Finite Group Databasebeta

← #32003539

Subgroups — #32003539

Order 18176.

1096 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×#17986075C211yesmaximal, characteristic, complemented
2C2×#17986072C211yesmaximal, characteristic, complemented
3C2×#17986068C211yesmaximal, characteristic, complemented
4C4×#14556102C211yesmaximal, characteristic
5#22589138C211yesmaximal, characteristic, complemented
6#22589063C211yesmaximal, characteristic, complemented
7#22588946C211yesmaximal, characteristic, complemented
8#22588946C211yesmaximal, characteristic, complemented
9#22588637C211yesmaximal, characteristic, complemented
10#22588637C211yesmaximal, characteristic, complemented
11#22588320C211yesmaximal, characteristic, complemented
12#22588212C211yesmaximal, characteristic, complemented
13#22588123C211yesmaximal, characteristic, complemented
14C8×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
15C2×C4×M16×C71C211yesmaximal, characteristic, complemented
16C22×#11765848C2211yescharacteristic
17C22×C8×D71C2211yescharacteristic
18C2×#14556102C411yescharacteristic
19C2×C4×D284C2211yescharacteristic
20C2×C4×C22⋊D71C2211yescharacteristic
21C2×C4×C22⋊D71C2211yescharacteristic
22#17986075—24no—
23#17986072—24no—
24#17986068—24no—
25C2×C4⋊(C71⋊C8)C2211yescharacteristic
26C2×C4⋊(C71⋊C8)C2211yescharacteristic
27C2×Dic71⋊C8C2211yescharacteristic
28C2×Dic71⋊C8C2211yescharacteristic
29C2×C22⋊(C71⋊C8)C2211yescharacteristic
30C2×C22⋊(C71⋊C8)C2211yescharacteristic
31C2×(C2×D71)⋊C8C2211yescharacteristic
32C2×(C2×D71)⋊C8C2211yescharacteristic
33C2×(C2×D71)⋊C8C2211yescharacteristic
34C2×(C2×D71)⋊C8C2211yescharacteristic
35C2×(C2×D71)⋊C8C2211yescharacteristic
36C2×(C2×D71)⋊C8C2211yescharacteristic
37C2×#14556038C2211yescharacteristic
38C2×C8×Dic71C2211yescharacteristic
39#17985901C411yescharacteristic
40#17985897C411yescharacteristic
41#17985890C411yescharacteristic
42#17985890C411yescharacteristic
43#17985878C411yescharacteristic
44#17985878C411yescharacteristic
45#17985859C411yescharacteristic
46C4×C4⋊Dic71C2211yescharacteristic
47C4×(C2×D71)⋊C4C2211yescharacteristic
48C4×(C2×D71)⋊C4C2211yescharacteristic
49#17985754C2211yescharacteristic
50#17985754C2211yescharacteristic
51#17985753C2211yescharacteristic
52#17985753C2211yescharacteristic
53#17985753C2211yescharacteristic
54#17985753C2211yescharacteristic
55C22×M16×C71C2211yescharacteristic
56C22×M16×C71C2211yescharacteristic
57C22×C42×C71C2211yescharacteristic
58C4×M16×C71—24no—
59C2×#97×C71C2211yescharacteristic
60C2×#97×C71C2211yescharacteristic
61C2×C4×C8×C71C2211yescharacteristic
62C2×C4×C8×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—22no—
71C22×C71⋊C8C2311yescharacteristic
72C22×C71⋊C8C2311yescharacteristic
73C22×C71⋊C8C2311yescharacteristic
74C22×C71⋊C8C2311yescharacteristic
75C2×C8×D71—22no—
76C2×C8×D71—22no—
77C2×C8×D71—22no—
78#14556102—24no—
79C4×D284—22no—
80C4×D284—22no—
81C4×C22⋊D71—22no—
82C4×C22⋊D71—22no—
83C4×C22⋊D71—22no—
84C4×C22⋊D71—22no—
85C2×C4⋊Dic71C2×C411yescharacteristic
86C2×C4⋊Dic71C2×C411yescharacteristic
87C2×C4⋊Dic71C2×C411yescharacteristic
88C2×Dic71⋊C4C2×C411yescharacteristic
89C2×Dic71⋊C4C2×C411yescharacteristic
90C2×C22⋊Dic71C2×C411yescharacteristic
91C2×C22⋊Dic71C2×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×(C2×D71)⋊C4C2×C411yescharacteristic
99C2×(C2×D71)⋊C4C2×C411yescharacteristic
100C2×C4×Dic71C2311yescharacteristic
101C2×C4×Dic71C2311yescharacteristic
102C4⋊(C71⋊C8)—22no—
103C4⋊(C71⋊C8)—22no—
104Dic71⋊C8—22no—
105Dic71⋊C8—22no—
106C22⋊(C71⋊C8)—22no—
107C22⋊(C71⋊C8)—22no—
108(C2×D71)⋊C8—22no—
109(C2×D71)⋊C8—22no—
110(C2×D71)⋊C8—22no—
111(C2×D71)⋊C8—22no—
112(C2×D71)⋊C8—22no—
113(C2×D71)⋊C8—22no—
114#14556038—22no—
115C8×Dic71—22no—
116C71⋊#95C2×C411yescharacteristic
117C71⋊#95C2×C411yescharacteristic
118C71⋊#95C2×C411yescharacteristic
119C71⋊#95C2×C411yescharacteristic
120C71⋊#95C2×C411yescharacteristic
121C71⋊#95C2×C411yescharacteristic
122C23×C4×C71C2×C411yescharacteristic
123C23×C4×C71C2×C411yescharacteristic
124C23×C4×C71C2311yescharacteristic
125C2×M16×C71—22no—
126C2×M16×C71—22no—
127C2×M16×C71—22no—
128C2×M16×C71—22no—
129C2×M16×C71—22no—
130C2×M16×C71D414yescomplemented
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
141#97×C71—22no—
142#97×C71D414yescomplemented
143C4×C8×C71—22no—
144C4×C8×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—41no—
155C2×C22⋊D71—41no—
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—21no—
186C2×C71⋊C8—21no—
187C8×D71—44no—
188C4⋊Dic71—22no—
189C4⋊Dic71—22no—
190C4⋊Dic71—41no—
191Dic71⋊C4—22no—
192Dic71⋊C4—22no—
193C22⋊Dic71—22no—
194C22⋊Dic71—22no—
195(C2×D71)⋊C4—22no—
196(C2×D71)⋊C4—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)⋊C4M1614yescomplemented
203C4×Dic71—21no—
204C4×Dic71—21no—
205C4×Dic71—21no—
206C4×Dic71—21no—
207C24×C71C22×C411yescharacteristic
208C22×C4×C71—21no—
209C22×C4×C71—21no—
210C22×C4×C71—21no—
211C22×C4×C71—21no—
212C22×C4×C71—22no—
213C22×C4×C71—22no—
214C22×C4×C71—22no—
215C22×C4×C71—22no—
216C22×C4×C71—41no—
217C22×C4×C71—41no—
218C22×C4×C71C22×C411yescharacteristic
219C22×C4×C71C22×C411yescharacteristic
220C22×C4×C71C22×C411yescharacteristic
221C22×C4×C71C22×C411yescharacteristic
222C22×C4×C71C22×C411yescharacteristic
223C22×C4×C71C2×D412yes—
224C22×C4×C71#4112yes—
225C22×C4×C71C2411yescharacteristic
226M16×C71—28no—
227M16×C71—28no—
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—
235C2×C8×C71C2×D412yes—
236C2×C8×C71C2×D412yes—
237C2×C8×C71C2×D412yes—
238C2×C8×C71#4112yes—
239C2×C8×C71#4112yes—
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×C71—21no—
251C23×C71—21no—
252C23×C71C4×D412yes—
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—21no—
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—21no—
278C2×C4×C71—22no—
279C2×C4×C71—22no—
280C2×C4×C71—22no—
281C2×C4×C71—22no—
282C2×C4×C71—44no—
283C2×C4×C71—44no—
284C2×C4×C71C4×D412yes—
285C2×C4×C71C4×D412yes—
286C2×C4×C71C4×D412yes—
287C2×C4×C71C2×M1612yes—
288C2×C4×C71#13112yes—
289C2×C4×C71C22×D411yescharacteristic
290C2×C4×C71C22×D411yescharacteristic
291C2×C4×C71C2×#4111yescharacteristic
292C2×C4×C71C2×#4111yescharacteristic
293C2×C4×C71C2×#4111yescharacteristic
294C2×C4×C71C2×#4111yescharacteristic
295C22⋊D71—44no—
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—22no—
327C8×C71#12114yescomplemented
328C71⋊C8—41no—
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×C4×D411yescharacteristic
340C22×C71C2×C4×D411yescharacteristic
341C22×C71C4×#4111yescharacteristic
342C22×C71C22×M1611yescharacteristic
343C22×C71C2×#13111yescharacteristic
344C22×C71#56811yescharacteristic
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—22no—
365C4×C71C2×#12111yescharacteristic
366C4×C71#52511yescharacteristic
367C4×C71#52911yescharacteristic
368C4×C71#53211yescharacteristic
369Dic71—22no—
370Dic71—41no—
371Dic71—41no—
372Dic71—41no—
373Dic71—41no—
374Dic71—41no—
375#21490—711nomaximal, Sylow
376C2×C71—42no—
377C2×C71C4×#12111yescharacteristic
378C2×C71#293311yescharacteristic
379C2×C71D4×M1611yescharacteristic
380C2×C71D4×M1611yescharacteristic
381C2×C71#293511yescharacteristic
382C2×C71#296511yescharacteristic
383C2×C71#296711yescharacteristic
384D71—42no—
385D71—81no—
386C2×#436—711no—
387C2×#435—711no—
388C2×#435—711no—
389C2×C4×M16D7111yescharacteristic, complemented
390C4×#121—711no—
391#1955—711no—
392#1940—711no—
393#1923—711no—
394#1923—711no—
395#1870—711no—
396#1870—711no—
397#1797—711no—
398#1771—711no—
399#1753—711no—
400C8×C22⋊C4—711no—
401C71#2149011yescharacteristic, complemented, Sylow
402C22×M16—711no—
403C22×M16C2×D7111yescharacteristic
404C22×M16C2×D7111yescharacteristic
405C23×C8—711no—
406C2×#121—711no—
407C2×C4×D4—711no—
408C2×C4×D4—711no—
409C2×C4×D4—711no—
410C22×C42C2×D7111yescharacteristic
411#436—1424no—
412#435—1424no—
413#435—1424no—
414C2×C4⋊C8—711no—
415C2×C4⋊C8—711no—
416C2×C4⋊C8—711no—
417C2×C4⋊C8—711no—
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—
426C4×M16—24no—
427C2×#97—711no—
428C2×#97C2×D7111yescharacteristic
429C2×#97C2×D7111yescharacteristic
430C2×C4×C8—711no—
431C2×C4×C8C2×D7111yescharacteristic
432C2×C4×C8C2×D7111yescharacteristic
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#336—711no—
448#336—711no—
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—22no—
458C2×M16—22no—
459C2×M16—22no—
460C2×M16—22no—
461C2×M16—22no—
462C2×M16—1422no—
463C2×M16—1422no—
464C2×M16—1422no—
465C2×M16D28414yescomplemented
466C22×C8—711no—
467C22×C8—711no—
468C22×C8—711no—
469C22×C8—711no—
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—1422no—
508C4⋊C8—1422no—
509C4⋊C8—1422no—
510C4⋊C8—1422no—
511C22⋊C8—1422no—
512C22⋊C8—1422no—
513C22⋊C8—1422no—
514C22⋊C8—1422no—
515C22⋊C8—1422no—
516C22⋊C8—1422no—
517C22⋊C8—1422no—
518C22⋊C8—1422no—
519#97—22no—
520#97—1422no—
521#97C22⋊D7114yescomplemented
522C4×C8—22no—
523C4×C8—22no—
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—2841no—
536C2×D4—2841no—
537C2×D4—1422no—
538C2×D4—1422no—
539C2×D4—1422no—
540C2×D4—1422no—
541C2×D4—1422no—
542C2×D4—1422no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—41no—
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—28no—
580M16—28no—
581M16—2844no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—2844no—
589C2×C8—1421no—
590C2×C8—1421no—
591C2×C8—1421no—
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×C8C2×C22⋊D7112yes—
602C2×C8C2×C22⋊D7112yes—
603C2×C8C2×D28412yes—
604C2×C8C2×D28412yes—
605C2×C8#1176586512yes—
606C2×C8#1176586512yes—
607C4⋊C4—2841no—
608C4⋊C4—1422no—
609C4⋊C4—1422no—
610C4⋊C4—1422no—
611C4⋊C4—1422no—
612C22⋊C4—714no—
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—
630C42C2×C22⋊D7112yes—
631C42#1176586512yes—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—712no—
639C23—1421no—
640C23—1421no—
641C23—1421no—
642C23—1421no—
643C23—1421no—
644C23—1421no—
645C23—1421no—
646C23—1421no—
647C23—1421no—
648C23—1421no—
649C23—1421no—
650C23—1421no—
651C23—1421no—
652C23C4×D28412yes—
653C23C22×C4×D7111yescharacteristic
654D4—2844no—
655D4—2844no—
656D4—2844no—
657C2×C4—21no—
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—21no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—44no—
672C2×C4—44no—
673C2×C4—2841no—
674C2×C4—2841no—
675C2×C4—2841no—
676C2×C4—2841no—
677C2×C4—2841no—
678C2×C4—2841no—
679C2×C4—2841no—
680C2×C4—2841no—
681C2×C4—712no—
682C2×C4—1421no—
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×C4C4×C22⋊D7112yes—
700C2×C4C4×C22⋊D7112yes—
701C2×C4C4×D28412yes—
702C2×C4M16×D7112yes—
703C2×C4#1455613612yes—
704C2×C4C22×C22⋊D7111yescharacteristic
705C2×C4C22×D28411yescharacteristic
706C2×C4C2×#1176586511yescharacteristic
707C2×C4C2×#1176586511yescharacteristic
708C2×C4C2×#1176586511yescharacteristic
709C2×C4C2×#1176586511yescharacteristic
710C8—22no—
711C8—22no—
712C8—22no—
713C8—2841no—
714C8—2841no—
715C8—2841no—
716C8—2841no—
717C8#1455610214yescomplemented
718C22—22no—
719C22—22no—
720C22—22no—
721C22—41no—
722C22—41no—
723C22—41no—
724C22—41no—
725C22—2841no—
726C22—2841no—
727C22—2841no—
728C22—2841no—
729C22—2841no—
730C22—2841no—
731C22—2841no—
732C22—2841no—
733C22—2841no—
734C22—2841no—
735C22—2841no—
736C22—1422no—
737C22—1422no—
738C22—1422no—
739C22C2×C4×C22⋊D7111yescharacteristic
740C22C2×C4×D28411yescharacteristic
741C22C4×#1176586511yescharacteristic
742C22C2×M16×D7111yescharacteristic
743C22C2×#1455613611yescharacteristic
744C22#1798676511yescharacteristic
745C22#1798676511yescharacteristic
746C4—22no—
747C4—22no—
748C4—22no—
749C4—22no—
750C4—22no—
751C4—2841no—
752C4—2841no—
753C4—2841no—
754C4—2841no—
755C4—2841no—
756C4—1422no—
757C4C2×#1455610211yescharacteristic
758C4#1798651011yescharacteristic
759C4#1798653311yescharacteristic
760C4#1798654911yescharacteristic
761C2—42no—
762C2—2842no—
763C2—5681no—
764C2C4×#1455610211yescharacteristic
765C2#2259706511yescharacteristic
766C2M16×C22⋊D7111yescharacteristic
767C2M16×D28411yescharacteristic
768C2#2259708611yescharacteristic
769C2#2259730211yescharacteristic
770C2#2259732511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D71
commutator, socleC23×C71C23×C4
FittingC2×C4×M16×C71C2
prime radicalC2×#14556102C4
cosocleC22×C4×C71C24
hypercenterC2×C4×M16D71
hypocenterC71#21490
LCSG ▷ C23×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×C4×M16

Complements

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

NH ≅ G/Ntype
1. C2×#17986075C2semidirect
2. C2×#17986072C2semidirect
3. C2×#17986068C2semidirect
5. #22589138C2semidirect
6. #22589063C2semidirect
7. #22588946C2semidirect
8. #22588946C2semidirect
9. #22588637C2semidirect
10. #22588637C2semidirect
11. #22588320C2semidirect
12. #22588212C2semidirect
13. #22588123C2semidirect
14. C8×(C2×D71)⋊C4C2semidirect
15. C2×C4×M16×C71C2semidirect
130. C2×M16×C71D4semidirect
142. #97×C71D4semidirect
202. (C2×D71)⋊C4M16semidirect
327. C8×C71#121semidirect
389. C2×C4×M16D71semidirect
401. C71#21490semidirect
465. C2×M16D284semidirect
521. #97C22⋊D71semidirect
717. C8#14556102semidirect

Maximal subgroups

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

subgroupindex
C2×#179860752
C2×#179860722
C2×#179860682
C4×#145561022
#225891382
#225890632
#225889462
#225886372
#225883202
#225882122
#225881232
C8×(C2×D71)⋊C42
C2×C4×M16×C712
#2149071