Finite Group Databasebeta

← C2×#22600834 #32876041

Subgroups — C2×#22600834 #32876041

Order 18176.

1962 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17986714C211yesmaximal, characteristic, complemented
2#22600834C2116yesmaximal, direct product factor
3C2×#17986409C211yesmaximal, characteristic, complemented
4C2×#17986323C211yesmaximal, characteristic, complemented
5C2×#17986320C211yesmaximal, characteristic, complemented
6C2×#17986320C211yesmaximal, characteristic, complemented
7C2×#17986312C211yesmaximal, characteristic, complemented
8C2×#17986296C211yesmaximal, characteristic, complemented
9C2×#17986279C211yesmaximal, characteristic, complemented
10C2×#17986250C211yesmaximal, characteristic, complemented
11C2×#17986233C211yesmaximal, characteristic, complemented
12C2×#17986109C211yesmaximal, characteristic, complemented
13C2×#17986071C211yesmaximal, characteristic, complemented
14C2×#17986039C211yesmaximal, characteristic, complemented
15C2×#17986035C211yesmaximal, characteristic, complemented
16C2×#553×C71C211yesmaximal, characteristic, complemented
17C22×#11765850C2211yescharacteristic
18C22×#11765849C2211yescharacteristic
19C23×C71⋊C8C2211yescharacteristic
20#17986714—24no—
21#17986714C2218yescomplemented
22C2×#14556128C2211yescharacteristic
23C2×#14556114—21no—
24C2×#14556114—21no—
25C2×#14556102C2211yescharacteristic
26C2×#14556102C2211yescharacteristic
27C2×#14556099—21no—
28C2×C4×D284C2211yescharacteristic
29C2×#14556087C2211yescharacteristic
30C2×#14556087C2211yescharacteristic
31C2×#14556086—21no—
32#17986409C2218yescomplemented
33#17986323C2218yescomplemented
34#17986320C2218yescomplemented
35#17986320C2218yescomplemented
36#17986312C2218yescomplemented
37#17986296C2218yescomplemented
38#17986279C2218yescomplemented
39#17986250C2218yescomplemented
40#17986233C2218yescomplemented
41#17986109C2218yescomplemented
42#17986071C2218yescomplemented
43#17986039C2218yescomplemented
44#17986035C2218yescomplemented
45C2×#14556061C2211yescharacteristic
46C2×#14556061C2211yescharacteristic
47C2×#14556061C2211yescharacteristic
48C2×#14556061C2211yescharacteristic
49C2×#14556061C2211yescharacteristic
50C2×#14556059C2211yescharacteristic
51C2×#14556059C2211yescharacteristic
52C2×#14556059C2211yescharacteristic
53C2×#14556059C2211yescharacteristic
54C2×C4⋊(C71⋊C8)C2211yescharacteristic
55C2×#14556049C2211yescharacteristic
56C2×#14556049C2211yescharacteristic
57C2×#14556049C2211yescharacteristic
58C2×#14556048C2211yescharacteristic
59C2×#14556048C2211yescharacteristic
60C2×#14556048C2211yescharacteristic
61C2×C22⋊(C71⋊C8)C2211yescharacteristic
62C2×C22⋊(C71⋊C8)C2211yescharacteristic
63C2×#14556039C2211yescharacteristic
64#553×C71—24no—
65#553×C71C2218yescomplemented
66C2×#126×C71—21no—
67C2×#125×C71C2211yescharacteristic
68C2×#123×C71—21no—
69C2×#121×C71—21no—
70C2×#121×C71C2211yescharacteristic
71C2×#121×C71C2211yescharacteristic
72C2×C4×D4×C71—21no—
73C2×C4×D4×C71C2211yescharacteristic
74C2×C4×D4×C71C2211yescharacteristic
75C2×#117×C71C2211yescharacteristic
76C22×C4⋊C4×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×D284C2311yescharacteristic
79C22×C22⋊D71—21no—
80C22×C22⋊D71—21no—
81C22×C4×D71—21no—
82C2×#11765850—24no—
83C2×#11765850C2314yes—
84C2×#11765849—24no—
85C2×#11765849C2314yes—
86C22×C71⋊C8—24no—
87C22×C71⋊C8C2314yes—
88C22×C71⋊C8C2311yescharacteristic
89C22×C71⋊C8C2311yescharacteristic
90C22×C71⋊C8C2311yescharacteristic
91C22×C71⋊C8C2311yescharacteristic
92#14556128—22no—
93#14556128C2314yes—
94#14556114—28no—
95#14556114—28no—
96#14556102—22no—
97#14556102—22no—
98#14556102C2314yes—
99#14556102C2314yes—
100#14556099—28no—
101C4×D284—22no—
102C4×D284C2314yes—
103#14556087—22no—
104#14556087—22no—
105#14556087C2314yes—
106#14556087C2314yes—
107#14556086—28no—
108C2×C4⋊Dic71—21no—
109C2×C4⋊Dic71C2311yescharacteristic
110C2×C4⋊Dic71C2311yescharacteristic
111C2×C4⋊Dic71C2311yescharacteristic
112C2×C22⋊Dic71—21no—
113C2×C22⋊Dic71—21no—
114C2×(C2×D71)⋊C4—21no—
115C2×(C2×D71)⋊C4—21no—
116C2×(C2×D71)⋊C4—21no—
117C2×C4×Dic71—21no—
118C2×C4×Dic71—21no—
119#14556061C2314yes—
120#14556061C2314yes—
121#14556061C2314yes—
122#14556061C2314yes—
123#14556061C2314yes—
124#14556059C2314yes—
125#14556059C2314yes—
126#14556059C2314yes—
127#14556059C2314yes—
128C4⋊(C71⋊C8)C2314yes—
129#14556049C2314yes—
130#14556049C2314yes—
131#14556049C2314yes—
132#14556048C2314yes—
133#14556048C2314yes—
134#14556048C2314yes—
135C22⋊(C71⋊C8)C2314yes—
136C22⋊(C71⋊C8)C2314yes—
137#14556039C2314yes—
138C22×D4×C71—21no—
139C22×D4×C71—21no—
140C22×D4×C71D411yescharacteristic
141C22×D4×C71C2311yescharacteristic
142C23×C4×C71—21no—
143C23×C4×C71—21no—
144C23×C4×C71C2311yescharacteristic
145C23×C4×C71C2311yescharacteristic
146#126×C71—28no—
147#125×C71—22no—
148#125×C71C2314yes—
149#123×C71—28no—
150#121×C71—28no—
151#121×C71—22no—
152#121×C71—22no—
153#121×C71C2314yes—
154#121×C71C2314yes—
155C4×D4×C71—28no—
156C4×D4×C71—22no—
157C4×D4×C71D414yes—
158C4×D4×C71C2314yes—
159C4×D4×C71C2314yes—
160#117×C71—22no—
161#117×C71C2314yes—
162C2×C4⋊C4×C71—21no—
163C2×C4⋊C4×C71—22no—
164C2×C4⋊C4×C71—21no—
165C2×C4⋊C4×C71—21no—
166C2×C4⋊C4×C71D411yescharacteristic
167C2×C4⋊C4×C71C2314yes—
168C2×C4⋊C4×C71C2311yescharacteristic
169C2×C4⋊C4×C71C2311yescharacteristic
170C2×C4⋊C4×C71C2311yescharacteristic
171C2×C22⋊C4×C71—21no—
172C2×C22⋊C4×C71—21no—
173C2×C22⋊C4×C71—21no—
174C2×C22⋊C4×C71—21no—
175C2×C22⋊C4×C71D411yescharacteristic
176C2×C22⋊C4×C71D411yescharacteristic
177C2×C42×C71—21no—
178C2×C42×C71C2311yescharacteristic
179C23×D71—21no—
180C2×Dic142—24no—
181C2×Dic142—82no—
182C2×D284—22no—
183C2×D284—22no—
184C2×D284—21no—
185C2×D284C2412yes—
186C2×C22⋊D71—24no—
187C2×C22⋊D71—24no—
188C2×C22⋊D71—82no—
189C2×C22⋊D71—82no—
190C22×Dic71—21no—
191C22×Dic71—21no—
192C22×Dic71—21no—
193C2×C4×D71—24no—
194C2×C4×D71—44no—
195#11765850—28no—
196#11765849—28no—
197C2×C71⋊C8—22no—
198C2×C71⋊C8—22no—
199C2×C71⋊C8—22no—
200C2×C71⋊C8—28no—
201C2×C71⋊C8#4114yes—
202C2×C71⋊C8C2412yes—
203C2×C71⋊C8C2412yes—
204C2×C71⋊C8C2412yes—
205C2×C71⋊C8C2412yes—
206C4⋊Dic71—24no—
207C4⋊Dic71—21no—
208C4⋊Dic71—21no—
209C4⋊Dic71—21no—
210C4⋊Dic71C2412yes—
211C4⋊Dic71C2412yes—
212C4⋊Dic71C2412yes—
213C22⋊Dic71—24no—
214C22⋊Dic71—24no—
215(C2×D71)⋊C4—24no—
216(C2×D71)⋊C4—24no—
217(C2×D71)⋊C4—24no—
218C4×Dic71—24no—
219C4×Dic71—24no—
220C24×C71—21no—
221C24×C71C2×D411yescharacteristic
222C24×C71C2×D411yescharacteristic
223C2×D4×C71—24no—
224C2×D4×C71—24no—
225C2×D4×C71—21no—
226C2×D4×C71—22no—
227C2×D4×C71—22no—
228C2×D4×C71—42no—
229C2×D4×C71—44no—
230C2×D4×C71—82no—
231C2×D4×C71C2×D414yes—
232C2×D4×C71C2412yes—
233C22×C4×C71—22no—
234C22×C4×C71—22no—
235C22×C4×C71—22no—
236C22×C4×C71—22no—
237C22×C4×C71—21no—
238C22×C4×C71—21no—
239C22×C4×C71—21no—
240C22×C4×C71—24no—
241C22×C4×C71—24no—
242C22×C4×C71—82no—
243C22×C4×C71—82no—
244C22×C4×C71C2×D411yescharacteristic
245C22×C4×C71C2×D411yescharacteristic
246C22×C4×C71C2×D411yescharacteristic
247C22×C4×C71C2×D411yescharacteristic
248C22×C4×C71C2×D412yes—
249C22×C4×C71C2×D412yes—
250C22×C4×C71C2412yes—
251C22×C4×C71C2412yes—
252C22×C4×C71C2411yescharacteristic
253C4⋊C4×C71—21no—
254C4⋊C4×C71—21no—
255C4⋊C4×C71—24no—
256C4⋊C4×C71—24no—
257C4⋊C4×C71—24no—
258C4⋊C4×C71—21no—
259C4⋊C4×C71C2×D414yes—
260C4⋊C4×C71C2412yes—
261C4⋊C4×C71C2412yes—
262C4⋊C4×C71C2412yes—
263C22⋊C4×C71—24no—
264C22⋊C4×C71—24no—
265C22⋊C4×C71—24no—
266C22⋊C4×C71—24no—
267C22⋊C4×C71C2×D414yes—
268C22⋊C4×C71C2×D414yes—
269C42×C71—24no—
270C42×C71C2×D412yes—
271C42×C71C2412yes—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—22no—
278C23×C71—22no—
279C23×C71—42no—
280C23×C71—42no—
281C23×C71—42no—
282C23×C71C22×D412yes—
283C23×C71C22×D412yes—
284C23×C71C22×D411yescharacteristic
285C22×D71—22no—
286C22×D71—42no—
287C22×D71—42no—
288C22×D71—42no—
289D4×C71—22no—
290D4×C71—22no—
291D4×C71—44no—
292D4×C71—48no—
293D4×C71—42no—
294D4×C71—84no—
295C2×C4×C71—22no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—24no—
300C2×C4×C71—24no—
301C2×C4×C71—22no—
302C2×C4×C71—22no—
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×C71—84no—
313C2×C4×C71C22×D412yes—
314C2×C4×C71C22×D412yes—
315C2×C4×C71C22×D412yes—
316C2×C4×C71C22×D412yes—
317C2×C4×C71C22×D411yescharacteristic
318C2×C4×C71C2×#4112yes—
319C2×C4×C712−1+412yes—
320C2×C4×C71C2511yescharacteristic
321C22⋊D71—84no—
322C22⋊D71—84no—
323C2×Dic71—22no—
324C2×Dic71—22no—
325C2×Dic71—22no—
326C2×Dic71—42no—
327C2×Dic71—42no—
328C2×Dic71—42no—
329D284—22no—
330D284—22no—
331D284—42no—
332C4×D71—48no—
333Dic142—84no—
334C71⋊C8—22no—
335C71⋊C8—22no—
336C71⋊C8—22no—
337C71⋊C8C2×#4114yes—
338C22×C71—22no—
339C22×C71—22no—
340C22×C71—22no—
341C22×C71—22no—
342C22×C71—22no—
343C22×C71—22no—
344C22×C71—44no—
345C22×C71—44no—
346C22×C71—42no—
347C22×C71—42no—
348C22×C71—42no—
349C22×C71—84no—
350C22×C71#54712yes—
351C22×C71#57512yes—
352C22×C71#57612yes—
353C22×C71C23×D411yescharacteristic
354C2×D71—42no—
355C2×D71—42no—
356C2×D71—42no—
357C2×D71—84no—
358C4×C71—22no—
359C4×C71—22no—
360C4×C71—22no—
361C4×C71—22no—
362C4×C71—42no—
363C4×C71—42no—
364C4×C71—42no—
365C4×C71#54712yes—
366C4×C71C22×#4111yescharacteristic
367C4×C71C2×2−1+411yescharacteristic
368Dic71—42no—
369Dic71—42no—
370Dic71—42no—
371C2×#3347—711nomaximal, Sylow
372C2×C71—42no—
373C2×C71—42no—
374C2×C71—82no—
375C2×C71#334714yescomplemented
376C2×C71C2×#54711yescharacteristic
377C2×C71C2×#57511yescharacteristic
378C2×C71C2×#57611yescharacteristic
379D71—82no—
380C2×#555—711no—
381C2×#553D7111yescharacteristic, complemented
382#3347—7116no—
383C2×#501—711no—
384C2×#482—711no—
385C2×#482—711no—
386C2×#482—711no—
387C2×#480—711no—
388C2×#478—711no—
389C2×#474—711no—
390C2×#469—711no—
391C2×#466—711no—
392C2×#442—711no—
393C2×#435—711no—
394C2×#428—711no—
395C2×#427—711no—
396C71C2×#334711yescharacteristic, complemented, Sylow
397C22×D8—711no—
398C22×M16—711no—
399C23×C8—711no—
400#555—718no—
401#555—1424no—
402#553—24no—
403#553C2×D7118yescomplemented
404C2×C4⋊Q8—711no—
405C2×#126—21no—
406C2×#125C2×D7111yescharacteristic
407C2×#124—1421no—
408C2×#124—1421no—
409C2×#123—21no—
410C2×#121—21no—
411C2×#121—711no—
412C2×#121—711no—
413C2×#121—1421no—
414C2×#121C2×D7111yescharacteristic
415C2×#121C2×D7111yescharacteristic
416C2×C4×D4—21no—
417C2×C4×D4—711no—
418C2×C4×D4C2×D7111yescharacteristic
419C2×C4×D4C2×D7111yescharacteristic
420C2×#117—711no—
421C2×#117—711no—
422C2×#117—1421no—
423C2×#117C2×D7111yescharacteristic
424C22×C4⋊C4C2×D7111yescharacteristic
425#501—718no—
426#482—718no—
427#482—718no—
428#482—718no—
429#480—718no—
430#478—718no—
431#474—718no—
432#469—718no—
433#466—718no—
434#442—718no—
435#435—718no—
436#428—718no—
437#427—718no—
438C2×#107—711no—
439C2×#107—711no—
440C2×#107—711no—
441C2×#107—711no—
442C2×#107—711no—
443C2×#106—711no—
444C2×#106—711no—
445C2×#106—711no—
446C2×#106—711no—
447C2×C4⋊C8—711no—
448C2×#102—711no—
449C2×#102—711no—
450C2×#102—711no—
451C2×#102—711no—
452C2×#102—711no—
453C2×#102—711no—
454C2×C22⋊C8—711no—
455C2×C22⋊C8—711no—
456C2×#97—711no—
457C22×Q8—1421no—
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—711no—
461C22×D4—1421no—
462C22×D4—1421no—
463C22×D4C22⋊D7111yescharacteristic
464C22×D4C22×D7111yescharacteristic
465C23×C4—21no—
466C23×C4—21no—
467C23×C4—1421no—
468C23×C4C22×D7111yescharacteristic
469C23×C4C22×D7111yescharacteristic
470C2×D8—714no—
471C2×D8—1424no—
472C2×M16—714no—
473C2×M16—1424no—
474C22×C8—711no—
475C22×C8—711no—
476C22×C8—714no—
477C22×C8—711no—
478C22×C8—711no—
479C22×C8—1424no—
480C4⋊Q8—714no—
481C4⋊Q8—1422no—
482#126—28no—
483#125—22no—
484#125C22×D7114yes—
485#124—1428no—
486#124—1428no—
487#123—28no—
488#121—28no—
489#121—22no—
490#121—22no—
491#121—714no—
492#121—714no—
493#121—1428no—
494#121—1422no—
495#121—1422no—
496#121C22×D7114yes—
497#121C22×D7114yes—
498C4×D4—28no—
499C4×D4—22no—
500C4×D4—714no—
501C4×D4—1422no—
502C4×D4C22⋊D7114yes—
503C4×D4C22×D7114yes—
504C4×D4C22×D7114yes—
505#117—22no—
506#117—714no—
507#117—714no—
508#117—1422no—
509#117—1422no—
510#117—1428no—
511#117C22×D7114yes—
512C2×C4⋊C4—21no—
513C2×C4⋊C4—22no—
514C2×C4⋊C4—21no—
515C2×C4⋊C4—21no—
516C2×C4⋊C4—711no—
517C2×C4⋊C4—711no—
518C2×C4⋊C4—711no—
519C2×C4⋊C4—1421no—
520C2×C4⋊C4C22⋊D7111yescharacteristic
521C2×C4⋊C4C22×D7111yescharacteristic
522C2×C4⋊C4C22×D7111yescharacteristic
523C2×C4⋊C4C22×D7114yes—
524C2×C4⋊C4C22×D7111yescharacteristic
525C2×C22⋊C4—21no—
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C22⋊C4—21no—
529C2×C22⋊C4—1421no—
530C2×C22⋊C4—1421no—
531C2×C22⋊C4—1421no—
532C2×C22⋊C4—1421no—
533C2×C22⋊C4—1421no—
534C2×C22⋊C4C22⋊D7111yescharacteristic
535C2×C22⋊C4C22⋊D7111yescharacteristic
536C2×C42—21no—
537C2×C42—1421no—
538C2×C42—1421no—
539C2×C42C22×D7111yescharacteristic
540#107—714no—
541#107—714no—
542#107—714no—
543#107—714no—
544#107—714no—
545#106—714no—
546#106—714no—
547#106—714no—
548#106—714no—
549C4⋊C8—714no—
550#102—714no—
551#102—714no—
552#102—714no—
553#102—714no—
554#102—714no—
555#102—714no—
556C22⋊C8—714no—
557C22⋊C8—714no—
558#97—714no—
559C24—21no—
560C24—1421no—
561C24C2×C22⋊D7111yescharacteristic
562C24C2×C22⋊D7111yescharacteristic
563C2×Q8—5682no—
564C2×Q8—1424no—
565C2×D4—24no—
566C2×D4—24no—
567C2×D4—21no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—42no—
571C2×D4—44no—
572C2×D4—82no—
573C2×D4—5682no—
574C2×D4—5682no—
575C2×D4—712no—
576C2×D4—1424no—
577C2×D4—1424no—
578C2×D4—1421no—
579C2×D4—1422no—
580C2×D4—1422no—
581C2×D4C2×C22⋊D7114yes—
582C2×D4C23×D7112yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—82no—
593C22×C4—82no—
594C22×C4—2844no—
595C22×C4—1421no—
596C22×C4—1421no—
597C22×C4—1421no—
598C22×C4—1424no—
599C22×C4C2×C22⋊D7112yes—
600C22×C4C2×C22⋊D7112yes—
601C22×C4C2×C22⋊D7111yescharacteristic
602C22×C4C2×C22⋊D7111yescharacteristic
603C22×C4C2×C22⋊D7111yescharacteristic
604C22×C4C2×C22⋊D7111yescharacteristic
605C22×C4C23×D7112yes—
606C22×C4C23×D7112yes—
607C22×C4C23×D7111yescharacteristic
608D8—1428no—
609M16—1428no—
610C2×C8—714no—
611C2×C8—712no—
612C2×C8—712no—
613C2×C8—712no—
614C2×C8—712no—
615C2×C8—1428no—
616C2×C8—1422no—
617C2×C8—1422no—
618C2×C8—1422no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—24no—
622C4⋊C4—24no—
623C4⋊C4—24no—
624C4⋊C4—21no—
625C4⋊C4—712no—
626C4⋊C4—712no—
627C4⋊C4—712no—
628C4⋊C4—1421no—
629C4⋊C4—1421no—
630C4⋊C4—1421no—
631C4⋊C4—1424no—
632C4⋊C4C2×C22⋊D7114yes—
633C4⋊C4C23×D7112yes—
634C4⋊C4C23×D7112yes—
635C4⋊C4C23×D7112yes—
636C22⋊C4—24no—
637C22⋊C4—24no—
638C22⋊C4—24no—
639C22⋊C4—24no—
640C22⋊C4—1424no—
641C22⋊C4—1424no—
642C22⋊C4—1424no—
643C22⋊C4—1424no—
644C22⋊C4—1424no—
645C22⋊C4C2×C22⋊D7114yes—
646C22⋊C4C2×C22⋊D7114yes—
647C42—24no—
648C42—1424no—
649C42—1424no—
650C42C2×C22⋊D7112yes—
651C42C23×D7112yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—2842no—
663C23—2842no—
664C23—2842no—
665C23—1422no—
666C23C22×C22⋊D7112yes—
667C23C22×C22⋊D7112yes—
668C23C22×C22⋊D7111yescharacteristic
669Q8—5684no—
670D4—22no—
671D4—22no—
672D4—44no—
673D4—48no—
674D4—42no—
675D4—84no—
676D4—2842no—
677D4—5684no—
678D4—5684no—
679D4—1422no—
680D4—1422no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—24no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—42no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—84no—
698C2×C4—84no—
699C2×C4—2848no—
700C2×C4—2842no—
701C2×C4—2842no—
702C2×C4—2842no—
703C2×C4—1422no—
704C2×C4—1422no—
705C2×C4—1422no—
706C2×C4C22×C22⋊D7112yes—
707C2×C4C22×C22⋊D7112yes—
708C2×C4C22×C22⋊D7112yes—
709C2×C4C22×C22⋊D7112yes—
710C2×C4C22×C22⋊D7111yescharacteristic
711C2×C4#41×D7112yes—
712C2×C4#1455617512yes—
713C2×C4C24×D7111yescharacteristic
714C8—714no—
715C8—1422no—
716C8—1422no—
717C8—1422no—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—42no—
727C22—42no—
728C22—42no—
729C22—84no—
730C22—2842no—
731C22—2842no—
732C22—2842no—
733C22—5684no—
734C22#1798664812yes—
735C22#1798679712yes—
736C22#1798680212yes—
737C22C23×C22⋊D7111yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—42no—
743C4—42no—
744C4—42no—
745C4—2842no—
746C4—2842no—
747C4—2842no—
748C4#1798664812yes—
749C4C2×#41×D7111yescharacteristic
750C4C2×#1455617511yescharacteristic
751C2—42no—
752C2—42no—
753C2—82no—
754C2—5682no—
755C2#2260083414yesdirect product factor
756C2C2×#1798664811yescharacteristic
757C2C2×#1798679711yescharacteristic
758C2C2×#1798680211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D71
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#553×C71C2
socleC23×C71C22×D4
hypercenterC2×#553D71
hypocenterC71C2×#3347
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#553

Complements

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

NH ≅ G/Ntype
1. C2×#17986714C2semidirect
2. #22600834C2direct (N × H)
3. C2×#17986409C2semidirect
4. C2×#17986323C2semidirect
5. C2×#17986320C2semidirect
6. C2×#17986320C2semidirect
7. C2×#17986312C2semidirect
8. C2×#17986296C2semidirect
9. C2×#17986279C2semidirect
10. C2×#17986250C2semidirect
11. C2×#17986233C2semidirect
12. C2×#17986109C2semidirect
13. C2×#17986071C2semidirect
14. C2×#17986039C2semidirect
15. C2×#17986035C2semidirect
16. C2×#553×C71C2semidirect
21. #17986714C22semidirect
32. #17986409C22semidirect
33. #17986323C22semidirect
34. #17986320C22semidirect
35. #17986320C22semidirect
36. #17986312C22semidirect
37. #17986296C22semidirect
38. #17986279C22semidirect
39. #17986250C22semidirect
40. #17986233C22semidirect
41. #17986109C22semidirect
42. #17986071C22semidirect
43. #17986039C22semidirect
44. #17986035C22semidirect
65. #553×C71C22semidirect
375. C2×C71#3347semidirect
381. C2×#553D71semidirect
396. C71C2×#3347semidirect
403. #553C2×D71semidirect
755. C2#22600834direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867142
#226008342
C2×#179864092
C2×#179863232
C2×#179863202
C2×#179863122
C2×#179862962
C2×#179862792
C2×#179862502
C2×#179862332
C2×#179861092
C2×#179860712
C2×#179860392
C2×#179860352
C2×#553×C712
C2×#334771