Finite Group Databasebeta

← C2×#22600842 #32876049

Subgroups — C2×#22600842 #32876049

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
2C2×#17986695C211yesmaximal, characteristic, complemented
3#22600842C2116yesmaximal, direct product factor
4C2×#17986408C211yesmaximal, characteristic, complemented
5C2×#17986324C211yesmaximal, characteristic, complemented
6C2×#17986324C211yesmaximal, characteristic, complemented
7C2×#17986324C211yesmaximal, characteristic, complemented
8C2×#17986313C211yesmaximal, characteristic, complemented
9C2×#17986300C211yesmaximal, characteristic, complemented
10C2×#17986280C211yesmaximal, characteristic, complemented
11C2×#17986252C211yesmaximal, characteristic, complemented
12C2×#17986235C211yesmaximal, characteristic, complemented
13C2×#17986112C211yesmaximal, characteristic, complemented
14C2×#17986041C211yesmaximal, characteristic, complemented
15C2×#17986037C211yesmaximal, characteristic, complemented
16C2×#435×C71C211yesmaximal, characteristic, complemented
17C22×D568C2211yescharacteristic
18#17986714—24no—
19#17986714C2218yescomplemented
20#17986695—24no—
21#17986695C2218yescomplemented
22C2×#14556128C2211yescharacteristic
23C2×#14556123—21no—
24C2×#14556120C2211yescharacteristic
25C2×#14556114—21no—
26C2×#14556114—21no—
27C2×#14556110—21no—
28C2×#14556102C2211yescharacteristic
29C2×#14556102C2211yescharacteristic
30C2×#14556102C2211yescharacteristic
31C2×#14556102C2211yescharacteristic
32C2×#14556100—21no—
33C2×#14556099—21no—
34C2×C4×D284C2211yescharacteristic
35C2×C4×D284C2211yescharacteristic
36C2×(C22⋊D71)⋊C4—21no—
37C2×#14556087C2211yescharacteristic
38C2×#14556087C2211yescharacteristic
39C2×#14556087C2211yescharacteristic
40C2×#14556086—21no—
41C22×C4⋊Dic71C2211yescharacteristic
42#17986408C2218yescomplemented
43#17986324C2218yescomplemented
44#17986324C2218yescomplemented
45#17986324C2218yescomplemented
46#17986313C2218yescomplemented
47#17986300C2218yescomplemented
48#17986280C2218yescomplemented
49#17986252C2218yescomplemented
50#17986235C2218yescomplemented
51#17986112C2218yescomplemented
52#17986041C2218yescomplemented
53#17986037C2218yescomplemented
54C2×#14556062C2211yescharacteristic
55C2×#14556062C2211yescharacteristic
56C2×#14556062C2211yescharacteristic
57C2×#14556062C2211yescharacteristic
58C2×#14556062C2211yescharacteristic
59C2×#14556060C2211yescharacteristic
60C2×#14556060C2211yescharacteristic
61C2×#14556060C2211yescharacteristic
62C2×#14556060C2211yescharacteristic
63C2×#14556050C2211yescharacteristic
64C2×#14556050C2211yescharacteristic
65C2×#14556050C2211yescharacteristic
66C2×#14556050C2211yescharacteristic
67C2×#14556050C2211yescharacteristic
68C2×#14556050C2211yescharacteristic
69C22×M16×C71C2211yescharacteristic
70C23×C8×C71C2211yescharacteristic
71C2×C4×D4×C71C2211yescharacteristic
72#435×C71C2218yescomplemented
73C2×C4⋊C8×C71C2211yescharacteristic
74C2×C22⋊C8×C71C2211yescharacteristic
75C2×C22⋊C8×C71C2211yescharacteristic
76C2×#97×C71C2211yescharacteristic
77C22×Dic142—21no—
78C22×D284C2311yescharacteristic
79C22×D284C2311yescharacteristic
80C22×C22⋊D71—21no—
81C22×C22⋊D71—21no—
82C22×C22⋊D71—21no—
83C22×C22⋊D71—21no—
84C23×Dic71—21no—
85C22×C4×D71—21no—
86C22×C4×D71—21no—
87C2×D568—24no—
88C2×D568C2314yes—
89#14556128—22no—
90#14556128C2314yes—
91#14556123—28no—
92#14556120—22no—
93#14556120C2314yes—
94#14556114—28no—
95#14556114—28no—
96#14556110—28no—
97#14556102—22no—
98#14556102—22no—
99#14556102—22no—
100#14556102—22no—
101#14556102C2314yes—
102#14556102C2314yes—
103#14556102C2314yes—
104#14556102C2314yes—
105#14556100—28no—
106#14556099—28no—
107C4×D284—22no—
108C4×D284—22no—
109C4×D284C2314yes—
110C4×D284C2314yes—
111(C22⋊D71)⋊C4—28no—
112#14556087—22no—
113#14556087—22no—
114#14556087—22no—
115#14556087C2314yes—
116#14556087C2314yes—
117#14556087C2314yes—
118#14556086—28no—
119C2×C4⋊Dic71—22no—
120C2×C4⋊Dic71—21no—
121C2×C4⋊Dic71—21no—
122C2×C4⋊Dic71C2314yes—
123C2×C4⋊Dic71C2311yescharacteristic
124C2×C4⋊Dic71C2311yescharacteristic
125C2×C4⋊Dic71C2311yescharacteristic
126C2×C4⋊Dic71C2311yescharacteristic
127C2×C4⋊Dic71C2311yescharacteristic
128C2×C4⋊Dic71C2311yescharacteristic
129C2×Dic71⋊C4—21no—
130C2×Dic71⋊C4—21no—
131C2×C22⋊Dic71—21no—
132C2×C22⋊Dic71—21no—
133C2×C22⋊Dic71—21no—
134C2×(C2×D71)⋊C4—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—21no—
140C2×C4×Dic71—21no—
141C2×C4×Dic71—21no—
142C2×C4×Dic71—21no—
143#14556062C2314yes—
144#14556062C2314yes—
145#14556062C2314yes—
146#14556062C2314yes—
147#14556062C2314yes—
148#14556060C2314yes—
149#14556060C2314yes—
150#14556060C2314yes—
151#14556060C2314yes—
152#14556050C2314yes—
153#14556050C2314yes—
154#14556050C2314yes—
155#14556050C2314yes—
156#14556050C2314yes—
157#14556050C2314yes—
158C22×D4×C71D411yescharacteristic
159C23×C4×C71C2311yescharacteristic
160C23×C4×C71C2311yescharacteristic
161C2×M16×C71—24no—
162C2×M16×C71C2314yes—
163C22×C8×C71—24no—
164C22×C8×C71C2311yescharacteristic
165C22×C8×C71C2311yescharacteristic
166C22×C8×C71C2311yescharacteristic
167C22×C8×C71C2314yes—
168C22×C8×C71C2311yescharacteristic
169C4×D4×C71D414yes—
170C4×D4×C71C2314yes—
171C2×C4⋊C4×C71D411yescharacteristic
172C2×C22⋊C4×C71D411yescharacteristic
173C2×C22⋊C4×C71D411yescharacteristic
174C2×C42×C71C2311yescharacteristic
175C4⋊C8×C71C2314yes—
176C22⋊C8×C71C2314yes—
177C22⋊C8×C71C2314yes—
178#97×C71C2314yes—
179C23×D71—21no—
180C23×D71—21no—
181C2×Dic142—24no—
182C2×Dic142—82no—
183C2×D284—22no—
184C2×D284—22no—
185C2×D284—22no—
186C2×D284—22no—
187C2×D284—21no—
188C2×D284—21no—
189C2×D284C2412yes—
190C2×D284C2412yes—
191C2×C22⋊D71—24no—
192C2×C22⋊D71—24no—
193C2×C22⋊D71—24no—
194C2×C22⋊D71—24no—
195C2×C22⋊D71—44no—
196C2×C22⋊D71—82no—
197C2×C22⋊D71—82no—
198C2×C22⋊D71—82no—
199C22×Dic71—21no—
200C22×Dic71—21no—
201C22×Dic71—21no—
202C22×Dic71—21no—
203C22×Dic71—21no—
204C22×Dic71—21no—
205C22×Dic71—24no—
206C22×Dic71—82no—
207C2×C4×D71—24no—
208C2×C4×D71—24no—
209C2×C4×D71—44no—
210C2×C4×D71—82no—
211D568—28no—
212C4⋊Dic71—21no—
213C4⋊Dic71—21no—
214C4⋊Dic71—24no—
215C4⋊Dic71—24no—
216C4⋊Dic71—21no—
217C4⋊Dic71—21no—
218C4⋊Dic71—21no—
219C4⋊Dic71—21no—
220C4⋊Dic71C2412yes—
221C4⋊Dic71C2412yes—
222C4⋊Dic71C2412yes—
223C4⋊Dic71C2412yes—
224C4⋊Dic71C2412yes—
225C4⋊Dic71C2412yes—
226Dic71⋊C4—24no—
227Dic71⋊C4—24no—
228C22⋊Dic71—24no—
229C22⋊Dic71—24no—
230C22⋊Dic71—24no—
231(C2×D71)⋊C4—24no—
232(C2×D71)⋊C4—24no—
233(C2×D71)⋊C4—24no—
234(C2×D71)⋊C4—24no—
235(C2×D71)⋊C4—24no—
236(C2×D71)⋊C4—24no—
237C4×Dic71—24no—
238C4×Dic71—24no—
239C4×Dic71—24no—
240C24×C71C2×D411yescharacteristic
241C24×C71C2×D411yescharacteristic
242C2×D4×C71—42no—
243C2×D4×C71C2×D414yes—
244C22×C4×C71—22no—
245C22×C4×C71—22no—
246C22×C4×C71—22no—
247C22×C4×C71—22no—
248C22×C4×C71C2×D411yescharacteristic
249C22×C4×C71C2×D411yescharacteristic
250C22×C4×C71C2×D411yescharacteristic
251C22×C4×C71C2×D411yescharacteristic
252C22×C4×C71C2×D412yes—
253C22×C4×C71C2×D412yes—
254C22×C4×C71C2412yes—
255C22×C4×C71C2412yes—
256C22×C4×C71C2411yescharacteristic
257M16×C71—28no—
258C2×C8×C71—22no—
259C2×C8×C71—22no—
260C2×C8×C71—22no—
261C2×C8×C71—28no—
262C2×C8×C71#4114yes—
263C2×C8×C71C2412yes—
264C2×C8×C71C2412yes—
265C2×C8×C71C2412yes—
266C2×C8×C71C2412yes—
267C4⋊C4×C71C2×D414yes—
268C22⋊C4×C71C2×D414yes—
269C22⋊C4×C71C2×D414yes—
270C42×C71C2×D412yes—
271C42×C71C2412yes—
272C23×C71—22no—
273C23×C71—22no—
274C23×C71—22no—
275C23×C71—22no—
276C23×C71—22no—
277C23×C71—22no—
278C23×C71C22×D412yes—
279C23×C71C22×D412yes—
280C23×C71C22×D411yescharacteristic
281C22×D71—22no—
282C22×D71—22no—
283C22×D71—42no—
284C22×D71—42no—
285C22×D71—42no—
286C22×D71—42no—
287C22×D71—42no—
288C22×D71—42no—
289D4×C71—44no—
290C2×C4×C71—22no—
291C2×C4×C71—22no—
292C2×C4×C71—22no—
293C2×C4×C71—22no—
294C2×C4×C71—24no—
295C2×C4×C71—24no—
296C2×C4×C71—22no—
297C2×C4×C71—22no—
298C2×C4×C71—22no—
299C2×C4×C71—22no—
300C2×C4×C71C22×D412yes—
301C2×C4×C71C22×D412yes—
302C2×C4×C71C22×D412yes—
303C2×C4×C71C22×D412yes—
304C2×C4×C71C22×D411yescharacteristic
305C2×C4×C71C2×#4112yes—
306C2×C4×C712−1+412yes—
307C2×C4×C71C2511yescharacteristic
308C22⋊D71—48no—
309C22⋊D71—84no—
310C22⋊D71—84no—
311C22⋊D71—84no—
312C2×Dic71—22no—
313C2×Dic71—22no—
314C2×Dic71—22no—
315C2×Dic71—22no—
316C2×Dic71—22no—
317C2×Dic71—22no—
318C2×Dic71—42no—
319C2×Dic71—42no—
320C2×Dic71—42no—
321C2×Dic71—42no—
322C2×Dic71—42no—
323C2×Dic71—42no—
324C2×Dic71—84no—
325D284—22no—
326D284—22no—
327D284—22no—
328D284—22no—
329D284—42no—
330D284—42no—
331C4×D71—48no—
332C4×D71—84no—
333Dic142—84no—
334C8×C71—22no—
335C8×C71—22no—
336C8×C71—22no—
337C8×C71C2×#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#54712yes—
347C22×C71#57512yes—
348C22×C71#57612yes—
349C22×C71C23×D411yescharacteristic
350C2×D71—42no—
351C2×D71—42no—
352C2×D71—42no—
353C2×D71—42no—
354C2×D71—42no—
355C2×D71—42no—
356C2×D71—84no—
357C2×D71—84no—
358C4×C71—22no—
359C4×C71—22no—
360C4×C71—22no—
361C4×C71—22no—
362C4×C71#54712yes—
363C4×C71C22×#4111yescharacteristic
364C4×C71C2×2−1+411yescharacteristic
365Dic71—42no—
366Dic71—42no—
367Dic71—42no—
368Dic71—42no—
369Dic71—42no—
370Dic71—42no—
371C2×#3347—711nomaximal, Sylow
372C2×C71—42no—
373C2×C71—42no—
374C2×C71#334714yescomplemented
375C2×C71C2×#54711yescharacteristic
376C2×C71C2×#57511yescharacteristic
377C2×C71C2×#57611yescharacteristic
378D71—82no—
379D71—82no—
380C2×#555—711no—
381C2×#553—711no—
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×#435D7111yescharacteristic, complemented
394C2×#428—711no—
395C2×#427—711no—
396C71C2×#334711yescharacteristic, complemented, Sylow
397C22×D8—711no—
398C22×M16C2×D7111yescharacteristic
399C23×C8C2×D7111yescharacteristic
400#555—718no—
401#555—1424no—
402#553—718no—
403#553—1424no—
404C2×C4⋊Q8—711no—
405C2×#126—1421no—
406C2×#125—711no—
407C2×#124—1421no—
408C2×#124—1421no—
409C2×#123—1421no—
410C2×#121—711no—
411C2×#121—711no—
412C2×#121—711no—
413C2×#121—711no—
414C2×#121—1421no—
415C2×#121—1421no—
416C2×C4×D4—711no—
417C2×C4×D4—711no—
418C2×C4×D4—1421no—
419C2×C4×D4C2×D7111yescharacteristic
420C2×#117—711no—
421C2×#117—711no—
422C2×#117—711no—
423C2×#117—1421no—
424C22×C4⋊C4—711no—
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#435C2×D7118yescomplemented
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⋊C8C2×D7111yescharacteristic
448C2×#102—711no—
449C2×#102—711no—
450C2×#102—711no—
451C2×#102—711no—
452C2×#102—711no—
453C2×#102—711no—
454C2×C22⋊C8C2×D7111yescharacteristic
455C2×C22⋊C8C2×D7111yescharacteristic
456C2×#97C2×D7111yescharacteristic
457C22×Q8—1421no—
458C22×D4—711no—
459C22×D4—711no—
460C22×D4—1421no—
461C22×D4—1421no—
462C22×D4—1421no—
463C22×D4—1421no—
464C22×D4D28411yescharacteristic
465C23×C4—1421no—
466C23×C4—1421no—
467C23×C4—1421no—
468C23×C4C22×D7111yescharacteristic
469C23×C4C22×D7111yescharacteristic
470C2×D8—714no—
471C2×D8—1424no—
472C2×M16—24no—
473C2×M16C22×D7114yes—
474C22×C8—24no—
475C22×C8C22×D7111yescharacteristic
476C22×C8C22×D7114yes—
477C22×C8C22×D7111yescharacteristic
478C22×C8C22×D7111yescharacteristic
479C22×C8C22×D7111yescharacteristic
480C4⋊Q8—714no—
481C4⋊Q8—1422no—
482#126—1428no—
483#125—714no—
484#125—1422no—
485#124—1428no—
486#124—1428no—
487#123—1428no—
488#121—714no—
489#121—714no—
490#121—714no—
491#121—714no—
492#121—1428no—
493#121—1428no—
494#121—1422no—
495#121—1422no—
496#121—1422no—
497#121—1422no—
498C4×D4—714no—
499C4×D4—714no—
500C4×D4—1428no—
501C4×D4—1422no—
502C4×D4—1422no—
503C4×D4D28414yes—
504C4×D4C22×D7114yes—
505#117—714no—
506#117—714no—
507#117—714no—
508#117—1422no—
509#117—1422no—
510#117—1422no—
511#117—1428no—
512C2×C4⋊C4—711no—
513C2×C4⋊C4—711no—
514C2×C4⋊C4—714no—
515C2×C4⋊C4—711no—
516C2×C4⋊C4—711no—
517C2×C4⋊C4—711no—
518C2×C4⋊C4—711no—
519C2×C4⋊C4—1421no—
520C2×C4⋊C4—1422no—
521C2×C4⋊C4—1421no—
522C2×C4⋊C4—1421no—
523C2×C4⋊C4—1421no—
524C2×C4⋊C4D28411yescharacteristic
525C2×C22⋊C4—1421no—
526C2×C22⋊C4—1421no—
527C2×C22⋊C4—1421no—
528C2×C22⋊C4—1421no—
529C2×C22⋊C4—1421no—
530C2×C22⋊C4—1421no—
531C2×C22⋊C4—1421no—
532C2×C22⋊C4—1421no—
533C2×C22⋊C4—1421no—
534C2×C22⋊C4D28411yescharacteristic
535C2×C22⋊C4D28411yescharacteristic
536C2×C42—1421no—
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⋊C8C22×D7114yes—
550#102—714no—
551#102—714no—
552#102—714no—
553#102—714no—
554#102—714no—
555#102—714no—
556C22⋊C8C22×D7114yes—
557C22⋊C8C22×D7114yes—
558#97C22×D7114yes—
559C24—1421no—
560C24—1421no—
561C24C2×D28411yescharacteristic
562C24C2×D28411yescharacteristic
563C2×Q8—5682no—
564C2×Q8—1424no—
565C2×D4—42no—
566C2×D4—2844no—
567C2×D4—5682no—
568C2×D4—5682no—
569C2×D4—5682no—
570C2×D4—712no—
571C2×D4—712no—
572C2×D4—1424no—
573C2×D4—1424no—
574C2×D4—1424no—
575C2×D4—1424no—
576C2×D4—1421no—
577C2×D4—1421no—
578C2×D4—1422no—
579C2×D4—1422no—
580C2×D4—1422no—
581C2×D4—1422no—
582C2×D4C2×D28414yes—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—2844no—
588C22×C4—5682no—
589C22×C4—5682no—
590C22×C4—1421no—
591C22×C4—1421no—
592C22×C4—1421no—
593C22×C4—1421no—
594C22×C4—1421no—
595C22×C4—1421no—
596C22×C4—1424no—
597C22×C4—1424no—
598C22×C4—1424no—
599C22×C4C2×D28412yes—
600C22×C4C2×D28412yes—
601C22×C4C2×D28411yescharacteristic
602C22×C4C2×D28411yescharacteristic
603C22×C4C2×D28411yescharacteristic
604C22×C4C2×D28411yescharacteristic
605C22×C4C23×D7112yes—
606C22×C4C23×D7112yes—
607C22×C4C23×D7111yescharacteristic
608D8—1428no—
609M16—28no—
610C2×C8—22no—
611C2×C8—22no—
612C2×C8—22no—
613C2×C8—28no—
614C2×C8#1176586414yes—
615C2×C8C23×D7112yes—
616C2×C8C23×D7112yes—
617C2×C8C23×D7112yes—
618C2×C8C23×D7112yes—
619C4⋊C4—712no—
620C4⋊C4—712no—
621C4⋊C4—712no—
622C4⋊C4—712no—
623C4⋊C4—712no—
624C4⋊C4—712no—
625C4⋊C4—1424no—
626C4⋊C4—1424no—
627C4⋊C4—1421no—
628C4⋊C4—1421no—
629C4⋊C4—1424no—
630C4⋊C4—1421no—
631C4⋊C4—1421no—
632C4⋊C4—1421no—
633C4⋊C4—1421no—
634C4⋊C4—1424no—
635C4⋊C4C2×D28414yes—
636C22⋊C4—1424no—
637C22⋊C4—1424no—
638C22⋊C4—1424no—
639C22⋊C4—1424no—
640C22⋊C4—1424no—
641C22⋊C4—1424no—
642C22⋊C4—1424no—
643C22⋊C4—1424no—
644C22⋊C4—1424no—
645C22⋊C4C2×D28414yes—
646C22⋊C4C2×D28414yes—
647C42—1424no—
648C42—1424no—
649C42—1424no—
650C42C2×D28412yes—
651C42C23×D7112yes—
652C23—22no—
653C23—22no—
654C23—22no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—2842no—
659C23—2842no—
660C23—2842no—
661C23—2842no—
662C23—2842no—
663C23—2842no—
664C23—1422no—
665C23—1422no—
666C23C22×D28412yes—
667C23C22×D28412yes—
668C23C22×D28411yescharacteristic
669Q8—5684no—
670D4—44no—
671D4—2848no—
672D4—2842no—
673D4—2842no—
674D4—5684no—
675D4—5684no—
676D4—5684no—
677D4—1422no—
678D4—1422no—
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—2848no—
692C2×C4—2842no—
693C2×C4—2842no—
694C2×C4—2842no—
695C2×C4—2842no—
696C2×C4—2842no—
697C2×C4—2842no—
698C2×C4—5684no—
699C2×C4—5684no—
700C2×C4—1422no—
701C2×C4—1422no—
702C2×C4—1422no—
703C2×C4—1422no—
704C2×C4—1422no—
705C2×C4—1422no—
706C2×C4C22×D28412yes—
707C2×C4C22×D28412yes—
708C2×C4C22×D28412yes—
709C2×C4C22×D28412yes—
710C2×C4C22×D28411yescharacteristic
711C2×C4C2×#1176586412yes—
712C2×C4#1455617512yes—
713C2×C4C24×D7111yescharacteristic
714C8—22no—
715C8—22no—
716C8—22no—
717C8C2×#1176586414yes—
718C22—22no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—22no—
723C22—22no—
724C22—44no—
725C22—44no—
726C22—2842no—
727C22—2842no—
728C22—2842no—
729C22—2842no—
730C22—2842no—
731C22—2842no—
732C22—5684no—
733C22—5684no—
734C22#1798665312yes—
735C22#1798679912yes—
736C22#1798680412yes—
737C22C23×D28411yescharacteristic
738C4—22no—
739C4—22no—
740C4—22no—
741C4—22no—
742C4—2842no—
743C4—2842no—
744C4—2842no—
745C4—2842no—
746C4—2842no—
747C4—2842no—
748C4#1798665312yes—
749C4C22×#1176586411yescharacteristic
750C4C2×#1455617511yescharacteristic
751C2—42no—
752C2—42no—
753C2—5682no—
754C2—5682no—
755C2#2260084214yesdirect product factor
756C2C2×#1798665311yescharacteristic
757C2C2×#1798679911yescharacteristic
758C2C2×#1798680411yescharacteristic
subgroupG/H
centerC23C22×D284
commutator, cosocleC2×C4×C71C25
FrattiniC2×C4C24×D71
FittingC2×#435×C71C2
socleC23×C71C22×D4
hypercenterC2×#435D71
hypocenterC71C2×#3347
LCSG ▷ C2×C4×C71 ▷ C2×C71 ▷ C71
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C2×#17986714C2semidirect
2. C2×#17986695C2semidirect
3. #22600842C2direct (N × H)
4. C2×#17986408C2semidirect
5. C2×#17986324C2semidirect
6. C2×#17986324C2semidirect
7. C2×#17986324C2semidirect
8. C2×#17986313C2semidirect
9. C2×#17986300C2semidirect
10. C2×#17986280C2semidirect
11. C2×#17986252C2semidirect
12. C2×#17986235C2semidirect
13. C2×#17986112C2semidirect
14. C2×#17986041C2semidirect
15. C2×#17986037C2semidirect
16. C2×#435×C71C2semidirect
19. #17986714C22semidirect
21. #17986695C22semidirect
42. #17986408C22semidirect
43. #17986324C22semidirect
44. #17986324C22semidirect
45. #17986324C22semidirect
46. #17986313C22semidirect
47. #17986300C22semidirect
48. #17986280C22semidirect
49. #17986252C22semidirect
50. #17986235C22semidirect
51. #17986112C22semidirect
52. #17986041C22semidirect
53. #17986037C22semidirect
72. #435×C71C22semidirect
374. C2×C71#3347semidirect
393. C2×#435D71semidirect
396. C71C2×#3347semidirect
435. #435C2×D71semidirect
755. C2#22600842direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#179867142
C2×#179866952
#226008422
C2×#179864082
C2×#179863242
C2×#179863132
C2×#179863002
C2×#179862802
C2×#179862522
C2×#179862352
C2×#179861122
C2×#179860412
C2×#179860372
C2×#435×C712
C2×#334771