Finite Group Databasebeta

← C2×#19146642 #25973199

Subgroups — C2×#19146642 #25973199

Order 11008.

2094 conjugacy classes of subgroups.

The subgroup lattice has 772 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583584C211yesmaximal, characteristic
2C2×Q8×C22⋊D43C211yesmaximal, characteristic
3#19146642C2116yesmaximal, direct product factor
4C2×#14583266C211yesmaximal, characteristic, complemented
5C2×#14583239C211yesmaximal, characteristic, complemented
6C2×#14583229C211yesmaximal, characteristic, complemented
7C2×#14583208C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic, complemented
9C2×#14583140C211yesmaximal, characteristic, complemented
10C2×#14583108C211yesmaximal, characteristic, complemented
11C2×#14583056C211yesmaximal, characteristic, complemented
12C2×#14583055C211yesmaximal, characteristic, complemented
13C2×#14583003C211yesmaximal, characteristic, complemented
14C2×#14582970C211yesmaximal, characteristic
15C2×#14582906C211yesmaximal, characteristic, complemented
16C22×#103×C43C211yesmaximal, characteristic, complemented
17C22×Q8×D43C2211yescharacteristic
18C22×Dic172C2211yescharacteristic
19C22×#10621885C2211yescharacteristic
20C22×#10621885C2211yescharacteristic
21C22×#10621872C2211yescharacteristic
22#14583584—24no—
23#14583584C2218yes—
24Q8×C22⋊D43—24no—
25Q8×C22⋊D43C2218yes—
26C2×#13063323—21no—
27C2×#13063323C2211yescharacteristic
28C2×#13063320—21no—
29C2×#13063316C2211yescharacteristic
30C2×#13063315—21no—
31C2×#13063308—21no—
32C2×#13063305C2211yescharacteristic
33C2×#13063304—21no—
34C2×#13063304C2211yescharacteristic
35C2×#13063304C2211yescharacteristic
36C2×#13063301—21no—
37C2×#13063301C2211yescharacteristic
38C2×Q8×Dic43C2211yescharacteristic
39C2×#13063290C2211yescharacteristic
40C2×C4×C22⋊D43—21no—
41C2×C4×C22⋊D43C2211yescharacteristic
42C2×#13063284—21no—
43C2×#13063283C2211yescharacteristic
44#14583266C2218yescomplemented
45#14583239C2218yescomplemented
46#14583229C2218yescomplemented
47#14583208C2218yescomplemented
48#14583156C2218yescomplemented
49#14583140C2218yescomplemented
50#14583108C2218yescomplemented
51#14583056C2218yescomplemented
52#14583055C2218yescomplemented
53#14583003C2218yescomplemented
54#14582970C2218yes—
55C2×#13063259C2211yescharacteristic
56C2×#13063256C2211yescharacteristic
57C2×#13063256C2211yescharacteristic
58C2×Dic43⋊C8C2211yescharacteristic
59#14582906C2218yescomplemented
60C2×#13063250C2211yescharacteristic
61C2×#13063250C2211yescharacteristic
62C2×#13063249C2211yescharacteristic
63C2×#13063249C2211yescharacteristic
64C2×#13063248C2211yescharacteristic
65C2×#13063248C2211yescharacteristic
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×#13063235C2211yescharacteristic
69C23×Q8×C43C2211yescharacteristic
70C23×C8×C43C2211yescharacteristic
71C22×C4⋊C4×C43C2211yescharacteristic
72C2×#103×C43C2211yescharacteristic
73C2×#103×C43C2211yescharacteristic
74C2×#103×C43C2211yescharacteristic
75C2×#103×C43C2211yescharacteristic
76C2×#103×C43C2218yescomplemented
77C22×Dic86—21no—
78C22×Dic86C2311yescharacteristic
79C22×Dic86C2311yescharacteristic
80C2×Q8×D43—22no—
81C2×Q8×D43—24no—
82C2×Q8×D43—42no—
83C2×Q8×D43C2314yes—
84C22×C22⋊D43D411yescharacteristic
85C22×C4×D43—21no—
86C22×C4×D43C2311yescharacteristic
87C2×Dic172—42no—
88C2×Dic172C2314yes—
89C2×#10621885—24no—
90C2×#10621885—42no—
91C2×#10621885C2314yes—
92C2×#10621885C2314yes—
93C2×#10621872—42no—
94C2×#10621872C2314yes—
95C22×C43⋊C8C2311yescharacteristic
96C22×C43⋊C8C2311yescharacteristic
97#13063323—28no—
98#13063323—22no—
99#13063323C2314yes—
100#13063320—28no—
101#13063316—22no—
102#13063316C2314yes—
103#13063315—28no—
104#13063308—28no—
105#13063305—22no—
106#13063305C2314yes—
107#13063304—22no—
108#13063304—22no—
109#13063304—28no—
110#13063304C2314yes—
111#13063304C2314yes—
112#13063301—22no—
113#13063301—28no—
114#13063301C2314yes—
115Q8×Dic43—22no—
116Q8×Dic43C2314yes—
117#13063290—22no—
118#13063290C2314yes—
119C4×C22⋊D43—28no—
120C4×C22⋊D43D414yes—
121C4×C22⋊D43C2314yes—
122#13063284—28no—
123#13063283—22no—
124#13063283C2314yes—
125C2×C4⋊Dic43—21no—
126C2×C4⋊Dic43—21no—
127C2×C4⋊Dic43—21no—
128C2×C4⋊Dic43C2311yescharacteristic
129C2×C4⋊Dic43C2311yescharacteristic
130C2×Dic43⋊C4—21no—
131C2×Dic43⋊C4—21no—
132C2×Dic43⋊C4—21no—
133C2×Dic43⋊C4—21no—
134C2×Dic43⋊C4—21no—
135C2×Dic43⋊C4—21no—
136C2×Dic43⋊C4—21no—
137C2×Dic43⋊C4D411yescharacteristic
138C2×C22⋊Dic43—21no—
139C2×C22⋊Dic43—21no—
140C2×C22⋊Dic43D411yescharacteristic
141C2×(C2×D43)⋊C4—21no—
142C2×(C2×D43)⋊C4—21no—
143C2×(C2×D43)⋊C4—21no—
144C2×(C2×D43)⋊C4D411yescharacteristic
145C2×C4×Dic43—21no—
146C2×C4×Dic43—21no—
147C2×C4×Dic43—21no—
148C2×C4×Dic43C2311yescharacteristic
149#13063259C2314yes—
150#13063256C2314yes—
151#13063256C2314yes—
152Dic43⋊C8C2314yes—
153#13063250C2314yes—
154#13063250C2314yes—
155#13063249C2314yes—
156#13063249C2314yes—
157#13063248C2314yes—
158#13063248C2314yes—
159C22⋊(C43⋊C8)C2314yes—
160(C2×D43)⋊C8C2314yes—
161#13063235C2314yes—
162C22×Q8×C43—22no—
163C22×Q8×C43—21no—
164C22×Q8×C43—24no—
165C22×Q8×C43—42no—
166C22×Q8×C43C2311yescharacteristic
167C22×Q8×C43C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C23×C4×C43—21no—
170C23×C4×C43—21no—
171C23×C4×C43C2311yescharacteristic
172C22×C8×C43—42no—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175C22×C8×C43C2314yes—
176C2×C4⋊C4×C43—22no—
177C2×C4⋊C4×C43—21no—
178C2×C4⋊C4×C43C2314yes—
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C4⋊C4×C43C2311yescharacteristic
181#103×C43C2314yes—
182#103×C43C2314yes—
183#103×C43C2314yes—
184#103×C43C2314yes—
185C24×C43C2×D411yescharacteristic
186C23×D43C2×D411yescharacteristic
187C2×Q8×C43—21no—
188C2×Q8×C43—24no—
189C2×Q8×C43—21no—
190C2×Q8×C43—22no—
191C2×Q8×C43—28no—
192C2×Q8×C43—22no—
193C2×Q8×C43—22no—
194C2×Q8×C43—44no—
195C2×Q8×C43—44no—
196C2×Q8×C43—48no—
197C2×Q8×C43#4114yes—
198C2×Q8×C43C2412yes—
199C2×Q8×C43C2412yes—
200C22×C4×C43—22no—
201C22×C4×C43—22no—
202C22×C4×C43—21no—
203C22×C4×C43—21no—
204C22×C4×C43—21no—
205C22×C4×C43—24no—
206C22×C4×C43—21no—
207C22×C4×C43—24no—
208C22×C4×C43—44no—
209C22×C4×C43—44no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D412yes—
212C22×C4×C43C2412yes—
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—24no—
215C2×C22⋊D43C2×D414yes—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—21no—
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D411yescharacteristic
223Q8×D43—28no—
224Q8×D43—44no—
225Q8×D43—48no—
226C2×C4×D43—22no—
227C2×C4×D43—22no—
228C2×C4×D43—24no—
229C2×C4×D43—44no—
230C2×C4×D43C2×D412yes—
231C2×C4×D43C2412yes—
232C2×Dic86—22no—
233C2×Dic86—22no—
234C2×Dic86—22no—
235C2×Dic86—22no—
236C2×Dic86—21no—
237C2×Dic86—21no—
238C2×Dic86—24no—
239C2×Dic86—44no—
240C2×Dic86C2412yes—
241C2×Dic86C2412yes—
242C2×C8×C43—22no—
243C2×C8×C43—22no—
244C2×C8×C43—44no—
245C2×C8×C43C2412yes—
246C2×C8×C43C2412yes—
247C4⋊C4×C43—21no—
248C4⋊C4×C43—21no—
249C4⋊C4×C43—24no—
250C4⋊C4×C43C2412yes—
251C4⋊C4×C43C2412yes—
252C22⋊Dic43—24no—
253C22⋊Dic43—24no—
254C22⋊Dic43C2×D414yes—
255#10621885—28no—
256#10621885—44no—
257(C2×D43)⋊C4—24no—
258(C2×D43)⋊C4—24no—
259(C2×D43)⋊C4—24no—
260(C2×D43)⋊C4C2×D414yes—
261C4⋊Dic43—21no—
262C4⋊Dic43—21no—
263C4⋊Dic43—24no—
264C4⋊Dic43—24no—
265C4⋊Dic43—24no—
266C4⋊Dic43C2412yes—
267C4⋊Dic43C2412yes—
268Dic43⋊C4—24no—
269Dic43⋊C4—24no—
270Dic43⋊C4—24no—
271Dic43⋊C4—24no—
272Dic43⋊C4—24no—
273Dic43⋊C4—24no—
274Dic43⋊C4—24no—
275Dic43⋊C4C2×D414yes—
276C4×Dic43—24no—
277C4×Dic43—24no—
278C4×Dic43—24no—
279C4×Dic43C2×D412yes—
280C4×Dic43C2412yes—
281C2×C43⋊C8—22no—
282C2×C43⋊C8—22no—
283C2×C43⋊C8C2412yes—
284C2×C43⋊C8C2412yes—
285Dic172—44no—
286#10621872—44no—
287C23×C43—22no—
288C23×C43—22no—
289C23×C43#13714yes—
290C23×C43C22×D412yes—
291C23×C43C22×D411yescharacteristic
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43C22×D412yes—
296Q8×C43—24no—
297Q8×C43—22no—
298Q8×C43—22no—
299Q8×C43—22no—
300Q8×C43—48no—
301Q8×C43—42no—
302Q8×C43C2×#4114yes—
303C2×C4×C43—24no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—24no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—48no—
313C2×C4×C43—42no—
314C2×C4×C43—48no—
315C2×C4×C43—42no—
316C2×C4×C43—42no—
317C2×C4×C43C22×D412yes—
318C2×C4×C43C22×D411yescharacteristic
319C2×C4×C43C2×#4112yes—
320C2×C4×C43H(5,𝔽2)12yes—
321C2×C4×C43C2511yescharacteristic
322C22⋊D43—28no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—42no—
331C2×Dic43—42no—
332C2×Dic43—42no—
333C2×Dic43—42no—
334C2×Dic43C22×D412yes—
335C2×Dic43C22×D412yes—
336C2×Dic43C22×D412yes—
337C4×D43—24no—
338C4×D43—22no—
339C4×D43—22no—
340C4×D43—48no—
341Dic86—22no—
342Dic86—22no—
343Dic86—22no—
344Dic86—22no—
345Dic86—48no—
346Dic86—42no—
347Dic86—42no—
348C8×C43—22no—
349C8×C43—22no—
350C43⋊C8—22no—
351C43⋊C8—22no—
352C2×#3312—431nomaximal, Sylow
353C22×C43—22no—
354C22×C43—28no—
355C22×C43—22no—
356C22×C43#54612yes—
357C22×C43C2×#13714yes—
358C22×C43C2×#13712yes—
359C22×C43#57812yes—
360C22×C43C23×D411yescharacteristic
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—44no—
365C4×C43—24no—
366C4×C43—22no—
367C4×C43—42no—
368C4×C43—42no—
369C4×C43—42no—
370C4×C43#54612yes—
371C4×C43C22×#4111yescharacteristic
372C4×C43C2×H(5,𝔽2)11yescharacteristic
373Dic43—22no—
374Dic43—22no—
375Dic43—22no—
376Dic43—42no—
377Dic43—42no—
378Dic43—42no—
379Dic43—42no—
380C2×#552—431no—
381C2×D4×Q8—431no—
382#3312—4316no—
383C2×#491—431no—
384C2×#485—431no—
385C2×#483—431no—
386C2×#479—431no—
387C2×#470—431no—
388C2×#467—431no—
389C2×#462—431no—
390C2×#451—431no—
391C2×#451—431no—
392C2×#441—431no—
393C2×#435—431no—
394C2×#419—431no—
395C22×#103D4311yescharacteristic, complemented
396C2×C43—24no—
397C2×C43#331214yescomplemented
398C2×C43C2×#54611yescharacteristic
399C2×C43C22×#13711yescharacteristic
400C2×C43C2×#57811yescharacteristic
401D43—42no—
402C23×Q8—431no—
403C23×Q8C2×D4311yescharacteristic
404C22×Q16—431no—
405C22×Q16—431no—
406C22×Q16—431no—
407C22×M16—431no—
408C23×C8C2×D4311yescharacteristic
409#552—438no—
410#552—864no—
411D4×Q8—438no—
412D4×Q8—864no—
413C2×C4⋊Q8—431no—
414C2×C4⋊Q8—861no—
415C2×#126—861no—
416C2×#125—431no—
417C2×#125—861no—
418C2×#123—861no—
419C2×C22⋊Q8—431no—
420C2×C22⋊Q8—431no—
421C2×C22⋊Q8—431no—
422C2×C22⋊Q8—431no—
423C2×C22⋊Q8—861no—
424C2×C22⋊Q8—861no—
425C2×C4×Q8—431no—
426C2×C4×Q8—431no—
427C2×C4×D4—431no—
428C2×C4×D4—861no—
429C2×#117—431no—
430C2×#117—861no—
431C22×C4⋊C4C2×D4311yescharacteristic
432#491—438no—
433#485—438no—
434#483—438no—
435#479—438no—
436#470—438no—
437#467—438no—
438#462—438no—
439#451—438no—
440#451—438no—
441#441—438no—
442#435—438no—
443C2×#107—431no—
444C2×#106—431no—
445C2×#106—431no—
446C2×C4⋊C8—431no—
447#419—438no—
448C2×#103—431no—
449C2×#103—431no—
450C2×#103—431no—
451C2×#103—431no—
452C2×#103—431no—
453C2×#103—431no—
454C2×#103C2×D4311yescharacteristic
455C2×#103C2×D4311yescharacteristic
456C2×#103C2×D4311yescharacteristic
457C2×#103C2×D4311yescharacteristic
458C2×#103C2×D4318yescomplemented
459C2×C22⋊C8—431no—
460C2×C22⋊C8—431no—
461C2×#97—431no—
462C43C2×#331211yescharacteristic, complemented, Sylow
463C22×Q8—21no—
464C22×Q8—22no—
465C22×Q8—24no—
466C22×Q8—42no—
467C22×Q8—434no—
468C22×Q8—431no—
469C22×Q8—431no—
470C22×Q8—861no—
471C22×Q8—862no—
472C22×Q8—864no—
473C22×Q8—1722no—
474C22×Q8C22×D4311yescharacteristic
475C22×Q8C22×D4314yes—
476C22×Q8C22×D4311yescharacteristic
477C22×D4—431no—
478C23×C4—21no—
479C23×C4—21no—
480C23×C4—431no—
481C23×C4—861no—
482C23×C4C22×D4311yescharacteristic
483C2×Q16—434no—
484C2×Q16—434no—
485C2×Q16—434no—
486C2×Q16—864no—
487C2×Q16—1722no—
488C2×Q16—1722no—
489C2×M16—434no—
490C2×M16—1722no—
491C22×C8—42no—
492C22×C8—431no—
493C22×C8—431no—
494C22×C8C22×D4311yescharacteristic
495C22×C8C22×D4311yescharacteristic
496C22×C8C22×D4314yes—
497C4⋊Q8—434no—
498C4⋊Q8—862no—
499C4⋊Q8—868no—
500#126—868no—
501#125—434no—
502#125—862no—
503#125—868no—
504#123—868no—
505C22⋊Q8—434no—
506C22⋊Q8—434no—
507C22⋊Q8—434no—
508C22⋊Q8—434no—
509C22⋊Q8—868no—
510C22⋊Q8—868no—
511C22⋊Q8—862no—
512C22⋊Q8—862no—
513C22⋊Q8—862no—
514C22⋊Q8—862no—
515C4×Q8—434no—
516C4×Q8—434no—
517C4×Q8—862no—
518C4×Q8—862no—
519C4×D4—434no—
520C4×D4—434no—
521C4×D4—868no—
522#117—434no—
523#117—868no—
524#117—862no—
525C2×C4⋊C4—21no—
526C2×C4⋊C4—22no—
527C2×C4⋊C4—431no—
528C2×C4⋊C4—431no—
529C2×C4⋊C4—431no—
530C2×C4⋊C4—861no—
531C2×C4⋊C4—861no—
532C2×C4⋊C4—861no—
533C2×C4⋊C4—861no—
534C2×C4⋊C4—861no—
535C2×C4⋊C4—861no—
536C2×C4⋊C4—861no—
537C2×C4⋊C4—861no—
538C2×C4⋊C4—861no—
539C2×C4⋊C4—861no—
540C2×C4⋊C4C22×D4311yescharacteristic
541C2×C4⋊C4C22×D4311yescharacteristic
542C2×C4⋊C4C22×D4314yes—
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×C42—431no—
551C2×C42—861no—
552C2×C42—861no—
553C2×C42—861no—
554#107—434no—
555#106—434no—
556#106—434no—
557C4⋊C8—434no—
558#103—434no—
559#103—434no—
560#103—434no—
561#103—434no—
562#103—434no—
563#103—434no—
564#103C22×D4314yes—
565#103C22×D4314yes—
566#103C22×D4314yes—
567#103C22×D4314yes—
568C22⋊C8—434no—
569C22⋊C8—434no—
570#97—434no—
571C24—431no—
572C24D4×D4311yescharacteristic
573C2×Q8—21no—
574C2×Q8—24no—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—28no—
578C2×Q8—22no—
579C2×Q8—22no—
580C2×Q8—44no—
581C2×Q8—44no—
582C2×Q8—48no—
583C2×Q8—432no—
584C2×Q8—432no—
585C2×Q8—864no—
586C2×Q8—861no—
587C2×Q8—861no—
588C2×Q8—868no—
589C2×Q8—862no—
590C2×Q8—862no—
591C2×Q8—862no—
592C2×Q8—862no—
593C2×Q8—1724no—
594C2×Q8—1724no—
595C2×Q8—1728no—
596C2×Q8#1062189814yes—
597C2×Q8C23×D4312yes—
598C2×Q8C23×D4312yes—
599C2×D4—434no—
600C2×D4—864no—
601C22×C4—21no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—24no—
605C22×C4—24no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—44no—
610C22×C4—44no—
611C22×C4—431no—
612C22×C4—431no—
613C22×C4—431no—
614C22×C4—432no—
615C22×C4—432no—
616C22×C4—864no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—861no—
620C22×C4—861no—
621C22×C4—861no—
622C22×C4—861no—
623C22×C4—1724no—
624C22×C4D4×D4312yes—
625C22×C4D4×D4311yescharacteristic
626C22×C4C23×D4312yes—
627C22×C4C23×D4311yescharacteristic
628Q16—868no—
629Q16—1724no—
630Q16—1724no—
631M16—1724no—
632C2×C8—22no—
633C2×C8—22no—
634C2×C8—44no—
635C2×C8—432no—
636C2×C8—432no—
637C2×C8—862no—
638C2×C8—862no—
639C2×C8C23×D4312yes—
640C2×C8C23×D4312yes—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—24no—
644C4⋊C4—434no—
645C4⋊C4—432no—
646C4⋊C4—432no—
647C4⋊C4—864no—
648C4⋊C4—864no—
649C4⋊C4—864no—
650C4⋊C4—864no—
651C4⋊C4—864no—
652C4⋊C4—864no—
653C4⋊C4—864no—
654C4⋊C4—864no—
655C4⋊C4—861no—
656C4⋊C4—861no—
657C4⋊C4—864no—
658C4⋊C4—864no—
659C4⋊C4C23×D4312yes—
660C4⋊C4C23×D4312yes—
661C22⋊C4—434no—
662C22⋊C4—434no—
663C22⋊C4—864no—
664C22⋊C4—864no—
665C22⋊C4—864no—
666C22⋊C4—864no—
667C22⋊C4—864no—
668C42—432no—
669C42—432no—
670C42—864no—
671C42—864no—
672C42—864no—
673C23—22no—
674C23—22no—
675C23—432no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23#1306335414yes—
680C23C2×D4×D4312yes—
681C23C2×D4×D4311yescharacteristic
682Q8—22no—
683Q8—24no—
684Q8—22no—
685Q8—22no—
686Q8—48no—
687Q8—42no—
688Q8—862no—
689Q8—862no—
690Q8—862no—
691Q8—862no—
692Q8—1728no—
693Q8—1722no—
694Q8—1722no—
695Q8C2×#1062189814yes—
696D4—868no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—24no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—48no—
707C2×C4—48no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—432no—
712C2×C4—432no—
713C2×C4—432no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—864no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—1728no—
725C2×C4—1722no—
726C2×C4—1722no—
727C2×C4—1722no—
728C2×C4—1722no—
729C2×C4C2×D4×D4312yes—
730C2×C4C2×D4×D4311yescharacteristic
731C2×C4C2×#1062189812yes—
732C2×C4#1306337012yes—
733C2×C4C24×D4311yescharacteristic
734C8—22no—
735C8—22no—
736C8—862no—
737C8—862no—
738C22—22no—
739C22—22no—
740C22—28no—
741C22—862no—
742C22—862no—
743C22—862no—
744C22—1724no—
745C22#1458353912yes—
746C22C2×#1306335414yes—
747C22C2×#1306335412yes—
748C22#1458371212yes—
749C22C22×D4×D4311yescharacteristic
750C4—22no—
751C4—24no—
752C4—42no—
753C4—42no—
754C4—42no—
755C4—862no—
756C4—862no—
757C4—862no—
758C4—1722no—
759C4—1722no—
760C4—1722no—
761C4—1722no—
762C4#1458353912yes—
763C4C22×#1062189811yescharacteristic
764C4C2×#1306337011yescharacteristic
765C2—24no—
766C2—1722no—
767C2#1914664214yesdirect product factor
768C2C2×#1458353911yescharacteristic
769C2C22×#1306335411yescharacteristic
770C2C2×#1458371211yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC22×#103×C43C2
socleC23×C43C22×D4
prime radicalC22×C22⋊D43D4
hypercenterC22×#103D43
hypocenterC43C2×#3312
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#103

Complements

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

NH ≅ G/Ntype
3. #19146642C2direct (N × H)
4. C2×#14583266C2semidirect
5. C2×#14583239C2semidirect
6. C2×#14583229C2semidirect
7. C2×#14583208C2semidirect
8. C2×#14583156C2semidirect
9. C2×#14583140C2semidirect
10. C2×#14583108C2semidirect
11. C2×#14583056C2semidirect
12. C2×#14583055C2semidirect
13. C2×#14583003C2semidirect
15. C2×#14582906C2semidirect
16. C22×#103×C43C2semidirect
44. #14583266C22semidirect
45. #14583239C22semidirect
46. #14583229C22semidirect
47. #14583208C22semidirect
48. #14583156C22semidirect
49. #14583140C22semidirect
50. #14583108C22semidirect
51. #14583056C22semidirect
52. #14583055C22semidirect
53. #14583003C22semidirect
59. #14582906C22semidirect
76. C2×#103×C43C22semidirect
395. C22×#103D43semidirect
397. C2×C43#3312semidirect
458. C2×#103C2×D43semidirect
462. C43C2×#3312semidirect
767. C2#19146642direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145835842
C2×Q8×C22⋊D432
#191466422
C2×#145832662
C2×#145832392
C2×#145832292
C2×#145832082
C2×#145831562
C2×#145831402
C2×#145831082
C2×#145830562
C2×#145830552
C2×#145830032
C2×#145829702
C2×#145829062
C22×#103×C432
C2×#331243