Finite Group Databasebeta

← C2×#19147663 #25977605

Subgroups — C2×#19147663 #25977605

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×#14583634C211yesmaximal, characteristic, complemented
2C2×#14583622C211yesmaximal, characteristic, complemented
3#19147663C2116yesmaximal, direct product factor
4C2×#14583293C211yesmaximal, characteristic, complemented
5C2×#14583288C211yesmaximal, characteristic
6C2×#14583283C211yesmaximal, characteristic, complemented
7C2×#14583122C211yesmaximal, characteristic, complemented
8C2×#14583122C211yesmaximal, characteristic, complemented
9C2×#14583100C211yesmaximal, characteristic, complemented
10C2×#14583115C211yesmaximal, characteristic, complemented
11C2×#14583115C211yesmaximal, characteristic, complemented
12C2×#14583105C211yesmaximal, characteristic, complemented
13C2×#14583012C211yesmaximal, characteristic, complemented
14C2×#14583007C211yesmaximal, characteristic, complemented
15C2×C4×#10621873C211yesmaximal, characteristic, complemented
16C2×C43×#446C211yesmaximal, characteristic, complemented
17C22×Dic172C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621873C2211yescharacteristic
22C22×#10621873C2211yescharacteristic
23C22×#10621873C2211yescharacteristic
24C22×D344C2211yescharacteristic
25C22×D344C2211yescharacteristic
26#14583634—24no—
27#14583634C2218yescomplemented
28#14583622—24no—
29#14583622C2218yescomplemented
30C2×#13063325C2211yescharacteristic
31C2×#13063322C2211yescharacteristic
32C2×#13063320—21no—
33C2×#13063320—21no—
34C2×#13063314—21no—
35C2×#13063313C2211yescharacteristic
36C2×#13063313C2211yescharacteristic
37C2×#13063313C2211yescharacteristic
38C2×#13063313C2211yescharacteristic
39C2×#13063310—21no—
40C2×#13063310—21no—
41C2×#13063301—21no—
42C2×C4×Dic86C2211yescharacteristic
43C2×C4×Dic86C2211yescharacteristic
44C2×C4×Dic86C2211yescharacteristic
45C2×C4×D172C2211yescharacteristic
46C2×C4×D172C2211yescharacteristic
47C2×C4×D172C2211yescharacteristic
48C2×#13063287—21no—
49C2×#13063283—21no—
50#14583293C2218yescomplemented
51#14583288C2218yes—
52#14583283C2218yescomplemented
53#14583122C2218yescomplemented
54#14583122C2218yescomplemented
55#14583115C2218yescomplemented
56#14583115C2218yescomplemented
57#14583105C2218yescomplemented
58#14583100C2218yescomplemented
59#14583012C2218yescomplemented
60#14583007C2218yescomplemented
61C4×#10621873C2218yescomplemented
62C2×#13063257C2211yescharacteristic
63C2×#13063250C2211yescharacteristic
64C2×#13063250C2211yescharacteristic
65C2×#13063250C2211yescharacteristic
66C2×#13063247C2211yescharacteristic
67C2×#13063247C2211yescharacteristic
68C2×#13063247C2211yescharacteristic
69C2×C4×Q8×C43C2211yescharacteristic
70C43×#446C2218yescomplemented
71C2×C4⋊C8×C43C2211yescharacteristic
72C2×C4⋊C8×C43C2211yescharacteristic
73C2×C4⋊C8×C43C2211yescharacteristic
74C2×#97×C43C2211yescharacteristic
75C2×#97×C43C2211yescharacteristic
76C2×C4×C8×C43C2211yescharacteristic
77C22×Dic86C2311yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×D172—21no—
81C22×D172—21no—
82C22×D172C2311yescharacteristic
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×C4×D43—21no—
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C2×Dic172—24no—
89C2×Dic172—42no—
90C2×Dic172C2314yes—
91C2×Dic172C2314yes—
92C2×#10621873—24no—
93C2×#10621873—42no—
94C2×#10621873—42no—
95C2×#10621873—42no—
96C2×#10621873—42no—
97C2×#10621873C2314yes—
98C2×#10621873C2314yes—
99C2×#10621873C2314yes—
100C2×#10621873C2314yes—
101C2×#10621873C2314yes—
102C2×D344—24no—
103C2×D344—42no—
104C2×D344C2314yes—
105C2×D344C2314yes—
106#13063325—22no—
107#13063325C2314yes—
108#13063322—22no—
109#13063322C2314yes—
110#13063320—28no—
111#13063320—28no—
112#13063314—28no—
113#13063313—22no—
114#13063313—22no—
115#13063313—22no—
116#13063313—22no—
117#13063313C2314yes—
118#13063313C2314yes—
119#13063313C2314yes—
120#13063313C2314yes—
121#13063310—28no—
122#13063310—28no—
123#13063301—28no—
124C4×Dic86—22no—
125C4×Dic86—22no—
126C4×Dic86—22no—
127C4×Dic86C2314yes—
128C4×Dic86C2314yes—
129C4×Dic86C2314yes—
130C4×D172—22no—
131C4×D172—22no—
132C4×D172—22no—
133C4×D172C2314yes—
134C4×D172C2314yes—
135C4×D172C2314yes—
136#13063287—28no—
137#13063283—28no—
138C2×C4⋊Dic43—21no—
139C2×C4⋊Dic43—21no—
140C2×C4⋊Dic43C2311yescharacteristic
141C2×C4⋊Dic43C2311yescharacteristic
142C2×Dic43⋊C4—21no—
143C2×Dic43⋊C4—21no—
144C2×Dic43⋊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×(C2×D43)⋊C4—21no—
152C2×(C2×D43)⋊C4—21no—
153C2×(C2×D43)⋊C4—21no—
154C2×(C2×D43)⋊C4—21no—
155C2×(C2×D43)⋊C4—21no—
156C2×C4×Dic43—21no—
157C2×C4×Dic43—21no—
158C2×C4×Dic43—21no—
159#13063257C2314yes—
160#13063250C2314yes—
161#13063250C2314yes—
162#13063250C2314yes—
163#13063247C2314yes—
164#13063247C2314yes—
165#13063247C2314yes—
166C22×Q8×C43D411yescharacteristic
167C22×C8×C43C2311yescharacteristic
168C22×C8×C43C2311yescharacteristic
169C22×C8×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C4×Q8×C43D414yes—
172C4×Q8×C43C2314yes—
173C2×C4⋊C4×C43D411yescharacteristic
174C2×C4⋊C4×C43D411yescharacteristic
175C2×C4⋊C4×C43D411yescharacteristic
176C2×C42×C43C2311yescharacteristic
177C2×C42×C43C2311yescharacteristic
178C2×C42×C43C2311yescharacteristic
179C4⋊C8×C43C2314yes—
180C4⋊C8×C43C2314yes—
181C4⋊C8×C43C2314yes—
182#97×C43C2314yes—
183#97×C43C2314yes—
184C4×C8×C43C2314yes—
185C23×D43—21no—
186C23×D43—21no—
187C23×D43—21no—
188C2×Q8×C43—42no—
189C2×Q8×C43C2×D414yes—
190C22×C4×C43C2×D411yescharacteristic
191C22×C4×C43C2×D411yescharacteristic
192C22×C4×C43C2×D411yescharacteristic
193C22×C4×C43C2×D411yescharacteristic
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C22×Dic43—21no—
198C22×Dic43—21no—
199C22×Dic43—21no—
200C22×Dic43—21no—
201C22×Dic43—21no—
202C2×D172—24no—
203C2×D172—21no—
204C2×D172—21no—
205C2×D172—21no—
206C2×D172—24no—
207C2×D172—22no—
208C2×D172—22no—
209C2×D172—22no—
210C2×D172—22no—
211C2×D172—22no—
212C2×D172—22no—
213C2×D172—44no—
214C2×D172—82no—
215C2×D172C2412yes—
216C2×D172C2412yes—
217C2×D172C2412yes—
218C2×C4×D43—24no—
219C2×C4×D43—24no—
220C2×C4×D43—24no—
221C2×C4×D43—44no—
222C2×C4×D43—82no—
223C2×C4×D43—82no—
224C2×Dic86—22no—
225C2×Dic86—22no—
226C2×Dic86—22no—
227C2×Dic86—22no—
228C2×Dic86—22no—
229C2×Dic86—22no—
230C2×Dic86—21no—
231C2×Dic86—21no—
232C2×Dic86—21no—
233C2×Dic86C2412yes—
234C2×Dic86C2412yes—
235C2×Dic86C2412yes—
236C2×C8×C43—22no—
237C2×C8×C43—22no—
238C2×C8×C43—22no—
239C2×C8×C43#4114yes—
240C2×C8×C43C2412yes—
241C2×C8×C43C2412yes—
242C2×C8×C43C2412yes—
243C2×C8×C43C2412yes—
244C4⋊C4×C43C2×D414yes—
245C4⋊C4×C43C2×D414yes—
246C4⋊C4×C43C2×D414yes—
247C42×C43C2×D412yes—
248C42×C43C2×D412yes—
249C42×C43C2×D412yes—
250C42×C43C2412yes—
251C42×C43C2412yes—
252C42×C43C2412yes—
253(C2×D43)⋊C4—24no—
254(C2×D43)⋊C4—24no—
255(C2×D43)⋊C4—24no—
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⋊Dic43—24no—
265C4⋊Dic43—24no—
266C4⋊Dic43—21no—
267C4⋊Dic43—21no—
268C4⋊Dic43C2412yes—
269C4⋊Dic43C2412yes—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273C4×Dic43—24no—
274C4×Dic43—24no—
275C4×Dic43—24no—
276Dic172—28no—
277Dic172—44no—
278D344—28no—
279D344—44no—
280#10621873—28no—
281#10621873—44no—
282#10621873—44no—
283#10621873—44no—
284#10621873—44no—
285C23×C43C22×D411yescharacteristic
286C22×D43—22no—
287C22×D43—22no—
288C22×D43—22no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43—42no—
297C22×D43—42no—
298Q8×C43—44no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43C22×D412yes—
306C2×C4×C43C22×D412yes—
307C2×C4×C43C22×D412yes—
308C2×C4×C43C22×D412yes—
309C2×C4×C43C22×D412yes—
310C2×C4×C43C22×D412yes—
311C2×C4×C43C22×D411yescharacteristic
312C2×C4×C43C2×#4112yes—
313C2×C4×C43H(5,𝔽2)12yes—
314C2×C4×C43C2511yescharacteristic
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—42no—
321C2×Dic43—42no—
322C2×Dic43—42no—
323C2×Dic43—42no—
324C2×Dic43—42no—
325D172—22no—
326D172—22no—
327D172—22no—
328D172—22no—
329D172—22no—
330D172—22no—
331D172—48no—
332D172—42no—
333D172—42no—
334D172—42no—
335D172—84no—
336C4×D43—48no—
337C4×D43—84no—
338C4×D43—84no—
339Dic86—22no—
340Dic86—22no—
341Dic86—22no—
342Dic86—22no—
343Dic86—22no—
344Dic86—22no—
345Dic86—42no—
346Dic86—42no—
347Dic86—42no—
348C8×C43—22no—
349C8×C43—22no—
350C8×C43—22no—
351C8×C43C2×#4114yes—
352C2×#3401—431nomaximal, Sylow
353C22×C43#55012yes—
354C22×C43#57512yes—
355C22×C43#57712yes—
356C22×C43C23×D411yescharacteristic
357C2×D43—42no—
358C2×D43—42no—
359C2×D43—42no—
360C2×D43—42no—
361C2×D43—42no—
362C2×D43—42no—
363C2×D43—42no—
364C2×D43—42no—
365C2×D43—42no—
366C2×D43—84no—
367C2×D43—84no—
368C2×D43—84no—
369C4×C43—22no—
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—22no—
373C4×C43—22no—
374C4×C43—22no—
375C4×C43#55012yes—
376C4×C43C22×#4111yescharacteristic
377C4×C43C2×H(5,𝔽2)11yescharacteristic
378Dic43—42no—
379Dic43—42no—
380Dic43—42no—
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×#446D4311yescharacteristic, complemented
396C2×#442—431no—
397C2×#441—431no—
398C2×C4×SD16—431no—
399C2×C43#340114yescomplemented
400C2×C43C2×#55011yescharacteristic
401C2×C43C2×#57511yescharacteristic
402C2×C43C2×#57711yescharacteristic
403D43—82no—
404D43—82no—
405D43—82no—
406C22×Q16—431no—
407C22×Q16—431no—
408C22×SD16—431no—
409C22×SD16—431no—
410C22×SD16—431no—
411C22×SD16—431no—
412C22×SD16—431no—
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—431no—
438C2×C4×D4—861no—
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#446C2×D4318yescomplemented
450#442—438no—
451#441—438no—
452C4×SD16—438no—
453C2×#106—431no—
454C2×C4⋊C8C2×D4311yescharacteristic
455C2×C4⋊C8C2×D4311yescharacteristic
456C2×C4⋊C8C2×D4311yescharacteristic
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#102—431no—
461C2×#102—431no—
462C2×#102—431no—
463C2×#97C2×D4311yescharacteristic
464C2×#97C2×D4311yescharacteristic
465C2×C4×C8C2×D4311yescharacteristic
466C43C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—431no—
468C22×Q8—431no—
469C22×Q8—431no—
470C22×Q8D17211yescharacteristic
471C22×D4—431no—
472C22×D4—431no—
473C22×D4—431no—
474C22×D4—861no—
475C22×D4—861no—
476C23×C4—861no—
477C23×C4—861no—
478C23×C4—861no—
479C2×Q16—434no—
480C2×Q16—434no—
481C2×Q16—864no—
482C2×Q16—1722no—
483C2×SD16—434no—
484C2×SD16—434no—
485C2×SD16—434no—
486C2×SD16—434no—
487C2×SD16—434no—
488C2×SD16—864no—
489C2×SD16—1722no—
490C2×SD16—1722no—
491C2×SD16—1722no—
492C2×SD16—1722no—
493C2×D8—434no—
494C2×D8—434no—
495C2×D8—864no—
496C2×D8—1722no—
497C22×C8C22×D4311yescharacteristic
498C22×C8C22×D4311yescharacteristic
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—868no—
512#124—862no—
513#124—862no—
514#124—862no—
515#124—862no—
516#123—868no—
517#123—868no—
518C22⋊Q8—868no—
519C4×Q8—434no—
520C4×Q8—434no—
521C4×Q8—434no—
522C4×Q8—862no—
523C4×Q8—862no—
524C4×Q8—862no—
525C4×Q8D17214yes—
526C4×Q8C22×D4314yes—
527C4×D4—434no—
528C4×D4—434no—
529C4×D4—434no—
530C4×D4—868no—
531C4×D4—862no—
532C4×D4—862no—
533C4×D4—862no—
534#117—868no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4—861no—
541C2×C4⋊C4—861no—
542C2×C4⋊C4D17211yescharacteristic
543C2×C4⋊C4D17211yescharacteristic
544C2×C4⋊C4D17211yescharacteristic
545C2×C22⋊C4—861no—
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—861no—
557C2×C42—861no—
558C2×C42—861no—
559C2×C42C22×D4311yescharacteristic
560C2×C42C22×D4311yescharacteristic
561C2×C42C22×D4311yescharacteristic
562#106—434no—
563C4⋊C8C22×D4314yes—
564C4⋊C8C22×D4314yes—
565C4⋊C8C22×D4314yes—
566#103—434no—
567#103—434no—
568#103—434no—
569#102—434no—
570#102—434no—
571#102—434no—
572#97C22×D4314yes—
573#97C22×D4314yes—
574C4×C8C22×D4314yes—
575C24—861no—
576C24—861no—
577C24—861no—
578C2×Q8—42no—
579C2×Q8—432no—
580C2×Q8—432no—
581C2×Q8—432no—
582C2×Q8—861no—
583C2×Q8—861no—
584C2×Q8—861no—
585C2×Q8—862no—
586C2×Q8—862no—
587C2×Q8—862no—
588C2×Q8—862no—
589C2×Q8—862no—
590C2×Q8—862no—
591C2×Q8C2×D17214yes—
592C2×D4—432no—
593C2×D4—432no—
594C2×D4—432no—
595C2×D4—864no—
596C2×D4—861no—
597C2×D4—864no—
598C2×D4—861no—
599C2×D4—861no—
600C2×D4—862no—
601C2×D4—862no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—862no—
605C2×D4—862no—
606C2×D4—3442no—
607C2×D4—1724no—
608C22×C4—861no—
609C22×C4—861no—
610C22×C4—861no—
611C22×C4—861no—
612C22×C4—861no—
613C22×C4—864no—
614C22×C4—864no—
615C22×C4—864no—
616C22×C4—3442no—
617C22×C4—3442no—
618C22×C4—1724no—
619C22×C4C2×D17211yescharacteristic
620C22×C4C2×D17211yescharacteristic
621C22×C4C2×D17211yescharacteristic
622C22×C4C2×D17211yescharacteristic
623C22×C4C2×D17211yescharacteristic
624C22×C4C2×D17211yescharacteristic
625C22×C4C23×D4311yescharacteristic
626Q16—868no—
627Q16—1724no—
628SD16—868no—
629SD16—1724no—
630SD16—1724no—
631SD16—1724no—
632SD16—1724no—
633D8—868no—
634D8—1724no—
635C2×C8—22no—
636C2×C8—22no—
637C2×C8—22no—
638C2×C8#1062190214yes—
639C2×C8C23×D4312yes—
640C2×C8C23×D4312yes—
641C2×C8C23×D4312yes—
642C2×C8C23×D4312yes—
643C4⋊C4—432no—
644C4⋊C4—432no—
645C4⋊C4—861no—
646C4⋊C4—861no—
647C4⋊C4—864no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4C2×D17214yes—
653C4⋊C4C2×D17214yes—
654C4⋊C4C2×D17214yes—
655C22⋊C4—864no—
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—864no—
667C42—864no—
668C42—864no—
669C42C2×D17212yes—
670C42C2×D17212yes—
671C42C2×D17212yes—
672C42C23×D4312yes—
673C42C23×D4312yes—
674C42C23×D4312yes—
675C23—862no—
676C23—862no—
677C23—862no—
678C23—1722no—
679C23—1722no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23—1722no—
687C23C22×D17211yescharacteristic
688Q8—44no—
689Q8—862no—
690Q8—862no—
691Q8—862no—
692Q8—862no—
693Q8—862no—
694Q8—862no—
695Q8—1722no—
696Q8—1722no—
697Q8—1722no—
698D4—862no—
699D4—862no—
700D4—862no—
701D4—862no—
702D4—862no—
703D4—862no—
704D4—3444no—
705D4—1728no—
706D4—1722no—
707D4—1722no—
708D4—1722no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—3444no—
721C2×C4—3444no—
722C2×C4—1728no—
723C2×C4—1722no—
724C2×C4—1722no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1722no—
728C2×C4C22×D17212yes—
729C2×C4C22×D17212yes—
730C2×C4C22×D17212yes—
731C2×C4C22×D17212yes—
732C2×C4C22×D17212yes—
733C2×C4C22×D17212yes—
734C2×C4C22×D17211yescharacteristic
735C2×C4C2×#1062190212yes—
736C2×C4#1306337112yes—
737C2×C4C24×D4311yescharacteristic
738C8—22no—
739C8—22no—
740C8—22no—
741C8C2×#1062190214yes—
742C22—3444no—
743C22—3444no—
744C22—3444no—
745C22—1722no—
746C22—1722no—
747C22—1722no—
748C22—1722no—
749C22—1722no—
750C22—1722no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22#1458357112yes—
755C22#1458369912yes—
756C22#1458371112yes—
757C22C23×D17211yescharacteristic
758C4—22no—
759C4—22no—
760C4—22no—
761C4—22no—
762C4—22no—
763C4—22no—
764C4—1722no—
765C4—1722no—
766C4—1722no—
767C4—1722no—
768C4—1722no—
769C4#1458357112yes—
770C4C22×#1062190211yescharacteristic
771C4C2×#1306337111yescharacteristic
772C2—3442no—
773C2—3442no—
774C2—3442no—
775C2#1914766314yesdirect product factor
776C2C2×#1458357111yescharacteristic
777C2C2×#1458369911yescharacteristic
778C2C2×#1458371111yescharacteristic
subgroupG/H
centerC23C22×D172
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#446C2
socleC23×C43C22×D4
prime radicalC2×#14583288C2
hypercenterC2×#446D43
hypocenterC43C2×#3401
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#14583634C2semidirect
2. C2×#14583622C2semidirect
3. #19147663C2direct (N × H)
4. C2×#14583293C2semidirect
6. C2×#14583283C2semidirect
7. C2×#14583122C2semidirect
8. C2×#14583122C2semidirect
9. C2×#14583100C2semidirect
10. C2×#14583115C2semidirect
11. C2×#14583115C2semidirect
12. C2×#14583105C2semidirect
13. C2×#14583012C2semidirect
14. C2×#14583007C2semidirect
15. C2×C4×#10621873C2semidirect
16. C2×C43×#446C2semidirect
27. #14583634C22semidirect
29. #14583622C22semidirect
50. #14583293C22semidirect
52. #14583283C22semidirect
53. #14583122C22semidirect
54. #14583122C22semidirect
55. #14583115C22semidirect
56. #14583115C22semidirect
57. #14583105C22semidirect
58. #14583100C22semidirect
59. #14583012C22semidirect
60. #14583007C22semidirect
61. C4×#10621873C22semidirect
70. C43×#446C22semidirect
395. C2×#446D43semidirect
399. C2×C43#3401semidirect
449. #446C2×D43semidirect
466. C43C2×#3401semidirect
775. C2#19147663direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145836342
C2×#145836222
#191476632
C2×#145832932
C2×#145832882
C2×#145832832
C2×#145831222
C2×#145831002
C2×#145831152
C2×#145831052
C2×#145830122
C2×#145830072
C2×C4×#106218732
C2×C43×#4462
C2×#340143