Finite Group Databasebeta

← #33103331

Subgroups — #33103331

Order 18688.

894 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618588C211yesmaximal, characteristic, complemented
2#416×D73C211yesmaximal, characteristic
3#22618378C211yesmaximal, characteristic
4#22610643C211yesmaximal, characteristic, complemented
5#22610641C211yesmaximal, characteristic, complemented
6#22610580C211yesmaximal, characteristic, complemented
7#22610578C211yesmaximal, characteristic, complemented
8#22610208C211yesmaximal, characteristic, complemented
9#22610029C211yesmaximal, characteristic, complemented
10#22609966C211yesmaximal, characteristic, complemented
11#22609873C211yesmaximal, characteristic
12#22609776C211yesmaximal, characteristic, complemented
13#22609773C211yesmaximal, characteristic, complemented
14#22609706C211yesmaximal, characteristic, complemented
15C73×#1866C211yesmaximal, characteristic, complemented
16C2×#41×D73C2211yescharacteristic
17C2×#14556598C2211yescharacteristic
18C22×C8×D73C2211yescharacteristic
19#117×D73C2211yescharacteristic
20#17988647—21no—
21#17988647—21no—
22#17988643—21no—
23#17988639—21no—
24C2×#14556527C2211yescharacteristic, complemented
25#17988614C2211yescharacteristic, complemented
26C2×#14556519C2211yescharacteristic
27C2×#14556518C2211yescharacteristic
28C2×#14556517C2211yescharacteristic
29#17988584C2211yescharacteristic
30#17988583C2211yescharacteristic
31#17988582C411yescharacteristic, complemented
32#17988582C411yescharacteristic, complemented
33#17988581C2211yescharacteristic
34#17988580C411yescharacteristic, complemented
35#17988580C411yescharacteristic, complemented
36#103×D73C411yescharacteristic, complemented
37#103×D73C411yescharacteristic, complemented
38#102×D73C411yescharacteristic, complemented
39#102×D73C411yescharacteristic, complemented
40#17988555—21no—
41#17988555C2211yescharacteristic
42#17988553—21no—
43#17988553C2211yescharacteristic
44#17988550—21no—
45#17988550C2211yescharacteristic
46#17988550C2211yescharacteristic
47C2×#14556503—21no—
48C2×#14556503C2211yescharacteristic
49#17988545C2211yescharacteristic, complemented
50#17988542C2211yescharacteristic, complemented
51C2×#14556502C2211yescharacteristic, complemented
52C2×#14556501C2211yescharacteristic, complemented
53C4×#11924005C2211yescharacteristic
54#17988351C2211yescharacteristic, complemented
55#17988351C2211yescharacteristic, complemented
56#17988348C2211yescharacteristic, complemented
57#17988347C2211yescharacteristic, complemented
58#17988346C2211yescharacteristic, complemented
59#17988341C2211yescharacteristic, complemented
60C2×#131×C73C2211yescharacteristic
61C2×#108×C73C2211yescharacteristic, complemented
62#424×C73C2211yescharacteristic, complemented
63C2×#104×C73C2211yescharacteristic
64#416×C73C2211yescharacteristic
65#339×C73C2211yescharacteristic, complemented
66#336×C73C2211yescharacteristic, complemented
67C2×#11924029C2×C411yescharacteristic
68C2×#11924028—21no—
69C2×#11924028C2311yescharacteristic
70C2×#11924027—21no—
71C2×#11924027C2×C411yescharacteristic
72#41×D73—22no—
73#41×D73—22no—
74#41×D73—41no—
75#41×D73—41no—
76C2×Q8×D73C2×C411yescharacteristic
77C2×D4×D73—21no—
78C2×D4×D73C2×C411yescharacteristic
79C22×C4×D73—21no—
80C22×C4×D73C2311yescharacteristic
81#14556598—22no—
82#14556598—41no—
83C2×#11924012—21no—
84C2×#11924012C2311yescharacteristic
85C2×#11924012C2311yescharacteristic
86C22×#10596831—21no—
87C22×#10596831C2311yescharacteristic
88C22×#10596831C2311yescharacteristic
89C2×C8×D73—41no—
90C2×C8×D73—41no—
91C2×C8×D73C2×C411yescharacteristic
92C2×C8×D73C2×C411yescharacteristic
93C2×C8×D73C2×C411yescharacteristic
94C2×C8×D73C2×C411yescharacteristic
95#14556550C2311yescharacteristic
96#14556549C2×C411yescharacteristic
97#14556549C2×C411yescharacteristic
98#14556548—21no—
99#14556547—21no—
100C4⋊C4×D73C2×C411yescharacteristic
101C4⋊C4×D73C2×C411yescharacteristic
102C2×#11924005—21no—
103C22⋊C4×D73—21no—
104C2×C4×Dic73C2311yescharacteristic
105C42×D73—21no—
106#14556527—41no—
107C4⋊#10596831—21no—
108C4⋊#10596831—21no—
109#14556519—41no—
110#14556518—22no—
111#14556517—41no—
112#14556516C2×C411yescharacteristic
113#14556516C2×C411yescharacteristic
114#14556515C2×C411yescharacteristic
115#14556515C2×C411yescharacteristic
116#14556514C2×C411yescharacteristic
117#14556514C2×C411yescharacteristic
118#14556513C2×C411yescharacteristic
119#14556513C2×C411yescharacteristic
120#14556512C2×C411yescharacteristic
121#14556512C2×C411yescharacteristic
122#14556511C2×C411yescharacteristic
123#14556511C2×C411yescharacteristic
124#14556503—21no—
125#14556503—21no—
126#14556503—21no—
127#14556503—21no—
128#14556503—21no—
129#14556503—21no—
130#14556503—21no—
131#14556503—21no—
132#14556503D411yescharacteristic
133#14556503D411yescharacteristic
134#14556503D411yescharacteristic
135#14556503D411yescharacteristic
136#14556502—41no—
137#14556501—21no—
138#14556501—21no—
139#14556501—41no—
140C8×Dic73—21no—
141C8×Dic73—21no—
142#14556498—21no—
143C2×#41×C73C2311yescharacteristic
144#131×C73—22no—
145#131×C73—41no—
146C2×M16×C73—21no—
147C2×M16×C73C2311yescharacteristic
148C2×M16×C73C2311yescharacteristic
149C22×C8×C73—21no—
150C22×C8×C73C2311yescharacteristic
151C22×C8×C73C2311yescharacteristic
152#117×C73C2311yescharacteristic
153C2×C42×C73C2311yescharacteristic
154#108×C73—41no—
155C4⋊C8×C73—21no—
156C4⋊C8×C73—21no—
157#104×C73—22no—
158#103×C73C2×C411yescharacteristic
159#103×C73C2×C411yescharacteristic
160#102×C73C2×C411yescharacteristic
161#102×C73C2×C411yescharacteristic
162C23×D73—21no—
163C23×D73#4111yescharacteristic
164#11924029—22no—
165#11924029—41no—
166#11924028—21no—
167#11924028—21no—
168#11924028—21no—
169#11924028—21no—
170#11924028—42no—
171#11924028—42no—
172#11924027—22no—
173#11924027—41no—
174#11924027—42no—
175#11924027—42no—
176C2×Dic146—21no—
177C2×Dic146C22×C411yescharacteristic
178Q8×D73—22no—
179Q8×D73—41no—
180C2×D292—21no—
181C2×D292C22×C411yescharacteristic
182C2×C22⋊D73—21no—
183C2×C22⋊D73—21no—
184C2×C22⋊D73—21no—
185D4×D73—22no—
186D4×D73—41no—
187D4×D73—42no—
188D4×D73—42no—
189C22×Dic73—21no—
190C22×Dic73—21no—
191C22×Dic73#4111yescharacteristic
192C2×C4×D73—21no—
193C2×C4×D73—21no—
194C2×C4×D73—21no—
195C2×C4×D73—21no—
196C2×C4×D73—21no—
197C2×C4×D73—21no—
198C2×C4×D73—21no—
199C2×C4×D73—21no—
200C2×C4×D73—21no—
201C2×C4×D73—42no—
202C2×C4×D73—42no—
203C2×C4×D73C22×C411yescharacteristic
204C2×C4×D73C22×C411yescharacteristic
205C2×C4×D73C2×D411yescharacteristic
206C2×C4×D73C2×D411yescharacteristic
207#11924012—21no—
208#11924012—21no—
209#11924012—21no—
210#11924012—21no—
211#11924012—42no—
212C2×#10596831—21no—
213C2×#10596831—21no—
214C2×#10596831—21no—
215C2×#10596831—21no—
216C2×#10596831—21no—
217C2×#10596831—21no—
218C2×#10596831—42no—
219C2×#10596831C22×C411yescharacteristic
220C2×#10596831C22×C411yescharacteristic
221C2×#10596831C2×D411yescharacteristic
222C2×#10596831C2×D411yescharacteristic
223C8×D73—41no—
224C8×D73—41no—
225C8×D73—41no—
226C8×D73—41no—
227C4⋊Dic73C22×C411yescharacteristic
228C4⋊Dic73C22×C411yescharacteristic
229#11924007—21no—
230#11924007—21no—
231C22⋊Dic73—21no—
232#11924005—21no—
233#11924005—21no—
234#11924005—42no—
235C4×Dic73—21no—
236C4×Dic73—21no—
237C4×Dic73—21no—
238C4×Dic73—21no—
239C4×Dic73—21no—
240#41×C73—21no—
241#41×C73—21no—
242#41×C73#4112yes—
243#41×C73#4112yes—
244C2×Q8×C73C22×C411yescharacteristic
245C2×D4×C73—21no—
246C2×D4×C73C22×C411yescharacteristic
247C22×C4×C73—21no—
248C22×C4×C73—21no—
249C22×C4×C73C2411yescharacteristic
250M16×C73—21no—
251M16×C73—21no—
252M16×C73—21no—
253M16×C73—21no—
254M16×C73—42no—
255C2×C8×C73—21no—
256C2×C8×C73—21no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—21no—
261C2×C8×C73—42no—
262C2×C8×C73C22×C411yescharacteristic
263C2×C8×C73C22×C411yescharacteristic
264C2×C8×C73C2×D411yescharacteristic
265C2×C8×C73C2×D411yescharacteristic
266C4⋊C4×C73C22×C411yescharacteristic
267C4⋊C4×C73C22×C411yescharacteristic
268C22⋊C4×C73—21no—
269C42×C73—21no—
270C42×C73—21no—
271C42×C73—21no—
272C23×C73—21no—
273C23×C73C2×#4111yescharacteristic
274C22×D73—21no—
275C22×D73—21no—
276C22×D73—22no—
277C22×D73—21no—
278C22×D73—41no—
279C22×D73—42no—
280C22×D73—42no—
281C22×D73—81no—
282C22×D73C4×D411yescharacteristic
283C22×D73C4×D411yescharacteristic
284Q8×C73—21no—
285Q8×C73#11712yes—
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—21no—
289D4×C73#11712yes—
290C2×C4×C73—21no—
291C2×C4×C73—22no—
292C2×C4×C73—22no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73C23×C411yescharacteristic
299C2×C4×C73C22×D411yescharacteristic
300C2×C4×C73C2×#4111yescharacteristic
301C2×C4×C73C2×#4111yescharacteristic
302C2×C4×C73H(5,𝔽2)11yescharacteristic
303C2×C4×C73H(5,𝔽2)11yescharacteristic
304C22⋊D73—42no—
305C22⋊D73—42no—
306C22⋊D73—41no—
307C22⋊D73—41no—
308C2×Dic73—21no—
309C2×Dic73—21no—
310C2×Dic73—21no—
311C2×Dic73—21no—
312C2×Dic73—21no—
313C2×Dic73—42no—
314C2×Dic73—41no—
315C2×Dic73—41no—
316C2×Dic73—41no—
317C2×Dic73C4×D411yescharacteristic
318C2×Dic73C4×D411yescharacteristic
319D292—21no—
320D292—21no—
321D292—42no—
322C4×D73—21no—
323C4×D73—21no—
324C4×D73—21no—
325C4×D73—21no—
326C4×D73—21no—
327C4×D73—21no—
328C4×D73—21no—
329C4×D73—21no—
330C4×D73—42no—
331C4×D73—42no—
332C4×D73—42no—
333C4×D73—41no—
334C4×D73—41no—
335C4×D73—81no—
336Dic146—21no—
337Dic146—21no—
338Dic146—42no—
339C8×C73—21no—
340C8×C73—21no—
341C8×C73—21no—
342C8×C73—21no—
343C8×C73—41no—
344C8×C73—41no—
345#10596831—21no—
346#10596831—21no—
347#10596831—21no—
348#10596831—21no—
349#10596831—41no—
350#10596831—41no—
351C22×C73—21no—
352C22×C73—21no—
353C22×C73—22no—
354C22×C73—41no—
355C22×C73—41no—
356C22×C73C2×C4×D411yescharacteristic
357C22×C73#55111yescharacteristic
358C22×C73#55111yescharacteristic
359C2×D73—21no—
360C2×D73—21no—
361C2×D73—21no—
362C2×D73—21no—
363C2×D73—21no—
364C2×D73—42no—
365C2×D73—42no—
366C2×D73—41no—
367C2×D73—41no—
368C2×D73—41no—
369C2×D73—84no—
370C2×D73#44412yes—
371C4×C73—22no—
372C4×C73—41no—
373C4×C73—41no—
374C4×C73—81no—
375C4×C73C2×#11711yescharacteristic
376C4×C73#51811yescharacteristic
377C4×C73#54611yescharacteristic
378C4×C73#54611yescharacteristic
379Dic73—21no—
380Dic73—21no—
381Dic73—41no—
382Dic73—41no—
383Dic73—41no—
384Dic73—81no—
385#22586—731nomaximal, Sylow
386C2×C73—21no—
387C2×C73—21no—
388C2×C73—42no—
389C2×C73#234211yescharacteristic
390C2×C73C2×#44411yescharacteristic
391C2×C73#295711yescharacteristic
392D73—22no—
393D73—41no—
394D73—81no—
395#2924—731no—
396C2×#416—731no—
397#2880—731no—
398#1938—731no—
399#1938—731no—
400#1929—731no—
401#1929—731no—
402#1866—731no—
403#1866D7311yescharacteristic, complemented
404#1826—731no—
405#1810—731no—
406#1789—731no—
407#1765—731no—
408#1765—731no—
409#1752—731no—
410C73#2258611yescharacteristic, complemented, Sylow
411C22×#41—731no—
412C2×#131—731no—
413C2×#131C2×D7311yescharacteristic
414C23×C8—731no—
415C2×#117—731no—
416#433—1461no—
417#433—1461no—
418#432—1461no—
419#431—1461no—
420C2×#108—731no—
421C2×#108C2×D7311yescharacteristic, complemented
422#424—731no—
423#424C2×D7311yescharacteristic, complemented
424C2×#104—731no—
425C2×#104—731no—
426C2×#104—731no—
427C2×#104C2×D7311yescharacteristic
428#416—731no—
429#416—731no—
430#416—731no—
431#416—731no—
432#416—731no—
433#416—731no—
434#416—731no—
435#416C2×D7311yescharacteristic
436C2×#103—731no—
437C2×#103—731no—
438C2×#102—731no—
439C2×#102—731no—
440#408—731no—
441#408—731no—
442#408—1461no—
443#408—1461no—
444#407—731no—
445#407—731no—
446#407—1461no—
447C2×C22⋊C8—731no—
448C2×C22⋊C8—1461no—
449#405—731no—
450#405—731no—
451C2×#97—731no—
452C2×#97—731no—
453C4×C22⋊C4—731no—
454#341—731no—
455#341—731no—
456#339—731no—
457#339—731no—
458#339—731no—
459#339C2×D7311yescharacteristic, complemented
460#336—731no—
461#336C2×D7311yescharacteristic, complemented
462C2×#41—2921no—
463C2×#41—2921no—
464C2×#41—731no—
465C2×#41—731no—
466C2×#41—731no—
467C2×#41—1461no—
468C2×#41—1462no—
469C2×#41—1462no—
470C2×#41—1461no—
471C2×#41C22×D7311yescharacteristic
472C22×Q8—731no—
473C22×D4—731no—
474C22×D4—1461no—
475C23×C4—731no—
476C23×C4—1461no—
477#131—22no—
478#131—41no—
479#131—2921no—
480#131—1462no—
481C2×M16—21no—
482C2×M16—731no—
483C2×M16—731no—
484C2×M16—1461no—
485C2×M16C22×D7311yescharacteristic
486C2×M16C22×D7311yescharacteristic
487C22×C8—21no—
488C22×C8—2921no—
489C22×C8—2921no—
490C22×C8—731no—
491C22×C8—731no—
492C22×C8—731no—
493C22×C8—731no—
494C22×C8—731no—
495C22×C8—731no—
496C22×C8—1461no—
497C22×C8C22×D7311yescharacteristic
498C22×C8C22×D7311yescharacteristic
499#117—731no—
500#117—731no—
501#117—731no—
502#117—1461no—
503#117—1461no—
504#117C22×D7311yescharacteristic
505C2×C4⋊C4—731no—
506C2×C4⋊C4—731no—
507C2×C22⋊C4—1461no—
508C2×C22⋊C4—1461no—
509C2×C42—731no—
510C2×C42—1461no—
511C2×C42C22×D7311yescharacteristic
512#108—41no—
513#108—2921no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—1461no—
517C4⋊C8—1461no—
518#104—22no—
519#104—2921no—
520#104—2921no—
521#104—1462no—
522#103—731no—
523#103—731no—
524#103—731no—
525#103—731no—
526#103—731no—
527#103—731no—
528#103C4×D7311yescharacteristic
529#103C4×D7311yescharacteristic
530#102—731no—
531#102—731no—
532#102—731no—
533#102—731no—
534#102—731no—
535#102—731no—
536#102C4×D7311yescharacteristic
537#102C4×D7311yescharacteristic
538C22⋊C8—731no—
539C22⋊C8—731no—
540C22⋊C8—731no—
541C22⋊C8—731no—
542C22⋊C8—1461no—
543C22⋊C8—1461no—
544C22⋊C8—1461no—
545C22⋊C8—1461no—
546C22⋊C8—1461no—
547C22⋊C8—1461no—
548C22⋊C8—1461no—
549C22⋊C8—1461no—
550#97—2921no—
551#97—2921no—
552#97—1461no—
553#97—1461no—
554C4×C8—1461no—
555C4×C8—1461no—
556#95—1461no—
557C24—731no—
558C24—1461no—
559#41—21no—
560#41—21no—
561#41—2922no—
562#41—2922no—
563#41—2922no—
564#41—2922no—
565#41—2921no—
566#41—2921no—
567#41—1462no—
568#41—1462no—
569#41—1461no—
570#41—1461no—
571#41—1461no—
572#41—1461no—
573#41#1192402712yes—
574#41#1192402912yes—
575C2×Q8—2921no—
576C2×Q8—731no—
577C2×Q8—1461no—
578C2×Q8—1462no—
579C2×Q8C2×C4×D7311yescharacteristic
580C2×D4—21no—
581C2×D4—2922no—
582C2×D4—2922no—
583C2×D4—2921no—
584C2×D4—731no—
585C2×D4—1461no—
586C2×D4—1461no—
587C2×D4—1461no—
588C2×D4—1461no—
589C2×D4—1462no—
590C2×D4C2×C4×D7311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—2922no—
594C22×C4—2922no—
595C22×C4—731no—
596C22×C4—731no—
597C22×C4—731no—
598C22×C4—731no—
599C22×C4—731no—
600C22×C4—1461no—
601C22×C4—1461no—
602C22×C4—1461no—
603C22×C4—1461no—
604C22×C4—1461no—
605C22×C4—1461no—
606C22×C4—1461no—
607C22×C4—1461no—
608C22×C4—1461no—
609C22×C4—1461no—
610C22×C4—1461no—
611C22×C4C23×D7311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—42no—
617M16—2922no—
618M16—1461no—
619M16—1461no—
620M16—1461no—
621M16—1461no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—42no—
629C2×C8—2921no—
630C2×C8—2921no—
631C2×C8—2921no—
632C2×C8—2921no—
633C2×C8—2922no—
634C2×C8—731no—
635C2×C8—731no—
636C2×C8—731no—
637C2×C8—731no—
638C2×C8—1461no—
639C2×C8—1461no—
640C2×C8—1461no—
641C2×C8—1461no—
642C2×C8—1461no—
643C2×C8—1461no—
644C2×C8C2×C4×D7311yescharacteristic
645C2×C8C2×C4×D7311yescharacteristic
646C2×C8D4×D7311yescharacteristic
647C2×C8D4×D7311yescharacteristic
648C4⋊C4—731no—
649C4⋊C4—731no—
650C4⋊C4—1461no—
651C4⋊C4—1461no—
652C4⋊C4C2×C4×D7311yescharacteristic
653C4⋊C4C2×C4×D7311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—2922no—
656C22⋊C4—1461no—
657C22⋊C4—1461no—
658C22⋊C4—1461no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—1461no—
663C42—1461no—
664C42—1461no—
665C42—1461no—
666C42—1461no—
667C23—21no—
668C23—2921no—
669C23—2922no—
670C23—2922no—
671C23—5841no—
672C23—731no—
673C23—731no—
674C23—1462no—
675C23—1461no—
676C23—1461no—
677C23—1461no—
678C23#41×D7311yescharacteristic
679Q8—21no—
680Q8—2922no—
681Q8—1461no—
682Q8—1461no—
683Q8#1455654912yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—2922no—
688D4—2922no—
689D4—2921no—
690D4—2921no—
691D4—2922no—
692D4—1461no—
693D4—1461no—
694D4#1455654912yes—
695C2×C4—21no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—2922no—
704C2×C4—2922no—
705C2×C4—2922no—
706C2×C4—2922no—
707C2×C4—2921no—
708C2×C4—2921no—
709C2×C4—2921no—
710C2×C4—2921no—
711C2×C4—2921no—
712C2×C4—5841no—
713C2×C4—731no—
714C2×C4—731no—
715C2×C4—1461no—
716C2×C4—1461no—
717C2×C4—1461no—
718C2×C4—1461no—
719C2×C4—1461no—
720C2×C4—1461no—
721C2×C4—1461no—
722C2×C4—1461no—
723C2×C4—1461no—
724C2×C4—1461no—
725C2×C4—1461no—
726C2×C4—1461no—
727C2×C4—1461no—
728C2×C4C22×C4×D7311yescharacteristic
729C2×C4C2×D4×D7311yescharacteristic
730C2×C4C2×#1192402711yescharacteristic
731C2×C4C2×#1192402911yescharacteristic
732C2×C4#1455663611yescharacteristic
733C2×C4#1455663711yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—41no—
739C8—41no—
740C8—2921no—
741C8—2921no—
742C8—1461no—
743C8—1461no—
744C8—1461no—
745C8—1461no—
746C22—21no—
747C22—21no—
748C22—22no—
749C22—41no—
750C22—41no—
751C22—2922no—
752C22—2922no—
753C22—2921no—
754C22—2921no—
755C22—2921no—
756C22—5844no—
757C22—732no—
758C22—1461no—
759C22—1461no—
760C22—1461no—
761C22—1461no—
762C22—1461no—
763C22C4×D4×D7311yescharacteristic
764C22#1798926011yescharacteristic
765C22#1798926411yescharacteristic
766C4—22no—
767C4—41no—
768C4—41no—
769C4—81no—
770C4—2921no—
771C4—2921no—
772C4—2921no—
773C4—5841no—
774C4—1461no—
775C4—1461no—
776C4C2×#1455654911yescharacteristic
777C4#1798905911yescharacteristic
778C4#1798922411yescharacteristic
779C4#1798922811yescharacteristic
780C2—21no—
781C2—21no—
782C2—42no—
783C2—2921no—
784C2—5841no—
785C2—1462no—
786C2#2261277811yescharacteristic
787C2#444×D7311yescharacteristic
788C2#2261884311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#1866C2
socleC22×C73C2×C4×D4
prime radicalC2×#41×D73C22
cosocleC22×C4×C73C24
hypercenter#1866D73
hypocenterC73#22586
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1866

Complements

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

NH ≅ G/Ntype
1. #22618588C2semidirect
4. #22610643C2semidirect
5. #22610641C2semidirect
6. #22610580C2semidirect
7. #22610578C2semidirect
8. #22610208C2semidirect
9. #22610029C2semidirect
10. #22609966C2semidirect
12. #22609776C2semidirect
13. #22609773C2semidirect
14. #22609706C2semidirect
15. C73×#1866C2semidirect
24. C2×#14556527C22semidirect
25. #17988614C22semidirect
31. #17988582C4semidirect
32. #17988582C4semidirect
34. #17988580C4semidirect
35. #17988580C4semidirect
36. #103×D73C4semidirect
37. #103×D73C4semidirect
38. #102×D73C4semidirect
39. #102×D73C4semidirect
49. #17988545C22semidirect
50. #17988542C22semidirect
51. C2×#14556502C22semidirect
52. C2×#14556501C22semidirect
54. #17988351C22semidirect
55. #17988351C22semidirect
56. #17988348C22semidirect
57. #17988347C22semidirect
58. #17988346C22semidirect
59. #17988341C22semidirect
61. C2×#108×C73C22semidirect
62. #424×C73C22semidirect
65. #339×C73C22semidirect
66. #336×C73C22semidirect
403. #1866D73semidirect
410. C73#22586semidirect
421. C2×#108C2×D73semidirect
423. #424C2×D73semidirect
459. #339C2×D73semidirect
461. #336C2×D73semidirect

Maximal subgroups

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

subgroupindex
#226185882
#416×D732
#226183782
#226106432
#226106412
#226105802
#226105782
#226102082
#226100292
#226099662
#226098732
#226097762
#226097732
#226097062
C73×#18662
#2258673