Finite Group Databasebeta

← #31919703

Subgroups — #31919703

Order 18176.

2366 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4⋊C4×D71C211yesmaximal, characteristic
2C2×#17985897C211yesmaximal, characteristic, complemented
3C2×#17985895C211yesmaximal, characteristic, complemented
4C2×#17985858C212yesmaximal
5C2×#17985856C211yesmaximal, characteristic
6C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
7#22586591C212yesmaximal, complemented
8#22586591C212yesmaximal, complemented
9#22586569C211yesmaximal, characteristic, complemented
10(C2×D71)⋊#95C212yesmaximal
11C71×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D71C2212yes—
13C23×C4×D71C2211yescharacteristic
14C22×C4⋊Dic71C2211yescharacteristic
15C22×C4⋊Dic71C2211yescharacteristic
16C22×Dic71⋊C4C2212yes—
17C22×Dic71⋊C4C2212yes—
18C22×Dic71⋊C4C2212yes—
19C2×C4⋊C4×D71—24no—
20C2×C4⋊C4×D71—24no—
21C2×C4⋊C4×D71C418yescomplemented
22C22×(C2×D71)⋊C4C2212yes—
23C22×(C2×D71)⋊C4C2211yescharacteristic
24C22×(C2×D71)⋊C4C2211yescharacteristic
25C22×C4×Dic71C2211yescharacteristic
26#17985897—24no—
27#17985895—24no—
28#17985858—28no—
29#17985856—24no—
30C4×(C2×D71)⋊C4—24no—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2211yescharacteristic
35C2×C71⋊#95C2211yescharacteristic
36C2×C71⋊#95C2212yes—
37C2×C71⋊#95C2212yes—
38C22×C4⋊C4×C71C2211yescharacteristic
39C22×C4⋊C4×C71C2211yescharacteristic
40C22×C42×C71C2211yescharacteristic
41C2×#95×C71C2212yes—
42C2×#95×C71C2212yes—
43C24×D71C2311yescharacteristic
44C23×Dic71C2312yes—
45C23×Dic71C2311yescharacteristic
46C23×Dic71C2311yescharacteristic
47C23×Dic71C2312yes—
48C23×Dic71C2311yescharacteristic
49C22×C4×D71—24no—
50C22×C4×D71—24no—
51C22×C4×D71—24no—
52C22×C4×D71—24no—
53C22×C4×D71—22no—
54C22×C4×D71—22no—
55C22×C4×D71—22no—
56C22×C4×D71—22no—
57C22×C4×D71—42no—
58C22×C4×D71—42no—
59C22×C4×D71C2×C418yes—
60C22×C4×D71C2×C414yes—
61C22×C4×D71D414yes—
62C22×C4×D71Q814yes—
63C2×C4⋊Dic71—22no—
64C2×C4⋊Dic71—22no—
65C2×C4⋊Dic71—22no—
66C2×C4⋊Dic71C2×C414yes—
67C2×C4⋊Dic71D414yes—
68C2×C4⋊Dic71D414yes—
69C2×Dic71⋊C4—24no—
70C2×Dic71⋊C4—24no—
71C2×Dic71⋊C4—24no—
72C2×Dic71⋊C4—24no—
73C2×Dic71⋊C4—24no—
74C2×Dic71⋊C4—24no—
75C2×Dic71⋊C4—42no—
76C2×Dic71⋊C4—42no—
77C2×Dic71⋊C4C2×C418yes—
78C4⋊C4×D71—232no—
79C2×(C2×D71)⋊C4—22no—
80C2×(C2×D71)⋊C4—22no—
81C2×(C2×D71)⋊C4—22no—
82C2×(C2×D71)⋊C4—22no—
83C2×(C2×D71)⋊C4—24no—
84C2×(C2×D71)⋊C4—24no—
85C2×(C2×D71)⋊C4—24no—
86C2×(C2×D71)⋊C4D414yes—
87C2×(C2×D71)⋊C4Q814yes—
88C2×C4×Dic71—22no—
89C2×C4×Dic71—22no—
90C2×C4×Dic71—22no—
91C71⋊#95—22no—
92C71⋊#95—22no—
93C71⋊#95—24no—
94C71⋊#95—24no—
95C71⋊#95—24no—
96C71⋊#95—24no—
97C71⋊#95—42no—
98C23×C4×C71C2312yes—
99C23×C4×C71C2312yes—
100C23×C4×C71C2311yescharacteristic
101C23×C4×C71C2311yescharacteristic
102C23×C4×C71C2311yescharacteristic
103C2×C4⋊C4×C71—22no—
104C2×C4⋊C4×C71—22no—
105C2×C4⋊C4×C71—22no—
106C2×C4⋊C4×C71—22no—
107C2×C4⋊C4×C71—22no—
108C2×C4⋊C4×C71C2×C414yes—
109C2×C42×C71—22no—
110C2×C42×C71—22no—
111C2×C42×C71—22no—
112#95×C71—24no—
113#95×C71—42no—
114C23×D71—21no—
115C23×D71—21no—
116C23×D71—21no—
117C23×D71—21no—
118C23×D71—21no—
119C23×D71—21no—
120C23×D71—21no—
121C23×D71—21no—
122C23×D71C22×C412yes—
123C23×D71C2×D412yes—
124C23×D71C2×D412yes—
125C23×D71C2×Q812yes—
126C23×D71C2×Q812yes—
127C23×D71#4112yes—
128C23×D71#4112yes—
129C22×Dic71—21no—
130C22×Dic71—21no—
131C22×Dic71—22no—
132C22×Dic71—22no—
133C22×Dic71—21no—
134C22×Dic71—21no—
135C22×Dic71—22no—
136C22×Dic71—22no—
137C22×Dic71—21no—
138C22×Dic71—21no—
139C22×Dic71—21no—
140C22×Dic71—21no—
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—21no—
144C22×Dic71—21no—
145C22×Dic71—21no—
146C22×Dic71—21no—
147C22×Dic71—21no—
148C22×Dic71—21no—
149C22×Dic71—22no—
150C22×Dic71—22no—
151C22×Dic71—22no—
152C22×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71C22×C414yes—
157C22×Dic71C22×C412yes—
158C22×Dic71C2×D412yes—
159C22×Dic71C2×D414yes—
160C22×Dic71C2×D414yes—
161C22×Dic71C2×D412yes—
162C22×Dic71C2×Q812yes—
163C22×Dic71C2×Q812yes—
164C2×C4×D71—28no—
165C2×C4×D71—28no—
166C2×C4×D71—28no—
167C2×C4×D71—28no—
168C2×C4×D71—28no—
169C2×C4×D71—28no—
170C2×C4×D71—216no—
171C2×C4×D71—216no—
172C2×C4×D71—48no—
173C2×C4×D71—48no—
174C2×C4×D71—48no—
175C2×C4×D71—48no—
176C2×C4×D71—48no—
177C2×C4×D71C4⋊C4116yescomplemented
178C4⋊Dic71—44no—
179C4⋊Dic71C22⋊C4116yescomplemented
180Dic71⋊C4—216no—
181Dic71⋊C4—48no—
182Dic71⋊C4—48no—
183(C2×D71)⋊C4—28no—
184(C2×D71)⋊C4—28no—
185(C2×D71)⋊C4—48no—
186C4×Dic71—44no—
187C24×C71C2411yescharacteristic
188C22×C4×C71—22no—
189C22×C4×C71—22no—
190C22×C4×C71—22no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—22no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—22no—
201C22×C4×C71—22no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—21no—
206C22×C4×C71—22no—
207C22×C4×C71—22no—
208C22×C4×C71—22no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71C22×C414yes—
214C22×C4×C71C22×C412yes—
215C22×C4×C71C2×D412yes—
216C22×C4×C71C2×D412yes—
217C22×C4×C71C2×D412yes—
218C22×C4×C71C2×D412yes—
219C22×C4×C71C2×Q812yes—
220C22×C4×C71C2×Q812yes—
221C22×C4×C71#4112yes—
222C22×C4×C71#4112yes—
223C4⋊C4×C71—28no—
224C4⋊C4×C71—44no—
225C42×C71—44no—
226C23×C71C23×C411yescharacteristic
227C23×C71C22×D411yescharacteristic
228C23×C71C22×D411yescharacteristic
229C23×C71C22×D411yescharacteristic
230C23×C71C22×D411yescharacteristic
231C23×C71C22×Q811yescharacteristic
232C23×C71C22×Q811yescharacteristic
233C23×C71C2×#4111yescharacteristic
234C23×C71C2×#4111yescharacteristic
235C23×C71C2×#4111yescharacteristic
236C23×C71C2×#4111yescharacteristic
237C23×C71H(5,𝔽2)11yescharacteristic
238C23×C71H(5,𝔽2)11yescharacteristic
239C23×C712−1+411yescharacteristic
240C23×C712−1+411yescharacteristic
241C22×D71—22no—
242C22×D71—22no—
243C22×D71—22no—
244C22×D71—22no—
245C22×D71—22no—
246C22×D71—22no—
247C22×D71—22no—
248C22×D71—22no—
249C22×D71—22no—
250C22×D71—22no—
251C22×D71—22no—
252C22×D71—22no—
253C22×D71—22no—
254C22×D71—22no—
255C22×D71—22no—
256C22×D71—22no—
257C22×D71—22no—
258C22×D71—22no—
259C22×D71—22no—
260C22×D71—22no—
261C22×D71—22no—
262C22×D71—22no—
263C22×D71—22no—
264C22×D71—22no—
265C22×D71—22no—
266C22×D71—22no—
267C22×D71—22no—
268C22×D71—22no—
269C22×D71C2×C4⋊C414yes—
270C22×D71C4×D414yes—
271C22×D71C4×Q814yes—
272C22×D71#12114yes—
273C22×D71C22⋊Q814yes—
274C22×D71#12514yes—
275C22×D71C4⋊Q814yes—
276C2×C4×C71—24no—
277C2×C4×C71—24no—
278C2×C4×C71—24no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—41no—
286C2×C4×C71—41no—
287C2×C4×C71—41no—
288C2×C4×C71—41no—
289C2×C4×C71—42no—
290C2×C4×C71—42no—
291C2×C4×C71—41no—
292C2×C4×C71—42no—
293C2×C4×C71—42no—
294C2×C4×C71—41no—
295C2×C4×C71—41no—
296C2×C4×C71—41no—
297C2×C4×C71—42no—
298C2×C4×C71—42no—
299C2×C4×C71—42no—
300C2×C4×C71—42no—
301C2×C4×C71—42no—
302C2×C4×C71—42no—
303C2×C4×C71—42no—
304C2×C4×C71C2×C22⋊C414yes—
305C2×C4×C71C2×C4⋊C414yes—
306C2×C4×C71#11714yes—
307C2×C4×C71#12114yes—
308C2×C4×C71#12114yes—
309C2×C4×C71C22⋊Q814yes—
310C2×C4×C71C22⋊Q814yes—
311C2×Dic71—22no—
312C2×Dic71—22no—
313C2×Dic71—24no—
314C2×Dic71—24no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—24no—
320C2×Dic71—24no—
321C2×Dic71—24no—
322C2×Dic71—24no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—41no—
330C2×Dic71—41no—
331C2×Dic71—41no—
332C2×Dic71—41no—
333C2×Dic71—41no—
334C2×Dic71—41no—
335C2×Dic71—41no—
336C2×Dic71—41no—
337C2×Dic71—42no—
338C2×Dic71—42no—
339C2×Dic71—42no—
340C2×Dic71—42no—
341C2×Dic71—42no—
342C2×Dic71—42no—
343C2×Dic71—42no—
344C2×Dic71C2×C22⋊C418yes—
345C2×Dic71C2×C4⋊C414yes—
346C4×D71—232no—
347C4×D71—432no—
348C22×C71C22×C22⋊C411yescharacteristic
349C22×C71C22×C4⋊C411yescharacteristic
350C22×C71C2×#11711yescharacteristic
351C22×C71C2×C4×D411yescharacteristic
352C22×C71C2×C4×Q811yescharacteristic
353C22×C71#51811yescharacteristic
354C22×C71#51911yescharacteristic
355C22×C71C2×#12111yescharacteristic
356C22×C71C2×#12111yescharacteristic
357C22×C71C2×#12111yescharacteristic
358C22×C71C2×C22⋊Q811yescharacteristic
359C22×C71C2×C22⋊Q811yescharacteristic
360C22×C71C2×C22⋊Q811yescharacteristic
361C22×C71C2×#12511yescharacteristic
362C22×C71C2×C4⋊Q811yescharacteristic
363C22×C71#53711yescharacteristic
364C22×C71#53711yescharacteristic
365C22×C71#54411yescharacteristic
366C22×C71#54411yescharacteristic
367C22×C71D4211yescharacteristic
368C22×C71D4211yescharacteristic
369C22×C71#54611yescharacteristic
370C22×C71#54611yescharacteristic
371C22×C71#54711yescharacteristic
372C22×C71#54711yescharacteristic
373C22×C71#54811yescharacteristic
374C22×C71#54811yescharacteristic
375C22×C71D4×Q811yescharacteristic
376C22×C71D4×Q811yescharacteristic
377C22×C71#55211yescharacteristic
378C22×C71#55211yescharacteristic
379C22×C71#55311yescharacteristic
380C22×C71#55311yescharacteristic
381C22×C71#55411yescharacteristic
382C22×C71#55411yescharacteristic
383C2×D71—24no—
384C2×D71—24no—
385C2×D71—24no—
386C2×D71—24no—
387C2×D71—24no—
388C2×D71—24no—
389C2×D71—24no—
390C2×D71—24no—
391C2×D71—24no—
392C2×D71—24no—
393C2×D71—24no—
394C2×D71—24no—
395C2×D71—24no—
396C2×D71—24no—
397C2×D71#38918yescomplemented
398C4×C71—44no—
399C4×C71—42no—
400C4×C71—42no—
401C4×C71—82no—
402C4×C71#38018yescomplemented
403Dic71—28no—
404Dic71—24no—
405Dic71—42no—
406Dic71—42no—
407Dic71—82no—
408#13907—711nomaximal, Sylow
409C2×C71C2×#38011yescharacteristic
410C2×C71C2×#38911yescharacteristic
411C2×C71#231611yescharacteristic
412C2×C71D4×C22⋊C411yescharacteristic
413C2×C71Q8×C22⋊C411yescharacteristic
414C2×C71#234411yescharacteristic
415C2×C71#234511yescharacteristic
416C2×C71#241611yescharacteristic
417C2×C71#241611yescharacteristic
418C2×C71#241711yescharacteristic
419C2×C71#241711yescharacteristic
420C2×C71#244011yescharacteristic
421C2×C71#244011yescharacteristic
422C2×C71#244211yescharacteristic
423C2×C71#244211yescharacteristic
424D71—28no—
425C23×C4⋊C4—711no—
426C2×#389—711no—
427C2×#389—711no—
428C2×#380—712no—
429C2×#380—711no—
430C2×C4×C22⋊C4—711no—
431#1441—712no—
432#1441—712no—
433C4⋊#95—711no—
434C4⋊#95D7111yescharacteristic, complemented
435C22⋊#95—712no—
436C71#1390711yescharacteristic, complemented, Sylow
437C24×C4—712no—
438C24×C4—711no—
439C22×C4⋊C4—712no—
440C22×C4⋊C4—712no—
441C22×C4⋊C4—711no—
442C22×C4⋊C4—712no—
443C22×C4⋊C4—718no—
444C22×C4⋊C4—711no—
445C22×C4⋊C4—1424no—
446C22×C4⋊C4—1424no—
447C22×C4⋊C4C2×D7111yescharacteristic
448C22×C4⋊C4C2×D7111yescharacteristic
449C22×C22⋊C4—711no—
450C22×C22⋊C4—711no—
451C22×C22⋊C4—712no—
452C22×C42—711no—
453C22×C42C2×D7111yescharacteristic
454#389—1424no—
455#389—1424no—
456#380—1428no—
457#380—1424no—
458C4×C22⋊C4—1424no—
459C2×#95—712no—
460C2×#95—712no—
461C2×#95—712no—
462C2×#95—712no—
463C2×#95—711no—
464C2×#95—711no—
465C2×#95—712no—
466C2×#95C2×D7112yes—
467C2×#95C2×D7112yes—
468C25—711no—
469C23×C4—2842no—
470C23×C4—2842no—
471C23×C4—718no—
472C23×C4—712no—
473C23×C4—711no—
474C23×C4—714no—
475C23×C4—714no—
476C23×C4—714no—
477C23×C4—711no—
478C23×C4—711no—
479C23×C4—712no—
480C23×C4—1424no—
481C23×C4—1424no—
482C23×C4—1424no—
483C23×C4—1424no—
484C23×C4—1422no—
485C23×C4—1422no—
486C23×C4—1422no—
487C23×C4—1422no—
488C23×C4C22×D7112yes—
489C23×C4C22×D7112yes—
490C23×C4C22×D7111yescharacteristic
491C23×C4C22×D7111yescharacteristic
492C23×C4C22×D7111yescharacteristic
493C2×C4⋊C4—22no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—22no—
498C2×C4⋊C4—2842no—
499C2×C4⋊C4—2842no—
500C2×C4⋊C4—714no—
501C2×C4⋊C4—714no—
502C2×C4⋊C4—714no—
503C2×C4⋊C4—718no—
504C2×C4⋊C4—14232no—
505C2×C4⋊C4—1424no—
506C2×C4⋊C4—1424no—
507C2×C4⋊C4—1424no—
508C2×C4⋊C4—1424no—
509C2×C4⋊C4—1422no—
510C2×C4⋊C4—1422no—
511C2×C4⋊C4—1422no—
512C2×C4⋊C4—1424no—
513C2×C4⋊C4—1424no—
514C2×C4⋊C4C4×D7114yes—
515C2×C22⋊C4—714no—
516C2×C22⋊C4—714no—
517C2×C22⋊C4—1424no—
518C2×C22⋊C4—1424no—
519C2×C22⋊C4—1424no—
520C2×C22⋊C4—1422no—
521C2×C22⋊C4—1422no—
522C2×C22⋊C4—1422no—
523C2×C22⋊C4—1422no—
524C2×C42—22no—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—1422no—
528C2×C42—1422no—
529C2×C42—1422no—
530#95—24no—
531#95—42no—
532#95—2842no—
533#95—1422no—
534#95—1422no—
535#95—1424no—
536#95—1424no—
537#95—1424no—
538#95—1424no—
539C24—712no—
540C24—712no—
541C24—712no—
542C24—712no—
543C24—712no—
544C24—712no—
545C24—712no—
546C24—1421no—
547C24—1421no—
548C24—1421no—
549C24—1421no—
550C24—1421no—
551C24—1421no—
552C24—1421no—
553C24—1421no—
554C24C23×D7111yescharacteristic
555C22×C4—22no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—2848no—
581C22×C4—2848no—
582C22×C4—2848no—
583C22×C4—2848no—
584C22×C4—2848no—
585C22×C4—714no—
586C22×C4—712no—
587C22×C4—712no—
588C22×C4—714no—
589C22×C4—714no—
590C22×C4—712no—
591C22×C4—7116no—
592C22×C4—712no—
593C22×C4—712no—
594C22×C4—14216no—
595C22×C4—14216no—
596C22×C4—1422no—
597C22×C4—1422no—
598C22×C4—1422no—
599C22×C4—1422no—
600C22×C4—1422no—
601C22×C4—1422no—
602C22×C4—1422no—
603C22×C4—1421no—
604C22×C4—1421no—
605C22×C4—1421no—
606C22×C4—1421no—
607C22×C4—1421no—
608C22×C4—1421no—
609C22×C4—1421no—
610C22×C4—1421no—
611C22×C4—1421no—
612C22×C4—1421no—
613C22×C4—1421no—
614C22×C4—1421no—
615C22×C4—1422no—
616C22×C4—1421no—
617C22×C4—1421no—
618C22×C4—1422no—
619C22×C4—1421no—
620C22×C4—1421no—
621C22×C4—1422no—
622C22×C4—1422no—
623C22×C4—1428no—
624C22×C4—1428no—
625C22×C4—1428no—
626C22×C4—1428no—
627C22×C4—1428no—
628C22×C4—1428no—
629C22×C4C2×C4×D7114yes—
630C22×C4C2×C4×D7112yes—
631C22×C4D4×D7112yes—
632C22×C4D4×D7112yes—
633C22×C4D4×D7112yes—
634C22×C4D4×D7112yes—
635C22×C4Q8×D7112yes—
636C22×C4Q8×D7112yes—
637C22×C4#1176586512yes—
638C22×C4#1176586512yes—
639C4⋊C4—28no—
640C4⋊C4—44no—
641C4⋊C4—2848no—
642C4⋊C4—2848no—
643C4⋊C4—2844no—
644C4⋊C4—7116no—
645C4⋊C4—14216no—
646C22⋊C4—2848no—
647C22⋊C4—1428no—
648C22⋊C4—1428no—
649C42—44no—
650C42—2844no—
651C23—714no—
652C23—714no—
653C23—714no—
654C23—714no—
655C23—714no—
656C23—714no—
657C23—714no—
658C23—1422no—
659C23—1422no—
660C23—1422no—
661C23—1422no—
662C23—1422no—
663C23—1422no—
664C23—1422no—
665C23—1422no—
666C23—1422no—
667C23—1422no—
668C23—1422no—
669C23—1422no—
670C23—1422no—
671C23—1422no—
672C23—1422no—
673C23—1422no—
674C23—1422no—
675C23—1422no—
676C23—1422no—
677C23—1422no—
678C23—1422no—
679C23—1422no—
680C23—1422no—
681C23—1422no—
682C23—1422no—
683C23—1422no—
684C23—1422no—
685C23—1422no—
686C23C22×C4×D7111yescharacteristic
687C23C2×D4×D7111yescharacteristic
688C23C2×D4×D7111yescharacteristic
689C23C2×D4×D7111yescharacteristic
690C23C2×D4×D7111yescharacteristic
691C23C2×Q8×D7111yescharacteristic
692C23C2×Q8×D7111yescharacteristic
693C23#41×D7111yescharacteristic
694C23#41×D7111yescharacteristic
695C23C2×#1176586511yescharacteristic
696C23C2×#1176586511yescharacteristic
697C23#1455617311yescharacteristic
698C23#1455617411yescharacteristic
699C23#1455617511yescharacteristic
700C23#1455617611yescharacteristic
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—22no—
706C2×C4—24no—
707C2×C4—24no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—28432no—
730C2×C4—2841no—
731C2×C4—2841no—
732C2×C4—2841no—
733C2×C4—2841no—
734C2×C4—2841no—
735C2×C4—2841no—
736C2×C4—2841no—
737C2×C4—2841no—
738C2×C4—2842no—
739C2×C4—2842no—
740C2×C4—2842no—
741C2×C4—2842no—
742C2×C4—2842no—
743C2×C4—2842no—
744C2×C4—2842no—
745C2×C4—718no—
746C2×C4—714no—
747C2×C4—1422no—
748C2×C4—1422no—
749C2×C4—1422no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4—1422no—
753C2×C4—1424no—
754C2×C4—1424no—
755C2×C4—1424no—
756C2×C4—1424no—
757C2×C4—1422no—
758C2×C4—1422no—
759C2×C4—1424no—
760C2×C4—1424no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—14232no—
766C2×C4C22⋊C4×D7114yes—
767C2×C4C4⋊C4×D7114yes—
768C2×C4#1455608514yes—
769C2×C4#1455610114yes—
770C2×C4#1455610114yes—
771C2×C4#1455610614yes—
772C2×C4#1455610614yes—
773C22—718no—
774C22—1424no—
775C22—1424no—
776C22—1424no—
777C22—1424no—
778C22—1424no—
779C22—1424no—
780C22—1424no—
781C22—1424no—
782C22—1424no—
783C22—1424no—
784C22—1424no—
785C22—1424no—
786C22—1424no—
787C22—1424no—
788C22C2×C22⋊C4×D7111yescharacteristic
789C22C2×C4⋊C4×D7111yescharacteristic
790C22C2×#1455608511yescharacteristic
791C22C4×D4×D7111yescharacteristic
792C22C4×Q8×D7111yescharacteristic
793C22#1798647111yescharacteristic
794C22#1798647511yescharacteristic
795C22#121×D7111yescharacteristic
796C22C2×#1455610111yescharacteristic
797C22C2×#1455610111yescharacteristic
798C22C22⋊Q8×D7111yescharacteristic
799C22C2×#1455610611yescharacteristic
800C22C2×#1455610611yescharacteristic
801C22#125×D7111yescharacteristic
802C22C4⋊Q8×D7111yescharacteristic
803C22#1798657811yescharacteristic
804C22#1798657911yescharacteristic
805C22#1798662611yescharacteristic
806C22#1798662911yescharacteristic
807C22#1798663311yescharacteristic
808C22#1798663411yescharacteristic
809C22#1798664211yescharacteristic
810C22#1798664611yescharacteristic
811C22#1798665011yescharacteristic
812C22#1798665411yescharacteristic
813C22#1798665711yescharacteristic
814C22#1798665911yescharacteristic
815C22#1798666211yescharacteristic
816C22#1798666411yescharacteristic
817C22#1798668811yescharacteristic
818C22#1798669011yescharacteristic
819C22#1798669311yescharacteristic
820C22#1798669911yescharacteristic
821C22#1798670411yescharacteristic
822C22#1798670911yescharacteristic
823C4—42no—
824C4—42no—
825C4—44no—
826C4—82no—
827C4—2842no—
828C4—2842no—
829C4—5682no—
830C4—1428no—
831C4—1424no—
832C4#1798585818yescomplemented
833C2—1428no—
834C2C2×#1798585811yescharacteristic
835C2#389×D7111yescharacteristic
836C2#2259095511yescharacteristic
837C2#2259116111yescharacteristic
838C2#2259117411yescharacteristic
839C2#2259120511yescharacteristic
840C2#2259121311yescharacteristic
841C2#2259178211yescharacteristic
842C2#2259178311yescharacteristic
843C2#2259179311yescharacteristic
844C2#2259179411yescharacteristic
845C2#2259204411yescharacteristic
846C2#2259204511yescharacteristic
847C2#2259206611yescharacteristic
848C2#2259206711yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC71×C4⋊#95C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC4⋊#95D71
hypocenterC71#13907
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#17985897C2semidirect
3. C2×#17985895C2semidirect
7. #22586591C2semidirect
8. #22586591C2semidirect
9. #22586569C2semidirect
11. C71×C4⋊#95C2semidirect
21. C2×C4⋊C4×D71C4semidirect
177. C2×C4×D71C4⋊C4semidirect
179. C4⋊Dic71C22⋊C4semidirect
397. C2×D71#389semidirect
402. C4×C71#380semidirect
434. C4⋊#95D71semidirect
436. C71#13907semidirect
832. C4#17985858semidirect

Maximal subgroups

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

subgroupindex
C22×C4⋊C4×D712
C2×#179858972
C2×#179858952
C2×#179858582
C2×#179858562
C2×C4×(C2×D71)⋊C42
#225865912
#225865692
(C2×D71)⋊#952
C71×C4⋊#952
#1390771