Finite Group Databasebeta

← C2×#22597081 #32861359

Subgroups — C2×#22597081 #32861359

Order 18176.

2850 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556136C211yesmaximal, characteristic, complemented
2C22×#14556134C211yesmaximal, characteristic, complemented
3C2×#17986546C211yesmaximal, characteristic
4#22597081C2116yesmaximal, direct product factor
5C2×#17986075C211yesmaximal, characteristic, complemented
6C2×#17986074C211yesmaximal, characteristic, complemented
7C2×#17986072C211yesmaximal, characteristic, complemented
8C2×#17986071C211yesmaximal, characteristic, complemented
9C2×#17986069C211yesmaximal, characteristic, complemented
10C2×C8×C22⋊D71C211yesmaximal, characteristic, complemented
11C2×(C22⋊D71)⋊C8C211yesmaximal, characteristic, complemented
12C2×C4⋊C8×D71C211yesmaximal, characteristic, complemented
13C2×#17985964C211yesmaximal, characteristic, complemented
14C2×#17985964C211yesmaximal, characteristic, complemented
15C2×#17985951C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×#11765865C2211yescharacteristic
19C2×#14556136—28no—
20C2×#14556136C2218yescomplemented
21C2×#14556134—28no—
22C2×#14556134C2218yescomplemented
23C22×#11765849C2211yescharacteristic
24C22×#11765848C2211yescharacteristic
25C22×#11765848C2211yescharacteristic
26C22×#11765848C2211yescharacteristic
27C22×#11765848C2211yescharacteristic
28C23×C71⋊C8C2211yescharacteristic
29C22×C8×D71C2211yescharacteristic
30C22×C8×D71C2211yescharacteristic
31C22×C8×D71C2211yescharacteristic
32C22×C8×D71C2211yescharacteristic
33#17986546C418yes—
34#17986546C2218yes—
35C2×#14556127C411yescharacteristic
36C2×#14556124C411yescharacteristic
37C2×#14556114C411yescharacteristic
38C2×#14556114C411yescharacteristic
39C2×#14556103C411yescharacteristic
40C2×#14556101C411yescharacteristic
41C2×#14556101C411yescharacteristic
42C2×#14556099C411yescharacteristic
43C2×C4×D284C2211yescharacteristic
44C2×C4×C22⋊D71C2211yescharacteristic
45C2×C4×C22⋊D71C2211yescharacteristic
46C2×C42×D71C2211yescharacteristic
47#17986075C2218yescomplemented
48#17986074C2218yescomplemented
49#17986072C2218yescomplemented
50#17986071C2218yescomplemented
51#17986069C2218yescomplemented
52C8×C22⋊D71C2218yescomplemented
53(C22⋊D71)⋊C8C2218yescomplemented
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×Dic71⋊C8C2211yescharacteristic
56C2×Dic71⋊C8C2211yescharacteristic
57C4⋊C8×D71C2218yescomplemented
58#17985964C2218yescomplemented
59#17985964C2218yescomplemented
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×(C2×D71)⋊C8C2211yescharacteristic
63C2×(C2×D71)⋊C8C2211yescharacteristic
64C2×(C2×D71)⋊C8C2211yescharacteristic
65C2×(C2×D71)⋊C8C2211yescharacteristic
66#17985951C2218yescomplemented
67C2×#14556039C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C2×C8×Dic71C2211yescharacteristic
70C22×M16×C71C2211yescharacteristic
71C23×C8×C71C2211yescharacteristic
72C2×C4×D4×C71C2211yescharacteristic
73#435×C71C2218yescomplemented
74C2×C4⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic
76C2×C22⋊C8×C71C2211yescharacteristic
77C2×#97×C71C2211yescharacteristic
78C2×#11765865—24no—
79C2×#11765865—24no—
80C2×#11765865—24no—
81C2×#11765865—24no—
82C2×#11765865C2×C414yes—
83C2×#11765865C2×C414yes—
84C2×#11765865C2314yes—
85C2×#11765865C2314yes—
86C22×Dic142C2×C411yescharacteristic
87C22×Dic142C2×C411yescharacteristic
88C22×D284C2×C411yescharacteristic
89C22×D284C2×C411yescharacteristic
90C22×D284C2×C411yescharacteristic
91C22×C22⋊D71C2×C411yescharacteristic
92C22×C22⋊D71C2×C411yescharacteristic
93C22×C22⋊D71C2×C411yescharacteristic
94C22×C22⋊D71C2×C411yescharacteristic
95C22×C22⋊D71C2×C411yescharacteristic
96C22×C22⋊D71C2×C411yescharacteristic
97C22×C4×D71C2×C411yescharacteristic
98C22×C4×D71C2×C411yescharacteristic
99C22×C4×D71C2311yescharacteristic
100C22×C4×D71C2311yescharacteristic
101C22×C4×D71C2311yescharacteristic
102#14556136—232no—
103#14556134—232no—
104C2×#11765849—24no—
105C2×#11765849C2314yes—
106C2×#11765848—24no—
107C2×#11765848—24no—
108C2×#11765848—24no—
109C2×#11765848D418yescomplemented
110C2×#11765848C2314yes—
111C2×#11765848C2314yes—
112C2×#11765848C2314yes—
113C2×#11765848C2314yes—
114C22×C71⋊C8—24no—
115C22×C71⋊C8C2314yes—
116C22×C71⋊C8C2311yescharacteristic
117C22×C71⋊C8C2311yescharacteristic
118C22×C71⋊C8C2311yescharacteristic
119C22×C71⋊C8C2311yescharacteristic
120C2×C8×D71—24no—
121C2×C8×D71—24no—
122C2×C8×D71—24no—
123C2×C8×D71—24no—
124C2×C8×D71C2314yes—
125C2×C8×D71C2314yes—
126C2×C8×D71C2314yes—
127C2×C8×D71C2314yes—
128#14556127C2×C418yes—
129#14556124C2×C418yes—
130#14556114C2×C418yes—
131#14556114C2×C418yes—
132#14556103C2×C418yes—
133#14556101C2×C418yes—
134#14556101C2×C418yes—
135#14556099C2×C418yes—
136C4×D284C2×C414yes—
137C4×D284C2314yes—
138C4×C22⋊D71C2×C414yes—
139C4×C22⋊D71C2×C414yes—
140C4×C22⋊D71C2314yes—
141C4×C22⋊D71C2314yes—
142C2×C4⋊Dic71C2×C411yescharacteristic
143C2×Dic71⋊C4C2×C411yescharacteristic
144C2×Dic71⋊C4C2×C411yescharacteristic
145C2×C22⋊Dic71C2×C411yescharacteristic
146C2×C22⋊Dic71C2×C411yescharacteristic
147C2×(C2×D71)⋊C4C2×C411yescharacteristic
148C2×(C2×D71)⋊C4C2×C411yescharacteristic
149C2×(C2×D71)⋊C4C2×C411yescharacteristic
150C2×(C2×D71)⋊C4C2×C411yescharacteristic
151C2×C4×Dic71C2×C411yescharacteristic
152C2×C4×Dic71C2×C411yescharacteristic
153C2×C4×Dic71C2311yescharacteristic
154C42×D71C2×C414yes—
155C42×D71C2314yes—
156C4⋊(C71⋊C8)C2314yes—
157Dic71⋊C8C2314yes—
158Dic71⋊C8C2314yes—
159C22⋊(C71⋊C8)C2314yes—
160C22⋊(C71⋊C8)C2314yes—
161(C2×D71)⋊C8C2314yes—
162(C2×D71)⋊C8C2314yes—
163(C2×D71)⋊C8C2314yes—
164(C2×D71)⋊C8C2314yes—
165#14556039C2314yes—
166C8×Dic71C2314yes—
167C8×Dic71C2314yes—
168C22×D4×C71C2×C411yescharacteristic
169C23×C4×C71C2311yescharacteristic
170C23×C4×C71C2311yescharacteristic
171C2×M16×C71—24no—
172C2×M16×C71C2314yes—
173C22×C8×C71—24no—
174C22×C8×C71C2311yescharacteristic
175C22×C8×C71C2311yescharacteristic
176C22×C8×C71C2311yescharacteristic
177C22×C8×C71C2314yes—
178C22×C8×C71C2311yescharacteristic
179C4×D4×C71C2×C414yes—
180C4×D4×C71C2314yes—
181C2×C4⋊C4×C71C2×C411yescharacteristic
182C2×C22⋊C4×C71C2×C411yescharacteristic
183C2×C22⋊C4×C71C2×C411yescharacteristic
184C2×C42×C71C2311yescharacteristic
185C4⋊C8×C71C2314yes—
186C22⋊C8×C71C2314yes—
187C22⋊C8×C71C2314yes—
188#97×C71C2314yes—
189C23×D71C22×C411yescharacteristic
190C23×D71C22×C411yescharacteristic
191C23×D71C22×C411yescharacteristic
192#11765865—216no—
193#11765865—216no—
194#11765865—28no—
195#11765865—28no—
196#11765865—28no—
197#11765865—28no—
198C2×Dic142—24no—
199C2×Dic142—24no—
200C2×Dic142C22×C414yes—
201C2×Dic142C22×C414yes—
202C2×D284—24no—
203C2×D284—24no—
204C2×D284—42no—
205C2×D284C22×C414yes—
206C2×D284C22×C414yes—
207C2×D284C22×C414yes—
208C2×C22⋊D71—24no—
209C2×C22⋊D71—24no—
210C2×C22⋊D71—24no—
211C2×C22⋊D71—24no—
212C2×C22⋊D71—24no—
213C2×C22⋊D71—24no—
214C2×C22⋊D71C22×C414yes—
215C2×C22⋊D71C22×C414yes—
216C2×C22⋊D71C22×C414yes—
217C2×C22⋊D71C22×C414yes—
218C2×C22⋊D71C22×C414yes—
219C2×C22⋊D71C22×C414yes—
220C22×Dic71C22×C411yescharacteristic
221C22×Dic71C22×C411yescharacteristic
222C22×Dic71C22×C411yescharacteristic
223C22×Dic71C22×C411yescharacteristic
224C22×Dic71C22×C411yescharacteristic
225C2×C4×D71—22no—
226C2×C4×D71—22no—
227C2×C4×D71—22no—
228C2×C4×D71—22no—
229C2×C4×D71—24no—
230C2×C4×D71—42no—
231C2×C4×D71C22×C414yes—
232C2×C4×D71C22×C412yes—
233C2×C4×D71C22×C412yes—
234C2×C4×D71C22×C414yes—
235C2×C4×D71C22×C412yes—
236C2×C4×D71C2×D414yes—
237C2×C4×D71#4114yes—
238C2×C4×D71C2412yes—
239C2×C4×D71C2412yes—
240C2×C4×D71C2412yes—
241#11765849—28no—
242#11765848—28no—
243#11765848—28no—
244#11765848—28no—
245#11765848C2×D4116yescomplemented
246C2×C71⋊C8—22no—
247C2×C71⋊C8—22no—
248C2×C71⋊C8—22no—
249C2×C71⋊C8—28no—
250C2×C71⋊C8C2×D414yes—
251C2×C71⋊C8C2412yes—
252C2×C71⋊C8C2412yes—
253C2×C71⋊C8C2412yes—
254C2×C71⋊C8C2412yes—
255C8×D71—28no—
256C8×D71—28no—
257C8×D71—28no—
258C8×D71—28no—
259C4⋊Dic71C22×C414yes—
260Dic71⋊C4C22×C414yes—
261Dic71⋊C4C22×C414yes—
262C22⋊Dic71C22×C414yes—
263C22⋊Dic71C22×C414yes—
264(C2×D71)⋊C4C22×C414yes—
265(C2×D71)⋊C4C22×C414yes—
266(C2×D71)⋊C4C22×C414yes—
267(C2×D71)⋊C4C22×C414yes—
268C4×Dic71C22×C412yes—
269C4×Dic71C22×C414yes—
270C4×Dic71C22×C414yes—
271C4×Dic71C2412yes—
272C24×C71C22×C411yescharacteristic
273C24×C71C22×C411yescharacteristic
274C2×D4×C71—42no—
275C2×D4×C71C22×C414yes—
276C22×C4×C71—22no—
277C22×C4×C71—22no—
278C22×C4×C71—22no—
279C22×C4×C71—22no—
280C22×C4×C71C22×C411yescharacteristic
281C22×C4×C71C22×C411yescharacteristic
282C22×C4×C71C22×C411yescharacteristic
283C22×C4×C71C22×C411yescharacteristic
284C22×C4×C71C22×C412yes—
285C22×C4×C71C22×C412yes—
286C22×C4×C71C2412yes—
287C22×C4×C71C2412yes—
288C22×C4×C71C2411yescharacteristic
289M16×C71—28no—
290C2×C8×C71—22no—
291C2×C8×C71—22no—
292C2×C8×C71—22no—
293C2×C8×C71—28no—
294C2×C8×C71C2×D414yes—
295C2×C8×C71C2412yes—
296C2×C8×C71C2412yes—
297C2×C8×C71C2412yes—
298C2×C8×C71C2412yes—
299C4⋊C4×C71C22×C414yes—
300C22⋊C4×C71C22×C414yes—
301C22⋊C4×C71C22×C414yes—
302C42×C71C22×C412yes—
303C42×C71C2412yes—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71—22no—
307C23×C71—22no—
308C23×C71—22no—
309C23×C71—22no—
310C23×C71C23×C412yes—
311C23×C71C23×C412yes—
312C23×C71C23×C411yescharacteristic
313C22×D71—22no—
314C22×D71—22no—
315C22×D71—22no—
316C22×D71—22no—
317C22×D71—22no—
318C22×D71—22no—
319C22×D71—22no—
320C22×D71—22no—
321C22×D71C4×D414yes—
322C22×D71C23×C412yes—
323C22×D71C23×C412yes—
324C22×D71C23×C412yes—
325D4×C71—44no—
326C2×C4×C71—22no—
327C2×C4×C71—22no—
328C2×C4×C71—22no—
329C2×C4×C71—22no—
330C2×C4×C71—24no—
331C2×C4×C71—24no—
332C2×C4×C71—22no—
333C2×C4×C71—22no—
334C2×C4×C71—22no—
335C2×C4×C71—22no—
336C2×C4×C71C23×C412yes—
337C2×C4×C71C23×C412yes—
338C2×C4×C71C23×C412yes—
339C2×C4×C71C23×C412yes—
340C2×C4×C71C23×C411yescharacteristic
341C2×C4×C71C22×D412yes—
342C2×C4×C71C2×#4112yes—
343C2×C4×C71C2511yescharacteristic
344C22⋊D71—28no—
345C22⋊D71—28no—
346C22⋊D71—28no—
347C22⋊D71—28no—
348C22⋊D71—28no—
349C22⋊D71—28no—
350C2×Dic71—22no—
351C2×Dic71—22no—
352C2×Dic71—22no—
353C2×Dic71C4×D414yes—
354C2×Dic71#13114yescomplemented
355C2×Dic71C23×C412yes—
356C2×Dic71C23×C412yes—
357C2×Dic71C23×C412yes—
358C2×Dic71C23×C412yes—
359C2×Dic71C23×C412yes—
360D284—28no—
361D284—28no—
362D284—44no—
363C4×D71—24no—
364C4×D71—24no—
365C4×D71—22no—
366C4×D71—22no—
367C4×D71—22no—
368C4×D71—22no—
369C4×D71—28no—
370C4×D71—44no—
371C4×D71C4×D418yes—
372C4×D71C22×D414yes—
373C4×D71C2×#4114yes—
374Dic142—28no—
375Dic142—28no—
376C8×C71—22no—
377C8×C71—22no—
378C8×C71—22no—
379C8×C71C22×D414yes—
380C71⋊C8—22no—
381C71⋊C8—22no—
382C71⋊C8—22no—
383C71⋊C8C22×D414yes—
384C22×C71—22no—
385C22×C71—22no—
386C22×C71—22no—
387C22×C71—22no—
388C22×C71—22no—
389C22×C71—22no—
390C22×C71—44no—
391C22×C71—44no—
392C22×C71C2×C4×D412yes—
393C22×C71C2×#13112yes—
394C22×C71#56812yes—
395C22×C71C24×C411yescharacteristic
396C2×D71—28no—
397C2×D71—22no—
398C2×D71—22no—
399C2×D71—22no—
400C2×D71—22no—
401C2×D71—22no—
402C2×D71—22no—
403C2×D71—22no—
404C2×D71—22no—
405C2×D71—44no—
406C2×D71—44no—
407C2×D71C2×C4×D414yes—
408C4×C71—22no—
409C4×C71—22no—
410C4×C71—22no—
411C4×C71—22no—
412C4×C71C2×C4×D412yes—
413C4×C71C23×D411yescharacteristic
414C4×C71C22×#4111yescharacteristic
415Dic71—22no—
416Dic71—22no—
417Dic71—22no—
418Dic71C2×C4×D414yes—
419Dic71C2×#13114yescomplemented
420C2×#2935—711nomaximal, Sylow
421C2×C71—42no—
422C2×C71—42no—
423C2×C71#293514yescomplemented
424C2×C71C22×C4×D411yescharacteristic
425C2×C71C22×#13111yescharacteristic
426C2×C71C2×#56811yescharacteristic
427D71—24no—
428D71—42no—
429D71—42no—
430C22×#131—711no—
431C22×#131—711no—
432C2×#532—711no—
433#2935—7116no—
434C2×#436—711no—
435C2×#436—711no—
436C2×#435—711no—
437C2×#435—711no—
438C2×#435—711no—
439C2×#435D7111yescharacteristic, complemented
440C2×C8×D4—711no—
441C2×C8×D4—711no—
442C22×C4⋊C8—711no—
443C2×#408—711no—
444C2×#408—711no—
445C2×C4×M16—711no—
446C71C2×#293511yescharacteristic, complemented, Sylow
447C22×#41—711no—
448C22×#41—711no—
449C2×#131—718no—
450C2×#131—718no—
451C2×#131—1428no—
452C2×#131—1428no—
453C22×M16—711no—
454C22×M16—711no—
455C22×M16—711no—
456C22×M16—711no—
457C22×M16—711no—
458C22×M16C2×D7111yescharacteristic
459C23×C8—711no—
460C23×C8—711no—
461C23×C8—711no—
462C23×C8—711no—
463C23×C8—711no—
464C23×C8C2×D7111yescharacteristic
465#532—718no—
466#532—718no—
467C2×C4⋊Q8—711no—
468C2×#127—711no—
469C2×#124—711no—
470C2×#124—711no—
471C2×#121—711no—
472C2×#121—711no—
473C2×#121—711no—
474C2×#121—711no—
475C2×C4×D4—711no—
476C2×C4×D4—711no—
477C2×C4×D4—711no—
478C2×C4×D4C2×D7111yescharacteristic
479C22×C42—711no—
480#436—718no—
481#436—718no—
482#435—718no—
483#435—718no—
484#435—718no—
485#435C2×D7118yescomplemented
486C8×D4—718no—
487C8×D4—718no—
488C2×C4⋊C8—711no—
489C2×C4⋊C8—711no—
490C2×C4⋊C8—711no—
491C2×C4⋊C8—718no—
492C2×C4⋊C8C2×D7111yescharacteristic
493#408—718no—
494#408—718no—
495C2×C22⋊C8—711no—
496C2×C22⋊C8—711no—
497C2×C22⋊C8—711no—
498C2×C22⋊C8—711no—
499C2×C22⋊C8—711no—
500C2×C22⋊C8—711no—
501C2×C22⋊C8C2×D7111yescharacteristic
502C2×C22⋊C8C2×D7111yescharacteristic
503C4×M16—718no—
504C2×#97—711no—
505C2×#97C2×D7111yescharacteristic
506C2×C4×C8—711no—
507C2×C4×C8—711no—
508C2×#41—714no—
509C2×#41—714no—
510C2×#41—714no—
511C2×#41—714no—
512C2×#41—1424no—
513C2×#41—1424no—
514C2×#41—1424no—
515C2×#41—1424no—
516C22×Q8—711no—
517C22×Q8—711no—
518C22×D4—711no—
519C22×D4—711no—
520C22×D4—711no—
521C22×D4—711no—
522C22×D4—711no—
523C22×D4—711no—
524C22×D4—711no—
525C22×D4—711no—
526C22×D4—711no—
527C22×D4C4×D7111yescharacteristic
528C23×C4—711no—
529C23×C4—711no—
530C23×C4—711no—
531C23×C4—711no—
532C23×C4—711no—
533C23×C4C22×D7111yescharacteristic
534C23×C4C22×D7111yescharacteristic
535#131—14232no—
536#131—14232no—
537C2×M16—24no—
538C2×M16—714no—
539C2×M16—718no—
540C2×M16—714no—
541C2×M16—714no—
542C2×M16—714no—
543C2×M16—714no—
544C2×M16—1424no—
545C2×M16—1424no—
546C2×M16—1424no—
547C2×M16—1424no—
548C2×M16C22×D7114yes—
549C22×C8—24no—
550C22×C8—711no—
551C22×C8—714no—
552C22×C8—711no—
553C22×C8—711no—
554C22×C8—711no—
555C22×C8—714no—
556C22×C8—714no—
557C22×C8—714no—
558C22×C8—714no—
559C22×C8—1424no—
560C22×C8—1424no—
561C22×C8—1424no—
562C22×C8—1424no—
563C22×C8—1424no—
564C22×C8C22×D7114yes—
565C22×C8C22×D7111yescharacteristic
566C22×C8C22×D7111yescharacteristic
567C22×C8C22×D7111yescharacteristic
568C22×C8C22×D7111yescharacteristic
569C4⋊Q8—718no—
570#127—718no—
571#124—718no—
572#124—718no—
573#121—718no—
574#121—718no—
575#121—718no—
576#121—718no—
577C4×D4—714no—
578C4×D4—714no—
579C4×D4—714no—
580C4×D4—714no—
581C4×D4—714no—
582C4×D4—714no—
583C4×D4C4×D7114yes—
584C4×D4C22×D7114yes—
585C2×C4⋊C4—711no—
586C2×C4⋊C4—711no—
587C2×C4⋊C4—711no—
588C2×C4⋊C4C4×D7111yescharacteristic
589C2×C22⋊C4—711no—
590C2×C22⋊C4—711no—
591C2×C22⋊C4—711no—
592C2×C22⋊C4—711no—
593C2×C22⋊C4—711no—
594C2×C22⋊C4—711no—
595C2×C22⋊C4C4×D7111yescharacteristic
596C2×C22⋊C4C4×D7111yescharacteristic
597C2×C42—711no—
598C2×C42—711no—
599C2×C42—711no—
600C2×C42—714no—
601C2×C42—714no—
602C2×C42C22×D7111yescharacteristic
603C4⋊C8—714no—
604C4⋊C8—714no—
605C4⋊C8—714no—
606C4⋊C8C22×D7114yes—
607C22⋊C8—714no—
608C22⋊C8—714no—
609C22⋊C8—714no—
610C22⋊C8—714no—
611C22⋊C8—714no—
612C22⋊C8—714no—
613C22⋊C8C22×D7114yes—
614C22⋊C8C22×D7114yes—
615#97—714no—
616#97C22×D7114yes—
617C4×C8—714no—
618C4×C8—714no—
619C24—711no—
620C24—711no—
621C24—711no—
622C24C2×C4×D7111yescharacteristic
623C24C2×C4×D7111yescharacteristic
624#41—1428no—
625#41—1428no—
626#41—1428no—
627#41—1428no—
628#41—14216no—
629#41—14216no—
630C2×Q8—714no—
631C2×Q8—714no—
632C2×Q8—1424no—
633C2×Q8—1424no—
634C2×D4—42no—
635C2×D4—2842no—
636C2×D4—714no—
637C2×D4—714no—
638C2×D4—714no—
639C2×D4—714no—
640C2×D4—714no—
641C2×D4—714no—
642C2×D4—714no—
643C2×D4—714no—
644C2×D4—714no—
645C2×D4—1424no—
646C2×D4—1424no—
647C2×D4—1424no—
648C2×D4—1424no—
649C2×D4—1424no—
650C2×D4—1424no—
651C2×D4—1424no—
652C2×D4—1424no—
653C2×D4C2×C4×D7114yes—
654C22×C4—22no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—2842no—
659C22×C4—714no—
660C22×C4—711no—
661C22×C4—711no—
662C22×C4—712no—
663C22×C4—714no—
664C22×C4—714no—
665C22×C4—712no—
666C22×C4—711no—
667C22×C4—711no—
668C22×C4—711no—
669C22×C4—714no—
670C22×C4—712no—
671C22×C4—712no—
672C22×C4—712no—
673C22×C4—712no—
674C22×C4—1424no—
675C22×C4—1422no—
676C22×C4—1422no—
677C22×C4—1422no—
678C22×C4—1422no—
679C22×C4C2×C4×D7111yescharacteristic
680C22×C4C2×C4×D7111yescharacteristic
681C22×C4C2×C4×D7111yescharacteristic
682C22×C4C2×C4×D7111yescharacteristic
683C22×C4C2×C4×D7112yes—
684C22×C4C2×C4×D7112yes—
685C22×C4C23×D7112yes—
686C22×C4C23×D7112yes—
687C22×C4C23×D7111yescharacteristic
688M16—28no—
689M16—7116no—
690M16—1428no—
691M16—1428no—
692M16—1428no—
693M16—1428no—
694C2×C8—22no—
695C2×C8—22no—
696C2×C8—22no—
697C2×C8—28no—
698C2×C8—714no—
699C2×C8—712no—
700C2×C8—712no—
701C2×C8—712no—
702C2×C8—712no—
703C2×C8—1428no—
704C2×C8—1428no—
705C2×C8—1428no—
706C2×C8—1428no—
707C2×C8—1422no—
708C2×C8—1422no—
709C2×C8—1422no—
710C2×C8—1428no—
711C2×C8D4×D7114yes—
712C2×C8C23×D7112yes—
713C2×C8C23×D7112yes—
714C2×C8C23×D7112yes—
715C2×C8C23×D7112yes—
716C4⋊C4—714no—
717C4⋊C4—714no—
718C4⋊C4—714no—
719C4⋊C4C2×C4×D7114yes—
720C22⋊C4—714no—
721C22⋊C4—714no—
722C22⋊C4—714no—
723C22⋊C4—714no—
724C22⋊C4—714no—
725C22⋊C4—714no—
726C22⋊C4C2×C4×D7114yes—
727C22⋊C4C2×C4×D7114yes—
728C42—712no—
729C42—714no—
730C42—714no—
731C42—712no—
732C42C2×C4×D7112yes—
733C42C23×D7112yes—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—712no—
741C23—714no—
742C23—712no—
743C23—712no—
744C23—1422no—
745C23—1422no—
746C23—1422no—
747C23—1422no—
748C23—1422no—
749C23—1422no—
750C23—1422no—
751C23—1422no—
752C23C22×C4×D7112yes—
753C23C22×C4×D7112yes—
754C23C22×C4×D7111yescharacteristic
755Q8—1428no—
756Q8—1428no—
757D4—44no—
758D4—2844no—
759D4—1428no—
760D4—1428no—
761D4—1428no—
762D4—1428no—
763D4—1428no—
764D4—1428no—
765D4—1428no—
766D4—1428no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—24no—
776C2×C4—24no—
777C2×C4—2844no—
778C2×C4—712no—
779C2×C4—712no—
780C2×C4—714no—
781C2×C4—714no—
782C2×C4—714no—
783C2×C4—714no—
784C2×C4—718no—
785C2×C4—712no—
786C2×C4—712no—
787C2×C4—712no—
788C2×C4—1428no—
789C2×C4—1422no—
790C2×C4—1422no—
791C2×C4—1422no—
792C2×C4—1422no—
793C2×C4—1422no—
794C2×C4—1422no—
795C2×C4—1422no—
796C2×C4—1424no—
797C2×C4—1424no—
798C2×C4C22×C4×D7112yes—
799C2×C4C22×C4×D7112yes—
800C2×C4C22×C4×D7112yes—
801C2×C4C22×C4×D7112yes—
802C2×C4C22×C4×D7111yescharacteristic
803C2×C4C2×D4×D7112yes—
804C2×C4#41×D7112yes—
805C2×C4C24×D7111yescharacteristic
806C8—22no—
807C8—22no—
808C8—22no—
809C8—714no—
810C8—1422no—
811C8—1422no—
812C8—1422no—
813C8C2×D4×D7114yes—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—44no—
821C22—44no—
822C22—2844no—
823C22—2844no—
824C22—714no—
825C22—1422no—
826C22—1422no—
827C22—1422no—
828C22—1422no—
829C22—1422no—
830C22—1422no—
831C22—1422no—
832C22—1422no—
833C22—1428no—
834C22C4×D4×D7112yes—
835C22#131×D7112yes—
836C22#1798676512yes—
837C22C23×C4×D7111yescharacteristic
838C4—22no—
839C4—22no—
840C4—22no—
841C4—22no—
842C4—714no—
843C4—714no—
844C4—1422no—
845C4—1422no—
846C4—1422no—
847C4C4×D4×D7112yes—
848C4C22×D4×D7111yescharacteristic
849C4C2×#41×D7111yescharacteristic
850C2—42no—
851C2—42no—
852C2—2842no—
853C2—2842no—
854C2—1424no—
855C2#2259708114yesdirect product factor
856C2C2×C4×D4×D7111yescharacteristic
857C2C2×#131×D7111yescharacteristic
858C2C2×#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×#2935
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#14556136C2semidirect
2. C22×#14556134C2semidirect
4. #22597081C2direct (N × H)
5. C2×#17986075C2semidirect
6. C2×#17986074C2semidirect
7. C2×#17986072C2semidirect
8. C2×#17986071C2semidirect
9. C2×#17986069C2semidirect
10. C2×C8×C22⋊D71C2semidirect
11. C2×(C22⋊D71)⋊C8C2semidirect
12. C2×C4⋊C8×D71C2semidirect
13. C2×#17985964C2semidirect
14. C2×#17985964C2semidirect
15. C2×#17985951C2semidirect
16. C2×#435×C71C2semidirect
20. C2×#14556136C22semidirect
22. C2×#14556134C22semidirect
47. #17986075C22semidirect
48. #17986074C22semidirect
49. #17986072C22semidirect
50. #17986071C22semidirect
51. #17986069C22semidirect
52. C8×C22⋊D71C22semidirect
53. (C22⋊D71)⋊C8C22semidirect
57. C4⋊C8×D71C22semidirect
58. #17985964C22semidirect
59. #17985964C22semidirect
66. #17985951C22semidirect
73. #435×C71C22semidirect
109. C2×#11765848D4semidirect
245. #11765848C2×D4semidirect
354. C2×Dic71#131semidirect
419. Dic71C2×#131semidirect
423. C2×C71#2935semidirect
439. C2×#435D71semidirect
446. C71C2×#2935semidirect
485. #435C2×D71semidirect
855. C2#22597081direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561362
C22×#145561342
C2×#179865462
#225970812
C2×#179860752
C2×#179860742
C2×#179860722
C2×#179860712
C2×#179860692
C2×C8×C22⋊D712
C2×(C22⋊D71)⋊C82
C2×C4⋊C8×D712
C2×#179859642
C2×#179859512
C2×#435×C712
C2×#293571