Finite Group Databasebeta

← #32158486

Subgroups — #32158486

Order 18176.

5050 conjugacy classes of subgroups.

The subgroup lattice has 736 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556176C211yesmaximal, characteristic
2C2×#17986475C211yesmaximal, characteristic, complemented
3C2×C4×Q8×D71C211yesmaximal, characteristic, complemented
4#22591180C213yesmaximal, complemented
5#22591178C211yesmaximal, characteristic, complemented
6#22591178C211yesmaximal, characteristic, complemented
7#22591177C213yesmaximal, complemented
8Q8×C22⋊Dic71C211yesmaximal, characteristic, complemented
9#22591174C213yesmaximal, complemented
10#22591174C213yesmaximal, complemented
11#22590931C213yesmaximal, complemented
12#22590929C213yesmaximal, complemented
13#22590829C213yesmaximal, complemented
14#22590826C213yesmaximal, 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#17986475—28no—
26C2×Q8×Dic71C2211yescharacteristic
27C2×Q8×Dic71C2211yescharacteristic
28C2×C4×Dic142C2213yes—
29C2×C4×Dic142C2213yes—
30C2×#14556093C2213yes—
31C2×#14556093C2213yes—
32C4×Q8×D71—28no—
33C2×#14556086C2213yes—
34C2×#14556085C2213yes—
35C2×C4⋊C4×D71C2213yes—
36C2×C42×D71C2213yes—
37#17985906C2213yes—
38#17985906C2213yes—
39#17985903C2213yes—
40#17985903C2213yes—
41#17985903C2216yes—
42#17985901C2213yes—
43#17985901C2213yes—
44#17985900C2213yes—
45#17985900C2213yes—
46#17985899C2213yes—
47#17985899C2213yes—
48#17985899C2216yes—
49#17985877C2213yes—
50#17985877C2213yes—
51#17985877C2216yes—
52#17985875C2211yescharacteristic
53#17985875C2213yes—
54#17985859C2213yes—
55#17985858C2216yes—
56#17985858C2216yes—
57#17985856C2213yes—
58#17985856C2213yes—
59C4×(C2×D71)⋊C4C2213yes—
60C4×(C2×D71)⋊C4C2213yes—
61C4×C22⋊Dic71C2213yes—
62#17985846C2216yes—
63#17985846C2216yes—
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×#11765866—24no—
75C2×#11765866—24no—
76C2×#11765866C2×C4124yes—
77C2×#11765866C2×C418yescomplemented
78C2×#11765865—212no—
79C2×#11765865—212no—
80C2×#11765865—212no—
81C2×#11765865—212no—
82C2×#11765865C2×C4124yes—
83C2×#11765865C2×C4124yescomplemented
84C22×Dic142C2313yes—
85C22×Dic142C2313yes—
86C2×Q8×D71—212no—
87C2×Q8×D71—212no—
88C2×Q8×D71C2×C418yes—
89C2×Q8×D71C2×C4124yescomplemented
90C2×Q8×D71D418yes—
91C2×Q8×D71D418yes—
92C22×D284C2313yes—
93C22×D284C2313yes—
94C22×C22⋊D71C2311yescharacteristic
95C22×C22⋊D71C2313yes—
96C22×C4×D71C2311yescharacteristic
97C22×C4×D71C2316yes—
98C22×C4×D71C2313yes—
99C22×C4×D71C2313yes—
100C22×C4×D71C2313yes—
101Q8×Dic71—24no—
102Q8×Dic71—24no—
103C4×Dic142—212no—
104C4×Dic142—212no—
105#14556093—212no—
106#14556093—212no—
107#14556086—212no—
108#14556085—212no—
109C2×C4⋊Dic71C2313yes—
110C2×C4⋊Dic71C2313yes—
111C2×Dic71⋊C4C2316yes—
112C2×Dic71⋊C4C2313yes—
113C2×Dic71⋊C4C2313yes—
114C4⋊C4×D71—212no—
115C2×C22⋊Dic71C2311yescharacteristic
116C2×C22⋊Dic71C2313yes—
117C2×(C2×D71)⋊C4C2313yes—
118C2×(C2×D71)⋊C4C2313yes—
119C2×(C2×D71)⋊C4C2311yescharacteristic
120C2×(C2×D71)⋊C4C2313yes—
121C2×(C2×D71)⋊C4C2316yes—
122C2×(C2×D71)⋊C4C2316yes—
123C2×(C2×D71)⋊C4C2313yes—
124C2×(C2×D71)⋊C4C2313yes—
125C2×C4×Dic71C2313yes—
126C2×C4×Dic71C2313yes—
127C2×C4×Dic71C2316yes—
128C2×C4×Dic71C2313yes—
129C2×C4×Dic71C2313yes—
130C42×D71—212no—
131C71⋊#95C2313yes—
132C71⋊#95C2316yes—
133C71⋊#95C2313yes—
134C71⋊#95C2311yescharacteristic
135C71⋊#95C2311yescharacteristic
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×D71C2413yes—
156C23×D71C2411yescharacteristic
157#11765866—232no—
158#11765866—296no—
159#11765865—296no—
160#11765865—296no—
161C2×Dic142—26no—
162C2×Dic142—26no—
163C2×Dic142C22×C4112yes—
164C2×Dic142C22×C4112yes—
165C2×Dic142C2×D4112yes—
166C2×Dic142C2×D4112yes—
167Q8×D71—296no—
168Q8×D71C22⋊C4164yescomplemented
169C2×D284—26no—
170C2×D284—26no—
171C2×D284—26no—
172C2×D284—26no—
173C2×D284C22×C4112yes—
174C2×D284C22×C4112yes—
175C2×C22⋊D71—22no—
176C2×C22⋊D71—22no—
177C2×C22⋊D71—26no—
178C2×C22⋊D71—26no—
179C2×C22⋊D71C22×C414yes—
180C2×C22⋊D71C22×C4112yes—
181C22×Dic71C2413yes—
182C22×Dic71C2411yescharacteristic
183C22×Dic71C2413yes—
184C22×Dic71C2411yescharacteristic
185C22×Dic71C2411yescharacteristic
186C22×Dic71C2413yes—
187C2×C4×D71—22no—
188C2×C4×D71—26no—
189C2×C4×D71—26no—
190C2×C4×D71—22no—
191C2×C4×D71—212no—
192C2×C4×D71—212no—
193C2×C4×D71—22no—
194C2×C4×D71—26no—
195C2×C4×D71—43no—
196C2×C4×D71—43no—
197C2×C4×D71C22×C4112yes—
198C2×C4×D71C22×C4124yes—
199C2×C4×D71C22×C4112yes—
200C2×C4×D71C2×D4112yes—
201C2×C4×D71C2×D4112yes—
202C4⋊Dic71—26no—
203C4⋊Dic71—26no—
204Dic71⋊C4—212no—
205Dic71⋊C4—26no—
206Dic71⋊C4—26no—
207C22⋊Dic71—22no—
208C22⋊Dic71—43no—
209(C2×D71)⋊C4—22no—
210(C2×D71)⋊C4—26no—
211(C2×D71)⋊C4—26no—
212(C2×D71)⋊C4—26no—
213(C2×D71)⋊C4—43no—
214(C2×D71)⋊C4—46no—
215(C2×D71)⋊C4—46no—
216(C2×D71)⋊C4—43no—
217C4×Dic71—26no—
218C4×Dic71—26no—
219C4×Dic71—26no—
220C4×Dic71—26no—
221C4×Dic71—212no—
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×C71C2411yescharacteristic
235C22×C4×C71C2413yes—
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—21no—
254C22×D71—21no—
255C22×D71—21no—
256C22×D71—21no—
257C22×D71—23no—
258C22×D71—23no—
259C22×D71—23no—
260C22×D71—23no—
261C22×D71—23no—
262C22×D71—23no—
263C22×D71C23×C416yes—
264C22×D71C23×C412yes—
265C22×D71C22×D412yes—
266C22×D71C22×D412yes—
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—23no—
279C2×C4×C71—23no—
280C2×C4×C71—23no—
281C2×C4×C71—21no—
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—28no—
289C22⋊D71—224no—
290C2×Dic71—21no—
291C2×Dic71—21no—
292C2×Dic71—21no—
293C2×Dic71—21no—
294C2×Dic71—21no—
295C2×Dic71—23no—
296C2×Dic71—23no—
297C2×Dic71—23no—
298C2×Dic71—21no—
299C2×Dic71—21no—
300C2×Dic71—23no—
301C2×Dic71—23no—
302C2×Dic71—23no—
303C2×Dic71C23×C412yes—
304C2×Dic71C23×C416yes—
305C2×Dic71C22×D416yes—
306C2×Dic71C22×D416yes—
307C2×Dic712−1+412yescomplemented
308D284—224no—
309D284—224no—
310C4×D71—28no—
311C4×D71—224no—
312C4×D71—248no—
313C4×D71—412no—
314C4×D71C2×C22⋊C4148yes—
315Dic142—224no—
316Dic142C2×C22⋊C4148yes—
317C22×C71—22no—
318C22×C71—22no—
319C22×C71—22no—
320C22×C71—41no—
321C22×C71—41no—
322C22×C71—41no—
323C22×C71—41no—
324C22×C71C24×C411yescharacteristic
325C22×C71C23×D411yescharacteristic
326C22×C71C23×D411yescharacteristic
327C22×C71C2×2−1+411yescharacteristic
328C22×C71C2×2−1+411yescharacteristic
329C22×C71#58511yescharacteristic
330C22×C71#58511yescharacteristic
331C2×D71—22no—
332C2×D71—22no—
333C2×D71—22no—
334C2×D71—22no—
335C2×D71—22no—
336C2×D71—22no—
337C2×D71—26no—
338C2×D71—26no—
339C2×D71—26no—
340C2×D71—43no—
341C2×D71—43no—
342C2×D71—43no—
343C2×D71—43no—
344C2×D71C22×C22⋊C414yes—
345C4×C71—26no—
346C4×C71—22no—
347C4×C71—43no—
348C4×C71—43no—
349C4×C71—41no—
350C4×C71C22×C22⋊C4112yes—
351Dic71—22no—
352Dic71—22no—
353Dic71—43no—
354Dic71—41no—
355Dic71—43no—
356Dic71C22×C22⋊C4112yes—
357#34257—711nomaximal, Sylow
358C2×C71—42no—
359C2×C71C23×C22⋊C411yescharacteristic
360C2×C71C4×2−1+411yescharacteristic
361C2×C71C4×2−1+411yescharacteristic
362C2×C71#348611yescharacteristic
363C2×C71#348711yescharacteristic
364C2×C71#349711yescharacteristic
365C2×C71#349711yescharacteristic
366D71—24no—
367D71—46no—
368C22×2−1+4—711no—
369C2×#519—711no—
370C22×C4×Q8—711no—
371#2341—713no—
372#2341—713no—
373#2341—711no—
374#2341—711no—
375Q8×C22⋊C4—713no—
376Q8×C22⋊C4—713no—
377Q8×C22⋊C4—711no—
378Q8×C22⋊C4D7111yescharacteristic, complemented
379#2311—713no—
380#2311—713no—
381#2297—713no—
382#2297—713no—
383C71#3425711yescharacteristic, complemented, Sylow
384C2×2−1+4—7116no—
385C2×2−1+4—1428no—
386C2×2−1+4—1428no—
387C22×#41—713no—
388C22×#41—711no—
389C22×#41—713no—
390C22×#41—713no—
391C23×Q8—711no—
392C23×Q8—713no—
393C23×Q8C2×D7111yescharacteristic
394#519—1428no—
395C2×C4×Q8—711no—
396C2×C4×Q8—711no—
397C2×C4×Q8—713no—
398C2×C4×Q8—713no—
399C2×C4×Q8—713no—
400C2×C4×Q8—713no—
401C2×C4×Q8—1428no—
402C2×C4×Q8C2×D7111yescharacteristic
403C2×C4×Q8C2×D7111yescharacteristic
404C2×#117—713no—
405C2×#117—713no—
406C22×C4⋊C4—713no—
407C22×C42—713no—
408#391—713no—
409#391—713no—
410#391—716no—
411#391—713no—
412#391—713no—
413#391C2×D7113yes—
414#391C2×D7113yes—
415#390—713no—
416#390—713no—
417#390—716no—
418#390—713no—
419#390—713no—
420#390—713no—
421#390—713no—
422#386—713no—
423#386—711no—
424#386—716no—
425#386—713no—
426#386—713no—
427#380—713no—
428#380—713no—
429#380—713no—
430#380—716no—
431#380—716no—
432#380C2×D7113yes—
433C4×C22⋊C4—713no—
434C4×C22⋊C4—713no—
435C4×C22⋊C4—713no—
436C4×C22⋊C4—716no—
437C4×C22⋊C4—716no—
438C4×C22⋊C4C2×D7113yes—
4392−1+4—142128no—
440C2×#41—7124no—
441C2×#41—718no—
442C2×#41—7124no—
443C2×#41—7124no—
444C2×#41—14212no—
445C2×#41—14212no—
446C2×#41—14212no—
447C2×#41—14212no—
448C2×#41—14212no—
449C2×#41—14212no—
450C2×#41—1424no—
451C2×#41—1424no—
452C22×Q8—24no—
453C22×Q8—24no—
454C22×Q8—718no—
455C22×Q8—718no—
456C22×Q8—718no—
457C22×Q8—7124no—
458C22×Q8—713no—
459C22×Q8—713no—
460C22×Q8—14212no—
461C22×Q8—14212no—
462C22×Q8C4×D7118yescomplemented
463C22×Q8C22×D7113yes—
464C22×Q8C22×D7111yescharacteristic
465C22×D4—711no—
466C22×D4—713no—
467C22×D4—713no—
468C22×D4—713no—
469C23×C4—713no—
470C23×C4—713no—
471C23×C4—716no—
472C23×C4—713no—
473C23×C4—711no—
474C23×C4C22×D7113yes—
475C4×Q8—24no—
476C4×Q8—24no—
477C4×Q8—14212no—
478C4×Q8—14212no—
479C4×Q8—14212no—
480C4×Q8—14212no—
481C4×Q8—1424no—
482C4×Q8—1424no—
483#117—14212no—
484#117—14212no—
485C2×C4⋊C4—716no—
486C2×C4⋊C4—713no—
487C2×C4⋊C4—713no—
488C2×C4⋊C4—713no—
489C2×C4⋊C4—713no—
490C2×C4⋊C4—14212no—
491C2×C4⋊C4C22×D7113yes—
492C2×C4⋊C4C22×D7113yes—
493C2×C22⋊C4—713no—
494C2×C22⋊C4—713no—
495C2×C22⋊C4—716no—
496C2×C22⋊C4—716no—
497C2×C22⋊C4—713no—
498C2×C22⋊C4—711no—
499C2×C22⋊C4—713no—
500C2×C22⋊C4—711no—
501C2×C22⋊C4—713no—
502C2×C22⋊C4—713no—
503C2×C22⋊C4C22×D7111yescharacteristic
504C2×C22⋊C4C22×D7113yes—
505C2×C42—716no—
506C2×C42—713no—
507C2×C42—713no—
508C2×C42—713no—
509C2×C42—713no—
510C2×C42—14212no—
511C2×C42C22×D7113yes—
512C2×C42C22×D7113yes—
513#95—711no—
514#95—711no—
515#95—713no—
516#95—713no—
517#95—713no—
518#95—713no—
519#95—716no—
520#95C22×D7113yes—
521#95C22×D7116yes—
522#95C22×D7113yes—
523C24—711no—
524C24—713no—
525C24C23×D7111yescharacteristic
526#41—14296no—
527#41—14296no—
528#41—14296no—
529#41—14232no—
530C2×Q8—232no—
531C2×Q8—26no—
532C2×Q8—26no—
533C2×Q8—7164no—
534C2×Q8—7112no—
535C2×Q8—7112no—
536C2×Q8—7112no—
537C2×Q8—7112no—
538C2×Q8—1426no—
539C2×Q8—1426no—
540C2×Q8—14296no—
541C2×Q8C2×C4×D71112yes—
542C2×Q8C2×C4×D7114yes—
543C2×Q8D4×D7114yes—
544C2×Q8D4×D7114yes—
545C2×D4—7112no—
546C2×D4—714no—
547C2×D4—7112no—
548C2×D4—7112no—
549C2×D4—1426no—
550C2×D4—1426no—
551C2×D4—1426no—
552C2×D4—1426no—
553C2×D4—1422no—
554C2×D4—1422no—
555C2×D4—1426no—
556C2×D4—1426no—
557C22×C4—26no—
558C22×C4—26no—
559C22×C4—2843no—
560C22×C4—2843no—
561C22×C4—713no—
562C22×C4—7112no—
563C22×C4—7112no—
564C22×C4—7112no—
565C22×C4—711no—
566C22×C4—711no—
567C22×C4—7124no—
568C22×C4—7112no—
569C22×C4—711no—
570C22×C4—713no—
571C22×C4—713no—
572C22×C4—1426no—
573C22×C4—1422no—
574C22×C4—14212no—
575C22×C4—14212no—
576C22×C4—1422no—
577C22×C4—1426no—
578C22×C4—1426no—
579C22×C4—1422no—
580C22×C4C2×C4×D71112yes—
581C22×C4C23×D7113yes—
582C22×C4C23×D7113yes—
583C22×C4C23×D7111yescharacteristic
584C22×C4C23×D7113yes—
585C22×C4C23×D7111yescharacteristic
586C22×C4C23×D7113yes—
587C4⋊C4—26no—
588C4⋊C4—26no—
589C4⋊C4—14212no—
590C4⋊C4—1426no—
591C4⋊C4—1426no—
592C4⋊C4—1426no—
593C4⋊C4—1426no—
594C22⋊C4—22no—
595C22⋊C4—43no—
596C22⋊C4—2846no—
597C22⋊C4—2843no—
598C22⋊C4—2843no—
599C22⋊C4—2846no—
600C22⋊C4—2843no—
601C22⋊C4—1426no—
602C22⋊C4—1422no—
603C22⋊C4—1426no—
604C22⋊C4—1422no—
605C22⋊C4—1426no—
606C42—26no—
607C42—26no—
608C42—1426no—
609C42—1426no—
610C42—14212no—
611C42—1426no—
612C42—1426no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—712no—
620C23—712no—
621C23—712no—
622C23—716no—
623C23—1423no—
624C23—1423no—
625C23—1423no—
626C23—1423no—
627C23—1423no—
628C23—1423no—
629C23—1421no—
630C23—1421no—
631C23—1421no—
632C23—1421no—
633C23C22×C4×D7112yes—
634C23C24×D7111yescharacteristic
635Q8—224no—
636Q8—7148no—
637Q8—14224no—
638Q8C22⋊C4×D71116yes—
639D4—14224no—
640D4—14224no—
641D4—1428no—
642D4—14224no—
643C2×C4—21no—
644C2×C4—23no—
645C2×C4—23no—
646C2×C4—21no—
647C2×C4—224no—
648C2×C4—21no—
649C2×C4—23no—
650C2×C4—23no—
651C2×C4—23no—
652C2×C4—21no—
653C2×C4—23no—
654C2×C4—23no—
655C2×C4—21no—
656C2×C4—23no—
657C2×C4—28412no—
658C2×C4—716no—
659C2×C4—716no—
660C2×C4—716no—
661C2×C4—7148no—
662C2×C4—712no—
663C2×C4—712no—
664C2×C4—14248no—
665C2×C4—1428no—
666C2×C4—1421no—
667C2×C4—1423no—
668C2×C4—1423no—
669C2×C4—1421no—
670C2×C4—1423no—
671C2×C4—1421no—
672C2×C4—1423no—
673C2×C4—1423no—
674C2×C4—1423no—
675C2×C4—1421no—
676C2×C4—1421no—
677C2×C4—1421no—
678C2×C4—1421no—
679C2×C4—14224no—
680C2×C4C22×C4×D7116yes—
681C2×C4C22×C4×D7116yes—
682C2×C4C2×D4×D7116yes—
683C2×C4C2×D4×D7116yes—
684C2×C4#1455617612yescomplemented
685C22—22no—
686C22—22no—
687C22—22no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22—41no—
692C22—2843no—
693C22—2843no—
694C22—2843no—
695C22—2843no—
696C22—714no—
697C22—1426no—
698C22—1426no—
699C22—1426no—
700C22—1422no—
701C22—1422no—
702C22—1422no—
703C22—1422no—
704C22—1422no—
705C22—1422no—
706C22C23×C4×D7111yescharacteristic
707C22C22×D4×D7111yescharacteristic
708C22C22×D4×D7111yescharacteristic
709C222−1+4×D7111yescharacteristic
710C22C2×#1455617611yescharacteristic
711C22#1798683511yescharacteristic
712C22#1798683611yescharacteristic
713C4—22no—
714C4—26no—
715C4—43no—
716C4—43no—
717C4—41no—
718C4—2843no—
719C4—2841no—
720C4—2843no—
721C4—7112no—
722C4—1422no—
723C4—1422no—
724C4C2×C22⋊C4×D71112yes—
725C2—42no—
726C2—2846no—
727C2—1424no—
728C2C22×C22⋊C4×D7111yescharacteristic
729C2#2260154911yescharacteristic
730C2C4×#1455617611yescharacteristic
731C2#2260199011yescharacteristic
732C2#2260199711yescharacteristic
733C2#2260210811yescharacteristic
734C2#2260211011yescharacteristic
subgroupG/H
center, FrattiniC23C24×D71
commutatorC22×C71C24×C4
FittingQ8×C22⋊C4×C71C2
socle, cosocleC23×C71C25
prime radicalC22×#14556176C2
hypercenterQ8×C22⋊C4D71
hypocenterC71#34257
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×#17986475C2semidirect
3. C2×C4×Q8×D71C2semidirect
4. #22591180C2semidirect
5. #22591178C2semidirect
6. #22591178C2semidirect
7. #22591177C2semidirect
8. Q8×C22⋊Dic71C2semidirect
9. #22591174C2semidirect
10. #22591174C2semidirect
11. #22590931C2semidirect
12. #22590929C2semidirect
13. #22590829C2semidirect
14. #22590826C2semidirect
15. Q8×C22⋊C4×C71C2semidirect
18. C2×#14556176C4semidirect
77. C2×#11765866C2×C4semidirect
83. C2×#11765865C2×C4semidirect
89. C2×Q8×D71C2×C4semidirect
140. C22×Q8×C71C2×C4semidirect
168. Q8×D71C22⋊C4semidirect
287. C2×C4×C712−1+4semidirect
307. C2×Dic712−1+4semidirect
378. Q8×C22⋊C4D71semidirect
383. C71#34257semidirect
462. C22×Q8C4×D71semidirect
684. 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×#179864752
C2×C4×Q8×D712
#225911802
#225911782
#225911772
Q8×C22⋊Dic712
#225911742
#225909312
#225909292
#225908292
#225908262
Q8×C22⋊C4×C712
#3425771