Finite Group Databasebeta

← C2×#22598589 #32865753

Subgroups — C2×#22598589 #32865753

Order 18176.

2210 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986607C211yesmaximal, characteristic, complemented
2C2×#17986471C211yesmaximal, characteristic
3#22598589C2116yesmaximal, direct product factor
4C2×#17986343C211yesmaximal, characteristic, complemented
5C2×#17986338C211yesmaximal, characteristic, complemented
6C2×#17986301C211yesmaximal, characteristic, complemented
7C2×#17986298C211yesmaximal, characteristic, complemented
8C2×#17986203C211yesmaximal, characteristic, complemented
9C2×#17986202C211yesmaximal, characteristic, complemented
10C2×#17986151C211yesmaximal, characteristic
11C2×#17986148C211yesmaximal, characteristic
12C2×#17986099C211yesmaximal, characteristic, complemented
13C2×#17986097C211yesmaximal, characteristic, complemented
14C2×C4×#11765854C211yesmaximal, characteristic, complemented
15C2×#17986058C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C71C211yesmaximal, characteristic, complemented
17C22×D4×D71C2211yescharacteristic
18C22×#11765854C2211yescharacteristic
19C22×#11765853C2211yescharacteristic
20C22×#11765852C2211yescharacteristic
21#17986607—24no—
22#17986607C2218yescomplemented
23C2×#14556126C2211yescharacteristic, complemented
24C2×#14556123—21no—
25C2×#14556122—21no—
26C2×#14556120—21no—
27C2×#14556119C2211yescharacteristic, complemented
28C2×#14556118—21no—
29C2×#14556108C2211yescharacteristic
30C2×#14556104C2211yescharacteristic
31#17986471—24no—
32#17986471C2218yes—
33C2×C4×Dic142C2211yescharacteristic, complemented
34C2×C4×D284C2211yescharacteristic
35C2×D4×Dic71C2211yescharacteristic
36C2×#14556090C2211yescharacteristic
37C2×C4×C22⋊D71—21no—
38C2×(C22⋊D71)⋊C4—21no—
39C2×#14556086C2211yescharacteristic
40C2×#14556085C2211yescharacteristic
41C22×(C2×D71)⋊C4—21no—
42C2×C22⋊C4×D71—21no—
43#17986343C2218yescomplemented
44#17986338C2218yescomplemented
45#17986301C2218yescomplemented
46#17986298C2218yescomplemented
47#17986203C2218yescomplemented
48#17986202C2218yescomplemented
49#17986151C2218yes—
50#17986148C2218yes—
51#17986099C2218yescomplemented
52#17986097C2218yescomplemented
53C4×#11765854C2218yescomplemented
54#17986058C2218yescomplemented
55C2×#14556061C2211yescharacteristic, complemented
56C2×#14556061C2211yescharacteristic, complemented
57C2×#14556060C2211yescharacteristic, complemented
58C2×Dic71⋊C8C2211yescharacteristic, complemented
59C2×Dic71⋊C8C2211yescharacteristic, complemented
60C2×#14556053C2211yescharacteristic, complemented
61C2×#14556052C2211yescharacteristic, complemented
62C2×#14556051C2211yescharacteristic, complemented
63C2×#14556050C2211yescharacteristic
64C2×#14556049C2211yescharacteristic
65C2×#14556048C2211yescharacteristic
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×#14556039C2211yescharacteristic, complemented
69C22×SD16×C71C2211yescharacteristic
70C2×C4×Q8×C71C2211yescharacteristic, complemented
71C2×C4×D4×C71C2211yescharacteristic
72C4×SD16×C71C2218yescomplemented
73C2×#106×C71C2211yescharacteristic, complemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic
76C2×C4×C8×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C22×Dic142C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C2×D4×D71—24no—
82C2×D4×D71—22no—
83C2×D4×D71—24no—
84C2×D4×D71C2314yes—
85C23×Dic71—21no—
86C22×C4×D71—21no—
87C22×C4×D71—21no—
88C22×C4×D71C2311yescharacteristic
89C2×#11765854—24no—
90C2×#11765854C2314yes—
91C2×#11765853—24no—
92C2×#11765853C2314yes—
93C2×#11765852—24no—
94C2×#11765852C2314yes—
95C22×C71⋊C8C2311yescharacteristic
96C22×C71⋊C8C2311yescharacteristic
97#14556126—22no—
98#14556126C2314yescomplemented
99#14556123—28no—
100#14556122—28no—
101#14556120—28no—
102#14556119—22no—
103#14556119C2314yescomplemented
104#14556118—28no—
105#14556108—22no—
106#14556108C2314yes—
107#14556104—22no—
108#14556104C2314yes—
109C4×Dic142—22no—
110C4×Dic142C2314yescomplemented
111C4×D284—22no—
112C4×D284C2314yes—
113D4×Dic71—22no—
114D4×Dic71C2314yes—
115#14556090—22no—
116#14556090C2314yes—
117C4×C22⋊D71—28no—
118(C22⋊D71)⋊C4—28no—
119#14556086—22no—
120#14556086C2314yes—
121#14556085D414yes—
122#14556085C2314yes—
123C2×C4⋊Dic71—21no—
124C2×C4⋊Dic71—21no—
125C2×C4⋊Dic71C2311yescharacteristic
126C2×C4⋊Dic71C2311yescharacteristic
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×Dic71⋊C4—21no—
132C2×Dic71⋊C4D411yescharacteristic
133C2×Dic71⋊C4D411yescharacteristic
134C2×C22⋊Dic71—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4—21no—
139C2×(C2×D71)⋊C4—28no—
140C2×(C2×D71)⋊C4—21no—
141C2×(C2×D71)⋊C4D411yescharacteristic
142C2×(C2×D71)⋊C4D411yescharacteristic
143C22⋊C4×D71—28no—
144C2×C4×Dic71—21no—
145C2×C4×Dic71—21no—
146C2×C4×Dic71C2311yescharacteristic
147#14556061C2314yescomplemented
148#14556061C2314yescomplemented
149#14556060C2314yescomplemented
150Dic71⋊C8C2314yescomplemented
151Dic71⋊C8C2314yescomplemented
152#14556053C2314yescomplemented
153#14556052C2314yescomplemented
154#14556051C2314yescomplemented
155#14556050C2314yes—
156#14556049C2314yes—
157#14556048C2314yes—
158(C2×D71)⋊C8C2314yes—
159(C2×D71)⋊C8C2314yes—
160#14556039C2314yescomplemented
161C22×Q8×C71C2311yescharacteristic
162C22×D4×C71C2311yescharacteristic
163C23×C4×C71—21no—
164C2×SD16×C71—24no—
165C2×SD16×C71C2314yes—
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2311yescharacteristic
168C4×Q8×C71—22no—
169C4×Q8×C71C2314yescomplemented
170C4×D4×C71—22no—
171C4×D4×C71C2314yes—
172C2×C4⋊C4×C71—21no—
173C2×C4⋊C4×C71C2311yescharacteristic
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C22⋊C4×C71—21no—
176C2×C42×C71—21no—
177C2×C42×C71C2311yescharacteristic
178#106×C71C2314yescomplemented
179#103×C71C2314yescomplemented
180#102×C71C2314yes—
181C4×C8×C71C2314yescomplemented
182C23×D71—21no—
183C23×D71—28no—
184C23×D71—24no—
185C23×D71—82no—
186C23×D71—82no—
187C23×D71C2×D411yescharacteristic
188C2×Dic142—22no—
189C2×Dic142—22no—
190C2×Dic142—21no—
191C2×Dic142C2412yes—
192C2×D284—21no—
193C2×D284—22no—
194C2×D284#4114yes—
195C2×D284C2412yes—
196C2×C22⋊D71—28no—
197C2×C22⋊D71—24no—
198D4×D71—216no—
199D4×D71—28no—
200D4×D71—28no—
201C22×Dic71—21no—
202C22×Dic71—21no—
203C22×Dic71—21no—
204C22×Dic71—24no—
205C22×Dic71—82no—
206C22×Dic71C2×D411yescharacteristic
207C22×Dic71C2×D411yescharacteristic
208C22×Dic71C2×D411yescharacteristic
209C2×C4×D71—22no—
210C2×C4×D71—22no—
211C2×C4×D71—24no—
212C2×C4×D71—24no—
213C2×C4×D71—82no—
214C2×C4×D71—82no—
215C2×C4×D71C2×D412yes—
216C2×C4×D71C2412yes—
217#11765854—28no—
218#11765853—28no—
219#11765852—28no—
220C2×C71⋊C8—22no—
221C2×C71⋊C8—22no—
222C2×C71⋊C8C2412yes—
223C2×C71⋊C8C2412yes—
224C4⋊Dic71—21no—
225C4⋊Dic71—21no—
226C4⋊Dic71—24no—
227C4⋊Dic71—24no—
228C4⋊Dic71C2412yes—
229C4⋊Dic71C2412yes—
230Dic71⋊C4—24no—
231Dic71⋊C4—24no—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234Dic71⋊C4—24no—
235Dic71⋊C4C2×D414yes—
236Dic71⋊C4C2×D414yes—
237C22⋊Dic71—24no—
238(C2×D71)⋊C4—24no—
239(C2×D71)⋊C4—24no—
240(C2×D71)⋊C4—24no—
241(C2×D71)⋊C4—24no—
242(C2×D71)⋊C4—24no—
243(C2×D71)⋊C4C2×D414yes—
244(C2×D71)⋊C4C2×D414yes—
245C4×Dic71—24no—
246C4×Dic71—24no—
247C4×Dic71C2×D412yes—
248C4×Dic71C2412yes—
249C24×C71—21no—
250C2×Q8×C71—21no—
251C2×Q8×C71—22no—
252C2×Q8×C71—22no—
253C2×Q8×C71C2412yes—
254C2×D4×C71—21no—
255C2×D4×C71—22no—
256C2×D4×C71#4114yes—
257C2×D4×C71C2412yes—
258C22×C4×C71—21no—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—24no—
262C22×C4×C71—82no—
263C22×C4×C71C2×D411yescharacteristic
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2411yescharacteristic
266SD16×C71—28no—
267C2×C8×C71—22no—
268C2×C8×C71—22no—
269C2×C8×C71C2412yes—
270C2×C8×C71C2412yes—
271C4⋊C4×C71—24no—
272C4⋊C4×C71—21no—
273C4⋊C4×C71—21no—
274C4⋊C4×C71C2412yes—
275C4⋊C4×C71C2412yes—
276C22⋊C4×C71—24no—
277C42×C71—24no—
278C42×C71C2×D412yes—
279C42×C71C2412yes—
280C23×C71—24no—
281C23×C71—22no—
282C23×C71—42no—
283C23×C71—42no—
284C23×C71C22×D411yescharacteristic
285C22×D71—22no—
286C22×D71—24no—
287C22×D71—22no—
288C22×D71—22no—
289C22×D71—22no—
290C22×D71—216no—
291C22×D71—42no—
292C22×D71—42no—
293C22×D71—84no—
294C22×D71—84no—
295C22×D71—816no—
296C22×D71C22×D412yes—
297Q8×C71—22no—
298Q8×C71—22no—
299Q8×C71—42no—
300D4×C71—24no—
301D4×C71—22no—
302D4×C71C2×#4114yes—
303C2×C4×C71—22no—
304C2×C4×C71—22no—
305C2×C4×C71—22no—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—42no—
309C2×C4×C71—42no—
310C2×C4×C71—42no—
311C2×C4×C71—84no—
312C2×C4×C71C22×D412yes—
313C2×C4×C71C22×D412yes—
314C2×C4×C71C22×D411yescharacteristic
315C2×C4×C71C2×#4112yes—
316C2×C4×C71C2×#4112yes—
317C2×C4×C71C2511yescharacteristic
318C22⋊D71—216no—
319C2×Dic71—22no—
320C2×Dic71—22no—
321C2×Dic71—22no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—42no—
326C2×Dic71—42no—
327C2×Dic71—42no—
328C2×Dic71—84no—
329C2×Dic71C22×D412yes—
330C2×Dic71C22×D412yes—
331C2×Dic71C22×D412yes—
332D284—24no—
333D284—22no—
334D284C2×#4114yes—
335C4×D71—24no—
336C4×D71—22no—
337C4×D71—22no—
338C4×D71—84no—
339C4×D71—84no—
340Dic142—22no—
341Dic142—22no—
342Dic142—42no—
343C8×C71—22no—
344C8×C71—22no—
345C71⋊C8—22no—
346C71⋊C8—22no—
347C22×C71—24no—
348C22×C71—48no—
349C22×C71—42no—
350C22×C71—42no—
351C22×C71#52512yes—
352C22×C71#57712yes—
353C22×C71#57712yes—
354C22×C71C23×D411yescharacteristic
355C2×D71—22no—
356C2×D71—24no—
357C2×D71—22no—
358C2×D71—22no—
359C2×D71—44no—
360C2×D71—48no—
361C2×D71—42no—
362C2×D71—42no—
363C2×D71—816no—
364C4×C71—22no—
365C4×C71—22no—
366C4×C71—42no—
367C4×C71—42no—
368C4×C71—42no—
369C4×C71#52512yes—
370C4×C71C22×#4111yescharacteristic
371C4×C71C22×#4111yescharacteristic
372Dic71—22no—
373Dic71—22no—
374Dic71—22no—
375Dic71—42no—
376Dic71—42no—
377Dic71—42no—
378C2×#3123—711nomaximal, Sylow
379C2×C71—44no—
380C2×C71#312314yescomplemented
381C2×C71C2×#52511yescharacteristic
382C2×C71C2×#57711yescharacteristic
383C2×C71C2×#57711yescharacteristic
384D71—42no—
385D71—44no—
386C2×#541—711no—
387C2×#518—711no—
388#3123—7116no—
389C2×#485—711no—
390C2×#485—711no—
391C2×#478—711no—
392C2×#478—711no—
393C2×#461—711no—
394C2×#461—711no—
395C2×#450—711no—
396C2×#450—711no—
397C2×#440—711no—
398C2×#440—711no—
399C2×C4×SD16—711no—
400C2×C4×SD16D7111yescharacteristic, complemented
401C2×#433—711no—
402C71C2×#312311yescharacteristic, complemented, Sylow
403C23×D4—711no—
404C22×SD16—711no—
405C22×SD16—711no—
406C22×SD16—711no—
407C22×SD16C2×D7111yescharacteristic
408#541—718no—
409#541—1424no—
410C2×C4⋊Q8—711no—
411C2×#126—1421no—
412C2×#126—1421no—
413C2×#125—711no—
414C2×#125—1421no—
415C2×#125—1421no—
416C2×C22⋊Q8—711no—
417C2×C22⋊Q8—711no—
418#518—718no—
419#518—1424no—
420C2×C4×Q8—711no—
421C2×C4×Q8C2×D7111yescharacteristic, complemented
422C2×C4×D4—711no—
423C2×C4×D4—711no—
424C2×C4×D4—711no—
425C2×C4×D4—1421no—
426C2×C4×D4—1421no—
427C2×C4×D4C2×D7111yescharacteristic
428C2×#117—711no—
429C2×#117—711no—
430C22×C22⋊C4—1421no—
431C22×C22⋊C4—1421no—
432#485—718no—
433#485—718no—
434#478—718no—
435#478—718no—
436#461—718no—
437#461—718no—
438#450—718no—
439#450—718no—
440#440—718no—
441#440—718no—
442C4×SD16—718no—
443C4×SD16C2×D7118yescomplemented
444#433—718no—
445C2×#107—711no—
446C2×#107—711no—
447C2×#106—711no—
448C2×#106C2×D7111yescharacteristic, complemented
449C2×C4⋊C8—711no—
450C2×C4⋊C8—711no—
451C2×#103—711no—
452C2×#103—711no—
453C2×#103—711no—
454C2×#103C2×D7111yescharacteristic, complemented
455C2×#102—711no—
456C2×#102—711no—
457C2×#102—711no—
458C2×#102C2×D7111yescharacteristic
459C2×C22⋊C8—711no—
460C2×C22⋊C8—711no—
461C2×#97—711no—
462C2×C4×C8C2×D7111yescharacteristic, complemented
463C25—1421no—
464C22×Q8—711no—
465C22×Q8C22×D7111yescharacteristic
466C22×D4—714no—
467C22×D4—711no—
468C22×D4—1422no—
469C22×D4—1421no—
470C22×D4—1424no—
471C22×D4—1424no—
472C22×D4C22×D7111yescharacteristic
473C23×C4—21no—
474C23×C4—711no—
475C23×C4—1421no—
476C23×C4—1421no—
477C23×C4—1421no—
478C2×SD16—24no—
479C2×SD16—714no—
480C2×SD16—714no—
481C2×SD16—714no—
482C2×SD16—1424no—
483C2×SD16—1424no—
484C2×SD16—1424no—
485C2×SD16C22×D7114yes—
486C22×C8—711no—
487C22×C8—711no—
488C22×C8C22×D7111yescharacteristic
489C22×C8C22×D7111yescharacteristic
490C4⋊Q8—714no—
491C4⋊Q8—1422no—
492#126—1428no—
493#126—1428no—
494#125—714no—
495#125—1428no—
496#125—1422no—
497#125—1428no—
498C22⋊Q8—714no—
499C22⋊Q8—714no—
500C22⋊Q8—1422no—
501C22⋊Q8—1422no—
502C4×Q8—22no—
503C4×Q8—714no—
504C4×Q8—1422no—
505C4×Q8C22×D7114yescomplemented
506C4×D4—22no—
507C4×D4—714no—
508C4×D4—714no—
509C4×D4—714no—
510C4×D4—1422no—
511C4×D4—1422no—
512C4×D4—1428no—
513C4×D4—1428no—
514C4×D4—1422no—
515C4×D4C22×D7114yes—
516#117—714no—
517#117—714no—
518#117—714no—
519#117—1422no—
520C2×C4⋊C4—21no—
521C2×C4⋊C4—711no—
522C2×C4⋊C4—711no—
523C2×C4⋊C4—711no—
524C2×C4⋊C4—711no—
525C2×C4⋊C4—1421no—
526C2×C4⋊C4—1421no—
527C2×C4⋊C4—1421no—
528C2×C4⋊C4—1421no—
529C2×C4⋊C4—1421no—
530C2×C4⋊C4—1421no—
531C2×C4⋊C4—1421no—
532C2×C4⋊C4C22×D7111yescharacteristic
533C2×C4⋊C4C22×D7111yescharacteristic
534C2×C22⋊C4—21no—
535C2×C22⋊C4—711no—
536C2×C22⋊C4—711no—
537C2×C22⋊C4—1428no—
538C2×C22⋊C4—1428no—
539C2×C22⋊C4—1421no—
540C2×C22⋊C4—1421no—
541C2×C22⋊C4—1421no—
542C2×C22⋊C4—1421no—
543C2×C22⋊C4—1421no—
544C2×C22⋊C4—1421no—
545C2×C42—21no—
546C2×C42—711no—
547C2×C42—1421no—
548C2×C42—1421no—
549C2×C42C22×D7111yescharacteristic
550#107—714no—
551#107—714no—
552#106—714no—
553#106C22×D7114yescomplemented
554C4⋊C8—714no—
555C4⋊C8—714no—
556#103—714no—
557#103—714no—
558#103—714no—
559#103C22×D7114yescomplemented
560#102—714no—
561#102—714no—
562#102—714no—
563#102C22×D7114yes—
564C22⋊C8—714no—
565C22⋊C8—714no—
566#97—714no—
567C4×C8C22×D7114yescomplemented
568C24—21no—
569C24—5682no—
570C24—5682no—
571C24—711no—
572C24—1424no—
573C24—1428no—
574C24—1421no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—22no—
578C2×Q8—712no—
579C2×Q8—1422no—
580C2×Q8—1422no—
581C2×Q8—1421no—
582C2×Q8C23×D7112yes—
583C2×D4—21no—
584C2×D4—22no—
585C2×D4—714no—
586C2×D4—712no—
587C2×D4—1424no—
588C2×D4—1428no—
589C2×D4—14216no—
590C2×D4—1428no—
591C2×D4—1428no—
592C2×D4—1421no—
593C2×D4—1422no—
594C2×D4#1176586514yes—
595C2×D4C23×D7112yes—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—24no—
600C22×C4—82no—
601C22×C4—5682no—
602C22×C4—5682no—
603C22×C4—5682no—
604C22×C4—711no—
605C22×C4—711no—
606C22×C4—711no—
607C22×C4—712no—
608C22×C4—712no—
609C22×C4—1424no—
610C22×C4—1421no—
611C22×C4—1421no—
612C22×C4—1421no—
613C22×C4—1424no—
614C22×C4—1424no—
615C22×C4—1422no—
616C22×C4—1422no—
617C22×C4D4×D7111yescharacteristic
618C22×C4D4×D7111yescharacteristic
619C22×C4C23×D7111yescharacteristic
620SD16—28no—
621SD16—1428no—
622SD16—1428no—
623SD16—1428no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—712no—
627C2×C8—712no—
628C2×C8—1422no—
629C2×C8—1422no—
630C2×C8C23×D7112yes—
631C2×C8C23×D7112yes—
632C4⋊C4—24no—
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—714no—
636C4⋊C4—714no—
637C4⋊C4—712no—
638C4⋊C4—712no—
639C4⋊C4—1424no—
640C4⋊C4—1424no—
641C4⋊C4—1424no—
642C4⋊C4—1424no—
643C4⋊C4—1424no—
644C4⋊C4—1424no—
645C4⋊C4—1424no—
646C4⋊C4—1421no—
647C4⋊C4—1421no—
648C4⋊C4C23×D7112yes—
649C4⋊C4C23×D7112yes—
650C22⋊C4—24no—
651C22⋊C4—714no—
652C22⋊C4—714no—
653C22⋊C4—1424no—
654C22⋊C4—1424no—
655C22⋊C4—1424no—
656C22⋊C4—1424no—
657C22⋊C4—1424no—
658C22⋊C4—1424no—
659C42—24no—
660C42—712no—
661C42—712no—
662C42—1424no—
663C42—1424no—
664C42D4×D7112yes—
665C42C23×D7112yes—
666C23—22no—
667C23—24no—
668C23—42no—
669C23—42no—
670C23—2842no—
671C23—2842no—
672C23—56816no—
673C23—5684no—
674C23—5684no—
675C23—712no—
676C23—14216no—
677C23—1422no—
678C23—1422no—
679C23—1424no—
680C23—1422no—
681C23—1422no—
682C23C2×D4×D7111yescharacteristic
683Q8—22no—
684Q8—22no—
685Q8—42no—
686Q8—2842no—
687Q8—1422no—
688Q8—1422no—
689D4—22no—
690D4—24no—
691D4—714no—
692D4—14216no—
693D4—1422no—
694D4—1424no—
695D4C2×#1176586514yes—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—42no—
702C2×C4—42no—
703C2×C4—42no—
704C2×C4—84no—
705C2×C4—2842no—
706C2×C4—2842no—
707C2×C4—2842no—
708C2×C4—5684no—
709C2×C4—5684no—
710C2×C4—5684no—
711C2×C4—712no—
712C2×C4—712no—
713C2×C4—712no—
714C2×C4—1422no—
715C2×C4—1422no—
716C2×C4—1422no—
717C2×C4—1422no—
718C2×C4—1422no—
719C2×C4—1422no—
720C2×C4—1422no—
721C2×C4—1422no—
722C2×C4—1424no—
723C2×C4C2×D4×D7112yes—
724C2×C4C2×D4×D7112yes—
725C2×C4C2×D4×D7111yescharacteristic
726C2×C4#41×D7112yes—
727C2×C4C2×#1176586512yes—
728C2×C4C24×D7111yescharacteristic
729C8—22no—
730C8—22no—
731C8—1422no—
732C8—1422no—
733C22—24no—
734C22—42no—
735C22—42no—
736C22—48no—
737C22—2842no—
738C22—2842no—
739C22—2848no—
740C22—2844no—
741C22—56816no—
742C22—1422no—
743C22—1422no—
744C22—1422no—
745C22—1424no—
746C22#1798650812yes—
747C22#1798680512yes—
748C22#1798680612yes—
749C22C22×D4×D7111yescharacteristic
750C4—22no—
751C4—22no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—2842no—
756C4—2842no—
757C4—2842no—
758C4—1422no—
759C4—1422no—
760C4—1422no—
761C4#1798650812yes—
762C4C2×#41×D7111yescharacteristic
763C4C22×#1176586511yescharacteristic
764C2—44no—
765C2—2844no—
766C2—2842no—
767C2#2259858914yesdirect product factor
768C2C2×#1798650811yescharacteristic
769C2C2×#1798680511yescharacteristic
770C2C2×#1798680611yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×C4×SD16×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×D71C22
hypercenterC2×C4×SD16D71
hypocenterC71C2×#3123
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#17986607C2semidirect
3. #22598589C2direct (N × H)
4. C2×#17986343C2semidirect
5. C2×#17986338C2semidirect
6. C2×#17986301C2semidirect
7. C2×#17986298C2semidirect
8. C2×#17986203C2semidirect
9. C2×#17986202C2semidirect
12. C2×#17986099C2semidirect
13. C2×#17986097C2semidirect
14. C2×C4×#11765854C2semidirect
15. C2×#17986058C2semidirect
16. C2×C4×SD16×C71C2semidirect
22. #17986607C22semidirect
23. C2×#14556126C22semidirect
27. C2×#14556119C22semidirect
33. C2×C4×Dic142C22semidirect
43. #17986343C22semidirect
44. #17986338C22semidirect
45. #17986301C22semidirect
46. #17986298C22semidirect
47. #17986203C22semidirect
48. #17986202C22semidirect
51. #17986099C22semidirect
52. #17986097C22semidirect
53. C4×#11765854C22semidirect
54. #17986058C22semidirect
55. C2×#14556061C22semidirect
56. C2×#14556061C22semidirect
57. C2×#14556060C22semidirect
58. C2×Dic71⋊C8C22semidirect
59. C2×Dic71⋊C8C22semidirect
60. C2×#14556053C22semidirect
61. C2×#14556052C22semidirect
62. C2×#14556051C22semidirect
68. C2×#14556039C22semidirect
70. C2×C4×Q8×C71C22semidirect
72. C4×SD16×C71C22semidirect
73. C2×#106×C71C22semidirect
74. C2×#103×C71C22semidirect
76. C2×C4×C8×C71C22semidirect
98. #14556126C23semidirect
103. #14556119C23semidirect
110. C4×Dic142C23semidirect
147. #14556061C23semidirect
148. #14556061C23semidirect
149. #14556060C23semidirect
150. Dic71⋊C8C23semidirect
151. Dic71⋊C8C23semidirect
152. #14556053C23semidirect
153. #14556052C23semidirect
154. #14556051C23semidirect
160. #14556039C23semidirect
169. C4×Q8×C71C23semidirect
178. #106×C71C23semidirect
179. #103×C71C23semidirect
181. C4×C8×C71C23semidirect
380. C2×C71#3123semidirect
400. C2×C4×SD16D71semidirect
402. C71C2×#3123semidirect
421. C2×C4×Q8C2×D71semidirect
443. C4×SD16C2×D71semidirect
448. C2×#106C2×D71semidirect
454. C2×#103C2×D71semidirect
462. C2×C4×C8C2×D71semidirect
505. C4×Q8C22×D71semidirect
553. #106C22×D71semidirect
559. #103C22×D71semidirect
567. C4×C8C22×D71semidirect
767. C2#22598589direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866072
C2×#179864712
#225985892
C2×#179863432
C2×#179863382
C2×#179863012
C2×#179862982
C2×#179862032
C2×#179862022
C2×#179861512
C2×#179861482
C2×#179860992
C2×#179860972
C2×C4×#117658542
C2×#179860582
C2×C4×SD16×C712
C2×#312371