Finite Group Databasebeta

← C2×#19145429 #25967219

Subgroups — C2×#19145429 #25967219

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×#14583411C211yesmaximal, characteristic
2C2×C22⋊Q8×D43C211yesmaximal, characteristic, complemented
3#19145429C2116yesmaximal, direct product factor
4C2×#14583236C211yesmaximal, characteristic, complemented
5C2×#14583219C211yesmaximal, characteristic, complemented
6C2×#14583240C211yesmaximal, characteristic, complemented
7C2×#14583158C211yesmaximal, characteristic, complemented
8C2×#14583156C211yesmaximal, characteristic, complemented
9C2×#14583148C211yesmaximal, characteristic, complemented
10C2×#14583146C211yesmaximal, characteristic, complemented
11C2×#14583063C211yesmaximal, characteristic, complemented
12C2×#14583059C211yesmaximal, characteristic, complemented
13C2×#14583056C211yesmaximal, characteristic, complemented
14C2×#14583039C211yesmaximal, characteristic, complemented
15C2×#14582861C211yesmaximal, characteristic, complemented
16C2×C43×#485C211yesmaximal, characteristic, complemented
17C22×#10621898C2211yescharacteristic
18C22×Q8×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C22×Dic172C2211yescharacteristic, complemented
21C22×#10621885C2211yescharacteristic, complemented
22C22×#10621873C2211yescharacteristic, complemented
23C22×#10621884C2211yescharacteristic, complemented
24C22×#10621872C2211yescharacteristic
25C22×#10621872C2211yescharacteristic
26#14583411—24no—
27#14583411C2218yes—
28C2×#13063309—21no—
29C2×#13063305C2211yescharacteristic
30C2×#13063305C2211yescharacteristic
31C2×#13063305C2211yescharacteristic
32C2×#13063304C2211yescharacteristic
33C2×#13063303—21no—
34C2×#13063302—21no—
35C2×#13063301C2211yescharacteristic
36C22⋊Q8×D43—24no—
37C22⋊Q8×D43C2218yescomplemented
38C2×#13063300C2211yescharacteristic
39C2×#13063300C2211yescharacteristic
40C2×#13063295—21no—
41C2×C4×D172—21no—
42C2×C4×D172—21no—
43C2×C4⋊C4×D43—21no—
44C2×C4⋊C4×D43C2211yescharacteristic
45C2×C22⋊C4×D43—21no—
46#14583240C2218yescomplemented
47#14583236C2218yescomplemented
48#14583219C2218yescomplemented
49#14583158C2218yescomplemented
50#14583156C2218yescomplemented
51#14583148C2218yescomplemented
52#14583146C2218yescomplemented
53#14583063C2218yescomplemented
54#14583059C2218yescomplemented
55#14583056C2218yescomplemented
56#14583039C2218yescomplemented
57C2×#13063258C2211yescharacteristic, complemented
58C2×#13063256C2211yescharacteristic, complemented
59C2×#13063250C2211yescharacteristic, complemented
60C2×#13063248C2211yescharacteristic, complemented
61C2×#13063248C2211yescharacteristic, complemented
62C2×#13063248C2211yescharacteristic, complemented
63C2×#13063247C2211yescharacteristic, complemented
64C2×#13063245C2211yescharacteristic, complemented
65#14582861C2218yescomplemented
66C2×C22⋊(C43⋊C8)C2211yescharacteristic
67C2×(C2×D43)⋊C8C2211yescharacteristic
68C2×(C2×D43)⋊C8C2211yescharacteristic
69C2×C22⋊Q8×C43C2211yescharacteristic
70C2×#117×C43C2211yescharacteristic
71C43×#485C2218yescomplemented
72C2×#107×C43C2211yescharacteristic, complemented
73C2×#106×C43C2211yescharacteristic, complemented
74C2×#103×C43C2211yescharacteristic, complemented
75C2×#103×C43C2211yescharacteristic, complemented
76C2×C22⋊C8×C43C2211yescharacteristic
77C24×D43D411yescharacteristic
78C2×#10621898—22no—
79C2×#10621898—42no—
80C2×#10621898—42no—
81C2×#10621898C2314yes—
82C22×Dic86—21no—
83C22×Dic86C2311yescharacteristic
84C22×Dic86C2311yescharacteristic
85C2×Q8×D43—22no—
86C2×Q8×D43—42no—
87C2×Q8×D43—42no—
88C2×Q8×D43C2314yes—
89C22×D172—21no—
90C22×D172—21no—
91C22×D172C2311yescharacteristic
92C22×C22⋊D43—21no—
93C23×Dic43D411yescharacteristic
94C22×C4×D43—21no—
95C22×C4×D43—21no—
96C22×C4×D43—21no—
97C22×C4×D43—42no—
98C22×C4×D43—42no—
99C22×C4×D43D411yescharacteristic
100C22×C4×D43D411yescharacteristic
101C22×C4×D43D414yes—
102C22×C4×D43C2311yescharacteristic
103C22×C4×D43C2311yescharacteristic
104C22×C4×D43C2314yes—
105C2×Dic172—42no—
106C2×Dic172C2314yescomplemented
107C2×#10621885—42no—
108C2×#10621885C2314yescomplemented
109C2×#10621873—42no—
110C2×#10621873C2314yescomplemented
111C2×#10621884—42no—
112C2×#10621884C2314yescomplemented
113C2×#10621872—42no—
114C2×#10621872—42no—
115C2×#10621872C2314yes—
116C2×#10621872C2314yes—
117C22×C43⋊C8C2311yescharacteristic
118C22×C43⋊C8C2311yescharacteristic
119#13063309—28no—
120#13063305—22no—
121#13063305—22no—
122#13063305—22no—
123#13063305C2314yes—
124#13063305C2314yes—
125#13063305C2314yes—
126#13063304—22no—
127#13063304C2314yes—
128#13063303—28no—
129#13063302—28no—
130#13063301—22no—
131#13063301C2314yes—
132#13063300—22no—
133#13063300—22no—
134#13063300C2314yes—
135#13063300C2314yes—
136#13063295—28no—
137C4×D172—28no—
138C4×D172—28no—
139C2×C4⋊Dic43—21no—
140C2×C4⋊Dic43—21no—
141C2×C4⋊Dic43—21no—
142C2×C4⋊Dic43C2311yescharacteristic
143C2×Dic43⋊C4—21no—
144C2×Dic43⋊C4—21no—
145C2×Dic43⋊C4—21no—
146C4⋊C4×D43—28no—
147C4⋊C4×D43—22no—
148C4⋊C4×D43C2314yes—
149C2×C22⋊Dic43—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—
156C22⋊C4×D43—28no—
157#13063258C2314yescomplemented
158#13063256C2314yescomplemented
159#13063250C2314yescomplemented
160#13063248C2314yescomplemented
161#13063248C2314yescomplemented
162#13063248C2314yescomplemented
163#13063247C2314yescomplemented
164#13063245C2314yescomplemented
165C22⋊(C43⋊C8)C2314yes—
166(C2×D43)⋊C8C2314yes—
167(C2×D43)⋊C8C2314yes—
168C22×Q8×C43C2311yescharacteristic
169C23×C4×C43C2311yescharacteristic
170C22×C8×C43C2311yescharacteristic
171C22×C8×C43C2311yescharacteristic
172C22⋊Q8×C43—22no—
173C22⋊Q8×C43C2314yes—
174#117×C43—22no—
175#117×C43C2314yes—
176C2×C4⋊C4×C43—21no—
177C2×C4⋊C4×C43C2311yescharacteristic
178C2×C4⋊C4×C43C2311yescharacteristic
179C2×C4⋊C4×C43C2311yescharacteristic
180C2×C22⋊C4×C43—21no—
181C2×C22⋊C4×C43—21no—
182C2×C42×C43—21no—
183#107×C43C2314yescomplemented
184#106×C43C2314yescomplemented
185#103×C43C2314yescomplemented
186#103×C43C2314yescomplemented
187C22⋊C8×C43C2314yes—
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—22no—
198C2×Q8×C43—22no—
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—21no—
206C22×C4×C43C2×D411yescharacteristic
207C22×C4×C43C2×D412yes—
208C22×C4×C43C2412yes—
209C22×C4×C43C2411yescharacteristic
210C2×C22⋊D43—24no—
211C2×C22⋊D43—44no—
212C22×Dic43—21no—
213C22×Dic43—21no—
214C22×Dic43—21no—
215C22×Dic43—42no—
216C22×Dic43C2×D411yescharacteristic
217C22×Dic43C2×D411yescharacteristic
218C22×Dic43C2×D414yes—
219Q8×D43—44no—
220Q8×D43—44no—
221Q8×D43—48no—
222#10621898—44no—
223#10621898—44no—
224#10621898—48no—
225C2×D172—21no—
226C2×D172—24no—
227C2×D172—24no—
228C2×D172—22no—
229C2×D172—22no—
230C2×D172—44no—
231C2×D172—44no—
232C2×D172C2412yes—
233C2×C4×D43—22no—
234C2×C4×D43—22no—
235C2×C4×D43—22no—
236C2×C4×D43—22no—
237C2×C4×D43—24no—
238C2×C4×D43—24no—
239C2×C4×D43—24no—
240C2×C4×D43—42no—
241C2×C4×D43—42no—
242C2×C4×D43—44no—
243C2×C4×D43—44no—
244C2×C4×D43—48no—
245C2×C4×D43—44no—
246C2×C4×D43—44no—
247C2×C4×D43—44no—
248C2×C4×D43C2×D412yes—
249C2×C4×D43C2×D412yes—
250C2×C4×D43C2×D414yes—
251C2×C4×D43C2×D414yes—
252C2×C4×D43C2412yes—
253C2×C4×D43C2412yes—
254C2×Dic86—22no—
255C2×Dic86—22no—
256C2×Dic86—22no—
257C2×Dic86—22no—
258C2×Dic86—21no—
259C2×Dic86—21no—
260C2×Dic86—24no—
261C2×Dic86—44no—
262C2×Dic86C2412yes—
263C2×Dic86C2412yes—
264C2×C8×C43—22no—
265C2×C8×C43—22no—
266C2×C8×C43C2412yes—
267C2×C8×C43C2412yes—
268C4⋊C4×C43—24no—
269C4⋊C4×C43—21no—
270C4⋊C4×C43—21no—
271C4⋊C4×C43—21no—
272C4⋊C4×C43C2412yes—
273C4⋊C4×C43C2412yes—
274C4⋊C4×C43C2412yes—
275C22⋊C4×C43—24no—
276C22⋊C4×C43—24no—
277C42×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—24no—
289C4⋊Dic43—24no—
290C4⋊Dic43—24no—
291C4⋊Dic43C2412yes—
292Dic43⋊C4—24no—
293Dic43⋊C4—24no—
294Dic43⋊C4—24no—
295C2×C43⋊C8—22no—
296C2×C43⋊C8—22no—
297C2×C43⋊C8C2412yes—
298C2×C43⋊C8C2412yes—
299Dic172—44no—
300#10621873—44no—
301#10621872—44no—
302#10621872—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—42no—
327C2×C4×C43—22no—
328C2×C4×C43—24no—
329C2×C4×C43—22no—
330C2×C4×C43—22no—
331C2×C4×C43—22no—
332C2×C4×C43—22no—
333C2×C4×C43—22no—
334C2×C4×C43—22no—
335C2×C4×C43—42no—
336C2×C4×C43—42no—
337C2×C4×C43—42no—
338C2×C4×C43—42no—
339C2×C4×C43C22×D412yes—
340C2×C4×C43C22×D411yescharacteristic
341C2×C4×C43H(5,𝔽2)12yes—
342C2×C4×C43H(5,𝔽2)12yes—
343C2×C4×C43C2511yescharacteristic
344C22⋊D43—48no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—44no—
351C2×Dic43—42no—
352C2×Dic43—42no—
353C2×Dic43—42no—
354C2×Dic43C22×D412yes—
355C2×Dic43C22×D412yes—
356D172—22no—
357D172—22no—
358D172—48no—
359D172—48no—
360D172—42no—
361C4×D43—24no—
362C4×D43—24no—
363C4×D43—22no—
364C4×D43—22no—
365C4×D43—22no—
366C4×D43—22no—
367C4×D43—44no—
368C4×D43—44no—
369C4×D43—48no—
370C4×D43—48no—
371C4×D43—48no—
372Dic86—22no—
373Dic86—22no—
374Dic86—22no—
375Dic86—22no—
376Dic86—48no—
377Dic86—42no—
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×#485D4311yescharacteristic, complemented
425C2×#470—431no—
426C2×#470—431no—
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×Q16—431no—
447C22×SD16—431no—
448C22×SD16—431no—
449C22×M16—431no—
450C22×M16—431no—
451#525—438no—
452#525—864no—
453C2×#123—861no—
454C2×C22⋊Q8—431no—
455C2×C22⋊Q8—431no—
456C2×C22⋊Q8—438no—
457C2×C22⋊Q8—431no—
458C2×C22⋊Q8—431no—
459C2×C22⋊Q8—431no—
460C2×C22⋊Q8—861no—
461C2×C22⋊Q8—861no—
462C2×C22⋊Q8—864no—
463C2×C22⋊Q8C2×D4311yescharacteristic
464C2×#121—431no—
465C2×#121—431no—
466C2×#120—861no—
467C2×C4×D4—861no—
468C2×C4×D4—861no—
469C2×#117C2×D4311yescharacteristic
470C22×C4⋊C4—431no—
471C22×C4⋊C4—861no—
472C22×C22⋊C4—861no—
473#485—438no—
474#485C2×D4318yescomplemented
475#484—438no—
476#481—438no—
477#470—438no—
478#470—438no—
479#468—438no—
480#468—438no—
481#452—438no—
482#452—438no—
483#451—438no—
484#448—438no—
485C2×#107—431no—
486C2×#107C2×D4311yescharacteristic, complemented
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⋊C8C2×D4311yescharacteristic
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—431no—
511C22×Q8—861no—
512C22×Q8—862no—
513C22×Q8—1722no—
514C22×Q8—1722no—
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—434no—
534C2×Q16—434no—
535C2×Q16—1722no—
536C2×Q16—1722no—
537C2×SD16—434no—
538C2×SD16—434no—
539C2×SD16—1722no—
540C2×SD16—1722no—
541C2×M16—434no—
542C2×M16—434no—
543C2×M16—1722no—
544C2×M16—1722no—
545C22×C8—431no—
546C22×C8—431no—
547C22×C8C22×D4311yescharacteristic
548C22×C8C22×D4311yescharacteristic
549#123—868no—
550C22⋊Q8—22no—
551C22⋊Q8—434no—
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⋊Q8—862no—
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—22no—
572#117C22×D4314yes—
573C2×C4⋊C4—21no—
574C2×C4⋊C4—431no—
575C2×C4⋊C4—434no—
576C2×C4⋊C4—862no—
577C2×C4⋊C4—868no—
578C2×C4⋊C4—861no—
579C2×C4⋊C4—861no—
580C2×C4⋊C4—861no—
581C2×C4⋊C4—861no—
582C2×C4⋊C4—861no—
583C2×C4⋊C4—861no—
584C2×C4⋊C4C22×D4311yescharacteristic
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—21no—
598#107—434no—
599#107C22×D4314yescomplemented
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⋊C8C22×D4314yes—
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—22no—
627C2×Q8—22no—
628C2×Q8—432no—
629C2×Q8—432no—
630C2×Q8—864no—
631C2×Q8—861no—
632C2×Q8—861no—
633C2×Q8—862no—
634C2×Q8—862no—
635C2×Q8—862no—
636C2×Q8—862no—
637C2×Q8—1724no—
638C2×Q8—1724no—
639C2×Q8—1724no—
640C2×Q8—1728no—
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—862no—
670C22×C4—862no—
671C22×C4—862no—
672C22×C4—862no—
673C22×C4—861no—
674C22×C4—861no—
675C22×C4—861no—
676C22×C4—864no—
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—1724no—
691Q16—1724no—
692SD16—1724no—
693SD16—1724no—
694M16—1724no—
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—21no—
706C4⋊C4—21no—
707C4⋊C4—21no—
708C4⋊C4—432no—
709C4⋊C4—864no—
710C4⋊C4—864no—
711C4⋊C4—864no—
712C4⋊C4—864no—
713C4⋊C4—864no—
714C4⋊C4—861no—
715C4⋊C4—864no—
716C4⋊C4C23×D4312yes—
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—24no—
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—42no—
753Q8—862no—
754Q8—862no—
755Q8—862no—
756Q8—862no—
757Q8—1728no—
758Q8—1722no—
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#1306337112yes—
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#1458346012yes—
827C22#137×D4312yes—
828C22#1458369612yes—
829C22C22×D4×D4311yescharacteristic
830C4—22no—
831C4—42no—
832C4—42no—
833C4—42no—
834C4—42no—
835C4—862no—
836C4—862no—
837C4—1722no—
838C4—1722no—
839C4—1722no—
840C4#1458346012yes—
841C4C2×#1306337111yescharacteristic
842C4C2×#1306337111yescharacteristic
843C2—42no—
844C2—864no—
845C2—3442no—
846C2—1722no—
847C2#1914542914yesdirect product factor
848C2C2×#1458346011yescharacteristic
849C2C2×#137×D4311yescharacteristic
850C2C2×#1458369611yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#485C2
socleC23×C43C22×D4
prime radicalC2×#14583411C2
hypercenterC2×#485D43
hypocenterC43C2×#3196
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#485

Complements

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

NH ≅ G/Ntype
2. C2×C22⋊Q8×D43C2semidirect
3. #19145429C2direct (N × H)
4. C2×#14583236C2semidirect
5. C2×#14583219C2semidirect
6. C2×#14583240C2semidirect
7. C2×#14583158C2semidirect
8. C2×#14583156C2semidirect
9. C2×#14583148C2semidirect
10. C2×#14583146C2semidirect
11. C2×#14583063C2semidirect
12. C2×#14583059C2semidirect
13. C2×#14583056C2semidirect
14. C2×#14583039C2semidirect
15. C2×#14582861C2semidirect
16. C2×C43×#485C2semidirect
20. C22×Dic172C22semidirect
21. C22×#10621885C22semidirect
22. C22×#10621873C22semidirect
23. C22×#10621884C22semidirect
37. C22⋊Q8×D43C22semidirect
46. #14583240C22semidirect
47. #14583236C22semidirect
48. #14583219C22semidirect
49. #14583158C22semidirect
50. #14583156C22semidirect
51. #14583148C22semidirect
52. #14583146C22semidirect
53. #14583063C22semidirect
54. #14583059C22semidirect
55. #14583056C22semidirect
56. #14583039C22semidirect
57. C2×#13063258C22semidirect
58. C2×#13063256C22semidirect
59. C2×#13063250C22semidirect
60. C2×#13063248C22semidirect
61. C2×#13063248C22semidirect
62. C2×#13063248C22semidirect
63. C2×#13063247C22semidirect
64. C2×#13063245C22semidirect
65. #14582861C22semidirect
71. C43×#485C22semidirect
72. C2×#107×C43C22semidirect
73. C2×#106×C43C22semidirect
74. C2×#103×C43C22semidirect
75. C2×#103×C43C22semidirect
106. C2×Dic172C23semidirect
108. C2×#10621885C23semidirect
110. C2×#10621873C23semidirect
112. C2×#10621884C23semidirect
157. #13063258C23semidirect
158. #13063256C23semidirect
159. #13063250C23semidirect
160. #13063248C23semidirect
161. #13063248C23semidirect
162. #13063248C23semidirect
163. #13063247C23semidirect
164. #13063245C23semidirect
183. #107×C43C23semidirect
184. #106×C43C23semidirect
185. #103×C43C23semidirect
186. #103×C43C23semidirect
424. C2×#485D43semidirect
435. C2×C43#3196semidirect
474. #485C2×D43semidirect
486. C2×#107C2×D43semidirect
488. C2×#106C2×D43semidirect
493. C2×#103C2×D43semidirect
494. C2×#103C2×D43semidirect
502. C43C2×#3196semidirect
599. #107C22×D43semidirect
601. #106C22×D43semidirect
606. #103C22×D43semidirect
607. #103C22×D43semidirect
847. C2#19145429direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834112
C2×C22⋊Q8×D432
#191454292
C2×#145832362
C2×#145832192
C2×#145832402
C2×#145831582
C2×#145831562
C2×#145831482
C2×#145831462
C2×#145830632
C2×#145830592
C2×#145830562
C2×#145830392
C2×#145828612
C2×C43×#4852
C2×#319643