic
831C2×C4C2×#1192400511yescharacteristic
832C2×C4C2×#1192400511yescharacteristic
833C2×C4C2×#1192400511yescharacteristic
834C2×C4C2×#1192400511yescharacteristic
835C2×C4C2×#1192400511yescharacteristic
836C2×C4C2×#1192400511yescharacteristic
837C2×C4C22×C4×D7311yescharacteristic
838C2×C4C22×C22⋊D7311yescharacteristic
839C2×C4C22×D29211yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—2921no—
845C8—2921no—
846C8—2921no—
847C8—2921no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—21no—
856C22—2921no—
857C22—2921no—
858C22—2921no—
859C22—2921no—
860C22—2921no—
861C22—2921no—
862C22—2921no—
863C22—2921no—
864C22—2921no—
865C22—11682no—
866C22—11682no—
867C22#1798860312yes—
868C22C22×#1192400511yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—21no—
876C4—21no—
877C4—21no—
878C4—21no—
879C4—21no—
880C4—21no—
881C4—2921no—
882C4—2921no—
883C4—2921no—
884C4—2921no—
885C4—2921no—
886C2—22no—
887C2—41no—
888C2—41no—
889C2—5841no—
890C2—5841no—
891C2—5841no—
892C2#2261840911yescharacteristic
893C2C2×#1798860311yescharacteristic
894C2#2261847911yescharacteristic
subgroupG/H
centerC22C22×#11924005
commutatorC2×C4×C73C23×C4
FrattiniC42C23×D73
FittingC73×#2970C2
socleC22×C73C22×C22⋊C4
prime radical#22623892C2
cosocleC42×C73C24
hypercenter#2970D73
hypocenterC73#17679
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. #22618582C2semidirect
3. #22608565C2semidirect
4. #22608563C2semidirect
5. #22608560C2semidirect
6. #22608554C2semidirect
7. #22608552C2semidirect
8. #22608549C2semidirect
9. #22608541C2semidirect
10. #22608536C2semidirect
11. #22608530C2semidirect
12. #22608528C2semidirect
13. #22608517C2semidirect
14. C2×#17988326C2semidirect
15. C73×#2970C2semidirect
40. #17988644C22semidirect
41. #17988644C22semidirect
42. #17988644C22semidirect
43. #17988644C22semidirect
46. C4×#11924012C22semidirect
47. C2×#14556502C22semidirect
48. #17988328C22semidirect
49. #17988328C22semidirect
50. #17988328C22semidirect
51. #17988328C22semidirect
56. #17988326C22semidirect
57. #17988326C22semidirect
58. #17988326C22semidirect
59. #17988326C22semidirect
60. #17988326C22semidirect
61. #17988326C22semidirect
62. #17988326C22semidirect
63. #17988326C22semidirect
69. #432×C73C22semidirect
70. #432×C73C22semidirect
71. #432×C73C22semidirect
72. C4×M16×C73C22semidirect
73. C2×#97×C73C22semidirect
74. C2×#97×C73C22semidirect
449. #2970D73semidirect
463. C73#17679semidirect
497. #432C2×D73semidirect
498. #432C2×D73semidirect
499. #432C2×D73semidirect
503. C4×M16C2×D73semidirect
505. C2×#97C2×D73semidirect
506. C2×#97C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226238922
#226185822
#226085652
#226085632
#226085602
#226085542
#226085522
#226085492
#226085412
#226085362
#226085302
#226085282
#226085172
C2×#179883262
C73×#29702
#1767973