Finite Group Databasebeta

← #1854×D71 #31998166

Subgroups — #1854×D71 #31998166

Order 18176.

1662 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#117×D71C211yesmaximal, characteristic
2C2×#107×D71C211yesmaximal, characteristic, complemented
3C2×#106×D71C211yesmaximal, characteristic, complemented
4C2×C22⋊C8×D71C211yesmaximal, characteristic
5#380×D71C211yesmaximal, characteristic
6#22588542C211yesmaximal, characteristic, complemented
7#22588541C211yesmaximal, characteristic, complemented
8#22588540C211yesmaximal, characteristic, complemented
9#22588539C211yesmaximal, characteristic, complemented
10#22588538C211yesmaximal, characteristic, complemented
11#22588537C211yesmaximal, characteristic, complemented
12#22588536C211yesmaximal, characteristic, complemented
13#340×D71C211yesmaximal, characteristic, complemented
14#340×D71C211yesmaximal, characteristic, complemented
15C71×#1854C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C22×C8×D71C2211yescharacteristic
19C2×#14556087C2211yescharacteristic
20C2×#14556086C2211yescharacteristic
21C2×#14556086C2211yescharacteristic
22C2×#14556085—21no—
23C2×#14556084—21no—
24#117×D71—24no—
25#117×D71—24no—
26C2×C4⋊C4×D71C2211yescharacteristic
27C2×C4⋊C4×D71C2211yescharacteristic
28C2×C4⋊C4×D71C2211yescharacteristic
29C2×C4⋊C4×D71C2211yescharacteristic
30C2×C22⋊C4×D71—21no—
31C2×C22⋊C4×D71—21no—
32C2×C42×D71—21no—
33C2×#14556062C2211yescharacteristic, complemented
34C2×#14556061C2211yescharacteristic, complemented
35C2×#14556061C2211yescharacteristic, complemented
36#107×D71—24no—
37C2×#14556060C2211yescharacteristic, complemented
38C2×#14556059C2211yescharacteristic, complemented
39C2×#14556059C2211yescharacteristic, complemented
40#106×D71—24no—
41C2×C22⋊(C71⋊C8)C2211yescharacteristic
42C2×(C2×D71)⋊C8C2211yescharacteristic
43C2×(C2×D71)⋊C8C2211yescharacteristic
44C22⋊C8×D71C418yescomplemented
45#17985859C2211yescharacteristic
46#17985858—21no—
47#17985857—21no—
48#17985856C2211yescharacteristic
49#17985856C2211yescharacteristic
50#95×D71—21no—
51#17985762C2211yescharacteristic, complemented
52#17985762C2211yescharacteristic, complemented
53#17985761C2211yescharacteristic, complemented
54#17985761C2211yescharacteristic, complemented
55#17985761C2211yescharacteristic, complemented
56#17985761C2211yescharacteristic, complemented
57C2×#117×C71C2211yescharacteristic
58C2×#107×C71C2211yescharacteristic, complemented
59C2×#106×C71C2211yescharacteristic, complemented
60C2×C22⋊C8×C71C2211yescharacteristic
61#380×C71C2211yescharacteristic
62#340×C71C2211yescharacteristic, complemented
63#340×C71C2211yescharacteristic, complemented
64C24×D71D411yescharacteristic
65C23×Dic71D411yescharacteristic
66C22×C4×D71—22no—
67C22×C4×D71—22no—
68C22×C4×D71—22no—
69C22×C4×D71—22no—
70C22×C4×D71—21no—
71C22×C4×D71—21no—
72C22×C4×D71—21no—
73C22×C4×D71—21no—
74C22×C4×D71C2×C414yes—
75C22×C4×D71D411yescharacteristic
76C22×C4×D71D411yescharacteristic
77C22×C4×D71Q814yes—
78C22×C4×D71C2311yescharacteristic
79C22×C4×D71C2311yescharacteristic
80C22×C71⋊C8C2311yescharacteristic
81C22×C71⋊C8C2311yescharacteristic
82C2×C8×D71—22no—
83C2×C8×D71—22no—
84C2×C8×D71—22no—
85C2×C8×D71—22no—
86C2×C8×D71C2×C414yes—
87C2×C8×D71C2×C414yes—
88#14556087—22no—
89#14556087—22no—
90#14556086—22no—
91#14556086—22no—
92#14556086—22no—
93#14556086—22no—
94#14556085—28no—
95#14556084—28no—
96C2×C4⋊Dic71C2311yescharacteristic
97C2×C4⋊Dic71C2311yescharacteristic
98C2×C4⋊Dic71C2311yescharacteristic
99C2×C4⋊Dic71C2311yescharacteristic
100C2×Dic71⋊C4—21no—
101C2×Dic71⋊C4—21no—
102C2×Dic71⋊C4—21no—
103C2×Dic71⋊C4—21no—
104C4⋊C4×D71—22no—
105C4⋊C4×D71—22no—
106C4⋊C4×D71—22no—
107C4⋊C4×D71—22no—
108C4⋊C4×D71—22no—
109C4⋊C4×D71—22no—
110C4⋊C4×D71D414yes—
111C4⋊C4×D71D414yes—
112C2×C22⋊Dic71—21no—
113C2×C22⋊Dic71—21no—
114C2×(C2×D71)⋊C4—21no—
115C2×(C2×D71)⋊C4—21no—
116C2×(C2×D71)⋊C4—21no—
117C2×(C2×D71)⋊C4—21no—
118C22⋊C4×D71—28no—
119C22⋊C4×D71—44no—
120C2×C4×Dic71—21no—
121C2×C4×Dic71—21no—
122C2×C4×Dic71—21no—
123C42×D71—28no—
124#14556062—22no—
125#14556061—22no—
126#14556061—22no—
127#14556060—22no—
128#14556059—22no—
129#14556059—22no—
130C22⋊(C71⋊C8)C2×C414yescomplemented
131(C2×D71)⋊C8C2×C414yescomplemented
132(C2×D71)⋊C8C2×C414yescomplemented
133C71⋊#95—21no—
134C71⋊#95—21no—
135C71⋊#95—21no—
136C23×C4×C71C2311yescharacteristic
137C22×C8×C71C2311yescharacteristic
138C22×C8×C71C2311yescharacteristic
139#117×C71—22no—
140#117×C71—22no—
141C2×C4⋊C4×C71C2311yescharacteristic
142C2×C4⋊C4×C71C2311yescharacteristic
143C2×C4⋊C4×C71C2311yescharacteristic
144C2×C4⋊C4×C71C2311yescharacteristic
145C2×C22⋊C4×C71—21no—
146C2×C22⋊C4×C71—21no—
147C2×C42×C71—21no—
148#107×C71—22no—
149#106×C71—22no—
150C22⋊C8×C71C2×C414yescomplemented
151#95×C71—21no—
152C23×D71—22no—
153C23×D71—22no—
154C23×D71—22no—
155C23×D71—22no—
156C23×D71—22no—
157C23×D71—22no—
158C23×D71C4⋊C414yes—
159C23×D71C2×D411yescharacteristic
160C23×D71C2×D411yescharacteristic
161C22×Dic71—22no—
162C22×Dic71—22no—
163C22×Dic71—21no—
164C22×Dic71—21no—
165C22×Dic71—21no—
166C22×Dic71—21no—
167C22×Dic71C4⋊C414yes—
168C22×Dic71C2×D411yescharacteristic
169C22×Dic71C2×D411yescharacteristic
170C2×C4×D71—22no—
171C2×C4×D71—22no—
172C2×C4×D71—21no—
173C2×C4×D71—21no—
174C2×C4×D71—21no—
175C2×C4×D71—21no—
176C2×C4×D71—22no—
177C2×C4×D71—22no—
178C2×C4×D71—28no—
179C2×C4×D71—28no—
180C2×C4×D71—28no—
181C2×C4×D71—28no—
182C2×C4×D71—24no—
183C2×C4×D71—24no—
184C2×C4×D71—42no—
185C2×C4×D71—42no—
186C2×C4×D71—42no—
187C2×C4×D71—42no—
188C2×C4×D71—42no—
189C2×C4×D71—42no—
190C2×C4×D71—42no—
191C2×C4×D71—42no—
192C2×C4×D71—42no—
193C2×C4×D71—42no—
194C2×C4×D71C4⋊C414yes—
195C2×C4×D71C4⋊C414yes—
196C2×C4×D71C22×C412yes—
197C2×C4×D71C22×C412yes—
198C2×C4×D71C2×D412yes—
199C2×C4×D71C2×D412yes—
200C2×C4×D71C2×Q812yes—
201C2×C4×D71C2×Q812yes—
202C2×C4×D71#4112yes—
203C2×C4×D71#4112yes—
204C2×C71⋊C8—21no—
205C2×C71⋊C8—21no—
206C2×C71⋊C8—21no—
207C2×C71⋊C8—21no—
208C2×C71⋊C8C22×C412yes—
209C2×C71⋊C8C22×C412yes—
210C8×D71—28no—
211C8×D71—28no—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214C4⋊Dic71—21no—
215C4⋊Dic71—21no—
216C4⋊Dic71—21no—
217C4⋊Dic71—21no—
218C4⋊Dic71C2×D412yes—
219C4⋊Dic71C2×D412yes—
220Dic71⋊C4—24no—
221Dic71⋊C4—24no—
222Dic71⋊C4—42no—
223Dic71⋊C4—42no—
224C22⋊Dic71—24no—
225C22⋊Dic71—42no—
226(C2×D71)⋊C4—24no—
227(C2×D71)⋊C4—24no—
228(C2×D71)⋊C4—42no—
229(C2×D71)⋊C4—42no—
230C4×Dic71—24no—
231C4×Dic71—24no—
232C4×Dic71—24no—
233C24×C71C2×D411yescharacteristic
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71C22×C412yes—
243C22×C4×C71C2×D411yescharacteristic
244C22×C4×C71C2×Q812yes—
245C22×C4×C71C2411yescharacteristic
246C2×C8×C71—21no—
247C2×C8×C71—21no—
248C2×C8×C71—21no—
249C2×C8×C71—21no—
250C2×C8×C71C22×C412yes—
251C2×C8×C71C22×C412yes—
252C4⋊C4×C71—21no—
253C4⋊C4×C71—21no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71—21no—
256C4⋊C4×C71—21no—
257C4⋊C4×C71—21no—
258C4⋊C4×C71C2×D412yes—
259C4⋊C4×C71C2×D412yes—
260C22⋊C4×C71—24no—
261C22⋊C4×C71—42no—
262C42×C71—24no—
263C23×C71—21no—
264C23×C71—21no—
265C23×C71—21no—
266C23×C71—21no—
267C23×C71—21no—
268C23×C71—21no—
269C23×C71C2×C4⋊C412yes—
270C23×C71C22×D411yescharacteristic
271C22×D71—21no—
272C22×D71—21no—
273C22×D71—21no—
274C22×D71—21no—
275C22×D71—21no—
276C22×D71—21no—
277C22×D71—28no—
278C22×D71—28no—
279C22×D71—28no—
280C22×D71—44no—
281C22×D71—44no—
282C22×D71—44no—
283C22×D71—44no—
284C22×D71C2×C4⋊C412yes—
285C22×D71C2×C4⋊C412yes—
286C22×D71#12012yes—
287C22×D71#12312yes—
288C22×D71#13512yes—
289C22×D71#13512yes—
290C22×D71AGL(1,ℤ/8)12yes—
291C22×D71#13712yes—
292C2×C4×C71—21no—
293C2×C4×C71—21no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—41no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
303C2×C4×C71—41no—
304C2×C4×C71—41no—
305C2×C4×C71—41no—
306C2×C4×C71—41no—
307C2×C4×C71—41no—
308C2×C4×C71—41no—
309C2×C4×C71—41no—
310C2×C4×C71C2×C4⋊C412yes—
311C2×C4×C71C23×C411yescharacteristic
312C2×C4×C71C22×D411yescharacteristic
313C2×C4×C71C22×D411yescharacteristic
314C2×C4×C71C22×Q811yescharacteristic
315C2×C4×C71C2×#4111yescharacteristic
316C2×C4×C71C2×#4111yescharacteristic
317C2×Dic71—21no—
318C2×Dic71—21no—
319C2×Dic71—28no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—41no—
323C2×Dic71—41no—
324C2×Dic71—41no—
325C2×Dic71—41no—
326C2×Dic71—41no—
327C2×Dic71—41no—
328C2×Dic71—41no—
329C2×Dic71—41no—
330C2×Dic71—41no—
331C2×Dic71—41no—
332C2×Dic71C2×C4⋊C412yes—
333C2×Dic71C2×C4⋊C412yes—
334C2×Dic71#12012yes—
335C2×Dic71#12312yes—
336C4×D71—28no—
337C4×D71—22no—
338C4×D71—22no—
339C4×D71—22no—
340C4×D71—22no—
341C4×D71—28no—
342C4×D71—48no—
343C4×D71—48no—
344C4×D71—84no—
345C4×D71—84no—
346C4×D71C4×D414yes—
347C4×D71C4×D414yes—
348C4×D71C22⋊Q814yes—
349C4×D71C22⋊Q814yes—
350C8×C71—22no—
351C8×C71—22no—
352C71⋊C8—22no—
353C71⋊C8—22no—
354C22×C71—22no—
355C22×C71—22no—
356C22×C71—22no—
357C22×C71—41no—
358C22×C71—41no—
359C22×C71—41no—
360C22×C71—41no—
361C22×C71C22×C4⋊C411yescharacteristic
362C22×C71C2×#12011yescharacteristic
363C22×C71C2×#12311yescharacteristic
364C22×C71C2×#13511yescharacteristic
365C22×C71C2×#13511yescharacteristic
366C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
367C22×C71C2×#13711yescharacteristic
368C2×D71—22no—
369C2×D71—22no—
370C2×D71—22no—
371C2×D71—41no—
372C2×D71—41no—
373C2×D71—41no—
374C2×D71—41no—
375C2×D71—416no—
376C2×D71#38514yes—
377C2×D71#42714yes—
378C2×D71#42814yes—
379C2×D71#44914yes—
380C2×D71#45214yes—
381C2×D71#48214yes—
382C2×D71#48514yes—
383C4×C71—22no—
384C4×C71—42no—
385C4×C71—42no—
386C4×C71—81no—
387C4×C71—81no—
388C4×C71C2×C4×D411yescharacteristic
389C4×C71C2×C4×D411yescharacteristic
390C4×C71C2×C22⋊Q811yescharacteristic
391C4×C71C2×C22⋊Q811yescharacteristic
392Dic71—22no—
393Dic71—42no—
394Dic71—42no—
395Dic71—81no—
396Dic71—81no—
397Dic71#38514yes—
398C2×#1854—711nomaximal, Sylow
399C2×C71—42no—
400C2×C71C2×#38511yescharacteristic
401C2×C71C2×#42711yescharacteristic
402C2×C71C2×#42811yescharacteristic
403C2×C71C2×#44911yescharacteristic
404C2×C71C2×#45211yescharacteristic
405C2×C71C2×#48211yescharacteristic
406C2×C71C2×#48511yescharacteristic
407D71—42no—
408D71#185418yesdirect product factor
409C22×#117—711no—
410C22×#107—711no—
411C22×#106—711no—
412C22×C22⋊C8—711no—
413C2×#380—711no—
414#1854—711no—
415#1854—711no—
416#1854—711no—
417#1854—711no—
418#1854—711no—
419#1854—711no—
420#1854—711no—
421#1854D7111yescharacteristic, direct product factor
422C2×#340—711no—
423C2×#340—711no—
424C71C2×#185411yescharacteristic, complemented, Sylow
425C24×C4—711no—
426C23×C8—711no—
427C23×C8—711no—
428C2×#117—711no—
429C2×#117—711no—
430C2×#117—711no—
431C2×#117—1421no—
432C2×#117—1421no—
433C2×#117—1424no—
434C2×#117—1424no—
435C2×#117C2×D7111yescharacteristic
436C22×C4⋊C4—711no—
437C22×C4⋊C4—711no—
438C22×C4⋊C4—711no—
439C22×C4⋊C4—711no—
440C22×C22⋊C4—1421no—
441C22×C22⋊C4—1421no—
442C22×C42—1421no—
443C2×#107—711no—
444C2×#107—711no—
445C2×#107—711no—
446C2×#107—1424no—
447C2×#107C2×D7111yescharacteristic, complemented
448C2×#106—711no—
449C2×#106—711no—
450C2×#106—711no—
451C2×#106—1424no—
452C2×#106C2×D7111yescharacteristic, complemented
453C2×C22⋊C8—711no—
454C2×C22⋊C8—711no—
455C2×C22⋊C8—711no—
456C2×C22⋊C8—718no—
457C2×C22⋊C8C2×D7111yescharacteristic
458#380—711no—
459#380—711no—
460#380—711no—
461#380—1421no—
462#380—1421no—
463#380C2×D7111yescharacteristic
464C2×#95—1421no—
465#340—711no—
466#340—711no—
467#340—711no—
468#340—711no—
469#340—711no—
470#340—711no—
471#340C2×D7111yescharacteristic, complemented
472#340C2×D7111yescharacteristic, complemented
473C25—711no—
474C23×C4—711no—
475C23×C4—711no—
476C23×C4—714no—
477C23×C4—711no—
478C23×C4—711no—
479C23×C4—714no—
480C23×C4—711no—
481C23×C4—1421no—
482C23×C4—1421no—
483C23×C4—1421no—
484C23×C4—1421no—
485C23×C4—1422no—
486C23×C4—1422no—
487C23×C4—1422no—
488C23×C4—1422no—
489C23×C4C22×D7111yescharacteristic
490C22×C8—711no—
491C22×C8—711no—
492C22×C8—714no—
493C22×C8—714no—
494C22×C8—1422no—
495C22×C8—1422no—
496C22×C8—1422no—
497C22×C8—1422no—
498C22×C8C22×D7111yescharacteristic
499C22×C8C22×D7111yescharacteristic
500#117—22no—
501#117—22no—
502#117—1428no—
503#117—1428no—
504#117—1422no—
505#117—1422no—
506#117—1422no—
507#117—1422no—
508#117—1422no—
509#117—1422no—
510C2×C4⋊C4—711no—
511C2×C4⋊C4—711no—
512C2×C4⋊C4—714no—
513C2×C4⋊C4—714no—
514C2×C4⋊C4—711no—
515C2×C4⋊C4—711no—
516C2×C4⋊C4—1422no—
517C2×C4⋊C4—1422no—
518C2×C4⋊C4—1422no—
519C2×C4⋊C4—1422no—
520C2×C4⋊C4—1422no—
521C2×C4⋊C4—1422no—
522C2×C4⋊C4—1421no—
523C2×C4⋊C4—1421no—
524C2×C4⋊C4—1421no—
525C2×C4⋊C4—1421no—
526C2×C4⋊C4C22×D7111yescharacteristic
527C2×C4⋊C4C22×D7111yescharacteristic
528C2×C4⋊C4C22×D7111yescharacteristic
529C2×C4⋊C4C22×D7111yescharacteristic
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—2844no—
533C2×C22⋊C4—1428no—
534C2×C22⋊C4—1421no—
535C2×C22⋊C4—1421no—
536C2×C22⋊C4—1421no—
537C2×C22⋊C4—1421no—
538C2×C22⋊C4—1421no—
539C2×C22⋊C4—1421no—
540C2×C42—21no—
541C2×C42—1428no—
542C2×C42—1421no—
543C2×C42—1421no—
544C2×C42—1421no—
545#107—22no—
546#107—1422no—
547#107—1422no—
548#107—1422no—
549#106—22no—
550#106—1422no—
551#106—1422no—
552#106—1422no—
553C22⋊C8—714no—
554C22⋊C8—714no—
555C22⋊C8—714no—
556C22⋊C8C4×D7114yescomplemented
557#95—21no—
558#95—1421no—
559#95—1421no—
560#95—1421no—
561C24—711no—
562C24—711no—
563C24—714no—
564C24—1422no—
565C24—1422no—
566C24—1422no—
567C24—1422no—
568C24—1422no—
569C24—1422no—
570C24D4×D7111yescharacteristic
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—2842no—
580C22×C4—2842no—
581C22×C4—2842no—
582C22×C4—2842no—
583C22×C4—2842no—
584C22×C4—2842no—
585C22×C4—2842no—
586C22×C4—2842no—
587C22×C4—2842no—
588C22×C4—2842no—
589C22×C4—711no—
590C22×C4—712no—
591C22×C4—712no—
592C22×C4—712no—
593C22×C4—712no—
594C22×C4—712no—
595C22×C4—712no—
596C22×C4—711no—
597C22×C4—714no—
598C22×C4—712no—
599C22×C4—712no—
600C22×C4—714no—
601C22×C4—714no—
602C22×C4—1424no—
603C22×C4—1424no—
604C22×C4—1422no—
605C22×C4—1422no—
606C22×C4—1428no—
607C22×C4—1428no—
608C22×C4—1428no—
609C22×C4—1428no—
610C22×C4—1422no—
611C22×C4—1422no—
612C22×C4—1421no—
613C22×C4—1421no—
614C22×C4—1421no—
615C22×C4—1421no—
616C22×C4—1422no—
617C22×C4—1422no—
618C22×C4—1421no—
619C22×C4—1421no—
620C22×C4—1421no—
621C22×C4—1421no—
622C22×C4C2×C4×D7112yes—
623C22×C4D4×D7111yescharacteristic
624C22×C4Q8×D7112yes—
625C22×C4C23×D7111yescharacteristic
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—712no—
631C2×C8—712no—
632C2×C8—1428no—
633C2×C8—1428no—
634C2×C8—1421no—
635C2×C8—1421no—
636C2×C8—1421no—
637C2×C8—1421no—
638C2×C8C2×C4×D7112yes—
639C2×C8C2×C4×D7112yes—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—2842no—
647C4⋊C4—2842no—
648C4⋊C4—712no—
649C4⋊C4—712no—
650C4⋊C4—1424no—
651C4⋊C4—1424no—
652C4⋊C4—1421no—
653C4⋊C4—1421no—
654C4⋊C4—1421no—
655C4⋊C4—1421no—
656C4⋊C4—1421no—
657C4⋊C4—1421no—
658C4⋊C4D4×D7112yes—
659C4⋊C4D4×D7112yes—
660C22⋊C4—24no—
661C22⋊C4—42no—
662C22⋊C4—2842no—
663C22⋊C4—2842no—
664C22⋊C4—2842no—
665C22⋊C4—1424no—
666C22⋊C4—1424no—
667C22⋊C4—1424no—
668C42—24no—
669C42—1424no—
670C42—1424no—
671C42—1424no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—2844no—
679C23—2844no—
680C23—2844no—
681C23—2844no—
682C23—712no—
683C23—712no—
684C23—712no—
685C23—712no—
686C23—712no—
687C23—712no—
688C23—712no—
689C23—712no—
690C23—1428no—
691C23—1428no—
692C23—1428no—
693C23—1421no—
694C23—1421no—
695C23—1421no—
696C23—1421no—
697C23—1421no—
698C23—1421no—
699C23C4⋊C4×D7112yes—
700C23C2×D4×D7111yescharacteristic
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—2848no—
720C2×C4—2848no—
721C2×C4—2841no—
722C2×C4—2841no—
723C2×C4—2841no—
724C2×C4—2841no—
725C2×C4—2841no—
726C2×C4—2841no—
727C2×C4—2841no—
728C2×C4—2841no—
729C2×C4—2841no—
730C2×C4—2841no—
731C2×C4—5684no—
732C2×C4—5684no—
733C2×C4—712no—
734C2×C4—712no—
735C2×C4—712no—
736C2×C4—714no—
737C2×C4—714no—
738C2×C4—714no—
739C2×C4—714no—
740C2×C4—712no—
741C2×C4—1428no—
742C2×C4—1428no—
743C2×C4—1422no—
744C2×C4—1422no—
745C2×C4—1428no—
746C2×C4—1421no—
747C2×C4—1421no—
748C2×C4—1422no—
749C2×C4—1422no—
750C2×C4—1422no—
751C2×C4—1422no—
752C2×C4C4⋊C4×D7112yes—
753C2×C4C22×C4×D7111yescharacteristic
754C2×C4C2×D4×D7111yescharacteristic
755C2×C4C2×D4×D7111yescharacteristic
756C2×C4C2×Q8×D7111yescharacteristic
757C2×C4#41×D7111yescharacteristic
758C2×C4#41×D7111yescharacteristic
759C8—22no—
760C8—22no—
761C8—1422no—
762C8—1422no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—28416no—
771C22—2841no—
772C22—2841no—
773C22—2841no—
774C22—2841no—
775C22—714no—
776C22—714no—
777C22—714no—
778C22—714no—
779C22—714no—
780C22—714no—
781C22—714no—
782C22—1422no—
783C22—1422no—
784C22—1422no—
785C22C2×C4⋊C4×D7111yescharacteristic
786C22#120×D7111yescharacteristic
787C22#123×D7111yescharacteristic
788C22#135×D7111yescharacteristic
789C22#135×D7111yescharacteristic
790C22AGL(1,ℤ/8)×D7111yescharacteristic
791C22#137×D7111yescharacteristic
792C4—22no—
793C4—42no—
794C4—42no—
795C4—81no—
796C4—81no—
797C4—2842no—
798C4—2842no—
799C4—5681no—
800C4—5681no—
801C4—714no—
802C4—1422no—
803C4C4×D4×D7111yescharacteristic
804C4C4×D4×D7111yescharacteristic
805C4C22⋊Q8×D7111yescharacteristic
806C4C22⋊Q8×D7111yescharacteristic
807C2—42no—
808C2—2842no—
809C2—718no—
810C2#385×D7111yescharacteristic
811C2#427×D7111yescharacteristic
812C2#428×D7111yescharacteristic
813C2#449×D7111yescharacteristic
814C2#452×D7111yescharacteristic
815C2#482×D7111yescharacteristic
816C2#485×D7111yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutatorC2×C4×C71C23×C4
FrattiniC22×C4C23×D71
FittingC71×#1854C2
socleC23×C71C22×D4
prime radicalC24×D71D4
cosocleC22×C4×C71C24
hypercenter#1854D71
hypocenterC71C2×#1854
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#107×D71C2semidirect
3. C2×#106×D71C2semidirect
6. #22588542C2semidirect
7. #22588541C2semidirect
8. #22588540C2semidirect
9. #22588539C2semidirect
10. #22588538C2semidirect
11. #22588537C2semidirect
12. #22588536C2semidirect
13. #340×D71C2semidirect
14. #340×D71C2semidirect
15. C71×#1854C2semidirect
33. C2×#14556062C22semidirect
34. C2×#14556061C22semidirect
35. C2×#14556061C22semidirect
37. C2×#14556060C22semidirect
38. C2×#14556059C22semidirect
39. C2×#14556059C22semidirect
44. C22⋊C8×D71C4semidirect
51. #17985762C22semidirect
52. #17985762C22semidirect
53. #17985761C22semidirect
54. #17985761C22semidirect
55. #17985761C22semidirect
56. #17985761C22semidirect
58. C2×#107×C71C22semidirect
59. C2×#106×C71C22semidirect
62. #340×C71C22semidirect
63. #340×C71C22semidirect
130. C22⋊(C71⋊C8)C2×C4semidirect
131. (C2×D71)⋊C8C2×C4semidirect
132. (C2×D71)⋊C8C2×C4semidirect
150. C22⋊C8×C71C2×C4semidirect
408. D71#1854direct (N × H)
421. #1854D71direct (N × H)
424. C71C2×#1854semidirect
447. C2×#107C2×D71semidirect
452. C2×#106C2×D71semidirect
471. #340C2×D71semidirect
472. #340C2×D71semidirect
556. C22⋊C8C4×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#117×D712
C2×#107×D712
C2×#106×D712
C2×C22⋊C8×D712
#380×D712
#225885422
#225885412
#225885402
#225885392
#225885382
#225885372
#225885362
#340×D712
C71×#18542
C2×#185471