Finite Group Databasebeta

← C2×#19145426 #25967216

Subgroups — C2×#19145426 #25967216

Order 11008.

2342 conjugacy classes of subgroups.

The subgroup lattice has 852 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583412C211yesmaximal, characteristic
2C2×C22⋊Q8×D43C211yesmaximal, characteristic, complemented
3#19145426C2116yesmaximal, direct product factor
4C2×#14583233C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583243C211yesmaximal, characteristic, complemented
7C2×#14583239C211yesmaximal, characteristic, complemented
8C2×#14583155C211yesmaximal, characteristic, complemented
9C2×#14583147C211yesmaximal, characteristic, complemented
10C2×#14583145C211yesmaximal, characteristic, complemented
11C2×#14583064C211yesmaximal, characteristic, complemented
12C2×#14583060C211yesmaximal, characteristic, complemented
13C2×#14583053C211yesmaximal, characteristic, complemented
14C2×#14583039C211yesmaximal, characteristic, complemented
15C2×#14582862C211yesmaximal, characteristic, complemented
16C2×C43×#470C211yesmaximal, characteristic, complemented
17C22×#10621902C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C22×#10621885C2211yescharacteristic, complemented
21C22×#10621873C2211yescharacteristic, complemented
22C22×#10621884C2211yescharacteristic, complemented
23C22×#10621877C2211yescharacteristic
24#14583412—24no—
25#14583412C2218yes—
26C2×#13063310—21no—
27C2×#13063305C2211yescharacteristic
28C2×#13063304C2211yescharacteristic
29C2×#13063303—21no—
30C2×#13063302—21no—
31C2×#13063301C2211yescharacteristic
32C2×#13063301C2211yescharacteristic
33C22⋊Q8×D43—24no—
34C22⋊Q8×D43C2218yescomplemented
35C2×#13063300C2211yescharacteristic
36C2×#13063299C2211yescharacteristic
37C2×#13063295—21no—
38C2×#13063287—21no—
39C2×(C22⋊D43)⋊C4—21no—
40C2×#13063283C2211yescharacteristic
41C2×C4⋊C4×D43—21no—
42C2×C4⋊C4×D43C2211yescharacteristic
43C2×C22⋊C4×D43—21no—
44#14583243C2218yescomplemented
45#14583239C2218yescomplemented
46#14583233C2218yescomplemented
47#14583219C2218yescomplemented
48#14583155C2218yescomplemented
49#14583147C2218yescomplemented
50#14583145C2218yescomplemented
51#14583064C2218yescomplemented
52#14583060C2218yescomplemented
53#14583053C2218yescomplemented
54#14583039C2218yescomplemented
55C2×#13063259C2211yescharacteristic, complemented
56C2×#13063258C2211yescharacteristic, complemented
57C2×#13063256C2211yescharacteristic, complemented
58C2×#13063250C2211yescharacteristic, complemented
59C2×#13063249C2211yescharacteristic, complemented
60C2×#13063249C2211yescharacteristic, complemented
61C2×#13063248C2211yescharacteristic, complemented
62C2×#13063247C2211yescharacteristic, complemented
63C2×#13063245C2211yescharacteristic, complemented
64#14582862C2218yescomplemented
65C2×(C2×D43)⋊C8C2211yescharacteristic
66C2×(C2×D43)⋊C8C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C22×Q16×C43C2211yescharacteristic, complemented
70C22×M16×C43C2211yescharacteristic
71C2×C22⋊Q8×C43C2211yescharacteristic
72C2×C22⋊Q8×C43C2211yescharacteristic
73C43×#470C2218yescomplemented
74C2×#106×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×#103×C43C2211yescharacteristic, complemented
77C24×D43D411yescharacteristic
78C2×#10621902—22no—
79C2×#10621902—42no—
80C2×#10621902—42no—
81C2×#10621902C2314yes—
82C22×Dic86—21no—
83C22×Dic86C2311yescharacteristic
84C2×Q8×D43—22no—
85C2×Q8×D43—42no—
86C2×Q8×D43—42no—
87C2×Q8×D43C2314yes—
88C22×D172—21no—
89C22×D172—21no—
90C22×D172C2311yescharacteristic
91C22×C22⋊D43—21no—
92C23×Dic43D411yescharacteristic
93C22×C4×D43—21no—
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—42no—
97C22×C4×D43—42no—
98C22×C4×D43D411yescharacteristic
99C22×C4×D43D414yes—
100C22×C4×D43D411yescharacteristic
101C22×C4×D43C2311yescharacteristic
102C22×C4×D43C2311yescharacteristic
103C22×C4×D43C2314yes—
104C2×#10621885—42no—
105C2×#10621885C2314yescomplemented
106C2×#10621873—42no—
107C2×#10621873C2314yescomplemented
108C2×#10621884—42no—
109C2×#10621884C2314yescomplemented
110C2×#10621877—42no—
111C2×#10621877C2314yes—
112C22×C43⋊C8C2311yescharacteristic
113C22×C43⋊C8C2311yescharacteristic
114#13063310—28no—
115#13063305—22no—
116#13063305C2314yes—
117#13063304—22no—
118#13063304C2314yes—
119#13063303—28no—
120#13063302—28no—
121#13063301—22no—
122#13063301—22no—
123#13063301C2314yes—
124#13063301C2314yes—
125#13063300—22no—
126#13063300C2314yes—
127#13063299—22no—
128#13063299C2314yes—
129#13063295—28no—
130#13063287—28no—
131(C22⋊D43)⋊C4—28no—
132#13063283—22no—
133#13063283C2314yes—
134C2×C4⋊Dic43—21no—
135C2×C4⋊Dic43C2311yescharacteristic
136C2×C4⋊Dic43C2311yescharacteristic
137C2×Dic43⋊C4—21no—
138C2×Dic43⋊C4—21no—
139C2×Dic43⋊C4—21no—
140C2×Dic43⋊C4—21no—
141C4⋊C4×D43—28no—
142C4⋊C4×D43—22no—
143C4⋊C4×D43C2314yes—
144C2×C22⋊Dic43—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—
151C22⋊C4×D43—28no—
152C2×C4×Dic43—21no—
153#13063259C2314yescomplemented
154#13063258C2314yescomplemented
155#13063256C2314yescomplemented
156#13063250C2314yescomplemented
157#13063249C2314yescomplemented
158#13063249C2314yescomplemented
159#13063248C2314yescomplemented
160#13063247C2314yescomplemented
161#13063245C2314yescomplemented
162(C2×D43)⋊C8C2314yes—
163(C2×D43)⋊C8C2314yes—
164(C2×D43)⋊C8C2314yes—
165(C2×D43)⋊C8C2314yes—
166C22×Q8×C43C2311yescharacteristic
167C22×Q8×C43C2311yescharacteristic
168C23×C4×C43C2311yescharacteristic
169C2×Q16×C43—42no—
170C2×Q16×C43C2314yescomplemented
171C2×M16×C43—42no—
172C2×M16×C43C2314yes—
173C22×C8×C43C2311yescharacteristic
174C22×C8×C43C2311yescharacteristic
175C22⋊Q8×C43—22no—
176C22⋊Q8×C43—22no—
177C22⋊Q8×C43C2314yes—
178C22⋊Q8×C43C2314yes—
179C2×C4⋊C4×C43—21no—
180C2×C4⋊C4×C43—21no—
181C2×C4⋊C4×C43C2311yescharacteristic
182C2×C4⋊C4×C43C2311yescharacteristic
183C2×C22⋊C4×C43—21no—
184C2×C22⋊C4×C43—21no—
185#106×C43C2314yescomplemented
186#103×C43C2314yescomplemented
187#103×C43C2314yescomplemented
188C24×C43C2×D411yescharacteristic
189C23×D43—24no—
190C23×D43—21no—
191C23×D43—42no—
192C23×D43—42no—
193C23×D43C2×D411yescharacteristic
194C23×D43C2×D411yescharacteristic
195C23×D43C2×D414yes—
196C2×Q8×C43—21no—
197C2×Q8×C43—21no—
198C2×Q8×C43—22no—
199C2×Q8×C43—22no—
200C2×Q8×C43—22no—
201C2×Q8×C43—22no—
202C2×Q8×C43C2412yes—
203C2×Q8×C43C2412yes—
204C22×C4×C43—22no—
205C22×C4×C43—22no—
206C22×C4×C43—21no—
207C22×C4×C43—21no—
208C22×C4×C43—21no—
209C22×C4×C43—21no—
210C22×C4×C43C2×D411yescharacteristic
211C22×C4×C43C2×D412yes—
212C22×C4×C43C2412yes—
213C22×C4×C43C2411yescharacteristic
214C2×C22⋊D43—24no—
215C2×C22⋊D43—44no—
216C22×Dic43—21no—
217C22×Dic43—21no—
218C22×Dic43—21no—
219C22×Dic43—42no—
220C22×Dic43C2×D411yescharacteristic
221C22×Dic43C2×D411yescharacteristic
222C22×Dic43C2×D414yes—
223#10621902—44no—
224#10621902—44no—
225#10621902—48no—
226Q8×D43—44no—
227Q8×D43—44no—
228Q8×D43—48no—
229C2×D172—21no—
230C2×D172—24no—
231C2×D172—24no—
232C2×D172—22no—
233C2×D172—22no—
234C2×D172—44no—
235C2×D172—44no—
236C2×D172C2412yes—
237C2×C4×D43—22no—
238C2×C4×D43—22no—
239C2×C4×D43—22no—
240C2×C4×D43—22no—
241C2×C4×D43—24no—
242C2×C4×D43—24no—
243C2×C4×D43—24no—
244C2×C4×D43—42no—
245C2×C4×D43—42no—
246C2×C4×D43—44no—
247C2×C4×D43—44no—
248C2×C4×D43—48no—
249C2×C4×D43—44no—
250C2×C4×D43—44no—
251C2×C4×D43—44no—
252C2×C4×D43C2×D412yes—
253C2×C4×D43C2×D412yes—
254C2×C4×D43C2×D414yes—
255C2×C4×D43C2×D414yes—
256C2×C4×D43C2412yes—
257C2×C4×D43C2412yes—
258C2×Dic86—22no—
259C2×Dic86—22no—
260C2×Dic86—21no—
261C2×Dic86—24no—
262C2×Dic86—44no—
263C2×Dic86C2412yes—
264Q16×C43—44no—
265M16×C43—44no—
266C2×C8×C43—22no—
267C2×C8×C43—22no—
268C2×C8×C43C2412yes—
269C2×C8×C43C2412yes—
270C4⋊C4×C43—24no—
271C4⋊C4×C43—24no—
272C4⋊C4×C43—21no—
273C4⋊C4×C43—21no—
274C4⋊C4×C43C2412yes—
275C4⋊C4×C43C2412yes—
276C22⋊C4×C43—24no—
277C22⋊C4×C43—24no—
278C22⋊Dic43—24no—
279#10621885—44no—
280#10621884—44no—
281(C2×D43)⋊C4—24no—
282(C2×D43)⋊C4—24no—
283(C2×D43)⋊C4—24no—
284(C2×D43)⋊C4—24no—
285(C2×D43)⋊C4—24no—
286(C2×D43)⋊C4—24no—
287C4⋊Dic43—21no—
288C4⋊Dic43—21no—
289C4⋊Dic43—24no—
290C4⋊Dic43C2412yes—
291C4⋊Dic43C2412yes—
292Dic43⋊C4—24no—
293Dic43⋊C4—24no—
294Dic43⋊C4—24no—
295Dic43⋊C4—24no—
296C4×Dic43—24no—
297#10621877—44no—
298C2×C43⋊C8—22no—
299C2×C43⋊C8—22no—
300C2×C43⋊C8C2412yes—
301C2×C43⋊C8C2412yes—
302#10621873—44no—
303C23×C43—22no—
304C23×C43—22no—
305C23×C43—22no—
306C23×C43C22×D412yes—
307C23×C43C22×D411yescharacteristic
308C22×D43—22no—
309C22×D43—22no—
310C22×D43—22no—
311C22×D43—22no—
312C22×D43—22no—
313C22×D43—28no—
314C22×D43—22no—
315C22×D43—44no—
316C22×D43—44no—
317C22×D43—416no—
318C22×D43—42no—
319C22×D43—42no—
320C22×D43—42no—
321C22×D43#13714yes—
322C22×D43C22×D412yes—
323C22×D43C22×D412yes—
324Q8×C43—22no—
325Q8×C43—22no—
326Q8×C43—22no—
327Q8×C43—22no—
328Q8×C43—42no—
329Q8×C43—42no—
330C2×C4×C43—22no—
331C2×C4×C43—24no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—22no—
336C2×C4×C43—22no—
337C2×C4×C43—22no—
338C2×C4×C43—42no—
339C2×C4×C43—42no—
340C2×C4×C43—42no—
341C2×C4×C43—42no—
342C2×C4×C43C22×D412yes—
343C2×C4×C43C22×D411yescharacteristic
344C2×C4×C43H(5,𝔽2)12yes—
345C2×C4×C43H(5,𝔽2)12yes—
346C2×C4×C43C2511yescharacteristic
347C22⋊D43—48no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—44no—
354C2×Dic43—42no—
355C2×Dic43—42no—
356C2×Dic43—42no—
357C2×Dic43C22×D412yes—
358C2×Dic43C22×D412yes—
359D172—22no—
360D172—22no—
361D172—48no—
362D172—48no—
363D172—42no—
364C4×D43—24no—
365C4×D43—24no—
366C4×D43—22no—
367C4×D43—22no—
368C4×D43—22no—
369C4×D43—22no—
370C4×D43—44no—
371C4×D43—44no—
372C4×D43—48no—
373C4×D43—48no—
374C4×D43—48no—
375Dic86—22no—
376Dic86—22no—
377Dic86—48no—
378Dic86—42no—
379C8×C43—22no—
380C8×C43—22no—
381C43⋊C8—22no—
382C43⋊C8—22no—
383C2×#3196—431nomaximal, Sylow
384C22×C43—22no—
385C22×C43—22no—
386C22×C43—22no—
387C22×C43—44no—
388C22×C43#53412yes—
389C22×C43C2×#13712yes—
390C22×C43#57512yes—
391C22×C43C23×D411yescharacteristic
392C2×D43—22no—
393C2×D43—28no—
394C2×D43—22no—
395C2×D43—22no—
396C2×D43—22no—
397C2×D43—22no—
398C2×D43—416no—
399C2×D43—44no—
400C2×D43—42no—
401C2×D43—42no—
402C2×D43—42no—
403C2×D43—84no—
404C2×D43C2×#13714yes—
405C4×C43—22no—
406C4×C43—42no—
407C4×C43—42no—
408C4×C43—42no—
409C4×C43—42no—
410C4×C43#53412yes—
411C4×C43C2×H(5,𝔽2)11yescharacteristic
412C4×C43C2×H(5,𝔽2)11yescharacteristic
413Dic43—22no—
414Dic43—22no—
415Dic43—42no—
416Dic43—42no—
417Dic43—42no—
418C2×#525—431no—
419C22×C22⋊Q8—431no—
420#3196—4316no—
421C2×#484—431no—
422C2×#481—431no—
423C2×#485—431no—
424C2×#485—431no—
425C2×#470—431no—
426C2×#470D4311yescharacteristic, complemented
427C2×#468—431no—
428C2×#468—431no—
429C2×#452—431no—
430C2×#452—431no—
431C2×#451—431no—
432C2×#448—431no—
433C2×#407—431no—
434C2×C43—42no—
435C2×C43#319614yescomplemented
436C2×C43C2×#53411yescharacteristic
437C2×C43C22×#13711yescharacteristic
438C2×C43C2×#57511yescharacteristic
439D43—24no—
440D43—42no—
441D43—82no—
442C22×#41—431no—
443C23×Q8—431no—
444C24×C4—431no—
445C22×Q16—431no—
446C22×Q16C2×D4311yescharacteristic, complemented
447C22×SD16—431no—
448C22×SD16—431no—
449C22×M16—431no—
450C22×M16C2×D4311yescharacteristic
451#525—438no—
452#525—864no—
453C2×#123—861no—
454C2×C22⋊Q8—431no—
455C2×C22⋊Q8—431no—
456C2×C22⋊Q8—431no—
457C2×C22⋊Q8—438no—
458C2×C22⋊Q8—431no—
459C2×C22⋊Q8—861no—
460C2×C22⋊Q8—861no—
461C2×C22⋊Q8—864no—
462C2×C22⋊Q8C2×D4311yescharacteristic
463C2×C22⋊Q8C2×D4311yescharacteristic
464C2×#121—431no—
465C2×#121—431no—
466C2×#120—861no—
467C2×C4×D4—861no—
468C2×C4×D4—861no—
469C2×#117—431no—
470C22×C4⋊C4—431no—
471C22×C4⋊C4—861no—
472C22×C22⋊C4—861no—
473#485—438no—
474#485—438no—
475#484—438no—
476#481—438no—
477#470—438no—
478#470C2×D4318yescomplemented
479#468—438no—
480#468—438no—
481#452—438no—
482#452—438no—
483#451—438no—
484#448—438no—
485C2×#107—431no—
486C2×#107—431no—
487C2×#106—431no—
488C2×#106C2×D4311yescharacteristic, complemented
489C2×#103—431no—
490C2×#103—431no—
491C2×#103—431no—
492C2×#103—431no—
493C2×#103C2×D4311yescharacteristic, complemented
494C2×#103C2×D4311yescharacteristic, complemented
495C2×#102—431no—
496C2×#102—431no—
497#407—438no—
498C2×C22⋊C8—431no—
499C2×C22⋊C8—431no—
500C2×C22⋊C8—431no—
501C2×C22⋊C8—431no—
502C43C2×#319611yescharacteristic, complemented, Sylow
503C25—431no—
504C2×#41—434no—
505C2×#41—862no—
506C2×#41—1722no—
507C2×#41—1722no—
508C22×Q8—434no—
509C22×Q8—431no—
510C22×Q8—861no—
511C22×Q8—862no—
512C22×Q8—1722no—
513C22×Q8—1722no—
514C22×Q8C22×D4311yescharacteristic
515C22×Q8C22×D4311yescharacteristic
516C22×D4—431no—
517C22×D4—861no—
518C22×D4—861no—
519C22×D4—861no—
520C23×C4—431no—
521C23×C4—431no—
522C23×C4—431no—
523C23×C4—431no—
524C23×C4—431no—
525C23×C4—434no—
526C23×C4—434no—
527C23×C4—861no—
528C23×C4—861no—
529C23×C4—861no—
530C23×C4—1722no—
531C23×C4—1722no—
532C23×C4C22×D4311yescharacteristic
533C2×Q16—42no—
534C2×Q16—434no—
535C2×Q16—1722no—
536C2×Q16C22×D4314yescomplemented
537C2×SD16—434no—
538C2×SD16—434no—
539C2×SD16—1722no—
540C2×SD16—1722no—
541C2×M16—42no—
542C2×M16—434no—
543C2×M16—1722no—
544C2×M16C22×D4314yes—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8C22×D4311yescharacteristic
548C22×C8C22×D4311yescharacteristic
549#123—868no—
550C22⋊Q8—22no—
551C22⋊Q8—22no—
552C22⋊Q8—434no—
553C22⋊Q8—434no—
554C22⋊Q8—434no—
555C22⋊Q8—434no—
556C22⋊Q8—868no—
557C22⋊Q8—868no—
558C22⋊Q8—862no—
559C22⋊Q8—862no—
560C22⋊Q8—862no—
561C22⋊Q8—862no—
562C22⋊Q8C22×D4314yes—
563C22⋊Q8C22×D4314yes—
564#121—434no—
565#121—434no—
566#121—862no—
567#121—862no—
568#120—868no—
569C4×D4—868no—
570C4×D4—868no—
571#117—434no—
572#117—862no—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—21no—
575C2×C4⋊C4—431no—
576C2×C4⋊C4—431no—
577C2×C4⋊C4—434no—
578C2×C4⋊C4—862no—
579C2×C4⋊C4—868no—
580C2×C4⋊C4—861no—
581C2×C4⋊C4—861no—
582C2×C4⋊C4—861no—
583C2×C4⋊C4—861no—
584C2×C4⋊C4—861no—
585C2×C4⋊C4C22×D4311yescharacteristic
586C2×C4⋊C4C22×D4311yescharacteristic
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—868no—
590C2×C22⋊C4—861no—
591C2×C22⋊C4—861no—
592C2×C22⋊C4—861no—
593C2×C22⋊C4—861no—
594C2×C22⋊C4—861no—
595C2×C22⋊C4—861no—
596C2×C22⋊C4—861no—
597C2×C42—861no—
598#107—434no—
599#107—434no—
600#106—434no—
601#106C22×D4314yescomplemented
602#103—434no—
603#103—434no—
604#103—434no—
605#103—434no—
606#103C22×D4314yescomplemented
607#103C22×D4314yescomplemented
608#102—434no—
609#102—434no—
610C22⋊C8—434no—
611C22⋊C8—434no—
612C22⋊C8—434no—
613C22⋊C8—434no—
614C24—431no—
615C24—431no—
616C24—434no—
617C24—864no—
618C24—861no—
619C24—1722no—
620C24—1722no—
621C24D4×D4311yescharacteristic
622#41—1724no—
623#41—1724no—
624#41—1728no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—22no—
628C2×Q8—22no—
629C2×Q8—22no—
630C2×Q8—22no—
631C2×Q8—432no—
632C2×Q8—864no—
633C2×Q8—861no—
634C2×Q8—862no—
635C2×Q8—862no—
636C2×Q8—1724no—
637C2×Q8—1724no—
638C2×Q8—1724no—
639C2×Q8—1728no—
640C2×Q8C23×D4312yes—
641C2×Q8C23×D4312yes—
642C2×D4—432no—
643C2×D4—864no—
644C2×D4—864no—
645C2×D4—864no—
646C2×D4—861no—
647C2×D4—862no—
648C2×D4—862no—
649C2×D4—1724no—
650C2×D4—1724no—
651C2×D4—1724no—
652C22×C4—22no—
653C22×C4—22no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—431no—
659C22×C4—431no—
660C22×C4—434no—
661C22×C4—432no—
662C22×C4—432no—
663C22×C4—432no—
664C22×C4—432no—
665C22×C4—434no—
666C22×C4—434no—
667C22×C4—864no—
668C22×C4—864no—
669C22×C4—864no—
670C22×C4—862no—
671C22×C4—862no—
672C22×C4—862no—
673C22×C4—862no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—861no—
677C22×C4—1728no—
678C22×C4—1724no—
679C22×C4—1724no—
680C22×C4—1722no—
681C22×C4—1722no—
682C22×C4—1724no—
683C22×C4—1724no—
684C22×C4—1724no—
685C22×C4—1722no—
686C22×C4D4×D4312yes—
687C22×C4D4×D4311yescharacteristic
688C22×C4C23×D4312yes—
689C22×C4C23×D4311yescharacteristic
690Q16—44no—
691Q16—1724no—
692SD16—1724no—
693SD16—1724no—
694M16—44no—
695M16—1724no—
696C2×C8—22no—
697C2×C8—22no—
698C2×C8—432no—
699C2×C8—432no—
700C2×C8—862no—
701C2×C8—862no—
702C2×C8C23×D4312yes—
703C2×C8C23×D4312yes—
704C4⋊C4—24no—
705C4⋊C4—24no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—432no—
709C4⋊C4—432no—
710C4⋊C4—864no—
711C4⋊C4—864no—
712C4⋊C4—864no—
713C4⋊C4—864no—
714C4⋊C4—861no—
715C4⋊C4—861no—
716C4⋊C4—864no—
717C4⋊C4C23×D4312yes—
718C4⋊C4C23×D4312yes—
719C22⋊C4—24no—
720C22⋊C4—24no—
721C22⋊C4—864no—
722C22⋊C4—864no—
723C22⋊C4—864no—
724C22⋊C4—864no—
725C22⋊C4—864no—
726C22⋊C4—864no—
727C22⋊C4—864no—
728C42—864no—
729C23—22no—
730C23—22no—
731C23—22no—
732C23—434no—
733C23—432no—
734C23—432no—
735C23—868no—
736C23—862no—
737C23—862no—
738C23—862no—
739C23—862no—
740C23—862no—
741C23—862no—
742C23—1724no—
743C23—1724no—
744C23—17216no—
745C23—1722no—
746C23—1722no—
747C23—1722no—
748C23C2×D4×D4312yes—
749C23C2×D4×D4311yescharacteristic
750Q8—22no—
751Q8—22no—
752Q8—22no—
753Q8—22no—
754Q8—42no—
755Q8—42no—
756Q8—862no—
757Q8—862no—
758Q8—1728no—
759Q8—1722no—
760D4—862no—
761D4—862no—
762D4—1728no—
763D4—1728no—
764D4—1728no—
765D4—1722no—
766C2×C4—22no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—42no—
775C2×C4—42no—
776C2×C4—42no—
777C2×C4—42no—
778C2×C4—432no—
779C2×C4—432no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—864no—
783C2×C4—864no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—862no—
787C2×C4—862no—
788C2×C4—862no—
789C2×C4—862no—
790C2×C4—862no—
791C2×C4—1724no—
792C2×C4—1724no—
793C2×C4—1728no—
794C2×C4—1728no—
795C2×C4—1728no—
796C2×C4—1724no—
797C2×C4—1722no—
798C2×C4—1722no—
799C2×C4—1722no—
800C2×C4C2×D4×D4312yes—
801C2×C4C2×D4×D4311yescharacteristic
802C2×C4#1306337012yes—
803C2×C4#1306337112yes—
804C2×C4C24×D4311yescharacteristic
805C8—22no—
806C8—22no—
807C8—862no—
808C8—862no—
809C22—22no—
810C22—22no—
811C22—22no—
812C22—44no—
813C22—434no—
814C22—862no—
815C22—862no—
816C22—868no—
817C22—862no—
818C22—862no—
819C22—862no—
820C22—3444no—
821C22—17216no—
822C22—1722no—
823C22—1722no—
824C22—1722no—
825C22—1724no—
826C22#1458345712yes—
827C22#137×D4312yes—
828C22#1458369812yes—
829C22C22×D4×D4311yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—862no—
836C4—862no—
837C4—1722no—
838C4—1722no—
839C4—1722no—
840C4#1458345712yes—
841C4C2×#1306337011yescharacteristic
842C4C2×#1306337111yescharacteristic
843C2—42no—
844C2—864no—
845C2—3442no—
846C2—1722no—
847C2#1914542614yesdirect product factor
848C2C2×#1458345711yescharacteristic
849C2C2×#137×D4311yescharacteristic
850C2C2×#1458369811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#470C2
socleC23×C43C22×D4
prime radicalC2×#14583412C2
hypercenterC2×#470D43
hypocenterC43C2×#3196
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×D43C2semidirect
3. #19145426C2direct (N × H)
4. C2×#14583233C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583243C2semidirect
7. C2×#14583239C2semidirect
8. C2×#14583155C2semidirect
9. C2×#14583147C2semidirect
10. C2×#14583145C2semidirect
11. C2×#14583064C2semidirect
12. C2×#14583060C2semidirect
13. C2×#14583053C2semidirect
14. C2×#14583039C2semidirect
15. C2×#14582862C2semidirect
16. C2×C43×#470C2semidirect
20. C22×#10621885C22semidirect
21. C22×#10621873C22semidirect
22. C22×#10621884C22semidirect
34. C22⋊Q8×D43C22semidirect
44. #14583243C22semidirect
45. #14583239C22semidirect
46. #14583233C22semidirect
47. #14583219C22semidirect
48. #14583155C22semidirect
49. #14583147C22semidirect
50. #14583145C22semidirect
51. #14583064C22semidirect
52. #14583060C22semidirect
53. #14583053C22semidirect
54. #14583039C22semidirect
55. C2×#13063259C22semidirect
56. C2×#13063258C22semidirect
57. C2×#13063256C22semidirect
58. C2×#13063250C22semidirect
59. C2×#13063249C22semidirect
60. C2×#13063249C22semidirect
61. C2×#13063248C22semidirect
62. C2×#13063247C22semidirect
63. C2×#13063245C22semidirect
64. #14582862C22semidirect
69. C22×Q16×C43C22semidirect
73. C43×#470C22semidirect
74. C2×#106×C43C22semidirect
75. C2×#103×C43C22semidirect
76. C2×#103×C43C22semidirect
105. C2×#10621885C23semidirect
107. C2×#10621873C23semidirect
109. C2×#10621884C23semidirect
153. #13063259C23semidirect
154. #13063258C23semidirect
155. #13063256C23semidirect
156. #13063250C23semidirect
157. #13063249C23semidirect
158. #13063249C23semidirect
159. #13063248C23semidirect
160. #13063247C23semidirect
161. #13063245C23semidirect
170. C2×Q16×C43C23semidirect
185. #106×C43C23semidirect
186. #103×C43C23semidirect
187. #103×C43C23semidirect
426. C2×#470D43semidirect
435. C2×C43#3196semidirect
446. C22×Q16C2×D43semidirect
478. #470C2×D43semidirect
488. C2×#106C2×D43semidirect
493. C2×#103C2×D43semidirect
494. C2×#103C2×D43semidirect
502. C43C2×#3196semidirect
536. C2×Q16C22×D43semidirect
601. #106C22×D43semidirect
606. #103C22×D43semidirect
607. #103C22×D43semidirect
847. C2#19145426direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834122
C2×C22⋊Q8×D432
#191454262
C2×#145832332
C2×#145832192
C2×#145832432
C2×#145832392
C2×#145831552
C2×#145831472
C2×#145831452
C2×#145830642
C2×#145830602
C2×#145830532
C2×#145830392
C2×#145828622
C2×C43×#4702
C2×#319643