Finite Group Databasebeta

← C2×#22598570 #32865732

Subgroups — C2×#22598570 #32865732

Order 18176.

2058 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×#17986622C211yesmaximal, characteristic
2C2×#17986477C211yesmaximal, characteristic, complemented
3#22598570C2116yesmaximal, direct product factor
4C2×#17986337C211yesmaximal, characteristic, complemented
5C2×#17986324C211yesmaximal, characteristic
6C2×#17986292C211yesmaximal, characteristic, complemented
7C2×#17986282C211yesmaximal, characteristic, complemented
8C2×#17986223C211yesmaximal, characteristic, complemented
9C2×#17986223C211yesmaximal, characteristic, complemented
10C2×#17986138C211yesmaximal, characteristic
11C2×#17986106C211yesmaximal, characteristic, complemented
12C2×#17986102C211yesmaximal, characteristic, complemented
13C2×Q16×Dic71C211yesmaximal, characteristic, complemented
14C2×#17986084C211yesmaximal, characteristic, complemented
15C2×#17986057C211yesmaximal, characteristic, complemented
16C2×#451×C71C211yesmaximal, characteristic, complemented
17C22×#11765852C2211yescharacteristic
18C22×#11765852C2211yescharacteristic
19#17986622—24no—
20#17986622C2218yes—
21C2×#14556127C2211yescharacteristic
22C2×#14556123—21no—
23C2×#14556117C2211yescharacteristic
24C2×#14556114—21no—
25C2×#14556110—21no—
26C2×#14556108—21no—
27C2×#14556102C2211yescharacteristic
28#17986477—24no—
29#17986477C2218yescomplemented
30C2×Q8×Dic71—21no—
31C2×Q8×Dic71—21no—
32C2×Q8×Dic71C2211yescharacteristic
33C2×Q8×Dic71C2211yescharacteristic
34C2×Q8×Dic71C2211yescharacteristic
35C2×Q8×Dic71C2211yescharacteristic
36C2×Q8×Dic71C2211yescharacteristic
37C2×#14556090C2211yescharacteristic
38C2×#14556087—21no—
39C2×#14556087—21no—
40C2×#14556087C2211yescharacteristic
41C2×#14556087C2211yescharacteristic
42#17986337C2218yescomplemented
43#17986324C2218yes—
44#17986292C2218yescomplemented
45#17986282C2218yescomplemented
46#17986223C2218yescomplemented
47#17986223C2218yescomplemented
48#17986138C2218yes—
49#17986106C2218yescomplemented
50#17986102C2218yescomplemented
51Q16×Dic71C2218yescomplemented
52#17986084C2218yescomplemented
53#17986057C2218yescomplemented
54C2×#14556062C2211yescharacteristic
55C2×#14556061C2211yescharacteristic
56C2×#14556060C2211yescharacteristic
57C2×#14556059C2211yescharacteristic
58C2×Dic71⋊C8C2211yescharacteristic
59C2×Dic71⋊C8C2211yescharacteristic
60C2×#14556052C2211yescharacteristic
61C2×#14556052C2211yescharacteristic
62C2×#14556052C2211yescharacteristic
63C2×#14556052C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556050C2211yescharacteristic
66C2×C22⋊(C71⋊C8)C2211yescharacteristic
67C2×#14556038C2211yescharacteristic
68C2×C8×Dic71C2211yescharacteristic
69C23×Q8×C71C2211yescharacteristic
70C22×Q16×C71C2211yescharacteristic
71C22×Q16×C71C2211yescharacteristic
72C2×C22⋊Q8×C71C2211yescharacteristic
73#451×C71C2218yescomplemented
74C2×#103×C71C2211yescharacteristic
75C2×#103×C71C2211yescharacteristic
76C2×C22⋊C8×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×D284C2311yescharacteristic
79C22×C22⋊D71—21no—
80C22×C4×D71—21no—
81C2×#11765852—24no—
82C2×#11765852—24no—
83C2×#11765852C2314yes—
84C2×#11765852C2314yes—
85C22×C71⋊C8C2311yescharacteristic
86C22×C71⋊C8C2311yescharacteristic
87#14556127—22no—
88#14556127C2314yes—
89#14556123—28no—
90#14556117—22no—
91#14556117C2314yes—
92#14556114—28no—
93#14556110—28no—
94#14556108—28no—
95#14556102—22no—
96#14556102C2314yes—
97Q8×Dic71—28no—
98Q8×Dic71—28no—
99Q8×Dic71—22no—
100Q8×Dic71—22no—
101Q8×Dic71—22no—
102Q8×Dic71—22no—
103Q8×Dic71—22no—
104Q8×Dic71C2314yes—
105Q8×Dic71C2314yes—
106Q8×Dic71C2314yes—
107Q8×Dic71C2314yes—
108Q8×Dic71C2314yes—
109#14556090—22no—
110#14556090C2314yes—
111#14556087—28no—
112#14556087—28no—
113#14556087—22no—
114#14556087D414yes—
115#14556087C2314yes—
116#14556087C2314yes—
117C2×C4⋊Dic71—21no—
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71—21no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71D411yescharacteristic
123C2×C4⋊Dic71D411yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×C4⋊Dic71C2311yescharacteristic
127C2×Dic71⋊C4—21no—
128C2×C22⋊Dic71—21no—
129C2×C22⋊Dic71D411yescharacteristic
130C2×C22⋊Dic71D411yescharacteristic
131C2×(C2×D71)⋊C4—21no—
132C2×(C2×D71)⋊C4—21no—
133C2×(C2×D71)⋊C4—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×C4×Dic71—21no—
136C2×C4×Dic71—21no—
137C2×C4×Dic71—21no—
138C2×C4×Dic71—21no—
139C2×C4×Dic71—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71C2311yescharacteristic
142C2×C4×Dic71C2311yescharacteristic
143#14556062C2314yes—
144#14556061C2314yes—
145#14556060C2314yes—
146#14556059C2314yes—
147Dic71⋊C8C2314yes—
148Dic71⋊C8C2314yes—
149#14556052C2314yes—
150#14556052C2314yes—
151#14556052C2314yes—
152#14556052C2314yes—
153#14556050C2314yes—
154#14556050C2314yes—
155C22⋊(C71⋊C8)C2314yes—
156#14556038C2314yes—
157C8×Dic71C2314yes—
158C22×Q8×C71—24no—
159C22×Q8×C71—24no—
160C22×Q8×C71—21no—
161C22×Q8×C71—22no—
162C22×Q8×C71C2314yes—
163C22×Q8×C71C2311yescharacteristic
164C22×Q8×C71C2311yescharacteristic
165C22×Q8×C71C2311yescharacteristic
166C23×C4×C71—21no—
167C23×C4×C71C2311yescharacteristic
168C2×Q16×C71—24no—
169C2×Q16×C71—24no—
170C2×Q16×C71C2314yes—
171C2×Q16×C71C2314yes—
172C22×C8×C71C2311yescharacteristic
173C22×C8×C71C2311yescharacteristic
174C22⋊Q8×C71—22no—
175C22⋊Q8×C71C2314yes—
176C2×C4⋊C4×C71—21no—
177C2×C4⋊C4×C71C2311yescharacteristic
178C2×C22⋊C4×C71—21no—
179#103×C71C2314yes—
180#103×C71C2314yes—
181C22⋊C8×C71C2314yes—
182C23×D71—21no—
183C2×Dic142—24no—
184C2×Dic142—82no—
185C2×D284—22no—
186C2×D284—22no—
187C2×D284—21no—
188C2×D284C2412yes—
189C2×C22⋊D71—24no—
190C2×C22⋊D71—82no—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C22×Dic71—21no—
194C22×Dic71C2×D411yescharacteristic
195C22×Dic71C2×D411yescharacteristic
196C22×Dic71C2×D411yescharacteristic
197C22×Dic71C2×D411yescharacteristic
198C2×C4×D71—24no—
199C2×C4×D71—82no—
200#11765852—28no—
201#11765852—28no—
202C2×C71⋊C8—22no—
203C2×C71⋊C8—22no—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C4⋊Dic71—21no—
207C4⋊Dic71—21no—
208C4⋊Dic71—21no—
209C4⋊Dic71—24no—
210C4⋊Dic71—24no—
211C4⋊Dic71—24no—
212C4⋊Dic71—24no—
213C4⋊Dic71—24no—
214C4⋊Dic71C2×D414yes—
215C4⋊Dic71C2×D414yes—
216C4⋊Dic71C2412yes—
217C4⋊Dic71C2412yes—
218C4⋊Dic71C2412yes—
219Dic71⋊C4—24no—
220C22⋊Dic71—24no—
221C22⋊Dic71C2×D414yes—
222C22⋊Dic71C2×D414yes—
223(C2×D71)⋊C4—24no—
224(C2×D71)⋊C4—24no—
225(C2×D71)⋊C4—24no—
226(C2×D71)⋊C4—24no—
227C4×Dic71—24no—
228C4×Dic71—24no—
229C4×Dic71—24no—
230C4×Dic71—24no—
231C4×Dic71—24no—
232C4×Dic71—24no—
233C4×Dic71C2×D412yes—
234C4×Dic71C2×D412yes—
235C4×Dic71C2412yes—
236C4×Dic71C2412yes—
237C24×C71C2×D411yescharacteristic
238C2×Q8×C71—216no—
239C2×Q8×C71—28no—
240C2×Q8×C71—28no—
241C2×Q8×C71—28no—
242C2×Q8×C71—24no—
243C2×Q8×C71—21no—
244C2×Q8×C71—21no—
245C2×Q8×C71—21no—
246C2×Q8×C71—22no—
247C2×Q8×C71—22no—
248C2×Q8×C71—22no—
249C2×Q8×C71—22no—
250C2×Q8×C71#4114yes—
251C2×Q8×C71#4114yes—
252C2×Q8×C71C2412yes—
253C2×Q8×C71C2412yes—
254C2×Q8×C71C2412yes—
255C22×C4×C71—28no—
256C22×C4×C71—21no—
257C22×C4×C71—21no—
258C22×C4×C71—24no—
259C22×C4×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—21no—
262C22×C4×C71—21no—
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71C2×D412yes—
265C22×C4×C71C2412yes—
266C22×C4×C71C2411yescharacteristic
267Q16×C71—28no—
268Q16×C71—28no—
269C2×C8×C71—22no—
270C2×C8×C71—22no—
271C2×C8×C71C2412yes—
272C2×C8×C71C2412yes—
273C4⋊C4×C71—24no—
274C4⋊C4×C71—21no—
275C4⋊C4×C71C2412yes—
276C22⋊C4×C71—24no—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—22no—
280C23×C71C22×D412yes—
281C23×C71C22×D411yescharacteristic
282C22×D71—22no—
283C22×D71—42no—
284C22×D71—42no—
285C22×D71—42no—
286Q8×C71—216no—
287Q8×C71—24no—
288Q8×C71—24no—
289Q8×C71—22no—
290Q8×C71—22no—
291Q8×C71—22no—
292Q8×C71—22no—
293Q8×C71—42no—
294Q8×C71C2×#4114yes—
295Q8×C71C2×#4114yes—
296C2×C4×C71—216no—
297C2×C4×C71—24no—
298C2×C4×C71—24no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—24no—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—42no—
308C2×C4×C71—42no—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D411yescharacteristic
311C2×C4×C71C2×#4112yes—
312C2×C4×C71C2×#4112yes—
313C2×C4×C71C2511yescharacteristic
314C22⋊D71—84no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—22no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—42no—
323C2×Dic71—42no—
324C2×Dic71—42no—
325C2×Dic71C22×D412yes—
326C2×Dic71C22×D412yes—
327C2×Dic71C22×D412yes—
328C2×Dic71C22×D412yes—
329D284—22no—
330D284—22no—
331D284—42no—
332C4×D71—84no—
333Dic142—84no—
334C8×C71—22no—
335C8×C71—22no—
336C71⋊C8—22no—
337C71⋊C8—22no—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—22no—
341C22×C71—44no—
342C22×C71#52512yes—
343C22×C71#57712yes—
344C22×C71#57812yes—
345C22×C71C23×D411yescharacteristic
346C2×D71—42no—
347C2×D71—42no—
348C2×D71—42no—
349C2×D71—84no—
350C4×C71—24no—
351C4×C71—24no—
352C4×C71—22no—
353C4×C71—42no—
354C4×C71—42no—
355C4×C71#52512yes—
356C4×C71C22×#4111yescharacteristic
357C4×C71C22×#4111yescharacteristic
358Dic71—22no—
359Dic71—22no—
360Dic71—22no—
361Dic71—22no—
362Dic71—42no—
363Dic71—42no—
364Dic71—42no—
365C2×#3121—711nomaximal, Sylow
366C2×C71—42no—
367C2×C71#312114yescomplemented
368C2×C71C2×#52511yescharacteristic
369C2×C71C2×#57711yescharacteristic
370C2×C71C2×#57811yescharacteristic
371D71—82no—
372C2×#542—711no—
373C2×#519—711no—
374#3121—7116no—
375C2×#485—711no—
376C2×#482—711no—
377C2×#477—711no—
378C2×#475—711no—
379C2×#464—711no—
380C2×#464—711no—
381C2×#451D7111yescharacteristic, complemented
382C2×#448—711no—
383C2×#441—711no—
384C2×#440—711no—
385C2×C4×Q16—711no—
386C2×C4×SD16—711no—
387C2×#433—711no—
388C71C2×#312111yescharacteristic, complemented, Sylow
389C23×Q8C2×D7111yescharacteristic
390C22×Q16C2×D7111yescharacteristic
391C22×Q16C2×D7111yescharacteristic
392C22×SD16—711no—
393C22×SD16—711no—
394#542—718no—
395#542—1424no—
396C2×C4⋊Q8—711no—
397C2×#126—1421no—
398C2×#124—711no—
399C2×#124—1421no—
400C2×#123—1421no—
401C2×C22⋊Q8—1421no—
402C2×C22⋊Q8C2×D7111yescharacteristic
403C2×#121—711no—
404#519—718no—
405#519—1424no—
406C2×C4×Q8—711no—
407C2×C4×Q8—711no—
408C2×C4×Q8—711no—
409C2×C4×Q8—711no—
410C2×C4×Q8—711no—
411C2×C4×Q8—1421no—
412C2×C4×Q8—1421no—
413C2×C4×D4—711no—
414C2×#117—711no—
415C2×#117—711no—
416C2×#117—1421no—
417C2×#117—1421no—
418#485—718no—
419#482—718no—
420#477—718no—
421#475—718no—
422#464—718no—
423#464—718no—
424#451C2×D7118yescomplemented
425#448—718no—
426#441—718no—
427#440—718no—
428C4×Q16—718no—
429C4×SD16—718no—
430#433—718no—
431C2×#107—711no—
432C2×#107—711no—
433C2×#106—711no—
434C2×#106—711no—
435C2×C4⋊C8—711no—
436C2×C4⋊C8—711no—
437C2×#103—711no—
438C2×#103—711no—
439C2×#103—711no—
440C2×#103—711no—
441C2×#103C2×D7111yescharacteristic
442C2×#103C2×D7111yescharacteristic
443C2×#102—711no—
444C2×#102—711no—
445C2×C22⋊C8—711no—
446C2×C22⋊C8C2×D7111yescharacteristic
447C2×#97—711no—
448C2×C4×C8—711no—
449C22×Q8—24no—
450C22×Q8—24no—
451C22×Q8—21no—
452C22×Q8—22no—
453C22×Q8—1421no—
454C22×Q8C22×D7111yescharacteristic
455C22×Q8C22×D7114yes—
456C22×Q8C22×D7111yescharacteristic
457C22×Q8C22×D7111yescharacteristic
458C22×D4—711no—
459C22×D4—1421no—
460C23×C4—21no—
461C23×C4—1421no—
462C23×C4C22×D7111yescharacteristic
463C2×Q16—24no—
464C2×Q16—24no—
465C2×Q16C22×D7114yes—
466C2×Q16C22×D7114yes—
467C2×SD16—714no—
468C2×SD16—714no—
469C2×SD16—1424no—
470C2×SD16—1424no—
471C22×C8—711no—
472C22×C8—711no—
473C22×C8C22×D7111yescharacteristic
474C22×C8C22×D7111yescharacteristic
475C4⋊Q8—714no—
476C4⋊Q8—1422no—
477#126—1428no—
478#124—714no—
479#124—1422no—
480#124—1428no—
481#123—1428no—
482C22⋊Q8—22no—
483C22⋊Q8—1428no—
484C22⋊Q8C22×D7114yes—
485#121—714no—
486#121—1422no—
487C4×Q8—714no—
488C4×Q8—714no—
489C4×Q8—714no—
490C4×Q8—714no—
491C4×Q8—714no—
492C4×Q8—1422no—
493C4×Q8—1422no—
494C4×Q8—1422no—
495C4×Q8—1422no—
496C4×Q8—1422no—
497C4×Q8—1428no—
498C4×Q8—1428no—
499C4×D4—714no—
500C4×D4—1422no—
501#117—714no—
502#117—714no—
503#117—714no—
504#117—1428no—
505#117—1428no—
506#117—1422no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—711no—
509C2×C4⋊C4—711no—
510C2×C4⋊C4—711no—
511C2×C4⋊C4—711no—
512C2×C4⋊C4—711no—
513C2×C4⋊C4—1421no—
514C2×C4⋊C4—1421no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1421no—
517C2×C4⋊C4—1421no—
518C2×C4⋊C4—1421no—
519C2×C4⋊C4C22×D7111yescharacteristic
520C2×C22⋊C4—21no—
521C2×C22⋊C4—711no—
522C2×C22⋊C4—711no—
523C2×C22⋊C4—1421no—
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C42—711no—
529C2×C42—711no—
530C2×C42—1421no—
531C2×C42—1421no—
532C2×C42—1421no—
533C2×C42—1421no—
534C2×C42—1421no—
535C2×C42—1421no—
536#107—714no—
537#107—714no—
538#106—714no—
539#106—714no—
540C4⋊C8—714no—
541C4⋊C8—714no—
542#103—714no—
543#103—714no—
544#103—714no—
545#103—714no—
546#103C22×D7114yes—
547#103C22×D7114yes—
548#102—714no—
549#102—714no—
550C22⋊C8—714no—
551C22⋊C8C22×D7114yes—
552#97—714no—
553C4×C8—714no—
554C24—1421no—
555C24D4×D7111yescharacteristic
556C2×Q8—216no—
557C2×Q8—28no—
558C2×Q8—28no—
559C2×Q8—28no—
560C2×Q8—24no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8—22no—
565C2×Q8—22no—
566C2×Q8—22no—
567C2×Q8—22no—
568C2×Q8—5682no—
569C2×Q8—1424no—
570C2×Q8#1176586414yes—
571C2×Q8#1176586414yes—
572C2×Q8C23×D7112yes—
573C2×Q8C23×D7112yes—
574C2×Q8C23×D7112yes—
575C2×D4—5682no—
576C2×D4—712no—
577C2×D4—1424no—
578C2×D4—1421no—
579C2×D4—1422no—
580C2×D4—1422no—
581C22×C4—28no—
582C22×C4—24no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—5682no—
590C22×C4—711no—
591C22×C4—711no—
592C22×C4—711no—
593C22×C4—711no—
594C22×C4—1424no—
595C22×C4—1421no—
596C22×C4—1421no—
597C22×C4—1421no—
598C22×C4D4×D7112yes—
599C22×C4D4×D7111yescharacteristic
600C22×C4C23×D7112yes—
601C22×C4C23×D7111yescharacteristic
602Q16—28no—
603Q16—28no—
604SD16—1428no—
605SD16—1428no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—712no—
609C2×C8—712no—
610C2×C8—1422no—
611C2×C8—1422no—
612C2×C8C23×D7112yes—
613C2×C8C23×D7112yes—
614C4⋊C4—24no—
615C4⋊C4—21no—
616C4⋊C4—714no—
617C4⋊C4—714no—
618C4⋊C4—712no—
619C4⋊C4—712no—
620C4⋊C4—712no—
621C4⋊C4—1424no—
622C4⋊C4—1424no—
623C4⋊C4—1424no—
624C4⋊C4—1424no—
625C4⋊C4—1424no—
626C4⋊C4—1424no—
627C4⋊C4—1421no—
628C4⋊C4—1421no—
629C4⋊C4—1421no—
630C4⋊C4C23×D7112yes—
631C22⋊C4—24no—
632C22⋊C4—714no—
633C22⋊C4—714no—
634C22⋊C4—1424no—
635C22⋊C4—1424no—
636C22⋊C4—1424no—
637C22⋊C4—1424no—
638C22⋊C4—1424no—
639C42—712no—
640C42—712no—
641C42—712no—
642C42—712no—
643C42—1424no—
644C42—1424no—
645C42—1424no—
646C42—1424no—
647C42—1424no—
648C42—1424no—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—2842no—
653C23—2842no—
654C23—2842no—
655C23—1422no—
656C23C2×D4×D7112yes—
657C23C2×D4×D7111yescharacteristic
658Q8—216no—
659Q8—22no—
660Q8—22no—
661Q8—24no—
662Q8—24no—
663Q8—22no—
664Q8—22no—
665Q8—42no—
666Q8—5684no—
667Q8C2×#1176586414yes—
668Q8C2×#1176586414yes—
669D4—2842no—
670D4—5684no—
671D4—1422no—
672D4—1422no—
673C2×C4—216no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—24no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—2842no—
687C2×C4—2842no—
688C2×C4—2842no—
689C2×C4—5684no—
690C2×C4—712no—
691C2×C4—712no—
692C2×C4—712no—
693C2×C4—712no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1422no—
697C2×C4—1422no—
698C2×C4—1422no—
699C2×C4—1422no—
700C2×C4—1422no—
701C2×C4C2×D4×D7112yes—
702C2×C4C2×D4×D7111yescharacteristic
703C2×C4C2×#1176586412yes—
704C2×C4C2×#1176586412yes—
705C2×C4C24×D7111yescharacteristic
706C8—22no—
707C8—22no—
708C8—1422no—
709C8—1422no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—2842no—
715C22—2842no—
716C22—2842no—
717C22—5684no—
718C22#1798650512yes—
719C22#1798680812yes—
720C22#1798681212yes—
721C22C22×D4×D7111yescharacteristic
722C4—24no—
723C4—24no—
724C4—22no—
725C4—42no—
726C4—42no—
727C4—2842no—
728C4—2842no—
729C4—2842no—
730C4—1422no—
731C4—1422no—
732C4—1422no—
733C4—1422no—
734C4#1798650512yes—
735C4C22×#1176586411yescharacteristic
736C4C22×#1176586411yescharacteristic
737C2—42no—
738C2—5682no—
739C2#2259857014yesdirect product factor
740C2C2×#1798650511yescharacteristic
741C2C2×#1798680811yescharacteristic
742C2C2×#1798681211yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#451×C71C2
socleC23×C71C22×D4
prime radicalC2×#14556102C22
hypercenterC2×#451D71
hypocenterC71C2×#3121
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
2. C2×#17986477C2semidirect
3. #22598570C2direct (N × H)
4. C2×#17986337C2semidirect
6. C2×#17986292C2semidirect
7. C2×#17986282C2semidirect
8. C2×#17986223C2semidirect
9. C2×#17986223C2semidirect
11. C2×#17986106C2semidirect
12. C2×#17986102C2semidirect
13. C2×Q16×Dic71C2semidirect
14. C2×#17986084C2semidirect
15. C2×#17986057C2semidirect
16. C2×#451×C71C2semidirect
29. #17986477C22semidirect
42. #17986337C22semidirect
44. #17986292C22semidirect
45. #17986282C22semidirect
46. #17986223C22semidirect
47. #17986223C22semidirect
49. #17986106C22semidirect
50. #17986102C22semidirect
51. Q16×Dic71C22semidirect
52. #17986084C22semidirect
53. #17986057C22semidirect
73. #451×C71C22semidirect
367. C2×C71#3121semidirect
381. C2×#451D71semidirect
388. C71C2×#3121semidirect
424. #451C2×D71semidirect
739. C2#22598570direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866222
C2×#179864772
#225985702
C2×#179863372
C2×#179863242
C2×#179862922
C2×#179862822
C2×#179862232
C2×#179861382
C2×#179861062
C2×#179861022
C2×Q16×Dic712
C2×#179860842
C2×#179860572
C2×#451×C712
C2×#312171