Finite Group Databasebeta

← C2×#22598556 #32865717

Subgroups — C2×#22598556 #32865717

Order 18176.

2070 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×#17986611C211yesmaximal, characteristic, complemented
2C2×#17986479C211yesmaximal, characteristic
3#22598556C2116yesmaximal, direct product factor
4C2×#17986335C211yesmaximal, characteristic, complemented
5C2×#17986330C211yesmaximal, characteristic, complemented
6C2×#17986307C211yesmaximal, characteristic, complemented
7C2×#17986300C211yesmaximal, characteristic, complemented
8C2×#17986210C211yesmaximal, characteristic, complemented
9C2×#17986205C211yesmaximal, characteristic, complemented
10C2×#17986163C211yesmaximal, characteristic
11C2×#17986163C211yesmaximal, characteristic
12C2×#17986107C211yesmaximal, characteristic, complemented
13C2×#17986101C211yesmaximal, characteristic, complemented
14C2×C4×Dic284C211yesmaximal, characteristic, complemented
15C2×C4×#11765854C211yesmaximal, characteristic, complemented
16C2×#433×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×Dic284C2211yescharacteristic
19C22×Dic284C2211yescharacteristic
20C22×#11765854C2211yescharacteristic
21C22×#11765854C2211yescharacteristic
22#17986611—24no—
23#17986611C2218yescomplemented
24C2×#14556128C2211yescharacteristic
25C2×#14556121—21no—
26C2×#14556121—21no—
27C2×#14556120C2211yescharacteristic
28C2×#14556118—21no—
29C2×#14556118—21no—
30C2×#14556107C2211yescharacteristic
31C2×#14556107C2211yescharacteristic
32#17986479—24no—
33#17986479C2218yes—
34C2×C4×Dic142C2211yescharacteristic
35C2×C4×Dic142C2211yescharacteristic
36C2×C4×Dic142C2211yescharacteristic
37C2×C4×Dic142C2211yescharacteristic
38C2×C4×D284C2211yescharacteristic
39C2×C4×D284C2211yescharacteristic
40C2×(C22⋊D71)⋊C4—21no—
41C2×(C22⋊D71)⋊C4—21no—
42C2×#14556086—21no—
43C22×C4⋊Dic71C2211yescharacteristic
44C2×C4⋊C4×D71—21no—
45#17986335C2218yescomplemented
46#17986330C2218yescomplemented
47#17986307C2218yescomplemented
48#17986300C2218yescomplemented
49#17986210C2218yescomplemented
50#17986205C2218yescomplemented
51#17986163C2218yes—
52#17986163C2218yes—
53#17986107C2218yescomplemented
54#17986101C2218yescomplemented
55C4×Dic284C2218yescomplemented
56C4×#11765854C2218yescomplemented
57C2×#14556062C2211yescharacteristic
58C2×#14556062C2211yescharacteristic
59C2×#14556060C2211yescharacteristic
60C2×#14556060C2211yescharacteristic
61C2×#14556053C2211yescharacteristic
62C2×#14556053C2211yescharacteristic
63C2×#14556053C2211yescharacteristic
64C2×#14556053C2211yescharacteristic
65C2×#14556053C2211yescharacteristic
66C2×#14556053C2211yescharacteristic
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2211yescharacteristic
69C2×#117×C71C2211yescharacteristic
70#433×C71C2218yescomplemented
71C2×C4⋊C8×C71C2211yescharacteristic
72C2×C4⋊C8×C71C2211yescharacteristic
73C2×C22⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×#97×C71C2211yescharacteristic
76C2×C4×C8×C71C2211yescharacteristic
77C2×#11765865—24no—
78C2×#11765865—24no—
79C2×#11765865—22no—
80C2×#11765865C2314yes—
81C22×Dic142C2311yescharacteristic
82C22×Dic142C2311yescharacteristic
83C22×Dic142C2311yescharacteristic
84C22×D284C2311yescharacteristic
85C22×C22⋊D71—21no—
86C23×Dic71—21no—
87C22×C4×D71—21no—
88C22×C4×D71—21no—
89C22×C4×D71—21no—
90C2×Dic284—24no—
91C2×Dic284—24no—
92C2×Dic284C2314yes—
93C2×Dic284C2314yes—
94C2×#11765854—24no—
95C2×#11765854—24no—
96C2×#11765854C2314yes—
97C2×#11765854C2314yes—
98#14556128—22no—
99#14556128C2314yes—
100#14556121—28no—
101#14556121—28no—
102#14556120—22no—
103#14556120C2314yes—
104#14556118—28no—
105#14556118—28no—
106#14556107—22no—
107#14556107—22no—
108#14556107C2314yes—
109#14556107C2314yes—
110C4×Dic142—22no—
111C4×Dic142—22no—
112C4×Dic142—22no—
113C4×Dic142—22no—
114C4×Dic142C2314yes—
115C4×Dic142C2314yes—
116C4×Dic142C2314yes—
117C4×Dic142C2314yes—
118C4×D284—22no—
119C4×D284—22no—
120C4×D284C2314yes—
121C4×D284C2314yes—
122(C22⋊D71)⋊C4—28no—
123(C22⋊D71)⋊C4—28no—
124#14556086—28no—
125C2×C4⋊Dic71—21no—
126C2×C4⋊Dic71—22no—
127C2×C4⋊Dic71—21no—
128C2×C4⋊Dic71—21no—
129C2×C4⋊Dic71C2314yes—
130C2×C4⋊Dic71C2311yescharacteristic
131C2×C4⋊Dic71C2311yescharacteristic
132C2×C4⋊Dic71C2311yescharacteristic
133C2×C4⋊Dic71C2311yescharacteristic
134C2×Dic71⋊C4—21no—
135C2×Dic71⋊C4—21no—
136C2×Dic71⋊C4—21no—
137C2×Dic71⋊C4—21no—
138C2×Dic71⋊C4—21no—
139C2×Dic71⋊C4—21no—
140C2×Dic71⋊C4—21no—
141C2×Dic71⋊C4—21no—
142C4⋊C4×D71—28no—
143C2×C22⋊Dic71—21no—
144C2×C22⋊Dic71—21no—
145C2×(C2×D71)⋊C4—21no—
146C2×(C2×D71)⋊C4—21no—
147C2×C4×Dic71—21no—
148C2×C4×Dic71—21no—
149C2×C4×Dic71—21no—
150C2×C4×Dic71—21no—
151#14556062C2314yes—
152#14556062C2314yes—
153#14556060C2314yes—
154#14556060C2314yes—
155#14556053C2314yes—
156#14556053C2314yes—
157#14556053C2314yes—
158#14556053C2314yes—
159#14556053C2314yes—
160#14556053C2314yes—
161#14556050C2314yes—
162#14556050C2314yes—
163C23×C4×C71C2311yescharacteristic
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2311yescharacteristic
168#117×C71D414yes—
169#117×C71C2314yes—
170C2×C4⋊C4×C71D411yescharacteristic
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C22⋊C4×C71D411yescharacteristic
173C2×C22⋊C4×C71D411yescharacteristic
174C2×C42×C71C2311yescharacteristic
175C2×C42×C71C2311yescharacteristic
176C4⋊C8×C71C2314yes—
177C4⋊C8×C71C2314yes—
178C22⋊C8×C71C2314yes—
179C22⋊C8×C71C2314yes—
180#97×C71C2314yes—
181C4×C8×C71C2314yes—
182C23×D71—21no—
183#11765865—216no—
184#11765865—28no—
185#11765865—28no—
186C2×Dic142—21no—
187C2×Dic142—22no—
188C2×Dic142—22no—
189C2×Dic142—22no—
190C2×Dic142—22no—
191C2×Dic142—22no—
192C2×Dic142—21no—
193C2×Dic142—21no—
194C2×Dic142#4114yes—
195C2×Dic142C2412yes—
196C2×Dic142C2412yes—
197C2×Dic142C2412yes—
198C2×D284—21no—
199C2×D284—22no—
200C2×D284#4114yes—
201C2×D284C2412yes—
202C2×C22⋊D71—28no—
203C2×C22⋊D71—24no—
204C22×Dic71—21no—
205C22×Dic71—21no—
206C22×Dic71—21no—
207C22×Dic71—21no—
208C22×Dic71—21no—
209C22×Dic71—21no—
210C22×Dic71—21no—
211C22×Dic71—24no—
212C22×Dic71—82no—
213C2×C4×D71—28no—
214C2×C4×D71—24no—
215C2×C4×D71—24no—
216C2×C4×D71—24no—
217C2×C4×D71—82no—
218C2×C4×D71—82no—
219Dic284—28no—
220Dic284—28no—
221#11765854—28no—
222#11765854—28no—
223C4⋊Dic71—24no—
224C4⋊Dic71—21no—
225C4⋊Dic71—21no—
226C4⋊Dic71—24no—
227C4⋊Dic71—24no—
228C4⋊Dic71—21no—
229C4⋊Dic71—21no—
230C4⋊Dic71C2412yes—
231C4⋊Dic71C2412yes—
232C4⋊Dic71C2412yes—
233C4⋊Dic71C2412yes—
234Dic71⋊C4—24no—
235Dic71⋊C4—24no—
236Dic71⋊C4—24no—
237Dic71⋊C4—24no—
238Dic71⋊C4—24no—
239Dic71⋊C4—24no—
240Dic71⋊C4—24no—
241Dic71⋊C4—24no—
242C22⋊Dic71—24no—
243C22⋊Dic71—24no—
244(C2×D71)⋊C4—24no—
245(C2×D71)⋊C4—24no—
246C4×Dic71—24no—
247C4×Dic71—24no—
248C4×Dic71—24no—
249C4×Dic71—24no—
250C24×C71C2×D411yescharacteristic
251C22×C4×C71—22no—
252C22×C4×C71—22no—
253C22×C4×C71C2×D411yescharacteristic
254C22×C4×C71C2×D411yescharacteristic
255C22×C4×C71C2×D411yescharacteristic
256C22×C4×C71C2×D412yes—
257C22×C4×C71C2×D411yescharacteristic
258C22×C4×C71C2×D411yescharacteristic
259C22×C4×C71C2412yes—
260C22×C4×C71C2411yescharacteristic
261C2×C8×C71—22no—
262C2×C8×C71—22no—
263C2×C8×C71—22no—
264C2×C8×C71—22no—
265C2×C8×C71C2412yes—
266C2×C8×C71C2412yes—
267C2×C8×C71C2412yes—
268C2×C8×C71C2412yes—
269C4⋊C4×C71C2×D414yes—
270C4⋊C4×C71C2×D414yes—
271C22⋊C4×C71C2×D414yes—
272C22⋊C4×C71C2×D414yes—
273C42×C71C2×D412yes—
274C42×C71C2×D412yes—
275C42×C71C2412yes—
276C42×C71C2412yes—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—22no—
280C23×C71C22×D412yes—
281C23×C71C22×D411yescharacteristic
282C22×D71—24no—
283C22×D71—22no—
284C22×D71—42no—
285C22×D71—42no—
286C2×C4×C71—22no—
287C2×C4×C71—22no—
288C2×C4×C71—22no—
289C2×C4×C71—22no—
290C2×C4×C71—22no—
291C2×C4×C71—24no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71C22×D412yes—
295C2×C4×C71C22×D412yes—
296C2×C4×C71C22×D412yes—
297C2×C4×C71C22×D412yes—
298C2×C4×C71C22×D412yes—
299C2×C4×C71C22×D411yescharacteristic
300C2×C4×C71C2×#4112yes—
301C2×C4×C71C2×#4112yes—
302C2×C4×C71C2511yescharacteristic
303C22⋊D71—216no—
304C2×Dic71—24no—
305C2×Dic71—22no—
306C2×Dic71—22no—
307C2×Dic71—22no—
308C2×Dic71—22no—
309C2×Dic71—22no—
310C2×Dic71—22no—
311C2×Dic71—22no—
312C2×Dic71—42no—
313C2×Dic71—42no—
314C2×Dic71—42no—
315C2×Dic71—42no—
316C2×Dic71—42no—
317C2×Dic71—42no—
318C2×Dic71—84no—
319D284—24no—
320D284—22no—
321D284C2×#4114yes—
322C4×D71—216no—
323C4×D71—84no—
324C4×D71—84no—
325Dic142—24no—
326Dic142—22no—
327Dic142—22no—
328Dic142—22no—
329Dic142—22no—
330Dic142—22no—
331Dic142—42no—
332Dic142—42no—
333Dic142C2×#4114yes—
334C8×C71—22no—
335C8×C71—22no—
336C8×C71—22no—
337C8×C71—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—24no—
347C2×D71—48no—
348C2×D71—42no—
349C2×D71—42no—
350C4×C71—22no—
351C4×C71—22no—
352C4×C71—22no—
353C4×C71—22no—
354C4×C71—22no—
355C4×C71#52512yes—
356C4×C71C22×#4111yescharacteristic
357C4×C71C22×#4111yescharacteristic
358Dic71—24no—
359Dic71—42no—
360Dic71—42no—
361Dic71—42no—
362Dic71—42no—
363Dic71—42no—
364Dic71—42no—
365C2×#3120—711nomaximal, Sylow
366C2×C71—42no—
367C2×C71#312014yescomplemented
368C2×C71C2×#52511yescharacteristic
369C2×C71C2×#57711yescharacteristic
370C2×C71C2×#57811yescharacteristic
371D71—44no—
372C2×#541—711no—
373C2×#520—711no—
374#3120—7116no—
375C2×#484—711no—
376C2×#483—711no—
377C2×#479—711no—
378C2×#478—711no—
379C2×#462—711no—
380C2×#461—711no—
381C2×#452—711no—
382C2×#452—711no—
383C2×#441—711no—
384C2×#440—711no—
385C2×C4×Q16—711no—
386C2×C4×SD16—711no—
387C2×#433D7111yescharacteristic, complemented
388C71C2×#312011yescharacteristic, complemented, Sylow
389C22×#41—711no—
390C22×Q16—711no—
391C22×Q16—711no—
392C22×SD16—711no—
393C22×SD16—711no—
394#541—718no—
395#541—1424no—
396C2×C4⋊Q8—711no—
397C2×#126—1421no—
398C2×#126—1421no—
399C2×#125—711no—
400C2×#125—1421no—
401C2×#125—1421no—
402C2×C22⋊Q8—711no—
403C2×C22⋊Q8—711no—
404#520—718no—
405#520—1424no—
406C2×C4×Q8—711no—
407C2×C4×Q8—711no—
408C2×C4×Q8—711no—
409C2×C4×Q8—711no—
410C2×C4×D4—711no—
411C2×C4×D4—711no—
412C2×C4×D4—1421no—
413C2×C4×D4—1421no—
414C2×#117—1421no—
415C2×#117C2×D7111yescharacteristic
416C22×C4⋊C4—711no—
417C22×C4⋊C4—1421no—
418#484—718no—
419#483—718no—
420#479—718no—
421#478—718no—
422#462—718no—
423#461—718no—
424#452—718no—
425#452—718no—
426#441—718no—
427#440—718no—
428C4×Q16—718no—
429C4×SD16—718no—
430#433C2×D7118yescomplemented
431C2×#107—711no—
432C2×#107—711no—
433C2×#106—711no—
434C2×#106—711no—
435C2×C4⋊C8C2×D7111yescharacteristic
436C2×C4⋊C8C2×D7111yescharacteristic
437C2×#103—711no—
438C2×#103—711no—
439C2×#103—711no—
440C2×#103—711no—
441C2×#103—711no—
442C2×#103—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×C22⋊C8C2×D7111yescharacteristic
446C2×C22⋊C8C2×D7111yescharacteristic
447C2×#97C2×D7111yescharacteristic
448C2×C4×C8C2×D7111yescharacteristic
449C2×#41—714no—
450C2×#41—1424no—
451C2×#41—1424no—
452C2×#41—1422no—
453C22×Q8—711no—
454C22×Q8—711no—
455C22×Q8—711no—
456C22×D4—711no—
457C22×D4—1421no—
458C23×C4—1421no—
459C23×C4—1421no—
460C23×C4—1421no—
461C23×C4—1421no—
462C23×C4C22×D7111yescharacteristic
463C2×Q16—714no—
464C2×Q16—714no—
465C2×Q16—1424no—
466C2×Q16—1424no—
467C2×SD16—714no—
468C2×SD16—714no—
469C2×SD16—1424no—
470C2×SD16—1424no—
471C22×C8C22×D7111yescharacteristic
472C22×C8C22×D7111yescharacteristic
473C22×C8C22×D7111yescharacteristic
474C22×C8C22×D7111yescharacteristic
475C4⋊Q8—714no—
476C4⋊Q8—1422no—
477#126—1428no—
478#126—1428no—
479#125—714no—
480#125—1428no—
481#125—1428no—
482#125—1422no—
483C22⋊Q8—714no—
484C22⋊Q8—714no—
485C22⋊Q8—1422no—
486C22⋊Q8—1422no—
487C4×Q8—714no—
488C4×Q8—714no—
489C4×Q8—714no—
490C4×Q8—714no—
491C4×Q8—1422no—
492C4×Q8—1422no—
493C4×Q8—1422no—
494C4×Q8—1422no—
495C4×D4—714no—
496C4×D4—714no—
497C4×D4—1428no—
498C4×D4—1428no—
499C4×D4—1422no—
500C4×D4—1422no—
501#117—1428no—
502#117D28414yes—
503#117C22×D7114yes—
504C2×C4⋊C4—711no—
505C2×C4⋊C4—711no—
506C2×C4⋊C4—714no—
507C2×C4⋊C4—711no—
508C2×C4⋊C4—711no—
509C2×C4⋊C4—1421no—
510C2×C4⋊C4—1422no—
511C2×C4⋊C4—1421no—
512C2×C4⋊C4—1421no—
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⋊C4—1421no—
520C2×C4⋊C4—1421no—
521C2×C4⋊C4—1428no—
522C2×C4⋊C4D28411yescharacteristic
523C2×C4⋊C4D28411yescharacteristic
524C2×C22⋊C4—1421no—
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4D28411yescharacteristic
529C2×C22⋊C4D28411yescharacteristic
530C2×C42—1421no—
531C2×C42—1421no—
532C2×C42—1421no—
533C2×C42—1421no—
534C2×C42C22×D7111yescharacteristic
535C2×C42C22×D7111yescharacteristic
536#107—714no—
537#107—714no—
538#106—714no—
539#106—714no—
540C4⋊C8C22×D7114yes—
541C4⋊C8C22×D7114yes—
542#103—714no—
543#103—714no—
544#103—714no—
545#103—714no—
546#103—714no—
547#103—714no—
548#102—714no—
549#102—714no—
550C22⋊C8C22×D7114yes—
551C22⋊C8C22×D7114yes—
552#97C22×D7114yes—
553C4×C8C22×D7114yes—
554C24—1421no—
555C24C2×D28411yescharacteristic
556#41—1428no—
557#41—1428no—
558#41—14216no—
559C2×Q8—714no—
560C2×Q8—712no—
561C2×Q8—712no—
562C2×Q8—712no—
563C2×Q8—1422no—
564C2×Q8—1422no—
565C2×Q8—1422no—
566C2×Q8—1422no—
567C2×Q8—1421no—
568C2×Q8—1421no—
569C2×Q8—1421no—
570C2×Q8—1422no—
571C2×D4—714no—
572C2×D4—712no—
573C2×D4—1428no—
574C2×D4—1424no—
575C2×D4—1421no—
576C2×D4—1422no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—5682no—
580C22×C4—5682no—
581C22×C4—5682no—
582C22×C4—1428no—
583C22×C4—1421no—
584C22×C4—1421no—
585C22×C4—1421no—
586C22×C4—1421no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1424no—
590C22×C4—1424no—
591C22×C4—1424no—
592C22×C4—1421no—
593C22×C4—1424no—
594C22×C4C2×D28412yes—
595C22×C4C2×D28411yescharacteristic
596C22×C4C2×D28411yescharacteristic
597C22×C4C2×D28411yescharacteristic
598C22×C4C2×D28411yescharacteristic
599C22×C4C2×D28411yescharacteristic
600C22×C4C23×D7112yes—
601C22×C4C23×D7111yescharacteristic
602Q16—1428no—
603Q16—1428no—
604SD16—1428no—
605SD16—1428no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8—22no—
609C2×C8—22no—
610C2×C8C23×D7112yes—
611C2×C8C23×D7112yes—
612C2×C8C23×D7112yes—
613C2×C8C23×D7112yes—
614C4⋊C4—712no—
615C4⋊C4—712no—
616C4⋊C4—712no—
617C4⋊C4—712no—
618C4⋊C4—1424no—
619C4⋊C4—1424no—
620C4⋊C4—1424no—
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⋊C4—1421no—
631C4⋊C4—1424no—
632C4⋊C4—1424no—
633C4⋊C4C2×D28414yes—
634C4⋊C4C2×D28414yes—
635C22⋊C4—1424no—
636C22⋊C4—1424no—
637C22⋊C4—1424no—
638C22⋊C4—1424no—
639C22⋊C4C2×D28414yes—
640C22⋊C4C2×D28414yes—
641C42—1424no—
642C42—1424no—
643C42—1424no—
644C42—1424no—
645C42C2×D28412yes—
646C42C2×D28412yes—
647C42C23×D7112yes—
648C42C23×D7112yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—2842no—
653C23—2842no—
654C23—1422no—
655C23—1424no—
656C23C22×D28412yes—
657C23C22×D28411yescharacteristic
658Q8—2842no—
659Q8—2842no—
660Q8—714no—
661Q8—1422no—
662Q8—1422no—
663Q8—1422no—
664Q8—1422no—
665Q8—1422no—
666Q8—1424no—
667D4—714no—
668D4—14216no—
669D4—1422no—
670D4—1424no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—2842no—
680C2×C4—2842no—
681C2×C4—2842no—
682C2×C4—2842no—
683C2×C4—2842no—
684C2×C4—2842no—
685C2×C4—5684no—
686C2×C4—5684no—
687C2×C4—5684no—
688C2×C4—14216no—
689C2×C4—1422no—
690C2×C4—1422no—
691C2×C4—1422no—
692C2×C4—1422no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1424no—
697C2×C4C22×D28412yes—
698C2×C4C22×D28412yes—
699C2×C4C22×D28412yes—
700C2×C4C22×D28412yes—
701C2×C4C22×D28412yes—
702C2×C4C22×D28411yescharacteristic
703C2×C4#41×D7112yes—
704C2×C4#41×D7112yes—
705C2×C4C24×D7111yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—2842no—
715C22—2842no—
716C22—2848no—
717C22—1424no—
718C22#1798651112yes—
719C22#1798681112yes—
720C22#1798681612yes—
721C22C23×D28411yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—2842no—
728C4—2842no—
729C4—2842no—
730C4—2842no—
731C4—2842no—
732C4—2842no—
733C4—1424no—
734C4#1798651112yes—
735C4C2×#41×D7111yescharacteristic
736C4C2×#41×D7111yescharacteristic
737C2—42no—
738C2—2844no—
739C2#2259855614yesdirect product factor
740C2C2×#1798651111yescharacteristic
741C2C2×#1798681111yescharacteristic
742C2C2×#1798681611yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#433×C71C2
socleC23×C71C22×D4
prime radicalC22×#11765865C22
hypercenterC2×#433D71
hypocenterC71C2×#3120
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#433

Complements

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

NH ≅ G/Ntype
1. C2×#17986611C2semidirect
3. #22598556C2direct (N × H)
4. C2×#17986335C2semidirect
5. C2×#17986330C2semidirect
6. C2×#17986307C2semidirect
7. C2×#17986300C2semidirect
8. C2×#17986210C2semidirect
9. C2×#17986205C2semidirect
12. C2×#17986107C2semidirect
13. C2×#17986101C2semidirect
14. C2×C4×Dic284C2semidirect
15. C2×C4×#11765854C2semidirect
16. C2×#433×C71C2semidirect
23. #17986611C22semidirect
45. #17986335C22semidirect
46. #17986330C22semidirect
47. #17986307C22semidirect
48. #17986300C22semidirect
49. #17986210C22semidirect
50. #17986205C22semidirect
53. #17986107C22semidirect
54. #17986101C22semidirect
55. C4×Dic284C22semidirect
56. C4×#11765854C22semidirect
70. #433×C71C22semidirect
367. C2×C71#3120semidirect
387. C2×#433D71semidirect
388. C71C2×#3120semidirect
430. #433C2×D71semidirect
739. C2#22598556direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866112
C2×#179864792
#225985562
C2×#179863352
C2×#179863302
C2×#179863072
C2×#179863002
C2×#179862102
C2×#179862052
C2×#179861632
C2×#179861072
C2×#179861012
C2×C4×Dic2842
C2×C4×#117658542
C2×#433×C712
C2×#312071