Finite Group Databasebeta

← C71×#15131 #31836003

Subgroups — C71×#15131 #31836003

Order 18176.

1814 conjugacy classes of subgroups.

The subgroup lattice has 830 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#396×C71C212yesmaximal
2C2×#389×C71C211yesmaximal, characteristic, complemented
3C2×#389×C71C211yesmaximal, characteristic, complemented
4C2×#384×C71C211yesmaximal, characteristic, complemented
5C2×#380×C71C211yesmaximal, characteristic
6C2×#380×C71C211yesmaximal, characteristic
7C2×C4×C22⋊C4×C71C211yesmaximal, characteristic
8C71×#1441C212yesmaximal, complemented
9C71×#1441C212yesmaximal, complemented
10C71×#1439C212yesmaximal
11C71×C4⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C71C2211yescharacteristic
13C22×C4⋊C4×C71C2211yescharacteristic
14C22×C4⋊C4×C71C2211yescharacteristic
15C22×C4⋊C4×C71C2212yes—
16C22×C4⋊C4×C71C2212yes—
17C22×C4⋊C4×C71C2212yes—
18C22×C4⋊C4×C71C2212yes—
19C22×C4⋊C4×C71C2211yescharacteristic
20C22×C4⋊C4×C71C2211yescharacteristic
21C22×C22⋊C4×C71C2212yes—
22C22×C22⋊C4×C71C2212yes—
23C22×C22⋊C4×C71C2211yescharacteristic
24C22×C22⋊C4×C71C2211yescharacteristic
25C22×C42×C71C2211yescharacteristic
26C22×C42×C71C2211yescharacteristic
27#396×C71—28no—
28#389×C71—24no—
29#389×C71—24no—
30#384×C71—24no—
31#380×C71—24no—
32#380×C71—24no—
33C4×C22⋊C4×C71—24no—
34C2×#95×C71C2212yes—
35C2×#95×C71C2212yes—
36C2×#95×C71C2212yes—
37C2×#95×C71C2212yes—
38C2×#95×C71C2212yes—
39C2×#95×C71C2211yescharacteristic
40C2×#95×C71C2211yescharacteristic
41C2×#95×C71C2212yes—
42C25×C71C2311yescharacteristic
43C23×C4×C71—22no—
44C23×C4×C71—22no—
45C23×C4×C71—22no—
46C23×C4×C71—22no—
47C23×C4×C71—22no—
48C23×C4×C71—22no—
49C23×C4×C71Q814yes—
50C23×C4×C71C2312yes—
51C23×C4×C71C2312yes—
52C23×C4×C71C2311yescharacteristic
53C23×C4×C71C2312yes—
54C23×C4×C71C2312yes—
55C23×C4×C71C2311yescharacteristic
56C23×C4×C71C2311yescharacteristic
57C23×C4×C71C2311yescharacteristic
58C23×C4×C71C2311yescharacteristic
59C23×C4×C71C2311yescharacteristic
60C2×C4⋊C4×C71—22no—
61C2×C4⋊C4×C71—22no—
62C2×C4⋊C4×C71—22no—
63C2×C4⋊C4×C71—22no—
64C2×C4⋊C4×C71—22no—
65C2×C4⋊C4×C71—22no—
66C2×C4⋊C4×C71—24no—
67C2×C4⋊C4×C71—24no—
68C2×C4⋊C4×C71—22no—
69C2×C4⋊C4×C71—24no—
70C2×C4⋊C4×C71—24no—
71C2×C4⋊C4×C71—22no—
72C2×C4⋊C4×C71—24no—
73C2×C4⋊C4×C71—24no—
74C2×C4⋊C4×C71—24no—
75C2×C4⋊C4×C71—24no—
76C2×C4⋊C4×C71—24no—
77C2×C4⋊C4×C71—22no—
78C2×C4⋊C4×C71—22no—
79C2×C4⋊C4×C71—42no—
80C2×C4⋊C4×C71—42no—
81C2×C4⋊C4×C71—42no—
82C2×C4⋊C4×C71D414yes—
83C2×C4⋊C4×C71D414yes—
84C2×C22⋊C4×C71—22no—
85C2×C22⋊C4×C71—22no—
86C2×C22⋊C4×C71—22no—
87C2×C22⋊C4×C71—22no—
88C2×C22⋊C4×C71—24no—
89C2×C22⋊C4×C71—24no—
90C2×C22⋊C4×C71—24no—
91C2×C22⋊C4×C71—24no—
92C2×C22⋊C4×C71—42no—
93C2×C22⋊C4×C71—42no—
94C2×C22⋊C4×C71D414yes—
95C2×C22⋊C4×C71Q814yes—
96C2×C42×C71—22no—
97C2×C42×C71—22no—
98C2×C42×C71—22no—
99C2×C42×C71—22no—
100C2×C42×C71—22no—
101C2×C42×C71D414yes—
102#95×C71—22no—
103#95×C71—22no—
104#95×C71—24no—
105#95×C71—24no—
106#95×C71—24no—
107#95×C71—24no—
108#95×C71—24no—
109#95×C71—42no—
110C24×C71—21no—
111C24×C71—21no—
112C24×C71—21no—
113C24×C71—21no—
114C24×C71—21no—
115C24×C71—21no—
116C24×C71—21no—
117C24×C71—21no—
118C24×C71—21no—
119C24×C71—21no—
120C24×C71—21no—
121C24×C71—21no—
122C24×C71C2×D412yes—
123C24×C71C2×Q812yes—
124C24×C71C2×Q812yes—
125C24×C71C2411yescharacteristic
126C22×C4×C71—21no—
127C22×C4×C71—21no—
128C22×C4×C71—21no—
129C22×C4×C71—21no—
130C22×C4×C71—21no—
131C22×C4×C71—21no—
132C22×C4×C71—21no—
133C22×C4×C71—21no—
134C22×C4×C71—21no—
135C22×C4×C71—21no—
136C22×C4×C71—21no—
137C22×C4×C71—21no—
138C22×C4×C71—21no—
139C22×C4×C71—21no—
140C22×C4×C71—22no—
141C22×C4×C71—22no—
142C22×C4×C71—21no—
143C22×C4×C71—22no—
144C22×C4×C71—22no—
145C22×C4×C71—21no—
146C22×C4×C71—21no—
147C22×C4×C71—21no—
148C22×C4×C71—21no—
149C22×C4×C71—22no—
150C22×C4×C71—22no—
151C22×C4×C71—22no—
152C22×C4×C71—22no—
153C22×C4×C71—21no—
154C22×C4×C71—21no—
155C22×C4×C71—21no—
156C22×C4×C71—21no—
157C22×C4×C71—22no—
158C22×C4×C71—22no—
159C22×C4×C71—21no—
160C22×C4×C71—22no—
161C22×C4×C71—21no—
162C22×C4×C71—22no—
163C22×C4×C71—21no—
164C22×C4×C71—28no—
165C22×C4×C71—28no—
166C22×C4×C71—28no—
167C22×C4×C71—22no—
168C22×C4×C71—22no—
169C22×C4×C71—22no—
170C22×C4×C71—22no—
171C22×C4×C71—22no—
172C22×C4×C71—22no—
173C22×C4×C71—22no—
174C22×C4×C71—22no—
175C22×C4×C71—22no—
176C22×C4×C71—22no—
177C22×C4×C71—22no—
178C22×C4×C71—22no—
179C22×C4×C71—22no—
180C22×C4×C71—22no—
181C22×C4×C71—44no—
182C22×C4×C71—44no—
183C22×C4×C71—44no—
184C22×C4×C71—44no—
185C22×C4×C71C2×D414yes—
186C22×C4×C71C2×D412yes—
187C22×C4×C71C2×D414yes—
188C22×C4×C71C2×D412yes—
189C22×C4×C71C2×D412yes—
190C22×C4×C71C2×D412yes—
191C22×C4×C71C2×D412yes—
192C22×C4×C71C2×D412yes—
193C22×C4×C71C2×D412yes—
194C22×C4×C71C2×Q812yes—
195C22×C4×C71C2×Q812yes—
196C22×C4×C71C2×Q812yes—
197C22×C4×C71C2×Q812yes—
198C22×C4×C71#4112yes—
199C22×C4×C71#4112yes—
200C22×C4×C71#4112yes—
201C22×C4×C71#4112yes—
202C22×C4×C71#4112yes—
203C4⋊C4×C71—28no—
204C4⋊C4×C71—28no—
205C4⋊C4×C71—48no—
206C4⋊C4×C71—48no—
207C4⋊C4×C71—48no—
208C4⋊C4×C71—48no—
209C4⋊C4×C71—44no—
210C4⋊C4×C71—44no—
211C22⋊C4×C71—28no—
212C22⋊C4×C71—28no—
213C22⋊C4×C71—48no—
214C22⋊C4×C71—48no—
215C42×C71—28no—
216C42×C71—44no—
217C23×C71—22no—
218C23×C71—22no—
219C23×C71—22no—
220C23×C71—22no—
221C23×C71—22no—
222C23×C71—22no—
223C23×C71—22no—
224C23×C71—22no—
225C23×C71—22no—
226C23×C71—22no—
227C23×C71—22no—
228C23×C71—22no—
229C23×C71—22no—
230C23×C71—22no—
231C23×C71—22no—
232C23×C71—22no—
233C23×C71—22no—
234C23×C71—22no—
235C23×C71—41no—
236C23×C71—41no—
237C23×C71—41no—
238C23×C71—41no—
239C23×C71—41no—
240C23×C71—41no—
241C23×C71—41no—
242C23×C71—41no—
243C23×C71—41no—
244C23×C71—41no—
245C23×C71—41no—
246C23×C71—41no—
247C23×C71—41no—
248C23×C71—41no—
249C23×C71—41no—
250C23×C71—41no—
251C23×C71C4⋊Q814yes—
252C23×C71C22×D411yescharacteristic
253C23×C71C22×D411yescharacteristic
254C23×C71C22×D411yescharacteristic
255C23×C71C22×D411yescharacteristic
256C23×C71C22×Q811yescharacteristic
257C23×C71C22×Q811yescharacteristic
258C23×C71C2×#4111yescharacteristic
259C23×C71C2×#4111yescharacteristic
260C23×C71C2×#4111yescharacteristic
261C23×C71C2×#4111yescharacteristic
262C23×C71C2×#4111yescharacteristic
263C23×C71H(5,𝔽2)11yescharacteristic
264C23×C71H(5,𝔽2)11yescharacteristic
265C23×C712−1+411yescharacteristic
266C23×C712−1+411yescharacteristic
267C2×C4×C71—22no—
268C2×C4×C71—22no—
269C2×C4×C71—22no—
270C2×C4×C71—22no—
271C2×C4×C71—22no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
276C2×C4×C71—22no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—24no—
281C2×C4×C71—24no—
282C2×C4×C71—22no—
283C2×C4×C71—22no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—24no—
287C2×C4×C71—24no—
288C2×C4×C71—22no—
289C2×C4×C71—24no—
290C2×C4×C71—24no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—41no—
295C2×C4×C71—41no—
296C2×C4×C71—42no—
297C2×C4×C71—41no—
298C2×C4×C71—41no—
299C2×C4×C71—41no—
300C2×C4×C71—41no—
301C2×C4×C71—42no—
302C2×C4×C71—41no—
303C2×C4×C71—42no—
304C2×C4×C71—41no—
305C2×C4×C71—42no—
306C2×C4×C71—42no—
307C2×C4×C71—41no—
308C2×C4×C71—42no—
309C2×C4×C71—42no—
310C2×C4×C71—41no—
311C2×C4×C71—41no—
312C2×C4×C71—42no—
313C2×C4×C71—41no—
314C2×C4×C71—416no—
315C2×C4×C71—42no—
316C2×C4×C71—42no—
317C2×C4×C71—42no—
318C2×C4×C71—42no—
319C2×C4×C71—42no—
320C2×C4×C71—42no—
321C2×C4×C71—42no—
322C2×C4×C71—42no—
323C2×C4×C71—42no—
324C2×C4×C71—42no—
325C2×C4×C71—42no—
326C2×C4×C71—42no—
327C2×C4×C71—42no—
328C2×C4×C71—42no—
329C2×C4×C71#12114yes—
330C2×C4×C71#12114yes—
331C2×C4×C71#12114yes—
332C2×C4×C71#12114yes—
333C2×C4×C71C22⋊Q814yes—
334C2×C4×C71C22⋊Q814yes—
335C2×C4×C71C22⋊Q814yes—
336C2×C4×C71C22⋊Q814yes—
337C2×C4×C71#12614yes—
338C22×C71—24no—
339C22×C71—24no—
340C22×C71—24no—
341C22×C71—42no—
342C22×C71—42no—
343C22×C71—42no—
344C22×C71—42no—
345C22×C71—42no—
346C22×C71—42no—
347C22×C71—42no—
348C22×C71—42no—
349C22×C71—42no—
350C22×C71—42no—
351C22×C71—42no—
352C22×C71—42no—
353C22×C71C2×#12111yescharacteristic
354C22×C71C2×#12111yescharacteristic
355C22×C71C2×#12111yescharacteristic
356C22×C71C2×#12111yescharacteristic
357C22×C71C2×C22⋊Q811yescharacteristic
358C22×C71C2×C22⋊Q811yescharacteristic
359C22×C71C2×C22⋊Q811yescharacteristic
360C22×C71C2×C22⋊Q811yescharacteristic
361C22×C71C2×#12611yescharacteristic
362C22×C71C2×C4⋊Q811yescharacteristic
363C22×C71#53211yescharacteristic
364C22×C71#53311yescharacteristic
365C22×C71#53311yescharacteristic
366C22×C71#53711yescharacteristic
367C22×C71#53711yescharacteristic
368C22×C71#54011yescharacteristic
369C22×C71#54111yescharacteristic
370C22×C71#54411yescharacteristic
371C22×C71#54411yescharacteristic
372C22×C71D4211yescharacteristic
373C22×C71D4211yescharacteristic
374C22×C71#54611yescharacteristic
375C22×C71#54711yescharacteristic
376C22×C71#54711yescharacteristic
377C22×C71#54711yescharacteristic
378C22×C71#54811yescharacteristic
379C22×C71D4×Q811yescharacteristic
380C22×C71D4×Q811yescharacteristic
381C22×C71#55011yescharacteristic
382C22×C71#55211yescharacteristic
383C22×C71#55311yescharacteristic
384C22×C71#55411yescharacteristic
385C22×C71#55411yescharacteristic
386C22×C71#55511yescharacteristic
387C22×C71#55611yescharacteristic
388C4×C71—24no—
389C4×C71—24no—
390C4×C71—42no—
391C4×C71—44no—
392C4×C71—42no—
393C4×C71—44no—
394C4×C71—42no—
395C4×C71—82no—
396C4×C71—82no—
397C4×C71#39618yescomplemented
398#15131C7111yesmaximal, characteristic, direct product factor, Sylow
399C2×C71—44no—
400C2×C71C2×#39611yescharacteristic
401C2×C71#241611yescharacteristic
402C2×C71#241711yescharacteristic
403C2×C71#242811yescharacteristic
404C2×C71#242911yescharacteristic
405C2×C71#243911yescharacteristic
406C2×C71#244011yescharacteristic
407C2×C71#244011yescharacteristic
408C2×C71#244111yescharacteristic
409C2×C71#249611yescharacteristic
410C2×C71#249711yescharacteristic
411C2×C71#253711yescharacteristic
412C2×C71#253811yescharacteristic
413C2×C71#262911yescharacteristic
414C2×C71#285711yescharacteristic
415C2×#396C2×C7112yes—
416C2×#389C2×C7111yescharacteristic, complemented
417C2×#389C2×C7111yescharacteristic, complemented
418C2×#384C2×C7111yescharacteristic, complemented
419C2×#380C2×C7111yescharacteristic
420C2×#380C2×C7111yescharacteristic
421C2×C4×C22⋊C4C2×C7111yescharacteristic
422#1441C2×C7112yescomplemented
423#1441C2×C7112yescomplemented
424#1439C2×C7112yes—
425C4⋊#95C2×C7111yescharacteristic, complemented
426C71#1513111yescharacteristic, direct product factor, Sylow
427C24×C4C22×C7111yescharacteristic
428C22×C4⋊C4C22×C7112yes—
429C22×C4⋊C4C22×C7111yescharacteristic
430C22×C4⋊C4C22×C7111yescharacteristic
431C22×C4⋊C4C22×C7112yes—
432C22×C4⋊C4C22×C7112yes—
433C22×C4⋊C4C22×C7112yes—
434C22×C4⋊C4C22×C7111yescharacteristic
435C22×C4⋊C4C22×C7111yescharacteristic
436C22×C22⋊C4C22×C7112yes—
437C22×C22⋊C4C22×C7112yes—
438C22×C22⋊C4C22×C7111yescharacteristic
439C22×C22⋊C4C22×C7111yescharacteristic
440C22×C42C22×C7111yescharacteristic
441C22×C42C22×C7111yescharacteristic
442#396—28no—
443#389—24no—
444#389—24no—
445#384—24no—
446#380—24no—
447#380—24no—
448C4×C22⋊C4—24no—
449C2×#95C22×C7112yes—
450C2×#95C22×C7112yes—
451C2×#95C22×C7112yes—
452C2×#95C22×C7111yescharacteristic
453C2×#95C22×C7111yescharacteristic
454C2×#95C22×C7112yes—
455C2×#95C22×C7112yes—
456C2×#95C22×C7112yes—
457C25C23×C7111yescharacteristic
458C23×C4—22no—
459C23×C4—22no—
460C23×C4—22no—
461C23×C4—22no—
462C23×C4—22no—
463C23×C4—22no—
464C23×C4Q8×C7114yes—
465C23×C4C23×C7112yes—
466C23×C4C23×C7112yes—
467C23×C4C23×C7112yes—
468C23×C4C23×C7112yes—
469C23×C4C23×C7111yescharacteristic
470C23×C4C23×C7111yescharacteristic
471C23×C4C23×C7111yescharacteristic
472C23×C4C23×C7111yescharacteristic
473C23×C4C23×C7111yescharacteristic
474C23×C4C23×C7111yescharacteristic
475C2×C4⋊C4—22no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—22no—
481C2×C4⋊C4—24no—
482C2×C4⋊C4—24no—
483C2×C4⋊C4—22no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—24no—
486C2×C4⋊C4—22no—
487C2×C4⋊C4—24no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—24no—
490C2×C4⋊C4—24no—
491C2×C4⋊C4—24no—
492C2×C4⋊C4—22no—
493C2×C4⋊C4—22no—
494C2×C4⋊C4—42no—
495C2×C4⋊C4—42no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4D4×C7114yes—
498C2×C4⋊C4D4×C7114yes—
499C2×C22⋊C4—22no—
500C2×C22⋊C4—22no—
501C2×C22⋊C4—22no—
502C2×C22⋊C4—22no—
503C2×C22⋊C4—24no—
504C2×C22⋊C4—24no—
505C2×C22⋊C4—24no—
506C2×C22⋊C4—24no—
507C2×C22⋊C4—42no—
508C2×C22⋊C4—42no—
509C2×C22⋊C4D4×C7114yes—
510C2×C22⋊C4Q8×C7114yes—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42D4×C7114yes—
517#95—22no—
518#95—22no—
519#95—24no—
520#95—24no—
521#95—24no—
522#95—24no—
523#95—24no—
524#95—42no—
525C24—21no—
526C24—21no—
527C24—21no—
528C24—21no—
529C24—21no—
530C24—21no—
531C24—21no—
532C24—21no—
533C24—21no—
534C24—21no—
535C24—21no—
536C24—21no—
537C24C2×D4×C7112yes—
538C24C2×Q8×C7112yes—
539C24C2×Q8×C7112yes—
540C24C24×C7111yescharacteristic
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—28no—
580C22×C4—28no—
581C22×C4—28no—
582C22×C4—22no—
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—44no—
597C22×C4—44no—
598C22×C4—44no—
599C22×C4—44no—
600C22×C4C2×D4×C7114yes—
601C22×C4C2×D4×C7112yes—
602C22×C4C2×D4×C7114yes—
603C22×C4C2×D4×C7112yes—
604C22×C4C2×D4×C7112yes—
605C22×C4C2×D4×C7112yes—
606C22×C4C2×D4×C7112yes—
607C22×C4C2×D4×C7112yes—
608C22×C4C2×D4×C7112yes—
609C22×C4C2×Q8×C7112yes—
610C22×C4C2×Q8×C7112yes—
611C22×C4C2×Q8×C7112yes—
612C22×C4C2×Q8×C7112yes—
613C22×C4#41×C7112yes—
614C22×C4#41×C7112yes—
615C22×C4#41×C7112yes—
616C22×C4#41×C7112yes—
617C22×C4#41×C7112yes—
618C4⋊C4—28no—
619C4⋊C4—28no—
620C4⋊C4—48no—
621C4⋊C4—48no—
622C4⋊C4—48no—
623C4⋊C4—48no—
624C4⋊C4—44no—
625C4⋊C4—44no—
626C22⋊C4—28no—
627C22⋊C4—28no—
628C22⋊C4—48no—
629C22⋊C4—48no—
630C42—28no—
631C42—44no—
632C23—22no—
633C23—22no—
634C23—22no—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—22no—
640C23—22no—
641C23—22no—
642C23—22no—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23C4⋊Q8×C7114yes—
667C23C22×D4×C7111yescharacteristic
668C23C22×D4×C7111yescharacteristic
669C23C22×D4×C7111yescharacteristic
670C23C22×D4×C7111yescharacteristic
671C23C22×Q8×C7111yescharacteristic
672C23C22×Q8×C7111yescharacteristic
673C23C2×#41×C7111yescharacteristic
674C23C2×#41×C7111yescharacteristic
675C23C2×#41×C7111yescharacteristic
676C23C2×#41×C7111yescharacteristic
677C23C2×#41×C7111yescharacteristic
678C23H(5,𝔽2)×C7111yescharacteristic
679C23H(5,𝔽2)×C7111yescharacteristic
680C232−1+4×C7111yescharacteristic
681C232−1+4×C7111yescharacteristic
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—24no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—24no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—42no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—41no—
723C2×C4—42no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—41no—
727C2×C4—42no—
728C2×C4—41no—
729C2×C4—416no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—42no—
741C2×C4—42no—
742C2×C4—42no—
743C2×C4—42no—
744C2×C4#121×C7114yes—
745C2×C4#121×C7114yes—
746C2×C4#121×C7114yes—
747C2×C4#121×C7114yes—
748C2×C4C22⋊Q8×C7114yes—
749C2×C4C22⋊Q8×C7114yes—
750C2×C4C22⋊Q8×C7114yes—
751C2×C4C22⋊Q8×C7114yes—
752C2×C4#126×C7114yes—
753C22—24no—
754C22—24no—
755C22—24no—
756C22—42no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—42no—
768C22C2×#121×C7111yescharacteristic
769C22C2×#121×C7111yescharacteristic
770C22C2×#121×C7111yescharacteristic
771C22C2×#121×C7111yescharacteristic
772C22C2×C22⋊Q8×C7111yescharacteristic
773C22C2×C22⋊Q8×C7111yescharacteristic
774C22C2×C22⋊Q8×C7111yescharacteristic
775C22C2×C22⋊Q8×C7111yescharacteristic
776C22C2×#126×C7111yescharacteristic
777C22C2×C4⋊Q8×C7111yescharacteristic
778C22#532×C7111yescharacteristic
779C22#533×C7111yescharacteristic
780C22#533×C7111yescharacteristic
781C22#537×C7111yescharacteristic
782C22#537×C7111yescharacteristic
783C22#540×C7111yescharacteristic
784C22#541×C7111yescharacteristic
785C22#544×C7111yescharacteristic
786C22#544×C7111yescharacteristic
787C22D42×C7111yescharacteristic
788C22D42×C7111yescharacteristic
789C22#546×C7111yescharacteristic
790C22#547×C7111yescharacteristic
791C22#547×C7111yescharacteristic
792C22#547×C7111yescharacteristic
793C22#548×C7111yescharacteristic
794C22D4×Q8×C7111yescharacteristic
795C22D4×Q8×C7111yescharacteristic
796C22#550×C7111yescharacteristic
797C22#552×C7111yescharacteristic
798C22#553×C7111yescharacteristic
799C22#554×C7111yescharacteristic
800C22#554×C7111yescharacteristic
801C22#555×C7111yescharacteristic
802C22#556×C7111yescharacteristic
803C4—24no—
804C4—24no—
805C4—42no—
806C4—44no—
807C4—42no—
808C4—42no—
809C4—44no—
810C4—82no—
811C4—82no—
812C4#396×C7118yescomplemented
813C2—44no—
814C2C2×#396×C7111yescharacteristic
815C2C71×#241611yescharacteristic
816C2C71×#241711yescharacteristic
817C2C71×#242811yescharacteristic
818C2C71×#242911yescharacteristic
819C2C71×#243911yescharacteristic
820C2C71×#244011yescharacteristic
821C2C71×#244011yescharacteristic
822C2C71×#244111yescharacteristic
823C2C71×#249611yescharacteristic
824C2C71×#249711yescharacteristic
825C2C71×#253711yescharacteristic
826C2C71×#253811yescharacteristic
827C2C71×#262911yescharacteristic
828C2C71×#285711yescharacteristic
subgroupG/H
center, socleC24×C71C24
commutator, Frattini, cosocleC24C24×C71
prime radicalC25×C71C23
LCSG ▷ C24 ▷ C1
UCSC1 ◁ C24×C71 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#389×C71C2semidirect
3. C2×#389×C71C2semidirect
4. C2×#384×C71C2semidirect
8. C71×#1441C2semidirect
9. C71×#1441C2semidirect
11. C71×C4⋊#95C2semidirect
397. C4×C71#396semidirect
398. #15131C71direct (N × H)
416. C2×#389C2×C71semidirect
417. C2×#389C2×C71semidirect
418. C2×#384C2×C71semidirect
422. #1441C2×C71semidirect
423. #1441C2×C71semidirect
425. C4⋊#95C2×C71semidirect
426. C71#15131direct (N × H)
812. C4#396×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#396×C712
C2×#389×C712
C2×#384×C712
C2×#380×C712
C2×C4×C22⋊C4×C712
C71×#14412
C71×#14392
C71×C4⋊#952
#1513171