Finite Group Databasebeta

← #33106762

Subgroups — #33106762

Order 18688.

1020 conjugacy classes of subgroups.

The subgroup lattice has 862 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
4C2×#17988604C211yesmaximal, characteristic, complemented
5#22610823C211yesmaximal, characteristic, complemented
6#22610638C211yesmaximal, characteristic, complemented
7#22610576C211yesmaximal, characteristic, complemented
8#22610377C211yesmaximal, characteristic, complemented
9#22610261C211yesmaximal, characteristic, complemented
10#22610258C211yesmaximal, characteristic, complemented
11#22610206C211yesmaximal, characteristic, complemented
12#22610135C211yesmaximal, characteristic, complemented
13#22609773C211yesmaximal, characteristic, complemented
14#22609699C211yesmaximal, characteristic, complemented
15C73×#2880C211yesmaximal, characteristic, complemented
16C2×#14556611C2211yescharacteristic
17C2×#14556611C2211yescharacteristic
18C2×#14556597C2211yescharacteristic, complemented
19C22×#11924012C2211yescharacteristic
20#17989098C2211yescharacteristic
21C2×#14556550C2211yescharacteristic
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
38#17988604—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×#14556501C2211yescharacteristic, 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
70#14556611—22no—
71#14556611—22no—
72#14556611—41no—
73#14556611—41no—
74C2×#11924018C2×C411yescharacteristic
75C2×#11924018C2×C411yescharacteristic
76C2×#11924016C2×C411yescharacteristic
77C2×#11924016C2×C411yescharacteristic
78C2×#11924015C2×C411yescharacteristic
79C2×#11924015C2×C411yescharacteristic
80C2×#11924013C2×C411yescharacteristic
81C2×#11924013C2×C411yescharacteristic
82#14556597—22no—
83#14556597—41no—
84C2×#11924012—22no—
85C2×#11924012—21no—
86C2×#11924012—41no—
87C2×#11924012C2311yescharacteristic
88C2×#11924012C2311yescharacteristic
89C2×#11924011—21no—
90C22×#10596831—21no—
91C22×#10596831C2311yescharacteristic
92C22×#10596831C2311yescharacteristic
93C2×C8×D73—21no—
94#14556574—21no—
95#14556570C2×C411yescharacteristic
96#14556570C2×C411yescharacteristic
97#14556565C2×C411yescharacteristic
98#14556565C2×C411yescharacteristic
99#14556560—21no—
100C4×C22⋊D73—21no—
101C4×C22⋊D73—21no—
102#14556550—22no—
103#14556550—41no—
104#14556550C2311yescharacteristic
105C2×C4⋊Dic73—21no—
106C2×C22⋊Dic73—21no—
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
120#14556515C2×C411yescharacteristic
121#14556515C2×C411yescharacteristic
122#14556515C2×C411yescharacteristic
123#14556512C2×C411yescharacteristic
124#14556512C2×C411yescharacteristic
125#14556512C2×C411yescharacteristic
126#14556512C2×C411yescharacteristic
127C22⋊#10596831C2×C411yescharacteristic
128C22⋊#10596831C2×C411yescharacteristic
129C22⋊#10596831C2×C411yescharacteristic
130C22⋊#10596831C2×C411yescharacteristic
131#14556503—21no—
132#14556503—21no—
133#14556501—21no—
134#14556501—41no—
135C8×Dic73—22no—
136C8×Dic73—21no—
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—21no—
185C2×C4×D73—21no—
186#11924018—22no—
187#11924018—41no—
188#11924016—22no—
189#11924016—41no—
190#11924015—22no—
191#11924015—41no—
192#11924013—22no—
193#11924013—41no—
194#11924012—21no—
195#11924012—21no—
196#11924012—21no—
197#11924012—42no—
198#11924012C2×D412yes—
199#11924011—42no—
200C2×#10596831—21no—
201C2×#10596831—21no—
202C2×#10596831—21no—
203C2×#10596831—21no—
204C2×#10596831—21no—
205C2×#10596831—21no—
206C2×#10596831—42no—
207C2×#10596831C22×C411yescharacteristic
208C2×#10596831C22×C411yescharacteristic
209C2×#10596831C22×C411yescharacteristic
210C2×#10596831C22×C411yescharacteristic
211C8×D73—42no—
212C4⋊Dic73—42no—
213C4⋊Dic73C22×C411yescharacteristic
214C4⋊Dic73C22×C411yescharacteristic
215#11924007—21no—
216#11924007—21no—
217C22⋊Dic73—21no—
218C22⋊Dic73—21no—
219C22⋊Dic73—21no—
220C22⋊Dic73—42no—
221#11924005—21no—
222#11924005—21no—
223C4×Dic73—21no—
224C4×Dic73—21no—
225C4×Dic73—21no—
226C4×Dic73—21no—
227C4×Dic73C2×D412yes—
228C24×C73—21no—
229C24×C73#4111yescharacteristic
230#41×C73—21no—
231#41×C73—21no—
232#41×C73—22no—
233#41×C73—22no—
234#41×C73—21no—
235#41×C73—21no—
236#41×C73—21no—
237#41×C73—21no—
238#41×C73—42no—
239#41×C73—42no—
240#41×C73—41no—
241#41×C73—41no—
242#41×C73—42no—
243#41×C73—42no—
244#41×C73C2×D412yes—
245#41×C73#4112yes—
246C2×Q8×C73—21no—
247C2×Q8×C73—22no—
248C2×Q8×C73—41no—
249C2×Q8×C73C22×C411yescharacteristic
250C2×Q8×C73C22×C411yescharacteristic
251C2×D4×C73—21no—
252C2×D4×C73—22no—
253C2×D4×C73—21no—
254C2×D4×C73—21no—
255C2×D4×C73—21no—
256C2×D4×C73—21no—
257C2×D4×C73—41no—
258C2×D4×C73—42no—
259C2×D4×C73—42no—
260C2×D4×C73C22×C411yescharacteristic
261C2×D4×C73C22×C411yescharacteristic
262C22×C4×C73—21no—
263C22×C4×C73—21no—
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—42no—
272C22×C4×C73—42no—
273C22×C4×C73C22×C411yescharacteristic
274C22×C4×C73C22×C411yescharacteristic
275C22×C4×C73C2×D411yescharacteristic
276C22×C4×C73C2×D411yescharacteristic
277C22×C4×C73#4111yescharacteristic
278C22×C4×C73C2411yescharacteristic
279M16×C73—21no—
280M16×C73—21no—
281M16×C73—21no—
282M16×C73—21no—
283M16×C73—42no—
284M16×C73—42no—
285C2×C8×C73—21no—
286C2×C8×C73—21no—
287C2×C8×C73—21no—
288C2×C8×C73—21no—
289C2×C8×C73—21no—
290C2×C8×C73—21no—
291C2×C8×C73—42no—
292C2×C8×C73—42no—
293C2×C8×C73C2×D411yescharacteristic
294C2×C8×C73C2×D411yescharacteristic
295C2×C8×C73C2×D411yescharacteristic
296C2×C8×C73C2×D411yescharacteristic
297C23×C73—21no—
298C23×C73—21no—
299C23×C73—21no—
300C23×C73—21no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—42no—
304C23×C73—42no—
305C23×C73—81no—
306C23×C73C4×D411yescharacteristic
307C23×C73C4×D411yescharacteristic
308C23×C73C2×#4111yescharacteristic
309C22×D73—21no—
310Q8×C73—21no—
311Q8×C73—21no—
312Q8×C73—21no—
313Q8×C73—42no—
314Q8×C73C4×D412yes—
315D4×C73—22no—
316D4×C73—22no—
317D4×C73—21no—
318D4×C73—21no—
319D4×C73—21no—
320D4×C73—42no—
321D4×C73—42no—
322D4×C73—42no—
323D4×C73—41no—
324D4×C73—41no—
325D4×C73C4×D412yes—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—22no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—22no—
337C2×C4×C73—21no—
338C2×C4×C73—21no—
339C2×C4×C73—21no—
340C2×C4×C73—42no—
341C2×C4×C73—42no—
342C2×C4×C73—42no—
343C2×C4×C73—41no—
344C2×C4×C73—41no—
345C2×C4×C73C4×D411yescharacteristic
346C2×C4×C73C4×D411yescharacteristic
347C2×C4×C73C23×C411yescharacteristic
348C2×C4×C73C22×D411yescharacteristic
349C2×C4×C73C22×D411yescharacteristic
350C2×C4×C73C2×#4111yescharacteristic
351C2×C4×C73H(5,𝔽2)11yescharacteristic
352C2×C4×C73H(5,𝔽2)11yescharacteristic
353C22⋊D73—42no—
354C22⋊D73—41no—
355C22⋊D73—41no—
356C22⋊D73—81no—
357C2×Dic73—21no—
358C2×Dic73—21no—
359C2×Dic73—21no—
360C2×Dic73—22no—
361C2×Dic73—41no—
362C2×Dic73—41no—
363C2×Dic73—41no—
364C2×Dic73—41no—
365C2×Dic73—41no—
366D292—21no—
367D292—21no—
368C4×D73—41no—
369C4×D73—41no—
370Dic146—21no—
371Dic146—21no—
372C8×C73—21no—
373C8×C73—21no—
374C8×C73—21no—
375C8×C73—21no—
376C8×C73—41no—
377C8×C73—41no—
378#10596831—21no—
379#10596831—21no—
380#10596831—21no—
381#10596831—21no—
382#10596831—22no—
383#10596831—41no—
384C22×C73—21no—
385C22×C73—21no—
386C22×C73—21no—
387C22×C73—21no—
388C22×C73—22no—
389C22×C73—21no—
390C22×C73—21no—
391C22×C73—21no—
392C22×C73—21no—
393C22×C73—41no—
394C22×C73—41no—
395C22×C73—41no—
396C22×C73—41no—
397C22×C73—41no—
398C22×C73—81no—
399C22×C73—81no—
400C22×C73—84no—
401C22×C73C2×C4×D411yescharacteristic
402C22×C73#54611yescharacteristic
403C22×C73#55111yescharacteristic
404C2×D73—41no—
405C2×D73—41no—
406C2×D73—41no—
407C4×C73—21no—
408C4×C73—21no—
409C4×C73—22no—
410C4×C73—41no—
411C4×C73C2×C4×D411yescharacteristic
412C4×C73#51811yescharacteristic
413C4×C73D4211yescharacteristic
414C4×C73#54611yescharacteristic
415Dic73—42no—
416Dic73—41no—
417Dic73—41no—
418Dic73—41no—
419Dic73—81no—
420#22889—731nomaximal, Sylow
421C2×C73—21no—
422C2×C73—21no—
423C2×C73—41no—
424C2×C73—41no—
425C2×C73—42no—
426C2×C73—81no—
427C2×C73#235811yescharacteristic
428C2×C73#295511yescharacteristic
429C2×C73#295711yescharacteristic
430D73—81no—
431#3002—731no—
432C2×#443—731no—
433#2933—731no—
434C2×#421—731no—
435#2880D7311yescharacteristic, complemented
436#1975—731no—
437#1937—731no—
438#1929—731no—
439#1897—731no—
440#1876—731no—
441#1876—731no—
442#1866—731no—
443#1855—731no—
444#1765—731no—
445#1750—731no—
446C73#2288911yescharacteristic, complemented, Sylow
447C22×#41C2×D7311yescharacteristic
448C2×#135—731no—
449C2×#135—731no—
450C2×#131—731no—
451C2×#131C2×D7311yescharacteristic
452C2×#131C2×D7311yescharacteristic
453C22×M16—731no—
454#525—731no—
455C2×#117—731no—
456#452—731no—
457#452—731no—
458#451—731no—
459#450—731no—
460#449—731no—
461#449—731no—
462#448—731no—
463#447—731no—
464#443—1464no—
465#436—1461no—
466#435—1461no—
467#435—1461no—
468C8×D4—1461no—
469C2×#108—731no—
470C2×#108—731no—
471#424—731no—
472#421—1464no—
473C2×#104—731no—
474C2×#104—731no—
475C2×#104—731no—
476C2×#104—731no—
477C2×#104—731no—
478C2×#104—731no—
479#416—731no—
480#416—731no—
481#408—21no—
482#408—21no—
483#408—731no—
484#408C2×D7311yescharacteristic
485#408C2×D7311yescharacteristic
486#407—21no—
487#407C2×D7311yescharacteristic
488C2×C22⋊C8—21no—
489C2×C22⋊C8—731no—
490C2×C22⋊C8C2×D7311yescharacteristic
491#405—731no—
492C2×#97—731no—
493C2×C4×C8—731no—
494#341—731no—
495#341—731no—
496#339—731no—
497#339—731no—
498#336—731no—
499#336—731no—
500C2×#41—21no—
501C2×#41—21no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—731no—
507C2×#41C4×D7311yescharacteristic
508C2×#41C4×D7311yescharacteristic
509C2×#41C22×D7311yescharacteristic
510C2×#41C22×D7311yescharacteristic
511C22×Q8C4×D7311yescharacteristic
512C22×D4—21no—
513C22×D4C4×D7311yescharacteristic
514C23×C4—21no—
515C23×C4C22×D7311yescharacteristic
516#135—2921no—
517#135—2921no—
518#135—1462no—
519#135—1462no—
520C2×Q16—731no—
521C2×Q16—731no—
522C2×SD16—731no—
523C2×SD16—731no—
524C2×SD16—731no—
525C2×SD16—731no—
526C2×D8—731no—
527C2×D8—731no—
528#131—22no—
529#131—22no—
530#131—41no—
531#131—41no—
532#131—2921no—
533#131—1462no—
534C2×M16—21no—
535C2×M16—21no—
536C2×M16—2921no—
537C2×M16—731no—
538C2×M16—731no—
539C2×M16—1462no—
540C2×M16—1461no—
541C2×M16—1461no—
542C2×M16C22×D7311yescharacteristic
543C2×M16C22×D7311yescharacteristic
544C22×C8—21no—
545C22×C8—21no—
546C22×C8—731no—
547C22×C8—731no—
548C22×C8—1461no—
549C22×C8—1461no—
550C22×C8C22×D7311yescharacteristic
551C22×C8C22×D7311yescharacteristic
552#123—1461no—
553C22⋊Q8—731no—
554C22⋊Q8—731no—
555#121—731no—
556#121—731no—
557#120—1461no—
558C4×D4—1461no—
559C4×D4—1461no—
560#117—2921no—
561#117—731no—
562#117—1462no—
563C2×C4⋊C4—1461no—
564C2×C22⋊C4—1461no—
565C2×C42—731no—
566C2×C42—731no—
567#108—2921no—
568#108—1462no—
569C4⋊C8—1461no—
570C4⋊C8—1461no—
571#104—2921no—
572#104—734no—
573#104—1462no—
574#104—1462no—
575#104—1462no—
576#104—1462no—
577#103—731no—
578#103—731no—
579#103—731no—
580#103—731no—
581#102—731no—
582#102—731no—
583#102—731no—
584#102—731no—
585C22⋊C8—21no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8—21no—
591C22⋊C8—731no—
592C22⋊C8—731no—
593C22⋊C8—731no—
594C22⋊C8—731no—
595C22⋊C8—1461no—
596C22⋊C8—1461no—
597C22⋊C8C22⋊D7311yescharacteristic
598C22⋊C8C22⋊D7311yescharacteristic
599C22⋊C8C22⋊D7311yescharacteristic
600C22⋊C8C22⋊D7311yescharacteristic
601#97—2921no—
602#97—1461no—
603C4×C8—1462no—
604C4×C8—1461no—
605C24—21no—
606C24#1192402811yescharacteristic
607#41—21no—
608#41—21no—
609#41—22no—
610#41—22no—
611#41—21no—
612#41—21no—
613#41—21no—
614#41—21no—
615#41—42no—
616#41—42no—
617#41—41no—
618#41—41no—
619#41—42no—
620#41—42no—
621#41—1461no—
622#41—1461no—
623#41—1461no—
624#41—1461no—
625#41D4×D7312yes—
626#41#1192402712yes—
627C2×Q8—21no—
628C2×Q8—22no—
629C2×Q8—41no—
630C2×Q8—731no—
631C2×Q8C2×C4×D7311yescharacteristic
632C2×Q8C2×C4×D7311yescharacteristic
633C2×D4—21no—
634C2×D4—22no—
635C2×D4—21no—
636C2×D4—21no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—41no—
640C2×D4—42no—
641C2×D4—42no—
642C2×D4—731no—
643C2×D4—1461no—
644C2×D4—1461no—
645C2×D4—1461no—
646C2×D4C2×C4×D7311yescharacteristic
647C2×D4C2×C4×D7311yescharacteristic
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—42no—
658C22×C4—42no—
659C22×C4—1461no—
660C22×C4—1461no—
661C22×C4—1461no—
662C22×C4C2×C4×D7311yescharacteristic
663C22×C4C2×C4×D7311yescharacteristic
664C22×C4C2×C22⋊D7311yescharacteristic
665C22×C4C2×C22⋊D7311yescharacteristic
666C22×C4#1192402811yescharacteristic
667C22×C4C23×D7311yescharacteristic
668Q16—2921no—
669Q16—1462no—
670SD16—2921no—
671SD16—2921no—
672SD16—1462no—
673SD16—1462no—
674D8—2921no—
675D8—1462no—
676M16—21no—
677M16—21no—
678M16—21no—
679M16—21no—
680M16—42no—
681M16—42no—
682M16—2922no—
683M16—2922no—
684M16—732no—
685M16—1461no—
686M16—1461no—
687M16—1461no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8—2922no—
697C2×C8—2922no—
698C2×C8—731no—
699C2×C8—731no—
700C2×C8—731no—
701C2×C8—731no—
702C2×C8—1461no—
703C2×C8—1461no—
704C2×C8—1461no—
705C2×C8—1461no—
706C2×C8—1461no—
707C2×C8—1461no—
708C2×C8C2×C22⋊D7311yescharacteristic
709C2×C8C2×C22⋊D7311yescharacteristic
710C2×C8C2×C22⋊D7311yescharacteristic
711C2×C8C2×C22⋊D7311yescharacteristic
712C4⋊C4—2922no—
713C4⋊C4—731no—
714C4⋊C4—731no—
715C4⋊C4—1461no—
716C4⋊C4—1461no—
717C22⋊C4—2922no—
718C22⋊C4—1461no—
719C22⋊C4—1461no—
720C22⋊C4—1461no—
721C22⋊C4—1461no—
722C22⋊C4—1461no—
723C42—732no—
724C42—1461no—
725C42—1461no—
726C42—1461no—
727C42—1461no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—41no—
733C23—41no—
734C23—42no—
735C23—42no—
736C23—81no—
737C23—1461no—
738C23C4×C22⋊D7311yescharacteristic
739C23C4×C22⋊D7311yescharacteristic
740C23C2×#1192402811yescharacteristic
741Q8—21no—
742Q8—21no—
743Q8—21no—
744Q8—42no—
745Q8—1461no—
746Q8—1461no—
747Q8#1455655112yes—
748D4—22no—
749D4—22no—
750D4—21no—
751D4—21no—
752D4—21no—
753D4—42no—
754D4—42no—
755D4—42no—
756D4—41no—
757D4—41no—
758D4—2922no—
759D4—2921no—
760D4—2921no—
761D4—5841no—
762D4—1461no—
763D4—1461no—
764D4#1455655112yes—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—22no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—2921no—
785C2×C4—2921no—
786C2×C4—2921no—
787C2×C4—2921no—
788C2×C4—2921no—
789C2×C4—2921no—
790C2×C4—2921no—
791C2×C4—1462no—
792C2×C4—1461no—
793C2×C4—1461no—
794C2×C4—1461no—
795C2×C4C4×C22⋊D7311yescharacteristic
796C2×C4C4×C22⋊D7311yescharacteristic
797C2×C4C22×C4×D7311yescharacteristic
798C2×C4C2×D4×D7311yescharacteristic
799C2×C4C22×C22⋊D7311yescharacteristic
800C2×C4C2×#1192402711yescharacteristic
801C2×C4#1455663611yescharacteristic
802C2×C4#1455663611yescharacteristic
803C8—21no—
804C8—21no—
805C8—21no—
806C8—21no—
807C8—41no—
808C8—41no—
809C8—2921no—
810C8—1462no—
811C8—1461no—
812C8—1461no—
813C8—1461no—
814C8—1461no—
815C22—21no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—22no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—81no—
830C22—81no—
831C22—84no—
832C22—2921no—
833C22—2921no—
834C22—2921no—
835C22C2×C4×C22⋊D7311yescharacteristic
836C22#1798922711yescharacteristic
837C22#1798926311yescharacteristic
838C4—21no—
839C4—21no—
840C4—22no—
841C4—41no—
842C4—2922no—
843C4—2921no—
844C4—2921no—
845C4—2921no—
846C4—5841no—
847C4C2×#1455655111yescharacteristic
848C4#1798906011yescharacteristic
849C4D4×C22⋊D7311yescharacteristic
850C4#1798923111yescharacteristic
851C2—21no—
852C2—21no—
853C2—41no—
854C2—41no—
855C2—42no—
856C2—81no—
857C2—5841no—
858C2#2261291011yescharacteristic
859C2#2261883211yescharacteristic
860C2#2261884611yescharacteristic
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#22889
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. C2×#17988604C2semidirect
5. #22610823C2semidirect
6. #22610638C2semidirect
7. #22610576C2semidirect
8. #22610377C2semidirect
9. #22610261C2semidirect
10. #22610258C2semidirect
11. #22610206C2semidirect
12. #22610135C2semidirect
13. #22609773C2semidirect
14. #22609699C2semidirect
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×#14556501C22semidirect
51. C2×C8×Dic73C22semidirect
52. #17988351C22semidirect
53. #17988351C22semidirect
54. #17988348C22semidirect
55. #17988348C22semidirect
56. #17988341C22semidirect
57. #17988341C22semidirect
116. #14556518D4semidirect
435. #2880D73semidirect
446. C73#22889semidirect

Maximal subgroups

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

subgroupindex
#226191492
C2×#179887022
#226186522
C2×#179886042
#226108232
#226106382
#226105762
#226103772
#226102612
#226102582
#226102062
#226101352
#226097732
#226096992
C73×#28802
#2288973