Finite Group Databasebeta

← C2×#22597003 #32861212

Subgroups — C2×#22597003 #32861212

Order 18176.

2178 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986467C211yesmaximal, characteristic
2#22597003C2116yesmaximal, direct product factor
3C2×#17986060C211yesmaximal, characteristic, complemented
4C2×#17986059C211yesmaximal, characteristic, complemented
5C2×#17986059C211yesmaximal, characteristic, complemented
6C2×#17986054C211yesmaximal, characteristic, complemented
7C2×#17986053C211yesmaximal, characteristic, complemented
8C2×#17986050C211yesmaximal, characteristic, complemented
9C2×#17986049C211yesmaximal, characteristic, complemented
10C2×#17986021C211yesmaximal, characteristic, complemented
11C2×C4⋊C8×D71C211yesmaximal, characteristic, complemented
12C2×#17985964C211yesmaximal, characteristic
13C2×#17985964C211yesmaximal, characteristic
14C2×#17985956C211yesmaximal, characteristic, complemented
15C2×#17985953C211yesmaximal, characteristic, complemented
16C2×#433×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×#11765848C2211yescharacteristic
19C22×#11765848C2211yescharacteristic
20C22×C8×D71C2211yescharacteristic
21C22×C8×D71C2211yescharacteristic
22#17986467C418yes—
23#17986467C2218yes—
24C2×#14556093C411yescharacteristic
25C2×#14556093C411yescharacteristic
26C2×#14556090C411yescharacteristic
27C2×#14556090C411yescharacteristic
28C2×(C22⋊D71)⋊C4C411yescharacteristic
29C2×(C22⋊D71)⋊C4C411yescharacteristic
30C2×(C22⋊D71)⋊C4C411yescharacteristic
31C2×(C22⋊D71)⋊C4C411yescharacteristic
32C2×#14556085C2211yescharacteristic
33C2×#14556085C2211yescharacteristic
34C22×C4×Dic71C2211yescharacteristic
35C2×C42×D71C2211yescharacteristic
36C2×C42×D71C2211yescharacteristic
37#17986060C2218yescomplemented
38#17986059C2218yescomplemented
39#17986059C2218yescomplemented
40#17986054C2218yescomplemented
41#17986053C2218yescomplemented
42#17986050C2218yescomplemented
43#17986049C2218yescomplemented
44#17986021C2218yescomplemented
45C2×C4⋊(C71⋊C8)C2211yescharacteristic
46C2×C4⋊(C71⋊C8)C2211yescharacteristic
47C2×Dic71⋊C8C2211yescharacteristic
48C2×Dic71⋊C8C2211yescharacteristic
49C2×Dic71⋊C8C2211yescharacteristic
50C2×Dic71⋊C8C2211yescharacteristic
51C4⋊C8×D71C2218yescomplemented
52#17985964C2218yes—
53#17985964C2218yes—
54C2×C22⋊(C71⋊C8)C2211yescharacteristic
55C2×C22⋊(C71⋊C8)C2211yescharacteristic
56C2×(C2×D71)⋊C8C2211yescharacteristic
57C2×(C2×D71)⋊C8C2211yescharacteristic
58C2×(C2×D71)⋊C8C2211yescharacteristic
59C2×(C2×D71)⋊C8C2211yescharacteristic
60#17985956C2218yescomplemented
61#17985953C2218yescomplemented
62C2×#14556039C2211yescharacteristic
63C2×#14556038C2211yescharacteristic
64C2×#14556038C2211yescharacteristic
65C2×C4×C71⋊C8C2211yescharacteristic
66C2×C8×Dic71C2211yescharacteristic
67C2×C8×Dic71C2211yescharacteristic
68C2×#117×C71C2211yescharacteristic
69#433×C71C2218yescomplemented
70C2×C4⋊C8×C71C2211yescharacteristic
71C2×C4⋊C8×C71C2211yescharacteristic
72C2×C22⋊C8×C71C2211yescharacteristic
73C2×C22⋊C8×C71C2211yescharacteristic
74C2×#97×C71C2211yescharacteristic
75C2×C4×C8×C71C2211yescharacteristic
76C2×#11765865—24no—
77C2×#11765865—24no—
78C2×#11765865C2×C414yes—
79C2×#11765865C2314yes—
80C22×Dic142C2×C411yescharacteristic
81C22×D284C2×C411yescharacteristic
82C22×C22⋊D71C2×C411yescharacteristic
83C22×C22⋊D71C2×C411yescharacteristic
84C23×Dic71C2×C411yescharacteristic
85C23×Dic71C2×C411yescharacteristic
86C22×C4×D71C2×C411yescharacteristic
87C22×C4×D71C2×C411yescharacteristic
88C22×C4×D71C2×C411yescharacteristic
89C22×C4×D71C2×C411yescharacteristic
90C22×C4×D71C2311yescharacteristic
91C22×C4×D71C2311yescharacteristic
92C2×#11765848—24no—
93C2×#11765848—24no—
94C2×#11765848C2314yes—
95C2×#11765848C2314yes—
96C22×C71⋊C8C2311yescharacteristic
97C22×C71⋊C8C2311yescharacteristic
98C22×C71⋊C8C2311yescharacteristic
99C22×C71⋊C8C2311yescharacteristic
100C2×C8×D71—24no—
101C2×C8×D71—24no—
102C2×C8×D71C2314yes—
103C2×C8×D71C2314yes—
104#14556093C2×C418yes—
105#14556093C2×C418yes—
106#14556090C2×C418yes—
107#14556090C2×C418yes—
108(C22⋊D71)⋊C4C2×C418yes—
109(C22⋊D71)⋊C4C2×C418yes—
110(C22⋊D71)⋊C4C2×C418yes—
111(C22⋊D71)⋊C4C2×C418yes—
112#14556085C2×C414yes—
113#14556085C2×C414yes—
114#14556085C2314yes—
115#14556085C2314yes—
116C2×Dic71⋊C4C2×C411yescharacteristic
117C2×Dic71⋊C4C2×C411yescharacteristic
118C2×Dic71⋊C4C2×C411yescharacteristic
119C2×Dic71⋊C4C2×C411yescharacteristic
120C2×(C2×D71)⋊C4C2×C411yescharacteristic
121C2×(C2×D71)⋊C4C2×C411yescharacteristic
122C2×(C2×D71)⋊C4C2×C411yescharacteristic
123C2×(C2×D71)⋊C4C2×C411yescharacteristic
124C2×C4×Dic71C2×C411yescharacteristic
125C2×C4×Dic71C2×C411yescharacteristic
126C2×C4×Dic71C2×C411yescharacteristic
127C2×C4×Dic71C2×C411yescharacteristic
128C2×C4×Dic71C2×C411yescharacteristic
129C2×C4×Dic71C2×C411yescharacteristic
130C2×C4×Dic71C2×C414yes—
131C2×C4×Dic71C2314yes—
132C2×C4×Dic71C2311yescharacteristic
133C2×C4×Dic71C2311yescharacteristic
134C42×D71C2×C414yes—
135C42×D71C2×C414yes—
136C42×D71C2314yes—
137C42×D71C2314yes—
138C4⋊(C71⋊C8)C2314yes—
139C4⋊(C71⋊C8)C2314yes—
140Dic71⋊C8C2314yes—
141Dic71⋊C8C2314yes—
142Dic71⋊C8C2314yes—
143Dic71⋊C8C2314yes—
144C22⋊(C71⋊C8)C2314yes—
145C22⋊(C71⋊C8)C2314yes—
146(C2×D71)⋊C8C2314yes—
147(C2×D71)⋊C8C2314yes—
148(C2×D71)⋊C8C2314yes—
149(C2×D71)⋊C8C2314yes—
150#14556039C2314yes—
151#14556038C2314yes—
152#14556038C2314yes—
153C4×C71⋊C8C2314yes—
154C8×Dic71C2314yes—
155C8×Dic71C2314yes—
156C23×C4×C71C2311yescharacteristic
157C22×C8×C71C2311yescharacteristic
158C22×C8×C71C2311yescharacteristic
159C22×C8×C71C2311yescharacteristic
160C22×C8×C71C2311yescharacteristic
161#117×C71C2×C414yes—
162#117×C71C2314yes—
163C2×C4⋊C4×C71C2×C411yescharacteristic
164C2×C4⋊C4×C71C2×C411yescharacteristic
165C2×C22⋊C4×C71C2×C411yescharacteristic
166C2×C22⋊C4×C71C2×C411yescharacteristic
167C2×C42×C71C2311yescharacteristic
168C2×C42×C71C2311yescharacteristic
169C4⋊C8×C71C2314yes—
170C4⋊C8×C71C2314yes—
171C22⋊C8×C71C2314yes—
172C22⋊C8×C71C2314yes—
173#97×C71C2314yes—
174C4×C8×C71C2314yes—
175C23×D71C22×C411yescharacteristic
176C23×D71C22×C411yescharacteristic
177#11765865—216no—
178#11765865—28no—
179#11765865—28no—
180C2×Dic142—24no—
181C2×Dic142C22×C414yes—
182C2×D284—24no—
183C2×D284C22×C414yes—
184C2×C22⋊D71—24no—
185C2×C22⋊D71—24no—
186C2×C22⋊D71C22×C414yes—
187C2×C22⋊D71C22×C414yes—
188C22×Dic71—24no—
189C22×Dic71—42no—
190C22×Dic71C22×C411yescharacteristic
191C22×Dic71C22×C411yescharacteristic
192C22×Dic71C22×C411yescharacteristic
193C22×Dic71C22×C411yescharacteristic
194C22×Dic71C22×C414yes—
195C22×Dic71C22×C414yes—
196C22×Dic71C22×C411yescharacteristic
197C22×Dic71C22×C411yescharacteristic
198C2×C4×D71—22no—
199C2×C4×D71—22no—
200C2×C4×D71—24no—
201C2×C4×D71—24no—
202C2×C4×D71—42no—
203C2×C4×D71—42no—
204C2×C4×D71C22×C414yes—
205C2×C4×D71C22×C414yes—
206C2×C4×D71C22×C412yes—
207C2×C4×D71C22×C414yes—
208C2×C4×D71C22×C414yes—
209C2×C4×D71C22×C412yes—
210C2×C4×D71#4114yes—
211C2×C4×D71#4114yes—
212C2×C4×D71C2412yes—
213C2×C4×D71C2412yes—
214#11765848—28no—
215#11765848—28no—
216C2×C71⋊C8—22no—
217C2×C71⋊C8—22no—
218C2×C71⋊C8—22no—
219C2×C71⋊C8—22no—
220C2×C71⋊C8C2412yes—
221C2×C71⋊C8C2412yes—
222C2×C71⋊C8C2412yes—
223C2×C71⋊C8C2412yes—
224C8×D71—28no—
225C8×D71—28no—
226Dic71⋊C4C22×C414yes—
227Dic71⋊C4C22×C414yes—
228Dic71⋊C4C22×C414yes—
229Dic71⋊C4C22×C414yes—
230(C2×D71)⋊C4C22×C414yes—
231(C2×D71)⋊C4C22×C414yes—
232(C2×D71)⋊C4C22×C414yes—
233(C2×D71)⋊C4C22×C414yes—
234C4×Dic71C22×C412yes—
235C4×Dic71C22×C414yes—
236C4×Dic71C22×C414yes—
237C4×Dic71C22×C414yes—
238C4×Dic71C22×C414yes—
239C4×Dic71C22×C412yes—
240C4×Dic71C22×C414yes—
241C4×Dic71C22×C414yes—
242C4×Dic71C2412yes—
243C4×Dic71C2412yes—
244C24×C71C22×C411yescharacteristic
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71C22×C411yescharacteristic
248C22×C4×C71C22×C411yescharacteristic
249C22×C4×C71C22×C411yescharacteristic
250C22×C4×C71C22×C411yescharacteristic
251C22×C4×C71C22×C411yescharacteristic
252C22×C4×C71C22×C412yes—
253C22×C4×C71C2412yes—
254C22×C4×C71C2411yescharacteristic
255C2×C8×C71—22no—
256C2×C8×C71—22no—
257C2×C8×C71—22no—
258C2×C8×C71—22no—
259C2×C8×C71C2412yes—
260C2×C8×C71C2412yes—
261C2×C8×C71C2412yes—
262C2×C8×C71C2412yes—
263C4⋊C4×C71C22×C414yes—
264C4⋊C4×C71C22×C414yes—
265C22⋊C4×C71C22×C414yes—
266C22⋊C4×C71C22×C414yes—
267C42×C71C22×C412yes—
268C42×C71C22×C412yes—
269C42×C71C2412yes—
270C42×C71C2412yes—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71C23×C412yes—
275C23×C71C23×C411yescharacteristic
276C22×D71—22no—
277C22×D71—22no—
278C22×D71—22no—
279C22×D71—22no—
280C22×D71—22no—
281C22×D71#11714yes—
282C22×D71C23×C412yes—
283C22×D71C23×C412yes—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—24no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71C23×C412yes—
293C2×C4×C71C23×C412yes—
294C2×C4×C71C23×C412yes—
295C2×C4×C71C23×C412yes—
296C2×C4×C71C23×C412yes—
297C2×C4×C71C23×C411yescharacteristic
298C2×C4×C71C2×#4112yes—
299C2×C4×C71C2×#4112yes—
300C2×C4×C71C2511yescharacteristic
301C22⋊D71—28no—
302C22⋊D71—28no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—28no—
308C2×Dic71—44no—
309C2×Dic71#11714yes—
310C2×Dic71#13114yes—
311C2×Dic71C23×C412yes—
312C2×Dic71C23×C412yes—
313C2×Dic71C23×C412yes—
314C2×Dic71C23×C412yes—
315C2×Dic71C23×C412yes—
316C2×Dic71C23×C412yes—
317D284—28no—
318C4×D71—24no—
319C4×D71—22no—
320C4×D71—22no—
321C4×D71—28no—
322C4×D71—28no—
323C4×D71—44no—
324C4×D71—44no—
325C4×D71#11718yes—
326C4×D71C2×#4114yes—
327C4×D71C2×#4114yes—
328Dic142—28no—
329C8×C71—22no—
330C8×C71—22no—
331C8×C71—22no—
332C8×C71—22no—
333C71⋊C8—22no—
334C71⋊C8—22no—
335C71⋊C8—22no—
336C71⋊C8—22no—
337C22×C71—22no—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—44no—
341C22×C71C2×#11712yes—
342C22×C71C2×#13112yes—
343C22×C71#56812yes—
344C22×C71C24×C411yescharacteristic
345C2×D71—28no—
346C2×D71—22no—
347C2×D71—22no—
348C2×D71—22no—
349C2×D71—22no—
350C2×D71—22no—
351C2×D71—44no—
352C2×D71C2×#11714yes—
353C4×C71—22no—
354C4×C71—22no—
355C4×C71—22no—
356C4×C71—22no—
357C4×C71—22no—
358C4×C71C2×#11712yes—
359C4×C71C22×#4111yescharacteristic
360C4×C71C22×#4111yescharacteristic
361Dic71—22no—
362Dic71—22no—
363Dic71—22no—
364Dic71—22no—
365Dic71C2×#11714yes—
366Dic71C2×#13114yes—
367C2×#2925—711nomaximal, Sylow
368C2×C71—42no—
369C2×C71#292514yescomplemented
370C2×C71C22×#11711yescharacteristic
371C2×C71C22×#13111yescharacteristic
372C2×C71C2×#56811yescharacteristic
373D71—24no—
374D71—42no—
375C2×C4×#41—711no—
376#2925—7116no—
377C2×#433—711no—
378C2×#433—711no—
379C2×#433—711no—
380C2×#433D7111yescharacteristic, complemented
381C2×#432—711no—
382C2×#432—711no—
383C2×#431—711no—
384C2×#431—711no—
385C2×#423—711no—
386C22×C4⋊C8—711no—
387C2×#408—711no—
388C2×#408—711no—
389C2×#405—711no—
390C2×#405—711no—
391C71C2×#292511yescharacteristic, complemented, Sylow
392C22×#41—711no—
393C22×M16—711no—
394C22×M16—711no—
395C23×C8—711no—
396C23×C8—711no—
397C4×#41—718no—
398C4×#41—718no—
399C2×C4×Q8—711no—
400C2×C4×Q8—711no—
401C2×C4×D4—711no—
402C2×C4×D4—711no—
403C2×C4×D4—711no—
404C2×C4×D4—711no—
405C2×C4×D4—711no—
406C2×C4×D4—711no—
407C2×#117—711no—
408C2×#117—711no—
409C2×#117C2×D7111yescharacteristic
410C22×C42—711no—
411C22×C42—711no—
412C22×C42—711no—
413#433—718no—
414#433—718no—
415#433—718no—
416#433C2×D7118yescomplemented
417#432—718no—
418#432—718no—
419#431—718no—
420#431—718no—
421#423—718no—
422C2×C4⋊C8—711no—
423C2×C4⋊C8—711no—
424C2×C4⋊C8—711no—
425C2×C4⋊C8—711no—
426C2×C4⋊C8—711no—
427C2×C4⋊C8—711no—
428C2×C4⋊C8—718no—
429C2×C4⋊C8C2×D7111yescharacteristic
430C2×C4⋊C8C2×D7111yescharacteristic
431#408—718no—
432#408—718no—
433C2×C22⋊C8—711no—
434C2×C22⋊C8—711no—
435C2×C22⋊C8—711no—
436C2×C22⋊C8—711no—
437C2×C22⋊C8—711no—
438C2×C22⋊C8—711no—
439C2×C22⋊C8C2×D7111yescharacteristic
440C2×C22⋊C8C2×D7111yescharacteristic
441#405—718no—
442#405—718no—
443C2×#97—711no—
444C2×#97—711no—
445C2×#97—711no—
446C2×#97C2×D7111yescharacteristic
447C2×C4×C8—711no—
448C2×C4×C8—711no—
449C2×C4×C8—711no—
450C2×C4×C8C2×D7111yescharacteristic
451C2×#41—714no—
452C2×#41—714no—
453C2×#41—1424no—
454C2×#41—1424no—
455C22×Q8—711no—
456C22×D4—711no—
457C22×D4—711no—
458C22×D4—711no—
459C23×C4—711no—
460C23×C4—711no—
461C23×C4—711no—
462C23×C4—711no—
463C23×C4—711no—
464C23×C4—711no—
465C23×C4—711no—
466C23×C4—711no—
467C23×C4C22×D7111yescharacteristic
468C2×M16—714no—
469C2×M16—714no—
470C2×M16—1424no—
471C2×M16—1424no—
472C22×C8—711no—
473C22×C8—711no—
474C22×C8—711no—
475C22×C8—711no—
476C22×C8—714no—
477C22×C8—714no—
478C22×C8—1424no—
479C22×C8—1424no—
480C22×C8C22×D7111yescharacteristic
481C22×C8C22×D7111yescharacteristic
482C22×C8C22×D7111yescharacteristic
483C22×C8C22×D7111yescharacteristic
484C4×Q8—718no—
485C4×Q8—718no—
486C4×D4—718no—
487C4×D4—718no—
488C4×D4—718no—
489C4×D4—718no—
490C4×D4—718no—
491C4×D4—718no—
492#117—714no—
493#117—714no—
494#117—714no—
495#117—714no—
496#117C4×D7114yes—
497#117C22×D7114yes—
498C2×C4⋊C4—711no—
499C2×C4⋊C4—711no—
500C2×C4⋊C4—711no—
501C2×C4⋊C4—711no—
502C2×C4⋊C4C4×D7111yescharacteristic
503C2×C4⋊C4C4×D7111yescharacteristic
504C2×C22⋊C4—711no—
505C2×C22⋊C4—711no—
506C2×C22⋊C4—711no—
507C2×C22⋊C4—711no—
508C2×C22⋊C4C4×D7111yescharacteristic
509C2×C22⋊C4C4×D7111yescharacteristic
510C2×C42—711no—
511C2×C42—711no—
512C2×C42—711no—
513C2×C42—711no—
514C2×C42—711no—
515C2×C42—711no—
516C2×C42—714no—
517C2×C42—714no—
518C2×C42—711no—
519C2×C42—711no—
520C2×C42—714no—
521C2×C42—714no—
522C2×C42—714no—
523C2×C42—714no—
524C2×C42C22×D7111yescharacteristic
525C2×C42C22×D7111yescharacteristic
526C4⋊C8—714no—
527C4⋊C8—714no—
528C4⋊C8—714no—
529C4⋊C8—714no—
530C4⋊C8—714no—
531C4⋊C8—714no—
532C4⋊C8C22×D7114yes—
533C4⋊C8C22×D7114yes—
534C22⋊C8—714no—
535C22⋊C8—714no—
536C22⋊C8—714no—
537C22⋊C8—714no—
538C22⋊C8—714no—
539C22⋊C8—714no—
540C22⋊C8C22×D7114yes—
541C22⋊C8C22×D7114yes—
542#97—714no—
543#97—714no—
544#97—714no—
545#97C22×D7114yes—
546C4×C8—714no—
547C4×C8—714no—
548C4×C8—714no—
549C4×C8C22×D7114yes—
550C24—711no—
551C24—711no—
552C24C2×C4×D7111yescharacteristic
553#41—1428no—
554#41—1428no—
555#41—14216no—
556C2×Q8—714no—
557C2×Q8—1424no—
558C2×D4—714no—
559C2×D4—714no—
560C2×D4—714no—
561C2×D4—1424no—
562C2×D4—1424no—
563C2×D4—1424no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—2842no—
567C22×C4—2842no—
568C22×C4—2842no—
569C22×C4—714no—
570C22×C4—714no—
571C22×C4—714no—
572C22×C4—711no—
573C22×C4—711no—
574C22×C4—712no—
575C22×C4—714no—
576C22×C4—714no—
577C22×C4—712no—
578C22×C4—711no—
579C22×C4—711no—
580C22×C4—711no—
581C22×C4—711no—
582C22×C4—714no—
583C22×C4—712no—
584C22×C4—714no—
585C22×C4—714no—
586C22×C4—712no—
587C22×C4—1424no—
588C22×C4—1424no—
589C22×C4—1424no—
590C22×C4—1422no—
591C22×C4—1422no—
592C22×C4C2×C4×D7111yescharacteristic
593C22×C4C2×C4×D7112yes—
594C22×C4C2×C4×D7111yescharacteristic
595C22×C4C2×C4×D7111yescharacteristic
596C22×C4C2×C4×D7111yescharacteristic
597C22×C4C2×C4×D7111yescharacteristic
598C22×C4C23×D7112yes—
599C22×C4C23×D7111yescharacteristic
600M16—1428no—
601M16—1428no—
602C2×C8—22no—
603C2×C8—22no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—712no—
607C2×C8—712no—
608C2×C8—712no—
609C2×C8—712no—
610C2×C8—1428no—
611C2×C8—1428no—
612C2×C8—1422no—
613C2×C8—1422no—
614C2×C8—1422no—
615C2×C8—1422no—
616C2×C8C23×D7112yes—
617C2×C8C23×D7112yes—
618C2×C8C23×D7112yes—
619C2×C8C23×D7112yes—
620C4⋊C4—714no—
621C4⋊C4—714no—
622C4⋊C4—714no—
623C4⋊C4—714no—
624C4⋊C4C2×C4×D7114yes—
625C4⋊C4C2×C4×D7114yes—
626C22⋊C4—714no—
627C22⋊C4—714no—
628C22⋊C4—714no—
629C22⋊C4—714no—
630C22⋊C4C2×C4×D7114yes—
631C22⋊C4C2×C4×D7114yes—
632C42—712no—
633C42—712no—
634C42—714no—
635C42—714no—
636C42—714no—
637C42—714no—
638C42—714no—
639C42—714no—
640C42—712no—
641C42—712no—
642C42C2×C4×D7112yes—
643C42C2×C4×D7112yes—
644C42C23×D7112yes—
645C42C23×D7112yes—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—712no—
650C23—714no—
651C23—712no—
652C23—1422no—
653C23—1422no—
654C23—1422no—
655C23—1422no—
656C23—1422no—
657C23C22×C4×D7112yes—
658C23C22×C4×D7111yescharacteristic
659Q8—1428no—
660D4—1428no—
661D4—1428no—
662D4—1428no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—24no—
671C2×C4—2844no—
672C2×C4—2844no—
673C2×C4—2844no—
674C2×C4—712no—
675C2×C4—712no—
676C2×C4—714no—
677C2×C4—714no—
678C2×C4—714no—
679C2×C4—714no—
680C2×C4—718no—
681C2×C4—712no—
682C2×C4—712no—
683C2×C4—712no—
684C2×C4—712no—
685C2×C4—1428no—
686C2×C4—1428no—
687C2×C4—1428no—
688C2×C4—1422no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1424no—
695C2×C4C22×C4×D7112yes—
696C2×C4C22×C4×D7112yes—
697C2×C4C22×C4×D7112yes—
698C2×C4C22×C4×D7112yes—
699C2×C4C22×C4×D7112yes—
700C2×C4C22×C4×D7111yescharacteristic
701C2×C4#41×D7112yes—
702C2×C4#41×D7112yes—
703C2×C4C24×D7111yescharacteristic
704C8—22no—
705C8—22no—
706C8—22no—
707C8—22no—
708C8—1422no—
709C8—1422no—
710C8—1422no—
711C8—1422no—
712C22—22no—
713C22—22no—
714C22—22no—
715C22—44no—
716C22—2844no—
717C22—714no—
718C22—1422no—
719C22—1422no—
720C22—1422no—
721C22—1422no—
722C22—1422no—
723C22—1428no—
724C22#117×D7112yes—
725C22#131×D7112yes—
726C22#1798676412yes—
727C22C23×C4×D7111yescharacteristic
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—22no—
733C4—714no—
734C4—714no—
735C4—1422no—
736C4—1422no—
737C4—1422no—
738C4—1422no—
739C4#117×D7112yes—
740C4C2×#41×D7111yescharacteristic
741C4C2×#41×D7111yescharacteristic
742C2—42no—
743C2—2842no—
744C2—1424no—
745C2#2259700314yesdirect product factor
746C2C2×#117×D7111yescharacteristic
747C2C2×#131×D7111yescharacteristic
748C2C2×#1798676411yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutatorC22×C71C24×C4
FrattiniC2×C4C24×D71
FittingC2×#433×C71C2
socleC23×C71C23×C4
prime radicalC22×#11765865C22
cosocleC2×C4×C71C25
hypercenterC2×#433D71
hypocenterC71C2×#2925
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #22597003C2direct (N × H)
3. C2×#17986060C2semidirect
4. C2×#17986059C2semidirect
5. C2×#17986059C2semidirect
6. C2×#17986054C2semidirect
7. C2×#17986053C2semidirect
8. C2×#17986050C2semidirect
9. C2×#17986049C2semidirect
10. C2×#17986021C2semidirect
11. C2×C4⋊C8×D71C2semidirect
14. C2×#17985956C2semidirect
15. C2×#17985953C2semidirect
16. C2×#433×C71C2semidirect
37. #17986060C22semidirect
38. #17986059C22semidirect
39. #17986059C22semidirect
40. #17986054C22semidirect
41. #17986053C22semidirect
42. #17986050C22semidirect
43. #17986049C22semidirect
44. #17986021C22semidirect
51. C4⋊C8×D71C22semidirect
60. #17985956C22semidirect
61. #17985953C22semidirect
69. #433×C71C22semidirect
369. C2×C71#2925semidirect
380. C2×#433D71semidirect
391. C71C2×#2925semidirect
416. #433C2×D71semidirect
745. C2#22597003direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179864672
#225970032
C2×#179860602
C2×#179860592
C2×#179860542
C2×#179860532
C2×#179860502
C2×#179860492
C2×#179860212
C2×C4⋊C8×D712
C2×#179859642
C2×#179859562
C2×#179859532
C2×#433×C712
C2×#292571