Finite Group Databasebeta

← #31919046

Subgroups — #31919046

Order 18176.

2022 conjugacy classes of subgroups.

The subgroup lattice has 1038 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17985892C211yesmaximal, characteristic
2C2×#17985874C211yesmaximal, characteristic
3C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊Dic71C211yesmaximal, characteristic, complemented
5C2×C22⋊C4×Dic71C211yesmaximal, characteristic
6C2×C22⋊C4×Dic71C211yesmaximal, characteristic
7#22586577C211yesmaximal, characteristic
8#22586577C211yesmaximal, characteristic
9#22586574C211yesmaximal, characteristic, complemented
10#22586574C211yesmaximal, characteristic, complemented
11#22586574C211yesmaximal, characteristic, complemented
12#22586572C211yesmaximal, characteristic, complemented
13C4×C71⋊#95C211yesmaximal, characteristic, complemented
14#95×Dic71C211yesmaximal, characteristic, complemented
15C2×#388×C71C211yesmaximal, characteristic
16C24×Dic71C2211yescharacteristic
17C22×C4⋊Dic71C2211yescharacteristic
18C22×C4⋊Dic71C2211yescharacteristic
19C22×C4⋊Dic71C2211yescharacteristic
20C22×C22⋊Dic71C2211yescharacteristic
21C22×C22⋊Dic71C2211yescharacteristic
22C22×C22⋊Dic71C2211yescharacteristic
23C22×C4×Dic71C2211yescharacteristic
24C22×C4×Dic71C2211yescharacteristic
25C22×C4×Dic71C2211yescharacteristic
26C22×C4×Dic71C2211yescharacteristic
27C22×C4×Dic71C2211yescharacteristic
28C22×C4×Dic71C2211yescharacteristic
29C22×C4×Dic71C2211yescharacteristic
30#17985892C418yescomplemented
31#17985874C418yescomplemented
32C4⋊C4×Dic71—24no—
33C4×C4⋊Dic71—24no—
34C22⋊C4×Dic71—24no—
35C22⋊C4×Dic71—24no—
36C2×C71⋊#95C2211yescharacteristic
37C2×C71⋊#95C2211yescharacteristic
38C2×C71⋊#95C2211yescharacteristic
39C2×C71⋊#95C2211yescharacteristic
40C2×C71⋊#95C2211yescharacteristic
41C2×C71⋊#95C2211yescharacteristic
42C2×C71⋊#95C2211yescharacteristic
43C2×C71⋊#95C2211yescharacteristic
44C2×C71⋊#95C2211yescharacteristic
45C2×C71⋊#95C2211yescharacteristic
46C2×C71⋊#95C2211yescharacteristic
47C2×C71⋊#95C2211yescharacteristic
48C2×C71⋊#95C2211yescharacteristic
49C2×C71⋊#95C2211yescharacteristic
50C22×C4⋊C4×C71C2211yescharacteristic
51C22×C22⋊C4×C71C2211yescharacteristic
52C22×C22⋊C4×C71C2211yescharacteristic
53C22×C22⋊C4×C71C2211yescharacteristic
54C22×C42×C71C2211yescharacteristic
55#388×C71C418yescomplemented
56C2×#95×C71C2211yescharacteristic
57C2×#95×C71C2211yescharacteristic
58C23×Dic71—22no—
59C23×Dic71—22no—
60C23×Dic71—22no—
61C23×Dic71—22no—
62C23×Dic71—41no—
63C23×Dic71—41no—
64C23×Dic71C2×C414yes—
65C23×Dic71C2311yescharacteristic
66C23×Dic71C2311yescharacteristic
67C23×Dic71C2311yescharacteristic
68C23×Dic71C2311yescharacteristic
69C23×Dic71C2311yescharacteristic
70C23×Dic71C2311yescharacteristic
71C23×Dic71C2311yescharacteristic
72C23×Dic71C2311yescharacteristic
73C2×C4⋊Dic71—22no—
74C2×C4⋊Dic71—22no—
75C2×C4⋊Dic71—22no—
76C2×C4⋊Dic71—22no—
77C2×C4⋊Dic71—22no—
78C2×C4⋊Dic71—22no—
79C2×C4⋊Dic71C2×C414yes—
80C2×C4⋊Dic71C2×C414yes—
81C2×C4⋊Dic71C2×C414yescomplemented
82C2×C22⋊Dic71—22no—
83C2×C22⋊Dic71—22no—
84C2×C22⋊Dic71—22no—
85C2×C22⋊Dic71—22no—
86C2×C22⋊Dic71—41no—
87C2×C22⋊Dic71—41no—
88C2×C22⋊Dic71C2×C414yes—
89C2×C22⋊Dic71C2×C414yes—
90C2×C22⋊Dic71C2×C414yes—
91C2×C4×Dic71—22no—
92C2×C4×Dic71—22no—
93C2×C4×Dic71—22no—
94C2×C4×Dic71—22no—
95C2×C4×Dic71—22no—
96C2×C4×Dic71—22no—
97C2×C4×Dic71—22no—
98C2×C4×Dic71—22no—
99C2×C4×Dic71—22no—
100C2×C4×Dic71—22no—
101C2×C4×Dic71—22no—
102C2×C4×Dic71—22no—
103C2×C4×Dic71—22no—
104C2×C4×Dic71—22no—
105C2×C4×Dic71—41no—
106C2×C4×Dic71—41no—
107C2×C4×Dic71—41no—
108C2×C4×Dic71—41no—
109C2×C4×Dic71—41no—
110C2×C4×Dic71—41no—
111C2×C4×Dic71C2×C414yescomplemented
112C71⋊#95—22no—
113C71⋊#95—22no—
114C71⋊#95—22no—
115C71⋊#95—22no—
116C71⋊#95—22no—
117C71⋊#95—22no—
118C71⋊#95—41no—
119C71⋊#95—41no—
120C71⋊#95C2×C414yes—
121C71⋊#95C2×C414yes—
122C71⋊#95C2×C414yescomplemented
123C71⋊#95C2×C414yescomplemented
124C71⋊#95D414yes—
125C71⋊#95D414yes—
126C25×C71C2311yescharacteristic
127C23×C4×C71C2311yescharacteristic
128C23×C4×C71C2311yescharacteristic
129C23×C4×C71C2311yescharacteristic
130C23×C4×C71C2311yescharacteristic
131C23×C4×C71C2311yescharacteristic
132C23×C4×C71C2311yescharacteristic
133C2×C4⋊C4×C71—22no—
134C2×C4⋊C4×C71—22no—
135C2×C4⋊C4×C71C2×C414yescomplemented
136C2×C22⋊C4×C71—22no—
137C2×C22⋊C4×C71—22no—
138C2×C22⋊C4×C71—22no—
139C2×C22⋊C4×C71—22no—
140C2×C22⋊C4×C71C2×C414yes—
141C2×C22⋊C4×C71C2×C414yes—
142C2×C22⋊C4×C71C2×C414yes—
143C2×C22⋊C4×C71C2×C414yes—
144C2×C22⋊C4×C71C2×C414yes—
145C2×C42×C71—22no—
146C2×C42×C71—22no—
147C2×C42×C71C2×C414yescomplemented
148#95×C71C2×C414yescomplemented
149#95×C71C2×C414yescomplemented
150C22×Dic71—21no—
151C22×Dic71—21no—
152C22×Dic71—21no—
153C22×Dic71—21no—
154C22×Dic71—21no—
155C22×Dic71—21no—
156C22×Dic71—21no—
157C22×Dic71—21no—
158C22×Dic71—21no—
159C22×Dic71—21no—
160C22×Dic71—21no—
161C22×Dic71—21no—
162C22×Dic71—21no—
163C22×Dic71—21no—
164C22×Dic71—21no—
165C22×Dic71—21no—
166C22×Dic71—21no—
167C22×Dic71—21no—
168C22×Dic71—21no—
169C22×Dic71—21no—
170C22×Dic71—21no—
171C22×Dic71—21no—
172C22×Dic71—21no—
173C22×Dic71—21no—
174C22×Dic71—21no—
175C22×Dic71—21no—
176C22×Dic71—21no—
177C22×Dic71—21no—
178C22×Dic71—21no—
179C22×Dic71—21no—
180C22×Dic71—21no—
181C22×Dic71—21no—
182C22×Dic71—21no—
183C22×Dic71—21no—
184C22×Dic71—21no—
185C22×Dic71—21no—
186C22×Dic71—21no—
187C22×Dic71—21no—
188C22×Dic71—21no—
189C22×Dic71—21no—
190C22×Dic71—28no—
191C22×Dic71—28no—
192C22×Dic71—44no—
193C22×Dic71—44no—
194C22×Dic71—44no—
195C22×Dic71—44no—
196C22×Dic71—44no—
197C22×Dic71C22×C412yes—
198C22×Dic71C22×C412yes—
199C22×Dic71C22×C412yes—
200C22×Dic71C22×C412yes—
201C22×Dic71C22×C412yes—
202C22×Dic71C22×C412yes—
203C22×Dic71C22×C412yes—
204C22×Dic71C22×C412yes—
205C22×Dic71C2×D412yes—
206C22×Dic71C2×D412yes—
207C22×Dic71C2×D412yes—
208C22×Dic71C2×D412yes—
209C22×Dic71#4112yes—
210C22×Dic71#4112yes—
211C22×Dic71#4112yes—
212C22×Dic71#4112yes—
213C4⋊Dic71—28no—
214C4⋊Dic71—28no—
215C4⋊Dic71—28no—
216C22⋊Dic71—28no—
217C22⋊Dic71—28no—
218C22⋊Dic71—44no—
219C4×Dic71—28no—
220C4×Dic71—44no—
221C4×Dic71—44no—
222C4×Dic71—44no—
223C4×Dic71—44no—
224C4×Dic71—44no—
225C4×Dic71—44no—
226C24×C71—21no—
227C24×C71—21no—
228C24×C71—21no—
229C24×C71—21no—
230C24×C71—21no—
231C24×C71—21no—
232C24×C71—21no—
233C24×C71—21no—
234C24×C71—21no—
235C24×C71—21no—
236C24×C71—21no—
237C24×C71—21no—
238C24×C71C22×C412yes—
239C24×C71C22×C412yes—
240C24×C71C22×C412yes—
241C24×C71C2411yescharacteristic
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71—21no—
246C22×C4×C71—21no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—21no—
252C22×C4×C71—21no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71—21no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71—21no—
263C22×C4×C71—21no—
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×C71C22×C412yes—
271C22×C4×C71C22×C412yes—
272C22×C4×C71C22×C412yes—
273C22×C4×C71C22×C412yes—
274C22×C4×C71C22×C412yes—
275C22×C4×C71C22×C412yes—
276C22×C4×C71C22×C412yes—
277C22×C4×C71C22×C412yes—
278C22×C4×C71C22×C412yes—
279C22×C4×C71C22×C412yes—
280C22×C4×C71C2×D412yes—
281C22×C4×C71C2×D412yes—
282C22×C4×C71#4112yes—
283C22×C4×C71#4112yes—
284C4⋊C4×C71—28no—
285C22⋊C4×C71—28no—
286C22⋊C4×C71—28no—
287C22⋊C4×C71C42116yescomplemented
288C42×C71—28no—
289C23×C71—22no—
290C23×C71—22no—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—22no—
299C23×C71—22no—
300C23×C71—22no—
301C23×C71—22no—
302C23×C71—22no—
303C23×C71—22no—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71—22no—
307C23×C71—41no—
308C23×C71—41no—
309C23×C71—41no—
310C23×C71—41no—
311C23×C71—41no—
312C23×C71—41no—
313C23×C71—41no—
314C23×C71—41no—
315C23×C71—41no—
316C23×C71—41no—
317C23×C71—41no—
318C23×C71—41no—
319C23×C71—41no—
320C23×C71—41no—
321C23×C71—41no—
322C23×C71—41no—
323C23×C71C2×C4214yes—
324C23×C71C23×C411yescharacteristic
325C23×C71C23×C411yescharacteristic
326C23×C71C23×C411yescharacteristic
327C23×C71C22×D411yescharacteristic
328C23×C71C22×D411yescharacteristic
329C23×C71C2×#4111yescharacteristic
330C23×C71C2×#4111yescharacteristic
331C23×C71C2×#4111yescharacteristic
332C23×C71C2×#4111yescharacteristic
333C23×C71C2×#4111yescharacteristic
334C23×C71C2×#4111yescharacteristic
335C23×C71H(5,𝔽2)11yescharacteristic
336C23×C71H(5,𝔽2)11yescharacteristic
337C23×C712−1+411yescharacteristic
338C23×C712−1+411yescharacteristic
339C2×C4×C71—22no—
340C2×C4×C71—22no—
341C2×C4×C71—22no—
342C2×C4×C71—22no—
343C2×C4×C71—22no—
344C2×C4×C71—22no—
345C2×C4×C71—22no—
346C2×C4×C71—22no—
347C2×C4×C71—22no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—22no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
353C2×C4×C71—22no—
354C2×C4×C71—22no—
355C2×C4×C71—22no—
356C2×C4×C71—22no—
357C2×C4×C71—22no—
358C2×C4×C71—22no—
359C2×C4×C71—22no—
360C2×C4×C71—22no—
361C2×C4×C71—22no—
362C2×C4×C71—22no—
363C2×C4×C71—22no—
364C2×C4×C71—22no—
365C2×C4×C71—22no—
366C2×C4×C71—22no—
367C2×C4×C71—22no—
368C2×C4×C71—22no—
369C2×C4×C71—41no—
370C2×C4×C71—41no—
371C2×C4×C71—41no—
372C2×C4×C71—41no—
373C2×C4×C71—41no—
374C2×C4×C71—41no—
375C2×C4×C71—41no—
376C2×C4×C71—41no—
377C2×C4×C71C2×C4214yes—
378C2×C4×C71C2×C4214yes—
379C2×C4×C71C4×D414yes—
380C2×C4×C71C4×D414yes—
381C2×Dic71—22no—
382C2×Dic71—22no—
383C2×Dic71—22no—
384C2×Dic71—22no—
385C2×Dic71—22no—
386C2×Dic71—22no—
387C2×Dic71—22no—
388C2×Dic71—22no—
389C2×Dic71—22no—
390C2×Dic71—22no—
391C2×Dic71—22no—
392C2×Dic71—22no—
393C2×Dic71—22no—
394C2×Dic71—22no—
395C2×Dic71—22no—
396C2×Dic71—22no—
397C2×Dic71—22no—
398C2×Dic71—22no—
399C2×Dic71—22no—
400C2×Dic71—22no—
401C2×Dic71—22no—
402C2×Dic71—22no—
403C2×Dic71—22no—
404C2×Dic71—22no—
405C2×Dic71—22no—
406C2×Dic71—22no—
407C2×Dic71—22no—
408C2×Dic71—22no—
409C2×Dic71—22no—
410C2×Dic71—22no—
411C2×Dic71—22no—
412C2×Dic71—22no—
413C2×Dic71—22no—
414C2×Dic71—22no—
415C2×Dic71—22no—
416C2×Dic71—22no—
417C2×Dic71—416no—
418C2×Dic71—41no—
419C2×Dic71—41no—
420C2×Dic71—41no—
421C2×Dic71—41no—
422C2×Dic71—41no—
423C2×Dic71—41no—
424C2×Dic71—41no—
425C2×Dic71—41no—
426C2×Dic71—41no—
427C2×Dic71—41no—
428C2×Dic71—41no—
429C2×Dic71—41no—
430C2×Dic71—41no—
431C2×Dic71—41no—
432C2×Dic71—41no—
433C2×Dic71—41no—
434C2×Dic71C4×D414yes—
435C2×Dic71C4×D414yes—
436C2×Dic71C4×D414yes—
437C2×Dic71C4×D414yes—
438C22×C71—24no—
439C22×C71—24no—
440C22×C71—24no—
441C22×C71—42no—
442C22×C71—42no—
443C22×C71—42no—
444C22×C71—42no—
445C22×C71—42no—
446C22×C71—42no—
447C22×C71—42no—
448C22×C71—42no—
449C22×C71—42no—
450C22×C71—42no—
451C22×C71—42no—
452C22×C71—42no—
453C22×C71C22×C4211yescharacteristic
454C22×C71C2×C4×D411yescharacteristic
455C22×C71C2×C4×D411yescharacteristic
456C22×C71C2×C4×D411yescharacteristic
457C22×C71C2×C4×D411yescharacteristic
458C22×C71C2×C4×D411yescharacteristic
459C22×C71C2×C4×D411yescharacteristic
460C22×C71C4×#4111yescharacteristic
461C22×C71C4×#4111yescharacteristic
462C22×C71C4×#4111yescharacteristic
463C22×C71C4×#4111yescharacteristic
464C22×C71C4×#4111yescharacteristic
465C22×C71C4×#4111yescharacteristic
466C22×C71#51811yescharacteristic
467C22×C71#51911yescharacteristic
468C22×C71#52011yescharacteristic
469C22×C71#52011yescharacteristic
470C22×C71#52011yescharacteristic
471C22×C71#52011yescharacteristic
472C22×C71D4211yescharacteristic
473C22×C71#54611yescharacteristic
474C22×C71#54611yescharacteristic
475C22×C71#54711yescharacteristic
476C22×C71#54711yescharacteristic
477C22×C71#54811yescharacteristic
478C22×C71#54811yescharacteristic
479C22×C71#55111yescharacteristic
480C22×C71#55111yescharacteristic
481C22×C71#55211yescharacteristic
482C22×C71#55211yescharacteristic
483C22×C71#55311yescharacteristic
484C22×C71#55311yescharacteristic
485C22×C71#55611yescharacteristic
486C22×C71#55611yescharacteristic
487C22×C71#55911yescharacteristic
488C4×C71—24no—
489C4×C71—24no—
490C4×C71—24no—
491C4×C71—24no—
492C4×C71—42no—
493C4×C71—42no—
494Dic71—24no—
495Dic71—24no—
496Dic71—24no—
497Dic71—24no—
498Dic71—42no—
499Dic71—42no—
500Dic71—42no—
501Dic71—42no—
502#13823—711nomaximal, Sylow
503C2×C71—44no—
504C2×C71C42×D411yescharacteristic
505C2×C71C42×D411yescharacteristic
506C2×C71#227411yescharacteristic
507C2×C71#235811yescharacteristic
508C2×C71#235911yescharacteristic
509C2×C71#235911yescharacteristic
510C2×C71#236111yescharacteristic
511C2×C71#236111yescharacteristic
512C2×C71#236211yescharacteristic
513C2×C71#236211yescharacteristic
514C2×C71#236711yescharacteristic
515C2×C71#236711yescharacteristic
516C2×C71#237311yescharacteristic
517C2×C71#237311yescharacteristic
518C2×C71#237411yescharacteristic
519C2×#388—711no—
520C2×#388D7111yescharacteristic
521C2×#385—711no—
522C2×C4×C4⋊C4—711no—
523C2×C4×C4⋊C4—711no—
524C2×C4×C22⋊C4—711no—
525C2×C4×C22⋊C4—711no—
526#1437—711no—
527#1437—711no—
528#1436—711no—
529#1436—711no—
530#1436—711no—
531#1436—711no—
532C4×#95—711no—
533C4×#95—711no—
534C71#1382311yescharacteristic, complemented, Sylow
535C24×C4—711no—
536C22×C4⋊C4—711no—
537C22×C4⋊C4—711no—
538C22×C4⋊C4—711no—
539C22×C4⋊C4C2×D7111yescharacteristic
540C22×C22⋊C4—711no—
541C22×C22⋊C4—711no—
542C22×C22⋊C4—711no—
543C22×C22⋊C4C2×D7111yescharacteristic
544C22×C22⋊C4C2×D7111yescharacteristic
545C22×C22⋊C4C2×D7111yescharacteristic
546C22×C42—711no—
547C22×C42—711no—
548C22×C42—711no—
549C22×C42—711no—
550C22×C42—711no—
551C22×C42—711no—
552C22×C42—711no—
553C22×C42C2×D7111yescharacteristic
554#388—718no—
555#388Dic7118yescomplemented
556#385—718no—
557C4×C4⋊C4—1424no—
558C4×C4⋊C4—1424no—
559C4×C22⋊C4—1424no—
560C4×C22⋊C4—1424no—
561C2×#95—711no—
562C2×#95—711no—
563C2×#95—711no—
564C2×#95—711no—
565C2×#95—711no—
566C2×#95—711no—
567C2×#95—711no—
568C2×#95—711no—
569C2×#95—711no—
570C2×#95—711no—
571C2×#95—711no—
572C2×#95—711no—
573C2×#95—711no—
574C2×#95—711no—
575C2×#95C2×D7111yescharacteristic
576C2×#95C2×D7111yescharacteristic
577C25C22×D7111yescharacteristic
578C23×C4—2841no—
579C23×C4—2841no—
580C23×C4—714no—
581C23×C4—711no—
582C23×C4—711no—
583C23×C4—711no—
584C23×C4—711no—
585C23×C4—711no—
586C23×C4—711no—
587C23×C4—711no—
588C23×C4—711no—
589C23×C4—1422no—
590C23×C4—1422no—
591C23×C4—1422no—
592C23×C4—1422no—
593C23×C4C22×D7111yescharacteristic
594C23×C4C22×D7111yescharacteristic
595C23×C4C22×D7111yescharacteristic
596C23×C4C22×D7111yescharacteristic
597C23×C4C22×D7111yescharacteristic
598C23×C4C22×D7111yescharacteristic
599C2×C4⋊C4—22no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—714no—
602C2×C4⋊C4—714no—
603C2×C4⋊C4—714no—
604C2×C4⋊C4—1422no—
605C2×C4⋊C4—1422no—
606C2×C4⋊C4—1422no—
607C2×C4⋊C4—1422no—
608C2×C4⋊C4—1422no—
609C2×C4⋊C4—1422no—
610C2×C4⋊C4C2×Dic7114yescomplemented
611C2×C22⋊C4—22no—
612C2×C22⋊C4—22no—
613C2×C22⋊C4—22no—
614C2×C22⋊C4—22no—
615C2×C22⋊C4—2841no—
616C2×C22⋊C4—2841no—
617C2×C22⋊C4—714no—
618C2×C22⋊C4—714no—
619C2×C22⋊C4—714no—
620C2×C22⋊C4—1422no—
621C2×C22⋊C4—1422no—
622C2×C22⋊C4—1422no—
623C2×C22⋊C4—1422no—
624C2×C22⋊C4C4×D7114yes—
625C2×C22⋊C4C4×D7114yes—
626C2×C22⋊C4C2×Dic7114yes—
627C2×C22⋊C4C2×Dic7114yes—
628C2×C22⋊C4C2×Dic7114yes—
629C2×C42—22no—
630C2×C42—22no—
631C2×C42—2841no—
632C2×C42—2841no—
633C2×C42—2841no—
634C2×C42—2841no—
635C2×C42—2841no—
636C2×C42—2841no—
637C2×C42—714no—
638C2×C42—1422no—
639C2×C42—1422no—
640C2×C42—1422no—
641C2×C42—1422no—
642C2×C42—1422no—
643C2×C42—1422no—
644C2×C42—1422no—
645C2×C42—1422no—
646C2×C42—1422no—
647C2×C42—1422no—
648C2×C42—1422no—
649C2×C42—1422no—
650C2×C42—1422no—
651C2×C42—1422no—
652C2×C42C2×Dic7114yescomplemented
653#95—2841no—
654#95—2841no—
655#95—714no—
656#95—714no—
657#95—714no—
658#95—714no—
659#95—714no—
660#95—714no—
661#95—1422no—
662#95—1422no—
663#95—1422no—
664#95—1422no—
665#95—1422no—
666#95—1422no—
667#95C2×Dic7114yescomplemented
668#95C2×Dic7114yescomplemented
669C24—21no—
670C24—21no—
671C24—21no—
672C24—21no—
673C24—21no—
674C24—21no—
675C24—21no—
676C24—21no—
677C24—21no—
678C24—21no—
679C24—21no—
680C24—21no—
681C24C2×C4×D7112yes—
682C24C2×C4×D7112yes—
683C24C22×Dic7112yes—
684C24C23×D7111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—2844no—
714C22×C4—2844no—
715C22×C4—2844no—
716C22×C4—2844no—
717C22×C4—2844no—
718C22×C4—712no—
719C22×C4—712no—
720C22×C4—712no—
721C22×C4—712no—
722C22×C4—712no—
723C22×C4—712no—
724C22×C4—712no—
725C22×C4—712no—
726C22×C4—712no—
727C22×C4—712no—
728C22×C4—712no—
729C22×C4—712no—
730C22×C4—712no—
731C22×C4—712no—
732C22×C4—712no—
733C22×C4—712no—
734C22×C4—1428no—
735C22×C4—1428no—
736C22×C4—1421no—
737C22×C4—1421no—
738C22×C4—1421no—
739C22×C4—1421no—
740C22×C4—1421no—
741C22×C4—1421no—
742C22×C4—1421no—
743C22×C4—1421no—
744C22×C4—1421no—
745C22×C4—1421no—
746C22×C4—1421no—
747C22×C4—1421no—
748C22×C4—1421no—
749C22×C4—1421no—
750C22×C4—1421no—
751C22×C4—1421no—
752C22×C4—1421no—
753C22×C4—1421no—
754C22×C4—1421no—
755C22×C4—1421no—
756C22×C4—1421no—
757C22×C4—1421no—
758C22×C4—1421no—
759C22×C4—1421no—
760C22×C4—1421no—
761C22×C4—1421no—
762C22×C4—1421no—
763C22×C4—1421no—
764C22×C4—1421no—
765C22×C4—1421no—
766C22×C4—1421no—
767C22×C4—1421no—
768C22×C4—1421no—
769C22×C4—1421no—
770C22×C4—1421no—
771C22×C4—1421no—
772C22×C4—1421no—
773C22×C4—1421no—
774C22×C4—1421no—
775C22×C4—1421no—
776C22×C4C2×C4×D7112yes—
777C22×C4C2×C4×D7112yes—
778C22×C4C2×C4×D7112yes—
779C22×C4C2×C4×D7112yes—
780C22×C4C22×Dic7112yes—
781C22×C4C22×Dic7112yes—
782C22×C4C22×Dic7112yes—
783C22×C4C22×Dic7112yes—
784C22×C4C22×Dic7112yes—
785C22×C4C22×Dic7112yes—
786C22×C4D4×D7112yes—
787C22×C4D4×D7112yes—
788C22×C4#1176586412yes—
789C22×C4#1176586412yes—
790C4⋊C4—28no—
791C4⋊C4—1428no—
792C4⋊C4—1428no—
793C4⋊C4—1428no—
794C22⋊C4—28no—
795C22⋊C4—28no—
796C22⋊C4—2844no—
797C22⋊C4—1428no—
798C22⋊C4—1428no—
799C22⋊C4C4×Dic71116yescomplemented
800C42—28no—
801C42—2844no—
802C42—2844no—
803C42—2844no—
804C42—2844no—
805C42—2844no—
806C42—2844no—
807C42—1428no—
808C23—22no—
809C23—22no—
810C23—22no—
811C23—22no—
812C23—22no—
813C23—22no—
814C23—22no—
815C23—22no—
816C23—22no—
817C23—22no—
818C23—22no—
819C23—22no—
820C23—22no—
821C23—22no—
822C23—22no—
823C23—22no—
824C23—22no—
825C23—22no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—41no—
841C23—41no—
842C23C2×C4×Dic7114yes—
843C23C22×C4×D7111yescharacteristic
844C23C22×C4×D7111yescharacteristic
845C23C23×Dic7111yescharacteristic
846C23C2×D4×D7111yescharacteristic
847C23C2×D4×D7111yescharacteristic
848C23#41×D7111yescharacteristic
849C23#41×D7111yescharacteristic
850C23#41×D7111yescharacteristic
851C23#41×D7111yescharacteristic
852C23C2×#1176586411yescharacteristic
853C23C2×#1176586411yescharacteristic
854C23#1455617411yescharacteristic
855C23#1455617411yescharacteristic
856C23#1455617511yescharacteristic
857C23#1455617511yescharacteristic
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—22no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—22no—
878C2×C4—22no—
879C2×C4—22no—
880C2×C4—22no—
881C2×C4—22no—
882C2×C4—22no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—22no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—41no—
892C2×C4—41no—
893C2×C4—41no—
894C2×C4—41no—
895C2×C4—41no—
896C2×C4—2841no—
897C2×C4—2841no—
898C2×C4—2841no—
899C2×C4—2841no—
900C2×C4—2841no—
901C2×C4—2841no—
902C2×C4—2841no—
903C2×C4—2841no—
904C2×C4—2841no—
905C2×C4—2841no—
906C2×C4—2841no—
907C2×C4—2841no—
908C2×C4—2841no—
909C2×C4—2841no—
910C2×C4—2841no—
911C2×C4—2841no—
912C2×C4—28416no—
913C2×C4—714no—
914C2×C4—714no—
915C2×C4—714no—
916C2×C4—714no—
917C2×C4—1422no—
918C2×C4—1422no—
919C2×C4—1422no—
920C2×C4—1422no—
921C2×C4—1422no—
922C2×C4—1422no—
923C2×C4—1422no—
924C2×C4—1422no—
925C2×C4—1422no—
926C2×C4—1422no—
927C2×C4—1422no—
928C2×C4—1422no—
929C2×C4—1422no—
930C2×C4—1422no—
931C2×C4—1422no—
932C2×C4—1422no—
933C2×C4—1422no—
934C2×C4—1422no—
935C2×C4—1422no—
936C2×C4—1422no—
937C2×C4—1422no—
938C2×C4—1422no—
939C2×C4—1422no—
940C2×C4—1422no—
941C2×C4—1422no—
942C2×C4—1422no—
943C2×C4—1422no—
944C2×C4—1422no—
945C2×C4—1422no—
946C2×C4—1422no—
947C2×C4—1422no—
948C2×C4—1422no—
949C2×C4—1422no—
950C2×C4—1422no—
951C2×C4—1422no—
952C2×C4—1422no—
953C2×C4C2×C4×Dic7114yes—
954C2×C4C2×C4×Dic7114yes—
955C2×C4D4×Dic7114yes—
956C2×C4D4×Dic7114yes—
957C22—24no—
958C22—24no—
959C22—24no—
960C22—42no—
961C22—42no—
962C22—42no—
963C22—42no—
964C22—42no—
965C22—42no—
966C22—42no—
967C22—42no—
968C22—42no—
969C22—42no—
970C22—42no—
971C22—42no—
972C22C22×C4×Dic7111yescharacteristic
973C22C4×D4×D7111yescharacteristic
974C22C4×D4×D7111yescharacteristic
975C22C4×D4×D7111yescharacteristic
976C22C4×D4×D7111yescharacteristic
977C22C2×D4×Dic7111yescharacteristic
978C22C2×D4×Dic7111yescharacteristic
979C22C4×#1176586411yescharacteristic
980C22C4×#1176586411yescharacteristic
981C22C4×#1176586411yescharacteristic
982C22C4×#1176586411yescharacteristic
983C22#41×Dic7111yescharacteristic
984C22#41×Dic7111yescharacteristic
985C22#1798647311yescharacteristic
986C22#1798647611yescharacteristic
987C22#1798647911yescharacteristic
988C22#1798647911yescharacteristic
989C22#1798648211yescharacteristic
990C22#1798648211yescharacteristic
991C22#1798663311yescharacteristic
992C22#1798664111yescharacteristic
993C22#1798664211yescharacteristic
994C22#1798664711yescharacteristic
995C22#1798664911yescharacteristic
996C22#1798665511yescharacteristic
997C22#1798665711yescharacteristic
998C22#1798667211yescharacteristic
999C22#1798667411yescharacteristic
1000C22#1798668511yescharacteristic
1001C22#1798668611yescharacteristic
1002C22#1798670011yescharacteristic
1003C22#1798670111yescharacteristic
1004C22#1798671611yescharacteristic
1005C22#1798671811yescharacteristic
1006C22#1798673111yescharacteristic
1007C4—24no—
1008C4—24no—
1009C4—24no—
1010C4—24no—
1011C4—42no—
1012C4—42no—
1013C4—2842no—
1014C4—2842no—
1015C4—2842no—
1016C4—2842no—
1017C4—1424no—
1018C4—1424no—
1019C4—1424no—
1020C4—1424no—
1021C2—44no—
1022C2C4×D4×Dic7111yescharacteristic
1023C2C4×D4×Dic7111yescharacteristic
1024C2#2259069611yescharacteristic
1025C2#2259131811yescharacteristic
1026C2#2259133111yescharacteristic
1027C2#2259133611yescharacteristic
1028C2#2259135311yescharacteristic
1029C2#2259136011yescharacteristic
1030C2#2259136411yescharacteristic
1031C2#2259137011yescharacteristic
1032C2#2259141411yescharacteristic
1033C2#2259141511yescharacteristic
1034C2#2259146411yescharacteristic
1035C2#2259146711yescharacteristic
1036C2#2259147011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC2×#388×C71C2
socle, cosocleC24×C71C24
prime radicalC25×C71C23
hypercenterC2×#388D71
hypocenterC71#13823
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic71C2semidirect
4. C2×C4×C4⋊Dic71C2semidirect
9. #22586574C2semidirect
10. #22586574C2semidirect
11. #22586574C2semidirect
12. #22586572C2semidirect
13. C4×C71⋊#95C2semidirect
14. #95×Dic71C2semidirect
30. #17985892C4semidirect
31. #17985874C4semidirect
55. #388×C71C4semidirect
81. C2×C4⋊Dic71C2×C4semidirect
111. C2×C4×Dic71C2×C4semidirect
122. C71⋊#95C2×C4semidirect
123. C71⋊#95C2×C4semidirect
135. C2×C4⋊C4×C71C2×C4semidirect
147. C2×C42×C71C2×C4semidirect
148. #95×C71C2×C4semidirect
149. #95×C71C2×C4semidirect
287. C22⋊C4×C71C42semidirect
534. C71#13823semidirect
555. #388Dic71semidirect
610. C2×C4⋊C4C2×Dic71semidirect
652. C2×C42C2×Dic71semidirect
667. #95C2×Dic71semidirect
668. #95C2×Dic71semidirect
799. C22⋊C4C4×Dic71semidirect

Maximal subgroups

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

subgroupindex
C2×#179858922
C2×#179858742
C2×C4⋊C4×Dic712
C2×C4×C4⋊Dic712
C2×C22⋊C4×Dic712
#225865772
#225865742
#225865722
C4×C71⋊#952
#95×Dic712
C2×#388×C712
#1382371