Finite Group Databasebeta

← #31999777

Subgroups — #31999777

Order 18176.

1226 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986024C211yesmaximal, characteristic, complemented
2C2×#17985961C211yesmaximal, characteristic
3C2×C22⋊C8×D71C211yesmaximal, characteristic
4C2×#17985956C211yesmaximal, characteristic, complemented
5#22590721C211yesmaximal, characteristic
6#22588954C211yesmaximal, characteristic, complemented
7#22588953C211yesmaximal, characteristic, complemented
8#22588950C211yesmaximal, characteristic, complemented
9#22588949C211yesmaximal, characteristic, complemented
10#22588948C211yesmaximal, characteristic, complemented
11#22588945C211yesmaximal, characteristic, complemented
12#22588944C211yesmaximal, characteristic, complemented
13#22588035C211yesmaximal, characteristic, complemented
14#22588035C211yesmaximal, characteristic, complemented
15C71×#1924C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20C22×C8×D71C2211yescharacteristic
21C2×#14556085C2211yescharacteristic
22C2×#14556085C2211yescharacteristic
23#17986024—24no—
24C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
25C2×Dic71⋊C8C2211yescharacteristic, complemented
26C2×Dic71⋊C8C2211yescharacteristic, complemented
27#17985961—24no—
28C2×C22⋊(C71⋊C8)C2211yescharacteristic
29C2×C22⋊(C71⋊C8)C2211yescharacteristic
30C2×(C2×D71)⋊C8C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C22⋊C8×D71—24no—
35#17985956—24no—
36C2×#14556038C2211yescharacteristic, complemented
37C2×C4×C71⋊C8C2211yescharacteristic, complemented
38C2×C8×Dic71C2211yescharacteristic, complemented
39#17985861C411yescharacteristic
40#17985861C411yescharacteristic
41#17985858C411yescharacteristic
42#17985858C411yescharacteristic
43#17985857C411yescharacteristic
44#17985857C411yescharacteristic
45#17985854C411yescharacteristic
46#17985854C411yescharacteristic
47C4×(C2×D71)⋊C4C2211yescharacteristic
48C4×(C2×D71)⋊C4C2211yescharacteristic
49C4×C22⋊Dic71C2211yescharacteristic
50#17985754C2211yescharacteristic, complemented
51#17985754C2211yescharacteristic, complemented
52#17985753C2211yescharacteristic, complemented
53#17985753C2211yescharacteristic, complemented
54#17985753C2211yescharacteristic, complemented
55#17985753C2211yescharacteristic, complemented
56C2×C4⋊C8×C71C2211yescharacteristic, complemented
57C2×C22⋊C8×C71C2211yescharacteristic
58C2×C22⋊C8×C71C2211yescharacteristic
59C2×#97×C71C2211yescharacteristic, complemented
60C4×C22⋊C4×C71C2211yescharacteristic
61#336×C71C2211yescharacteristic, complemented
62#336×C71C2211yescharacteristic, complemented
63C24×D71C2×C411yescharacteristic
64C23×Dic71C2×C411yescharacteristic
65C22×C4×D71—22no—
66C22×C4×D71—22no—
67C22×C4×D71—22no—
68C22×C4×D71—22no—
69C22×C4×D71—22no—
70C22×C4×D71—22no—
71C22×C4×D71C2×C411yescharacteristic
72C22×C4×D71C2×C411yescharacteristic
73C22×C4×D71C2311yescharacteristic
74C22×C4×D71C2311yescharacteristic
75C2×#11765848—22no—
76C2×#11765848—22no—
77C2×#11765848—22no—
78C2×#11765848—22no—
79C2×#11765848—22no—
80C2×#11765848D414yes—
81C22×C71⋊C8C2311yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C22×C71⋊C8C2311yescharacteristic
84C22×C71⋊C8C2311yescharacteristic
85C2×C8×D71—22no—
86C2×C8×D71—22no—
87C2×C8×D71—22no—
88C2×C8×D71—22no—
89C2×C8×D71—22no—
90C2×C8×D71D414yes—
91#14556085—22no—
92#14556085—22no—
93#14556085—22no—
94#14556085—22no—
95C2×Dic71⋊C4C2×C411yescharacteristic
96C2×Dic71⋊C4C2×C411yescharacteristic
97C2×Dic71⋊C4C2×C411yescharacteristic
98C2×Dic71⋊C4C2×C411yescharacteristic
99C2×C22⋊Dic71C2×C411yescharacteristic
100C2×C22⋊Dic71C2×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×(C2×D71)⋊C4C2×C411yescharacteristic
107C2×(C2×D71)⋊C4C2×C411yescharacteristic
108C2×(C2×D71)⋊C4C2×C411yescharacteristic
109C2×C4×Dic71C2311yescharacteristic
110C2×C4×Dic71C2311yescharacteristic
111C4⋊(C71⋊C8)—22no—
112Dic71⋊C8—22no—
113Dic71⋊C8—22no—
114C22⋊(C71⋊C8)—22no—
115C22⋊(C71⋊C8)—22no—
116(C2×D71)⋊C8—22no—
117(C2×D71)⋊C8—22no—
118(C2×D71)⋊C8—22no—
119(C2×D71)⋊C8—22no—
120#14556038—22no—
121C4×C71⋊C8—22no—
122C8×Dic71—22no—
123C71⋊#95C2×C411yescharacteristic
124C71⋊#95C2×C411yescharacteristic
125C71⋊#95C2×C411yescharacteristic
126C71⋊#95C2×C411yescharacteristic
127C71⋊#95C2×C411yescharacteristic
128C71⋊#95C2×C411yescharacteristic
129C23×C4×C71C2311yescharacteristic
130C22×C8×C71C2311yescharacteristic
131C22×C8×C71C2311yescharacteristic
132C22×C8×C71C2311yescharacteristic
133C22×C8×C71C2311yescharacteristic
134C2×C22⋊C4×C71C2×C411yescharacteristic
135C2×C22⋊C4×C71C2×C411yescharacteristic
136C2×C42×C71C2311yescharacteristic
137C2×C42×C71C2311yescharacteristic
138C4⋊C8×C71—22no—
139C22⋊C8×C71—22no—
140C22⋊C8×C71—22no—
141#97×C71—22no—
142#95×C71C2×C411yescharacteristic
143#95×C71C2×C411yescharacteristic
144C23×D71—22no—
145C23×D71—22no—
146C23×D71—22no—
147C23×D71—22no—
148C23×D71—22no—
149C23×D71—41no—
150C23×D71—41no—
151C23×D71C22×C411yescharacteristic
152C23×D71C22×C411yescharacteristic
153C22×Dic71—22no—
154C22×Dic71—22no—
155C22×Dic71—22no—
156C22×Dic71C22×C411yescharacteristic
157C22×Dic71C22×C411yescharacteristic
158C22×Dic71C22×C411yescharacteristic
159C22×Dic71C22×C411yescharacteristic
160C22×Dic71C22×C411yescharacteristic
161C22×Dic71C22×C411yescharacteristic
162C2×C4×D71—22no—
163C2×C4×D71—22no—
164C2×C4×D71—22no—
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—22no—
172C2×C4×D71—22no—
173C2×C4×D71—22no—
174C2×C4×D71—44no—
175C2×C4×D71—44no—
176C2×C4×D71—44no—
177C2×C4×D71—44no—
178C2×C4×D71C2×D412yes—
179C2×C4×D71C2×D412yes—
180C2×C4×D71#4112yes—
181C2×C4×D71#4112yes—
182C2×C4×D71#4112yes—
183C2×C4×D71#4112yes—
184#11765848—28no—
185#11765848—44no—
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⋊C8C2×D412yes—
197C2×C71⋊C8C2×D412yes—
198C8×D71—28no—
199C8×D71—44no—
200Dic71⋊C4—22no—
201Dic71⋊C4—22no—
202Dic71⋊C4—22no—
203Dic71⋊C4—22no—
204C22⋊Dic71—22no—
205C22⋊Dic71—41no—
206(C2×D71)⋊C4—22no—
207(C2×D71)⋊C4—22no—
208(C2×D71)⋊C4—22no—
209(C2×D71)⋊C4—22no—
210(C2×D71)⋊C4—22no—
211(C2×D71)⋊C4—22no—
212(C2×D71)⋊C4—41no—
213(C2×D71)⋊C4—41no—
214C4×Dic71—21no—
215C4×Dic71—21no—
216C4×Dic71—21no—
217C4×Dic71—21no—
218C24×C71C22×C411yescharacteristic
219C22×C4×C71—21no—
220C22×C4×C71—21no—
221C22×C4×C71—21no—
222C22×C4×C71—21no—
223C22×C4×C71—21no—
224C22×C4×C71—21no—
225C22×C4×C71C22×C411yescharacteristic
226C22×C4×C71C22×C411yescharacteristic
227C22×C4×C71C22×C411yescharacteristic
228C22×C4×C71C22×C411yescharacteristic
229C22×C4×C71C22×C411yescharacteristic
230C22×C4×C71C2411yescharacteristic
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×C71—21no—
239C2×C8×C71—21no—
240C2×C8×C71—21no—
241C2×C8×C71C2×D412yes—
242C2×C8×C71C2×D412yes—
243C22⋊C4×C71—22no—
244C22⋊C4×C71—41no—
245C42×C71—21no—
246C42×C71—21no—
247C42×C71—21no—
248C42×C71—21no—
249C23×C71—21no—
250C23×C71—21no—
251C23×C71—21no—
252C23×C71—21no—
253C23×C71—21no—
254C23×C71—21no—
255C23×C71#13112yes—
256C23×C71C23×C411yescharacteristic
257C22×D71—21no—
258C22×D71—21no—
259C22×D71—21no—
260C22×D71—21no—
261C22×D71—28no—
262C22×D71—21no—
263C22×D71—21no—
264C22×D71—21no—
265C22×D71—21no—
266C22×D71—21no—
267C22×D71—21no—
268C22×D71—44no—
269C22×D71—44no—
270C22×D71—44no—
271C22×D71—44no—
272C22×D71—44no—
273C22×D71—44no—
274C22×D71#11712yes—
275C22×D71C4×D412yes—
276C22×D71C4×D412yes—
277C22×D71#13112yes—
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—21no—
289C2×C4×C71—21no—
290C2×C4×C71—21no—
291C2×C4×C71—21no—
292C2×C4×C71—21no—
293C2×C4×C71—41no—
294C2×C4×C71—41no—
295C2×C4×C71—41no—
296C2×C4×C71—41no—
297C2×C4×C71C22×D411yescharacteristic
298C2×C4×C71C22×D411yescharacteristic
299C2×C4×C71C2×#4111yescharacteristic
300C2×C4×C71C2×#4111yescharacteristic
301C2×C4×C71C2×#4111yescharacteristic
302C2×C4×C71C2×#4111yescharacteristic
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×Dic71—21no—
315C2×Dic71—21no—
316C2×Dic71—21no—
317C2×Dic71—21no—
318C2×Dic71—44no—
319C2×Dic71#11712yes—
320C2×Dic71C4×D412yes—
321C2×Dic71C4×D412yes—
322C4×D71—44no—
323C4×D71—41no—
324C4×D71—41no—
325C4×D71—41no—
326C4×D71—41no—
327C4×D71—44no—
328C4×D71#12114yes—
329C4×D71#12314yes—
330C4×D71#12414yes—
331C4×D71#12614yes—
332C8×C71—22no—
333C8×C71—22no—
334C8×C71—41no—
335C8×C71—41no—
336C71⋊C8—22no—
337C71⋊C8—22no—
338C71⋊C8—41no—
339C71⋊C8—41no—
340C22×C71—22no—
341C22×C71—22no—
342C22×C71—22no—
343C22×C71—41no—
344C22×C71—41no—
345C22×C71—41no—
346C22×C71—41no—
347C22×C71C2×#11711yescharacteristic
348C22×C71C2×C4×D411yescharacteristic
349C22×C71C2×C4×D411yescharacteristic
350C22×C71C2×#13111yescharacteristic
351C22×C71C2×#13111yescharacteristic
352C22×C71#56811yescharacteristic
353C22×C71#56811yescharacteristic
354C2×D71—22no—
355C2×D71—22no—
356C2×D71—22no—
357C2×D71—22no—
358C2×D71—22no—
359C2×D71—22no—
360C2×D71—22no—
361C2×D71—22no—
362C2×D71—22no—
363C2×D71—416no—
364C2×D71—41no—
365C2×D71—41no—
366C2×D71—41no—
367C2×D71—41no—
368C2×D71#38814yes—
369C4×C71—41no—
370C4×C71—41no—
371C4×C71—41no—
372C4×C71—41no—
373C4×C71—41no—
374C4×C71C2×#12111yescharacteristic
375C4×C71C2×#12311yescharacteristic
376C4×C71C2×#12411yescharacteristic
377C4×C71C2×#12611yescharacteristic
378Dic71—41no—
379Dic71—41no—
380Dic71—41no—
381Dic71—41no—
382Dic71—41no—
383Dic71#38814yes—
384#21050—711nomaximal, Sylow
385C2×C71—42no—
386C2×C71C2×#38811yescharacteristic
387C2×C71#292411yescharacteristic
388C2×C71#292411yescharacteristic
389C2×C71#292911yescharacteristic
390C2×C71#293011yescharacteristic
391C2×C71#293311yescharacteristic
392C2×C71#293311yescharacteristic
393D71—24no—
394D71—42no—
395C2×#424—711no—
396C2×#407—711no—
397C22×C22⋊C8—711no—
398C2×#405—711no—
399#2280—711no—
400#1924—711no—
401#1924—711no—
402#1924—711no—
403#1924D7111yescharacteristic, complemented
404#1923—711no—
405#1923—711no—
406#1923—711no—
407#1923—711no—
408#1729—711no—
409#1729—711no—
410C71#2105011yescharacteristic, complemented, Sylow
411C24×C4—711no—
412C22×M16—711no—
413C22×M16—711no—
414C23×C8—711no—
415C23×C8—711no—
416C2×#117—711no—
417C2×#117—711no—
418#424—1424no—
419C2×C4⋊C8—711no—
420C2×C4⋊C8—711no—
421C2×C4⋊C8—711no—
422C2×C4⋊C8C2×D7111yescharacteristic, complemented
423#407—1424no—
424C2×C22⋊C8—711no—
425C2×C22⋊C8—711no—
426C2×C22⋊C8—711no—
427C2×C22⋊C8—711no—
428C2×C22⋊C8—711no—
429C2×C22⋊C8—711no—
430C2×C22⋊C8—1424no—
431C2×C22⋊C8C2×D7111yescharacteristic
432C2×C22⋊C8C2×D7111yescharacteristic
433#405—1424no—
434C2×#97—711no—
435C2×#97C2×D7111yescharacteristic, complemented
436C2×C4×C8—711no—
437C2×C4×C8—711no—
438#381—711no—
439#381—711no—
440#380—711no—
441#380—711no—
442#380—711no—
443#380—711no—
444#379—711no—
445#379—711no—
446C4×C22⋊C4—711no—
447C4×C22⋊C4—711no—
448C4×C22⋊C4—711no—
449C4×C22⋊C4C2×D7111yescharacteristic
450#336—711no—
451#336—711no—
452#336—711no—
453#336—711no—
454#336—711no—
455#336—711no—
456#336C2×D7111yescharacteristic, complemented
457#336C2×D7111yescharacteristic, complemented
458C25—711no—
459C23×C4—711no—
460C23×C4—711no—
461C23×C4—711no—
462C23×C4—711no—
463C23×C4—711no—
464C23×C4—1422no—
465C23×C4—1422no—
466C23×C4—1422no—
467C23×C4—1422no—
468C23×C4—1422no—
469C23×C4—1422no—
470C23×C4C22×D7111yescharacteristic
471C2×M16—714no—
472C2×M16—1422no—
473C2×M16—1422no—
474C2×M16—1422no—
475C2×M16—1422no—
476C2×M16—1422no—
477C22×C8—711no—
478C22×C8—711no—
479C22×C8—714no—
480C22×C8—711no—
481C22×C8—711no—
482C22×C8—1422no—
483C22×C8—1422no—
484C22×C8—1422no—
485C22×C8—1422no—
486C22×C8—1422no—
487C22×C8C22×D7111yescharacteristic
488C22×C8C22×D7111yescharacteristic
489C22×C8C22×D7111yescharacteristic
490C22×C8C22×D7111yescharacteristic
491#117—1422no—
492#117—1422no—
493#117—1422no—
494#117—1422no—
495C2×C4⋊C4—711no—
496C2×C4⋊C4—711no—
497C2×C4⋊C4—711no—
498C2×C4⋊C4—711no—
499C2×C22⋊C4—711no—
500C2×C22⋊C4—711no—
501C2×C22⋊C4—711no—
502C2×C22⋊C4—711no—
503C2×C22⋊C4—711no—
504C2×C22⋊C4—711no—
505C2×C22⋊C4—711no—
506C2×C22⋊C4—711no—
507C2×C22⋊C4—711no—
508C2×C22⋊C4—711no—
509C2×C22⋊C4C4×D7111yescharacteristic
510C2×C22⋊C4C4×D7111yescharacteristic
511C2×C42—711no—
512C2×C42—711no—
513C2×C42C22×D7111yescharacteristic
514C2×C42C22×D7111yescharacteristic
515C4⋊C8—22no—
516C4⋊C8—1422no—
517C4⋊C8—1422no—
518C4⋊C8—1422no—
519C22⋊C8—22no—
520C22⋊C8—22no—
521C22⋊C8—1422no—
522C22⋊C8—1422no—
523C22⋊C8—1422no—
524C22⋊C8—1422no—
525C22⋊C8—1422no—
526C22⋊C8—1422no—
527#97—22no—
528#97—1422no—
529C4×C8—1422no—
530C4×C8—1422no—
531#95—711no—
532#95—711no—
533#95—711no—
534#95—711no—
535#95—711no—
536#95—711no—
537#95C4×D7111yescharacteristic
538#95C4×D7111yescharacteristic
539C24—2841no—
540C24—2841no—
541C24—711no—
542C24—711no—
543C24—1422no—
544C24—1422no—
545C24—1422no—
546C24—1422no—
547C24—1422no—
548C24C2×C4×D7111yescharacteristic
549C22×C4—21no—
550C22×C4—21no—
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—711no—
560C22×C4—712no—
561C22×C4—712no—
562C22×C4—712no—
563C22×C4—712no—
564C22×C4—712no—
565C22×C4—712no—
566C22×C4—711no—
567C22×C4—711no—
568C22×C4—711no—
569C22×C4—711no—
570C22×C4—711no—
571C22×C4—1422no—
572C22×C4—1422no—
573C22×C4—1422no—
574C22×C4—1422no—
575C22×C4—1422no—
576C22×C4—1422no—
577C22×C4—1422no—
578C22×C4—1422no—
579C22×C4—1422no—
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
592M16—2844no—
593M16—1428no—
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—2844no—
605C2×C8—712no—
606C2×C8—712no—
607C2×C8—1428no—
608C2×C8—1421no—
609C2×C8—1421no—
610C2×C8—1421no—
611C2×C8—1421no—
612C2×C8—1421no—
613C2×C8—1421no—
614C2×C8—1421no—
615C2×C8—1421no—
616C2×C8—1421no—
617C2×C8—1421no—
618C2×C8D4×D7112yes—
619C2×C8D4×D7112yes—
620C4⋊C4—1422no—
621C4⋊C4—1422no—
622C4⋊C4—1422no—
623C4⋊C4—1422no—
624C22⋊C4—22no—
625C22⋊C4—41no—
626C22⋊C4—2841no—
627C22⋊C4—2841no—
628C22⋊C4—2841no—
629C22⋊C4—1422no—
630C22⋊C4—1422no—
631C22⋊C4—1422no—
632C22⋊C4—1422no—
633C22⋊C4—1422no—
634C22⋊C4—1422no—
635C22⋊C4—1422no—
636C42—21no—
637C42—21no—
638C42—21no—
639C42—21no—
640C42—1421no—
641C42—1421no—
642C42—1421no—
643C42—1421no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—2844no—
651C23—2844no—
652C23—2844no—
653C23—2844no—
654C23—2844no—
655C23—2844no—
656C23—712no—
657C23—712no—
658C23—712no—
659C23—712no—
660C23—1428no—
661C23—1421no—
662C23—1421no—
663C23—1421no—
664C23—1421no—
665C23—1421no—
666C23—1421no—
667C23—1421no—
668C23—1421no—
669C23—1421no—
670C23—1421no—
671C23#1455613612yes—
672C23C22×C4×D7111yescharacteristic
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—2844no—
693C2×C4—2844no—
694C2×C4—2844no—
695C2×C4—2841no—
696C2×C4—2841no—
697C2×C4—2841no—
698C2×C4—2841no—
699C2×C4—712no—
700C2×C4—712no—
701C2×C4—712no—
702C2×C4—714no—
703C2×C4—714no—
704C2×C4—714no—
705C2×C4—714no—
706C2×C4—1421no—
707C2×C4—1421no—
708C2×C4—1421no—
709C2×C4—1421no—
710C2×C4—1421no—
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×C4C2×D4×D7111yescharacteristic
722C2×C4C2×D4×D7111yescharacteristic
723C2×C4#41×D7111yescharacteristic
724C2×C4#41×D7111yescharacteristic
725C2×C4#41×D7111yescharacteristic
726C2×C4#41×D7111yescharacteristic
727C8—22no—
728C8—22no—
729C8—41no—
730C8—41no—
731C8—2841no—
732C8—2841no—
733C8—1422no—
734C8—1422no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—28416no—
743C22—2841no—
744C22—2841no—
745C22—2841no—
746C22—2841no—
747C22—714no—
748C22—1422no—
749C22—1422no—
750C22—1422no—
751C22—1422no—
752C22—1422no—
753C22—1422no—
754C22—1422no—
755C22—1422no—
756C22—1422no—
757C22#117×D7111yescharacteristic
758C22C4×D4×D7111yescharacteristic
759C22C4×D4×D7111yescharacteristic
760C22#131×D7111yescharacteristic
761C22C2×#1455613611yescharacteristic
762C22#1798676411yescharacteristic
763C22#1798676511yescharacteristic
764C4—41no—
765C4—41no—
766C4—41no—
767C4—41no—
768C4—41no—
769C4—2841no—
770C4—2841no—
771C4—2841no—
772C4—2841no—
773C4—2841no—
774C4—714no—
775C4#121×D7111yescharacteristic
776C4#123×D7111yescharacteristic
777C4#124×D7111yescharacteristic
778C4#126×D7111yescharacteristic
779C2—42no—
780C2—2842no—
781C2—1424no—
782C2#388×D7111yescharacteristic
783C2#2259699611yescharacteristic
784C2#2259699911yescharacteristic
785C2#2259703111yescharacteristic
786C2#2259704011yescharacteristic
787C2#2259706311yescharacteristic
788C2#2259706611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1924C2
prime radicalC24×D71C2×C4
cosocleC22×C4×C71C24
hypercenter#1924D71
hypocenterC71#21050
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#17986024C2semidirect
4. C2×#17985956C2semidirect
6. #22588954C2semidirect
7. #22588953C2semidirect
8. #22588950C2semidirect
9. #22588949C2semidirect
10. #22588948C2semidirect
11. #22588945C2semidirect
12. #22588944C2semidirect
13. #22588035C2semidirect
14. #22588035C2semidirect
15. C71×#1924C2semidirect
24. C2×C4⋊(C71⋊C8)C22semidirect
25. C2×Dic71⋊C8C22semidirect
26. C2×Dic71⋊C8C22semidirect
36. C2×#14556038C22semidirect
37. C2×C4×C71⋊C8C22semidirect
38. C2×C8×Dic71C22semidirect
50. #17985754C22semidirect
51. #17985754C22semidirect
52. #17985753C22semidirect
53. #17985753C22semidirect
54. #17985753C22semidirect
55. #17985753C22semidirect
56. C2×C4⋊C8×C71C22semidirect
59. C2×#97×C71C22semidirect
61. #336×C71C22semidirect
62. #336×C71C22semidirect
403. #1924D71semidirect
410. C71#21050semidirect
422. C2×C4⋊C8C2×D71semidirect
435. C2×#97C2×D71semidirect
456. #336C2×D71semidirect
457. #336C2×D71semidirect

Maximal subgroups

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

subgroupindex
C2×#179860242
C2×#179859612
C2×C22⋊C8×D712
C2×#179859562
#225907212
#225889542
#225889532
#225889502
#225889492
#225889482
#225889452
#225889442
#225880352
C71×#19242
#2105071