Finite Group Databasebeta

← C2×#22602811 #32905081

Subgroups — C2×#22602811 #32905081

Order 18176.

7182 conjugacy classes of subgroups.

The subgroup lattice has 884 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602811C2132yesmaximal, direct product factor
2C2×#17986745C214yesmaximal, complemented
3C2×#17986734C211yesmaximal, characteristic, complemented
4C2×#17986734C212yesmaximal, complemented
5C2×#17986727C211yesmaximal, characteristic, complemented
6C2×#17986709C212yesmaximal, complemented
7C2×#17986671C211yesmaximal, characteristic, complemented
8C2×Q8×D284C211yesmaximal, characteristic, complemented
9C2×#17986659C212yesmaximal, complemented
10C2×#17986651C212yesmaximal, complemented
11C2×#17986623C212yesmaximal, complemented
12C2×#17986620C212yesmaximal, complemented
13C2×#17986604C212yesmaximal, complemented
14C2×#17986597C214yesmaximal, complemented
15C2×#17986574C212yesmaximal, complemented
16C2×#17986549C211yesmaximal, characteristic, complemented
17C2×#17986533C211yesmaximal, characteristic, complemented
18C2×#533×C71C211yesmaximal, characteristic, complemented
19C22×#11765866C2212yes—
20C22×#11765865C2212yes—
21C22×Q8×D71C2212yes—
22#17986745C22164yescomplemented
23#17986734C22116yescomplemented
24#17986734C22132yescomplemented
25#17986727C22116yescomplemented
26#17986709C22132yescomplemented
27#17986671C22116yescomplemented
28Q8×D284C22116yescomplemented
29#17986659C22132yescomplemented
30#17986651C22132yescomplemented
31#17986623C22132yescomplemented
32#17986620C22132yescomplemented
33#17986604C22132yescomplemented
34#17986597C22164yescomplemented
35#17986574C22132yescomplemented
36#17986549C22116yescomplemented
37C2×#14556128C2212yes—
38C2×#14556128C2211yescharacteristic
39C2×#14556126C2212yes—
40C2×#14556125C2211yescharacteristic
41C2×#14556125C2212yes—
42#17986533C22116yescomplemented
43C2×#14556123C2214yes—
44C2×#14556122C2212yes—
45C2×#14556120C2211yescharacteristic
46C2×#14556120C2212yes—
47C2×#14556118C2214yes—
48C2×#14556117C2212yes—
49C2×#14556117C2214yes—
50C2×#14556116C2211yescharacteristic
51C2×#14556116C2212yes—
52C2×#14556116C2212yes—
53C2×#14556114C2214yes—
54C2×#14556113C2214yes—
55C2×#14556113C2214yes—
56C2×#14556113C2214yes—
57C2×#14556113C2214yes—
58C2×#14556113C2214yes—
59C2×#14556111C2212yes—
60C2×#14556110C2214yes—
61C2×#14556108C2212yes—
62C2×#14556108C2214yes—
63C2×#14556107C2211yescharacteristic
64C2×#14556106C2214yes—
65C2×#14556106C2214yes—
66C2×#14556106C2214yes—
67C2×#14556104C2214yes—
68C2×#14556103C2212yes—
69C2×#14556103C2214yes—
70C2×#14556102C2211yescharacteristic
71C2×#14556102C2212yes—
72C2×#14556102C2212yes—
73C2×#14556101C2214yes—
74C2×#14556101C2214yes—
75C2×C4×Dic142C2211yescharacteristic
76C2×C4×Dic142C2212yes—
77C2×#14556093C2212yes—
78C2×C4×D284C2211yescharacteristic
79C2×C4×D284C2212yes—
80C2×C4×D284C2212yes—
81C2×C4×D284C2212yes—
82C2×C4×D284C2212yes—
83C2×C4×D284C2212yes—
84C2×#14556090C2212yes—
85C2×#14556090C2214yes—
86C2×C4×C22⋊D71C2212yes—
87C2×#14556085C2212yes—
88C2×C4⋊C4×D71C2214yes—
89#533×C71C22116yescomplemented
90C2×C4⋊Q8×C71C2211yescharacteristic
91C2×C4⋊Q8×C71C2211yescharacteristic
92C2×#125×C71C2212yes—
93C2×C22⋊Q8×C71C2211yescharacteristic
94C2×C22⋊Q8×C71C2211yescharacteristic
95C2×C22⋊Q8×C71C2212yes—
96C2×C4×Q8×C71C2211yescharacteristic
97C2×C4×Q8×C71C2211yescharacteristic
98C2×C4×Q8×C71C2212yes—
99C2×#117×C71C2212yes—
100C22×C42×C71C2211yescharacteristic
101C2×#11765866—48no—
102C2×#11765866C23116yes—
103C2×#11765865—48no—
104C2×#11765865C23116yes—
105C22×Dic142C2312yes—
106C22×Dic142C2311yescharacteristic
107C22×Dic142C2314yes—
108C2×Q8×D71—48no—
109C2×Q8×D71C23116yes—
110C22×D284C2312yes—
111C22×D284C2311yescharacteristic
112C22×D284C2312yes—
113C22×D284C2314yes—
114C22×D284C2314yes—
115C22×D284C2312yes—
116C22×C22⋊D71C2314yes—
117C22×C22⋊D71C2312yes—
118C22×C4×D71C2312yes—
119C22×C4×D71C2314yes—
120C22×C4×D71C2314yes—
121C22×C4×D71C2314yes—
122C22×C4×D71C2314yes—
123#14556128C23116yes—
124#14556128C2318yes—
125#14556126C23116yes—
126#14556125C23116yes—
127#14556125C2318yes—
128#14556123C23132yes—
129#14556122C23116yes—
130#14556120C23116yes—
131#14556120C2318yes—
132#14556118C23132yes—
133#14556117C23116yes—
134#14556117C23132yes—
135#14556116C23116yes—
136#14556116C23116yes—
137#14556116C2318yes—
138#14556114C23132yes—
139#14556113C23132yes—
140#14556113C23132yes—
141#14556113C23132yes—
142#14556113C23132yes—
143#14556113C23132yes—
144#14556111C23116yes—
145#14556110C23132yes—
146#14556108C23132yes—
147#14556108C23116yes—
148#14556107C2318yes—
149#14556106C23132yes—
150#14556106C23132yes—
151#14556106C23132yes—
152#14556104C23132yes—
153#14556103C23132yes—
154#14556103C23116yes—
155#14556102C2318yes—
156#14556102C23116yes—
157#14556102C23116yes—
158#14556101C23132yes—
159#14556101C23132yes—
160C4×Dic142C23116yes—
161C4×Dic142C2318yes—
162#14556093C23116yes—
163C4×D284C23116yes—
164C4×D284C23116yes—
165C4×D284C23116yes—
166C4×D284C23116yes—
167C4×D284C2318yes—
168C4×D284C23116yes—
169#14556090C23132yes—
170#14556090C23116yes—
171C4×C22⋊D71C23116yes—
172#14556085C23116yes—
173C2×C4⋊Dic71C2314yes—
174C2×C4⋊Dic71C2311yescharacteristic
175C2×C4⋊Dic71C2311yescharacteristic
176C2×C4⋊Dic71C2312yes—
177C2×C4⋊Dic71C2312yes—
178C2×Dic71⋊C4C2312yes—
179C2×Dic71⋊C4C2314yes—
180C2×Dic71⋊C4C2312yes—
181C2×Dic71⋊C4C2312yes—
182C2×Dic71⋊C4C2314yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2312yes—
185C4⋊C4×D71C23132yes—
186C2×C22⋊Dic71C2312yes—
187C2×(C2×D71)⋊C4C2312yes—
188C2×(C2×D71)⋊C4C2312yes—
189C2×(C2×D71)⋊C4C2312yes—
190C2×(C2×D71)⋊C4C2314yes—
191C2×(C2×D71)⋊C4C2314yes—
192C2×(C2×D71)⋊C4C2314yes—
193C2×(C2×D71)⋊C4C2314yes—
194C2×(C2×D71)⋊C4C2314yes—
195C2×(C2×D71)⋊C4C2314yes—
196C2×(C2×D71)⋊C4C2314yes—
197C2×(C2×D71)⋊C4C2312yes—
198C2×C4×Dic71C2312yes—
199C2×C4×Dic71C2314yes—
200C22×Q8×C71C2311yescharacteristic
201C22×Q8×C71C2311yescharacteristic
202C22×Q8×C71C2312yes—
203C23×C4×C71C2311yescharacteristic
204C23×C4×C71C2311yescharacteristic
205C23×C4×C71C2311yescharacteristic
206C4⋊Q8×C71C2318yes—
207C4⋊Q8×C71C2318yes—
208#125×C71C23116yes—
209C22⋊Q8×C71C2318yes—
210C22⋊Q8×C71C2318yes—
211C22⋊Q8×C71C23116yes—
212C4×Q8×C71C2318yes—
213C4×Q8×C71C2318yes—
214C4×Q8×C71C23116yes—
215#117×C71C23116yes—
216C2×C4⋊C4×C71C2312yes—
217C2×C4⋊C4×C71C2312yes—
218C2×C4⋊C4×C71C2312yes—
219C2×C4⋊C4×C71C2312yes—
220C2×C4⋊C4×C71C2312yes—
221C2×C4⋊C4×C71C2312yes—
222C2×C4⋊C4×C71C2311yescharacteristic
223C2×C4⋊C4×C71C2311yescharacteristic
224C2×C4⋊C4×C71C2312yes—
225C2×C22⋊C4×C71C2312yes—
226C2×C22⋊C4×C71C2312yes—
227C2×C42×C71C2311yescharacteristic
228C2×C42×C71C2311yescharacteristic
229C2×C42×C71C2311yescharacteristic
230C2×C42×C71C2311yescharacteristic
231C2×C42×C71C2318yes—
232C2×C42×C71C2312yes—
233C2×C42×C71C2312yes—
234C23×D71C2412yes—
235C23×D71C2414yes—
236#11765866—432no—
237#11765865—432no—
238C2×Dic142—28no—
239C2×Dic142—24no—
240C2×Dic142—48no—
241C2×Dic142C2418yes—
242C2×Dic142C2414yes—
243C2×Dic142C24116yes—
244Q8×D71—432no—
245C2×D284—28no—
246C2×D284—24no—
247C2×D284—28no—
248C2×D284—44no—
249C2×D284—48no—
250C2×D284—48no—
251C2×D284C2418yes—
252C2×D284C2414yes—
253C2×D284C2418yes—
254C2×D284C24116yes—
255C2×D284C24116yes—
256C2×D284C2418yes—
257C2×C22⋊D71—44no—
258C2×C22⋊D71—48no—
259C2×C22⋊D71C24116yes—
260C2×C22⋊D71C2418yes—
261C22×Dic71C2412yes—
262C22×Dic71C2414yes—
263C22×Dic71C2412yes—
264C22×Dic71C2412yes—
265C2×C4×D71—28no—
266C2×C4×D71—48no—
267C2×C4×D71—48no—
268C2×C4×D71—48no—
269C2×C4×D71—48no—
270C2×C4×D71C2418yes—
271C2×C4×D71C24116yes—
272C2×C4×D71C24116yes—
273C2×C4×D71C24116yes—
274C2×C4×D71C24116yes—
275C4⋊Dic71C24116yes—
276C4⋊Dic71C2414yes—
277C4⋊Dic71C2414yes—
278C4⋊Dic71C2418yes—
279C4⋊Dic71C2418yes—
280Dic71⋊C4C2418yes—
281Dic71⋊C4C24116yes—
282Dic71⋊C4C2418yes—
283Dic71⋊C4C2418yes—
284Dic71⋊C4C24116yes—
285Dic71⋊C4C24116yes—
286Dic71⋊C4C2418yes—
287C22⋊Dic71C2418yes—
288(C2×D71)⋊C4C2418yes—
289(C2×D71)⋊C4C2418yes—
290(C2×D71)⋊C4C2418yes—
291(C2×D71)⋊C4C24116yes—
292(C2×D71)⋊C4C24116yes—
293(C2×D71)⋊C4C24116yes—
294(C2×D71)⋊C4C24116yes—
295(C2×D71)⋊C4C24116yes—
296(C2×D71)⋊C4C24116yes—
297(C2×D71)⋊C4C24116yes—
298(C2×D71)⋊C4C2418yes—
299C4×Dic71C2418yes—
300C4×Dic71C24116yes—
301C24×C71C2411yescharacteristic
302C2×Q8×C71—24no—
303C2×Q8×C71—24no—
304C2×Q8×C71—44no—
305C2×Q8×C71C2414yes—
306C2×Q8×C71C2414yes—
307C2×Q8×C71C2418yes—
308C22×C4×C71—24no—
309C22×C4×C71—24no—
310C22×C4×C71—42no—
311C22×C4×C71C2411yescharacteristic
312C22×C4×C71C2412yes—
313C22×C4×C71C2412yes—
314C22×C4×C71C2412yes—
315C22×C4×C71C2411yescharacteristic
316C22×C4×C71C2412yes—
317C22×C4×C71C2414yes—
318C22×C4×C71C2411yescharacteristic
319C22×C4×C71C2411yescharacteristic
320C22×C4×C71C2414yes—
321C22×C4×C71C2414yes—
322C22×C4×C71C2411yescharacteristic
323C22×C4×C71C2411yescharacteristic
324C4⋊C4×C71C2418yes—
325C4⋊C4×C71C2418yes—
326C4⋊C4×C71C2418yes—
327C4⋊C4×C71C2418yes—
328C4⋊C4×C71C2418yes—
329C4⋊C4×C71C2418yes—
330C4⋊C4×C71C2414yes—
331C4⋊C4×C71C2414yes—
332C4⋊C4×C71C2418yes—
333C22⋊C4×C71C2418yes—
334C22⋊C4×C71C2418yes—
335C42×C71C2414yes—
336C42×C71C2414yes—
337C42×C71C2414yes—
338C42×C71C2414yes—
339C42×C71C2418yes—
340C42×C71C2418yes—
341C23×C71—22no—
342C23×C71—22no—
343C23×C71—22no—
344C23×C71C2512yes—
345C23×C71C2511yescharacteristic
346C22×D71—24no—
347C22×D71—28no—
348C22×D71—24no—
349C22×D71—28no—
350C22×D71—28no—
351C22×D71—24no—
352C22×D71C2514yes—
353C22×D71C2518yes—
354Q8×C71—28no—
355Q8×C71—28no—
356Q8×C71—48no—
357C2×C4×C71—22no—
358C2×C4×C71—24no—
359C2×C4×C71—24no—
360C2×C4×C71—22no—
361C2×C4×C71—22no—
362C2×C4×C71—22no—
363C2×C4×C71—24no—
364C2×C4×C71—24no—
365C2×C4×C71—28no—
366C2×C4×C71—28no—
367C2×C4×C71—44no—
368C2×C4×C71H(5,𝔽2)14yes—
369C2×C4×C712−1+414yes—
370C2×C4×C71C2512yes—
371C2×C4×C71C2512yes—
372C2×C4×C71C2512yes—
373C2×C4×C71C2512yes—
374C2×C4×C71C2514yes—
375C2×C4×C71C2514yes—
376C2×C4×C71C2514yes—
377C2×C4×C71C2514yes—
378C2×C4×C71C2512yes—
379C2×C4×C71C2512yes—
380C22⋊D71—48no—
381C22⋊D71—416no—
382C2×Dic71—24no—
383C2×Dic71—28no—
384C2×Dic71—24no—
385C2×Dic71—24no—
386C2×Dic71C2514yes—
387C2×Dic71C2514yes—
388C2×Dic71C2518yes—
389C2×Dic71C2514yes—
390D284—216no—
391D284—28no—
392D284—216no—
393D284—48no—
394D284—416no—
395D284—416no—
396C4×D71—216no—
397C4×D71—416no—
398C4×D71—416no—
399C4×D71—416no—
400C4×D71—416no—
401Dic142—216no—
402Dic142—28no—
403Dic142—416no—
404C22×C71—22no—
405C22×C71—22no—
406C22×C71—22no—
407C22×C71—44no—
408C22×C71C2×H(5,𝔽2)12yes—
409C22×C71C2×2−1+412yes—
410C22×C71#58512yes—
411C22×C71C2611yescharacteristic
412C2×D71—24no—
413C2×D71—28no—
414C2×D71—24no—
415C2×D71—28no—
416C2×D71—28no—
417C2×D71—24no—
418C2×D71—48no—
419C2×D71—416no—
420C4×C71—24no—
421C4×C71—22no—
422C4×C71—24no—
423C4×C71—22no—
424C4×C71—24no—
425C4×C71—22no—
426C4×C71—24no—
427C4×C71—22no—
428C4×C71C2×H(5,𝔽2)14yes—
429C4×C71C2×2−1+414yes—
430Dic71—28no—
431Dic71—24no—
432Dic71—24no—
433Dic71—24no—
434C2×#3554—711nomaximal, Sylow
435C2×C71—42no—
436C2×C71#355414yescomplemented
437C2×C71C22×H(5,𝔽2)11yescharacteristic
438C2×C71C22×2−1+411yescharacteristic
439C2×C71C2×#58511yescharacteristic
440D71—44no—
441D71—48no—
442#3554—7132no—
443C2×#562—714no—
444C2×#559—712no—
445C2×#559—711no—
446C2×#557—711no—
447C2×#554—712no—
448C2×#550—711no—
449C2×D4×Q8—711no—
450C2×#548—712no—
451C2×#547—712no—
452C2×#542—712no—
453C2×#542—712no—
454C2×#540—712no—
455C2×#539—714no—
456C2×#536—712no—
457C2×#533D7111yescharacteristic, complemented
458C2×#532—711no—
459C2×#529—711no—
460C71C2×#355411yescharacteristic, complemented, Sylow
461C22×#41—712no—
462C22×#41—712no—
463C23×Q8—712no—
464#562—7164no—
465#559—7132no—
466#559—7116no—
467#557—7116no—
468#554—7132no—
469#550—7116no—
470D4×Q8—7116no—
471#548—7132no—
472#547—7132no—
473#542—7132no—
474#542—7132no—
475#540—7132no—
476#539—7164no—
477#536—7132no—
478#533C2×D71116yescomplemented
479#532—7116no—
480C2×C4⋊Q8—712no—
481C2×C4⋊Q8—711no—
482C2×C4⋊Q8—712no—
483C2×C4⋊Q8C2×D7111yescharacteristic
484C2×C4⋊Q8C2×D7111yescharacteristic
485C2×#127—711no—
486C2×#127—712no—
487#529—7116no—
488C2×#126—714no—
489C2×#126—712no—
490C2×#125—714no—
491C2×#125—711no—
492C2×#125—712no—
493C2×#125C2×D7112yes—
494C2×#124—712no—
495C2×#124—714no—
496C2×#124—714no—
497C2×#124—711no—
498C2×#124—712no—
499C2×#124—712no—
500C2×#123—712no—
501C2×#123—714no—
502C2×#123—714no—
503C2×#123—714no—
504C2×#123—714no—
505C2×#123—714no—
506C2×#123—714no—
507C2×C22⋊Q8—714no—
508C2×C22⋊Q8—711no—
509C2×C22⋊Q8—714no—
510C2×C22⋊Q8—714no—
511C2×C22⋊Q8—714no—
512C2×C22⋊Q8—714no—
513C2×C22⋊Q8—712no—
514C2×C22⋊Q8C2×D7111yescharacteristic
515C2×C22⋊Q8C2×D7111yescharacteristic
516C2×C22⋊Q8C2×D7112yes—
517C2×#121—711no—
518C2×#121—712no—
519C2×#121—712no—
520C2×#121—714no—
521C2×#121—712no—
522C2×#121—714no—
523C2×#121—714no—
524C2×C4×Q8—712no—
525C2×C4×Q8—711no—
526C2×C4×Q8—712no—
527C2×C4×Q8C2×D7111yescharacteristic
528C2×C4×Q8C2×D7111yescharacteristic
529C2×C4×Q8C2×D7112yes—
530C2×C4×D4—712no—
531C2×C4×D4—714no—
532C2×C4×D4—712no—
533C2×C4×D4—711no—
534C2×C4×D4—712no—
535C2×C4×D4—712no—
536C2×C4×D4—712no—
537C2×C4×D4—712no—
538C2×C4×D4—712no—
539C2×#117—712no—
540C2×#117C2×D7112yes—
541C22×C4⋊C4—714no—
542C22×C42C2×D7111yescharacteristic
543C2×#41—2848no—
544C2×#41—2848no—
545C2×#41—7116no—
546C2×#41—7116no—
547C22×Q8—2848no—
548C22×Q8—7116no—
549C22×Q8—714no—
550C22×Q8—711no—
551C22×Q8—712no—
552C22×Q8C22×D7111yescharacteristic
553C22×Q8C22×D7111yescharacteristic
554C22×Q8C22×D7112yes—
555C22×D4—712no—
556C22×D4—714no—
557C22×D4—712no—
558C22×D4—714no—
559C22×D4—714no—
560C22×D4—711no—
561C22×D4—712no—
562C22×D4—712no—
563C23×C4—714no—
564C23×C4—714no—
565C23×C4—714no—
566C23×C4—714no—
567C23×C4—712no—
568C23×C4C22×D7111yescharacteristic
569C23×C4C22×D7111yescharacteristic
570C23×C4C22×D7111yescharacteristic
571C4⋊Q8—7116no—
572C4⋊Q8—718no—
573C4⋊Q8—7116no—
574C4⋊Q8C22×D7118yes—
575C4⋊Q8C22×D7118yes—
576#127—718no—
577#127—7116no—
578#126—7132no—
579#126—7116no—
580#125—7132no—
581#125—718no—
582#125—7116no—
583#125C22×D71116yes—
584#124—7116no—
585#124—7132no—
586#124—7132no—
587#124—718no—
588#124—7116no—
589#124—7116no—
590#123—7116no—
591#123—7132no—
592#123—7132no—
593#123—7132no—
594#123—7132no—
595#123—7132no—
596#123—7132no—
597C22⋊Q8—7132no—
598C22⋊Q8—718no—
599C22⋊Q8—7132no—
600C22⋊Q8—7132no—
601C22⋊Q8—7132no—
602C22⋊Q8—7132no—
603C22⋊Q8—7116no—
604C22⋊Q8C22×D7118yes—
605C22⋊Q8C22×D7118yes—
606C22⋊Q8C22×D71116yes—
607#121—718no—
608#121—7116no—
609#121—7116no—
610#121—7132no—
611#121—7116no—
612#121—7132no—
613#121—7132no—
614C4×Q8—7116no—
615C4×Q8—718no—
616C4×Q8—7116no—
617C4×Q8C22×D7118yes—
618C4×Q8C22×D7118yes—
619C4×Q8C22×D71116yes—
620C4×D4—7116no—
621C4×D4—7132no—
622C4×D4—7116no—
623C4×D4—718no—
624C4×D4—7116no—
625C4×D4—7116no—
626C4×D4—7116no—
627C4×D4—7116no—
628C4×D4—7116no—
629#117—7116no—
630#117C22×D71116yes—
631C2×C4⋊C4—712no—
632C2×C4⋊C4—714no—
633C2×C4⋊C4—714no—
634C2×C4⋊C4—712no—
635C2×C4⋊C4—712no—
636C2×C4⋊C4—711no—
637C2×C4⋊C4—711no—
638C2×C4⋊C4—712no—
639C2×C4⋊C4—712no—
640C2×C4⋊C4—714no—
641C2×C4⋊C4—714no—
642C2×C4⋊C4—712no—
643C2×C4⋊C4—7132no—
644C2×C4⋊C4C22×D7112yes—
645C2×C4⋊C4C22×D7112yes—
646C2×C4⋊C4C22×D7112yes—
647C2×C4⋊C4C22×D7112yes—
648C2×C4⋊C4C22×D7111yescharacteristic
649C2×C4⋊C4C22×D7111yescharacteristic
650C2×C4⋊C4C22×D7112yes—
651C2×C4⋊C4C22×D7112yes—
652C2×C4⋊C4C22×D7112yes—
653C2×C22⋊C4—712no—
654C2×C22⋊C4—712no—
655C2×C22⋊C4—712no—
656C2×C22⋊C4—712no—
657C2×C22⋊C4—712no—
658C2×C22⋊C4—714no—
659C2×C22⋊C4—714no—
660C2×C22⋊C4—714no—
661C2×C22⋊C4—714no—
662C2×C22⋊C4—714no—
663C2×C22⋊C4—714no—
664C2×C22⋊C4—714no—
665C2×C22⋊C4C22×D7112yes—
666C2×C22⋊C4C22×D7112yes—
667C2×C42—712no—
668C2×C42—714no—
669C2×C42C22×D7111yescharacteristic
670C2×C42C22×D7112yes—
671C2×C42C22×D7112yes—
672C2×C42C22×D7111yescharacteristic
673C2×C42C22×D7111yescharacteristic
674C2×C42C22×D7111yescharacteristic
675C2×C42C22×D7118yes—
676C24—712no—
677C24—714no—
678C24C23×D7111yescharacteristic
679#41—28432no—
680#41—28432no—
681C2×Q8—24no—
682C2×Q8—24no—
683C2×Q8—44no—
684C2×Q8—2848no—
685C2×Q8—28432no—
686C2×Q8—7116no—
687C2×Q8—714no—
688C2×Q8—718no—
689C2×Q8—1428no—
690C2×Q8—1424no—
691C2×Q8C23×D7114yes—
692C2×Q8C23×D7114yes—
693C2×Q8C23×D7118yes—
694C2×D4—2844no—
695C2×D4—2848no—
696C2×D4—2848no—
697C2×D4—2844no—
698C2×D4—2848no—
699C2×D4—718no—
700C2×D4—7116no—
701C2×D4—718no—
702C2×D4—7116no—
703C2×D4—7116no—
704C2×D4—714no—
705C2×D4—718no—
706C2×D4—718no—
707C2×D4—1428no—
708C2×D4—1424no—
709C2×D4—1428no—
710C22×C4—24no—
711C22×C4—24no—
712C22×C4—42no—
713C22×C4—2848no—
714C22×C4—2848no—
715C22×C4—2848no—
716C22×C4—2848no—
717C22×C4—7116no—
718C22×C4—7116no—
719C22×C4—7116no—
720C22×C4—7116no—
721C22×C4—712no—
722C22×C4—712no—
723C22×C4—714no—
724C22×C4—712no—
725C22×C4—718no—
726C22×C4—1428no—
727C22×C4C23×D7114yes—
728C22×C4C23×D7114yes—
729C22×C4C23×D7112yes—
730C22×C4C23×D7111yescharacteristic
731C22×C4C23×D7111yescharacteristic
732C22×C4C23×D7111yescharacteristic
733C22×C4C23×D7111yescharacteristic
734C22×C4C23×D7112yes—
735C22×C4C23×D7112yes—
736C22×C4C23×D7112yes—
737C22×C4C23×D7114yes—
738C22×C4C23×D7111yescharacteristic
739C22×C4C23×D7111yescharacteristic
740C4⋊C4—718no—
741C4⋊C4—7116no—
742C4⋊C4—718no—
743C4⋊C4—718no—
744C4⋊C4—7116no—
745C4⋊C4—7116no—
746C4⋊C4—718no—
747C4⋊C4—7116no—
748C4⋊C4—714no—
749C4⋊C4—714no—
750C4⋊C4—718no—
751C4⋊C4—718no—
752C4⋊C4C23×D7118yes—
753C4⋊C4C23×D7118yes—
754C4⋊C4C23×D7118yes—
755C4⋊C4C23×D7118yes—
756C4⋊C4C23×D7114yes—
757C4⋊C4C23×D7114yes—
758C4⋊C4C23×D7118yes—
759C4⋊C4C23×D7118yes—
760C4⋊C4C23×D7118yes—
761C22⋊C4—718no—
762C22⋊C4—718no—
763C22⋊C4—718no—
764C22⋊C4—718no—
765C22⋊C4—718no—
766C22⋊C4—7116no—
767C22⋊C4—7116no—
768C22⋊C4—7116no—
769C22⋊C4—7116no—
770C22⋊C4—7116no—
771C22⋊C4—7116no—
772C22⋊C4—7116no—
773C22⋊C4C23×D7118yes—
774C22⋊C4C23×D7118yes—
775C42—718no—
776C42—7116no—
777C42C23×D7114yes—
778C42C23×D7114yes—
779C42C23×D7114yes—
780C42C23×D7114yes—
781C42C23×D7118yes—
782C42C23×D7118yes—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—714no—
787C23—718no—
788C23—1424no—
789C23—1428no—
790C23—1424no—
791C23—1428no—
792C23—1428no—
793C23—1424no—
794C23C24×D7112yes—
795C23C24×D7111yescharacteristic
796Q8—28no—
797Q8—28no—
798Q8—48no—
799Q8—28416no—
800Q8—14216no—
801Q8—1428no—
802D4—28416no—
803D4—2848no—
804D4—28416no—
805D4—28416no—
806D4—2848no—
807D4—14216no—
808D4—1428no—
809D4—14216no—
810C2×C4—22no—
811C2×C4—24no—
812C2×C4—24no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—24no—
817C2×C4—24no—
818C2×C4—28no—
819C2×C4—28no—
820C2×C4—44no—
821C2×C4—28416no—
822C2×C4—28416no—
823C2×C4—28416no—
824C2×C4—28416no—
825C2×C4—714no—
826C2×C4—714no—
827C2×C4—718no—
828C2×C4—714no—
829C2×C4—1424no—
830C2×C4—1428no—
831C2×C4—1424no—
832C2×C4—1424no—
833C2×C4—14216no—
834C2×C4#1455617414yes—
835C2×C4#1455617614yes—
836C2×C4C24×D7114yes—
837C2×C4C24×D7112yes—
838C2×C4C24×D7112yes—
839C2×C4C24×D7112yes—
840C2×C4C24×D7112yes—
841C2×C4C24×D7114yes—
842C2×C4C24×D7114yes—
843C2×C4C24×D7114yes—
844C2×C4C24×D7112yes—
845C2×C4C24×D7112yes—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—44no—
850C22—2848no—
851C22—28416no—
852C22—1424no—
853C22—1428no—
854C22—1424no—
855C22—1428no—
856C22—1428no—
857C22—1424no—
858C22C2×#1455617412yes—
859C22C2×#1455617612yes—
860C22#1798683512yes—
861C22C25×D7111yescharacteristic
862C4—22no—
863C4—24no—
864C4—24no—
865C4—22no—
866C4—22no—
867C4—22no—
868C4—24no—
869C4—24no—
870C4—1424no—
871C4—1428no—
872C4—1424no—
873C4—1424no—
874C4C2×#1455617414yes—
875C4C2×#1455617614yes—
876C2—42no—
877C2—2844no—
878C2—2848no—
879C2#2260281114yesdirect product factor
880C2C22×#1455617411yescharacteristic
881C2C22×#1455617611yescharacteristic
882C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#533×C71C2
socleC23×C71C25
hypercenterC2×#533D71
hypocenterC71C2×#3554
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22602811C2direct (N × H)
2. C2×#17986745C2semidirect
3. C2×#17986734C2semidirect
4. C2×#17986734C2semidirect
5. C2×#17986727C2semidirect
6. C2×#17986709C2semidirect
7. C2×#17986671C2semidirect
8. C2×Q8×D284C2semidirect
9. C2×#17986659C2semidirect
10. C2×#17986651C2semidirect
11. C2×#17986623C2semidirect
12. C2×#17986620C2semidirect
13. C2×#17986604C2semidirect
14. C2×#17986597C2semidirect
15. C2×#17986574C2semidirect
16. C2×#17986549C2semidirect
17. C2×#17986533C2semidirect
18. C2×#533×C71C2semidirect
22. #17986745C22semidirect
23. #17986734C22semidirect
24. #17986734C22semidirect
25. #17986727C22semidirect
26. #17986709C22semidirect
27. #17986671C22semidirect
28. Q8×D284C22semidirect
29. #17986659C22semidirect
30. #17986651C22semidirect
31. #17986623C22semidirect
32. #17986620C22semidirect
33. #17986604C22semidirect
34. #17986597C22semidirect
35. #17986574C22semidirect
36. #17986549C22semidirect
42. #17986533C22semidirect
89. #533×C71C22semidirect
436. C2×C71#3554semidirect
457. C2×#533D71semidirect
460. C71C2×#3554semidirect
478. #533C2×D71semidirect
879. C2#22602811direct (N × H)

Maximal subgroups

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

subgroupindex
#226028112
C2×#179867452
C2×#179867342
C2×#179867272
C2×#179867092
C2×#179866712
C2×Q8×D2842
C2×#179866592
C2×#179866512
C2×#179866232
C2×#179866202
C2×#179866042
C2×#179865972
C2×#179865742
C2×#179865492
C2×#179865332
C2×#533×C712
C2×#355471