Finite Group Databasebeta

← C2×#19146012 #25969513

Subgroups — C2×#19146012 #25969513

Order 11008.

1946 conjugacy classes of subgroups.

The subgroup lattice has 782 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583521C211yesmaximal, characteristic, complemented
2C2×#14583505C211yesmaximal, characteristic, complemented
3#19146012C2116yesmaximal, direct product factor
4C2×#14583196C211yesmaximal, characteristic, complemented
5C2×#14583188C211yesmaximal, characteristic, complemented
6C2×#14583178C211yesmaximal, characteristic, complemented
7C2×#14583153C211yesmaximal, characteristic, complemented
8C2×#14583148C211yesmaximal, characteristic, complemented
9C2×#14583136C211yesmaximal, characteristic, complemented
10C2×#14583131C211yesmaximal, characteristic, complemented
11C2×#14583099C211yesmaximal, characteristic, complemented
12C2×#14583117C211yesmaximal, characteristic, complemented
13C2×#14583117C211yesmaximal, characteristic, complemented
14C2×#14583095C211yesmaximal, characteristic, complemented
15C2×#14582924C211yesmaximal, characteristic, complemented
16C2×C43×#479C211yesmaximal, characteristic, complemented
17C22×#10621884C2211yescharacteristic
18C22×#10621884C2211yescharacteristic
19C22×D344C2211yescharacteristic
20C22×D344C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22C22×C8×D43C2211yescharacteristic
23#14583521—24no—
24#14583521C2218yescomplemented
25#14583505—24no—
26#14583505C2218yescomplemented
27C2×#13063324C2211yescharacteristic
28C2×#13063322C2211yescharacteristic
29C2×#13063319—21no—
30C2×#13063314C2211yescharacteristic
31C2×#13063313—21no—
32C2×#13063310—21no—
33C2×#13063310—21no—
34C2×#13063310—21no—
35C2×#13063303—21no—
36C2×#13063301C2211yescharacteristic
37C2×#13063300—21no—
38C2×#13063300—21no—
39C2×#13063300C2211yescharacteristic
40C2×#13063300C2211yescharacteristic
41C2×#13063300C2211yescharacteristic
42C2×C4×D172C2211yescharacteristic
43C2×#13063287C2211yescharacteristic
44C2×#13063287C2211yescharacteristic
45C2×#13063282C2211yescharacteristic
46#14583196C2218yescomplemented
47#14583188C2218yescomplemented
48#14583178C2218yescomplemented
49#14583153C2218yescomplemented
50#14583148C2218yescomplemented
51#14583136C2218yescomplemented
52#14583131C2218yescomplemented
53#14583117C2218yescomplemented
54#14583117C2218yescomplemented
55#14583099C2218yescomplemented
56#14583095C2218yescomplemented
57C2×#13063258C2211yescharacteristic
58C2×#13063256C2211yescharacteristic
59#14582924C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063247C2211yescharacteristic
64C2×#13063247C2211yescharacteristic
65C2×#13063245C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×#13063245C2211yescharacteristic
68C2×#13063245C2211yescharacteristic
69C2×#125×C43C2211yescharacteristic
70C2×C4×Q8×C43C2211yescharacteristic
71C43×#479C2218yescomplemented
72C2×#107×C43C2211yescharacteristic
73C2×#106×C43C2211yescharacteristic
74C2×C4⋊C8×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2211yescharacteristic
77C22×Dic86—21no—
78C22×D172—21no—
79C22×D172—21no—
80C22×D172—21no—
81C22×D172—21no—
82C22×D172—21no—
83C22×D172C2311yescharacteristic
84C22×D172C2311yescharacteristic
85C22×D172C2311yescharacteristic
86C22×C4×D43—21no—
87C22×C4×D43—21no—
88C22×C4×D43—21no—
89C22×C4×D43C2311yescharacteristic
90C2×#10621884—42no—
91C2×#10621884—42no—
92C2×#10621884C2314yes—
93C2×#10621884C2314yes—
94C2×D344—42no—
95C2×D344—42no—
96C2×D344C2314yes—
97C2×D344C2314yes—
98C2×#10621872—42no—
99C2×#10621872C2314yes—
100C22×C43⋊C8C2311yescharacteristic
101C22×C43⋊C8C2311yescharacteristic
102C2×C8×D43—42no—
103C2×C8×D43C2314yes—
104#13063324—22no—
105#13063324C2314yes—
106#13063322—22no—
107#13063322C2314yes—
108#13063319—28no—
109#13063314—22no—
110#13063314C2314yes—
111#13063313—28no—
112#13063310—28no—
113#13063310—28no—
114#13063310—28no—
115#13063303—28no—
116#13063301—22no—
117#13063301C2314yes—
118#13063300—22no—
119#13063300—22no—
120#13063300—22no—
121#13063300—28no—
122#13063300—28no—
123#13063300C2314yes—
124#13063300C2314yes—
125#13063300C2314yes—
126C4×D172—22no—
127C4×D172C2314yes—
128#13063287—22no—
129#13063287—22no—
130#13063287C2314yes—
131#13063287C2314yes—
132#13063282D414yes—
133#13063282C2314yes—
134C2×C4⋊Dic43C2311yescharacteristic
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4D411yescharacteristic
138C2×Dic43⋊C4D411yescharacteristic
139C2×(C2×D43)⋊C4—21no—
140C2×(C2×D43)⋊C4—21no—
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—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)⋊C4D411yescharacteristic
149C2×(C2×D43)⋊C4D411yescharacteristic
150C2×C4×Dic43C2311yescharacteristic
151#13063258C2314yes—
152#13063256C2314yes—
153C4⋊(C43⋊C8)C2314yes—
154Dic43⋊C8C2314yes—
155Dic43⋊C8C2314yes—
156#13063247C2314yes—
157#13063247C2314yes—
158#13063245C2314yes—
159#13063245C2314yes—
160#13063245C2314yes—
161#13063245C2314yes—
162C22×Q8×C43C2311yescharacteristic
163C22×C8×C43C2311yescharacteristic
164C22×C8×C43C2311yescharacteristic
165#125×C43—22no—
166#125×C43C2314yes—
167C4×Q8×C43—22no—
168C4×Q8×C43C2314yes—
169C2×C4⋊C4×C43—21no—
170C2×C4⋊C4×C43—21no—
171C2×C4⋊C4×C43—21no—
172C2×C4⋊C4×C43C2311yescharacteristic
173C2×C4⋊C4×C43C2311yescharacteristic
174C2×C4⋊C4×C43C2311yescharacteristic
175C2×C42×C43—21no—
176C2×C42×C43C2311yescharacteristic
177#107×C43C2314yes—
178#106×C43C2314yes—
179C4⋊C8×C43C2314yes—
180#103×C43C2314yes—
181#103×C43C2314yes—
182C23×D43—21no—
183C23×D43—21no—
184C23×D43—21no—
185C23×D43C2×D411yescharacteristic
186C2×Q8×C43—21no—
187C2×Q8×C43—22no—
188C2×Q8×C43—22no—
189C2×Q8×C43C2412yes—
190C22×C4×C43—21no—
191C22×C4×C43—21no—
192C22×C4×C43—21no—
193C22×C4×C43—21no—
194C22×C4×C43C2×D411yescharacteristic
195C22×C4×C43C2×D411yescharacteristic
196C22×C4×C43C2411yescharacteristic
197C22×Dic43—21no—
198C22×Dic43C2×D411yescharacteristic
199C22×Dic43C2×D411yescharacteristic
200C22×Dic43C2×D411yescharacteristic
201C2×D172—21no—
202C2×D172—21no—
203C2×D172—21no—
204C2×D172—24no—
205C2×D172—24no—
206C2×D172—24no—
207C2×D172—24no—
208C2×D172—24no—
209C2×D172—22no—
210C2×D172—22no—
211C2×D172—22no—
212C2×D172—22no—
213C2×D172—22no—
214C2×D172—22no—
215C2×D172—82no—
216C2×D172—82no—
217C2×D172—82no—
218C2×D172—82no—
219C2×D172—82no—
220C2×D172C2412yes—
221C2×D172C2412yes—
222C2×D172C2412yes—
223C2×C4×D43—22no—
224C2×C4×D43—22no—
225C2×C4×D43—24no—
226C2×C4×D43—24no—
227C2×C4×D43—24no—
228C2×C4×D43—82no—
229C2×C4×D43—82no—
230C2×C4×D43—82no—
231C2×C4×D43C2×D412yes—
232C2×C4×D43C2412yes—
233C2×Dic86—24no—
234C2×Dic86—82no—
235C2×C8×C43—22no—
236C2×C8×C43—22no—
237C2×C8×C43C2412yes—
238C2×C8×C43C2412yes—
239C4⋊C4×C43—24no—
240C4⋊C4×C43—24no—
241C4⋊C4×C43—24no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43—21no—
244C4⋊C4×C43—21no—
245C4⋊C4×C43C2412yes—
246C4⋊C4×C43C2412yes—
247C4⋊C4×C43C2412yes—
248C42×C43—24no—
249C42×C43C2×D412yes—
250C42×C43C2412yes—
251#10621884—44no—
252#10621884—44no—
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)⋊C4C2×D414yes—
263(C2×D43)⋊C4C2×D414yes—
264C4⋊Dic43—21no—
265C4⋊Dic43C2412yes—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4C2×D414yes—
269Dic43⋊C4C2×D414yes—
270C4×Dic43C2×D412yes—
271C4×Dic43C2412yes—
272C2×C43⋊C8—22no—
273C2×C43⋊C8—22no—
274C2×C43⋊C8C2412yes—
275C2×C43⋊C8C2412yes—
276D344—44no—
277D344—44no—
278#10621872—44no—
279C8×D43—44no—
280C23×C43C22×D411yescharacteristic
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43—42no—
288C22×D43—42no—
289C22×D43—42no—
290C22×D43—42no—
291C22×D43—42no—
292C22×D43—42no—
293C22×D43—42no—
294C22×D43—42no—
295C22×D43—42no—
296C22×D43C22×D412yes—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—42no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—42no—
307C2×C4×C43—42no—
308C2×C4×C43—42no—
309C2×C4×C43—42no—
310C2×C4×C43C22×D412yes—
311C2×C4×C43C22×D412yes—
312C2×C4×C43C22×D411yescharacteristic
313C2×C4×C43H(5,𝔽2)12yes—
314C2×C4×C432−1+412yes—
315C2×C4×C43C2511yescharacteristic
316C2×Dic43—22no—
317C2×Dic43—22no—
318C2×Dic43—22no—
319C2×Dic43—22no—
320C2×Dic43—42no—
321C2×Dic43C22×D412yes—
322C2×Dic43C22×D412yes—
323C2×Dic43C22×D412yes—
324D172—22no—
325D172—22no—
326D172—22no—
327D172—22no—
328D172—22no—
329D172—22no—
330D172—42no—
331D172—42no—
332D172—42no—
333D172—84no—
334D172—84no—
335D172—84no—
336D172—84no—
337D172—84no—
338C4×D43—24no—
339C4×D43—22no—
340C4×D43—22no—
341C4×D43—84no—
342C4×D43—84no—
343C4×D43—84no—
344Dic86—84no—
345C8×C43—22no—
346C8×C43—22no—
347C43⋊C8—22no—
348C43⋊C8—22no—
349C2×#3257—431nomaximal, Sylow
350C22×C43#53712yes—
351C22×C43#57612yes—
352C22×C43#57712yes—
353C22×C43C23×D411yescharacteristic
354C2×D43—22no—
355C2×D43—22no—
356C2×D43—22no—
357C2×D43—44no—
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—42no—
367C2×D43—84no—
368C2×D43—84no—
369C2×D43—84no—
370C4×C43—22no—
371C4×C43—22no—
372C4×C43—42no—
373C4×C43—42no—
374C4×C43—42no—
375C4×C43—42no—
376C4×C43#53712yes—
377C4×C43C2×H(5,𝔽2)11yescharacteristic
378C4×C43C2×2−1+411yescharacteristic
379Dic43—22no—
380Dic43—22no—
381Dic43—22no—
382Dic43—42no—
383C2×#542—431no—
384C2×#540—431no—
385#3257—4316no—
386C2×#479D4311yescharacteristic, complemented
387C2×#478—431no—
388C2×#476—431no—
389C2×#474—431no—
390C2×#469—431no—
391C2×#468—431no—
392C2×#466—431no—
393C2×#465—431no—
394C2×#460—431no—
395C2×#463—431no—
396C2×#463—431no—
397C2×#459—431no—
398C2×#424—431no—
399C2×C43#325714yescomplemented
400C2×C43C2×#53711yescharacteristic
401C2×C43C2×#57611yescharacteristic
402C2×C43C2×#57711yescharacteristic
403D43—42no—
404D43—82no—
405D43—82no—
406D43—82no—
407C22×SD16—431no—
408C22×SD16—431no—
409C22×D8—431no—
410C22×D8—431no—
411C22×M16—431no—
412C23×C8—431no—
413#542—438no—
414#542—864no—
415#540—438no—
416#540—864no—
417C2×C4⋊Q8—431no—
418C2×#127—431no—
419C2×#126—861no—
420C2×#125C2×D4311yescharacteristic
421C2×#124—431no—
422C2×#124—861no—
423C2×#123—861no—
424C2×#123—861no—
425C2×#123—861no—
426C2×C22⋊Q8—431no—
427C2×C22⋊Q8—861no—
428C2×#121—431no—
429C2×#121—431no—
430C2×#121—431no—
431C2×#121—861no—
432C2×#121—861no—
433C2×C4×Q8C2×D4311yescharacteristic
434C2×C4×D4—431no—
435C2×C4×D4—431no—
436C2×C4×D4—431no—
437C2×#117—431no—
438#479C2×D4318yescomplemented
439#478—438no—
440#476—438no—
441#474—438no—
442#469—438no—
443#468—438no—
444#466—438no—
445#465—438no—
446#463—438no—
447#463—438no—
448#460—438no—
449#459—438no—
450C2×#107—431no—
451C2×#107C2×D4311yescharacteristic
452C2×#106—431no—
453C2×#106C2×D4311yescharacteristic
454#424—438no—
455C2×C4⋊C8—431no—
456C2×C4⋊C8—431no—
457C2×C4⋊C8—431no—
458C2×C4⋊C8C2×D4311yescharacteristic
459C2×#103C2×D4311yescharacteristic
460C2×#103C2×D4311yescharacteristic
461C2×#102—431no—
462C2×#102—431no—
463C2×#102—431no—
464C2×#102—431no—
465C2×#102—431no—
466C2×#102—431no—
467C43C2×#325711yescharacteristic, complemented, Sylow
468C22×Q8—861no—
469C22×Q8C22×D4311yescharacteristic
470C22×D4—431no—
471C22×D4—431no—
472C22×D4—431no—
473C22×D4—861no—
474C22×D4—861no—
475C22×D4—861no—
476C22×D4—861no—
477C22×D4—861no—
478C23×C4—431no—
479C23×C4—861no—
480C23×C4—861no—
481C23×C4—861no—
482C2×SD16—434no—
483C2×SD16—434no—
484C2×SD16—1722no—
485C2×SD16—1722no—
486C2×D8—434no—
487C2×D8—434no—
488C2×D8—1722no—
489C2×D8—1722no—
490C2×M16—434no—
491C2×M16—1722no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8—434no—
495C22×C8—1722no—
496C22×C8C22×D4311yescharacteristic
497C22×C8C22×D4311yescharacteristic
498C4⋊Q8—434no—
499C4⋊Q8—862no—
500#127—434no—
501#127—862no—
502#126—868no—
503#125—22no—
504#125C22×D4314yes—
505#124—434no—
506#124—868no—
507#124—862no—
508#123—868no—
509#123—868no—
510#123—868no—
511C22⋊Q8—434no—
512C22⋊Q8—868no—
513C22⋊Q8—862no—
514#121—434no—
515#121—434no—
516#121—434no—
517#121—868no—
518#121—868no—
519#121—862no—
520#121—862no—
521#121—862no—
522C4×Q8—22no—
523C4×Q8C22×D4314yes—
524C4×D4—434no—
525C4×D4—434no—
526C4×D4—434no—
527C4×D4—862no—
528C4×D4—862no—
529C4×D4—862no—
530#117—434no—
531#117—434no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4—21no—
534C2×C4⋊C4—21no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4C22×D4311yescharacteristic
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4311yescharacteristic
543C2×C22⋊C4—431no—
544C2×C22⋊C4—431no—
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×C42—21no—
555C2×C42—431no—
556C2×C42C22×D4311yescharacteristic
557#107—434no—
558#107C22×D4314yes—
559#106—434no—
560#106C22×D4314yes—
561C4⋊C8—434no—
562C4⋊C8—434no—
563C4⋊C8—434no—
564C4⋊C8C22×D4314yes—
565#103C22×D4314yes—
566#103C22×D4314yes—
567#102—434no—
568#102—434no—
569#102—434no—
570#102—434no—
571#102—434no—
572#102—434no—
573C24—431no—
574C24—861no—
575C24—861no—
576C24—861no—
577C2×Q8—21no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—864no—
581C2×Q8—3442no—
582C2×Q8C23×D4312yes—
583C2×D4—432no—
584C2×D4—432no—
585C2×D4—432no—
586C2×D4—864no—
587C2×D4—864no—
588C2×D4—864no—
589C2×D4—864no—
590C2×D4—864no—
591C2×D4—861no—
592C2×D4—861no—
593C2×D4—861no—
594C2×D4—862no—
595C2×D4—862no—
596C2×D4—862no—
597C2×D4—862no—
598C2×D4—862no—
599C2×D4—862no—
600C2×D4—3442no—
601C2×D4—3442no—
602C2×D4—3442no—
603C2×D4—3442no—
604C2×D4—3442no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—431no—
610C22×C4—431no—
611C22×C4—431no—
612C22×C4—432no—
613C22×C4—432no—
614C22×C4—864no—
615C22×C4—864no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—861no—
619C22×C4—864no—
620C22×C4—3442no—
621C22×C4—3442no—
622C22×C4—3442no—
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4C23×D4311yescharacteristic
626SD16—1724no—
627SD16—1724no—
628D8—1724no—
629D8—1724no—
630M16—1724no—
631C2×C8—22no—
632C2×C8—22no—
633C2×C8—432no—
634C2×C8—432no—
635C2×C8—862no—
636C2×C8—862no—
637C2×C8—1724no—
638C2×C8C23×D4312yes—
639C2×C8C23×D4312yes—
640C4⋊C4—24no—
641C4⋊C4—24no—
642C4⋊C4—24no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—21no—
646C4⋊C4—434no—
647C4⋊C4—434no—
648C4⋊C4—432no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4—861no—
652C4⋊C4C23×D4312yes—
653C4⋊C4C23×D4312yes—
654C4⋊C4C23×D4312yes—
655C22⋊C4—434no—
656C22⋊C4—434no—
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—
669C42D4×D4312yes—
670C42C23×D4312yes—
671C23—432no—
672C23—862no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—862no—
678C23—1722no—
679C23—1722no—
680C23—1722no—
681C23—1722no—
682C23—1722no—
683C23—1722no—
684C23—1722no—
685C23—1722no—
686C23—1722no—
687C23C2×D4×D4311yescharacteristic
688Q8—22no—
689Q8—22no—
690Q8—42no—
691Q8—3444no—
692D4—862no—
693D4—862no—
694D4—862no—
695D4—862no—
696D4—862no—
697D4—862no—
698D4—3444no—
699D4—3444no—
700D4—3444no—
701D4—3444no—
702D4—3444no—
703D4—1722no—
704D4—1722no—
705D4—1722no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—42no—
713C2×C4—42no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—432no—
717C2×C4—432no—
718C2×C4—432no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—864no—
725C2×C4—862no—
726C2×C4—3444no—
727C2×C4—3444no—
728C2×C4—3444no—
729C2×C4—1722no—
730C2×C4C2×D4×D4312yes—
731C2×C4C2×D4×D4312yes—
732C2×C4C2×D4×D4311yescharacteristic
733C2×C4#1306337112yes—
734C2×C4#1306337312yes—
735C2×C4C24×D4311yescharacteristic
736C8—22no—
737C8—22no—
738C8—862no—
739C8—862no—
740C22—862no—
741C22—862no—
742C22—862no—
743C22—3444no—
744C22—3444no—
745C22—3444no—
746C22—1722no—
747C22—1722no—
748C22—1722no—
749C22—1722no—
750C22—1722no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22—1722no—
755C22—1724no—
756C22#1458347912yes—
757C22#1458370112yes—
758C22#1458370812yes—
759C22C22×D4×D4311yescharacteristic
760C4—22no—
761C4—22no—
762C4—42no—
763C4—42no—
764C4—42no—
765C4—42no—
766C4—862no—
767C4—862no—
768C4—862no—
769C4—1722no—
770C4#1458347912yes—
771C4C2×#1306337111yescharacteristic
772C4C2×#1306337311yescharacteristic
773C2—3442no—
774C2—3442no—
775C2—3442no—
776C2—1722no—
777C2#1914601214yesdirect product factor
778C2C2×#1458347911yescharacteristic
779C2C2×#1458370111yescharacteristic
780C2C2×#1458370811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#479C2
socleC23×C43C22×D4
hypercenterC2×#479D43
hypocenterC43C2×#3257
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#479

Complements

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

NH ≅ G/Ntype
1. C2×#14583521C2semidirect
2. C2×#14583505C2semidirect
3. #19146012C2direct (N × H)
4. C2×#14583196C2semidirect
5. C2×#14583188C2semidirect
6. C2×#14583178C2semidirect
7. C2×#14583153C2semidirect
8. C2×#14583148C2semidirect
9. C2×#14583136C2semidirect
10. C2×#14583131C2semidirect
11. C2×#14583099C2semidirect
12. C2×#14583117C2semidirect
13. C2×#14583117C2semidirect
14. C2×#14583095C2semidirect
15. C2×#14582924C2semidirect
16. C2×C43×#479C2semidirect
24. #14583521C22semidirect
26. #14583505C22semidirect
46. #14583196C22semidirect
47. #14583188C22semidirect
48. #14583178C22semidirect
49. #14583153C22semidirect
50. #14583148C22semidirect
51. #14583136C22semidirect
52. #14583131C22semidirect
53. #14583117C22semidirect
54. #14583117C22semidirect
55. #14583099C22semidirect
56. #14583095C22semidirect
59. #14582924C22semidirect
71. C43×#479C22semidirect
386. C2×#479D43semidirect
399. C2×C43#3257semidirect
438. #479C2×D43semidirect
467. C43C2×#3257semidirect
777. C2#19146012direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835212
C2×#145835052
#191460122
C2×#145831962
C2×#145831882
C2×#145831782
C2×#145831532
C2×#145831482
C2×#145831362
C2×#145831312
C2×#145830992
C2×#145831172
C2×#145830952
C2×#145829242
C2×C43×#4792
C2×#325743