Finite Group Databasebeta

← C2×#19147657 #25977599

Subgroups — C2×#19147657 #25977599

Order 11008.

2002 conjugacy classes of subgroups.

The subgroup lattice has 780 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583632C211yesmaximal, characteristic, complemented
2C2×#14583621C211yesmaximal, characteristic, complemented
3#19147657C2116yesmaximal, direct product factor
4C2×#14583290C211yesmaximal, characteristic, complemented
5C2×#14583285C211yesmaximal, characteristic
6C2×#14583283C211yesmaximal, characteristic, complemented
7C2×#14583124C211yesmaximal, characteristic, complemented
8C2×#14583121C211yesmaximal, characteristic, complemented
9C2×#14583098C211yesmaximal, characteristic, complemented
10C2×#14583114C211yesmaximal, characteristic, complemented
11C2×#14583113C211yesmaximal, characteristic, complemented
12C2×#14583103C211yesmaximal, characteristic, complemented
13C2×#14583029C211yesmaximal, characteristic, complemented
14C2×#14583010C211yesmaximal, characteristic, complemented
15C2×#14583005C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C43C211yesmaximal, characteristic, complemented
17C22×Dic172C2211yescharacteristic
18C22×#10621885C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621884C2211yescharacteristic
23C22×D344C2211yescharacteristic
24C22×#10621882C2211yescharacteristic
25#14583632—24no—
26#14583632C2218yescomplemented
27#14583621—24no—
28#14583621C2218yescomplemented
29C2×#13063323C2211yescharacteristic
30C2×#13063321C2211yescharacteristic
31C2×#13063320—21no—
32C2×#13063319—21no—
33C2×#13063314C2211yescharacteristic
34C2×#13063313C2211yescharacteristic
35C2×#13063313C2211yescharacteristic
36C2×#13063312C2211yescharacteristic
37C2×#13063311—21no—
38C2×#13063308—21no—
39C2×#13063307—21no—
40C2×#13063303—21no—
41C2×C4×Dic86C2211yescharacteristic
42C2×#13063290C2211yescharacteristic
43C2×#13063290C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063287C2211yescharacteristic
46C2×C4×C22⋊D43—21no—
47C2×#13063282—21no—
48#14583290C2218yescomplemented
49#14583285C2218yes—
50#14583283C2218yescomplemented
51#14583124C2218yescomplemented
52#14583121C2218yescomplemented
53#14583114C2218yescomplemented
54#14583113C2218yescomplemented
55#14583103C2218yescomplemented
56#14583098C2218yescomplemented
57#14583029C2218yescomplemented
58#14583010C2218yescomplemented
59#14583005C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C22×SD16×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C4×SD16×C43C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86D411yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C22×C4×D43—21no—
85C22×C4×D43—21no—
86C2×Dic172—24no—
87C2×Dic172C2314yes—
88C2×#10621885—42no—
89C2×#10621885C2314yes—
90C2×#10621873—42no—
91C2×#10621873—42no—
92C2×#10621873C2314yes—
93C2×#10621873C2314yes—
94C2×#10621883—42no—
95C2×#10621883C2314yes—
96C2×#10621884—42no—
97C2×#10621884C2314yes—
98C2×D344—24no—
99C2×D344C2314yes—
100C2×#10621882—42no—
101C2×#10621882C2314yes—
102C22×C43⋊C8C2311yescharacteristic
103C22×C43⋊C8C2311yescharacteristic
104#13063323—22no—
105#13063323C2314yes—
106#13063321—22no—
107#13063321C2314yes—
108#13063320—28no—
109#13063319—28no—
110#13063314—22no—
111#13063314C2314yes—
112#13063313—22no—
113#13063313—22no—
114#13063313C2314yes—
115#13063313C2314yes—
116#13063312—22no—
117#13063312C2314yes—
118#13063311—28no—
119#13063308—28no—
120#13063307—28no—
121#13063303—28no—
122C4×Dic86D414yes—
123C4×Dic86C2314yes—
124#13063290—22no—
125#13063290—22no—
126#13063290C2314yes—
127#13063290C2314yes—
128#13063287—22no—
129#13063287—22no—
130#13063287C2314yes—
131#13063287C2314yes—
132C4×C22⋊D43—28no—
133#13063282—28no—
134C2×C4⋊Dic43D411yescharacteristic
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4D411yescharacteristic
140C2×Dic43⋊C4D411yescharacteristic
141C2×C22⋊Dic43—21no—
142C2×C22⋊Dic43—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4—21no—
145C2×(C2×D43)⋊C4—21no—
146C2×(C2×D43)⋊C4—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×(C2×D43)⋊C4—21no—
151C2×C4×Dic43—21no—
152C2×C4×Dic43—21no—
153C2×C4×Dic43C2311yescharacteristic
154C2×C4×Dic43C2311yescharacteristic
155C4⋊(C43⋊C8)C2314yes—
156Dic43⋊C8C2314yes—
157Dic43⋊C8C2314yes—
158#13063248C2314yes—
159#13063248C2314yes—
160#13063245C2314yes—
161#13063245C2314yes—
162#13063235C2314yes—
163#13063235C2314yes—
164C22×Q8×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43—21no—
167C2×SD16×C43—24no—
168C2×SD16×C43C2314yes—
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C4×Q8×C43—22no—
172C4×Q8×C43C2314yes—
173C4×D4×C43—22no—
174C4×D4×C43C2314yes—
175C2×C4⋊C4×C43—21no—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C42×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#106×C43C2314yes—
182#103×C43C2314yes—
183#102×C43C2314yes—
184C4×C8×C43C2314yes—
185C24×C43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C2×Q8×C43—21no—
189C2×Q8×C43—22no—
190C2×Q8×C43—22no—
191C2×Q8×C43C2412yes—
192C2×D4×C43—21no—
193C2×D4×C43—22no—
194C2×D4×C43—22no—
195C2×D4×C43C2412yes—
196C22×C4×C43—24no—
197C22×C4×C43—21no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—82no—
201C22×C4×C43C2×D411yescharacteristic
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2411yescharacteristic
204C2×C22⋊D43—24no—
205C2×C22⋊D43—24no—
206C2×C22⋊D43—44no—
207C2×C22⋊D43—82no—
208C22×Dic43—21no—
209C22×Dic43—21no—
210C22×Dic43C2×D411yescharacteristic
211C22×Dic43C2×D411yescharacteristic
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C2×D172—21no—
215C2×D172—21no—
216C2×D172—22no—
217C2×D172—22no—
218C2×D172—22no—
219C2×D172—22no—
220C2×D172C2412yes—
221C2×D172C2412yes—
222C2×C4×D43—24no—
223C2×C4×D43—24no—
224C2×C4×D43—44no—
225C2×C4×D43—82no—
226C2×Dic86—22no—
227C2×Dic86—22no—
228C2×Dic86—22no—
229C2×Dic86—22no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—42no—
233C2×Dic86C2×D414yes—
234C2×Dic86C2412yes—
235C2×Dic86C2412yes—
236SD16×C43—28no—
237C2×C8×C43—22no—
238C2×C8×C43#4114yes—
239C2×C8×C43C2412yes—
240C2×C8×C43C2412yes—
241C4⋊C4×C43—24no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43C2412yes—
245C4⋊C4×C43C2412yes—
246C22⋊C4×C43—24no—
247C42×C43—24no—
248C42×C43C2×D412yes—
249C42×C43C2412yes—
250C22⋊Dic43—24no—
251C22⋊Dic43—24no—
252#10621885—44no—
253#10621884—44no—
254#10621883—44no—
255#10621882—44no—
256(C2×D43)⋊C4—24no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262(C2×D43)⋊C4—24no—
263(C2×D43)⋊C4—24no—
264C4⋊Dic43C2×D414yes—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4—24no—
269Dic43⋊C4C2×D414yes—
270Dic43⋊C4C2×D414yes—
271C4×Dic43—24no—
272C4×Dic43—24no—
273C4×Dic43C2×D412yes—
274C4×Dic43C2×D412yes—
275C4×Dic43C2412yes—
276C4×Dic43C2412yes—
277C2×C43⋊C8—22no—
278C2×C43⋊C8—22no—
279C2×C43⋊C8C2412yes—
280C2×C43⋊C8C2412yes—
281Dic172—28no—
282D344—28no—
283#10621873—44no—
284#10621873—44no—
285C23×C43—22no—
286C23×C43—42no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43C22×D411yescharacteristic
290C22×D43—22no—
291C22×D43—22no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—42no—
297C22×D43—42no—
298Q8×C43—22no—
299Q8×C43—22no—
300Q8×C43—42no—
301D4×C43—22no—
302D4×C43—22no—
303D4×C43—42no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—42no—
312C2×C4×C43—84no—
313C2×C4×C43C22×D412yes—
314C2×C4×C43C22×D412yes—
315C2×C4×C43C22×D411yescharacteristic
316C2×C4×C43C2×#4112yes—
317C2×C4×C43H(5,𝔽2)12yes—
318C2×C4×C43C2511yescharacteristic
319C22⋊D43—48no—
320C22⋊D43—84no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—42no—
328C2×Dic43—42no—
329C2×Dic43C22×D412yes—
330C2×Dic43C22×D412yes—
331C2×Dic43C22×D412yes—
332C2×Dic43C22×D412yes—
333D172—22no—
334D172—22no—
335D172—22no—
336D172—22no—
337D172—42no—
338D172—42no—
339C4×D43—48no—
340C4×D43—84no—
341Dic86—22no—
342Dic86—22no—
343Dic86—22no—
344Dic86—22no—
345Dic86—44no—
346Dic86—42no—
347Dic86—42no—
348C8×C43—22no—
349C8×C43C2×#4114yes—
350C43⋊C8—22no—
351C43⋊C8—22no—
352C2×#3401—431nomaximal, Sylow
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—84no—
357C22×C43#55012yes—
358C22×C43#57512yes—
359C22×C43#57712yes—
360C22×C43C23×D411yescharacteristic
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—84no—
368C2×D43—84no—
369C4×C43—22no—
370C4×C43—22no—
371C4×C43—42no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43#55012yes—
375C4×C43C22×#4111yescharacteristic
376C4×C43C2×H(5,𝔽2)11yescharacteristic
377Dic43—22no—
378Dic43—22no—
379Dic43—22no—
380Dic43—22no—
381Dic43—42no—
382Dic43—42no—
383C2×#559—431no—
384C2×#556—431no—
385#3401—4316no—
386C2×#497—431no—
387C2×#496—431no—
388C2×#495—431no—
389C2×#464—431no—
390C2×#464—431no—
391C2×#460—431no—
392C2×#463—431no—
393C2×#463—431no—
394C2×#461—431no—
395C2×#446—431no—
396C2×#442—431no—
397C2×#441—431no—
398C2×C4×SD16D4311yescharacteristic, complemented
399C2×C43—82no—
400C2×C43#340114yescomplemented
401C2×C43C2×#55011yescharacteristic
402C2×C43C2×#57511yescharacteristic
403C2×C43C2×#57711yescharacteristic
404D43—82no—
405D43—82no—
406C22×Q16—431no—
407C22×Q16—431no—
408C22×SD16—431no—
409C22×SD16—431no—
410C22×SD16—431no—
411C22×SD16—431no—
412C22×SD16C2×D4311yescharacteristic
413C22×D8—431no—
414C22×D8—431no—
415#559—438no—
416#559—864no—
417#556—438no—
418#556—864no—
419C2×C4⋊Q8—431no—
420C2×#127—431no—
421C2×#126—861no—
422C2×#126—861no—
423C2×#124—431no—
424C2×#124—431no—
425C2×#124—431no—
426C2×#124—431no—
427C2×#124—861no—
428C2×#123—861no—
429C2×#123—861no—
430C2×C22⋊Q8—861no—
431C2×C4×Q8—431no—
432C2×C4×Q8—431no—
433C2×C4×Q8—431no—
434C2×C4×Q8C2×D4311yescharacteristic
435C2×C4×D4—431no—
436C2×C4×D4—431no—
437C2×C4×D4—861no—
438C2×C4×D4C2×D4311yescharacteristic
439C2×#117—861no—
440#497—438no—
441#496—438no—
442#495—438no—
443#464—438no—
444#464—438no—
445#463—438no—
446#463—438no—
447#461—438no—
448#460—438no—
449#446—438no—
450#442—438no—
451#441—438no—
452C4×SD16C2×D4318yescomplemented
453C2×#106C2×D4311yescharacteristic
454C2×C4⋊C8—431no—
455C2×C4⋊C8—431no—
456C2×C4⋊C8—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103C2×D4311yescharacteristic
460C2×#102—431no—
461C2×#102—431no—
462C2×#102C2×D4311yescharacteristic
463C2×#97—431no—
464C2×#97—431no—
465C2×C4×C8C2×D4311yescharacteristic
466C43C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—431no—
468C22×Q8—431no—
469C22×Q8—431no—
470C22×Q8C22×D4311yescharacteristic
471C22×D4—431no—
472C22×D4—431no—
473C22×D4—861no—
474C22×D4—861no—
475C22×D4C22×D4311yescharacteristic
476C23×C4—21no—
477C23×C4—861no—
478C23×C4—861no—
479C2×Q16—434no—
480C2×Q16—434no—
481C2×Q16—864no—
482C2×Q16—1722no—
483C2×SD16—24no—
484C2×SD16—434no—
485C2×SD16—434no—
486C2×SD16—434no—
487C2×SD16—434no—
488C2×SD16—1722no—
489C2×SD16—1722no—
490C2×SD16—1722no—
491C2×SD16—1722no—
492C2×SD16C22×D4314yes—
493C2×D8—434no—
494C2×D8—434no—
495C2×D8—864no—
496C2×D8—1722no—
497C22×C8—431no—
498C22×C8—431no—
499C22×C8C22×D4311yescharacteristic
500C22×C8C22×D4311yescharacteristic
501C4⋊Q8—434no—
502C4⋊Q8—862no—
503#127—434no—
504#127—862no—
505#126—868no—
506#126—868no—
507#124—434no—
508#124—434no—
509#124—434no—
510#124—434no—
511#124—862no—
512#124—862no—
513#124—868no—
514#124—862no—
515#124—862no—
516#123—868no—
517#123—868no—
518C22⋊Q8—868no—
519C4×Q8—22no—
520C4×Q8—434no—
521C4×Q8—434no—
522C4×Q8—434no—
523C4×Q8—434no—
524C4×Q8—862no—
525C4×Q8—862no—
526C4×Q8C22×D4314yes—
527C4×D4—22no—
528C4×D4—434no—
529C4×D4—434no—
530C4×D4—862no—
531C4×D4—862no—
532C4×D4—868no—
533C4×D4C22×D4314yes—
534#117—868no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—431no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4—861no—
543C2×C4⋊C4C22×D4311yescharacteristic
544C2×C4⋊C4C22×D4311yescharacteristic
545C2×C22⋊C4—21no—
546C2×C22⋊C4—861no—
547C2×C22⋊C4—861no—
548C2×C22⋊C4—861no—
549C2×C22⋊C4—861no—
550C2×C22⋊C4—861no—
551C2×C22⋊C4—861no—
552C2×C22⋊C4—861no—
553C2×C22⋊C4—861no—
554C2×C22⋊C4—861no—
555C2×C22⋊C4—861no—
556C2×C42—21no—
557C2×C42—431no—
558C2×C42—431no—
559C2×C42—861no—
560C2×C42—861no—
561C2×C42C22×D4311yescharacteristic
562#106C22×D4314yes—
563C4⋊C8—434no—
564C4⋊C8—434no—
565C4⋊C8—434no—
566#103—434no—
567#103—434no—
568#103C22×D4314yes—
569#102—434no—
570#102—434no—
571#102C22×D4314yes—
572#97—434no—
573#97—434no—
574C4×C8C22×D4314yes—
575C24—21no—
576C24—861no—
577C24—861no—
578C2×Q8—21no—
579C2×Q8—22no—
580C2×Q8—22no—
581C2×Q8—434no—
582C2×Q8—432no—
583C2×Q8—432no—
584C2×Q8—861no—
585C2×Q8—861no—
586C2×Q8—862no—
587C2×Q8—862no—
588C2×Q8—862no—
589C2×Q8—862no—
590C2×Q8—1722no—
591C2×Q8C23×D4312yes—
592C2×D4—21no—
593C2×D4—22no—
594C2×D4—22no—
595C2×D4—432no—
596C2×D4—432no—
597C2×D4—864no—
598C2×D4—864no—
599C2×D4—861no—
600C2×D4—861no—
601C2×D4—862no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—3442no—
606C2×D4—1724no—
607C2×D4C23×D4312yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—24no—
612C22×C4—82no—
613C22×C4—431no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—864no—
618C22×C4—864no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—3442no—
622C22×C4—1724no—
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4C23×D4311yescharacteristic
626Q16—868no—
627Q16—1724no—
628SD16—28no—
629SD16—1724no—
630SD16—1724no—
631SD16—1724no—
632SD16—1724no—
633D8—868no—
634D8—1724no—
635C2×C8—22no—
636C2×C8—432no—
637C2×C8—432no—
638C2×C8—862no—
639C2×C8—862no—
640C2×C8#1062189814yes—
641C2×C8C23×D4312yes—
642C2×C8C23×D4312yes—
643C4⋊C4—24no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—434no—
647C4⋊C4—434no—
648C4⋊C4—434no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4—864no—
653C4⋊C4C23×D4312yes—
654C4⋊C4C23×D4312yes—
655C22⋊C4—24no—
656C22⋊C4—864no—
657C22⋊C4—864no—
658C22⋊C4—864no—
659C22⋊C4—864no—
660C22⋊C4—864no—
661C22⋊C4—864no—
662C22⋊C4—864no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C22⋊C4—864no—
666C42—24no—
667C42—432no—
668C42—432no—
669C42—432no—
670C42—432no—
671C42—864no—
672C42—864no—
673C42D4×D4312yes—
674C42C23×D4312yes—
675C23—22no—
676C23—42no—
677C23—42no—
678C23—42no—
679C23—862no—
680C23—862no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23—1722no—
687C23C2×D4×D4311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—862no—
692Q8—862no—
693Q8—862no—
694Q8—862no—
695Q8—1724no—
696Q8—1722no—
697Q8—1722no—
698D4—22no—
699D4—22no—
700D4—42no—
701D4—862no—
702D4—862no—
703D4—862no—
704D4—862no—
705D4—3444no—
706D4—1728no—
707D4—1722no—
708D4—1722no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—84no—
718C2×C4—432no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—432no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—3444no—
729C2×C4—1728no—
730C2×C4—1722no—
731C2×C4—1722no—
732C2×C4C2×D4×D4312yes—
733C2×C4C2×D4×D4312yes—
734C2×C4C2×D4×D4311yescharacteristic
735C2×C4C2×#1062189812yes—
736C2×C4#1306337112yes—
737C2×C4C24×D4311yescharacteristic
738C8—22no—
739C8—862no—
740C8—862no—
741C8C2×#1062189814yes—
742C22—42no—
743C22—42no—
744C22—42no—
745C22—84no—
746C22—3444no—
747C22—3444no—
748C22—1722no—
749C22—1722no—
750C22—1722no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22#1458357012yes—
755C22#1458369612yes—
756C22#1458370512yes—
757C22C22×D4×D4311yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—42no—
762C4—42no—
763C4—862no—
764C4—862no—
765C4—862no—
766C4—862no—
767C4—1722no—
768C4—1722no—
769C4#1458357012yes—
770C4C22×#1062189811yescharacteristic
771C4C2×#1306337111yescharacteristic
772C2—82no—
773C2—3442no—
774C2—3442no—
775C2#1914765714yesdirect product factor
776C2C2×#1458357011yescharacteristic
777C2C2×#1458369611yescharacteristic
778C2C2×#1458370511yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C4×SD16×C43C2
socleC23×C43C22×D4
prime radicalC2×#14583285C2
hypercenterC2×C4×SD16D43
hypocenterC43C2×#3401
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
1. C2×#14583632C2semidirect
2. C2×#14583621C2semidirect
3. #19147657C2direct (N × H)
4. C2×#14583290C2semidirect
6. C2×#14583283C2semidirect
7. C2×#14583124C2semidirect
8. C2×#14583121C2semidirect
9. C2×#14583098C2semidirect
10. C2×#14583114C2semidirect
11. C2×#14583113C2semidirect
12. C2×#14583103C2semidirect
13. C2×#14583029C2semidirect
14. C2×#14583010C2semidirect
15. C2×#14583005C2semidirect
16. C2×C4×SD16×C43C2semidirect
26. #14583632C22semidirect
28. #14583621C22semidirect
48. #14583290C22semidirect
50. #14583283C22semidirect
51. #14583124C22semidirect
52. #14583121C22semidirect
53. #14583114C22semidirect
54. #14583113C22semidirect
55. #14583103C22semidirect
56. #14583098C22semidirect
57. #14583029C22semidirect
58. #14583010C22semidirect
59. #14583005C22semidirect
72. C4×SD16×C43C22semidirect
398. C2×C4×SD16D43semidirect
400. C2×C43#3401semidirect
452. C4×SD16C2×D43semidirect
466. C43C2×#3401semidirect
775. C2#19147657direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836322
C2×#145836212
#191476572
C2×#145832902
C2×#145832852
C2×#145832832
C2×#145831242
C2×#145831212
C2×#145830982
C2×#145831142
C2×#145831132
C2×#145831032
C2×#145830292
C2×#145830102
C2×#145830052
C2×C4×SD16×C432
C2×#340143