Finite Group Databasebeta

← C2×#22598548 #32865709

Subgroups — C2×#22598548 #32865709

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×#17986479C211yesmaximal, characteristic
2#22598548C2116yesmaximal, direct product factor
3C2×#17986332C211yesmaximal, characteristic, complemented
4C2×#17986327C211yesmaximal, characteristic, complemented
5C2×#17986303C211yesmaximal, characteristic, complemented
6C2×#17986296C211yesmaximal, characteristic, complemented
7C2×#17986206C211yesmaximal, characteristic, complemented
8C2×#17986201C211yesmaximal, characteristic, complemented
9C2×#17986159C211yesmaximal, characteristic
10C2×#17986159C211yesmaximal, characteristic
11C2×#17986104C211yesmaximal, characteristic, complemented
12C2×#17986097C211yesmaximal, characteristic, complemented
13C2×C4×#11765855C211yesmaximal, characteristic, complemented
14C2×C4×#11765852C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#541×C71C211yesmaximal, characteristic, complemented
17C22×#11765865C2211yescharacteristic
18C22×#11765855C2211yescharacteristic
19C22×#11765855C2211yescharacteristic
20C22×#11765852C2211yescharacteristic
21C22×#11765852C2211yescharacteristic
22#17986479—24no—
23#17986479C2218yes—
24C2×C4×Dic142C2211yescharacteristic
25C2×C4×Dic142C2211yescharacteristic
26C2×C4×D284C2211yescharacteristic
27C2×C4×D284C2211yescharacteristic
28C2×(C22⋊D71)⋊C4—21no—
29C2×(C22⋊D71)⋊C4—21no—
30C2×#14556086—21no—
31C22×C4⋊Dic71C2211yescharacteristic
32C2×C4⋊C4×D71—21no—
33#17986332C2218yescomplemented
34#17986327C2218yescomplemented
35#17986303C2218yescomplemented
36#17986296C2218yescomplemented
37#17986206C2218yescomplemented
38#17986201C2218yescomplemented
39#17986159C2218yes—
40#17986159C2218yes—
41#17986104C2218yescomplemented
42#17986097C2218yescomplemented
43C4×#11765855C2218yescomplemented
44C4×#11765852C2218yescomplemented
45#17986060C2218yescomplemented
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556059C2211yescharacteristic
49C2×#14556059C2211yescharacteristic
50C2×C4⋊(C71⋊C8)C2211yescharacteristic
51C2×C4⋊(C71⋊C8)C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556052C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556051C2211yescharacteristic
57C2×#14556051C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic
63C2×C4×C71⋊C8C2211yescharacteristic
64#541×C71—24no—
65#541×C71C2218yescomplemented
66C2×C4⋊Q8×C71C2211yescharacteristic
67C2×#126×C71—21no—
68C2×#126×C71—21no—
69C2×#125×C71—21no—
70C2×#125×C71—21no—
71C2×#125×C71C2211yescharacteristic
72C2×C22⋊Q8×C71C2211yescharacteristic
73C2×C22⋊Q8×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×Q8×C71C2211yescharacteristic
76C2×#117×C71C2211yescharacteristic
77C2×#11765865—24no—
78C2×#11765865—24no—
79C2×#11765865—22no—
80C2×#11765865C2314yes—
81C22×Dic142C2311yescharacteristic
82C22×D284C2311yescharacteristic
83C22×C22⋊D71—21no—
84C23×Dic71—21no—
85C22×C4×D71—21no—
86C22×C4×D71—21no—
87C22×C4×D71—21no—
88C2×#11765855—24no—
89C2×#11765855—24no—
90C2×#11765855C2314yes—
91C2×#11765855C2314yes—
92C2×#11765852—24no—
93C2×#11765852—24no—
94C2×#11765852C2314yes—
95C2×#11765852C2314yes—
96C22×C71⋊C8C2311yescharacteristic
97C22×C71⋊C8C2311yescharacteristic
98C22×C71⋊C8C2311yescharacteristic
99C22×C71⋊C8C2311yescharacteristic
100C4×Dic142—22no—
101C4×Dic142—22no—
102C4×Dic142C2314yes—
103C4×Dic142C2314yes—
104C4×D284—22no—
105C4×D284—22no—
106C4×D284C2314yes—
107C4×D284C2314yes—
108(C22⋊D71)⋊C4—28no—
109(C22⋊D71)⋊C4—28no—
110#14556086—28no—
111C2×C4⋊Dic71—21no—
112C2×C4⋊Dic71—22no—
113C2×C4⋊Dic71C2314yes—
114C2×C4⋊Dic71C2311yescharacteristic
115C2×C4⋊Dic71C2311yescharacteristic
116C2×Dic71⋊C4—21no—
117C2×Dic71⋊C4—21no—
118C4⋊C4×D71—28no—
119C2×(C2×D71)⋊C4—21no—
120C2×(C2×D71)⋊C4—21no—
121C2×C4×Dic71—21no—
122C2×C4×Dic71—21no—
123#14556061C2314yes—
124#14556061C2314yes—
125#14556059C2314yes—
126#14556059C2314yes—
127C4⋊(C71⋊C8)C2314yes—
128C4⋊(C71⋊C8)C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131#14556052C2314yes—
132#14556052C2314yes—
133#14556051C2314yes—
134#14556051C2314yes—
135#14556048C2314yes—
136#14556048C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138C22⋊(C71⋊C8)C2314yes—
139#14556039C2314yes—
140C4×C71⋊C8C2314yes—
141C22×Q8×C71C2311yescharacteristic
142C22×Q8×C71C2311yescharacteristic
143C23×C4×C71C2311yescharacteristic
144C4⋊Q8×C71—22no—
145C4⋊Q8×C71C2314yes—
146#126×C71—28no—
147#126×C71—28no—
148#125×C71—28no—
149#125×C71—28no—
150#125×C71—22no—
151#125×C71C2314yes—
152C22⋊Q8×C71—22no—
153C22⋊Q8×C71—22no—
154C22⋊Q8×C71C2314yes—
155C22⋊Q8×C71C2314yes—
156C4×Q8×C71—22no—
157C4×Q8×C71—22no—
158C4×Q8×C71C2314yes—
159C4×Q8×C71C2314yes—
160#117×C71D414yes—
161#117×C71C2314yes—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—21no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71—21no—
167C2×C4⋊C4×C71—21no—
168C2×C4⋊C4×C71—21no—
169C2×C4⋊C4×C71—21no—
170C2×C4⋊C4×C71D411yescharacteristic
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C4⋊C4×C71C2311yescharacteristic
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71—21no—
176C2×C22⋊C4×C71D411yescharacteristic
177C2×C22⋊C4×C71D411yescharacteristic
178C2×C42×C71—21no—
179C2×C42×C71—21no—
180C2×C42×C71C2311yescharacteristic
181C2×C42×C71C2311yescharacteristic
182C23×D71—21no—
183#11765865—216no—
184#11765865—28no—
185#11765865—28no—
186C2×Dic142—21no—
187C2×Dic142—22no—
188C2×Dic142#4114yes—
189C2×Dic142C2412yes—
190C2×D284—21no—
191C2×D284—22no—
192C2×D284#4114yes—
193C2×D284C2412yes—
194C2×C22⋊D71—28no—
195C2×C22⋊D71—24no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C22×Dic71—24no—
200C22×Dic71—82no—
201C2×C4×D71—28no—
202C2×C4×D71—24no—
203C2×C4×D71—24no—
204C2×C4×D71—24no—
205C2×C4×D71—82no—
206C2×C4×D71—82no—
207#11765855—28no—
208#11765855—28no—
209#11765852—28no—
210#11765852—28no—
211C2×C71⋊C8—22no—
212C2×C71⋊C8—22no—
213C2×C71⋊C8—22no—
214C2×C71⋊C8—22no—
215C2×C71⋊C8C2412yes—
216C2×C71⋊C8C2412yes—
217C2×C71⋊C8C2412yes—
218C2×C71⋊C8C2412yes—
219C4⋊Dic71—24no—
220C4⋊Dic71—21no—
221C4⋊Dic71—21no—
222C4⋊Dic71C2412yes—
223C4⋊Dic71C2412yes—
224Dic71⋊C4—24no—
225Dic71⋊C4—24no—
226(C2×D71)⋊C4—24no—
227(C2×D71)⋊C4—24no—
228C4×Dic71—24no—
229C4×Dic71—24no—
230C24×C71C2×D411yescharacteristic
231C2×Q8×C71—21no—
232C2×Q8×C71—21no—
233C2×Q8×C71—22no—
234C2×Q8×C71—22no—
235C2×Q8×C71—22no—
236C2×Q8×C71—22no—
237C2×Q8×C71C2412yes—
238C2×Q8×C71C2412yes—
239C22×C4×C71—22no—
240C22×C4×C71—22no—
241C22×C4×C71—21no—
242C22×C4×C71—21no—
243C22×C4×C71—21no—
244C22×C4×C71—21no—
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2×D412yes—
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2412yes—
252C22×C4×C71C2411yescharacteristic
253C4⋊C4×C71—24no—
254C4⋊C4×C71—24no—
255C4⋊C4×C71—24no—
256C4⋊C4×C71—24no—
257C4⋊C4×C71—24no—
258C4⋊C4×C71—24no—
259C4⋊C4×C71—24no—
260C4⋊C4×C71—24no—
261C4⋊C4×C71—21no—
262C4⋊C4×C71—21no—
263C4⋊C4×C71C2×D414yes—
264C4⋊C4×C71C2×D414yes—
265C4⋊C4×C71C2412yes—
266C4⋊C4×C71C2412yes—
267C22⋊C4×C71—24no—
268C22⋊C4×C71—24no—
269C22⋊C4×C71C2×D414yes—
270C22⋊C4×C71C2×D414yes—
271C42×C71—24no—
272C42×C71—24no—
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—
286Q8×C71—22no—
287Q8×C71—22no—
288Q8×C71—22no—
289Q8×C71—22no—
290Q8×C71—42no—
291Q8×C71—42no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—22no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—24no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71—22no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
303C2×C4×C71—22no—
304C2×C4×C71—42no—
305C2×C4×C71—42no—
306C2×C4×C71—42no—
307C2×C4×C71—42no—
308C2×C4×C71C22×D412yes—
309C2×C4×C71C22×D412yes—
310C2×C4×C71C22×D412yes—
311C2×C4×C71C22×D412yes—
312C2×C4×C71C22×D412yes—
313C2×C4×C71C22×D411yescharacteristic
314C2×C4×C71C2×#4112yes—
315C2×C4×C71C2×#4112yes—
316C2×C4×C71C2511yescharacteristic
317C22⋊D71—216no—
318C2×Dic71—24no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—42no—
323C2×Dic71—42no—
324C2×Dic71—84no—
325D284—24no—
326D284—22no—
327D284C2×#4114yes—
328C4×D71—216no—
329C4×D71—84no—
330C4×D71—84no—
331Dic142—24no—
332Dic142—22no—
333Dic142C2×#4114yes—
334C71⋊C8—22no—
335C71⋊C8—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—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—42no—
356C4×C71—42no—
357C4×C71—42no—
358C4×C71—42no—
359C4×C71#52512yes—
360C4×C71C22×#4111yescharacteristic
361C4×C71C22×#4111yescharacteristic
362Dic71—24no—
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×#541D7111yescharacteristic, complemented
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×#433—711no—
388C71C2×#312011yescharacteristic, complemented, Sylow
389C22×#41—711no—
390C22×Q16—711no—
391C22×Q16—711no—
392C22×SD16—711no—
393C22×SD16—711no—
394#541—24no—
395#541C2×D7118yescomplemented
396C2×C4⋊Q8C2×D7111yescharacteristic
397C2×#126—21no—
398C2×#126—21no—
399C2×#125—21no—
400C2×#125—21no—
401C2×#125C2×D7111yescharacteristic
402C2×C22⋊Q8C2×D7111yescharacteristic
403C2×C22⋊Q8C2×D7111yescharacteristic
404#520—718no—
405#520—1424no—
406C2×C4×Q8—711no—
407C2×C4×Q8—711no—
408C2×C4×Q8C2×D7111yescharacteristic
409C2×C4×Q8C2×D7111yescharacteristic
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#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×#103—711no—
442C2×#103—711no—
443C2×#102—711no—
444C2×#102—711no—
445C2×C22⋊C8—711no—
446C2×C22⋊C8—711no—
447C2×#97—711no—
448C2×C4×C8—711no—
449C2×#41—714no—
450C2×#41—1424no—
451C2×#41—1424no—
452C2×#41—1422no—
453C22×Q8—711no—
454C22×Q8C22×D7111yescharacteristic
455C22×Q8C22×D7111yescharacteristic
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×C8—711no—
472C22×C8—711no—
473C22×C8—711no—
474C22×C8—711no—
475C4⋊Q8—22no—
476C4⋊Q8C22×D7114yes—
477#126—28no—
478#126—28no—
479#125—28no—
480#125—28no—
481#125—22no—
482#125C22×D7114yes—
483C22⋊Q8—22no—
484C22⋊Q8—22no—
485C22⋊Q8C22×D7114yes—
486C22⋊Q8C22×D7114yes—
487C4×Q8—22no—
488C4×Q8—22no—
489C4×Q8—714no—
490C4×Q8—714no—
491C4×Q8—1422no—
492C4×Q8—1422no—
493C4×Q8C22×D7114yes—
494C4×Q8C22×D7114yes—
495C4×D4—714no—
496C4×D4—714no—
497C4×D4—1428no—
498C4×D4—1428no—
499C4×D4—1422no—
500C4×D4—1422no—
501#117—1428no—
502#117C22⋊D7114yes—
503#117C22×D7114yes—
504C2×C4⋊C4—21no—
505C2×C4⋊C4—21no—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—21no—
509C2×C4⋊C4—21no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4—711no—
513C2×C4⋊C4—711no—
514C2×C4⋊C4—714no—
515C2×C4⋊C4—1421no—
516C2×C4⋊C4—1422no—
517C2×C4⋊C4—1421no—
518C2×C4⋊C4—1421no—
519C2×C4⋊C4—1428no—
520C2×C4⋊C4C22⋊D7111yescharacteristic
521C2×C4⋊C4C22⋊D7111yescharacteristic
522C2×C4⋊C4C22×D7111yescharacteristic
523C2×C4⋊C4C22×D7111yescharacteristic
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4C22⋊D7111yescharacteristic
529C2×C22⋊C4C22⋊D7111yescharacteristic
530C2×C42—21no—
531C2×C42—21no—
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⋊C8—714no—
541C4⋊C8—714no—
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⋊C8—714no—
551C22⋊C8—714no—
552#97—714no—
553C4×C8—714no—
554C24—1421no—
555C24C2×C22⋊D7111yescharacteristic
556#41—1428no—
557#41—1428no—
558#41—14216no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—22no—
562C2×Q8—22no—
563C2×Q8—22no—
564C2×Q8—22no—
565C2×Q8—714no—
566C2×Q8—712no—
567C2×Q8—1421no—
568C2×Q8—1422no—
569C2×Q8C23×D7112yes—
570C2×Q8C23×D7112yes—
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—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—5682no—
584C22×C4—5682no—
585C22×C4—5682no—
586C22×C4—1428no—
587C22×C4—1421no—
588C22×C4—1421no—
589C22×C4—1424no—
590C22×C4—1424no—
591C22×C4—1424no—
592C22×C4—1421no—
593C22×C4—1424no—
594C22×C4C2×C22⋊D7112yes—
595C22×C4C2×C22⋊D7111yescharacteristic
596C22×C4C2×C22⋊D7111yescharacteristic
597C22×C4C2×C22⋊D7111yescharacteristic
598C22×C4C2×C22⋊D7111yescharacteristic
599C22×C4C2×C22⋊D7111yescharacteristic
600C22×C4C23×D7112yes—
601C22×C4C23×D7111yescharacteristic
602Q16—1428no—
603Q16—1428no—
604SD16—1428no—
605SD16—1428no—
606C2×C8—712no—
607C2×C8—712no—
608C2×C8—712no—
609C2×C8—712no—
610C2×C8—1422no—
611C2×C8—1422no—
612C2×C8—1422no—
613C2×C8—1422no—
614C4⋊C4—24no—
615C4⋊C4—24no—
616C4⋊C4—24no—
617C4⋊C4—24no—
618C4⋊C4—24no—
619C4⋊C4—24no—
620C4⋊C4—24no—
621C4⋊C4—24no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—712no—
625C4⋊C4—712no—
626C4⋊C4—1424no—
627C4⋊C4—1424no—
628C4⋊C4—1424no—
629C4⋊C4—1421no—
630C4⋊C4—1421no—
631C4⋊C4C2×C22⋊D7114yes—
632C4⋊C4C2×C22⋊D7114yes—
633C4⋊C4C23×D7112yes—
634C4⋊C4C23×D7112yes—
635C22⋊C4—24no—
636C22⋊C4—24no—
637C22⋊C4—1424no—
638C22⋊C4—1424no—
639C22⋊C4C2×C22⋊D7114yes—
640C22⋊C4C2×C22⋊D7114yes—
641C42—24no—
642C42—24no—
643C42—1424no—
644C42—1424no—
645C42C2×C22⋊D7112yes—
646C42C2×C22⋊D7112yes—
647C42C23×D7112yes—
648C42C23×D7112yes—
649C23—22no—
650C23—22no—
651C23—22no—
652C23—2842no—
653C23—2842no—
654C23—1422no—
655C23—1424no—
656C23C22×C22⋊D7112yes—
657C23C22×C22⋊D7111yescharacteristic
658Q8—22no—
659Q8—22no—
660Q8—22no—
661Q8—22no—
662Q8—42no—
663Q8—42no—
664Q8—714no—
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—22no—
680C2×C4—22no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—42no—
684C2×C4—42no—
685C2×C4—42no—
686C2×C4—42no—
687C2×C4—2842no—
688C2×C4—2842no—
689C2×C4—5684no—
690C2×C4—5684no—
691C2×C4—5684no—
692C2×C4—14216no—
693C2×C4—1422no—
694C2×C4—1422no—
695C2×C4—1422no—
696C2×C4—1424no—
697C2×C4C22×C22⋊D7112yes—
698C2×C4C22×C22⋊D7112yes—
699C2×C4C22×C22⋊D7112yes—
700C2×C4C22×C22⋊D7112yes—
701C2×C4C22×C22⋊D7112yes—
702C2×C4C22×C22⋊D7111yescharacteristic
703C2×C4#41×D7112yes—
704C2×C4#41×D7112yes—
705C2×C4C24×D7111yescharacteristic
706C8—1422no—
707C8—1422no—
708C8—1422no—
709C8—1422no—
710C22—22no—
711C22—22no—
712C22—22no—
713C22—44no—
714C22—2842no—
715C22—2842no—
716C22—2848no—
717C22—1424no—
718C22#1798650612yes—
719C22#1798680712yes—
720C22#1798681412yes—
721C22C23×C22⋊D7111yescharacteristic
722C4—22no—
723C4—22no—
724C4—22no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—2842no—
732C4—2842no—
733C4—1424no—
734C4#1798650612yes—
735C4C2×#41×D7111yescharacteristic
736C4C2×#41×D7111yescharacteristic
737C2—42no—
738C2—2844no—
739C2#2259854814yesdirect product factor
740C2C2×#1798650611yescharacteristic
741C2C2×#1798680711yescharacteristic
742C2C2×#1798681411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#541×C71C2
socleC23×C71C22×D4
prime radicalC22×#11765865C22
hypercenterC2×#541D71
hypocenterC71C2×#3120
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#541

Complements

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

NH ≅ G/Ntype
2. #22598548C2direct (N × H)
3. C2×#17986332C2semidirect
4. C2×#17986327C2semidirect
5. C2×#17986303C2semidirect
6. C2×#17986296C2semidirect
7. C2×#17986206C2semidirect
8. C2×#17986201C2semidirect
11. C2×#17986104C2semidirect
12. C2×#17986097C2semidirect
13. C2×C4×#11765855C2semidirect
14. C2×C4×#11765852C2semidirect
15. C2×#17986060C2semidirect
16. C2×#541×C71C2semidirect
33. #17986332C22semidirect
34. #17986327C22semidirect
35. #17986303C22semidirect
36. #17986296C22semidirect
37. #17986206C22semidirect
38. #17986201C22semidirect
41. #17986104C22semidirect
42. #17986097C22semidirect
43. C4×#11765855C22semidirect
44. C4×#11765852C22semidirect
45. #17986060C22semidirect
65. #541×C71C22semidirect
367. C2×C71#3120semidirect
372. C2×#541D71semidirect
388. C71C2×#3120semidirect
395. #541C2×D71semidirect
739. C2#22598548direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179864792
#225985482
C2×#179863322
C2×#179863272
C2×#179863032
C2×#179862962
C2×#179862062
C2×#179862012
C2×#179861592
C2×#179861042
C2×#179860972
C2×C4×#117658552
C2×C4×#117658522
C2×#179860602
C2×#541×C712
C2×#312071