Finite Group Databasebeta

← #32019576

Subgroups — #32019576

Order 18176.

1098 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986072C211yesmaximal, characteristic, complemented
2C2×#17986067C211yesmaximal, characteristic, complemented
3C2×(C22⋊D71)⋊C8C211yesmaximal, characteristic, complemented
4C22×C4⋊(C71⋊C8)C211yesmaximal, characteristic, complemented
5C4×#14556102C211yesmaximal, characteristic
6#22589138C211yesmaximal, characteristic, complemented
7#22589063C211yesmaximal, characteristic, complemented
8#22588954C211yesmaximal, characteristic, complemented
9#22588947C211yesmaximal, characteristic, complemented
10#22588630C211yesmaximal, characteristic, complemented
11#22588630C211yesmaximal, characteristic, complemented
12#22588524C211yesmaximal, characteristic, complemented
13#22588519C211yesmaximal, characteristic, complemented
14#22588212C211yesmaximal, characteristic, complemented
15C71×#1749C211yesmaximal, characteristic, complemented
16C22×#11765848C2211yescharacteristic
17C23×C71⋊C8C2211yescharacteristic
18C23×C71⋊C8C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20C2×#14556102C411yescharacteristic
21C2×C4×D284C2211yescharacteristic
22C2×C4×C22⋊D71C2211yescharacteristic
23C2×C4×C22⋊D71C2211yescharacteristic
24#17986072—24no—
25#17986067—24no—
26(C22⋊D71)⋊C8—24no—
27C2×C4⋊(C71⋊C8)—24no—
28C2×C4⋊(C71⋊C8)C2211yescharacteristic
29C2×C4⋊(C71⋊C8)C2211yescharacteristic
30C2×C4⋊(C71⋊C8)C2211yescharacteristic
31C2×C4⋊(C71⋊C8)C2211yescharacteristic
32C2×Dic71⋊C8C2211yescharacteristic
33C2×Dic71⋊C8C2211yescharacteristic
34C2×(C2×D71)⋊C8C2211yescharacteristic
35C2×(C2×D71)⋊C8C2211yescharacteristic
36C2×(C2×D71)⋊C8C2211yescharacteristic
37C2×(C2×D71)⋊C8C2211yescharacteristic
38C2×(C2×D71)⋊C8C2211yescharacteristic
39C2×(C2×D71)⋊C8C2211yescharacteristic
40C2×#14556038C2211yescharacteristic
41C2×C8×Dic71C2211yescharacteristic
42#17985901C411yescharacteristic
43#17985897C411yescharacteristic
44#17985890C411yescharacteristic
45#17985890C411yescharacteristic
46#17985878C411yescharacteristic
47#17985878C411yescharacteristic
48#17985859C411yescharacteristic
49C4×C4⋊Dic71C2211yescharacteristic
50C4×(C2×D71)⋊C4C2211yescharacteristic
51C4×(C2×D71)⋊C4C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54#17985753C2211yescharacteristic
55#17985753C2211yescharacteristic
56C22×C42×C71C2211yescharacteristic
57C2×C22⋊C8×C71C2211yescharacteristic
58C2×C22⋊C8×C71C2211yescharacteristic
59C2×#97×C71C2211yescharacteristic
60C2×#97×C71C2211yescharacteristic
61#336×C71C2211yescharacteristic
62#336×C71C2211yescharacteristic
63C22×D284C2×C411yescharacteristic
64C22×C22⋊D71C2×C411yescharacteristic
65C22×C22⋊D71C2×C411yescharacteristic
66C22×C4×D71C2311yescharacteristic
67C22×C4×D71C2311yescharacteristic
68C2×#11765848—22no—
69C2×#11765848—22no—
70C2×#11765848—41no—
71C22×C71⋊C8—22no—
72C22×C71⋊C8—22no—
73C22×C71⋊C8—22no—
74C22×C71⋊C8—22no—
75C22×C71⋊C8—41no—
76C22×C71⋊C8—41no—
77C22×C71⋊C8C2311yescharacteristic
78C22×C71⋊C8C2311yescharacteristic
79C22×C71⋊C8C2311yescharacteristic
80C22×C71⋊C8C2311yescharacteristic
81C2×C8×D71—22no—
82C2×C8×D71—22no—
83C2×C8×D71—41no—
84#14556102—24no—
85C4×D284—22no—
86C4×D284—22no—
87C4×C22⋊D71—22no—
88C4×C22⋊D71—22no—
89C4×C22⋊D71—22no—
90C4×C22⋊D71—22no—
91C2×C4⋊Dic71C2×C411yescharacteristic
92C2×C4⋊Dic71C2×C411yescharacteristic
93C2×C4⋊Dic71C2×C411yescharacteristic
94C2×Dic71⋊C4C2×C411yescharacteristic
95C2×Dic71⋊C4C2×C411yescharacteristic
96C2×C22⋊Dic71C2×C411yescharacteristic
97C2×C22⋊Dic71C2×C411yescharacteristic
98C2×(C2×D71)⋊C4C2×C411yescharacteristic
99C2×(C2×D71)⋊C4C2×C411yescharacteristic
100C2×(C2×D71)⋊C4C2×C411yescharacteristic
101C2×(C2×D71)⋊C4C2×C411yescharacteristic
102C2×(C2×D71)⋊C4C2×C411yescharacteristic
103C2×(C2×D71)⋊C4C2×C411yescharacteristic
104C2×(C2×D71)⋊C4C2×C411yescharacteristic
105C2×(C2×D71)⋊C4C2×C411yescharacteristic
106C2×C4×Dic71C2311yescharacteristic
107C2×C4×Dic71C2311yescharacteristic
108C4⋊(C71⋊C8)—22no—
109C4⋊(C71⋊C8)—22no—
110C4⋊(C71⋊C8)—22no—
111C4⋊(C71⋊C8)D414yescomplemented
112Dic71⋊C8—22no—
113Dic71⋊C8—22no—
114(C2×D71)⋊C8—22no—
115(C2×D71)⋊C8—22no—
116(C2×D71)⋊C8—22no—
117(C2×D71)⋊C8—22no—
118(C2×D71)⋊C8—41no—
119(C2×D71)⋊C8—41no—
120#14556038—22no—
121C8×Dic71—22no—
122C71⋊#95C2×C411yescharacteristic
123C71⋊#95C2×C411yescharacteristic
124C71⋊#95C2×C411yescharacteristic
125C71⋊#95C2×C411yescharacteristic
126C71⋊#95C2×C411yescharacteristic
127C71⋊#95C2×C411yescharacteristic
128C23×C4×C71C2×C411yescharacteristic
129C23×C4×C71C2×C411yescharacteristic
130C23×C4×C71C2311yescharacteristic
131C22×C8×C71C2311yescharacteristic
132C22×C8×C71C2311yescharacteristic
133C22×C8×C71C2311yescharacteristic
134C22×C8×C71C2311yescharacteristic
135C2×C42×C71—22no—
136C2×C42×C71—22no—
137C2×C42×C71C2×C411yescharacteristic
138C2×C42×C71C2×C411yescharacteristic
139C2×C42×C71C2311yescharacteristic
140C2×C42×C71C2311yescharacteristic
141C22⋊C8×C71—22no—
142C22⋊C8×C71D414yescomplemented
143#97×C71—22no—
144#97×C71—22no—
145C23×D71C22×C411yescharacteristic
146C23×D71C22×C411yescharacteristic
147C2×D284—22no—
148C2×D284—22no—
149C2×D284—41no—
150C2×C22⋊D71—22no—
151C2×C22⋊D71—22no—
152C2×C22⋊D71—22no—
153C2×C22⋊D71—22no—
154C2×C22⋊D71—22no—
155C2×C22⋊D71M1614yescomplemented
156C22×Dic71C22×C411yescharacteristic
157C22×Dic71C22×C411yescharacteristic
158C22×Dic71C22×C411yescharacteristic
159C22×Dic71C22×C411yescharacteristic
160C22×Dic71C22×C411yescharacteristic
161C22×Dic71C22×C411yescharacteristic
162C2×C4×D71—21no—
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—21no—
170C2×C4×D71—21no—
171C2×C4×D71—21no—
172C2×C4×D71—21no—
173C2×C4×D71—21no—
174#11765848—44no—
175C2×C71⋊C8—21no—
176C2×C71⋊C8—21no—
177C2×C71⋊C8—21no—
178C2×C71⋊C8—21no—
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—44no—
186C2×C71⋊C8—44no—
187C2×C71⋊C8C2×D412yes—
188C2×C71⋊C8C2×D412yes—
189C8×D71—44no—
190C4⋊Dic71—22no—
191C4⋊Dic71—22no—
192C4⋊Dic71—41no—
193Dic71⋊C4—22no—
194Dic71⋊C4—22no—
195C22⋊Dic71—22no—
196C22⋊Dic71—22no—
197(C2×D71)⋊C4—22no—
198(C2×D71)⋊C4—22no—
199(C2×D71)⋊C4—22no—
200(C2×D71)⋊C4—22no—
201(C2×D71)⋊C4—22no—
202(C2×D71)⋊C4—22no—
203(C2×D71)⋊C4—22no—
204(C2×D71)⋊C4—22no—
205C4×Dic71—21no—
206C4×Dic71—21no—
207C4×Dic71—21no—
208C4×Dic71—21no—
209C24×C71C22×C411yescharacteristic
210C22×C4×C71—22no—
211C22×C4×C71—22no—
212C22×C4×C71—22no—
213C22×C4×C71—21no—
214C22×C4×C71—21no—
215C22×C4×C71—21no—
216C22×C4×C71—21no—
217C22×C4×C71—22no—
218C22×C4×C71—22no—
219C22×C4×C71—41no—
220C22×C4×C71C22×C411yescharacteristic
221C22×C4×C71C22×C411yescharacteristic
222C22×C4×C71C22×C411yescharacteristic
223C22×C4×C71C22×C411yescharacteristic
224C22×C4×C71C22×C411yescharacteristic
225C22×C4×C71C2×D412yes—
226C22×C4×C71#4112yes—
227C22×C4×C71C2411yescharacteristic
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—
237C2×C8×C71—21no—
238C2×C8×C71C2×D412yes—
239C2×C8×C71C2×D412yes—
240C42×C71—22no—
241C42×C71—22no—
242C42×C71—21no—
243C42×C71—21no—
244C42×C71C2×D412yes—
245C42×C71#4112yes—
246C23×C71—21no—
247C23×C71—21no—
248C23×C71—21no—
249C23×C71—21no—
250C23×C71C4×D412yes—
251C23×C71C2×M1612yes—
252C23×C71#13112yes—
253C23×C71C23×C411yescharacteristic
254C22×D71—21no—
255C22×D71—21no—
256C22×D71—21no—
257C22×D71—21no—
258C22×D71—21no—
259C22×D71—21no—
260C22×D71—21no—
261C22×D71—21no—
262C22×D71—21no—
263C22×D71—21no—
264C22×D71—21no—
265C22×D71—21no—
266C22×D71—21no—
267C22×D71C2×M1612yes—
268C2×C4×C71—28no—
269C2×C4×C71—21no—
270C2×C4×C71—21no—
271C2×C4×C71—21no—
272C2×C4×C71—21no—
273C2×C4×C71—21no—
274C2×C4×C71—21no—
275C2×C4×C71—21no—
276C2×C4×C71—21no—
277C2×C4×C71—22no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—21no—
282C2×C4×C71—21no—
283C2×C4×C71—21no—
284C2×C4×C71—44no—
285C2×C4×C71C4×D412yes—
286C2×C4×C71C4×D412yes—
287C2×C4×C71C4×D412yes—
288C2×C4×C71#13112yes—
289C2×C4×C71C22×D411yescharacteristic
290C2×C4×C71C22×D411yescharacteristic
291C2×C4×C71C2×#4111yescharacteristic
292C2×C4×C71C2×#4111yescharacteristic
293C2×C4×C71H(5,𝔽2)11yescharacteristic
294C2×C4×C712−1+411yescharacteristic
295C22⋊D71—28no—
296C22⋊D71—44no—
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—21no—
313C2×Dic71—21no—
314C2×Dic71C2×M1612yes—
315D284—44no—
316C4×D71—41no—
317C4×D71—41no—
318C4×D71—41no—
319C4×D71—41no—
320C4×D71—41no—
321C4×D71—41no—
322C4×D71—41no—
323C4×D71—41no—
324C8×C71—22no—
325C8×C71—22no—
326C8×C71—41no—
327C8×C71—41no—
328C71⋊C8—22no—
329C71⋊C8—22no—
330C71⋊C8—41no—
331C71⋊C8—41no—
332C22×C71—22no—
333C22×C71—22no—
334C22×C71—22no—
335C22×C71—22no—
336C22×C71—22no—
337C22×C71—22no—
338C22×C71#43514yescomplemented
339C22×C71C2×C4×D411yescharacteristic
340C22×C71C2×C4×D411yescharacteristic
341C22×C71#52011yescharacteristic
342C22×C71C22×M1611yescharacteristic
343C22×C71C2×#13111yescharacteristic
344C22×C71C2×#13111yescharacteristic
345C22×C71#56811yescharacteristic
346C2×D71—22no—
347C2×D71—22no—
348C2×D71—22no—
349C2×D71—41no—
350C2×D71—41no—
351C2×D71—41no—
352C2×D71—41no—
353C2×D71—41no—
354C2×D71—41no—
355C2×D71—41no—
356C2×D71—41no—
357C2×D71—41no—
358C2×D71—41no—
359C2×D71—41no—
360C4×C71—22no—
361C4×C71—22no—
362C4×C71—22no—
363C4×C71—22no—
364C4×C71—41no—
365C4×C71D4211yescharacteristic
366C4×C71#54711yescharacteristic
367C4×C71#54811yescharacteristic
368C4×C71#55311yescharacteristic
369Dic71—22no—
370Dic71—41no—
371Dic71—41no—
372Dic71—41no—
373Dic71—41no—
374Dic71—41no—
375#22987—711nomaximal, Sylow
376C2×C71—24no—
377C2×C71#236111yescharacteristic
378C2×C71C2×#43511yescharacteristic
379C2×C71#292911yescharacteristic
380C2×C71D4×M1611yescharacteristic
381C2×C71#293511yescharacteristic
382C2×C71#299011yescharacteristic
383C2×C71#299211yescharacteristic
384D71—42no—
385D71—81no—
386C2×#435—711no—
387C2×#435—711no—
388C2×C8×D4—711no—
389C22×C4⋊C8—711no—
390C4×#121—711no—
391#1955—711no—
392#1940—711no—
393#1924—711no—
394#1923—711no—
395#1869—711no—
396#1869—711no—
397#1851—711no—
398#1850—711no—
399#1771—711no—
400#1749D7111yescharacteristic, complemented
401C71#2298711yescharacteristic, complemented, Sylow
402C22×M16—711no—
403C23×C8—711no—
404C23×C8—711no—
405C23×C8—711no—
406C2×#121—711no—
407C2×C4×D4—711no—
408C2×C4×D4—711no—
409C2×C4×D4—711no—
410C22×C42C2×D7111yescharacteristic
411#435—1424no—
412#435—1424no—
413C8×D4—1424no—
414C2×C4⋊C8—711no—
415C2×C4⋊C8—711no—
416C2×C4⋊C8—711no—
417C2×C4⋊C8—711no—
418C2×C4⋊C8—711no—
419C2×C4⋊C8—711no—
420C2×C4⋊C8—1424no—
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⋊C8C2×D7111yescharacteristic
428C2×C22⋊C8C2×D7111yescharacteristic
429C2×#97—711no—
430C2×#97C2×D7111yescharacteristic
431C2×#97C2×D7111yescharacteristic
432C2×C4×C8—711no—
433#390—711no—
434#389—711no—
435#388—711no—
436#388—711no—
437#386—711no—
438#386—711no—
439#380—711no—
440C4×C4⋊C4—711no—
441C4×C22⋊C4—711no—
442C4×C22⋊C4—711no—
443#336—711no—
444#336—711no—
445#336—711no—
446#336—711no—
447#336C2×D7111yescharacteristic
448#336C2×D7111yescharacteristic
449C22×D4—711no—
450C22×D4—711no—
451C22×D4—711no—
452C23×C4—711no—
453C23×C4—711no—
454C23×C4C4×D7111yescharacteristic
455C23×C4C4×D7111yescharacteristic
456C23×C4C22×D7111yescharacteristic
457C2×M16—2841no—
458C2×M16—1422no—
459C2×M16—1422no—
460C22×C8—2841no—
461C22×C8—2841no—
462C22×C8—2841no—
463C22×C8—711no—
464C22×C8—711no—
465C22×C8—711no—
466C22×C8—711no—
467C22×C8—1422no—
468C22×C8—1422no—
469C22×C8—1422no—
470C22×C8—1422no—
471C22×C8—1422no—
472C22×C8—1422no—
473C22×C8C22×D7111yescharacteristic
474C22×C8C22×D7111yescharacteristic
475C22×C8C22×D7111yescharacteristic
476C22×C8C22×D7111yescharacteristic
477#121—1424no—
478C4×D4—1422no—
479C4×D4—1422no—
480C4×D4—1422no—
481C4×D4—1422no—
482C4×D4—1422no—
483C4×D4—1422no—
484C2×C4⋊C4—711no—
485C2×C4⋊C4—711no—
486C2×C4⋊C4—711no—
487C2×C4⋊C4—711no—
488C2×C4⋊C4—711no—
489C2×C22⋊C4—711no—
490C2×C22⋊C4—711no—
491C2×C22⋊C4—711no—
492C2×C22⋊C4—711no—
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×C42—22no—
500C2×C42—22no—
501C2×C42—711no—
502C2×C42—711no—
503C2×C42C4×D7111yescharacteristic
504C2×C42C4×D7111yescharacteristic
505C2×C42C22×D7111yescharacteristic
506C2×C42C22×D7111yescharacteristic
507C4⋊C8—714no—
508C4⋊C8—1422no—
509C4⋊C8—1422no—
510C4⋊C8—1422no—
511C4⋊C8—1422no—
512C4⋊C8—1422no—
513C22⋊C8—22no—
514C22⋊C8—2841no—
515C22⋊C8—2841no—
516C22⋊C8—1422no—
517C22⋊C8—1422no—
518C22⋊C8—1422no—
519C22⋊C8—1422no—
520C22⋊C8D28414yescomplemented
521#97—22no—
522#97—22no—
523#97—1422no—
524C4×C8—1422no—
525#95—711no—
526#95—711no—
527#95—711no—
528#95—711no—
529#95—711no—
530#95—711no—
531C24—711no—
532C24—711no—
533C24C2×C4×D7111yescharacteristic
534C2×D4—2841no—
535C2×D4—714no—
536C2×D4—1422no—
537C2×D4—1422no—
538C2×D4—1422no—
539C2×D4—1422no—
540C2×D4—1422no—
541C2×D4—1422no—
542C2×D4—1422no—
543C22×C4—22no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—41no—
553C22×C4—711no—
554C22×C4—711no—
555C22×C4—711no—
556C22×C4—711no—
557C22×C4—711no—
558C22×C4—711no—
559C22×C4—1421no—
560C22×C4—1421no—
561C22×C4—1421no—
562C22×C4—1421no—
563C22×C4—1421no—
564C22×C4—1421no—
565C22×C4—1421no—
566C22×C4—1421no—
567C22×C4—1421no—
568C22×C4—1421no—
569C22×C4—1421no—
570C22×C4—1421no—
571C22×C4C2×C4×D7111yescharacteristic
572C22×C4C2×C4×D7111yescharacteristic
573C22×C4C2×C4×D7111yescharacteristic
574C22×C4C2×C4×D7111yescharacteristic
575C22×C4C2×C4×D7111yescharacteristic
576C22×C4C2×D28412yes—
577C22×C4#1176586512yes—
578C22×C4C23×D7111yescharacteristic
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—2844no—
591C2×C8—2844no—
592C2×C8—2844no—
593C2×C8—712no—
594C2×C8—712no—
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×C8—1421no—
604C2×C8—1421no—
605C2×C8C2×D28412yes—
606C2×C8C2×D28412yes—
607C4⋊C4—2841no—
608C4⋊C4—1422no—
609C4⋊C4—1422no—
610C4⋊C4—1422no—
611C4⋊C4—1422no—
612C22⋊C4—1422no—
613C22⋊C4—1422no—
614C22⋊C4—1422no—
615C22⋊C4—1422no—
616C22⋊C4—1422no—
617C22⋊C4—1422no—
618C22⋊C4—1422no—
619C22⋊C4—1422no—
620C22⋊C4—1422no—
621C22⋊C4—1422no—
622C42—21no—
623C42—21no—
624C42—22no—
625C42—22no—
626C42—1421no—
627C42—1421no—
628C42—1421no—
629C42—1421no—
630C42D4×D7112yes—
631C42#1176586412yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—712no—
637C23—1421no—
638C23—1421no—
639C23—1421no—
640C23—1421no—
641C23—1421no—
642C23—1421no—
643C23—1421no—
644C23—1421no—
645C23—1421no—
646C23—1421no—
647C23—1421no—
648C23—1421no—
649C23—1421no—
650C23C4×D28412yes—
651C23M16×D7112yes—
652C23#1455613612yes—
653C23C22×C4×D7111yescharacteristic
654D4—2844no—
655D4—2844no—
656D4—1428no—
657C2×C4—28no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—44no—
674C2×C4—2841no—
675C2×C4—2841no—
676C2×C4—2841no—
677C2×C4—2841no—
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(C22⋊D71)⋊C412yes—
701C2×C4(C22⋊D71)⋊C412yes—
702C2×C4C4×D28412yes—
703C2×C4#1455613612yes—
704C2×C4C2×D4×D7111yescharacteristic
705C2×C4C22×D28411yescharacteristic
706C2×C4C2×#1176586411yescharacteristic
707C2×C4C2×#1176586511yescharacteristic
708C2×C4#1455617411yescharacteristic
709C2×C4#1455617511yescharacteristic
710C8—22no—
711C8—22no—
712C8—41no—
713C8—41no—
714C8—2841no—
715C8—2841no—
716C8—1422no—
717C8—1422no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—2841no—
725C22—2841no—
726C22—2841no—
727C22—2841no—
728C22—2841no—
729C22—2841no—
730C22—2841no—
731C22—2841no—
732C22—2841no—
733C22—2841no—
734C22—2841no—
735C22—1422no—
736C22—1422no—
737C22—1422no—
738C22#1798607214yescomplemented
739C22C2×(C22⋊D71)⋊C411yescharacteristic
740C22C2×C4×D28411yescharacteristic
741C22#1798647911yescharacteristic
742C22C2×M16×D7111yescharacteristic
743C22C2×#1455613611yescharacteristic
744C22C2×#1455613611yescharacteristic
745C22#1798676511yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—41no—
751C4—2841no—
752C4—2841no—
753C4—2841no—
754C4—2841no—
755C4—2841no—
756C4—1422no—
757C4D4×D28411yescharacteristic
758C4#1798665311yescharacteristic
759C4#1798665811yescharacteristic
760C4#1798669511yescharacteristic
761C2—24no—
762C2—2842no—
763C2—5681no—
764C2#2259135411yescharacteristic
765C2C2×#1798607211yescharacteristic
766C2#2259703011yescharacteristic
767C2#2259707211yescharacteristic
768C2#2259708611yescharacteristic
769C2#2259746711yescharacteristic
770C2#2259748111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1749C2
prime radicalC2×#14556102C4
cosocleC22×C4×C71C24
hypercenter#1749D71
hypocenterC71#22987
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1749

Complements

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

NH ≅ G/Ntype
1. C2×#17986072C2semidirect
2. C2×#17986067C2semidirect
3. C2×(C22⋊D71)⋊C8C2semidirect
4. C22×C4⋊(C71⋊C8)C2semidirect
6. #22589138C2semidirect
7. #22589063C2semidirect
8. #22588954C2semidirect
9. #22588947C2semidirect
10. #22588630C2semidirect
11. #22588630C2semidirect
12. #22588524C2semidirect
13. #22588519C2semidirect
14. #22588212C2semidirect
15. C71×#1749C2semidirect
111. C4⋊(C71⋊C8)D4semidirect
142. C22⋊C8×C71D4semidirect
155. C2×C22⋊D71M16semidirect
338. C22×C71#435semidirect
400. #1749D71semidirect
401. C71#22987semidirect
520. C22⋊C8D284semidirect
738. C22#17986072semidirect

Maximal subgroups

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

subgroupindex
C2×#179860722
C2×#179860672
C2×(C22⋊D71)⋊C82
C22×C4⋊(C71⋊C8)2
C4×#145561022
#225891382
#225890632
#225889542
#225889472
#225886302
#225885242
#225885192
#225882122
C71×#17492
#2298771