Finite Group Databasebeta

← #32158504

Subgroups — #32158504

Order 18176.

5106 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556176C211yesmaximal, characteristic
2C2×#17986481C211yesmaximal, characteristic, complemented
3C2×C4×#11765866C211yesmaximal, characteristic, complemented
4Q8×C22⋊Dic71C211yesmaximal, characteristic, complemented
5Q8×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
6Q8×(C2×D71)⋊C4C211yesmaximal, characteristic, complemented
7#22591171C213yesmaximal, complemented
8#22591169C213yesmaximal, complemented
9#22591169C213yesmaximal, complemented
10#22591168C213yesmaximal, complemented
11#22590929C213yesmaximal, complemented
12#22590923C213yesmaximal, complemented
13#22590826C213yesmaximal, complemented
14#391×D71C213yesmaximal, complemented
15Q8×C22⋊C4×C71C211yesmaximal, characteristic, complemented
16C2×#14556176—28no—
17C2×#14556176—28no—
18C2×#14556176C4116yescomplemented
19C22×#11765866C2213yes—
20C22×#11765866C2211yescharacteristic
21C22×#11765865C2213yes—
22C22×#11765865C2213yes—
23C22×Q8×D71C2213yes—
24C22×Q8×D71C2211yescharacteristic
25#17986481—28no—
26C4×#11765866—28no—
27C2×Q8×Dic71C2211yescharacteristic
28C2×Q8×Dic71C2211yescharacteristic
29C2×C4×D284C2213yes—
30C2×C4×D284C2213yes—
31C2×#14556090C2213yes—
32C2×#14556090C2213yes—
33C2×#14556086C2213yes—
34C2×#14556085C2213yes—
35C2×C4⋊C4×D71C2213yes—
36C2×C42×D71C2213yes—
37#17985906C2213yes—
38#17985906C2213yes—
39#17985905C2213yes—
40#17985905C2213yes—
41#17985904C2213yes—
42#17985904C2213yes—
43#17985903C2213yes—
44#17985903C2216yes—
45#17985903C2213yes—
46#17985899C2211yescharacteristic
47#17985899C2213yes—
48#17985877C2213yes—
49#17985877C2213yes—
50#17985877C2216yes—
51#17985875C2213yes—
52#17985875C2213yes—
53#17985875C2216yes—
54#17985861C2216yes—
55#17985861C2216yes—
56#17985859C2213yes—
57#17985856C2213yes—
58#17985856C2213yes—
59C4×(C2×D71)⋊C4C2213yes—
60C4×(C2×D71)⋊C4C2213yes—
61C4×C22⋊Dic71C2213yes—
62#95×D71C2216yes—
63#95×D71C2216yes—
64C23×Q8×C71C2211yescharacteristic
65C2×C4×Q8×C71C2211yescharacteristic
66C2×C4×Q8×C71C2211yescharacteristic
67#391×C71C2213yes—
68#391×C71C2213yes—
69#380×C71C2213yes—
70C4×C22⋊C4×C71C2213yes—
71#14556176—2128no—
72C2×#11765866—212no—
73C2×#11765866—212no—
74C2×#11765866C2×C418yes—
75C2×#11765866C2×C4124yescomplemented
76C2×#11765866D418yes—
77C2×#11765866D418yes—
78C2×#11765865—212no—
79C2×#11765865—212no—
80C2×#11765865—212no—
81C2×#11765865—212no—
82C2×#11765865C2×C4124yescomplemented
83C2×#11765865C2×C4124yescomplemented
84C22×Dic142C2313yes—
85C22×Dic142C2313yes—
86C2×Q8×D71—212no—
87C2×Q8×D71—212no—
88C2×Q8×D71—24no—
89C2×Q8×D71—24no—
90C2×Q8×D71C2×C4124yescomplemented
91C2×Q8×D71C2×C418yescomplemented
92C22×D284C2313yes—
93C22×D284C2313yes—
94C22×C22⋊D71C2313yes—
95C22×C22⋊D71C2311yescharacteristic
96C22×C4×D71C2313yes—
97C22×C4×D71C2313yes—
98C22×C4×D71C2316yes—
99C22×C4×D71C2313yes—
100C22×C4×D71C2316yes—
101C22×C4×D71C2313yes—
102Q8×Dic71—24no—
103Q8×Dic71—24no—
104C4×D284—212no—
105C4×D284—212no—
106#14556090—212no—
107#14556090—212no—
108#14556086—212no—
109#14556085—212no—
110C2×C4⋊Dic71C2313yes—
111C2×C4⋊Dic71C2313yes—
112C2×Dic71⋊C4C2313yes—
113C2×Dic71⋊C4C2311yescharacteristic
114C4⋊C4×D71—212no—
115C2×C22⋊Dic71C2311yescharacteristic
116C2×C22⋊Dic71C2313yes—
117C2×(C2×D71)⋊C4C2311yescharacteristic
118C2×(C2×D71)⋊C4C2311yescharacteristic
119C2×(C2×D71)⋊C4C2313yes—
120C2×(C2×D71)⋊C4C2313yes—
121C2×(C2×D71)⋊C4C2316yes—
122C2×(C2×D71)⋊C4C2313yes—
123C2×(C2×D71)⋊C4C2313yes—
124C2×C4×Dic71C2313yes—
125C2×C4×Dic71C2313yes—
126C2×C4×Dic71C2311yescharacteristic
127C2×C4×Dic71C2313yes—
128C42×D71—212no—
129C71⋊#95C2313yes—
130C71⋊#95C2313yes—
131C71⋊#95C2313yes—
132C71⋊#95C2316yes—
133C71⋊#95C2316yes—
134C71⋊#95C2316yes—
135C71⋊#95C2313yes—
136C71⋊#95C2313yes—
137C71⋊#95C2313yes—
138C22×Q8×C71—24no—
139C22×Q8×C71—24no—
140C22×Q8×C71C2×C418yescomplemented
141C22×Q8×C71C2313yes—
142C22×Q8×C71C2311yescharacteristic
143C23×C4×C71C2313yes—
144C4×Q8×C71—24no—
145C4×Q8×C71—24no—
146C2×C4⋊C4×C71C2313yes—
147C2×C4⋊C4×C71C2313yes—
148C2×C22⋊C4×C71C2311yescharacteristic
149C2×C22⋊C4×C71C2313yes—
150C2×C42×C71C2313yes—
151C2×C42×C71C2313yes—
152#95×C71C2313yes—
153#95×C71C2316yes—
154#95×C71C2313yes—
155C23×D71C2411yescharacteristic
156C23×D71C2413yes—
157#11765866—296no—
158#11765866C22⋊C4164yescomplemented
159#11765865—296no—
160#11765865—296no—
161C2×Dic142—26no—
162C2×Dic142—26no—
163C2×Dic142—26no—
164C2×Dic142—26no—
165C2×Dic142C22×C4112yes—
166C2×Dic142C22×C4112yes—
167Q8×D71—232no—
168Q8×D71—296no—
169C2×D284—26no—
170C2×D284—26no—
171C2×D284C22×C4112yes—
172C2×D284C22×C4112yes—
173C2×D284C2×D4112yes—
174C2×D284C2×D4112yes—
175C2×C22⋊D71—26no—
176C2×C22⋊D71—26no—
177C2×C22⋊D71—22no—
178C2×C22⋊D71—22no—
179C2×C22⋊D71C22×C4112yes—
180C2×C22⋊D71C22×C414yes—
181C22×Dic71C2413yes—
182C22×Dic71C2413yes—
183C22×Dic71C2411yescharacteristic
184C22×Dic71C2413yes—
185C22×Dic71C2411yescharacteristic
186C22×Dic71C2411yescharacteristic
187C2×C4×D71—212no—
188C2×C4×D71—212no—
189C2×C4×D71—26no—
190C2×C4×D71—26no—
191C2×C4×D71—26no—
192C2×C4×D71—26no—
193C2×C4×D71—26no—
194C2×C4×D71—26no—
195C2×C4×D71—212no—
196C2×C4×D71—43no—
197C2×C4×D71—43no—
198C2×C4×D71—46no—
199C2×C4×D71—46no—
200C2×C4×D71C22×C4124yes—
201C2×C4×D71C22×C4112yes—
202C2×C4×D71C22×C4112yes—
203C2×C4×D71C2×D4112yes—
204C2×C4×D71C2×D4112yes—
205C4⋊Dic71—26no—
206C4⋊Dic71—26no—
207Dic71⋊C4—26no—
208Dic71⋊C4—22no—
209C22⋊Dic71—22no—
210C22⋊Dic71—43no—
211(C2×D71)⋊C4—26no—
212(C2×D71)⋊C4—26no—
213(C2×D71)⋊C4—212no—
214(C2×D71)⋊C4—22no—
215(C2×D71)⋊C4—22no—
216(C2×D71)⋊C4—43no—
217(C2×D71)⋊C4—43no—
218C4×Dic71—26no—
219C4×Dic71—26no—
220C4×Dic71—22no—
221C4×Dic71—26no—
222C24×C71C2411yescharacteristic
223C2×Q8×C71—232no—
224C2×Q8×C71—26no—
225C2×Q8×C71—26no—
226C2×Q8×C71C22×C4112yes—
227C2×Q8×C71C22×C414yes—
228C2×Q8×C71C2×D414yes—
229C2×Q8×C71C2×D414yes—
230C22×C4×C71—26no—
231C22×C4×C71—26no—
232C22×C4×C71C22×C4112yes—
233C22×C4×C71C2413yes—
234C22×C4×C71C2413yes—
235C22×C4×C71C2411yescharacteristic
236C22×C4×C71C2413yes—
237C22×C4×C71C2411yescharacteristic
238C22×C4×C71C2413yes—
239C4⋊C4×C71—26no—
240C4⋊C4×C71—26no—
241C22⋊C4×C71—22no—
242C22⋊C4×C71—43no—
243C42×C71—26no—
244C42×C71—26no—
245C23×C71—21no—
246C23×C71—21no—
247C23×C71—21no—
248C23×C71—21no—
249C23×C71—21no—
250C23×C71—21no—
251C23×C71C23×C412yes—
252C23×C71C2511yescharacteristic
253C22×D71—23no—
254C22×D71—23no—
255C22×D71—23no—
256C22×D71—23no—
257C22×D71—21no—
258C22×D71—21no—
259C22×D71—21no—
260C22×D71—21no—
261C22×D71—21no—
262C22×D71—21no—
263C22×D71C23×C412yes—
264C22×D71C23×C416yes—
265C22×D71C22×D416yes—
266C22×D71C22×D416yes—
267Q8×C71—224no—
268Q8×C71C2×C22⋊C4116yes—
269C2×C4×C71—21no—
270C2×C4×C71—23no—
271C2×C4×C71—23no—
272C2×C4×C71—21no—
273C2×C4×C71—224no—
274C2×C4×C71—21no—
275C2×C4×C71—23no—
276C2×C4×C71—23no—
277C2×C4×C71—21no—
278C2×C4×C71—21no—
279C2×C4×C71—23no—
280C2×C4×C71—23no—
281C2×C4×C71—23no—
282C2×C4×C71—23no—
283C2×C4×C71C23×C416yes—
284C2×C4×C71C23×C416yes—
285C2×C4×C71C22×D416yes—
286C2×C4×C71C22×D416yes—
287C2×C4×C712−1+412yescomplemented
288C22⋊D71—224no—
289C22⋊D71—28no—
290C2×Dic71—21no—
291C2×Dic71—23no—
292C2×Dic71—23no—
293C2×Dic71—21no—
294C2×Dic71—21no—
295C2×Dic71—23no—
296C2×Dic71—23no—
297C2×Dic71—21no—
298C2×Dic71—21no—
299C2×Dic71—23no—
300C2×Dic71—23no—
301C2×Dic71—23no—
302C2×Dic71—23no—
303C2×Dic71C23×C416yes—
304C2×Dic71C23×C412yes—
305C2×Dic71C22×D412yes—
306C2×Dic71C22×D412yes—
307C2×Dic712−1+412yescomplemented
308D284—224no—
309D284C2×C22⋊C4148yes—
310C4×D71—248no—
311C4×D71—224no—
312C4×D71—412no—
313C4×D71—412no—
314C4×D71—812no—
315C4×D71C2×C22⋊C4148yes—
316Dic142—224no—
317Dic142—224no—
318C22×C71—22no—
319C22×C71—22no—
320C22×C71—22no—
321C22×C71—41no—
322C22×C71—41no—
323C22×C71—41no—
324C22×C71—41no—
325C22×C71C24×C411yescharacteristic
326C22×C71C23×D411yescharacteristic
327C22×C71C23×D411yescharacteristic
328C22×C71C2×2−1+411yescharacteristic
329C22×C71C2×2−1+411yescharacteristic
330C22×C71#58511yescharacteristic
331C22×C71#58511yescharacteristic
332C2×D71—26no—
333C2×D71—26no—
334C2×D71—26no—
335C2×D71—26no—
336C2×D71—26no—
337C2×D71—26no—
338C2×D71—22no—
339C2×D71—22no—
340C2×D71—22no—
341C2×D71—41no—
342C2×D71—41no—
343C2×D71—41no—
344C2×D71—41no—
345C2×D71C22×C22⋊C4112yes—
346C4×C71—26no—
347C4×C71—22no—
348C4×C71—43no—
349C4×C71—41no—
350C4×C71—43no—
351C4×C71C22×C22⋊C4112yes—
352Dic71—26no—
353Dic71—22no—
354Dic71—43no—
355Dic71—41no—
356Dic71—43no—
357Dic71C22×C22⋊C414yes—
358#34259—711nomaximal, Sylow
359C2×C71—42no—
360C2×C71C23×C22⋊C411yescharacteristic
361C2×C71C4×2−1+411yescharacteristic
362C2×C71C4×2−1+411yescharacteristic
363C2×C71#348911yescharacteristic
364C2×C71#348911yescharacteristic
365C2×C71#349911yescharacteristic
366C2×C71#350011yescharacteristic
367D71—212no—
368D71—42no—
369C22×2−1+4—711no—
370C2×#520—711no—
371C2×C4×#41—711no—
372Q8×C22⋊C4—711no—
373Q8×C22⋊C4—711no—
374Q8×C22⋊C4—711no—
375Q8×C22⋊C4D7111yescharacteristic, complemented
376#2339—713no—
377#2339—713no—
378#2339—713no—
379#2339—713no—
380#2311—713no—
381#2310—713no—
382#2297—713no—
383C2×#391—713no—
384C71#3425911yescharacteristic, complemented, Sylow
385C2×2−1+4—7116no—
386C2×2−1+4—1428no—
387C2×2−1+4—1428no—
388C22×#41—711no—
389C22×#41—713no—
390C22×#41—713no—
391C22×#41—713no—
392C23×Q8—713no—
393C23×Q8—711no—
394C23×Q8C2×D7111yescharacteristic
395#520—1428no—
396C4×#41—1428no—
397C2×C4×Q8—711no—
398C2×C4×Q8—711no—
399C2×C4×Q8C2×D7111yescharacteristic
400C2×C4×Q8C2×D7111yescharacteristic
401C2×C4×D4—713no—
402C2×C4×D4—713no—
403C2×C4×D4—713no—
404C2×C4×D4—713no—
405C2×#117—713no—
406C2×#117—713no—
407C22×C4⋊C4—713no—
408C22×C42—713no—
409#391—713no—
410#391—713no—
411#391—713no—
412#391—713no—
413#391—713no—
414#391—713no—
415#391—713no—
416#391—716no—
417#391—713no—
418#391C2×D7113yes—
419#391C2×D7113yes—
420#390—713no—
421#390—711no—
422#386—716no—
423#386—713no—
424#386—713no—
425#386—716no—
426#386—713no—
427#386—713no—
428#381—716no—
429#381—716no—
430#380—713no—
431#380—713no—
432#380—713no—
433#380C2×D7113yes—
434C4×C22⋊C4—713no—
435C4×C22⋊C4—713no—
436C4×C22⋊C4—713no—
437C4×C22⋊C4C2×D7113yes—
438C2×#95—716no—
439C2×#95—716no—
4402−1+4—142128no—
441C2×#41—718no—
442C2×#41—7124no—
443C2×#41—718no—
444C2×#41—718no—
445C2×#41—7124no—
446C2×#41—7124no—
447C2×#41—14212no—
448C2×#41—14212no—
449C2×#41—14212no—
450C2×#41—14212no—
451C2×#41—14212no—
452C2×#41—14212no—
453C22×Q8—24no—
454C22×Q8—24no—
455C22×Q8—7124no—
456C22×Q8—718no—
457C22×Q8—713no—
458C22×Q8—713no—
459C22×Q8—14212no—
460C22×Q8—14212no—
461C22×Q8—1424no—
462C22×Q8—1424no—
463C22×Q8C4×D7118yescomplemented
464C22×Q8C22×D7113yes—
465C22×Q8C22×D7111yescharacteristic
466C22×D4—713no—
467C22×D4—711no—
468C22×D4—713no—
469C22×D4—713no—
470C23×C4—716no—
471C23×C4—713no—
472C23×C4—713no—
473C23×C4—713no—
474C23×C4—716no—
475C23×C4—713no—
476C23×C4C22×D7113yes—
477C4×Q8—24no—
478C4×Q8—24no—
479C4×Q8—1424no—
480C4×Q8—1424no—
481C4×D4—14212no—
482C4×D4—14212no—
483C4×D4—14212no—
484C4×D4—14212no—
485#117—14212no—
486#117—14212no—
487C2×C4⋊C4—713no—
488C2×C4⋊C4—713no—
489C2×C4⋊C4—711no—
490C2×C4⋊C4—713no—
491C2×C4⋊C4—14212no—
492C2×C4⋊C4C22×D7113yes—
493C2×C4⋊C4C22×D7113yes—
494C2×C22⋊C4—713no—
495C2×C22⋊C4—713no—
496C2×C22⋊C4—713no—
497C2×C22⋊C4—711no—
498C2×C22⋊C4—713no—
499C2×C22⋊C4—716no—
500C2×C22⋊C4—713no—
501C2×C22⋊C4—711no—
502C2×C22⋊C4—711no—
503C2×C22⋊C4C22×D7111yescharacteristic
504C2×C22⋊C4C22×D7113yes—
505C2×C42—713no—
506C2×C42—713no—
507C2×C42—713no—
508C2×C42—711no—
509C2×C42—14212no—
510C2×C42C22×D7113yes—
511C2×C42C22×D7113yes—
512#95—713no—
513#95—713no—
514#95—713no—
515#95—716no—
516#95—716no—
517#95—716no—
518#95—713no—
519#95—713no—
520#95—713no—
521#95C22×D7113yes—
522#95C22×D7116yes—
523#95C22×D7113yes—
524C24—713no—
525C24—711no—
526C24C23×D7111yescharacteristic
527#41—7164no—
528#41—14296no—
529#41—14296no—
530#41—14296no—
531C2×Q8—232no—
532C2×Q8—26no—
533C2×Q8—26no—
534C2×Q8—7112no—
535C2×Q8—7112no—
536C2×Q8—1426no—
537C2×Q8—1426no—
538C2×Q8—14296no—
539C2×Q8—14232no—
540C2×Q8—1426no—
541C2×Q8—1426no—
542C2×Q8C2×C4×D71112yes—
543C2×Q8C2×C4×D7114yes—
544C2×Q8D4×D7114yes—
545C2×Q8D4×D7114yes—
546C2×D4—714no—
547C2×D4—7112no—
548C2×D4—7112no—
549C2×D4—7112no—
550C2×D4—7112no—
551C2×D4—7112no—
552C2×D4—1426no—
553C2×D4—1426no—
554C2×D4—1422no—
555C2×D4—1422no—
556C2×D4—1426no—
557C2×D4—1426no—
558C22×C4—26no—
559C22×C4—26no—
560C22×C4—2843no—
561C22×C4—2843no—
562C22×C4—2846no—
563C22×C4—2846no—
564C22×C4—711no—
565C22×C4—7112no—
566C22×C4—7112no—
567C22×C4—7112no—
568C22×C4—713no—
569C22×C4—711no—
570C22×C4—7124no—
571C22×C4—7112no—
572C22×C4—711no—
573C22×C4—713no—
574C22×C4—713no—
575C22×C4—1426no—
576C22×C4—1426no—
577C22×C4—1426no—
578C22×C4—14212no—
579C22×C4—14212no—
580C22×C4—14212no—
581C22×C4—1426no—
582C22×C4—1426no—
583C22×C4—1426no—
584C22×C4C2×C4×D71112yes—
585C22×C4C23×D7113yes—
586C22×C4C23×D7111yescharacteristic
587C22×C4C23×D7113yes—
588C22×C4C23×D7113yes—
589C22×C4C23×D7111yescharacteristic
590C22×C4C23×D7113yes—
591C4⋊C4—26no—
592C4⋊C4—26no—
593C4⋊C4—1426no—
594C4⋊C4—1422no—
595C4⋊C4—1426no—
596C4⋊C4—1426no—
597C22⋊C4—22no—
598C22⋊C4—43no—
599C22⋊C4—2843no—
600C22⋊C4—2843no—
601C22⋊C4—2843no—
602C22⋊C4—1422no—
603C22⋊C4—1426no—
604C22⋊C4—14212no—
605C22⋊C4—1426no—
606C22⋊C4—1422no—
607C22⋊C4—1422no—
608C42—26no—
609C42—26no—
610C42—1422no—
611C42—1426no—
612C42—1426no—
613C42—1426no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—716no—
621C23—716no—
622C23—716no—
623C23—712no—
624C23—1421no—
625C23—1421no—
626C23—1421no—
627C23—1421no—
628C23—1421no—
629C23—1421no—
630C23—1423no—
631C23—1423no—
632C23—1423no—
633C23—1423no—
634C23C22×C4×D7112yes—
635C23C24×D7111yescharacteristic
636Q8—224no—
637Q8—14224no—
638Q8—14224no—
639Q8C22⋊C4×D71116yes—
640D4—7148no—
641D4—14224no—
642D4—1428no—
643D4—14224no—
644C2×C4—21no—
645C2×C4—23no—
646C2×C4—23no—
647C2×C4—21no—
648C2×C4—224no—
649C2×C4—21no—
650C2×C4—23no—
651C2×C4—23no—
652C2×C4—21no—
653C2×C4—23no—
654C2×C4—21no—
655C2×C4—23no—
656C2×C4—23no—
657C2×C4—23no—
658C2×C4—28412no—
659C2×C4—28412no—
660C2×C4—56812no—
661C2×C4—712no—
662C2×C4—712no—
663C2×C4—712no—
664C2×C4—7148no—
665C2×C4—716no—
666C2×C4—712no—
667C2×C4—14248no—
668C2×C4—1421no—
669C2×C4—1423no—
670C2×C4—1423no—
671C2×C4—1421no—
672C2×C4—1421no—
673C2×C4—1423no—
674C2×C4—1423no—
675C2×C4—1423no—
676C2×C4—1423no—
677C2×C4—1421no—
678C2×C4—1423no—
679C2×C4—1423no—
680C2×C4—1421no—
681C2×C4—14224no—
682C2×C4C22×C4×D7116yes—
683C2×C4C22×C4×D7116yes—
684C2×C4C2×D4×D7116yes—
685C2×C4C2×D4×D7116yes—
686C2×C4#1455617612yescomplemented
687C22—22no—
688C22—22no—
689C22—22no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—41no—
694C22—2841no—
695C22—2841no—
696C22—2841no—
697C22—2841no—
698C22—7112no—
699C22—1422no—
700C22—1422no—
701C22—1422no—
702C22—1426no—
703C22—1426no—
704C22—1426no—
705C22—1426no—
706C22—1426no—
707C22—1426no—
708C22C23×C4×D7111yescharacteristic
709C22C22×D4×D7111yescharacteristic
710C22C22×D4×D7111yescharacteristic
711C222−1+4×D7111yescharacteristic
712C22C2×#1455617611yescharacteristic
713C22#1798683511yescharacteristic
714C22#1798683611yescharacteristic
715C4—26no—
716C4—22no—
717C4—43no—
718C4—41no—
719C4—43no—
720C4—2843no—
721C4—2841no—
722C4—2843no—
723C4—714no—
724C4—1426no—
725C4—1422no—
726C4C2×C22⋊C4×D71112yes—
727C2—42no—
728C2—2842no—
729C2—14212no—
730C2C22×C22⋊C4×D7111yescharacteristic
731C2#2260154911yescharacteristic
732C2C4×#1455617611yescharacteristic
733C2#2260201711yescharacteristic
734C2#2260201911yescharacteristic
735C2#2260212411yescharacteristic
736C2#2260213111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingQ8×C22⋊C4×C71C2
socle, cosocleC23×C71C25
prime radicalC22×#14556176C2
hypercenterQ8×C22⋊C4D71
hypocenterC71#34259
LCSG ▷ C22×C71 ▷ C71
UCSC1 ◁ C23 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#17986481C2semidirect
3. C2×C4×#11765866C2semidirect
4. Q8×C22⋊Dic71C2semidirect
5. Q8×(C2×D71)⋊C4C2semidirect
6. Q8×(C2×D71)⋊C4C2semidirect
7. #22591171C2semidirect
8. #22591169C2semidirect
9. #22591169C2semidirect
10. #22591168C2semidirect
11. #22590929C2semidirect
12. #22590923C2semidirect
13. #22590826C2semidirect
14. #391×D71C2semidirect
15. Q8×C22⋊C4×C71C2semidirect
18. C2×#14556176C4semidirect
75. C2×#11765866C2×C4semidirect
82. C2×#11765865C2×C4semidirect
83. C2×#11765865C2×C4semidirect
90. C2×Q8×D71C2×C4semidirect
91. C2×Q8×D71C2×C4semidirect
140. C22×Q8×C71C2×C4semidirect
158. #11765866C22⋊C4semidirect
287. C2×C4×C712−1+4semidirect
307. C2×Dic712−1+4semidirect
375. Q8×C22⋊C4D71semidirect
384. C71#34259semidirect
463. C22×Q8C4×D71semidirect
686. C2×C4#14556176semidirect

Maximal subgroups

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

subgroupindex
C22×#145561762
C2×#179864812
C2×C4×#117658662
Q8×C22⋊Dic712
Q8×(C2×D71)⋊C42
#225911712
#225911692
#225911682
#225909292
#225909232
#225908262
#391×D712
Q8×C22⋊C4×C712
#3425971