Finite Group Databasebeta

← C2×#22598124 #32864949

Subgroups — C2×#22598124 #32864949

Order 18176.

2162 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×#17986552C211yesmaximal, characteristic, complemented
2C2×#41×Dic71C211yesmaximal, characteristic
3#22598124C2116yesmaximal, direct product factor
4C2×#17986308C211yesmaximal, characteristic, complemented
5C2×#17986304C211yesmaximal, characteristic, complemented
6C2×#17986292C211yesmaximal, characteristic, complemented
7C2×#17986282C211yesmaximal, characteristic, complemented
8C2×#17986301C211yesmaximal, characteristic, complemented
9C2×#17986297C211yesmaximal, characteristic, complemented
10C2×#17986287C211yesmaximal, characteristic, complemented
11C2×#17986277C211yesmaximal, characteristic, complemented
12C2×#17986037C211yesmaximal, characteristic, complemented
13C2×#17986035C211yesmaximal, characteristic, complemented
14C22×Dic71⋊C8C211yesmaximal, characteristic, complemented
15C2×#17985995C211yesmaximal, characteristic
16C2×#416×C71C211yesmaximal, characteristic
17C23×C71⋊C8C2211yescharacteristic
18#17986552—24no—
19#17986552C2218yescomplemented
20C2×#14556127C2211yescharacteristic
21C2×#14556127C2211yescharacteristic
22C2×#14556119C2211yescharacteristic
23C2×#14556119C2211yescharacteristic
24C2×#14556105—21no—
25C2×#14556105—21no—
26#41×Dic71—24no—
27#41×Dic71C2218yes—
28C2×Q8×Dic71C2211yescharacteristic
29C2×Q8×Dic71C2211yescharacteristic
30C2×C4×Dic142—21no—
31C2×C4×Dic142—21no—
32C2×D4×Dic71—21no—
33C2×D4×Dic71—21no—
34C2×D4×Dic71C2211yescharacteristic
35C2×D4×Dic71C2211yescharacteristic
36C2×#14556087—21no—
37C2×#14556087C2211yescharacteristic
38C2×#14556087C2211yescharacteristic
39C22×C4×Dic71—21no—
40C22×C4×Dic71C2211yescharacteristic
41#17986308C2218yescomplemented
42#17986304C2218yescomplemented
43#17986301C2218yescomplemented
44#17986297C2218yescomplemented
45#17986292C2218yescomplemented
46#17986287C2218yescomplemented
47#17986282C2218yescomplemented
48#17986277C2218yescomplemented
49#17986037C2218yescomplemented
50#17986035C2218yescomplemented
51C2×#14556062C2211yescharacteristic
52C2×#14556062C2211yescharacteristic
53C2×#14556061C2211yescharacteristic
54C2×#14556061C2211yescharacteristic
55C2×#14556060C2211yescharacteristic
56C2×#14556060C2211yescharacteristic
57C2×#14556059C2211yescharacteristic
58C2×#14556059C2211yescharacteristic
59C2×Dic71⋊C8C2211yescharacteristic
60C2×Dic71⋊C8C2211yescharacteristic
61C2×Dic71⋊C8C2211yescharacteristic
62C2×Dic71⋊C8C2211yescharacteristic
63C2×Dic71⋊C8C2218yescomplemented
64#17985995C2218yes—
65C2×#14556052C2211yescharacteristic
66C2×#14556052C2211yescharacteristic
67C2×#14556049C2211yescharacteristic
68C2×#14556049C2211yescharacteristic
69C22×#41×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71C2×#117×C71C2211yescharacteristic
72#416×C71C2218yes—
73C2×#103×C71C2211yescharacteristic
74C2×#103×C71C2211yescharacteristic
75C2×#102×C71C2211yescharacteristic
76C2×#102×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142—21no—
79C23×Dic71—21no—
80C23×Dic71—21no—
81C23×Dic71D411yescharacteristic
82C23×Dic71D411yescharacteristic
83C22×C71⋊C8—24no—
84C22×C71⋊C8C2311yescharacteristic
85C22×C71⋊C8C2311yescharacteristic
86C22×C71⋊C8C2314yes—
87#14556127—22no—
88#14556127—22no—
89#14556127C2314yes—
90#14556127C2314yes—
91#14556119—22no—
92#14556119—22no—
93#14556119C2314yes—
94#14556119C2314yes—
95#14556105—28no—
96#14556105—28no—
97Q8×Dic71—22no—
98Q8×Dic71—22no—
99Q8×Dic71C2314yes—
100Q8×Dic71C2314yes—
101C4×Dic142—28no—
102C4×Dic142—28no—
103D4×Dic71—28no—
104D4×Dic71—28no—
105D4×Dic71—22no—
106D4×Dic71—22no—
107D4×Dic71C2314yes—
108D4×Dic71C2314yes—
109#14556087—28no—
110#14556087—22no—
111#14556087—22no—
112#14556087C2314yes—
113#14556087C2314yes—
114C2×C4⋊Dic71—21no—
115C2×C4⋊Dic71—21no—
116C2×C4⋊Dic71—21no—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71C2311yescharacteristic
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×C4⋊Dic71C2311yescharacteristic
122C2×Dic71⋊C4—21no—
123C2×Dic71⋊C4—21no—
124C2×Dic71⋊C4—21no—
125C2×Dic71⋊C4—21no—
126C2×C22⋊Dic71—21no—
127C2×C22⋊Dic71—21no—
128C2×C22⋊Dic71—21no—
129C2×C22⋊Dic71—21no—
130C2×C4×Dic71—21no—
131C2×C4×Dic71—21no—
132C2×C4×Dic71—28no—
133C2×C4×Dic71—21no—
134C2×C4×Dic71—21no—
135C2×C4×Dic71D411yescharacteristic
136C2×C4×Dic71D411yescharacteristic
137C2×C4×Dic71D414yes—
138C2×C4×Dic71C2311yescharacteristic
139C2×C4×Dic71C2311yescharacteristic
140C2×C4×Dic71C2314yes—
141#14556062C2314yes—
142#14556062C2314yes—
143#14556061C2314yes—
144#14556061C2314yes—
145#14556060C2314yes—
146#14556060C2314yes—
147#14556059C2314yes—
148#14556059C2314yes—
149Dic71⋊C8C2314yes—
150Dic71⋊C8C2314yes—
151Dic71⋊C8C2314yes—
152Dic71⋊C8C2314yes—
153#14556052C2314yes—
154#14556052C2314yes—
155#14556049C2314yes—
156#14556049C2314yes—
157C2×#41×C71—22no—
158C2×#41×C71—24no—
159C2×#41×C71Q818yescomplemented
160C2×#41×C71C2314yes—
161C22×Q8×C71C2311yescharacteristic
162C22×D4×C71—21no—
163C22×D4×C71C2311yescharacteristic
164C23×C4×C71—21no—
165C23×C4×C71C2311yescharacteristic
166C22×C8×C71—24no—
167C22×C8×C71C2311yescharacteristic
168C22×C8×C71C2311yescharacteristic
169C22×C8×C71C2314yes—
170#117×C71—22no—
171#117×C71C2314yes—
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C42×C71—21no—
176#103×C71C2314yes—
177#103×C71C2314yes—
178#102×C71C2314yes—
179#102×C71C2314yes—
180C2×Dic142—24no—
181C2×Dic142—24no—
182C2×Dic142—44no—
183C2×Dic142—44no—
184C22×Dic71—24no—
185C22×Dic71—21no—
186C22×Dic71—21no—
187C22×Dic71—21no—
188C22×Dic71—21no—
189C22×Dic71—24no—
190C22×Dic71—24no—
191C22×Dic71—42no—
192C22×Dic71—44no—
193C22×Dic71—44no—
194C22×Dic71C2×D411yescharacteristic
195C22×Dic71C2×D411yescharacteristic
196C22×Dic71C2×D411yescharacteristic
197C22×Dic71C2×D414yes—
198C22×Dic71C2×D414yes—
199C22×Dic71C2×D411yescharacteristic
200C2×C71⋊C8—22no—
201C2×C71⋊C8—22no—
202C2×C71⋊C8—28no—
203C2×C71⋊C8C2412yes—
204C2×C71⋊C8C2412yes—
205C4⋊Dic71—21no—
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71—21no—
209C4⋊Dic71—24no—
210C4⋊Dic71—24no—
211C4⋊Dic71—24no—
212C4⋊Dic71—24no—
213C4⋊Dic71C2412yes—
214C4⋊Dic71C2412yes—
215C4⋊Dic71C2412yes—
216C4⋊Dic71C2412yes—
217Dic71⋊C4—24no—
218Dic71⋊C4—24no—
219Dic71⋊C4—24no—
220Dic71⋊C4—24no—
221C22⋊Dic71—24no—
222C22⋊Dic71—24no—
223C22⋊Dic71—24no—
224C22⋊Dic71—24no—
225C4×Dic71—24no—
226C4×Dic71—24no—
227C4×Dic71—24no—
228C4×Dic71—24no—
229C4×Dic71C2×D414yes—
230C4×Dic71C2×D414yes—
231C4×Dic71C2×D412yes—
232C4×Dic71C2×D412yes—
233C4×Dic71C2412yes—
234C4×Dic71C2412yes—
235C24×C71—21no—
236C24×C71C2×D411yescharacteristic
237#41×C71—216no—
238#41×C71—28no—
239#41×C71C2×Q8116yescomplemented
240C2×Q8×C71—21no—
241C2×Q8×C71—22no—
242C2×Q8×C71C2×Q814yes—
243C2×Q8×C71C2412yes—
244C2×D4×C71—28no—
245C2×D4×C71—24no—
246C2×D4×C71—21no—
247C2×D4×C71—22no—
248C2×D4×C71C2×Q814yes—
249C2×D4×C71C2412yes—
250C22×C4×C71—21no—
251C22×C4×C71—28no—
252C22×C4×C71—24no—
253C22×C4×C71—21no—
254C22×C4×C71—21no—
255C22×C4×C71C2×D412yes—
256C22×C4×C71C2×D411yescharacteristic
257C22×C4×C71C2×Q814yes—
258C22×C4×C71#4114yes—
259C22×C4×C71C2411yescharacteristic
260C22×C4×C71C2412yes—
261C2×C8×C71—22no—
262C2×C8×C71—22no—
263C2×C8×C71—28no—
264C2×C8×C71C2412yes—
265C2×C8×C71C2412yes—
266C4⋊C4×C71—21no—
267C4⋊C4×C71—21no—
268C4⋊C4×C71C2412yes—
269C4⋊C4×C71C2412yes—
270C22⋊C4×C71—24no—
271C42×C71—24no—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—24no—
275C23×C71—22no—
276C23×C71—42no—
277C23×C71—42no—
278C23×C71C22⋊Q814yes—
279C23×C71C22×D412yes—
280C23×C71C22×D411yescharacteristic
281Q8×C71—24no—
282Q8×C71—22no—
283Q8×C71C22×Q814yes—
284D4×C71—216no—
285D4×C71—24no—
286D4×C71—22no—
287D4×C71C22×Q814yes—
288C2×C4×C71—24no—
289C2×C4×C71—22no—
290C2×C4×C71—216no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—42no—
294C2×C4×C71—42no—
295C2×C4×C71C22⋊Q814yes—
296C2×C4×C71C22⋊Q818yes—
297C2×C4×C71C22×D412yes—
298C2×C4×C71C22×D411yescharacteristic
299C2×C4×C71C22×Q812yes—
300C2×C4×C71C22×Q814yes—
301C2×C4×C71C2×#4112yes—
302C2×C4×C71C2×#4114yes—
303C2×C4×C71C2511yescharacteristic
304C2×Dic71—22no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—28no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—44no—
313C2×Dic71—48no—
314C2×Dic71—42no—
315C2×Dic71—42no—
316C2×Dic71—42no—
317C2×Dic71—42no—
318C2×Dic71—48no—
319C2×Dic71#13514yes—
320C2×Dic71C22×D412yes—
321C2×Dic71C22×D412yes—
322C2×Dic71C22×D412yes—
323C2×Dic71C22×D412yes—
324Dic142—48no—
325Dic142—48no—
326C8×C71—22no—
327C8×C71—22no—
328C71⋊C8—22no—
329C71⋊C8—22no—
330C22×C71—28no—
331C22×C71—22no—
332C22×C71—22no—
333C22×C71—24no—
334C22×C71—48no—
335C22×C71—42no—
336C22×C71—42no—
337C22×C71C2×C22⋊Q814yes—
338C22×C71C2×C22⋊Q812yes—
339C22×C71C2×#13512yes—
340C22×C71#57512yes—
341C22×C71C23×D411yescharacteristic
342C4×C71—24no—
343C4×C71—42no—
344C4×C71—42no—
345C4×C71C2×C22⋊Q814yes—
346C4×C71C2×C22⋊Q812yes—
347C4×C71C23×Q811yescharacteristic
348C4×C71C22×#4111yescharacteristic
349Dic71—22no—
350Dic71—22no—
351Dic71—22no—
352Dic71—42no—
353Dic71—42no—
354Dic71—42no—
355Dic71—42no—
356Dic71C2×#13514yes—
357C2×#3076—711nomaximal, Sylow
358C2×C71—24no—
359C2×C71—44no—
360C2×C71#307614yescomplemented
361C2×C71C22×C22⋊Q811yescharacteristic
362C2×C71C22×#13511yescharacteristic
363C2×C71C2×#57511yescharacteristic
364C2×#533—711no—
365C2×C4×#41—711no—
366#3076—7116no—
367C2×#479—711no—
368C2×#479—711no—
369C2×#477—711no—
370C2×#475—711no—
371C2×#478—711no—
372C2×#478—711no—
373C2×#476—711no—
374C2×#474—711no—
375C2×#427—711no—
376C2×#427—711no—
377C22×C4⋊C8—711no—
378C2×#416—711no—
379C2×#416D7111yescharacteristic
380C71C2×#307611yescharacteristic, complemented, Sylow
381C22×#41C2×D7111yescharacteristic
382C23×C8—711no—
383C23×C8C2×D7111yescharacteristic
384#533—718no—
385#533—1424no—
386C2×C4⋊Q8—711no—
387C2×C4⋊Q8—711no—
388C2×#125—711no—
389C2×#125—711no—
390C2×C22⋊Q8—1421no—
391C2×C22⋊Q8—1421no—
392C4×#41—718no—
393C4×#41—1424no—
394C2×C4×Q8—711no—
395C2×C4×Q8—711no—
396C2×C4×Q8—1421no—
397C2×C4×Q8—1421no—
398C2×C4×D4—711no—
399C2×C4×D4—711no—
400C2×C4×D4—1421no—
401C2×C4×D4—1421no—
402C2×#117—711no—
403C2×#117—711no—
404C2×#117—1421no—
405C2×#117C2×D7111yescharacteristic
406C22×C42—711no—
407C22×C42—1421no—
408#479—718no—
409#479—718no—
410#478—718no—
411#478—718no—
412#477—718no—
413#476—718no—
414#475—718no—
415#474—718no—
416#427—718no—
417#427—718no—
418C2×#107—711no—
419C2×#107—711no—
420C2×#107—711no—
421C2×#107—711no—
422C2×#106—711no—
423C2×#106—711no—
424C2×#106—711no—
425C2×#106—711no—
426C2×C4⋊C8—711no—
427C2×C4⋊C8—711no—
428C2×C4⋊C8—711no—
429C2×C4⋊C8—711no—
430C2×C4⋊C8—718no—
431#416—718no—
432#416C2×D7118yes—
433C2×#103—711no—
434C2×#103—711no—
435C2×#103C2×D7111yescharacteristic
436C2×#103C2×D7111yescharacteristic
437C2×#102—711no—
438C2×#102—711no—
439C2×#102C2×D7111yescharacteristic
440C2×#102C2×D7111yescharacteristic
441C2×#41—22no—
442C2×#41—24no—
443C2×#41Dic14218yescomplemented
444C2×#41C22×D7114yes—
445C22×Q8—1421no—
446C22×Q8—1421no—
447C22×Q8C22×D7111yescharacteristic
448C22×D4—21no—
449C22×D4C22×D7111yescharacteristic
450C23×C4—21no—
451C23×C4—711no—
452C23×C4—711no—
453C23×C4—1421no—
454C23×C4—1421no—
455C23×C4C22×D7111yescharacteristic
456C22×C8—24no—
457C22×C8—711no—
458C22×C8—711no—
459C22×C8—714no—
460C22×C8—1424no—
461C22×C8C22×D7111yescharacteristic
462C22×C8C22×D7111yescharacteristic
463C22×C8C22×D7114yes—
464C4⋊Q8—714no—
465C4⋊Q8—714no—
466C4⋊Q8—1422no—
467C4⋊Q8—1422no—
468#125—714no—
469#125—714no—
470#125—1422no—
471#125—1422no—
472C22⋊Q8—1428no—
473C22⋊Q8—1428no—
474C4×Q8—714no—
475C4×Q8—714no—
476C4×Q8—1428no—
477C4×Q8—1428no—
478C4×Q8—1422no—
479C4×Q8—1422no—
480C4×D4—714no—
481C4×D4—714no—
482C4×D4—1422no—
483C4×D4—1422no—
484C4×D4—1428no—
485C4×D4—1428no—
486#117—22no—
487#117—714no—
488#117—714no—
489#117—1428no—
490#117—1422no—
491#117—1422no—
492#117C22×D7114yes—
493C2×C4⋊C4—711no—
494C2×C4⋊C4—711no—
495C2×C4⋊C4—711no—
496C2×C4⋊C4—711no—
497C2×C4⋊C4—1421no—
498C2×C4⋊C4—1421no—
499C2×C4⋊C4—1421no—
500C2×C4⋊C4—1421no—
501C2×C4⋊C4—1421no—
502C2×C4⋊C4—1421no—
503C2×C4⋊C4—1421no—
504C2×C4⋊C4—1421no—
505C2×C4⋊C4C22×D7111yescharacteristic
506C2×C4⋊C4C22×D7111yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—1421no—
509C2×C22⋊C4—1421no—
510C2×C22⋊C4—1421no—
511C2×C22⋊C4—1421no—
512C2×C42—21no—
513C2×C42—714no—
514C2×C42—711no—
515C2×C42—711no—
516C2×C42—711no—
517C2×C42—711no—
518C2×C42—714no—
519C2×C42—1428no—
520C2×C42—1421no—
521C2×C42—1421no—
522C2×C42—1421no—
523C2×C42—1421no—
524#107—714no—
525#107—714no—
526#107—714no—
527#107—714no—
528#106—714no—
529#106—714no—
530#106—714no—
531#106—714no—
532C4⋊C8—714no—
533C4⋊C8—714no—
534C4⋊C8—714no—
535C4⋊C8—714no—
536#103—714no—
537#103—714no—
538#103C22×D7114yes—
539#103C22×D7114yes—
540#102—714no—
541#102—714no—
542#102C22×D7114yes—
543#102C22×D7114yes—
544C24—21no—
545C24D4×D7111yescharacteristic
546#41—28no—
547#41—216no—
548#41C2×Dic142116yescomplemented
549C2×Q8—21no—
550C2×Q8—22no—
551C2×Q8—2844no—
552C2×Q8—2844no—
553C2×Q8—1424no—
554C2×Q8—1424no—
555C2×Q8C2×Dic14214yes—
556C2×Q8C23×D7112yes—
557C2×D4—24no—
558C2×D4—28no—
559C2×D4—21no—
560C2×D4—22no—
561C2×D4C2×Dic14214yes—
562C2×D4C23×D7112yes—
563C22×C4—21no—
564C22×C4—24no—
565C22×C4—28no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—2844no—
569C22×C4—2844no—
570C22×C4—2842no—
571C22×C4—714no—
572C22×C4—711no—
573C22×C4—711no—
574C22×C4—711no—
575C22×C4—711no—
576C22×C4—714no—
577C22×C4—1424no—
578C22×C4—1424no—
579C22×C4—1421no—
580C22×C4—1421no—
581C22×C4—1421no—
582C22×C4—1421no—
583C22×C4—1424no—
584C22×C4D4×D7112yes—
585C22×C4D4×D7111yescharacteristic
586C22×C4C2×Dic14214yes—
587C22×C4#1176586414yes—
588C22×C4C23×D7111yescharacteristic
589C22×C4C23×D7112yes—
590C2×C8—22no—
591C2×C8—22no—
592C2×C8—28no—
593C2×C8—712no—
594C2×C8—712no—
595C2×C8—1422no—
596C2×C8—1422no—
597C2×C8—1428no—
598C2×C8C23×D7112yes—
599C2×C8C23×D7112yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—712no—
603C4⋊C4—712no—
604C4⋊C4—712no—
605C4⋊C4—712no—
606C4⋊C4—1424no—
607C4⋊C4—1424no—
608C4⋊C4—1424no—
609C4⋊C4—1424no—
610C4⋊C4—1424no—
611C4⋊C4—1424no—
612C4⋊C4—1424no—
613C4⋊C4—1424no—
614C4⋊C4—1421no—
615C4⋊C4—1421no—
616C4⋊C4—1421no—
617C4⋊C4—1421no—
618C4⋊C4C23×D7112yes—
619C4⋊C4C23×D7112yes—
620C22⋊C4—24no—
621C22⋊C4—1424no—
622C22⋊C4—1424no—
623C22⋊C4—1424no—
624C22⋊C4—1424no—
625C42—24no—
626C42—714no—
627C42—714no—
628C42—712no—
629C42—712no—
630C42—712no—
631C42—712no—
632C42—1424no—
633C42—1424no—
634C42—1424no—
635C42—1424no—
636C23—22no—
637C23—22no—
638C23—22no—
639C23—24no—
640C23—42no—
641C23—42no—
642C23#1455610514yes—
643C23C2×D4×D7112yes—
644C23C2×D4×D7111yescharacteristic
645Q8—22no—
646Q8—24no—
647Q8—2848no—
648Q8—2848no—
649Q8C22×Dic14214yes—
650D4—216no—
651D4—22no—
652D4—24no—
653D4C22×Dic14214yes—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—216no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—2842no—
662C2×C4—2842no—
663C2×C4—2842no—
664C2×C4—2842no—
665C2×C4—2848no—
666C2×C4—2848no—
667C2×C4—2844no—
668C2×C4—712no—
669C2×C4—714no—
670C2×C4—712no—
671C2×C4—712no—
672C2×C4—712no—
673C2×C4—1422no—
674C2×C4—1422no—
675C2×C4—1422no—
676C2×C4—1422no—
677C2×C4—1428no—
678C2×C4—1422no—
679C2×C4—1422no—
680C2×C4—1422no—
681C2×C4#1455610514yes—
682C2×C4#1455610518yes—
683C2×C4C2×D4×D7112yes—
684C2×C4C2×D4×D7111yescharacteristic
685C2×C4C22×Dic14212yes—
686C2×C4C22×Dic14214yes—
687C2×C4C2×#1176586412yes—
688C2×C4C2×#1176586414yes—
689C2×C4C24×D7111yescharacteristic
690C8—22no—
691C8—22no—
692C8—1422no—
693C8—1422no—
694C22—22no—
695C22—22no—
696C22—28no—
697C22—24no—
698C22—42no—
699C22—42no—
700C22—48no—
701C22C2×#1455610514yes—
702C22C2×#1455610512yes—
703C22#135×D7112yes—
704C22#1798679612yes—
705C22C22×D4×D7111yescharacteristic
706C4—24no—
707C4—42no—
708C4—42no—
709C4—2842no—
710C4—2842no—
711C4—2842no—
712C4—2842no—
713C4—714no—
714C4—1422no—
715C4—1422no—
716C4—1422no—
717C4C2×#1455610514yes—
718C4C2×#1455610512yes—
719C4C23×Dic14211yescharacteristic
720C4C22×#1176586411yescharacteristic
721C2—24no—
722C2—44no—
723C2#2259812414yesdirect product factor
724C2C22×#1455610511yescharacteristic
725C2C2×#135×D7111yescharacteristic
726C2C2×#1798679611yescharacteristic
subgroupG/H
centerC22×C4D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#416×C71C2
socleC23×C71C22×D4
prime radicalC22×#41×C71C22
hypercenterC2×#416D71
hypocenterC71C2×#3076
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
1. C2×#17986552C2semidirect
3. #22598124C2direct (N × H)
4. C2×#17986308C2semidirect
5. C2×#17986304C2semidirect
6. C2×#17986292C2semidirect
7. C2×#17986282C2semidirect
8. C2×#17986301C2semidirect
9. C2×#17986297C2semidirect
10. C2×#17986287C2semidirect
11. C2×#17986277C2semidirect
12. C2×#17986037C2semidirect
13. C2×#17986035C2semidirect
14. C22×Dic71⋊C8C2semidirect
19. #17986552C22semidirect
41. #17986308C22semidirect
42. #17986304C22semidirect
43. #17986301C22semidirect
44. #17986297C22semidirect
45. #17986292C22semidirect
46. #17986287C22semidirect
47. #17986282C22semidirect
48. #17986277C22semidirect
49. #17986037C22semidirect
50. #17986035C22semidirect
63. C2×Dic71⋊C8C22semidirect
159. C2×#41×C71Q8semidirect
239. #41×C71C2×Q8semidirect
360. C2×C71#3076semidirect
380. C71C2×#3076semidirect
443. C2×#41Dic142semidirect
548. #41C2×Dic142semidirect
723. C2#22598124direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865522
C2×#41×Dic712
#225981242
C2×#179863082
C2×#179863042
C2×#179862922
C2×#179862822
C2×#179863012
C2×#179862972
C2×#179862872
C2×#179862772
C2×#179860372
C2×#179860352
C22×Dic71⋊C82
C2×#179859952
C2×#416×C712
C2×#307671