Finite Group Databasebeta

← C2×#22602249 #32905825

Subgroups — C2×#22602249 #32905825

Order 18176.

7758 conjugacy classes of subgroups.

The subgroup lattice has 924 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22602249C2132yesmaximal, direct product factor
2C2×#17986720C212yesmaximal, complemented
3C2×#17986713C212yesmaximal, complemented
4C2×#17986707C212yesmaximal, complemented
5C2×#17986692C214yesmaximal, complemented
6C2×#17986655C214yesmaximal, complemented
7C2×#17986649C212yesmaximal, complemented
8C2×#17986622C212yesmaximal, complemented
9C2×#17986616C212yesmaximal, complemented
10C2×#17986577C211yesmaximal, characteristic, complemented
11C2×#17986551C212yesmaximal, complemented
12C2×#17986545C211yesmaximal, characteristic, complemented
13C2×#17986544C212yesmaximal, complemented
14C22×#14556127C211yesmaximal, characteristic, complemented
15C2×#17986482C211yesmaximal, characteristic, complemented
16C2×#17986480C211yesmaximal, characteristic, complemented
17C2×#41×Dic71C211yesmaximal, characteristic, complemented
18C2×#537×C71C211yesmaximal, characteristic, complemented
19C22×#11765865C2211yescharacteristic
20C22×#11765864C2214yes—
21C23×Dic142C2212yes—
22#17986720C22132yescomplemented
23#17986713C22132yescomplemented
24#17986707C22132yescomplemented
25#17986692C22164yescomplemented
26#17986655C22164yescomplemented
27#17986649C22132yescomplemented
28#17986622C22132yescomplemented
29#17986616C22132yescomplemented
30#17986577C22116yescomplemented
31#17986551C22132yescomplemented
32#17986545C22116yescomplemented
33#17986544C22132yescomplemented
34C2×#14556127C2212yes—
35C2×#14556127C2212yes—
36C2×#14556127C2212yes—
37C2×#14556127C2212yes—
38C2×#14556127C22116yescomplemented
39C2×#14556126C2211yescharacteristic
40C2×#14556124C2211yescharacteristic
41C2×#14556123C2214yes—
42C2×#14556121C2214yes—
43C2×#14556118C2214yes—
44C2×#14556117C2211yescharacteristic
45C2×#14556115C2214yes—
46C2×#14556115C2211yescharacteristic
47C2×#14556114C2214yes—
48C2×#14556114C2214yes—
49C2×#14556110C2214yes—
50C2×#14556109C2214yes—
51C2×#14556108C2214yes—
52C2×#14556107C2212yes—
53C2×#14556105C2214yes—
54C2×#14556105C2214yes—
55C2×#14556104C2212yes—
56C2×#14556102C2212yes—
57C2×#14556100C2212yes—
58C2×#14556100C2214yes—
59C2×#14556100C2212yes—
60C2×#14556100C2214yes—
61C2×#14556099C2212yes—
62#17986482C22116yescomplemented
63#17986480C22116yescomplemented
64#41×Dic71C22116yescomplemented
65C2×Q8×Dic71C2211yescharacteristic
66C2×Q8×Dic71C2211yescharacteristic
67C2×Q8×Dic71C2212yes—
68C2×#14556093C2212yes—
69C2×#14556093C2214yes—
70C2×D4×Dic71C2211yescharacteristic
71C2×D4×Dic71C2212yes—
72C2×D4×Dic71C2212yes—
73C2×D4×Dic71C2211yescharacteristic
74C2×D4×Dic71C2214yes—
75C2×D4×Dic71C2212yes—
76C2×#14556090C2212yes—
77C2×C4×C22⋊D71C2214yes—
78C2×C4×C22⋊D71C2212yes—
79C2×C4×C22⋊D71C2212yes—
80C2×(C22⋊D71)⋊C4C2214yes—
81C2×#14556087C2211yescharacteristic
82C2×#14556087C2212yes—
83C2×#14556087C2212yes—
84C2×#14556086C2212yes—
85C2×#14556084C2214yes—
86C22×C4⋊Dic71C2212yes—
87C22×C4⋊Dic71C2211yescharacteristic
88C22×Dic71⋊C4C2212yes—
89C2×C4⋊C4×D71C2212yes—
90C22×C4×Dic71C2211yescharacteristic
91C22×C4×Dic71C2212yes—
92C22×#41×C71C2211yescharacteristic
93C22×#41×C71C2211yescharacteristic
94#537×C71C22116yescomplemented
95C2×C22⋊Q8×C71C2212yes—
96C2×C22⋊Q8×C71C2212yes—
97C2×#121×C71C2212yes—
98C2×#121×C71C2214yes—
99C2×#121×C71C2212yes—
100C22×C4⋊C4×C71C2211yescharacteristic
101C2×#11765865—28no—
102C2×#11765865C2318yes—
103C2×#11765864—416no—
104C2×#11765864C23132yes—
105C22×Dic142—48no—
106C22×Dic142C2314yes—
107C22×Dic142C2311yescharacteristic
108C22×Dic142C23116yes—
109C22×Dic142C2314yes—
110C22×D284C2311yescharacteristic
111C22×C22⋊D71C2312yes—
112C22×C22⋊D71C2312yes—
113C22×C22⋊D71C2312yes—
114C22×C22⋊D71C2314yes—
115C23×Dic71C2311yescharacteristic
116C23×Dic71C2312yes—
117C23×Dic71C2311yescharacteristic
118C23×Dic71C2312yes—
119C23×Dic71C2312yes—
120C23×Dic71C2314yes—
121C22×C4×D71C2312yes—
122C22×C4×D71C2314yes—
123#14556127C23116yes—
124#14556127C23116yes—
125#14556127C23116yes—
126#14556127C23116yes—
127#14556126C2318yes—
128#14556124C2318yes—
129#14556123C23132yes—
130#14556121C23132yes—
131#14556118C23132yes—
132#14556117C2318yes—
133#14556115C2318yes—
134#14556115C23132yes—
135#14556114C23132yes—
136#14556114C23132yes—
137#14556110C23132yes—
138#14556109C23132yes—
139#14556108C23132yes—
140#14556107C23116yes—
141#14556105C23132yes—
142#14556105C23132yes—
143#14556104C23116yes—
144#14556102C23116yes—
145#14556100C23132yes—
146#14556100C23116yes—
147#14556100C23116yes—
148#14556100C23132yes—
149#14556099C23116yes—
150Q8×Dic71C23116yes—
151Q8×Dic71C2318yes—
152Q8×Dic71C2318yes—
153#14556093C23116yes—
154#14556093C23132yes—
155D4×Dic71C23116yes—
156D4×Dic71C2318yes—
157D4×Dic71C23116yes—
158D4×Dic71C23132yes—
159D4×Dic71C23116yes—
160D4×Dic71C2318yes—
161#14556090C23116yes—
162C4×C22⋊D71C23116yes—
163C4×C22⋊D71C23132yes—
164C4×C22⋊D71C23116yes—
165(C22⋊D71)⋊C4C23132yes—
166#14556087C23116yes—
167#14556087C23116yes—
168#14556087C2318yes—
169#14556086C23116yes—
170#14556084C23132yes—
171C2×C4⋊Dic71C2318yes—
172C2×C4⋊Dic71C23116yes—
173C2×C4⋊Dic71C2311yescharacteristic
174C2×C4⋊Dic71C2312yes—
175C2×C4⋊Dic71C2312yes—
176C2×C4⋊Dic71C2314yes—
177C2×C4⋊Dic71C2311yescharacteristic
178C2×C4⋊Dic71C2312yes—
179C2×C4⋊Dic71C2312yes—
180C2×Dic71⋊C4C23116yes—
181C2×Dic71⋊C4C2314yes—
182C2×Dic71⋊C4C2314yes—
183C2×Dic71⋊C4C2314yes—
184C2×Dic71⋊C4C2312yes—
185C2×Dic71⋊C4C2312yes—
186C2×Dic71⋊C4C2314yes—
187C4⋊C4×D71C23116yes—
188C2×C22⋊Dic71C2314yes—
189C2×C22⋊Dic71C2312yes—
190C2×C22⋊Dic71C2314yes—
191C2×C22⋊Dic71C2312yes—
192C2×C22⋊Dic71C2312yes—
193C2×C22⋊Dic71C2312yes—
194C2×C22⋊Dic71C2312yes—
195C2×(C2×D71)⋊C4C2314yes—
196C2×(C2×D71)⋊C4C2314yes—
197C2×(C2×D71)⋊C4C2312yes—
198C2×(C2×D71)⋊C4C2312yes—
199C2×C4×Dic71C2311yescharacteristic
200C2×C4×Dic71C2312yes—
201C2×C4×Dic71C2311yescharacteristic
202C2×C4×Dic71C2312yes—
203C2×C4×Dic71C2311yescharacteristic
204C2×C4×Dic71C2311yescharacteristic
205C2×C4×Dic71C2312yes—
206C2×C4×Dic71C2318yes—
207C2×C4×Dic71C23116yes—
208C2×C4×Dic71C2314yes—
209C2×C4×Dic71C2314yes—
210C2×#41×C71—28no—
211C2×#41×C71—28no—
212C2×#41×C71C2318yes—
213C2×#41×C71C2318yes—
214C22×Q8×C71C2311yescharacteristic
215C22×Q8×C71C2311yescharacteristic
216C22×D4×C71C2311yescharacteristic
217C22×D4×C71C2312yes—
218C22×D4×C71C2312yes—
219C22×D4×C71C2311yescharacteristic
220C22×D4×C71C2314yes—
221C23×C4×C71C2312yes—
222C23×C4×C71C2312yes—
223C23×C4×C71C2312yes—
224C23×C4×C71C2311yescharacteristic
225C22⋊Q8×C71C23116yes—
226C22⋊Q8×C71C23116yes—
227#121×C71C23116yes—
228#121×C71C23116yes—
229#121×C71C23132yes—
230C2×C4⋊C4×C71C2312yes—
231C2×C4⋊C4×C71C2312yes—
232C2×C4⋊C4×C71C2318yes—
233C2×C4⋊C4×C71C2314yes—
234C2×C22⋊C4×C71C2314yes—
235C2×C22⋊C4×C71C2314yes—
236C23×D71C2412yes—
237#11765865—232no—
238#11765864—464no—
239C2×Dic142—24no—
240C2×Dic142—216no—
241C2×Dic142—432no—
242C2×Dic142—48no—
243C2×Dic142C24116yes—
244C2×Dic142C2414yes—
245C2×Dic142C24116yes—
246C2×D284—24no—
247C2×D284C2414yes—
248C2×C22⋊D71—28no—
249C2×C22⋊D71—28no—
250C2×C22⋊D71—28no—
251C2×C22⋊D71—48no—
252C2×C22⋊D71C2418yes—
253C2×C22⋊D71C2418yes—
254C2×C22⋊D71C2418yes—
255C2×C22⋊D71C24116yes—
256C22×Dic71—24no—
257C22×Dic71—28no—
258C22×Dic71—24no—
259C22×Dic71—28no—
260C22×Dic71—44no—
261C22×Dic71—48no—
262C22×Dic71C2412yes—
263C22×Dic71C2412yes—
264C22×Dic71C2414yes—
265C22×Dic71C2411yescharacteristic
266C22×Dic71C2414yes—
267C22×Dic71C2418yes—
268C22×Dic71C2412yes—
269C22×Dic71C2411yescharacteristic
270C22×Dic71C2414yes—
271C22×Dic71C2418yes—
272C22×Dic71C2418yes—
273C22×Dic71C24116yes—
274C22×Dic71C2411yescharacteristic
275C22×Dic71C2411yescharacteristic
276C2×C4×D71—28no—
277C2×C4×D71—48no—
278C2×C4×D71C2418yes—
279C2×C4×D71C24116yes—
280C4⋊Dic71C2414yes—
281C4⋊Dic71C2418yes—
282C4⋊Dic71C2418yes—
283C4⋊Dic71C24116yes—
284C4⋊Dic71C2414yes—
285C4⋊Dic71C2418yes—
286C4⋊Dic71C2418yes—
287Dic71⋊C4C24116yes—
288Dic71⋊C4C24116yes—
289Dic71⋊C4C24116yes—
290Dic71⋊C4C2418yes—
291Dic71⋊C4C2418yes—
292Dic71⋊C4C24116yes—
293C22⋊Dic71C24116yes—
294C22⋊Dic71C2418yes—
295C22⋊Dic71C24116yes—
296C22⋊Dic71C2418yes—
297C22⋊Dic71C2418yes—
298C22⋊Dic71C2418yes—
299C22⋊Dic71C2418yes—
300(C2×D71)⋊C4C24116yes—
301(C2×D71)⋊C4C24116yes—
302(C2×D71)⋊C4C2418yes—
303(C2×D71)⋊C4C2418yes—
304C4×Dic71C2414yes—
305C4×Dic71C2418yes—
306C4×Dic71C2414yes—
307C4×Dic71C2418yes—
308C4×Dic71C2414yes—
309C4×Dic71C2414yes—
310C4×Dic71C2418yes—
311C4×Dic71C24116yes—
312C4×Dic71C24116yes—
313C24×C71C2412yes—
314C24×C71C2412yes—
315C24×C71C2411yescharacteristic
316#41×C71—232no—
317#41×C71—232no—
318C2×Q8×C71—24no—
319C2×Q8×C71—24no—
320C2×Q8×C71C2414yes—
321C2×Q8×C71C2414yes—
322C2×D4×C71—28no—
323C2×D4×C71—28no—
324C2×D4×C71—24no—
325C2×D4×C71—24no—
326C2×D4×C71—48no—
327C2×D4×C71C2414yes—
328C2×D4×C71C2418yes—
329C2×D4×C71C2418yes—
330C2×D4×C71C2414yes—
331C2×D4×C71C24116yes—
332C22×C4×C71—28no—
333C22×C4×C71—28no—
334C22×C4×C71—44no—
335C22×C4×C71#4118yescomplemented
336C22×C4×C71C2414yes—
337C22×C4×C71C2412yes—
338C22×C4×C71C2412yes—
339C22×C4×C71C2418yes—
340C22×C4×C71C2418yes—
341C22×C4×C71C2418yes—
342C22×C4×C71C2411yescharacteristic
343C22×C4×C71C2411yescharacteristic
344C22×C4×C71C2414yes—
345C4⋊C4×C71C2418yes—
346C4⋊C4×C71C2418yes—
347C4⋊C4×C71C24116yes—
348C22⋊C4×C71C24116yes—
349C22⋊C4×C71C24116yes—
350C23×C71—22no—
351C23×C71—22no—
352C23×C71—24no—
353C23×C71—24no—
354C23×C71—24no—
355C23×C71—24no—
356C23×C71—24no—
357C23×C71—24no—
358C23×C71C2×#4114yes—
359C23×C71C2514yes—
360C23×C71C2514yes—
361C23×C71C2512yes—
362C23×C71C2511yescharacteristic
363C22×D71—24no—
364C22×D71—24no—
365C22×D71—24no—
366C22×D71C2514yes—
367Q8×C71—28no—
368Q8×C71—28no—
369D4×C71—216no—
370D4×C71—216no—
371D4×C71—28no—
372D4×C71—28no—
373D4×C71—416no—
374C2×C4×C71—24no—
375C2×C4×C71—24no—
376C2×C4×C71—28no—
377C2×C4×C71—216no—
378C2×C4×C71—216no—
379C2×C4×C71—48no—
380C2×C4×C71C2×#4114yes—
381C2×C4×C71C2×#4114yes—
382C2×C4×C71C2×#41116yescomplemented
383C2×C4×C71C2518yes—
384C2×C4×C71C2514yes—
385C2×C4×C71C2514yes—
386C2×C4×C71C2512yes—
387C2×C4×C71C2512yes—
388C22⋊D71—216no—
389C22⋊D71—216no—
390C22⋊D71—216no—
391C22⋊D71—416no—
392C2×Dic71—24no—
393C2×Dic71—24no—
394C2×Dic71—22no—
395C2×Dic71—28no—
396C2×Dic71—24no—
397C2×Dic71—22no—
398C2×Dic71—28no—
399C2×Dic71—216no—
400C2×Dic71—28no—
401C2×Dic71—216no—
402C2×Dic71—48no—
403C2×Dic71—416no—
404C2×Dic71H(5,𝔽2)14yes—
405C2×Dic712−1+414yes—
406C2×Dic71C2514yes—
407C2×Dic71C2512yes—
408C2×Dic71C2512yes—
409C2×Dic71C2514yes—
410C2×Dic71C2514yes—
411C2×Dic71C2518yes—
412C2×Dic71C2512yes—
413C2×Dic71C2512yes—
414D284—28no—
415C4×D71—216no—
416C4×D71—416no—
417Dic142—28no—
418Dic142—232no—
419Dic142—416no—
420C22×C71—22no—
421C22×C71—22no—
422C22×C71—28no—
423C22×C71—24no—
424C22×C71—24no—
425C22×C71—24no—
426C22×C71—24no—
427C22×C71—24no—
428C22×C71—24no—
429C22×C71—48no—
430C22×C71—48no—
431C22×C71C22×#4114yes—
432C22×C71C22×#4112yes—
433C22×C71C2×H(5,𝔽2)12yes—
434C22×C71C2×2−1+412yes—
435C22×C71C2611yescharacteristic
436C2×D71—24no—
437C2×D71—24no—
438C2×D71—24no—
439C2×D71—48no—
440C4×C71—24no—
441C4×C71—24no—
442C4×C71—28no—
443C4×C71C22×#4114yes—
444C4×C71C22×#4114yes—
445Dic71—24no—
446Dic71—28no—
447Dic71—22no—
448Dic71—24no—
449Dic71—24no—
450Dic71—22no—
451Dic71C2×H(5,𝔽2)14yes—
452Dic71C2×2−1+414yes—
453C2×#3511—711nomaximal, Sylow
454C2×C71—24no—
455C2×C71—44no—
456C2×C71—44no—
457C2×C71#351114yescomplemented
458C2×C71C23×#4111yescharacteristic
459C2×C71C22×H(5,𝔽2)11yescharacteristic
460C2×C71C22×2−1+411yescharacteristic
461D71—44no—
462#3511—7132no—
463C2×#556—712no—
464C2×#555—712no—
465C2×#554—712no—
466C2×#553—714no—
467C2×#548—714no—
468C2×#547—712no—
469C2×#542—712no—
470C2×#542—712no—
471C2×#537—711no—
472C2×#537D7111yescharacteristic, complemented
473C2×#533—712no—
474C2×#532—711no—
475C2×#532—712no—
476C22×C4⋊Q8—711no—
477C2×#520—711no—
478C2×#520—711no—
479C2×C4×#41—711no—
480C71C2×#351111yescharacteristic, complemented, Sylow
481C22×#41—714no—
482C22×#41—711no—
483C22×#41C2×D7111yescharacteristic
484C22×#41C2×D7111yescharacteristic
485C23×Q8—712no—
486#556—7132no—
487#555—7132no—
488#554—7132no—
489#553—7164no—
490#548—7164no—
491#547—7132no—
492#542—7132no—
493#542—7132no—
494#537—7116no—
495#537C2×D71116yescomplemented
496#533—7132no—
497#532—7116no—
498#532—7132no—
499C2×C4⋊Q8—711no—
500C2×C4⋊Q8—712no—
501C2×C4⋊Q8—712no—
502C2×C4⋊Q8—712no—
503C2×C4⋊Q8—712no—
504C2×C4⋊Q8—7116no—
505C2×#127—711no—
506C2×#126—714no—
507C2×#126—714no—
508C2×#125—714no—
509C2×#124—711no—
510C2×#124—711no—
511C2×#124—714no—
512C2×#124—714no—
513C2×#124—714no—
514C2×#123—714no—
515C2×#123—714no—
516C2×C22⋊Q8—712no—
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—712no—
524C2×#121—712no—
525C2×#121—714no—
526C2×#121—712no—
527C2×#121—714no—
528C2×#121—712no—
529C2×#121C2×D7112yes—
530C2×#121C2×D7112yes—
531C2×#121C2×D7114yes—
532#520—7116no—
533#520—7116no—
534C4×#41—7116no—
535C2×C4×Q8—711no—
536C2×C4×Q8—711no—
537C2×C4×Q8—712no—
538C2×C4×Q8—712no—
539C2×C4×Q8—714no—
540C2×C4×D4—711no—
541C2×C4×D4—712no—
542C2×C4×D4—712no—
543C2×C4×D4—711no—
544C2×C4×D4—712no—
545C2×C4×D4—714no—
546C2×C4×D4—714no—
547C2×C4×D4—712no—
548C2×C4×D4—712no—
549C2×C4×D4—712no—
550C2×C4×D4—714no—
551C2×#117—711no—
552C2×#117—712no—
553C2×#117—712no—
554C2×#117—712no—
555C2×#117—714no—
556C22×C4⋊C4—711no—
557C22×C4⋊C4—712no—
558C22×C4⋊C4—712no—
559C22×C4⋊C4—712no—
560C22×C4⋊C4C2×D7111yescharacteristic
561C22×C42—711no—
562C22×C42—712no—
563C2×#41—28no—
564C2×#41—28no—
565C2×#41—28416no—
566C2×#41—7132no—
567C2×#41—718no—
568C2×#41—1428no—
569C2×#41C22×D7118yes—
570C2×#41C22×D7118yes—
571C22×Q8—2848no—
572C22×Q8—714no—
573C22×Q8—7116no—
574C22×Q8—711no—
575C22×Q8—714no—
576C22×Q8C22×D7111yescharacteristic
577C22×Q8C22×D7111yescharacteristic
578C22×D4—714no—
579C22×D4—712no—
580C22×D4—712no—
581C22×D4—712no—
582C22×D4—711no—
583C22×D4C22×D7112yes—
584C22×D4C22×D7112yes—
585C22×D4C22×D7111yescharacteristic
586C22×D4C22×D7111yescharacteristic
587C22×D4C22×D7114yes—
588C23×C4—712no—
589C23×C4—714no—
590C23×C4—714no—
591C23×C4—711no—
592C23×C4—712no—
593C23×C4—711no—
594C23×C4—712no—
595C23×C4—712no—
596C23×C4C22×D7112yes—
597C23×C4C22×D7112yes—
598C23×C4C22×D7112yes—
599C23×C4C22×D7111yescharacteristic
600C4⋊Q8—718no—
601C4⋊Q8—7116no—
602C4⋊Q8—7116no—
603C4⋊Q8—7116no—
604C4⋊Q8—7116no—
605#127—718no—
606#126—7132no—
607#126—7132no—
608#125—7132no—
609#124—718no—
610#124—718no—
611#124—7132no—
612#124—7132no—
613#124—7132no—
614#123—7132no—
615#123—7132no—
616C22⋊Q8—7116no—
617C22⋊Q8—7116no—
618C22⋊Q8—7132no—
619C22⋊Q8—7132no—
620C22⋊Q8—7132no—
621C22⋊Q8C22×D71116yes—
622C22⋊Q8C22×D71116yes—
623#121—7116no—
624#121—7116no—
625#121—7132no—
626#121—7116no—
627#121—7132no—
628#121—7116no—
629#121C22×D71116yes—
630#121C22×D71116yes—
631#121C22×D71132yes—
632C4×Q8—718no—
633C4×Q8—718no—
634C4×Q8—7116no—
635C4×Q8—7116no—
636C4×Q8—7132no—
637C4×D4—718no—
638C4×D4—7116no—
639C4×D4—7116no—
640C4×D4—718no—
641C4×D4—7116no—
642C4×D4—7132no—
643C4×D4—7132no—
644C4×D4—7116no—
645C4×D4—7116no—
646C4×D4—7116no—
647C4×D4—7132no—
648#117—718no—
649#117—7116no—
650#117—7116no—
651#117—7116no—
652#117—7132no—
653C2×C4⋊C4—711no—
654C2×C4⋊C4—712no—
655C2×C4⋊C4—714no—
656C2×C4⋊C4—712no—
657C2×C4⋊C4—714no—
658C2×C4⋊C4—714no—
659C2×C4⋊C4—718no—
660C2×C4⋊C4—7116no—
661C2×C4⋊C4—714no—
662C2×C4⋊C4—7116no—
663C2×C4⋊C4—711no—
664C2×C4⋊C4—712no—
665C2×C4⋊C4—712no—
666C2×C4⋊C4—712no—
667C2×C4⋊C4—712no—
668C2×C4⋊C4—714no—
669C2×C4⋊C4—7116no—
670C2×C4⋊C4C22×D7112yes—
671C2×C4⋊C4C22×D7112yes—
672C2×C4⋊C4C22×D7118yes—
673C2×C4⋊C4C22×D7114yes—
674C2×C22⋊C4—712no—
675C2×C22⋊C4—714no—
676C2×C22⋊C4—712no—
677C2×C22⋊C4—712no—
678C2×C22⋊C4—714no—
679C2×C22⋊C4—712no—
680C2×C22⋊C4—712no—
681C2×C22⋊C4—714no—
682C2×C22⋊C4—714no—
683C2×C22⋊C4—712no—
684C2×C22⋊C4—712no—
685C2×C22⋊C4C22×D7114yes—
686C2×C22⋊C4C22×D7114yes—
687C2×C42—712no—
688C2×C42—714no—
689C2×C42—714no—
690C2×C42—711no—
691C2×C42—712no—
692C2×C42—711no—
693C2×C42—711no—
694C2×C42—712no—
695C2×C42—718no—
696C2×C42—7116no—
697C2×C42—711no—
698C24—712no—
699C24C23×D7112yes—
700C24C23×D7112yes—
701C24C23×D7111yescharacteristic
702#41—232no—
703#41—232no—
704#41—28464no—
705#41—14232no—
706C2×Q8—24no—
707C2×Q8—24no—
708C2×Q8—2848no—
709C2×Q8—28432no—
710C2×Q8—7116no—
711C2×Q8—714no—
712C2×Q8—7116no—
713C2×Q8—14216no—
714C2×Q8—1424no—
715C2×Q8C23×D7114yes—
716C2×Q8C23×D7114yes—
717C2×D4—28no—
718C2×D4—28no—
719C2×D4—24no—
720C2×D4—24no—
721C2×D4—48no—
722C2×D4—2848no—
723C2×D4—7116no—
724C2×D4—718no—
725C2×D4—718no—
726C2×D4—718no—
727C2×D4—714no—
728C2×D4—1428no—
729C2×D4—1428no—
730C2×D4—1428no—
731C2×D4—1424no—
732C2×D4C23×D7118yes—
733C2×D4C23×D7118yes—
734C2×D4C23×D7114yes—
735C2×D4C23×D7114yes—
736C2×D4C23×D71116yes—
737C22×C4—28no—
738C22×C4—28no—
739C22×C4—44no—
740C22×C4—2848no—
741C22×C4—2844no—
742C22×C4—2848no—
743C22×C4—718no—
744C22×C4—7116no—
745C22×C4—7116no—
746C22×C4—711no—
747C22×C4—711no—
748C22×C4—714no—
749C22×C4—718no—
750C22×C4—714no—
751C22×C4—718no—
752C22×C4—712no—
753C22×C4—711no—
754C22×C4—711no—
755C22×C4—712no—
756C22×C4—712no—
757C22×C4—714no—
758C22×C4—718no—
759C22×C4—1424no—
760C22×C4—1428no—
761C22×C4—1424no—
762C22×C4—1428no—
763C22×C4—1428no—
764C22×C4#1176586418yescomplemented
765C22×C4C23×D7118yes—
766C22×C4C23×D7118yes—
767C22×C4C23×D7112yes—
768C22×C4C23×D7112yes—
769C22×C4C23×D7114yes—
770C22×C4C23×D7118yes—
771C22×C4C23×D7111yescharacteristic
772C22×C4C23×D7111yescharacteristic
773C22×C4C23×D7114yes—
774C4⋊C4—7116no—
775C4⋊C4—7116no—
776C4⋊C4—7116no—
777C4⋊C4—718no—
778C4⋊C4—718no—
779C4⋊C4—7116no—
780C4⋊C4—714no—
781C4⋊C4—718no—
782C4⋊C4—718no—
783C4⋊C4—7116no—
784C4⋊C4—714no—
785C4⋊C4—718no—
786C4⋊C4—718no—
787C4⋊C4C23×D7118yes—
788C4⋊C4C23×D7118yes—
789C4⋊C4C23×D71116yes—
790C22⋊C4—718no—
791C22⋊C4—7116no—
792C22⋊C4—718no—
793C22⋊C4—718no—
794C22⋊C4—7116no—
795C22⋊C4—718no—
796C22⋊C4—718no—
797C22⋊C4—7116no—
798C22⋊C4—7116no—
799C22⋊C4—718no—
800C22⋊C4—718no—
801C22⋊C4C23×D71116yes—
802C22⋊C4C23×D71116yes—
803C42—714no—
804C42—718no—
805C42—714no—
806C42—718no—
807C42—714no—
808C42—714no—
809C42—718no—
810C42—7116no—
811C42—7116no—
812C23—22no—
813C23—22no—
814C23—24no—
815C23—24no—
816C23—24no—
817C23—24no—
818C23—24no—
819C23—24no—
820C23—714no—
821C23—1424no—
822C23—1424no—
823C23—1424no—
824C23C2×#1176586414yes—
825C23C24×D7114yes—
826C23C24×D7114yes—
827C23C24×D7112yes—
828C23C24×D7111yescharacteristic
829Q8—28no—
830Q8—28no—
831Q8—28416no—
832Q8—14232no—
833Q8—1428no—
834D4—216no—
835D4—216no—
836D4—28no—
837D4—28no—
838D4—416no—
839D4—28416no—
840D4—14216no—
841D4—14216no—
842D4—14216no—
843D4—1428no—
844C2×C4—24no—
845C2×C4—24no—
846C2×C4—28no—
847C2×C4—216no—
848C2×C4—216no—
849C2×C4—48no—
850C2×C4—28416no—
851C2×C4—2848no—
852C2×C4—28416no—
853C2×C4—714no—
854C2×C4—714no—
855C2×C4—712no—
856C2×C4—712no—
857C2×C4—714no—
858C2×C4—712no—
859C2×C4—712no—
860C2×C4—714no—
861C2×C4—714no—
862C2×C4—718no—
863C2×C4—1428no—
864C2×C4—14216no—
865C2×C4—1428no—
866C2×C4—14216no—
867C2×C4—1424no—
868C2×C4—1424no—
869C2×C4—1428no—
870C2×C4—1422no—
871C2×C4—1424no—
872C2×C4—1422no—
873C2×C4—14216no—
874C2×C4C2×#1176586414yes—
875C2×C4C2×#1176586414yes—
876C2×C4C2×#11765864116yescomplemented
877C2×C4C24×D7114yes—
878C2×C4C24×D7114yes—
879C2×C4C24×D7118yes—
880C2×C4C24×D7112yes—
881C2×C4C24×D7112yes—
882C22—28no—
883C22—22no—
884C22—22no—
885C22—24no—
886C22—24no—
887C22—24no—
888C22—24no—
889C22—24no—
890C22—24no—
891C22—48no—
892C22—48no—
893C22—2848no—
894C22—1424no—
895C22—1424no—
896C22—1424no—
897C22C22×#1176586414yes—
898C22C22×#1176586412yes—
899C22H(5,𝔽2)×D7112yes—
900C222−1+4×D7112yes—
901C22C25×D7111yescharacteristic
902C4—24no—
903C4—24no—
904C4—28no—
905C4—714no—
906C4—714no—
907C4—1424no—
908C4—1424no—
909C4—1428no—
910C4—1422no—
911C4—1424no—
912C4—1422no—
913C4C22×#1176586414yes—
914C4C22×#1176586414yes—
915C2—24no—
916C2—44no—
917C2—44no—
918C2—2844no—
919C2#2260224914yesdirect product factor
920C2C23×#1176586411yescharacteristic
921C2C2×H(5,𝔽2)×D7111yescharacteristic
922C2C2×2−1+4×D7111yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#537×C71C2
socleC23×C71C25
hypercenterC2×#537D71
hypocenterC71C2×#3511
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #22602249C2direct (N × H)
2. C2×#17986720C2semidirect
3. C2×#17986713C2semidirect
4. C2×#17986707C2semidirect
5. C2×#17986692C2semidirect
6. C2×#17986655C2semidirect
7. C2×#17986649C2semidirect
8. C2×#17986622C2semidirect
9. C2×#17986616C2semidirect
10. C2×#17986577C2semidirect
11. C2×#17986551C2semidirect
12. C2×#17986545C2semidirect
13. C2×#17986544C2semidirect
14. C22×#14556127C2semidirect
15. C2×#17986482C2semidirect
16. C2×#17986480C2semidirect
17. C2×#41×Dic71C2semidirect
18. C2×#537×C71C2semidirect
22. #17986720C22semidirect
23. #17986713C22semidirect
24. #17986707C22semidirect
25. #17986692C22semidirect
26. #17986655C22semidirect
27. #17986649C22semidirect
28. #17986622C22semidirect
29. #17986616C22semidirect
30. #17986577C22semidirect
31. #17986551C22semidirect
32. #17986545C22semidirect
33. #17986544C22semidirect
38. C2×#14556127C22semidirect
62. #17986482C22semidirect
63. #17986480C22semidirect
64. #41×Dic71C22semidirect
94. #537×C71C22semidirect
335. C22×C4×C71#41semidirect
382. C2×C4×C71C2×#41semidirect
457. C2×C71#3511semidirect
472. C2×#537D71semidirect
480. C71C2×#3511semidirect
495. #537C2×D71semidirect
764. C22×C4#11765864semidirect
876. C2×C4C2×#11765864semidirect
919. C2#22602249direct (N × H)

Maximal subgroups

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

subgroupindex
#226022492
C2×#179867202
C2×#179867132
C2×#179867072
C2×#179866922
C2×#179866552
C2×#179866492
C2×#179866222
C2×#179866162
C2×#179865772
C2×#179865512
C2×#179865452
C2×#179865442
C22×#145561272
C2×#179864822
C2×#179864802
C2×#41×Dic712
C2×#537×C712
C2×#351171