Finite Group Databasebeta

← #32018219

Subgroups — #32018219

Order 18176.

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#22597558C211yesmaximal, characteristic
2C2×#17986113C211yesmaximal, characteristic, complemented
3#22597065C211yesmaximal, characteristic, complemented
4#22596789C211yesmaximal, characteristic, complemented
5#22589225C211yesmaximal, characteristic, complemented
6#22589041C211yesmaximal, characteristic, complemented
7#22588991C211yesmaximal, characteristic, complemented
8#22588783C211yesmaximal, characteristic, complemented
9#22588665C211yesmaximal, characteristic, complemented
10#22588664C211yesmaximal, characteristic, complemented
11#22588613C211yesmaximal, characteristic, complemented
12#22588545C211yesmaximal, characteristic, complemented
13#22588178C211yesmaximal, characteristic, complemented
14C4×C22⋊(C71⋊C8)C211yesmaximal, characteristic, complemented
15C22×#104×C71C211yesmaximal, characteristic, complemented
16C2×#14556148C2211yescharacteristic
17C2×#14556148C2211yescharacteristic
18C2×#14556136C2211yescharacteristic, complemented
19C2×#14556135C2211yescharacteristic
20C2×#14556135C2211yescharacteristic
21#17986510C2211yescharacteristic
22#17986161C411yescharacteristic, complemented
23#17986161C411yescharacteristic, complemented
24#17986155C411yescharacteristic, complemented
25#17986150C411yescharacteristic, complemented
26#17986144C411yescharacteristic, complemented
27#17986144C411yescharacteristic, complemented
28#17986138C411yescharacteristic, complemented
29#17986133C411yescharacteristic, complemented
30#17986113—24no—
31#17986075—21no—
32#17986070—21no—
33#17986068—21no—
34C8×C22⋊D71—21no—
35C2×#14556063C2211yescharacteristic, complemented
36C2×#14556063C2211yescharacteristic, complemented
37#17986027C2211yescharacteristic, complemented
38C2×#14556056C2211yescharacteristic, complemented
39C2×#14556056C2211yescharacteristic, complemented
40#17985995C2211yescharacteristic
41#17985995C2211yescharacteristic
42#17985967C2211yescharacteristic, complemented
43#17985966—21no—
44#17985966—21no—
45#17985966C2211yescharacteristic
46#17985966C2211yescharacteristic
47#17985963—21no—
48#17985963C2211yescharacteristic
49C2×C22⋊(C71⋊C8)—21no—
50C2×C22⋊(C71⋊C8)C2211yescharacteristic
51C2×C22⋊(C71⋊C8)C2211yescharacteristic
52#17985957C2211yescharacteristic, complemented
53C2×C4×C71⋊C8C2211yescharacteristic, complemented
54C2×C4×C71⋊C8C2211yescharacteristic, complemented
55#17985763C2211yescharacteristic, complemented
56#17985763C2211yescharacteristic, complemented
57#17985759C2211yescharacteristic, complemented
58#17985759C2211yescharacteristic, complemented
59#17985754C2211yescharacteristic, complemented
60#17985754C2211yescharacteristic, complemented
61C22×#41×C71C2211yescharacteristic
62C22×M16×C71C2211yescharacteristic
63C22×C42×C71C2211yescharacteristic
64C2×#104×C71—24no—
65C2×#104×C71C2211yescharacteristic
66C2×#104×C71C2211yescharacteristic
67C2×#104×C71C2211yescharacteristic
68C2×#104×C71C2211yescharacteristic
69C2×#11765865C2311yescharacteristic
70#14556148—22no—
71#14556148—22no—
72#14556148—41no—
73#14556148—41no—
74C2×#11765855C2×C411yescharacteristic, complemented
75C2×#11765855C2×C411yescharacteristic, complemented
76C2×#11765853C2×C411yescharacteristic, complemented
77C2×#11765853C2×C411yescharacteristic, complemented
78C2×#11765852C2×C411yescharacteristic, complemented
79C2×#11765852C2×C411yescharacteristic, complemented
80C2×#11765850C2×C411yescharacteristic, complemented
81C2×#11765850C2×C411yescharacteristic, complemented
82#14556136—22no—
83#14556136—41no—
84#14556135—22no—
85#14556135—22no—
86#14556135—41no—
87#14556135—41no—
88C2×#11765849—21no—
89C2×#11765849—21no—
90C2×#11765849C2311yescharacteristic
91C2×#11765849C2311yescharacteristic
92C2×#11765848—21no—
93C22×C71⋊C8—21no—
94C22×C71⋊C8—21no—
95C22×C71⋊C8C2311yescharacteristic
96C22×C71⋊C8C2311yescharacteristic
97C22×C71⋊C8C2311yescharacteristic
98C22×C71⋊C8C2311yescharacteristic
99C2×C8×D71—21no—
100#14556111—21no—
101#14556107C2×C411yescharacteristic
102#14556107C2×C411yescharacteristic
103#14556102C2×C411yescharacteristic
104#14556102C2×C411yescharacteristic
105#14556097—21no—
106C4×C22⋊D71—21no—
107C4×C22⋊D71—21no—
108#14556087C2311yescharacteristic
109#14556063—22no—
110#14556063—41no—
111Dic71⋊C8—21no—
112Dic71⋊C8—21no—
113#14556056—22no—
114#14556056—41no—
115#14556052C2×C411yescharacteristic, complemented
116#14556052C2×C411yescharacteristic, complemented
117#14556052C2×C411yescharacteristic, complemented
118#14556052C2×C411yescharacteristic, complemented
119#14556049C2×C411yescharacteristic, complemented
120#14556049C2×C411yescharacteristic, complemented
121#14556049C2×C411yescharacteristic, complemented
122#14556049C2×C411yescharacteristic, complemented
123C22⋊(C71⋊C8)—21no—
124C22⋊(C71⋊C8)—21no—
125C22⋊(C71⋊C8)—21no—
126C22⋊(C71⋊C8)—21no—
127C22⋊(C71⋊C8)—21no—
128C22⋊(C71⋊C8)—21no—
129C22⋊(C71⋊C8)C2×C411yescharacteristic
130C22⋊(C71⋊C8)C2×C411yescharacteristic
131C22⋊(C71⋊C8)C2×C411yescharacteristic
132C22⋊(C71⋊C8)C2×C411yescharacteristic
133C22⋊(C71⋊C8)D411yescharacteristic
134C22⋊(C71⋊C8)D411yescharacteristic
135C22⋊(C71⋊C8)D411yescharacteristic
136C22⋊(C71⋊C8)D411yescharacteristic
137(C2×D71)⋊C8—21no—
138(C2×D71)⋊C8—21no—
139#14556038—21no—
140C4×C71⋊C8—22no—
141C4×C71⋊C8—41no—
142C8×Dic71—21no—
143C2×#41×C71—21no—
144C2×#41×C71—21no—
145C2×#41×C71—22no—
146C2×#41×C71—22no—
147C2×#41×C71—41no—
148C2×#41×C71—41no—
149C2×#41×C71C2×C411yescharacteristic
150C2×#41×C71C2×C411yescharacteristic
151C2×#41×C71C2311yescharacteristic
152C2×#41×C71C2311yescharacteristic
153C22×Q8×C71C2×C411yescharacteristic
154C22×D4×C71—21no—
155C22×D4×C71C2×C411yescharacteristic
156C23×C4×C71—21no—
157C23×C4×C71—21no—
158C23×C4×C71C2311yescharacteristic
159C2×M16×C71—21no—
160C2×M16×C71—22no—
161C2×M16×C71—41no—
162C2×M16×C71C2311yescharacteristic
163C2×M16×C71C2311yescharacteristic
164C22×C8×C71—21no—
165C2×C42×C71—22no—
166C2×C42×C71—21no—
167C2×C42×C71—41no—
168C2×C42×C71C2311yescharacteristic
169C2×C42×C71C2311yescharacteristic
170#104×C71—22no—
171#104×C71—22no—
172#104×C71—22no—
173#104×C71D414yescomplemented
174#11765865—21no—
175#11765865—21no—
176#11765865—21no—
177#11765865—21no—
178C2×Dic142C22×C411yescharacteristic
179C2×D284C22×C411yescharacteristic
180C2×C22⋊D71—21no—
181C2×C22⋊D71—21no—
182C2×C22⋊D71—21no—
183C2×C4×D71—21no—
184#11765855—22no—
185#11765855—41no—
186#11765853—22no—
187#11765853—41no—
188#11765852—22no—
189#11765852—41no—
190#11765850—22no—
191#11765850—41no—
192#11765849—21no—
193#11765849—21no—
194#11765849—21no—
195#11765849—21no—
196#11765849—42no—
197#11765849—42no—
198#11765848—42no—
199C2×C71⋊C8—21no—
200C2×C71⋊C8—21no—
201C2×C71⋊C8—21no—
202C2×C71⋊C8—21no—
203C2×C71⋊C8—21no—
204C2×C71⋊C8—21no—
205C2×C71⋊C8—21no—
206C2×C71⋊C8—21no—
207C2×C71⋊C8—21no—
208C2×C71⋊C8—21no—
209C2×C71⋊C8—42no—
210C2×C71⋊C8—42no—
211C2×C71⋊C8C22×C411yescharacteristic
212C2×C71⋊C8C22×C411yescharacteristic
213C2×C71⋊C8C22×C411yescharacteristic
214C2×C71⋊C8C22×C411yescharacteristic
215C2×C71⋊C8C2×D411yescharacteristic
216C2×C71⋊C8C2×D411yescharacteristic
217C2×C71⋊C8C2×D411yescharacteristic
218C2×C71⋊C8C2×D411yescharacteristic
219C8×D71—42no—
220C4⋊Dic71C22×C411yescharacteristic
221C4⋊Dic71C22×C411yescharacteristic
222Dic71⋊C4—21no—
223Dic71⋊C4—21no—
224C22⋊Dic71—21no—
225C22⋊Dic71—21no—
226C22⋊Dic71—21no—
227(C2×D71)⋊C4—21no—
228(C2×D71)⋊C4—21no—
229C4×Dic71—21no—
230C24×C71—21no—
231C24×C71#4111yescharacteristic
232#41×C71—21no—
233#41×C71—21no—
234#41×C71—22no—
235#41×C71—22no—
236#41×C71—21no—
237#41×C71—21no—
238#41×C71—21no—
239#41×C71—21no—
240#41×C71—42no—
241#41×C71—42no—
242#41×C71—41no—
243#41×C71—41no—
244#41×C71—42no—
245#41×C71—42no—
246#41×C71C2×D412yes—
247#41×C71#4112yes—
248C2×Q8×C71—21no—
249C2×Q8×C71—22no—
250C2×Q8×C71—41no—
251C2×Q8×C71C22×C411yescharacteristic
252C2×Q8×C71C22×C411yescharacteristic
253C2×D4×C71—21no—
254C2×D4×C71—22no—
255C2×D4×C71—21no—
256C2×D4×C71—21no—
257C2×D4×C71—21no—
258C2×D4×C71—21no—
259C2×D4×C71—41no—
260C2×D4×C71—42no—
261C2×D4×C71—42no—
262C2×D4×C71C22×C411yescharacteristic
263C2×D4×C71C22×C411yescharacteristic
264C22×C4×C71—21no—
265C22×C4×C71—21no—
266C22×C4×C71—21no—
267C22×C4×C71—21no—
268C22×C4×C71—21no—
269C22×C4×C71—21no—
270C22×C4×C71—24no—
271C22×C4×C71—21no—
272C22×C4×C71—21no—
273C22×C4×C71—21no—
274C22×C4×C71—21no—
275C22×C4×C71—21no—
276C22×C4×C71—42no—
277C22×C4×C71—42no—
278C22×C4×C71—42no—
279C22×C4×C71—42no—
280C22×C4×C71C22×C411yescharacteristic
281C22×C4×C71C22×C411yescharacteristic
282C22×C4×C71C2×D411yescharacteristic
283C22×C4×C71C2×D411yescharacteristic
284C22×C4×C71#4111yescharacteristic
285C22×C4×C71C2411yescharacteristic
286M16×C71—21no—
287M16×C71—21no—
288M16×C71—21no—
289M16×C71—42no—
290M16×C71C2×D412yes—
291C2×C8×C71—21no—
292C2×C8×C71—21no—
293C2×C8×C71—42no—
294C42×C71—21no—
295C42×C71—21no—
296C42×C71—21no—
297C42×C71—42no—
298C42×C71C2×D412yes—
299C23×C71—21no—
300C23×C71—21no—
301C23×C71—21no—
302C23×C71—22no—
303C23×C71—21no—
304C23×C71—41no—
305C23×C71—42no—
306C23×C71—42no—
307C23×C71—81no—
308C23×C71C4×D411yescharacteristic
309C23×C71C4×D411yescharacteristic
310C23×C71C2×#4111yescharacteristic
311C22×D71—21no—
312Q8×C71—21no—
313Q8×C71—21no—
314Q8×C71—21no—
315Q8×C71—42no—
316Q8×C71C4×D412yes—
317D4×C71—22no—
318D4×C71—22no—
319D4×C71—21no—
320D4×C71—21no—
321D4×C71—21no—
322D4×C71—42no—
323D4×C71—42no—
324D4×C71—42no—
325D4×C71—41no—
326D4×C71—41no—
327D4×C71C4×D412yes—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—21no—
331C2×C4×C71—22no—
332C2×C4×C71—21no—
333C2×C4×C71—21no—
334C2×C4×C71—21no—
335C2×C4×C71—21no—
336C2×C4×C71—21no—
337C2×C4×C71—21no—
338C2×C4×C71—21no—
339C2×C4×C71—21no—
340C2×C4×C71—22no—
341C2×C4×C71—21no—
342C2×C4×C71—21no—
343C2×C4×C71—22no—
344C2×C4×C71—22no—
345C2×C4×C71—21no—
346C2×C4×C71—42no—
347C2×C4×C71—42no—
348C2×C4×C71—42no—
349C2×C4×C71—48no—
350C2×C4×C71—41no—
351C2×C4×C71—41no—
352C2×C4×C71—41no—
353C2×C4×C71—41no—
354C2×C4×C71C4×D411yescharacteristic
355C2×C4×C71C4×D411yescharacteristic
356C2×C4×C71C23×C411yescharacteristic
357C2×C4×C71C22×D411yescharacteristic
358C2×C4×C71C22×D411yescharacteristic
359C2×C4×C71C2×#4111yescharacteristic
360C2×C4×C71H(5,𝔽2)11yescharacteristic
361C2×C4×C71H(5,𝔽2)11yescharacteristic
362C22⋊D71—41no—
363C22⋊D71—41no—
364C22⋊D71—42no—
365C22⋊D71—81no—
366C2×Dic71—21no—
367C2×Dic71—21no—
368C2×Dic71—21no—
369D284—21no—
370D284—21no—
371C4×D71—41no—
372C4×D71—41no—
373Dic142—21no—
374Dic142—21no—
375C8×C71—22no—
376C8×C71—41no—
377C71⋊C8—21no—
378C71⋊C8—21no—
379C71⋊C8—21no—
380C71⋊C8—21no—
381C71⋊C8—21no—
382C71⋊C8—21no—
383C71⋊C8—21no—
384C71⋊C8—21no—
385C71⋊C8—41no—
386C71⋊C8—41no—
387C22×C71—21no—
388C22×C71—21no—
389C22×C71—21no—
390C22×C71—21no—
391C22×C71—21no—
392C22×C71—22no—
393C22×C71—21no—
394C22×C71—21no—
395C22×C71—42no—
396C22×C71—42no—
397C22×C71—41no—
398C22×C71—41no—
399C22×C71—41no—
400C22×C71—41no—
401C22×C71—41no—
402C22×C71—84no—
403C22×C71#44312yescomplemented
404C22×C71C2×C4×D411yescharacteristic
405C22×C71#54611yescharacteristic
406C22×C71#55111yescharacteristic
407C2×D71—41no—
408C2×D71—41no—
409C2×D71—41no—
410C4×C71—24no—
411C4×C71—21no—
412C4×C71—21no—
413C4×C71—22no—
414C4×C71—42no—
415C4×C71—41no—
416C4×C71C2×C4×D411yescharacteristic
417C4×C71#51811yescharacteristic
418C4×C71D4211yescharacteristic
419C4×C71#54611yescharacteristic
420Dic71—41no—
421Dic71—41no—
422Dic71—41no—
423#22888—711nomaximal, Sylow
424C2×C71—21no—
425C2×C71—22no—
426C2×C71—21no—
427C2×C71—41no—
428C2×C71—42no—
429C2×C71—81no—
430C2×C71#235811yescharacteristic
431C2×C71C2×#44311yescharacteristic
432C2×C71#295611yescharacteristic
433D71—81no—
434#3002—711no—
435C2×#443—711no—
436#2933—711no—
437C22×#104D7111yescharacteristic, complemented
438#2880—711no—
439#1974—711no—
440#1937—711no—
441#1929—711no—
442#1896—711no—
443#1876—711no—
444#1876—711no—
445#1866—711no—
446#1855—711no—
447#1764—711no—
448C4×C22⋊C8—711no—
449C71#2288811yescharacteristic, complemented, Sylow
450C22×#41C2×D7111yescharacteristic
451C2×#135—711no—
452C2×#135—711no—
453C2×#131—711no—
454C2×#131—711no—
455C2×#131—711no—
456C22×M16C2×D7111yescharacteristic
457#525—711no—
458C22×C42C2×D7111yescharacteristic
459#452—711no—
460#452—711no—
461#451—711no—
462#450—711no—
463#449—711no—
464#449—711no—
465#448—711no—
466#447—711no—
467#443—1424no—
468#436—1421no—
469#435—1421no—
470#435—1421no—
471C8×D4—1421no—
472C2×#108—711no—
473C2×#108—711no—
474#424—711no—
475C2×#104—24no—
476C2×#104—711no—
477C2×#104—711no—
478C2×#104C2×D7111yescharacteristic
479C2×#104C2×D7111yescharacteristic
480C2×#104C2×D7111yescharacteristic
481C2×#104C2×D7111yescharacteristic
482#416—711no—
483#416—711no—
484#408—711no—
485#408—711no—
486#408—711no—
487#408—1421no—
488#408—1421no—
489#407—711no—
490#407—1421no—
491C2×C22⋊C8—711no—
492C2×C22⋊C8—711no—
493C2×C22⋊C8—1421no—
494#405—711no—
495C2×C4×C8—711no—
496C2×C4×C8—711no—
497#341—711no—
498#341—711no—
499#339—711no—
500#339—711no—
501#336—711no—
502#336—711no—
503C2×#41—21no—
504C2×#41—21no—
505C2×#41—22no—
506C2×#41—22no—
507C2×#41—41no—
508C2×#41—41no—
509C2×#41—711no—
510C2×#41C4×D7111yescharacteristic
511C2×#41C4×D7111yescharacteristic
512C2×#41C22×D7111yescharacteristic
513C2×#41C22×D7111yescharacteristic
514C22×Q8C4×D7111yescharacteristic
515C22×D4—21no—
516C22×D4C4×D7111yescharacteristic
517C23×C4—21no—
518C23×C4—21no—
519C23×C4C22×D7111yescharacteristic
520#135—2841no—
521#135—2841no—
522#135—1422no—
523#135—1422no—
524C2×Q16—711no—
525C2×Q16—711no—
526C2×SD16—711no—
527C2×SD16—711no—
528C2×SD16—711no—
529C2×SD16—711no—
530C2×D8—711no—
531C2×D8—711no—
532#131—2841no—
533#131—2841no—
534#131—2841no—
535#131—1422no—
536#131—1422no—
537#131—1422no—
538C2×M16—21no—
539C2×M16—22no—
540C2×M16—41no—
541C2×M16—711no—
542C2×M16—711no—
543C2×M16—1421no—
544C2×M16—1421no—
545C2×M16—1421no—
546C2×M16C22×D7111yescharacteristic
547C2×M16C22×D7111yescharacteristic
548C22×C8—21no—
549C22×C8—711no—
550C22×C8—711no—
551C22×C8—711no—
552C22×C8—711no—
553C22×C8—1421no—
554C22×C8—1421no—
555C22×C8—1421no—
556#123—1421no—
557C22⋊Q8—711no—
558C22⋊Q8—711no—
559#121—711no—
560#121—711no—
561#120—1421no—
562C4×D4—1421no—
563C4×D4—1421no—
564#117—711no—
565C2×C42—22no—
566C2×C42—21no—
567C2×C42—41no—
568C2×C42C22×D7111yescharacteristic
569C2×C42C22×D7111yescharacteristic
570#108—2841no—
571#108—1422no—
572C4⋊C8—1421no—
573C4⋊C8—1421no—
574#104—22no—
575#104—22no—
576#104—22no—
577#104—2841no—
578#104—1422no—
579#104C22⋊D7114yescomplemented
580#103—711no—
581#103—711no—
582#103—711no—
583#103—711no—
584#102—711no—
585#102—711no—
586#102—711no—
587#102—711no—
588C22⋊C8—711no—
589C22⋊C8—711no—
590C22⋊C8—711no—
591C22⋊C8—711no—
592C22⋊C8—711no—
593C22⋊C8—711no—
594C22⋊C8—711no—
595C22⋊C8—711no—
596C22⋊C8—1421no—
597C22⋊C8—1421no—
598C22⋊C8—1421no—
599C22⋊C8—1421no—
600C22⋊C8—1421no—
601C22⋊C8—1421no—
602C22⋊C8—1421no—
603C22⋊C8—1421no—
604#97—1421no—
605C4×C8—2841no—
606C4×C8—1421no—
607C4×C8—1422no—
608C24—21no—
609C24#1176586411yescharacteristic
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—1421no—
625#41—1421no—
626#41—1421no—
627#41—1421no—
628#41C2×C22⋊D7112yes—
629#41#1176586512yes—
630C2×Q8—21no—
631C2×Q8—22no—
632C2×Q8—41no—
633C2×Q8—711no—
634C2×Q8C2×C4×D7111yescharacteristic
635C2×Q8C2×C4×D7111yescharacteristic
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—711no—
646C2×D4—1421no—
647C2×D4—1421no—
648C2×D4—1421no—
649C2×D4C2×C4×D7111yescharacteristic
650C2×D4C2×C4×D7111yescharacteristic
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—24no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—21no—
663C22×C4—42no—
664C22×C4—42no—
665C22×C4—42no—
666C22×C4—42no—
667C22×C4—1421no—
668C22×C4C2×C4×D7111yescharacteristic
669C22×C4C2×C4×D7111yescharacteristic
670C22×C4D4×D7111yescharacteristic
671C22×C4D4×D7111yescharacteristic
672C22×C4#1176586411yescharacteristic
673C22×C4C23×D7111yescharacteristic
674Q16—2841no—
675Q16—1422no—
676SD16—2841no—
677SD16—2841no—
678SD16—1422no—
679SD16—1422no—
680D8—2841no—
681D8—1422no—
682M16—21no—
683M16—21no—
684M16—21no—
685M16—42no—
686M16—2842no—
687M16—2842no—
688M16—2842no—
689M16—1421no—
690M16—1421no—
691M16—1421no—
692M16—1421no—
693M16C2×C22⋊D7112yes—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—42no—
697C2×C8—2842no—
698C2×C8—2842no—
699C2×C8—2842no—
700C2×C8—711no—
701C2×C8—711no—
702C2×C8—711no—
703C2×C8—711no—
704C2×C8—711no—
705C2×C8—711no—
706C2×C8—711no—
707C2×C8—711no—
708C2×C8—1421no—
709C2×C8—1421no—
710C2×C8—1421no—
711C2×C8—1421no—
712C2×C8—1421no—
713C2×C8—1421no—
714C2×C8—1421no—
715C2×C8—1421no—
716C2×C8—1421no—
717C2×C8—1421no—
718C4⋊C4—711no—
719C4⋊C4—711no—
720C4⋊C4—1421no—
721C4⋊C4—1421no—
722C22⋊C4—1421no—
723C22⋊C4—1421no—
724C22⋊C4—1421no—
725C22⋊C4—1421no—
726C22⋊C4—1421no—
727C42—21no—
728C42—21no—
729C42—21no—
730C42—42no—
731C42—1421no—
732C42C2×C22⋊D7112yes—
733C23—22no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—41no—
739C23—42no—
740C23—42no—
741C23—81no—
742C23—1421no—
743C23(C22⋊D71)⋊C411yescharacteristic
744C23(C22⋊D71)⋊C411yescharacteristic
745C23C2×#1176586411yescharacteristic
746Q8—21no—
747Q8—21no—
748Q8—21no—
749Q8—42no—
750Q8—1421no—
751Q8—1421no—
752Q8C4×C22⋊D7112yes—
753D4—22no—
754D4—22no—
755D4—21no—
756D4—21no—
757D4—21no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—41no—
762D4—41no—
763D4—2842no—
764D4—2841no—
765D4—2841no—
766D4—5681no—
767D4—1421no—
768D4—1421no—
769D4C4×C22⋊D7112yes—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—22no—
778C2×C4—21no—
779C2×C4—22no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—22no—
787C2×C4—21no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—48no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—2841no—
797C2×C4—2841no—
798C2×C4—1421no—
799C2×C4—1421no—
800C2×C4—1421no—
801C2×C4(C22⋊D71)⋊C411yescharacteristic
802C2×C4(C22⋊D71)⋊C411yescharacteristic
803C2×C4C22×C4×D7111yescharacteristic
804C2×C4C2×D4×D7111yescharacteristic
805C2×C4C22×C22⋊D7111yescharacteristic
806C2×C4C2×#1176586511yescharacteristic
807C2×C4#1455617311yescharacteristic
808C2×C4#1455617311yescharacteristic
809C8—22no—
810C8—41no—
811C8—2841no—
812C8—2841no—
813C8—1421no—
814C8—1421no—
815C8—1421no—
816C8—1421no—
817C8—1421no—
818C8—1421no—
819C8—1421no—
820C8—1421no—
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—2841no—
838C22—2841no—
839C22—2841no—
840C22#1798611312yescomplemented
841C22C2×(C22⋊D71)⋊C411yescharacteristic
842C22#1798664311yescharacteristic
843C22#1798667511yescharacteristic
844C4—24no—
845C4—21no—
846C4—21no—
847C4—22no—
848C4—42no—
849C4—41no—
850C4—2841no—
851C4—2841no—
852C4—2841no—
853C4C2×C4×C22⋊D7111yescharacteristic
854C4#1798647211yescharacteristic
855C4D4×C22⋊D7111yescharacteristic
856C4#1798663911yescharacteristic
857C2—21no—
858C2—22no—
859C2—21no—
860C2—41no—
861C2—42no—
862C2—81no—
863C2—5681no—
864C2#2259131911yescharacteristic
865C2C2×#1798611311yescharacteristic
866C2#2259724611yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC22×#104×C71C2
socleC22×C71C2×C4×D4
prime radical#22597558C2
cosocleC22×C4×C71C24
hypercenterC22×#104D71
hypocenterC71#22888
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C22×#104

Complements

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

NH ≅ G/Ntype
2. C2×#17986113C2semidirect
3. #22597065C2semidirect
4. #22596789C2semidirect
5. #22589225C2semidirect
6. #22589041C2semidirect
7. #22588991C2semidirect
8. #22588783C2semidirect
9. #22588665C2semidirect
10. #22588664C2semidirect
11. #22588613C2semidirect
12. #22588545C2semidirect
13. #22588178C2semidirect
14. C4×C22⋊(C71⋊C8)C2semidirect
15. C22×#104×C71C2semidirect
18. C2×#14556136C22semidirect
22. #17986161C4semidirect
23. #17986161C4semidirect
24. #17986155C4semidirect
25. #17986150C4semidirect
26. #17986144C4semidirect
27. #17986144C4semidirect
28. #17986138C4semidirect
29. #17986133C4semidirect
35. C2×#14556063C22semidirect
36. C2×#14556063C22semidirect
37. #17986027C22semidirect
38. C2×#14556056C22semidirect
39. C2×#14556056C22semidirect
42. #17985967C22semidirect
52. #17985957C22semidirect
53. C2×C4×C71⋊C8C22semidirect
54. C2×C4×C71⋊C8C22semidirect
55. #17985763C22semidirect
56. #17985763C22semidirect
57. #17985759C22semidirect
58. #17985759C22semidirect
59. #17985754C22semidirect
60. #17985754C22semidirect
74. C2×#11765855C2×C4semidirect
75. C2×#11765855C2×C4semidirect
76. C2×#11765853C2×C4semidirect
77. C2×#11765853C2×C4semidirect
78. C2×#11765852C2×C4semidirect
79. C2×#11765852C2×C4semidirect
80. C2×#11765850C2×C4semidirect
81. C2×#11765850C2×C4semidirect
115. #14556052C2×C4semidirect
116. #14556052C2×C4semidirect
117. #14556052C2×C4semidirect
118. #14556052C2×C4semidirect
119. #14556049C2×C4semidirect
120. #14556049C2×C4semidirect
121. #14556049C2×C4semidirect
122. #14556049C2×C4semidirect
173. #104×C71D4semidirect
403. C22×C71#443semidirect
437. C22×#104D71semidirect
449. C71#22888semidirect
579. #104C22⋊D71semidirect
840. C22#17986113semidirect

Maximal subgroups

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

subgroupindex
#225975582
C2×#179861132
#225970652
#225967892
#225892252
#225890412
#225889912
#225887832
#225886652
#225886642
#225886132
#225885452
#225881782
C4×C22⋊(C71⋊C8)2
C22×#104×C712
#2288871