Finite Group Databasebeta

← C2×#22602723 #32905150

Subgroups — C2×#22602723 #32905150

Order 18176.

7182 conjugacy classes of subgroups.

The subgroup lattice has 904 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602723C2132yesmaximal, direct product factor
2C2×#17986745C214yesmaximal, complemented
3C2×#17986715C211yesmaximal, characteristic, complemented
4C2×#17986712C212yesmaximal, complemented
5C2×#17986710C211yesmaximal, characteristic, complemented
6C2×#17986693C212yesmaximal, complemented
7C2×#17986690C212yesmaximal, complemented
8C2×#17986664C211yesmaximal, characteristic, complemented
9C2×#17986661C212yesmaximal, complemented
10C2×#17986652C211yesmaximal, characteristic, complemented
11C2×#17986629C212yesmaximal, complemented
12C2×#17986621C214yesmaximal, complemented
13C2×#17986605C212yesmaximal, complemented
14C2×#17986579C212yesmaximal, complemented
15C2×#17986572C212yesmaximal, complemented
16C2×#17986549C211yesmaximal, characteristic, complemented
17C2×#17986533C211yesmaximal, characteristic, complemented
18C2×#533×C71C211yesmaximal, characteristic, complemented
19C22×#11765866C2212yes—
20C22×#11765865C2212yes—
21C22×Q8×D71C2212yes—
22#17986745C22164yescomplemented
23#17986715C22116yescomplemented
24#17986712C22132yescomplemented
25#17986710C22116yescomplemented
26#17986693C22132yescomplemented
27#17986690C22132yescomplemented
28#17986664C22116yescomplemented
29#17986661C22132yescomplemented
30#17986652C22116yescomplemented
31#17986629C22132yescomplemented
32#17986621C22164yescomplemented
33#17986605C22132yescomplemented
34#17986579C22132yescomplemented
35#17986572C22132yescomplemented
36#17986549C22116yescomplemented
37C2×#14556128C2211yescharacteristic
38C2×#14556127C2212yes—
39C2×#14556127C2214yes—
40C2×#14556125C2211yescharacteristic
41#17986533C22116yescomplemented
42C2×#14556122C2214yes—
43C2×#14556122C2212yes—
44C2×#14556120C2211yescharacteristic
45C2×#14556119C2212yes—
46C2×#14556118C2214yes—
47C2×#14556117C2214yes—
48C2×#14556116C2211yescharacteristic
49C2×#14556116C2214yes—
50C2×#14556116C2212yes—
51C2×#14556114C2214yes—
52C2×#14556113C2214yes—
53C2×#14556113C2214yes—
54C2×#14556113C2214yes—
55C2×#14556111C2212yes—
56C2×#14556110C2214yes—
57C2×#14556108C2214yes—
58C2×#14556108C2212yes—
59C2×#14556107C2211yescharacteristic
60C2×#14556106C2214yes—
61C2×#14556106C2214yes—
62C2×#14556104C2212yes—
63C2×#14556104C2212yes—
64C2×#14556104C2214yes—
65C2×#14556103C2212yes—
66C2×#14556103C2212yes—
67C2×#14556103C2214yes—
68C2×#14556103C2212yes—
69C2×#14556103C2214yes—
70C2×#14556102C2211yescharacteristic
71C2×#14556102C2211yescharacteristic
72C2×#14556102C2211yescharacteristic
73C2×#14556102C2212yes—
74C2×#14556101C2214yes—
75C2×#14556101C2214yes—
76C2×C4×Dic142C2211yescharacteristic
77C2×C4×D284C2211yescharacteristic
78C2×C4×D284C2211yescharacteristic
79C2×C4×D284C2212yes—
80C2×C4×D284C2214yes—
81C2×C4×D284C2211yescharacteristic
82C2×#14556090C2212yes—
83C2×#14556090C2212yes—
84C2×C4×C22⋊D71C2212yes—
85C2×#14556086C2212yes—
86C2×#14556086C2212yes—
87C2×#14556085C2212yes—
88C2×#14556085C2214yes—
89C2×C4⋊C4×D71C2212yes—
90C2×C4⋊C4×D71C2212yes—
91#533×C71C22116yescomplemented
92C2×C4⋊Q8×C71C2211yescharacteristic
93C2×C4⋊Q8×C71C2211yescharacteristic
94C2×#125×C71C2212yes—
95C2×C22⋊Q8×C71C2212yes—
96C2×C22⋊Q8×C71C2212yes—
97C2×C4×Q8×C71C2212yes—
98C2×C4×Q8×C71C2212yes—
99C2×#117×C71C2212yes—
100C22×C42×C71C2211yescharacteristic
101C2×#11765866—48no—
102C2×#11765866C23116yes—
103C2×#11765865—48no—
104C2×#11765865C23116yes—
105C22×Dic142C2311yescharacteristic
106C22×Dic142C2314yes—
107C22×Dic142C2312yes—
108C2×Q8×D71—48no—
109C2×Q8×D71C23116yes—
110C22×D284C2311yescharacteristic
111C22×D284C2311yescharacteristic
112C22×D284C2311yescharacteristic
113C22×D284C2312yes—
114C22×D284C2314yes—
115C22×D284C2314yes—
116C22×D284C2312yes—
117C22×C22⋊D71C2312yes—
118C22×C22⋊D71C2312yes—
119C22×C22⋊D71C2312yes—
120C22×C4×D71C2312yes—
121C22×C4×D71C2312yes—
122C22×C4×D71C2312yes—
123C22×C4×D71C2314yes—
124C22×C4×D71C2314yes—
125C22×C4×D71C2314yes—
126#14556128C2318yes—
127#14556127C23132yes—
128#14556127C23116yes—
129#14556125C2318yes—
130#14556122C23116yes—
131#14556122C23132yes—
132#14556120C2318yes—
133#14556119C23116yes—
134#14556118C23132yes—
135#14556117C23132yes—
136#14556116C23116yes—
137#14556116C23132yes—
138#14556116C2318yes—
139#14556114C23132yes—
140#14556113C23132yes—
141#14556113C23132yes—
142#14556113C23132yes—
143#14556111C23116yes—
144#14556110C23132yes—
145#14556108C23116yes—
146#14556108C23132yes—
147#14556107C2318yes—
148#14556106C23132yes—
149#14556106C23132yes—
150#14556104C23116yes—
151#14556104C23116yes—
152#14556104C23132yes—
153#14556103C23132yes—
154#14556103C23116yes—
155#14556103C23116yes—
156#14556103C23132yes—
157#14556103C23116yes—
158#14556102C2318yes—
159#14556102C2318yes—
160#14556102C2318yes—
161#14556102C23116yes—
162#14556101C23132yes—
163#14556101C23132yes—
164C4×Dic142C2318yes—
165C4×D284C23132yes—
166C4×D284C2318yes—
167C4×D284C2318yes—
168C4×D284C23116yes—
169C4×D284C2318yes—
170#14556090C23116yes—
171#14556090C23116yes—
172C4×C22⋊D71C23116yes—
173#14556086C23116yes—
174#14556086C23116yes—
175#14556085C23116yes—
176#14556085C23132yes—
177C2×C4⋊Dic71C2311yescharacteristic
178C2×C4⋊Dic71C2311yescharacteristic
179C2×C4⋊Dic71C2311yescharacteristic
180C2×C4⋊Dic71C2311yescharacteristic
181C2×C4⋊Dic71C2312yes—
182C2×C4⋊Dic71C2314yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2314yes—
185C2×Dic71⋊C4C2312yes—
186C2×Dic71⋊C4C2314yes—
187C2×Dic71⋊C4C2312yes—
188C2×Dic71⋊C4C2312yes—
189C2×Dic71⋊C4C2312yes—
190C4⋊C4×D71C23116yes—
191C4⋊C4×D71C23116yes—
192C2×C22⋊Dic71C2312yes—
193C2×(C2×D71)⋊C4C2312yes—
194C2×(C2×D71)⋊C4C2312yes—
195C2×(C2×D71)⋊C4C2312yes—
196C2×(C2×D71)⋊C4C2314yes—
197C2×(C2×D71)⋊C4C2314yes—
198C2×(C2×D71)⋊C4C2314yes—
199C2×(C2×D71)⋊C4C2312yes—
200C2×(C2×D71)⋊C4C2314yes—
201C2×(C2×D71)⋊C4C2314yes—
202C2×(C2×D71)⋊C4C2312yes—
203C2×(C2×D71)⋊C4C2312yes—
204C2×(C2×D71)⋊C4C2312yes—
205C2×(C2×D71)⋊C4C2312yes—
206C2×C4×Dic71C2314yes—
207C2×C4×Dic71C2312yes—
208C22×Q8×C71C2312yes—
209C22×Q8×C71C2312yes—
210C23×C4×C71C2311yescharacteristic
211C23×C4×C71C2311yescharacteristic
212C23×C4×C71C2311yescharacteristic
213C4⋊Q8×C71C2318yes—
214C4⋊Q8×C71C2318yes—
215#125×C71C23116yes—
216C22⋊Q8×C71C23116yes—
217C22⋊Q8×C71C23116yes—
218C4×Q8×C71C23116yes—
219C4×Q8×C71C23116yes—
220#117×C71C23116yes—
221C2×C4⋊C4×C71C2312yes—
222C2×C4⋊C4×C71C2312yes—
223C2×C4⋊C4×C71C2314yes—
224C2×C4⋊C4×C71C2314yes—
225C2×C4⋊C4×C71C2312yes—
226C2×C4⋊C4×C71C2312yes—
227C2×C22⋊C4×C71C2314yes—
228C2×C42×C71C2311yescharacteristic
229C2×C42×C71C2311yescharacteristic
230C2×C42×C71C2311yescharacteristic
231C2×C42×C71C2311yescharacteristic
232C2×C42×C71C2318yes—
233C2×C42×C71C2314yes—
234C23×D71C2412yes—
235C23×D71C2412yes—
236C23×D71C2412yes—
237#11765866—432no—
238#11765865—432no—
239C2×Dic142—24no—
240C2×Dic142—48no—
241C2×Dic142—44no—
242C2×Dic142C2414yes—
243C2×Dic142C24116yes—
244C2×Dic142C2418yes—
245Q8×D71—432no—
246C2×D284—24no—
247C2×D284—24no—
248C2×D284—24no—
249C2×D284—44no—
250C2×D284—48no—
251C2×D284—44no—
252C2×D284—48no—
253C2×D284C2414yes—
254C2×D284C2414yes—
255C2×D284C2414yes—
256C2×D284C2418yes—
257C2×D284C24116yes—
258C2×D284C24116yes—
259C2×D284C2418yes—
260C2×C22⋊D71—44no—
261C2×C22⋊D71—44no—
262C2×C22⋊D71—44no—
263C2×C22⋊D71C2418yes—
264C2×C22⋊D71C2418yes—
265C2×C22⋊D71C2418yes—
266C22×Dic71C2412yes—
267C22×Dic71C2412yes—
268C22×Dic71C2412yes—
269C22×Dic71C2412yes—
270C22×Dic71C2412yes—
271C2×C4×D71—28no—
272C2×C4×D71—28no—
273C2×C4×D71—28no—
274C2×C4×D71—48no—
275C2×C4×D71—48no—
276C2×C4×D71—48no—
277C2×C4×D71C2418yes—
278C2×C4×D71C2418yes—
279C2×C4×D71C2418yes—
280C2×C4×D71C24116yes—
281C2×C4×D71C24116yes—
282C2×C4×D71C24116yes—
283C4⋊Dic71C2414yes—
284C4⋊Dic71C2414yes—
285C4⋊Dic71C2414yes—
286C4⋊Dic71C2414yes—
287C4⋊Dic71C2418yes—
288C4⋊Dic71C24116yes—
289Dic71⋊C4C24116yes—
290Dic71⋊C4C24116yes—
291Dic71⋊C4C2418yes—
292Dic71⋊C4C24116yes—
293Dic71⋊C4C2418yes—
294Dic71⋊C4C2418yes—
295Dic71⋊C4C2418yes—
296C22⋊Dic71C2418yes—
297(C2×D71)⋊C4C2418yes—
298(C2×D71)⋊C4C2418yes—
299(C2×D71)⋊C4C2418yes—
300(C2×D71)⋊C4C24116yes—
301(C2×D71)⋊C4C24116yes—
302(C2×D71)⋊C4C24116yes—
303(C2×D71)⋊C4C2418yes—
304(C2×D71)⋊C4C24116yes—
305(C2×D71)⋊C4C24116yes—
306(C2×D71)⋊C4C2418yes—
307(C2×D71)⋊C4C2418yes—
308(C2×D71)⋊C4C2418yes—
309(C2×D71)⋊C4C2418yes—
310C4×Dic71C24116yes—
311C4×Dic71C2418yes—
312C24×C71C2411yescharacteristic
313C2×Q8×C71—28no—
314C2×Q8×C71—44no—
315C2×Q8×C71C2418yes—
316C2×Q8×C71C2418yes—
317C22×C4×C71—24no—
318C22×C4×C71—24no—
319C22×C4×C71—42no—
320C22×C4×C71C2414yes—
321C22×C4×C71C2414yes—
322C22×C4×C71C2411yescharacteristic
323C22×C4×C71C2411yescharacteristic
324C22×C4×C71C2414yes—
325C22×C4×C71C2411yescharacteristic
326C22×C4×C71C2411yescharacteristic
327C22×C4×C71C2414yes—
328C22×C4×C71C2414yes—
329C22×C4×C71C2411yescharacteristic
330C22×C4×C71C2411yescharacteristic
331C4⋊C4×C71C2418yes—
332C4⋊C4×C71C2418yes—
333C4⋊C4×C71C24116yes—
334C4⋊C4×C71C24116yes—
335C4⋊C4×C71C2418yes—
336C4⋊C4×C71C2418yes—
337C22⋊C4×C71C24116yes—
338C42×C71C2414yes—
339C42×C71C2414yes—
340C42×C71C2414yes—
341C42×C71C2414yes—
342C42×C71C24116yes—
343C23×C71—22no—
344C23×C71—22no—
345C23×C71—22no—
346C23×C71C2512yes—
347C23×C71C2511yescharacteristic
348C22×D71—24no—
349C22×D71—24no—
350C22×D71—24no—
351C22×D71—24no—
352C22×D71—24no—
353C22×D71—24no—
354C22×D71—24no—
355C22×D71—24no—
356C22×D71—24no—
357C22×D71C2514yes—
358C22×D71C2514yes—
359C22×D71C2514yes—
360Q8×C71—216no—
361Q8×C71—48no—
362C2×C4×C71—22no—
363C2×C4×C71—28no—
364C2×C4×C71—22no—
365C2×C4×C71—22no—
366C2×C4×C71—22no—
367C2×C4×C71—28no—
368C2×C4×C71—28no—
369C2×C4×C71—28no—
370C2×C4×C71—44no—
371C2×C4×C71H(5,𝔽2)14yes—
372C2×C4×C712−1+414yes—
373C2×C4×C71C2512yes—
374C2×C4×C71C2512yes—
375C2×C4×C71C2512yes—
376C2×C4×C71C2512yes—
377C2×C4×C71C2518yes—
378C2×C4×C71C2518yes—
379C2×C4×C71C2512yes—
380C2×C4×C71C2512yes—
381C22⋊D71—48no—
382C22⋊D71—48no—
383C22⋊D71—48no—
384C2×Dic71—24no—
385C2×Dic71—24no—
386C2×Dic71—24no—
387C2×Dic71—24no—
388C2×Dic71—24no—
389C2×Dic71C2514yes—
390C2×Dic71C2514yes—
391C2×Dic71C2514yes—
392C2×Dic71C2514yes—
393C2×Dic71C2514yes—
394D284—28no—
395D284—28no—
396D284—28no—
397D284—416no—
398D284—48no—
399D284—48no—
400D284—416no—
401C4×D71—216no—
402C4×D71—216no—
403C4×D71—216no—
404C4×D71—416no—
405C4×D71—416no—
406C4×D71—416no—
407Dic142—28no—
408Dic142—416no—
409Dic142—48no—
410C22×C71—22no—
411C22×C71—22no—
412C22×C71—22no—
413C22×C71—44no—
414C22×C71C2×H(5,𝔽2)12yes—
415C22×C71C2×2−1+412yes—
416C22×C71#58512yes—
417C22×C71C2611yescharacteristic
418C2×D71—24no—
419C2×D71—24no—
420C2×D71—24no—
421C2×D71—24no—
422C2×D71—24no—
423C2×D71—24no—
424C2×D71—24no—
425C2×D71—24no—
426C2×D71—24no—
427C2×D71—48no—
428C2×D71—48no—
429C2×D71—48no—
430C4×C71—22no—
431C4×C71—28no—
432C4×C71—22no—
433C4×C71—28no—
434C4×C71—22no—
435C4×C71—22no—
436C4×C71C2×H(5,𝔽2)14yes—
437C4×C71C2×2−1+414yes—
438Dic71—24no—
439Dic71—24no—
440Dic71—24no—
441Dic71—24no—
442Dic71—24no—
443C2×#3547—711nomaximal, Sylow
444C2×C71—42no—
445C2×C71#354714yescomplemented
446C2×C71C22×H(5,𝔽2)11yescharacteristic
447C2×C71C22×2−1+411yescharacteristic
448C2×C71C2×#58511yescharacteristic
449D71—44no—
450D71—44no—
451D71—44no—
452#3547—7132no—
453C2×#562—714no—
454C2×#555—711no—
455C2×#555—712no—
456C2×#554—711no—
457C2×#553—712no—
458C2×#552—712no—
459C2×D4×Q8—711no—
460C2×#548—712no—
461C2×#547—711no—
462C2×#544—712no—
463C2×#542—714no—
464C2×#540—712no—
465C2×#537—712no—
466C2×#536—712no—
467C2×#533D7111yescharacteristic, complemented
468C2×#532—711no—
469C2×#529—711no—
470C71C2×#354711yescharacteristic, complemented, Sylow
471C22×#41—712no—
472C22×#41—712no—
473C23×Q8—712no—
474#562—7164no—
475#555—7116no—
476#555—7132no—
477#554—7116no—
478#553—7132no—
479#552—7132no—
480D4×Q8—7116no—
481#548—7132no—
482#547—7116no—
483#544—7132no—
484#542—7164no—
485#540—7132no—
486#537—7132no—
487#536—7132no—
488#533C2×D71116yescomplemented
489#532—7116no—
490C2×C4⋊Q8—714no—
491C2×C4⋊Q8—712no—
492C2×C4⋊Q8—711no—
493C2×C4⋊Q8C2×D7111yescharacteristic
494C2×C4⋊Q8C2×D7111yescharacteristic
495C2×#127—711no—
496#529—7116no—
497C2×#126—712no—
498C2×#126—714no—
499C2×#125—714no—
500C2×#125—712no—
501C2×#125—711no—
502C2×#125C2×D7112yes—
503C2×#124—714no—
504C2×#124—714no—
505C2×#124—711no—
506C2×#124—712no—
507C2×#124—714no—
508C2×#123—712no—
509C2×#123—714no—
510C2×#123—714no—
511C2×#123—714no—
512C2×#123—714no—
513C2×C22⋊Q8—712no—
514C2×C22⋊Q8—712no—
515C2×C22⋊Q8—714no—
516C2×C22⋊Q8—711no—
517C2×C22⋊Q8—712no—
518C2×C22⋊Q8—714no—
519C2×C22⋊Q8—714no—
520C2×C22⋊Q8—714no—
521C2×C22⋊Q8C2×D7112yes—
522C2×C22⋊Q8C2×D7112yes—
523C2×#121—711no—
524C2×#121—711no—
525C2×#121—711no—
526C2×#121—712no—
527C2×#121—714no—
528C2×#121—712no—
529C2×#121—712no—
530C2×#121—714no—
531C2×#121—712no—
532C2×#121—714no—
533C2×#121—714no—
534C2×C4×Q8—711no—
535C2×C4×Q8C2×D7112yes—
536C2×C4×Q8C2×D7112yes—
537C2×C4×D4—712no—
538C2×C4×D4—712no—
539C2×C4×D4—712no—
540C2×C4×D4—711no—
541C2×C4×D4—711no—
542C2×C4×D4—712no—
543C2×C4×D4—711no—
544C2×C4×D4—714no—
545C2×#117—712no—
546C2×#117—712no—
547C2×#117—712no—
548C2×#117—714no—
549C2×#117C2×D7112yes—
550C22×C4⋊C4—712no—
551C22×C4⋊C4—712no—
552C22×C42C2×D7111yescharacteristic
553C2×#41—2848no—
554C2×#41—2848no—
555C2×#41—7116no—
556C2×#41—7116no—
557C22×Q8—2848no—
558C22×Q8—7116no—
559C22×Q8—714no—
560C22×Q8—712no—
561C22×Q8—711no—
562C22×Q8C22×D7112yes—
563C22×Q8C22×D7112yes—
564C22×D4—712no—
565C22×D4—712no—
566C22×D4—712no—
567C22×D4—714no—
568C22×D4—712no—
569C22×D4—714no—
570C22×D4—712no—
571C22×D4—711no—
572C22×D4—711no—
573C22×D4—711no—
574C23×C4—714no—
575C23×C4—714no—
576C23×C4—714no—
577C23×C4—712no—
578C23×C4—712no—
579C23×C4—712no—
580C23×C4C22×D7111yescharacteristic
581C23×C4C22×D7111yescharacteristic
582C23×C4C22×D7111yescharacteristic
583C4⋊Q8—7132no—
584C4⋊Q8—7116no—
585C4⋊Q8—718no—
586C4⋊Q8C22×D7118yes—
587C4⋊Q8C22×D7118yes—
588#127—718no—
589#126—7116no—
590#126—7132no—
591#125—7132no—
592#125—7116no—
593#125—718no—
594#125C22×D71116yes—
595#124—7132no—
596#124—7132no—
597#124—718no—
598#124—7116no—
599#124—7132no—
600#123—7116no—
601#123—7132no—
602#123—7132no—
603#123—7132no—
604#123—7132no—
605C22⋊Q8—7116no—
606C22⋊Q8—7116no—
607C22⋊Q8—7132no—
608C22⋊Q8—718no—
609C22⋊Q8—7116no—
610C22⋊Q8—7132no—
611C22⋊Q8—7132no—
612C22⋊Q8—7132no—
613C22⋊Q8C22×D71116yes—
614C22⋊Q8C22×D71116yes—
615#121—718no—
616#121—718no—
617#121—718no—
618#121—7116no—
619#121—7132no—
620#121—7116no—
621#121—7116no—
622#121—7132no—
623#121—7116no—
624#121—7132no—
625#121—7132no—
626C4×Q8—718no—
627C4×Q8C22×D71116yes—
628C4×Q8C22×D71116yes—
629C4×D4—7116no—
630C4×D4—7116no—
631C4×D4—7116no—
632C4×D4—718no—
633C4×D4—718no—
634C4×D4—7116no—
635C4×D4—718no—
636C4×D4—7132no—
637#117—7116no—
638#117—7116no—
639#117—7116no—
640#117—7132no—
641#117C22×D71116yes—
642C2×C4⋊C4—711no—
643C2×C4⋊C4—711no—
644C2×C4⋊C4—714no—
645C2×C4⋊C4—714no—
646C2×C4⋊C4—711no—
647C2×C4⋊C4—711no—
648C2×C4⋊C4—712no—
649C2×C4⋊C4—714no—
650C2×C4⋊C4—712no—
651C2×C4⋊C4—712no—
652C2×C4⋊C4—712no—
653C2×C4⋊C4—714no—
654C2×C4⋊C4—712no—
655C2×C4⋊C4—7116no—
656C2×C4⋊C4—7116no—
657C2×C4⋊C4C22×D7112yes—
658C2×C4⋊C4C22×D7112yes—
659C2×C4⋊C4C22×D7112yes—
660C2×C4⋊C4C22×D7114yes—
661C2×C4⋊C4C22×D7114yes—
662C2×C4⋊C4C22×D7112yes—
663C2×C22⋊C4—712no—
664C2×C22⋊C4—712no—
665C2×C22⋊C4—712no—
666C2×C22⋊C4—712no—
667C2×C22⋊C4—714no—
668C2×C22⋊C4—714no—
669C2×C22⋊C4—714no—
670C2×C22⋊C4—712no—
671C2×C22⋊C4—712no—
672C2×C22⋊C4—714no—
673C2×C22⋊C4—712no—
674C2×C22⋊C4—714no—
675C2×C22⋊C4—712no—
676C2×C22⋊C4—712no—
677C2×C22⋊C4C22×D7114yes—
678C2×C42—714no—
679C2×C42—712no—
680C2×C42C22×D7111yescharacteristic
681C2×C42C22×D7114yes—
682C2×C42C22×D7111yescharacteristic
683C2×C42C22×D7111yescharacteristic
684C2×C42C22×D7111yescharacteristic
685C2×C42C22×D7118yes—
686C24—712no—
687C24—712no—
688C24—712no—
689C24C23×D7111yescharacteristic
690#41—28432no—
691#41—28432no—
692C2×Q8—28no—
693C2×Q8—44no—
694C2×Q8—2848no—
695C2×Q8—2844no—
696C2×Q8—28432no—
697C2×Q8—7116no—
698C2×Q8—718no—
699C2×Q8—714no—
700C2×Q8—1424no—
701C2×Q8C23×D7118yes—
702C2×Q8C23×D7118yes—
703C2×D4—2844no—
704C2×D4—2848no—
705C2×D4—2844no—
706C2×D4—2848no—
707C2×D4—2844no—
708C2×D4—2844no—
709C2×D4—2844no—
710C2×D4—718no—
711C2×D4—718no—
712C2×D4—718no—
713C2×D4—7116no—
714C2×D4—718no—
715C2×D4—7116no—
716C2×D4—718no—
717C2×D4—714no—
718C2×D4—714no—
719C2×D4—714no—
720C2×D4—1424no—
721C2×D4—1424no—
722C2×D4—1424no—
723C22×C4—24no—
724C22×C4—24no—
725C22×C4—42no—
726C22×C4—2848no—
727C22×C4—2848no—
728C22×C4—2848no—
729C22×C4—7116no—
730C22×C4—7116no—
731C22×C4—7116no—
732C22×C4—712no—
733C22×C4—712no—
734C22×C4—712no—
735C22×C4—712no—
736C22×C4—712no—
737C22×C4—718no—
738C22×C4—718no—
739C22×C4—718no—
740C22×C4—1428no—
741C22×C4—1428no—
742C22×C4—1428no—
743C22×C4C23×D7114yes—
744C22×C4C23×D7114yes—
745C22×C4C23×D7114yes—
746C22×C4C23×D7111yescharacteristic
747C22×C4C23×D7111yescharacteristic
748C22×C4C23×D7111yescharacteristic
749C22×C4C23×D7111yescharacteristic
750C22×C4C23×D7114yes—
751C22×C4C23×D7114yes—
752C22×C4C23×D7111yescharacteristic
753C22×C4C23×D7111yescharacteristic
754C4⋊C4—7116no—
755C4⋊C4—7116no—
756C4⋊C4—718no—
757C4⋊C4—7116no—
758C4⋊C4—718no—
759C4⋊C4—718no—
760C4⋊C4—718no—
761C4⋊C4—714no—
762C4⋊C4—714no—
763C4⋊C4—714no—
764C4⋊C4—714no—
765C4⋊C4—718no—
766C4⋊C4—7116no—
767C4⋊C4C23×D7118yes—
768C4⋊C4C23×D7118yes—
769C4⋊C4C23×D7118yes—
770C4⋊C4C23×D71116yes—
771C4⋊C4C23×D71116yes—
772C4⋊C4C23×D7118yes—
773C22⋊C4—718no—
774C22⋊C4—718no—
775C22⋊C4—718no—
776C22⋊C4—718no—
777C22⋊C4—7116no—
778C22⋊C4—7116no—
779C22⋊C4—7116no—
780C22⋊C4—718no—
781C22⋊C4—718no—
782C22⋊C4—7116no—
783C22⋊C4—718no—
784C22⋊C4—7116no—
785C22⋊C4—718no—
786C22⋊C4—718no—
787C22⋊C4C23×D71116yes—
788C42—7116no—
789C42—718no—
790C42C23×D7114yes—
791C42C23×D7114yes—
792C42C23×D7114yes—
793C42C23×D7114yes—
794C42C23×D71116yes—
795C23—22no—
796C23—22no—
797C23—22no—
798C23—714no—
799C23—714no—
800C23—714no—
801C23—1424no—
802C23—1424no—
803C23—1424no—
804C23—1424no—
805C23—1424no—
806C23—1424no—
807C23—1424no—
808C23—1424no—
809C23—1424no—
810C23C24×D7112yes—
811C23C24×D7111yescharacteristic
812Q8—216no—
813Q8—48no—
814Q8—28416no—
815Q8—2848no—
816Q8—1428no—
817D4—2848no—
818D4—28416no—
819D4—2848no—
820D4—28416no—
821D4—2848no—
822D4—2848no—
823D4—2848no—
824D4—1428no—
825D4—1428no—
826D4—1428no—
827C2×C4—22no—
828C2×C4—28no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—28no—
833C2×C4—28no—
834C2×C4—28no—
835C2×C4—44no—
836C2×C4—28416no—
837C2×C4—28416no—
838C2×C4—28416no—
839C2×C4—714no—
840C2×C4—714no—
841C2×C4—714no—
842C2×C4—714no—
843C2×C4—714no—
844C2×C4—1424no—
845C2×C4—1424no—
846C2×C4—1424no—
847C2×C4—1424no—
848C2×C4—1424no—
849C2×C4—14216no—
850C2×C4—14216no—
851C2×C4—14216no—
852C2×C4#1455617414yes—
853C2×C4#1455617614yes—
854C2×C4C24×D7118yes—
855C2×C4C24×D7112yes—
856C2×C4C24×D7112yes—
857C2×C4C24×D7112yes—
858C2×C4C24×D7112yes—
859C2×C4C24×D7118yes—
860C2×C4C24×D7112yes—
861C2×C4C24×D7112yes—
862C22—22no—
863C22—22no—
864C22—22no—
865C22—44no—
866C22—2848no—
867C22—2848no—
868C22—2848no—
869C22—1424no—
870C22—1424no—
871C22—1424no—
872C22—1424no—
873C22—1424no—
874C22—1424no—
875C22—1424no—
876C22—1424no—
877C22—1424no—
878C22C2×#1455617412yes—
879C22C2×#1455617612yes—
880C22#1798683512yes—
881C22C25×D7111yescharacteristic
882C4—22no—
883C4—28no—
884C4—22no—
885C4—22no—
886C4—22no—
887C4—28no—
888C4—1424no—
889C4—1424no—
890C4—1424no—
891C4—1424no—
892C4—1424no—
893C4C2×#1455617414yes—
894C4C2×#1455617614yes—
895C2—42no—
896C2—2844no—
897C2—2844no—
898C2—2844no—
899C2#2260272314yesdirect product factor
900C2C22×#1455617411yescharacteristic
901C2C22×#1455617611yescharacteristic
902C2C2×#1798683511yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#533×C71C2
socleC23×C71C25
hypercenterC2×#533D71
hypocenterC71C2×#3547
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
1. #22602723C2direct (N × H)
2. C2×#17986745C2semidirect
3. C2×#17986715C2semidirect
4. C2×#17986712C2semidirect
5. C2×#17986710C2semidirect
6. C2×#17986693C2semidirect
7. C2×#17986690C2semidirect
8. C2×#17986664C2semidirect
9. C2×#17986661C2semidirect
10. C2×#17986652C2semidirect
11. C2×#17986629C2semidirect
12. C2×#17986621C2semidirect
13. C2×#17986605C2semidirect
14. C2×#17986579C2semidirect
15. C2×#17986572C2semidirect
16. C2×#17986549C2semidirect
17. C2×#17986533C2semidirect
18. C2×#533×C71C2semidirect
22. #17986745C22semidirect
23. #17986715C22semidirect
24. #17986712C22semidirect
25. #17986710C22semidirect
26. #17986693C22semidirect
27. #17986690C22semidirect
28. #17986664C22semidirect
29. #17986661C22semidirect
30. #17986652C22semidirect
31. #17986629C22semidirect
32. #17986621C22semidirect
33. #17986605C22semidirect
34. #17986579C22semidirect
35. #17986572C22semidirect
36. #17986549C22semidirect
41. #17986533C22semidirect
91. #533×C71C22semidirect
445. C2×C71#3547semidirect
467. C2×#533D71semidirect
470. C71C2×#3547semidirect
488. #533C2×D71semidirect
899. C2#22602723direct (N × H)

Maximal subgroups

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

subgroupindex
#226027232
C2×#179867452
C2×#179867152
C2×#179867122
C2×#179867102
C2×#179866932
C2×#179866902
C2×#179866642
C2×#179866612
C2×#179866522
C2×#179866292
C2×#179866212
C2×#179866052
C2×#179865792
C2×#179865722
C2×#179865492
C2×#179865332
C2×#533×C712
C2×#354771