Finite Group Databasebeta

← C2×#22600526 #32874202

Subgroups — C2×#22600526 #32874202

Order 18176.

2178 conjugacy classes of subgroups.

The subgroup lattice has 812 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986714C211yesmaximal, characteristic, complemented
2#22600526C2116yesmaximal, direct product factor
3C2×#17986358C211yesmaximal, characteristic, complemented
4C2×#17986337C211yesmaximal, characteristic, complemented
5C2×#17986320C211yesmaximal, characteristic, complemented
6C2×#17986284C211yesmaximal, characteristic, complemented
7C2×#17986250C211yesmaximal, characteristic, complemented
8C2×#17986230C211yesmaximal, characteristic, complemented
9C2×#17986211C211yesmaximal, characteristic, complemented
10C2×#17986144C211yesmaximal, characteristic, complemented
11C2×#17986138C211yesmaximal, characteristic, complemented
12C2×#17986097C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986008C211yesmaximal, characteristic, complemented
15C2×#17985995C211yesmaximal, characteristic, complemented
16C2×#548×C71C211yesmaximal, characteristic, complemented
17C22×#11765852C2211yescharacteristic
18C22×#11765852C2211yescharacteristic
19C22×#11765850C2211yescharacteristic
20C22×#11765849C2211yescharacteristic
21C23×C71⋊C8C2211yescharacteristic
22#17986714—24no—
23#17986714C2218yescomplemented
24C2×#14556128C2211yescharacteristic
25C2×#14556114—21no—
26C2×#14556114—21no—
27C2×#14556102C2211yescharacteristic
28C2×#14556102C2211yescharacteristic
29C2×#14556099—21no—
30C2×C4×D284C2211yescharacteristic
31C2×#14556087C2211yescharacteristic
32C2×#14556087C2211yescharacteristic
33C2×#14556086—21no—
34#17986358C2218yescomplemented
35#17986337C2218yescomplemented
36#17986320C2218yescomplemented
37#17986284C2218yescomplemented
38#17986250C2218yescomplemented
39#17986230C2218yescomplemented
40#17986211C2218yescomplemented
41#17986144C2218yescomplemented
42#17986138C2218yescomplemented
43#17986097C2218yescomplemented
44#17986071C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556059C2211yescharacteristic
47C2×#14556059C2211yescharacteristic
48C2×C4⋊(C71⋊C8)C2211yescharacteristic
49#17986008C2218yescomplemented
50#17985995C2218yescomplemented
51C2×#14556052C2211yescharacteristic
52C2×#14556052C2211yescharacteristic
53C2×#14556052C2211yescharacteristic
54C2×#14556052C2211yescharacteristic
55C2×#14556052C2211yescharacteristic
56C2×#14556052C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556049C2211yescharacteristic
59C2×#14556049C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64C22×#41×C71C2211yescharacteristic
65C23×Q8×C71C2211yescharacteristic
66#548×C71—24no—
67#548×C71C2218yescomplemented
68C2×#124×C71—21no—
69C2×#124×C71C2211yescharacteristic
70C2×C22⋊Q8×C71—21no—
71C2×C22⋊Q8×C71C2211yescharacteristic
72C2×#121×C71—21no—
73C2×#121×C71C2211yescharacteristic
74C2×C4×Q8×C71C2211yescharacteristic
75C2×C4×D4×C71—21no—
76C2×C4×D4×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×D284C2311yescharacteristic
79C22×C22⋊D71—21no—
80C22×C22⋊D71—21no—
81C22×C4×D71—21no—
82C2×#11765852—24no—
83C2×#11765852—42no—
84C2×#11765852C2314yes—
85C2×#11765852C2314yes—
86C2×#11765850—42no—
87C2×#11765850C2314yes—
88C2×#11765849—42no—
89C2×#11765849C2314yes—
90C22×C71⋊C8—42no—
91C22×C71⋊C8C2311yescharacteristic
92C22×C71⋊C8C2311yescharacteristic
93C22×C71⋊C8C2311yescharacteristic
94C22×C71⋊C8C2311yescharacteristic
95C22×C71⋊C8C2314yes—
96#14556128—22no—
97#14556128C2314yes—
98#14556114—28no—
99#14556114—28no—
100#14556102—22no—
101#14556102—22no—
102#14556102C2314yes—
103#14556102C2314yes—
104#14556099—28no—
105C4×D284—22no—
106C4×D284C2314yes—
107#14556087—22no—
108#14556087—22no—
109#14556087C2314yes—
110#14556087C2314yes—
111#14556086—28no—
112C2×C4⋊Dic71—21no—
113C2×C4⋊Dic71C2311yescharacteristic
114C2×C4⋊Dic71C2311yescharacteristic
115C2×C4⋊Dic71C2311yescharacteristic
116C2×C22⋊Dic71—21no—
117C2×C22⋊Dic71—21no—
118C2×(C2×D71)⋊C4—21no—
119C2×(C2×D71)⋊C4—21no—
120C2×(C2×D71)⋊C4—21no—
121C2×C4×Dic71—21no—
122C2×C4×Dic71—21no—
123#14556061C2314yes—
124#14556059C2314yes—
125#14556059C2314yes—
126C4⋊(C71⋊C8)C2314yes—
127#14556052C2314yes—
128#14556052C2314yes—
129#14556052C2314yes—
130#14556052C2314yes—
131#14556052C2314yes—
132#14556052C2314yes—
133#14556049C2314yes—
134#14556049C2314yes—
135#14556049C2314yes—
136#14556048C2314yes—
137C22⋊(C71⋊C8)C2314yes—
138C22⋊(C71⋊C8)C2314yes—
139#14556039C2314yes—
140C2×#41×C71—22no—
141C2×#41×C71—24no—
142C2×#41×C71—42no—
143C2×#41×C71C2314yes—
144C22×Q8×C71—21no—
145C22×Q8×C71—22no—
146C22×Q8×C71—24no—
147C22×Q8×C71—42no—
148C22×Q8×C71C2311yescharacteristic
149C22×Q8×C71C2314yes—
150C22×Q8×C71C2311yescharacteristic
151C22×D4×C71—21no—
152C22×D4×C71—21no—
153C22×D4×C71D411yescharacteristic
154C22×D4×C71C2311yescharacteristic
155C23×C4×C71—21no—
156C23×C4×C71—21no—
157C23×C4×C71C2311yescharacteristic
158C23×C4×C71C2311yescharacteristic
159#124×C71—28no—
160#124×C71—22no—
161#124×C71C2314yes—
162C22⋊Q8×C71—22no—
163C22⋊Q8×C71—28no—
164C22⋊Q8×C71C2314yes—
165#121×C71—28no—
166#121×C71—22no—
167#121×C71C2314yes—
168C4×Q8×C71—22no—
169C4×Q8×C71C2314yes—
170C4×D4×C71—28no—
171C4×D4×C71D414yes—
172C4×D4×C71C2314yes—
173C2×C4⋊C4×C71—21no—
174C2×C4⋊C4×C71—21no—
175C2×C4⋊C4×C71D411yescharacteristic
176C2×C4⋊C4×C71C2311yescharacteristic
177C2×C22⋊C4×C71—21no—
178C2×C22⋊C4×C71—21no—
179C2×C22⋊C4×C71—21no—
180C2×C22⋊C4×C71—21no—
181C2×C22⋊C4×C71D411yescharacteristic
182C2×C22⋊C4×C71D411yescharacteristic
183C2×C42×C71—21no—
184C2×C42×C71C2311yescharacteristic
185C23×D71—21no—
186C2×Dic142—24no—
187C2×Dic142—82no—
188C2×D284—22no—
189C2×D284—22no—
190C2×D284—21no—
191C2×D284C2412yes—
192C2×C22⋊D71—24no—
193C2×C22⋊D71—24no—
194C2×C22⋊D71—82no—
195C2×C22⋊D71—82no—
196C22×Dic71—21no—
197C22×Dic71—21no—
198C22×Dic71—21no—
199C2×C4×D71—24no—
200C2×C4×D71—44no—
201#11765852—28no—
202#11765852—44no—
203#11765850—44no—
204#11765849—44no—
205C2×C71⋊C8—22no—
206C2×C71⋊C8—22no—
207C2×C71⋊C8—22no—
208C2×C71⋊C8—22no—
209C2×C71⋊C8—44no—
210C2×C71⋊C8C2412yes—
211C2×C71⋊C8C2412yes—
212C2×C71⋊C8C2412yes—
213C2×C71⋊C8C2412yes—
214C4⋊Dic71—24no—
215C4⋊Dic71—21no—
216C4⋊Dic71—21no—
217C4⋊Dic71—21no—
218C4⋊Dic71C2412yes—
219C4⋊Dic71C2412yes—
220C4⋊Dic71C2412yes—
221C22⋊Dic71—24no—
222C22⋊Dic71—24no—
223(C2×D71)⋊C4—24no—
224(C2×D71)⋊C4—24no—
225(C2×D71)⋊C4—24no—
226C4×Dic71—24no—
227C4×Dic71—24no—
228C24×C71—21no—
229C24×C71C2×D411yescharacteristic
230C24×C71C2×D411yescharacteristic
231#41×C71—28no—
232#41×C71—44no—
233#41×C71—48no—
234C2×Q8×C71—21no—
235C2×Q8×C71—24no—
236C2×Q8×C71—21no—
237C2×Q8×C71—22no—
238C2×Q8×C71—28no—
239C2×Q8×C71—22no—
240C2×Q8×C71—22no—
241C2×Q8×C71—44no—
242C2×Q8×C71—44no—
243C2×Q8×C71—48no—
244C2×Q8×C71#4114yes—
245C2×Q8×C71C2412yes—
246C2×Q8×C71C2412yes—
247C2×D4×C71—24no—
248C2×D4×C71—24no—
249C2×D4×C71—21no—
250C2×D4×C71—22no—
251C2×D4×C71—22no—
252C2×D4×C71—42no—
253C2×D4×C71—44no—
254C2×D4×C71—44no—
255C2×D4×C71C2×D414yes—
256C2×D4×C71C2412yes—
257C22×C4×C71—21no—
258C22×C4×C71—22no—
259C22×C4×C71—22no—
260C22×C4×C71—22no—
261C22×C4×C71—22no—
262C22×C4×C71—21no—
263C22×C4×C71—21no—
264C22×C4×C71—24no—
265C22×C4×C71—24no—
266C22×C4×C71—44no—
267C22×C4×C71—44no—
268C22×C4×C71C2×D411yescharacteristic
269C22×C4×C71C2×D411yescharacteristic
270C22×C4×C71C2×D411yescharacteristic
271C22×C4×C71C2×D411yescharacteristic
272C22×C4×C71C2×D412yes—
273C22×C4×C71C2×D412yes—
274C22×C4×C71C2412yes—
275C22×C4×C71C2412yes—
276C22×C4×C71C2411yescharacteristic
277C4⋊C4×C71—24no—
278C4⋊C4×C71—24no—
279C4⋊C4×C71—21no—
280C4⋊C4×C71C2×D414yes—
281C4⋊C4×C71C2412yes—
282C22⋊C4×C71—24no—
283C22⋊C4×C71—24no—
284C22⋊C4×C71—24no—
285C22⋊C4×C71—24no—
286C22⋊C4×C71C2×D414yes—
287C22⋊C4×C71C2×D414yes—
288C42×C71—24no—
289C42×C71C2×D412yes—
290C42×C71C2412yes—
291C23×C71—22no—
292C23×C71—22no—
293C23×C71—22no—
294C23×C71—22no—
295C23×C71—22no—
296C23×C71—22no—
297C23×C71—22no—
298C23×C71—42no—
299C23×C71—42no—
300C23×C71—42no—
301C23×C71C22×D412yes—
302C23×C71C22×D412yes—
303C23×C71C22×D411yescharacteristic
304C22×D71—22no—
305C22×D71—42no—
306C22×D71—42no—
307C22×D71—42no—
308Q8×C71—24no—
309Q8×C71—22no—
310Q8×C71—22no—
311Q8×C71—22no—
312Q8×C71—48no—
313Q8×C71—42no—
314Q8×C71C2×#4114yes—
315D4×C71—22no—
316D4×C71—22no—
317D4×C71—44no—
318D4×C71—48no—
319D4×C71—48no—
320D4×C71—42no—
321C2×C4×C71—22no—
322C2×C4×C71—22no—
323C2×C4×C71—24no—
324C2×C4×C71—22no—
325C2×C4×C71—22no—
326C2×C4×C71—22no—
327C2×C4×C71—24no—
328C2×C4×C71—24no—
329C2×C4×C71—22no—
330C2×C4×C71—22no—
331C2×C4×C71—22no—
332C2×C4×C71—22no—
333C2×C4×C71—22no—
334C2×C4×C71—22no—
335C2×C4×C71—48no—
336C2×C4×C71—48no—
337C2×C4×C71—42no—
338C2×C4×C71—42no—
339C2×C4×C71C22×D412yes—
340C2×C4×C71C22×D412yes—
341C2×C4×C71C22×D412yes—
342C2×C4×C71C22×D412yes—
343C2×C4×C71C22×D411yescharacteristic
344C2×C4×C71C2×#4112yes—
345C2×C4×C71H(5,𝔽2)12yes—
346C2×C4×C71C2511yescharacteristic
347C22⋊D71—84no—
348C22⋊D71—84no—
349C2×Dic71—22no—
350C2×Dic71—22no—
351C2×Dic71—22no—
352C2×Dic71—42no—
353C2×Dic71—42no—
354C2×Dic71—42no—
355D284—22no—
356D284—22no—
357D284—42no—
358C4×D71—48no—
359Dic142—84no—
360C71⋊C8—22no—
361C71⋊C8—22no—
362C71⋊C8—22no—
363C71⋊C8—22no—
364C22×C71—22no—
365C22×C71—22no—
366C22×C71—22no—
367C22×C71—22no—
368C22×C71—22no—
369C22×C71—22no—
370C22×C71—44no—
371C22×C71—44no—
372C22×C71—42no—
373C22×C71—42no—
374C22×C71—42no—
375C22×C71—84no—
376C22×C71#54612yes—
377C22×C71#57512yes—
378C22×C71#57712yes—
379C22×C71C23×D411yescharacteristic
380C2×D71—42no—
381C2×D71—42no—
382C2×D71—42no—
383C2×D71—84no—
384C4×C71—22no—
385C4×C71—22no—
386C4×C71—24no—
387C4×C71—22no—
388C4×C71—22no—
389C4×C71—42no—
390C4×C71—42no—
391C4×C71#54612yes—
392C4×C71C22×#4111yescharacteristic
393C4×C71C2×H(5,𝔽2)11yescharacteristic
394Dic71—42no—
395Dic71—42no—
396Dic71—42no—
397C2×#3321—711nomaximal, Sylow
398C2×C71—42no—
399C2×C71—42no—
400C2×C71—82no—
401C2×C71#332114yescomplemented
402C2×C71C2×#54611yescharacteristic
403C2×C71C2×#57511yescharacteristic
404C2×C71C2×#57711yescharacteristic
405D71—82no—
406C2×#555—711no—
407C2×#548D7111yescharacteristic, complemented
408#3321—7116no—
409C2×#489—711no—
410C2×#485—711no—
411C2×#482—711no—
412C2×#475—711no—
413C2×#469—711no—
414C2×#465—711no—
415C2×#463—711no—
416C2×#449—711no—
417C2×#448—711no—
418C2×#440—711no—
419C2×#435—711no—
420C2×#419—711no—
421C2×#416—711no—
422C71C2×#332111yescharacteristic, complemented, Sylow
423C22×#41C2×D7111yescharacteristic
424C23×Q8C2×D7111yescharacteristic
425C22×SD16—711no—
426C22×SD16—711no—
427C22×D8—711no—
428C22×M16—711no—
429C23×C8—711no—
430#555—718no—
431#555—1424no—
432#548—24no—
433#548C2×D7118yescomplemented
434C2×C4⋊Q8—711no—
435C2×#124—21no—
436C2×#124—1421no—
437C2×#124—1421no—
438C2×#124C2×D7111yescharacteristic
439C2×C22⋊Q8—21no—
440C2×C22⋊Q8C2×D7111yescharacteristic
441C2×#121—21no—
442C2×#121—711no—
443C2×#121—711no—
444C2×#121—1421no—
445C2×#121C2×D7111yescharacteristic
446C2×C4×Q8C2×D7111yescharacteristic
447C2×C4×D4—21no—
448C2×C4×D4—711no—
449C2×C4×D4C2×D7111yescharacteristic
450C2×#117—711no—
451C2×#117—711no—
452C2×#117—1421no—
453#489—718no—
454#485—718no—
455#482—718no—
456#475—718no—
457#469—718no—
458#465—718no—
459#463—718no—
460#449—718no—
461#448—718no—
462#440—718no—
463#435—718no—
464C2×#107—711no—
465C2×#106—711no—
466C2×#106—711no—
467C2×C4⋊C8—711no—
468#419—718no—
469#416—718no—
470C2×#103—711no—
471C2×#103—711no—
472C2×#103—711no—
473C2×#103—711no—
474C2×#103—711no—
475C2×#103—711no—
476C2×#102—711no—
477C2×#102—711no—
478C2×#102—711no—
479C2×#102—711no—
480C2×C22⋊C8—711no—
481C2×C22⋊C8—711no—
482C2×#97—711no—
483C2×#41—22no—
484C2×#41—24no—
485C2×#41—42no—
486C2×#41C22×D7114yes—
487C22×Q8—21no—
488C22×Q8—22no—
489C22×Q8—24no—
490C22×Q8—42no—
491C22×Q8—1421no—
492C22×Q8C22×D7111yescharacteristic
493C22×Q8C22×D7114yes—
494C22×Q8C22×D7111yescharacteristic
495C22×D4—21no—
496C22×D4—21no—
497C22×D4—711no—
498C22×D4—1421no—
499C22×D4—1421no—
500C22×D4C22⋊D7111yescharacteristic
501C22×D4C22×D7111yescharacteristic
502C23×C4—21no—
503C23×C4—21no—
504C23×C4—1421no—
505C23×C4C22×D7111yescharacteristic
506C23×C4C22×D7111yescharacteristic
507C2×SD16—2842no—
508C2×SD16—714no—
509C2×SD16—714no—
510C2×SD16—1424no—
511C2×D8—2842no—
512C2×D8—714no—
513C2×M16—2842no—
514C2×M16—714no—
515C22×C8—2842no—
516C22×C8—714no—
517C22×C8—711no—
518C22×C8—711no—
519C22×C8—711no—
520C22×C8—711no—
521C4⋊Q8—714no—
522C4⋊Q8—1422no—
523#124—28no—
524#124—22no—
525#124—1428no—
526#124—1428no—
527#124C22×D7114yes—
528C22⋊Q8—22no—
529C22⋊Q8—28no—
530C22⋊Q8C22×D7114yes—
531#121—28no—
532#121—22no—
533#121—714no—
534#121—714no—
535#121—1428no—
536#121—1422no—
537#121—1422no—
538#121C22×D7114yes—
539C4×Q8—22no—
540C4×Q8C22×D7114yes—
541C4×D4—28no—
542C4×D4—714no—
543C4×D4—1422no—
544C4×D4C22⋊D7114yes—
545C4×D4C22×D7114yes—
546#117—714no—
547#117—714no—
548#117—1422no—
549#117—1422no—
550#117—1428no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—711no—
554C2×C4⋊C4—711no—
555C2×C4⋊C4—711no—
556C2×C4⋊C4—1421no—
557C2×C4⋊C4C22⋊D7111yescharacteristic
558C2×C4⋊C4C22×D7111yescharacteristic
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—1421no—
564C2×C22⋊C4—1421no—
565C2×C22⋊C4—1421no—
566C2×C22⋊C4—1421no—
567C2×C22⋊C4—1421no—
568C2×C22⋊C4C22⋊D7111yescharacteristic
569C2×C22⋊C4C22⋊D7111yescharacteristic
570C2×C42—21no—
571C2×C42—1421no—
572C2×C42—1421no—
573C2×C42C22×D7111yescharacteristic
574#107—714no—
575#106—714no—
576#106—714no—
577C4⋊C8—714no—
578#103—714no—
579#103—714no—
580#103—714no—
581#103—714no—
582#103—714no—
583#103—714no—
584#102—714no—
585#102—714no—
586#102—714no—
587#102—714no—
588C22⋊C8—714no—
589C22⋊C8—714no—
590#97—714no—
591C24—21no—
592C24—1421no—
593C24C2×C22⋊D7111yescharacteristic
594C24C2×C22⋊D7111yescharacteristic
595#41—28no—
596#41—44no—
597#41—48no—
598C2×Q8—21no—
599C2×Q8—24no—
600C2×Q8—21no—
601C2×Q8—22no—
602C2×Q8—28no—
603C2×Q8—22no—
604C2×Q8—22no—
605C2×Q8—44no—
606C2×Q8—44no—
607C2×Q8—48no—
608C2×Q8—5682no—
609C2×Q8—1424no—
610C2×Q8#1176586414yes—
611C2×Q8C23×D7112yes—
612C2×Q8C23×D7112yes—
613C2×D4—24no—
614C2×D4—24no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—44no—
621C2×D4—5682no—
622C2×D4—5682no—
623C2×D4—712no—
624C2×D4—1424no—
625C2×D4—1424no—
626C2×D4—1421no—
627C2×D4—1422no—
628C2×D4—1422no—
629C2×D4C2×C22⋊D7114yes—
630C2×D4C23×D7112yes—
631C22×C4—21no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—24no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—24no—
640C22×C4—44no—
641C22×C4—44no—
642C22×C4—2844no—
643C22×C4—1421no—
644C22×C4—1421no—
645C22×C4—1421no—
646C22×C4—1424no—
647C22×C4C2×C22⋊D7112yes—
648C22×C4C2×C22⋊D7112yes—
649C22×C4C2×C22⋊D7111yescharacteristic
650C22×C4C2×C22⋊D7111yescharacteristic
651C22×C4C2×C22⋊D7111yescharacteristic
652C22×C4C2×C22⋊D7111yescharacteristic
653C22×C4C23×D7112yes—
654C22×C4C23×D7112yes—
655C22×C4C23×D7111yescharacteristic
656SD16—2844no—
657SD16—1428no—
658D8—2844no—
659M16—2844no—
660C2×C8—2844no—
661C2×C8—712no—
662C2×C8—712no—
663C2×C8—712no—
664C2×C8—712no—
665C2×C8—1422no—
666C2×C8—1422no—
667C2×C8—1422no—
668C2×C8—1422no—
669C4⋊C4—24no—
670C4⋊C4—24no—
671C4⋊C4—21no—
672C4⋊C4—712no—
673C4⋊C4—712no—
674C4⋊C4—712no—
675C4⋊C4—1421no—
676C4⋊C4—1421no—
677C4⋊C4—1421no—
678C4⋊C4—1424no—
679C4⋊C4C2×C22⋊D7114yes—
680C4⋊C4C23×D7112yes—
681C22⋊C4—24no—
682C22⋊C4—24no—
683C22⋊C4—24no—
684C22⋊C4—24no—
685C22⋊C4—1424no—
686C22⋊C4—1424no—
687C22⋊C4—1424no—
688C22⋊C4—1424no—
689C22⋊C4—1424no—
690C22⋊C4C2×C22⋊D7114yes—
691C22⋊C4C2×C22⋊D7114yes—
692C42—24no—
693C42—1424no—
694C42—1424no—
695C42C2×C22⋊D7112yes—
696C42C23×D7112yes—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—22no—
703C23—22no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—2842no—
708C23—2842no—
709C23—2842no—
710C23—1422no—
711C23C22×C22⋊D7112yes—
712C23C22×C22⋊D7112yes—
713C23C22×C22⋊D7111yescharacteristic
714Q8—22no—
715Q8—24no—
716Q8—22no—
717Q8—22no—
718Q8—48no—
719Q8—42no—
720Q8—5684no—
721Q8C2×#1176586414yes—
722D4—22no—
723D4—22no—
724D4—44no—
725D4—48no—
726D4—48no—
727D4—42no—
728D4—2842no—
729D4—5684no—
730D4—5684no—
731D4—1422no—
732D4—1422no—
733C2×C4—22no—
734C2×C4—22no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—24no—
744C2×C4—24no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—48no—
748C2×C4—48no—
749C2×C4—42no—
750C2×C4—42no—
751C2×C4—2848no—
752C2×C4—2842no—
753C2×C4—2842no—
754C2×C4—2842no—
755C2×C4—1422no—
756C2×C4—1422no—
757C2×C4—1422no—
758C2×C4C22×C22⋊D7112yes—
759C2×C4C22×C22⋊D7112yes—
760C2×C4C22×C22⋊D7112yes—
761C2×C4C22×C22⋊D7112yes—
762C2×C4C22×C22⋊D7111yescharacteristic
763C2×C4C2×#1176586412yes—
764C2×C4#1455617312yes—
765C2×C4C24×D7111yescharacteristic
766C8—1422no—
767C8—1422no—
768C8—1422no—
769C8—1422no—
770C22—22no—
771C22—22no—
772C22—22no—
773C22—22no—
774C22—22no—
775C22—22no—
776C22—44no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—2842no—
783C22—2842no—
784C22—2842no—
785C22—5684no—
786C22#1798664312yes—
787C22#1798679712yes—
788C22#1798680712yes—
789C22C23×C22⋊D7111yescharacteristic
790C4—22no—
791C4—22no—
792C4—24no—
793C4—22no—
794C4—22no—
795C4—42no—
796C4—42no—
797C4—2842no—
798C4—2842no—
799C4—2842no—
800C4#1798664312yes—
801C4C22×#1176586411yescharacteristic
802C4C2×#1455617311yescharacteristic
803C2—42no—
804C2—42no—
805C2—82no—
806C2—5682no—
807C2#2260052614yesdirect product factor
808C2C2×#1798664311yescharacteristic
809C2C2×#1798679711yescharacteristic
810C2C2×#1798680711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#548×C71C2
socleC23×C71C22×D4
hypercenterC2×#548D71
hypocenterC71C2×#3321
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#548

Complements

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

NH ≅ G/Ntype
1. C2×#17986714C2semidirect
2. #22600526C2direct (N × H)
3. C2×#17986358C2semidirect
4. C2×#17986337C2semidirect
5. C2×#17986320C2semidirect
6. C2×#17986284C2semidirect
7. C2×#17986250C2semidirect
8. C2×#17986230C2semidirect
9. C2×#17986211C2semidirect
10. C2×#17986144C2semidirect
11. C2×#17986138C2semidirect
12. C2×#17986097C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986008C2semidirect
15. C2×#17985995C2semidirect
16. C2×#548×C71C2semidirect
23. #17986714C22semidirect
34. #17986358C22semidirect
35. #17986337C22semidirect
36. #17986320C22semidirect
37. #17986284C22semidirect
38. #17986250C22semidirect
39. #17986230C22semidirect
40. #17986211C22semidirect
41. #17986144C22semidirect
42. #17986138C22semidirect
43. #17986097C22semidirect
44. #17986071C22semidirect
49. #17986008C22semidirect
50. #17985995C22semidirect
67. #548×C71C22semidirect
401. C2×C71#3321semidirect
407. C2×#548D71semidirect
422. C71C2×#3321semidirect
433. #548C2×D71semidirect
807. C2#22600526direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867142
#226005262
C2×#179863582
C2×#179863372
C2×#179863202
C2×#179862842
C2×#179862502
C2×#179862302
C2×#179862112
C2×#179861442
C2×#179861382
C2×#179860972
C2×#179860712
C2×#179860082
C2×#179859952
C2×#548×C712
C2×#332171