Finite Group Databasebeta

← #32014380

Subgroups — #32014380

Order 18176.

1212 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986051C211yesmaximal, characteristic, complemented
2C2×#17985962C211yesmaximal, characteristic
3C4×C22⋊C4×D71C211yesmaximal, characteristic
4#22588954C211yesmaximal, characteristic, complemented
5#22588952C211yesmaximal, characteristic, complemented
6#22588947C211yesmaximal, characteristic, complemented
7#22588945C211yesmaximal, characteristic, complemented
8#22588525C211yesmaximal, characteristic, complemented
9#22588407C211yesmaximal, characteristic, complemented
10#22588317C211yesmaximal, characteristic, complemented
11#22588249C211yesmaximal, characteristic
12#22588126C211yesmaximal, characteristic, complemented
13#22588121C211yesmaximal, characteristic, complemented
14#22588101C211yesmaximal, characteristic, complemented
15C71×#1851C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C22×#11765849C2211yescharacteristic
18C2×C22⋊C4×D71C411yescharacteristic
19C2×C22⋊C4×D71C411yescharacteristic
20C2×C42×D71C2211yescharacteristic
21C2×C42×D71C2211yescharacteristic
22#17986051—24no—
23C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
24C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
25#17985962—24no—
26C2×C22⋊(C71⋊C8)C2211yescharacteristic
27C2×(C2×D71)⋊C8C2211yescharacteristic
28C2×(C2×D71)⋊C8C2211yescharacteristic
29C2×(C2×D71)⋊C8C2211yescharacteristic
30C2×(C2×D71)⋊C8C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×(C2×D71)⋊C8C2211yescharacteristic
35C2×#14556038C2211yescharacteristic, complemented
36C2×#14556038C2211yescharacteristic, complemented
37C2×C8×Dic71C2211yescharacteristic, complemented
38C2×C8×Dic71C2211yescharacteristic, complemented
39C22⋊C4×Dic71C411yescharacteristic
40C22⋊C4×Dic71C411yescharacteristic
41C4×(C2×D71)⋊C4C2211yescharacteristic
42C4×(C2×D71)⋊C4C2211yescharacteristic
43C4×C22⋊Dic71C2211yescharacteristic
44#17985846C411yescharacteristic
45#17985846C411yescharacteristic
46#95×D71C411yescharacteristic
47#95×D71C411yescharacteristic
48#17985754C2211yescharacteristic, complemented
49#17985754C2211yescharacteristic, complemented
50#17985753C2211yescharacteristic, complemented
51#17985753C2211yescharacteristic, complemented
52#17985753C2211yescharacteristic, complemented
53#17985753C2211yescharacteristic, complemented
54C22×M16×C71C2211yescharacteristic
55C2×C4⋊C8×C71C2211yescharacteristic, complemented
56C2×C4⋊C8×C71C2211yescharacteristic, complemented
57C2×C22⋊C8×C71C2211yescharacteristic
58C4×C22⋊C4×C71C2211yescharacteristic
59#336×C71C2211yescharacteristic, complemented
60#336×C71C2211yescharacteristic, complemented
61C24×D71C2×C411yescharacteristic
62C23×Dic71C2×C411yescharacteristic
63C22×C4×D71—22no—
64C22×C4×D71—22no—
65C22×C4×D71—22no—
66C22×C4×D71—22no—
67C22×C4×D71—41no—
68C22×C4×D71—41no—
69C22×C4×D71C2×C411yescharacteristic
70C22×C4×D71C2×C411yescharacteristic
71C22×C4×D71C2×C411yescharacteristic
72C22×C4×D71C2×C411yescharacteristic
73C22×C4×D71C2×C411yescharacteristic
74C22×C4×D71C2×C411yescharacteristic
75C22×C4×D71C2311yescharacteristic
76C22×C4×D71C2311yescharacteristic
77C2×#11765849—22no—
78C2×#11765849—22no—
79C2×#11765849—41no—
80C22×C71⋊C8C2311yescharacteristic
81C22×C71⋊C8C2311yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C22×C71⋊C8C2311yescharacteristic
84C2×C22⋊Dic71C2×C411yescharacteristic
85C2×C22⋊Dic71C2×C411yescharacteristic
86C2×(C2×D71)⋊C4C2×C411yescharacteristic
87C2×(C2×D71)⋊C4C2×C411yescharacteristic
88C2×(C2×D71)⋊C4C2×C411yescharacteristic
89C2×(C2×D71)⋊C4C2×C411yescharacteristic
90C22⋊C4×D71—24no—
91C22⋊C4×D71—24no—
92C2×C4×Dic71C2×C411yescharacteristic
93C2×C4×Dic71C2×C411yescharacteristic
94C2×C4×Dic71C2×C411yescharacteristic
95C2×C4×Dic71C2×C411yescharacteristic
96C2×C4×Dic71C2311yescharacteristic
97C2×C4×Dic71C2311yescharacteristic
98C42×D71—22no—
99C42×D71—22no—
100C42×D71—41no—
101C42×D71—41no—
102C4⋊(C71⋊C8)—22no—
103C4⋊(C71⋊C8)—41no—
104C22⋊(C71⋊C8)—22no—
105(C2×D71)⋊C8—22no—
106(C2×D71)⋊C8—22no—
107(C2×D71)⋊C8—22no—
108(C2×D71)⋊C8—22no—
109(C2×D71)⋊C8—22no—
110(C2×D71)⋊C8—41no—
111(C2×D71)⋊C8—41no—
112(C2×D71)⋊C8D414yes—
113#14556038—41no—
114#14556038—41no—
115C8×Dic71—22no—
116C8×Dic71—22no—
117C71⋊#95C2×C411yescharacteristic
118C71⋊#95C2×C411yescharacteristic
119C71⋊#95C2×C411yescharacteristic
120C71⋊#95C2×C411yescharacteristic
121C71⋊#95C2×C411yescharacteristic
122C71⋊#95C2×C411yescharacteristic
123C23×C4×C71C2311yescharacteristic
124C2×M16×C71—22no—
125C2×M16×C71—22no—
126C2×M16×C71—41no—
127C22×C8×C71C2311yescharacteristic
128C22×C8×C71C2311yescharacteristic
129C22×C8×C71C2311yescharacteristic
130C22×C8×C71C2311yescharacteristic
131C2×C22⋊C4×C71C2×C411yescharacteristic
132C2×C22⋊C4×C71C2×C411yescharacteristic
133C2×C42×C71C2311yescharacteristic
134C2×C42×C71C2311yescharacteristic
135C4⋊C8×C71—22no—
136C4⋊C8×C71—41no—
137C22⋊C8×C71—22no—
138#95×C71C2×C411yescharacteristic
139#95×C71C2×C411yescharacteristic
140C23×D71—22no—
141C23×D71—22no—
142C23×D71—22no—
143C23×D71—22no—
144C23×D71—22no—
145C23×D71—41no—
146C23×D71—41no—
147C23×D71C22×C411yescharacteristic
148C23×D71C22×C411yescharacteristic
149C22×Dic71—22no—
150C22×Dic71—22no—
151C22×Dic71—41no—
152C22×Dic71C22×C411yescharacteristic
153C22×Dic71C22×C411yescharacteristic
154C22×Dic71C22×C411yescharacteristic
155C22×Dic71C22×C411yescharacteristic
156C22×Dic71C22×C411yescharacteristic
157C22×Dic71C22×C411yescharacteristic
158C2×C4×D71—22no—
159C2×C4×D71—22no—
160C2×C4×D71—21no—
161C2×C4×D71—21no—
162C2×C4×D71—21no—
163C2×C4×D71—21no—
164C2×C4×D71—22no—
165C2×C4×D71—22no—
166C2×C4×D71—22no—
167C2×C4×D71—22no—
168C2×C4×D71—22no—
169C2×C4×D71—22no—
170C2×C4×D71—22no—
171C2×C4×D71—21no—
172C2×C4×D71—21no—
173C2×C4×D71—21no—
174C2×C4×D71—21no—
175C2×C4×D71—21no—
176C2×C4×D71—21no—
177C2×C4×D71—22no—
178C2×C4×D71—22no—
179C2×C4×D71—44no—
180C2×C4×D71—44no—
181C2×C4×D71—44no—
182C2×C4×D71—44no—
183C2×C4×D71—41no—
184C2×C4×D71—41no—
185C2×C4×D71—41no—
186C2×C4×D71—41no—
187C2×C4×D71—41no—
188C2×C4×D71—41no—
189C2×C4×D71M1614yescomplemented
190C2×C4×D71C2×D412yes—
191C2×C4×D71#4112yes—
192#11765849—44no—
193C2×C71⋊C8—21no—
194C2×C71⋊C8—21no—
195C2×C71⋊C8—21no—
196C2×C71⋊C8—21no—
197C2×C71⋊C8—21no—
198C2×C71⋊C8—21no—
199C2×C71⋊C8—21no—
200C2×C71⋊C8—21no—
201C2×C71⋊C8—21no—
202C2×C71⋊C8—21no—
203C2×C71⋊C8—21no—
204C2×C71⋊C8C2×D412yes—
205C22⋊Dic71—22no—
206C22⋊Dic71—22no—
207(C2×D71)⋊C4—22no—
208(C2×D71)⋊C4—22no—
209(C2×D71)⋊C4—22no—
210(C2×D71)⋊C4M1614yescomplemented
211C4×Dic71—21no—
212C4×Dic71—21no—
213C4×Dic71—21no—
214C4×Dic71—21no—
215C4×Dic71—22no—
216C4×Dic71—22no—
217C4×Dic71—41no—
218C4×Dic71—41no—
219C24×C71C22×C411yescharacteristic
220C22×C4×C71—21no—
221C22×C4×C71—21no—
222C22×C4×C71—21no—
223C22×C4×C71—21no—
224C22×C4×C71C22×C411yescharacteristic
225C22×C4×C71C22×C411yescharacteristic
226C22×C4×C71C22×C411yescharacteristic
227C22×C4×C71C22×C411yescharacteristic
228C22×C4×C71C22×C411yescharacteristic
229C22×C4×C71#4112yes—
230C22×C4×C71#4112yes—
231C22×C4×C71C2411yescharacteristic
232M16×C71—44no—
233C2×C8×C71—21no—
234C2×C8×C71—21no—
235C2×C8×C71—21no—
236C2×C8×C71—21no—
237C2×C8×C71—21no—
238C2×C8×C71—21no—
239C2×C8×C71—21no—
240C2×C8×C71—21no—
241C2×C8×C71—21no—
242C2×C8×C71—21no—
243C2×C8×C71—21no—
244C2×C8×C71C2×D412yes—
245C22⋊C4×C71—22no—
246C22⋊C4×C71—22no—
247C42×C71—21no—
248C42×C71—21no—
249C42×C71—21no—
250C42×C71—21no—
251C23×C71—21no—
252C23×C71—21no—
253C23×C71—21no—
254C23×C71—21no—
255C23×C71—21no—
256C23×C71—21no—
257C23×C71#11712yes—
258C23×C71C23×C411yescharacteristic
259C22×D71—21no—
260C22×D71—21no—
261C22×D71—21no—
262C22×D71—21no—
263C22×D71—28no—
264C22×D71—21no—
265C22×D71—21no—
266C22×D71—21no—
267C22×D71—21no—
268C22×D71—21no—
269C22×D71—21no—
270C22×D71—44no—
271C22×D71—44no—
272C22×D71—44no—
273C22×D71—44no—
274C22×D71—44no—
275C22×D71—44no—
276C22×D71C4×D412yes—
277C22×D71C2×M1612yes—
278C22×D71C2×M1612yes—
279C22×D71#13112yes—
280C2×C4×C71—21no—
281C2×C4×C71—21no—
282C2×C4×C71—21no—
283C2×C4×C71—21no—
284C2×C4×C71—21no—
285C2×C4×C71—21no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—21no—
291C2×C4×C71—21no—
292C2×C4×C71—21no—
293C2×C4×C71—21no—
294C2×C4×C71—21no—
295C2×C4×C71—21no—
296C2×C4×C71#11712yes—
297C2×C4×C71C2×M1612yes—
298C2×C4×C71C2×M1612yes—
299C2×C4×C71C22×D411yescharacteristic
300C2×C4×C71C2×#4111yescharacteristic
301C2×C4×C71C2×#4111yescharacteristic
302C2×C4×C71C2×#4111yescharacteristic
303C2×C4×C71H(5,𝔽2)11yescharacteristic
304C2×C4×C71H(5,𝔽2)11yescharacteristic
305C2×Dic71—21no—
306C2×Dic71—21no—
307C2×Dic71—21no—
308C2×Dic71—21no—
309C2×Dic71—21no—
310C2×Dic71—21no—
311C2×Dic71—21no—
312C2×Dic71—21no—
313C2×Dic71—21no—
314C2×Dic71—21no—
315C2×Dic71—21no—
316C2×Dic71—21no—
317C2×Dic71—21no—
318C2×Dic71—21no—
319C2×Dic71—21no—
320C2×Dic71—44no—
321C2×Dic71C4×D412yes—
322C2×Dic71C2×M1612yes—
323C2×Dic71C2×M1612yes—
324C4×D71—28no—
325C4×D71—22no—
326C4×D71—22no—
327C4×D71—22no—
328C4×D71—22no—
329C4×D71—44no—
330C4×D71—44no—
331C4×D71—44no—
332C4×D71—44no—
333C4×D71—44no—
334C4×D71—41no—
335C4×D71—41no—
336C4×D71—41no—
337C4×D71—41no—
338C8×C71—22no—
339C8×C71—41no—
340C8×C71—41no—
341C8×C71—41no—
342C71⋊C8—22no—
343C71⋊C8—41no—
344C71⋊C8—41no—
345C71⋊C8—41no—
346C22×C71—22no—
347C22×C71—22no—
348C22×C71—22no—
349C22×C71—41no—
350C22×C71—41no—
351C22×C71—41no—
352C22×C71—41no—
353C22×C71C2×#11711yescharacteristic
354C22×C71C2×C4×D411yescharacteristic
355C22×C71#51811yescharacteristic
356C22×C71C22×M1611yescharacteristic
357C22×C71C22×M1611yescharacteristic
358C22×C71C2×#13111yescharacteristic
359C22×C71#56811yescharacteristic
360C2×D71—22no—
361C2×D71—22no—
362C2×D71—22no—
363C2×D71—22no—
364C2×D71—22no—
365C2×D71—22no—
366C2×D71—22no—
367C2×D71—22no—
368C2×D71—22no—
369C2×D71—416no—
370C2×D71—41no—
371C2×D71—41no—
372C2×D71—41no—
373C2×D71—41no—
374C2×D71#43514yes—
375C4×C71—22no—
376C4×C71—22no—
377C4×C71—22no—
378C4×C71—41no—
379C4×C71—41no—
380C4×C71#54611yescharacteristic
381C4×C71#54611yescharacteristic
382C4×C71#55111yescharacteristic
383C4×C71#55111yescharacteristic
384Dic71—22no—
385Dic71—22no—
386Dic71—22no—
387Dic71—41no—
388Dic71—41no—
389Dic71—41no—
390#22553—711nomaximal, Sylow
391C2×C71—42no—
392C2×C71#234211yescharacteristic
393C2×C71#292011yescharacteristic
394C2×C71#292411yescharacteristic
395C2×C71C2×#43511yescharacteristic
396C2×C71D4×M1611yescharacteristic
397C2×C71#297411yescharacteristic
398C2×C71#297511yescharacteristic
399D71—24no—
400D71—42no—
401C2×#431—711no—
402C2×#407—711no—
403C2×C4×C22⋊C4—711no—
404#1924—711no—
405#1924—711no—
406#1923—711no—
407#1923—711no—
408#1851—711no—
409#1851D7111yescharacteristic, complemented
410#1817—711no—
411#1797—711no—
412#1779—711no—
413#1753—711no—
414#1753—711no—
415#1749—711no—
416C71#2255311yescharacteristic, complemented, Sylow
417C24×C4—711no—
418C22×M16—711no—
419C22×M16C2×D7111yescharacteristic
420C22×C22⋊C4—711no—
421C22×C22⋊C4—711no—
422C22×C42—711no—
423C22×C42—711no—
424#431—1424no—
425C2×C4⋊C8—711no—
426C2×C4⋊C8—711no—
427C2×C4⋊C8C2×D7111yescharacteristic, complemented
428C2×C4⋊C8C2×D7111yescharacteristic, complemented
429#407—1424no—
430C2×C22⋊C8—711no—
431C2×C22⋊C8—711no—
432C2×C22⋊C8—711no—
433C2×C22⋊C8—711no—
434C2×C22⋊C8—711no—
435C2×C22⋊C8—711no—
436C2×C22⋊C8—711no—
437C2×C22⋊C8—711no—
438C2×C22⋊C8—711no—
439C2×C22⋊C8C2×D7111yescharacteristic
440C2×#97—711no—
441C2×#97—711no—
442C2×C4×C8—711no—
443C2×C4×C8—711no—
444C4×C22⋊C4—711no—
445C4×C22⋊C4—711no—
446C4×C22⋊C4—711no—
447C4×C22⋊C4—711no—
448C4×C22⋊C4—711no—
449C4×C22⋊C4—711no—
450C4×C22⋊C4—711no—
451C4×C22⋊C4C2×D7111yescharacteristic
452C2×#95—711no—
453C2×#95—711no—
454#336—711no—
455#336—711no—
456#336—711no—
457#336—711no—
458#336—711no—
459#336—711no—
460#336C2×D7111yescharacteristic, complemented
461#336C2×D7111yescharacteristic, complemented
462C25—711no—
463C23×C4—2841no—
464C23×C4—2841no—
465C23×C4—711no—
466C23×C4—711no—
467C23×C4—711no—
468C23×C4—711no—
469C23×C4—711no—
470C23×C4—711no—
471C23×C4—711no—
472C23×C4—711no—
473C23×C4—711no—
474C23×C4—1422no—
475C23×C4—1422no—
476C23×C4—1422no—
477C23×C4—1422no—
478C23×C4C22×D7111yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C2×M16—2841no—
483C2×M16—1422no—
484C2×M16—1422no—
485C22×C8—711no—
486C22×C8—711no—
487C22×C8—711no—
488C22×C8—711no—
489C22×C8C22×D7111yescharacteristic
490C22×C8C22×D7111yescharacteristic
491C22×C8C22×D7111yescharacteristic
492C22×C8C22×D7111yescharacteristic
493C2×C22⋊C4—711no—
494C2×C22⋊C4—711no—
495C2×C22⋊C4—711no—
496C2×C22⋊C4—711no—
497C2×C22⋊C4—711no—
498C2×C22⋊C4—711no—
499C2×C22⋊C4—1424no—
500C2×C22⋊C4—1424no—
501C2×C22⋊C4C4×D7111yescharacteristic
502C2×C22⋊C4C4×D7111yescharacteristic
503C2×C42—2841no—
504C2×C42—2841no—
505C2×C42—711no—
506C2×C42—711no—
507C2×C42—711no—
508C2×C42—711no—
509C2×C42—711no—
510C2×C42—711no—
511C2×C42—1422no—
512C2×C42—1422no—
513C2×C42C22×D7111yescharacteristic
514C2×C42C22×D7111yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—41no—
517C4⋊C8—2841no—
518C4⋊C8—1422no—
519C22⋊C8—22no—
520C22⋊C8—2841no—
521C22⋊C8—2841no—
522C22⋊C8—714no—
523C22⋊C8—1422no—
524C22⋊C8—1422no—
525C22⋊C8—1422no—
526C22⋊C8—1422no—
527C22⋊C8—1422no—
528C22⋊C8—1422no—
529#97—2841no—
530#97—2841no—
531C4×C8—1422no—
532C4×C8—1422no—
533#95—711no—
534#95—711no—
535#95—711no—
536#95—711no—
537#95—711no—
538#95—711no—
539#95C4×D7111yescharacteristic
540#95C4×D7111yescharacteristic
541C24—2841no—
542C24—2841no—
543C24—711no—
544C24—711no—
545C24—1422no—
546C24—1422no—
547C24—1422no—
548C24—1422no—
549C24—1422no—
550C24C2×C4×D7111yescharacteristic
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—2844no—
556C22×C4—2844no—
557C22×C4—2844no—
558C22×C4—2844no—
559C22×C4—2841no—
560C22×C4—2841no—
561C22×C4—2841no—
562C22×C4—2841no—
563C22×C4—2841no—
564C22×C4—2841no—
565C22×C4—2841no—
566C22×C4—711no—
567C22×C4—711no—
568C22×C4—711no—
569C22×C4—712no—
570C22×C4—712no—
571C22×C4—714no—
572C22×C4—711no—
573C22×C4—711no—
574C22×C4—711no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1422no—
580C22×C4—1422no—
581C22×C4—1422no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4—1422no—
585C22×C4—1421no—
586C22×C4—1421no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1421no—
590C22×C4—1421no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1421no—
595C22×C4—1421no—
596C22×C4—1421no—
597C22×C4—1421no—
598C22×C4C2×C4×D7111yescharacteristic
599C22×C4C2×C4×D7111yescharacteristic
600C22×C4C2×C4×D7111yescharacteristic
601C22×C4C2×C4×D7111yescharacteristic
602C22×C4C2×C4×D7111yescharacteristic
603C22×C4#1176586412yes—
604C22×C4#1176586612yes—
605C22×C4C23×D7111yescharacteristic
606M16—44no—
607M16—2844no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—712no—
620C2×C8—1421no—
621C2×C8—1421no—
622C2×C8—1421no—
623C2×C8—1421no—
624C2×C8—1421no—
625C2×C8—1421no—
626C2×C8—1421no—
627C2×C8—1421no—
628C2×C8—1421no—
629C2×C8—1421no—
630C2×C8—1421no—
631C2×C8D4×D7112yes—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—714no—
635C22⋊C4—1422no—
636C22⋊C4—1422no—
637C22⋊C4—1422no—
638C22⋊C4—1422no—
639C22⋊C4—1422no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—2841no—
645C42—2841no—
646C42—1422no—
647C42—1422no—
648C42—1421no—
649C42—1421no—
650C42—1421no—
651C42—1421no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—2844no—
659C23—2844no—
660C23—2844no—
661C23—2844no—
662C23—2844no—
663C23—2844no—
664C23—712no—
665C23—712no—
666C23—712no—
667C23—712no—
668C23—1428no—
669C23—1421no—
670C23—1421no—
671C23—1421no—
672C23—1421no—
673C23—1421no—
674C23—1421no—
675C23—1421no—
676C23—1421no—
677C23—1421no—
678C23—1421no—
679C23#1455608612yes—
680C23C22×C4×D7111yescharacteristic
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—2844no—
698C2×C4—2844no—
699C2×C4—2844no—
700C2×C4—2844no—
701C2×C4—2844no—
702C2×C4—2844no—
703C2×C4—2841no—
704C2×C4—2841no—
705C2×C4—2841no—
706C2×C4—2841no—
707C2×C4—712no—
708C2×C4—712no—
709C2×C4—712no—
710C2×C4—1428no—
711C2×C4—1421no—
712C2×C4—1421no—
713C2×C4—1421no—
714C2×C4—1421no—
715C2×C4—1421no—
716C2×C4—1421no—
717C2×C4—1421no—
718C2×C4—1421no—
719C2×C4—1421no—
720C2×C4—1421no—
721C2×C4—1421no—
722C2×C4—1421no—
723C2×C4—1421no—
724C2×C4—1421no—
725C2×C4—1421no—
726C2×C4—1422no—
727C2×C4—1422no—
728C2×C4—1422no—
729C2×C4—1422no—
730C2×C4#1455608612yes—
731C2×C4M16×D7112yes—
732C2×C4M16×D7112yes—
733C2×C4C2×D4×D7111yescharacteristic
734C2×C4#41×D7111yescharacteristic
735C2×C4C2×#1176586411yescharacteristic
736C2×C4C2×#1176586611yescharacteristic
737C2×C4#1455617311yescharacteristic
738C2×C4#1455617411yescharacteristic
739C8—22no—
740C8—41no—
741C8—41no—
742C8—41no—
743C8—2841no—
744C8—2841no—
745C8—2841no—
746C8—1422no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—28416no—
755C22—2841no—
756C22—2841no—
757C22—2841no—
758C22—2841no—
759C22—714no—
760C22—1422no—
761C22—1422no—
762C22—1422no—
763C22—1422no—
764C22—1422no—
765C22—1422no—
766C22—1422no—
767C22—1422no—
768C22—1422no—
769C22C2×#1455608611yescharacteristic
770C22C4×D4×D7111yescharacteristic
771C22#1798647111yescharacteristic
772C22C2×M16×D7111yescharacteristic
773C22C2×M16×D7111yescharacteristic
774C22#131×D7111yescharacteristic
775C22#1798676411yescharacteristic
776C4—22no—
777C4—22no—
778C4—22no—
779C4—41no—
780C4—41no—
781C4—2841no—
782C4—2841no—
783C4—2841no—
784C4—1422no—
785C4—1422no—
786C4—1422no—
787C4#1798663611yescharacteristic
788C4#1798664011yescharacteristic
789C4#1798667211yescharacteristic
790C4#1798667611yescharacteristic
791C2—42no—
792C2—2842no—
793C2—1424no—
794C2#2259118711yescharacteristic
795C2#2259697211yescharacteristic
796C2#2259699711yescharacteristic
797C2#435×D7111yescharacteristic
798C2#2259707611yescharacteristic
799C2#2259737011yescharacteristic
800C2#2259737811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1851C2
prime radicalC24×D71C2×C4
cosocleC22×C4×C71C24
hypercenter#1851D71
hypocenterC71#22553
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#17986051C2semidirect
4. #22588954C2semidirect
5. #22588952C2semidirect
6. #22588947C2semidirect
7. #22588945C2semidirect
8. #22588525C2semidirect
9. #22588407C2semidirect
10. #22588317C2semidirect
12. #22588126C2semidirect
13. #22588121C2semidirect
14. #22588101C2semidirect
15. C71×#1851C2semidirect
23. C2×C4⋊(C71⋊C8)C22semidirect
24. C2×C4⋊(C71⋊C8)C22semidirect
35. C2×#14556038C22semidirect
36. C2×#14556038C22semidirect
37. C2×C8×Dic71C22semidirect
38. C2×C8×Dic71C22semidirect
48. #17985754C22semidirect
49. #17985754C22semidirect
50. #17985753C22semidirect
51. #17985753C22semidirect
52. #17985753C22semidirect
53. #17985753C22semidirect
55. C2×C4⋊C8×C71C22semidirect
56. C2×C4⋊C8×C71C22semidirect
59. #336×C71C22semidirect
60. #336×C71C22semidirect
189. C2×C4×D71M16semidirect
210. (C2×D71)⋊C4M16semidirect
409. #1851D71semidirect
416. C71#22553semidirect
427. C2×C4⋊C8C2×D71semidirect
428. C2×C4⋊C8C2×D71semidirect
460. #336C2×D71semidirect
461. #336C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860512
C2×#179859622
C4×C22⋊C4×D712
#225889542
#225889522
#225889472
#225889452
#225885252
#225884072
#225883172
#225882492
#225881262
#225881212
#225881012
C71×#18512
#2255371