Finite Group Databasebeta

← #32013800

Subgroups — #32013800

Order 18176.

1390 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986071C211yesmaximal, characteristic, complemented
2#22591269C211yesmaximal, characteristic, complemented
3#22589314C211yesmaximal, characteristic, complemented
4#22589289C211yesmaximal, characteristic, complemented
5#22588779C211yesmaximal, characteristic, complemented
6#22588769C211yesmaximal, characteristic, complemented
7#22588663C211yesmaximal, characteristic, complemented
8#22588658C211yesmaximal, characteristic, complemented
9#22588430C211yesmaximal, characteristic, complemented
10#22588426C211yesmaximal, characteristic, complemented
11#22588350C211yesmaximal, characteristic, complemented
12#22588165C211yesmaximal, characteristic, complemented
13#22588059C211yesmaximal, characteristic, complemented
14C2×#17985761C211yesmaximal, characteristic, complemented
15C2×#547×C71C211yesmaximal, characteristic
16C22×#11765849C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C2×#14556087C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20#17986071—24no—
21C2×C4⋊(C71⋊C8)C2211yescharacteristic
22C2×#14556049C2211yescharacteristic
23C2×#14556049C2211yescharacteristic
24C2×#14556049C2211yescharacteristic
25C2×#14556049C2211yescharacteristic
26C2×C22⋊(C71⋊C8)C2211yescharacteristic
27C2×C22⋊(C71⋊C8)C2211yescharacteristic
28C2×#14556039C2211yescharacteristic
29#17985892—21no—
30#17985885—21no—
31#17985879—21no—
32#17985865C2211yescharacteristic
33#17985859C2211yescharacteristic
34#17985859C2211yescharacteristic
35C4×C4⋊Dic71C2211yescharacteristic
36C22⋊C4×Dic71—21no—
37#17985761C2211yescharacteristic
38#17985761C2211yescharacteristic
39#17985761C2211yescharacteristic
40#17985761C2211yescharacteristic
41#17985761C2211yescharacteristic
42#17985761C2211yescharacteristic
43#17985761C2211yescharacteristic
44#17985761C2211yescharacteristic
45#17985761C2211yescharacteristic
46#17985761C2211yescharacteristic
47#17985761C2211yescharacteristic
48#17985761C2211yescharacteristic
49C22×#41×C71—21no—
50#547×C71—24no—
51#547×C71C418yescomplemented
52C2×C4⋊Q8×C71C2211yescharacteristic
53C2×#123×C71—21no—
54C2×#123×C71—21no—
55C2×C22⋊Q8×C71—21no—
56C2×#121×C71C2211yescharacteristic
57C2×#121×C71C2211yescharacteristic
58C2×C4×D4×C71C2211yescharacteristic
59C2×C4×D4×C71C2211yescharacteristic
60C22×C4⋊C4×C71C2211yescharacteristic
61C22×C4⋊C4×C71C2211yescharacteristic
62C23×Dic71—21no—
63C2×#11765849—22no—
64C2×#11765849—22no—
65C2×#11765849—41no—
66C22×C71⋊C8—22no—
67C22×C71⋊C8—22no—
68C22×C71⋊C8—41no—
69C22×C71⋊C8C2311yescharacteristic
70C22×C71⋊C8C2311yescharacteristic
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73#14556087—22no—
74#14556087—41no—
75C2×C4⋊Dic71—22no—
76C2×C4⋊Dic71—21no—
77C2×C4⋊Dic71—41no—
78C2×C4⋊Dic71C2311yescharacteristic
79C2×C4⋊Dic71C2311yescharacteristic
80C2×C4⋊Dic71C2311yescharacteristic
81C2×C4⋊Dic71C2311yescharacteristic
82C2×C22⋊Dic71—21no—
83C2×C22⋊Dic71—21no—
84C2×C22⋊Dic71—21no—
85C2×C4×Dic71—21no—
86C2×C4×Dic71—21no—
87C4⋊(C71⋊C8)—22no—
88#14556049—22no—
89#14556049—22no—
90#14556049—41no—
91#14556049—41no—
92C22⋊(C71⋊C8)—22no—
93C22⋊(C71⋊C8)—22no—
94#14556039—22no—
95C71⋊#95—21no—
96C71⋊#95—21no—
97C71⋊#95—21no—
98C71⋊#95—21no—
99C71⋊#95—21no—
100C2×#41×C71—28no—
101C2×#41×C71—44no—
102C2×#41×C71—44no—
103C22×Q8×C71—21no—
104C22×D4×C71—21no—
105C22×D4×C71—21no—
106C22×D4×C71D411yescharacteristic
107C22×D4×C71C2311yescharacteristic
108C23×C4×C71—21no—
109C23×C4×C71—21no—
110C23×C4×C71—21no—
111C23×C4×C71C2311yescharacteristic
112C23×C4×C71C2311yescharacteristic
113C4⋊Q8×C71—22no—
114C4⋊Q8×C71C2×C414yescomplemented
115#123×C71—28no—
116#123×C71—28no—
117C22⋊Q8×C71—28no—
118#121×C71—22no—
119#121×C71—22no—
120#121×C71C2×C414yes—
121#121×C71C2×C414yescomplemented
122C4×D4×C71—22no—
123C4×D4×C71C2×C414yes—
124C4×D4×C71C2×C414yescomplemented
125C4×D4×C71D414yes—
126C2×C4⋊C4×C71—21no—
127C2×C4⋊C4×C71—21no—
128C2×C4⋊C4×C71—22no—
129C2×C4⋊C4×C71—22no—
130C2×C4⋊C4×C71—21no—
131C2×C4⋊C4×C71C2×C414yes—
132C2×C4⋊C4×C71C2×C414yescomplemented
133C2×C4⋊C4×C71D411yescharacteristic
134C2×C4⋊C4×C71C2311yescharacteristic
135C2×C4⋊C4×C71C2311yescharacteristic
136C2×C4⋊C4×C71C2311yescharacteristic
137C2×C22⋊C4×C71—21no—
138C2×C22⋊C4×C71—21no—
139C2×C22⋊C4×C71—21no—
140C2×C22⋊C4×C71D411yescharacteristic
141C2×C22⋊C4×C71D411yescharacteristic
142C2×C42×C71C2311yescharacteristic
143C22×Dic71—21no—
144C22×Dic71—21no—
145C22×Dic71—21no—
146C22×Dic71—21no—
147C22×Dic71—42no—
148C22×Dic71—42no—
149C22×Dic71—81no—
150#11765849—44no—
151C2×C71⋊C8—21no—
152C2×C71⋊C8—21no—
153C2×C71⋊C8—21no—
154C2×C71⋊C8—21no—
155C2×C71⋊C8—21no—
156C2×C71⋊C8—21no—
157C2×C71⋊C8—21no—
158C2×C71⋊C8—21no—
159C2×C71⋊C8—21no—
160C2×C71⋊C8—21no—
161C2×C71⋊C8—21no—
162C2×C71⋊C8—44no—
163C2×C71⋊C8#4112yescomplemented
164C4⋊Dic71—21no—
165C4⋊Dic71—21no—
166C4⋊Dic71—21no—
167C4⋊Dic71—21no—
168C4⋊Dic71—21no—
169C4⋊Dic71—21no—
170C4⋊Dic71—21no—
171C4⋊Dic71—42no—
172C4⋊Dic71#4112yescomplemented
173C22⋊Dic71—42no—
174C22⋊Dic71—42no—
175C22⋊Dic71—81no—
176C4×Dic71—42no—
177C4×Dic71—81no—
178C24×C71—21no—
179C24×C71C2×D411yescharacteristic
180C24×C71C2×D411yescharacteristic
181#41×C71—432no—
182C2×Q8×C71—24no—
183C2×Q8×C71—42no—
184C2×Q8×C71—42no—
185C2×D4×C71—22no—
186C2×D4×C71—22no—
187C2×D4×C71—24no—
188C2×D4×C71—24no—
189C2×D4×C71—21no—
190C2×D4×C71—21no—
191C2×D4×C71—21no—
192C2×D4×C71—21no—
193C2×D4×C71—21no—
194C2×D4×C71—42no—
195C2×D4×C71—42no—
196C2×D4×C71—42no—
197C2×D4×C71—42no—
198C2×D4×C71C22⋊C414yes—
199C2×D4×C71C22×C412yes—
200C22×C4×C71—21no—
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—21no—
206C22×C4×C71—21no—
207C22×C4×C71—21no—
208C22×C4×C71—24no—
209C22×C4×C71—24no—
210C22×C4×C71—21no—
211C22×C4×C71—21no—
212C22×C4×C71—21no—
213C22×C4×C71—24no—
214C22×C4×C71—42no—
215C22×C4×C71—42no—
216C22×C4×C71—42no—
217C22×C4×C71—42no—
218C22×C4×C71—42no—
219C22×C4×C71—42no—
220C22×C4×C71C22×C412yes—
221C22×C4×C71C22×C412yes—
222C22×C4×C71C2×D411yescharacteristic
223C22×C4×C71C2×D411yescharacteristic
224C22×C4×C71C2×D411yescharacteristic
225C22×C4×C71C2×D411yescharacteristic
226C22×C4×C71C2×D412yes—
227C22×C4×C71C2×D412yes—
228C22×C4×C71C2411yescharacteristic
229C4⋊C4×C71—24no—
230C4⋊C4×C71—24no—
231C4⋊C4×C71—24no—
232C4⋊C4×C71—21no—
233C4⋊C4×C71—21no—
234C4⋊C4×C71—21no—
235C4⋊C4×C71C22⋊C414yes—
236C4⋊C4×C71C22×C412yes—
237C4⋊C4×C71C22×C412yes—
238C4⋊C4×C71C22×C412yes—
239C22⋊C4×C71—24no—
240C22⋊C4×C71—24no—
241C22⋊C4×C71—24no—
242C22⋊C4×C71C22⋊C414yes—
243C22⋊C4×C71C22⋊C414yes—
244C42×C71C22×C412yes—
245C42×C71C2×D412yes—
246C23×C71—21no—
247C23×C71—21no—
248C23×C71—21no—
249C23×C71—21no—
250C23×C71—21no—
251C23×C71—21no—
252C23×C71—21no—
253C23×C71—21no—
254C23×C71—21no—
255C23×C71—21no—
256C23×C71—22no—
257C23×C71—41no—
258C23×C71—41no—
259C23×C71—41no—
260C23×C71—41no—
261C23×C71—41no—
262C23×C71—41no—
263C23×C71C2×C22⋊C412yes—
264C23×C71C2×C22⋊C412yes—
265C23×C71AGL(1,ℤ/8)12yes—
266C23×C71AGL(1,ℤ/8)12yes—
267C23×C71C22×D411yescharacteristic
268Q8×C71—48no—
269D4×C71—28no—
270D4×C71—22no—
271D4×C71—22no—
272D4×C71—48no—
273D4×C71—48no—
274D4×C71—41no—
275D4×C71—41no—
276C2×C4×C71—21no—
277C2×C4×C71—21no—
278C2×C4×C71—21no—
279C2×C4×C71—21no—
280C2×C4×C71—21no—
281C2×C4×C71—21no—
282C2×C4×C71—21no—
283C2×C4×C71—21no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—48no—
296C2×C4×C71—48no—
297C2×C4×C71—41no—
298C2×C4×C71—41no—
299C2×C4×C71—41no—
300C2×C4×C71—41no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
303C2×C4×C71—48no—
304C2×C4×C71C2×C22⋊C412yes—
305C2×C4×C71C2×C22⋊C412yes—
306C2×C4×C71C2×C22⋊C412yes—
307C2×C4×C71C2×C22⋊C412yes—
308C2×C4×C71C23×C411yescharacteristic
309C2×C4×C71C22×D411yescharacteristic
310C2×C4×C71C2×#4111yescharacteristic
311C2×C4×C71C2×#4111yescharacteristic
312C2×C4×C71H(5,𝔽2)11yescharacteristic
313C2×C4×C712−1+411yescharacteristic
314C2×Dic71—22no—
315C2×Dic71—41no—
316C2×Dic71—41no—
317C2×Dic71—41no—
318C2×Dic71—41no—
319C2×Dic71—41no—
320C2×Dic71—41no—
321C2×Dic71—41no—
322C2×Dic71—41no—
323C2×Dic71—41no—
324C2×Dic71—41no—
325C2×Dic71—41no—
326C2×Dic71—84no—
327C71⋊C8—22no—
328C71⋊C8—41no—
329C71⋊C8—41no—
330C71⋊C8—41no—
331C22×C71—22no—
332C22×C71—22no—
333C22×C71—22no—
334C22×C71—22no—
335C22×C71—22no—
336C22×C71—22no—
337C22×C71—22no—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—41no—
341C22×C71—41no—
342C22×C71—41no—
343C22×C71—41no—
344C22×C71—42no—
345C22×C71—42no—
346C22×C71—42no—
347C22×C71—81no—
348C22×C71—81no—
349C22×C71—81no—
350C22×C71—81no—
351C22×C71#41814yes—
352C22×C71C22×C22⋊C411yescharacteristic
353C22×C71#54611yescharacteristic
354C22×C71#54711yescharacteristic
355C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
356C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
357C22×C71#57711yescharacteristic
358C22×C71#57811yescharacteristic
359C4×C71—22no—
360C4×C71—22no—
361C4×C71—22no—
362C4×C71—22no—
363C4×C71—42no—
364C4×C71—42no—
365C4×C71—42no—
366C4×C71C4×#4111yescharacteristic
367C4×C71#52011yescharacteristic
368C4×C71#54611yescharacteristic
369C4×C71#54711yescharacteristic
370Dic71—42no—
371Dic71—81no—
372Dic71—81no—
373Dic71—81no—
374#22495—711nomaximal, Sylow
375C2×C71—24no—
376C2×C71—42no—
377C2×C71—82no—
378C2×C71#233911yescharacteristic
379C2×C71C2×#41811yescharacteristic
380C2×C71#289811yescharacteristic
381C2×C71#330611yescharacteristic
382C2×C71#330811yescharacteristic
383C2×C71#334311yescharacteristic
384C2×C71#334511yescharacteristic
385C2×#547D7111yescharacteristic
386C2×#435—711no—
387#2352—711no—
388#1993—711no—
389#1987—711no—
390#1895—711no—
391#1893—711no—
392#1875—711no—
393#1874—711no—
394#1824—711no—
395#1823—711no—
396#1804—711no—
397#1762—711no—
398#1736—711no—
399C2×#340—711no—
400C71#2249511yescharacteristic, complemented, Sylow
401C22×#41—21no—
402C22×M16—711no—
403C23×C8—711no—
404#547—24no—
405#547Dic7118yescomplemented
406C2×C4⋊Q8C2×D7111yescharacteristic
407C2×#123—21no—
408C2×#123—21no—
409C2×C22⋊Q8—21no—
410C2×#121C2×D7111yescharacteristic
411C2×#121C2×D7111yescharacteristic
412C2×C4×D4C2×D7111yescharacteristic
413C2×C4×D4C2×D7111yescharacteristic
414C2×#117—711no—
415C22×C4⋊C4—711no—
416C22×C4⋊C4C2×D7111yescharacteristic
417C22×C4⋊C4C2×D7111yescharacteristic
418#435—1424no—
419C2×C4⋊C8—711no—
420C2×#102—711no—
421C2×#102—711no—
422C2×#102—711no—
423C2×#102—711no—
424C2×C22⋊C8—711no—
425C2×C22⋊C8—711no—
426C2×#97—711no—
427#388—1421no—
428#387—1421no—
429#386—1421no—
430#382—711no—
431#380—711no—
432#380—711no—
433C4×C4⋊C4—711no—
434C4×C22⋊C4—1421no—
435#340—711no—
436#340—711no—
437#340—711no—
438#340—711no—
439#340—711no—
440#340—711no—
441#340—711no—
442#340—711no—
443#340—711no—
444#340—711no—
445#340—711no—
446#340—711no—
447C2×#41—28no—
448C2×#41—44no—
449C2×#41—44no—
450C22×Q8—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C22⋊D7111yescharacteristic
454C22×D4C22×D7111yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—21no—
458C23×C4—1421no—
459C23×C4C22×D7111yescharacteristic
460C23×C4C22×D7111yescharacteristic
461C2×M16—2841no—
462C2×M16—1422no—
463C2×M16—1422no—
464C22×C8—2841no—
465C22×C8—711no—
466C22×C8—711no—
467C22×C8—711no—
468C22×C8—711no—
469C22×C8—1422no—
470C22×C8—1422no—
471C4⋊Q8—22no—
472C4⋊Q8C2×Dic7114yescomplemented
473#123—28no—
474#123—28no—
475C22⋊Q8—28no—
476#121—22no—
477#121—22no—
478#121C2×Dic7114yes—
479#121C2×Dic7114yescomplemented
480C4×D4—22no—
481C4×D4C2×Dic7114yes—
482C4×D4C2×Dic7114yescomplemented
483C4×D4C22⋊D7114yes—
484#117—2841no—
485#117—1422no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—2841no—
492C2×C4⋊C4—711no—
493C2×C4⋊C4—711no—
494C2×C4⋊C4—711no—
495C2×C4⋊C4—711no—
496C2×C4⋊C4—1421no—
497C2×C4⋊C4—1422no—
498C2×C4⋊C4C2×Dic7114yes—
499C2×C4⋊C4C2×Dic7114yescomplemented
500C2×C4⋊C4C22⋊D7111yescharacteristic
501C2×C4⋊C4C22×D7111yescharacteristic
502C2×C4⋊C4C22×D7111yescharacteristic
503C2×C4⋊C4C22×D7111yescharacteristic
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
506C2×C22⋊C4—21no—
507C2×C22⋊C4—1421no—
508C2×C22⋊C4—1421no—
509C2×C22⋊C4—1421no—
510C2×C22⋊C4C22⋊D7111yescharacteristic
511C2×C22⋊C4C22⋊D7111yescharacteristic
512C2×C42—1421no—
513C2×C42—1421no—
514C2×C42C22×D7111yescharacteristic
515C4⋊C8—1422no—
516#102—2841no—
517#102—2841no—
518#102—1422no—
519#102—1422no—
520C22⋊C8—1422no—
521C22⋊C8—1422no—
522#97—1422no—
523#95—1421no—
524#95—1421no—
525#95—1421no—
526#95—1421no—
527#95—1421no—
528C24—21no—
529C24C2×C22⋊D7111yescharacteristic
530C24C2×C22⋊D7111yescharacteristic
531#41—432no—
532C2×Q8—24no—
533C2×Q8—42no—
534C2×Q8—42no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—24no—
538C2×D4—24no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—42no—
545C2×D4—42no—
546C2×D4—42no—
547C2×D4—42no—
548C2×D4C22⋊Dic7114yes—
549C2×D4C22×Dic7112yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—24no—
563C22×C4—24no—
564C22×C4—42no—
565C22×C4—42no—
566C22×C4—42no—
567C22×C4—42no—
568C22×C4—42no—
569C22×C4—42no—
570C22×C4—2842no—
571C22×C4—2842no—
572C22×C4—5681no—
573C22×C4—1421no—
574C22×C4—1421no—
575C22×C4—1421no—
576C22×C4—1421no—
577C22×C4C22×Dic7112yes—
578C22×C4C22×Dic7112yes—
579C22×C4C2×C22⋊D7112yes—
580C22×C4C2×C22⋊D7112yes—
581C22×C4C2×C22⋊D7111yescharacteristic
582C22×C4C2×C22⋊D7111yescharacteristic
583C22×C4C2×C22⋊D7111yescharacteristic
584C22×C4C2×C22⋊D7111yescharacteristic
585C22×C4C23×D7111yescharacteristic
586M16—2844no—
587C2×C8—2844no—
588C2×C8—712no—
589C2×C8—1421no—
590C2×C8—1421no—
591C2×C8—1421no—
592C2×C8—1421no—
593C2×C8—1421no—
594C2×C8—1421no—
595C2×C8—1421no—
596C2×C8—1421no—
597C2×C8—1421no—
598C2×C8—1421no—
599C2×C8—1421no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—24no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—2842no—
607C4⋊C4—712no—
608C4⋊C4—1421no—
609C4⋊C4—1421no—
610C4⋊C4—1421no—
611C4⋊C4—1421no—
612C4⋊C4—1421no—
613C4⋊C4—1421no—
614C4⋊C4—1421no—
615C4⋊C4C22⋊Dic7114yes—
616C4⋊C4C22×Dic7112yes—
617C4⋊C4C22×Dic7112yes—
618C4⋊C4C22×Dic7112yes—
619C22⋊C4—24no—
620C22⋊C4—24no—
621C22⋊C4—24no—
622C22⋊C4—2842no—
623C22⋊C4—2842no—
624C22⋊C4—5681no—
625C22⋊C4C22⋊Dic7114yes—
626C22⋊C4C22⋊Dic7114yes—
627C42—2842no—
628C42—5681no—
629C42C22×Dic7112yes—
630C42C2×C22⋊D7112yes—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23C2×C22⋊Dic7112yes—
649C23C2×C22⋊Dic7112yes—
650C23#1455615412yes—
651C23#1455615412yes—
652C23C22×C22⋊D7111yescharacteristic
653Q8—48no—
654D4—28no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—48no—
659D4—41no—
660D4—41no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—48no—
681C2×C4—48no—
682C2×C4—48no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—2841no—
690C2×C4—2841no—
691C2×C4—2841no—
692C2×C4—2841no—
693C2×C4—2841no—
694C2×C4—2841no—
695C2×C4—2841no—
696C2×C4—2841no—
697C2×C4—2841no—
698C2×C4—2841no—
699C2×C4—2841no—
700C2×C4—5684no—
701C2×C4—1422no—
702C2×C4C2×C22⋊Dic7112yes—
703C2×C4C2×C22⋊Dic7112yes—
704C2×C4C2×C22⋊Dic7112yes—
705C2×C4C2×C22⋊Dic7112yes—
706C2×C4C23×Dic7111yescharacteristic
707C2×C4C22×C22⋊D7111yescharacteristic
708C2×C4#41×D7111yescharacteristic
709C2×C4#41×D7111yescharacteristic
710C2×C4#1455617411yescharacteristic
711C2×C4#1455617511yescharacteristic
712C8—2841no—
713C8—2841no—
714C8—2841no—
715C8—1422no—
716C22—22no—
717C22—22no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—22no—
725C22—41no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—81no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22#1798600414yes—
737C22C22×C22⋊Dic7111yescharacteristic
738C22#1798663711yescharacteristic
739C22#1798664811yescharacteristic
740C22C2×#1455615411yescharacteristic
741C22C2×#1455615411yescharacteristic
742C22#1798680711yescharacteristic
743C22#1798681411yescharacteristic
744C4—22no—
745C4—22no—
746C4—22no—
747C4—22no—
748C4—42no—
749C4—42no—
750C4—42no—
751C4—2842no—
752C4—5681no—
753C4—5681no—
754C4—5681no—
755C4#41×Dic7111yescharacteristic
756C4#1798648211yescharacteristic
757C4#1798663711yescharacteristic
758C4#1798664811yescharacteristic
759C2—24no—
760C2—42no—
761C2—82no—
762C2#2259117011yescharacteristic
763C2C2×#1798600411yescharacteristic
764C2#2259687311yescharacteristic
765C2#2260029511yescharacteristic
766C2#2260032511yescharacteristic
767C2#2260077411yescharacteristic
768C2#2260081011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
Fitting, prime radicalC2×#547×C71C2
socleC23×C71C22×D4
cosocleC22×C4×C71C24
hypercenterC2×#547D71
hypocenterC71#22495
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#547

Complements

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

NH ≅ G/Ntype
1. C2×#17986071C2semidirect
2. #22591269C2semidirect
3. #22589314C2semidirect
4. #22589289C2semidirect
5. #22588779C2semidirect
6. #22588769C2semidirect
7. #22588663C2semidirect
8. #22588658C2semidirect
9. #22588430C2semidirect
10. #22588426C2semidirect
11. #22588350C2semidirect
12. #22588165C2semidirect
13. #22588059C2semidirect
14. C2×#17985761C2semidirect
51. #547×C71C4semidirect
114. C4⋊Q8×C71C2×C4semidirect
121. #121×C71C2×C4semidirect
124. C4×D4×C71C2×C4semidirect
132. C2×C4⋊C4×C71C2×C4semidirect
163. C2×C71⋊C8#41semidirect
172. C4⋊Dic71#41semidirect
400. C71#22495semidirect
405. #547Dic71semidirect
472. C4⋊Q8C2×Dic71semidirect
479. #121C2×Dic71semidirect
482. C4×D4C2×Dic71semidirect
499. C2×C4⋊C4C2×Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860712
#225912692
#225893142
#225892892
#225887792
#225887692
#225886632
#225886582
#225884302
#225884262
#225883502
#225881652
#225880592
C2×#179857612
C2×#547×C712
#2249571