Finite Group Databasebeta

← #32007474

Subgroups — #32007474

Order 18176.

1122 conjugacy classes of subgroups.

The subgroup lattice has 786 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×C22⋊C4×D71C211yesmaximal, characteristic
2#22588949C211yesmaximal, characteristic, complemented
3#22588948C211yesmaximal, characteristic, complemented
4#22588947C211yesmaximal, characteristic, complemented
5#22588946C211yesmaximal, characteristic, complemented
6#22588945C211yesmaximal, characteristic, complemented
7#22588944C211yesmaximal, characteristic, complemented
8#22588943C211yesmaximal, characteristic, complemented
9#22588319C211yesmaximal, characteristic, complemented
10#22588317C211yesmaximal, characteristic, complemented
11#22588249C211yesmaximal, characteristic
12#22588249C211yesmaximal, characteristic
13C4×(C2×D71)⋊C8C211yesmaximal, characteristic, complemented
14#22588097C211yesmaximal, characteristic, complemented
15C71×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C2×C22⋊C4×D71C411yescharacteristic
18C2×C22⋊C4×D71C411yescharacteristic
19C2×C42×D71C2211yescharacteristic
20C2×C42×D71C2211yescharacteristic
21C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
22C2×Dic71⋊C8C2211yescharacteristic, complemented
23C2×Dic71⋊C8C2211yescharacteristic, complemented
24C2×C22⋊(C71⋊C8)C2211yescharacteristic
25C2×C22⋊(C71⋊C8)C2211yescharacteristic
26C2×(C2×D71)⋊C8C2211yescharacteristic
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×C4×C71⋊C8C2211yescharacteristic, complemented
35C2×C8×Dic71C2211yescharacteristic, complemented
36C2×C8×Dic71C2211yescharacteristic, complemented
37C22⋊C4×Dic71C411yescharacteristic
38C22⋊C4×Dic71C411yescharacteristic
39C4×(C2×D71)⋊C4C2211yescharacteristic
40C4×(C2×D71)⋊C4C2211yescharacteristic
41C4×C22⋊Dic71C2211yescharacteristic
42#17985846C411yescharacteristic
43#17985846C411yescharacteristic
44#95×D71C411yescharacteristic
45#95×D71C411yescharacteristic
46#17985754C2211yescharacteristic, complemented
47#17985754C2211yescharacteristic, complemented
48#17985753C2211yescharacteristic, complemented
49#17985753C2211yescharacteristic, complemented
50#17985753C2211yescharacteristic, complemented
51#17985753C2211yescharacteristic, complemented
52C2×C4⋊C8×C71C2211yescharacteristic, complemented
53C2×C22⋊C8×C71C2211yescharacteristic
54C2×C22⋊C8×C71C2211yescharacteristic
55C2×C4×C8×C71C2211yescharacteristic, complemented
56C4×C22⋊C4×C71C2211yescharacteristic
57#336×C71C2211yescharacteristic, complemented
58#336×C71C2211yescharacteristic, complemented
59C24×D71C2×C411yescharacteristic
60C23×Dic71C2×C411yescharacteristic
61C22×C4×D71—22no—
62C22×C4×D71—22no—
63C22×C4×D71—41no—
64C22×C4×D71—41no—
65C22×C4×D71—41no—
66C22×C4×D71—41no—
67C22×C4×D71C2×C411yescharacteristic
68C22×C4×D71C2×C411yescharacteristic
69C22×C4×D71C2×C411yescharacteristic
70C22×C4×D71C2×C411yescharacteristic
71C22×C4×D71C2×C411yescharacteristic
72C22×C4×D71C2×C411yescharacteristic
73C22×C4×D71C2311yescharacteristic
74C22×C4×D71C2311yescharacteristic
75C22×C71⋊C8C2311yescharacteristic
76C22×C71⋊C8C2311yescharacteristic
77C22×C71⋊C8C2311yescharacteristic
78C22×C71⋊C8C2311yescharacteristic
79C2×C22⋊Dic71C2×C411yescharacteristic
80C2×C22⋊Dic71C2×C411yescharacteristic
81C2×(C2×D71)⋊C4C2×C411yescharacteristic
82C2×(C2×D71)⋊C4C2×C411yescharacteristic
83C2×(C2×D71)⋊C4C2×C411yescharacteristic
84C2×(C2×D71)⋊C4C2×C411yescharacteristic
85C22⋊C4×D71—24no—
86C22⋊C4×D71C818yescomplemented
87C2×C4×Dic71C2×C411yescharacteristic
88C2×C4×Dic71C2×C411yescharacteristic
89C2×C4×Dic71C2×C411yescharacteristic
90C2×C4×Dic71C2×C411yescharacteristic
91C2×C4×Dic71C2311yescharacteristic
92C2×C4×Dic71C2311yescharacteristic
93C42×D71—41no—
94C42×D71—41no—
95C42×D71—41no—
96C42×D71—41no—
97C4⋊(C71⋊C8)—41no—
98Dic71⋊C8—41no—
99Dic71⋊C8—41no—
100C22⋊(C71⋊C8)—41no—
101C22⋊(C71⋊C8)—41no—
102(C2×D71)⋊C8—22no—
103(C2×D71)⋊C8—22no—
104(C2×D71)⋊C8—22no—
105(C2×D71)⋊C8—22no—
106(C2×D71)⋊C8—41no—
107(C2×D71)⋊C8—41no—
108(C2×D71)⋊C8—41no—
109(C2×D71)⋊C8—41no—
110C4×C71⋊C8—41no—
111C8×Dic71—41no—
112C8×Dic71—41no—
113C71⋊#95C2×C411yescharacteristic
114C71⋊#95C2×C411yescharacteristic
115C71⋊#95C2×C411yescharacteristic
116C71⋊#95C2×C411yescharacteristic
117C71⋊#95C2×C411yescharacteristic
118C71⋊#95C2×C411yescharacteristic
119C23×C4×C71C2311yescharacteristic
120C22×C8×C71C2311yescharacteristic
121C22×C8×C71C2311yescharacteristic
122C22×C8×C71C2311yescharacteristic
123C22×C8×C71C2311yescharacteristic
124C2×C22⋊C4×C71C2×C411yescharacteristic
125C2×C22⋊C4×C71C2×C411yescharacteristic
126C2×C42×C71C2311yescharacteristic
127C2×C42×C71C2311yescharacteristic
128C4⋊C8×C71—41no—
129C22⋊C8×C71—41no—
130C22⋊C8×C71—41no—
131C4×C8×C71—41no—
132#95×C71C2×C411yescharacteristic
133#95×C71C2×C411yescharacteristic
134C23×D71—22no—
135C23×D71—22no—
136C23×D71—41no—
137C23×D71—41no—
138C23×D71—41no—
139C23×D71—41no—
140C23×D71C2×C814yes—
141C23×D71C22×C411yescharacteristic
142C23×D71C22×C411yescharacteristic
143C22×Dic71—22no—
144C22×Dic71—41no—
145C22×Dic71—41no—
146C22×Dic71C22×C411yescharacteristic
147C22×Dic71C22×C411yescharacteristic
148C22×Dic71C22×C411yescharacteristic
149C22×Dic71C22×C411yescharacteristic
150C22×Dic71C22×C411yescharacteristic
151C22×Dic71C22×C411yescharacteristic
152C2×C4×D71—21no—
153C2×C4×D71—21no—
154C2×C4×D71—21no—
155C2×C4×D71—21no—
156C2×C4×D71—22no—
157C2×C4×D71—22no—
158C2×C4×D71—21no—
159C2×C4×D71—21no—
160C2×C4×D71—21no—
161C2×C4×D71—21no—
162C2×C4×D71—21no—
163C2×C4×D71—21no—
164C2×C4×D71—22no—
165C2×C4×D71—44no—
166C2×C4×D71—44no—
167C2×C4×D71—44no—
168C2×C4×D71—44no—
169C2×C4×D71—41no—
170C2×C4×D71—41no—
171C2×C4×D71—41no—
172C2×C4×D71—41no—
173C2×C4×D71—41no—
174C2×C4×D71—41no—
175C2×C4×D71—41no—
176C2×C4×D71—41no—
177C2×C4×D71—41no—
178C2×C4×D71—41no—
179C2×C4×D71—41no—
180C2×C4×D71—41no—
181C2×C4×D71C2×C814yes—
182C2×C4×D71C2×C814yes—
183C2×C4×D71M1614yes—
184C2×C4×D71#4112yes—
185C2×C4×D71#4112yes—
186C2×C71⋊C8—21no—
187C2×C71⋊C8—21no—
188C2×C71⋊C8—21no—
189C2×C71⋊C8—21no—
190C2×C71⋊C8—21no—
191C2×C71⋊C8—21no—
192C2×C71⋊C8—21no—
193C2×C71⋊C8—21no—
194C2×C71⋊C8—21no—
195C2×C71⋊C8—21no—
196C2×C71⋊C8—21no—
197C2×C71⋊C8—21no—
198C22⋊Dic71—22no—
199C22⋊Dic71C2×C814yes—
200(C2×D71)⋊C4—22no—
201(C2×D71)⋊C4—22no—
202(C2×D71)⋊C4C2×C814yes—
203(C2×D71)⋊C4C2×C814yes—
204C4×Dic71—21no—
205C4×Dic71—21no—
206C4×Dic71—21no—
207C4×Dic71—21no—
208C4×Dic71—41no—
209C4×Dic71—41no—
210C4×Dic71—41no—
211C4×Dic71—41no—
212C24×C71C22×C411yescharacteristic
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×C71C22×C411yescharacteristic
220C22×C4×C71C22×C411yescharacteristic
221C22×C4×C71C22×C411yescharacteristic
222C22×C4×C71C22×C411yescharacteristic
223C22×C4×C71C22×C411yescharacteristic
224C22×C4×C71C2411yescharacteristic
225C2×C8×C71—21no—
226C2×C8×C71—21no—
227C2×C8×C71—21no—
228C2×C8×C71—21no—
229C2×C8×C71—21no—
230C2×C8×C71—21no—
231C2×C8×C71—21no—
232C2×C8×C71—21no—
233C2×C8×C71—21no—
234C2×C8×C71—21no—
235C2×C8×C71—21no—
236C2×C8×C71—21no—
237C22⋊C4×C71—22no—
238C22⋊C4×C71C2×C814yes—
239C42×C71—21no—
240C42×C71—21no—
241C42×C71—21no—
242C42×C71—21no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71—21no—
246C23×C71—21no—
247C23×C71—21no—
248C23×C71—21no—
249C23×C71C22×C812yes—
250C23×C71C23×C411yescharacteristic
251C22×D71—21no—
252C22×D71—21no—
253C22×D71—21no—
254C22×D71—21no—
255C22×D71—21no—
256C22×D71—21no—
257C22×D71—21no—
258C22×D71—21no—
259C22×D71—21no—
260C22×D71—21no—
261C22×D71—28no—
262C22×D71—44no—
263C22×D71—44no—
264C22×D71—44no—
265C22×D71—44no—
266C22×D71—44no—
267C22×D71—44no—
268C22×D71#11712yes—
269C22×D71C22×C812yes—
270C22×D71C22×C812yes—
271C22×D71C2×M1612yes—
272C2×C4×C71—21no—
273C2×C4×C71—21no—
274C2×C4×C71—21no—
275C2×C4×C71—21no—
276C2×C4×C71—21no—
277C2×C4×C71—21no—
278C2×C4×C71—21no—
279C2×C4×C71—21no—
280C2×C4×C71—21no—
281C2×C4×C71—21no—
282C2×C4×C71—21no—
283C2×C4×C71—21no—
284C2×C4×C71—41no—
285C2×C4×C71—41no—
286C2×C4×C71—41no—
287C2×C4×C71—41no—
288C2×C4×C71C22×C812yes—
289C2×C4×C71C22×C812yes—
290C2×C4×C71C2×M1612yes—
291C2×C4×C71C2×#4111yescharacteristic
292C2×C4×C71C2×#4111yescharacteristic
293C2×C4×C71H(5,𝔽2)11yescharacteristic
294C2×C4×C71H(5,𝔽2)11yescharacteristic
295C2×C4×C71H(5,𝔽2)11yescharacteristic
296C2×C4×C71H(5,𝔽2)11yescharacteristic
297C2×Dic71—21no—
298C2×Dic71—21no—
299C2×Dic71—21no—
300C2×Dic71—21no—
301C2×Dic71—21no—
302C2×Dic71—21no—
303C2×Dic71—21no—
304C2×Dic71—21no—
305C2×Dic71—21no—
306C2×Dic71—21no—
307C2×Dic71—21no—
308C2×Dic71—21no—
309C2×Dic71—21no—
310C2×Dic71—21no—
311C2×Dic71—44no—
312C2×Dic71#11712yes—
313C2×Dic71C22×C812yes—
314C2×Dic71C22×C812yes—
315C2×Dic71C2×M1612yes—
316C4×D71—22no—
317C4×D71—22no—
318C4×D71—22no—
319C4×D71—22no—
320C4×D71—44no—
321C4×D71—44no—
322C4×D71—44no—
323C4×D71—44no—
324C4×D71—44no—
325C4×D71—44no—
326C4×D71—41no—
327C4×D71—41no—
328C4×D71—41no—
329C4×D71—41no—
330C8×C71—41no—
331C8×C71—41no—
332C8×C71—41no—
333C8×C71—41no—
334C71⋊C8—41no—
335C71⋊C8—41no—
336C71⋊C8—41no—
337C71⋊C8—41no—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—22no—
341C22×C71—41no—
342C22×C71—41no—
343C22×C71—41no—
344C22×C71—41no—
345C22×C71C2×#11711yescharacteristic
346C22×C71#51811yescharacteristic
347C22×C71#51811yescharacteristic
348C22×C71C23×C811yescharacteristic
349C22×C71C22×M1611yescharacteristic
350C22×C71#56811yescharacteristic
351C22×C71#56811yescharacteristic
352C2×D71—22no—
353C2×D71—22no—
354C2×D71—22no—
355C2×D71—22no—
356C2×D71—22no—
357C2×D71—22no—
358C2×D71—22no—
359C2×D71—22no—
360C2×D71—22no—
361C2×D71—416no—
362C2×D71—41no—
363C2×D71—41no—
364C2×D71—41no—
365C2×D71—41no—
366C2×D71#43114yes—
367C4×C71—22no—
368C4×C71—22no—
369C4×C71—22no—
370C4×C71—41no—
371C4×C71—41no—
372C4×C71#53811yescharacteristic
373C4×C71#53811yescharacteristic
374C4×C71#53811yescharacteristic
375C4×C71#53811yescharacteristic
376Dic71—22no—
377Dic71—22no—
378Dic71—22no—
379Dic71—22no—
380Dic71—41no—
381Dic71—41no—
382#21902—711nomaximal, Sylow
383C2×C71—42no—
384C2×C71#231211yescharacteristic
385C2×C71C2×#43111yescharacteristic
386C2×C71#292111yescharacteristic
387C2×C71#297211yescharacteristic
388C2×C71#297211yescharacteristic
389C2×C71#297311yescharacteristic
390C2×C71#297511yescharacteristic
391D71—24no—
392D71—42no—
393C2×C4×C22⋊C4—711no—
394#1923—711no—
395#1923—711no—
396#1923—711no—
397#1923—711no—
398#1923—711no—
399#1923—711no—
400#1923—711no—
401#1923D7111yescharacteristic, complemented
402#1797—711no—
403#1797—711no—
404#1779—711no—
405#1779—711no—
406C4×C22⋊C8—711no—
407C4×C22⋊C8—711no—
408C71#2190211yescharacteristic, complemented, Sylow
409C24×C4—711no—
410C22×C22⋊C4—711no—
411C22×C22⋊C4—711no—
412C22×C42—711no—
413C22×C42—711no—
414C2×C4⋊C8—711no—
415C2×C4⋊C8—711no—
416C2×C4⋊C8—711no—
417C2×C4⋊C8C2×D7111yescharacteristic, complemented
418C2×C22⋊C8—711no—
419C2×C22⋊C8—711no—
420C2×C22⋊C8—711no—
421C2×C22⋊C8—711no—
422C2×C22⋊C8—711no—
423C2×C22⋊C8—711no—
424C2×C22⋊C8—711no—
425C2×C22⋊C8—711no—
426C2×C22⋊C8—711no—
427C2×C22⋊C8—711no—
428C2×C22⋊C8C2×D7111yescharacteristic
429C2×C22⋊C8C2×D7111yescharacteristic
430C2×C4×C8—711no—
431C2×C4×C8—711no—
432C2×C4×C8—711no—
433C2×C4×C8C2×D7111yescharacteristic, complemented
434C4×C22⋊C4—711no—
435C4×C22⋊C4—711no—
436C4×C22⋊C4—711no—
437C4×C22⋊C4—711no—
438C4×C22⋊C4—711no—
439C4×C22⋊C4—711no—
440C4×C22⋊C4—711no—
441C4×C22⋊C4C2×D7111yescharacteristic
442C2×#95—711no—
443C2×#95—711no—
444#336—711no—
445#336—711no—
446#336—711no—
447#336—711no—
448#336—711no—
449#336—711no—
450#336C2×D7111yescharacteristic, complemented
451#336C2×D7111yescharacteristic, complemented
452C25—711no—
453C23×C4—2841no—
454C23×C4—2841no—
455C23×C4—2841no—
456C23×C4—2841no—
457C23×C4—711no—
458C23×C4—711no—
459C23×C4—711no—
460C23×C4—711no—
461C23×C4—711no—
462C23×C4—711no—
463C23×C4—711no—
464C23×C4—711no—
465C23×C4—711no—
466C23×C4—1422no—
467C23×C4—1422no—
468C23×C4C22×D7111yescharacteristic
469C22×C8—711no—
470C22×C8—711no—
471C22×C8—711no—
472C22×C8—711no—
473C22×C8C22×D7111yescharacteristic
474C22×C8C22×D7111yescharacteristic
475C22×C8C22×D7111yescharacteristic
476C22×C8C22×D7111yescharacteristic
477C2×C22⋊C4—711no—
478C2×C22⋊C4—711no—
479C2×C22⋊C4—711no—
480C2×C22⋊C4—718no—
481C2×C22⋊C4—711no—
482C2×C22⋊C4—711no—
483C2×C22⋊C4—711no—
484C2×C22⋊C4—1424no—
485C2×C22⋊C4C4×D7111yescharacteristic
486C2×C22⋊C4C4×D7111yescharacteristic
487C2×C42—2841no—
488C2×C42—2841no—
489C2×C42—2841no—
490C2×C42—2841no—
491C2×C42—711no—
492C2×C42—711no—
493C2×C42—711no—
494C2×C42—711no—
495C2×C42—711no—
496C2×C42—711no—
497C2×C42C22×D7111yescharacteristic
498C2×C42C22×D7111yescharacteristic
499C4⋊C8—41no—
500C4⋊C8—2841no—
501C4⋊C8—2841no—
502C4⋊C8—2841no—
503C22⋊C8—41no—
504C22⋊C8—41no—
505C22⋊C8—2841no—
506C22⋊C8—2841no—
507C22⋊C8—2841no—
508C22⋊C8—2841no—
509C22⋊C8—2841no—
510C22⋊C8—2841no—
511C22⋊C8—1422no—
512C22⋊C8—1422no—
513C22⋊C8—1422no—
514C22⋊C8—1422no—
515C4×C8—41no—
516C4×C8—2841no—
517C4×C8—2841no—
518C4×C8—2841no—
519#95—711no—
520#95—711no—
521#95—711no—
522#95—711no—
523#95—711no—
524#95—711no—
525#95C4×D7111yescharacteristic
526#95C4×D7111yescharacteristic
527C24—2841no—
528C24—2841no—
529C24—2841no—
530C24—2841no—
531C24—714no—
532C24—711no—
533C24—711no—
534C24—1422no—
535C24—1422no—
536C24C2×C4×D7111yescharacteristic
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—2841no—
544C22×C4—2841no—
545C22×C4—2841no—
546C22×C4—2841no—
547C22×C4—2841no—
548C22×C4—2841no—
549C22×C4—2841no—
550C22×C4—2841no—
551C22×C4—2841no—
552C22×C4—2841no—
553C22×C4—2841no—
554C22×C4—2841no—
555C22×C4—2844no—
556C22×C4—2844no—
557C22×C4—2844no—
558C22×C4—2844no—
559C22×C4—2841no—
560C22×C4—2841no—
561C22×C4—714no—
562C22×C4—714no—
563C22×C4—714no—
564C22×C4—711no—
565C22×C4—711no—
566C22×C4—711no—
567C22×C4—711no—
568C22×C4—712no—
569C22×C4—712no—
570C22×C4—711no—
571C22×C4—711no—
572C22×C4—1422no—
573C22×C4—1422no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4—1421no—
577C22×C4—1421no—
578C22×C4—1421no—
579C22×C4—1421no—
580C22×C4—1421no—
581C22×C4—1421no—
582C22×C4—1421no—
583C22×C4—1421no—
584C22×C4—1421no—
585C22×C4—1421no—
586C22×C4C2×C4×D7111yescharacteristic
587C22×C4C2×C4×D7111yescharacteristic
588C22×C4C2×C4×D7111yescharacteristic
589C22×C4C2×C4×D7111yescharacteristic
590C22×C4C2×C4×D7111yescharacteristic
591C22×C4C23×D7111yescharacteristic
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—1421no—
605C2×C8—1421no—
606C2×C8—1421no—
607C2×C8—1421no—
608C2×C8—1421no—
609C2×C8—1421no—
610C2×C8—1421no—
611C2×C8—1421no—
612C2×C8—1421no—
613C2×C8—1421no—
614C2×C8—1421no—
615C2×C8—1421no—
616C22⋊C4—22no—
617C22⋊C4—714no—
618C22⋊C4—714no—
619C22⋊C4—714no—
620C22⋊C4—1422no—
621C22⋊C4—1422no—
622C22⋊C4—1422no—
623C22⋊C4C8×D7114yes—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—2841no—
629C42—2841no—
630C42—2841no—
631C42—2841no—
632C42—1421no—
633C42—1421no—
634C42—1421no—
635C42—1421no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—2844no—
643C23—2844no—
644C23—2844no—
645C23—2844no—
646C23—2844no—
647C23—2844no—
648C23—712no—
649C23—712no—
650C23—712no—
651C23—712no—
652C23—1428no—
653C23—1421no—
654C23—1421no—
655C23—1421no—
656C23—1421no—
657C23—1421no—
658C23—1421no—
659C23—1421no—
660C23—1421no—
661C23—1421no—
662C23—1421no—
663C23C2×C8×D7112yes—
664C23C22×C4×D7111yescharacteristic
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—2844no—
682C2×C4—2844no—
683C2×C4—2844no—
684C2×C4—2844no—
685C2×C4—2844no—
686C2×C4—2844no—
687C2×C4—2844no—
688C2×C4—2841no—
689C2×C4—2841no—
690C2×C4—2841no—
691C2×C4—2841no—
692C2×C4—712no—
693C2×C4—712no—
694C2×C4—712no—
695C2×C4—712no—
696C2×C4—1421no—
697C2×C4—1421no—
698C2×C4—1421no—
699C2×C4—1421no—
700C2×C4—1421no—
701C2×C4—1421no—
702C2×C4—1421no—
703C2×C4—1421no—
704C2×C4—1421no—
705C2×C4—1421no—
706C2×C4—1421no—
707C2×C4—1421no—
708C2×C4—1421no—
709C2×C4—1421no—
710C2×C4—1422no—
711C2×C4—1422no—
712C2×C4—1422no—
713C2×C4—1422no—
714C2×C4C2×C8×D7112yes—
715C2×C4C2×C8×D7112yes—
716C2×C4M16×D7112yes—
717C2×C4#41×D7111yescharacteristic
718C2×C4#41×D7111yescharacteristic
719C2×C4#1455617311yescharacteristic
720C2×C4#1455617311yescharacteristic
721C2×C4#1455617411yescharacteristic
722C2×C4#1455617411yescharacteristic
723C8—41no—
724C8—41no—
725C8—41no—
726C8—41no—
727C8—2841no—
728C8—2841no—
729C8—2841no—
730C8—2841no—
731C22—22no—
732C22—22no—
733C22—22no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—28416no—
739C22—2841no—
740C22—2841no—
741C22—2841no—
742C22—2841no—
743C22—714no—
744C22—1422no—
745C22—1422no—
746C22—1422no—
747C22—1422no—
748C22—1422no—
749C22—1422no—
750C22—1422no—
751C22—1422no—
752C22—1422no—
753C22#117×D7111yescharacteristic
754C22#1798647111yescharacteristic
755C22#1798647111yescharacteristic
756C22C22×C8×D7111yescharacteristic
757C22C2×M16×D7111yescharacteristic
758C22#1798676411yescharacteristic
759C22#1798676411yescharacteristic
760C4—22no—
761C4—22no—
762C4—22no—
763C4—41no—
764C4—41no—
765C4—2841no—
766C4—2841no—
767C4—1422no—
768C4—1422no—
769C4—1422no—
770C4—1422no—
771C4#1798658111yescharacteristic
772C4#1798658311yescharacteristic
773C4#1798658511yescharacteristic
774C4#1798658811yescharacteristic
775C2—42no—
776C2—2842no—
777C2—1424no—
778C2#2259093411yescharacteristic
779C2#431×D7111yescharacteristic
780C2#2259697411yescharacteristic
781C2#2259736111yescharacteristic
782C2#2259736111yescharacteristic
783C2#2259736511yescharacteristic
784C2#2259737811yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutatorC22×C71C23×C8
FittingC71×#1923C2
socleC23×C71C23×C4
prime radicalC24×D71C2×C4
cosocleC22×C4×C71C24
hypercenter#1923D71
hypocenterC71#21902
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #22588949C2semidirect
3. #22588948C2semidirect
4. #22588947C2semidirect
5. #22588946C2semidirect
6. #22588945C2semidirect
7. #22588944C2semidirect
8. #22588943C2semidirect
9. #22588319C2semidirect
10. #22588317C2semidirect
13. C4×(C2×D71)⋊C8C2semidirect
14. #22588097C2semidirect
15. C71×#1923C2semidirect
21. C2×C4⋊(C71⋊C8)C22semidirect
22. C2×Dic71⋊C8C22semidirect
23. C2×Dic71⋊C8C22semidirect
34. C2×C4×C71⋊C8C22semidirect
35. C2×C8×Dic71C22semidirect
36. C2×C8×Dic71C22semidirect
46. #17985754C22semidirect
47. #17985754C22semidirect
48. #17985753C22semidirect
49. #17985753C22semidirect
50. #17985753C22semidirect
51. #17985753C22semidirect
52. C2×C4⋊C8×C71C22semidirect
55. C2×C4×C8×C71C22semidirect
57. #336×C71C22semidirect
58. #336×C71C22semidirect
86. C22⋊C4×D71C8semidirect
401. #1923D71semidirect
408. C71#21902semidirect
417. C2×C4⋊C8C2×D71semidirect
433. C2×C4×C8C2×D71semidirect
450. #336C2×D71semidirect
451. #336C2×D71semidirect

Maximal subgroups

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

subgroupindex
C4×C22⋊C4×D712
#225889492
#225889482
#225889472
#225889462
#225889452
#225889442
#225889432
#225883192
#225883172
#225882492
C4×(C2×D71)⋊C82
#225880972
C71×#19232
#2190271