Finite Group Databasebeta

← C2×#22598251 #32865217

Subgroups — C2×#22598251 #32865217

Order 18176.

2378 conjugacy classes of subgroups.

The subgroup lattice has 802 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986506C211yesmaximal, characteristic
2C2×#117×D71C211yesmaximal, characteristic, complemented
3#22598251C2116yesmaximal, direct product factor
4C2×#17986333C211yesmaximal, characteristic, complemented
5C2×#17986316C211yesmaximal, characteristic, complemented
6C2×#17986339C211yesmaximal, characteristic, complemented
7C2×#17986338C211yesmaximal, characteristic, complemented
8C2×#17986322C211yesmaximal, characteristic, complemented
9C2×#17986321C211yesmaximal, characteristic, complemented
10C2×#17986328C211yesmaximal, characteristic, complemented
11C2×#17986311C211yesmaximal, characteristic, complemented
12C2×#17986037C211yesmaximal, characteristic, complemented
13C2×#17986035C211yesmaximal, characteristic, complemented
14C2×#17985995C211yesmaximal, characteristic, complemented
15C22×(C2×D71)⋊C8C211yesmaximal, characteristic, complemented
16C2×#416×C71C211yesmaximal, characteristic, complemented
17C23×C4×D71C2211yescharacteristic
18C23×C71⋊C8C2211yescharacteristic
19#17986506—24no—
20#17986506C2218yes—
21C2×#14556109—21no—
22C2×#14556104C2211yescharacteristic
23C2×#14556104C2211yescharacteristic
24C2×#14556099C2211yescharacteristic
25C2×#14556099C2211yescharacteristic
26C2×#14556096—21no—
27C2×C4×C22⋊D71—21no—
28C2×C4×C22⋊D71—21no—
29C2×#14556087C2211yescharacteristic
30C2×#14556087C2211yescharacteristic
31C2×#14556086C2211yescharacteristic
32C2×#14556086C2211yescharacteristic
33C2×#14556085—21no—
34C2×#14556084—21no—
35#117×D71—24no—
36#117×D71C2218yescomplemented
37C2×C4⋊C4×D71C2211yescharacteristic
38C2×C4⋊C4×D71C2211yescharacteristic
39C2×C22⋊C4×D71—21no—
40C2×C42×D71—21no—
41#17986339C2218yescomplemented
42#17986338C2218yescomplemented
43#17986333C2218yescomplemented
44#17986328C2218yescomplemented
45#17986322C2218yescomplemented
46#17986321C2218yescomplemented
47#17986316C2218yescomplemented
48#17986311C2218yescomplemented
49#17986037C2218yescomplemented
50#17986035C2218yescomplemented
51C2×#14556062C2211yescharacteristic, complemented
52C2×#14556062C2211yescharacteristic, complemented
53C2×#14556061C2211yescharacteristic, complemented
54C2×#14556061C2211yescharacteristic, complemented
55C2×#14556060C2211yescharacteristic, complemented
56C2×#14556060C2211yescharacteristic, complemented
57C2×#14556059C2211yescharacteristic, complemented
58C2×#14556059C2211yescharacteristic, complemented
59#17985995C2218yescomplemented
60C2×#14556052C2211yescharacteristic, complemented
61C2×#14556052C2211yescharacteristic, complemented
62C2×#14556049C2211yescharacteristic, complemented
63C2×#14556049C2211yescharacteristic, complemented
64C2×(C2×D71)⋊C8C2211yescharacteristic
65C2×(C2×D71)⋊C8C2211yescharacteristic
66C2×(C2×D71)⋊C8C2211yescharacteristic
67C2×(C2×D71)⋊C8C2211yescharacteristic
68C2×(C2×D71)⋊C8C2218yescomplemented
69C22×#41×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71C2×#117×C71C2211yescharacteristic
72#416×C71C2218yescomplemented
73C2×#103×C71C2211yescharacteristic, complemented
74C2×#103×C71C2211yescharacteristic, complemented
75C2×#102×C71C2211yescharacteristic, complemented
76C2×#102×C71C2211yescharacteristic, complemented
77C24×D71D411yescharacteristic
78C22×C22⋊D71—21no—
79C22×C22⋊D71—21no—
80C23×Dic71D411yescharacteristic
81C22×C4×D71—21no—
82C22×C4×D71—21no—
83C22×C4×D71—24no—
84C22×C4×D71—24no—
85C22×C4×D71D411yescharacteristic
86C22×C4×D71D414yes—
87C22×C4×D71D411yescharacteristic
88C22×C4×D71C2311yescharacteristic
89C22×C4×D71C2314yes—
90C22×C4×D71C2311yescharacteristic
91C22×C71⋊C8—24no—
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2314yes—
95#14556109—28no—
96#14556104—22no—
97#14556104—22no—
98#14556104C2314yes—
99#14556104C2314yes—
100#14556099—22no—
101#14556099—22no—
102#14556099C2314yes—
103#14556099C2314yes—
104#14556096—28no—
105C4×C22⋊D71—28no—
106C4×C22⋊D71—28no—
107#14556087—22no—
108#14556087—22no—
109#14556087C2314yes—
110#14556087C2314yes—
111#14556086—22no—
112#14556086—22no—
113#14556086C2314yes—
114#14556086C2314yes—
115#14556085—28no—
116#14556084—28no—
117C2×C4⋊Dic71C2311yescharacteristic
118C2×C4⋊Dic71C2311yescharacteristic
119C2×C4⋊Dic71C2311yescharacteristic
120C2×C4⋊Dic71C2311yescharacteristic
121C2×Dic71⋊C4—21no—
122C2×Dic71⋊C4—21no—
123C2×Dic71⋊C4—21no—
124C2×Dic71⋊C4—21no—
125C4⋊C4×D71—22no—
126C4⋊C4×D71—22no—
127C4⋊C4×D71C2314yes—
128C4⋊C4×D71C2314yes—
129C2×C22⋊Dic71—21no—
130C2×C22⋊Dic71—21no—
131C2×C22⋊Dic71—21no—
132C2×C22⋊Dic71—21no—
133C2×(C2×D71)⋊C4—21no—
134C2×(C2×D71)⋊C4—21no—
135C2×(C2×D71)⋊C4—21no—
136C2×(C2×D71)⋊C4—21no—
137C22⋊C4×D71—28no—
138C2×C4×Dic71—21no—
139C2×C4×Dic71—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71—21no—
142C42×D71—28no—
143#14556062C2314yescomplemented
144#14556062C2314yescomplemented
145#14556061C2314yescomplemented
146#14556061C2314yescomplemented
147#14556060C2314yescomplemented
148#14556060C2314yescomplemented
149#14556059C2314yescomplemented
150#14556059C2314yescomplemented
151#14556052C2314yescomplemented
152#14556052C2314yescomplemented
153#14556049C2314yescomplemented
154#14556049C2314yescomplemented
155(C2×D71)⋊C8C2314yes—
156(C2×D71)⋊C8C2314yes—
157(C2×D71)⋊C8C2314yes—
158(C2×D71)⋊C8C2314yes—
159C2×#41×C71—22no—
160C2×#41×C71—24no—
161C2×#41×C71—24no—
162C2×#41×C71C2314yes—
163C22×Q8×C71C2311yescharacteristic
164C22×D4×C71—21no—
165C22×D4×C71C2311yescharacteristic
166C23×C4×C71—21no—
167C23×C4×C71C2311yescharacteristic
168C22×C8×C71—24no—
169C22×C8×C71C2311yescharacteristic
170C22×C8×C71C2311yescharacteristic
171C22×C8×C71C2314yes—
172#117×C71—22no—
173#117×C71C2314yes—
174C2×C4⋊C4×C71C2311yescharacteristic
175C2×C4⋊C4×C71C2311yescharacteristic
176C2×C22⋊C4×C71—21no—
177C2×C42×C71—21no—
178#103×C71C2314yescomplemented
179#103×C71C2314yescomplemented
180#102×C71C2314yescomplemented
181#102×C71C2314yescomplemented
182C23×D71—24no—
183C23×D71—24no—
184C23×D71—42no—
185C23×D71C2×D411yescharacteristic
186C23×D71C2×D414yes—
187C23×D71C2×D411yescharacteristic
188C2×C22⋊D71—24no—
189C2×C22⋊D71—24no—
190C2×C22⋊D71—44no—
191C2×C22⋊D71—44no—
192C22×Dic71—24no—
193C22×Dic71—21no—
194C22×Dic71—21no—
195C22×Dic71—21no—
196C22×Dic71—21no—
197C22×Dic71C2×D411yescharacteristic
198C22×Dic71C2×D411yescharacteristic
199C22×Dic71C2×D414yes—
200C2×C4×D71—24no—
201C2×C4×D71—24no—
202C2×C4×D71—216no—
203C2×C4×D71—22no—
204C2×C4×D71—22no—
205C2×C4×D71—28no—
206C2×C4×D71—22no—
207C2×C4×D71—22no—
208C2×C4×D71—28no—
209C2×C4×D71—24no—
210C2×C4×D71—24no—
211C2×C4×D71—44no—
212C2×C4×D71—44no—
213C2×C4×D71C2×D414yes—
214C2×C4×D71C2×D412yes—
215C2×C4×D71C2×D414yes—
216C2×C4×D71C2×D412yes—
217C2×C4×D71C2412yes—
218C2×C4×D71C2412yes—
219C2×C71⋊C8—22no—
220C2×C71⋊C8—22no—
221C2×C71⋊C8—28no—
222C2×C71⋊C8C2412yes—
223C2×C71⋊C8C2412yes—
224C4⋊Dic71—21no—
225C4⋊Dic71—21no—
226C4⋊Dic71—21no—
227C4⋊Dic71—21no—
228C4⋊Dic71C2412yes—
229C4⋊Dic71C2412yes—
230C4⋊Dic71C2412yes—
231C4⋊Dic71C2412yes—
232Dic71⋊C4—24no—
233Dic71⋊C4—24no—
234Dic71⋊C4—24no—
235Dic71⋊C4—24no—
236C22⋊Dic71—24no—
237C22⋊Dic71—24no—
238C22⋊Dic71—24no—
239C22⋊Dic71—24no—
240(C2×D71)⋊C4—24no—
241(C2×D71)⋊C4—24no—
242(C2×D71)⋊C4—24no—
243(C2×D71)⋊C4—24no—
244C4×Dic71—24no—
245C4×Dic71—24no—
246C4×Dic71—24no—
247C4×Dic71—24no—
248C24×C71—21no—
249C24×C71C2×D411yescharacteristic
250#41×C71—28no—
251#41×C71—28no—
252#41×C71—48no—
253C2×Q8×C71—21no—
254C2×Q8×C71—22no—
255C2×Q8×C71—22no—
256C2×Q8×C71C2412yes—
257C2×D4×C71—24no—
258C2×D4×C71—21no—
259C2×D4×C71—22no—
260C2×D4×C71—22no—
261C2×D4×C71—44no—
262C2×D4×C71C2412yes—
263C22×C4×C71—21no—
264C22×C4×C71—21no—
265C22×C4×C71—21no—
266C22×C4×C71—24no—
267C22×C4×C71—44no—
268C22×C4×C71C2×D412yes—
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71#4114yes—
271C22×C4×C71#4114yes—
272C22×C4×C71C2411yescharacteristic
273C22×C4×C71C2412yes—
274C2×C8×C71—22no—
275C2×C8×C71—22no—
276C2×C8×C71—28no—
277C2×C8×C71C2412yes—
278C2×C8×C71C2412yes—
279C4⋊C4×C71—21no—
280C4⋊C4×C71—21no—
281C4⋊C4×C71C2412yes—
282C4⋊C4×C71C2412yes—
283C22⋊C4×C71—24no—
284C42×C71—24no—
285C23×C71—22no—
286C23×C71—22no—
287C23×C71—22no—
288C23×C71—42no—
289C23×C71—42no—
290C23×C71—42no—
291C23×C71#12314yes—
292C23×C71C22×D412yes—
293C23×C71C22×D411yescharacteristic
294C22×D71—22no—
295C22×D71—22no—
296C22×D71—28no—
297C22×D71—22no—
298C22×D71—22no—
299C22×D71—22no—
300C22×D71—28no—
301C22×D71—44no—
302C22×D71—416no—
303C22×D71#13514yes—
304C22×D71C22×D412yes—
305C22×D71C22×D412yes—
306Q8×C71—22no—
307Q8×C71—22no—
308Q8×C71—42no—
309D4×C71—22no—
310D4×C71—22no—
311D4×C71—48no—
312D4×C71—42no—
313C2×C4×C71—22no—
314C2×C4×C71—22no—
315C2×C4×C71—22no—
316C2×C4×C71—42no—
317C2×C4×C71—42no—
318C2×C4×C71—42no—
319C2×C4×C71—48no—
320C2×C4×C71#12314yes—
321C2×C4×C71#12318yes—
322C2×C4×C71C22×D412yes—
323C2×C4×C71C22×D411yescharacteristic
324C2×C4×C71C2×#4112yes—
325C2×C4×C71C2×#4114yes—
326C2×C4×C71C2×#4112yes—
327C2×C4×C71C2×#4114yes—
328C2×C4×C71C2511yescharacteristic
329C22⋊D71—48no—
330C22⋊D71—48no—
331C2×Dic71—28no—
332C2×Dic71—22no—
333C2×Dic71—22no—
334C2×Dic71—22no—
335C2×Dic71—22no—
336C2×Dic71—22no—
337C2×Dic71—22no—
338C2×Dic71—42no—
339C2×Dic71—42no—
340C2×Dic71—42no—
341C2×Dic71—42no—
342C2×Dic71C22×D412yes—
343C2×Dic71C22×D412yes—
344C4×D71—28no—
345C4×D71—28no—
346C4×D71—24no—
347C4×D71—24no—
348C4×D71—22no—
349C4×D71—22no—
350C4×D71—22no—
351C4×D71—22no—
352C4×D71—48no—
353C4×D71—48no—
354C8×C71—22no—
355C8×C71—22no—
356C71⋊C8—22no—
357C71⋊C8—22no—
358C22×C71—28no—
359C22×C71—22no—
360C22×C71—22no—
361C22×C71—42no—
362C22×C71—42no—
363C22×C71—42no—
364C22×C71—84no—
365C22×C71C2×#12314yes—
366C22×C71C2×#12312yes—
367C22×C71C2×#13512yes—
368C22×C71#57512yes—
369C22×C71C23×D411yescharacteristic
370C2×D71—28no—
371C2×D71—22no—
372C2×D71—22no—
373C2×D71—22no—
374C2×D71—22no—
375C2×D71—22no—
376C2×D71—416no—
377C2×D71—44no—
378C2×D71C2×#13514yes—
379C4×C71—42no—
380C4×C71—42no—
381C4×C71—42no—
382C4×C71C2×#12314yes—
383C4×C71C2×#12312yes—
384C4×C71C22×#4111yescharacteristic
385C4×C71C22×#4111yescharacteristic
386Dic71—22no—
387Dic71—22no—
388Dic71—42no—
389Dic71—42no—
390Dic71—42no—
391Dic71—42no—
392C2×#3091—711nomaximal, Sylow
393C2×C71—24no—
394C2×C71—82no—
395C2×C71#309114yescomplemented
396C2×C71C22×#12311yescharacteristic
397C2×C71C22×#13511yescharacteristic
398C2×C71C2×#57511yescharacteristic
399D71—24no—
400D71—42no—
401C2×#525—711no—
402C22×#117—711no—
403#3091—7116no—
404C2×#484—711no—
405C2×#481—711no—
406C2×#485—711no—
407C2×#485—711no—
408C2×#482—711no—
409C2×#482—711no—
410C2×#483—711no—
411C2×#480—711no—
412C2×#427—711no—
413C2×#427—711no—
414C2×#416—711no—
415C2×#416D7111yescharacteristic, complemented
416C22×C22⋊C8—711no—
417C71C2×#309111yescharacteristic, complemented, Sylow
418C22×#41C2×D7111yescharacteristic
419C24×C4—711no—
420C23×C8—711no—
421C23×C8C2×D7111yescharacteristic
422#525—718no—
423#525—1424no—
424C2×#123—1421no—
425C2×C22⋊Q8—711no—
426C2×C22⋊Q8—711no—
427C2×#121—711no—
428C2×#121—711no—
429C2×#120—1421no—
430C2×C4×D4—1421no—
431C2×C4×D4—1421no—
432C2×#117—711no—
433C2×#117—711no—
434C2×#117—718no—
435C2×#117—711no—
436C2×#117—711no—
437C2×#117—1421no—
438C2×#117—1421no—
439C2×#117—1424no—
440C2×#117C2×D7111yescharacteristic
441C22×C4⋊C4—711no—
442C22×C4⋊C4—711no—
443C22×C22⋊C4—1421no—
444C22×C42—1421no—
445#485—718no—
446#485—718no—
447#484—718no—
448#483—718no—
449#482—718no—
450#482—718no—
451#481—718no—
452#480—718no—
453#427—718no—
454#427—718no—
455C2×#107—711no—
456C2×#107—711no—
457C2×#107—711no—
458C2×#107—711no—
459C2×#106—711no—
460C2×#106—711no—
461C2×#106—711no—
462C2×#106—711no—
463#416—718no—
464#416C2×D7118yescomplemented
465C2×#103—711no—
466C2×#103—711no—
467C2×#103C2×D7111yescharacteristic, complemented
468C2×#103C2×D7111yescharacteristic, complemented
469C2×#102—711no—
470C2×#102—711no—
471C2×#102C2×D7111yescharacteristic, complemented
472C2×#102C2×D7111yescharacteristic, complemented
473C2×C22⋊C8—711no—
474C2×C22⋊C8—711no—
475C2×C22⋊C8—711no—
476C2×C22⋊C8—711no—
477C2×C22⋊C8—718no—
478C25—711no—
479C2×#41—22no—
480C2×#41—24no—
481C2×#41—24no—
482C2×#41C22×D7114yes—
483C22×Q8C22×D7111yescharacteristic
484C22×D4—21no—
485C22×D4—1421no—
486C22×D4—1421no—
487C22×D4C22×D7111yescharacteristic
488C23×C4—21no—
489C23×C4—711no—
490C23×C4—714no—
491C23×C4—711no—
492C23×C4—711no—
493C23×C4—711no—
494C23×C4—711no—
495C23×C4—714no—
496C23×C4—1421no—
497C23×C4—1421no—
498C23×C4—1424no—
499C23×C4—1424no—
500C23×C4C22×D7111yescharacteristic
501C22×C8—24no—
502C22×C8—711no—
503C22×C8—711no—
504C22×C8—714no—
505C22×C8—1424no—
506C22×C8C22×D7111yescharacteristic
507C22×C8C22×D7111yescharacteristic
508C22×C8C22×D7114yes—
509#123—1428no—
510C22⋊Q8—714no—
511C22⋊Q8—714no—
512C22⋊Q8—1422no—
513C22⋊Q8—1422no—
514#121—714no—
515#121—714no—
516#121—1422no—
517#121—1422no—
518#120—1428no—
519C4×D4—1428no—
520C4×D4—1428no—
521#117—22no—
522#117—714no—
523#117—714no—
524#117—714no—
525#117—714no—
526#117—1428no—
527#117—1428no—
528#117—1422no—
529#117—1422no—
530#117—1422no—
531#117—1422no—
532#117C22×D7114yes—
533C2×C4⋊C4—711no—
534C2×C4⋊C4—711no—
535C2×C4⋊C4—711no—
536C2×C4⋊C4—711no—
537C2×C4⋊C4—714no—
538C2×C4⋊C4—714no—
539C2×C4⋊C4—1422no—
540C2×C4⋊C4—1422no—
541C2×C4⋊C4—1421no—
542C2×C4⋊C4—1421no—
543C2×C4⋊C4—1421no—
544C2×C4⋊C4—1421no—
545C2×C4⋊C4C22×D7111yescharacteristic
546C2×C4⋊C4C22×D7111yescharacteristic
547C2×C22⋊C4—21no—
548C2×C22⋊C4—1428no—
549C2×C22⋊C4—1421no—
550C2×C22⋊C4—1421no—
551C2×C22⋊C4—1421no—
552C2×C22⋊C4—1421no—
553C2×C22⋊C4—1421no—
554C2×C22⋊C4—1421no—
555C2×C22⋊C4—1421no—
556C2×C22⋊C4—1421no—
557C2×C42—21no—
558C2×C42—1428no—
559C2×C42—1421no—
560C2×C42—1421no—
561C2×C42—1421no—
562C2×C42—1421no—
563#107—714no—
564#107—714no—
565#107—714no—
566#107—714no—
567#106—714no—
568#106—714no—
569#106—714no—
570#106—714no—
571#103—714no—
572#103—714no—
573#103C22×D7114yescomplemented
574#103C22×D7114yescomplemented
575#102—714no—
576#102—714no—
577#102C22×D7114yescomplemented
578#102C22×D7114yescomplemented
579C22⋊C8—714no—
580C22⋊C8—714no—
581C22⋊C8—714no—
582C22⋊C8—714no—
583C24—21no—
584C24—2842no—
585C24—714no—
586C24—711no—
587C24—711no—
588C24—1424no—
589C24—1424no—
590C24D4×D7111yescharacteristic
591#41—28no—
592#41—28no—
593#41—48no—
594C2×Q8—21no—
595C2×Q8—22no—
596C2×Q8—22no—
597C2×Q8C23×D7112yes—
598C2×D4—24no—
599C2×D4—21no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—44no—
603C2×D4—2844no—
604C2×D4—2844no—
605C2×D4—1424no—
606C2×D4—1424no—
607C2×D4C23×D7112yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—44no—
613C22×C4—2844no—
614C22×C4—2844no—
615C22×C4—711no—
616C22×C4—711no—
617C22×C4—714no—
618C22×C4—714no—
619C22×C4—712no—
620C22×C4—714no—
621C22×C4—712no—
622C22×C4—712no—
623C22×C4—712no—
624C22×C4—1424no—
625C22×C4—1424no—
626C22×C4—1421no—
627C22×C4—1421no—
628C22×C4—1421no—
629C22×C4—1421no—
630C22×C4—1424no—
631C22×C4—1422no—
632C22×C4—1422no—
633C22×C4—1428no—
634C22×C4—1422no—
635C22×C4—1422no—
636C22×C4—1428no—
637C22×C4—1424no—
638C22×C4—1424no—
639C22×C4—14216no—
640C22×C4D4×D7112yes—
641C22×C4D4×D7111yescharacteristic
642C22×C4#1176586414yes—
643C22×C4#1176586514yes—
644C22×C4C23×D7111yescharacteristic
645C22×C4C23×D7112yes—
646C2×C8—22no—
647C2×C8—22no—
648C2×C8—28no—
649C2×C8—712no—
650C2×C8—712no—
651C2×C8—1422no—
652C2×C8—1422no—
653C2×C8—1428no—
654C2×C8C23×D7112yes—
655C2×C8C23×D7112yes—
656C4⋊C4—21no—
657C4⋊C4—21no—
658C4⋊C4—712no—
659C4⋊C4—712no—
660C4⋊C4—712no—
661C4⋊C4—712no—
662C4⋊C4—1424no—
663C4⋊C4—1424no—
664C4⋊C4—1424no—
665C4⋊C4—1424no—
666C4⋊C4—1421no—
667C4⋊C4—1421no—
668C4⋊C4—1421no—
669C4⋊C4—1421no—
670C4⋊C4C23×D7112yes—
671C4⋊C4C23×D7112yes—
672C22⋊C4—24no—
673C22⋊C4—1424no—
674C22⋊C4—1424no—
675C22⋊C4—1424no—
676C22⋊C4—1424no—
677C22⋊C4—1424no—
678C22⋊C4—1424no—
679C22⋊C4—1424no—
680C22⋊C4—1424no—
681C42—24no—
682C42—1424no—
683C42—1424no—
684C42—1424no—
685C42—1424no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—42no—
690C23—42no—
691C23—42no—
692C23—28416no—
693C23—2844no—
694C23—712no—
695C23—714no—
696C23—712no—
697C23—1428no—
698C23—1428no—
699C23—1422no—
700C23—1422no—
701C23—1422no—
702C23—1422no—
703C23—1422no—
704C23#1455611014yes—
705C23C2×D4×D7112yes—
706C23C2×D4×D7111yescharacteristic
707Q8—22no—
708Q8—22no—
709Q8—42no—
710D4—22no—
711D4—22no—
712D4—48no—
713D4—42no—
714D4—2848no—
715D4—2848no—
716C2×C4—22no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—48no—
723C2×C4—2848no—
724C2×C4—2848no—
725C2×C4—2842no—
726C2×C4—2842no—
727C2×C4—2842no—
728C2×C4—2842no—
729C2×C4—712no—
730C2×C4—712no—
731C2×C4—1422no—
732C2×C4—1422no—
733C2×C4—1422no—
734C2×C4—1422no—
735C2×C4—1428no—
736C2×C4—1422no—
737C2×C4—1422no—
738C2×C4—1422no—
739C2×C4—1422no—
740C2×C4—1422no—
741C2×C4—1422no—
742C2×C4—1428no—
743C2×C4—1428no—
744C2×C4—1424no—
745C2×C4—1424no—
746C2×C4#1455611014yes—
747C2×C4#1455611018yes—
748C2×C4C2×D4×D7112yes—
749C2×C4C2×D4×D7111yescharacteristic
750C2×C4C2×#1176586412yes—
751C2×C4C2×#1176586414yes—
752C2×C4C2×#1176586512yes—
753C2×C4C2×#1176586514yes—
754C2×C4C24×D7111yescharacteristic
755C8—22no—
756C8—22no—
757C8—1422no—
758C8—1422no—
759C22—22no—
760C22—22no—
761C22—28no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—84no—
766C22—28416no—
767C22—2844no—
768C22—714no—
769C22—1422no—
770C22—1422no—
771C22—1422no—
772C22—1422no—
773C22—1422no—
774C22—1428no—
775C22C2×#1455611014yes—
776C22C2×#1455611012yes—
777C22#135×D7112yes—
778C22#1798679612yes—
779C22C22×D4×D7111yescharacteristic
780C4—42no—
781C4—42no—
782C4—42no—
783C4—2842no—
784C4—2842no—
785C4—2842no—
786C4—2842no—
787C4—1422no—
788C4—1422no—
789C4C2×#1455611014yes—
790C4C2×#1455611012yes—
791C4C22×#1176586411yescharacteristic
792C4C22×#1176586511yescharacteristic
793C2—24no—
794C2—82no—
795C2—2842no—
796C2—1424no—
797C2#2259825114yesdirect product factor
798C2C22×#1455611011yescharacteristic
799C2C2×#135×D7111yescharacteristic
800C2C2×#1798679611yescharacteristic
subgroupG/H
centerC22×C4D4×D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#416×C71C2
socleC23×C71C22×D4
prime radicalC2×#17986506C2
hypercenterC2×#416D71
hypocenterC71C2×#3091
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C2×#416

Complements

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

NH ≅ G/Ntype
2. C2×#117×D71C2semidirect
3. #22598251C2direct (N × H)
4. C2×#17986333C2semidirect
5. C2×#17986316C2semidirect
6. C2×#17986339C2semidirect
7. C2×#17986338C2semidirect
8. C2×#17986322C2semidirect
9. C2×#17986321C2semidirect
10. C2×#17986328C2semidirect
11. C2×#17986311C2semidirect
12. C2×#17986037C2semidirect
13. C2×#17986035C2semidirect
14. C2×#17985995C2semidirect
15. C22×(C2×D71)⋊C8C2semidirect
16. C2×#416×C71C2semidirect
36. #117×D71C22semidirect
41. #17986339C22semidirect
42. #17986338C22semidirect
43. #17986333C22semidirect
44. #17986328C22semidirect
45. #17986322C22semidirect
46. #17986321C22semidirect
47. #17986316C22semidirect
48. #17986311C22semidirect
49. #17986037C22semidirect
50. #17986035C22semidirect
51. C2×#14556062C22semidirect
52. C2×#14556062C22semidirect
53. C2×#14556061C22semidirect
54. C2×#14556061C22semidirect
55. C2×#14556060C22semidirect
56. C2×#14556060C22semidirect
57. C2×#14556059C22semidirect
58. C2×#14556059C22semidirect
59. #17985995C22semidirect
60. C2×#14556052C22semidirect
61. C2×#14556052C22semidirect
62. C2×#14556049C22semidirect
63. C2×#14556049C22semidirect
68. C2×(C2×D71)⋊C8C22semidirect
72. #416×C71C22semidirect
73. C2×#103×C71C22semidirect
74. C2×#103×C71C22semidirect
75. C2×#102×C71C22semidirect
76. C2×#102×C71C22semidirect
143. #14556062C23semidirect
144. #14556062C23semidirect
145. #14556061C23semidirect
146. #14556061C23semidirect
147. #14556060C23semidirect
148. #14556060C23semidirect
149. #14556059C23semidirect
150. #14556059C23semidirect
151. #14556052C23semidirect
152. #14556052C23semidirect
153. #14556049C23semidirect
154. #14556049C23semidirect
178. #103×C71C23semidirect
179. #103×C71C23semidirect
180. #102×C71C23semidirect
181. #102×C71C23semidirect
395. C2×C71#3091semidirect
415. C2×#416D71semidirect
417. C71C2×#3091semidirect
464. #416C2×D71semidirect
467. C2×#103C2×D71semidirect
468. C2×#103C2×D71semidirect
471. C2×#102C2×D71semidirect
472. C2×#102C2×D71semidirect
573. #103C22×D71semidirect
574. #103C22×D71semidirect
577. #102C22×D71semidirect
578. #102C22×D71semidirect
797. C2#22598251direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179865062
C2×#117×D712
#225982512
C2×#179863332
C2×#179863162
C2×#179863392
C2×#179863382
C2×#179863222
C2×#179863212
C2×#179863282
C2×#179863112
C2×#179860372
C2×#179860352
C2×#179859952
C22×(C2×D71)⋊C82
C2×#416×C712
C2×#309171