Finite Group Databasebeta

← #32013985

Subgroups — #32013985

Order 18176.

1292 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D71C211yesmaximal, characteristic
2C2×#17986128C211yesmaximal, characteristic, complemented
3C2×#17986127C211yesmaximal, characteristic, complemented
4#22589281C211yesmaximal, characteristic, complemented
5#22589278C211yesmaximal, characteristic, complemented
6#22589278C211yesmaximal, characteristic, complemented
7#22589274C211yesmaximal, characteristic, complemented
8#22589274C211yesmaximal, characteristic, complemented
9#22588319C211yesmaximal, characteristic
10#22588319C211yesmaximal, characteristic
11#22588317C211yesmaximal, characteristic
12#22588103C211yesmaximal, characteristic
13#22588101C211yesmaximal, characteristic
14#22588097C211yesmaximal, characteristic
15C71×#1985C211yesmaximal, characteristic, complemented
16C22×Q8×D71C411yescharacteristic
17C2×Q8×Dic71C411yescharacteristic
18C2×C4×Dic142C2211yescharacteristic
19C2×C4×Dic142C2211yescharacteristic
20C2×C4×Dic142C2211yescharacteristic
21C2×#14556093C411yescharacteristic
22C2×#14556093C411yescharacteristic
23C2×#14556093C411yescharacteristic
24C4×Q8×D71—24no—
25C4×Q8×D71—24no—
26C2×C4⋊C4×D71C411yescharacteristic
27C2×C4⋊C4×D71C411yescharacteristic
28C2×C4⋊C4×D71C411yescharacteristic
29C2×C42×D71C2211yescharacteristic
30C2×C42×D71C2211yescharacteristic
31C2×C42×D71C2211yescharacteristic
32#17986128—24no—
33#17986127—24no—
34C2×C4⋊(C71⋊C8)C2211yescharacteristic
35C2×Dic71⋊C8C2211yescharacteristic
36C2×Dic71⋊C8C2211yescharacteristic
37C2×Dic71⋊C8C2211yescharacteristic
38C2×Dic71⋊C8C2211yescharacteristic
39C2×(C2×D71)⋊C8C2211yescharacteristic
40C2×(C2×D71)⋊C8C2211yescharacteristic
41C2×(C2×D71)⋊C8C2211yescharacteristic
42C2×(C2×D71)⋊C8C2211yescharacteristic
43C2×#14556039C2211yescharacteristic
44C2×#14556038C2211yescharacteristic
45C2×#14556038C2211yescharacteristic
46C2×C8×Dic71C2211yescharacteristic
47C2×C8×Dic71C2211yescharacteristic
48#17985754C2211yescharacteristic
49#17985754C2211yescharacteristic
50#17985754C2211yescharacteristic
51#17985754C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54#17985753C2211yescharacteristic
55#17985753C2211yescharacteristic
56C2×C4×Q8×C71C2211yescharacteristic
57C2×C4⋊C8×C71C2211yescharacteristic
58C2×#97×C71C2211yescharacteristic
59#336×C71C2211yescharacteristic
60#336×C71C2211yescharacteristic
61#336×C71C2211yescharacteristic
62#336×C71C2211yescharacteristic
63C22×Dic142C2×C411yescharacteristic
64C22×Dic142C2×C411yescharacteristic
65C22×Dic142C2×C411yescharacteristic
66C2×Q8×D71—24no—
67C2×Q8×D71—24no—
68C2×Q8×D71—24no—
69C22×C4×D71C2×C411yescharacteristic
70C22×C4×D71C2×C411yescharacteristic
71C22×C4×D71C2×C411yescharacteristic
72C22×C4×D71C2×C411yescharacteristic
73C22×C4×D71C2×C411yescharacteristic
74C22×C4×D71C2×C411yescharacteristic
75C22×C4×D71C2311yescharacteristic
76C22×C71⋊C8C2311yescharacteristic
77C22×C71⋊C8C2311yescharacteristic
78C22×C71⋊C8C2311yescharacteristic
79C22×C71⋊C8C2311yescharacteristic
80Q8×Dic71—24no—
81C4×Dic142—22no—
82C4×Dic142—22no—
83C4×Dic142—22no—
84C4×Dic142—22no—
85C4×Dic142D414yes—
86C4×Dic142D414yes—
87#14556093—24no—
88#14556093—24no—
89#14556093—24no—
90C2×C4⋊Dic71C2×C411yescharacteristic
91C2×C4⋊Dic71C2×C411yescharacteristic
92C2×C4⋊Dic71C2×C411yescharacteristic
93C2×Dic71⋊C4C2×C411yescharacteristic
94C2×Dic71⋊C4C2×C411yescharacteristic
95C2×Dic71⋊C4C2×C411yescharacteristic
96C2×Dic71⋊C4C2×C411yescharacteristic
97C2×Dic71⋊C4C2×C411yescharacteristic
98C2×Dic71⋊C4C2×C411yescharacteristic
99C4⋊C4×D71—24no—
100C4⋊C4×D71—24no—
101C4⋊C4×D71—24no—
102C2×C4×Dic71C2×C411yescharacteristic
103C2×C4×Dic71C2×C411yescharacteristic
104C2×C4×Dic71C2×C411yescharacteristic
105C2×C4×Dic71C2×C411yescharacteristic
106C2×C4×Dic71C2×C411yescharacteristic
107C2×C4×Dic71C2×C411yescharacteristic
108C2×C4×Dic71C2311yescharacteristic
109C2×C4×Dic71C2311yescharacteristic
110C2×C4×Dic71C2311yescharacteristic
111C42×D71—22no—
112C42×D71—22no—
113C42×D71—22no—
114C42×D71—22no—
115C42×D71—22no—
116C42×D71—22no—
117C4⋊(C71⋊C8)—22no—
118Dic71⋊C8—22no—
119Dic71⋊C8—22no—
120Dic71⋊C8—22no—
121Dic71⋊C8—22no—
122(C2×D71)⋊C8—22no—
123(C2×D71)⋊C8—22no—
124(C2×D71)⋊C8—22no—
125(C2×D71)⋊C8Q814yescomplemented
126#14556039—22no—
127#14556038—22no—
128#14556038—22no—
129C8×Dic71—22no—
130C8×Dic71—22no—
131C22×Q8×C71C2×C411yescharacteristic
132C22×C8×C71C2311yescharacteristic
133C22×C8×C71C2311yescharacteristic
134C22×C8×C71C2311yescharacteristic
135C22×C8×C71C2311yescharacteristic
136C4×Q8×C71—22no—
137C4×Q8×C71—22no—
138C2×C4⋊C4×C71C2×C411yescharacteristic
139C2×C4⋊C4×C71C2×C411yescharacteristic
140C2×C4⋊C4×C71C2×C411yescharacteristic
141C2×C42×C71C2311yescharacteristic
142C2×C42×C71C2311yescharacteristic
143C2×C42×C71C2311yescharacteristic
144C4⋊C8×C71—22no—
145#97×C71—22no—
146C23×D71C22×C411yescharacteristic
147C2×Dic142—22no—
148C2×Dic142—22no—
149C2×Dic142—22no—
150C2×Dic142—22no—
151C2×Dic142—22no—
152C2×Dic142—22no—
153C2×Dic142—22no—
154C2×Dic142C22⋊C414yes—
155C2×Dic142M1614yes—
156Q8×D71—232no—
157C22×Dic71C22×C411yescharacteristic
158C22×Dic71C22×C411yescharacteristic
159C22×Dic71C22×C411yescharacteristic
160C22×Dic71C22×C411yescharacteristic
161C22×Dic71C22×C411yescharacteristic
162C22×Dic71C22×C411yescharacteristic
163C22×Dic71C22×C411yescharacteristic
164C2×C4×D71—22no—
165C2×C4×D71—22no—
166C2×C4×D71—22no—
167C2×C4×D71—22no—
168C2×C4×D71—21no—
169C2×C4×D71—21no—
170C2×C4×D71—21no—
171C2×C4×D71—21no—
172C2×C4×D71—22no—
173C2×C4×D71—22no—
174C2×C4×D71—22no—
175C2×C4×D71—22no—
176C2×C4×D71—22no—
177C2×C4×D71—22no—
178C2×C4×D71—22no—
179C2×C4×D71—22no—
180C2×C4×D71—22no—
181C2×C4×D71—22no—
182C2×C4×D71—41no—
183C2×C4×D71—41no—
184C2×C4×D71—41no—
185C2×C4×D71M1614yes—
186C2×C4×D71C2×Q812yes—
187C2×C4×D71#4112yes—
188C2×C71⋊C8—21no—
189C2×C71⋊C8—21no—
190C2×C71⋊C8—21no—
191C2×C71⋊C8—21no—
192C2×C71⋊C8—21no—
193C2×C71⋊C8—21no—
194C2×C71⋊C8—21no—
195C2×C71⋊C8—21no—
196C2×C71⋊C8—21no—
197C2×C71⋊C8—21no—
198C2×C71⋊C8—21no—
199C2×C71⋊C8C2×Q812yescomplemented
200C4⋊Dic71—22no—
201C4⋊Dic71—22no—
202C4⋊Dic71C22⋊C414yes—
203Dic71⋊C4—22no—
204Dic71⋊C4—22no—
205Dic71⋊C4—22no—
206Dic71⋊C4—22no—
207Dic71⋊C4C22⋊C414yes—
208Dic71⋊C4C22⋊C414yes—
209C4×Dic71—22no—
210C4×Dic71—22no—
211C4×Dic71—21no—
212C4×Dic71—21no—
213C4×Dic71—22no—
214C4×Dic71—22no—
215C4×Dic71—22no—
216C4×Dic71—22no—
217C4×Dic71C2×D412yes—
218C4×Dic71C2×D412yes—
219C4×Dic71C2×D412yes—
220C4×Dic71C2×D412yes—
221C2×Q8×C71—22no—
222C2×Q8×C71—22no—
223C2×Q8×C71—22no—
224C22×C4×C71C22×C411yescharacteristic
225C22×C4×C71C22×C411yescharacteristic
226C22×C4×C71C22×C411yescharacteristic
227C22×C4×C71C22×C411yescharacteristic
228C22×C4×C71C22×C411yescharacteristic
229C22×C4×C71C22×C411yescharacteristic
230C22×C4×C71C2411yescharacteristic
231C2×C8×C71—21no—
232C2×C8×C71—21no—
233C2×C8×C71—21no—
234C2×C8×C71—21no—
235C2×C8×C71—21no—
236C2×C8×C71—21no—
237C2×C8×C71—21no—
238C2×C8×C71—21no—
239C2×C8×C71—21no—
240C2×C8×C71—21no—
241C2×C8×C71—21no—
242C2×C8×C71C2×Q812yescomplemented
243C4⋊C4×C71—22no—
244C4⋊C4×C71—22no—
245C4⋊C4×C71—22no—
246C42×C71—21no—
247C42×C71—21no—
248C42×C71—21no—
249C42×C71—21no—
250C42×C71C2×D412yes—
251C42×C71C2×D412yes—
252C23×C71C23×C411yescharacteristic
253C22×D71—21no—
254C22×D71—21no—
255C22×D71—21no—
256C22×D71—21no—
257C22×D71C4×Q812yes—
258C22×D71C2×M1612yes—
259C22×D71#13112yes—
260Q8×C71—28no—
261C2×C4×C71—21no—
262C2×C4×C71—21no—
263C2×C4×C71—21no—
264C2×C4×C71—21no—
265C2×C4×C71—21no—
266C2×C4×C71—21no—
267C2×C4×C71—21no—
268C2×C4×C71—21no—
269C2×C4×C71—21no—
270C2×C4×C71—21no—
271C2×C4×C71—21no—
272C2×C4×C71—21no—
273C2×C4×C71—21no—
274C2×C4×C71—21no—
275C2×C4×C71C2×C22⋊C412yes—
276C2×C4×C71C2×C22⋊C412yes—
277C2×C4×C71C2×M1612yes—
278C2×C4×C71C2×M1612yes—
279C2×C4×C71C22×D411yescharacteristic
280C2×C4×C71C22×D411yescharacteristic
281C2×C4×C71C22×Q811yescharacteristic
282C2×C4×C71C2×#4111yescharacteristic
283C2×C4×C712−1+411yescharacteristic
284C2×C4×C712−1+411yescharacteristic
285C2×Dic71—21no—
286C2×Dic71—21no—
287C2×Dic71—21no—
288C2×Dic71—21no—
289C2×Dic71—21no—
290C2×Dic71—21no—
291C2×Dic71—21no—
292C2×Dic71—21no—
293C2×Dic71—21no—
294C2×Dic71—21no—
295C2×Dic71—21no—
296C2×Dic71—21no—
297C2×Dic71—21no—
298C2×Dic71C2×C22⋊C412yes—
299C2×Dic71C2×C22⋊C412yes—
300C2×Dic71C2×C22⋊C412yes—
301C2×Dic71C2×C22⋊C412yes—
302C2×Dic71C4×Q812yes—
303C2×Dic71C2×M1612yes—
304C2×Dic71C2×M1612yes—
305C2×Dic71C2×M1612yes—
306C4×D71—28no—
307C4×D71—28no—
308C4×D71—22no—
309C4×D71—22no—
310C4×D71—22no—
311C4×D71—22no—
312C4×D71—28no—
313C4×D71—44no—
314C4×D71—44no—
315C4×D71—44no—
316Dic142—28no—
317Dic142—28no—
318Dic142—28no—
319C8×C71—22no—
320C8×C71—41no—
321C8×C71—41no—
322C8×C71—41no—
323C71⋊C8—22no—
324C71⋊C8—41no—
325C71⋊C8—41no—
326C71⋊C8—41no—
327C22×C71C22×C22⋊C411yescharacteristic
328C22×C71C2×C4×Q811yescharacteristic
329C22×C71#51911yescharacteristic
330C22×C71C22×M1611yescharacteristic
331C22×C71C22×M1611yescharacteristic
332C22×C71C2×#13111yescharacteristic
333C22×C71#56811yescharacteristic
334C2×D71—22no—
335C2×D71—22no—
336C2×D71—22no—
337C2×D71—22no—
338C2×D71—22no—
339C2×D71—22no—
340C2×D71#44614yescomplemented
341C4×C71—22no—
342C4×C71—22no—
343C4×C71—22no—
344C4×C71—22no—
345C4×C71—41no—
346C4×C71—41no—
347C4×C71#54811yescharacteristic
348C4×C71#54811yescharacteristic
349C4×C71D4×Q811yescharacteristic
350C4×C71D4×Q811yescharacteristic
351Dic71—22no—
352Dic71—22no—
353Dic71—22no—
354Dic71—22no—
355Dic71—22no—
356Dic71—41no—
357Dic71#40714yes—
358#22510—711nomaximal, Sylow
359C2×C71Q8×C22⋊C411yescharacteristic
360C2×C71C2×#40711yescharacteristic
361C2×C71#288011yescharacteristic
362C2×C71C2×#44611yescharacteristic
363C2×C71Q8×M1611yescharacteristic
364C2×C71#298311yescharacteristic
365C2×C71#298411yescharacteristic
366D71—24no—
367C22×C4×Q8—711no—
368C2×#446—711no—
369C2×#446—711no—
370#1985—711no—
371#1985—711no—
372#1985—711no—
373#1985D7111yescharacteristic, complemented
374#1984—711no—
375#1984—711no—
376#1797—711no—
377#1797—711no—
378#1797—711no—
379#1749—711no—
380#1749—711no—
381C4×C22⋊C8—711no—
382C71#2251011yescharacteristic, complemented, Sylow
383C23×Q8—711no—
384C2×C4×Q8—711no—
385C2×C4×Q8—711no—
386C2×C4×Q8—711no—
387C2×C4×Q8—711no—
388C2×C4×Q8—711no—
389C2×C4×Q8—711no—
390C2×C4×Q8—711no—
391C2×C4×Q8—1424no—
392C2×C4×Q8—1424no—
393C2×C4×Q8C2×D7111yescharacteristic
394C22×C4⋊C4—711no—
395C22×C4⋊C4—711no—
396C22×C4⋊C4—711no—
397C22×C42—711no—
398C22×C42—711no—
399C22×C42—711no—
400#446—1424no—
401#446—1424no—
402C2×C4⋊C8—711no—
403C2×C4⋊C8—711no—
404C2×C4⋊C8—711no—
405C2×C4⋊C8—711no—
406C2×C4⋊C8—711no—
407C2×C4⋊C8C2×D7111yescharacteristic
408C2×C22⋊C8—711no—
409C2×C22⋊C8—711no—
410C2×C22⋊C8—711no—
411C2×C22⋊C8—711no—
412C2×#97—711no—
413C2×#97—711no—
414C2×#97—711no—
415C2×#97C2×D7111yescharacteristic
416C2×C4×C8—711no—
417C2×C4×C8—711no—
418#336—711no—
419#336—711no—
420#336—711no—
421#336—711no—
422#336—711no—
423#336—711no—
424#336—711no—
425#336—711no—
426#336C2×D7111yescharacteristic
427#336C2×D7111yescharacteristic
428#336C2×D7111yescharacteristic
429#336C2×D7111yescharacteristic
430C22×Q8—711no—
431C22×Q8—711no—
432C22×Q8—711no—
433C22×Q8—1424no—
434C22×Q8—1424no—
435C22×Q8—1424no—
436C22×Q8C4×D7111yescharacteristic
437C23×C4—711no—
438C23×C4—711no—
439C23×C4—711no—
440C23×C4—711no—
441C23×C4—711no—
442C23×C4—711no—
443C23×C4—711no—
444C22×C8—711no—
445C22×C8—711no—
446C22×C8—711no—
447C22×C8—711no—
448C22×C8C22×D7111yescharacteristic
449C22×C8C22×D7111yescharacteristic
450C22×C8C22×D7111yescharacteristic
451C22×C8C22×D7111yescharacteristic
452C4×Q8—22no—
453C4×Q8—22no—
454C4×Q8—714no—
455C4×Q8—714no—
456C4×Q8—1422no—
457C4×Q8—1422no—
458C4×Q8—1422no—
459C4×Q8—1422no—
460C4×Q8—1424no—
461C4×Q8—1424no—
462C4×Q8—1424no—
463C4×Q8—1424no—
464C2×C4⋊C4—711no—
465C2×C4⋊C4—711no—
466C2×C4⋊C4—711no—
467C2×C4⋊C4—711no—
468C2×C4⋊C4—711no—
469C2×C4⋊C4—711no—
470C2×C4⋊C4—711no—
471C2×C4⋊C4—711no—
472C2×C4⋊C4—711no—
473C2×C4⋊C4—1424no—
474C2×C4⋊C4—1424no—
475C2×C4⋊C4—1424no—
476C2×C4⋊C4C4×D7111yescharacteristic
477C2×C4⋊C4C4×D7111yescharacteristic
478C2×C4⋊C4C4×D7111yescharacteristic
479C2×C42—711no—
480C2×C42—711no—
481C2×C42—711no—
482C2×C42—711no—
483C2×C42—711no—
484C2×C42—711no—
485C2×C42—711no—
486C2×C42—711no—
487C2×C42—711no—
488C2×C42—1422no—
489C2×C42—1422no—
490C2×C42—1422no—
491C2×C42—1422no—
492C2×C42—1422no—
493C2×C42—1422no—
494C2×C42C22×D7111yescharacteristic
495C2×C42C22×D7111yescharacteristic
496C2×C42C22×D7111yescharacteristic
497C4⋊C8—22no—
498C4⋊C8—1422no—
499C4⋊C8—1422no—
500C4⋊C8—1422no—
501C4⋊C8—1422no—
502C4⋊C8—1422no—
503C22⋊C8—714no—
504C22⋊C8—1422no—
505C22⋊C8—1422no—
506C22⋊C8—1422no—
507#97—22no—
508#97—1422no—
509#97—1422no—
510#97—1422no—
511C4×C8—1422no—
512C4×C8—1422no—
513C24—711no—
514C2×Q8—22no—
515C2×Q8—22no—
516C2×Q8—22no—
517C2×Q8—714no—
518C2×Q8—714no—
519C2×Q8—1422no—
520C2×Q8—1422no—
521C2×Q8—1422no—
522C2×Q8—1422no—
523C2×Q8—1422no—
524C2×Q8—1422no—
525C2×Q8—14232no—
526C2×Q8—1422no—
527C22×C4—2841no—
528C22×C4—2841no—
529C22×C4—2841no—
530C22×C4—711no—
531C22×C4—711no—
532C22×C4—711no—
533C22×C4—711no—
534C22×C4—711no—
535C22×C4—711no—
536C22×C4—712no—
537C22×C4—712no—
538C22×C4—714no—
539C22×C4—711no—
540C22×C4—1422no—
541C22×C4—1422no—
542C22×C4—1422no—
543C22×C4—1422no—
544C22×C4—1422no—
545C22×C4—1422no—
546C22×C4—1422no—
547C22×C4—1422no—
548C22×C4—1422no—
549C22×C4—1422no—
550C22×C4—1422no—
551C22×C4—1422no—
552C22×C4—1421no—
553C22×C4—1421no—
554C22×C4—1421no—
555C22×C4—1421no—
556C22×C4—1422no—
557C22×C4—1422no—
558C22×C4C2×C4×D7111yescharacteristic
559C22×C4C2×C4×D7111yescharacteristic
560C22×C4C2×C4×D7111yescharacteristic
561C22×C4C2×C4×D7111yescharacteristic
562C22×C4C2×C4×D7111yescharacteristic
563C22×C4C2×C4×D7111yescharacteristic
564C22×C4C23×D7111yescharacteristic
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—712no—
577C2×C8—1421no—
578C2×C8—1421no—
579C2×C8—1421no—
580C2×C8—1421no—
581C2×C8—1421no—
582C2×C8—1421no—
583C2×C8—1421no—
584C2×C8—1421no—
585C2×C8—1421no—
586C2×C8—1421no—
587C2×C8—1421no—
588C2×C8Q8×D7112yescomplemented
589C4⋊C4—22no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—714no—
593C4⋊C4—714no—
594C4⋊C4—714no—
595C4⋊C4—1422no—
596C4⋊C4—1422no—
597C4⋊C4—1422no—
598C4⋊C4—1422no—
599C4⋊C4—1422no—
600C4⋊C4—1422no—
601C42—21no—
602C42—21no—
603C42—21no—
604C42—21no—
605C42—712no—
606C42—712no—
607C42—712no—
608C42—712no—
609C42—1422no—
610C42—1422no—
611C42—1422no—
612C42—1422no—
613C42—1421no—
614C42—1421no—
615C42—1422no—
616C42—1422no—
617C42D4×D7112yes—
618C42D4×D7112yes—
619C23—712no—
620C23—712no—
621C23—712no—
622C23—1421no—
623C23—1421no—
624C23—1421no—
625C23—1421no—
626C23C22×C4×D7111yescharacteristic
627Q8—28no—
628Q8—1428no—
629Q8—1428no—
630Q8—1428no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—2844no—
646C2×C4—2844no—
647C2×C4—2844no—
648C2×C4—712no—
649C2×C4—712no—
650C2×C4—712no—
651C2×C4—712no—
652C2×C4—712no—
653C2×C4—712no—
654C2×C4—712no—
655C2×C4—712no—
656C2×C4—1428no—
657C2×C4—1428no—
658C2×C4—1428no—
659C2×C4—1421no—
660C2×C4—1421no—
661C2×C4—1421no—
662C2×C4—1421no—
663C2×C4—1421no—
664C2×C4—1421no—
665C2×C4—1421no—
666C2×C4—1421no—
667C2×C4—1421no—
668C2×C4—1421no—
669C2×C4—1421no—
670C2×C4—1421no—
671C2×C4—1421no—
672C2×C4—1422no—
673C2×C4—1422no—
674C2×C4—1422no—
675C2×C4—1422no—
676C2×C4C22⋊C4×D7112yes—
677C2×C4C22⋊C4×D7112yes—
678C2×C4M16×D7112yes—
679C2×C4M16×D7112yes—
680C2×C4C2×D4×D7111yescharacteristic
681C2×C4C2×D4×D7111yescharacteristic
682C2×C4C2×Q8×D7111yescharacteristic
683C2×C4#41×D7111yescharacteristic
684C2×C4#1455617511yescharacteristic
685C2×C4#1455617611yescharacteristic
686C8—22no—
687C8—41no—
688C8—41no—
689C8—41no—
690C8—2841no—
691C8—2841no—
692C8—2841no—
693C8—1422no—
694C22—714no—
695C22—1422no—
696C22—1422no—
697C22—1422no—
698C22—1422no—
699C22—1422no—
700C22—1422no—
701C22C2×C22⋊C4×D7111yescharacteristic
702C22C4×Q8×D7111yescharacteristic
703C22#1798647511yescharacteristic
704C22C2×M16×D7111yescharacteristic
705C22C2×M16×D7111yescharacteristic
706C22#131×D7111yescharacteristic
707C22#1798676411yescharacteristic
708C4—22no—
709C4—22no—
710C4—22no—
711C4—22no—
712C4—41no—
713C4—41no—
714C4—2841no—
715C4—714no—
716C4—1422no—
717C4—1422no—
718C4—1422no—
719C4—1422no—
720C4—1422no—
721C4#1798665711yescharacteristic
722C4#1798665911yescharacteristic
723C4#1798666211yescharacteristic
724C4#1798666411yescharacteristic
725C2—1424no—
726C2#2259117411yescharacteristic
727C2#407×D7111yescharacteristic
728C2#2259678811yescharacteristic
729C2#446×D7111yescharacteristic
730C2#2259729211yescharacteristic
731C2#2259742211yescharacteristic
732C2#2259742611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1985C2
prime radicalC23×D71C22×C4
cosocleC22×C4×C71C24
hypercenter#1985D71
hypocenterC71#22510
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. C2×#17986128C2semidirect
3. C2×#17986127C2semidirect
4. #22589281C2semidirect
5. #22589278C2semidirect
6. #22589278C2semidirect
7. #22589274C2semidirect
8. #22589274C2semidirect
15. C71×#1985C2semidirect
125. (C2×D71)⋊C8Q8semidirect
199. C2×C71⋊C8C2×Q8semidirect
242. C2×C8×C71C2×Q8semidirect
340. C2×D71#446semidirect
373. #1985D71semidirect
382. C71#22510semidirect
588. C2×C8Q8×D71semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D712
C2×#179861282
C2×#179861272
#225892812
#225892782
#225892742
#225883192
#225883172
#225881032
#225881012
#225880972
C71×#19852
#2251071