Finite Group Databasebeta

← C2×#22600209 #32873840

Subgroups — C2×#22600209 #32873840

Order 18176.

2158 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986707C211yesmaximal, characteristic
2C2×Q8×C22⋊D71C211yesmaximal, characteristic
3#22600209C2116yesmaximal, direct product factor
4C2×#17986348C211yesmaximal, characteristic, complemented
5C2×#17986335C211yesmaximal, characteristic, complemented
6C2×#17986333C211yesmaximal, characteristic, complemented
7C2×#17986292C211yesmaximal, characteristic, complemented
8C2×#17986238C211yesmaximal, characteristic, complemented
9C2×#17986237C211yesmaximal, characteristic, complemented
10C2×#17986207C211yesmaximal, characteristic, complemented
11C2×#17986153C211yesmaximal, characteristic, complemented
12C2×Q16×Dic71C211yesmaximal, characteristic, complemented
13C2×(C22⋊D71)⋊C8C211yesmaximal, characteristic
14C22×#14556052C211yesmaximal, characteristic, complemented
15C2×#103×D71C211yesmaximal, characteristic, complemented
16C2×#451×C71C211yesmaximal, characteristic, complemented
17C22×Q8×D71C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C23×C71⋊C8C2211yescharacteristic
20C22×C8×D71C2211yescharacteristic
21#17986707—24no—
22#17986707C2218yes—
23Q8×C22⋊D71—24no—
24Q8×C22⋊D71C2218yes—
25C2×#14556127C2211yescharacteristic
26C2×#14556126—21no—
27C2×#14556126C2211yescharacteristic
28C2×#14556118—21no—
29C2×#14556108—21no—
30C2×#14556107—21no—
31C2×#14556107C2211yescharacteristic
32C2×#14556105—21no—
33C2×#14556104—21no—
34C2×#14556104C2211yescharacteristic
35C2×#14556104C2211yescharacteristic
36C2×Q8×Dic71C2211yescharacteristic
37C2×Q8×Dic71C2211yescharacteristic
38C2×C4×C22⋊D71—21no—
39C2×C4×C22⋊D71C2211yescharacteristic
40C2×(C22⋊D71)⋊C4—21no—
41C22×C4⋊Dic71C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic
43#17986348C2218yescomplemented
44#17986335C2218yescomplemented
45#17986333C2218yescomplemented
46#17986292C2218yescomplemented
47#17986238C2218yescomplemented
48#17986237C2218yescomplemented
49#17986207C2218yescomplemented
50#17986153C2218yescomplemented
51Q16×Dic71C2218yescomplemented
52(C22⋊D71)⋊C8C2218yes—
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×Dic71⋊C8C2211yescharacteristic
57C2×#14556053C2211yescharacteristic
58C2×#14556053C2211yescharacteristic
59C2×#14556052C2211yescharacteristic
60C2×#14556052C2211yescharacteristic
61C2×#14556052C2211yescharacteristic
62C2×#14556052C2211yescharacteristic
63C2×#14556052C2211yescharacteristic
64C2×#14556052C2218yescomplemented
65C2×#14556051C2211yescharacteristic
66#103×D71C2218yescomplemented
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C23×Q8×C71C2211yescharacteristic
70C22×Q16×C71C2211yescharacteristic
71C22×Q16×C71C2211yescharacteristic
72C2×C22⋊Q8×C71C2211yescharacteristic
73#451×C71C2218yescomplemented
74C2×#103×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×C22⋊C8×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C2×Q8×D71—22no—
81C2×Q8×D71—24no—
82C2×Q8×D71—42no—
83C2×Q8×D71C2314yes—
84C22×C22⋊D71D411yescharacteristic
85C23×Dic71—21no—
86C22×C4×D71—21no—
87C22×C4×D71—21no—
88C22×C4×D71C2311yescharacteristic
89C2×#11765855—42no—
90C2×#11765855C2314yes—
91C22×C71⋊C8—42no—
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2314yes—
95C2×C8×D71—42no—
96C2×C8×D71C2314yes—
97#14556127—22no—
98#14556127C2314yes—
99#14556126—28no—
100#14556126—22no—
101#14556126C2314yes—
102#14556118—28no—
103#14556108—28no—
104#14556107—28no—
105#14556107—22no—
106#14556107C2314yes—
107#14556105—28no—
108#14556104—22no—
109#14556104—22no—
110#14556104—28no—
111#14556104C2314yes—
112#14556104C2314yes—
113Q8×Dic71—22no—
114Q8×Dic71—22no—
115Q8×Dic71C2314yes—
116Q8×Dic71C2314yes—
117C4×C22⋊D71—28no—
118C4×C22⋊D71D414yes—
119C4×C22⋊D71C2314yes—
120(C22⋊D71)⋊C4—28no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71—21no—
123C2×C4⋊Dic71—22no—
124C2×C4⋊Dic71—21no—
125C2×C4⋊Dic71C2314yes—
126C2×C4⋊Dic71C2311yescharacteristic
127C2×C4⋊Dic71C2311yescharacteristic
128C2×C4⋊Dic71C2311yescharacteristic
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4—21no—
133C2×Dic71⋊C4—21no—
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4D411yescharacteristic
137C4⋊C4×D71—22no—
138C4⋊C4×D71C2314yes—
139C2×C22⋊Dic71—21no—
140C2×C22⋊Dic71D411yescharacteristic
141C2×(C2×D71)⋊C4—21no—
142C2×(C2×D71)⋊C4—21no—
143C2×(C2×D71)⋊C4D411yescharacteristic
144C2×C4×Dic71—21no—
145C2×C4×Dic71—21no—
146C2×C4×Dic71C2311yescharacteristic
147#14556062C2314yes—
148#14556062C2314yes—
149#14556061C2314yes—
150Dic71⋊C8C2314yes—
151#14556053C2314yes—
152#14556053C2314yes—
153#14556052C2314yes—
154#14556052C2314yes—
155#14556052C2314yes—
156#14556052C2314yes—
157#14556052C2314yes—
158#14556051C2314yes—
159(C2×D71)⋊C8C2314yes—
160C8×Dic71C2314yes—
161C22×Q8×C71—22no—
162C22×Q8×C71—21no—
163C22×Q8×C71—24no—
164C22×Q8×C71—42no—
165C22×Q8×C71C2311yescharacteristic
166C22×Q8×C71C2311yescharacteristic
167C22×Q8×C71C2314yes—
168C22×Q8×C71C2311yescharacteristic
169C23×C4×C71—21no—
170C23×C4×C71C2311yescharacteristic
171C2×Q16×C71—24no—
172C2×Q16×C71—42no—
173C2×Q16×C71C2314yes—
174C2×Q16×C71C2314yes—
175C22×C8×C71C2311yescharacteristic
176C22×C8×C71C2311yescharacteristic
177C22⋊Q8×C71—22no—
178C22⋊Q8×C71C2314yes—
179C2×C4⋊C4×C71—21no—
180C2×C4⋊C4×C71C2311yescharacteristic
181C2×C22⋊C4×C71—21no—
182#103×C71C2314yes—
183#103×C71C2314yes—
184C22⋊C8×C71C2314yes—
185C23×D71C2×D411yescharacteristic
186C2×Dic142—22no—
187C2×Dic142—22no—
188C2×Dic142—21no—
189C2×Dic142—24no—
190C2×Dic142—24no—
191C2×Dic142—44no—
192C2×Dic142—82no—
193C2×Dic142C2412yes—
194Q8×D71—28no—
195Q8×D71—44no—
196Q8×D71—48no—
197C2×C22⋊D71Q1618yescomplemented
198C2×C22⋊D71C2×D414yes—
199C22×Dic71—21no—
200C22×Dic71—21no—
201C22×Dic71—21no—
202C22×Dic71—21no—
203C22×Dic71—24no—
204C22×Dic71—82no—
205C22×Dic71C2×D411yescharacteristic
206C22×Dic71C2×D411yescharacteristic
207C22×Dic71C2×D411yescharacteristic
208C2×C4×D71—22no—
209C2×C4×D71—22no—
210C2×C4×D71—24no—
211C2×C4×D71—24no—
212C2×C4×D71—44no—
213C2×C4×D71—82no—
214C2×C4×D71C2×D412yes—
215C2×C4×D71C2412yes—
216#11765855—44no—
217C2×C71⋊C8—22no—
218C2×C71⋊C8—22no—
219C2×C71⋊C8—44no—
220C2×C71⋊C8C2412yes—
221C2×C71⋊C8C2412yes—
222C8×D71—44no—
223C4⋊Dic71—21no—
224C4⋊Dic71—21no—
225C4⋊Dic71—24no—
226C4⋊Dic71—21no—
227C4⋊Dic71—24no—
228C4⋊Dic71—24no—
229C4⋊Dic71C2412yes—
230C4⋊Dic71C2412yes—
231C4⋊Dic71C2412yes—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234Dic71⋊C4—24no—
235Dic71⋊C4—24no—
236Dic71⋊C4—24no—
237Dic71⋊C4—24no—
238Dic71⋊C4—24no—
239Dic71⋊C4C2×D414yes—
240C22⋊Dic71—24no—
241C22⋊Dic71C2×D414yes—
242(C2×D71)⋊C4—24no—
243(C2×D71)⋊C4—24no—
244(C2×D71)⋊C4C2×D414yes—
245C4×Dic71—24no—
246C4×Dic71—24no—
247C4×Dic71C2×D412yes—
248C4×Dic71C2412yes—
249C24×C71C2×D411yescharacteristic
250C2×Q8×C71—21no—
251C2×Q8×C71—21no—
252C2×Q8×C71—24no—
253C2×Q8×C71—21no—
254C2×Q8×C71—22no—
255C2×Q8×C71—28no—
256C2×Q8×C71—22no—
257C2×Q8×C71—22no—
258C2×Q8×C71—22no—
259C2×Q8×C71—22no—
260C2×Q8×C71—44no—
261C2×Q8×C71—44no—
262C2×Q8×C71—48no—
263C2×Q8×C71#4114yes—
264C2×Q8×C71C2412yes—
265C2×Q8×C71C2412yes—
266C2×Q8×C71C2412yes—
267C22×C4×C71—21no—
268C22×C4×C71—22no—
269C22×C4×C71—22no—
270C22×C4×C71—21no—
271C22×C4×C71—21no—
272C22×C4×C71—21no—
273C22×C4×C71—24no—
274C22×C4×C71—44no—
275C22×C4×C71C2×D411yescharacteristic
276C22×C4×C71C2×D412yes—
277C22×C4×C71C2412yes—
278C22×C4×C71C2411yescharacteristic
279Q16×C71—28no—
280Q16×C71—44no—
281C2×C8×C71—22no—
282C2×C8×C71—22no—
283C2×C8×C71C2412yes—
284C2×C8×C71C2412yes—
285C4⋊C4×C71—24no—
286C4⋊C4×C71—21no—
287C4⋊C4×C71C2412yes—
288C22⋊C4×C71—24no—
289C23×C71—22no—
290C23×C71—22no—
291C23×C71C2×Q1614yes—
292C23×C71C22×D412yes—
293C23×C71C22×D411yescharacteristic
294C22×D71—22no—
295C22×D71—22no—
296C22×D71C2×Q1614yes—
297C22×D71C22×D412yes—
298Q8×C71—24no—
299Q8×C71—22no—
300Q8×C71—22no—
301Q8×C71—22no—
302Q8×C71—22no—
303Q8×C71—22no—
304Q8×C71—48no—
305Q8×C71—42no—
306Q8×C71—42no—
307Q8×C71C2×#4114yes—
308C2×C4×C71—22no—
309C2×C4×C71—24no—
310C2×C4×C71—22no—
311C2×C4×C71—24no—
312C2×C4×C71—22no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—48no—
318C2×C4×C71—42no—
319C2×C4×C71—42no—
320C2×C4×C71—42no—
321C2×C4×C71C22×D412yes—
322C2×C4×C71C22×D411yescharacteristic
323C2×C4×C71C2×#4112yes—
324C2×C4×C71H(5,𝔽2)12yes—
325C2×C4×C71C2511yescharacteristic
326C22⋊D71C2×Q16116yescomplemented
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—42no—
334C2×Dic71—42no—
335C2×Dic71—42no—
336C2×Dic71—42no—
337C2×Dic71—84no—
338C2×Dic71C2×Q1614yes—
339C2×Dic71C22×D412yes—
340C2×Dic71C22×D412yes—
341C2×Dic71C22×D412yes—
342C4×D71—24no—
343C4×D71—22no—
344C4×D71—22no—
345C4×D71—48no—
346C4×D71—84no—
347Dic142—22no—
348Dic142—22no—
349Dic142—48no—
350Dic142—42no—
351Dic142—84no—
352C8×C71—22no—
353C8×C71—22no—
354C71⋊C8—22no—
355C71⋊C8—22no—
356C22×C71—22no—
357C22×C71—28no—
358C22×C71—22no—
359C22×C71#54612yes—
360C22×C71C22×Q1614yes—
361C22×C71C22×Q1612yes—
362C22×C71#57712yes—
363C22×C71C23×D411yescharacteristic
364C2×D71—22no—
365C2×D71—28no—
366C2×D71—22no—
367C2×D71C22×Q1614yes—
368C4×C71—24no—
369C4×C71—22no—
370C4×C71—42no—
371C4×C71—42no—
372C4×C71—42no—
373C4×C71#54612yes—
374C4×C71C22×#4111yescharacteristic
375C4×C71C2×H(5,𝔽2)11yescharacteristic
376Dic71—22no—
377Dic71—22no—
378Dic71—42no—
379Dic71—42no—
380Dic71—42no—
381Dic71—42no—
382Dic71C22×Q1614yes—
383C2×#3299—711nomaximal, Sylow
384C2×C71—24no—
385C2×C71#329914yescomplemented
386C2×C71C2×#54611yescharacteristic
387C2×C71C23×Q1611yescharacteristic
388C2×C71C2×#57711yescharacteristic
389D71—24no—
390C2×#554—711no—
391C2×D4×Q8—711no—
392#3299—7116no—
393C2×#487—711no—
394C2×#484—711no—
395C2×#484—711no—
396C2×#477—711no—
397C2×#467—711no—
398C2×#467—711no—
399C2×#462—711no—
400C2×#451—711no—
401C2×#451D7111yescharacteristic, complemented
402C2×C4×Q16—711no—
403C2×C8×D4—711no—
404C22×#103—711no—
405C22×#103—711no—
406C71C2×#329911yescharacteristic, complemented, Sylow
407C23×Q8—711no—
408C23×Q8C2×D7111yescharacteristic
409C22×Q16—711no—
410C22×Q16C2×D7111yescharacteristic
411C22×Q16C2×D7111yescharacteristic
412C23×C8—711no—
413C23×C8—711no—
414#554—718no—
415#554—1424no—
416D4×Q8—718no—
417D4×Q8—1424no—
418C2×C4⋊Q8—711no—
419C2×C4⋊Q8—711no—
420C2×C4⋊Q8—1421no—
421C2×#125—1421no—
422C2×C22⋊Q8—711no—
423C2×C22⋊Q8—711no—
424C2×C22⋊Q8—711no—
425C2×C22⋊Q8—1421no—
426C2×C22⋊Q8—1421no—
427C2×C22⋊Q8—1421no—
428C2×C22⋊Q8—1421no—
429C2×C22⋊Q8C2×D7111yescharacteristic
430C2×C4×Q8—711no—
431C2×C4×Q8—711no—
432C2×C4×D4—711no—
433C2×C4×D4—1421no—
434C2×C4×D4—1421no—
435C22×C4⋊C4—711no—
436C22×C4⋊C4—711no—
437#487—718no—
438#484—718no—
439#484—718no—
440#477—718no—
441#467—718no—
442#467—718no—
443#462—718no—
444#451—718no—
445#451C2×D7118yescomplemented
446C4×Q16—718no—
447C8×D4—718no—
448C2×#107—711no—
449C2×#107—711no—
450C2×#107—711no—
451C2×C4⋊C8—711no—
452C2×#103—711no—
453C2×#103—711no—
454C2×#103—711no—
455C2×#103—711no—
456C2×#103—718no—
457C2×#103—711no—
458C2×#103—711no—
459C2×#103—711no—
460C2×#103—711no—
461C2×#103—718no—
462C2×#103C2×D7111yescharacteristic
463C2×#103C2×D7111yescharacteristic
464C2×C22⋊C8—711no—
465C2×C22⋊C8C2×D7111yescharacteristic
466C2×C4×C8—711no—
467C22×Q8—21no—
468C22×Q8—22no—
469C22×Q8—24no—
470C22×Q8—42no—
471C22×Q8—2842no—
472C22×Q8—714no—
473C22×Q8—711no—
474C22×Q8—1421no—
475C22×Q8—1421no—
476C22×Q8—1424no—
477C22×Q8—1422no—
478C22×Q8C22×D7111yescharacteristic
479C22×Q8C22×D7111yescharacteristic
480C22×Q8C22×D7114yes—
481C22×Q8C22×D7111yescharacteristic
482C22×D4—711no—
483C23×C4—21no—
484C23×C4—711no—
485C23×C4—1421no—
486C23×C4—1421no—
487C23×C4—1421no—
488C23×C4C22×D7111yescharacteristic
489C2×Q16—24no—
490C2×Q16—42no—
491C2×Q16—2842no—
492C2×Q16—714no—
493C2×Q16C22×D7114yes—
494C2×Q16C22×D7114yes—
495C22×C8—2842no—
496C22×C8—2842no—
497C22×C8—714no—
498C22×C8—714no—
499C22×C8—711no—
500C22×C8—711no—
501C22×C8C22×D7111yescharacteristic
502C22×C8C22×D7111yescharacteristic
503C4⋊Q8—714no—
504C4⋊Q8—714no—
505C4⋊Q8—1422no—
506C4⋊Q8—1422no—
507C4⋊Q8—1428no—
508#125—1428no—
509C22⋊Q8—22no—
510C22⋊Q8—714no—
511C22⋊Q8—714no—
512C22⋊Q8—714no—
513C22⋊Q8—1428no—
514C22⋊Q8—1428no—
515C22⋊Q8—1428no—
516C22⋊Q8—1428no—
517C22⋊Q8—1422no—
518C22⋊Q8—1422no—
519C22⋊Q8—1422no—
520C22⋊Q8C22×D7114yes—
521C4×Q8—714no—
522C4×Q8—714no—
523C4×Q8—1422no—
524C4×Q8—1422no—
525C4×D4—714no—
526C4×D4—714no—
527C4×D4—1428no—
528C4×D4—1428no—
529C2×C4⋊C4—21no—
530C2×C4⋊C4—711no—
531C2×C4⋊C4—711no—
532C2×C4⋊C4—711no—
533C2×C4⋊C4—714no—
534C2×C4⋊C4—711no—
535C2×C4⋊C4—714no—
536C2×C4⋊C4—1422no—
537C2×C4⋊C4—1421no—
538C2×C4⋊C4—1421no—
539C2×C4⋊C4—1421no—
540C2×C4⋊C4—1421no—
541C2×C4⋊C4—1421no—
542C2×C4⋊C4—1421no—
543C2×C4⋊C4—1421no—
544C2×C4⋊C4—1421no—
545C2×C4⋊C4—1421no—
546C2×C4⋊C4—1422no—
547C2×C4⋊C4—1421no—
548C2×C4⋊C4C22×D7111yescharacteristic
549C2×C22⋊C4—21no—
550C2×C22⋊C4—711no—
551C2×C22⋊C4—711no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4—1421no—
555C2×C42—711no—
556C2×C42—1421no—
557C2×C42—1421no—
558#107—714no—
559#107—714no—
560#107—714no—
561C4⋊C8—714no—
562#103—714no—
563#103—714no—
564#103—714no—
565#103—714no—
566#103—714no—
567#103—714no—
568#103—714no—
569#103—714no—
570#103C22×D7114yes—
571#103C22×D7114yes—
572C22⋊C8—714no—
573C22⋊C8C22×D7114yes—
574C4×C8—714no—
575C24—711no—
576C24D4×D7111yescharacteristic
577C2×Q8—21no—
578C2×Q8—21no—
579C2×Q8—24no—
580C2×Q8—21no—
581C2×Q8—22no—
582C2×Q8—28no—
583C2×Q8—22no—
584C2×Q8—22no—
585C2×Q8—22no—
586C2×Q8—22no—
587C2×Q8—44no—
588C2×Q8—44no—
589C2×Q8—48no—
590C2×Q8—2844no—
591C2×Q8—2848no—
592C2×Q8—2844no—
593C2×Q8—5682no—
594C2×Q8—712no—
595C2×Q8—1424no—
596C2×Q8—1424no—
597C2×Q8—1428no—
598C2×Q8—1422no—
599C2×Q8—1422no—
600C2×Q8—1421no—
601C2×Q8#1176586414yes—
602C2×Q8C23×D7112yes—
603C2×Q8C23×D7112yes—
604C2×Q8C23×D7112yes—
605C2×D4—714no—
606C2×D4—718no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—24no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—44no—
615C22×C4—2844no—
616C22×C4—5682no—
617C22×C4—5682no—
618C22×C4—711no—
619C22×C4—711no—
620C22×C4—711no—
621C22×C4—712no—
622C22×C4—712no—
623C22×C4—1424no—
624C22×C4—1424no—
625C22×C4—1421no—
626C22×C4—1421no—
627C22×C4—1421no—
628C22×C4—1421no—
629C22×C4—1424no—
630C22×C4—1422no—
631C22×C4—1422no—
632C22×C4D4×D7112yes—
633C22×C4D4×D7111yescharacteristic
634C22×C4C23×D7112yes—
635C22×C4C23×D7111yescharacteristic
636Q16—28no—
637Q16—44no—
638Q16—2844no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—2844no—
642C2×C8—2844no—
643C2×C8—712no—
644C2×C8—712no—
645C2×C8—1422no—
646C2×C8—1422no—
647C2×C8C23×D7112yes—
648C2×C8C23×D7112yes—
649C4⋊C4—24no—
650C4⋊C4—21no—
651C4⋊C4—714no—
652C4⋊C4—712no—
653C4⋊C4—712no—
654C4⋊C4—712no—
655C4⋊C4—1424no—
656C4⋊C4—1424no—
657C4⋊C4—1424no—
658C4⋊C4—1424no—
659C4⋊C4—1424no—
660C4⋊C4—1424no—
661C4⋊C4—1424no—
662C4⋊C4—1424no—
663C4⋊C4—1424no—
664C4⋊C4—1421no—
665C4⋊C4—1424no—
666C4⋊C4—1421no—
667C4⋊C4—1421no—
668C4⋊C4C23×D7112yes—
669C22⋊C4—24no—
670C22⋊C4—714no—
671C22⋊C4—714no—
672C22⋊C4—1424no—
673C22⋊C4—1424no—
674C22⋊C4—1424no—
675C42—712no—
676C42—712no—
677C42—1424no—
678C42—1424no—
679C23—22no—
680C23—22no—
681C23—712no—
682C23—714no—
683C23—1422no—
684C23—1422no—
685C23Q16×D7114yes—
686C23C2×D4×D7112yes—
687C23C2×D4×D7111yescharacteristic
688Q8—22no—
689Q8—24no—
690Q8—22no—
691Q8—22no—
692Q8—22no—
693Q8—22no—
694Q8—48no—
695Q8—42no—
696Q8—42no—
697Q8—2848no—
698Q8—2842no—
699Q8—5684no—
700Q8—1422no—
701Q8—1422no—
702Q8C2×#1176586414yes—
703D4—7116no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—2848no—
718C2×C4—2842no—
719C2×C4—2842no—
720C2×C4—2842no—
721C2×C4—2842no—
722C2×C4—5684no—
723C2×C4—5684no—
724C2×C4—712no—
725C2×C4—714no—
726C2×C4—712no—
727C2×C4—712no—
728C2×C4—1422no—
729C2×C4—1422no—
730C2×C4—1422no—
731C2×C4—1422no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1422no—
736C2×C4—1424no—
737C2×C4C2×D4×D7112yes—
738C2×C4C2×D4×D7111yescharacteristic
739C2×C4C2×#1176586412yes—
740C2×C4#1455617312yes—
741C2×C4C24×D7111yescharacteristic
742C8—22no—
743C8—22no—
744C8—1422no—
745C8—1422no—
746C22—28no—
747C22—22no—
748C22—22no—
749C22—714no—
750C22—1428no—
751C22—1422no—
752C22—1422no—
753C22#1798663612yes—
754C22C2×Q16×D7114yes—
755C22C2×Q16×D7112yes—
756C22#1798680812yes—
757C22C22×D4×D7111yescharacteristic
758C4—22no—
759C4—24no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—2842no—
764C4—2842no—
765C4—2842no—
766C4—2842no—
767C4—714no—
768C4—1422no—
769C4—1422no—
770C4#1798663612yes—
771C4C22×#1176586411yescharacteristic
772C4C2×#1455617311yescharacteristic
773C2—24no—
774C2—1424no—
775C2#2260020914yesdirect product factor
776C2C2×#1798663611yescharacteristic
777C2C22×Q16×D7111yescharacteristic
778C2C2×#1798680811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#451×C71C2
socleC23×C71C22×D4
prime radicalC22×C22⋊D71D4
hypercenterC2×#451D71
hypocenterC71C2×#3299
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
3. #22600209C2direct (N × H)
4. C2×#17986348C2semidirect
5. C2×#17986335C2semidirect
6. C2×#17986333C2semidirect
7. C2×#17986292C2semidirect
8. C2×#17986238C2semidirect
9. C2×#17986237C2semidirect
10. C2×#17986207C2semidirect
11. C2×#17986153C2semidirect
12. C2×Q16×Dic71C2semidirect
14. C22×#14556052C2semidirect
15. C2×#103×D71C2semidirect
16. C2×#451×C71C2semidirect
43. #17986348C22semidirect
44. #17986335C22semidirect
45. #17986333C22semidirect
46. #17986292C22semidirect
47. #17986238C22semidirect
48. #17986237C22semidirect
49. #17986207C22semidirect
50. #17986153C22semidirect
51. Q16×Dic71C22semidirect
64. C2×#14556052C22semidirect
66. #103×D71C22semidirect
73. #451×C71C22semidirect
197. C2×C22⋊D71Q16semidirect
326. C22⋊D71C2×Q16semidirect
385. C2×C71#3299semidirect
401. C2×#451D71semidirect
406. C71C2×#3299semidirect
445. #451C2×D71semidirect
775. C2#22600209direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867072
C2×Q8×C22⋊D712
#226002092
C2×#179863482
C2×#179863352
C2×#179863332
C2×#179862922
C2×#179862382
C2×#179862372
C2×#179862072
C2×#179861532
C2×Q16×Dic712
C2×(C22⋊D71)⋊C82
C22×#145560522
C2×#103×D712
C2×#451×C712
C2×#329971