Finite Group Databasebeta

← #33106747

Subgroups — #33106747

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#22619149C211yesmaximal, characteristic
2C2×#17988702C211yesmaximal, characteristic, complemented
3#22618652C211yesmaximal, characteristic, complemented
4C22×#14556518C211yesmaximal, characteristic, complemented
5#22610818C211yesmaximal, characteristic, complemented
6#22610638C211yesmaximal, characteristic, complemented
7#22610576C211yesmaximal, characteristic, complemented
8#22610372C211yesmaximal, characteristic, complemented
9#22610261C211yesmaximal, characteristic, complemented
10#22610258C211yesmaximal, characteristic, complemented
11#22610206C211yesmaximal, characteristic, complemented
12#22610135C211yesmaximal, characteristic, complemented
13#22609766C211yesmaximal, characteristic, complemented
14C22⋊C8×Dic73C211yesmaximal, characteristic, complemented
15C73×#2880C211yesmaximal, characteristic, complemented
16C2×#14556611C2211yescharacteristic
17C2×#14556611C2211yescharacteristic
18C2×#14556597C2211yescharacteristic, complemented
19C22×#11924012C2211yescharacteristic
20#17989098C2211yescharacteristic
21C22×C4×Dic73C2211yescharacteristic
22#17988749C411yescharacteristic, complemented
23#17988749C411yescharacteristic, complemented
24#17988743C411yescharacteristic, complemented
25#17988738C411yescharacteristic, complemented
26#17988732C411yescharacteristic, complemented
27#17988732C411yescharacteristic, complemented
28#17988726C411yescharacteristic, complemented
29#17988721C411yescharacteristic, complemented
30#17988702—24no—
31#17988662—21no—
32#17988661—21no—
33#17988655—21no—
34#17988650—21no—
35C2×#14556526C2211yescharacteristic, complemented
36C2×#14556526C2211yescharacteristic, complemented
37#17988613C2211yescharacteristic, complemented
38C2×#14556518—24no—
39C2×#14556518C2211yescharacteristic
40C2×#14556518C2211yescharacteristic
41C2×#14556518C2211yescharacteristic
42C2×#14556518C2211yescharacteristic
43C2×#14556517C2211yescharacteristic, complemented
44C2×#14556517C2211yescharacteristic, complemented
45#17988583C2211yescharacteristic
46#17988583C2211yescharacteristic
47#17988553C2211yescharacteristic, complemented
48C2×C22⋊#10596831C2211yescharacteristic
49#17988542C2211yescharacteristic, complemented
50C2×C8×Dic73C2211yescharacteristic, complemented
51C2×C8×Dic73C2211yescharacteristic, complemented
52#17988351C2211yescharacteristic, complemented
53#17988351C2211yescharacteristic, complemented
54#17988348C2211yescharacteristic, complemented
55#17988348C2211yescharacteristic, complemented
56#17988341C2211yescharacteristic, complemented
57#17988341C2211yescharacteristic, complemented
58C22×#41×C73C2211yescharacteristic
59C2×#131×C73C2211yescharacteristic
60C2×#131×C73C2211yescharacteristic
61#408×C73—21no—
62#408×C73—21no—
63#408×C73C2211yescharacteristic
64#408×C73C2211yescharacteristic
65#407×C73—21no—
66#407×C73C2211yescharacteristic
67C2×C22⋊C8×C73—21no—
68C2×C22⋊C8×C73C2211yescharacteristic
69C2×#11924028C2311yescharacteristic
70C23×Dic73—21no—
71#14556611—22no—
72#14556611—22no—
73#14556611—41no—
74#14556611—41no—
75C2×#11924018C2×C411yescharacteristic, complemented
76C2×#11924018C2×C411yescharacteristic, complemented
77C2×#11924016C2×C411yescharacteristic, complemented
78C2×#11924016C2×C411yescharacteristic, complemented
79C2×#11924015C2×C411yescharacteristic, complemented
80C2×#11924015C2×C411yescharacteristic, complemented
81C2×#11924013C2×C411yescharacteristic, complemented
82C2×#11924013C2×C411yescharacteristic, complemented
83#14556597—22no—
84#14556597—41no—
85C2×#11924012—22no—
86C2×#11924012—21no—
87C2×#11924012—41no—
88C2×#11924012C2311yescharacteristic
89C2×#11924012C2311yescharacteristic
90C2×#11924011—21no—
91C22×#10596831—21no—
92C22×#10596831C2311yescharacteristic
93C22×#10596831C2311yescharacteristic
94C2×C8×D73—21no—
95#14556574—21no—
96#14556570C2×C411yescharacteristic
97#14556570C2×C411yescharacteristic
98#14556565C2×C411yescharacteristic
99#14556565C2×C411yescharacteristic
100#14556560—21no—
101C4×C22⋊D73—21no—
102C4×C22⋊D73—21no—
103#14556550C2311yescharacteristic
104C2×C4×Dic73—22no—
105C2×C4×Dic73—21no—
106C2×C4×Dic73—41no—
107C2×C4×Dic73C2311yescharacteristic
108C2×C4×Dic73C2311yescharacteristic
109#14556526—22no—
110#14556526—41no—
111#14556520—21no—
112#14556520—21no—
113#14556518—22no—
114#14556518—22no—
115#14556518—22no—
116#14556518D414yescomplemented
117#14556517—22no—
118#14556517—41no—
119#14556515C2×C411yescharacteristic, complemented
120#14556515C2×C411yescharacteristic, complemented
121#14556515C2×C411yescharacteristic, complemented
122#14556515C2×C411yescharacteristic, complemented
123#14556512C2×C411yescharacteristic, complemented
124#14556512C2×C411yescharacteristic, complemented
125#14556512C2×C411yescharacteristic, complemented
126#14556512C2×C411yescharacteristic, complemented
127C22⋊#10596831C2×C411yescharacteristic
128C22⋊#10596831C2×C411yescharacteristic
129C22⋊#10596831C2×C411yescharacteristic
130C22⋊#10596831C2×C411yescharacteristic
131#14556503—21no—
132#14556503—21no—
133#14556501—21no—
134C8×Dic73—22no—
135C8×Dic73—21no—
136C8×Dic73—41no—
137C2×#41×C73—21no—
138C2×#41×C73—21no—
139C2×#41×C73—22no—
140C2×#41×C73—22no—
141C2×#41×C73—41no—
142C2×#41×C73—41no—
143C2×#41×C73C2×C411yescharacteristic
144C2×#41×C73C2×C411yescharacteristic
145C2×#41×C73C2311yescharacteristic
146C2×#41×C73C2311yescharacteristic
147C22×Q8×C73C2×C411yescharacteristic
148C22×D4×C73—21no—
149C22×D4×C73C2×C411yescharacteristic
150C23×C4×C73—21no—
151C23×C4×C73C2311yescharacteristic
152#131×C73—22no—
153#131×C73—22no—
154#131×C73—41no—
155#131×C73—41no—
156C2×M16×C73—21no—
157C2×M16×C73—21no—
158C2×M16×C73C2311yescharacteristic
159C2×M16×C73C2311yescharacteristic
160C22×C8×C73—21no—
161C22×C8×C73—21no—
162C22×C8×C73C2311yescharacteristic
163C22×C8×C73C2311yescharacteristic
164C22⋊C8×C73—21no—
165C22⋊C8×C73—21no—
166C22⋊C8×C73—21no—
167C22⋊C8×C73—21no—
168C22⋊C8×C73—21no—
169C22⋊C8×C73—21no—
170C22⋊C8×C73D411yescharacteristic
171C22⋊C8×C73D411yescharacteristic
172C22⋊C8×C73D411yescharacteristic
173C22⋊C8×C73D411yescharacteristic
174#11924028—21no—
175#11924028—21no—
176#11924028—21no—
177#11924028—21no—
178C2×Dic146C22×C411yescharacteristic
179C2×D292C22×C411yescharacteristic
180C2×C22⋊D73—21no—
181C2×C22⋊D73—21no—
182C2×C22⋊D73—21no—
183C22×Dic73—21no—
184C22×Dic73—24no—
185C22×Dic73—21no—
186C22×Dic73—42no—
187C22×Dic73—42no—
188C2×C4×D73—21no—
189#11924018—22no—
190#11924018—41no—
191#11924016—22no—
192#11924016—41no—
193#11924015—22no—
194#11924015—41no—
195#11924013—22no—
196#11924013—41no—
197#11924012—21no—
198#11924012—21no—
199#11924012—21no—
200#11924012—42no—
201#11924012C2×D412yes—
202#11924011—42no—
203C2×#10596831—21no—
204C2×#10596831—21no—
205C2×#10596831—21no—
206C2×#10596831—21no—
207C2×#10596831—21no—
208C2×#10596831—21no—
209C2×#10596831—42no—
210C2×#10596831C22×C411yescharacteristic
211C2×#10596831C22×C411yescharacteristic
212C2×#10596831C22×C411yescharacteristic
213C2×#10596831C22×C411yescharacteristic
214C8×D73—42no—
215C4⋊Dic73C22×C411yescharacteristic
216C4⋊Dic73C22×C411yescharacteristic
217#11924007—21no—
218#11924007—21no—
219C22⋊Dic73—21no—
220C22⋊Dic73—21no—
221C22⋊Dic73—21no—
222#11924005—21no—
223#11924005—21no—
224C4×Dic73—21no—
225C4×Dic73—21no—
226C4×Dic73—21no—
227C4×Dic73—21no—
228C4×Dic73—42no—
229C4×Dic73C2×D412yes—
230C24×C73—21no—
231C24×C73#4111yescharacteristic
232#41×C73—21no—
233#41×C73—21no—
234#41×C73—22no—
235#41×C73—22no—
236#41×C73—21no—
237#41×C73—21no—
238#41×C73—21no—
239#41×C73—21no—
240#41×C73—42no—
241#41×C73—42no—
242#41×C73—41no—
243#41×C73—41no—
244#41×C73—42no—
245#41×C73—42no—
246#41×C73C2×D412yes—
247#41×C73#4112yes—
248C2×Q8×C73—21no—
249C2×Q8×C73—22no—
250C2×Q8×C73—41no—
251C2×Q8×C73C22×C411yescharacteristic
252C2×Q8×C73C22×C411yescharacteristic
253C2×D4×C73—21no—
254C2×D4×C73—22no—
255C2×D4×C73—21no—
256C2×D4×C73—21no—
257C2×D4×C73—21no—
258C2×D4×C73—21no—
259C2×D4×C73—41no—
260C2×D4×C73—42no—
261C2×D4×C73—42no—
262C2×D4×C73C22×C411yescharacteristic
263C2×D4×C73C22×C411yescharacteristic
264C22×C4×C73—21no—
265C22×C4×C73—21no—
266C22×C4×C73—21no—
267C22×C4×C73—21no—
268C22×C4×C73—21no—
269C22×C4×C73—21no—
270C22×C4×C73—21no—
271C22×C4×C73—21no—
272C22×C4×C73—21no—
273C22×C4×C73—42no—
274C22×C4×C73—42no—
275C22×C4×C73C22×C411yescharacteristic
276C22×C4×C73C22×C411yescharacteristic
277C22×C4×C73C2×D411yescharacteristic
278C22×C4×C73C2×D411yescharacteristic
279C22×C4×C73#4111yescharacteristic
280C22×C4×C73C2411yescharacteristic
281M16×C73—21no—
282M16×C73—21no—
283M16×C73—21no—
284M16×C73—21no—
285M16×C73—42no—
286M16×C73—42no—
287C2×C8×C73—21no—
288C2×C8×C73—21no—
289C2×C8×C73—21no—
290C2×C8×C73—21no—
291C2×C8×C73—21no—
292C2×C8×C73—21no—
293C2×C8×C73—42no—
294C2×C8×C73—42no—
295C2×C8×C73C2×D411yescharacteristic
296C2×C8×C73C2×D411yescharacteristic
297C2×C8×C73C2×D411yescharacteristic
298C2×C8×C73C2×D411yescharacteristic
299C23×C73—21no—
300C23×C73—21no—
301C23×C73—21no—
302C23×C73—22no—
303C23×C73—21no—
304C23×C73—41no—
305C23×C73—42no—
306C23×C73—42no—
307C23×C73—81no—
308C23×C73C4×D411yescharacteristic
309C23×C73C4×D411yescharacteristic
310C23×C73C2×#4111yescharacteristic
311C22×D73—21no—
312Q8×C73—21no—
313Q8×C73—21no—
314Q8×C73—21no—
315Q8×C73—42no—
316Q8×C73C4×D412yes—
317D4×C73—22no—
318D4×C73—22no—
319D4×C73—21no—
320D4×C73—21no—
321D4×C73—21no—
322D4×C73—42no—
323D4×C73—42no—
324D4×C73—42no—
325D4×C73—41no—
326D4×C73—41no—
327D4×C73C4×D412yes—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—22no—
336C2×C4×C73—21no—
337C2×C4×C73—21no—
338C2×C4×C73—22no—
339C2×C4×C73—21no—
340C2×C4×C73—21no—
341C2×C4×C73—21no—
342C2×C4×C73—42no—
343C2×C4×C73—42no—
344C2×C4×C73—42no—
345C2×C4×C73—41no—
346C2×C4×C73—41no—
347C2×C4×C73C4×D411yescharacteristic
348C2×C4×C73C4×D411yescharacteristic
349C2×C4×C73C23×C411yescharacteristic
350C2×C4×C73C22×D411yescharacteristic
351C2×C4×C73C22×D411yescharacteristic
352C2×C4×C73C2×#4111yescharacteristic
353C2×C4×C73H(5,𝔽2)11yescharacteristic
354C2×C4×C73H(5,𝔽2)11yescharacteristic
355C22⋊D73—41no—
356C22⋊D73—41no—
357C22⋊D73—42no—
358C22⋊D73—81no—
359C2×Dic73—22no—
360C2×Dic73—22no—
361C2×Dic73—22no—
362C2×Dic73—22no—
363C2×Dic73—21no—
364C2×Dic73—21no—
365C2×Dic73—21no—
366C2×Dic73—48no—
367C2×Dic73—41no—
368C2×Dic73—41no—
369D292—21no—
370D292—21no—
371C4×D73—41no—
372C4×D73—41no—
373Dic146—21no—
374Dic146—21no—
375C8×C73—21no—
376C8×C73—21no—
377C8×C73—21no—
378C8×C73—21no—
379C8×C73—41no—
380C8×C73—41no—
381#10596831—21no—
382#10596831—21no—
383#10596831—21no—
384#10596831—21no—
385#10596831—22no—
386#10596831—41no—
387C22×C73—21no—
388C22×C73—21no—
389C22×C73—21no—
390C22×C73—21no—
391C22×C73—21no—
392C22×C73—22no—
393C22×C73—21no—
394C22×C73—21no—
395C22×C73—42no—
396C22×C73—42no—
397C22×C73—41no—
398C22×C73—41no—
399C22×C73—41no—
400C22×C73—41no—
401C22×C73—41no—
402C22×C73—84no—
403C22×C73#44312yescomplemented
404C22×C73C2×C4×D411yescharacteristic
405C22×C73#54611yescharacteristic
406C22×C73#55111yescharacteristic
407C2×D73—41no—
408C2×D73—41no—
409C2×D73—41no—
410C4×C73—21no—
411C4×C73—21no—
412C4×C73—22no—
413C4×C73—41no—
414C4×C73C2×C4×D411yescharacteristic
415C4×C73#51811yescharacteristic
416C4×C73D4211yescharacteristic
417C4×C73#54611yescharacteristic
418Dic73—24no—
419Dic73—42no—
420Dic73—41no—
421Dic73—41no—
422Dic73—41no—
423#22888—731nomaximal, Sylow
424C2×C73—21no—
425C2×C73—22no—
426C2×C73—21no—
427C2×C73—41no—
428C2×C73—42no—
429C2×C73—81no—
430C2×C73#235811yescharacteristic
431C2×C73C2×#44311yescharacteristic
432C2×C73#295611yescharacteristic
433D73—81no—
434#3002—731no—
435C2×#443—731no—
436#2933—731no—
437C22×#104—731no—
438#2880D7311yescharacteristic, complemented
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⋊C8—731no—
449C73#2288811yescharacteristic, complemented, Sylow
450C22×#41C2×D7311yescharacteristic
451C2×#135—731no—
452C2×#135—731no—
453C2×#131—731no—
454C2×#131C2×D7311yescharacteristic
455C2×#131C2×D7311yescharacteristic
456C22×M16—731no—
457#525—731no—
458C22×C42—731no—
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—21no—
485#408—21no—
486#408—731no—
487#408C2×D7311yescharacteristic
488#408C2×D7311yescharacteristic
489#407—21no—
490#407C2×D7311yescharacteristic
491C2×C22⋊C8—21no—
492C2×C22⋊C8—731no—
493C2×C22⋊C8C2×D7311yescharacteristic
494#405—731no—
495C2×C4×C8—731no—
496C2×C4×C8—731no—
497#341—731no—
498#341—731no—
499#339—731no—
500#339—731no—
501#336—731no—
502#336—731no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—731no—
510C2×#41C4×D7311yescharacteristic
511C2×#41C4×D7311yescharacteristic
512C2×#41C22×D7311yescharacteristic
513C2×#41C22×D7311yescharacteristic
514C22×Q8C4×D7311yescharacteristic
515C22×D4—21no—
516C22×D4C4×D7311yescharacteristic
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—22no—
533#131—22no—
534#131—41no—
535#131—41no—
536#131—2921no—
537#131—1462no—
538C2×M16—21no—
539C2×M16—21no—
540C2×M16—2921no—
541C2×M16—731no—
542C2×M16—731no—
543C2×M16—1462no—
544C2×M16—1461no—
545C2×M16—1461no—
546C2×M16C22×D7311yescharacteristic
547C2×M16C22×D7311yescharacteristic
548C22×C8—21no—
549C22×C8—21no—
550C22×C8—731no—
551C22×C8—731no—
552C22×C8—1461no—
553C22×C8—1461no—
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—2921no—
566C2×C42—731no—
567C2×C42—731no—
568C2×C42—1461no—
569C2×C42—1462no—
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—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—21no—
592C22⋊C8—21no—
593C22⋊C8—21no—
594C22⋊C8—731no—
595C22⋊C8—731no—
596C22⋊C8—731no—
597C22⋊C8—731no—
598C22⋊C8—1461no—
599C22⋊C8—1461no—
600C22⋊C8C22⋊D7311yescharacteristic
601C22⋊C8C22⋊D7311yescharacteristic
602C22⋊C8C22⋊D7311yescharacteristic
603C22⋊C8C22⋊D7311yescharacteristic
604#97—1461no—
605C4×C8—2921no—
606C4×C8—1462no—
607C4×C8—1461no—
608C24—21no—
609C24#1192402811yescharacteristic
610#41—21no—
611#41—21no—
612#41—22no—
613#41—22no—
614#41—21no—
615#41—21no—
616#41—21no—
617#41—21no—
618#41—42no—
619#41—42no—
620#41—41no—
621#41—41no—
622#41—42no—
623#41—42no—
624#41—1461no—
625#41—1461no—
626#41—1461no—
627#41—1461no—
628#41D4×D7312yes—
629#41#1192402712yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8—731no—
634C2×Q8C2×C4×D7311yescharacteristic
635C2×Q8C2×C4×D7311yescharacteristic
636C2×D4—21no—
637C2×D4—22no—
638C2×D4—21no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—41no—
643C2×D4—42no—
644C2×D4—42no—
645C2×D4—731no—
646C2×D4—1461no—
647C2×D4—1461no—
648C2×D4—1461no—
649C2×D4C2×C4×D7311yescharacteristic
650C2×D4C2×C4×D7311yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—42no—
661C22×C4—42no—
662C22×C4—2922no—
663C22×C4—2922no—
664C22×C4—1464no—
665C22×C4—1461no—
666C22×C4—1461no—
667C22×C4—1461no—
668C22×C4C2×C4×D7311yescharacteristic
669C22×C4C2×C4×D7311yescharacteristic
670C22×C4C2×C22⋊D7311yescharacteristic
671C22×C4C2×C22⋊D7311yescharacteristic
672C22×C4#1192402811yescharacteristic
673C22×C4C23×D7311yescharacteristic
674Q16—2921no—
675Q16—1462no—
676SD16—2921no—
677SD16—2921no—
678SD16—1462no—
679SD16—1462no—
680D8—2921no—
681D8—1462no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—21no—
686M16—42no—
687M16—42no—
688M16—2922no—
689M16—2922no—
690M16—732no—
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—42no—
701C2×C8—42no—
702C2×C8—2922no—
703C2×C8—2922no—
704C2×C8—731no—
705C2×C8—731no—
706C2×C8—731no—
707C2×C8—731no—
708C2×C8—1461no—
709C2×C8—1461no—
710C2×C8—1461no—
711C2×C8—1461no—
712C2×C8—1461no—
713C2×C8—1461no—
714C2×C8C2×C22⋊D7311yescharacteristic
715C2×C8C2×C22⋊D7311yescharacteristic
716C2×C8C2×C22⋊D7311yescharacteristic
717C2×C8C2×C22⋊D7311yescharacteristic
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—2922no—
728C42—732no—
729C42—1461no—
730C42—1461no—
731C42—1461no—
732C42—1461no—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—81no—
742C23—1461no—
743C23C4×C22⋊D7311yescharacteristic
744C23C4×C22⋊D7311yescharacteristic
745C23C2×#1192402811yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—42no—
750Q8—1461no—
751Q8—1461no—
752Q8#1455655112yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—2922no—
764D4—2921no—
765D4—2921no—
766D4—5841no—
767D4—1461no—
768D4—1461no—
769D4#1455655112yes—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—22no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—42no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—2921no—
790C2×C4—2921no—
791C2×C4—2928no—
792C2×C4—2921no—
793C2×C4—2921no—
794C2×C4—1462no—
795C2×C4—1461no—
796C2×C4—1461no—
797C2×C4—1461no—
798C2×C4—1462no—
799C2×C4—1462no—
800C2×C4—1462no—
801C2×C4C4×C22⋊D7311yescharacteristic
802C2×C4C4×C22⋊D7311yescharacteristic
803C2×C4C22×C4×D7311yescharacteristic
804C2×C4C2×D4×D7311yescharacteristic
805C2×C4C22×C22⋊D7311yescharacteristic
806C2×C4C2×#1192402711yescharacteristic
807C2×C4#1455663611yescharacteristic
808C2×C4#1455663611yescharacteristic
809C8—21no—
810C8—21no—
811C8—21no—
812C8—21no—
813C8—41no—
814C8—41no—
815C8—2921no—
816C8—1462no—
817C8—1461no—
818C8—1461no—
819C8—1461no—
820C8—1461no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—22no—
827C22—21no—
828C22—21no—
829C22—42no—
830C22—42no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—41no—
836C22—84no—
837C22—2921no—
838C22—2921no—
839C22—2921no—
840C22#1798870212yescomplemented
841C22C2×C4×C22⋊D7311yescharacteristic
842C22#1798922711yescharacteristic
843C22#1798926311yescharacteristic
844C4—21no—
845C4—21no—
846C4—22no—
847C4—41no—
848C4—2922no—
849C4—2921no—
850C4—2921no—
851C4—2921no—
852C4—1464no—
853C4C2×#1455655111yescharacteristic
854C4#1798906011yescharacteristic
855C4D4×C22⋊D7311yescharacteristic
856C4#1798923111yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—5841no—
864C2#2261291011yescharacteristic
865C2C2×#1798870211yescharacteristic
866C2#2261883811yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D73
commutatorC2×C4×C73C23×C4
FrattiniC22×C4C23×D73
FittingC73×#2880C2
socleC22×C73C2×C4×D4
prime radical#22619149C2
cosocleC22×C4×C73C24
hypercenter#2880D73
hypocenterC73#22888
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C22⋊C8 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. C2×#17988702C2semidirect
3. #22618652C2semidirect
4. C22×#14556518C2semidirect
5. #22610818C2semidirect
6. #22610638C2semidirect
7. #22610576C2semidirect
8. #22610372C2semidirect
9. #22610261C2semidirect
10. #22610258C2semidirect
11. #22610206C2semidirect
12. #22610135C2semidirect
13. #22609766C2semidirect
14. C22⋊C8×Dic73C2semidirect
15. C73×#2880C2semidirect
18. C2×#14556597C22semidirect
22. #17988749C4semidirect
23. #17988749C4semidirect
24. #17988743C4semidirect
25. #17988738C4semidirect
26. #17988732C4semidirect
27. #17988732C4semidirect
28. #17988726C4semidirect
29. #17988721C4semidirect
35. C2×#14556526C22semidirect
36. C2×#14556526C22semidirect
37. #17988613C22semidirect
43. C2×#14556517C22semidirect
44. C2×#14556517C22semidirect
47. #17988553C22semidirect
49. #17988542C22semidirect
50. C2×C8×Dic73C22semidirect
51. C2×C8×Dic73C22semidirect
52. #17988351C22semidirect
53. #17988351C22semidirect
54. #17988348C22semidirect
55. #17988348C22semidirect
56. #17988341C22semidirect
57. #17988341C22semidirect
75. C2×#11924018C2×C4semidirect
76. C2×#11924018C2×C4semidirect
77. C2×#11924016C2×C4semidirect
78. C2×#11924016C2×C4semidirect
79. C2×#11924015C2×C4semidirect
80. C2×#11924015C2×C4semidirect
81. C2×#11924013C2×C4semidirect
82. C2×#11924013C2×C4semidirect
116. #14556518D4semidirect
119. #14556515C2×C4semidirect
120. #14556515C2×C4semidirect
121. #14556515C2×C4semidirect
122. #14556515C2×C4semidirect
123. #14556512C2×C4semidirect
124. #14556512C2×C4semidirect
125. #14556512C2×C4semidirect
126. #14556512C2×C4semidirect
403. C22×C73#443semidirect
438. #2880D73semidirect
449. C73#22888semidirect
840. C22#17988702semidirect

Maximal subgroups

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

subgroupindex
#226191492
C2×#179887022
#226186522
C22×#145565182
#226108182
#226106382
#226105762
#226103722
#226102612
#226102582
#226102062
#226101352
#226097662
C22⋊C8×Dic732
C73×#28802
#2288873