Finite Group Databasebeta

← #31999765

Subgroups — #31999765

Order 18176.

1330 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986021C211yesmaximal, characteristic, complemented
2C2×#17985961C211yesmaximal, characteristic
3C2×#17985961C211yesmaximal, characteristic
4C2×C4×#11765848C211yesmaximal, characteristic, complemented
5C4×C22⋊C4×D71C211yesmaximal, characteristic
6#22588956C211yesmaximal, characteristic, complemented
7#22588954C211yesmaximal, characteristic, complemented
8#22588952C211yesmaximal, characteristic, complemented
9#22588950C211yesmaximal, characteristic, complemented
10#22588948C211yesmaximal, characteristic, complemented
11#22588946C211yesmaximal, characteristic, complemented
12#22588944C211yesmaximal, characteristic, complemented
13#22588032C211yesmaximal, characteristic, complemented
14#22588032C211yesmaximal, characteristic, complemented
15C71×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D71C2211yescharacteristic
17C22×#11765848C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×#11765848C2211yescharacteristic
20C22×#11765848C2211yescharacteristic
21C2×C22⋊C4×D71C411yescharacteristic
22C2×C22⋊C4×D71C411yescharacteristic
23C2×C42×D71C2211yescharacteristic
24C2×C42×D71C2211yescharacteristic
25#17986021—24no—
26C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
27C2×Dic71⋊C8C2211yescharacteristic, complemented
28C2×Dic71⋊C8C2211yescharacteristic, complemented
29#17985961—24no—
30#17985961—24no—
31C2×C22⋊(C71⋊C8)C2211yescharacteristic
32C2×C22⋊(C71⋊C8)C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×(C2×D71)⋊C8C2211yescharacteristic
35C2×(C2×D71)⋊C8C2211yescharacteristic
36C2×(C2×D71)⋊C8C2211yescharacteristic
37C4×#11765848—24no—
38C2×#14556038C2211yescharacteristic, complemented
39C2×#14556038C2211yescharacteristic, complemented
40C2×C4×C71⋊C8C2211yescharacteristic, complemented
41C22⋊C4×Dic71C411yescharacteristic
42C22⋊C4×Dic71C411yescharacteristic
43C4×(C2×D71)⋊C4C2211yescharacteristic
44C4×(C2×D71)⋊C4C2211yescharacteristic
45C4×C22⋊Dic71C2211yescharacteristic
46#17985846C411yescharacteristic
47#17985846C411yescharacteristic
48#95×D71C411yescharacteristic
49#95×D71C411yescharacteristic
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×C4×C8×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×D71C2×C411yescharacteristic
74C22×C4×D71C2×C411yescharacteristic
75C22×C4×D71C2×C411yescharacteristic
76C22×C4×D71C2×C411yescharacteristic
77C22×C4×D71C2311yescharacteristic
78C22×C4×D71C2311yescharacteristic
79C2×#11765848—22no—
80C2×#11765848—22no—
81C2×#11765848—22no—
82C2×#11765848—22no—
83C2×#11765848—22no—
84C2×#11765848—22no—
85C2×#11765848—22no—
86C2×#11765848—22no—
87C2×#11765848—22no—
88C2×#11765848—22no—
89C2×#11765848D414yes—
90C2×#11765848D414yes—
91C22×C71⋊C8C2311yescharacteristic
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95C2×C22⋊Dic71C2×C411yescharacteristic
96C2×C22⋊Dic71C2×C411yescharacteristic
97C2×(C2×D71)⋊C4C2×C411yescharacteristic
98C2×(C2×D71)⋊C4C2×C411yescharacteristic
99C2×(C2×D71)⋊C4C2×C411yescharacteristic
100C2×(C2×D71)⋊C4C2×C411yescharacteristic
101C22⋊C4×D71—24no—
102C22⋊C4×D71—24no—
103C2×C4×Dic71C2×C411yescharacteristic
104C2×C4×Dic71C2×C411yescharacteristic
105C2×C4×Dic71C2×C411yescharacteristic
106C2×C4×Dic71C2×C411yescharacteristic
107C2×C4×Dic71C2311yescharacteristic
108C2×C4×Dic71C2311yescharacteristic
109C42×D71—22no—
110C42×D71—22no—
111C42×D71—22no—
112C42×D71—22no—
113C4⋊(C71⋊C8)—22no—
114Dic71⋊C8—22no—
115Dic71⋊C8—22no—
116C22⋊(C71⋊C8)—22no—
117C22⋊(C71⋊C8)—22no—
118(C2×D71)⋊C8—22no—
119(C2×D71)⋊C8—22no—
120(C2×D71)⋊C8—22no—
121(C2×D71)⋊C8—22no—
122#14556038—22no—
123#14556038—22no—
124C4×C71⋊C8—22no—
125C71⋊#95C2×C411yescharacteristic
126C71⋊#95C2×C411yescharacteristic
127C71⋊#95C2×C411yescharacteristic
128C71⋊#95C2×C411yescharacteristic
129C71⋊#95C2×C411yescharacteristic
130C71⋊#95C2×C411yescharacteristic
131C23×C4×C71C2311yescharacteristic
132C22×C8×C71C2311yescharacteristic
133C22×C8×C71C2311yescharacteristic
134C22×C8×C71C2311yescharacteristic
135C22×C8×C71C2311yescharacteristic
136C2×C22⋊C4×C71C2×C411yescharacteristic
137C2×C22⋊C4×C71C2×C411yescharacteristic
138C2×C42×C71C2311yescharacteristic
139C2×C42×C71C2311yescharacteristic
140C4⋊C8×C71—22no—
141C22⋊C8×C71—22no—
142C22⋊C8×C71—22no—
143C4×C8×C71—22no—
144#95×C71C2×C411yescharacteristic
145#95×C71C2×C411yescharacteristic
146C23×D71—22no—
147C23×D71—22no—
148C23×D71—22no—
149C23×D71—22no—
150C23×D71—22no—
151C23×D71—41no—
152C23×D71—41no—
153C23×D71C22×C411yescharacteristic
154C23×D71C22×C411yescharacteristic
155C22×Dic71—22no—
156C22×Dic71—22no—
157C22×Dic71—22no—
158C22×Dic71C22×C411yescharacteristic
159C22×Dic71C22×C411yescharacteristic
160C22×Dic71C22×C411yescharacteristic
161C22×Dic71C22×C411yescharacteristic
162C22×Dic71C22×C411yescharacteristic
163C22×Dic71C22×C411yescharacteristic
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—22no—
172C2×C4×D71—22no—
173C2×C4×D71—22no—
174C2×C4×D71—21no—
175C2×C4×D71—21no—
176C2×C4×D71—21no—
177C2×C4×D71—21no—
178C2×C4×D71—21no—
179C2×C4×D71—21no—
180C2×C4×D71—22no—
181C2×C4×D71—22no—
182C2×C4×D71—22no—
183C2×C4×D71—22no—
184C2×C4×D71—41no—
185C2×C4×D71—41no—
186C2×C4×D71—41no—
187C2×C4×D71—41no—
188C2×C4×D71—44no—
189C2×C4×D71—44no—
190C2×C4×D71—44no—
191C2×C4×D71—44no—
192C2×C4×D71C2×D412yes—
193C2×C4×D71C2×D412yes—
194C2×C4×D71#4112yes—
195C2×C4×D71#4112yes—
196C2×C4×D71#4112yes—
197C2×C4×D71#4112yes—
198#11765848—28no—
199#11765848—28no—
200#11765848—44no—
201#11765848—44no—
202C2×C71⋊C8—21no—
203C2×C71⋊C8—21no—
204C2×C71⋊C8—21no—
205C2×C71⋊C8—21no—
206C2×C71⋊C8—21no—
207C2×C71⋊C8—21no—
208C2×C71⋊C8—21no—
209C2×C71⋊C8—21no—
210C2×C71⋊C8—21no—
211C2×C71⋊C8—21no—
212C2×C71⋊C8C2×D412yes—
213C2×C71⋊C8C2×D412yes—
214C22⋊Dic71—22no—
215C22⋊Dic71—22no—
216(C2×D71)⋊C4—22no—
217(C2×D71)⋊C4—22no—
218(C2×D71)⋊C4—22no—
219(C2×D71)⋊C4M1614yescomplemented
220C4×Dic71—21no—
221C4×Dic71—21no—
222C4×Dic71—21no—
223C4×Dic71—21no—
224C4×Dic71—22no—
225C4×Dic71—22no—
226C4×Dic71—22no—
227C4×Dic71—22no—
228C24×C71C22×C411yescharacteristic
229C22×C4×C71—21no—
230C22×C4×C71—21no—
231C22×C4×C71—21no—
232C22×C4×C71—21no—
233C22×C4×C71—21no—
234C22×C4×C71—21no—
235C22×C4×C71C22×C411yescharacteristic
236C22×C4×C71C22×C411yescharacteristic
237C22×C4×C71C22×C411yescharacteristic
238C22×C4×C71C22×C411yescharacteristic
239C22×C4×C71C22×C411yescharacteristic
240C22×C4×C71C2411yescharacteristic
241C2×C8×C71—21no—
242C2×C8×C71—21no—
243C2×C8×C71—21no—
244C2×C8×C71—21no—
245C2×C8×C71—21no—
246C2×C8×C71—21no—
247C2×C8×C71—21no—
248C2×C8×C71—21no—
249C2×C8×C71—21no—
250C2×C8×C71—21no—
251C2×C8×C71C2×D412yes—
252C2×C8×C71C2×D412yes—
253C22⋊C4×C71—22no—
254C22⋊C4×C71M1614yescomplemented
255C42×C71—21no—
256C42×C71—21no—
257C42×C71—21no—
258C42×C71—21no—
259C23×C71—21no—
260C23×C71—21no—
261C23×C71—21no—
262C23×C71—21no—
263C23×C71—21no—
264C23×C71—21no—
265C23×C71C2×M1612yes—
266C23×C71C23×C411yescharacteristic
267C22×D71—21no—
268C22×D71—21no—
269C22×D71—21no—
270C22×D71—21no—
271C22×D71—28no—
272C22×D71—21no—
273C22×D71—21no—
274C22×D71—21no—
275C22×D71—21no—
276C22×D71—21no—
277C22×D71—21no—
278C22×D71—44no—
279C22×D71—44no—
280C22×D71—44no—
281C22×D71—44no—
282C22×D71—44no—
283C22×D71—44no—
284C22×D71#11712yes—
285C22×D71C4×D412yes—
286C22×D71C4×D412yes—
287C22×D71C2×M1612yes—
288C2×C4×C71—21no—
289C2×C4×C71—21no—
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—21no—
297C2×C4×C71—21no—
298C2×C4×C71—21no—
299C2×C4×C71—21no—
300C2×C4×C71—41no—
301C2×C4×C71—41no—
302C2×C4×C71—41no—
303C2×C4×C71—41no—
304C2×C4×C71C2×M1612yes—
305C2×C4×C71C2×M1612yes—
306C2×C4×C71C2×M1612yes—
307C2×C4×C71C22×D411yescharacteristic
308C2×C4×C71C22×D411yescharacteristic
309C2×C4×C71C2×#4111yescharacteristic
310C2×C4×C71C2×#4111yescharacteristic
311C2×C4×C71C2×#4111yescharacteristic
312C2×C4×C71C2×#4111yescharacteristic
313C2×Dic71—21no—
314C2×Dic71—21no—
315C2×Dic71—21no—
316C2×Dic71—21no—
317C2×Dic71—21no—
318C2×Dic71—21no—
319C2×Dic71—21no—
320C2×Dic71—21no—
321C2×Dic71—21no—
322C2×Dic71—21no—
323C2×Dic71—21no—
324C2×Dic71—21no—
325C2×Dic71—21no—
326C2×Dic71—21no—
327C2×Dic71—44no—
328C2×Dic71#11712yes—
329C2×Dic71C4×D412yes—
330C2×Dic71C4×D412yes—
331C2×Dic71C2×M1612yes—
332C4×D71—44no—
333C4×D71—44no—
334C4×D71—44no—
335C4×D71—44no—
336C4×D71—44no—
337C4×D71—41no—
338C4×D71—41no—
339C4×D71—41no—
340C4×D71—41no—
341C4×D71—44no—
342C4×D71#12114yes—
343C4×D71#12314yes—
344C4×D71#12414yes—
345C4×D71#12614yes—
346C8×C71—22no—
347C8×C71—22no—
348C8×C71—41no—
349C8×C71—41no—
350C71⋊C8—22no—
351C71⋊C8—22no—
352C71⋊C8—41no—
353C71⋊C8—41no—
354C22×C71—22no—
355C22×C71—22no—
356C22×C71—22no—
357C22×C71—41no—
358C22×C71—41no—
359C22×C71—41no—
360C22×C71—41no—
361C22×C71C2×#11711yescharacteristic
362C22×C71C2×C4×D411yescharacteristic
363C22×C71C2×C4×D411yescharacteristic
364C22×C71C22×M1611yescharacteristic
365C22×C71C22×M1611yescharacteristic
366C22×C71#56811yescharacteristic
367C22×C71#56811yescharacteristic
368C2×D71—22no—
369C2×D71—22no—
370C2×D71—22no—
371C2×D71—22no—
372C2×D71—22no—
373C2×D71—22no—
374C2×D71—22no—
375C2×D71—22no—
376C2×D71—22no—
377C2×D71—416no—
378C2×D71—41no—
379C2×D71—41no—
380C2×D71—41no—
381C2×D71—41no—
382C2×D71#38814yes—
383C4×C71—22no—
384C4×C71—22no—
385C4×C71—22no—
386C4×C71—41no—
387C4×C71—41no—
388C4×C71C2×#12111yescharacteristic
389C4×C71C2×#12311yescharacteristic
390C4×C71C2×#12411yescharacteristic
391C4×C71C2×#12611yescharacteristic
392Dic71—22no—
393Dic71—41no—
394Dic71—41no—
395Dic71—41no—
396Dic71—41no—
397Dic71#38814yes—
398#21049—711nomaximal, Sylow
399C2×C71—42no—
400C2×C71C2×#38811yescharacteristic
401C2×C71#292011yescharacteristic
402C2×C71#292111yescharacteristic
403C2×C71D4×M1611yescharacteristic
404C2×C71D4×M1611yescharacteristic
405C2×C71D4×M1611yescharacteristic
406C2×C71D4×M1611yescharacteristic
407D71—24no—
408D71—42no—
409C2×#423—711no—
410C2×#407—711no—
411C2×#407—711no—
412C2×C4×M16—711no—
413C2×C4×C22⋊C4—711no—
414#1924—711no—
415#1924—711no—
416#1924—711no—
417#1924—711no—
418#1923—711no—
419#1923—711no—
420#1923—711no—
421#1923D7111yescharacteristic, complemented
422#1728—711no—
423#1728—711no—
424C71#2104911yescharacteristic, complemented, Sylow
425C24×C4—711no—
426C22×M16—711no—
427C22×M16—711no—
428C22×M16—711no—
429C22×M16—711no—
430C22×C22⋊C4—711no—
431C22×C22⋊C4—711no—
432C22×C42—711no—
433C22×C42—711no—
434#423—1424no—
435C2×C4⋊C8—711no—
436C2×C4⋊C8—711no—
437C2×C4⋊C8—711no—
438C2×C4⋊C8C2×D7111yescharacteristic, complemented
439#407—1424no—
440#407—1424no—
441C2×C22⋊C8—711no—
442C2×C22⋊C8—711no—
443C2×C22⋊C8—711no—
444C2×C22⋊C8—711no—
445C2×C22⋊C8—711no—
446C2×C22⋊C8—711no—
447C2×C22⋊C8C2×D7111yescharacteristic
448C2×C22⋊C8C2×D7111yescharacteristic
449C4×M16—1424no—
450C2×#97—711no—
451C2×#97—711no—
452C2×C4×C8—711no—
453C2×C4×C8C2×D7111yescharacteristic, complemented
454C4×C22⋊C4—711no—
455C4×C22⋊C4—711no—
456C4×C22⋊C4—711no—
457C4×C22⋊C4—711no—
458C4×C22⋊C4—711no—
459C4×C22⋊C4—711no—
460C4×C22⋊C4—711no—
461C4×C22⋊C4C2×D7111yescharacteristic
462C2×#95—711no—
463C2×#95—711no—
464#336—711no—
465#336—711no—
466#336—711no—
467#336—711no—
468#336—711no—
469#336—711no—
470#336C2×D7111yescharacteristic, complemented
471#336C2×D7111yescharacteristic, complemented
472C25—711no—
473C23×C4—711no—
474C23×C4—711no—
475C23×C4—711no—
476C23×C4—711no—
477C23×C4—711no—
478C23×C4—711no—
479C23×C4—711no—
480C23×C4—711no—
481C23×C4—711no—
482C23×C4—1422no—
483C23×C4—1422no—
484C23×C4—1422no—
485C23×C4—1422no—
486C23×C4—1422no—
487C23×C4—1422no—
488C23×C4C22×D7111yescharacteristic
489C2×M16—714no—
490C2×M16—714no—
491C2×M16—1422no—
492C2×M16—1422no—
493C2×M16—1422no—
494C2×M16—1422no—
495C2×M16—1422no—
496C2×M16—1422no—
497C2×M16—1422no—
498C2×M16—1422no—
499C2×M16—1422no—
500C2×M16—1422no—
501C22×C8—711no—
502C22×C8—711no—
503C22×C8—711no—
504C22×C8—711no—
505C22×C8C22×D7111yescharacteristic
506C22×C8C22×D7111yescharacteristic
507C22×C8C22×D7111yescharacteristic
508C22×C8C22×D7111yescharacteristic
509C2×C22⋊C4—711no—
510C2×C22⋊C4—711no—
511C2×C22⋊C4—711no—
512C2×C22⋊C4—711no—
513C2×C22⋊C4—711no—
514C2×C22⋊C4—711no—
515C2×C22⋊C4—1424no—
516C2×C22⋊C4—1424no—
517C2×C22⋊C4C4×D7111yescharacteristic
518C2×C22⋊C4C4×D7111yescharacteristic
519C2×C42—711no—
520C2×C42—711no—
521C2×C42—711no—
522C2×C42—711no—
523C2×C42—711no—
524C2×C42—711no—
525C2×C42—1422no—
526C2×C42—1422no—
527C2×C42—1422no—
528C2×C42—1422no—
529C2×C42C22×D7111yescharacteristic
530C2×C42C22×D7111yescharacteristic
531C4⋊C8—22no—
532C4⋊C8—1422no—
533C4⋊C8—1422no—
534C4⋊C8—1422no—
535C22⋊C8—22no—
536C22⋊C8—22no—
537C22⋊C8—1422no—
538C22⋊C8—1422no—
539C22⋊C8—1422no—
540C22⋊C8—1422no—
541C22⋊C8—1422no—
542C22⋊C8—1422no—
543#97—1422no—
544#97—1422no—
545C4×C8—22no—
546C4×C8—1422no—
547#95—711no—
548#95—711no—
549#95—711no—
550#95—711no—
551#95—711no—
552#95—711no—
553#95C4×D7111yescharacteristic
554#95C4×D7111yescharacteristic
555C24—2841no—
556C24—2841no—
557C24—711no—
558C24—711no—
559C24—1422no—
560C24—1422no—
561C24—1422no—
562C24—1422no—
563C24—1422no—
564C24C2×C4×D7111yescharacteristic
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—2841no—
572C22×C4—2841no—
573C22×C4—2841no—
574C22×C4—2841no—
575C22×C4—2844no—
576C22×C4—2844no—
577C22×C4—2844no—
578C22×C4—2844no—
579C22×C4—711no—
580C22×C4—712no—
581C22×C4—712no—
582C22×C4—712no—
583C22×C4—712no—
584C22×C4—712no—
585C22×C4—712no—
586C22×C4—711no—
587C22×C4—711no—
588C22×C4—711no—
589C22×C4—711no—
590C22×C4—711no—
591C22×C4—1422no—
592C22×C4—1422no—
593C22×C4—1422no—
594C22×C4—1422no—
595C22×C4—1422no—
596C22×C4—1422no—
597C22×C4—1422no—
598C22×C4—1422no—
599C22×C4—1422no—
600C22×C4—1422no—
601C22×C4—1422no—
602C22×C4—1422no—
603C22×C4—1422no—
604C22×C4—1422no—
605C22×C4—1421no—
606C22×C4—1421no—
607C22×C4—1421no—
608C22×C4—1421no—
609C22×C4—1421no—
610C22×C4—1421no—
611C22×C4—1422no—
612C22×C4—1422no—
613C22×C4—1422no—
614C22×C4C2×C4×D7111yescharacteristic
615C22×C4C2×C4×D7111yescharacteristic
616C22×C4C2×C4×D7111yescharacteristic
617C22×C4C2×C4×D7111yescharacteristic
618C22×C4C2×C4×D7111yescharacteristic
619C22×C4C23×D7111yescharacteristic
620M16—2844no—
621M16—2844no—
622M16—1428no—
623M16—1428no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—712no—
635C2×C8—712no—
636C2×C8—1421no—
637C2×C8—1421no—
638C2×C8—1421no—
639C2×C8—1421no—
640C2×C8—1421no—
641C2×C8—1421no—
642C2×C8—1421no—
643C2×C8—1421no—
644C2×C8—1421no—
645C2×C8—1421no—
646C2×C8D4×D7112yes—
647C2×C8D4×D7112yes—
648C22⋊C4—22no—
649C22⋊C4—714no—
650C22⋊C4—1422no—
651C22⋊C4—1422no—
652C22⋊C4—1422no—
653C22⋊C4—1422no—
654C22⋊C4—1422no—
655C22⋊C4#1176584814yescomplemented
656C42—21no—
657C42—21no—
658C42—21no—
659C42—21no—
660C42—1422no—
661C42—1422no—
662C42—1422no—
663C42—1422no—
664C42—1421no—
665C42—1421no—
666C42—1421no—
667C42—1421no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—2844no—
675C23—2844no—
676C23—2844no—
677C23—2844no—
678C23—2844no—
679C23—2844no—
680C23—712no—
681C23—712no—
682C23—712no—
683C23—712no—
684C23—1428no—
685C23—1421no—
686C23—1421no—
687C23—1421no—
688C23—1421no—
689C23—1421no—
690C23—1421no—
691C23—1421no—
692C23—1421no—
693C23—1421no—
694C23—1421no—
695C23C2×#1176584812yes—
696C23C22×C4×D7111yescharacteristic
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—2844no—
714C2×C4—2844no—
715C2×C4—2844no—
716C2×C4—2844no—
717C2×C4—2844no—
718C2×C4—2844no—
719C2×C4—2844no—
720C2×C4—2841no—
721C2×C4—2841no—
722C2×C4—2841no—
723C2×C4—2841no—
724C2×C4—712no—
725C2×C4—712no—
726C2×C4—712no—
727C2×C4—714no—
728C2×C4—714no—
729C2×C4—714no—
730C2×C4—714no—
731C2×C4—712no—
732C2×C4—1421no—
733C2×C4—1421no—
734C2×C4—1421no—
735C2×C4—1421no—
736C2×C4—1421no—
737C2×C4—1421no—
738C2×C4—1421no—
739C2×C4—1421no—
740C2×C4—1421no—
741C2×C4—1421no—
742C2×C4—1421no—
743C2×C4—1421no—
744C2×C4—1421no—
745C2×C4—1421no—
746C2×C4M16×D7112yes—
747C2×C4C2×#1176584812yes—
748C2×C4C2×#1176584812yes—
749C2×C4C2×D4×D7111yescharacteristic
750C2×C4C2×D4×D7111yescharacteristic
751C2×C4#41×D7111yescharacteristic
752C2×C4#41×D7111yescharacteristic
753C2×C4#41×D7111yescharacteristic
754C2×C4#41×D7111yescharacteristic
755C8—22no—
756C8—22no—
757C8—41no—
758C8—41no—
759C8—2841no—
760C8—2841no—
761C8—1422no—
762C8—1422no—
763C22—22no—
764C22—22no—
765C22—22no—
766C22—41no—
767C22—41no—
768C22—41no—
769C22—41no—
770C22—28416no—
771C22—2841no—
772C22—2841no—
773C22—2841no—
774C22—2841no—
775C22—714no—
776C22—1422no—
777C22—1422no—
778C22—1422no—
779C22—1422no—
780C22—1422no—
781C22—1422no—
782C22—1422no—
783C22—1422no—
784C22—1422no—
785C22#117×D7111yescharacteristic
786C22C4×D4×D7111yescharacteristic
787C22C4×D4×D7111yescharacteristic
788C22C2×M16×D7111yescharacteristic
789C22C22×#1176584811yescharacteristic
790C22#1798676411yescharacteristic
791C22#1798676411yescharacteristic
792C4—22no—
793C4—22no—
794C4—22no—
795C4—41no—
796C4—41no—
797C4—2841no—
798C4—2841no—
799C4—2841no—
800C4—2841no—
801C4—714no—
802C4—1422no—
803C4#121×D7111yescharacteristic
804C4#123×D7111yescharacteristic
805C4#124×D7111yescharacteristic
806C4#126×D7111yescharacteristic
807C2—42no—
808C2—2842no—
809C2—1424no—
810C2#388×D7111yescharacteristic
811C2#2259696811yescharacteristic
812C2#2259697411yescharacteristic
813C2D4×#1176584811yescharacteristic
814C2D4×#1176584811yescharacteristic
815C2#2259707311yescharacteristic
816C2#2259707611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC71×#1923C2
prime radicalC24×D71C2×C4
cosocleC22×C4×C71C24
hypercenter#1923D71
hypocenterC71#21049
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
1. C2×#17986021C2semidirect
4. C2×C4×#11765848C2semidirect
6. #22588956C2semidirect
7. #22588954C2semidirect
8. #22588952C2semidirect
9. #22588950C2semidirect
10. #22588948C2semidirect
11. #22588946C2semidirect
12. #22588944C2semidirect
13. #22588032C2semidirect
14. #22588032C2semidirect
15. C71×#1923C2semidirect
26. C2×C4⋊(C71⋊C8)C22semidirect
27. C2×Dic71⋊C8C22semidirect
28. C2×Dic71⋊C8C22semidirect
38. C2×#14556038C22semidirect
39. C2×#14556038C22semidirect
40. C2×C4×C71⋊C8C22semidirect
50. #17985754C22semidirect
51. #17985754C22semidirect
52. #17985753C22semidirect
53. #17985753C22semidirect
54. #17985753C22semidirect
55. #17985753C22semidirect
56. C2×C4⋊C8×C71C22semidirect
59. C2×C4×C8×C71C22semidirect
61. #336×C71C22semidirect
62. #336×C71C22semidirect
219. (C2×D71)⋊C4M16semidirect
254. C22⋊C4×C71M16semidirect
421. #1923D71semidirect
424. C71#21049semidirect
438. C2×C4⋊C8C2×D71semidirect
453. C2×C4×C8C2×D71semidirect
470. #336C2×D71semidirect
471. #336C2×D71semidirect
655. C22⋊C4#11765848semidirect

Maximal subgroups

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

subgroupindex
C2×#179860212
C2×#179859612
C2×C4×#117658482
C4×C22⋊C4×D712
#225889562
#225889542
#225889522
#225889502
#225889482
#225889462
#225889442
#225880322
C71×#19232
#2104971