Finite Group Databasebeta

← C2×#22597408 #32862226

Subgroups — C2×#22597408 #32862226

Order 18176.

2186 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986546C211yesmaximal, characteristic
2#22597408C2116yesmaximal, direct product factor
3C2×#17986073C211yesmaximal, characteristic, complemented
4C2×#17986072C211yesmaximal, characteristic, complemented
5C2×#17986071C211yesmaximal, characteristic, complemented
6C2×#17986070C211yesmaximal, characteristic, complemented
7C2×#17986069C211yesmaximal, characteristic, complemented
8C2×#17986068C211yesmaximal, characteristic, complemented
9C2×#17986067C211yesmaximal, characteristic, complemented
10C2×#17986055C211yesmaximal, characteristic, complemented
11C2×#17986054C211yesmaximal, characteristic, complemented
12C2×#17985967C211yesmaximal, characteristic, complemented
13C2×#17985965C211yesmaximal, characteristic, complemented
14C2×#17985964C211yesmaximal, characteristic, complemented
15C2×#17985964C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×#11765865C2211yescharacteristic
19C22×#11765849C2211yescharacteristic
20C22×#11765848C2211yescharacteristic
21C22×#11765848C2211yescharacteristic
22C23×C71⋊C8C2211yescharacteristic
23C22×C8×D71C2211yescharacteristic
24C22×C8×D71C2211yescharacteristic
25#17986546C418yes—
26#17986546C2218yes—
27C2×#14556127C411yescharacteristic
28C2×#14556124C411yescharacteristic
29C2×#14556114C411yescharacteristic
30C2×#14556114C411yescharacteristic
31C2×#14556103C411yescharacteristic
32C2×#14556101C411yescharacteristic
33C2×#14556101C411yescharacteristic
34C2×#14556099C411yescharacteristic
35C2×C4×D284C2211yescharacteristic
36C2×C4×C22⋊D71C2211yescharacteristic
37C2×C4×C22⋊D71C2211yescharacteristic
38C2×C42×D71C2211yescharacteristic
39#17986073C2218yescomplemented
40#17986072C2218yescomplemented
41#17986071C2218yescomplemented
42#17986070C2218yescomplemented
43#17986069C2218yescomplemented
44#17986068C2218yescomplemented
45#17986067C2218yescomplemented
46#17986055C2218yescomplemented
47#17986054C2218yescomplemented
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49C2×Dic71⋊C8C2211yescharacteristic
50C2×Dic71⋊C8C2211yescharacteristic
51#17985967C2218yescomplemented
52#17985965C2218yescomplemented
53#17985964C2218yescomplemented
54#17985964C2218yescomplemented
55C2×C22⋊(C71⋊C8)C2211yescharacteristic
56C2×C22⋊(C71⋊C8)C2211yescharacteristic
57C2×(C2×D71)⋊C8C2211yescharacteristic
58C2×(C2×D71)⋊C8C2211yescharacteristic
59C2×(C2×D71)⋊C8C2211yescharacteristic
60C2×(C2×D71)⋊C8C2211yescharacteristic
61C2×(C2×D71)⋊C8C2211yescharacteristic
62C2×(C2×D71)⋊C8C2211yescharacteristic
63C2×(C2×D71)⋊C8C2211yescharacteristic
64C2×(C2×D71)⋊C8C2211yescharacteristic
65C2×#14556039C2211yescharacteristic
66C2×#14556038C2211yescharacteristic
67C2×#14556038C2211yescharacteristic
68C22×M16×C71C2211yescharacteristic
69C23×C8×C71C2211yescharacteristic
70C2×C4×D4×C71C2211yescharacteristic
71#435×C71C2218yescomplemented
72C2×C4⋊C8×C71C2211yescharacteristic
73C2×C22⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×#97×C71C2211yescharacteristic
76C2×#11765865—42no—
77C2×#11765865—42no—
78C2×#11765865—42no—
79C2×#11765865—42no—
80C2×#11765865C2×C414yes—
81C2×#11765865C2×C414yes—
82C2×#11765865C2314yes—
83C2×#11765865C2314yes—
84C22×Dic142C2×C411yescharacteristic
85C22×Dic142C2×C411yescharacteristic
86C22×D284C2×C411yescharacteristic
87C22×D284C2×C411yescharacteristic
88C22×D284C2×C411yescharacteristic
89C22×C22⋊D71C2×C411yescharacteristic
90C22×C22⋊D71C2×C411yescharacteristic
91C22×C22⋊D71C2×C411yescharacteristic
92C22×C22⋊D71C2×C411yescharacteristic
93C22×C22⋊D71C2×C411yescharacteristic
94C22×C22⋊D71C2×C411yescharacteristic
95C22×C4×D71C2×C411yescharacteristic
96C22×C4×D71C2×C411yescharacteristic
97C22×C4×D71C2311yescharacteristic
98C22×C4×D71C2311yescharacteristic
99C22×C4×D71C2311yescharacteristic
100C2×#11765849—42no—
101C2×#11765849C2314yes—
102C2×#11765848—42no—
103C2×#11765848—42no—
104C2×#11765848C2314yes—
105C2×#11765848C2314yes—
106C22×C71⋊C8—42no—
107C22×C71⋊C8C2311yescharacteristic
108C22×C71⋊C8C2311yescharacteristic
109C22×C71⋊C8C2311yescharacteristic
110C22×C71⋊C8C2311yescharacteristic
111C22×C71⋊C8C2314yes—
112C2×C8×D71—42no—
113C2×C8×D71—42no—
114C2×C8×D71C2314yes—
115C2×C8×D71C2314yes—
116#14556127C2×C418yes—
117#14556124C2×C418yes—
118#14556114C2×C418yes—
119#14556114C2×C418yes—
120#14556103C2×C418yes—
121#14556101C2×C418yes—
122#14556101C2×C418yes—
123#14556099C2×C418yes—
124C4×D284C2×C414yes—
125C4×D284C2314yes—
126C4×C22⋊D71C2×C414yes—
127C4×C22⋊D71C2×C414yes—
128C4×C22⋊D71C2314yes—
129C4×C22⋊D71C2314yes—
130C2×C4⋊Dic71C2×C411yescharacteristic
131C2×Dic71⋊C4C2×C411yescharacteristic
132C2×Dic71⋊C4C2×C411yescharacteristic
133C2×C22⋊Dic71C2×C411yescharacteristic
134C2×C22⋊Dic71C2×C411yescharacteristic
135C2×(C2×D71)⋊C4C2×C411yescharacteristic
136C2×(C2×D71)⋊C4C2×C411yescharacteristic
137C2×(C2×D71)⋊C4C2×C411yescharacteristic
138C2×(C2×D71)⋊C4C2×C411yescharacteristic
139C2×C4×Dic71C2×C411yescharacteristic
140C2×C4×Dic71C2×C411yescharacteristic
141C2×C4×Dic71C2311yescharacteristic
142C42×D71C2×C414yes—
143C42×D71C2314yes—
144C4⋊(C71⋊C8)C2314yes—
145Dic71⋊C8C2314yes—
146Dic71⋊C8C2314yes—
147C22⋊(C71⋊C8)C2314yes—
148C22⋊(C71⋊C8)C2314yes—
149(C2×D71)⋊C8C2314yes—
150(C2×D71)⋊C8C2314yes—
151(C2×D71)⋊C8C2314yes—
152(C2×D71)⋊C8C2314yes—
153(C2×D71)⋊C8C2314yes—
154(C2×D71)⋊C8C2314yes—
155(C2×D71)⋊C8C2314yes—
156(C2×D71)⋊C8C2314yes—
157#14556039C2314yes—
158#14556038C2314yes—
159#14556038C2314yes—
160C22×D4×C71C2×C411yescharacteristic
161C23×C4×C71C2311yescharacteristic
162C23×C4×C71C2311yescharacteristic
163C2×M16×C71—42no—
164C2×M16×C71C2314yes—
165C22×C8×C71—42no—
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2311yescharacteristic
168C22×C8×C71C2311yescharacteristic
169C22×C8×C71C2311yescharacteristic
170C22×C8×C71C2314yes—
171C4×D4×C71C2×C414yes—
172C4×D4×C71C2314yes—
173C2×C4⋊C4×C71C2×C411yescharacteristic
174C2×C22⋊C4×C71C2×C411yescharacteristic
175C2×C22⋊C4×C71C2×C411yescharacteristic
176C2×C42×C71C2311yescharacteristic
177C4⋊C8×C71C2314yes—
178C22⋊C8×C71C2314yes—
179C22⋊C8×C71C2314yes—
180#97×C71C2314yes—
181C23×D71C22×C411yescharacteristic
182C23×D71C22×C411yescharacteristic
183C23×D71C22×C411yescharacteristic
184#11765865—48no—
185#11765865—48no—
186#11765865—44no—
187#11765865—44no—
188#11765865—44no—
189#11765865—44no—
190C2×Dic142—42no—
191C2×Dic142—42no—
192C2×Dic142C22×C414yes—
193C2×Dic142C22×C414yes—
194C2×D284—42no—
195C2×D284—42no—
196C2×D284—42no—
197C2×D284C22×C414yes—
198C2×D284C22×C414yes—
199C2×D284C22×C414yes—
200C2×C22⋊D71—42no—
201C2×C22⋊D71—42no—
202C2×C22⋊D71—42no—
203C2×C22⋊D71—42no—
204C2×C22⋊D71—42no—
205C2×C22⋊D71—42no—
206C2×C22⋊D71C22×C414yes—
207C2×C22⋊D71C22×C414yes—
208C2×C22⋊D71C22×C414yes—
209C2×C22⋊D71C22×C414yes—
210C2×C22⋊D71C22×C414yes—
211C2×C22⋊D71C22×C414yes—
212C22×Dic71C22×C411yescharacteristic
213C22×Dic71C22×C411yescharacteristic
214C22×Dic71C22×C411yescharacteristic
215C22×Dic71C22×C411yescharacteristic
216C22×Dic71C22×C411yescharacteristic
217C2×C4×D71—22no—
218C2×C4×D71—22no—
219C2×C4×D71—22no—
220C2×C4×D71—22no—
221C2×C4×D71—22no—
222C2×C4×D71—22no—
223C2×C4×D71—42no—
224C2×C4×D71—42no—
225C2×C4×D71C22×C412yes—
226C2×C4×D71C22×C412yes—
227C2×C4×D71C22×C412yes—
228C2×C4×D71C22×C414yes—
229C2×C4×D71C22×C414yes—
230C2×C4×D71C2412yes—
231C2×C4×D71C2412yes—
232C2×C4×D71C2412yes—
233#11765849—44no—
234#11765848—44no—
235#11765848—44no—
236C2×C71⋊C8—22no—
237C2×C71⋊C8—22no—
238C2×C71⋊C8—22no—
239C2×C71⋊C8—22no—
240C2×C71⋊C8—44no—
241C2×C71⋊C8C2412yes—
242C2×C71⋊C8C2412yes—
243C2×C71⋊C8C2412yes—
244C2×C71⋊C8C2412yes—
245C8×D71—44no—
246C8×D71—44no—
247C4⋊Dic71C22×C414yes—
248Dic71⋊C4C22×C414yes—
249Dic71⋊C4C22×C414yes—
250C22⋊Dic71C22×C414yes—
251C22⋊Dic71C22×C414yes—
252(C2×D71)⋊C4C22×C414yes—
253(C2×D71)⋊C4C22×C414yes—
254(C2×D71)⋊C4C22×C414yes—
255(C2×D71)⋊C4C22×C414yes—
256C4×Dic71C22×C412yes—
257C4×Dic71C22×C414yes—
258C4×Dic71C22×C414yes—
259C4×Dic71C2412yes—
260C24×C71C22×C411yescharacteristic
261C24×C71C22×C411yescharacteristic
262C2×D4×C71—42no—
263C2×D4×C71C22×C414yes—
264C22×C4×C71—22no—
265C22×C4×C71—22no—
266C22×C4×C71—22no—
267C22×C4×C71—22no—
268C22×C4×C71C22×C411yescharacteristic
269C22×C4×C71C22×C411yescharacteristic
270C22×C4×C71C22×C411yescharacteristic
271C22×C4×C71C22×C411yescharacteristic
272C22×C4×C71C22×C412yes—
273C22×C4×C71C22×C412yes—
274C22×C4×C71C2412yes—
275C22×C4×C71C2412yes—
276C22×C4×C71C2411yescharacteristic
277M16×C71—44no—
278C2×C8×C71—22no—
279C2×C8×C71—22no—
280C2×C8×C71—22no—
281C2×C8×C71—22no—
282C2×C8×C71—44no—
283C2×C8×C71C2412yes—
284C2×C8×C71C2412yes—
285C2×C8×C71C2412yes—
286C2×C8×C71C2412yes—
287C4⋊C4×C71C22×C414yes—
288C22⋊C4×C71C22×C414yes—
289C22⋊C4×C71C22×C414yes—
290C42×C71C22×C412yes—
291C42×C71C2412yes—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71C23×C412yes—
299C23×C71C23×C412yes—
300C23×C71C23×C411yescharacteristic
301C22×D71—22no—
302C22×D71—22no—
303C22×D71—22no—
304C22×D71—22no—
305C22×D71—22no—
306C22×D71—22no—
307C22×D71—22no—
308C22×D71—22no—
309C22×D71—22no—
310C22×D71C23×C412yes—
311C22×D71C23×C412yes—
312C22×D71C23×C412yes—
313D4×C71—44no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—22no—
317C2×C4×C71—22no—
318C2×C4×C71—24no—
319C2×C4×C71—24no—
320C2×C4×C71—22no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—22no—
324C2×C4×C71C23×C412yes—
325C2×C4×C71C23×C412yes—
326C2×C4×C71C23×C412yes—
327C2×C4×C71C23×C412yes—
328C2×C4×C71C23×C411yescharacteristic
329C2×C4×C71H(5,𝔽2)12yes—
330C2×C4×C71H(5,𝔽2)12yes—
331C2×C4×C71C2511yescharacteristic
332C22⋊D71—44no—
333C22⋊D71—44no—
334C22⋊D71—44no—
335C22⋊D71—44no—
336C22⋊D71—44no—
337C22⋊D71—44no—
338C2×Dic71—22no—
339C2×Dic71—22no—
340C2×Dic71—22no—
341C2×Dic71—22no—
342C2×Dic71—22no—
343C2×Dic71C23×C412yes—
344C2×Dic71C23×C412yes—
345C2×Dic71C23×C412yes—
346C2×Dic71C23×C412yes—
347C2×Dic71C23×C412yes—
348D284—44no—
349D284—44no—
350D284—44no—
351C4×D71—24no—
352C4×D71—24no—
353C4×D71—24no—
354C4×D71—22no—
355C4×D71—22no—
356C4×D71—22no—
357C4×D71—22no—
358C4×D71—22no—
359C4×D71—22no—
360C4×D71—44no—
361C4×D71—44no—
362Dic142—44no—
363Dic142—44no—
364C8×C71—22no—
365C8×C71—22no—
366C8×C71—22no—
367C8×C71—22no—
368C71⋊C8—22no—
369C71⋊C8—22no—
370C71⋊C8—22no—
371C71⋊C8—22no—
372C22×C71—22no—
373C22×C71—22no—
374C22×C71—22no—
375C22×C71—22no—
376C22×C71—22no—
377C22×C71—22no—
378C22×C71—44no—
379C22×C71—44no—
380C22×C71#51812yes—
381C22×C71#56812yes—
382C22×C71#56812yes—
383C22×C71C24×C411yescharacteristic
384C2×D71—22no—
385C2×D71—22no—
386C2×D71—22no—
387C2×D71—22no—
388C2×D71—22no—
389C2×D71—22no—
390C2×D71—22no—
391C2×D71—22no—
392C2×D71—22no—
393C2×D71—44no—
394C2×D71—44no—
395C2×D71—44no—
396C4×C71—22no—
397C4×C71—22no—
398C4×C71—22no—
399C4×C71—22no—
400C4×C71#51812yes—
401C4×C71C2×H(5,𝔽2)11yescharacteristic
402C4×C71C2×H(5,𝔽2)11yescharacteristic
403Dic71—22no—
404Dic71—22no—
405Dic71—22no—
406Dic71—22no—
407Dic71—22no—
408C2×#2980—711nomaximal, Sylow
409C2×C71—42no—
410C2×C71—42no—
411C2×C71#298014yescomplemented
412C2×C71C2×#51811yescharacteristic
413C2×C71C2×#56811yescharacteristic
414C2×C71C2×#56811yescharacteristic
415D71—42no—
416D71—42no—
417D71—42no—
418C2×#532—711no—
419#2980—7116no—
420C2×#435—711no—
421C2×#435—711no—
422C2×#435—711no—
423C2×#435—711no—
424C2×#435—711no—
425C2×#435—711no—
426C2×#435—711no—
427C2×#435D7111yescharacteristic, complemented
428C2×#432—711no—
429C2×#432—711no—
430C2×#408—711no—
431C2×#408—711no—
432C2×#408—711no—
433C2×#408—711no—
434C71C2×#298011yescharacteristic, complemented, Sylow
435C22×#41—711no—
436C22×#41—711no—
437C22×M16—711no—
438C22×M16—711no—
439C22×M16—711no—
440C22×M16C2×D7111yescharacteristic
441C23×C8—711no—
442C23×C8—711no—
443C23×C8—711no—
444C23×C8C2×D7111yescharacteristic
445#532—718no—
446#532—718no—
447C2×C4⋊Q8—711no—
448C2×#127—711no—
449C2×#124—711no—
450C2×#124—711no—
451C2×#121—711no—
452C2×#121—711no—
453C2×#121—711no—
454C2×#121—711no—
455C2×C4×D4—711no—
456C2×C4×D4—711no—
457C2×C4×D4—711no—
458C2×C4×D4C2×D7111yescharacteristic
459C22×C42—711no—
460#435—718no—
461#435—718no—
462#435—718no—
463#435—718no—
464#435—718no—
465#435—718no—
466#435—718no—
467#435C2×D7118yescomplemented
468#432—718no—
469#432—718no—
470C2×C4⋊C8—711no—
471C2×C4⋊C8—711no—
472C2×C4⋊C8—711no—
473C2×C4⋊C8C2×D7111yescharacteristic
474#408—718no—
475#408—718no—
476#408—718no—
477#408—718no—
478C2×C22⋊C8—711no—
479C2×C22⋊C8—711no—
480C2×C22⋊C8—711no—
481C2×C22⋊C8—711no—
482C2×C22⋊C8—711no—
483C2×C22⋊C8—711no—
484C2×C22⋊C8—711no—
485C2×C22⋊C8—711no—
486C2×C22⋊C8—711no—
487C2×C22⋊C8—711no—
488C2×C22⋊C8C2×D7111yescharacteristic
489C2×C22⋊C8C2×D7111yescharacteristic
490C2×#97—711no—
491C2×#97—711no—
492C2×#97—711no—
493C2×#97C2×D7111yescharacteristic
494C2×#41—2842no—
495C2×#41—2842no—
496C2×#41—2842no—
497C2×#41—2842no—
498C2×#41—714no—
499C2×#41—714no—
500C2×#41—714no—
501C2×#41—714no—
502C22×Q8—711no—
503C22×Q8—711no—
504C22×D4—711no—
505C22×D4—711no—
506C22×D4—711no—
507C22×D4—711no—
508C22×D4—711no—
509C22×D4—711no—
510C22×D4—711no—
511C22×D4—711no—
512C22×D4—711no—
513C22×D4C4×D7111yescharacteristic
514C23×C4—711no—
515C23×C4—711no—
516C23×C4—711no—
517C23×C4—711no—
518C23×C4—711no—
519C23×C4C22×D7111yescharacteristic
520C23×C4C22×D7111yescharacteristic
521C2×M16—42no—
522C2×M16—2842no—
523C2×M16—2842no—
524C2×M16—2842no—
525C2×M16—714no—
526C2×M16—714no—
527C2×M16—714no—
528C2×M16C22×D7114yes—
529C22×C8—42no—
530C22×C8—2842no—
531C22×C8—2842no—
532C22×C8—2842no—
533C22×C8—714no—
534C22×C8—714no—
535C22×C8—714no—
536C22×C8—711no—
537C22×C8—711no—
538C22×C8—711no—
539C22×C8—711no—
540C22×C8C22×D7111yescharacteristic
541C22×C8C22×D7111yescharacteristic
542C22×C8C22×D7111yescharacteristic
543C22×C8C22×D7111yescharacteristic
544C22×C8C22×D7114yes—
545C4⋊Q8—718no—
546#127—718no—
547#124—718no—
548#124—718no—
549#121—718no—
550#121—718no—
551#121—718no—
552#121—718no—
553C4×D4—714no—
554C4×D4—714no—
555C4×D4—714no—
556C4×D4—714no—
557C4×D4—714no—
558C4×D4—714no—
559C4×D4C4×D7114yes—
560C4×D4C22×D7114yes—
561C2×C4⋊C4—711no—
562C2×C4⋊C4—711no—
563C2×C4⋊C4—711no—
564C2×C4⋊C4C4×D7111yescharacteristic
565C2×C22⋊C4—711no—
566C2×C22⋊C4—711no—
567C2×C22⋊C4—711no—
568C2×C22⋊C4—711no—
569C2×C22⋊C4—711no—
570C2×C22⋊C4—711no—
571C2×C22⋊C4C4×D7111yescharacteristic
572C2×C22⋊C4C4×D7111yescharacteristic
573C2×C42—711no—
574C2×C42—711no—
575C2×C42—711no—
576C2×C42—714no—
577C2×C42—714no—
578C2×C42C22×D7111yescharacteristic
579C4⋊C8—714no—
580C4⋊C8—714no—
581C4⋊C8—714no—
582C4⋊C8C22×D7114yes—
583C22⋊C8—714no—
584C22⋊C8—714no—
585C22⋊C8—714no—
586C22⋊C8—714no—
587C22⋊C8—714no—
588C22⋊C8—714no—
589C22⋊C8—714no—
590C22⋊C8—714no—
591C22⋊C8—714no—
592C22⋊C8—714no—
593C22⋊C8C22×D7114yes—
594C22⋊C8C22×D7114yes—
595#97—714no—
596#97—714no—
597#97—714no—
598#97C22×D7114yes—
599C24—711no—
600C24—711no—
601C24—711no—
602C24C2×C4×D7111yescharacteristic
603C24C2×C4×D7111yescharacteristic
604#41—2844no—
605#41—2844no—
606#41—2844no—
607#41—2844no—
608#41—2848no—
609#41—2848no—
610C2×Q8—2842no—
611C2×Q8—2842no—
612C2×Q8—714no—
613C2×Q8—714no—
614C2×D4—42no—
615C2×D4—2842no—
616C2×D4—2842no—
617C2×D4—2842no—
618C2×D4—2842no—
619C2×D4—2842no—
620C2×D4—2842no—
621C2×D4—2842no—
622C2×D4—2842no—
623C2×D4—2842no—
624C2×D4—714no—
625C2×D4—714no—
626C2×D4—714no—
627C2×D4—714no—
628C2×D4—714no—
629C2×D4—714no—
630C2×D4—714no—
631C2×D4—714no—
632C2×D4—714no—
633C2×D4C2×C4×D7114yes—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—2842no—
639C22×C4—2842no—
640C22×C4—714no—
641C22×C4—714no—
642C22×C4—711no—
643C22×C4—711no—
644C22×C4—711no—
645C22×C4—711no—
646C22×C4—711no—
647C22×C4—712no—
648C22×C4—712no—
649C22×C4—712no—
650C22×C4—712no—
651C22×C4—712no—
652C22×C4—712no—
653C22×C4—1422no—
654C22×C4—1422no—
655C22×C4—1422no—
656C22×C4—1422no—
657C22×C4—1422no—
658C22×C4—1422no—
659C22×C4C2×C4×D7111yescharacteristic
660C22×C4C2×C4×D7111yescharacteristic
661C22×C4C2×C4×D7111yescharacteristic
662C22×C4C2×C4×D7111yescharacteristic
663C22×C4C2×C4×D7112yes—
664C22×C4C2×C4×D7112yes—
665C22×C4C23×D7112yes—
666C22×C4C23×D7112yes—
667C22×C4C23×D7111yescharacteristic
668M16—44no—
669M16—2844no—
670M16—2844no—
671M16—2844no—
672C2×C8—22no—
673C2×C8—22no—
674C2×C8—22no—
675C2×C8—22no—
676C2×C8—44no—
677C2×C8—2844no—
678C2×C8—2844no—
679C2×C8—2844no—
680C2×C8—712no—
681C2×C8—712no—
682C2×C8—712no—
683C2×C8—712no—
684C2×C8—1422no—
685C2×C8—1422no—
686C2×C8—1422no—
687C2×C8—1422no—
688C2×C8C23×D7112yes—
689C2×C8C23×D7112yes—
690C2×C8C23×D7112yes—
691C2×C8C23×D7112yes—
692C4⋊C4—714no—
693C4⋊C4—714no—
694C4⋊C4—714no—
695C4⋊C4C2×C4×D7114yes—
696C22⋊C4—714no—
697C22⋊C4—714no—
698C22⋊C4—714no—
699C22⋊C4—714no—
700C22⋊C4—714no—
701C22⋊C4—714no—
702C22⋊C4C2×C4×D7114yes—
703C22⋊C4C2×C4×D7114yes—
704C42—712no—
705C42—714no—
706C42—714no—
707C42—712no—
708C42C2×C4×D7112yes—
709C42C23×D7112yes—
710C23—22no—
711C23—22no—
712C23—22no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—712no—
717C23—712no—
718C23—712no—
719C23—1422no—
720C23—1422no—
721C23—1422no—
722C23—1422no—
723C23—1422no—
724C23—1422no—
725C23—1422no—
726C23—1422no—
727C23—1422no—
728C23C22×C4×D7112yes—
729C23C22×C4×D7112yes—
730C23C22×C4×D7111yescharacteristic
731Q8—2844no—
732Q8—2844no—
733D4—44no—
734D4—2844no—
735D4—2844no—
736D4—2844no—
737D4—2844no—
738D4—2844no—
739D4—2844no—
740D4—2844no—
741D4—2844no—
742D4—2844no—
743C2×C4—22no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—24no—
752C2×C4—24no—
753C2×C4—2844no—
754C2×C4—2844no—
755C2×C4—712no—
756C2×C4—712no—
757C2×C4—712no—
758C2×C4—712no—
759C2×C4—712no—
760C2×C4—1422no—
761C2×C4—1422no—
762C2×C4—1422no—
763C2×C4—1422no—
764C2×C4—1422no—
765C2×C4—1422no—
766C2×C4—1422no—
767C2×C4—1422no—
768C2×C4—1422no—
769C2×C4—1422no—
770C2×C4—1422no—
771C2×C4—1424no—
772C2×C4—1424no—
773C2×C4—1424no—
774C2×C4C22×C4×D7112yes—
775C2×C4C22×C4×D7112yes—
776C2×C4C22×C4×D7112yes—
777C2×C4C22×C4×D7112yes—
778C2×C4C22×C4×D7111yescharacteristic
779C2×C4#1455617312yes—
780C2×C4#1455617412yes—
781C2×C4C24×D7111yescharacteristic
782C8—22no—
783C8—22no—
784C8—22no—
785C8—22no—
786C8—1422no—
787C8—1422no—
788C8—1422no—
789C8—1422no—
790C22—22no—
791C22—22no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—22no—
796C22—44no—
797C22—44no—
798C22—2844no—
799C22—2844no—
800C22—2844no—
801C22—1422no—
802C22—1422no—
803C22—1422no—
804C22—1422no—
805C22—1422no—
806C22—1422no—
807C22—1422no—
808C22—1422no—
809C22—1422no—
810C22#1798647112yes—
811C22#1798676412yes—
812C22#1798676512yes—
813C22C23×C4×D7111yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—1422no—
819C4—1422no—
820C4—1422no—
821C4—1422no—
822C4—1422no—
823C4#1798647112yes—
824C4C2×#1455617311yescharacteristic
825C4C2×#1455617411yescharacteristic
826C2—42no—
827C2—42no—
828C2—2842no—
829C2—2842no—
830C2—2842no—
831C2#2259740814yesdirect product factor
832C2C2×#1798647111yescharacteristic
833C2C2×#1798676411yescharacteristic
834C2C2×#1798676511yescharacteristic
subgroupG/H
centerC22×C4C23×D71
commutatorC22×C71C24×C4
FrattiniC2×C4C24×D71
FittingC2×#435×C71C2
socleC23×C71C23×C4
prime radicalC2×#17986546C2
cosocleC2×C4×C71C25
hypercenterC2×#435D71
hypocenterC71C2×#2980
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. #22597408C2direct (N × H)
3. C2×#17986073C2semidirect
4. C2×#17986072C2semidirect
5. C2×#17986071C2semidirect
6. C2×#17986070C2semidirect
7. C2×#17986069C2semidirect
8. C2×#17986068C2semidirect
9. C2×#17986067C2semidirect
10. C2×#17986055C2semidirect
11. C2×#17986054C2semidirect
12. C2×#17985967C2semidirect
13. C2×#17985965C2semidirect
14. C2×#17985964C2semidirect
15. C2×#17985964C2semidirect
16. C2×#435×C71C2semidirect
39. #17986073C22semidirect
40. #17986072C22semidirect
41. #17986071C22semidirect
42. #17986070C22semidirect
43. #17986069C22semidirect
44. #17986068C22semidirect
45. #17986067C22semidirect
46. #17986055C22semidirect
47. #17986054C22semidirect
51. #17985967C22semidirect
52. #17985965C22semidirect
53. #17985964C22semidirect
54. #17985964C22semidirect
71. #435×C71C22semidirect
411. C2×C71#2980semidirect
427. C2×#435D71semidirect
434. C71C2×#2980semidirect
467. #435C2×D71semidirect
831. C2#22597408direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865462
#225974082
C2×#179860732
C2×#179860722
C2×#179860712
C2×#179860702
C2×#179860692
C2×#179860682
C2×#179860672
C2×#179860552
C2×#179860542
C2×#179859672
C2×#179859652
C2×#179859642
C2×#435×C712
C2×#298071