Finite Group Databasebeta

← C2×#548×D71 #32904382

Subgroups — C2×#548×D71 #32904382

Order 18176.

12142 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×#41×D71C211yesmaximal, characteristic, complemented
2C23×Q8×D71C211yesmaximal, characteristic, complemented
3C2×#17986661C211yesmaximal, characteristic, complemented
4C2×#17986660C211yesmaximal, characteristic, complemented
5C2×#17986659C213yesmaximal, complemented
6C2×#17986658C213yesmaximal, complemented
7C2×#17986657C213yesmaximal, complemented
8C2×#17986656C211yesmaximal, characteristic, complemented
9C2×#17986655C213yesmaximal, complemented
10#548×D71C2132yesmaximal, direct product factor
11C2×#124×D71C213yesmaximal, complemented
12C2×C22⋊Q8×D71C213yesmaximal, complemented
13C2×#121×D71C213yesmaximal, complemented
14C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
15C2×C4×D4×D71C213yesmaximal, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C22×#11765866C2211yescharacteristic, complemented
18C22×#11765865C2213yescomplemented
19C22×#11765864C2213yescomplemented
20C2×#41×D71—216no—
21C2×#41×D71C22116yescomplemented
22C23×Dic142C2213yescomplemented
23C22×Q8×D71—216no—
24C22×Q8×D71C2213yes—
25C22×Q8×D71C2211yescharacteristic
26C22×Q8×D71C22116yescomplemented
27C22×Q8×D71C2211yescharacteristic, complemented
28C22×Q8×D71C2213yescomplemented
29C22×D4×D71C2213yes—
30C22×D4×D71C2213yes—
31C23×C4×D71C2213yes—
32C23×C4×D71C2213yes—
33#17986661C22116yescomplemented
34#17986660C22116yescomplemented
35#17986659C22148yescomplemented
36#17986658C22148yescomplemented
37#17986657C22148yescomplemented
38#17986656C22116yescomplemented
39#17986655C22148yescomplemented
40C2×#14556117C2213yescomplemented
41C2×#14556116C2213yescomplemented
42C2×#14556115C2213yescomplemented
43C2×#14556114C2216yescomplemented
44C2×#14556114C2216yescomplemented
45#124×D71C22148yescomplemented
46C2×#14556108C2213yescomplemented
47C2×#14556107C2213yescomplemented
48C2×#14556106C2216yescomplemented
49C2×#14556105C2216yescomplemented
50C2×#14556104C2213yescomplemented
51C22⋊Q8×D71C22148yescomplemented
52C2×#14556103C2213yescomplemented
53C2×#14556102C2213yescomplemented
54C2×#14556101C2216yescomplemented
55C2×#14556100C2216yescomplemented
56C2×#14556099C2213yescomplemented
57#121×D71C22148yescomplemented
58C2×Q8×Dic71C2211yescharacteristic, complemented
59C2×C4×Dic142C2213yescomplemented
60C2×#14556093C2213yescomplemented
61C4×Q8×D71C22116yescomplemented
62C2×C4×D284C2213yescomplemented
63C2×D4×Dic71C2213yescomplemented
64C2×#14556090C2213yescomplemented
65C2×C4×C22⋊D71C2213yescomplemented
66C2×C4×C22⋊D71C2213yescomplemented
67C2×(C22⋊D71)⋊C4C2213yescomplemented
68C2×(C22⋊D71)⋊C4C2213yescomplemented
69C4×D4×D71C22148yescomplemented
70C2×C4⋊C4×D71C2213yes—
71C2×C4⋊C4×D71C2213yes—
72C2×C22⋊C4×D71C2211yescharacteristic
73C2×C22⋊C4×D71C2213yes—
74C2×C22⋊C4×D71C2216yes—
75C2×C42×D71C2213yes—
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×D71C2311yescharacteristic
86C2×#11765866—28no—
87C2×#11765866C2318yescomplemented
88C2×#11765865—224no—
89C2×#11765865C23124yescomplemented
90C2×#11765864—224no—
91C2×#11765864C23124yescomplemented
92#41×D71—2128no—
93C22×Dic142—224no—
94C22×Dic142C2316yes—
95C22×Dic142C2313yes—
96C22×Dic142C2313yes—
97C22×Dic142C23124yescomplemented
98C2×Q8×D71—224no—
99C2×Q8×D71—2128no—
100C2×Q8×D71—224no—
101C2×Q8×D71—28no—
102C2×Q8×D71D4116yescomplemented
103C2×Q8×D71C23124yes—
104C2×Q8×D71C2318yes—
105C2×Q8×D71C2318yescomplemented
106C2×Q8×D71C23124yescomplemented
107C22×D284C2313yes—
108C22×D284C2313yes—
109C22×C22⋊D71C2316yes—
110C22×C22⋊D71C2313yes—
111C22×C22⋊D71C2313yes—
112C2×D4×D71—224no—
113C2×D4×D71—224no—
114C2×D4×D71C23124yes—
115C2×D4×D71C23124yes—
116C23×Dic71C2313yes—
117C23×Dic71C2313yes—
118C22×C4×D71—224no—
119C22×C4×D71—224no—
120C22×C4×D71C2311yescharacteristic
121C22×C4×D71C2313yes—
122C22×C4×D71C23124yes—
123C22×C4×D71C2313yes—
124C22×C4×D71C2313yes—
125C22×C4×D71C23124yes—
126C22×C4×D71C2313yes—
127C22×C4×D71C2313yes—
128C22×C4×D71C2313yes—
129C22×C4×D71C2311yescharacteristic
130C22×C4×D71C2313yes—
131#14556117C23124yescomplemented
132#14556116C23124yescomplemented
133#14556115C23124yescomplemented
134#14556114C23148yescomplemented
135#14556114C23148yescomplemented
136#14556108C23124yescomplemented
137#14556107C23124yescomplemented
138#14556106C23148yescomplemented
139#14556105C23148yescomplemented
140#14556104C23124yescomplemented
141#14556103C23124yescomplemented
142#14556102C23124yescomplemented
143#14556101C23148yescomplemented
144#14556100C23148yescomplemented
145#14556099C23124yescomplemented
146Q8×Dic71C2318yescomplemented
147C4×Dic142C23124yescomplemented
148#14556093C23124yescomplemented
149C4×D284C23124yescomplemented
150D4×Dic71C23124yescomplemented
151#14556090C23124yescomplemented
152C4×C22⋊D71C23124yescomplemented
153C4×C22⋊D71C23124yescomplemented
154(C22⋊D71)⋊C4C23124yescomplemented
155(C22⋊D71)⋊C4C23124yescomplemented
156C2×C4⋊Dic71C2313yes—
157C2×C4⋊Dic71C2313yes—
158C2×Dic71⋊C4C2313yes—
159C2×Dic71⋊C4C2313yes—
160C2×Dic71⋊C4C2316yes—
161C4⋊C4×D71C23124yes—
162C4⋊C4×D71C23124yes—
163C2×C22⋊Dic71C2311yescharacteristic
164C2×C22⋊Dic71C2313yes—
165C2×C22⋊Dic71C2316yes—
166C2×(C2×D71)⋊C4C2311yescharacteristic
167C2×(C2×D71)⋊C4C2313yes—
168C2×(C2×D71)⋊C4C2311yescharacteristic
169C2×(C2×D71)⋊C4C2313yes—
170C2×(C2×D71)⋊C4C2316yes—
171C2×(C2×D71)⋊C4C2316yes—
172C22⋊C4×D71C2318yes—
173C22⋊C4×D71C23124yes—
174C22⋊C4×D71C23148yes—
175C2×C4×Dic71C2313yes—
176C2×C4×Dic71C2313yes—
177C2×C4×Dic71C2313yes—
178C42×D71C23124yes—
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—24no—
201C23×D71—24no—
202C23×D71—212no—
203C23×D71—212no—
204C23×D71—212no—
205C23×D71#4118yescomplemented
206C23×D71C24112yes—
207C23×D71C2413yes—
208C23×D71C2414yes—
209C23×D71C2411yescharacteristic
210C23×D71C2411yescharacteristic
211#11765866—232no—
212#11765865—296no—
213#11765864—296no—
214C2×Dic142—212no—
215C2×Dic142—224no—
216C2×Dic142—296no—
217C2×Dic142C2×D4124yescomplemented
218C2×Dic142C24124yes—
219C2×Dic142C24112yes—
220C2×Dic142C24112yes—
221Q8×D71—232no—
222Q8×D71—296no—
223Q8×D71—296no—
224Q8×D71C2×D4164yescomplemented
225C2×D284—212no—
226C2×D284—212no—
227C2×D284C24112yes—
228C2×D284C24112yes—
229C2×C22⋊D71—212no—
230C2×C22⋊D71—212no—
231C2×C22⋊D71—224no—
232C2×C22⋊D71C24124yes—
233C2×C22⋊D71C24112yes—
234C2×C22⋊D71C24112yes—
235D4×D71—296no—
236D4×D71—296no—
237C22×Dic71—212no—
238C22×Dic71—212no—
239C22×Dic71C2411yescharacteristic
240C22×Dic71C2413yes—
241C22×Dic71C24112yes—
242C22×Dic71C24112yes—
243C22×Dic71C2413yes—
244C22×Dic71C2411yescharacteristic
245C22×Dic71C2413yes—
246C2×C4×D71—24no—
247C2×C4×D71—212no—
248C2×C4×D71—212no—
249C2×C4×D71—24no—
250C2×C4×D71—212no—
251C2×C4×D71—212no—
252C2×C4×D71—212no—
253C2×C4×D71—212no—
254C2×C4×D71—296no—
255C2×C4×D71—296no—
256C2×C4×D71C2×D4124yes—
257C2×C4×D71C2414yes—
258C2×C4×D71C24112yes—
259C2×C4×D71C24112yes—
260C2×C4×D71C24112yes—
261C2×C4×D71C24112yes—
262C2×C4×D71C24112yes—
263C2×C4×D71C24112yes—
264C2×C4×D71C2414yes—
265C2×C4×D71C24112yes—
266C4⋊Dic71C24112yes—
267C4⋊Dic71C24112yes—
268Dic71⋊C4C24112yes—
269Dic71⋊C4C24112yes—
270Dic71⋊C4C24124yes—
271C22⋊Dic71C2414yes—
272C22⋊Dic71C24112yes—
273C22⋊Dic71C24124yes—
274(C2×D71)⋊C4C2414yes—
275(C2×D71)⋊C4C24112yes—
276(C2×D71)⋊C4C2414yes—
277(C2×D71)⋊C4C24112yes—
278(C2×D71)⋊C4C24124yes—
279(C2×D71)⋊C4C24124yes—
280C4×Dic71C24112yes—
281C4×Dic71C24112yes—
282C4×Dic71C24112yes—
283C24×C71C2413yes—
284C24×C71C2411yescharacteristic
285#41×C71—232no—
286C2×Q8×C71—232no—
287C2×Q8×C71—212no—
288C2×Q8×C71C2×D418yescomplemented
289C2×Q8×C71C24112yes—
290C2×Q8×C71C2414yes—
291C2×D4×C71—212no—
292C2×D4×C71—212no—
293C2×D4×C71C24112yes—
294C2×D4×C71C24112yes—
295C22×C4×C71—212no—
296C22×C4×C71—212no—
297C22×C4×C71C2411yescharacteristic
298C22×C4×C71C2413yes—
299C22×C4×C71C24112yes—
300C22×C4×C71C24112yes—
301C22×C4×C71C2413yes—
302C22×C4×C71C2411yescharacteristic
303C22×C4×C71C2413yes—
304C4⋊C4×C71C24112yes—
305C4⋊C4×C71C24112yes—
306C22⋊C4×C71C2414yes—
307C22⋊C4×C71C24112yes—
308C22⋊C4×C71C24124yes—
309C42×C71C24112yes—
310C23×C71—22no—
311C23×C71—22no—
312C23×C71—26no—
313C23×C71—26no—
314C23×C71—26no—
315C23×C71C2×#4114yescomplemented
316C23×C71C2516yes—
317C23×C71C2512yes—
318C23×C71C2511yescharacteristic
319C22×D71—22no—
320C22×D71—22no—
321C22×D71—232no—
322C22×D71—28no—
323C22×D71—28no—
324C22×D71—26no—
325C22×D71—26no—
326C22×D71—26no—
327C22×D71—224no—
328C22×D71—224no—
329C22×D71—224no—
330C22×D71—448no—
331C22×D71C22×D414yes—
332C22×D71C2×#4114yes—
333C22×D71C2×#41116yescomplemented
334C22×D71C2×#4114yescomplemented
335C22×D712−1+414yes—
336C22×D71C2516yes—
337C22×D71C2512yes—
338C22×D71C2512yes—
339Q8×C71—224no—
340Q8×C71C22×D4116yescomplemented
341D4×C71—224no—
342D4×C71—224no—
343C2×C4×C71—22no—
344C2×C4×C71—26no—
345C2×C4×C71—26no—
346C2×C4×C71—22no—
347C2×C4×C71—224no—
348C2×C4×C71—224no—
349C2×C4×C71C22×D4112yes—
350C2×C4×C71C2512yes—
351C2×C4×C71C2516yes—
352C2×C4×C71C2516yes—
353C2×C4×C71C2512yes—
354C2×C4×C71C2516yes—
355C22⋊D71—224no—
356C22⋊D71—224no—
357C22⋊D71—248no—
358C2×Dic71—22no—
359C2×Dic71—26no—
360C2×Dic71—26no—
361C2×Dic71—22no—
362C2×Dic71—224no—
363C2×Dic71—224no—
364C2×Dic71C22×D4112yes—
365C2×Dic71C2512yes—
366C2×Dic71C2516yes—
367C2×Dic71C2516yes—
368C2×Dic71C2512yes—
369C2×Dic71C2516yes—
370D284—224no—
371D284—224no—
372C4×D71—28no—
373C4×D71—224no—
374C4×D71—224no—
375C4×D71—28no—
376C4×D71—224no—
377C4×D71—224no—
378C4×D71—224no—
379C4×D71—224no—
380C4×D71C22×D4148yes—
381Dic142—224no—
382Dic142—248no—
383Dic142C22×D4148yescomplemented
384C22×C71—22no—
385C22×C71—22no—
386C22×C71—28no—
387C22×C71—26no—
388C22×C71—26no—
389C22×C71—26no—
390C22×C71—412no—
391C22×C71C23×D412yes—
392C22×C71C22×#4112yes—
393C22×C71C22×#4114yescomplemented
394C22×C71C2×2−1+412yes—
395C22×C71C2611yescharacteristic
396C2×D71—22no—
397C2×D71—22no—
398C2×D71—28no—
399C2×D71—232no—
400C2×D71—26no—
401C2×D71—26no—
402C2×D71—26no—
403C2×D71—412no—
404C2×D71—448no—
405C2×D71#548116yesdirect product factor
406C2×D71C23×D414yes—
407C2×D71C22×#4114yes—
408C2×D71C22×#4114yescomplemented
409C2×D71C2×2−1+414yes—
410C4×C71—26no—
411C4×C71—22no—
412C4×C71—26no—
413C4×C71—22no—
414C4×C71C23×D4112yes—
415Dic71—26no—
416Dic71—22no—
417Dic71—26no—
418Dic71—22no—
419Dic71C23×D4112yes—
420C22×#548—711nomaximal, Sylow
421C2×C71—24no—
422C2×C71—46no—
423C2×C71C2×#54814yescomplemented
424C2×C71C24×D411yescharacteristic
425C2×C71C23×#4111yescharacteristic
426C2×C71C22×2−1+411yescharacteristic
427D71—24no—
428D71—46no—
429D71C2×#54818yesdirect product factor
430C23×#41—711no—
431C24×Q8—711no—
432C2×#548—711no—
433C2×#548—711no—
434C2×#548—7132no—
435C2×#548—713no—
436C2×#548—713no—
437C2×#548—713no—
438C2×#548—711no—
439C2×#548—713no—
440C2×#548D7111yescharacteristic, direct product factor
441C22×#124—713no—
442C22×C22⋊Q8—713no—
443C22×#121—713no—
444C22×C4×Q8—711no—
445C22×C4×D4—713no—
446C71C22×#54811yescharacteristic, complemented, Sylow
447C22×#41—7116no—
448C22×#41—711no—
449C22×#41—713no—
450C22×#41—713no—
451C22×#41—14216no—
452C22×#41C2×D7111yescharacteristic, complemented
453C23×Q8—711no—
454C23×Q8—713no—
455C23×Q8—713no—
456C23×Q8—711no—
457C23×Q8—7116no—
458C23×Q8—713no—
459C23×Q8—14216no—
460C23×Q8C2×D7111yescharacteristic, complemented
461C23×D4—713no—
462C23×D4—713no—
463C24×C4—713no—
464C24×C4—713no—
465#548—7116no—
466#548—7116no—
467#548—7148no—
468#548—7148no—
469#548—7148no—
470#548—7116no—
471#548—7148no—
472#548C2×D71116yesdirect product factor
473C2×#124—713no—
474C2×#124—713no—
475C2×#124—7148no—
476C2×#124—716no—
477C2×#124—716no—
478C2×#124—713no—
479C2×#124C2×D7113yescomplemented
480C2×C22⋊Q8—713no—
481C2×C22⋊Q8—713no—
482C2×C22⋊Q8—7148no—
483C2×C22⋊Q8—716no—
484C2×C22⋊Q8—713no—
485C2×C22⋊Q8—716no—
486C2×C22⋊Q8C2×D7113yescomplemented
487C2×#121—713no—
488C2×#121—716no—
489C2×#121—713no—
490C2×#121—7148no—
491C2×#121—713no—
492C2×#121—716no—
493C2×#121C2×D7113yescomplemented
494C2×C4×Q8—711no—
495C2×C4×Q8—7116no—
496C2×C4×Q8—713no—
497C2×C4×Q8—713no—
498C2×C4×Q8C2×D7111yescharacteristic, complemented
499C2×C4×D4—713no—
500C2×C4×D4—713no—
501C2×C4×D4—713no—
502C2×C4×D4—7148no—
503C2×C4×D4—713no—
504C2×C4×D4—713no—
505C2×C4×D4—713no—
506C2×C4×D4—713no—
507C2×C4×D4C2×D7113yescomplemented
508C22×C4⋊C4—713no—
509C22×C4⋊C4—713no—
510C22×C22⋊C4—711no—
511C22×C22⋊C4—713no—
512C22×C22⋊C4—716no—
513C22×C42—713no—
514C25—711no—
515C25—713no—
516C2×#41—28no—
517C2×#41—718no—
518C2×#41—7124no—
519C2×#41—7124no—
520C2×#41—14224no—
521C2×#41—14224no—
522C2×#41—142128no—
523C2×#41—1428no—
524C2×#41C22×D7118yescomplemented
525C22×Q8—28no—
526C22×Q8—7116no—
527C22×Q8—718no—
528C22×Q8—7124no—
529C22×Q8—7124no—
530C22×Q8—718no—
531C22×Q8—713no—
532C22×Q8—716no—
533C22×Q8—713no—
534C22×Q8—7124no—
535C22×Q8—14224no—
536C22×Q8—14224no—
537C22×Q8—142128no—
538C22×Q8—14224no—
539C22×Q8—1428no—
540C22×Q8C22×D7113yes—
541C22×Q8C22×D7111yescharacteristic
542C22×Q8C22×D7118yescomplemented
543C22×D4—713no—
544C22×D4—713no—
545C22×D4—716no—
546C22×D4—7124no—
547C22×D4—7124no—
548C22×D4—713no—
549C22×D4—713no—
550C22×D4—14224no—
551C22×D4—14224no—
552C22×D4C22×D7113yes—
553C22×D4C22×D7113yes—
554C23×C4—713no—
555C23×C4—713no—
556C23×C4—713no—
557C23×C4—711no—
558C23×C4—713no—
559C23×C4—713no—
560C23×C4—711no—
561C23×C4—713no—
562C23×C4—7124no—
563C23×C4—713no—
564C23×C4—713no—
565C23×C4—7124no—
566C23×C4—713no—
567C23×C4—14224no—
568C23×C4—14224no—
569C23×C4C22×D7113yes—
570C23×C4C22×D7113yes—
571#124—7124no—
572#124—7124no—
573#124—7148no—
574#124—7148no—
575#124—7124no—
576#124C22×D71124yescomplemented
577C22⋊Q8—7124no—
578C22⋊Q8—7124no—
579C22⋊Q8—7148no—
580C22⋊Q8—7124no—
581C22⋊Q8—7148no—
582C22⋊Q8C22×D71124yescomplemented
583#121—7124no—
584#121—7148no—
585#121—7124no—
586#121—7124no—
587#121—7148no—
588#121C22×D71124yescomplemented
589C4×Q8—718no—
590C4×Q8—7124no—
591C4×Q8—7124no—
592C4×Q8C22×D7118yescomplemented
593C4×D4—7124no—
594C4×D4—7124no—
595C4×D4—7124no—
596C4×D4—7124no—
597C4×D4—7124no—
598C4×D4—7124no—
599C4×D4—7124no—
600C4×D4C22×D71124yescomplemented
601C2×C4⋊C4—713no—
602C2×C4⋊C4—713no—
603C2×C4⋊C4—713no—
604C2×C4⋊C4—716no—
605C2×C4⋊C4—713no—
606C2×C4⋊C4—7124no—
607C2×C4⋊C4—7124no—
608C2×C4⋊C4C22×D7113yes—
609C2×C4⋊C4C22×D7113yes—
610C2×C22⋊C4—711no—
611C2×C22⋊C4—713no—
612C2×C22⋊C4—716no—
613C2×C22⋊C4—711no—
614C2×C22⋊C4—711no—
615C2×C22⋊C4—713no—
616C2×C22⋊C4—713no—
617C2×C22⋊C4—716no—
618C2×C22⋊C4—716no—
619C2×C22⋊C4—718no—
620C2×C22⋊C4—7124no—
621C2×C22⋊C4—7148no—
622C2×C22⋊C4C22×D7111yescharacteristic
623C2×C22⋊C4C22×D7113yes—
624C2×C22⋊C4C22×D7116yes—
625C2×C42—713no—
626C2×C42—713no—
627C2×C42—713no—
628C2×C42—7124no—
629C2×C42C22×D7113yes—
630C24—711no—
631C24—718no—
632C24—714no—
633C24—711no—
634C24—7112no—
635C24—713no—
636C24—14212no—
637C24—14212no—
638C24—14212no—
639C24—1424no—
640C24—1424no—
641C24C23×D7113yes—
642C24C23×D7111yescharacteristic
643#41—232no—
644#41—14296no—
645#41—14296no—
646#41—14232no—
647C2×Q8—232no—
648C2×Q8—212no—
649C2×Q8—7164no—
650C2×Q8—7124no—
651C2×Q8—7112no—
652C2×Q8—7124no—
653C2×Q8—7112no—
654C2×Q8—14224no—
655C2×Q8—14296no—
656C2×Q8—14296no—
657C2×Q8—14296no—
658C2×Q8—14232no—
659C2×Q8—14212no—
660C2×Q8D4×D7118yescomplemented
661C2×Q8C23×D71112yes—
662C2×Q8C23×D7114yes—
663C2×D4—212no—
664C2×D4—212no—
665C2×D4—7112no—
666C2×D4—7112no—
667C2×D4—7124no—
668C2×D4—7112no—
669C2×D4—7112no—
670C2×D4—14212no—
671C2×D4—14296no—
672C2×D4—14224no—
673C2×D4—14296no—
674C2×D4—14212no—
675C2×D4—14212no—
676C2×D4—14212no—
677C2×D4C23×D71112yes—
678C2×D4C23×D71112yes—
679C22×C4—212no—
680C22×C4—212no—
681C22×C4—713no—
682C22×C4—7124no—
683C22×C4—7112no—
684C22×C4—7112no—
685C22×C4—7112no—
686C22×C4—711no—
687C22×C4—713no—
688C22×C4—713no—
689C22×C4—711no—
690C22×C4—714no—
691C22×C4—7112no—
692C22×C4—7112no—
693C22×C4—714no—
694C22×C4—7112no—
695C22×C4—7112no—
696C22×C4—7112no—
697C22×C4—7112no—
698C22×C4—14212no—
699C22×C4—14296no—
700C22×C4—14212no—
701C22×C4—14296no—
702C22×C4—1424no—
703C22×C4—1424no—
704C22×C4—14212no—
705C22×C4—14212no—
706C22×C4—14212no—
707C22×C4—14212no—
708C22×C4—14212no—
709C22×C4—14212no—
710C22×C4C23×D71112yes—
711C22×C4C23×D71112yes—
712C22×C4C23×D7111yescharacteristic
713C22×C4C23×D7113yes—
714C22×C4C23×D7113yes—
715C22×C4C23×D7111yescharacteristic
716C22×C4C23×D7113yes—
717C4⋊C4—7112no—
718C4⋊C4—7112no—
719C4⋊C4—7124no—
720C4⋊C4—7112no—
721C4⋊C4—7112no—
722C4⋊C4C23×D71112yes—
723C4⋊C4C23×D71112yes—
724C22⋊C4—714no—
725C22⋊C4—7112no—
726C22⋊C4—7124no—
727C22⋊C4—714no—
728C22⋊C4—714no—
729C22⋊C4—7112no—
730C22⋊C4—7112no—
731C22⋊C4—7124no—
732C22⋊C4—7124no—
733C22⋊C4C23×D7114yes—
734C22⋊C4C23×D71112yes—
735C22⋊C4C23×D71124yes—
736C42—7112no—
737C42—7112no—
738C42—7112no—
739C42C23×D71112yes—
740C23—22no—
741C23—22no—
742C23—26no—
743C23—26no—
744C23—26no—
745C23—28448no—
746C23—714no—
747C23—714no—
748C23—714no—
749C23—712no—
750C23—714no—
751C23—7116no—
752C23—712no—
753C23—716no—
754C23—14224no—
755C23—14224no—
756C23—14224no—
757C23—1428no—
758C23—14232no—
759C23—1428no—
760C23—1426no—
761C23—1426no—
762C23—1426no—
763C23—1422no—
764C23—1422no—
765C23#41×D7114yescomplemented
766C23C24×D7116yes—
767C23C24×D7112yes—
768C23C24×D7111yescharacteristic
769Q8—224no—
770Q8—7148no—
771Q8—14248no—
772Q8—14224no—
773Q8C2×D4×D71116yescomplemented
774D4—224no—
775D4—224no—
776D4—14224no—
777D4—14248no—
778D4—14224no—
779D4—14224no—
780D4—14224no—
781C2×C4—22no—
782C2×C4—26no—
783C2×C4—26no—
784C2×C4—22no—
785C2×C4—224no—
786C2×C4—224no—
787C2×C4—7112no—
788C2×C4—716no—
789C2×C4—7148no—
790C2×C4—712no—
791C2×C4—716no—
792C2×C4—716no—
793C2×C4—712no—
794C2×C4—14224no—
795C2×C4—14224no—
796C2×C4—1428no—
797C2×C4—14224no—
798C2×C4—14224no—
799C2×C4—1428no—
800C2×C4—14224no—
801C2×C4—14224no—
802C2×C4—1422no—
803C2×C4—1426no—
804C2×C4—1426no—
805C2×C4—1422no—
806C2×C4—14224no—
807C2×C4—14224no—
808C2×C4C2×D4×D71112yes—
809C2×C4C24×D7112yes—
810C2×C4C24×D7116yes—
811C2×C4C24×D7116yes—
812C2×C4C24×D7112yes—
813C2×C4C24×D7116yes—
814C22—28no—
815C22—22no—
816C22—22no—
817C22—26no—
818C22—26no—
819C22—26no—
820C22—412no—
821C22—28448no—
822C22—28412no—
823C22—7116no—
824C22—714no—
825C22—714no—
826C22—714no—
827C22—714no—
828C22—14232no—
829C22—1426no—
830C22—1426no—
831C22—1426no—
832C22—1428no—
833C22—1422no—
834C22—1422no—
835C22C22×D4×D7112yes—
836C22C2×#41×D7112yes—
837C22C2×#41×D7114yescomplemented
838C222−1+4×D7112yes—
839C22C25×D7111yescharacteristic
840C4—22no—
841C4—26no—
842C4—26no—
843C4—22no—
844C4—7112no—
845C4—1422no—
846C4—1426no—
847C4—1426no—
848C4—1422no—
849C4C22×D4×D71112yes—
850C2—24no—
851C2—46no—
852C2—2846no—
853C2—718no—
854C2—1424no—
855C2#548×D7114yesdirect product factor
856C2C23×D4×D7111yescharacteristic
857C2C22×#41×D7111yescharacteristic
858C2C2×2−1+4×D7111yescharacteristic
subgroupG/H
centerC23C24×D71
commutator, cosocleC22×C71C26
FrattiniC22C25×D71
FittingC2×#548×C71C2
socleC23×C71C25
hypercenterC2×#548D71
hypocenterC71C22×#548
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C22×#41×D71C2semidirect
2. C23×Q8×D71C2semidirect
3. C2×#17986661C2semidirect
4. C2×#17986660C2semidirect
5. C2×#17986659C2semidirect
6. C2×#17986658C2semidirect
7. C2×#17986657C2semidirect
8. C2×#17986656C2semidirect
9. C2×#17986655C2semidirect
10. #548×D71C2direct (N × H)
11. C2×#124×D71C2semidirect
12. C2×C22⋊Q8×D71C2semidirect
13. C2×#121×D71C2semidirect
14. C2×C4×Q8×D71C2semidirect
15. C2×C4×D4×D71C2semidirect
16. C2×#548×C71C2semidirect
17. C22×#11765866C22semidirect
18. C22×#11765865C22semidirect
19. C22×#11765864C22semidirect
21. C2×#41×D71C22semidirect
22. C23×Dic142C22semidirect
26. C22×Q8×D71C22semidirect
27. C22×Q8×D71C22semidirect
28. C22×Q8×D71C22semidirect
33. #17986661C22semidirect
34. #17986660C22semidirect
35. #17986659C22semidirect
36. #17986658C22semidirect
37. #17986657C22semidirect
38. #17986656C22semidirect
39. #17986655C22semidirect
40. C2×#14556117C22semidirect
41. C2×#14556116C22semidirect
42. C2×#14556115C22semidirect
43. C2×#14556114C22semidirect
44. C2×#14556114C22semidirect
45. #124×D71C22semidirect
46. C2×#14556108C22semidirect
47. C2×#14556107C22semidirect
48. C2×#14556106C22semidirect
49. C2×#14556105C22semidirect
50. C2×#14556104C22semidirect
51. C22⋊Q8×D71C22semidirect
52. C2×#14556103C22semidirect
53. C2×#14556102C22semidirect
54. C2×#14556101C22semidirect
55. C2×#14556100C22semidirect
56. C2×#14556099C22semidirect
57. #121×D71C22semidirect
58. C2×Q8×Dic71C22semidirect
59. C2×C4×Dic142C22semidirect
60. C2×#14556093C22semidirect
61. C4×Q8×D71C22semidirect
62. C2×C4×D284C22semidirect
63. C2×D4×Dic71C22semidirect
64. C2×#14556090C22semidirect
65. C2×C4×C22⋊D71C22semidirect
66. C2×C4×C22⋊D71C22semidirect
67. C2×(C22⋊D71)⋊C4C22semidirect
68. C2×(C22⋊D71)⋊C4C22semidirect
69. C4×D4×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
87. C2×#11765866C23semidirect
89. C2×#11765865C23semidirect
91. C2×#11765864C23semidirect
97. C22×Dic142C23semidirect
102. C2×Q8×D71D4semidirect
105. C2×Q8×D71C23semidirect
106. C2×Q8×D71C23semidirect
131. #14556117C23semidirect
132. #14556116C23semidirect
133. #14556115C23semidirect
134. #14556114C23semidirect
135. #14556114C23semidirect
136. #14556108C23semidirect
137. #14556107C23semidirect
138. #14556106C23semidirect
139. #14556105C23semidirect
140. #14556104C23semidirect
141. #14556103C23semidirect
142. #14556102C23semidirect
143. #14556101C23semidirect
144. #14556100C23semidirect
145. #14556099C23semidirect
146. Q8×Dic71C23semidirect
147. C4×Dic142C23semidirect
148. #14556093C23semidirect
149. C4×D284C23semidirect
150. D4×Dic71C23semidirect
151. #14556090C23semidirect
152. C4×C22⋊D71C23semidirect
153. C4×C22⋊D71C23semidirect
154. (C22⋊D71)⋊C4C23semidirect
155. (C22⋊D71)⋊C4C23semidirect
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
205. C23×D71#41semidirect
217. C2×Dic142C2×D4semidirect
224. Q8×D71C2×D4semidirect
288. C2×Q8×C71C2×D4semidirect
315. C23×C71C2×#41semidirect
333. C22×D71C2×#41semidirect
334. C22×D71C2×#41semidirect
340. Q8×C71C22×D4semidirect
383. Dic142C22×D4semidirect
393. C22×C71C22×#41semidirect
405. C2×D71#548direct (N × H)
408. C2×D71C22×#41semidirect
423. C2×C71C2×#548semidirect
429. D71C2×#548direct (N × H)
440. C2×#548D71direct (N × H)
446. C71C22×#548semidirect
452. C22×#41C2×D71semidirect
460. C23×Q8C2×D71semidirect
472. #548C2×D71direct (N × H)
479. C2×#124C2×D71semidirect
486. C2×C22⋊Q8C2×D71semidirect
493. C2×#121C2×D71semidirect
498. C2×C4×Q8C2×D71semidirect
507. C2×C4×D4C2×D71semidirect
524. C2×#41C22×D71semidirect
542. C22×Q8C22×D71semidirect
576. #124C22×D71semidirect
582. C22⋊Q8C22×D71semidirect
588. #121C22×D71semidirect
592. C4×Q8C22×D71semidirect
600. C4×D4C22×D71semidirect
660. C2×Q8D4×D71semidirect
765. C23#41×D71semidirect
773. Q8C2×D4×D71semidirect
837. C22C2×#41×D71semidirect
855. C2#548×D71direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#41×D712
C23×Q8×D712
C2×#179866612
C2×#179866602
C2×#179866592
C2×#179866582
C2×#179866572
C2×#179866562
C2×#179866552
#548×D712
C2×#124×D712
C2×C22⋊Q8×D712
C2×#121×D712
C2×C4×Q8×D712
C2×C4×D4×D712
C2×#548×C712
C22×#54871