Finite Group Databasebeta

← C71×#22423 #31843295

Subgroups — C71×#22423 #31843295

Order 18176.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C71C211yesmaximal, characteristic
2C2×#435×C71C211yesmaximal, characteristic, complemented
3C2×#418×C71C211yesmaximal, characteristic, complemented
4C22×#102×C71C211yesmaximal, characteristic, complemented
5C71×#2352C211yesmaximal, characteristic, complemented
6C71×#1982C211yesmaximal, characteristic, complemented
7C71×#1961C211yesmaximal, characteristic, complemented
8C71×#1895C211yesmaximal, characteristic, complemented
9C71×#1893C211yesmaximal, characteristic, complemented
10C71×#1875C211yesmaximal, characteristic, complemented
11C71×#1874C211yesmaximal, characteristic, complemented
12C71×#1804C211yesmaximal, characteristic, complemented
13C71×#1786C211yesmaximal, characteristic, complemented
14C71×#1786C211yesmaximal, characteristic, complemented
15C71×#1762C211yesmaximal, characteristic, complemented
16C23×D4×C71—21no—
17C23×D4×C71C2211yescharacteristic
18C23×D4×C71C2211yescharacteristic
19C22×M16×C71C2211yescharacteristic, complemented
20C23×C8×C71C2211yescharacteristic, complemented
21D42×C71—24no—
22D42×C71C418yescomplemented
23C2×#127×C71C2211yescharacteristic
24C2×#121×C71—21no—
25C2×#121×C71C2211yescharacteristic
26C2×#121×C71C2211yescharacteristic
27C2×#120×C71—21no—
28C2×#120×C71—21no—
29C2×C4×D4×C71C2211yescharacteristic
30C2×C4×D4×C71C2211yescharacteristic
31C2×#117×C71C2211yescharacteristic, complemented
32C22×C4⋊C4×C71C2211yescharacteristic, complemented
33#435×C71—24no—
34C2×C4⋊C8×C71C2211yescharacteristic, complemented
35#418×C71—24no—
36C2×#102×C71—24no—
37C2×#102×C71C2211yescharacteristic
38C2×#102×C71C2211yescharacteristic
39C2×#102×C71C2211yescharacteristic
40C2×#102×C71C2211yescharacteristic
41C2×#102×C71C2211yescharacteristic, complemented
42C2×#102×C71C2211yescharacteristic, complemented
43C2×#102×C71C2211yescharacteristic, complemented
44C2×#102×C71C2211yescharacteristic, complemented
45C2×#102×C71C2211yescharacteristic, complemented
46C2×#102×C71C2211yescharacteristic, complemented
47C2×#102×C71C2211yescharacteristic, complemented
48C2×#102×C71C2211yescharacteristic, complemented
49C2×C22⋊C8×C71C2211yescharacteristic, complemented
50C2×C22⋊C8×C71C2211yescharacteristic, complemented
51C2×#97×C71C2211yescharacteristic, complemented
52#388×C71—21no—
53#387×C71—21no—
54#386×C71—21no—
55#382×C71C2211yescharacteristic, complemented
56#380×C71C2211yescharacteristic, complemented
57#380×C71C2211yescharacteristic, complemented
58C4×C4⋊C4×C71C2211yescharacteristic, complemented
59C4×C22⋊C4×C71—21no—
60#340×C71C2211yescharacteristic, complemented
61#340×C71C2211yescharacteristic, complemented
62#340×C71C2211yescharacteristic, complemented
63#340×C71C2211yescharacteristic, complemented
64C25×C71—21no—
65C25×C71—21no—
66C22×D4×C71—22no—
67C22×D4×C71—22no—
68C22×D4×C71—22no—
69C22×D4×C71—22no—
70C22×D4×C71—21no—
71C22×D4×C71—21no—
72C22×D4×C71—28no—
73C22×D4×C71—21no—
74C22×D4×C71—21no—
75C22×D4×C71—21no—
76C22×D4×C71—22no—
77C22×D4×C71—22no—
78C22×D4×C71—21no—
79C22×D4×C71—41no—
80C22×D4×C71—41no—
81C22×D4×C71—41no—
82C22×D4×C71—41no—
83C22×D4×C71—44no—
84C22×D4×C71—44no—
85C22×D4×C71C2×C414yes—
86C22×D4×C71C2×C414yescomplemented
87C22×D4×C71D411yescharacteristic
88C22×D4×C71C2311yescharacteristic
89C22×D4×C71C2311yescharacteristic
90C22×D4×C71C2311yescharacteristic
91C23×C4×C71—21no—
92C23×C4×C71—21no—
93C23×C4×C71C2311yescharacteristic
94C23×C4×C71C2311yescharacteristic
95C2×M16×C71—22no—
96C2×M16×C71—22no—
97C2×M16×C71—41no—
98C22×C8×C71—22no—
99C22×C8×C71—22no—
100C22×C8×C71—41no—
101C22×C8×C71C2311yescharacteristic
102C22×C8×C71C2311yescharacteristic
103C22×C8×C71C2311yescharacteristic
104C22×C8×C71C2311yescharacteristic
105#127×C71—22no—
106#127×C71C2×C414yescomplemented
107#121×C71—22no—
108#121×C71—22no—
109#121×C71—28no—
110#121×C71C2×C414yes—
111#121×C71C2×C414yescomplemented
112#120×C71—28no—
113#120×C71—28no—
114C4×D4×C71—22no—
115C4×D4×C71C2×C414yes—
116C4×D4×C71C2×C414yescomplemented
117C4×D4×C71D414yes—
118#117×C71—22no—
119#117×C71—41no—
120C2×C4⋊C4×C71—22no—
121C2×C4⋊C4×C71—21no—
122C2×C4⋊C4×C71—41no—
123C2×C4⋊C4×C71D411yescharacteristic
124C2×C4⋊C4×C71C2311yescharacteristic
125C2×C4⋊C4×C71C2311yescharacteristic
126C2×C4⋊C4×C71C2311yescharacteristic
127C2×C4⋊C4×C71C2311yescharacteristic
128C2×C4⋊C4×C71C2311yescharacteristic
129C2×C22⋊C4×C71—21no—
130C2×C22⋊C4×C71—21no—
131C2×C22⋊C4×C71—21no—
132C2×C22⋊C4×C71—21no—
133C2×C22⋊C4×C71—21no—
134C2×C22⋊C4×C71—21no—
135C2×C22⋊C4×C71D411yescharacteristic
136C2×C22⋊C4×C71D411yescharacteristic
137C2×C42×C71—21no—
138C2×C42×C71—21no—
139C2×C42×C71C2311yescharacteristic
140C4⋊C8×C71—22no—
141#102×C71—22no—
142#102×C71—22no—
143#102×C71—22no—
144#102×C71—22no—
145#102×C71—22no—
146#102×C71—22no—
147#102×C71—22no—
148#102×C71—41no—
149#102×C71—41no—
150#102×C71—41no—
151#102×C71—41no—
152#102×C71D414yescomplemented
153C22⋊C8×C71—22no—
154C22⋊C8×C71—22no—
155#97×C71—22no—
156#95×C71—21no—
157#95×C71—21no—
158#95×C71—21no—
159#95×C71—21no—
160#95×C71—21no—
161C24×C71—21no—
162C24×C71—21no—
163C24×C71—21no—
164C24×C71—24no—
165C24×C71—24no—
166C24×C71—42no—
167C24×C71—42no—
168C24×C71—42no—
169C24×C71—42no—
170C24×C71—42no—
171C24×C71—42no—
172C24×C71—42no—
173C24×C71—42no—
174C24×C71—81no—
175C24×C71—81no—
176C24×C71—81no—
177C24×C71—81no—
178C24×C71C2×D411yescharacteristic
179C24×C71C2×D411yescharacteristic
180C2×D4×C71—22no—
181C2×D4×C71—22no—
182C2×D4×C71—28no—
183C2×D4×C71—28no—
184C2×D4×C71—24no—
185C2×D4×C71—24no—
186C2×D4×C71—24no—
187C2×D4×C71—24no—
188C2×D4×C71—24no—
189C2×D4×C71—24no—
190C2×D4×C71—21no—
191C2×D4×C71—21no—
192C2×D4×C71—21no—
193C2×D4×C71—21no—
194C2×D4×C71—21no—
195C2×D4×C71—21no—
196C2×D4×C71—21no—
197C2×D4×C71—21no—
198C2×D4×C71—21no—
199C2×D4×C71—21no—
200C2×D4×C71—21no—
201C2×D4×C71—21no—
202C2×D4×C71—21no—
203C2×D4×C71—44no—
204C2×D4×C71—44no—
205C2×D4×C71—44no—
206C2×D4×C71—44no—
207C2×D4×C71—44no—
208C2×D4×C71—44no—
209C2×D4×C71—42no—
210C2×D4×C71—42no—
211C2×D4×C71—42no—
212C2×D4×C71—42no—
213C2×D4×C71—42no—
214C2×D4×C71—42no—
215C2×D4×C71—432no—
216C2×D4×C71—42no—
217C2×D4×C71—42no—
218C2×D4×C71—42no—
219C2×D4×C71—42no—
220C2×D4×C71—81no—
221C2×D4×C71—81no—
222C2×D4×C71C22⋊C414yes—
223C2×D4×C71C22×C412yes—
224C2×D4×C71C22×C412yes—
225C2×D4×C71C22×C412yes—
226C2×D4×C71C2×D412yes—
227C2×D4×C71#4112yes—
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—21no—
238C22×C4×C71—24no—
239C22×C4×C71—21no—
240C22×C4×C71—21no—
241C22×C4×C71—21no—
242C22×C4×C71—42no—
243C22×C4×C71—42no—
244C22×C4×C71—42no—
245C22×C4×C71—42no—
246C22×C4×C71—81no—
247C22×C4×C71C22×C412yes—
248C22×C4×C71C22×C412yes—
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D411yescharacteristic
253C22×C4×C71C2×D412yes—
254C22×C4×C71C2×D412yes—
255C22×C4×C71C2411yescharacteristic
256M16×C71—44no—
257C2×C8×C71—21no—
258C2×C8×C71—21no—
259C2×C8×C71—21no—
260C2×C8×C71—21no—
261C2×C8×C71—21no—
262C2×C8×C71—21no—
263C2×C8×C71—21no—
264C2×C8×C71—21no—
265C2×C8×C71—21no—
266C2×C8×C71—21no—
267C2×C8×C71—21no—
268C2×C8×C71—44no—
269C2×C8×C71C2×D412yescomplemented
270C4⋊C4×C71—21no—
271C4⋊C4×C71—21no—
272C4⋊C4×C71—21no—
273C4⋊C4×C71—21no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71—21no—
277C4⋊C4×C71—21no—
278C4⋊C4×C71—42no—
279C4⋊C4×C71C22⋊C414yes—
280C4⋊C4×C71C22×C412yes—
281C4⋊C4×C71C2×D412yescomplemented
282C22⋊C4×C71—24no—
283C22⋊C4×C71—24no—
284C22⋊C4×C71—24no—
285C22⋊C4×C71—42no—
286C22⋊C4×C71—42no—
287C22⋊C4×C71—81no—
288C22⋊C4×C71C22⋊C414yes—
289C22⋊C4×C71C22⋊C414yes—
290C42×C71—42no—
291C42×C71—81no—
292C42×C71C22×C412yes—
293C42×C71C2×D412yes—
294C23×C71—21no—
295C23×C71—21no—
296C23×C71—21no—
297C23×C71—21no—
298C23×C71—22no—
299C23×C71—21no—
300C23×C71—22no—
301C23×C71—21no—
302C23×C71—22no—
303C23×C71—21no—
304C23×C71—21no—
305C23×C71—21no—
306C23×C71—21no—
307C23×C71—22no—
308C23×C71—22no—
309C23×C71—48no—
310C23×C71—48no—
311C23×C71—48no—
312C23×C71—41no—
313C23×C71—41no—
314C23×C71—41no—
315C23×C71—41no—
316C23×C71—41no—
317C23×C71—41no—
318C23×C71—41no—
319C23×C71—41no—
320C23×C71—41no—
321C23×C71—41no—
322C23×C71—41no—
323C23×C71—41no—
324C23×C71—41no—
325C23×C71—41no—
326C23×C71—41no—
327C23×C71—41no—
328C23×C71—48no—
329C23×C71—84no—
330C23×C71—84no—
331C23×C71—84no—
332C23×C71—84no—
333C23×C71—84no—
334C23×C71—84no—
335C23×C71—84no—
336C23×C71—84no—
337C23×C71—84no—
338C23×C71—84no—
339C23×C71C2×C22⋊C412yes—
340C23×C71C2×C22⋊C412yes—
341C23×C71AGL(1,ℤ/8)12yes—
342C23×C71AGL(1,ℤ/8)12yes—
343C23×C71C22×D411yescharacteristic
344D4×C71—28no—
345D4×C71—22no—
346D4×C71—22no—
347D4×C71—22no—
348D4×C71—22no—
349D4×C71—22no—
350D4×C71—22no—
351D4×C71—22no—
352D4×C71—48no—
353D4×C71—48no—
354D4×C71—48no—
355D4×C71—48no—
356D4×C71—48no—
357D4×C71—41no—
358D4×C71—41no—
359D4×C71—41no—
360D4×C71—41no—
361D4×C71—84no—
362D4×C71C4×D414yes—
363C2×C4×C71—21no—
364C2×C4×C71—21no—
365C2×C4×C71—21no—
366C2×C4×C71—21no—
367C2×C4×C71—21no—
368C2×C4×C71—21no—
369C2×C4×C71—21no—
370C2×C4×C71—21no—
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—48no—
382C2×C4×C71—41no—
383C2×C4×C71—41no—
384C2×C4×C71—41no—
385C2×C4×C71—41no—
386C2×C4×C71—41no—
387C2×C4×C71—41no—
388C2×C4×C71—41no—
389C2×C4×C71—41no—
390C2×C4×C71—41no—
391C2×C4×C71—41no—
392C2×C4×C71—41no—
393C2×C4×C71—41no—
394C2×C4×C71—41no—
395C2×C4×C71—84no—
396C2×C4×C71C2×C22⋊C412yes—
397C2×C4×C71C2×C22⋊C412yes—
398C2×C4×C71C2×C22⋊C412yes—
399C2×C4×C71C2×C22⋊C412yes—
400C2×C4×C71C23×C411yescharacteristic
401C2×C4×C71C22×D411yescharacteristic
402C2×C4×C71C22×D411yescharacteristic
403C2×C4×C71C2×#4111yescharacteristic
404C2×C4×C71H(5,𝔽2)11yescharacteristic
405C2×C4×C71H(5,𝔽2)11yescharacteristic
406C8×C71—22no—
407C8×C71—41no—
408C8×C71—41no—
409C8×C71—41no—
410C22×C71—22no—
411C22×C71—22no—
412C22×C71—22no—
413C22×C71—22no—
414C22×C71—22no—
415C22×C71—22no—
416C22×C71—22no—
417C22×C71—24no—
418C22×C71—22no—
419C22×C71—22no—
420C22×C71—42no—
421C22×C71—42no—
422C22×C71—41no—
423C22×C71—42no—
424C22×C71—41no—
425C22×C71—42no—
426C22×C71—41no—
427C22×C71—42no—
428C22×C71—41no—
429C22×C71—42no—
430C22×C71—42no—
431C22×C71—42no—
432C22×C71—42no—
433C22×C71—42no—
434C22×C71—42no—
435C22×C71—42no—
436C22×C71—816no—
437C22×C71—816no—
438C22×C71—81no—
439C22×C71—81no—
440C22×C71—81no—
441C22×C71—81no—
442C22×C71—81no—
443C22×C71—81no—
444C22×C71—81no—
445C22×C71—81no—
446C22×C71#41814yescomplemented
447C22×C71C22×C22⋊C411yescharacteristic
448C22×C71D4211yescharacteristic
449C22×C71#54611yescharacteristic
450C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C71C2×AGL(1,ℤ/8)11yescharacteristic
452C22×C71#57611yescharacteristic
453C22×C71#57711yescharacteristic
454C4×C71—22no—
455C4×C71—22no—
456C4×C71—22no—
457C4×C71—22no—
458C4×C71—42no—
459C4×C71—42no—
460C4×C71—81no—
461C4×C71—81no—
462C4×C71—81no—
463C4×C71C2×C4×D411yescharacteristic
464C4×C71#51811yescharacteristic
465C4×C71D4211yescharacteristic
466C4×C71#54611yescharacteristic
467#22423C7111yesmaximal, characteristic, direct product factor, Sylow
468C2×C71—24no—
469C2×C71—42no—
470C2×C71—44no—
471C2×C71—82no—
472C2×C71—82no—
473C2×C71D4×C22⋊C411yescharacteristic
474C2×C71C2×#41811yescharacteristic
475C2×C71#289711yescharacteristic
476C2×C71#326411yescharacteristic
477C2×C71#326511yescharacteristic
478C2×C71#331011yescharacteristic
479C2×C71#331811yescharacteristic
480C2×D42C2×C7111yescharacteristic
481C2×#435C2×C7111yescharacteristic, complemented
482C2×#418C2×C7111yescharacteristic, complemented
483C22×#102C2×C7111yescharacteristic, complemented
484#2352C2×C7111yescharacteristic, complemented
485#1982C2×C7111yescharacteristic, complemented
486#1961C2×C7111yescharacteristic, complemented
487#1895C2×C7111yescharacteristic, complemented
488#1893C2×C7111yescharacteristic, complemented
489#1875C2×C7111yescharacteristic, complemented
490#1874C2×C7111yescharacteristic, complemented
491#1804C2×C7111yescharacteristic, complemented
492#1786C2×C7111yescharacteristic, complemented
493#1786C2×C7111yescharacteristic, complemented
494#1762C2×C7111yescharacteristic, complemented
495C71#2242311yescharacteristic, direct product factor, Sylow
496C23×D4—21no—
497C23×D4C22×C7111yescharacteristic
498C23×D4C22×C7111yescharacteristic
499C22×M16C22×C7111yescharacteristic, complemented
500C23×C8C22×C7111yescharacteristic, complemented
501D42—24no—
502D42C4×C7118yescomplemented
503C2×#127C22×C7111yescharacteristic
504C2×#121—21no—
505C2×#121C22×C7111yescharacteristic
506C2×#121C22×C7111yescharacteristic
507C2×#120—21no—
508C2×#120—21no—
509C2×C4×D4C22×C7111yescharacteristic
510C2×C4×D4C22×C7111yescharacteristic
511C2×#117C22×C7111yescharacteristic, complemented
512C22×C4⋊C4C22×C7111yescharacteristic, complemented
513#435—24no—
514C2×C4⋊C8C22×C7111yescharacteristic, complemented
515#418—24no—
516C2×#102—24no—
517C2×#102C22×C7111yescharacteristic
518C2×#102C22×C7111yescharacteristic
519C2×#102C22×C7111yescharacteristic
520C2×#102C22×C7111yescharacteristic
521C2×#102C22×C7111yescharacteristic, complemented
522C2×#102C22×C7111yescharacteristic, complemented
523C2×#102C22×C7111yescharacteristic, complemented
524C2×#102C22×C7111yescharacteristic, complemented
525C2×#102C22×C7111yescharacteristic, complemented
526C2×#102C22×C7111yescharacteristic, complemented
527C2×#102C22×C7111yescharacteristic, complemented
528C2×#102C22×C7111yescharacteristic, complemented
529C2×C22⋊C8C22×C7111yescharacteristic, complemented
530C2×C22⋊C8C22×C7111yescharacteristic, complemented
531C2×#97C22×C7111yescharacteristic, complemented
532#388—21no—
533#387—21no—
534#386—21no—
535#382C22×C7111yescharacteristic, complemented
536#380C22×C7111yescharacteristic, complemented
537#380C22×C7111yescharacteristic, complemented
538C4×C4⋊C4C22×C7111yescharacteristic, complemented
539C4×C22⋊C4—21no—
540#340C22×C7111yescharacteristic, complemented
541#340C22×C7111yescharacteristic, complemented
542#340C22×C7111yescharacteristic, complemented
543#340C22×C7111yescharacteristic, complemented
544C25—21no—
545C25—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4C2×C4×C7114yes—
566C22×D4C2×C4×C7114yescomplemented
567C22×D4D4×C7111yescharacteristic
568C22×D4C23×C7111yescharacteristic
569C22×D4C23×C7111yescharacteristic
570C22×D4C23×C7111yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4C23×C7111yescharacteristic
574C23×C4C23×C7111yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C7111yescharacteristic
582C22×C8C23×C7111yescharacteristic
583C22×C8C23×C7111yescharacteristic
584C22×C8C23×C7111yescharacteristic
585#127—22no—
586#127C2×C4×C7114yescomplemented
587#121—22no—
588#121—22no—
589#121—28no—
590#121C2×C4×C7114yes—
591#121C2×C4×C7114yescomplemented
592#120—28no—
593#120—28no—
594C4×D4—22no—
595C4×D4C2×C4×C7114yes—
596C4×D4C2×C4×C7114yescomplemented
597C4×D4D4×C7114yes—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4D4×C7111yescharacteristic
604C2×C4⋊C4C23×C7111yescharacteristic
605C2×C4⋊C4C23×C7111yescharacteristic
606C2×C4⋊C4C23×C7111yescharacteristic
607C2×C4⋊C4C23×C7111yescharacteristic
608C2×C4⋊C4C23×C7111yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4D4×C7111yescharacteristic
616C2×C22⋊C4D4×C7111yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C23×C7111yescharacteristic
620C4⋊C8—22no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630#102—41no—
631#102—41no—
632#102D4×C7114yescomplemented
633C22⋊C8—22no—
634C22⋊C8—22no—
635#97—22no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×D4×C7111yescharacteristic
659C24C2×D4×C7111yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊C4×C7114yes—
703C2×D4C22×C4×C7112yes—
704C2×D4C22×C4×C7112yes—
705C2×D4C22×C4×C7112yes—
706C2×D4C2×D4×C7112yes—
707C2×D4#41×C7112yes—
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—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—81no—
727C22×C4C22×C4×C7112yes—
728C22×C4C22×C4×C7112yes—
729C22×C4C2×D4×C7111yescharacteristic
730C22×C4C2×D4×C7111yescharacteristic
731C22×C4C2×D4×C7111yescharacteristic
732C22×C4C2×D4×C7111yescharacteristic
733C22×C4C2×D4×C7112yes—
734C22×C4C2×D4×C7112yes—
735C22×C4C24×C7111yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—44no—
749C2×C8C2×D4×C7112yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—42no—
759C4⋊C4C22⋊C4×C7114yes—
760C4⋊C4C22×C4×C7112yes—
761C4⋊C4C2×D4×C7112yescomplemented
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4C22⋊C4×C7114yes—
769C22⋊C4C22⋊C4×C7114yes—
770C42—42no—
771C42—81no—
772C42C22×C4×C7112yes—
773C42C2×D4×C7112yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—48no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊C4×C7112yes—
820C23C2×C22⋊C4×C7112yes—
821C23AGL(1,ℤ/8)×C7112yes—
822C23AGL(1,ℤ/8)×C7112yes—
823C23C22×D4×C7111yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4C4×D4×C7114yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—84no—
876C2×C4C2×C22⋊C4×C7112yes—
877C2×C4C2×C22⋊C4×C7112yes—
878C2×C4C2×C22⋊C4×C7112yes—
879C2×C4C2×C22⋊C4×C7112yes—
880C2×C4C23×C4×C7111yescharacteristic
881C2×C4C22×D4×C7111yescharacteristic
882C2×C4C22×D4×C7111yescharacteristic
883C2×C4C2×#41×C7111yescharacteristic
884C2×C4H(5,𝔽2)×C7111yescharacteristic
885C2×C4H(5,𝔽2)×C7111yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—42no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22#418×C7114yescomplemented
927C22C22×C22⋊C4×C7111yescharacteristic
928C22D42×C7111yescharacteristic
929C22#546×C7111yescharacteristic
930C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
931C22C2×AGL(1,ℤ/8)×C7111yescharacteristic
932C22#576×C7111yescharacteristic
933C22#577×C7111yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×C4×D4×C7111yescharacteristic
944C4#518×C7111yescharacteristic
945C4D42×C7111yescharacteristic
946C4#546×C7111yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊C4×C7111yescharacteristic
953C2C2×#418×C7111yescharacteristic
954C2C71×#289711yescharacteristic
955C2C71×#326411yescharacteristic
956C2C71×#326511yescharacteristic
957C2C71×#331011yescharacteristic
958C2C71×#331811yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutatorC2×C4C23×C4×C71
Frattini, cosocleC22×C4C24×C71
prime radicalC2×D42×C71C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ C2×C4×D4×C71 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#435×C71C2semidirect
3. C2×#418×C71C2semidirect
4. C22×#102×C71C2semidirect
5. C71×#2352C2semidirect
6. C71×#1982C2semidirect
7. C71×#1961C2semidirect
8. C71×#1895C2semidirect
9. C71×#1893C2semidirect
10. C71×#1875C2semidirect
11. C71×#1874C2semidirect
12. C71×#1804C2semidirect
13. C71×#1786C2semidirect
14. C71×#1786C2semidirect
15. C71×#1762C2semidirect
19. C22×M16×C71C22semidirect
20. C23×C8×C71C22semidirect
22. D42×C71C4semidirect
31. C2×#117×C71C22semidirect
32. C22×C4⋊C4×C71C22semidirect
34. C2×C4⋊C8×C71C22semidirect
41. C2×#102×C71C22semidirect
42. C2×#102×C71C22semidirect
43. C2×#102×C71C22semidirect
44. C2×#102×C71C22semidirect
45. C2×#102×C71C22semidirect
46. C2×#102×C71C22semidirect
47. C2×#102×C71C22semidirect
48. C2×#102×C71C22semidirect
49. C2×C22⋊C8×C71C22semidirect
50. C2×C22⋊C8×C71C22semidirect
51. C2×#97×C71C22semidirect
55. #382×C71C22semidirect
56. #380×C71C22semidirect
57. #380×C71C22semidirect
58. C4×C4⋊C4×C71C22semidirect
60. #340×C71C22semidirect
61. #340×C71C22semidirect
62. #340×C71C22semidirect
63. #340×C71C22semidirect
86. C22×D4×C71C2×C4semidirect
106. #127×C71C2×C4semidirect
111. #121×C71C2×C4semidirect
116. C4×D4×C71C2×C4semidirect
152. #102×C71D4semidirect
269. C2×C8×C71C2×D4semidirect
281. C4⋊C4×C71C2×D4semidirect
446. C22×C71#418semidirect
467. #22423C71direct (N × H)
481. C2×#435C2×C71semidirect
482. C2×#418C2×C71semidirect
483. C22×#102C2×C71semidirect
484. #2352C2×C71semidirect
485. #1982C2×C71semidirect
486. #1961C2×C71semidirect
487. #1895C2×C71semidirect
488. #1893C2×C71semidirect
489. #1875C2×C71semidirect
490. #1874C2×C71semidirect
491. #1804C2×C71semidirect
492. #1786C2×C71semidirect
493. #1786C2×C71semidirect
494. #1762C2×C71semidirect
495. C71#22423direct (N × H)
499. C22×M16C22×C71semidirect
500. C23×C8C22×C71semidirect
502. D42C4×C71semidirect
511. C2×#117C22×C71semidirect
512. C22×C4⋊C4C22×C71semidirect
514. C2×C4⋊C8C22×C71semidirect
521. C2×#102C22×C71semidirect
522. C2×#102C22×C71semidirect
523. C2×#102C22×C71semidirect
524. C2×#102C22×C71semidirect
525. C2×#102C22×C71semidirect
526. C2×#102C22×C71semidirect
527. C2×#102C22×C71semidirect
528. C2×#102C22×C71semidirect
529. C2×C22⋊C8C22×C71semidirect
530. C2×C22⋊C8C22×C71semidirect
531. C2×#97C22×C71semidirect
535. #382C22×C71semidirect
536. #380C22×C71semidirect
537. #380C22×C71semidirect
538. C4×C4⋊C4C22×C71semidirect
540. #340C22×C71semidirect
541. #340C22×C71semidirect
542. #340C22×C71semidirect
543. #340C22×C71semidirect
566. C22×D4C2×C4×C71semidirect
586. #127C2×C4×C71semidirect
591. #121C2×C4×C71semidirect
596. C4×D4C2×C4×C71semidirect
632. #102D4×C71semidirect
749. C2×C8C2×D4×C71semidirect
761. C4⋊C4C2×D4×C71semidirect
926. C22#418×C71semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C712
C2×#435×C712
C2×#418×C712
C22×#102×C712
C71×#23522
C71×#19822
C71×#19612
C71×#18952
C71×#18932
C71×#18752
C71×#18742
C71×#18042
C71×#17862
C71×#17622
#2242371