Finite Group Databasebeta

← C2×#22600727 #32875908

Subgroups — C2×#22600727 #32875908

Order 18176.

1942 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986707C211yesmaximal, characteristic
2C2×#17986704C211yesmaximal, characteristic
3#22600727C2116yesmaximal, direct product factor
4C2×#17986403C211yesmaximal, characteristic, complemented
5C2×#17986336C211yesmaximal, characteristic, complemented
6C2×#17986335C211yesmaximal, characteristic, complemented
7C2×#17986333C211yesmaximal, characteristic, complemented
8C2×#17986293C211yesmaximal, characteristic, complemented
9C2×#17986292C211yesmaximal, characteristic, complemented
10C2×#17986239C211yesmaximal, characteristic, complemented
11C2×#17986238C211yesmaximal, characteristic, complemented
12C2×#17986091C211yesmaximal, characteristic, complemented
13C2×(C22⋊D71)⋊C8C211yesmaximal, characteristic
14C22×#14556061C211yesmaximal, characteristic, complemented
15C2×#107×D71C211yesmaximal, characteristic, complemented
16C2×#484×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic
18C23×C71⋊C8C2211yescharacteristic
19C22×C8×D71C2211yescharacteristic
20#17986707—24no—
21#17986707C2218yes—
22#17986704—24no—
23#17986704C2218yes—
24C2×#14556127C2211yescharacteristic
25C2×#14556127C2211yescharacteristic
26C2×#14556118—21no—
27C2×#14556118—21no—
28C2×#14556108—21no—
29C2×#14556108C2211yescharacteristic
30C2×#14556107—21no—
31C2×#14556107C2211yescharacteristic
32C2×#14556106—21no—
33C2×#14556105—21no—
34C2×#14556104C2211yescharacteristic
35C2×Q8×Dic71C2211yescharacteristic
36C2×#14556093C2211yescharacteristic
37C2×C4×C22⋊D71—21no—
38C2×C4×C22⋊D71C2211yescharacteristic
39C2×(C22⋊D71)⋊C4—21no—
40C22×C4⋊Dic71C2211yescharacteristic
41C2×C4⋊C4×D71C2211yescharacteristic
42C2×C4⋊C4×D71C2211yescharacteristic
43#17986403C2218yescomplemented
44#17986336C2218yescomplemented
45#17986335C2218yescomplemented
46#17986333C2218yescomplemented
47#17986293C2218yescomplemented
48#17986292C2218yescomplemented
49#17986239C2218yescomplemented
50#17986238C2218yescomplemented
51#17986091C2218yescomplemented
52(C22⋊D71)⋊C8C2218yes—
53C2×#14556062C2211yescharacteristic
54C2×#14556062C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556061C2211yescharacteristic
57C2×#14556061C2211yescharacteristic
58C2×#14556061C2211yescharacteristic
59C2×#14556061C2211yescharacteristic
60C2×#14556061C2218yescomplemented
61#107×D71C2218yescomplemented
62C2×Dic71⋊C8C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556052C2211yescharacteristic
66C2×#14556051C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C2×C22⋊Q8×C71C2211yescharacteristic
70C22×C4⋊C4×C71C2211yescharacteristic
71#484×C71C2218yescomplemented
72C2×#107×C71C2211yescharacteristic
73C2×#107×C71C2211yescharacteristic
74C2×#103×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×C22⋊C8×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C22×Dic142C2311yescharacteristic
80C22×C22⋊D71D411yescharacteristic
81C23×Dic71—21no—
82C22×C4×D71—21no—
83C22×C4×D71—21no—
84C22×C4×D71C2311yescharacteristic
85C2×#11765855—24no—
86C2×#11765855C2314yes—
87C22×C71⋊C8—24no—
88C22×C71⋊C8C2314yes—
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91C2×C8×D71—24no—
92C2×C8×D71C2314yes—
93#14556127—22no—
94#14556127—22no—
95#14556127C2314yes—
96#14556127C2314yes—
97#14556118—28no—
98#14556118—28no—
99#14556108—22no—
100#14556108—28no—
101#14556108C2314yes—
102#14556107—28no—
103#14556107—22no—
104#14556107C2314yes—
105#14556106—28no—
106#14556105—28no—
107#14556104—22no—
108#14556104C2314yes—
109Q8×Dic71—22no—
110Q8×Dic71C2314yes—
111#14556093—22no—
112#14556093C2314yes—
113C4×C22⋊D71—28no—
114C4×C22⋊D71D414yes—
115C4×C22⋊D71C2314yes—
116(C22⋊D71)⋊C4—28no—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71—22no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71C2314yes—
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4D411yescharacteristic
133C4⋊C4×D71—22no—
134C4⋊C4×D71—22no—
135C4⋊C4×D71C2314yes—
136C4⋊C4×D71C2314yes—
137C2×C22⋊Dic71—21no—
138C2×C22⋊Dic71D411yescharacteristic
139C2×(C2×D71)⋊C4—21no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4D411yescharacteristic
142C2×C4×Dic71—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71C2311yescharacteristic
145#14556062C2314yes—
146#14556062C2314yes—
147#14556061C2314yes—
148#14556061C2314yes—
149#14556061C2314yes—
150#14556061C2314yes—
151#14556061C2314yes—
152Dic71⋊C8C2314yes—
153#14556053C2314yes—
154#14556053C2314yes—
155#14556052C2314yes—
156#14556051C2314yes—
157(C2×D71)⋊C8C2314yes—
158C8×Dic71C2314yes—
159C22×Q8×C71C2311yescharacteristic
160C23×C4×C71—21no—
161C23×C4×C71C2311yescharacteristic
162C22×C8×C71C2311yescharacteristic
163C22×C8×C71C2311yescharacteristic
164C22⋊Q8×C71—22no—
165C22⋊Q8×C71C2314yes—
166C2×C4⋊C4×C71—22no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C4⋊C4×C71C2311yescharacteristic
172C2×C4⋊C4×C71C2314yes—
173C2×C22⋊C4×C71—21no—
174#107×C71C2314yes—
175#107×C71C2314yes—
176#103×C71C2314yes—
177#103×C71C2314yes—
178C22⋊C8×C71C2314yes—
179C23×D71C2×D411yescharacteristic
180C2×Dic142—22no—
181C2×Dic142—22no—
182C2×Dic142—21no—
183C2×Dic142—24no—
184C2×Dic142—24no—
185C2×Dic142—82no—
186C2×Dic142—82no—
187C2×Dic142C2412yes—
188C2×C22⋊D71Q1618yescomplemented
189C2×C22⋊D71C2×D414yes—
190C22×Dic71—21no—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71—24no—
195C22×Dic71—82no—
196C22×Dic71C2×D411yescharacteristic
197C22×Dic71C2×D411yescharacteristic
198C22×Dic71C2×D411yescharacteristic
199C2×C4×D71—22no—
200C2×C4×D71—22no—
201C2×C4×D71—24no—
202C2×C4×D71—24no—
203C2×C4×D71—82no—
204C2×C4×D71—82no—
205C2×C4×D71C2×D412yes—
206C2×C4×D71C2412yes—
207#11765855—28no—
208C2×C71⋊C8—22no—
209C2×C71⋊C8—28no—
210C2×C71⋊C8#4114yes—
211C2×C71⋊C8C2412yes—
212C2×C71⋊C8C2412yes—
213C8×D71—28no—
214C4⋊Dic71—21no—
215C4⋊Dic71—21no—
216C4⋊Dic71—21no—
217C4⋊Dic71—24no—
218C4⋊Dic71—24no—
219C4⋊Dic71—24no—
220C4⋊Dic71C2412yes—
221C4⋊Dic71C2412yes—
222C4⋊Dic71C2412yes—
223Dic71⋊C4—24no—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230Dic71⋊C4C2×D414yes—
231C22⋊Dic71—24no—
232C22⋊Dic71C2×D414yes—
233(C2×D71)⋊C4—24no—
234(C2×D71)⋊C4—24no—
235(C2×D71)⋊C4C2×D414yes—
236C4×Dic71—24no—
237C4×Dic71—24no—
238C4×Dic71C2×D412yes—
239C4×Dic71C2412yes—
240C24×C71C2×D411yescharacteristic
241C2×Q8×C71—21no—
242C2×Q8×C71—22no—
243C2×Q8×C71—22no—
244C2×Q8×C71C2412yes—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71—21no—
248C22×C4×C71—21no—
249C22×C4×C71—21no—
250C22×C4×C71—21no—
251C22×C4×C71—24no—
252C22×C4×C71—82no—
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D412yes—
255C22×C4×C71C2412yes—
256C22×C4×C71C2411yescharacteristic
257C2×C8×C71—22no—
258C2×C8×C71—22no—
259C2×C8×C71C2412yes—
260C2×C8×C71C2412yes—
261C4⋊C4×C71—21no—
262C4⋊C4×C71—24no—
263C4⋊C4×C71—21no—
264C4⋊C4×C71—24no—
265C4⋊C4×C71—21no—
266C4⋊C4×C71C2412yes—
267C4⋊C4×C71C2412yes—
268C4⋊C4×C71C2412yes—
269C22⋊C4×C71—24no—
270C23×C71—22no—
271C23×C71—22no—
272C23×C71C2×Q1614yes—
273C23×C71C22×D412yes—
274C23×C71C22×D411yescharacteristic
275C22×D71—22no—
276C22×D71—22no—
277C22×D71C2×Q1614yes—
278C22×D71C22×D412yes—
279Q8×C71—22no—
280Q8×C71—22no—
281Q8×C71—42no—
282C2×C4×C71—22no—
283C2×C4×C71—24no—
284C2×C4×C71—22no—
285C2×C4×C71—22no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—42no—
291C2×C4×C71—42no—
292C2×C4×C71—42no—
293C2×C4×C71—42no—
294C2×C4×C71—84no—
295C2×C4×C71C22×D412yes—
296C2×C4×C71C22×D411yescharacteristic
297C2×C4×C71C2×#4112yes—
298C2×C4×C712−1+412yes—
299C2×C4×C71C2511yescharacteristic
300C22⋊D71C2×Q16116yescomplemented
301C2×Dic71—22no—
302C2×Dic71—22no—
303C2×Dic71—22no—
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—42no—
308C2×Dic71—42no—
309C2×Dic71—42no—
310C2×Dic71—42no—
311C2×Dic71—84no—
312C2×Dic71C2×Q1614yes—
313C2×Dic71C22×D412yes—
314C2×Dic71C22×D412yes—
315C2×Dic71C22×D412yes—
316C4×D71—24no—
317C4×D71—22no—
318C4×D71—22no—
319C4×D71—84no—
320C4×D71—84no—
321Dic142—22no—
322Dic142—22no—
323Dic142—42no—
324Dic142—84no—
325Dic142—84no—
326C8×C71—22no—
327C8×C71—22no—
328C71⋊C8—22no—
329C71⋊C8C2×#4114yes—
330C22×C71—28no—
331C22×C71—22no—
332C22×C71—22no—
333C22×C71#54712yes—
334C22×C71C22×Q1614yes—
335C22×C71C22×Q1612yes—
336C22×C71#57612yes—
337C22×C71C23×D411yescharacteristic
338C2×D71—28no—
339C2×D71—22no—
340C2×D71—22no—
341C2×D71C22×Q1614yes—
342C4×C71—22no—
343C4×C71—42no—
344C4×C71—42no—
345C4×C71—42no—
346C4×C71—42no—
347C4×C71#54712yes—
348C4×C71C22×#4111yescharacteristic
349C4×C71C2×2−1+411yescharacteristic
350Dic71—22no—
351Dic71—22no—
352Dic71—42no—
353Dic71—42no—
354Dic71—42no—
355Dic71—42no—
356Dic71C22×Q1614yes—
357C2×#3338—711nomaximal, Sylow
358C2×C71—24no—
359C2×C71#333814yescomplemented
360C2×C71C2×#54711yescharacteristic
361C2×C71C23×Q1611yescharacteristic
362C2×C71C2×#57611yescharacteristic
363D71—24no—
364C2×#554—711no—
365C2×#554—711no—
366#3338—7116no—
367C2×#500—711no—
368C2×#484—711no—
369C2×#484—711no—
370C2×#484—711no—
371C2×#484D7111yescharacteristic, complemented
372C2×#477—711no—
373C2×#477—711no—
374C2×#467—711no—
375C2×#467—711no—
376C2×C4×Q16—711no—
377C2×C8×D4—711no—
378C22×#107—711no—
379C22×#107—711no—
380C71C2×#333811yescharacteristic, complemented, Sylow
381C22×Q16—711no—
382C23×C8—711no—
383C23×C8—711no—
384#554—718no—
385#554—718no—
386#554—1424no—
387#554—1424no—
388C2×C4⋊Q8—711no—
389C2×C4⋊Q8—711no—
390C2×#125—1421no—
391C2×#125—1421no—
392C2×C22⋊Q8—711no—
393C2×C22⋊Q8—711no—
394C2×C22⋊Q8—711no—
395C2×C22⋊Q8—1421no—
396C2×C22⋊Q8—1421no—
397C2×C22⋊Q8—1421no—
398C2×C22⋊Q8—1421no—
399C2×C22⋊Q8C2×D7111yescharacteristic
400C2×C4×Q8—711no—
401C2×C4×Q8—711no—
402C2×C4×D4—711no—
403C2×C4×D4—1421no—
404C2×C4×D4—1421no—
405C22×C4⋊C4—711no—
406C22×C4⋊C4—711no—
407C22×C4⋊C4—711no—
408C22×C4⋊C4C2×D7111yescharacteristic
409#500—718no—
410#484—718no—
411#484—718no—
412#484—718no—
413#484C2×D7118yescomplemented
414#477—718no—
415#477—718no—
416#467—718no—
417#467—718no—
418C4×Q16—718no—
419C8×D4—718no—
420C2×#107—711no—
421C2×#107—711no—
422C2×#107—711no—
423C2×#107—711no—
424C2×#107—718no—
425C2×#107—711no—
426C2×#107—711no—
427C2×#107—711no—
428C2×#107—718no—
429C2×#107C2×D7111yescharacteristic
430C2×#107C2×D7111yescharacteristic
431C2×C4⋊C8—711no—
432C2×#103—711no—
433C2×#103—711no—
434C2×#103—711no—
435C2×#103—711no—
436C2×#103C2×D7111yescharacteristic
437C2×#103C2×D7111yescharacteristic
438C2×C22⋊C8—711no—
439C2×C22⋊C8C2×D7111yescharacteristic
440C2×C4×C8—711no—
441C22×Q8—711no—
442C22×Q8—1421no—
443C22×Q8—1421no—
444C22×Q8C22×D7111yescharacteristic
445C22×D4—711no—
446C23×C4—21no—
447C23×C4—711no—
448C23×C4—1421no—
449C23×C4—1421no—
450C23×C4—1421no—
451C23×C4C22×D7111yescharacteristic
452C2×Q16—714no—
453C2×Q16—1424no—
454C22×C8—711no—
455C22×C8—711no—
456C22×C8—714no—
457C22×C8—714no—
458C22×C8—1424no—
459C22×C8—1424no—
460C22×C8C22×D7111yescharacteristic
461C22×C8C22×D7111yescharacteristic
462C4⋊Q8—714no—
463C4⋊Q8—714no—
464C4⋊Q8—1422no—
465C4⋊Q8—1422no—
466#125—1428no—
467#125—1428no—
468C22⋊Q8—22no—
469C22⋊Q8—714no—
470C22⋊Q8—714no—
471C22⋊Q8—714no—
472C22⋊Q8—1428no—
473C22⋊Q8—1428no—
474C22⋊Q8—1428no—
475C22⋊Q8—1428no—
476C22⋊Q8—1422no—
477C22⋊Q8—1422no—
478C22⋊Q8—1422no—
479C22⋊Q8C22×D7114yes—
480C4×Q8—714no—
481C4×Q8—714no—
482C4×Q8—1422no—
483C4×Q8—1422no—
484C4×D4—714no—
485C4×D4—714no—
486C4×D4—1428no—
487C4×D4—1428no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4—711no—
492C2×C4⋊C4—711no—
493C2×C4⋊C4—711no—
494C2×C4⋊C4—711no—
495C2×C4⋊C4—714no—
496C2×C4⋊C4—714no—
497C2×C4⋊C4—714no—
498C2×C4⋊C4—1422no—
499C2×C4⋊C4—1422no—
500C2×C4⋊C4—1421no—
501C2×C4⋊C4—1421no—
502C2×C4⋊C4—1421no—
503C2×C4⋊C4—1421no—
504C2×C4⋊C4—1421no—
505C2×C4⋊C4—1421no—
506C2×C4⋊C4—1421no—
507C2×C4⋊C4—1421no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4—1422no—
510C2×C4⋊C4—1421no—
511C2×C4⋊C4C22×D7111yescharacteristic
512C2×C4⋊C4C22×D7111yescharacteristic
513C2×C4⋊C4C22×D7111yescharacteristic
514C2×C4⋊C4C22×D7114yes—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—711no—
517C2×C22⋊C4—711no—
518C2×C22⋊C4—1421no—
519C2×C22⋊C4—1421no—
520C2×C22⋊C4—1421no—
521C2×C42—711no—
522C2×C42—1421no—
523C2×C42—1421no—
524#107—714no—
525#107—714no—
526#107—714no—
527#107—714no—
528#107—714no—
529#107—714no—
530#107—714no—
531#107C22×D7114yes—
532#107C22×D7114yes—
533C4⋊C8—714no—
534#103—714no—
535#103—714no—
536#103—714no—
537#103—714no—
538#103C22×D7114yes—
539#103C22×D7114yes—
540C22⋊C8—714no—
541C22⋊C8C22×D7114yes—
542C4×C8—714no—
543C24—711no—
544C24D4×D7111yescharacteristic
545C2×Q8—21no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—5682no—
549C2×Q8—5682no—
550C2×Q8—712no—
551C2×Q8—1424no—
552C2×Q8—1424no—
553C2×Q8—1422no—
554C2×Q8—1422no—
555C2×Q8—1421no—
556C2×Q8C23×D7112yes—
557C2×D4—714no—
558C2×D4—718no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—24no—
566C22×C4—82no—
567C22×C4—5682no—
568C22×C4—5682no—
569C22×C4—5682no—
570C22×C4—711no—
571C22×C4—711no—
572C22×C4—711no—
573C22×C4—712no—
574C22×C4—712no—
575C22×C4—1424no—
576C22×C4—1424no—
577C22×C4—1421no—
578C22×C4—1421no—
579C22×C4—1421no—
580C22×C4—1421no—
581C22×C4—1424no—
582C22×C4—1422no—
583C22×C4—1422no—
584C22×C4D4×D7112yes—
585C22×C4D4×D7111yescharacteristic
586C22×C4C23×D7112yes—
587C22×C4C23×D7111yescharacteristic
588Q16—1428no—
589C2×C8—22no—
590C2×C8—22no—
591C2×C8—714no—
592C2×C8—712no—
593C2×C8—712no—
594C2×C8—1428no—
595C2×C8—1428no—
596C2×C8—1422no—
597C2×C8C23×D7112yes—
598C2×C8C23×D7112yes—
599C4⋊C4—21no—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—24no—
603C4⋊C4—21no—
604C4⋊C4—714no—
605C4⋊C4—712no—
606C4⋊C4—712no—
607C4⋊C4—712no—
608C4⋊C4—1424no—
609C4⋊C4—1424no—
610C4⋊C4—1424no—
611C4⋊C4—1424no—
612C4⋊C4—1424no—
613C4⋊C4—1424no—
614C4⋊C4—1424no—
615C4⋊C4—1424no—
616C4⋊C4—1424no—
617C4⋊C4—1421no—
618C4⋊C4—1424no—
619C4⋊C4—1421no—
620C4⋊C4—1421no—
621C4⋊C4C23×D7112yes—
622C4⋊C4C23×D7112yes—
623C4⋊C4C23×D7112yes—
624C22⋊C4—24no—
625C22⋊C4—714no—
626C22⋊C4—714no—
627C22⋊C4—1424no—
628C22⋊C4—1424no—
629C22⋊C4—1424no—
630C42—712no—
631C42—712no—
632C42—1424no—
633C42—1424no—
634C23—22no—
635C23—22no—
636C23—712no—
637C23—714no—
638C23—1422no—
639C23—1422no—
640C23Q16×D7114yes—
641C23C2×D4×D7112yes—
642C23C2×D4×D7111yescharacteristic
643Q8—22no—
644Q8—22no—
645Q8—42no—
646Q8—2842no—
647Q8—5684no—
648Q8—5684no—
649Q8—1422no—
650Q8—1422no—
651D4—7116no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—2842no—
666C2×C4—2842no—
667C2×C4—2842no—
668C2×C4—2842no—
669C2×C4—5684no—
670C2×C4—5684no—
671C2×C4—5684no—
672C2×C4—712no—
673C2×C4—714no—
674C2×C4—712no—
675C2×C4—712no—
676C2×C4—1422no—
677C2×C4—1422no—
678C2×C4—1422no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4—1422no—
682C2×C4—1422no—
683C2×C4—1422no—
684C2×C4—1424no—
685C2×C4C2×D4×D7112yes—
686C2×C4C2×D4×D7111yescharacteristic
687C2×C4#41×D7112yes—
688C2×C4#1455617512yes—
689C2×C4C24×D7111yescharacteristic
690C8—22no—
691C8—22no—
692C8—714no—
693C8—1422no—
694C22—28no—
695C22—22no—
696C22—22no—
697C22—714no—
698C22—1428no—
699C22—1422no—
700C22—1422no—
701C22#1798664712yes—
702C22C2×Q16×D7114yes—
703C22C2×Q16×D7112yes—
704C22#1798680312yes—
705C22C22×D4×D7111yescharacteristic
706C4—22no—
707C4—42no—
708C4—42no—
709C4—42no—
710C4—42no—
711C4—2842no—
712C4—2842no—
713C4—2842no—
714C4—2842no—
715C4—714no—
716C4—1422no—
717C4—1422no—
718C4#1798664712yes—
719C4C2×#41×D7111yescharacteristic
720C4C2×#1455617511yescharacteristic
721C2—24no—
722C2—1424no—
723C2#2260072714yesdirect product factor
724C2C2×#1798664711yescharacteristic
725C2C22×Q16×D7111yescharacteristic
726C2C2×#1798680311yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#484×C71C2
socleC23×C71C22×D4
prime radicalC22×C22⋊D71D4
hypercenterC2×#484D71
hypocenterC71C2×#3338
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#484

Complements

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

NH ≅ G/Ntype
3. #22600727C2direct (N × H)
4. C2×#17986403C2semidirect
5. C2×#17986336C2semidirect
6. C2×#17986335C2semidirect
7. C2×#17986333C2semidirect
8. C2×#17986293C2semidirect
9. C2×#17986292C2semidirect
10. C2×#17986239C2semidirect
11. C2×#17986238C2semidirect
12. C2×#17986091C2semidirect
14. C22×#14556061C2semidirect
15. C2×#107×D71C2semidirect
16. C2×#484×C71C2semidirect
43. #17986403C22semidirect
44. #17986336C22semidirect
45. #17986335C22semidirect
46. #17986333C22semidirect
47. #17986293C22semidirect
48. #17986292C22semidirect
49. #17986239C22semidirect
50. #17986238C22semidirect
51. #17986091C22semidirect
60. C2×#14556061C22semidirect
61. #107×D71C22semidirect
71. #484×C71C22semidirect
188. C2×C22⋊D71Q16semidirect
300. C22⋊D71C2×Q16semidirect
359. C2×C71#3338semidirect
371. C2×#484D71semidirect
380. C71C2×#3338semidirect
413. #484C2×D71semidirect
723. C2#22600727direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867072
C2×#179867042
#226007272
C2×#179864032
C2×#179863362
C2×#179863352
C2×#179863332
C2×#179862932
C2×#179862922
C2×#179862392
C2×#179862382
C2×#179860912
C2×(C22⋊D71)⋊C82
C22×#145560612
C2×#107×D712
C2×#484×C712
C2×#333871