Finite Group Databasebeta

← #33106756

Subgroups — #33106756

Order 18688.

1070 conjugacy classes of subgroups.

The subgroup lattice has 868 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22619153C211yesmaximal, characteristic
2C2×#17988705C211yesmaximal, characteristic, complemented
3#22618652C211yesmaximal, characteristic, complemented
4C22×#14556519C211yesmaximal, characteristic, complemented
5#22618377C211yesmaximal, characteristic, complemented
6#22610819C211yesmaximal, characteristic, complemented
7#22610635C211yesmaximal, characteristic, complemented
8#22610580C211yesmaximal, characteristic, complemented
9#22610374C211yesmaximal, characteristic, complemented
10#22610257C211yesmaximal, characteristic, complemented
11#22610257C211yesmaximal, characteristic, complemented
12#22610209C211yesmaximal, characteristic, complemented
13#22610138C211yesmaximal, characteristic, complemented
14#22609768C211yesmaximal, characteristic, complemented
15C4×C22⋊C8×C73C211yesmaximal, characteristic, complemented
16C22×#11924028C2211yescharacteristic
17C2×#14556613C2211yescharacteristic
18C2×#14556613C2211yescharacteristic
19C2×#14556597C2211yescharacteristic
20C2×#14556597C2211yescharacteristic
21C2×#14556597C2211yescharacteristic, complemented
22C22×#11924012C2211yescharacteristic
23#17989098C2211yescharacteristic
24#17988751C411yescharacteristic, complemented
25#17988751C411yescharacteristic, complemented
26#17988745C411yescharacteristic, complemented
27#17988740C411yescharacteristic, complemented
28#17988734C411yescharacteristic, complemented
29#17988734C411yescharacteristic, complemented
30#17988728C411yescharacteristic, complemented
31#17988723C411yescharacteristic, complemented
32#17988705—24no—
33#17988662—21no—
34#17988661—21no—
35#17988655—21no—
36#17988650—21no—
37C2×#14556527C2211yescharacteristic, complemented
38C2×#14556527C2211yescharacteristic, complemented
39#17988613C2211yescharacteristic, complemented
40C2×#14556519—24no—
41C2×#14556519C2211yescharacteristic
42C2×#14556519C2211yescharacteristic
43C2×#14556519C2211yescharacteristic
44C2×#14556519C2211yescharacteristic
45C2×#14556519C2211yescharacteristic, complemented
46C2×#14556519C2211yescharacteristic, complemented
47#17988584C2211yescharacteristic
48#17988584C2211yescharacteristic
49#17988553C2211yescharacteristic
50#17988553C2211yescharacteristic
51#17988553C2211yescharacteristic, complemented
52#17988552—21no—
53#17988552—21no—
54#17988551C2211yescharacteristic
55#17988549—21no—
56C22⋊C8×D73—21no—
57#17988542C2211yescharacteristic, complemented
58#17988352C2211yescharacteristic, complemented
59#17988352C2211yescharacteristic, complemented
60#17988347C2211yescharacteristic, complemented
61#17988347C2211yescharacteristic, complemented
62C22×C42×C73C2211yescharacteristic
63C2×C22⋊C8×C73C2211yescharacteristic
64C2×C22⋊C8×C73C2211yescharacteristic
65C2×C4×C8×C73C2211yescharacteristic, complemented
66C2×C4×C8×C73C2211yescharacteristic, complemented
67#336×C73C2211yescharacteristic, complemented
68#336×C73C2211yescharacteristic, complemented
69C2×#11924028—22no—
70C2×#11924028—22no—
71C2×#11924028—21no—
72C2×#11924028—21no—
73C2×#11924028—41no—
74C2×#11924028—41no—
75C2×#11924028C2×C411yescharacteristic
76C2×#11924028C2×C411yescharacteristic
77C2×#11924028C2311yescharacteristic
78C2×#11924028C2311yescharacteristic
79C2×#11924028C2311yescharacteristic
80C22×Dic146C2×C411yescharacteristic
81C22×D292C2×C411yescharacteristic
82C22×C22⋊D73—21no—
83C22×C4×D73—21no—
84#14556613—22no—
85#14556613—22no—
86#14556613—41no—
87#14556613—41no—
88C2×Dic292C2×C411yescharacteristic, complemented
89C2×Dic292C2×C411yescharacteristic, complemented
90C2×#11924017C2×C411yescharacteristic, complemented
91C2×#11924017C2×C411yescharacteristic, complemented
92C2×#11924017C2×C411yescharacteristic, complemented
93C2×#11924017C2×C411yescharacteristic, complemented
94C2×D584C2×C411yescharacteristic, complemented
95C2×D584C2×C411yescharacteristic, complemented
96#14556597—22no—
97#14556597—22no—
98#14556597—22no—
99#14556597—41no—
100#14556597—41no—
101#14556597—41no—
102C2×#11924012—22no—
103C2×#11924012—21no—
104C2×#11924012—41no—
105C2×#11924012C2311yescharacteristic
106C2×#11924012C2311yescharacteristic
107C2×#11924012C2311yescharacteristic
108C2×#11924012C2311yescharacteristic
109C2×#11924011—21no—
110C2×#11924011—21no—
111C2×#11924011—21no—
112C22×#10596831—21no—
113C2×C8×D73—21no—
114C2×C8×D73—21no—
115C2×C8×D73—21no—
116#14556574—21no—
117#14556570C2×C411yescharacteristic
118#14556570C2×C411yescharacteristic
119#14556565C2×C411yescharacteristic
120#14556565C2×C411yescharacteristic
121#14556560—21no—
122C4×C22⋊D73—21no—
123C4×C22⋊D73—21no—
124#14556550C2311yescharacteristic
125#14556527—22no—
126#14556527—41no—
127#14556520—21no—
128#14556520—21no—
129#14556519—22no—
130#14556519—22no—
131#14556519—22no—
132#14556519—22no—
133#14556519—41no—
134#14556519D414yescomplemented
135#14556516C2×C411yescharacteristic, complemented
136#14556516C2×C411yescharacteristic, complemented
137#14556516C2×C411yescharacteristic, complemented
138#14556516C2×C411yescharacteristic, complemented
139#14556513C2×C411yescharacteristic, complemented
140#14556513C2×C411yescharacteristic, complemented
141#14556513C2×C411yescharacteristic, complemented
142#14556513C2×C411yescharacteristic, complemented
143C22⋊#10596831—21no—
144C22⋊#10596831—21no—
145#14556503—21no—
146#14556503—21no—
147#14556503—21no—
148#14556503—21no—
149#14556503—21no—
150#14556503—21no—
151#14556501—21no—
152C8×Dic73—21no—
153C23×C4×C73—21no—
154C23×C4×C73C2311yescharacteristic
155C22×C8×C73C2311yescharacteristic
156C22×C8×C73C2311yescharacteristic
157C22×C8×C73C2311yescharacteristic
158C22×C8×C73C2311yescharacteristic
159C2×C42×C73—22no—
160C2×C42×C73—21no—
161C2×C42×C73—41no—
162C2×C42×C73C2311yescharacteristic
163C2×C42×C73C2311yescharacteristic
164C22⋊C8×C73C2×C411yescharacteristic
165C22⋊C8×C73C2×C411yescharacteristic
166C22⋊C8×C73C2×C411yescharacteristic
167C22⋊C8×C73C2×C411yescharacteristic
168C22⋊C8×C73D411yescharacteristic
169C22⋊C8×C73D411yescharacteristic
170C22⋊C8×C73D411yescharacteristic
171C22⋊C8×C73D411yescharacteristic
172C4×C8×C73—22no—
173C4×C8×C73—41no—
174C23×D73—21no—
175#11924028—21no—
176#11924028—21no—
177#11924028—21no—
178#11924028—21no—
179#11924028—21no—
180#11924028—21no—
181#11924028—21no—
182#11924028—21no—
183#11924028—21no—
184#11924028—21no—
185#11924028—22no—
186#11924028—22no—
187#11924028—41no—
188#11924028—41no—
189#11924028—42no—
190#11924028—42no—
191#11924028—42no—
192#11924028—42no—
193#11924028C2×D412yes—
194#11924028#4112yes—
195C2×Dic146—22no—
196C2×Dic146—21no—
197C2×Dic146—41no—
198C2×Dic146C22×C411yescharacteristic
199C2×Dic146C22×C411yescharacteristic
200C2×Dic146C22×C411yescharacteristic
201C2×D292—22no—
202C2×D292—21no—
203C2×D292—41no—
204C2×D292C22×C411yescharacteristic
205C2×D292C22×C411yescharacteristic
206C2×D292C22×C411yescharacteristic
207C2×C22⋊D73—21no—
208C2×C22⋊D73—21no—
209C2×C22⋊D73—21no—
210C2×C22⋊D73—21no—
211C2×C22⋊D73—21no—
212C2×C22⋊D73—21no—
213C2×C22⋊D73—21no—
214C2×C22⋊D73—42no—
215C2×C22⋊D73—42no—
216C22×Dic73—21no—
217C2×C4×D73—21no—
218C2×C4×D73—21no—
219C2×C4×D73—21no—
220C2×C4×D73—21no—
221C2×C4×D73—21no—
222C2×C4×D73—42no—
223C2×C4×D73—42no—
224Dic292—22no—
225Dic292—41no—
226#11924017—22no—
227#11924017—22no—
228#11924017—41no—
229#11924017—41no—
230D584—22no—
231D584—41no—
232#11924012—21no—
233#11924012—21no—
234#11924012—21no—
235#11924012—21no—
236#11924012—21no—
237#11924012—21no—
238#11924012—21no—
239#11924012—42no—
240#11924012C2×D412yes—
241#11924011—42no—
242#11924011—42no—
243#11924011—42no—
244C2×#10596831—21no—
245C2×#10596831—21no—
246C2×#10596831—21no—
247C2×#10596831—21no—
248C2×#10596831—42no—
249C8×D73—42no—
250C8×D73—42no—
251C8×D73—42no—
252C4⋊Dic73C22×C411yescharacteristic
253C4⋊Dic73C22×C411yescharacteristic
254#11924007—21no—
255#11924007—21no—
256C22⋊Dic73—21no—
257C22⋊Dic73—21no—
258C22⋊Dic73—21no—
259#11924005—21no—
260#11924005—21no—
261C4×Dic73—21no—
262C24×C73#4111yescharacteristic
263C22×C4×C73—21no—
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—24no—
269C22×C4×C73—21no—
270C22×C4×C73—42no—
271C22×C4×C73—42no—
272C22×C4×C73C22×C411yescharacteristic
273C22×C4×C73C22×C411yescharacteristic
274C22×C4×C73C2×D411yescharacteristic
275C22×C4×C73C2×D411yescharacteristic
276C22×C4×C73#4111yescharacteristic
277C22×C4×C73C2411yescharacteristic
278C2×C8×C73—21no—
279C2×C8×C73—21no—
280C2×C8×C73—21no—
281C2×C8×C73—21no—
282C2×C8×C73—21no—
283C2×C8×C73—21no—
284C2×C8×C73—21no—
285C2×C8×C73—21no—
286C2×C8×C73C22×C411yescharacteristic
287C2×C8×C73C22×C411yescharacteristic
288C2×C8×C73C22×C411yescharacteristic
289C2×C8×C73C22×C411yescharacteristic
290C2×C8×C73C2×D411yescharacteristic
291C2×C8×C73C2×D411yescharacteristic
292C2×C8×C73C2×D411yescharacteristic
293C2×C8×C73C2×D411yescharacteristic
294C42×C73—21no—
295C42×C73—21no—
296C42×C73—21no—
297C42×C73—42no—
298C42×C73C2×D412yes—
299C23×C73—21no—
300C23×C73—21no—
301C23×C73—22no—
302C23×C73—41no—
303C23×C73C4×D411yescharacteristic
304C23×C73C4×D411yescharacteristic
305C23×C73C2×#4111yescharacteristic
306C22×D73—21no—
307C22×D73—21no—
308C22×D73—21no—
309C22×D73—42no—
310C22×D73—42no—
311C22×D73—81no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—22no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—22no—
326C2×C4×C73—48no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73C4×D411yescharacteristic
330C2×C4×C73C4×D411yescharacteristic
331C2×C4×C73C23×C411yescharacteristic
332C2×C4×C73C22×D411yescharacteristic
333C2×C4×C73C22×D411yescharacteristic
334C2×C4×C73C2×#4111yescharacteristic
335C2×C4×C73H(5,𝔽2)11yescharacteristic
336C2×C4×C73H(5,𝔽2)11yescharacteristic
337C22⋊D73—22no—
338C22⋊D73—22no—
339C22⋊D73—42no—
340C22⋊D73—42no—
341C22⋊D73—41no—
342C22⋊D73—41no—
343C22⋊D73—41no—
344C22⋊D73—41no—
345C22⋊D73—42no—
346C22⋊D73—81no—
347C2×Dic73—21no—
348C2×Dic73—21no—
349C2×Dic73—21no—
350C2×Dic73—21no—
351C2×Dic73—21no—
352C2×Dic73—42no—
353D292—21no—
354D292—21no—
355D292—21no—
356D292—21no—
357D292—21no—
358D292—42no—
359D292C4×D412yes—
360C4×D73—22no—
361C4×D73—22no—
362C4×D73—42no—
363C4×D73—42no—
364C4×D73—41no—
365C4×D73—41no—
366C4×D73—41no—
367C4×D73—41no—
368Dic146—21no—
369Dic146—21no—
370Dic146—21no—
371Dic146—21no—
372Dic146—21no—
373Dic146—42no—
374Dic146C4×D412yes—
375C8×C73—21no—
376C8×C73—21no—
377C8×C73—21no—
378C8×C73—21no—
379C8×C73—21no—
380C8×C73—21no—
381C8×C73—21no—
382C8×C73—21no—
383#10596831—22no—
384#10596831—41no—
385#10596831—41no—
386#10596831—41no—
387C22×C73—21no—
388C22×C73—21no—
389C22×C73—21no—
390C22×C73—21no—
391C22×C73—21no—
392C22×C73—21no—
393C22×C73—21no—
394C22×C73—42no—
395C22×C73—42no—
396C22×C73#44312yescomplemented
397C22×C73C2×C4×D411yescharacteristic
398C22×C73#54611yescharacteristic
399C22×C73#55111yescharacteristic
400C2×D73—22no—
401C2×D73—41no—
402C2×D73—41no—
403C2×D73—41no—
404C2×D73—41no—
405C2×D73—41no—
406C2×D73—41no—
407C2×D73—41no—
408C2×D73—41no—
409C2×D73—84no—
410C4×C73—24no—
411C4×C73—21no—
412C4×C73—21no—
413C4×C73—42no—
414C4×C73C2×C4×D411yescharacteristic
415C4×C73#51811yescharacteristic
416C4×C73D4211yescharacteristic
417C4×C73#54611yescharacteristic
418Dic73—22no—
419Dic73—41no—
420Dic73—41no—
421Dic73—41no—
422Dic73—41no—
423#22888—731nomaximal, Sylow
424C2×C73—21no—
425C2×C73—22no—
426C2×C73—21no—
427C2×C73—41no—
428C2×C73#235811yescharacteristic
429C2×C73C2×#44311yescharacteristic
430C2×C73#295611yescharacteristic
431D73—42no—
432D73—81no—
433D73—81no—
434#3002—731no—
435C2×#443—731no—
436#2933—731no—
437C22×#104—731no—
438#2880—731no—
439#1974—731no—
440#1937—731no—
441#1929—731no—
442#1896—731no—
443#1876—731no—
444#1876—731no—
445#1866—731no—
446#1855—731no—
447#1764—731no—
448C4×C22⋊C8D7311yescharacteristic, complemented
449C73#2288811yescharacteristic, complemented, Sylow
450C22×#41—731no—
451C2×#135—731no—
452C2×#135—731no—
453C2×#131—731no—
454C2×#131—731no—
455C2×#131—731no—
456C22×M16—731no—
457#525—731no—
458C22×C42C2×D7311yescharacteristic
459#452—731no—
460#452—731no—
461#451—731no—
462#450—731no—
463#449—731no—
464#449—731no—
465#448—731no—
466#447—731no—
467#443—1464no—
468#436—1461no—
469#435—1461no—
470#435—1461no—
471C8×D4—1461no—
472C2×#108—731no—
473C2×#108—731no—
474#424—731no—
475C2×#104—731no—
476C2×#104—731no—
477C2×#104—731no—
478C2×#104—731no—
479C2×#104—731no—
480C2×#104—731no—
481C2×#104—1464no—
482#416—731no—
483#416—731no—
484#408—731no—
485#408—731no—
486#408—731no—
487#408—1461no—
488#408—1461no—
489#407—731no—
490#407—1461no—
491C2×C22⋊C8—1461no—
492C2×C22⋊C8C2×D7311yescharacteristic
493C2×C22⋊C8C2×D7311yescharacteristic
494#405—731no—
495C2×C4×C8C2×D7311yescharacteristic, complemented
496C2×C4×C8C2×D7311yescharacteristic, complemented
497#341—731no—
498#341—731no—
499#339—731no—
500#339—731no—
501#336C2×D7311yescharacteristic, complemented
502#336C2×D7311yescharacteristic, complemented
503C2×#41—2921no—
504C2×#41—2921no—
505C2×#41—731no—
506C2×#41—731no—
507C2×#41—731no—
508C2×#41—731no—
509C2×#41—731no—
510C2×#41—1462no—
511C2×#41—1462no—
512C2×#41—1461no—
513C2×#41—1461no—
514C22×Q8—731no—
515C22×D4—731no—
516C22×D4—1461no—
517C23×C4—21no—
518C23×C4—1461no—
519C23×C4C22×D7311yescharacteristic
520#135—2921no—
521#135—2921no—
522#135—1462no—
523#135—1462no—
524C2×Q16—731no—
525C2×Q16—731no—
526C2×SD16—731no—
527C2×SD16—731no—
528C2×SD16—731no—
529C2×SD16—731no—
530C2×D8—731no—
531C2×D8—731no—
532#131—2921no—
533#131—2921no—
534#131—2921no—
535#131—1462no—
536#131—1462no—
537#131—1462no—
538C2×M16—2921no—
539C2×M16—731no—
540C2×M16—731no—
541C2×M16—731no—
542C2×M16—731no—
543C2×M16—1462no—
544C2×M16—1461no—
545C2×M16—1461no—
546C2×M16—1461no—
547C2×M16—1461no—
548C22×C8—1461no—
549C22×C8—1461no—
550C22×C8—1461no—
551C22×C8—1461no—
552C22×C8C22×D7311yescharacteristic
553C22×C8C22×D7311yescharacteristic
554C22×C8C22×D7311yescharacteristic
555C22×C8C22×D7311yescharacteristic
556#123—1461no—
557C22⋊Q8—731no—
558C22⋊Q8—731no—
559#121—731no—
560#121—731no—
561#120—1461no—
562C4×D4—1461no—
563C4×D4—1461no—
564#117—731no—
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C22×D7311yescharacteristic
569C2×C42C22×D7311yescharacteristic
570#108—2921no—
571#108—1462no—
572C4⋊C8—1461no—
573C4⋊C8—1461no—
574#104—2921no—
575#104—734no—
576#104—1462no—
577#104—1462no—
578#104—1462no—
579#104—1462no—
580#103—731no—
581#103—731no—
582#103—731no—
583#103—731no—
584#102—731no—
585#102—731no—
586#102—731no—
587#102—731no—
588C22⋊C8—1461no—
589C22⋊C8—1461no—
590C22⋊C8—1461no—
591C22⋊C8—1461no—
592C22⋊C8—1461no—
593C22⋊C8—1461no—
594C22⋊C8—1461no—
595C22⋊C8—1461no—
596C22⋊C8C4×D7311yescharacteristic
597C22⋊C8C4×D7311yescharacteristic
598C22⋊C8C4×D7311yescharacteristic
599C22⋊C8C4×D7311yescharacteristic
600C22⋊C8D29211yescharacteristic
601C22⋊C8D29211yescharacteristic
602C22⋊C8D29211yescharacteristic
603C22⋊C8D29211yescharacteristic
604#97—1461no—
605C4×C8—22no—
606C4×C8—41no—
607C4×C8—1461no—
608C24—1461no—
609C24#1192402811yescharacteristic
610#41—2922no—
611#41—2922no—
612#41—2921no—
613#41—2921no—
614#41—2922no—
615#41—2922no—
616#41—732no—
617#41—732no—
618#41—1462no—
619#41—1462no—
620#41—1461no—
621#41—1461no—
622#41—1461no—
623#41—1461no—
624#41—1461no—
625#41—1461no—
626#41—1461no—
627#41—1461no—
628#41—1461no—
629#41—1461no—
630C2×Q8—2921no—
631C2×Q8—731no—
632C2×Q8—731no—
633C2×Q8—731no—
634C2×Q8—1462no—
635C2×Q8—1461no—
636C2×D4—2921no—
637C2×D4—2922no—
638C2×D4—2922no—
639C2×D4—731no—
640C2×D4—731no—
641C2×D4—731no—
642C2×D4—1462no—
643C2×D4—1461no—
644C2×D4—1461no—
645C2×D4—1461no—
646C2×D4—1461no—
647C2×D4—1461no—
648C2×D4—1461no—
649C2×D4—1461no—
650C2×D4—1461no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—24no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—2922no—
661C22×C4—2922no—
662C22×C4—1461no—
663C22×C4—1461no—
664C22×C4—1461no—
665C22×C4—1461no—
666C22×C4—1461no—
667C22×C4—1461no—
668C22×C4C2×C4×D7311yescharacteristic
669C22×C4C2×C4×D7311yescharacteristic
670C22×C4C2×D29211yescharacteristic
671C22×C4C2×D29211yescharacteristic
672C22×C4#1192402811yescharacteristic
673C22×C4C23×D7311yescharacteristic
674Q16—2921no—
675Q16—1462no—
676SD16—2921no—
677SD16—2921no—
678SD16—1462no—
679SD16—1462no—
680D8—2921no—
681D8—1462no—
682M16—2922no—
683M16—2922no—
684M16—2922no—
685M16—2922no—
686M16—732no—
687M16—1461no—
688M16—1461no—
689M16—1461no—
690M16—1461no—
691M16—1461no—
692M16—1461no—
693M16—1461no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8—21no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—2922no—
703C2×C8—2922no—
704C2×C8—2922no—
705C2×C8—2922no—
706C2×C8—1461no—
707C2×C8—1461no—
708C2×C8—1461no—
709C2×C8—1461no—
710C2×C8C2×C4×D7311yescharacteristic
711C2×C8C2×C4×D7311yescharacteristic
712C2×C8C2×C4×D7311yescharacteristic
713C2×C8C2×C4×D7311yescharacteristic
714C2×C8C2×D29211yescharacteristic
715C2×C8C2×D29211yescharacteristic
716C2×C8C2×D29211yescharacteristic
717C2×C8C2×D29211yescharacteristic
718C4⋊C4—731no—
719C4⋊C4—731no—
720C4⋊C4—1461no—
721C4⋊C4—1461no—
722C22⋊C4—1461no—
723C22⋊C4—1461no—
724C22⋊C4—1461no—
725C22⋊C4—1461no—
726C22⋊C4—1461no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—42no—
731C42—1461no—
732C42D4×D7312yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—41no—
737C23—2922no—
738C23—2922no—
739C23—5841no—
740C23—1461no—
741C23—1461no—
742C23—1461no—
743C23C4×D29211yescharacteristic
744C23C4×D29211yescharacteristic
745C23C2×#1192402811yescharacteristic
746Q8—2922no—
747Q8—732no—
748Q8—1461no—
749Q8—1461no—
750Q8—1461no—
751Q8—1461no—
752Q8—1461no—
753D4—2922no—
754D4—2922no—
755D4—2922no—
756D4—2921no—
757D4—2921no—
758D4—2921no—
759D4—2921no—
760D4—2922no—
761D4—5841no—
762D4—732no—
763D4—1462no—
764D4—1462no—
765D4—1461no—
766D4—1461no—
767D4—1461no—
768D4—1461no—
769D4—1461no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—22no—
784C2×C4—48no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—2922no—
788C2×C4—2922no—
789C2×C4—2922no—
790C2×C4—2921no—
791C2×C4—2921no—
792C2×C4—2921no—
793C2×C4—2921no—
794C2×C4—1461no—
795C2×C4—1461no—
796C2×C4—1461no—
797C2×C4—1461no—
798C2×C4—1461no—
799C2×C4—1462no—
800C2×C4—1462no—
801C2×C4C4×D29211yescharacteristic
802C2×C4C4×D29211yescharacteristic
803C2×C4C22×C4×D7311yescharacteristic
804C2×C4C2×D4×D7311yescharacteristic
805C2×C4C22×D29211yescharacteristic
806C2×C4#41×D7311yescharacteristic
807C2×C4#1455663611yescharacteristic
808C2×C4#1455663711yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—21no—
814C8—21no—
815C8—21no—
816C8—21no—
817C8—2921no—
818C8—2921no—
819C8—2921no—
820C8—1462no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—21no—
827C22—21no—
828C22—42no—
829C22—42no—
830C22—2921no—
831C22—2921no—
832C22—2921no—
833C22—2921no—
834C22—2921no—
835C22—2921no—
836C22—2921no—
837C22—2921no—
838C22—5844no—
839C22—1462no—
840C22#1798870512yescomplemented
841C22C2×C4×D29211yescharacteristic
842C22#1798922711yescharacteristic
843C22#1798926111yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—42no—
848C4—2921no—
849C4—2921no—
850C4—2921no—
851C4—2921no—
852C4—1462no—
853C4C4×D4×D7311yescharacteristic
854C4#1798905911yescharacteristic
855C4D4×D29211yescharacteristic
856C4#1798923211yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—2922no—
862C2—5841no—
863C2—5841no—
864C2#2261291311yescharacteristic
865C2C2×#1798870511yescharacteristic
866C2#2261884211yescharacteristic
subgroupG/H
centerC2×C4C22×D292
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC4×C22⋊C8×C73C2
socleC22×C73C2×C4×D4
prime radical#22619153C2
cosocleC22×C4×C73C24
hypercenterC4×C22⋊C8D73
hypocenterC73#22888
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ C4×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#17988705C2semidirect
3. #22618652C2semidirect
4. C22×#14556519C2semidirect
5. #22618377C2semidirect
6. #22610819C2semidirect
7. #22610635C2semidirect
8. #22610580C2semidirect
9. #22610374C2semidirect
10. #22610257C2semidirect
11. #22610257C2semidirect
12. #22610209C2semidirect
13. #22610138C2semidirect
14. #22609768C2semidirect
15. C4×C22⋊C8×C73C2semidirect
21. C2×#14556597C22semidirect
24. #17988751C4semidirect
25. #17988751C4semidirect
26. #17988745C4semidirect
27. #17988740C4semidirect
28. #17988734C4semidirect
29. #17988734C4semidirect
30. #17988728C4semidirect
31. #17988723C4semidirect
37. C2×#14556527C22semidirect
38. C2×#14556527C22semidirect
39. #17988613C22semidirect
45. C2×#14556519C22semidirect
46. C2×#14556519C22semidirect
51. #17988553C22semidirect
57. #17988542C22semidirect
58. #17988352C22semidirect
59. #17988352C22semidirect
60. #17988347C22semidirect
61. #17988347C22semidirect
65. C2×C4×C8×C73C22semidirect
66. C2×C4×C8×C73C22semidirect
67. #336×C73C22semidirect
68. #336×C73C22semidirect
88. C2×Dic292C2×C4semidirect
89. C2×Dic292C2×C4semidirect
90. C2×#11924017C2×C4semidirect
91. C2×#11924017C2×C4semidirect
92. C2×#11924017C2×C4semidirect
93. C2×#11924017C2×C4semidirect
94. C2×D584C2×C4semidirect
95. C2×D584C2×C4semidirect
134. #14556519D4semidirect
135. #14556516C2×C4semidirect
136. #14556516C2×C4semidirect
137. #14556516C2×C4semidirect
138. #14556516C2×C4semidirect
139. #14556513C2×C4semidirect
140. #14556513C2×C4semidirect
141. #14556513C2×C4semidirect
142. #14556513C2×C4semidirect
396. C22×C73#443semidirect
448. C4×C22⋊C8D73semidirect
449. C73#22888semidirect
495. C2×C4×C8C2×D73semidirect
496. C2×C4×C8C2×D73semidirect
501. #336C2×D73semidirect
502. #336C2×D73semidirect
840. C22#17988705semidirect

Maximal subgroups

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

subgroupindex
#226191532
C2×#179887052
#226186522
C22×#145565192
#226183772
#226108192
#226106352
#226105802
#226103742
#226102572
#226102092
#226101382
#226097682
C4×C22⋊C8×C732
#2288873