Finite Group Databasebeta

← C2×#22599434 #32868807

Subgroups — C2×#22599434 #32868807

Order 18176.

2278 conjugacy classes of subgroups.

The subgroup lattice has 862 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986620C211yesmaximal, characteristic, complemented
2#22599434C2116yesmaximal, direct product factor
3C2×#17986386C211yesmaximal, characteristic, complemented
4C2×#17986381C211yesmaximal, characteristic, complemented
5C2×#17986358C211yesmaximal, characteristic, complemented
6C2×#17986345C211yesmaximal, characteristic, complemented
7C2×#17986218C211yesmaximal, characteristic, complemented
8C2×#17986196C211yesmaximal, characteristic, complemented
9C2×#17986211C211yesmaximal, characteristic, complemented
10C2×#17986191C211yesmaximal, characteristic, complemented
11C2×#17986161C211yesmaximal, characteristic, complemented
12C2×#17986144C211yesmaximal, characteristic, complemented
13C2×#17986150C211yesmaximal, characteristic, complemented
14C2×#17986133C211yesmaximal, characteristic, complemented
15C2×#17986060C211yesmaximal, characteristic, complemented
16C2×#535×C71C211yesmaximal, characteristic, complemented
17C22×#11765855C2211yescharacteristic, complemented
18C22×#11765853C2211yescharacteristic
19C22×#11765853C2211yescharacteristic
20C22×#11765853C2211yescharacteristic, complemented
21C22×#11765852C2211yescharacteristic, complemented
22C22×#11765850C2211yescharacteristic
23C22×#11765850C2211yescharacteristic
24C22×#11765850C2211yescharacteristic, complemented
25#17986620—24no—
26#17986620C2218yescomplemented
27C2×#14556128C2211yescharacteristic, complemented
28C2×#14556123—21no—
29C2×#14556116C2211yescharacteristic, complemented
30C2×#14556114—21no—
31C2×#14556110—21no—
32C2×#14556107C2211yescharacteristic
33C2×#14556106—21no—
34C2×#14556102C2211yescharacteristic
35C2×C4×Dic142C2211yescharacteristic, complemented
36C2×C4×D284C2211yescharacteristic, complemented
37#17986386C2218yescomplemented
38#17986381C2218yescomplemented
39#17986358C2218yescomplemented
40#17986345C2218yescomplemented
41#17986218C2218yescomplemented
42#17986211C2218yescomplemented
43#17986196C2218yescomplemented
44#17986191C2218yescomplemented
45#17986161C2218yescomplemented
46#17986150C2218yescomplemented
47#17986144C2218yescomplemented
48#17986133C2218yescomplemented
49#17986060C2218yescomplemented
50C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
51C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
52C2×#14556052C2211yescharacteristic, complemented
53C2×#14556052C2211yescharacteristic, complemented
54C2×#14556049C2211yescharacteristic
55C2×#14556049C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556049C2211yescharacteristic, complemented
59C2×#14556049C2211yescharacteristic, complemented
60C2×C22⋊(C71⋊C8)C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×#14556039C2211yescharacteristic, complemented
63C2×C4×C71⋊C8C2211yescharacteristic, complemented
64C22×#41×C71C2211yescharacteristic
65C23×D4×C71C2211yescharacteristic
66#535×C71—24no—
67#535×C71C2218yescomplemented
68C2×#127×C71C2211yescharacteristic
69C2×#127×C71C2211yescharacteristic
70C2×#124×C71C2211yescharacteristic
71C2×#124×C71C2211yescharacteristic
72C2×#121×C71—21no—
73C2×#121×C71—21no—
74C2×#120×C71—21no—
75C2×#120×C71—21no—
76C2×#117×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C22×C4×D71—21no—
82C2×#11765855—42no—
83C2×#11765855C2314yescomplemented
84C2×#11765853—42no—
85C2×#11765853—42no—
86C2×#11765853—42no—
87C2×#11765853C2314yes—
88C2×#11765853C2314yes—
89C2×#11765853C2314yescomplemented
90C2×#11765852—42no—
91C2×#11765852C2314yescomplemented
92C2×#11765850—42no—
93C2×#11765850—42no—
94C2×#11765850—42no—
95C2×#11765850C2314yes—
96C2×#11765850C2314yes—
97C2×#11765850C2314yescomplemented
98C22×C71⋊C8C2311yescharacteristic
99C22×C71⋊C8C2311yescharacteristic
100C22×C71⋊C8C2311yescharacteristic
101C22×C71⋊C8C2311yescharacteristic
102#14556128—22no—
103#14556128C2314yescomplemented
104#14556123—28no—
105#14556116—22no—
106#14556116C2314yescomplemented
107#14556114—28no—
108#14556110—28no—
109#14556107—22no—
110#14556107C2314yes—
111#14556106—28no—
112#14556102—22no—
113#14556102C2314yes—
114C4×Dic142—22no—
115C4×Dic142C2314yescomplemented
116C4×D284—22no—
117C4×D284C2314yescomplemented
118C2×C4⋊Dic71—21no—
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×Dic71⋊C4—21no—
122C2×Dic71⋊C4—21no—
123C2×C22⋊Dic71—21no—
124C2×(C2×D71)⋊C4—21no—
125C2×(C2×D71)⋊C4—21no—
126C2×(C2×D71)⋊C4—21no—
127C2×(C2×D71)⋊C4—21no—
128C2×C4×Dic71—21no—
129C4⋊(C71⋊C8)C2314yescomplemented
130C4⋊(C71⋊C8)C2314yescomplemented
131#14556052C2314yescomplemented
132#14556052C2314yescomplemented
133#14556049C2314yes—
134#14556049C2314yes—
135#14556049C2314yes—
136#14556049C2314yes—
137#14556049C2314yescomplemented
138#14556049C2314yescomplemented
139C22⋊(C71⋊C8)C2314yes—
140C22⋊(C71⋊C8)C2314yes—
141#14556039C2314yescomplemented
142C4×C71⋊C8C2314yescomplemented
143C25×C71—21no—
144C2×#41×C71—22no—
145C2×#41×C71—42no—
146C2×#41×C71—42no—
147C2×#41×C71C2314yes—
148C22×Q8×C71C2311yescharacteristic
149C22×D4×C71—21no—
150C22×D4×C71—21no—
151C22×D4×C71—22no—
152C22×D4×C71—21no—
153C22×D4×C71—21no—
154C22×D4×C71—21no—
155C22×D4×C71—21no—
156C22×D4×C71—42no—
157C22×D4×C71—42no—
158C22×D4×C71C2311yescharacteristic
159C22×D4×C71C2311yescharacteristic
160C22×D4×C71C2311yescharacteristic
161C22×D4×C71C2314yes—
162C23×C4×C71—21no—
163C23×C4×C71C2311yescharacteristic
164#127×C71—22no—
165#127×C71—22no—
166#127×C71C2314yes—
167#127×C71C2314yes—
168#124×C71—22no—
169#124×C71—22no—
170#124×C71C2314yes—
171#124×C71C2314yes—
172#121×C71—28no—
173#121×C71—28no—
174#120×C71—28no—
175#120×C71—28no—
176#117×C71D414yes—
177#117×C71C2314yes—
178C2×C4⋊C4×C71D411yescharacteristic
179C2×C4⋊C4×C71D411yescharacteristic
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71—21no—
182C2×C22⋊C4×C71—21no—
183C2×C22⋊C4×C71—21no—
184C2×C22⋊C4×C71D411yescharacteristic
185C2×C22⋊C4×C71D411yescharacteristic
186C2×C42×C71C2311yescharacteristic
187C2×C42×C71C2311yescharacteristic
188C23×D71—21no—
189C2×Dic142—22no—
190C2×Dic142—22no—
191C2×Dic142—21no—
192C2×Dic142—24no—
193C2×Dic142—82no—
194C2×Dic142C2412yes—
195C2×D284—22no—
196C2×D284—22no—
197C2×D284—21no—
198C2×D284C2412yes—
199C2×C22⋊D71—24no—
200C2×C22⋊D71—82no—
201C22×Dic71—21no—
202C22×Dic71—21no—
203C22×Dic71—21no—
204C2×C4×D71—24no—
205C2×C4×D71—82no—
206#11765855—44no—
207#11765853—44no—
208#11765853—44no—
209#11765853—44no—
210#11765852—44no—
211#11765850—44no—
212#11765850—44no—
213#11765850—44no—
214C2×C71⋊C8—22no—
215C2×C71⋊C8—22no—
216C2×C71⋊C8—22no—
217C2×C71⋊C8—22no—
218C2×C71⋊C8C2412yes—
219C2×C71⋊C8C2412yes—
220C2×C71⋊C8C2412yes—
221C2×C71⋊C8C2412yes—
222C4⋊Dic71—24no—
223C4⋊Dic71—21no—
224C4⋊Dic71—21no—
225C4⋊Dic71C2412yes—
226C4⋊Dic71C2412yes—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229C22⋊Dic71—24no—
230(C2×D71)⋊C4—24no—
231(C2×D71)⋊C4—24no—
232(C2×D71)⋊C4—24no—
233(C2×D71)⋊C4—24no—
234C4×Dic71—24no—
235C24×C71—21no—
236C24×C71—21no—
237C24×C71—21no—
238C24×C71—24no—
239C24×C71—44no—
240C24×C71—82no—
241C24×C71—82no—
242C24×C71C2×D411yescharacteristic
243#41×C71—44no—
244#41×C71—44no—
245#41×C71—48no—
246C2×Q8×C71—21no—
247C2×Q8×C71—22no—
248C2×Q8×C71—22no—
249C2×Q8×C71C2412yes—
250C2×D4×C71—24no—
251C2×D4×C71—24no—
252C2×D4×C71—21no—
253C2×D4×C71—21no—
254C2×D4×C71—21no—
255C2×D4×C71—24no—
256C2×D4×C71—24no—
257C2×D4×C71—24no—
258C2×D4×C71—24no—
259C2×D4×C71—22no—
260C2×D4×C71—22no—
261C2×D4×C71—22no—
262C2×D4×C71—22no—
263C2×D4×C71—22no—
264C2×D4×C71—22no—
265C2×D4×C71—44no—
266C2×D4×C71—44no—
267C2×D4×C71—44no—
268C2×D4×C71—48no—
269C2×D4×C71—44no—
270C2×D4×C71—82no—
271C2×D4×C71—82no—
272C2×D4×C71—82no—
273C2×D4×C71—82no—
274C2×D4×C71C2412yes—
275C2×D4×C71C2412yes—
276C2×D4×C71C2412yes—
277C22×C4×C71—22no—
278C22×C4×C71—22no—
279C22×C4×C71—21no—
280C22×C4×C71—24no—
281C22×C4×C71—44no—
282C22×C4×C71C2×D411yescharacteristic
283C22×C4×C71C2×D411yescharacteristic
284C22×C4×C71C2×D411yescharacteristic
285C22×C4×C71C2×D411yescharacteristic
286C22×C4×C71C2×D411yescharacteristic
287C22×C4×C71C2×D412yes—
288C22×C4×C71C2412yes—
289C22×C4×C71C2411yescharacteristic
290C4⋊C4×C71C2×D414yes—
291C4⋊C4×C71C2×D414yes—
292C22⋊C4×C71—24no—
293C22⋊C4×C71—24no—
294C22⋊C4×C71—24no—
295C22⋊C4×C71—24no—
296C22⋊C4×C71C2×D414yes—
297C22⋊C4×C71C2×D414yes—
298C42×C71C2×D412yes—
299C42×C71C2×D412yes—
300C42×C71C2412yes—
301C42×C71C2412yes—
302C23×C71—22no—
303C23×C71—22no—
304C23×C71—22no—
305C23×C71—22no—
306C23×C71—22no—
307C23×C71—22no—
308C23×C71—48no—
309C23×C71—42no—
310C23×C71—42no—
311C23×C71—42no—
312C23×C71—42no—
313C23×C71—42no—
314C23×C71—42no—
315C23×C71—42no—
316C23×C71—42no—
317C23×C71—42no—
318C23×C71—84no—
319C23×C71—84no—
320C23×C71—816no—
321C23×C71C22×D412yes—
322C23×C71C22×D411yescharacteristic
323C22×D71—22no—
324C22×D71—42no—
325C22×D71—42no—
326C22×D71—42no—
327Q8×C71—22no—
328Q8×C71—22no—
329Q8×C71—42no—
330D4×C71—22no—
331D4×C71—22no—
332D4×C71—22no—
333D4×C71—22no—
334D4×C71—22no—
335D4×C71—22no—
336D4×C71—48no—
337D4×C71—48no—
338D4×C71—42no—
339D4×C71—42no—
340D4×C71—42no—
341D4×C71—84no—
342D4×C71—84no—
343D4×C71—84no—
344D4×C71—84no—
345C2×C4×C71—22no—
346C2×C4×C71—22no—
347C2×C4×C71—22no—
348C2×C4×C71—22no—
349C2×C4×C71—22no—
350C2×C4×C71—24no—
351C2×C4×C71—22no—
352C2×C4×C71—22no—
353C2×C4×C71—22no—
354C2×C4×C71—48no—
355C2×C4×C71—42no—
356C2×C4×C71C22×D412yes—
357C2×C4×C71C22×D412yes—
358C2×C4×C71C22×D412yes—
359C2×C4×C71C22×D412yes—
360C2×C4×C71C22×D412yes—
361C2×C4×C71C22×D411yescharacteristic
362C2×C4×C71H(5,𝔽2)12yes—
363C2×C4×C71H(5,𝔽2)12yes—
364C2×C4×C71C2511yescharacteristic
365C22⋊D71—84no—
366C2×Dic71—22no—
367C2×Dic71—22no—
368C2×Dic71—22no—
369C2×Dic71—42no—
370C2×Dic71—42no—
371C2×Dic71—42no—
372D284—22no—
373D284—22no—
374D284—42no—
375C4×D71—84no—
376Dic142—22no—
377Dic142—22no—
378Dic142—42no—
379Dic142—84no—
380C71⋊C8—22no—
381C71⋊C8—22no—
382C71⋊C8—22no—
383C71⋊C8—22no—
384C22×C71—22no—
385C22×C71—22no—
386C22×C71—22no—
387C22×C71—44no—
388C22×C71—42no—
389C22×C71—42no—
390C22×C71—42no—
391C22×C71—42no—
392C22×C71—42no—
393C22×C71—42no—
394C22×C71—42no—
395C22×C71—42no—
396C22×C71—42no—
397C22×C71—816no—
398C22×C71—84no—
399C22×C71—84no—
400C22×C71—84no—
401C22×C71#53512yes—
402C22×C71#57612yes—
403C22×C71#57712yes—
404C22×C71C23×D411yescharacteristic
405C2×D71—42no—
406C2×D71—42no—
407C2×D71—42no—
408C2×D71—84no—
409C4×C71—22no—
410C4×C71—22no—
411C4×C71—22no—
412C4×C71—22no—
413C4×C71—22no—
414C4×C71—42no—
415C4×C71#53512yes—
416C4×C71C2×H(5,𝔽2)11yescharacteristic
417C4×C71C2×H(5,𝔽2)11yescharacteristic
418Dic71—42no—
419Dic71—42no—
420Dic71—42no—
421C2×#3224—711nomaximal, Sylow
422C2×C71—42no—
423C2×C71—82no—
424C2×C71—82no—
425C2×C71—82no—
426C2×C71#322414yescomplemented
427C2×C71C2×#53511yescharacteristic
428C2×C71C2×#57611yescharacteristic
429C2×C71C2×#57711yescharacteristic
430D71—82no—
431C2×#542—711no—
432C2×#535D7111yescharacteristic, complemented
433#3224—7116no—
434C2×#496—711no—
435C2×#495—711no—
436C2×#489—711no—
437C2×#486—711no—
438C2×#464—711no—
439C2×#460—711no—
440C2×#463—711no—
441C2×#459—711no—
442C2×#452—711no—
443C2×#449—711no—
444C2×#450—711no—
445C2×#447—711no—
446C2×#433—711no—
447C71C2×#322411yescharacteristic, complemented, Sylow
448C22×#41C2×D7111yescharacteristic
449C23×D4C2×D7111yescharacteristic
450C22×Q16—711no—
451C22×SD16—711no—
452C22×SD16—711no—
453C22×SD16—711no—
454C22×SD16—711no—
455C22×D8—711no—
456C22×D8—711no—
457C22×D8—711no—
458#542—718no—
459#542—1424no—
460#535—24no—
461#535C2×D7118yescomplemented
462C2×C4⋊Q8—711no—
463C2×#127C2×D7111yescharacteristic
464C2×#127C2×D7111yescharacteristic
465C2×#126—1421no—
466C2×#124—711no—
467C2×#124—1421no—
468C2×#124C2×D7111yescharacteristic
469C2×#124C2×D7111yescharacteristic
470C2×#123—1421no—
471C2×C22⋊Q8—711no—
472C2×C22⋊Q8—1421no—
473C2×#121—21no—
474C2×#121—21no—
475C2×#121—711no—
476C2×#120—21no—
477C2×#120—21no—
478C2×C4×Q8—711no—
479C2×C4×D4—711no—
480C2×#117C2×D7111yescharacteristic
481#496—718no—
482#495—718no—
483#489—718no—
484#486—718no—
485#464—718no—
486#463—718no—
487#460—718no—
488#459—718no—
489#452—718no—
490#450—718no—
491#449—718no—
492#447—718no—
493#433—718no—
494C2×C4⋊C8—711no—
495C2×C4⋊C8—711no—
496C2×#103—711no—
497C2×#103—711no—
498C2×#102—711no—
499C2×#102—711no—
500C2×#102—711no—
501C2×#102—711no—
502C2×#102—711no—
503C2×#102—711no—
504C2×C22⋊C8—711no—
505C2×C22⋊C8—711no—
506C2×#97—711no—
507C2×C4×C8—711no—
508C25—21no—
509C2×#41—22no—
510C2×#41—42no—
511C2×#41—42no—
512C2×#41C22×D7114yes—
513C22×Q8—711no—
514C22×Q8—1421no—
515C22×Q8C22×D7111yescharacteristic
516C22×D4—21no—
517C22×D4—21no—
518C22×D4—22no—
519C22×D4—21no—
520C22×D4—21no—
521C22×D4—21no—
522C22×D4—21no—
523C22×D4—42no—
524C22×D4—42no—
525C22×D4—711no—
526C22×D4—1421no—
527C22×D4C22×D7111yescharacteristic
528C22×D4C22×D7111yescharacteristic
529C22×D4C22×D7111yescharacteristic
530C22×D4C22×D7114yes—
531C23×C4—21no—
532C23×C4—1421no—
533C23×C4C22×D7111yescharacteristic
534C2×Q16—2842no—
535C2×Q16—714no—
536C2×SD16—2842no—
537C2×SD16—2842no—
538C2×SD16—2842no—
539C2×SD16—2842no—
540C2×SD16—714no—
541C2×SD16—714no—
542C2×SD16—714no—
543C2×SD16—714no—
544C2×D8—2842no—
545C2×D8—2842no—
546C2×D8—2842no—
547C2×D8—714no—
548C2×D8—714no—
549C2×D8—714no—
550C22×C8—711no—
551C22×C8—711no—
552C22×C8—711no—
553C22×C8—711no—
554C4⋊Q8—714no—
555C4⋊Q8—1422no—
556#127—22no—
557#127—22no—
558#127C22×D7114yes—
559#127C22×D7114yes—
560#126—1428no—
561#124—22no—
562#124—22no—
563#124—714no—
564#124—1428no—
565#124—1422no—
566#124C22×D7114yes—
567#124C22×D7114yes—
568#123—1428no—
569C22⋊Q8—714no—
570C22⋊Q8—1422no—
571C22⋊Q8—1428no—
572#121—28no—
573#121—28no—
574#121—714no—
575#121—1422no—
576#120—28no—
577#120—28no—
578C4×Q8—714no—
579C4×Q8—1422no—
580C4×D4—714no—
581C4×D4—1422no—
582#117C22⋊D7114yes—
583#117C22×D7114yes—
584C2×C4⋊C4—711no—
585C2×C4⋊C4—711no—
586C2×C4⋊C4—1421no—
587C2×C4⋊C4—1421no—
588C2×C4⋊C4—1421no—
589C2×C4⋊C4C22⋊D7111yescharacteristic
590C2×C4⋊C4C22⋊D7111yescharacteristic
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—1421no—
596C2×C22⋊C4—1421no—
597C2×C22⋊C4—1421no—
598C2×C22⋊C4—1421no—
599C2×C22⋊C4—1421no—
600C2×C22⋊C4C22⋊D7111yescharacteristic
601C2×C22⋊C4C22⋊D7111yescharacteristic
602C2×C42—1421no—
603C2×C42C22×D7111yescharacteristic
604C2×C42C22×D7111yescharacteristic
605C4⋊C8—714no—
606C4⋊C8—714no—
607#103—714no—
608#103—714no—
609#102—714no—
610#102—714no—
611#102—714no—
612#102—714no—
613#102—714no—
614#102—714no—
615C22⋊C8—714no—
616C22⋊C8—714no—
617#97—714no—
618C4×C8—714no—
619C24—21no—
620C24—21no—
621C24—21no—
622C24—24no—
623C24—44no—
624C24—82no—
625C24—82no—
626C24—1421no—
627C24C2×C22⋊D7111yescharacteristic
628#41—44no—
629#41—44no—
630#41—48no—
631C2×Q8—21no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—5682no—
635C2×Q8—712no—
636C2×Q8—1422no—
637C2×Q8—1422no—
638C2×Q8—1421no—
639C2×Q8—1424no—
640C2×Q8C23×D7112yes—
641C2×D4—24no—
642C2×D4—24no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—24no—
647C2×D4—24no—
648C2×D4—24no—
649C2×D4—24no—
650C2×D4—22no—
651C2×D4—22no—
652C2×D4—22no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—44no—
657C2×D4—44no—
658C2×D4—44no—
659C2×D4—48no—
660C2×D4—44no—
661C2×D4—82no—
662C2×D4—82no—
663C2×D4—82no—
664C2×D4—82no—
665C2×D4—5682no—
666C2×D4—712no—
667C2×D4—1424no—
668C2×D4—1421no—
669C2×D4—1422no—
670C2×D4—1422no—
671C2×D4C23×D7112yes—
672C2×D4C23×D7112yes—
673C2×D4C23×D7112yes—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—21no—
677C22×C4—24no—
678C22×C4—44no—
679C22×C4—5682no—
680C22×C4—1421no—
681C22×C4—1421no—
682C22×C4—1421no—
683C22×C4—1424no—
684C22×C4C2×C22⋊D7112yes—
685C22×C4C2×C22⋊D7111yescharacteristic
686C22×C4C2×C22⋊D7111yescharacteristic
687C22×C4C2×C22⋊D7111yescharacteristic
688C22×C4C2×C22⋊D7111yescharacteristic
689C22×C4C2×C22⋊D7111yescharacteristic
690C22×C4C23×D7112yes—
691C22×C4C23×D7111yescharacteristic
692Q16—2844no—
693SD16—2844no—
694SD16—2844no—
695SD16—2844no—
696SD16—2844no—
697D8—2844no—
698D8—2844no—
699D8—2844no—
700C2×C8—712no—
701C2×C8—712no—
702C2×C8—712no—
703C2×C8—712no—
704C2×C8—1422no—
705C2×C8—1422no—
706C2×C8—1422no—
707C2×C8—1422no—
708C4⋊C4—712no—
709C4⋊C4—712no—
710C4⋊C4—1424no—
711C4⋊C4—1424no—
712C4⋊C4—1421no—
713C4⋊C4—1421no—
714C4⋊C4—1424no—
715C4⋊C4C2×C22⋊D7114yes—
716C4⋊C4C2×C22⋊D7114yes—
717C22⋊C4—24no—
718C22⋊C4—24no—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—1424no—
722C22⋊C4—1424no—
723C22⋊C4—1424no—
724C22⋊C4—1424no—
725C22⋊C4—1424no—
726C22⋊C4C2×C22⋊D7114yes—
727C22⋊C4C2×C22⋊D7114yes—
728C42—1424no—
729C42C2×C22⋊D7112yes—
730C42C2×C22⋊D7112yes—
731C42C23×D7112yes—
732C42C23×D7112yes—
733C23—22no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—48no—
740C23—42no—
741C23—42no—
742C23—42no—
743C23—42no—
744C23—42no—
745C23—42no—
746C23—42no—
747C23—42no—
748C23—42no—
749C23—84no—
750C23—84no—
751C23—816no—
752C23—2842no—
753C23—2842no—
754C23—2842no—
755C23—1422no—
756C23C22×C22⋊D7112yes—
757C23C22×C22⋊D7111yescharacteristic
758Q8—22no—
759Q8—22no—
760Q8—42no—
761Q8—2842no—
762Q8—5684no—
763Q8—1422no—
764Q8—1422no—
765D4—22no—
766D4—22no—
767D4—22no—
768D4—22no—
769D4—22no—
770D4—22no—
771D4—48no—
772D4—48no—
773D4—42no—
774D4—42no—
775D4—42no—
776D4—84no—
777D4—84no—
778D4—84no—
779D4—84no—
780D4—2842no—
781D4—5684no—
782D4—1422no—
783D4—1422no—
784C2×C4—22no—
785C2×C4—22no—
786C2×C4—22no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—24no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—48no—
794C2×C4—42no—
795C2×C4—2842no—
796C2×C4—2842no—
797C2×C4—2842no—
798C2×C4—5684no—
799C2×C4—1422no—
800C2×C4—1422no—
801C2×C4—1422no—
802C2×C4C22×C22⋊D7112yes—
803C2×C4C22×C22⋊D7112yes—
804C2×C4C22×C22⋊D7112yes—
805C2×C4C22×C22⋊D7112yes—
806C2×C4C22×C22⋊D7112yes—
807C2×C4C22×C22⋊D7111yescharacteristic
808C2×C4#1455617312yes—
809C2×C4#1455617312yes—
810C2×C4C24×D7111yescharacteristic
811C8—1422no—
812C8—1422no—
813C8—1422no—
814C8—1422no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—44no—
819C22—42no—
820C22—42no—
821C22—42no—
822C22—42no—
823C22—42no—
824C22—42no—
825C22—42no—
826C22—42no—
827C22—42no—
828C22—816no—
829C22—84no—
830C22—84no—
831C22—84no—
832C22—2842no—
833C22—2842no—
834C22—2842no—
835C22—5684no—
836C22#1798656612yes—
837C22#1798680212yes—
838C22#1798681012yes—
839C22C23×C22⋊D7111yescharacteristic
840C4—22no—
841C4—22no—
842C4—22no—
843C4—22no—
844C4—22no—
845C4—42no—
846C4—2842no—
847C4—2842no—
848C4—2842no—
849C4#1798656612yes—
850C4C2×#1455617311yescharacteristic
851C4C2×#1455617311yescharacteristic
852C2—42no—
853C2—82no—
854C2—82no—
855C2—82no—
856C2—5682no—
857C2#2259943414yesdirect product factor
858C2C2×#1798656611yescharacteristic
859C2C2×#1798680211yescharacteristic
860C2C2×#1798681011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#535×C71C2
socleC23×C71C22×D4
hypercenterC2×#535D71
hypocenterC71C2×#3224
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×#117 ◁ C2×#535

Complements

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

NH ≅ G/Ntype
1. C2×#17986620C2semidirect
2. #22599434C2direct (N × H)
3. C2×#17986386C2semidirect
4. C2×#17986381C2semidirect
5. C2×#17986358C2semidirect
6. C2×#17986345C2semidirect
7. C2×#17986218C2semidirect
8. C2×#17986196C2semidirect
9. C2×#17986211C2semidirect
10. C2×#17986191C2semidirect
11. C2×#17986161C2semidirect
12. C2×#17986144C2semidirect
13. C2×#17986150C2semidirect
14. C2×#17986133C2semidirect
15. C2×#17986060C2semidirect
16. C2×#535×C71C2semidirect
17. C22×#11765855C22semidirect
20. C22×#11765853C22semidirect
21. C22×#11765852C22semidirect
24. C22×#11765850C22semidirect
26. #17986620C22semidirect
27. C2×#14556128C22semidirect
29. C2×#14556116C22semidirect
35. C2×C4×Dic142C22semidirect
36. C2×C4×D284C22semidirect
37. #17986386C22semidirect
38. #17986381C22semidirect
39. #17986358C22semidirect
40. #17986345C22semidirect
41. #17986218C22semidirect
42. #17986211C22semidirect
43. #17986196C22semidirect
44. #17986191C22semidirect
45. #17986161C22semidirect
46. #17986150C22semidirect
47. #17986144C22semidirect
48. #17986133C22semidirect
49. #17986060C22semidirect
50. C2×C4⋊(C71⋊C8)C22semidirect
51. C2×C4⋊(C71⋊C8)C22semidirect
52. C2×#14556052C22semidirect
53. C2×#14556052C22semidirect
58. C2×#14556049C22semidirect
59. C2×#14556049C22semidirect
62. C2×#14556039C22semidirect
63. C2×C4×C71⋊C8C22semidirect
67. #535×C71C22semidirect
83. C2×#11765855C23semidirect
89. C2×#11765853C23semidirect
91. C2×#11765852C23semidirect
97. C2×#11765850C23semidirect
103. #14556128C23semidirect
106. #14556116C23semidirect
115. C4×Dic142C23semidirect
117. C4×D284C23semidirect
129. C4⋊(C71⋊C8)C23semidirect
130. C4⋊(C71⋊C8)C23semidirect
131. #14556052C23semidirect
132. #14556052C23semidirect
137. #14556049C23semidirect
138. #14556049C23semidirect
141. #14556039C23semidirect
142. C4×C71⋊C8C23semidirect
426. C2×C71#3224semidirect
432. C2×#535D71semidirect
447. C71C2×#3224semidirect
461. #535C2×D71semidirect
857. C2#22599434direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866202
#225994342
C2×#179863862
C2×#179863812
C2×#179863582
C2×#179863452
C2×#179862182
C2×#179861962
C2×#179862112
C2×#179861912
C2×#179861612
C2×#179861442
C2×#179861502
C2×#179861332
C2×#179860602
C2×#535×C712
C2×#322471