Finite Group Databasebeta

← C2×#22600825 #32876031

Subgroups — C2×#22600825 #32876031

Order 18176.

1942 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986706C211yesmaximal, characteristic, complemented
2#22600825C2116yesmaximal, direct product factor
3C2×#17986409C211yesmaximal, characteristic, complemented
4C2×#17986334C211yesmaximal, characteristic, complemented
5C2×#17986315C211yesmaximal, characteristic, complemented
6C2×#17986340C211yesmaximal, characteristic, complemented
7C2×#17986310C211yesmaximal, characteristic, complemented
8C2×#17986303C211yesmaximal, characteristic, complemented
9C2×#17986279C211yesmaximal, characteristic, complemented
10C2×#17986243C211yesmaximal, characteristic, complemented
11C2×#17986226C211yesmaximal, characteristic, complemented
12C2×#17986099C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986042C211yesmaximal, characteristic, complemented
15C22×#14556061C211yesmaximal, characteristic, complemented
16C2×#553×C71C211yesmaximal, characteristic
17C22×#11765853C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19C23×C71⋊C8C2211yescharacteristic
20#17986706—24no—
21#17986706C2218yescomplemented
22C2×#14556128C2211yescharacteristic
23C2×#14556119—21no—
24C2×#14556107C2211yescharacteristic
25C2×#14556107C2211yescharacteristic
26C2×#14556105—21no—
27C2×#14556105—21no—
28C2×C4×Dic142C2211yescharacteristic
29C2×D4×Dic71—21no—
30C22×C4⋊Dic71C2211yescharacteristic
31C22×C4⋊Dic71C2211yescharacteristic
32#17986409C2218yescomplemented
33#17986340C2218yescomplemented
34#17986334C2218yescomplemented
35#17986315C2218yescomplemented
36#17986310C2218yescomplemented
37#17986303C2218yescomplemented
38#17986279C2218yescomplemented
39#17986243C2218yescomplemented
40#17986226C2218yescomplemented
41#17986099C2218yescomplemented
42#17986071C2218yescomplemented
43#17986042C2218yescomplemented
44C2×#14556061C2211yescharacteristic
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556061C2211yescharacteristic
50C2×#14556061C2218yescomplemented
51C2×#14556059C2211yescharacteristic
52C2×#14556059C2211yescharacteristic
53C2×#14556059C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556051C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556051C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556049C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64#553×C71—24no—
65#553×C71C2218yes—
66C2×#126×C71—21no—
67C2×#125×C71C2211yescharacteristic
68C2×#123×C71—21no—
69C2×#121×C71—21no—
70C2×#121×C71C2211yescharacteristic
71C2×#121×C71C2211yescharacteristic
72C2×C4×D4×C71—21no—
73C2×C4×D4×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×#117×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C23×Dic71—21no—
80C23×Dic71—21no—
81C2×#11765853—24no—
82C2×#11765853C2314yes—
83C2×#11765849—24no—
84C2×#11765849C2314yes—
85C22×C71⋊C8—24no—
86C22×C71⋊C8C2314yes—
87C22×C71⋊C8C2311yescharacteristic
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91#14556128—22no—
92#14556128C2314yes—
93#14556119—28no—
94#14556107—22no—
95#14556107—22no—
96#14556107C2314yes—
97#14556107C2314yes—
98#14556105—28no—
99#14556105—28no—
100C4×Dic142—22no—
101C4×Dic142C2314yes—
102D4×Dic71—28no—
103C2×C4⋊Dic71—22no—
104C2×C4⋊Dic71—22no—
105C2×C4⋊Dic71—21no—
106C2×C4⋊Dic71—21no—
107C2×C4⋊Dic71—21no—
108C2×C4⋊Dic71C2314yes—
109C2×C4⋊Dic71C2314yes—
110C2×C4⋊Dic71C2311yescharacteristic
111C2×C4⋊Dic71C2311yescharacteristic
112C2×C4⋊Dic71C2311yescharacteristic
113C2×Dic71⋊C4—21no—
114C2×Dic71⋊C4—21no—
115C2×Dic71⋊C4—21no—
116C2×C22⋊Dic71—21no—
117C2×C22⋊Dic71—21no—
118C2×C4×Dic71—21no—
119#14556061C2314yes—
120#14556061C2314yes—
121#14556061C2314yes—
122#14556061C2314yes—
123#14556061C2314yes—
124#14556061C2314yes—
125#14556059C2314yes—
126#14556059C2314yes—
127#14556059C2314yes—
128C4⋊(C71⋊C8)C2314yes—
129#14556051C2314yes—
130#14556051C2314yes—
131#14556051C2314yes—
132#14556049C2314yes—
133#14556049C2314yes—
134#14556049C2314yes—
135C22⋊(C71⋊C8)C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137#14556039C2314yes—
138C22×D4×C71—21no—
139C22×D4×C71—21no—
140C22×D4×C71D411yescharacteristic
141C22×D4×C71C2311yescharacteristic
142C23×C4×C71—21no—
143C23×C4×C71—21no—
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146#126×C71—28no—
147#125×C71—22no—
148#125×C71C2314yes—
149#123×C71—28no—
150#121×C71—28no—
151#121×C71—22no—
152#121×C71—22no—
153#121×C71C2314yes—
154#121×C71C2314yes—
155C4×D4×C71—28no—
156C4×D4×C71—22no—
157C4×D4×C71D414yes—
158C4×D4×C71C2314yes—
159C4×D4×C71C2314yes—
160#117×C71—22no—
161#117×C71C2314yes—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—22no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71D411yescharacteristic
167C2×C4⋊C4×C71C2314yes—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C22⋊C4×C71—21no—
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71D411yescharacteristic
176C2×C22⋊C4×C71D411yescharacteristic
177C2×C42×C71—21no—
178C2×C42×C71C2311yescharacteristic
179C2×Dic142—22no—
180C2×Dic142—22no—
181C2×Dic142—21no—
182C2×Dic142—24no—
183C2×Dic142—82no—
184C2×Dic142C2412yes—
185C22×Dic71—21no—
186C22×Dic71—21no—
187C22×Dic71—21no—
188C22×Dic71—21no—
189C22×Dic71—24no—
190C22×Dic71—24no—
191C22×Dic71—82no—
192C22×Dic71—82no—
193#11765853—28no—
194#11765849—28no—
195C2×C71⋊C8—22no—
196C2×C71⋊C8—22no—
197C2×C71⋊C8—22no—
198C2×C71⋊C8—28no—
199C2×C71⋊C8#4114yes—
200C2×C71⋊C8C2412yes—
201C2×C71⋊C8C2412yes—
202C2×C71⋊C8C2412yes—
203C2×C71⋊C8C2412yes—
204C4⋊Dic71—21no—
205C4⋊Dic71—24no—
206C4⋊Dic71—24no—
207C4⋊Dic71—21no—
208C4⋊Dic71—21no—
209C4⋊Dic71—24no—
210C4⋊Dic71C2412yes—
211C4⋊Dic71C2412yes—
212C4⋊Dic71C2412yes—
213Dic71⋊C4—24no—
214Dic71⋊C4—24no—
215Dic71⋊C4—24no—
216C22⋊Dic71—24no—
217C22⋊Dic71—24no—
218C4×Dic71—24no—
219C24×C71—21no—
220C24×C71C2×D411yescharacteristic
221C24×C71C2×D411yescharacteristic
222C2×D4×C71—24no—
223C2×D4×C71—24no—
224C2×D4×C71—24no—
225C2×D4×C71—21no—
226C2×D4×C71—22no—
227C2×D4×C71—22no—
228C2×D4×C71—44no—
229C2×D4×C71—82no—
230C2×D4×C71C2×D414yes—
231C2×D4×C71C2412yes—
232C22×C4×C71—22no—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—21no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—24no—
240C22×C4×C71—24no—
241C22×C4×C71—82no—
242C22×C4×C71—82no—
243C22×C4×C71C2×D411yescharacteristic
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D412yes—
248C22×C4×C71C2×D412yes—
249C22×C4×C71C2412yes—
250C22×C4×C71C2412yes—
251C22×C4×C71C2411yescharacteristic
252C4⋊C4×C71—21no—
253C4⋊C4×C71—21no—
254C4⋊C4×C71—24no—
255C4⋊C4×C71—24no—
256C4⋊C4×C71—24no—
257C4⋊C4×C71—21no—
258C4⋊C4×C71C2×D414yes—
259C4⋊C4×C71C2412yes—
260C4⋊C4×C71C2412yes—
261C4⋊C4×C71C2412yes—
262C22⋊C4×C71—24no—
263C22⋊C4×C71—24no—
264C22⋊C4×C71—24no—
265C22⋊C4×C71—24no—
266C22⋊C4×C71C2×D414yes—
267C22⋊C4×C71C2×D414yes—
268C42×C71—24no—
269C42×C71C2×D412yes—
270C42×C71C2412yes—
271C23×C71—22no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—42no—
278C23×C71—42no—
279C23×C71—42no—
280C23×C71#13714yes—
281C23×C71C22×D412yes—
282C23×C71C22×D412yes—
283C23×C71C22×D411yescharacteristic
284D4×C71—28no—
285D4×C71—22no—
286D4×C71—22no—
287D4×C71—48no—
288D4×C71—42no—
289D4×C71—84no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—24no—
295C2×C4×C71—24no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—42no—
304C2×C4×C71—42no—
305C2×C4×C71—42no—
306C2×C4×C71—84no—
307C2×C4×C71—84no—
308C2×C4×C71C22×D412yes—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D412yes—
311C2×C4×C71C22×D412yes—
312C2×C4×C71C22×D411yescharacteristic
313C2×C4×C71C2×#4112yes—
314C2×C4×C712−1+412yes—
315C2×C4×C71C2511yescharacteristic
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—22no—
320C2×Dic71—42no—
321C2×Dic71—42no—
322C2×Dic71—42no—
323C2×Dic71—42no—
324C2×Dic71—84no—
325C2×Dic71—84no—
326Dic142—22no—
327Dic142—22no—
328Dic142—42no—
329Dic142—84no—
330C71⋊C8—22no—
331C71⋊C8—22no—
332C71⋊C8—22no—
333C71⋊C8C2×#4114yes—
334C22×C71—28no—
335C22×C71—22no—
336C22×C71—22no—
337C22×C71—22no—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—44no—
341C22×C71—42no—
342C22×C71—42no—
343C22×C71—42no—
344C22×C71—84no—
345C22×C71#54712yes—
346C22×C71C2×#13714yes—
347C22×C71C2×#13712yes—
348C22×C71#57612yes—
349C22×C71C23×D411yescharacteristic
350C4×C71—22no—
351C4×C71—22no—
352C4×C71—22no—
353C4×C71—22no—
354C4×C71—42no—
355C4×C71—42no—
356C4×C71—42no—
357C4×C71#54712yes—
358C4×C71C22×#4111yescharacteristic
359C4×C71C2×2−1+411yescharacteristic
360Dic71—42no—
361Dic71—42no—
362Dic71—42no—
363Dic71—42no—
364C2×#3346—711nomaximal, Sylow
365C2×C71—24no—
366C2×C71—42no—
367C2×C71—82no—
368C2×C71#334614yescomplemented
369C2×C71C2×#54711yescharacteristic
370C2×C71C22×#13711yescharacteristic
371C2×C71C2×#57611yescharacteristic
372C2×#554—711no—
373C2×#553D7111yescharacteristic
374#3346—7116no—
375C2×#501—711no—
376C2×#484—711no—
377C2×#481—711no—
378C2×#485—711no—
379C2×#480—711no—
380C2×#479—711no—
381C2×#474—711no—
382C2×#468—711no—
383C2×#465—711no—
384C2×#440—711no—
385C2×#435—711no—
386C2×#428—711no—
387C22×#107—711no—
388C71C2×#334611yescharacteristic, complemented, Sylow
389C22×SD16—711no—
390C22×M16—711no—
391C23×C8—711no—
392#554—718no—
393#554—1424no—
394#553—24no—
395#553C2×D7118yes—
396C2×C4⋊Q8—711no—
397C2×#126—21no—
398C2×#125—1421no—
399C2×#125C2×D7111yescharacteristic
400C2×#123—21no—
401C2×C22⋊Q8—711no—
402C2×C22⋊Q8—711no—
403C2×C22⋊Q8—1421no—
404C2×C22⋊Q8—1421no—
405C2×#121—21no—
406C2×#121C2×D7111yescharacteristic
407C2×#121C2×D7111yescharacteristic
408C2×C4×Q8—711no—
409C2×C4×D4—21no—
410C2×C4×D4—1421no—
411C2×C4×D4C2×D7111yescharacteristic
412C2×C4×D4C2×D7111yescharacteristic
413C2×#117C2×D7111yescharacteristic
414C22×C4⋊C4—711no—
415C22×C4⋊C4—711no—
416C22×C4⋊C4C2×D7111yescharacteristic
417#501—718no—
418#485—718no—
419#484—718no—
420#481—718no—
421#480—718no—
422#479—718no—
423#474—718no—
424#468—718no—
425#465—718no—
426#440—718no—
427#435—718no—
428#428—718no—
429C2×#107—711no—
430C2×#107—711no—
431C2×#107—711no—
432C2×#107—711no—
433C2×#107—718no—
434C2×#107—711no—
435C2×#107—711no—
436C2×#106—711no—
437C2×#106—711no—
438C2×#106—711no—
439C2×C4⋊C8—711no—
440C2×#103—711no—
441C2×#103—711no—
442C2×#103—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×#102—711no—
446C2×C22⋊C8—711no—
447C2×C22⋊C8—711no—
448C2×#97—711no—
449C22×Q8—711no—
450C22×Q8—1421no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4C22⋊D7111yescharacteristic
454C22×D4C22×D7111yescharacteristic
455C23×C4—21no—
456C23×C4—21no—
457C23×C4—1421no—
458C23×C4—1421no—
459C23×C4C22×D7111yescharacteristic
460C23×C4C22×D7111yescharacteristic
461C2×SD16—714no—
462C2×SD16—1424no—
463C2×M16—714no—
464C2×M16—1424no—
465C22×C8—711no—
466C22×C8—711no—
467C22×C8—714no—
468C22×C8—711no—
469C22×C8—711no—
470C22×C8—1424no—
471C4⋊Q8—714no—
472C4⋊Q8—1422no—
473#126—28no—
474#125—22no—
475#125—1428no—
476#125C22×D7114yes—
477#123—28no—
478C22⋊Q8—714no—
479C22⋊Q8—714no—
480C22⋊Q8—1422no—
481C22⋊Q8—1422no—
482C22⋊Q8—1428no—
483C22⋊Q8—1428no—
484#121—28no—
485#121—22no—
486#121—22no—
487#121C22×D7114yes—
488#121C22×D7114yes—
489C4×Q8—714no—
490C4×Q8—1422no—
491C4×D4—28no—
492C4×D4—22no—
493C4×D4—1428no—
494C4×D4C22⋊D7114yes—
495C4×D4C22×D7114yes—
496C4×D4C22×D7114yes—
497#117—22no—
498#117C22×D7114yes—
499C2×C4⋊C4—21no—
500C2×C4⋊C4—22no—
501C2×C4⋊C4—21no—
502C2×C4⋊C4—21no—
503C2×C4⋊C4—711no—
504C2×C4⋊C4—711no—
505C2×C4⋊C4—711no—
506C2×C4⋊C4—714no—
507C2×C4⋊C4—714no—
508C2×C4⋊C4—1421no—
509C2×C4⋊C4—1421no—
510C2×C4⋊C4—1422no—
511C2×C4⋊C4—1422no—
512C2×C4⋊C4—1421no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4C22⋊D7111yescharacteristic
517C2×C4⋊C4C22×D7111yescharacteristic
518C2×C4⋊C4C22×D7111yescharacteristic
519C2×C4⋊C4C22×D7114yes—
520C2×C4⋊C4C22×D7111yescharacteristic
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—21no—
524C2×C22⋊C4—21no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4C22⋊D7111yescharacteristic
528C2×C22⋊C4C22⋊D7111yescharacteristic
529C2×C42—21no—
530C2×C42—1421no—
531C2×C42C22×D7111yescharacteristic
532#107—714no—
533#107—714no—
534#107—714no—
535#107—714no—
536#107—714no—
537#107—714no—
538#106—714no—
539#106—714no—
540#106—714no—
541C4⋊C8—714no—
542#103—714no—
543#103—714no—
544#103—714no—
545#102—714no—
546#102—714no—
547#102—714no—
548C22⋊C8—714no—
549C22⋊C8—714no—
550#97—714no—
551C24—21no—
552C24C2×C22⋊D7111yescharacteristic
553C24C2×C22⋊D7111yescharacteristic
554C2×Q8—5682no—
555C2×Q8—712no—
556C2×Q8—1422no—
557C2×Q8—1422no—
558C2×Q8—1421no—
559C2×Q8—1424no—
560C2×D4—24no—
561C2×D4—24no—
562C2×D4—24no—
563C2×D4—21no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—44no—
567C2×D4—82no—
568C2×D4C2×C22⋊D7114yes—
569C2×D4C23×D7112yes—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—24no—
578C22×C4—24no—
579C22×C4—82no—
580C22×C4—82no—
581C22×C4—5682no—
582C22×C4—5682no—
583C22×C4—1421no—
584C22×C4—1421no—
585C22×C4—1421no—
586C22×C4—1421no—
587C22×C4—1424no—
588C22×C4—1424no—
589C22×C4C2×C22⋊D7112yes—
590C22×C4C2×C22⋊D7112yes—
591C22×C4C2×C22⋊D7111yescharacteristic
592C22×C4C2×C22⋊D7111yescharacteristic
593C22×C4C2×C22⋊D7111yescharacteristic
594C22×C4C2×C22⋊D7111yescharacteristic
595C22×C4C23×D7112yes—
596C22×C4C23×D7112yes—
597C22×C4C23×D7111yescharacteristic
598SD16—1428no—
599M16—1428no—
600C2×C8—714no—
601C2×C8—712no—
602C2×C8—712no—
603C2×C8—712no—
604C2×C8—712no—
605C2×C8—1428no—
606C2×C8—1422no—
607C2×C8—1422no—
608C2×C8—1422no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—24no—
612C4⋊C4—24no—
613C4⋊C4—24no—
614C4⋊C4—21no—
615C4⋊C4—712no—
616C4⋊C4—712no—
617C4⋊C4—712no—
618C4⋊C4—1424no—
619C4⋊C4—1424no—
620C4⋊C4—1424no—
621C4⋊C4—1421no—
622C4⋊C4—1424no—
623C4⋊C4—1424no—
624C4⋊C4—1421no—
625C4⋊C4—1421no—
626C4⋊C4—1424no—
627C4⋊C4C2×C22⋊D7114yes—
628C4⋊C4C23×D7112yes—
629C4⋊C4C23×D7112yes—
630C4⋊C4C23×D7112yes—
631C22⋊C4—24no—
632C22⋊C4—24no—
633C22⋊C4—24no—
634C22⋊C4—24no—
635C22⋊C4—1424no—
636C22⋊C4—1424no—
637C22⋊C4C2×C22⋊D7114yes—
638C22⋊C4C2×C22⋊D7114yes—
639C42—24no—
640C42—1424no—
641C42C2×C22⋊D7112yes—
642C42C23×D7112yes—
643C23—22no—
644C23—22no—
645C23—22no—
646C23—22no—
647C23—22no—
648C23—22no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23#1455615814yes—
653C23C22×C22⋊D7112yes—
654C23C22×C22⋊D7112yes—
655C23C22×C22⋊D7111yescharacteristic
656Q8—2842no—
657Q8—5684no—
658Q8—1422no—
659Q8—1422no—
660D4—28no—
661D4—22no—
662D4—22no—
663D4—48no—
664D4—42no—
665D4—84no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—42no—
680C2×C4—42no—
681C2×C4—42no—
682C2×C4—84no—
683C2×C4—84no—
684C2×C4—2842no—
685C2×C4—2842no—
686C2×C4—2842no—
687C2×C4—2842no—
688C2×C4—5684no—
689C2×C4—5684no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4C22×C22⋊D7112yes—
695C2×C4C22×C22⋊D7112yes—
696C2×C4C22×C22⋊D7112yes—
697C2×C4C22×C22⋊D7112yes—
698C2×C4C22×C22⋊D7111yescharacteristic
699C2×C4#41×D7112yes—
700C2×C4#1455617512yes—
701C2×C4C24×D7111yescharacteristic
702C8—714no—
703C8—1422no—
704C8—1422no—
705C8—1422no—
706C22—22no—
707C22—22no—
708C22—28no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—44no—
713C22—42no—
714C22—42no—
715C22—42no—
716C22—84no—
717C22#1798664812yes—
718C22C2×#1455615814yes—
719C22C2×#1455615812yes—
720C22#1798680212yes—
721C22C23×C22⋊D7111yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—42no—
727C4—42no—
728C4—42no—
729C4—2842no—
730C4—2842no—
731C4—2842no—
732C4—2842no—
733C4#1798664812yes—
734C4C2×#41×D7111yescharacteristic
735C4C2×#1455617511yescharacteristic
736C2—24no—
737C2—42no—
738C2—82no—
739C2#2260082514yesdirect product factor
740C2C2×#1798664811yescharacteristic
741C2C22×#1455615811yescharacteristic
742C2C2×#1798680211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
Fitting, prime radicalC2×#553×C71C2
socleC23×C71C22×D4
hypercenterC2×#553D71
hypocenterC71C2×#3346
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#17986706C2semidirect
2. #22600825C2direct (N × H)
3. C2×#17986409C2semidirect
4. C2×#17986334C2semidirect
5. C2×#17986315C2semidirect
6. C2×#17986340C2semidirect
7. C2×#17986310C2semidirect
8. C2×#17986303C2semidirect
9. C2×#17986279C2semidirect
10. C2×#17986243C2semidirect
11. C2×#17986226C2semidirect
12. C2×#17986099C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986042C2semidirect
15. C22×#14556061C2semidirect
21. #17986706C22semidirect
32. #17986409C22semidirect
33. #17986340C22semidirect
34. #17986334C22semidirect
35. #17986315C22semidirect
36. #17986310C22semidirect
37. #17986303C22semidirect
38. #17986279C22semidirect
39. #17986243C22semidirect
40. #17986226C22semidirect
41. #17986099C22semidirect
42. #17986071C22semidirect
43. #17986042C22semidirect
50. C2×#14556061C22semidirect
368. C2×C71#3346semidirect
388. C71C2×#3346semidirect
739. C2#22600825direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867062
#226008252
C2×#179864092
C2×#179863342
C2×#179863152
C2×#179863402
C2×#179863102
C2×#179863032
C2×#179862792
C2×#179862432
C2×#179862262
C2×#179860992
C2×#179860712
C2×#179860422
C22×#145560612
C2×#553×C712
C2×#334671