Finite Group Databasebeta

← C71×#14004 #31834876

Subgroups — C71×#14004 #31834876

Order 18176.

2106 conjugacy classes of subgroups.

The subgroup lattice has 1070 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#389×C71C211yesmaximal, characteristic, complemented
2C2×#385×C71C211yesmaximal, characteristic
3C2×#385×C71C211yesmaximal, characteristic
4C2×#385×C71C211yesmaximal, characteristic
5C2×#380×C71C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C71C211yesmaximal, characteristic
7C22×#95×C71C211yesmaximal, characteristic
8C71×#1444C211yesmaximal, characteristic, complemented
9C71×#1442C211yesmaximal, characteristic, complemented
10C71×#1441C211yesmaximal, characteristic, complemented
11C71×#1441C211yesmaximal, characteristic, complemented
12C71×#1436C211yesmaximal, characteristic, complemented
13C71×#1436C211yesmaximal, characteristic, complemented
14C71×C4⋊#95C211yesmaximal, characteristic, complemented
15C71×C22⋊#95C211yesmaximal, characteristic
16C24×C4×C71C2211yescharacteristic
17C24×C4×C71C2211yescharacteristic
18C24×C4×C71C2211yescharacteristic
19C22×C4⋊C4×C71C2211yescharacteristic
20C22×C4⋊C4×C71C2211yescharacteristic
21C22×C4⋊C4×C71C2211yescharacteristic
22C22×C4⋊C4×C71C2211yescharacteristic
23C22×C4⋊C4×C71C2211yescharacteristic
24C22×C4⋊C4×C71C2211yescharacteristic
25C22×C4⋊C4×C71C2211yescharacteristic
26C22×C4⋊C4×C71C2211yescharacteristic
27C22×C22⋊C4×C71C2211yescharacteristic
28C22×C22⋊C4×C71C2211yescharacteristic
29C22×C22⋊C4×C71C2211yescharacteristic
30C22×C22⋊C4×C71C2211yescharacteristic
31C22×C42×C71C2211yescharacteristic
32C22×C42×C71C2211yescharacteristic
33#389×C71—24no—
34#385×C71—24no—
35#385×C71—24no—
36#385×C71C418yescomplemented
37#380×C71—24no—
38C4×C22⋊C4×C71—24no—
39C2×#95×C71—24no—
40C2×#95×C71C2211yescharacteristic
41C2×#95×C71C2211yescharacteristic
42C2×#95×C71C2211yescharacteristic
43C2×#95×C71C2211yescharacteristic
44C2×#95×C71C2211yescharacteristic
45C2×#95×C71C2211yescharacteristic
46C2×#95×C71C2211yescharacteristic
47C2×#95×C71C2211yescharacteristic
48C2×#95×C71C2211yescharacteristic
49C2×#95×C71C2211yescharacteristic
50C2×#95×C71C2211yescharacteristic
51C2×#95×C71C2211yescharacteristic
52C2×#95×C71C2211yescharacteristic
53C2×#95×C71C2211yescharacteristic
54C2×#95×C71C2211yescharacteristic
55C2×#95×C71C2211yescharacteristic
56C2×#95×C71C2211yescharacteristic
57C2×#95×C71C2211yescharacteristic
58C25×C71C2311yescharacteristic
59C23×C4×C71—22no—
60C23×C4×C71—22no—
61C23×C4×C71—22no—
62C23×C4×C71—22no—
63C23×C4×C71—22no—
64C23×C4×C71—22no—
65C23×C4×C71—22no—
66C23×C4×C71—22no—
67C23×C4×C71—22no—
68C23×C4×C71—22no—
69C23×C4×C71—22no—
70C23×C4×C71—22no—
71C23×C4×C71—22no—
72C23×C4×C71—41no—
73C23×C4×C71—41no—
74C23×C4×C71—41no—
75C23×C4×C71—41no—
76C23×C4×C71—41no—
77C23×C4×C71—41no—
78C23×C4×C71C2×C414yes—
79C23×C4×C71Q814yes—
80C23×C4×C71C2311yescharacteristic
81C23×C4×C71C2311yescharacteristic
82C23×C4×C71C2311yescharacteristic
83C23×C4×C71C2311yescharacteristic
84C23×C4×C71C2311yescharacteristic
85C23×C4×C71C2311yescharacteristic
86C23×C4×C71C2311yescharacteristic
87C23×C4×C71C2311yescharacteristic
88C23×C4×C71C2311yescharacteristic
89C23×C4×C71C2311yescharacteristic
90C23×C4×C71C2311yescharacteristic
91C23×C4×C71C2311yescharacteristic
92C23×C4×C71C2311yescharacteristic
93C23×C4×C71C2311yescharacteristic
94C2×C4⋊C4×C71—22no—
95C2×C4⋊C4×C71—22no—
96C2×C4⋊C4×C71—22no—
97C2×C4⋊C4×C71—22no—
98C2×C4⋊C4×C71—22no—
99C2×C4⋊C4×C71—22no—
100C2×C4⋊C4×C71—22no—
101C2×C4⋊C4×C71—22no—
102C2×C4⋊C4×C71—22no—
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×C71—41no—
109C2×C4⋊C4×C71—41no—
110C2×C4⋊C4×C71—41no—
111C2×C4⋊C4×C71—41no—
112C2×C4⋊C4×C71—41no—
113C2×C4⋊C4×C71—41no—
114C2×C4⋊C4×C71—41no—
115C2×C4⋊C4×C71—41no—
116C2×C4⋊C4×C71C2×C414yescomplemented
117C2×C4⋊C4×C71C2×C414yescomplemented
118C2×C22⋊C4×C71—22no—
119C2×C22⋊C4×C71—22no—
120C2×C22⋊C4×C71—22no—
121C2×C22⋊C4×C71—22no—
122C2×C22⋊C4×C71—22no—
123C2×C22⋊C4×C71—22no—
124C2×C22⋊C4×C71—22no—
125C2×C22⋊C4×C71C2×C414yes—
126C2×C22⋊C4×C71C2×C414yes—
127C2×C22⋊C4×C71D414yes—
128C2×C22⋊C4×C71D414yes—
129C2×C22⋊C4×C71Q814yes—
130C2×C42×C71—22no—
131C2×C42×C71—22no—
132C2×C42×C71—22no—
133C2×C42×C71—22no—
134C2×C42×C71—41no—
135C2×C42×C71—41no—
136#95×C71—22no—
137#95×C71—22no—
138#95×C71—22no—
139#95×C71—22no—
140#95×C71—22no—
141#95×C71—22no—
142#95×C71—22no—
143#95×C71—22no—
144#95×C71—22no—
145#95×C71—22no—
146#95×C71—22no—
147#95×C71—22no—
148#95×C71—22no—
149#95×C71—41no—
150#95×C71—41no—
151#95×C71C2×C414yescomplemented
152#95×C71C2×C414yescomplemented
153#95×C71D414yes—
154C24×C71—21no—
155C24×C71—21no—
156C24×C71—21no—
157C24×C71—21no—
158C24×C71—21no—
159C24×C71—21no—
160C24×C71—21no—
161C24×C71—21no—
162C24×C71C22×C412yes—
163C24×C71C2×D412yes—
164C24×C71C2×D412yes—
165C24×C71C2×Q812yes—
166C24×C71C2×Q812yes—
167C24×C71#4112yes—
168C24×C71#4112yes—
169C24×C71C2411yescharacteristic
170C22×C4×C71—21no—
171C22×C4×C71—21no—
172C22×C4×C71—21no—
173C22×C4×C71—21no—
174C22×C4×C71—21no—
175C22×C4×C71—21no—
176C22×C4×C71—21no—
177C22×C4×C71—21no—
178C22×C4×C71—21no—
179C22×C4×C71—21no—
180C22×C4×C71—21no—
181C22×C4×C71—21no—
182C22×C4×C71—21no—
183C22×C4×C71—21no—
184C22×C4×C71—21no—
185C22×C4×C71—21no—
186C22×C4×C71—28no—
187C22×C4×C71—28no—
188C22×C4×C71—28no—
189C22×C4×C71—21no—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—21no—
195C22×C4×C71—21no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—21no—
199C22×C4×C71—21no—
200C22×C4×C71—21no—
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—21no—
210C22×C4×C71—21no—
211C22×C4×C71—21no—
212C22×C4×C71—21no—
213C22×C4×C71—21no—
214C22×C4×C71—21no—
215C22×C4×C71—21no—
216C22×C4×C71—21no—
217C22×C4×C71—21no—
218C22×C4×C71—21no—
219C22×C4×C71—21no—
220C22×C4×C71—21no—
221C22×C4×C71—21no—
222C22×C4×C71—21no—
223C22×C4×C71—21no—
224C22×C4×C71—21no—
225C22×C4×C71—21no—
226C22×C4×C71—21no—
227C22×C4×C71—21no—
228C22×C4×C71—21no—
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71—21no—
236C22×C4×C71—21no—
237C22×C4×C71—28no—
238C22×C4×C71—28no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
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—44no—
254C22×C4×C71—44no—
255C22×C4×C71—44no—
256C22×C4×C71—44no—
257C22×C4×C71—44no—
258C22×C4×C71—44no—
259C22×C4×C71—44no—
260C22×C4×C71—44no—
261C22×C4×C71—44no—
262C22×C4×C71—44no—
263C22×C4×C71—44no—
264C22×C4×C71—44no—
265C22×C4×C71—44no—
266C22×C4×C71—44no—
267C22×C4×C71—44no—
268C22×C4×C71—44no—
269C22×C4×C71C22×C412yes—
270C22×C4×C71C22×C412yes—
271C22×C4×C71C22×C412yes—
272C22×C4×C71C22×C412yes—
273C22×C4×C71C22×C412yes—
274C22×C4×C71C22×C412yes—
275C22×C4×C71C2×D412yes—
276C22×C4×C71C2×D412yes—
277C22×C4×C71C2×D412yes—
278C22×C4×C71C2×D412yes—
279C22×C4×C71C2×D412yes—
280C22×C4×C71C2×D412yes—
281C22×C4×C71C2×D412yes—
282C22×C4×C71C2×Q812yes—
283C22×C4×C71C2×Q812yes—
284C22×C4×C71C2×Q812yes—
285C22×C4×C71C2×Q812yes—
286C22×C4×C71#4112yes—
287C22×C4×C71#4112yes—
288C22×C4×C71#4112yes—
289C4⋊C4×C71—28no—
290C4⋊C4×C71—44no—
291C4⋊C4×C71—44no—
292C4⋊C4×C71—44no—
293C4⋊C4×C71—44no—
294C4⋊C4×C71—44no—
295C4⋊C4×C71—44no—
296C4⋊C4×C71—44no—
297C22⋊C4×C71—28no—
298C22⋊C4×C71—28no—
299C22⋊C4×C71—44no—
300C22⋊C4×C71C4⋊C4116yescomplemented
301C42×C71—44no—
302C42×C71—44no—
303C23×C71—22no—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71—22no—
307C23×C71—22no—
308C23×C71—22no—
309C23×C71—22no—
310C23×C71—22no—
311C23×C71—22no—
312C23×C71—22no—
313C23×C71—22no—
314C23×C71—22no—
315C23×C71—22no—
316C23×C71—22no—
317C23×C71—22no—
318C23×C71—22no—
319C23×C71—22no—
320C23×C71—22no—
321C23×C71—22no—
322C23×C71—22no—
323C23×C71—22no—
324C23×C71—22no—
325C23×C71—22no—
326C23×C71—22no—
327C23×C71—22no—
328C23×C71—22no—
329C23×C71—22no—
330C23×C71—22no—
331C23×C71C2×C4⋊C414yes—
332C23×C71C4×D414yes—
333C23×C71C4×Q814yes—
334C23×C71#12114yes—
335C23×C71C22⋊Q814yes—
336C23×C71#12514yes—
337C23×C71C4⋊Q814yes—
338C23×C71C23×C411yescharacteristic
339C23×C71C22×D411yescharacteristic
340C23×C71C22×D411yescharacteristic
341C23×C71C22×D411yescharacteristic
342C23×C71C22×Q811yescharacteristic
343C23×C71C22×Q811yescharacteristic
344C23×C71C2×#4111yescharacteristic
345C23×C71C2×#4111yescharacteristic
346C23×C71C2×#4111yescharacteristic
347C23×C71C2×#4111yescharacteristic
348C23×C71C2×#4111yescharacteristic
349C23×C71H(5,𝔽2)11yescharacteristic
350C23×C71H(5,𝔽2)11yescharacteristic
351C23×C71H(5,𝔽2)11yescharacteristic
352C23×C712−1+411yescharacteristic
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—22no—
370C2×C4×C71—22no—
371C2×C4×C71—22no—
372C2×C4×C71—22no—
373C2×C4×C71—22no—
374C2×C4×C71—22no—
375C2×C4×C71—22no—
376C2×C4×C71—22no—
377C2×C4×C71—22no—
378C2×C4×C71—22no—
379C2×C4×C71—22no—
380C2×C4×C71—22no—
381C2×C4×C71—22no—
382C2×C4×C71—22no—
383C2×C4×C71—22no—
384C2×C4×C71—22no—
385C2×C4×C71—22no—
386C2×C4×C71—22no—
387C2×C4×C71—22no—
388C2×C4×C71—22no—
389C2×C4×C71—22no—
390C2×C4×C71—22no—
391C2×C4×C71—22no—
392C2×C4×C71—22no—
393C2×C4×C71—22no—
394C2×C4×C71—22no—
395C2×C4×C71—22no—
396C2×C4×C71—22no—
397C2×C4×C71—22no—
398C2×C4×C71—22no—
399C2×C4×C71—22no—
400C2×C4×C71—22no—
401C2×C4×C71—416no—
402C2×C4×C71—416no—
403C2×C4×C71—416no—
404C2×C4×C71—41no—
405C2×C4×C71—41no—
406C2×C4×C71—41no—
407C2×C4×C71—41no—
408C2×C4×C71—41no—
409C2×C4×C71—41no—
410C2×C4×C71—41no—
411C2×C4×C71—41no—
412C2×C4×C71—41no—
413C2×C4×C71—41no—
414C2×C4×C71—41no—
415C2×C4×C71—41no—
416C2×C4×C71—41no—
417C2×C4×C71—41no—
418C2×C4×C71—41no—
419C2×C4×C71—41no—
420C2×C4×C71—41no—
421C2×C4×C71—41no—
422C2×C4×C71—41no—
423C2×C4×C71—41no—
424C2×C4×C71—41no—
425C2×C4×C71—41no—
426C2×C4×C71—41no—
427C2×C4×C71—41no—
428C2×C4×C71—41no—
429C2×C4×C71—41no—
430C2×C4×C71—41no—
431C2×C4×C71—41no—
432C2×C4×C71—41no—
433C2×C4×C71—41no—
434C2×C4×C71—41no—
435C2×C4×C71—41no—
436C2×C4×C71—41no—
437C2×C4×C71—41no—
438C2×C4×C71—41no—
439C2×C4×C71—41no—
440C2×C4×C71—41no—
441C2×C4×C71—41no—
442C2×C4×C71—41no—
443C2×C4×C71—41no—
444C2×C4×C71—41no—
445C2×C4×C71—41no—
446C2×C4×C71—41no—
447C2×C4×C71—41no—
448C2×C4×C71—41no—
449C2×C4×C71—41no—
450C2×C4×C71C2×C4⋊C414yes—
451C2×C4×C71C2×C4⋊C414yes—
452C2×C4×C71C4×D414yes—
453C2×C4×C71C22⋊Q814yes—
454C22×C71—24no—
455C22×C71—24no—
456C22×C71—24no—
457C22×C71—24no—
458C22×C71—24no—
459C22×C71—24no—
460C22×C71—24no—
461C22×C71—24no—
462C22×C71—24no—
463C22×C71—24no—
464C22×C71—24no—
465C22×C71—24no—
466C22×C71—24no—
467C22×C71—24no—
468C22×C71#38918yescomplemented
469C22×C71C22×C4⋊C411yescharacteristic
470C22×C71C2×C4×D411yescharacteristic
471C22×C71C2×C4×D411yescharacteristic
472C22×C71C2×C4×Q811yescharacteristic
473C22×C71C4×#4111yescharacteristic
474C22×C71#51811yescharacteristic
475C22×C71#52011yescharacteristic
476C22×C71C2×#12111yescharacteristic
477C22×C71C2×C22⋊Q811yescharacteristic
478C22×C71C2×C22⋊Q811yescharacteristic
479C22×C71#52511yescharacteristic
480C22×C71C2×#12511yescharacteristic
481C22×C71#52911yescharacteristic
482C22×C71C2×C4⋊Q811yescharacteristic
483C22×C71#53311yescharacteristic
484C22×C71#53811yescharacteristic
485C22×C71#53911yescharacteristic
486C22×C71#54311yescharacteristic
487C22×C71#54411yescharacteristic
488C22×C71D4211yescharacteristic
489C22×C71D4211yescharacteristic
490C22×C71#54611yescharacteristic
491C22×C71#54611yescharacteristic
492C22×C71#54611yescharacteristic
493C22×C71#54611yescharacteristic
494C22×C71#54611yescharacteristic
495C22×C71#54711yescharacteristic
496C22×C71#54711yescharacteristic
497C22×C71D4×Q811yescharacteristic
498C22×C71#55111yescharacteristic
499C22×C71#55111yescharacteristic
500C22×C71#55211yescharacteristic
501C22×C71#55411yescharacteristic
502C22×C71#55411yescharacteristic
503C22×C71#55411yescharacteristic
504C4×C71—24no—
505C4×C71—24no—
506C4×C71—24no—
507C4×C71—24no—
508C4×C71—42no—
509C4×C71—42no—
510C4×C71—42no—
511C4×C71—42no—
512C4×C71—42no—
513C4×C71—42no—
514C4×C71—42no—
515C4×C71—42no—
516C4×C71—81no—
517C4×C71—81no—
518#14004C7111yesmaximal, characteristic, direct product factor, Sylow
519C2×C71—28no—
520C2×C71C2×#38911yescharacteristic
521C2×C71C4×C22⋊Q811yescharacteristic
522C2×C71#232911yescharacteristic
523C2×C71D4×C4⋊C411yescharacteristic
524C2×C71#234911yescharacteristic
525C2×C71#235811yescharacteristic
526C2×C71#235911yescharacteristic
527C2×C71#242411yescharacteristic
528C2×C71#242511yescharacteristic
529C2×C71#243711yescharacteristic
530C2×C71#243811yescharacteristic
531C2×C71#244011yescharacteristic
532C2×C71#247311yescharacteristic
533C2×C71#250511yescharacteristic
534C2×C71#254911yescharacteristic
535C2×#389C2×C7111yescharacteristic, complemented
536C2×#385C2×C7111yescharacteristic
537C2×#385C2×C7111yescharacteristic
538C2×#385C2×C7111yescharacteristic
539C2×#380C2×C7111yescharacteristic
540C2×C4×C22⋊C4C2×C7111yescharacteristic
541C22×#95C2×C7111yescharacteristic
542#1444C2×C7111yescharacteristic, complemented
543#1442C2×C7111yescharacteristic, complemented
544#1441C2×C7111yescharacteristic, complemented
545#1441C2×C7111yescharacteristic, complemented
546#1436C2×C7111yescharacteristic, complemented
547#1436C2×C7111yescharacteristic, complemented
548C4⋊#95C2×C7111yescharacteristic, complemented
549C22⋊#95C2×C7111yescharacteristic
550C71#1400411yescharacteristic, direct product factor, Sylow
551C24×C4C22×C7111yescharacteristic
552C24×C4C22×C7111yescharacteristic
553C24×C4C22×C7111yescharacteristic
554C22×C4⋊C4C22×C7111yescharacteristic
555C22×C4⋊C4C22×C7111yescharacteristic
556C22×C4⋊C4C22×C7111yescharacteristic
557C22×C4⋊C4C22×C7111yescharacteristic
558C22×C4⋊C4C22×C7111yescharacteristic
559C22×C4⋊C4C22×C7111yescharacteristic
560C22×C4⋊C4C22×C7111yescharacteristic
561C22×C4⋊C4C22×C7111yescharacteristic
562C22×C22⋊C4C22×C7111yescharacteristic
563C22×C22⋊C4C22×C7111yescharacteristic
564C22×C22⋊C4C22×C7111yescharacteristic
565C22×C22⋊C4C22×C7111yescharacteristic
566C22×C42C22×C7111yescharacteristic
567C22×C42C22×C7111yescharacteristic
568#389—24no—
569#385—24no—
570#385—24no—
571#385C4×C7118yescomplemented
572#380—24no—
573C4×C22⋊C4—24no—
574C2×#95—24no—
575C2×#95C22×C7111yescharacteristic
576C2×#95C22×C7111yescharacteristic
577C2×#95C22×C7111yescharacteristic
578C2×#95C22×C7111yescharacteristic
579C2×#95C22×C7111yescharacteristic
580C2×#95C22×C7111yescharacteristic
581C2×#95C22×C7111yescharacteristic
582C2×#95C22×C7111yescharacteristic
583C2×#95C22×C7111yescharacteristic
584C2×#95C22×C7111yescharacteristic
585C2×#95C22×C7111yescharacteristic
586C2×#95C22×C7111yescharacteristic
587C2×#95C22×C7111yescharacteristic
588C2×#95C22×C7111yescharacteristic
589C2×#95C22×C7111yescharacteristic
590C2×#95C22×C7111yescharacteristic
591C2×#95C22×C7111yescharacteristic
592C2×#95C22×C7111yescharacteristic
593C25C23×C7111yescharacteristic
594C23×C4—22no—
595C23×C4—22no—
596C23×C4—22no—
597C23×C4—22no—
598C23×C4—22no—
599C23×C4—22no—
600C23×C4—22no—
601C23×C4—22no—
602C23×C4—22no—
603C23×C4—22no—
604C23×C4—22no—
605C23×C4—22no—
606C23×C4—22no—
607C23×C4—41no—
608C23×C4—41no—
609C23×C4—41no—
610C23×C4—41no—
611C23×C4—41no—
612C23×C4—41no—
613C23×C4C2×C4×C7114yes—
614C23×C4Q8×C7114yes—
615C23×C4C23×C7111yescharacteristic
616C23×C4C23×C7111yescharacteristic
617C23×C4C23×C7111yescharacteristic
618C23×C4C23×C7111yescharacteristic
619C23×C4C23×C7111yescharacteristic
620C23×C4C23×C7111yescharacteristic
621C23×C4C23×C7111yescharacteristic
622C23×C4C23×C7111yescharacteristic
623C23×C4C23×C7111yescharacteristic
624C23×C4C23×C7111yescharacteristic
625C23×C4C23×C7111yescharacteristic
626C23×C4C23×C7111yescharacteristic
627C23×C4C23×C7111yescharacteristic
628C23×C4C23×C7111yescharacteristic
629C2×C4⋊C4—22no—
630C2×C4⋊C4—22no—
631C2×C4⋊C4—22no—
632C2×C4⋊C4—22no—
633C2×C4⋊C4—22no—
634C2×C4⋊C4—22no—
635C2×C4⋊C4—22no—
636C2×C4⋊C4—22no—
637C2×C4⋊C4—22no—
638C2×C4⋊C4—22no—
639C2×C4⋊C4—22no—
640C2×C4⋊C4—22no—
641C2×C4⋊C4—22no—
642C2×C4⋊C4—22no—
643C2×C4⋊C4—41no—
644C2×C4⋊C4—41no—
645C2×C4⋊C4—41no—
646C2×C4⋊C4—41no—
647C2×C4⋊C4—41no—
648C2×C4⋊C4—41no—
649C2×C4⋊C4—41no—
650C2×C4⋊C4—41no—
651C2×C4⋊C4C2×C4×C7114yescomplemented
652C2×C4⋊C4C2×C4×C7114yescomplemented
653C2×C22⋊C4—22no—
654C2×C22⋊C4—22no—
655C2×C22⋊C4—22no—
656C2×C22⋊C4—22no—
657C2×C22⋊C4—22no—
658C2×C22⋊C4—22no—
659C2×C22⋊C4—22no—
660C2×C22⋊C4C2×C4×C7114yes—
661C2×C22⋊C4C2×C4×C7114yes—
662C2×C22⋊C4D4×C7114yes—
663C2×C22⋊C4D4×C7114yes—
664C2×C22⋊C4Q8×C7114yes—
665C2×C42—22no—
666C2×C42—22no—
667C2×C42—22no—
668C2×C42—22no—
669C2×C42—41no—
670C2×C42—41no—
671#95—22no—
672#95—22no—
673#95—22no—
674#95—22no—
675#95—22no—
676#95—22no—
677#95—22no—
678#95—22no—
679#95—22no—
680#95—22no—
681#95—22no—
682#95—22no—
683#95—22no—
684#95—41no—
685#95—41no—
686#95C2×C4×C7114yescomplemented
687#95C2×C4×C7114yescomplemented
688#95D4×C7114yes—
689C24—21no—
690C24—21no—
691C24—21no—
692C24—21no—
693C24—21no—
694C24—21no—
695C24—21no—
696C24—21no—
697C24C22×C4×C7112yes—
698C24C2×D4×C7112yes—
699C24C2×D4×C7112yes—
700C24C2×Q8×C7112yes—
701C24C2×Q8×C7112yes—
702C24#41×C7112yes—
703C24#41×C7112yes—
704C24C24×C7111yescharacteristic
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—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—28no—
722C22×C4—28no—
723C22×C4—28no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—21no—
736C22×C4—21no—
737C22×C4—21no—
738C22×C4—21no—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—21no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—21no—
756C22×C4—21no—
757C22×C4—21no—
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—28no—
773C22×C4—28no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—21no—
783C22×C4—21no—
784C22×C4—21no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—44no—
789C22×C4—44no—
790C22×C4—44no—
791C22×C4—44no—
792C22×C4—44no—
793C22×C4—44no—
794C22×C4—44no—
795C22×C4—44no—
796C22×C4—44no—
797C22×C4—44no—
798C22×C4—44no—
799C22×C4—44no—
800C22×C4—44no—
801C22×C4—44no—
802C22×C4—44no—
803C22×C4—44no—
804C22×C4C22×C4×C7112yes—
805C22×C4C22×C4×C7112yes—
806C22×C4C22×C4×C7112yes—
807C22×C4C22×C4×C7112yes—
808C22×C4C22×C4×C7112yes—
809C22×C4C22×C4×C7112yes—
810C22×C4C2×D4×C7112yes—
811C22×C4C2×D4×C7112yes—
812C22×C4C2×D4×C7112yes—
813C22×C4C2×D4×C7112yes—
814C22×C4C2×D4×C7112yes—
815C22×C4C2×D4×C7112yes—
816C22×C4C2×D4×C7112yes—
817C22×C4C2×Q8×C7112yes—
818C22×C4C2×Q8×C7112yes—
819C22×C4C2×Q8×C7112yes—
820C22×C4C2×Q8×C7112yes—
821C22×C4#41×C7112yes—
822C22×C4#41×C7112yes—
823C22×C4#41×C7112yes—
824C4⋊C4—28no—
825C4⋊C4—44no—
826C4⋊C4—44no—
827C4⋊C4—44no—
828C4⋊C4—44no—
829C4⋊C4—44no—
830C4⋊C4—44no—
831C4⋊C4—44no—
832C22⋊C4—28no—
833C22⋊C4—28no—
834C22⋊C4—44no—
835C22⋊C4C4⋊C4×C71116yescomplemented
836C42—44no—
837C42—44no—
838C23—22no—
839C23—22no—
840C23—22no—
841C23—22no—
842C23—22no—
843C23—22no—
844C23—22no—
845C23—22no—
846C23—22no—
847C23—22no—
848C23—22no—
849C23—22no—
850C23—22no—
851C23—22no—
852C23—22no—
853C23—22no—
854C23—22no—
855C23—22no—
856C23—22no—
857C23—22no—
858C23—22no—
859C23—22no—
860C23—22no—
861C23—22no—
862C23—22no—
863C23—22no—
864C23—22no—
865C23—22no—
866C23C2×C4⋊C4×C7114yes—
867C23C4×D4×C7114yes—
868C23C4×Q8×C7114yes—
869C23#121×C7114yes—
870C23C22⋊Q8×C7114yes—
871C23#125×C7114yes—
872C23C4⋊Q8×C7114yes—
873C23C23×C4×C7111yescharacteristic
874C23C22×D4×C7111yescharacteristic
875C23C22×D4×C7111yescharacteristic
876C23C22×D4×C7111yescharacteristic
877C23C22×Q8×C7111yescharacteristic
878C23C22×Q8×C7111yescharacteristic
879C23C2×#41×C7111yescharacteristic
880C23C2×#41×C7111yescharacteristic
881C23C2×#41×C7111yescharacteristic
882C23C2×#41×C7111yescharacteristic
883C23C2×#41×C7111yescharacteristic
884C23H(5,𝔽2)×C7111yescharacteristic
885C23H(5,𝔽2)×C7111yescharacteristic
886C23H(5,𝔽2)×C7111yescharacteristic
887C232−1+4×C7111yescharacteristic
888C2×C4—22no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—22no—
892C2×C4—22no—
893C2×C4—22no—
894C2×C4—22no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—22no—
900C2×C4—22no—
901C2×C4—22no—
902C2×C4—22no—
903C2×C4—22no—
904C2×C4—22no—
905C2×C4—22no—
906C2×C4—22no—
907C2×C4—22no—
908C2×C4—22no—
909C2×C4—22no—
910C2×C4—22no—
911C2×C4—22no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—22no—
917C2×C4—22no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—22no—
924C2×C4—22no—
925C2×C4—22no—
926C2×C4—22no—
927C2×C4—22no—
928C2×C4—22no—
929C2×C4—22no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—22no—
934C2×C4—22no—
935C2×C4—22no—
936C2×C4—416no—
937C2×C4—416no—
938C2×C4—416no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—41no—
947C2×C4—41no—
948C2×C4—41no—
949C2×C4—41no—
950C2×C4—41no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—41no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—41no—
962C2×C4—41no—
963C2×C4—41no—
964C2×C4—41no—
965C2×C4—41no—
966C2×C4—41no—
967C2×C4—41no—
968C2×C4—41no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4C2×C4⋊C4×C7114yes—
986C2×C4C2×C4⋊C4×C7114yes—
987C2×C4C4×D4×C7114yes—
988C2×C4C22⋊Q8×C7114yes—
989C22—24no—
990C22—24no—
991C22—24no—
992C22—24no—
993C22—24no—
994C22—24no—
995C22—24no—
996C22—24no—
997C22—24no—
998C22—24no—
999C22—24no—
1000C22—24no—
1001C22—24no—
1002C22—24no—
1003C22#389×C7118yescomplemented
1004C22C22×C4⋊C4×C7111yescharacteristic
1005C22C2×C4×D4×C7111yescharacteristic
1006C22C2×C4×D4×C7111yescharacteristic
1007C22C2×C4×Q8×C7111yescharacteristic
1008C22C4×#41×C7111yescharacteristic
1009C22#518×C7111yescharacteristic
1010C22#520×C7111yescharacteristic
1011C22C2×#121×C7111yescharacteristic
1012C22C2×C22⋊Q8×C7111yescharacteristic
1013C22C2×C22⋊Q8×C7111yescharacteristic
1014C22#525×C7111yescharacteristic
1015C22C2×#125×C7111yescharacteristic
1016C22#529×C7111yescharacteristic
1017C22C2×C4⋊Q8×C7111yescharacteristic
1018C22#533×C7111yescharacteristic
1019C22#538×C7111yescharacteristic
1020C22#539×C7111yescharacteristic
1021C22#543×C7111yescharacteristic
1022C22#544×C7111yescharacteristic
1023C22D42×C7111yescharacteristic
1024C22D42×C7111yescharacteristic
1025C22#546×C7111yescharacteristic
1026C22#546×C7111yescharacteristic
1027C22#546×C7111yescharacteristic
1028C22#546×C7111yescharacteristic
1029C22#546×C7111yescharacteristic
1030C22#547×C7111yescharacteristic
1031C22#547×C7111yescharacteristic
1032C22D4×Q8×C7111yescharacteristic
1033C22#551×C7111yescharacteristic
1034C22#551×C7111yescharacteristic
1035C22#552×C7111yescharacteristic
1036C22#554×C7111yescharacteristic
1037C22#554×C7111yescharacteristic
1038C22#554×C7111yescharacteristic
1039C4—24no—
1040C4—24no—
1041C4—24no—
1042C4—24no—
1043C4—42no—
1044C4—42no—
1045C4—42no—
1046C4—42no—
1047C4—42no—
1048C4—42no—
1049C4—42no—
1050C4—42no—
1051C4—81no—
1052C4—81no—
1053C2—28no—
1054C2C2×#389×C7111yescharacteristic
1055C2C4×C22⋊Q8×C7111yescharacteristic
1056C2C71×#232911yescharacteristic
1057C2D4×C4⋊C4×C7111yescharacteristic
1058C2C71×#234911yescharacteristic
1059C2C71×#235811yescharacteristic
1060C2C71×#235911yescharacteristic
1061C2C71×#242411yescharacteristic
1062C2C71×#242511yescharacteristic
1063C2C71×#243711yescharacteristic
1064C2C71×#243811yescharacteristic
1065C2C71×#244011yescharacteristic
1066C2C71×#247311yescharacteristic
1067C2C71×#250511yescharacteristic
1068C2C71×#254911yescharacteristic
subgroupG/H
center, socleC24×C71C24
commutatorC23C23×C4×C71
Frattini, cosocleC24C24×C71
prime radicalC25×C71C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#389×C71C2semidirect
8. C71×#1444C2semidirect
9. C71×#1442C2semidirect
10. C71×#1441C2semidirect
11. C71×#1441C2semidirect
12. C71×#1436C2semidirect
13. C71×#1436C2semidirect
14. C71×C4⋊#95C2semidirect
36. #385×C71C4semidirect
116. C2×C4⋊C4×C71C2×C4semidirect
117. C2×C4⋊C4×C71C2×C4semidirect
151. #95×C71C2×C4semidirect
152. #95×C71C2×C4semidirect
300. C22⋊C4×C71C4⋊C4semidirect
468. C22×C71#389semidirect
518. #14004C71direct (N × H)
535. C2×#389C2×C71semidirect
542. #1444C2×C71semidirect
543. #1442C2×C71semidirect
544. #1441C2×C71semidirect
545. #1441C2×C71semidirect
546. #1436C2×C71semidirect
547. #1436C2×C71semidirect
548. C4⋊#95C2×C71semidirect
550. C71#14004direct (N × H)
571. #385C4×C71semidirect
651. C2×C4⋊C4C2×C4×C71semidirect
652. C2×C4⋊C4C2×C4×C71semidirect
686. #95C2×C4×C71semidirect
687. #95C2×C4×C71semidirect
835. C22⋊C4C4⋊C4×C71semidirect
1003. C22#389×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#389×C712
C2×#385×C712
C2×#380×C712
C2×C4×C22⋊C4×C712
C22×#95×C712
C71×#14442
C71×#14422
C71×#14412
C71×#14362
C71×C4⋊#952
C71×C22⋊#952
#1400471