Finite Group Databasebeta

← C2×#22602006 #32905759

Subgroups — C2×#22602006 #32905759

Order 18176.

12366 conjugacy classes of subgroups.

The subgroup lattice has 864 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556174C211yesmaximal, characteristic, complemented
2C23×#11765866C211yesmaximal, characteristic, complemented
3#22602006C2132yesmaximal, direct product factor
4C2×#17986671C211yesmaximal, characteristic, complemented
5C2×#17986668C211yesmaximal, characteristic, complemented
6C2×#17986660C211yesmaximal, characteristic, complemented
7C2×#17986642C213yesmaximal, complemented
8C2×#17986640C213yesmaximal, complemented
9C2×D4×D284C213yesmaximal, complemented
10C2×#17986633C213yesmaximal, complemented
11C2×#17986579C213yesmaximal, complemented
12C2×#17986567C213yesmaximal, complemented
13C2×#17986508C213yesmaximal, complemented
14C2×#121×D71C213yesmaximal, complemented
15C2×#17986481C211yesmaximal, characteristic, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C2×#14556174—216no—
18C2×#14556174C22116yescomplemented
19C22×#11765866—216no—
20C22×#11765866C2211yescharacteristic
21C22×#11765866C2213yescomplemented
22C22×#11765866C2211yescharacteristic, complemented
23C22×#11765866C2211yescharacteristic, complemented
24C22×#11765866C2213yescomplemented
25C22×#11765866C22116yescomplemented
26C22×#11765865C2213yescomplemented
27C23×D284C2213yescomplemented
28C23×D284C2213yescomplemented
29C22×D4×D71C2213yescomplemented
30C22×D4×D71C2213yescomplemented
31C22×D4×D71C2216yescomplemented
32C23×C4×D71C2213yescomplemented
33#17986671C22116yescomplemented
34#17986668C22116yescomplemented
35#17986660C22116yescomplemented
36#17986642C22148yescomplemented
37#17986640C22148yescomplemented
38D4×D284C22148yescomplemented
39#17986633C22148yescomplemented
40#17986579C22148yescomplemented
41#17986567C22148yescomplemented
42C2×#14556125C2213yescomplemented
43C2×#14556124C2213yescomplemented
44C2×#14556117C2213yescomplemented
45#17986508C22148yescomplemented
46C2×#14556113C2213yescomplemented
47C2×#14556110C2213yescomplemented
48C2×#14556106C2213yescomplemented
49C2×#14556105C2211yescharacteristic, complemented
50C2×#14556104C2213yescomplemented
51C2×#14556103C2213yescomplemented
52C2×#14556103C2216yescomplemented
53C2×#14556103C2213yescomplemented
54C2×#14556102C2213yescomplemented
55C2×#14556102C2213yescomplemented
56C2×#14556101C2216yescomplemented
57C2×#14556101C2216yescomplemented
58C2×#14556101C2213yescomplemented
59C2×#14556100C2213yescomplemented
60C2×#14556099C2213yescomplemented
61#121×D71C22148yescomplemented
62C2×#14556098C2216yescomplemented
63C2×#14556098C2213yescomplemented
64C2×#14556098C2216yescomplemented
65C2×#14556096C2213yescomplemented
66#17986481C22116yescomplemented
67C2×Q8×Dic71C2211yescharacteristic, complemented
68C2×C4×D284C2213yescomplemented
69C2×C4×D284C2213yescomplemented
70C2×#14556090C2213yescomplemented
71C2×C4×C22⋊D71C2213yescomplemented
72C2×C4×C22⋊D71C2213yescomplemented
73C2×#14556085C2213yescomplemented
74C2×C4⋊C4×D71C2213yescomplemented
75C2×C22⋊C4×D71C2216yescomplemented
76C22×#41×C71C2211yescharacteristic, complemented
77C23×Q8×C71C2211yescharacteristic, complemented
78#548×C71C22116yescomplemented
79C2×#124×C71C2213yescomplemented
80C2×C22⋊Q8×C71C2213yescomplemented
81C2×#121×C71C2213yescomplemented
82C2×C4×Q8×C71C2211yescharacteristic, complemented
83C2×C4×D4×C71C2213yescomplemented
84C24×D71C2313yes—
85C24×D71C2316yes—
86#14556174—2128no—
87C2×#11765866—2128no—
88C2×#11765866—224no—
89C2×#11765866—224no—
90C2×#11765866—28no—
91C2×#11765866—28no—
92C2×#11765866D4116yescomplemented
93C2×#11765866C2318yes—
94C2×#11765866C23124yescomplemented
95C2×#11765866C23124yescomplemented
96C2×#11765866C2318yescomplemented
97C2×#11765866C2318yescomplemented
98C2×#11765865—224no—
99C2×#11765865C23124yescomplemented
100C22×Dic142C2311yescharacteristic
101C22×D284—224no—
102C22×D284—224no—
103C22×D284C2313yes—
104C22×D284C2313yes—
105C22×D284C2316yes—
106C22×D284C2313yes—
107C22×D284C2316yes—
108C22×D284C2313yes—
109C22×D284C2313yes—
110C22×D284C23124yescomplemented
111C22×D284C23124yescomplemented
112C22×C22⋊D71C2313yes—
113C22×C22⋊D71C2313yes—
114C22×C22⋊D71C2313yes—
115C22×C22⋊D71C2316yes—
116C22×C22⋊D71C2313yes—
117C2×D4×D71—224no—
118C2×D4×D71—224no—
119C2×D4×D71—424no—
120C2×D4×D71C23124yescomplemented
121C2×D4×D71C23124yescomplemented
122C2×D4×D71C23148yescomplemented
123C23×Dic71C2311yescharacteristic
124C22×C4×D71—224no—
125C22×C4×D71C2313yes—
126C22×C4×D71C2313yes—
127C22×C4×D71C2313yes—
128C22×C4×D71C2313yes—
129C22×C4×D71C2316yes—
130C22×C4×D71C2313yes—
131C22×C4×D71C23124yescomplemented
132#14556125C23124yescomplemented
133#14556124C23124yescomplemented
134#14556117C23124yescomplemented
135#14556113C23124yescomplemented
136#14556110C23124yescomplemented
137#14556106C23124yescomplemented
138#14556105C2318yescomplemented
139#14556104C23124yescomplemented
140#14556103C23124yescomplemented
141#14556103C23148yescomplemented
142#14556103C23124yescomplemented
143#14556102C23124yescomplemented
144#14556102C23124yescomplemented
145#14556101C23124yescomplemented
146#14556101C23148yescomplemented
147#14556101C23148yescomplemented
148#14556100C23124yescomplemented
149#14556099C23124yescomplemented
150#14556098C23148yescomplemented
151#14556098C23148yescomplemented
152#14556098C23124yescomplemented
153#14556096C23124yescomplemented
154Q8×Dic71C2318yescomplemented
155C4×D284C23124yescomplemented
156C4×D284C23124yescomplemented
157#14556090C23124yescomplemented
158C4×C22⋊D71C23124yescomplemented
159C4×C22⋊D71C23124yescomplemented
160#14556085C23124yescomplemented
161C2×C4⋊Dic71C2313yes—
162C2×C4⋊Dic71C2311yescharacteristic
163C2×Dic71⋊C4C2313yes—
164C2×Dic71⋊C4C2311yescharacteristic
165C2×Dic71⋊C4C2311yescharacteristic
166C2×Dic71⋊C4C2313yes—
167C4⋊C4×D71C23124yescomplemented
168C2×C22⋊Dic71C2313yes—
169C2×C22⋊Dic71C2311yescharacteristic
170C2×(C2×D71)⋊C4C2313yes—
171C2×(C2×D71)⋊C4C2316yes—
172C2×(C2×D71)⋊C4C2313yes—
173C2×(C2×D71)⋊C4C2313yes—
174C2×(C2×D71)⋊C4C2313yes—
175C2×(C2×D71)⋊C4C2313yes—
176C2×(C2×D71)⋊C4C2313yes—
177C22⋊C4×D71C23148yescomplemented
178C2×C4×Dic71C2313yes—
179C2×#41×C71—28no—
180C2×#41×C71C2318yescomplemented
181C22×Q8×C71—28no—
182C22×Q8×C71C2313yes—
183C22×Q8×C71C2311yescharacteristic
184C22×Q8×C71C2318yescomplemented
185C22×D4×C71C2313yes—
186C22×D4×C71C2313yes—
187C23×C4×C71C2313yes—
188C23×C4×C71C2313yes—
189#124×C71C23124yescomplemented
190C22⋊Q8×C71C23124yescomplemented
191#121×C71C23124yescomplemented
192C4×Q8×C71C2318yescomplemented
193C4×D4×C71C23124yescomplemented
194C2×C4⋊C4×C71C2313yes—
195C2×C4⋊C4×C71C2313yes—
196C2×C22⋊C4×C71C2311yescharacteristic
197C2×C22⋊C4×C71C2313yes—
198C2×C22⋊C4×C71C2316yes—
199C2×C42×C71C2313yes—
200C23×D71—212no—
201C23×D71—212no—
202C23×D71—224no—
203C23×D71—46no—
204C23×D71—412no—
205C23×D71—412no—
206C23×D71C2413yes—
207C23×D71C2413yes—
208C23×D71C24112yes—
209C23×D71C2413yes—
210C23×D71C24124yes—
211#11765866—232no—
212#11765866—232no—
213#11765866—296no—
214#11765866—296no—
215#11765866C2×D4164yescomplemented
216#11765865—296no—
217C2×Dic142—24no—
218C2×Dic142C2414yes—
219C2×D284—212no—
220C2×D284—224no—
221C2×D284—212no—
222C2×D284—212no—
223C2×D284—296no—
224C2×D284—296no—
225C2×D284—412no—
226C2×D284—46no—
227C2×D284C2×D4124yescomplemented
228C2×D284C24112yes—
229C2×D284C24112yes—
230C2×D284C24124yes—
231C2×D284C24112yes—
232C2×D284C24124yes—
233C2×D284C24112yes—
234C2×D284C24112yes—
235C2×C22⋊D71—212no—
236C2×C22⋊D71—212no—
237C2×C22⋊D71—212no—
238C2×C22⋊D71—412no—
239C2×C22⋊D71—46no—
240C2×C22⋊D71C24112yes—
241C2×C22⋊D71C24112yes—
242C2×C22⋊D71C24112yes—
243C2×C22⋊D71C24124yes—
244C2×C22⋊D71C24112yes—
245D4×D71—296no—
246D4×D71—296no—
247D4×D71—496no—
248C22×Dic71—24no—
249C22×Dic71C2411yescharacteristic
250C22×Dic71C2411yescharacteristic
251C22×Dic71C2413yes—
252C22×Dic71C2414yes—
253C22×Dic71C2411yescharacteristic
254C22×Dic71C2411yescharacteristic
255C2×C4×D71—212no—
256C2×C4×D71—212no—
257C2×C4×D71—212no—
258C2×C4×D71—212no—
259C2×C4×D71—296no—
260C2×C4×D71—412no—
261C2×C4×D71C2×D4124yescomplemented
262C2×C4×D71C24112yes—
263C2×C4×D71C24112yes—
264C2×C4×D71C24112yes—
265C2×C4×D71C24112yes—
266C2×C4×D71C24124yes—
267C2×C4×D71C24112yes—
268C4⋊Dic71C24112yes—
269C4⋊Dic71C2414yes—
270Dic71⋊C4C24112yes—
271Dic71⋊C4C2414yes—
272Dic71⋊C4C2414yes—
273Dic71⋊C4C24112yes—
274C22⋊Dic71C24112yes—
275C22⋊Dic71C2414yes—
276(C2×D71)⋊C4C24112yes—
277(C2×D71)⋊C4C24124yes—
278(C2×D71)⋊C4C24112yes—
279(C2×D71)⋊C4C24112yes—
280(C2×D71)⋊C4C24112yes—
281(C2×D71)⋊C4C24112yes—
282(C2×D71)⋊C4C24112yes—
283C4×Dic71C24112yes—
284C24×C71C2413yes—
285C24×C71C2411yescharacteristic
286#41×C71—232no—
287C2×Q8×C71—232no—
288C2×Q8×C71—212no—
289C2×Q8×C71C2×D418yescomplemented
290C2×Q8×C71C24112yes—
291C2×Q8×C71C2414yes—
292C2×D4×C71—212no—
293C2×D4×C71—212no—
294C2×D4×C71C24112yes—
295C2×D4×C71C24112yes—
296C22×C4×C71—212no—
297C22×C4×C71—212no—
298C22×C4×C71C2413yes—
299C22×C4×C71C2413yes—
300C22×C4×C71C24112yes—
301C22×C4×C71C2411yescharacteristic
302C22×C4×C71C2411yescharacteristic
303C22×C4×C71C24112yes—
304C22×C4×C71C2413yes—
305C4⋊C4×C71C24112yes—
306C4⋊C4×C71C24112yes—
307C22⋊C4×C71C2414yes—
308C22⋊C4×C71C24112yes—
309C22⋊C4×C71C24124yes—
310C42×C71C24112yes—
311C23×C71—22no—
312C23×C71—22no—
313C23×C71—26no—
314C23×C71—26no—
315C23×C71—26no—
316C23×C71H(5,𝔽2)14yescomplemented
317C23×C71C2516yes—
318C23×C71C2512yes—
319C23×C71C2511yescharacteristic
320C22×D71—26no—
321C22×D71—26no—
322C22×D71—26no—
323C22×D71—26no—
324C22×D71—26no—
325C22×D71—26no—
326C22×D71—224no—
327C22×D71—26no—
328C22×D71—26no—
329C22×D71—224no—
330C22×D71—248no—
331C22×D71—412no—
332C22×D71—424no—
333C22×D71—424no—
334C22×D71—448no—
335C22×D71—848no—
336C22×D71C22×D4112yes—
337C22×D71C2516yes—
338C22×D71C2516yes—
339C22×D71C2516yes—
340Q8×C71—224no—
341Q8×C71C22×D4116yescomplemented
342D4×C71—224no—
343D4×C71—224no—
344C2×C4×C71—22no—
345C2×C4×C71—26no—
346C2×C4×C71—26no—
347C2×C4×C71—22no—
348C2×C4×C71—224no—
349C2×C4×C71—224no—
350C2×C4×C71C22×D4112yes—
351C2×C4×C71C2512yes—
352C2×C4×C71C2516yes—
353C2×C4×C71C2516yes—
354C2×C4×C71C2512yes—
355C2×C4×C71C2516yes—
356C22⋊D71—224no—
357C22⋊D71—224no—
358C22⋊D71—224no—
359C22⋊D71—424no—
360C22⋊D71—412no—
361C2×Dic71—22no—
362C2×Dic71—22no—
363C2×Dic71—26no—
364C2×Dic71—22no—
365C2×Dic71—28no—
366C2×Dic71C22×D414yes—
367C2×Dic71C2512yes—
368C2×Dic71C2516yes—
369C2×Dic71C2512yes—
370C2×Dic71C2512yes—
371C2×Dic71C2512yes—
372D284—224no—
373D284—248no—
374D284—224no—
375D284—224no—
376D284—424no—
377D284—412no—
378D284C22×D4148yescomplemented
379C4×D71—224no—
380C4×D71—224no—
381C4×D71—224no—
382C4×D71—224no—
383C4×D71—424no—
384C4×D71C22×D4148yescomplemented
385Dic142—28no—
386C22×C71—22no—
387C22×C71—22no—
388C22×C71—28no—
389C22×C71—26no—
390C22×C71—26no—
391C22×C71—26no—
392C22×C71—412no—
393C22×C71C23×D412yes—
394C22×C71C2×H(5,𝔽2)12yes—
395C22×C71C2×H(5,𝔽2)14yescomplemented
396C22×C71#58512yes—
397C22×C71C2611yescharacteristic
398C2×D71—26no—
399C2×D71—26no—
400C2×D71—224no—
401C2×D71—26no—
402C2×D71—26no—
403C2×D71—26no—
404C2×D71—26no—
405C2×D71—26no—
406C2×D71—26no—
407C2×D71—448no—
408C2×D71—412no—
409C2×D71—412no—
410C2×D71—848no—
411C2×D71C23×D4112yes—
412C4×C71—22no—
413C4×C71—26no—
414C4×C71—26no—
415C4×C71—22no—
416C4×C71C23×D4112yes—
417Dic71—22no—
418Dic71—22no—
419Dic71—26no—
420Dic71—22no—
421Dic71C23×D414yes—
422C2×#3488—711nomaximal, Sylow
423C2×C71—24no—
424C2×C71—46no—
425C2×C71#348814yescomplemented
426C2×C71C24×D411yescharacteristic
427C2×C71C22×H(5,𝔽2)11yescharacteristic
428C2×C71C2×#58511yescharacteristic
429D71—212no—
430D71—46no—
431D71—46no—
432C22×H(5,𝔽2)—711no—
433C23×#41—711no—
434#3488—7132no—
435C2×#550—711no—
436C2×#550—711no—
437C2×#548—711no—
438C2×#548D7111yescharacteristic, complemented
439C2×#546—713no—
440C2×#546—713no—
441C2×D42—713no—
442C2×D42—713no—
443C2×#537—713no—
444C2×#535—713no—
445C2×#525—713no—
446C22×#121—713no—
447C2×#520—711no—
448C71C2×#348811yescharacteristic, complemented, Sylow
449C2×H(5,𝔽2)—7116no—
450C2×H(5,𝔽2)—14216no—
451C22×#41—711no—
452C22×#41—713no—
453C22×#41—713no—
454C22×#41—711no—
455C22×#41—711no—
456C22×#41—7116no—
457C22×#41—713no—
458C22×#41—14216no—
459C22×#41C2×D7111yescharacteristic, complemented
460C23×Q8C2×D7111yescharacteristic, complemented
461C23×D4—716no—
462C23×D4—713no—
463C23×D4—713no—
464C23×D4—713no—
465C23×D4—713no—
466C24×C4—713no—
467#550—7116no—
468#550—7116no—
469#548—7116no—
470#548C2×D71116yescomplemented
471#546—7148no—
472#546—7148no—
473D42—7148no—
474D42—7148no—
475#537—7148no—
476#535—7148no—
477C2×#127—713no—
478C2×#127—713no—
479C2×#124—713no—
480C2×#124C2×D7113yescomplemented
481#525—7148no—
482C2×#123—713no—
483C2×#123—713no—
484C2×C22⋊Q8—713no—
485C2×C22⋊Q8—713no—
486C2×C22⋊Q8—711no—
487C2×C22⋊Q8C2×D7113yescomplemented
488C2×#121—713no—
489C2×#121—713no—
490C2×#121—713no—
491C2×#121—713no—
492C2×#121—7148no—
493C2×#121—713no—
494C2×#121—716no—
495C2×#121—713no—
496C2×#121—716no—
497C2×#121—713no—
498C2×#121—716no—
499C2×#121C2×D7113yescomplemented
500C2×#120—713no—
501C2×#120—713no—
502C2×#120—716no—
503C2×#120—716no—
504#520—7116no—
505C2×C4×Q8—711no—
506C2×C4×Q8C2×D7111yescharacteristic, complemented
507C2×C4×D4—713no—
508C2×C4×D4—713no—
509C2×C4×D4—713no—
510C2×C4×D4—713no—
511C2×C4×D4—713no—
512C2×C4×D4C2×D7113yescomplemented
513C2×#117—713no—
514C22×C4⋊C4—713no—
515C22×C22⋊C4—716no—
516C25—716no—
517C25—713no—
518H(5,𝔽2)—142128no—
519C2×#41—28no—
520C2×#41—7116no—
521C2×#41—718no—
522C2×#41—7124no—
523C2×#41—7124no—
524C2×#41—718no—
525C2×#41—718no—
526C2×#41—7124no—
527C2×#41—14224no—
528C2×#41—14224no—
529C2×#41—14224no—
530C2×#41—142128no—
531C2×#41—1428no—
532C2×#41—1428no—
533C2×#41C22×D7118yescomplemented
534C22×Q8—28no—
535C22×Q8—711no—
536C22×Q8C22×D7113yes—
537C22×Q8C22×D7111yescharacteristic
538C22×Q8C22×D7118yescomplemented
539C22×D4—28424no—
540C22×D4—713no—
541C22×D4—716no—
542C22×D4—7148no—
543C22×D4—713no—
544C22×D4—713no—
545C22×D4—713no—
546C22×D4—7124no—
547C22×D4—7124no—
548C22×D4—713no—
549C22×D4—716no—
550C22×D4—713no—
551C22×D4—716no—
552C22×D4—713no—
553C22×D4—713no—
554C22×D4—713no—
555C22×D4—7124no—
556C22×D4—7124no—
557C22×D4—14224no—
558C22×D4—14224no—
559C22×D4—14224no—
560C22×D4—14224no—
561C22×D4C22×D7113yes—
562C22×D4C22×D7113yes—
563C23×C4—716no—
564C23×C4—713no—
565C23×C4—711no—
566C23×C4—713no—
567C23×C4—713no—
568C23×C4—713no—
569C23×C4—713no—
570C23×C4—7124no—
571C23×C4—14224no—
572C23×C4C22×D7113yes—
573C23×C4C22×D7113yes—
574#127—7124no—
575#127—7124no—
576#124—7124no—
577#124C22×D71124yescomplemented
578#123—7124no—
579#123—7124no—
580C22⋊Q8—7124no—
581C22⋊Q8—7124no—
582C22⋊Q8—718no—
583C22⋊Q8C22×D71124yescomplemented
584#121—7124no—
585#121—7124no—
586#121—7124no—
587#121—7124no—
588#121—7124no—
589#121—7148no—
590#121—7124no—
591#121—7148no—
592#121—7124no—
593#121—7148no—
594#121C22×D71124yescomplemented
595#120—7124no—
596#120—7124no—
597#120—7148no—
598#120—7148no—
599C4×Q8—718no—
600C4×Q8C22×D7118yescomplemented
601C4×D4—7124no—
602C4×D4—7124no—
603C4×D4—7124no—
604C4×D4—7124no—
605C4×D4—7124no—
606C4×D4C22×D71124yescomplemented
607#117—7124no—
608C2×C4⋊C4—713no—
609C2×C4⋊C4—713no—
610C2×C4⋊C4—711no—
611C2×C4⋊C4—711no—
612C2×C4⋊C4—711no—
613C2×C4⋊C4—713no—
614C2×C4⋊C4—7124no—
615C2×C4⋊C4C22×D7113yes—
616C2×C4⋊C4C22×D7113yes—
617C2×C22⋊C4—713no—
618C2×C22⋊C4—711no—
619C2×C22⋊C4—713no—
620C2×C22⋊C4—716no—
621C2×C22⋊C4—713no—
622C2×C22⋊C4—713no—
623C2×C22⋊C4—713no—
624C2×C22⋊C4—713no—
625C2×C22⋊C4—713no—
626C2×C22⋊C4—7148no—
627C2×C22⋊C4C22×D7116yes—
628C2×C22⋊C4C22×D7111yescharacteristic
629C2×C22⋊C4C22×D7113yes—
630C2×C42—713no—
631C2×C42C22×D7113yes—
632C24—2846no—
633C24—28412no—
634C24—28412no—
635C24—7124no—
636C24—7112no—
637C24—713no—
638C24—713no—
639C24—713no—
640C24—14212no—
641C24—14224no—
642C24—14212no—
643C24C23×D7113yes—
644C24C23×D7111yescharacteristic
645#41—232no—
646#41—7164no—
647#41—14296no—
648#41—14296no—
649#41—14296no—
650#41—14232no—
651#41—14232no—
652C2×Q8—232no—
653C2×Q8—212no—
654C2×Q8—714no—
655C2×Q8—1424no—
656C2×Q8D4×D7118yescomplemented
657C2×Q8C23×D71112yes—
658C2×Q8C23×D7114yes—
659C2×D4—212no—
660C2×D4—212no—
661C2×D4—28412no—
662C2×D4—2846no—
663C2×D4—28496no—
664C2×D4—28412no—
665C2×D4—2846no—
666C2×D4—7112no—
667C2×D4—7124no—
668C2×D4—7112no—
669C2×D4—7112no—
670C2×D4—7112no—
671C2×D4—7124no—
672C2×D4—7112no—
673C2×D4—7124no—
674C2×D4—7112no—
675C2×D4—7124no—
676C2×D4—7112no—
677C2×D4—7112no—
678C2×D4—7112no—
679C2×D4—14296no—
680C2×D4—14296no—
681C2×D4—14212no—
682C2×D4—14224no—
683C2×D4—14296no—
684C2×D4—14212no—
685C2×D4—14296no—
686C2×D4—14212no—
687C2×D4—14212no—
688C2×D4—14212no—
689C2×D4—14212no—
690C2×D4C23×D71112yes—
691C2×D4C23×D71112yes—
692C22×C4—212no—
693C22×C4—212no—
694C22×C4—28412no—
695C22×C4—7124no—
696C22×C4—711no—
697C22×C4—7124no—
698C22×C4—7112no—
699C22×C4—714no—
700C22×C4—711no—
701C22×C4—713no—
702C22×C4—711no—
703C22×C4—711no—
704C22×C4—7112no—
705C22×C4—7112no—
706C22×C4—7112no—
707C22×C4—7112no—
708C22×C4—14212no—
709C22×C4—14296no—
710C22×C4—14212no—
711C22×C4—1424no—
712C22×C4—14212no—
713C22×C4—14212no—
714C22×C4C23×D71112yes—
715C22×C4C23×D71112yes—
716C22×C4C23×D7111yescharacteristic
717C22×C4C23×D7113yes—
718C22×C4C23×D7113yes—
719C22×C4C23×D7111yescharacteristic
720C22×C4C23×D7113yes—
721C4⋊C4—7112no—
722C4⋊C4—714no—
723C4⋊C4—714no—
724C4⋊C4—7112no—
725C4⋊C4—7112no—
726C4⋊C4—714no—
727C4⋊C4C23×D71112yes—
728C4⋊C4C23×D71112yes—
729C22⋊C4—7112no—
730C22⋊C4—714no—
731C22⋊C4—7112no—
732C22⋊C4—7124no—
733C22⋊C4—7112no—
734C22⋊C4—7112no—
735C22⋊C4—7112no—
736C22⋊C4—7112no—
737C22⋊C4—7112no—
738C22⋊C4C23×D71124yes—
739C22⋊C4C23×D7114yes—
740C22⋊C4C23×D71112yes—
741C42—7112no—
742C42C23×D71112yes—
743C23—22no—
744C23—22no—
745C23—26no—
746C23—26no—
747C23—26no—
748C23—28448no—
749C23—28412no—
750C23—28424no—
751C23—28424no—
752C23—56848no—
753C23—7112no—
754C23—716no—
755C23—716no—
756C23—716no—
757C23—14224no—
758C23—14248no—
759C23—1426no—
760C23—1426no—
761C23—1426no—
762C23—1426no—
763C23—14224no—
764C23—1426no—
765C23—1426no—
766C23—1426no—
767C23—1426no—
768C23#1455617414yescomplemented
769C23C24×D7116yes—
770C23C24×D7112yes—
771C23C24×D7111yescharacteristic
772Q8—224no—
773Q8—1428no—
774Q8C2×D4×D71116yescomplemented
775D4—224no—
776D4—224no—
777D4—28424no—
778D4—28412no—
779D4—28424no—
780D4—28412no—
781D4—7148no—
782D4—14224no—
783D4—14248no—
784D4—14224no—
785D4—14224no—
786D4—14224no—
787D4—14224no—
788D4—14224no—
789C2×C4—22no—
790C2×C4—26no—
791C2×C4—26no—
792C2×C4—22no—
793C2×C4—224no—
794C2×C4—224no—
795C2×C4—28424no—
796C2×C4—714no—
797C2×C4—712no—
798C2×C4—7148no—
799C2×C4—712no—
800C2×C4—716no—
801C2×C4—712no—
802C2×C4—712no—
803C2×C4—14224no—
804C2×C4—14224no—
805C2×C4—1428no—
806C2×C4—1422no—
807C2×C4—1422no—
808C2×C4—1426no—
809C2×C4—1422no—
810C2×C4—14224no—
811C2×C4—14224no—
812C2×C4C2×D4×D71112yes—
813C2×C4C24×D7112yes—
814C2×C4C24×D7116yes—
815C2×C4C24×D7116yes—
816C2×C4C24×D7112yes—
817C2×C4C24×D7116yes—
818C22—28no—
819C22—22no—
820C22—22no—
821C22—26no—
822C22—26no—
823C22—26no—
824C22—412no—
825C22—28448no—
826C22—28412no—
827C22—28412no—
828C22—56848no—
829C22—7112no—
830C22—1426no—
831C22—1426no—
832C22—1426no—
833C22—1426no—
834C22—1426no—
835C22—1426no—
836C22—14224no—
837C22—1426no—
838C22—1426no—
839C22C22×D4×D7112yes—
840C22C2×#1455617412yes—
841C22C2×#1455617414yescomplemented
842C22#1798683612yes—
843C22C25×D7111yescharacteristic
844C4—22no—
845C4—26no—
846C4—26no—
847C4—22no—
848C4—714no—
849C4—1422no—
850C4—1422no—
851C4—1426no—
852C4—1422no—
853C4C22×D4×D71112yes—
854C2—24no—
855C2—46no—
856C2—2846no—
857C2—2846no—
858C2—14212no—
859C2#2260200614yesdirect product factor
860C2C23×D4×D7111yescharacteristic
861C2C22×#1455617411yescharacteristic
862C2C2×#1798683611yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#548×C71C2
socleC23×C71C25
hypercenterC2×#548D71
hypocenterC71C2×#3488
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#14556174C2semidirect
2. C23×#11765866C2semidirect
3. #22602006C2direct (N × H)
4. C2×#17986671C2semidirect
5. C2×#17986668C2semidirect
6. C2×#17986660C2semidirect
7. C2×#17986642C2semidirect
8. C2×#17986640C2semidirect
9. C2×D4×D284C2semidirect
10. C2×#17986633C2semidirect
11. C2×#17986579C2semidirect
12. C2×#17986567C2semidirect
13. C2×#17986508C2semidirect
14. C2×#121×D71C2semidirect
15. C2×#17986481C2semidirect
16. C2×#548×C71C2semidirect
18. C2×#14556174C22semidirect
21. C22×#11765866C22semidirect
22. C22×#11765866C22semidirect
23. C22×#11765866C22semidirect
24. C22×#11765866C22semidirect
25. C22×#11765866C22semidirect
26. C22×#11765865C22semidirect
27. C23×D284C22semidirect
28. C23×D284C22semidirect
29. C22×D4×D71C22semidirect
30. C22×D4×D71C22semidirect
31. C22×D4×D71C22semidirect
32. C23×C4×D71C22semidirect
33. #17986671C22semidirect
34. #17986668C22semidirect
35. #17986660C22semidirect
36. #17986642C22semidirect
37. #17986640C22semidirect
38. D4×D284C22semidirect
39. #17986633C22semidirect
40. #17986579C22semidirect
41. #17986567C22semidirect
42. C2×#14556125C22semidirect
43. C2×#14556124C22semidirect
44. C2×#14556117C22semidirect
45. #17986508C22semidirect
46. C2×#14556113C22semidirect
47. C2×#14556110C22semidirect
48. C2×#14556106C22semidirect
49. C2×#14556105C22semidirect
50. C2×#14556104C22semidirect
51. C2×#14556103C22semidirect
52. C2×#14556103C22semidirect
53. C2×#14556103C22semidirect
54. C2×#14556102C22semidirect
55. C2×#14556102C22semidirect
56. C2×#14556101C22semidirect
57. C2×#14556101C22semidirect
58. C2×#14556101C22semidirect
59. C2×#14556100C22semidirect
60. C2×#14556099C22semidirect
61. #121×D71C22semidirect
62. C2×#14556098C22semidirect
63. C2×#14556098C22semidirect
64. C2×#14556098C22semidirect
65. C2×#14556096C22semidirect
66. #17986481C22semidirect
67. C2×Q8×Dic71C22semidirect
68. C2×C4×D284C22semidirect
69. C2×C4×D284C22semidirect
70. C2×#14556090C22semidirect
71. C2×C4×C22⋊D71C22semidirect
72. C2×C4×C22⋊D71C22semidirect
73. C2×#14556085C22semidirect
74. C2×C4⋊C4×D71C22semidirect
75. C2×C22⋊C4×D71C22semidirect
76. C22×#41×C71C22semidirect
77. C23×Q8×C71C22semidirect
78. #548×C71C22semidirect
79. C2×#124×C71C22semidirect
80. C2×C22⋊Q8×C71C22semidirect
81. C2×#121×C71C22semidirect
82. C2×C4×Q8×C71C22semidirect
83. C2×C4×D4×C71C22semidirect
92. C2×#11765866D4semidirect
94. C2×#11765866C23semidirect
95. C2×#11765866C23semidirect
96. C2×#11765866C23semidirect
97. C2×#11765866C23semidirect
99. C2×#11765865C23semidirect
110. C22×D284C23semidirect
111. C22×D284C23semidirect
120. C2×D4×D71C23semidirect
121. C2×D4×D71C23semidirect
122. C2×D4×D71C23semidirect
131. C22×C4×D71C23semidirect
132. #14556125C23semidirect
133. #14556124C23semidirect
134. #14556117C23semidirect
135. #14556113C23semidirect
136. #14556110C23semidirect
137. #14556106C23semidirect
138. #14556105C23semidirect
139. #14556104C23semidirect
140. #14556103C23semidirect
141. #14556103C23semidirect
142. #14556103C23semidirect
143. #14556102C23semidirect
144. #14556102C23semidirect
145. #14556101C23semidirect
146. #14556101C23semidirect
147. #14556101C23semidirect
148. #14556100C23semidirect
149. #14556099C23semidirect
150. #14556098C23semidirect
151. #14556098C23semidirect
152. #14556098C23semidirect
153. #14556096C23semidirect
154. Q8×Dic71C23semidirect
155. C4×D284C23semidirect
156. C4×D284C23semidirect
157. #14556090C23semidirect
158. C4×C22⋊D71C23semidirect
159. C4×C22⋊D71C23semidirect
160. #14556085C23semidirect
167. C4⋊C4×D71C23semidirect
177. C22⋊C4×D71C23semidirect
180. C2×#41×C71C23semidirect
184. C22×Q8×C71C23semidirect
189. #124×C71C23semidirect
190. C22⋊Q8×C71C23semidirect
191. #121×C71C23semidirect
192. C4×Q8×C71C23semidirect
193. C4×D4×C71C23semidirect
215. #11765866C2×D4semidirect
227. C2×D284C2×D4semidirect
261. C2×C4×D71C2×D4semidirect
289. C2×Q8×C71C2×D4semidirect
316. C23×C71H(5,𝔽2)semidirect
341. Q8×C71C22×D4semidirect
378. D284C22×D4semidirect
384. C4×D71C22×D4semidirect
395. C22×C71C2×H(5,𝔽2)semidirect
425. C2×C71#3488semidirect
438. C2×#548D71semidirect
448. C71C2×#3488semidirect
459. C22×#41C2×D71semidirect
460. C23×Q8C2×D71semidirect
470. #548C2×D71semidirect
480. C2×#124C2×D71semidirect
487. C2×C22⋊Q8C2×D71semidirect
499. C2×#121C2×D71semidirect
506. C2×C4×Q8C2×D71semidirect
512. C2×C4×D4C2×D71semidirect
533. C2×#41C22×D71semidirect
538. C22×Q8C22×D71semidirect
577. #124C22×D71semidirect
583. C22⋊Q8C22×D71semidirect
594. #121C22×D71semidirect
600. C4×Q8C22×D71semidirect
606. C4×D4C22×D71semidirect
656. C2×Q8D4×D71semidirect
768. C23#14556174semidirect
774. Q8C2×D4×D71semidirect
841. C22C2×#14556174semidirect
859. C2#22602006direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#145561742
C23×#117658662
#226020062
C2×#179866712
C2×#179866682
C2×#179866602
C2×#179866422
C2×#179866402
C2×D4×D2842
C2×#179866332
C2×#179865792
C2×#179865672
C2×#179865082
C2×#121×D712
C2×#179864812
C2×#548×C712
C2×#348871