Finite Group Databasebeta

← C2×#22598590 #32865754

Subgroups — C2×#22598590 #32865754

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×#17986610C211yesmaximal, characteristic, complemented
2C2×#17986471C211yesmaximal, characteristic
3#22598590C2116yesmaximal, direct product factor
4C2×#17986339C211yesmaximal, characteristic, complemented
5C2×#17986338C211yesmaximal, characteristic, complemented
6C2×#17986300C211yesmaximal, characteristic, complemented
7C2×#17986299C211yesmaximal, characteristic, complemented
8C2×#17986201C211yesmaximal, characteristic, complemented
9C2×#17986148C211yesmaximal, characteristic
10C2×#17986148C211yesmaximal, characteristic
11C2×#17986102C211yesmaximal, characteristic, complemented
12C2×#17986100C211yesmaximal, characteristic, complemented
13C2×SD16×Dic71C211yesmaximal, characteristic, complemented
14C2×#17986084C211yesmaximal, characteristic, complemented
15C2×#17986059C211yesmaximal, characteristic, complemented
16C2×#461×C71C211yesmaximal, characteristic, complemented
17C22×D4×D71C2211yescharacteristic
18C22×#11765852C2211yescharacteristic
19C22×#11765852C2211yescharacteristic
20#17986610—24no—
21#17986610C2218yescomplemented
22C2×#14556123—21no—
23C2×#14556123—21no—
24C2×#14556120C2211yescharacteristic, complemented
25C2×#14556118—21no—
26C2×#14556118—21no—
27C2×#14556104C2211yescharacteristic
28C2×#14556104C2211yescharacteristic
29#17986471—24no—
30#17986471C2218yes—
31C2×Q8×Dic71C2211yescharacteristic, complemented
32C2×Q8×Dic71C2211yescharacteristic, complemented
33C2×C4×D284C2211yescharacteristic
34C2×D4×Dic71C2211yescharacteristic
35C2×#14556090C2211yescharacteristic
36C2×C4×C22⋊D71—21no—
37C2×(C22⋊D71)⋊C4—21no—
38C2×#14556086C2211yescharacteristic
39C2×#14556085C2211yescharacteristic
40C22×(C2×D71)⋊C4—21no—
41C2×C22⋊C4×D71—21no—
42#17986339C2218yescomplemented
43#17986338C2218yescomplemented
44#17986300C2218yescomplemented
45#17986299C2218yescomplemented
46#17986201C2218yescomplemented
47#17986148C2218yes—
48#17986148C2218yes—
49#17986102C2218yescomplemented
50#17986100C2218yescomplemented
51SD16×Dic71C2218yescomplemented
52#17986084C2218yescomplemented
53#17986059C2218yescomplemented
54C2×#14556062C2211yescharacteristic, complemented
55C2×#14556061C2211yescharacteristic, complemented
56C2×#14556060C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×C4⋊(C71⋊C8)C2211yescharacteristic, complemented
59C2×#14556052C2211yescharacteristic, complemented
60C2×#14556052C2211yescharacteristic, complemented
61C2×#14556050C2211yescharacteristic
62C2×#14556050C2211yescharacteristic
63C2×#14556049C2211yescharacteristic
64C2×#14556049C2211yescharacteristic
65C2×(C2×D71)⋊C8C2211yescharacteristic
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×#14556038C2211yescharacteristic, complemented
68C2×C8×Dic71C2211yescharacteristic, complemented
69C22×SD16×C71C2211yescharacteristic
70C22×SD16×C71C2211yescharacteristic
71C2×C4⋊Q8×C71C2211yescharacteristic, complemented
72C2×C4×D4×C71C2211yescharacteristic
73#461×C71C2218yescomplemented
74C2×C4⋊C8×C71C2211yescharacteristic, complemented
75C2×#103×C71C2211yescharacteristic, complemented
76C2×#103×C71C2211yescharacteristic, complemented
77C24×D71—21no—
78C22×D284C2311yescharacteristic
79C22×C22⋊D71—21no—
80C2×D4×D71—24no—
81C2×D4×D71—22no—
82C2×D4×D71—24no—
83C2×D4×D71C2314yes—
84C23×Dic71—21no—
85C22×C4×D71—21no—
86C22×C4×D71—21no—
87C22×C4×D71C2311yescharacteristic
88C2×#11765852—24no—
89C2×#11765852—24no—
90C2×#11765852C2314yes—
91C2×#11765852C2314yes—
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94#14556123—28no—
95#14556123—28no—
96#14556120—22no—
97#14556120C2314yescomplemented
98#14556118—28no—
99#14556118—28no—
100#14556104—22no—
101#14556104—22no—
102#14556104C2314yes—
103#14556104C2314yes—
104Q8×Dic71—22no—
105Q8×Dic71—22no—
106Q8×Dic71C2314yescomplemented
107Q8×Dic71C2314yescomplemented
108C4×D284—22no—
109C4×D284C2314yes—
110D4×Dic71—22no—
111D4×Dic71C2314yes—
112#14556090—22no—
113#14556090C2314yes—
114C4×C22⋊D71—28no—
115(C22⋊D71)⋊C4—28no—
116#14556086—22no—
117#14556086C2314yes—
118#14556085D414yes—
119#14556085C2314yes—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71C2311yescharacteristic
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×Dic71⋊C4—21no—
126C2×Dic71⋊C4—21no—
127C2×Dic71⋊C4—21no—
128C2×Dic71⋊C4—21no—
129C2×Dic71⋊C4D411yescharacteristic
130C2×Dic71⋊C4D411yescharacteristic
131C2×C22⋊Dic71—21no—
132C2×(C2×D71)⋊C4—21no—
133C2×(C2×D71)⋊C4—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—28no—
137C2×(C2×D71)⋊C4—21no—
138C2×(C2×D71)⋊C4D411yescharacteristic
139C2×(C2×D71)⋊C4D411yescharacteristic
140C22⋊C4×D71—28no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71—21no—
143C2×C4×Dic71—21no—
144C2×C4×Dic71C2311yescharacteristic
145#14556062C2314yescomplemented
146#14556061C2314yescomplemented
147#14556060C2314yescomplemented
148#14556059C2314yescomplemented
149C4⋊(C71⋊C8)C2314yescomplemented
150#14556052C2314yescomplemented
151#14556052C2314yescomplemented
152#14556050C2314yes—
153#14556050C2314yes—
154#14556049C2314yes—
155#14556049C2314yes—
156(C2×D71)⋊C8C2314yes—
157(C2×D71)⋊C8C2314yes—
158#14556038C2314yescomplemented
159C8×Dic71C2314yescomplemented
160C22×Q8×C71C2311yescharacteristic
161C22×Q8×C71C2311yescharacteristic
162C22×D4×C71C2311yescharacteristic
163C23×C4×C71—21no—
164C2×SD16×C71—24no—
165C2×SD16×C71—24no—
166C2×SD16×C71C2314yes—
167C2×SD16×C71C2314yes—
168C22×C8×C71C2311yescharacteristic
169C22×C8×C71C2311yescharacteristic
170C4⋊Q8×C71—22no—
171C4⋊Q8×C71C2314yescomplemented
172C4×D4×C71—22no—
173C4×D4×C71C2314yes—
174C2×C4⋊C4×C71—21no—
175C2×C4⋊C4×C71—21no—
176C2×C4⋊C4×C71C2311yescharacteristic
177C2×C22⋊C4×C71—21no—
178C2×C42×C71C2311yescharacteristic
179C4⋊C8×C71C2314yescomplemented
180#103×C71C2314yescomplemented
181#103×C71C2314yescomplemented
182C23×D71—21no—
183C23×D71—28no—
184C23×D71—24no—
185C23×D71—82no—
186C23×D71—82no—
187C23×D71C2×D411yescharacteristic
188C2×D284—21no—
189C2×D284—22no—
190C2×D284#4114yes—
191C2×D284C2412yes—
192C2×C22⋊D71—28no—
193C2×C22⋊D71—24no—
194D4×D71—216no—
195D4×D71—28no—
196D4×D71—28no—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C22×Dic71—21no—
200C22×Dic71—24no—
201C22×Dic71—82no—
202C22×Dic71C2×D411yescharacteristic
203C22×Dic71C2×D411yescharacteristic
204C22×Dic71C2×D411yescharacteristic
205C2×C4×D71—22no—
206C2×C4×D71—22no—
207C2×C4×D71—24no—
208C2×C4×D71—24no—
209C2×C4×D71—82no—
210C2×C4×D71—82no—
211C2×C4×D71C2×D412yes—
212C2×C4×D71C2412yes—
213#11765852—28no—
214#11765852—28no—
215C2×C71⋊C8—22no—
216C2×C71⋊C8—22no—
217C2×C71⋊C8C2412yes—
218C2×C71⋊C8C2412yes—
219C4⋊Dic71—21no—
220C4⋊Dic71—21no—
221C4⋊Dic71—21no—
222C4⋊Dic71—24no—
223C4⋊Dic71—24no—
224C4⋊Dic71C2412yes—
225C4⋊Dic71C2412yes—
226C4⋊Dic71C2412yes—
227Dic71⋊C4—24no—
228Dic71⋊C4—24no—
229Dic71⋊C4—24no—
230Dic71⋊C4—24no—
231Dic71⋊C4C2×D414yes—
232Dic71⋊C4C2×D414yes—
233C22⋊Dic71—24no—
234(C2×D71)⋊C4—24no—
235(C2×D71)⋊C4—24no—
236(C2×D71)⋊C4—24no—
237(C2×D71)⋊C4—24no—
238(C2×D71)⋊C4—24no—
239(C2×D71)⋊C4C2×D414yes—
240(C2×D71)⋊C4C2×D414yes—
241C4×Dic71—24no—
242C4×Dic71—24no—
243C4×Dic71—24no—
244C4×Dic71C2×D412yes—
245C4×Dic71C2412yes—
246C24×C71—21no—
247C2×Q8×C71—21no—
248C2×Q8×C71—21no—
249C2×Q8×C71—22no—
250C2×Q8×C71—22no—
251C2×Q8×C71—22no—
252C2×Q8×C71—22no—
253C2×Q8×C71C2412yes—
254C2×Q8×C71C2412yes—
255C2×D4×C71—21no—
256C2×D4×C71—22no—
257C2×D4×C71#4114yes—
258C2×D4×C71C2412yes—
259C22×C4×C71—21no—
260C22×C4×C71—21no—
261C22×C4×C71—21no—
262C22×C4×C71—24no—
263C22×C4×C71—82no—
264C22×C4×C71C2×D411yescharacteristic
265C22×C4×C71C2×D411yescharacteristic
266C22×C4×C71C2411yescharacteristic
267SD16×C71—28no—
268SD16×C71—28no—
269C2×C8×C71—22no—
270C2×C8×C71—22no—
271C2×C8×C71C2412yes—
272C2×C8×C71C2412yes—
273C4⋊C4×C71—24no—
274C4⋊C4×C71—24no—
275C4⋊C4×C71—21no—
276C4⋊C4×C71C2412yes—
277C22⋊C4×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—22no—
300Q8×C71—22no—
301Q8×C71—42no—
302Q8×C71—42no—
303D4×C71—24no—
304D4×C71—22no—
305D4×C71C2×#4114yes—
306C2×C4×C71—22no—
307C2×C4×C71—22no—
308C2×C4×C71—22no—
309C2×C4×C71—22no—
310C2×C4×C71—22no—
311C2×C4×C71—42no—
312C2×C4×C71—42no—
313C2×C4×C71—42no—
314C2×C4×C71—84no—
315C2×C4×C71C22×D412yes—
316C2×C4×C71C22×D412yes—
317C2×C4×C71C22×D411yescharacteristic
318C2×C4×C71C2×#4112yes—
319C2×C4×C71C2×#4112yes—
320C2×C4×C71C2511yescharacteristic
321C22⋊D71—216no—
322C2×Dic71—22no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—22no—
327C2×Dic71—22no—
328C2×Dic71—42no—
329C2×Dic71—42no—
330C2×Dic71—42no—
331C2×Dic71—84no—
332C2×Dic71C22×D412yes—
333C2×Dic71C22×D412yes—
334C2×Dic71C22×D412yes—
335D284—24no—
336D284—22no—
337D284C2×#4114yes—
338C4×D71—24no—
339C4×D71—22no—
340C4×D71—22no—
341C4×D71—84no—
342C4×D71—84no—
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×#461D7111yescharacteristic, complemented
395C2×#450—711no—
396C2×#450—711no—
397C2×#440—711no—
398C2×#440—711no—
399C2×C4×SD16—711no—
400C2×C4×SD16—711no—
401C2×#433—711no—
402C71C2×#312311yescharacteristic, complemented, Sylow
403C23×D4—711no—
404C22×SD16—711no—
405C22×SD16—711no—
406C22×SD16C2×D7111yescharacteristic
407C22×SD16C2×D7111yescharacteristic
408#541—718no—
409#541—1424no—
410C2×C4⋊Q8C2×D7111yescharacteristic, complemented
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×Q8—711no—
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#461C2×D7118yescomplemented
438#450—718no—
439#450—718no—
440#440—718no—
441#440—718no—
442C4×SD16—718no—
443C4×SD16—718no—
444#433—718no—
445C2×#107—711no—
446C2×#107—711no—
447C2×#106—711no—
448C2×#106—711no—
449C2×C4⋊C8—711no—
450C2×C4⋊C8C2×D7111yescharacteristic, complemented
451C2×#103—711no—
452C2×#103—711no—
453C2×#103C2×D7111yescharacteristic, complemented
454C2×#103C2×D7111yescharacteristic, complemented
455C2×#102—711no—
456C2×#102—711no—
457C2×#102—711no—
458C2×#102—711no—
459C2×C22⋊C8—711no—
460C2×C22⋊C8—711no—
461C2×#97—711no—
462C2×C4×C8—711no—
463C25—1421no—
464C22×Q8C22×D7111yescharacteristic
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—24no—
480C2×SD16—714no—
481C2×SD16—714no—
482C2×SD16—1424no—
483C2×SD16—1424no—
484C2×SD16C22×D7114yes—
485C2×SD16C22×D7114yes—
486C22×C8—711no—
487C22×C8—711no—
488C22×C8C22×D7111yescharacteristic
489C22×C8C22×D7111yescharacteristic
490C4⋊Q8—22no—
491C4⋊Q8C22×D7114yescomplemented
492#126—1428no—
493#126—1428no—
494#125—714no—
495#125—1428no—
496#125—1428no—
497#125—1422no—
498C22⋊Q8—714no—
499C22⋊Q8—714no—
500C22⋊Q8—1422no—
501C22⋊Q8—1422no—
502C4×Q8—714no—
503C4×Q8—714no—
504C4×Q8—1422no—
505C4×Q8—1422no—
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—21no—
522C2×C4⋊C4—711no—
523C2×C4⋊C4—711no—
524C2×C4⋊C4—711no—
525C2×C4⋊C4—711no—
526C2×C4⋊C4—711no—
527C2×C4⋊C4—1421no—
528C2×C4⋊C4—1421no—
529C2×C4⋊C4—1421no—
530C2×C4⋊C4—1421no—
531C2×C4⋊C4—1421no—
532C2×C4⋊C4—1421no—
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—711no—
546C2×C42—1421no—
547C2×C42—1421no—
548C2×C42—1421no—
549C2×C42C22×D7111yescharacteristic
550#107—714no—
551#107—714no—
552#106—714no—
553#106—714no—
554C4⋊C8—714no—
555C4⋊C8C22×D7114yescomplemented
556#103—714no—
557#103—714no—
558#103C22×D7114yescomplemented
559#103C22×D7114yescomplemented
560#102—714no—
561#102—714no—
562#102—714no—
563#102—714no—
564C22⋊C8—714no—
565C22⋊C8—714no—
566#97—714no—
567C4×C8—714no—
568C24—21no—
569C24—5682no—
570C24—5682no—
571C24—711no—
572C24—1424no—
573C24—1428no—
574C24—1421no—
575C2×Q8—21no—
576C2×Q8—21no—
577C2×Q8—22no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8C23×D7112yes—
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#1176586414yes—
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—28no—
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—24no—
634C4⋊C4—21no—
635C4⋊C4—714no—
636C4⋊C4—714no—
637C4⋊C4—712no—
638C4⋊C4—712no—
639C4⋊C4—712no—
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⋊C4—1421no—
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—712no—
660C42—712no—
661C42—1424no—
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—22no—
686Q8—22no—
687Q8—42no—
688Q8—42no—
689D4—22no—
690D4—24no—
691D4—714no—
692D4—14216no—
693D4—1422no—
694D4—1424no—
695D4C2×#1176586414yes—
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×#1176586412yes—
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#1798650912yes—
747C22#1798680512yes—
748C22#1798680812yes—
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#1798650912yes—
762C4C2×#41×D7111yescharacteristic
763C4C22×#1176586411yescharacteristic
764C2—44no—
765C2—2844no—
766C2—2842no—
767C2#2259859014yesdirect product factor
768C2C2×#1798650911yescharacteristic
769C2C2×#1798680511yescharacteristic
770C2C2×#1798680811yescharacteristic
subgroupG/H
centerC23C2×D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#461×C71C2
socleC23×C71C22×D4
prime radicalC22×D4×D71C22
hypercenterC2×#461D71
hypocenterC71C2×#3123
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#17986610C2semidirect
3. #22598590C2direct (N × H)
4. C2×#17986339C2semidirect
5. C2×#17986338C2semidirect
6. C2×#17986300C2semidirect
7. C2×#17986299C2semidirect
8. C2×#17986201C2semidirect
11. C2×#17986102C2semidirect
12. C2×#17986100C2semidirect
13. C2×SD16×Dic71C2semidirect
14. C2×#17986084C2semidirect
15. C2×#17986059C2semidirect
16. C2×#461×C71C2semidirect
21. #17986610C22semidirect
24. C2×#14556120C22semidirect
31. C2×Q8×Dic71C22semidirect
32. C2×Q8×Dic71C22semidirect
42. #17986339C22semidirect
43. #17986338C22semidirect
44. #17986300C22semidirect
45. #17986299C22semidirect
46. #17986201C22semidirect
49. #17986102C22semidirect
50. #17986100C22semidirect
51. SD16×Dic71C22semidirect
52. #17986084C22semidirect
53. #17986059C22semidirect
54. C2×#14556062C22semidirect
55. C2×#14556061C22semidirect
56. C2×#14556060C22semidirect
57. C2×#14556059C22semidirect
58. C2×C4⋊(C71⋊C8)C22semidirect
59. C2×#14556052C22semidirect
60. C2×#14556052C22semidirect
67. C2×#14556038C22semidirect
68. C2×C8×Dic71C22semidirect
71. C2×C4⋊Q8×C71C22semidirect
73. #461×C71C22semidirect
74. C2×C4⋊C8×C71C22semidirect
75. C2×#103×C71C22semidirect
76. C2×#103×C71C22semidirect
97. #14556120C23semidirect
106. Q8×Dic71C23semidirect
107. Q8×Dic71C23semidirect
145. #14556062C23semidirect
146. #14556061C23semidirect
147. #14556060C23semidirect
148. #14556059C23semidirect
149. C4⋊(C71⋊C8)C23semidirect
150. #14556052C23semidirect
151. #14556052C23semidirect
158. #14556038C23semidirect
159. C8×Dic71C23semidirect
171. C4⋊Q8×C71C23semidirect
179. C4⋊C8×C71C23semidirect
180. #103×C71C23semidirect
181. #103×C71C23semidirect
380. C2×C71#3123semidirect
394. C2×#461D71semidirect
402. C71C2×#3123semidirect
410. C2×C4⋊Q8C2×D71semidirect
437. #461C2×D71semidirect
450. C2×C4⋊C8C2×D71semidirect
453. C2×#103C2×D71semidirect
454. C2×#103C2×D71semidirect
491. C4⋊Q8C22×D71semidirect
555. C4⋊C8C22×D71semidirect
558. #103C22×D71semidirect
559. #103C22×D71semidirect
767. C2#22598590direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179866102
C2×#179864712
#225985902
C2×#179863392
C2×#179863382
C2×#179863002
C2×#179862992
C2×#179862012
C2×#179861482
C2×#179861022
C2×#179861002
C2×SD16×Dic712
C2×#179860842
C2×#179860592
C2×#461×C712
C2×#312371