Finite Group Databasebeta

← C2×#22597432 #32862405

Subgroups — C2×#22597432 #32862405

Order 18176.

1750 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986552C211yesmaximal, characteristic
2#22597432C2116yesmaximal, direct product factor
3C2×#17986129C211yesmaximal, characteristic, complemented
4C2×#17986128C211yesmaximal, characteristic, complemented
5C2×#17986128C211yesmaximal, characteristic, complemented
6C2×#17986127C211yesmaximal, characteristic, complemented
7C2×#17986127C211yesmaximal, characteristic, complemented
8C2×#17986126C211yesmaximal, characteristic, complemented
9C2×C8×Dic142C211yesmaximal, characteristic, complemented
10C2×#17986123C211yesmaximal, characteristic, complemented
11C2×#17986060C211yesmaximal, characteristic
12C2×#17986057C211yesmaximal, characteristic
13C2×#17986057C211yesmaximal, characteristic
14C2×#17986053C211yesmaximal, characteristic
15C2×#17986049C211yesmaximal, characteristic
16C2×#433×C71C211yesmaximal, characteristic
17#17986552C418yes—
18#17986552C2218yes—
19C2×#14556127C411yescharacteristic
20C2×#14556127C411yescharacteristic
21C2×#14556119C411yescharacteristic
22C2×#14556119C411yescharacteristic
23C2×#14556105C411yescharacteristic
24C2×#14556105C411yescharacteristic
25C2×#14556105C411yescharacteristic
26C2×#14556105C411yescharacteristic
27C2×C4×Dic142C2211yescharacteristic
28C2×C4×Dic142C2211yescharacteristic
29C2×C4×Dic142C2211yescharacteristic
30C2×C4×Dic142C2211yescharacteristic
31C2×#14556087C2211yescharacteristic
32C22×C4×Dic71C2211yescharacteristic
33#17986129C2218yescomplemented
34#17986128C2218yescomplemented
35#17986128C2218yescomplemented
36#17986127C2218yescomplemented
37#17986127C2218yescomplemented
38#17986126C2218yescomplemented
39C8×Dic142C2218yescomplemented
40#17986123C2218yescomplemented
41#17986060C2218yes—
42#17986057C2218yes—
43#17986057C2218yes—
44#17986053C2218yes—
45#17986049C2218yes—
46C2×C4⋊(C71⋊C8)C2211yescharacteristic
47C2×C4⋊(C71⋊C8)C2211yescharacteristic
48C2×Dic71⋊C8C2211yescharacteristic
49C2×Dic71⋊C8C2211yescharacteristic
50C2×Dic71⋊C8C2211yescharacteristic
51C2×Dic71⋊C8C2211yescharacteristic
52C2×Dic71⋊C8C2211yescharacteristic
53C2×Dic71⋊C8C2211yescharacteristic
54C2×Dic71⋊C8C2211yescharacteristic
55C2×Dic71⋊C8C2211yescharacteristic
56C2×C22⋊(C71⋊C8)C2211yescharacteristic
57C2×C22⋊(C71⋊C8)C2211yescharacteristic
58C2×#14556039C2211yescharacteristic
59C2×#14556038C2211yescharacteristic
60C2×#14556038C2211yescharacteristic
61C2×#14556038C2211yescharacteristic
62C2×#14556038C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64C2×C8×Dic71C2211yescharacteristic
65C2×C8×Dic71C2211yescharacteristic
66C2×C8×Dic71C2211yescharacteristic
67C2×C8×Dic71C2211yescharacteristic
68C2×#117×C71C2211yescharacteristic
69#433×C71C2218yes—
70C2×C4⋊C8×C71C2211yescharacteristic
71C2×C4⋊C8×C71C2211yescharacteristic
72C2×C22⋊C8×C71C2211yescharacteristic
73C2×C22⋊C8×C71C2211yescharacteristic
74C2×#97×C71C2211yescharacteristic
75C2×C4×C8×C71C2211yescharacteristic
76C22×Dic142C2×C411yescharacteristic
77C22×Dic142C2×C411yescharacteristic
78C22×Dic142C2×C411yescharacteristic
79C22×Dic142C2×C411yescharacteristic
80C23×Dic71C2×C411yescharacteristic
81C23×Dic71C2×C411yescharacteristic
82C22×C71⋊C8C2311yescharacteristic
83C22×C71⋊C8C2311yescharacteristic
84C22×C71⋊C8C2311yescharacteristic
85C22×C71⋊C8C2311yescharacteristic
86#14556127C2×C418yes—
87#14556127C2×C418yes—
88#14556119C2×C418yes—
89#14556119C2×C418yes—
90#14556105C2×C418yes—
91#14556105C2×C418yes—
92#14556105C2×C418yes—
93#14556105C2×C418yes—
94C4×Dic142C2×C414yes—
95C4×Dic142C2×C414yes—
96C4×Dic142C2×C414yes—
97C4×Dic142C2×C414yes—
98C4×Dic142C2314yes—
99C4×Dic142C2314yes—
100C4×Dic142C2314yes—
101C4×Dic142C2314yes—
102#14556087C2×C414yes—
103#14556087C2314yes—
104C2×C4⋊Dic71C2×C411yescharacteristic
105C2×C4⋊Dic71C2×C411yescharacteristic
106C2×C4⋊Dic71C2×C411yescharacteristic
107C2×C4⋊Dic71C2×C411yescharacteristic
108C2×C4⋊Dic71C2×C411yescharacteristic
109C2×C4⋊Dic71C2×C411yescharacteristic
110C2×Dic71⋊C4C2×C411yescharacteristic
111C2×Dic71⋊C4C2×C411yescharacteristic
112C2×Dic71⋊C4C2×C411yescharacteristic
113C2×Dic71⋊C4C2×C411yescharacteristic
114C2×Dic71⋊C4C2×C411yescharacteristic
115C2×Dic71⋊C4C2×C411yescharacteristic
116C2×Dic71⋊C4C2×C411yescharacteristic
117C2×Dic71⋊C4C2×C411yescharacteristic
118C2×C22⋊Dic71C2×C411yescharacteristic
119C2×C22⋊Dic71C2×C411yescharacteristic
120C2×C4×Dic71C2×C411yescharacteristic
121C2×C4×Dic71C2×C411yescharacteristic
122C2×C4×Dic71C2×C414yes—
123C2×C4×Dic71C2314yes—
124C2×C4×Dic71C2311yescharacteristic
125C2×C4×Dic71C2311yescharacteristic
126C2×C4×Dic71C2311yescharacteristic
127C2×C4×Dic71C2311yescharacteristic
128C4⋊(C71⋊C8)C2314yes—
129C4⋊(C71⋊C8)C2314yes—
130Dic71⋊C8C2314yes—
131Dic71⋊C8C2314yes—
132Dic71⋊C8C2314yes—
133Dic71⋊C8C2314yes—
134Dic71⋊C8C2314yes—
135Dic71⋊C8C2314yes—
136Dic71⋊C8C2314yes—
137Dic71⋊C8C2314yes—
138C22⋊(C71⋊C8)C2314yes—
139C22⋊(C71⋊C8)C2314yes—
140#14556039C2314yes—
141#14556038C2314yes—
142#14556038C2314yes—
143#14556038C2314yes—
144#14556038C2314yes—
145C4×C71⋊C8C2314yes—
146C8×Dic71C2314yes—
147C8×Dic71C2314yes—
148C8×Dic71C2314yes—
149C8×Dic71C2314yes—
150C23×C4×C71C2311yescharacteristic
151C22×C8×C71C2311yescharacteristic
152C22×C8×C71C2311yescharacteristic
153C22×C8×C71C2311yescharacteristic
154C22×C8×C71C2311yescharacteristic
155#117×C71C2×C414yes—
156#117×C71C2314yes—
157C2×C4⋊C4×C71C2×C411yescharacteristic
158C2×C4⋊C4×C71C2×C411yescharacteristic
159C2×C22⋊C4×C71C2×C411yescharacteristic
160C2×C22⋊C4×C71C2×C411yescharacteristic
161C2×C42×C71C2311yescharacteristic
162C2×C42×C71C2311yescharacteristic
163C4⋊C8×C71C2314yes—
164C4⋊C8×C71C2314yes—
165C22⋊C8×C71C2314yes—
166C22⋊C8×C71C2314yes—
167#97×C71C2314yes—
168C4×C8×C71C2314yes—
169C2×Dic142—24no—
170C2×Dic142—24no—
171C2×Dic142—42no—
172C2×Dic142—42no—
173C2×Dic142C22×C414yes—
174C2×Dic142C22×C414yes—
175C2×Dic142C22×C414yes—
176C2×Dic142C22×C414yes—
177C22×Dic71—24no—
178C22×Dic71—42no—
179C22×Dic71C22×C411yescharacteristic
180C22×Dic71C22×C411yescharacteristic
181C22×Dic71C22×C411yescharacteristic
182C22×Dic71C22×C414yes—
183C22×Dic71C22×C411yescharacteristic
184C22×Dic71C22×C411yescharacteristic
185C22×Dic71C22×C411yescharacteristic
186C22×Dic71C22×C411yescharacteristic
187C22×Dic71C22×C414yes—
188C22×Dic71C22×C411yescharacteristic
189C2×C71⋊C8—22no—
190C2×C71⋊C8—22no—
191C2×C71⋊C8—22no—
192C2×C71⋊C8—22no—
193C2×C71⋊C8C2412yes—
194C2×C71⋊C8C2412yes—
195C2×C71⋊C8C2412yes—
196C2×C71⋊C8C2412yes—
197C4⋊Dic71C22×C414yes—
198C4⋊Dic71C22×C414yes—
199C4⋊Dic71C22×C414yes—
200C4⋊Dic71C22×C414yes—
201C4⋊Dic71C22×C414yes—
202C4⋊Dic71C22×C414yes—
203Dic71⋊C4C22×C414yes—
204Dic71⋊C4C22×C414yes—
205Dic71⋊C4C22×C414yes—
206Dic71⋊C4C22×C414yes—
207Dic71⋊C4C22×C414yes—
208Dic71⋊C4C22×C414yes—
209Dic71⋊C4C22×C414yes—
210Dic71⋊C4C22×C414yes—
211C22⋊Dic71C22×C414yes—
212C22⋊Dic71C22×C414yes—
213C4×Dic71C22×C412yes—
214C4×Dic71C22×C412yes—
215C4×Dic71C22×C414yes—
216C4×Dic71C22×C414yes—
217C4×Dic71C22×C412yes—
218C4×Dic71C22×C412yes—
219C4×Dic71C2412yes—
220C4×Dic71C2412yes—
221C4×Dic71C2412yes—
222C4×Dic71C2412yes—
223C24×C71C22×C411yescharacteristic
224C22×C4×C71—22no—
225C22×C4×C71—22no—
226C22×C4×C71C22×C411yescharacteristic
227C22×C4×C71C22×C411yescharacteristic
228C22×C4×C71C22×C411yescharacteristic
229C22×C4×C71C22×C411yescharacteristic
230C22×C4×C71C22×C411yescharacteristic
231C22×C4×C71C22×C412yes—
232C22×C4×C71C2412yes—
233C22×C4×C71C2411yescharacteristic
234C2×C8×C71—22no—
235C2×C8×C71—22no—
236C2×C8×C71—22no—
237C2×C8×C71—22no—
238C2×C8×C71C2412yes—
239C2×C8×C71C2412yes—
240C2×C8×C71C2412yes—
241C2×C8×C71C2412yes—
242C4⋊C4×C71C22×C414yes—
243C4⋊C4×C71C22×C414yes—
244C22⋊C4×C71C22×C414yes—
245C22⋊C4×C71C22×C414yes—
246C42×C71C22×C412yes—
247C42×C71C22×C412yes—
248C42×C71C2412yes—
249C42×C71C2412yes—
250C23×C71—22no—
251C23×C71—22no—
252C23×C71—22no—
253C23×C71C23×C412yes—
254C23×C71C23×C411yescharacteristic
255C2×C4×C71—22no—
256C2×C4×C71—22no—
257C2×C4×C71—22no—
258C2×C4×C71—22no—
259C2×C4×C71—22no—
260C2×C4×C71—24no—
261C2×C4×C71—22no—
262C2×C4×C71—22no—
263C2×C4×C71C23×C412yes—
264C2×C4×C71C23×C412yes—
265C2×C4×C71C23×C412yes—
266C2×C4×C71C23×C412yes—
267C2×C4×C71C23×C412yes—
268C2×C4×C71C23×C411yescharacteristic
269C2×C4×C712−1+412yes—
270C2×C4×C712−1+412yes—
271C2×C4×C71C2511yescharacteristic
272C2×Dic71—22no—
273C2×Dic71—22no—
274C2×Dic71—22no—
275C2×Dic71—22no—
276C2×Dic71—22no—
277C2×Dic71—22no—
278C2×Dic71—22no—
279C2×Dic71—28no—
280C2×Dic71—44no—
281C2×Dic71#13114yes—
282C2×Dic71C23×C412yes—
283C2×Dic71C23×C412yes—
284C2×Dic71C23×C412yes—
285C2×Dic71C23×C412yes—
286C2×Dic71C23×C412yes—
287C2×Dic71C23×C412yes—
288C2×Dic71C23×C412yes—
289C2×Dic71C23×C412yes—
290Dic142—28no—
291Dic142—28no—
292Dic142—44no—
293Dic142—44no—
294C8×C71—22no—
295C8×C71—22no—
296C8×C71—22no—
297C8×C71—22no—
298C71⋊C8—22no—
299C71⋊C8—22no—
300C71⋊C8—22no—
301C71⋊C8—22no—
302C22×C71—22no—
303C22×C71—22no—
304C22×C71—22no—
305C22×C71—44no—
306C22×C71#51912yes—
307C22×C71C2×#13112yes—
308C22×C71#56812yes—
309C22×C71C24×C411yescharacteristic
310C4×C71—22no—
311C4×C71—22no—
312C4×C71—22no—
313C4×C71—22no—
314C4×C71—22no—
315C4×C71#51912yes—
316C4×C71C2×2−1+411yescharacteristic
317C4×C71C2×2−1+411yescharacteristic
318Dic71—22no—
319Dic71—22no—
320Dic71—22no—
321Dic71—22no—
322Dic71—22no—
323Dic71—22no—
324Dic71—22no—
325Dic71C2×#13114yes—
326C2×#2985—711nomaximal, Sylow
327C2×C71—42no—
328C2×C71#298514yescomplemented
329C2×C71C2×#51911yescharacteristic
330C2×C71C22×#13111yescharacteristic
331C2×C71C2×#56811yescharacteristic
332C2×#533—711no—
333#2985—7116no—
334C2×#446—711no—
335C2×#446—711no—
336C2×#446—711no—
337C2×#446—711no—
338C2×#446—711no—
339C2×#446—711no—
340C2×C8×Q8—711no—
341C2×C8×Q8—711no—
342C2×#433—711no—
343C2×#433—711no—
344C2×#433—711no—
345C2×#433D7111yescharacteristic
346C2×#432—711no—
347C2×#431—711no—
348C71C2×#298511yescharacteristic, complemented, Sylow
349#533—718no—
350#533—718no—
351C2×C4⋊Q8—711no—
352C2×C4⋊Q8—711no—
353C2×#125—711no—
354C2×#125—711no—
355C2×C22⋊Q8—711no—
356C2×C22⋊Q8—711no—
357C2×C22⋊Q8—711no—
358C2×C22⋊Q8—711no—
359C2×C4×Q8—711no—
360C2×C4×Q8—711no—
361C2×C4×Q8—711no—
362C2×C4×Q8—711no—
363C2×#117—711no—
364C2×#117C2×D7111yescharacteristic
365C22×C42—711no—
366#446—718no—
367#446—718no—
368#446—718no—
369#446—718no—
370#446—718no—
371#446—718no—
372C8×Q8—718no—
373C8×Q8—718no—
374#433—718no—
375#433—718no—
376#433—718no—
377#433C2×D7118yes—
378#432—718no—
379#431—718no—
380C2×C4⋊C8—711no—
381C2×C4⋊C8—711no—
382C2×C4⋊C8—711no—
383C2×C4⋊C8—711no—
384C2×C4⋊C8—711no—
385C2×C4⋊C8—711no—
386C2×C4⋊C8—711no—
387C2×C4⋊C8—711no—
388C2×C4⋊C8—711no—
389C2×C4⋊C8—711no—
390C2×C4⋊C8C2×D7111yescharacteristic
391C2×C4⋊C8C2×D7111yescharacteristic
392C2×C22⋊C8—711no—
393C2×C22⋊C8—711no—
394C2×C22⋊C8C2×D7111yescharacteristic
395C2×C22⋊C8C2×D7111yescharacteristic
396C2×#97—711no—
397C2×#97—711no—
398C2×#97—711no—
399C2×#97—711no—
400C2×#97—711no—
401C2×#97C2×D7111yescharacteristic
402C2×C4×C8—711no—
403C2×C4×C8—711no—
404C2×C4×C8—711no—
405C2×C4×C8—711no—
406C2×C4×C8—711no—
407C2×C4×C8C2×D7111yescharacteristic
408C22×Q8—711no—
409C22×Q8—711no—
410C22×Q8—711no—
411C22×Q8—711no—
412C23×C4—711no—
413C23×C4—711no—
414C23×C4C22×D7111yescharacteristic
415C22×C8—711no—
416C22×C8—711no—
417C22×C8—711no—
418C22×C8—711no—
419C22×C8C22×D7111yescharacteristic
420C22×C8C22×D7111yescharacteristic
421C22×C8C22×D7111yescharacteristic
422C22×C8C22×D7111yescharacteristic
423C4⋊Q8—718no—
424C4⋊Q8—718no—
425#125—718no—
426#125—718no—
427C22⋊Q8—718no—
428C22⋊Q8—718no—
429C22⋊Q8—718no—
430C22⋊Q8—718no—
431C4×Q8—714no—
432C4×Q8—714no—
433C4×Q8—714no—
434C4×Q8—714no—
435C4×Q8—714no—
436C4×Q8—714no—
437C4×Q8—714no—
438C4×Q8—714no—
439#117—714no—
440#117—714no—
441#117C4×D7114yes—
442#117C22×D7114yes—
443C2×C4⋊C4—711no—
444C2×C4⋊C4—711no—
445C2×C4⋊C4—711no—
446C2×C4⋊C4—711no—
447C2×C4⋊C4—711no—
448C2×C4⋊C4—711no—
449C2×C4⋊C4—711no—
450C2×C4⋊C4—711no—
451C2×C4⋊C4—711no—
452C2×C4⋊C4—711no—
453C2×C4⋊C4—711no—
454C2×C4⋊C4—711no—
455C2×C4⋊C4—711no—
456C2×C4⋊C4—711no—
457C2×C4⋊C4C4×D7111yescharacteristic
458C2×C4⋊C4C4×D7111yescharacteristic
459C2×C22⋊C4—711no—
460C2×C22⋊C4—711no—
461C2×C22⋊C4C4×D7111yescharacteristic
462C2×C22⋊C4C4×D7111yescharacteristic
463C2×C42—711no—
464C2×C42—711no—
465C2×C42—714no—
466C2×C42—714no—
467C2×C42—711no—
468C2×C42—711no—
469C2×C42—711no—
470C2×C42—711no—
471C2×C42C22×D7111yescharacteristic
472C2×C42C22×D7111yescharacteristic
473C4⋊C8—714no—
474C4⋊C8—714no—
475C4⋊C8—714no—
476C4⋊C8—714no—
477C4⋊C8—714no—
478C4⋊C8—714no—
479C4⋊C8—714no—
480C4⋊C8—714no—
481C4⋊C8—714no—
482C4⋊C8—714no—
483C4⋊C8C22×D7114yes—
484C4⋊C8C22×D7114yes—
485C22⋊C8—714no—
486C22⋊C8—714no—
487C22⋊C8C22×D7114yes—
488C22⋊C8C22×D7114yes—
489#97—714no—
490#97—714no—
491#97—714no—
492#97—714no—
493#97—714no—
494#97C22×D7114yes—
495C4×C8—714no—
496C4×C8—714no—
497C4×C8—714no—
498C4×C8—714no—
499C4×C8—714no—
500C4×C8C22×D7114yes—
501C24C2×C4×D7111yescharacteristic
502C2×Q8—2842no—
503C2×Q8—2842no—
504C2×Q8—714no—
505C2×Q8—714no—
506C2×Q8—714no—
507C2×Q8—714no—
508C2×Q8—1424no—
509C2×Q8—1424no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—2842no—
513C22×C4—714no—
514C22×C4—711no—
515C22×C4—711no—
516C22×C4—711no—
517C22×C4—711no—
518C22×C4—714no—
519C22×C4—711no—
520C22×C4—711no—
521C22×C4—711no—
522C22×C4—711no—
523C22×C4—1424no—
524C22×C4C2×C4×D7111yescharacteristic
525C22×C4C2×C4×D7112yes—
526C22×C4C2×C4×D7111yescharacteristic
527C22×C4C2×C4×D7111yescharacteristic
528C22×C4C2×C4×D7111yescharacteristic
529C22×C4C2×C4×D7111yescharacteristic
530C22×C4C23×D7112yes—
531C22×C4C23×D7111yescharacteristic
532C2×C8—22no—
533C2×C8—22no—
534C2×C8—22no—
535C2×C8—22no—
536C2×C8—712no—
537C2×C8—712no—
538C2×C8—712no—
539C2×C8—712no—
540C2×C8—1422no—
541C2×C8—1422no—
542C2×C8—1422no—
543C2×C8—1422no—
544C2×C8C23×D7112yes—
545C2×C8C23×D7112yes—
546C2×C8C23×D7112yes—
547C2×C8C23×D7112yes—
548C4⋊C4—714no—
549C4⋊C4—714no—
550C4⋊C4—714no—
551C4⋊C4—714no—
552C4⋊C4—714no—
553C4⋊C4—714no—
554C4⋊C4—714no—
555C4⋊C4—714no—
556C4⋊C4—714no—
557C4⋊C4—714no—
558C4⋊C4—714no—
559C4⋊C4—714no—
560C4⋊C4—714no—
561C4⋊C4—714no—
562C4⋊C4C2×C4×D7114yes—
563C4⋊C4C2×C4×D7114yes—
564C22⋊C4—714no—
565C22⋊C4—714no—
566C22⋊C4C2×C4×D7114yes—
567C22⋊C4C2×C4×D7114yes—
568C42—712no—
569C42—712no—
570C42—714no—
571C42—714no—
572C42—712no—
573C42—712no—
574C42—712no—
575C42—712no—
576C42—712no—
577C42—712no—
578C42C2×C4×D7112yes—
579C42C2×C4×D7112yes—
580C42C23×D7112yes—
581C42C23×D7112yes—
582C23—22no—
583C23—22no—
584C23—22no—
585C23C22×C4×D7112yes—
586C23C22×C4×D7111yescharacteristic
587Q8—2844no—
588Q8—2844no—
589Q8—1428no—
590Q8—1428no—
591C2×C4—22no—
592C2×C4—22no—
593C2×C4—22no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—2844no—
600C2×C4—712no—
601C2×C4—714no—
602C2×C4—712no—
603C2×C4—712no—
604C2×C4—712no—
605C2×C4—712no—
606C2×C4—712no—
607C2×C4—712no—
608C2×C4—712no—
609C2×C4—1428no—
610C2×C4—1422no—
611C2×C4—1422no—
612C2×C4—1422no—
613C2×C4—1422no—
614C2×C4—1422no—
615C2×C4—1422no—
616C2×C4—1422no—
617C2×C4C22×C4×D7112yes—
618C2×C4C22×C4×D7112yes—
619C2×C4C22×C4×D7112yes—
620C2×C4C22×C4×D7112yes—
621C2×C4C22×C4×D7112yes—
622C2×C4C22×C4×D7111yescharacteristic
623C2×C4#1455617512yes—
624C2×C4#1455617512yes—
625C2×C4C24×D7111yescharacteristic
626C8—22no—
627C8—22no—
628C8—22no—
629C8—22no—
630C8—1422no—
631C8—1422no—
632C8—1422no—
633C8—1422no—
634C22—22no—
635C22—22no—
636C22—22no—
637C22—44no—
638C22#1798647612yes—
639C22#131×D7112yes—
640C22#1798676412yes—
641C22C23×C4×D7111yescharacteristic
642C4—22no—
643C4—22no—
644C4—22no—
645C4—22no—
646C4—22no—
647C4—714no—
648C4—1422no—
649C4—1422no—
650C4—1422no—
651C4—1422no—
652C4—1422no—
653C4—1422no—
654C4—1422no—
655C4#1798647612yes—
656C4C2×#1455617511yescharacteristic
657C4C2×#1455617511yescharacteristic
658C2—42no—
659C2#2259743214yesdirect product factor
660C2C2×#1798647611yescharacteristic
661C2C2×#131×D7111yescharacteristic
662C2C2×#1798676411yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutatorC22×C71C24×C4
FrattiniC2×C4C24×D71
FittingC2×#433×C71C2
socleC23×C71C23×C4
prime radicalC24×C71C22×C4
cosocleC2×C4×C71C25
hypercenterC2×#433D71
hypocenterC71C2×#2985
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
2. #22597432C2direct (N × H)
3. C2×#17986129C2semidirect
4. C2×#17986128C2semidirect
5. C2×#17986128C2semidirect
6. C2×#17986127C2semidirect
7. C2×#17986127C2semidirect
8. C2×#17986126C2semidirect
9. C2×C8×Dic142C2semidirect
10. C2×#17986123C2semidirect
33. #17986129C22semidirect
34. #17986128C22semidirect
35. #17986128C22semidirect
36. #17986127C22semidirect
37. #17986127C22semidirect
38. #17986126C22semidirect
39. C8×Dic142C22semidirect
40. #17986123C22semidirect
328. C2×C71#2985semidirect
348. C71C2×#2985semidirect
659. C2#22597432direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865522
#225974322
C2×#179861292
C2×#179861282
C2×#179861272
C2×#179861262
C2×C8×Dic1422
C2×#179861232
C2×#179860602
C2×#179860572
C2×#179860532
C2×#179860492
C2×#433×C712
C2×#298571