Finite Group Databasebeta

← #31918873

Subgroups — #31918873

Order 18176.

2182 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556086C211yesmaximal, characteristic
2C2×#17985856C211yesmaximal, characteristic
3C2×C4⋊C4×Dic71C211yesmaximal, characteristic, complemented
4C2×C4×(C2×D71)⋊C4C211yesmaximal, characteristic
5#22586578C212yesmaximal
6#22586576C212yesmaximal
7#22586570C211yesmaximal, characteristic, complemented
8#22586569C211yesmaximal, characteristic, complemented
9#22586564C212yesmaximal, complemented
10C4×C71⋊#95C212yesmaximal, complemented
11C2×C4×C4⋊C4×C71C211yesmaximal, characteristic, complemented
12C23×C4×D71C2211yescharacteristic
13C2×#14556086—24no—
14C2×#14556086—24no—
15C2×#14556086C418yescomplemented
16C22×C4⋊Dic71C2211yescharacteristic
17C22×C4⋊Dic71C2211yescharacteristic
18C22×(C2×D71)⋊C4C2212yes—
19C22×(C2×D71)⋊C4C2211yescharacteristic
20C22×(C2×D71)⋊C4C2211yescharacteristic
21C22×(C2×D71)⋊C4C2212yes—
22C22×C4×Dic71C2212yes—
23C22×C4×Dic71C2212yes—
24C22×C4×Dic71C2211yescharacteristic
25#17985856C418yescomplemented
26C4⋊C4×Dic71—24no—
27C4×(C2×D71)⋊C4C418yescomplemented
28C2×C71⋊#95C2212yes—
29C2×C71⋊#95C2212yes—
30C2×C71⋊#95C2212yes—
31C2×C71⋊#95C2212yes—
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2211yescharacteristic
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2211yescharacteristic
36C22×C4⋊C4×C71C2211yescharacteristic
37C22×C4⋊C4×C71C2211yescharacteristic
38C22×C42×C71C2212yes—
39C22×C42×C71C2211yescharacteristic
40C4×C4⋊C4×C71—24no—
41C2×#95×C71C2212yes—
42C24×D71C2311yescharacteristic
43C23×Dic71C2311yescharacteristic
44C23×Dic71C2312yes—
45C23×Dic71C2312yes—
46C23×Dic71C2311yescharacteristic
47C23×Dic71C2311yescharacteristic
48C22×C4×D71—22no—
49C22×C4×D71—22no—
50C22×C4×D71—22no—
51C22×C4×D71—22no—
52C22×C4×D71C2×C414yes—
53C22×C4×D71C2×C414yes—
54C22×C4×D71C2×C414yes—
55#14556086—232no—
56C2×C4⋊Dic71—22no—
57C2×C4⋊Dic71—22no—
58C2×C4⋊Dic71—22no—
59C2×C4⋊Dic71—22no—
60C2×C4⋊Dic71C2×C414yes—
61C2×C4⋊Dic71C2×C414yes—
62C2×(C2×D71)⋊C4—22no—
63C2×(C2×D71)⋊C4—22no—
64C2×(C2×D71)⋊C4—24no—
65C2×(C2×D71)⋊C4—24no—
66C2×(C2×D71)⋊C4—22no—
67C2×(C2×D71)⋊C4—22no—
68C2×(C2×D71)⋊C4—42no—
69C2×(C2×D71)⋊C4—42no—
70C2×(C2×D71)⋊C4C2×C414yes—
71C2×(C2×D71)⋊C4C2×C414yes—
72C2×(C2×D71)⋊C4C2×C418yes—
73C2×(C2×D71)⋊C4C2×C418yes—
74C2×C4×Dic71—24no—
75C2×C4×Dic71—22no—
76C2×C4×Dic71—24no—
77C2×C4×Dic71—24no—
78C2×C4×Dic71—24no—
79C2×C4×Dic71—22no—
80C2×C4×Dic71—42no—
81C2×C4×Dic71C2×C414yes—
82C2×C4×Dic71C2×C418yes—
83C71⋊#95—24no—
84C71⋊#95—24no—
85C71⋊#95—24no—
86C71⋊#95—42no—
87C71⋊#95—42no—
88C71⋊#95C2×C414yes—
89C71⋊#95C2×C414yes—
90C71⋊#95C2×C418yes—
91C23×C4×C71C2312yes—
92C23×C4×C71C2311yescharacteristic
93C23×C4×C71C2312yes—
94C23×C4×C71C2311yescharacteristic
95C23×C4×C71C2311yescharacteristic
96C2×C4⋊C4×C71—22no—
97C2×C4⋊C4×C71—22no—
98C2×C4⋊C4×C71C2×C414yes—
99C2×C4⋊C4×C71C2×C414yes—
100C2×C4⋊C4×C71D414yes—
101C2×C4⋊C4×C71D414yes—
102C2×C42×C71—22no—
103C2×C42×C71—22no—
104C2×C42×C71—24no—
105C2×C42×C71—24no—
106C2×C42×C71—42no—
107C2×C42×C71C2×C414yes—
108#95×C71—24no—
109C23×D71—21no—
110C23×D71—21no—
111C23×D71—21no—
112C23×D71—21no—
113C23×D71—21no—
114C23×D71—21no—
115C23×D71—21no—
116C23×D71—21no—
117C23×D71—21no—
118C23×D71—21no—
119C23×D71—21no—
120C23×D71—21no—
121C23×D71C22×C412yes—
122C23×D71C22×C412yes—
123C23×D71C22×C412yes—
124C22×Dic71—21no—
125C22×Dic71—21no—
126C22×Dic71—21no—
127C22×Dic71—21no—
128C22×Dic71—21no—
129C22×Dic71—21no—
130C22×Dic71—21no—
131C22×Dic71—21no—
132C22×Dic71—21no—
133C22×Dic71—22no—
134C22×Dic71—22no—
135C22×Dic71—22no—
136C22×Dic71—22no—
137C22×Dic71—22no—
138C22×Dic71—22no—
139C22×Dic71—22no—
140C22×Dic71—21no—
141C22×Dic71—21no—
142C22×Dic71—21no—
143C22×Dic71—22no—
144C22×Dic71—22no—
145C22×Dic71—21no—
146C22×Dic71—22no—
147C22×Dic71—22no—
148C22×Dic71—21no—
149C22×Dic71—22no—
150C22×Dic71C22×C412yes—
151C22×Dic71C22×C414yes—
152C22×Dic71C22×C414yes—
153C22×Dic71C22×C412yes—
154C22×Dic71C22×C412yes—
155C22×Dic71C22×C412yes—
156C22×Dic71C22×C412yes—
157C22×Dic71#4112yes—
158C22×Dic71#4112yes—
159C2×C4×D71—28no—
160C2×C4×D71—28no—
161C2×C4×D71—28no—
162C2×C4×D71—28no—
163C2×C4×D71—28no—
164C2×C4×D71—28no—
165C2×C4×D71C42116yescomplemented
166C4⋊Dic71—28no—
167C4⋊Dic71—28no—
168(C2×D71)⋊C4—216no—
169(C2×D71)⋊C4—28no—
170(C2×D71)⋊C4—28no—
171(C2×D71)⋊C4—48no—
172C4×Dic71—216no—
173C4×Dic71—28no—
174C4×Dic71—48no—
175C24×C71C2411yescharacteristic
176C22×C4×C71—21no—
177C22×C4×C71—22no—
178C22×C4×C71—21no—
179C22×C4×C71—22no—
180C22×C4×C71—21no—
181C22×C4×C71—22no—
182C22×C4×C71—22no—
183C22×C4×C71—21no—
184C22×C4×C71—21no—
185C22×C4×C71—22no—
186C22×C4×C71—22no—
187C22×C4×C71—21no—
188C22×C4×C71—22no—
189C22×C4×C71—22no—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—22no—
193C22×C4×C71—21no—
194C22×C4×C71—22no—
195C22×C4×C71—21no—
196C22×C4×C71C22×C412yes—
197C22×C4×C71C22×C414yes—
198C22×C4×C71C22×C414yes—
199C22×C4×C71C22×C412yes—
200C22×C4×C71C22×C412yes—
201C22×C4×C71C22×C412yes—
202C22×C4×C71C22×C412yes—
203C22×C4×C71C2×D414yes—
204C22×C4×C71C2×D412yes—
205C22×C4×C71C2×D414yes—
206C22×C4×C71C2×D412yes—
207C22×C4×C71#4112yes—
208C22×C4×C71#4112yes—
209C22×C4×C71#4112yes—
210C22×C4×C71#4112yes—
211C4⋊C4×C71—28no—
212C4⋊C4×C71C22⋊C4116yescomplemented
213C42×C71—28no—
214C42×C71—48no—
215C23×C71C23×C411yescharacteristic
216C23×C71C23×C411yescharacteristic
217C23×C71C23×C411yescharacteristic
218C23×C71C22×D411yescharacteristic
219C23×C71C22×D411yescharacteristic
220C23×C71C2×#4111yescharacteristic
221C23×C71C2×#4111yescharacteristic
222C23×C71C2×#4111yescharacteristic
223C23×C71C2×#4111yescharacteristic
224C23×C71C2×#4111yescharacteristic
225C23×C71C2×#4111yescharacteristic
226C23×C71H(5,𝔽2)11yescharacteristic
227C23×C71H(5,𝔽2)11yescharacteristic
228C23×C712−1+411yescharacteristic
229C23×C712−1+411yescharacteristic
230C22×D71—22no—
231C22×D71—22no—
232C22×D71—22no—
233C22×D71—22no—
234C22×D71—22no—
235C22×D71—22no—
236C22×D71—22no—
237C22×D71—22no—
238C22×D71—22no—
239C22×D71—22no—
240C22×D71—22no—
241C22×D71—22no—
242C22×D71—22no—
243C22×D71—22no—
244C22×D71—22no—
245C22×D71—22no—
246C22×D71—22no—
247C22×D71—22no—
248C22×D71—41no—
249C22×D71—41no—
250C22×D71—41no—
251C22×D71—41no—
252C22×D71—41no—
253C22×D71—41no—
254C22×D71—41no—
255C22×D71—41no—
256C22×D71—41no—
257C22×D71—41no—
258C22×D71—41no—
259C22×D71—41no—
260C22×D71—41no—
261C22×D71—41no—
262C22×D71—41no—
263C22×D71—41no—
264C22×D71C2×C4214yes—
265C2×C4×C71—22no—
266C2×C4×C71—24no—
267C2×C4×C71—24no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—24no—
271C2×C4×C71—24no—
272C2×C4×C71—24no—
273C2×C4×C71—24no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—24no—
280C2×C4×C71—24no—
281C2×C4×C71—24no—
282C2×C4×C71—22no—
283C2×C4×C71—42no—
284C2×C4×C71—41no—
285C2×C4×C71—41no—
286C2×C4×C71—42no—
287C2×C4×C71—42no—
288C2×C4×C71—41no—
289C2×C4×C71—42no—
290C2×C4×C71—41no—
291C2×C4×C71C2×C4214yes—
292C2×C4×C71C2×C22⋊C418yes—
293C2×C4×C71C2×C22⋊C414yes—
294C2×C4×C71#11714yes—
295C2×C4×C71#11714yescomplemented
296C2×C4×C71C4×D414yes—
297C2×C4×C71C4×D414yes—
298C2×C4×C71C4×D414yes—
299C2×C4×C71C4×D414yes—
300C2×Dic71—22no—
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—24no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—24no—
316C2×Dic71—24no—
317C2×Dic71—24no—
318C2×Dic71—24no—
319C2×Dic71—22no—
320C2×Dic71—24no—
321C2×Dic71—42no—
322C2×Dic71—41no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325C2×Dic71—42no—
326C2×Dic71—42no—
327C2×Dic71—41no—
328C2×Dic71—42no—
329C2×Dic71—42no—
330C2×Dic71—42no—
331C2×Dic71—41no—
332C2×Dic71—41no—
333C2×Dic71C2×C4214yes—
334C2×Dic71#11714yescomplemented
335C4×D71—232no—
336C22×C71C22×C4211yescharacteristic
337C22×C71C22×C22⋊C411yescharacteristic
338C22×C71C2×#11711yescharacteristic
339C22×C71C2×#11711yescharacteristic
340C22×C71C2×#11711yescharacteristic
341C22×C71C2×C4×D411yescharacteristic
342C22×C71C2×C4×D411yescharacteristic
343C22×C71C2×C4×D411yescharacteristic
344C22×C71C2×C4×D411yescharacteristic
345C22×C71C4×#4111yescharacteristic
346C22×C71C4×#4111yescharacteristic
347C22×C71C4×#4111yescharacteristic
348C22×C71C4×#4111yescharacteristic
349C22×C71#51811yescharacteristic
350C22×C71#51911yescharacteristic
351C22×C71#52011yescharacteristic
352C22×C71#52011yescharacteristic
353C22×C71#52011yescharacteristic
354C22×C71#52011yescharacteristic
355C22×C71#54611yescharacteristic
356C22×C71#54611yescharacteristic
357C22×C71#54711yescharacteristic
358C22×C71#54711yescharacteristic
359C22×C71#54811yescharacteristic
360C22×C71#54811yescharacteristic
361C22×C71#55011yescharacteristic
362C22×C71#55011yescharacteristic
363C22×C71#55211yescharacteristic
364C22×C71#55211yescharacteristic
365C22×C71#55311yescharacteristic
366C22×C71#55311yescharacteristic
367C22×C71#55511yescharacteristic
368C22×C71#55511yescharacteristic
369C22×C71#55611yescharacteristic
370C22×C71#55611yescharacteristic
371C2×D71—24no—
372C2×D71—24no—
373C2×D71—24no—
374C2×D71—42no—
375C2×D71—42no—
376C2×D71—42no—
377C2×D71—42no—
378C2×D71—42no—
379C2×D71—42no—
380C2×D71—42no—
381C2×D71—42no—
382C2×D71—42no—
383C2×D71—42no—
384C2×D71—42no—
385C2×D71—42no—
386C4×C71—28no—
387C4×C71—24no—
388C4×C71—42no—
389C4×C71—44no—
390C4×C71C4×C22⋊C418yes—
391Dic71—24no—
392Dic71—24no—
393Dic71—44no—
394Dic71—42no—
395Dic71—44no—
396#13801—711nomaximal, Sylow
397C2×C71C2×C4×C22⋊C411yescharacteristic
398C2×C71C4×#11711yescharacteristic
399C2×C71#227411yescharacteristic
400C2×C71#233911yescharacteristic
401C2×C71#234111yescharacteristic
402C2×C71#234611yescharacteristic
403C2×C71#234711yescharacteristic
404C2×C71#235211yescharacteristic
405C2×C71#235211yescharacteristic
406C2×C71#235411yescharacteristic
407C2×C71#235411yescharacteristic
408C2×C71#236211yescharacteristic
409C2×C71#236211yescharacteristic
410C2×C71#236311yescharacteristic
411C2×C71#236311yescharacteristic
412D71—44no—
413C22×#117—711no—
414C2×#380—711no—
415C2×C4×C4⋊C4—711no—
416C2×C4×C4⋊C4D7111yescharacteristic, complemented
417C2×C4×C22⋊C4—711no—
418#1437—712no—
419#1437—712no—
420C4⋊#95—711no—
421C4⋊#95—711no—
422#1434—712no—
423C4×#95—712no—
424C71#1380111yescharacteristic, complemented, Sylow
425C24×C4—711no—
426C2×#117—718no—
427C2×#117—1424no—
428C2×#117—1424no—
429C22×C4⋊C4—711no—
430C22×C4⋊C4—711no—
431C22×C4⋊C4C2×D7111yescharacteristic
432C22×C4⋊C4C2×D7111yescharacteristic
433C22×C22⋊C4—712no—
434C22×C22⋊C4—712no—
435C22×C22⋊C4—711no—
436C22×C22⋊C4—711no—
437C22×C42—712no—
438C22×C42—712no—
439C22×C42—711no—
440C22×C42C2×D7112yes—
441C22×C42C2×D7111yescharacteristic
442#380—718no—
443C4×C4⋊C4—24no—
444C4×C4⋊C4—1424no—
445C4×C22⋊C4—718no—
446C2×#95—712no—
447C2×#95—712no—
448C2×#95—711no—
449C2×#95—712no—
450C2×#95—711no—
451C2×#95—712no—
452C2×#95—712no—
453C2×#95—712no—
454C2×#95C2×D7112yes—
455C25—711no—
456C23×C4—711no—
457C23×C4—711no—
458C23×C4—714no—
459C23×C4—714no—
460C23×C4—714no—
461C23×C4—712no—
462C23×C4—712no—
463C23×C4—711no—
464C23×C4—1422no—
465C23×C4—1422no—
466C23×C4—1422no—
467C23×C4—1422no—
468C23×C4C22×D7112yes—
469C23×C4C22×D7111yescharacteristic
470C23×C4C22×D7112yes—
471C23×C4C22×D7111yescharacteristic
472C23×C4C22×D7111yescharacteristic
473#117—14232no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—714no—
477C2×C4⋊C4—714no—
478C2×C4⋊C4—1422no—
479C2×C4⋊C4—1422no—
480C2×C4⋊C4—1422no—
481C2×C4⋊C4—1422no—
482C2×C4⋊C4C4×D7114yes—
483C2×C4⋊C4C4×D7114yes—
484C2×C4⋊C4D28414yes—
485C2×C4⋊C4C22⋊D7114yes—
486C2×C22⋊C4—2842no—
487C2×C22⋊C4—2842no—
488C2×C22⋊C4—718no—
489C2×C22⋊C4—718no—
490C2×C22⋊C4—714no—
491C2×C22⋊C4—714no—
492C2×C22⋊C4—1422no—
493C2×C22⋊C4—1422no—
494C2×C22⋊C4—1424no—
495C2×C22⋊C4—1424no—
496C2×C22⋊C4—1422no—
497C2×C22⋊C4—1422no—
498C2×C42—22no—
499C2×C42—22no—
500C2×C42—24no—
501C2×C42—24no—
502C2×C42—42no—
503C2×C42—2842no—
504C2×C42—718no—
505C2×C42—714no—
506C2×C42—1424no—
507C2×C42—1424no—
508C2×C42—1424no—
509C2×C42—1424no—
510C2×C42—1422no—
511C2×C42—1422no—
512C2×C42C4×D7114yes—
513#95—24no—
514#95—2842no—
515#95—2842no—
516#95—714no—
517#95—714no—
518#95—718no—
519#95—1424no—
520#95—1424no—
521#95—1424no—
522C24—712no—
523C24—712no—
524C24—712no—
525C24—1421no—
526C24—1421no—
527C24—1421no—
528C24—1421no—
529C24—1421no—
530C24—1421no—
531C24—1421no—
532C24—1421no—
533C24—1421no—
534C24—1421no—
535C24—1421no—
536C24—1421no—
537C24C23×D7111yescharacteristic
538C22×C4—21no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—712no—
559C22×C4—712no—
560C22×C4—712no—
561C22×C4—712no—
562C22×C4—712no—
563C22×C4—712no—
564C22×C4—7116no—
565C22×C4—712no—
566C22×C4—714no—
567C22×C4—714no—
568C22×C4—1422no—
569C22×C4—1421no—
570C22×C4—1422no—
571C22×C4—1422no—
572C22×C4—1422no—
573C22×C4—1422no—
574C22×C4—1421no—
575C22×C4—1421no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1421no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1421no—
583C22×C4—1422no—
584C22×C4—1421no—
585C22×C4—1422no—
586C22×C4—1421no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1421no—
590C22×C4—1421no—
591C22×C4—1421no—
592C22×C4—1421no—
593C22×C4—1421no—
594C22×C4—1428no—
595C22×C4—1428no—
596C22×C4—1428no—
597C22×C4—1428no—
598C22×C4—1428no—
599C22×C4—1428no—
600C22×C4C2×C4×D7112yes—
601C22×C4C2×C4×D7114yes—
602C22×C4C2×C4×D7114yes—
603C22×C4C2×C4×D7112yes—
604C22×C4C2×C4×D7112yes—
605C22×C4C2×C4×D7112yes—
606C22×C4C2×C4×D7112yes—
607C22×C4C2×C22⋊D7114yes—
608C22×C4C2×C22⋊D7112yes—
609C22×C4C2×D28414yes—
610C22×C4C2×D28412yes—
611C22×C4#1176586412yes—
612C22×C4#1176586512yes—
613C22×C4#1176586512yes—
614C22×C4#1176586612yes—
615C4⋊C4—28no—
616C4⋊C4—1428no—
617C4⋊C4—1428no—
618C4⋊C4(C2×D71)⋊C4116yescomplemented
619C22⋊C4—2848no—
620C22⋊C4—1428no—
621C22⋊C4—14216no—
622C22⋊C4—1428no—
623C42—28no—
624C42—48no—
625C42—2848no—
626C42—14216no—
627C42—1428no—
628C23—2841no—
629C23—2841no—
630C23—2841no—
631C23—2841no—
632C23—2841no—
633C23—2841no—
634C23—2841no—
635C23—2841no—
636C23—2841no—
637C23—2841no—
638C23—2841no—
639C23—2841no—
640C23—2841no—
641C23—2841no—
642C23—2841no—
643C23—2841no—
644C23—714no—
645C23—1422no—
646C23—1422no—
647C23—1422no—
648C23—1422no—
649C23—1422no—
650C23—1422no—
651C23—1422no—
652C23—1422no—
653C23—1422no—
654C23—1422no—
655C23—1422no—
656C23—1422no—
657C23—1422no—
658C23—1422no—
659C23—1422no—
660C23—1422no—
661C23—1422no—
662C23—1422no—
663C23C22×C4×D7111yescharacteristic
664C23C22×C4×D7111yescharacteristic
665C23C22×C4×D7111yescharacteristic
666C23C22×C22⋊D7111yescharacteristic
667C23C22×D28411yescharacteristic
668C23#41×D7111yescharacteristic
669C23#41×D7111yescharacteristic
670C23C2×#1176586411yescharacteristic
671C23C2×#1176586511yescharacteristic
672C23C2×#1176586511yescharacteristic
673C23C2×#1176586611yescharacteristic
674C23#1455617311yescharacteristic
675C23#1455617411yescharacteristic
676C23#1455617511yescharacteristic
677C23#1455617611yescharacteristic
678C2×C4—22no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—24no—
682C2×C4—24no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—24no—
688C2×C4—24no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—24no—
693C2×C4—24no—
694C2×C4—24no—
695C2×C4—22no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—41no—
704C2×C4—2842no—
705C2×C4—2841no—
706C2×C4—2842no—
707C2×C4—2842no—
708C2×C4—2842no—
709C2×C4—2841no—
710C2×C4—2842no—
711C2×C4—2842no—
712C2×C4—2842no—
713C2×C4—2842no—
714C2×C4—2841no—
715C2×C4—2841no—
716C2×C4—714no—
717C2×C4—714no—
718C2×C4—1424no—
719C2×C4—1422no—
720C2×C4—1422no—
721C2×C4—1424no—
722C2×C4—1424no—
723C2×C4—1424no—
724C2×C4—1424no—
725C2×C4—1422no—
726C2×C4—1424no—
727C2×C4—1422no—
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—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—14232no—
740C2×C4C42×D7114yes—
741C2×C4C2×(C2×D71)⋊C418yes—
742C2×C4C2×(C2×D71)⋊C414yes—
743C2×C4#1455608514yes—
744C2×C4#1455608614yescomplemented
745C2×C4C4×C22⋊D7114yes—
746C2×C4C4×C22⋊D7114yes—
747C2×C4C4×D28414yes—
748C2×C4C4×D28414yes—
749C22—2842no—
750C22—2842no—
751C22—2842no—
752C22—2842no—
753C22—2842no—
754C22—2842no—
755C22—2842no—
756C22—2842no—
757C22—2842no—
758C22—2842no—
759C22—2842no—
760C22—2842no—
761C22—1424no—
762C22—1424no—
763C22—1424no—
764C22C2×C42×D7111yescharacteristic
765C22C22×(C2×D71)⋊C411yescharacteristic
766C22#117×D7111yescharacteristic
767C22C2×#1455608511yescharacteristic
768C22C2×#1455608611yescharacteristic
769C22C2×C4×C22⋊D7111yescharacteristic
770C22C2×C4×C22⋊D7111yescharacteristic
771C22C2×C4×D28411yescharacteristic
772C22C2×C4×D28411yescharacteristic
773C22C4×#1176586411yescharacteristic
774C22C4×#1176586411yescharacteristic
775C22C4×#1176586611yescharacteristic
776C22C4×#1176586611yescharacteristic
777C22#1798647111yescharacteristic
778C22#1798647511yescharacteristic
779C22#1798647811yescharacteristic
780C22#1798647911yescharacteristic
781C22#1798648011yescharacteristic
782C22#1798648111yescharacteristic
783C22#1798664311yescharacteristic
784C22#1798664411yescharacteristic
785C22#1798664811yescharacteristic
786C22#1798665311yescharacteristic
787C22#1798666011yescharacteristic
788C22#1798666111yescharacteristic
789C22#1798666811yescharacteristic
790C22#1798667111yescharacteristic
791C22#1798668411yescharacteristic
792C22#1798669011yescharacteristic
793C22#1798669711yescharacteristic
794C22#1798669911yescharacteristic
795C22#1798671211yescharacteristic
796C22#1798671411yescharacteristic
797C22#1798671711yescharacteristic
798C22#1798672211yescharacteristic
799C4—24no—
800C4—28no—
801C4—42no—
802C4—44no—
803C4—2842no—
804C4—2844no—
805C4—2844no—
806C4—1424no—
807C4—1424no—
808C4C4×(C2×D71)⋊C418yes—
809C2—2844no—
810C2C2×C4×(C2×D71)⋊C411yescharacteristic
811C2C4×#1455608611yescharacteristic
812C2#2259069411yescharacteristic
813C2#2259116511yescharacteristic
814C2#2259117811yescharacteristic
815C2#2259122111yescharacteristic
816C2#2259122911yescharacteristic
817C2#2259126511yescharacteristic
818C2#2259127211yescharacteristic
819C2#2259128711yescharacteristic
820C2#2259129011yescharacteristic
821C2#2259136311yescharacteristic
822C2#2259136911yescharacteristic
823C2#2259137411yescharacteristic
824C2#2259138011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC22×C71C22×C42
FittingC2×C4×C4⋊C4×C71C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC2×C4×C4⋊C4D71
hypocenterC71#13801
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×C4⋊C4×Dic71C2semidirect
7. #22586570C2semidirect
8. #22586569C2semidirect
9. #22586564C2semidirect
10. C4×C71⋊#95C2semidirect
11. C2×C4×C4⋊C4×C71C2semidirect
15. C2×#14556086C4semidirect
25. #17985856C4semidirect
27. C4×(C2×D71)⋊C4C4semidirect
165. C2×C4×D71C42semidirect
212. C4⋊C4×C71C22⋊C4semidirect
295. C2×C4×C71#117semidirect
334. C2×Dic71#117semidirect
416. C2×C4×C4⋊C4D71semidirect
424. C71#13801semidirect
618. C4⋊C4(C2×D71)⋊C4semidirect
744. C2×C4#14556086semidirect

Maximal subgroups

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

subgroupindex
C22×#145560862
C2×#179858562
C2×C4⋊C4×Dic712
C2×C4×(C2×D71)⋊C42
#225865782
#225865762
#225865702
#225865692
#225865642
C4×C71⋊#952
C2×C4×C4⋊C4×C712
#1380171