Finite Group Databasebeta

← C2×#19147666 #25977608

Subgroups — C2×#19147666 #25977608

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×#14583619C211yesmaximal, characteristic, complemented
3#19147666C2116yesmaximal, direct product factor
4C2×#14583293C211yesmaximal, characteristic, complemented
5C2×#14583287C211yesmaximal, characteristic
6C2×#14583282C211yesmaximal, characteristic, complemented
7C2×#14583120C211yesmaximal, characteristic, complemented
8C2×#14583120C211yesmaximal, characteristic, complemented
9C2×#14583098C211yesmaximal, characteristic, complemented
10C2×#14583114C211yesmaximal, characteristic, complemented
11C2×#14583113C211yesmaximal, characteristic, complemented
12C2×#14583104C211yesmaximal, characteristic, complemented
13C2×#14583027C211yesmaximal, characteristic, complemented
14C2×#14583005C211yesmaximal, characteristic, complemented
15C2×#14582986C211yesmaximal, characteristic, complemented
16C2×C43×#442C211yesmaximal, characteristic, complemented
17C22×Dic172C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621873C2211yescharacteristic
20C22×#10621873C2211yescharacteristic
21C22×#10621883C2211yescharacteristic
22C22×#10621883C2211yescharacteristic
23C22×#10621883C2211yescharacteristic
24C22×#10621882C2211yescharacteristic
25#14583632—24no—
26#14583632C2218yescomplemented
27#14583619—24no—
28#14583619C2218yescomplemented
29C2×#13063325C2211yescharacteristic
30C2×#13063321C2211yescharacteristic
31C2×#13063318—21no—
32C2×#13063318—21no—
33C2×#13063313C2211yescharacteristic
34C2×#13063312C2211yescharacteristic
35C2×#13063312C2211yescharacteristic
36C2×#13063312C2211yescharacteristic
37C2×#13063311—21no—
38C2×#13063308—21no—
39C2×#13063307—21no—
40C2×#13063304—21no—
41C2×C4×Dic86C2211yescharacteristic
42C2×#13063290C2211yescharacteristic
43C2×#13063290C2211yescharacteristic
44C2×#13063290C2211yescharacteristic
45C2×#13063287C2211yescharacteristic
46C2×C4×C22⋊D43—21no—
47C2×#13063284—21no—
48#14583293C2218yescomplemented
49#14583287C2218yes—
50#14583282C2218yescomplemented
51#14583120C2218yescomplemented
52#14583120C2218yescomplemented
53#14583114C2218yescomplemented
54#14583113C2218yescomplemented
55#14583104C2218yescomplemented
56#14583098C2218yescomplemented
57#14583027C2218yescomplemented
58#14583005C2218yescomplemented
59#14582986C2218yescomplemented
60C2×C4⋊(C43⋊C8)C2211yescharacteristic
61C2×Dic43⋊C8C2211yescharacteristic
62C2×Dic43⋊C8C2211yescharacteristic
63C2×#13063248C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×#13063245C2211yescharacteristic
67C2×#13063235C2211yescharacteristic
68C2×C8×Dic43C2211yescharacteristic
69C22×D8×C43C2211yescharacteristic
70C2×C4×D4×C43C2211yescharacteristic
71C2×C4×D4×C43C2211yescharacteristic
72C43×#442C2218yescomplemented
73C2×#106×C43C2211yescharacteristic
74C2×#102×C43C2211yescharacteristic
75C2×#102×C43C2211yescharacteristic
76C2×#97×C43C2211yescharacteristic
77C22×Dic86D411yescharacteristic
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C22×Dic86C2311yescharacteristic
81C22×D172C2311yescharacteristic
82C22×C22⋊D43—21no—
83C22×C22⋊D43—21no—
84C22×C4×D43—21no—
85C2×Dic172—24no—
86C2×Dic172—42no—
87C2×Dic172C2314yes—
88C2×Dic172C2314yes—
89C2×#10621873—24no—
90C2×#10621873—42no—
91C2×#10621873C2314yes—
92C2×#10621873C2314yes—
93C2×#10621883—42no—
94C2×#10621883—42no—
95C2×#10621883—42no—
96C2×#10621883C2314yes—
97C2×#10621883C2314yes—
98C2×#10621883C2314yes—
99C2×#10621882—42no—
100C2×#10621882C2314yes—
101C22×C43⋊C8C2311yescharacteristic
102C22×C43⋊C8C2311yescharacteristic
103#13063325—22no—
104#13063325C2314yes—
105#13063321—22no—
106#13063321C2314yes—
107#13063318—28no—
108#13063318—28no—
109#13063313—22no—
110#13063313C2314yes—
111#13063312—22no—
112#13063312—22no—
113#13063312—22no—
114#13063312C2314yes—
115#13063312C2314yes—
116#13063312C2314yes—
117#13063311—28no—
118#13063308—28no—
119#13063307—28no—
120#13063304—28no—
121C4×Dic86D414yes—
122C4×Dic86C2314yes—
123#13063290—22no—
124#13063290—22no—
125#13063290—22no—
126#13063290C2314yes—
127#13063290C2314yes—
128#13063290C2314yes—
129#13063287—22no—
130#13063287C2314yes—
131C4×C22⋊D43—28no—
132#13063284—28no—
133C2×C4⋊Dic43—21no—
134C2×C4⋊Dic43—21no—
135C2×C4⋊Dic43D411yescharacteristic
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×C22⋊Dic43—21no—
144C2×C22⋊Dic43—21no—
145C2×C22⋊Dic43—21no—
146C2×C22⋊Dic43—21no—
147C2×(C2×D43)⋊C4—21no—
148C2×(C2×D43)⋊C4—21no—
149C2×(C2×D43)⋊C4—21no—
150C2×C4×Dic43—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#13063248C2314yes—
161#13063245C2314yes—
162#13063235C2314yes—
163C8×Dic43C2314yes—
164C22×D4×C43C2311yescharacteristic
165C22×D4×C43C2311yescharacteristic
166C23×C4×C43—21no—
167C23×C4×C43—21no—
168C2×D8×C43—24no—
169C2×D8×C43C2314yes—
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C4×D4×C43—22no—
173C4×D4×C43—22no—
174C4×D4×C43C2314yes—
175C4×D4×C43C2314yes—
176C2×C4⋊C4×C43C2311yescharacteristic
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C22⋊C4×C43—21no—
179C2×C22⋊C4×C43—21no—
180C2×C42×C43C2311yescharacteristic
181#106×C43C2314yes—
182#102×C43C2314yes—
183#102×C43C2314yes—
184#97×C43C2314yes—
185C24×C43—21no—
186C24×C43—21no—
187C23×D43—21no—
188C2×D4×C43—21no—
189C2×D4×C43—21no—
190C2×D4×C43—22no—
191C2×D4×C43—22no—
192C2×D4×C43—22no—
193C2×D4×C43—22no—
194C2×D4×C43C2412yes—
195C2×D4×C43C2412yes—
196C22×C4×C43—24no—
197C22×C4×C43—24no—
198C22×C4×C43—21no—
199C22×C4×C43—21no—
200C22×C4×C43—44no—
201C22×C4×C43—82no—
202C22×C4×C43C2×D411yescharacteristic
203C22×C4×C43C2×D411yescharacteristic
204C22×C4×C43C2411yescharacteristic
205C2×C22⋊D43—24no—
206C2×C22⋊D43—24no—
207C2×C22⋊D43—44no—
208C2×C22⋊D43—82no—
209C22×Dic43—21no—
210C22×Dic43—21no—
211C22×Dic43—21no—
212C22×Dic43C2×D411yescharacteristic
213C22×Dic43C2×D411yescharacteristic
214C22×Dic43C2×D411yescharacteristic
215C22×Dic43C2×D411yescharacteristic
216C2×D172—21no—
217C2×D172—22no—
218C2×D172—22no—
219C2×D172C2412yes—
220C2×C4×D43—24no—
221C2×C4×D43—82no—
222C2×Dic86—22no—
223C2×Dic86—22no—
224C2×Dic86—22no—
225C2×Dic86—22no—
226C2×Dic86—22no—
227C2×Dic86—22no—
228C2×Dic86—21no—
229C2×Dic86—21no—
230C2×Dic86—21no—
231C2×Dic86—42no—
232C2×Dic86C2×D414yes—
233C2×Dic86C2412yes—
234C2×Dic86C2412yes—
235C2×Dic86C2412yes—
236D8×C43—28no—
237C2×C8×C43—22no—
238C2×C8×C43#4114yes—
239C2×C8×C43C2412yes—
240C2×C8×C43C2412yes—
241C4⋊C4×C43—21no—
242C4⋊C4×C43—21no—
243C4⋊C4×C43C2412yes—
244C4⋊C4×C43C2412yes—
245C22⋊C4×C43—24no—
246C22⋊C4×C43—24no—
247C42×C43C2×D412yes—
248C42×C43C2412yes—
249C22⋊Dic43—24no—
250C22⋊Dic43—24no—
251C22⋊Dic43—24no—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254C22⋊Dic43—24no—
255#10621883—44no—
256#10621883—44no—
257#10621883—44no—
258#10621882—44no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4—24no—
261(C2×D43)⋊C4—24no—
262C4⋊Dic43—24no—
263C4⋊Dic43—24no—
264C4⋊Dic43C2×D414yes—
265Dic43⋊C4—24no—
266Dic43⋊C4—24no—
267Dic43⋊C4—24no—
268Dic43⋊C4C2×D414yes—
269Dic43⋊C4C2×D414yes—
270C4×Dic43—24no—
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—
282Dic172—44no—
283#10621873—28no—
284#10621873—44no—
285C23×C43—22no—
286C23×C43—22no—
287C23×C43—42no—
288C23×C43—42no—
289C23×C43—42no—
290C23×C43—42no—
291C23×C43—42no—
292C23×C43—42no—
293C23×C43C22×D411yescharacteristic
294C22×D43—22no—
295C22×D43—42no—
296C22×D43—42no—
297C22×D43—42no—
298D4×C43—22no—
299D4×C43—22no—
300D4×C43—22no—
301D4×C43—22no—
302D4×C43—42no—
303D4×C43—42no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—48no—
309C2×C4×C43—42no—
310C2×C4×C43—42no—
311C2×C4×C43—84no—
312C2×C4×C43C22×D412yes—
313C2×C4×C43C22×D412yes—
314C2×C4×C43C22×D411yescharacteristic
315C2×C4×C43C2×#4112yes—
316C2×C4×C43H(5,𝔽2)12yes—
317C2×C4×C43C2511yescharacteristic
318C22⋊D43—48no—
319C22⋊D43—84no—
320C2×Dic43—22no—
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×Dic43—42no—
330C2×Dic43C22×D412yes—
331C2×Dic43C22×D412yes—
332C2×Dic43C22×D412yes—
333C2×Dic43C22×D412yes—
334D172—22no—
335D172—22no—
336D172—42no—
337C4×D43—84no—
338Dic86—22no—
339Dic86—22no—
340Dic86—22no—
341Dic86—22no—
342Dic86—22no—
343Dic86—22no—
344Dic86—44no—
345Dic86—42no—
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—42no—
357C22×C43—42no—
358C22×C43—42no—
359C22×C43—84no—
360C22×C43—84no—
361C22×C43#55012yes—
362C22×C43#57512yes—
363C22×C43#57712yes—
364C22×C43C23×D411yescharacteristic
365C2×D43—42no—
366C2×D43—42no—
367C2×D43—42no—
368C2×D43—84no—
369C4×C43—22no—
370C4×C43—22no—
371C4×C43—42no—
372C4×C43—42no—
373C4×C43#55012yes—
374C4×C43C22×#4111yescharacteristic
375C4×C43C2×H(5,𝔽2)11yescharacteristic
376Dic43—22no—
377Dic43—22no—
378Dic43—22no—
379Dic43—22no—
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×#446—431no—
396C2×#442D4311yescharacteristic, complemented
397C2×#441—431no—
398C2×C4×SD16—431no—
399C2×C43—82no—
400C2×C43—82no—
401C2×C43#340114yescomplemented
402C2×C43C2×#55011yescharacteristic
403C2×C43C2×#57511yescharacteristic
404C2×C43C2×#57711yescharacteristic
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×D8C2×D4311yescharacteristic
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×Q8—431no—
435C2×C4×D4—431no—
436C2×C4×D4—861no—
437C2×C4×D4C2×D4311yescharacteristic
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#442C2×D4318yescomplemented
451#441—438no—
452C4×SD16—438no—
453C2×#106C2×D4311yescharacteristic
454C2×C4⋊C8—431no—
455C2×C4⋊C8—431no—
456C2×C4⋊C8—431no—
457C2×#103—431no—
458C2×#103—431no—
459C2×#103—431no—
460C2×#102—431no—
461C2×#102C2×D4311yescharacteristic
462C2×#102C2×D4311yescharacteristic
463C2×#97—431no—
464C2×#97C2×D4311yescharacteristic
465C2×C4×C8—431no—
466C43C2×#340111yescharacteristic, complemented, Sylow
467C22×Q8—431no—
468C22×Q8—431no—
469C22×Q8—431no—
470C22×Q8—431no—
471C22×D4—431no—
472C22×D4—861no—
473C22×D4—861no—
474C22×D4C22×D4311yescharacteristic
475C22×D4C22×D4311yescharacteristic
476C23×C4—21no—
477C23×C4—21no—
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—24no—
494C2×D8—434no—
495C2×D8—1722no—
496C2×D8C22×D4314yes—
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—862no—
514#124—868no—
515#124—862no—
516#123—868no—
517#123—868no—
518C22⋊Q8—868no—
519C4×Q8—434no—
520C4×Q8—434no—
521C4×Q8—434no—
522C4×Q8—434no—
523C4×Q8—434no—
524C4×Q8—862no—
525C4×Q8—862no—
526C4×Q8—862no—
527C4×D4—22no—
528C4×D4—22no—
529C4×D4—434no—
530C4×D4—862no—
531C4×D4—868no—
532C4×D4C22×D4314yes—
533C4×D4C22×D4314yes—
534#117—868no—
535C2×C4⋊C4—431no—
536C2×C4⋊C4—431no—
537C2×C4⋊C4—431no—
538C2×C4⋊C4—861no—
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—21no—
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—431no—
557C2×C42—431no—
558C2×C42—861no—
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#103—434no—
569#102—434no—
570#102C22×D4314yes—
571#102C22×D4314yes—
572#97—434no—
573#97C22×D4314yes—
574C4×C8—434no—
575C24—21no—
576C24—21no—
577C24—861no—
578C2×Q8—434no—
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×Q8—1722no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—22no—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—432no—
599C2×D4—864no—
600C2×D4—864no—
601C2×D4—861no—
602C2×D4—862no—
603C2×D4—862no—
604C2×D4—3442no—
605C2×D4—1724no—
606C2×D4C23×D4312yes—
607C2×D4C23×D4312yes—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—24no—
611C22×C4—24no—
612C22×C4—44no—
613C22×C4—82no—
614C22×C4—431no—
615C22×C4—431no—
616C22×C4—431no—
617C22×C4—431no—
618C22×C4—864no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—3442no—
623C22×C4D4×D4311yescharacteristic
624C22×C4D4×D4311yescharacteristic
625C22×C4C23×D4311yescharacteristic
626Q16—868no—
627Q16—1724no—
628SD16—868no—
629SD16—1724no—
630SD16—1724no—
631SD16—1724no—
632SD16—1724no—
633D8—28no—
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—21no—
644C4⋊C4—21no—
645C4⋊C4—434no—
646C4⋊C4—434no—
647C4⋊C4—434no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4—864no—
653C4⋊C4C23×D4312yes—
654C4⋊C4C23×D4312yes—
655C22⋊C4—24no—
656C22⋊C4—24no—
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—432no—
667C42—432no—
668C42—432no—
669C42—432no—
670C42—864no—
671C42—864no—
672C42—864no—
673C42D4×D4312yes—
674C42C23×D4312yes—
675C23—22no—
676C23—22no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—862no—
684C23—1722no—
685C23—1722no—
686C23—1722no—
687C23C2×D4×D4311yescharacteristic
688Q8—862no—
689Q8—862no—
690Q8—862no—
691Q8—862no—
692Q8—862no—
693Q8—862no—
694Q8—1724no—
695Q8—1722no—
696Q8—1722no—
697Q8—1722no—
698D4—22no—
699D4—22no—
700D4—22no—
701D4—22no—
702D4—42no—
703D4—42no—
704D4—862no—
705D4—862no—
706D4—3444no—
707D4—1728no—
708D4—1722no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—48no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—84no—
717C2×C4—432no—
718C2×C4—432no—
719C2×C4—432no—
720C2×C4—432no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—3444no—
729C2×C4—1722no—
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—42no—
746C22—42no—
747C22—42no—
748C22—84no—
749C22—84no—
750C22—3444no—
751C22—1722no—
752C22—1722no—
753C22—1722no—
754C22#1458357012yes—
755C22#1458369512yes—
756C22#1458370912yes—
757C22C22×D4×D4311yescharacteristic
758C4—22no—
759C4—22no—
760C4—42no—
761C4—42no—
762C4—862no—
763C4—862no—
764C4—862no—
765C4—862no—
766C4—1722no—
767C4—1722no—
768C4—1722no—
769C4#1458357012yes—
770C4C22×#1062189811yescharacteristic
771C4C2×#1306337111yescharacteristic
772C2—82no—
773C2—82no—
774C2—3442no—
775C2#1914766614yesdirect product factor
776C2C2×#1458357011yescharacteristic
777C2C2×#1458369511yescharacteristic
778C2C2×#1458370911yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#442C2
socleC23×C43C22×D4
prime radicalC2×#14583287C2
hypercenterC2×#442D43
hypocenterC43C2×#3401
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#14583632C2semidirect
2. C2×#14583619C2semidirect
3. #19147666C2direct (N × H)
4. C2×#14583293C2semidirect
6. C2×#14583282C2semidirect
7. C2×#14583120C2semidirect
8. C2×#14583120C2semidirect
9. C2×#14583098C2semidirect
10. C2×#14583114C2semidirect
11. C2×#14583113C2semidirect
12. C2×#14583104C2semidirect
13. C2×#14583027C2semidirect
14. C2×#14583005C2semidirect
15. C2×#14582986C2semidirect
16. C2×C43×#442C2semidirect
26. #14583632C22semidirect
28. #14583619C22semidirect
48. #14583293C22semidirect
50. #14583282C22semidirect
51. #14583120C22semidirect
52. #14583120C22semidirect
53. #14583114C22semidirect
54. #14583113C22semidirect
55. #14583104C22semidirect
56. #14583098C22semidirect
57. #14583027C22semidirect
58. #14583005C22semidirect
59. #14582986C22semidirect
72. C43×#442C22semidirect
396. C2×#442D43semidirect
401. C2×C43#3401semidirect
450. #442C2×D43semidirect
466. C43C2×#3401semidirect
775. C2#19147666direct (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×#145836192
#191476662
C2×#145832932
C2×#145832872
C2×#145832822
C2×#145831202
C2×#145830982
C2×#145831142
C2×#145831132
C2×#145831042
C2×#145830272
C2×#145830052
C2×#145829862
C2×C43×#4422
C2×#340143