Finite Group Databasebeta

← #32014466

Subgroups — #32014466

Order 18176.

1060 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986059C211yesmaximal, characteristic, complemented
2C2×#17985962C211yesmaximal, characteristic
3#22590721C211yesmaximal, characteristic
4#22588954C211yesmaximal, characteristic, complemented
5#22588954C211yesmaximal, characteristic, complemented
6#22588945C211yesmaximal, characteristic, complemented
7#22588945C211yesmaximal, characteristic, complemented
8#22588525C211yesmaximal, characteristic, complemented
9#22588410C211yesmaximal, characteristic, complemented
10#22588321C211yesmaximal, characteristic, complemented
11#22588249C211yesmaximal, characteristic
12#22588126C211yesmaximal, characteristic, complemented
13#22588121C211yesmaximal, characteristic, complemented
14#22588105C211yesmaximal, characteristic, complemented
15C71×#1851C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C22×#11765849C2211yescharacteristic
18C2×#14556085C2211yescharacteristic
19C2×#14556085C2211yescharacteristic
20#17986059—24no—
21C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
22C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
23#17985962—24no—
24C2×C22⋊(C71⋊C8)C2211yescharacteristic
25C2×(C2×D71)⋊C8C2211yescharacteristic
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×#14556038C2211yescharacteristic, complemented
34C2×#14556038C2211yescharacteristic, complemented
35C2×C8×Dic71C2211yescharacteristic, complemented
36C2×C8×Dic71C2211yescharacteristic, complemented
37#17985861C411yescharacteristic
38#17985861C411yescharacteristic
39#17985858C411yescharacteristic
40#17985858C411yescharacteristic
41#17985857C411yescharacteristic
42#17985857C411yescharacteristic
43#17985854C411yescharacteristic
44#17985854C411yescharacteristic
45C4×(C2×D71)⋊C4C2211yescharacteristic
46C4×(C2×D71)⋊C4C2211yescharacteristic
47C4×C22⋊Dic71C2211yescharacteristic
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×D71C2311yescharacteristic
72C22×C4×D71C2311yescharacteristic
73C2×#11765849—22no—
74C2×#11765849—22no—
75C2×#11765849—41no—
76C22×C71⋊C8C2311yescharacteristic
77C22×C71⋊C8C2311yescharacteristic
78C22×C71⋊C8C2311yescharacteristic
79C22×C71⋊C8C2311yescharacteristic
80#14556085—22no—
81#14556085—22no—
82#14556085—41no—
83#14556085—41no—
84C2×Dic71⋊C4C2×C411yescharacteristic
85C2×Dic71⋊C4C2×C411yescharacteristic
86C2×Dic71⋊C4C2×C411yescharacteristic
87C2×Dic71⋊C4C2×C411yescharacteristic
88C2×C22⋊Dic71C2×C411yescharacteristic
89C2×C22⋊Dic71C2×C411yescharacteristic
90C2×(C2×D71)⋊C4C2×C411yescharacteristic
91C2×(C2×D71)⋊C4C2×C411yescharacteristic
92C2×(C2×D71)⋊C4C2×C411yescharacteristic
93C2×(C2×D71)⋊C4C2×C411yescharacteristic
94C2×(C2×D71)⋊C4C2×C411yescharacteristic
95C2×(C2×D71)⋊C4C2×C411yescharacteristic
96C2×(C2×D71)⋊C4C2×C411yescharacteristic
97C2×(C2×D71)⋊C4C2×C411yescharacteristic
98C2×C4×Dic71C2311yescharacteristic
99C2×C4×Dic71C2311yescharacteristic
100C4⋊(C71⋊C8)—22no—
101C4⋊(C71⋊C8)—41no—
102C22⋊(C71⋊C8)—22no—
103(C2×D71)⋊C8—22no—
104(C2×D71)⋊C8—22no—
105(C2×D71)⋊C8—22no—
106(C2×D71)⋊C8—22no—
107(C2×D71)⋊C8—22no—
108(C2×D71)⋊C8—41no—
109(C2×D71)⋊C8—41no—
110(C2×D71)⋊C8D414yes—
111#14556038—22no—
112#14556038—41no—
113C8×Dic71—22no—
114C8×Dic71—41no—
115C71⋊#95C2×C411yescharacteristic
116C71⋊#95C2×C411yescharacteristic
117C71⋊#95C2×C411yescharacteristic
118C71⋊#95C2×C411yescharacteristic
119C71⋊#95C2×C411yescharacteristic
120C71⋊#95C2×C411yescharacteristic
121C23×C4×C71C2311yescharacteristic
122C2×M16×C71—22no—
123C2×M16×C71—22no—
124C2×M16×C71—41no—
125C22×C8×C71C2311yescharacteristic
126C22×C8×C71C2311yescharacteristic
127C22×C8×C71C2311yescharacteristic
128C22×C8×C71C2311yescharacteristic
129C2×C22⋊C4×C71C2×C411yescharacteristic
130C2×C22⋊C4×C71C2×C411yescharacteristic
131C2×C42×C71C2311yescharacteristic
132C2×C42×C71C2311yescharacteristic
133C4⋊C8×C71—22no—
134C4⋊C8×C71—41no—
135C22⋊C8×C71—22no—
136#95×C71C2×C411yescharacteristic
137#95×C71C2×C411yescharacteristic
138C23×D71—22no—
139C23×D71—22no—
140C23×D71—22no—
141C23×D71—41no—
142C23×D71—41no—
143C23×D71—41no—
144C23×D71—41no—
145C23×D71C22×C411yescharacteristic
146C23×D71C22×C411yescharacteristic
147C22×Dic71—22no—
148C22×Dic71—22no—
149C22×Dic71—41no—
150C22×Dic71C22×C411yescharacteristic
151C22×Dic71C22×C411yescharacteristic
152C22×Dic71C22×C411yescharacteristic
153C22×Dic71C22×C411yescharacteristic
154C22×Dic71C22×C411yescharacteristic
155C22×Dic71C22×C411yescharacteristic
156C2×C4×D71—21no—
157C2×C4×D71—21no—
158C2×C4×D71—21no—
159C2×C4×D71—21no—
160C2×C4×D71—22no—
161C2×C4×D71—22no—
162C2×C4×D71—22no—
163C2×C4×D71—21no—
164C2×C4×D71—21no—
165C2×C4×D71—21no—
166C2×C4×D71—21no—
167C2×C4×D71—21no—
168C2×C4×D71—21no—
169C2×C4×D71—22no—
170C2×C4×D71—44no—
171C2×C4×D71—44no—
172C2×C4×D71—44no—
173C2×C4×D71—44no—
174C2×C4×D71—41no—
175C2×C4×D71—41no—
176C2×C4×D71C2×D412yes—
177C2×C4×D71#4112yes—
178#11765849—44no—
179C2×C71⋊C8—21no—
180C2×C71⋊C8—21no—
181C2×C71⋊C8—21no—
182C2×C71⋊C8—21no—
183C2×C71⋊C8—21no—
184C2×C71⋊C8—21no—
185C2×C71⋊C8—21no—
186C2×C71⋊C8—21no—
187C2×C71⋊C8—21no—
188C2×C71⋊C8—21no—
189C2×C71⋊C8—21no—
190C2×C71⋊C8C2×D412yes—
191Dic71⋊C4—22no—
192Dic71⋊C4—22no—
193Dic71⋊C4—41no—
194Dic71⋊C4—41no—
195C22⋊Dic71—41no—
196C22⋊Dic71—41no—
197(C2×D71)⋊C4—22no—
198(C2×D71)⋊C4—22no—
199(C2×D71)⋊C4—22no—
200(C2×D71)⋊C4—22no—
201(C2×D71)⋊C4—41no—
202(C2×D71)⋊C4—41no—
203(C2×D71)⋊C4—41no—
204(C2×D71)⋊C4—41no—
205C4×Dic71—21no—
206C4×Dic71—21no—
207C4×Dic71—21no—
208C4×Dic71—21no—
209C24×C71C22×C411yescharacteristic
210C22×C4×C71—21no—
211C22×C4×C71—21no—
212C22×C4×C71—21no—
213C22×C4×C71—21no—
214C22×C4×C71C22×C411yescharacteristic
215C22×C4×C71C22×C411yescharacteristic
216C22×C4×C71C22×C411yescharacteristic
217C22×C4×C71C22×C411yescharacteristic
218C22×C4×C71C22×C411yescharacteristic
219C22×C4×C71#4112yes—
220C22×C4×C71#4112yes—
221C22×C4×C71C2411yescharacteristic
222M16×C71—44no—
223C2×C8×C71—21no—
224C2×C8×C71—21no—
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×C71C2×D412yes—
235C22⋊C4×C71—41no—
236C22⋊C4×C71—41no—
237C42×C71—21no—
238C42×C71—21no—
239C42×C71—21no—
240C42×C71—21no—
241C23×C71—21no—
242C23×C71—21no—
243C23×C71—21no—
244C23×C71—21no—
245C23×C71—21no—
246C23×C71—21no—
247C23×C71#11712yes—
248C23×C71C23×C411yescharacteristic
249C22×D71—21no—
250C22×D71—21no—
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—44no—
262C22×D71—44no—
263C22×D71—44no—
264C22×D71—44no—
265C22×D71—44no—
266C22×D71—44no—
267C22×D71—44no—
268C22×D71C4×D412yes—
269C22×D71#13112yes—
270C2×C4×C71—21no—
271C2×C4×C71—21no—
272C2×C4×C71—22no—
273C2×C4×C71—22no—
274C2×C4×C71—22no—
275C2×C4×C71—22no—
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—21no—
285C2×C4×C71—21no—
286C2×C4×C71—21no—
287C2×C4×C71—21no—
288C2×C4×C71#11712yes—
289C2×C4×C71C22×D411yescharacteristic
290C2×C4×C71C2×#4111yescharacteristic
291C2×C4×C71C2×#4111yescharacteristic
292C2×C4×C71C2×#4111yescharacteristic
293C2×C4×C71H(5,𝔽2)11yescharacteristic
294C2×C4×C71H(5,𝔽2)11yescharacteristic
295C2×Dic71—21no—
296C2×Dic71—21no—
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—21no—
312C2×Dic71—44no—
313C2×Dic71C4×D412yes—
314C4×D71—22no—
315C4×D71—22no—
316C4×D71—22no—
317C4×D71—22no—
318C4×D71—44no—
319C4×D71—44no—
320C4×D71—41no—
321C4×D71—41no—
322C4×D71—41no—
323C4×D71—41no—
324C8×C71—22no—
325C8×C71—41no—
326C8×C71—41no—
327C8×C71—41no—
328C71⋊C8—22no—
329C71⋊C8—41no—
330C71⋊C8—41no—
331C71⋊C8—41no—
332C22×C71—22no—
333C22×C71—22no—
334C22×C71—22no—
335C22×C71—41no—
336C22×C71—41no—
337C22×C71—41no—
338C22×C71—41no—
339C22×C71C2×#11711yescharacteristic
340C22×C71C2×C4×D411yescharacteristic
341C22×C71#51811yescharacteristic
342C22×C71C2×#13111yescharacteristic
343C22×C71#56811yescharacteristic
344C22×C71#56811yescharacteristic
345C22×C71#56811yescharacteristic
346C2×D71—22no—
347C2×D71—22no—
348C2×D71—22no—
349C2×D71—22no—
350C2×D71—22no—
351C2×D71—22no—
352C2×D71—416no—
353C2×D71—41no—
354C2×D71—41no—
355C2×D71—41no—
356C2×D71—41no—
357C2×D71—41no—
358C2×D71—41no—
359C2×D71—41no—
360C2×D71—41no—
361C4×C71—22no—
362C4×C71—41no—
363C4×C71—41no—
364C4×C71—41no—
365C4×C71—41no—
366C4×C71#54611yescharacteristic
367C4×C71#54611yescharacteristic
368C4×C71#55111yescharacteristic
369C4×C71#55111yescharacteristic
370Dic71—22no—
371Dic71—41no—
372Dic71—41no—
373Dic71—41no—
374Dic71—41no—
375Dic71—41no—
376#22559—711nomaximal, Sylow
377C2×C71—42no—
378C2×C71#234211yescharacteristic
379C2×C71#292111yescharacteristic
380C2×C71#292411yescharacteristic
381C2×C71#293011yescharacteristic
382C2×C71#293311yescharacteristic
383C2×C71#297611yescharacteristic
384C2×C71#297811yescharacteristic
385D71—42no—
386D71—42no—
387C2×#433—711no—
388C2×#407—711no—
389#2280—711no—
390#1924—711no—
391#1924—711no—
392#1923—711no—
393#1923—711no—
394#1851—711no—
395#1851D7111yescharacteristic, complemented
396#1818—711no—
397#1798—711no—
398#1779—711no—
399#1753—711no—
400#1753—711no—
401#1750—711no—
402C71#2255911yescharacteristic, complemented, Sylow
403C24×C4—711no—
404C22×M16—711no—
405C22×M16C2×D7111yescharacteristic
406C2×#117—711no—
407C2×#117—711no—
408#433—1424no—
409C2×C4⋊C8—711no—
410C2×C4⋊C8—711no—
411C2×C4⋊C8C2×D7111yescharacteristic, complemented
412C2×C4⋊C8C2×D7111yescharacteristic, complemented
413#407—1424no—
414C2×C22⋊C8—711no—
415C2×C22⋊C8—711no—
416C2×C22⋊C8—711no—
417C2×C22⋊C8—711no—
418C2×C22⋊C8—711no—
419C2×C22⋊C8—711no—
420C2×C22⋊C8—711no—
421C2×C22⋊C8—711no—
422C2×C22⋊C8—711no—
423C2×C22⋊C8C2×D7111yescharacteristic
424C2×#97—711no—
425C2×#97—711no—
426C2×C4×C8—711no—
427C2×C4×C8—711no—
428#381—711no—
429#381—711no—
430#380—711no—
431#380—711no—
432#380—711no—
433#380—711no—
434#379—711no—
435#379—711no—
436C4×C22⋊C4—711no—
437C4×C22⋊C4—711no—
438C4×C22⋊C4—711no—
439C4×C22⋊C4C2×D7111yescharacteristic
440#336—711no—
441#336—711no—
442#336—711no—
443#336—711no—
444#336—711no—
445#336—711no—
446#336C2×D7111yescharacteristic, complemented
447#336C2×D7111yescharacteristic, complemented
448C25—711no—
449C23×C4—2841no—
450C23×C4—2841no—
451C23×C4—711no—
452C23×C4—711no—
453C23×C4—711no—
454C23×C4—711no—
455C23×C4—711no—
456C23×C4—1422no—
457C23×C4—1422no—
458C23×C4—1422no—
459C23×C4—1422no—
460C23×C4C22×D7111yescharacteristic
461C2×M16—22no—
462C2×M16—22no—
463C2×M16—41no—
464C2×M16—2841no—
465C2×M16—1422no—
466C2×M16—1422no—
467C22×C8—711no—
468C22×C8—711no—
469C22×C8—711no—
470C22×C8—711no—
471C22×C8C22×D7111yescharacteristic
472C22×C8C22×D7111yescharacteristic
473C22×C8C22×D7111yescharacteristic
474C22×C8C22×D7111yescharacteristic
475#117—2841no—
476#117—2841no—
477#117—1422no—
478#117—1422no—
479C2×C4⋊C4—711no—
480C2×C4⋊C4—711no—
481C2×C4⋊C4—711no—
482C2×C4⋊C4—711no—
483C2×C22⋊C4—711no—
484C2×C22⋊C4—711no—
485C2×C22⋊C4—711no—
486C2×C22⋊C4—711no—
487C2×C22⋊C4—711no—
488C2×C22⋊C4—711no—
489C2×C22⋊C4—711no—
490C2×C22⋊C4—711no—
491C2×C22⋊C4—711no—
492C2×C22⋊C4—711no—
493C2×C22⋊C4C4×D7111yescharacteristic
494C2×C22⋊C4C4×D7111yescharacteristic
495C2×C42—711no—
496C2×C42—711no—
497C2×C42C22×D7111yescharacteristic
498C2×C42C22×D7111yescharacteristic
499C4⋊C8—22no—
500C4⋊C8—41no—
501C4⋊C8—2841no—
502C4⋊C8—1422no—
503C22⋊C8—22no—
504C22⋊C8—2841no—
505C22⋊C8—2841no—
506C22⋊C8—714no—
507C22⋊C8—1422no—
508C22⋊C8—1422no—
509C22⋊C8—1422no—
510C22⋊C8—1422no—
511C22⋊C8—1422no—
512C22⋊C8—1422no—
513#97—2841no—
514#97—1422no—
515C4×C8—2841no—
516C4×C8—1422no—
517#95—711no—
518#95—711no—
519#95—711no—
520#95—711no—
521#95—711no—
522#95—711no—
523#95C4×D7111yescharacteristic
524#95C4×D7111yescharacteristic
525C24—2841no—
526C24—2841no—
527C24—2841no—
528C24—2841no—
529C24—711no—
530C24—711no—
531C24—1422no—
532C24—1422no—
533C24—1422no—
534C24C2×C4×D7111yescharacteristic
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—2844no—
540C22×C4—2844no—
541C22×C4—2844no—
542C22×C4—2844no—
543C22×C4—2841no—
544C22×C4—2841no—
545C22×C4—2841no—
546C22×C4—711no—
547C22×C4—712no—
548C22×C4—712no—
549C22×C4—711no—
550C22×C4—711no—
551C22×C4—711no—
552C22×C4—711no—
553C22×C4—711no—
554C22×C4—1422no—
555C22×C4—1422no—
556C22×C4—1422no—
557C22×C4—1422no—
558C22×C4—1421no—
559C22×C4—1421no—
560C22×C4—1421no—
561C22×C4—1421no—
562C22×C4—1421no—
563C22×C4—1421no—
564C22×C4—1422no—
565C22×C4—1422no—
566C22×C4—1421no—
567C22×C4—1421no—
568C22×C4—1421no—
569C22×C4—1421no—
570C22×C4C2×C4×D7111yescharacteristic
571C22×C4C2×C4×D7111yescharacteristic
572C22×C4C2×C4×D7111yescharacteristic
573C22×C4C2×C4×D7111yescharacteristic
574C22×C4C2×C4×D7111yescharacteristic
575C22×C4#1176586412yes—
576C22×C4#1176586612yes—
577C22×C4C23×D7111yescharacteristic
578M16—44no—
579M16—2844no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—712no—
592C2×C8—1421no—
593C2×C8—1421no—
594C2×C8—1421no—
595C2×C8—1421no—
596C2×C8—1421no—
597C2×C8—1421no—
598C2×C8—1421no—
599C2×C8—1421no—
600C2×C8—1421no—
601C2×C8—1421no—
602C2×C8—1421no—
603C2×C8D4×D7112yes—
604C4⋊C4—2841no—
605C4⋊C4—2841no—
606C4⋊C4—1422no—
607C4⋊C4—1422no—
608C22⋊C4—41no—
609C22⋊C4—41no—
610C22⋊C4—2841no—
611C22⋊C4—2841no—
612C22⋊C4—2841no—
613C22⋊C4—2841no—
614C22⋊C4—2841no—
615C22⋊C4—2841no—
616C22⋊C4—1422no—
617C22⋊C4—1422no—
618C22⋊C4—1422no—
619C22⋊C4—1422no—
620C42—21no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—1421no—
625C42—1421no—
626C42—1421no—
627C42—1421no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—2844no—
635C23—2844no—
636C23—2844no—
637C23—2844no—
638C23—2844no—
639C23—2844no—
640C23—2844no—
641C23—712no—
642C23—712no—
643C23—1421no—
644C23—1421no—
645C23—1421no—
646C23—1421no—
647C23—1421no—
648C23—1421no—
649C23—1421no—
650C23—1421no—
651C23—1421no—
652C23—1421no—
653C23—1421no—
654C23—1421no—
655C23#1455608612yes—
656C23C22×C4×D7111yescharacteristic
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—21no—
664C2×C4—21no—
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—2844no—
676C2×C4—2844no—
677C2×C4—2844no—
678C2×C4—2841no—
679C2×C4—2841no—
680C2×C4—2841no—
681C2×C4—2841no—
682C2×C4—712no—
683C2×C4—1421no—
684C2×C4—1421no—
685C2×C4—1421no—
686C2×C4—1421no—
687C2×C4—1421no—
688C2×C4—1421no—
689C2×C4—1421no—
690C2×C4—1421no—
691C2×C4—1421no—
692C2×C4—1421no—
693C2×C4—1421no—
694C2×C4—1421no—
695C2×C4—1421no—
696C2×C4—1421no—
697C2×C4—1421no—
698C2×C4—1421no—
699C2×C4—1421no—
700C2×C4—1422no—
701C2×C4—1422no—
702C2×C4—1422no—
703C2×C4—1422no—
704C2×C4#1455608612yes—
705C2×C4C2×D4×D7111yescharacteristic
706C2×C4#41×D7111yescharacteristic
707C2×C4C2×#1176586411yescharacteristic
708C2×C4C2×#1176586611yescharacteristic
709C2×C4#1455617311yescharacteristic
710C2×C4#1455617411yescharacteristic
711C8—22no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—2841no—
716C8—2841no—
717C8—2841no—
718C8—1422no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—41no—
726C22—28416no—
727C22—2841no—
728C22—2841no—
729C22—2841no—
730C22—2841no—
731C22—2841no—
732C22—2841no—
733C22—2841no—
734C22—2841no—
735C22—1422no—
736C22—1422no—
737C22—1422no—
738C22—1422no—
739C22—1422no—
740C22—1422no—
741C22C2×#1455608611yescharacteristic
742C22C4×D4×D7111yescharacteristic
743C22#1798647111yescharacteristic
744C22#131×D7111yescharacteristic
745C22#1798676411yescharacteristic
746C22#1798676511yescharacteristic
747C22#1798676511yescharacteristic
748C4—22no—
749C4—41no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—2841no—
754C4—2841no—
755C4—2841no—
756C4—2841no—
757C4—2841no—
758C4—1422no—
759C4#1798663611yescharacteristic
760C4#1798664011yescharacteristic
761C4#1798667211yescharacteristic
762C4#1798667611yescharacteristic
763C2—42no—
764C2—2842no—
765C2—2842no—
766C2#2259118711yescharacteristic
767C2#2259697711yescharacteristic
768C2#2259699711yescharacteristic
769C2#2259704011yescharacteristic
770C2#2259706311yescharacteristic
771C2#2259738711yescharacteristic
772C2#2259739711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1851C2
prime radicalC24×D71C2×C4
cosocleC22×C4×C71C24
hypercenter#1851D71
hypocenterC71#22559
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1851

Complements

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

NH ≅ G/Ntype
1. C2×#17986059C2semidirect
4. #22588954C2semidirect
5. #22588954C2semidirect
6. #22588945C2semidirect
7. #22588945C2semidirect
8. #22588525C2semidirect
9. #22588410C2semidirect
10. #22588321C2semidirect
12. #22588126C2semidirect
13. #22588121C2semidirect
14. #22588105C2semidirect
15. C71×#1851C2semidirect
21. C2×C4⋊(C71⋊C8)C22semidirect
22. C2×C4⋊(C71⋊C8)C22semidirect
33. C2×#14556038C22semidirect
34. C2×#14556038C22semidirect
35. C2×C8×Dic71C22semidirect
36. 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
395. #1851D71semidirect
402. C71#22559semidirect
411. C2×C4⋊C8C2×D71semidirect
412. C2×C4⋊C8C2×D71semidirect
446. #336C2×D71semidirect
447. #336C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860592
C2×#179859622
#225907212
#225889542
#225889452
#225885252
#225884102
#225883212
#225882492
#225881262
#225881212
#225881052
C71×#18512
#2255971