Finite Group Databasebeta

← C71×#23580 #31844452

Subgroups — C71×#23580 #31844452

Order 18176.

1242 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#540×C71C211yesmaximal, characteristic, complemented
2C2×#442×C71C211yesmaximal, characteristic, complemented
3C2×C4×D8×C71C211yesmaximal, characteristic, complemented
4C71×#2324C211yesmaximal, characteristic, complemented
5C71×#2059C211yesmaximal, characteristic, complemented
6C71×#2041C211yesmaximal, characteristic, complemented
7C71×#2034C211yesmaximal, characteristic, complemented
8C71×#2033C211yesmaximal, characteristic, complemented
9C71×#2025C211yesmaximal, characteristic, complemented
10C71×#2011C211yesmaximal, characteristic, complemented
11C71×#1999C211yesmaximal, characteristic, complemented
12C71×#1999C211yesmaximal, characteristic, complemented
13C71×#1762C211yesmaximal, characteristic, complemented
14C4×#102×C71C211yesmaximal, characteristic, complemented
15C71×#1750C211yesmaximal, characteristic, complemented
16C22×D8×C71C2211yescharacteristic
17C22×D8×C71C2211yescharacteristic
18#540×C71—24no—
19#540×C71—24no—
20C2×#127×C71C2211yescharacteristic
21C2×#125×C71C2211yescharacteristic
22C2×#123×C71—21no—
23C2×#123×C71—21no—
24C2×#121×C71—21no—
25C2×#121×C71—21no—
26C2×#121×C71C2211yescharacteristic
27C2×#121×C71C2211yescharacteristic
28C2×#121×C71C2211yescharacteristic
29C2×C4×D4×C71C2211yescharacteristic
30C2×C4×D4×C71C2211yescharacteristic
31C2×C4×D4×C71C2211yescharacteristic
32C2×#117×C71C2211yescharacteristic
33#442×C71—24no—
34C4×D8×C71—24no—
35C2×#107×C71C2211yescharacteristic
36C2×#106×C71C2211yescharacteristic
37C2×#102×C71C2211yescharacteristic
38C2×#102×C71C2211yescharacteristic
39C2×#102×C71C2211yescharacteristic
40C2×#102×C71C2211yescharacteristic
41C2×#102×C71C2211yescharacteristic
42C2×#102×C71C2211yescharacteristic
43C2×#102×C71C2211yescharacteristic
44C2×#102×C71C2211yescharacteristic
45C2×C22⋊C8×C71C2211yescharacteristic
46C2×C22⋊C8×C71C2211yescharacteristic
47C2×#97×C71C2211yescharacteristic
48C2×C4×C8×C71C2211yescharacteristic
49#390×C71—21no—
50#390×C71C2211yescharacteristic
51#389×C71C2211yescharacteristic
52#388×C71—21no—
53#386×C71—21no—
54#385×C71—21no—
55#380×C71C2211yescharacteristic
56C4×C4⋊C4×C71C2211yescharacteristic
57#340×C71C2211yescharacteristic
58#340×C71C2211yescharacteristic
59#340×C71C2211yescharacteristic
60#340×C71C2211yescharacteristic
61#336×C71C2211yescharacteristic
62#336×C71C2211yescharacteristic
63C22×D4×C71—21no—
64C22×D4×C71—21no—
65C22×D4×C71—21no—
66C22×D4×C71—21no—
67C22×D4×C71—21no—
68C22×D4×C71C2311yescharacteristic
69C22×D4×C71C2311yescharacteristic
70C22×D4×C71C2311yescharacteristic
71C23×C4×C71—21no—
72C23×C4×C71—21no—
73C23×C4×C71—21no—
74C23×C4×C71C2311yescharacteristic
75C2×D8×C71—22no—
76C2×D8×C71—22no—
77C2×D8×C71—22no—
78C2×D8×C71—22no—
79C2×D8×C71—22no—
80C2×D8×C71—22no—
81C22×C8×C71C2311yescharacteristic
82C22×C8×C71C2311yescharacteristic
83C22×C8×C71C2311yescharacteristic
84C22×C8×C71C2311yescharacteristic
85#127×C71—22no—
86#127×C71—22no—
87#125×C71—22no—
88#125×C71—22no—
89#123×C71—28no—
90#123×C71—28no—
91#121×C71—28no—
92#121×C71—28no—
93#121×C71—22no—
94#121×C71—22no—
95#121×C71—22no—
96#121×C71—22no—
97#121×C71—22no—
98#121×C71—22no—
99C4×D4×C71—22no—
100C4×D4×C71—22no—
101C4×D4×C71—22no—
102C4×D4×C71—22no—
103C4×D4×C71D414yescomplemented
104C4×D4×C71D414yescomplemented
105#117×C71—22no—
106#117×C71—22no—
107C2×C4⋊C4×C71—21no—
108C2×C4⋊C4×C71—21no—
109C2×C4⋊C4×C71—21no—
110C2×C4⋊C4×C71D411yescharacteristic
111C2×C4⋊C4×C71D411yescharacteristic
112C2×C4⋊C4×C71C2311yescharacteristic
113C2×C4⋊C4×C71C2311yescharacteristic
114C2×C4⋊C4×C71C2311yescharacteristic
115C2×C4⋊C4×C71C2311yescharacteristic
116C2×C4⋊C4×C71C2311yescharacteristic
117C2×C22⋊C4×C71—21no—
118C2×C22⋊C4×C71—21no—
119C2×C22⋊C4×C71—21no—
120C2×C22⋊C4×C71—21no—
121C2×C22⋊C4×C71—21no—
122C2×C22⋊C4×C71—21no—
123C2×C22⋊C4×C71—21no—
124C2×C22⋊C4×C71—21no—
125C2×C22⋊C4×C71—21no—
126C2×C22⋊C4×C71D411yescharacteristic
127C2×C22⋊C4×C71D411yescharacteristic
128C2×C42×C71—21no—
129C2×C42×C71C2311yescharacteristic
130C2×C42×C71C2311yescharacteristic
131#107×C71—22no—
132#106×C71—22no—
133#102×C71—22no—
134#102×C71—22no—
135#102×C71—22no—
136#102×C71—22no—
137#102×C71—22no—
138#102×C71—22no—
139#102×C71—22no—
140#102×C71—22no—
141C22⋊C8×C71—22no—
142C22⋊C8×C71—22no—
143#97×C71—22no—
144C4×C8×C71—22no—
145#95×C71—21no—
146#95×C71—21no—
147#95×C71—21no—
148C24×C71—21no—
149C24×C71—21no—
150C24×C71—21no—
151C24×C71C2×D411yescharacteristic
152C2×D4×C71—24no—
153C2×D4×C71—24no—
154C2×D4×C71—24no—
155C2×D4×C71—24no—
156C2×D4×C71—24no—
157C2×D4×C71—21no—
158C2×D4×C71—21no—
159C2×D4×C71—21no—
160C2×D4×C71—21no—
161C2×D4×C71—21no—
162C2×D4×C71—21no—
163C2×D4×C71—21no—
164C2×D4×C71—21no—
165C2×D4×C71—21no—
166C2×D4×C71—21no—
167C2×D4×C71—21no—
168C2×D4×C71—21no—
169C2×D4×C71—21no—
170C2×D4×C71—21no—
171C2×D4×C71—21no—
172C2×D4×C71—81no—
173C2×D4×C71—81no—
174C2×D4×C71—81no—
175C2×D4×C71—81no—
176C2×D4×C71—81no—
177C2×D4×C71—81no—
178C2×D4×C71—81no—
179C2×D4×C71—81no—
180C2×D4×C71—81no—
181C2×D4×C71—81no—
182C2×D4×C71C2×D412yes—
183C2×D4×C71C2×D412yes—
184C2×D4×C71#4112yes—
185C22×C4×C71—21no—
186C22×C4×C71—21no—
187C22×C4×C71—21no—
188C22×C4×C71—21no—
189C22×C4×C71—21no—
190C22×C4×C71—21no—
191C22×C4×C71—21no—
192C22×C4×C71—21no—
193C22×C4×C71—21no—
194C22×C4×C71—24no—
195C22×C4×C71—24no—
196C22×C4×C71—21no—
197C22×C4×C71—21no—
198C22×C4×C71—42no—
199C22×C4×C71—81no—
200C22×C4×C71—81no—
201C22×C4×C71—81no—
202C22×C4×C71—81no—
203C22×C4×C71—81no—
204C22×C4×C71—81no—
205C22×C4×C71C2×D411yescharacteristic
206C22×C4×C71C2×D411yescharacteristic
207C22×C4×C71C2×D411yescharacteristic
208C22×C4×C71C2×D411yescharacteristic
209C22×C4×C71C2×D411yescharacteristic
210C22×C4×C71C2411yescharacteristic
211D8×C71—28no—
212D8×C71—28no—
213C2×C8×C71—21no—
214C2×C8×C71—21no—
215C2×C8×C71—21no—
216C2×C8×C71—21no—
217C2×C8×C71—21no—
218C2×C8×C71—21no—
219C2×C8×C71—21no—
220C2×C8×C71—21no—
221C2×C8×C71—21no—
222C2×C8×C71—21no—
223C2×C8×C71#4112yes—
224C2×C8×C71#4112yes—
225C4⋊C4×C71—24no—
226C4⋊C4×C71—24no—
227C4⋊C4×C71—22no—
228C4⋊C4×C71—22no—
229C4⋊C4×C71—21no—
230C4⋊C4×C71—21no—
231C4⋊C4×C71—21no—
232C4⋊C4×C71—21no—
233C4⋊C4×C71—21no—
234C4⋊C4×C71—21no—
235C4⋊C4×C71—21no—
236C4⋊C4×C71—81no—
237C4⋊C4×C71C2×D412yes—
238C4⋊C4×C71C2×D412yes—
239C4⋊C4×C71#4112yes—
240C22⋊C4×C71—24no—
241C22⋊C4×C71—24no—
242C22⋊C4×C71—24no—
243C22⋊C4×C71—24no—
244C22⋊C4×C71—24no—
245C22⋊C4×C71—22no—
246C22⋊C4×C71—22no—
247C22⋊C4×C71—42no—
248C22⋊C4×C71—81no—
249C22⋊C4×C71—81no—
250C22⋊C4×C71—81no—
251C42×C71—21no—
252C42×C71—21no—
253C42×C71—81no—
254C42×C71C2×D412yes—
255C42×C71C2×D412yes—
256C23×C71—21no—
257C23×C71—22no—
258C23×C71—22no—
259C23×C71—22no—
260C23×C71—21no—
261C23×C71—21no—
262C23×C71—21no—
263C23×C71—21no—
264C23×C71—21no—
265C23×C71—21no—
266C23×C71—41no—
267C23×C71—41no—
268C23×C71—41no—
269C23×C71—41no—
270C23×C71—41no—
271C23×C71—41no—
272C23×C71—41no—
273C23×C71—41no—
274C23×C71—41no—
275C23×C71—41no—
276C23×C71—41no—
277C23×C71—41no—
278C23×C71—41no—
279C23×C71—41no—
280C23×C71—41no—
281C23×C71—41no—
282C23×C71—41no—
283C23×C71—41no—
284C23×C71C22×D411yescharacteristic
285D4×C71—22no—
286D4×C71—22no—
287D4×C71—22no—
288D4×C71—22no—
289D4×C71—22no—
290D4×C71—22no—
291D4×C71—41no—
292D4×C71—41no—
293D4×C71—41no—
294D4×C71—41no—
295D4×C71—41no—
296D4×C71—41no—
297D4×C71—84no—
298D4×C71—84no—
299D4×C71—84no—
300D4×C71—84no—
301D4×C71—84no—
302C2×C4×C71—21no—
303C2×C4×C71—21no—
304C2×C4×C71—21no—
305C2×C4×C71—21no—
306C2×C4×C71—21no—
307C2×C4×C71—21no—
308C2×C4×C71—21no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—21no—
312C2×C4×C71—22no—
313C2×C4×C71—21no—
314C2×C4×C71—21no—
315C2×C4×C71—21no—
316C2×C4×C71—21no—
317C2×C4×C71—21no—
318C2×C4×C71—41no—
319C2×C4×C71—41no—
320C2×C4×C71—41no—
321C2×C4×C71—41no—
322C2×C4×C71—41no—
323C2×C4×C71—41no—
324C2×C4×C71—41no—
325C2×C4×C71—41no—
326C2×C4×C71—41no—
327C2×C4×C71—41no—
328C2×C4×C71—41no—
329C2×C4×C71—41no—
330C2×C4×C71—41no—
331C2×C4×C71—41no—
332C2×C4×C71—41no—
333C2×C4×C71—41no—
334C2×C4×C71—84no—
335C2×C4×C71—84no—
336C2×C4×C71—84no—
337C2×C4×C71#12012yes—
338C2×C4×C71#12012yes—
339C2×C4×C71C22×D411yescharacteristic
340C2×C4×C71C22×D411yescharacteristic
341C2×C4×C71C2×#4111yescharacteristic
342C2×C4×C71C2×#4111yescharacteristic
343C2×C4×C71C2×#4111yescharacteristic
344C2×C4×C71C2×#4111yescharacteristic
345C8×C71—22no—
346C8×C71—22no—
347C8×C71—41no—
348C8×C71—41no—
349C22×C71—41no—
350C22×C71—42no—
351C22×C71—41no—
352C22×C71—42no—
353C22×C71—41no—
354C22×C71—42no—
355C22×C71—42no—
356C22×C71—42no—
357C22×C71—41no—
358C22×C71—41no—
359C22×C71—42no—
360C22×C71—41no—
361C22×C71—42no—
362C22×C71—42no—
363C22×C71—41no—
364C22×C71—42no—
365C22×C71—81no—
366C22×C71—81no—
367C22×C71—81no—
368C22×C71—81no—
369C22×C71—81no—
370C22×C71—81no—
371C22×C71—81no—
372C22×C71—81no—
373C22×C71—81no—
374C22×C71—81no—
375C22×C71—81no—
376C22×C71—81no—
377C22×C71C2×#12011yescharacteristic
378C22×C71#52511yescharacteristic
379C22×C71#53211yescharacteristic
380C22×C71#57611yescharacteristic
381C22×C71#57611yescharacteristic
382C22×C71#57611yescharacteristic
383C22×C71#57711yescharacteristic
384C4×C71—22no—
385C4×C71—22no—
386C4×C71—42no—
387C4×C71—41no—
388C4×C71—41no—
389C4×C71—42no—
390C4×C71—41no—
391C4×C71—42no—
392C4×C71—81no—
393C4×C71—81no—
394C4×C71#52511yescharacteristic
395C4×C71#52511yescharacteristic
396C4×C71#53211yescharacteristic
397C4×C71#53211yescharacteristic
398#23580C7111yesmaximal, characteristic, direct product factor, Sylow
399C2×C71—81no—
400C2×C71—82no—
401C2×C71—82no—
402C2×C71—82no—
403C2×C71#238811yescharacteristic
404C2×C71#300811yescharacteristic
405C2×C71#301211yescharacteristic
406C2×C71#311911yescharacteristic
407C2×C71#312211yescharacteristic
408C2×C71#317611yescharacteristic
409C2×C71#317911yescharacteristic
410C2×#540C2×C7111yescharacteristic, complemented
411C2×#442C2×C7111yescharacteristic, complemented
412C2×C4×D8C2×C7111yescharacteristic, complemented
413#2324C2×C7111yescharacteristic, complemented
414#2059C2×C7111yescharacteristic, complemented
415#2041C2×C7111yescharacteristic, complemented
416#2034C2×C7111yescharacteristic, complemented
417#2033C2×C7111yescharacteristic, complemented
418#2025C2×C7111yescharacteristic, complemented
419#2011C2×C7111yescharacteristic, complemented
420#1999C2×C7111yescharacteristic, complemented
421#1999C2×C7111yescharacteristic, complemented
422#1762C2×C7111yescharacteristic, complemented
423C4×#102C2×C7111yescharacteristic, complemented
424#1750C2×C7111yescharacteristic, complemented
425C71#2358011yescharacteristic, direct product factor, Sylow
426C22×D8C22×C7111yescharacteristic
427C22×D8C22×C7111yescharacteristic
428#540—24no—
429#540—24no—
430C2×#127C22×C7111yescharacteristic
431C2×#125C22×C7111yescharacteristic
432C2×#123—21no—
433C2×#123—21no—
434C2×#121—21no—
435C2×#121—21no—
436C2×#121C22×C7111yescharacteristic
437C2×#121C22×C7111yescharacteristic
438C2×#121C22×C7111yescharacteristic
439C2×C4×D4C22×C7111yescharacteristic
440C2×C4×D4C22×C7111yescharacteristic
441C2×C4×D4C22×C7111yescharacteristic
442C2×#117C22×C7111yescharacteristic
443#442—24no—
444C4×D8—24no—
445C2×#107C22×C7111yescharacteristic
446C2×#106C22×C7111yescharacteristic
447C2×#102C22×C7111yescharacteristic
448C2×#102C22×C7111yescharacteristic
449C2×#102C22×C7111yescharacteristic
450C2×#102C22×C7111yescharacteristic
451C2×#102C22×C7111yescharacteristic
452C2×#102C22×C7111yescharacteristic
453C2×#102C22×C7111yescharacteristic
454C2×#102C22×C7111yescharacteristic
455C2×C22⋊C8C22×C7111yescharacteristic
456C2×C22⋊C8C22×C7111yescharacteristic
457C2×#97C22×C7111yescharacteristic
458C2×C4×C8C22×C7111yescharacteristic
459#390—21no—
460#390C22×C7111yescharacteristic
461#389C22×C7111yescharacteristic
462#388—21no—
463#386—21no—
464#385—21no—
465#380C22×C7111yescharacteristic
466C4×C4⋊C4C22×C7111yescharacteristic
467#340C22×C7111yescharacteristic
468#340C22×C7111yescharacteristic
469#340C22×C7111yescharacteristic
470#340C22×C7111yescharacteristic
471#336C22×C7111yescharacteristic
472#336C22×C7111yescharacteristic
473C22×D4—21no—
474C22×D4—21no—
475C22×D4—21no—
476C22×D4—21no—
477C22×D4—21no—
478C22×D4C23×C7111yescharacteristic
479C22×D4C23×C7111yescharacteristic
480C22×D4C23×C7111yescharacteristic
481C23×C4—21no—
482C23×C4—21no—
483C23×C4—21no—
484C23×C4C23×C7111yescharacteristic
485C2×D8—22no—
486C2×D8—22no—
487C2×D8—22no—
488C2×D8—22no—
489C2×D8—22no—
490C2×D8—22no—
491C22×C8C23×C7111yescharacteristic
492C22×C8C23×C7111yescharacteristic
493C22×C8C23×C7111yescharacteristic
494C22×C8C23×C7111yescharacteristic
495#127—22no—
496#127—22no—
497#125—22no—
498#125—22no—
499#123—28no—
500#123—28no—
501#121—28no—
502#121—28no—
503#121—22no—
504#121—22no—
505#121—22no—
506#121—22no—
507#121—22no—
508#121—22no—
509C4×D4—22no—
510C4×D4—22no—
511C4×D4—22no—
512C4×D4—22no—
513C4×D4D4×C7114yescomplemented
514C4×D4D4×C7114yescomplemented
515#117—22no—
516#117—22no—
517C2×C4⋊C4—21no—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4D4×C7111yescharacteristic
521C2×C4⋊C4D4×C7111yescharacteristic
522C2×C4⋊C4C23×C7111yescharacteristic
523C2×C4⋊C4C23×C7111yescharacteristic
524C2×C4⋊C4C23×C7111yescharacteristic
525C2×C4⋊C4C23×C7111yescharacteristic
526C2×C4⋊C4C23×C7111yescharacteristic
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—21no—
530C2×C22⋊C4—21no—
531C2×C22⋊C4—21no—
532C2×C22⋊C4—21no—
533C2×C22⋊C4—21no—
534C2×C22⋊C4—21no—
535C2×C22⋊C4—21no—
536C2×C22⋊C4D4×C7111yescharacteristic
537C2×C22⋊C4D4×C7111yescharacteristic
538C2×C42—21no—
539C2×C42C23×C7111yescharacteristic
540C2×C42C23×C7111yescharacteristic
541#107—22no—
542#106—22no—
543#102—22no—
544#102—22no—
545#102—22no—
546#102—22no—
547#102—22no—
548#102—22no—
549#102—22no—
550#102—22no—
551C22⋊C8—22no—
552C22⋊C8—22no—
553#97—22no—
554C4×C8—22no—
555#95—21no—
556#95—21no—
557#95—21no—
558C24—21no—
559C24—21no—
560C24—21no—
561C24C2×D4×C7111yescharacteristic
562C2×D4—24no—
563C2×D4—24no—
564C2×D4—24no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—21no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—81no—
583C2×D4—81no—
584C2×D4—81no—
585C2×D4—81no—
586C2×D4—81no—
587C2×D4—81no—
588C2×D4—81no—
589C2×D4—81no—
590C2×D4—81no—
591C2×D4—81no—
592C2×D4C2×D4×C7112yes—
593C2×D4C2×D4×C7112yes—
594C2×D4#41×C7112yes—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—42no—
609C22×C4—81no—
610C22×C4—81no—
611C22×C4—81no—
612C22×C4—81no—
613C22×C4—81no—
614C22×C4—81no—
615C22×C4C2×D4×C7111yescharacteristic
616C22×C4C2×D4×C7111yescharacteristic
617C22×C4C2×D4×C7111yescharacteristic
618C22×C4C2×D4×C7111yescharacteristic
619C22×C4C2×D4×C7111yescharacteristic
620C22×C4C24×C7111yescharacteristic
621D8—28no—
622D8—28no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8#41×C7112yes—
634C2×C8#41×C7112yes—
635C4⋊C4—24no—
636C4⋊C4—24no—
637C4⋊C4—22no—
638C4⋊C4—22no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—81no—
647C4⋊C4C2×D4×C7112yes—
648C4⋊C4C2×D4×C7112yes—
649C4⋊C4#41×C7112yes—
650C22⋊C4—24no—
651C22⋊C4—24no—
652C22⋊C4—24no—
653C22⋊C4—24no—
654C22⋊C4—24no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—42no—
658C22⋊C4—81no—
659C22⋊C4—81no—
660C22⋊C4—81no—
661C42—21no—
662C42—21no—
663C42—81no—
664C42C2×D4×C7112yes—
665C42C2×D4×C7112yes—
666C23—21no—
667C23—22no—
668C23—22no—
669C23—22no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—41no—
683C23—41no—
684C23—41no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—41no—
689C23—41no—
690C23—41no—
691C23—41no—
692C23—41no—
693C23—41no—
694C23C22×D4×C7111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—84no—
708D4—84no—
709D4—84no—
710D4—84no—
711D4—84no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—21no—
722C2×C4—22no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—84no—
745C2×C4—84no—
746C2×C4—84no—
747C2×C4#120×C7112yes—
748C2×C4#120×C7112yes—
749C2×C4C22×D4×C7111yescharacteristic
750C2×C4C22×D4×C7111yescharacteristic
751C2×C4C2×#41×C7111yescharacteristic
752C2×C4C2×#41×C7111yescharacteristic
753C2×C4C2×#41×C7111yescharacteristic
754C2×C4C2×#41×C7111yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C22—41no—
760C22—42no—
761C22—41no—
762C22—42no—
763C22—41no—
764C22—42no—
765C22—42no—
766C22—42no—
767C22—41no—
768C22—41no—
769C22—42no—
770C22—41no—
771C22—42no—
772C22—42no—
773C22—41no—
774C22—42no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—81no—
781C22—81no—
782C22—81no—
783C22—81no—
784C22—81no—
785C22—81no—
786C22—81no—
787C22C2×#120×C7111yescharacteristic
788C22#525×C7111yescharacteristic
789C22#532×C7111yescharacteristic
790C22#576×C7111yescharacteristic
791C22#576×C7111yescharacteristic
792C22#576×C7111yescharacteristic
793C22#577×C7111yescharacteristic
794C4—22no—
795C4—22no—
796C4—42no—
797C4—41no—
798C4—41no—
799C4—42no—
800C4—41no—
801C4—42no—
802C4—81no—
803C4—81no—
804C4#525×C7111yescharacteristic
805C4#525×C7111yescharacteristic
806C4#532×C7111yescharacteristic
807C4#532×C7111yescharacteristic
808C2—81no—
809C2—82no—
810C2—82no—
811C2—82no—
812C2C71×#238811yescharacteristic
813C2C71×#300811yescharacteristic
814C2C71×#301211yescharacteristic
815C2C71×#311911yescharacteristic
816C2C71×#312211yescharacteristic
817C2C71×#317611yescharacteristic
818C2C71×#317911yescharacteristic
subgroupG/H
center, socleC23×C71C22×D4
commutator, Frattini, cosocleC22×C4C24×C71
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C71 ◁ C2×#117×C71 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#540×C71C2semidirect
2. C2×#442×C71C2semidirect
3. C2×C4×D8×C71C2semidirect
4. C71×#2324C2semidirect
5. C71×#2059C2semidirect
6. C71×#2041C2semidirect
7. C71×#2034C2semidirect
8. C71×#2033C2semidirect
9. C71×#2025C2semidirect
10. C71×#2011C2semidirect
11. C71×#1999C2semidirect
12. C71×#1999C2semidirect
13. C71×#1762C2semidirect
14. C4×#102×C71C2semidirect
15. C71×#1750C2semidirect
103. C4×D4×C71D4semidirect
104. C4×D4×C71D4semidirect
398. #23580C71direct (N × H)
410. C2×#540C2×C71semidirect
411. C2×#442C2×C71semidirect
412. C2×C4×D8C2×C71semidirect
413. #2324C2×C71semidirect
414. #2059C2×C71semidirect
415. #2041C2×C71semidirect
416. #2034C2×C71semidirect
417. #2033C2×C71semidirect
418. #2025C2×C71semidirect
419. #2011C2×C71semidirect
420. #1999C2×C71semidirect
421. #1999C2×C71semidirect
422. #1762C2×C71semidirect
423. C4×#102C2×C71semidirect
424. #1750C2×C71semidirect
425. C71#23580direct (N × H)
513. C4×D4D4×C71semidirect
514. C4×D4D4×C71semidirect

Maximal subgroups

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

subgroupindex
C2×#540×C712
C2×#442×C712
C2×C4×D8×C712
C71×#23242
C71×#20592
C71×#20412
C71×#20342
C71×#20332
C71×#20252
C71×#20112
C71×#19992
C71×#17622
C4×#102×C712
C71×#17502
#2358071