Finite Group Databasebeta

← #31928697

Subgroups — #31928697

Order 18176.

2574 conjugacy classes of subgroups.

The subgroup lattice has 878 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C42×D71C211yesmaximal, characteristic
2C2×#17985898C211yesmaximal, characteristic, complemented
3C2×#17985897C211yesmaximal, characteristic, complemented
4C2×#17985873C212yesmaximal
5C2×#17985856C211yesmaximal, characteristic
6C2×#17985856C211yesmaximal, characteristic
7#22586575C212yesmaximal, complemented
8#22586574C212yesmaximal, complemented
9#22586569C211yesmaximal, characteristic, complemented
10(C2×D71)⋊#95C212yesmaximal
11C71×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×C4×D71C2211yescharacteristic
13C23×C4×D71C2211yescharacteristic
14C23×C4×D71C2211yescharacteristic
15C22×C4⋊Dic71C2212yes—
16C22×C4⋊Dic71C2211yescharacteristic
17C22×C4⋊Dic71C2211yescharacteristic
18C22×Dic71⋊C4C2212yes—
19C22×(C2×D71)⋊C4C2212yes—
20C22×(C2×D71)⋊C4C2212yes—
21C22×C4×Dic71C2211yescharacteristic
22C22×C4×Dic71C2211yescharacteristic
23C22×C4×Dic71C2211yescharacteristic
24C2×C42×D71—24no—
25C2×C42×D71—24no—
26C2×C42×D71—24no—
27#17985898—24no—
28#17985897—24no—
29#17985873—28no—
30#17985856—24no—
31#17985856C418yescomplemented
32C2×C71⋊#95C2212yes—
33C2×C71⋊#95C2212yes—
34C2×C71⋊#95C2212yes—
35C2×C71⋊#95C2212yes—
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×Dic71C2312yes—
46C23×Dic71C2311yescharacteristic
47C23×Dic71C2311yescharacteristic
48C23×Dic71C2311yescharacteristic
49C22×C4×D71—22no—
50C22×C4×D71—22no—
51C22×C4×D71—22no—
52C22×C4×D71—22no—
53C22×C4×D71—22no—
54C22×C4×D71—22no—
55C22×C4×D71—22no—
56C22×C4×D71—22no—
57C22×C4×D71—22no—
58C22×C4×D71—22no—
59C22×C4×D71—22no—
60C22×C4×D71—22no—
61C22×C4×D71—22no—
62C22×C4×D71—22no—
63C22×C4×D71—22no—
64C22×C4×D71—22no—
65C22×C4×D71C2×C414yes—
66C22×C4×D71D414yes—
67C22×C4×D71D414yes—
68C22×C4×D71Q814yes—
69C22×C4×D71Q814yes—
70C2×C4⋊Dic71—24no—
71C2×C4⋊Dic71—24no—
72C2×C4⋊Dic71—24no—
73C2×C4⋊Dic71—22no—
74C2×C4⋊Dic71—22no—
75C2×C4⋊Dic71—22no—
76C2×C4⋊Dic71—22no—
77C2×C4⋊Dic71—22no—
78C2×C4⋊Dic71C2×C414yescomplemented
79C2×Dic71⋊C4—24no—
80C2×Dic71⋊C4—24no—
81C2×Dic71⋊C4—24no—
82C2×(C2×D71)⋊C4—24no—
83C2×(C2×D71)⋊C4—24no—
84C2×(C2×D71)⋊C4—24no—
85C2×(C2×D71)⋊C4—24no—
86C2×(C2×D71)⋊C4—24no—
87C2×(C2×D71)⋊C4C2×C418yes—
88C2×C4×Dic71—22no—
89C2×C4×Dic71—22no—
90C2×C4×Dic71—22no—
91C2×C4×Dic71—22no—
92C2×C4×Dic71—22no—
93C2×C4×Dic71—22no—
94C2×C4×Dic71—22no—
95C2×C4×Dic71—22no—
96C2×C4×Dic71D414yes—
97C42×D71—232no—
98C71⋊#95—24no—
99C71⋊#95—24no—
100C71⋊#95—24no—
101C71⋊#95—24no—
102C71⋊#95—24no—
103C71⋊#95C2×C418yescomplemented
104C23×C4×C71C2312yes—
105C23×C4×C71C2312yes—
106C23×C4×C71C2311yescharacteristic
107C23×C4×C71C2311yescharacteristic
108C23×C4×C71C2311yescharacteristic
109C2×C4⋊C4×C71—22no—
110C2×C4⋊C4×C71—22no—
111C2×C4⋊C4×C71—22no—
112C2×C4⋊C4×C71—22no—
113C2×C4⋊C4×C71—22no—
114C2×C4⋊C4×C71C2×C414yescomplemented
115C2×C42×C71—22no—
116C2×C42×C71—22no—
117C2×C42×C71D414yes—
118#95×C71—24no—
119#95×C71—24no—
120C23×D71—21no—
121C23×D71—21no—
122C23×D71—21no—
123C23×D71—21no—
124C23×D71—21no—
125C23×D71—21no—
126C23×D71—21no—
127C23×D71—21no—
128C23×D71C22×C412yes—
129C23×D71C2×D412yes—
130C23×D71C2×D412yes—
131C23×D71C2×Q812yes—
132C23×D71C2×Q812yes—
133C23×D71#4112yes—
134C23×D71#4112yes—
135C22×Dic71—21no—
136C22×Dic71—21no—
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—22no—
148C22×Dic71—22no—
149C22×Dic71—22no—
150C22×Dic71—22no—
151C22×Dic71—22no—
152C22×Dic71—22no—
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71—22no—
159C22×Dic71—22no—
160C22×Dic71C22×C414yes—
161C22×Dic71C22×C412yes—
162C22×Dic71C2×D412yes—
163C22×Dic71C2×D412yes—
164C22×Dic71C2×D412yes—
165C22×Dic71C2×D412yes—
166C22×Dic71C2×Q812yes—
167C22×Dic71C2×Q812yes—
168C22×Dic71#4112yes—
169C22×Dic71#4112yes—
170C2×C4×D71—28no—
171C2×C4×D71—28no—
172C2×C4×D71—28no—
173C2×C4×D71—28no—
174C2×C4×D71—28no—
175C2×C4×D71—28no—
176C2×C4×D71—28no—
177C2×C4×D71—28no—
178C2×C4×D71—28no—
179C2×C4×D71—28no—
180C2×C4×D71—28no—
181C2×C4×D71—28no—
182C2×C4×D71—28no—
183C2×C4×D71—28no—
184C2×C4×D71—28no—
185C2×C4×D71—28no—
186C2×C4×D71—28no—
187C2×C4×D71—28no—
188C2×C4×D71—28no—
189C2×C4×D71—28no—
190C2×C4×D71C4⋊C4116yescomplemented
191C4⋊Dic71—28no—
192C4⋊Dic71—44no—
193C4⋊Dic71—48no—
194Dic71⋊C4—48no—
195(C2×D71)⋊C4—216no—
196(C2×D71)⋊C4—48no—
197C4×Dic71—28no—
198C4×Dic71—28no—
199C4×Dic71—28no—
200C24×C71C2411yescharacteristic
201C22×C4×C71—21no—
202C22×C4×C71—21no—
203C22×C4×C71—21no—
204C22×C4×C71—21no—
205C22×C4×C71—21no—
206C22×C4×C71—21no—
207C22×C4×C71—21no—
208C22×C4×C71—21no—
209C22×C4×C71—22no—
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—22no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—22no—
220C22×C4×C71—22no—
221C22×C4×C71—22no—
222C22×C4×C71C22×C414yes—
223C22×C4×C71C22×C412yes—
224C22×C4×C71C2×D412yes—
225C22×C4×C71C2×D412yes—
226C22×C4×C71C2×D412yes—
227C22×C4×C71C2×D412yes—
228C22×C4×C71C2×D412yes—
229C22×C4×C71C2×D412yes—
230C22×C4×C71C2×Q812yes—
231C22×C4×C71C2×Q812yes—
232C22×C4×C71#4112yes—
233C22×C4×C71#4112yes—
234C22×C4×C71#4112yes—
235C22×C4×C71#4112yes—
236C4⋊C4×C71—28no—
237C4⋊C4×C71—44no—
238C42×C71—28no—
239C23×C71C23×C411yescharacteristic
240C23×C71C22×D411yescharacteristic
241C23×C71C22×D411yescharacteristic
242C23×C71C22×D411yescharacteristic
243C23×C71C22×D411yescharacteristic
244C23×C71C22×Q811yescharacteristic
245C23×C71C22×Q811yescharacteristic
246C23×C71C2×#4111yescharacteristic
247C23×C71C2×#4111yescharacteristic
248C23×C71C2×#4111yescharacteristic
249C23×C71C2×#4111yescharacteristic
250C23×C71C2×#4111yescharacteristic
251C23×C71C2×#4111yescharacteristic
252C23×C71C2×#4111yescharacteristic
253C23×C71C2×#4111yescharacteristic
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×D71—22no—
270C22×D71—22no—
271C22×D71—22no—
272C22×D71—22no—
273C22×D71—22no—
274C22×D71—22no—
275C22×D71—22no—
276C22×D71—22no—
277C22×D71—22no—
278C22×D71—22no—
279C22×D71—22no—
280C22×D71—22no—
281C22×D71—22no—
282C22×D71C2×C4⋊C414yes—
283C22×D71C4×D414yes—
284C22×D71C4×Q814yes—
285C22×D71#12114yes—
286C22×D71C22⋊Q814yes—
287C22×D71#12514yes—
288C22×D71C4⋊Q814yes—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
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—22no—
301C2×C4×C71—24no—
302C2×C4×C71—24no—
303C2×C4×C71—24no—
304C2×C4×C71—42no—
305C2×C4×C71—42no—
306C2×C4×C71—42no—
307C2×C4×C71—42no—
308C2×C4×C71—42no—
309C2×C4×C71—42no—
310C2×C4×C71—42no—
311C2×C4×C71—42no—
312C2×C4×C71—42no—
313C2×C4×C71—42no—
314C2×C4×C71—42no—
315C2×C4×C71C2×C4⋊C414yes—
316C2×C4×C71C4×D414yes—
317C2×C4×C71C4×D414yes—
318C2×C4×C71#12014yes—
319C2×C4×C71#12114yes—
320C2×C4×C71C22⋊Q814yes—
321C2×C4×C71C22⋊Q814yes—
322C2×C4×C71C22⋊Q814yes—
323C2×C4×C71#12314yes—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—22no—
329C2×Dic71—22no—
330C2×Dic71—22no—
331C2×Dic71—22no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—24no—
343C2×Dic71—24no—
344C2×Dic71—24no—
345C2×Dic71—42no—
346C2×Dic71—42no—
347C2×Dic71—42no—
348C2×Dic71—42no—
349C2×Dic71—42no—
350C2×Dic71—42no—
351C2×Dic71—42no—
352C2×Dic71—42no—
353C2×Dic71—42no—
354C2×Dic71—42no—
355C2×Dic71—42no—
356C2×Dic71C2×C4⋊C414yes—
357C2×Dic71#12114yes—
358C2×Dic71C22⋊Q814yes—
359C4×D71—232no—
360C4×D71—232no—
361C4×D71—232no—
362C22×C71C22×C4⋊C411yescharacteristic
363C22×C71C2×C4×D411yescharacteristic
364C22×C71C2×C4×D411yescharacteristic
365C22×C71C2×C4×D411yescharacteristic
366C22×C71C2×C4×Q811yescharacteristic
367C22×C71C4×#4111yescharacteristic
368C22×C71C4×#4111yescharacteristic
369C22×C71C2×#12011yescharacteristic
370C22×C71C2×#12111yescharacteristic
371C22×C71C2×#12111yescharacteristic
372C22×C71C2×#12111yescharacteristic
373C22×C71C2×C22⋊Q811yescharacteristic
374C22×C71C2×C22⋊Q811yescharacteristic
375C22×C71C2×C22⋊Q811yescharacteristic
376C22×C71C2×C22⋊Q811yescharacteristic
377C22×C71C2×C22⋊Q811yescharacteristic
378C22×C71C2×#12311yescharacteristic
379C22×C71#52511yescharacteristic
380C22×C71#52511yescharacteristic
381C22×C71#52511yescharacteristic
382C22×C71#52511yescharacteristic
383C22×C71#52511yescharacteristic
384C22×C71#52511yescharacteristic
385C22×C71C2×#12511yescharacteristic
386C22×C71#52911yescharacteristic
387C22×C71#52911yescharacteristic
388C22×C71#52911yescharacteristic
389C22×C71#52911yescharacteristic
390C22×C71C2×C4⋊Q811yescharacteristic
391C22×C71#53211yescharacteristic
392C22×C71#53211yescharacteristic
393C22×C71#53311yescharacteristic
394C22×C71#53311yescharacteristic
395C22×C71#53311yescharacteristic
396C22×C71#53311yescharacteristic
397C2×D71—24no—
398C2×D71—24no—
399C2×D71—24no—
400C2×D71—24no—
401C2×D71—24no—
402C2×D71—24no—
403C2×D71—24no—
404C2×D71—24no—
405C2×D71—24no—
406C2×D71—24no—
407C2×D71—24no—
408C2×D71—24no—
409C2×D71—24no—
410C2×D71—24no—
411C2×D71#38918yescomplemented
412C4×C71—24no—
413C4×C71—24no—
414C4×C71—44no—
415C4×C71—82no—
416C4×C71#38518yescomplemented
417Dic71—24no—
418Dic71—24no—
419Dic71—24no—
420Dic71—44no—
421Dic71—82no—
422#14697—711nomaximal, Sylow
423C2×C71C2×#38511yescharacteristic
424C2×C71C2×#38911yescharacteristic
425C2×C71#229611yescharacteristic
426C2×C71C4×#12111yescharacteristic
427C2×C71C4×#12111yescharacteristic
428C2×C71C4×C22⋊Q811yescharacteristic
429C2×C71C4×C22⋊Q811yescharacteristic
430C2×C71#284711yescharacteristic
431C2×C71#284811yescharacteristic
432C2×C71#285111yescharacteristic
433C2×C71#285111yescharacteristic
434C2×C71#285411yescharacteristic
435C2×C71#285511yescharacteristic
436C2×C71#285711yescharacteristic
437C2×C71#285711yescharacteristic
438D71—28no—
439C23×C42—711no—
440C2×#389—711no—
441C2×#389—711no—
442C2×#385—712no—
443C2×#380—711no—
444C2×#380—711no—
445#1436—712no—
446#1436—712no—
447C4⋊#95—711no—
448C4⋊#95D7111yescharacteristic, complemented
449C22⋊#95—712no—
450C71#1469711yescharacteristic, complemented, Sylow
451C24×C4—711no—
452C24×C4—711no—
453C24×C4—711no—
454C22×C4⋊C4—711no—
455C22×C4⋊C4—712no—
456C22×C4⋊C4—712no—
457C22×C4⋊C4—711no—
458C22×C4⋊C4C2×D7111yescharacteristic
459C22×C4⋊C4C2×D7111yescharacteristic
460C22×C22⋊C4—712no—
461C22×C22⋊C4—712no—
462C22×C42—711no—
463C22×C42—711no—
464C22×C42—711no—
465C22×C42—1424no—
466C22×C42—1424no—
467C22×C42—1424no—
468C22×C42C2×D7111yescharacteristic
469#389—1424no—
470#389—1424no—
471#385—1428no—
472#380—718no—
473#380—1424no—
474C2×#95—712no—
475C2×#95—712no—
476C2×#95—712no—
477C2×#95—712no—
478C2×#95—712no—
479C2×#95—712no—
480C2×#95C2×D7112yes—
481C2×#95C2×D7112yes—
482C25—711no—
483C23×C4—711no—
484C23×C4—711no—
485C23×C4—711no—
486C23×C4—714no—
487C23×C4—714no—
488C23×C4—714no—
489C23×C4—712no—
490C23×C4—714no—
491C23×C4—714no—
492C23×C4—712no—
493C23×C4—1422no—
494C23×C4—1422no—
495C23×C4—1422no—
496C23×C4—1422no—
497C23×C4—1422no—
498C23×C4—1422no—
499C23×C4—1422no—
500C23×C4—1422no—
501C23×C4—1422no—
502C23×C4—1422no—
503C23×C4—1422no—
504C23×C4—1422no—
505C23×C4—1422no—
506C23×C4—1422no—
507C23×C4—1422no—
508C23×C4—1422no—
509C23×C4C22×D7112yes—
510C23×C4C22×D7112yes—
511C23×C4C22×D7111yescharacteristic
512C23×C4C22×D7111yescharacteristic
513C23×C4C22×D7111yescharacteristic
514C2×C4⋊C4—22no—
515C2×C4⋊C4—22no—
516C2×C4⋊C4—22no—
517C2×C4⋊C4—22no—
518C2×C4⋊C4—22no—
519C2×C4⋊C4—714no—
520C2×C4⋊C4—1424no—
521C2×C4⋊C4—1424no—
522C2×C4⋊C4—1424no—
523C2×C4⋊C4—1422no—
524C2×C4⋊C4—1424no—
525C2×C4⋊C4—1422no—
526C2×C4⋊C4—1424no—
527C2×C4⋊C4—1422no—
528C2×C4⋊C4—1424no—
529C2×C4⋊C4—1422no—
530C2×C4⋊C4—1422no—
531C2×C4⋊C4C4×D7114yescomplemented
532C2×C22⋊C4—718no—
533C2×C22⋊C4—1424no—
534C2×C22⋊C4—1424no—
535C2×C22⋊C4—1424no—
536C2×C22⋊C4—1424no—
537C2×C22⋊C4—1424no—
538C2×C42—22no—
539C2×C42—22no—
540C2×C42—714no—
541C2×C42—14232no—
542C2×C42—1422no—
543C2×C42—1422no—
544C2×C42—1422no—
545C2×C42—1422no—
546C2×C42—1422no—
547C2×C42—1422no—
548C2×C42—1422no—
549C2×C42—1422no—
550C2×C42D28414yes—
551#95—24no—
552#95—24no—
553#95—718no—
554#95—1424no—
555#95—1424no—
556#95—1424no—
557#95—1424no—
558#95—1424no—
559C24—712no—
560C24—712no—
561C24—712no—
562C24—712no—
563C24—712no—
564C24—712no—
565C24—712no—
566C24—1421no—
567C24—1421no—
568C24—1421no—
569C24—1421no—
570C24—1421no—
571C24—1421no—
572C24—1421no—
573C24—1421no—
574C24C23×D7111yescharacteristic
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—712no—
597C22×C4—712no—
598C22×C4—712no—
599C22×C4—712no—
600C22×C4—712no—
601C22×C4—712no—
602C22×C4—712no—
603C22×C4—712no—
604C22×C4—712no—
605C22×C4—7116no—
606C22×C4—714no—
607C22×C4—1428no—
608C22×C4—1428no—
609C22×C4—1428no—
610C22×C4—1428no—
611C22×C4—1428no—
612C22×C4—1428no—
613C22×C4—1428no—
614C22×C4—1428no—
615C22×C4—1428no—
616C22×C4—1428no—
617C22×C4—1428no—
618C22×C4—1428no—
619C22×C4—1422no—
620C22×C4—1422no—
621C22×C4—1422no—
622C22×C4—1422no—
623C22×C4—1422no—
624C22×C4—1422no—
625C22×C4—1422no—
626C22×C4—1422no—
627C22×C4—1422no—
628C22×C4—1422no—
629C22×C4—1422no—
630C22×C4—1422no—
631C22×C4—1422no—
632C22×C4—1421no—
633C22×C4—1421no—
634C22×C4—1421no—
635C22×C4—1421no—
636C22×C4—1421no—
637C22×C4—1421no—
638C22×C4—1421no—
639C22×C4—1421no—
640C22×C4—1421no—
641C22×C4—1421no—
642C22×C4—1421no—
643C22×C4—1421no—
644C22×C4—1428no—
645C22×C4—1428no—
646C22×C4—1428no—
647C22×C4—1428no—
648C22×C4—1428no—
649C22×C4—1428no—
650C22×C4—1428no—
651C22×C4—1428no—
652C22×C4C2×C4×D7114yes—
653C22×C4C2×C4×D7112yes—
654C22×C4D4×D7112yes—
655C22×C4D4×D7112yes—
656C22×C4D4×D7112yes—
657C22×C4C2×D28412yes—
658C22×C4C2×D28412yes—
659C22×C4C2×D28412yes—
660C22×C4Q8×D7112yes—
661C22×C4Q8×D7112yes—
662C22×C4#1176586412yes—
663C22×C4#1176586412yes—
664C22×C4#1176586512yes—
665C22×C4#1176586612yes—
666C4⋊C4—28no—
667C4⋊C4—44no—
668C4⋊C4—2848no—
669C4⋊C4—2844no—
670C4⋊C4—2848no—
671C4⋊C4—1428no—
672C22⋊C4—2848no—
673C22⋊C4—14216no—
674C42—28no—
675C42—1428no—
676C42—1428no—
677C42—1428no—
678C23—714no—
679C23—714no—
680C23—714no—
681C23—714no—
682C23—714no—
683C23—714no—
684C23—714no—
685C23—1422no—
686C23—1422no—
687C23—1422no—
688C23—1422no—
689C23—1422no—
690C23—1422no—
691C23—1422no—
692C23—1422no—
693C23—1422no—
694C23—1422no—
695C23—1422no—
696C23—1422no—
697C23—1422no—
698C23—1422no—
699C23—1422no—
700C23—1422no—
701C23—1422no—
702C23—1422no—
703C23—1422no—
704C23—1422no—
705C23—1422no—
706C23—1422no—
707C23—1422no—
708C23—1422no—
709C23—1422no—
710C23—1422no—
711C23—1422no—
712C23—1422no—
713C23C22×C4×D7111yescharacteristic
714C23C2×D4×D7111yescharacteristic
715C23C2×D4×D7111yescharacteristic
716C23C2×D4×D7111yescharacteristic
717C23C22×D28411yescharacteristic
718C23C2×Q8×D7111yescharacteristic
719C23C2×Q8×D7111yescharacteristic
720C23#41×D7111yescharacteristic
721C23#41×D7111yescharacteristic
722C23#41×D7111yescharacteristic
723C23#41×D7111yescharacteristic
724C23C2×#1176586411yescharacteristic
725C23C2×#1176586411yescharacteristic
726C23C2×#1176586511yescharacteristic
727C23C2×#1176586611yescharacteristic
728C2×C4—22no—
729C2×C4—22no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—22no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—24no—
741C2×C4—24no—
742C2×C4—24no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—42no—
748C2×C4—42no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—42no—
752C2×C4—42no—
753C2×C4—42no—
754C2×C4—2842no—
755C2×C4—2842no—
756C2×C4—2842no—
757C2×C4—2842no—
758C2×C4—2842no—
759C2×C4—2842no—
760C2×C4—2842no—
761C2×C4—2842no—
762C2×C4—2842no—
763C2×C4—2842no—
764C2×C4—2842no—
765C2×C4—714no—
766C2×C4—714no—
767C2×C4—714no—
768C2×C4—14232no—
769C2×C4—14232no—
770C2×C4—1424no—
771C2×C4—1424no—
772C2×C4—1424no—
773C2×C4—1422no—
774C2×C4—1422no—
775C2×C4—1422no—
776C2×C4—1422no—
777C2×C4—1422no—
778C2×C4—1422no—
779C2×C4—1422no—
780C2×C4—1422no—
781C2×C4—1422no—
782C2×C4—1422no—
783C2×C4—1422no—
784C2×C4—1422no—
785C2×C4—1422no—
786C2×C4—1422no—
787C2×C4—1422no—
788C2×C4—1422no—
789C2×C4—1422no—
790C2×C4—1422no—
791C2×C4—14232no—
792C2×C4C4⋊C4×D7114yes—
793C2×C4(C22⋊D71)⋊C414yes—
794C2×C4C4×D28414yes—
795C2×C4#1455609814yes—
796C2×C4#1455610314yes—
797C2×C4#1455610614yes—
798C2×C4#1455610814yes—
799C2×C4#1455610814yes—
800C2×C4#1455611014yes—
801C22—718no—
802C22—1424no—
803C22—1424no—
804C22—1424no—
805C22—1424no—
806C22—1424no—
807C22—1424no—
808C22—1424no—
809C22—1424no—
810C22—1424no—
811C22—1424no—
812C22—1424no—
813C22—1424no—
814C22—1424no—
815C22—1424no—
816C22C2×C4⋊C4×D7111yescharacteristic
817C22C4×D4×D7111yescharacteristic
818C22C2×(C22⋊D71)⋊C411yescharacteristic
819C22C2×C4×D28411yescharacteristic
820C22C4×Q8×D7111yescharacteristic
821C22C4×#1176586411yescharacteristic
822C22C4×#1176586611yescharacteristic
823C22C2×#1455609811yescharacteristic
824C22#121×D7111yescharacteristic
825C22#121×D7111yescharacteristic
826C22C2×#1455610311yescharacteristic
827C22C22⋊Q8×D7111yescharacteristic
828C22C22⋊Q8×D7111yescharacteristic
829C22C2×#1455610611yescharacteristic
830C22C2×#1455610811yescharacteristic
831C22C2×#1455610811yescharacteristic
832C22C2×#1455611011yescharacteristic
833C22#1798650911yescharacteristic
834C22#1798650911yescharacteristic
835C22#1798651111yescharacteristic
836C22#1798651111yescharacteristic
837C22#1798651211yescharacteristic
838C22#1798651211yescharacteristic
839C22#125×D7111yescharacteristic
840C22#1798652811yescharacteristic
841C22#1798652811yescharacteristic
842C22#1798653111yescharacteristic
843C22#1798653611yescharacteristic
844C22C4⋊Q8×D7111yescharacteristic
845C22#1798654611yescharacteristic
846C22#1798654711yescharacteristic
847C22#1798655311yescharacteristic
848C22#1798655411yescharacteristic
849C22#1798655411yescharacteristic
850C22#1798655511yescharacteristic
851C4—24no—
852C4—24no—
853C4—44no—
854C4—82no—
855C4—2844no—
856C4—5682no—
857C4—1424no—
858C4—1424no—
859C4—1424no—
860C4#1798587318yescomplemented
861C2—1428no—
862C2C2×#1798587311yescharacteristic
863C2#389×D7111yescharacteristic
864C2#2259082111yescharacteristic
865C2C4×#1455610311yescharacteristic
866C2#2259085611yescharacteristic
867C2C4×#1455610811yescharacteristic
868C2#2259087811yescharacteristic
869C2#2259662311yescharacteristic
870C2#2259662811yescharacteristic
871C2#2259664911yescharacteristic
872C2#2259665111yescharacteristic
873C2#2259667011yescharacteristic
874C2#2259668111yescharacteristic
875C2#2259669111yescharacteristic
876C2#2259669311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D71
commutatorC23×C71C23×C4
FittingC71×C4⋊#95C2
socle, cosocleC24×C71C24
prime radicalC24×D71C23
hypercenterC4⋊#95D71
hypocenterC71#14697
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C2×#17985898C2semidirect
3. C2×#17985897C2semidirect
7. #22586575C2semidirect
8. #22586574C2semidirect
9. #22586569C2semidirect
11. C71×C4⋊#95C2semidirect
31. #17985856C4semidirect
78. C2×C4⋊Dic71C2×C4semidirect
103. C71⋊#95C2×C4semidirect
114. C2×C4⋊C4×C71C2×C4semidirect
190. C2×C4×D71C4⋊C4semidirect
411. C2×D71#389semidirect
416. C4×C71#385semidirect
448. C4⋊#95D71semidirect
450. C71#14697semidirect
531. C2×C4⋊C4C4×D71semidirect
860. C4#17985873semidirect

Maximal subgroups

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

subgroupindex
C22×C42×D712
C2×#179858982
C2×#179858972
C2×#179858732
C2×#179858562
#225865752
#225865742
#225865692
(C2×D71)⋊#952
C71×C4⋊#952
#1469771