Finite Group Databasebeta

← C2×#19138409 #25264082

Subgroups — C2×#19138409 #25264082

Order 11008.

3830 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
1C22×#13063305C211yesmaximal, characteristic, complemented
2C22×#13063303C211yesmaximal, characteristic, complemented
3C22×C4×D172C211yesmaximal, characteristic
4C22×C4⋊C4×D43C211yesmaximal, characteristic, complemented
5#19138409C2116yesmaximal, direct product factor
6C2×#14582836C211yesmaximal, characteristic, complemented
7C2×#14582831C211yesmaximal, characteristic, complemented
8C2×#14582821C211yesmaximal, characteristic, complemented
9C2×#14582820C211yesmaximal, characteristic, complemented
10C2×#14582797C211yesmaximal, characteristic, complemented
11C2×#14582777C211yesmaximal, characteristic
12C2×#14582777C211yesmaximal, characteristic
13C2×#14582773C211yesmaximal, characteristic, complemented
14C2×#14582773C211yesmaximal, characteristic, complemented
15C2×#14582773C211yesmaximal, characteristic, complemented
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×D172C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C23×C4×D43C2211yescharacteristic
23C2×#13063305—28no—
24C2×#13063305C2218yescomplemented
25C2×#13063303—28no—
26C2×#13063303C2218yescomplemented
27C2×C4×D172—28no—
28C2×C4×D172C2218yes—
29C22×C4⋊Dic43C2211yescharacteristic
30C22×C4⋊Dic43C2211yescharacteristic
31C22×C4⋊Dic43C2211yescharacteristic
32C22×C4⋊Dic43C2211yescharacteristic
33C22×C4⋊Dic43C2211yescharacteristic
34C22×C4⋊Dic43C2211yescharacteristic
35C22×Dic43⋊C4C2211yescharacteristic
36C22×Dic43⋊C4C2211yescharacteristic
37C22×Dic43⋊C4C2211yescharacteristic
38C22×Dic43⋊C4C2211yescharacteristic
39C2×C4⋊C4×D43—28no—
40C2×C4⋊C4×D43C2218yescomplemented
41C22×(C2×D43)⋊C4C2211yescharacteristic
42C22×(C2×D43)⋊C4C2211yescharacteristic
43C22×(C2×D43)⋊C4C2211yescharacteristic
44C22×(C2×D43)⋊C4C2211yescharacteristic
45C22×(C2×D43)⋊C4C2211yescharacteristic
46C22×(C2×D43)⋊C4C2211yescharacteristic
47C22×(C2×D43)⋊C4C2211yescharacteristic
48C22×(C2×D43)⋊C4C2211yescharacteristic
49#14582836C2218yescomplemented
50#14582831C2218yescomplemented
51#14582821C2218yescomplemented
52#14582820C2218yescomplemented
53#14582797C2218yescomplemented
54#14582777C2218yes—
55#14582777C2218yes—
56#14582773C2218yescomplemented
57#14582773C2218yescomplemented
58#14582773C2218yescomplemented
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2211yescharacteristic
61C2×C43⋊#95C2211yescharacteristic
62C2×C43⋊#95C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C42×C43C2211yescharacteristic
66C43×#387C2218yescomplemented
67C2×#95×C43C2211yescharacteristic
68C2×#95×C43C2211yescharacteristic
69C2×#95×C43C2211yescharacteristic
70C2×#95×C43C2211yescharacteristic
71C24×D43C2311yescharacteristic
72C24×D43C2311yescharacteristic
73C22×Dic86—24no—
74C22×Dic86—24no—
75C22×Dic86—42no—
76C22×Dic86C2314yes—
77C22×D172—24no—
78C22×D172—24no—
79C22×D172Q818yescomplemented
80C22×D172C2314yes—
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C23×Dic43C2311yescharacteristic
86C23×Dic43C2311yescharacteristic
87C22×C4×D43—24no—
88C22×C4×D43—24no—
89C22×C4×D43—24no—
90C22×C4×D43—24no—
91C22×C4×D43—24no—
92C22×C4×D43—24no—
93C22×C4×D43—24no—
94C22×C4×D43—24no—
95C22×C4×D43—24no—
96C22×C4×D43—42no—
97C22×C4×D43—42no—
98C22×C4×D43—42no—
99C22×C4×D43C2314yes—
100C22×C4×D43C2314yes—
101C22×C4×D43C2314yes—
102C22×C4×D43C2314yes—
103#13063305—232no—
104#13063303—232no—
105C4×D172—232no—
106C2×C4⋊Dic43—24no—
107C2×C4⋊Dic43—24no—
108C2×C4⋊Dic43—24no—
109C2×C4⋊Dic43—24no—
110C2×C4⋊Dic43—24no—
111C2×C4⋊Dic43—42no—
112C2×C4⋊Dic43C2314yes—
113C2×C4⋊Dic43C2314yes—
114C2×C4⋊Dic43C2314yes—
115C2×C4⋊Dic43C2314yes—
116C2×C4⋊Dic43C2314yes—
117C2×C4⋊Dic43C2314yes—
118C2×Dic43⋊C4—24no—
119C2×Dic43⋊C4—24no—
120C2×Dic43⋊C4—24no—
121C2×Dic43⋊C4—24no—
122C2×Dic43⋊C4C2314yes—
123C2×Dic43⋊C4C2314yes—
124C2×Dic43⋊C4C2314yes—
125C2×Dic43⋊C4C2314yes—
126C4⋊C4×D43—232no—
127C2×(C2×D43)⋊C4—24no—
128C2×(C2×D43)⋊C4—24no—
129C2×(C2×D43)⋊C4—24no—
130C2×(C2×D43)⋊C4—24no—
131C2×(C2×D43)⋊C4—24no—
132C2×(C2×D43)⋊C4—24no—
133C2×(C2×D43)⋊C4—42no—
134C2×(C2×D43)⋊C4D418yes—
135C2×(C2×D43)⋊C4C2314yes—
136C2×(C2×D43)⋊C4C2314yes—
137C2×(C2×D43)⋊C4C2314yes—
138C2×(C2×D43)⋊C4C2314yes—
139C2×(C2×D43)⋊C4C2314yes—
140C2×(C2×D43)⋊C4C2314yes—
141C2×(C2×D43)⋊C4C2314yes—
142C2×(C2×D43)⋊C4C2314yes—
143C43⋊#95C2314yes—
144C43⋊#95C2314yes—
145C43⋊#95C2314yes—
146C43⋊#95C2314yes—
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C23×C4×C43C2311yescharacteristic
150C23×C4×C43C2311yescharacteristic
151C23×C4×C43C2311yescharacteristic
152C23×C4×C43C2311yescharacteristic
153C23×C4×C43C2311yescharacteristic
154C2×C4⋊C4×C43—24no—
155C2×C4⋊C4×C43D418yescomplemented
156C2×C4⋊C4×C43C2314yes—
157C2×C4⋊C4×C43C2314yes—
158C2×C42×C43—24no—
159C2×C42×C43C2314yes—
160#95×C43C2314yes—
161#95×C43C2314yes—
162#95×C43C2314yes—
163#95×C43C2314yes—
164C24×C43C2411yescharacteristic
165C23×D43—22no—
166C23×D43—22no—
167C23×D43—22no—
168C23×D43—22no—
169C23×D43—22no—
170C23×D43—22no—
171C23×D43—22no—
172C23×D43—22no—
173C23×D43—22no—
174C23×D43—22no—
175C23×D43C2×D414yes—
176C23×D43C2×Q814yes—
177C23×D43C2×Q814yes—
178C23×D43#4114yes—
179C23×D43C2412yes—
180C23×D43C2412yes—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—22no—
186C22×C4×C43—22no—
187C22×C4×C43—22no—
188C22×C4×C43—22no—
189C22×C4×C43—22no—
190C22×C4×C43—22no—
191C22×C4×C43—22no—
192C22×C4×C43—22no—
193C22×C4×C43—22no—
194C22×C4×C43—22no—
195C22×C4×C43—22no—
196C22×C4×C43—22no—
197C22×C4×C43C2×D414yes—
198C22×C4×C43C2×D414yes—
199C22×C4×C43C2×D414yes—
200C22×C4×C43C2×D414yes—
201C22×C4×C43C2×Q814yes—
202C22×C4×C43C2412yes—
203C22×C4×C43C2412yes—
204C22×C4×C43C2412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2412yes—
207C22×C4×C43C2412yes—
208C22×C4×C43C2412yes—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—22no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43—22no—
224C22×Dic43—22no—
225C22×Dic43C2×D414yes—
226C22×Dic43#4114yes—
227C22×Dic43C2412yes—
228C22×Dic43C2412yes—
229C22×Dic43C2412yes—
230C22×Dic43C2412yes—
231C22×Dic43C2412yes—
232C22×Dic43C2412yes—
233C2×D172—232no—
234C2×D172—28no—
235C2×D172—28no—
236C2×D172C2×Q8116yescomplemented
237C2×C4×D43—232no—
238C2×C4×D43—28no—
239C2×C4×D43—28no—
240C2×C4×D43—28no—
241C2×C4×D43—28no—
242C2×C4×D43—28no—
243C2×C4×D43—28no—
244C2×C4×D43—28no—
245C2×C4×D43—28no—
246C2×C4×D43—28no—
247C2×C4×D43—44no—
248C2×C4×D43—44no—
249C2×C4×D43—44no—
250C2×C4×D43—416no—
251C2×C4×D43—416no—
252C2×C4×D43—416no—
253C2×Dic86—28no—
254C2×Dic86—28no—
255C2×Dic86—44no—
256C2×Dic86—416no—
257C4⋊C4×C43—28no—
258C4⋊C4×C43C2×D4116yescomplemented
259C42×C43—28no—
260(C2×D43)⋊C4—28no—
261(C2×D43)⋊C4—28no—
262(C2×D43)⋊C4—28no—
263(C2×D43)⋊C4—28no—
264(C2×D43)⋊C4—28no—
265(C2×D43)⋊C4—28no—
266(C2×D43)⋊C4—44no—
267(C2×D43)⋊C4C2×D4116yes—
268C4⋊Dic43—28no—
269C4⋊Dic43—28no—
270C4⋊Dic43—28no—
271C4⋊Dic43—28no—
272C4⋊Dic43—28no—
273C4⋊Dic43—44no—
274Dic43⋊C4—28no—
275Dic43⋊C4—28no—
276Dic43⋊C4—28no—
277Dic43⋊C4—28no—
278C23×C43C22×D412yes—
279C23×C43C22×D412yes—
280C23×C43C22×Q812yes—
281C23×C43C2×#4112yes—
282C23×C43C2×#4112yes—
283C23×C43H(5,𝔽2)12yes—
284C23×C432−1+412yes—
285C23×C43C2511yescharacteristic
286C22×D43—28no—
287C22×D43—28no—
288C22×D43—28no—
289C22×D43—28no—
290C22×D43—28no—
291C22×D43—28no—
292C22×D43—22no—
293C22×D43—22no—
294C22×D43—22no—
295C22×D43—22no—
296C22×D43—28no—
297C22×D43—28no—
298C22×D43—28no—
299C22×D43—22no—
300C22×D43—22no—
301C22×D43—22no—
302C22×D43—22no—
303C22×D43—22no—
304C22×D43—22no—
305C22×D43—44no—
306C22×D43—44no—
307C22×D43—44no—
308C22×D43—44no—
309C22×D43C22⋊Q8116yescomplemented
310C22×D43C22×D414yes—
311C22×D43C22×Q814yes—
312C22×D43C22×Q814yes—
313C22×D43C2×#4114yes—
314C2×C4×C43—28no—
315C2×C4×C43—28no—
316C2×C4×C43—28no—
317C2×C4×C43—28no—
318C2×C4×C43—28no—
319C2×C4×C43—22no—
320C2×C4×C43—22no—
321C2×C4×C43—22no—
322C2×C4×C43—22no—
323C2×C4×C43—22no—
324C2×C4×C43—22no—
325C2×C4×C43—22no—
326C2×C4×C43—22no—
327C2×C4×C43—22no—
328C2×C4×C43—22no—
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—44no—
336C2×C4×C43—44no—
337C2×C4×C43C22×D414yes—
338C2×C4×C43C22×D414yes—
339C2×C4×C43C22×D414yes—
340C2×C4×C43C22×D414yes—
341C2×C4×C43C22×Q814yes—
342C2×Dic43—28no—
343C2×Dic43—28no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—22no—
352C2×Dic43—22no—
353C2×Dic43—22no—
354C2×Dic43—22no—
355C2×Dic43—22no—
356C2×Dic43—22no—
357C2×Dic43—22no—
358C2×Dic43—22no—
359C2×Dic43—22no—
360C2×Dic43—44no—
361C2×Dic43—44no—
362C2×Dic43—44no—
363C2×Dic43—44no—
364C2×Dic43C22×D414yes—
365C2×Dic43C2×#4114yes—
366D172—232no—
367C4×D43—232no—
368C4×D43—416no—
369C4×D43—416no—
370C4×D43—416no—
371Dic86—416no—
372C2×#2449—431nomaximal, Sylow
373C22×C43C2×C22⋊Q814yes—
374C22×C43#52514yes—
375C22×C43#53914yes—
376C22×C43D4214yes—
377C22×C43#54714yes—
378C22×C43D4×Q814yes—
379C22×C43#55414yes—
380C22×C43C23×D411yescharacteristic
381C22×C43C23×D411yescharacteristic
382C22×C43C23×Q811yescharacteristic
383C22×C43C22×#4111yescharacteristic
384C22×C43C22×#4111yescharacteristic
385C22×C43C2×H(5,𝔽2)11yescharacteristic
386C22×C43C2×2−1+411yescharacteristic
387C2×D43—24no—
388C2×D43—24no—
389C2×D43—24no—
390C2×D43—24no—
391C2×D43—24no—
392C2×D43—24no—
393C2×D43—232no—
394C2×D43—24no—
395C2×D43—24no—
396C2×D43—24no—
397C2×D43—42no—
398C2×D43—42no—
399C2×D43—42no—
400C2×D43—42no—
401C2×D43—416no—
402C2×D43C2×C22⋊Q818yescomplemented
403C4×C43—24no—
404C4×C43—24no—
405C4×C43—24no—
406C4×C43—24no—
407C4×C43—24no—
408C4×C43—42no—
409C4×C43—42no—
410Dic43—24no—
411Dic43—24no—
412Dic43—42no—
413Dic43—42no—
414Dic43—42no—
415Dic43—42no—
416C22×C22⋊Q8—431no—
417C22×C22⋊Q8—431no—
418C22×C4×D4—431no—
419C23×C4⋊C4—431no—
420#2449—4316no—
421C2×#399—431no—
422C2×#398—431no—
423C2×#396—431no—
424C2×#395—431no—
425C2×#389—431no—
426C2×#387D4311yescharacteristic, complemented
427C2×#386—431no—
428C2×#386—431no—
429C2×#385—431no—
430C2×#385—431no—
431C2×#385—431no—
432C2×C43#244918yescomplemented
433C2×C43C22×C22⋊Q811yescharacteristic
434C2×C43C2×#52511yescharacteristic
435C2×C43C2×#53911yescharacteristic
436C2×C43C2×D4211yescharacteristic
437C2×C43C2×#54711yescharacteristic
438C2×C43C2×D4×Q811yescharacteristic
439C2×C43C2×#55411yescharacteristic
440D43—28no—
441D43—44no—
442C23×Q8—431no—
443C23×D4—431no—
444C24×C4—431no—
445C24×C4—431no—
446C24×C4—431no—
447C24×C4—431no—
448C2×C22⋊Q8—438no—
449C2×C22⋊Q8—438no—
450C2×C22⋊Q8—868no—
451C2×C22⋊Q8—868no—
452C2×C4×D4—438no—
453C2×C4×D4—868no—
454C22×C4⋊C4—431no—
455C22×C4⋊C4—431no—
456C22×C4⋊C4—431no—
457C22×C4⋊C4—431no—
458C22×C4⋊C4—431no—
459C22×C4⋊C4—431no—
460C22×C4⋊C4—431no—
461C22×C4⋊C4—431no—
462C22×C4⋊C4—431no—
463C22×C4⋊C4—431no—
464C22×C4⋊C4—438no—
465C22×C4⋊C4—868no—
466C22×C4⋊C4C2×D4311yescharacteristic
467C22×C4⋊C4C2×D4311yescharacteristic
468C22×C22⋊C4—431no—
469C22×C22⋊C4—431no—
470C22×C22⋊C4—431no—
471C22×C22⋊C4—431no—
472C22×C22⋊C4—431no—
473C22×C22⋊C4—431no—
474C22×C22⋊C4—431no—
475C22×C22⋊C4—431no—
476C22×C42C2×D4311yescharacteristic
477#399—438no—
478#398—438no—
479#396—438no—
480#395—438no—
481#389—438no—
482#387C2×D4318yescomplemented
483#386—438no—
484#386—438no—
485#385—438no—
486#385—438no—
487#385—438no—
488C2×#95—431no—
489C2×#95—431no—
490C2×#95—431no—
491C2×#95—431no—
492C2×#95C2×D4311yescharacteristic
493C2×#95C2×D4311yescharacteristic
494C2×#95C2×D4311yescharacteristic
495C2×#95C2×D4311yescharacteristic
496C43C2×#244911yescharacteristic, complemented, Sylow
497C25—431no—
498C25—431no—
499C22×Q8—434no—
500C22×Q8—864no—
501C22×Q8—864no—
502C22×Q8—1722no—
503C22×D4—438no—
504C22×D4—434no—
505C22×D4—864no—
506C22×D4—864no—
507C23×C4—431no—
508C23×C4—431no—
509C23×C4—431no—
510C23×C4—431no—
511C23×C4—431no—
512C23×C4—431no—
513C23×C4—434no—
514C23×C4—434no—
515C23×C4—434no—
516C23×C4—434no—
517C23×C4—864no—
518C23×C4—864no—
519C23×C4—864no—
520C23×C4—864no—
521C23×C4—864no—
522C23×C4—864no—
523C23×C4—864no—
524C23×C4—864no—
525C23×C4—864no—
526C23×C4—1722no—
527C23×C4—1722no—
528C23×C4—1722no—
529C23×C4C22×D4311yescharacteristic
530C23×C4C22×D4311yescharacteristic
531C23×C4C22×D4311yescharacteristic
532C23×C4C22×D4311yescharacteristic
533C23×C4C22×D4311yescharacteristic
534C23×C4C22×D4311yescharacteristic
535C23×C4C22×D4311yescharacteristic
536C22⋊Q8—8632no—
537C22⋊Q8—8632no—
538C4×D4—8632no—
539C2×C4⋊C4—24no—
540C2×C4⋊C4—434no—
541C2×C4⋊C4—434no—
542C2×C4⋊C4—434no—
543C2×C4⋊C4—434no—
544C2×C4⋊C4—434no—
545C2×C4⋊C4—434no—
546C2×C4⋊C4—434no—
547C2×C4⋊C4—434no—
548C2×C4⋊C4—434no—
549C2×C4⋊C4—434no—
550C2×C4⋊C4—864no—
551C2×C4⋊C4—864no—
552C2×C4⋊C4—864no—
553C2×C4⋊C4—864no—
554C2×C4⋊C4—864no—
555C2×C4⋊C4—864no—
556C2×C4⋊C4—864no—
557C2×C4⋊C4—864no—
558C2×C4⋊C4—864no—
559C2×C4⋊C4—8632no—
560C2×C4⋊C4—1722no—
561C2×C4⋊C4D17218yescomplemented
562C2×C4⋊C4C22×D4314yes—
563C2×C4⋊C4C22×D4314yes—
564C2×C22⋊C4—438no—
565C2×C22⋊C4—434no—
566C2×C22⋊C4—434no—
567C2×C22⋊C4—434no—
568C2×C22⋊C4—434no—
569C2×C22⋊C4—434no—
570C2×C22⋊C4—434no—
571C2×C22⋊C4—434no—
572C2×C22⋊C4—434no—
573C2×C22⋊C4—864no—
574C2×C22⋊C4—864no—
575C2×C22⋊C4—864no—
576C2×C22⋊C4—864no—
577C2×C22⋊C4—864no—
578C2×C22⋊C4—864no—
579C2×C22⋊C4—1722no—
580C2×C42—24no—
581C2×C42C22×D4314yes—
582#95—434no—
583#95—434no—
584#95—434no—
585#95—434no—
586#95C22×D4314yes—
587#95C22×D4314yes—
588#95C22×D4314yes—
589#95C22×D4314yes—
590C24—434no—
591C24—434no—
592C24—434no—
593C24—432no—
594C24—434no—
595C24—432no—
596C24—862no—
597C24—862no—
598C24—862no—
599C24—862no—
600C24—862no—
601C24—862no—
602C24—862no—
603C24—862no—
604C24—862no—
605C24—862no—
606C24C23×D4311yescharacteristic
607C2×Q8—868no—
608C2×Q8—868no—
609C2×Q8—1724no—
610C2×Q8—17216no—
611C2×D4—4316no—
612C2×D4—868no—
613C2×D4—8632no—
614C2×D4—868no—
615C22×C4—22no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—434no—
632C22×C4—434no—
633C22×C4—432no—
634C22×C4—432no—
635C22×C4—432no—
636C22×C4—432no—
637C22×C4—432no—
638C22×C4—432no—
639C22×C4—868no—
640C22×C4—868no—
641C22×C4—868no—
642C22×C4—8632no—
643C22×C4—868no—
644C22×C4—868no—
645C22×C4—862no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—868no—
650C22×C4—862no—
651C22×C4—862no—
652C22×C4—862no—
653C22×C4—862no—
654C22×C4—862no—
655C22×C4—862no—
656C22×C4—862no—
657C22×C4—862no—
658C22×C4—862no—
659C22×C4—862no—
660C22×C4—862no—
661C22×C4—862no—
662C22×C4—868no—
663C22×C4—868no—
664C22×C4—868no—
665C22×C4—1724no—
666C22×C4—1724no—
667C22×C4—1724no—
668C22×C4—17216no—
669C22×C4—17216no—
670C22×C4—17216no—
671C22×C4C2×D17214yes—
672C22×C4C2×D17214yes—
673C22×C4C2×D17214yes—
674C22×C4D4×D4314yes—
675C22×C4Q8×D4314yes—
676C22×C4C23×D4312yes—
677C22×C4C23×D4312yes—
678C22×C4C23×D4312yes—
679C22×C4C23×D4312yes—
680C22×C4C23×D4312yes—
681C22×C4C23×D4312yes—
682C22×C4C23×D4312yes—
683C4⋊C4—28no—
684C4⋊C4—868no—
685C4⋊C4—868no—
686C4⋊C4—868no—
687C4⋊C4—868no—
688C4⋊C4—868no—
689C4⋊C4—868no—
690C4⋊C4—868no—
691C4⋊C4—868no—
692C4⋊C4—868no—
693C4⋊C4—1724no—
694C4⋊C4C2×D172116yescomplemented
695C22⋊C4—4316no—
696C22⋊C4—868no—
697C22⋊C4—868no—
698C22⋊C4—868no—
699C22⋊C4—868no—
700C22⋊C4—868no—
701C22⋊C4—868no—
702C22⋊C4—1724no—
703C42—28no—
704C23—4316no—
705C23—434no—
706C23—434no—
707C23—434no—
708C23—434no—
709C23—868no—
710C23—868no—
711C23—868no—
712C23—862no—
713C23—862no—
714C23—862no—
715C23—862no—
716C23—868no—
717C23—868no—
718C23—868no—
719C23—868no—
720C23—868no—
721C23—868no—
722C23—862no—
723C23—862no—
724C23—862no—
725C23—862no—
726C23—862no—
727C23—862no—
728C23—1724no—
729C23—1724no—
730C23—1724no—
731C23—1724no—
732C23C2×D4×D4312yes—
733C23C22×D17212yes—
734C23C2×Q8×D4312yes—
735C23#41×D4312yes—
736C23#41×D4312yes—
737C23#1306337112yes—
738C23#1306337212yes—
739C23C24×D4311yescharacteristic
740Q8—17216no—
741D4—8632no—
742C2×C4—28no—
743C2×C4—28no—
744C2×C4—22no—
745C2×C4—22no—
746C2×C4—22no—
747C2×C4—22no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—22no—
753C2×C4—22no—
754C2×C4—28no—
755C2×C4—28no—
756C2×C4—28no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—22no—
761C2×C4—22no—
762C2×C4—22no—
763C2×C4—44no—
764C2×C4—44no—
765C2×C4—434no—
766C2×C4—434no—
767C2×C4—8632no—
768C2×C4—868no—
769C2×C4—862no—
770C2×C4—862no—
771C2×C4—862no—
772C2×C4—862no—
773C2×C4—868no—
774C2×C4—862no—
775C2×C4—862no—
776C2×C4—862no—
777C2×C4—862no—
778C2×C4—862no—
779C2×C4—862no—
780C2×C4—862no—
781C2×C4—862no—
782C2×C4—862no—
783C2×C4—862no—
784C2×C4—862no—
785C2×C4—862no—
786C2×C4—17216no—
787C2×C4—17216no—
788C2×C4—17216no—
789C2×C4—1724no—
790C2×C4—1724no—
791C2×C4—1724no—
792C2×C4—1724no—
793C2×C4C2×D4×D4314yes—
794C2×C4C22×D17214yes—
795C2×C4C22×D17214yes—
796C2×C4C22×D17214yes—
797C2×C4C2×Q8×D4314yes—
798C22—438no—
799C22—864no—
800C22—864no—
801C22—864no—
802C22—864no—
803C22—864no—
804C22—8632no—
805C22—864no—
806C22—864no—
807C22—864no—
808C22—864no—
809C22—1722no—
810C22—1722no—
811C22—1722no—
812C22—17216no—
813C22—1722no—
814C22C22⋊Q8×D4314yes—
815C22#1458341114yes—
816C22#1458349014yes—
817C22D4×D17214yes—
818C22#1458354714yes—
819C22Q8×D17214yes—
820C22#1458360514yes—
821C22C22×D4×D4311yescharacteristic
822C22C23×D17211yescharacteristic
823C22C22×Q8×D4311yescharacteristic
824C22C2×#41×D4311yescharacteristic
825C22C2×#41×D4311yescharacteristic
826C22C2×#1306337111yescharacteristic
827C22C2×#1306337211yescharacteristic
828C4—24no—
829C4—24no—
830C4—24no—
831C4—24no—
832C4—24no—
833C4—42no—
834C4—42no—
835C4—864no—
836C4—864no—
837C4—1722no—
838C4—1722no—
839C4—1722no—
840C4—1722no—
841C2—868no—
842C2—1724no—
843C2#1913840918yesdirect product factor
844C2C2×C22⋊Q8×D4311yescharacteristic
845C2C2×#1458341111yescharacteristic
846C2C2×#1458349011yescharacteristic
847C2C2×D4×D17211yescharacteristic
848C2C2×#1458354711yescharacteristic
849C2C2×Q8×D17211yescharacteristic
850C2C2×#1458360511yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC23×D172C22
hypercenterC2×#387D43
hypocenterC43C2×#2449
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
1. C22×#13063305C2semidirect
2. C22×#13063303C2semidirect
4. C22×C4⋊C4×D43C2semidirect
5. #19138409C2direct (N × H)
6. C2×#14582836C2semidirect
7. C2×#14582831C2semidirect
8. C2×#14582821C2semidirect
9. C2×#14582820C2semidirect
10. C2×#14582797C2semidirect
13. C2×#14582773C2semidirect
14. C2×#14582773C2semidirect
15. C2×#14582773C2semidirect
16. C2×C43×#387C2semidirect
24. C2×#13063305C22semidirect
26. C2×#13063303C22semidirect
40. C2×C4⋊C4×D43C22semidirect
49. #14582836C22semidirect
50. #14582831C22semidirect
51. #14582821C22semidirect
52. #14582820C22semidirect
53. #14582797C22semidirect
56. #14582773C22semidirect
57. #14582773C22semidirect
58. #14582773C22semidirect
66. C43×#387C22semidirect
79. C22×D172Q8semidirect
155. C2×C4⋊C4×C43D4semidirect
236. C2×D172C2×Q8semidirect
258. C4⋊C4×C43C2×D4semidirect
309. C22×D43C22⋊Q8semidirect
402. C2×D43C2×C22⋊Q8semidirect
426. C2×#387D43semidirect
432. C2×C43#2449semidirect
482. #387C2×D43semidirect
496. C43C2×#2449semidirect
561. C2×C4⋊C4D172semidirect
694. C4⋊C4C2×D172semidirect
843. C2#19138409direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633052
C22×#130633032
C22×C4×D1722
C22×C4⋊C4×D432
#191384092
C2×#145828362
C2×#145828312
C2×#145828212
C2×#145828202
C2×#145827972
C2×#145827772
C2×#145827732
C2×C43×#3872
C2×#244943