Finite Group Databasebeta

← C2×#19137581 #25256094

Subgroups — C2×#19137581 #25256094

Order 11008.

3830 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063306C211yesmaximal, characteristic
2C22×#13063281C211yesmaximal, characteristic, complemented
3#19137581C2116yesmaximal, direct product factor
4C2×#14582794C211yesmaximal, characteristic, complemented
5C2×#14582793C211yesmaximal, characteristic, complemented
6C2×#14582787C211yesmaximal, characteristic, complemented
7C2×#14582783C211yesmaximal, characteristic, complemented
8C2×#14582780C211yesmaximal, characteristic, complemented
9C2×#14582779C211yesmaximal, characteristic
10C2×#14582772C211yesmaximal, characteristic, complemented
11C2×#14582772C211yesmaximal, characteristic, complemented
12C2×C4×Dic43⋊C4C211yesmaximal, characteristic, complemented
13C2×C22⋊C4×Dic43C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
15C22×C43⋊#95C211yesmaximal, characteristic, complemented
16C22×C4×D4×C43C211yesmaximal, characteristic
17C24×Dic43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C2×#13063306C4116yescomplemented
20C2×#13063306C2218yes—
21C2×#13063281—28no—
22C2×#13063281C2218yescomplemented
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×C22⋊Dic43C2211yescharacteristic
31C22×C22⋊Dic43C2211yescharacteristic
32C22×C22⋊Dic43C2211yescharacteristic
33C22×C22⋊Dic43C2211yescharacteristic
34C22×C22⋊Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37C22×C4×Dic43C2211yescharacteristic
38C22×C4×Dic43C2211yescharacteristic
39#14582794C2218yescomplemented
40#14582793C2218yescomplemented
41#14582787C2218yescomplemented
42#14582783C2218yescomplemented
43#14582780C2218yescomplemented
44#14582779C2218yes—
45#14582772C2218yescomplemented
46#14582772C2218yescomplemented
47C4×Dic43⋊C4C2218yescomplemented
48C22⋊C4×Dic43C2218yescomplemented
49C4×C22⋊Dic43C2218yescomplemented
50C2×C43⋊#95C2211yescharacteristic
51C2×C43⋊#95C2211yescharacteristic
52C2×C43⋊#95C2211yescharacteristic
53C2×C43⋊#95C2211yescharacteristic
54C2×C43⋊#95C2211yescharacteristic
55C2×C43⋊#95C2211yescharacteristic
56C2×C43⋊#95C2211yescharacteristic
57C2×C43⋊#95C2211yescharacteristic
58C2×C43⋊#95C2211yescharacteristic
59C2×C43⋊#95C2211yescharacteristic
60C2×C43⋊#95C2218yescomplemented
61C23×D4×C43C2211yescharacteristic
62C24×C4×C43C2211yescharacteristic
63C24×C4×C43C2211yescharacteristic
64C2×C4×D4×C43—28no—
65C2×C4×D4×C43C2218yes—
66C22×C4⋊C4×C43C2211yescharacteristic
67C22×C22⋊C4×C43C2211yescharacteristic
68C22×C22⋊C4×C43C2211yescharacteristic
69C22×C42×C43C2211yescharacteristic
70C23×Dic43—24no—
71C23×Dic43—24no—
72C23×Dic43—24no—
73C23×Dic43—24no—
74C23×Dic43—42no—
75C23×Dic43C2×C418yescomplemented
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2314yes—
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2314yes—
85C23×Dic43C2311yescharacteristic
86#13063306C2×C4164yescomplemented
87#13063281—232no—
88C2×Dic43⋊C4—24no—
89C2×Dic43⋊C4—24no—
90C2×Dic43⋊C4—24no—
91C2×Dic43⋊C4—42no—
92C2×Dic43⋊C4C2×C418yescomplemented
93C2×Dic43⋊C4C2×C418yescomplemented
94C2×Dic43⋊C4C2314yes—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2314yes—
97C2×Dic43⋊C4C2314yes—
98C2×Dic43⋊C4C2314yes—
99C2×Dic43⋊C4C2314yes—
100C2×C22⋊Dic43—24no—
101C2×C22⋊Dic43—24no—
102C2×C22⋊Dic43—42no—
103C2×C22⋊Dic43C2×C418yescomplemented
104C2×C22⋊Dic43C2×C418yescomplemented
105C2×C22⋊Dic43C2×C418yescomplemented
106C2×C22⋊Dic43C2314yes—
107C2×C22⋊Dic43C2314yes—
108C2×C22⋊Dic43C2314yes—
109C2×C22⋊Dic43C2314yes—
110C2×C22⋊Dic43C2314yes—
111C2×C22⋊Dic43C2314yes—
112C2×C4×Dic43—24no—
113C2×C4×Dic43—24no—
114C2×C4×Dic43—24no—
115C2×C4×Dic43—42no—
116C2×C4×Dic43C2314yes—
117C2×C4×Dic43C2314yes—
118C2×C4×Dic43C2314yes—
119C2×C4×Dic43C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C25×C43C2311yescharacteristic
131C25×C43C2311yescharacteristic
132C22×D4×C43—24no—
133C22×D4×C43—24no—
134C22×D4×C43C2×C418yes—
135C22×D4×C43C2314yes—
136C23×C4×C43—24no—
137C23×C4×C43—24no—
138C23×C4×C43—24no—
139C23×C4×C43—24no—
140C23×C4×C43—42no—
141C23×C4×C43—42no—
142C23×C4×C43C2311yescharacteristic
143C23×C4×C43C2314yes—
144C23×C4×C43C2314yes—
145C23×C4×C43C2311yescharacteristic
146C23×C4×C43C2311yescharacteristic
147C23×C4×C43C2311yescharacteristic
148C23×C4×C43C2311yescharacteristic
149C4×D4×C43—232no—
150C2×C4⋊C4×C43—24no—
151C2×C4⋊C4×C43C2314yes—
152C2×C22⋊C4×C43—24no—
153C2×C22⋊C4×C43D418yes—
154C2×C22⋊C4×C43C2314yes—
155C2×C22⋊C4×C43C2314yes—
156C2×C42×C43—24no—
157C2×C42×C43C2314yes—
158C24×C43—22no—
159C24×C43—22no—
160C24×C43—22no—
161C24×C43—22no—
162C24×C43—22no—
163C24×C43—22no—
164C24×C43—22no—
165C24×C43—22no—
166C24×C43—22no—
167C24×C43—22no—
168C24×C43C22×C414yes—
169C24×C43C22×C414yes—
170C24×C43C2×D414yes—
171C24×C43#4114yes—
172C24×C43C2412yes—
173C24×C43C2412yes—
174C24×C43C2411yescharacteristic
175C2×D4×C43—232no—
176C2×D4×C43—28no—
177C2×D4×C43—28no—
178C2×D4×C43C22×C4116yes—
179C22×C4×C43—28no—
180C22×C4×C43—28no—
181C22×C4×C43—28no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43—22no—
185C22×C4×C43—28no—
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—44no—
195C22×C4×C43—44no—
196C22×C4×C43—416no—
197C22×C4×C43—416no—
198C22×C4×C43C22×C414yes—
199C22×C4×C43C2×D414yes—
200C22×C4×C43C2×D414yes—
201C22×C4×C43#4114yes—
202C22×C4×C43C2412yes—
203C22×C4×C43C2412yes—
204C22×C4×C43C2412yes—
205C22×C4×C43C2412yes—
206C22×C4×C43C2412yes—
207C22×Dic43—28no—
208C22×Dic43—232no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—28no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43—22no—
216C22×Dic43—28no—
217C22×Dic43—22no—
218C22×Dic43—22no—
219C22×Dic43—22no—
220C22×Dic43—22no—
221C22×Dic43—22no—
222C22×Dic43—22no—
223C22×Dic43—28no—
224C22×Dic43—22no—
225C22×Dic43—22no—
226C22×Dic43—22no—
227C22×Dic43—22no—
228C22×Dic43—22no—
229C22×Dic43—22no—
230C22×Dic43—22no—
231C22×Dic43—44no—
232C22×Dic43—416no—
233C22×Dic43C22×C414yes—
234C22×Dic43C22×C414yes—
235C22×Dic43C22×C414yes—
236C22×Dic43C22×C414yes—
237C22×Dic43C22×C4116yescomplemented
238C22×Dic43#4114yes—
239C22×Dic43C2412yes—
240C22×Dic43C2412yes—
241C22×Dic43C2412yes—
242C22×Dic43C2412yes—
243C22×Dic43C2412yes—
244C22×Dic43C2412yes—
245C22×Dic43C2412yes—
246C22×Dic43C2412yes—
247C4⋊C4×C43—28no—
248C22⋊C4×C43—28no—
249C22⋊C4×C43C2×D4116yes—
250C42×C43—28no—
251C22⋊Dic43—28no—
252C22⋊Dic43—28no—
253C22⋊Dic43—44no—
254C22⋊Dic43C22×C4116yescomplemented
255C22⋊Dic43C22×C4116yescomplemented
256C22⋊Dic43C22×C4116yescomplemented
257Dic43⋊C4—28no—
258Dic43⋊C4—28no—
259Dic43⋊C4—28no—
260Dic43⋊C4—44no—
261Dic43⋊C4C22×C4116yescomplemented
262Dic43⋊C4C22×C4116yescomplemented
263C4×Dic43—28no—
264C4×Dic43—28no—
265C4×Dic43—28no—
266C4×Dic43—44no—
267C23×C43—28no—
268C23×C43—28no—
269C23×C43—28no—
270C23×C43—28no—
271C23×C43—28no—
272C23×C43—28no—
273C23×C43—22no—
274C23×C43—22no—
275C23×C43—22no—
276C23×C43—22no—
277C23×C43—28no—
278C23×C43—28no—
279C23×C43—28no—
280C23×C43—22no—
281C23×C43—22no—
282C23×C43—22no—
283C23×C43—22no—
284C23×C43—22no—
285C23×C43—22no—
286C23×C43—44no—
287C23×C43—44no—
288C23×C43—44no—
289C23×C43—44no—
290C23×C43C4×D4116yes—
291C23×C43C23×C414yes—
292C23×C43C23×C414yes—
293C23×C43C23×C412yes—
294C23×C43C22×D414yes—
295C23×C43C22×D412yes—
296C23×C43C2×#4112yes—
297C23×C43C2×#4112yes—
298C23×C43C2×#4114yes—
299C23×C43C2×#4112yes—
300C23×C43H(5,𝔽2)12yes—
301C23×C432−1+412yes—
302C23×C43C2511yescharacteristic
303D4×C43—232no—
304C2×C4×C43—28no—
305C2×C4×C43—28no—
306C2×C4×C43—28no—
307C2×C4×C43—28no—
308C2×C4×C43—22no—
309C2×C4×C43—22no—
310C2×C4×C43—22no—
311C2×C4×C43—22no—
312C2×C4×C43—22no—
313C2×C4×C43—22no—
314C2×C4×C43—22no—
315C2×C4×C43—22no—
316C2×C4×C43—22no—
317C2×C4×C43—22no—
318C2×C4×C43—22no—
319C2×C4×C43—416no—
320C2×C4×C43—416no—
321C2×C4×C43—44no—
322C2×C4×C43C23×C414yes—
323C2×C4×C43C22×D414yes—
324C2×C4×C43C22×D414yes—
325C2×C4×C43C2×#4114yes—
326C2×Dic43—28no—
327C2×Dic43—28no—
328C2×Dic43—232no—
329C2×Dic43—28no—
330C2×Dic43—28no—
331C2×Dic43—28no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—22no—
338C2×Dic43—22no—
339C2×Dic43—22no—
340C2×Dic43—22no—
341C2×Dic43—22no—
342C2×Dic43—22no—
343C2×Dic43—22no—
344C2×Dic43—22no—
345C2×Dic43—22no—
346C2×Dic43—22no—
347C2×Dic43—22no—
348C2×Dic43—22no—
349C2×Dic43—22no—
350C2×Dic43—22no—
351C2×Dic43—416no—
352C2×Dic43—44no—
353C2×Dic43—44no—
354C2×Dic43—44no—
355C2×Dic43C23×C414yes—
356C2×Dic43C23×C414yes—
357C2×Dic43C23×C414yes—
358C2×Dic43C23×C414yes—
359C2×Dic43C2×#4114yes—
360C2×#2359—431nomaximal, Sylow
361C22×C43—232no—
362C22×C43—24no—
363C22×C43—24no—
364C22×C43—24no—
365C22×C43—24no—
366C22×C43—24no—
367C22×C43—24no—
368C22×C43—24no—
369C22×C43—24no—
370C22×C43—24no—
371C22×C43—416no—
372C22×C43—42no—
373C22×C43—42no—
374C22×C43—42no—
375C22×C43—42no—
376C22×C43C2×C4×D418yes—
377C22×C43C2×C4×D414yes—
378C22×C43C4×#4114yes—
379C22×C43#52014yes—
380C22×C43#54614yes—
381C22×C43#54714yes—
382C22×C43#55114yes—
383C22×C43#55214yes—
384C22×C43C24×C411yescharacteristic
385C22×C43C23×D411yescharacteristic
386C22×C43C22×#4111yescharacteristic
387C22×C43C22×#4111yescharacteristic
388C22×C43C22×#4111yescharacteristic
389C22×C43C2×H(5,𝔽2)11yescharacteristic
390C22×C43C2×2−1+411yescharacteristic
391C4×C43—24no—
392C4×C43—24no—
393C4×C43—24no—
394C4×C43—24no—
395C4×C43—42no—
396Dic43—24no—
397Dic43—24no—
398Dic43—24no—
399Dic43—24no—
400Dic43—24no—
401Dic43—42no—
402Dic43—42no—
403Dic43—42no—
404C22×#123—431no—
405C22×C4×D4D4311yescharacteristic
406C22×#117—431no—
407#2359—4316no—
408C2×#389—431no—
409C2×#388—431no—
410C2×#388—431no—
411C2×#387—431no—
412C2×#387—431no—
413C2×#386—431no—
414C2×#385—431no—
415C2×#385—431no—
416C2×C4×C4⋊C4—431no—
417C2×C4×C22⋊C4—431no—
418C2×C4×C22⋊C4—431no—
419C22×#95—431no—
420C2×C43—28no—
421C2×C43—44no—
422C2×C43#235918yescomplemented
423C2×C43C22×C4×D411yescharacteristic
424C2×C43C2×C4×#4111yescharacteristic
425C2×C43C2×#52011yescharacteristic
426C2×C43C2×#54611yescharacteristic
427C2×C43C2×#54711yescharacteristic
428C2×C43C2×#55111yescharacteristic
429C2×C43C2×#55211yescharacteristic
430C23×D4C2×D4311yescharacteristic
431C24×C4—431no—
432C24×C4—431no—
433C24×C4C2×D4311yescharacteristic
434C24×C4C2×D4311yescharacteristic
435C2×#123—438no—
436C2×#123—4316no—
437C2×C4×D4—28no—
438C2×C4×D4C2×D4318yes—
439C2×#117—438no—
440C2×#117—868no—
441C22×C4⋊C4—431no—
442C22×C4⋊C4—431no—
443C22×C4⋊C4—431no—
444C22×C4⋊C4—431no—
445C22×C4⋊C4—431no—
446C22×C4⋊C4—431no—
447C22×C4⋊C4C2×D4311yescharacteristic
448C22×C22⋊C4—431no—
449C22×C22⋊C4—431no—
450C22×C22⋊C4—431no—
451C22×C22⋊C4—431no—
452C22×C22⋊C4—431no—
453C22×C22⋊C4—431no—
454C22×C22⋊C4C2×D4311yescharacteristic
455C22×C22⋊C4C2×D4311yescharacteristic
456C22×C42—431no—
457C22×C42—431no—
458C22×C42—431no—
459C22×C42—431no—
460C22×C42C2×D4311yescharacteristic
461#389—438no—
462#388—438no—
463#388—438no—
464#387—438no—
465#387—438no—
466#386—438no—
467#385—438no—
468#385—438no—
469C4×C4⋊C4—438no—
470C4×C22⋊C4—438no—
471C4×C22⋊C4—438no—
472C2×#95—438no—
473C2×#95—431no—
474C2×#95—431no—
475C2×#95—431no—
476C2×#95—431no—
477C2×#95—431no—
478C2×#95—431no—
479C2×#95—431no—
480C2×#95—431no—
481C2×#95—431no—
482C2×#95—431no—
483C43C2×#235911yescharacteristic, complemented, Sylow
484C25C22×D4311yescharacteristic
485C25C22×D4311yescharacteristic
486C22×D4—24no—
487C22×D4—24no—
488C22×D4C4×D4318yes—
489C22×D4C22×D4314yes—
490C23×C4—24no—
491C23×C4—24no—
492C23×C4—24no—
493C23×C4—24no—
494C23×C4—42no—
495C23×C4—42no—
496C23×C4—438no—
497C23×C4—434no—
498C23×C4—431no—
499C23×C4—431no—
500C23×C4—431no—
501C23×C4—431no—
502C23×C4—431no—
503C23×C4—431no—
504C23×C4—431no—
505C23×C4—431no—
506C23×C4—434no—
507C23×C4—864no—
508C23×C4—864no—
509C23×C4—864no—
510C23×C4—864no—
511C23×C4—1722no—
512C23×C4C22×D4311yescharacteristic
513C23×C4C22×D4314yes—
514C23×C4C22×D4314yes—
515C23×C4C22×D4311yescharacteristic
516C23×C4C22×D4311yescharacteristic
517C23×C4C22×D4311yescharacteristic
518C23×C4C22×D4311yescharacteristic
519#123—4364no—
520C4×D4—232no—
521#117—8632no—
522C2×C4⋊C4—24no—
523C2×C4⋊C4—438no—
524C2×C4⋊C4—438no—
525C2×C4⋊C4—434no—
526C2×C4⋊C4—434no—
527C2×C4⋊C4—434no—
528C2×C4⋊C4—434no—
529C2×C4⋊C4—434no—
530C2×C4⋊C4—434no—
531C2×C4⋊C4—864no—
532C2×C4⋊C4—864no—
533C2×C4⋊C4—864no—
534C2×C4⋊C4—1722no—
535C2×C4⋊C4C22×D4314yes—
536C2×C22⋊C4—24no—
537C2×C22⋊C4—438no—
538C2×C22⋊C4—438no—
539C2×C22⋊C4—438no—
540C2×C22⋊C4—434no—
541C2×C22⋊C4—434no—
542C2×C22⋊C4—434no—
543C2×C22⋊C4—434no—
544C2×C22⋊C4—434no—
545C2×C22⋊C4—434no—
546C2×C22⋊C4—864no—
547C2×C22⋊C4—864no—
548C2×C22⋊C4—1722no—
549C2×C22⋊C4C22⋊D4318yes—
550C2×C22⋊C4C22×D4314yes—
551C2×C22⋊C4C22×D4314yes—
552C2×C42—24no—
553C2×C42—434no—
554C2×C42—434no—
555C2×C42—434no—
556C2×C42—434no—
557C2×C42—864no—
558C2×C42—864no—
559C2×C42—864no—
560C2×C42—1722no—
561C2×C42C22×D4314yes—
562#95—434no—
563#95—434no—
564#95—434no—
565#95—434no—
566#95—434no—
567#95—434no—
568#95—434no—
569#95—434no—
570#95—434no—
571#95—434no—
572C24—22no—
573C24—22no—
574C24—22no—
575C24—22no—
576C24—22no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24C2×C4×D4314yes—
583C24C2×C4×D4314yes—
584C24#1062189814yes—
585C24C2×C22⋊D4314yes—
586C24C23×D4312yes—
587C24C23×D4312yes—
588C24C23×D4311yescharacteristic
589C2×D4—232no—
590C2×D4—28no—
591C2×D4—28no—
592C2×D4C2×C4×D43116yes—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—28no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—28no—
606C22×C4—28no—
607C22×C4—28no—
608C22×C4—44no—
609C22×C4—44no—
610C22×C4—416no—
611C22×C4—416no—
612C22×C4—434no—
613C22×C4—434no—
614C22×C4—434no—
615C22×C4—434no—
616C22×C4—4316no—
617C22×C4—434no—
618C22×C4—432no—
619C22×C4—432no—
620C22×C4—432no—
621C22×C4—432no—
622C22×C4—432no—
623C22×C4—432no—
624C22×C4—432no—
625C22×C4—432no—
626C22×C4—868no—
627C22×C4—8632no—
628C22×C4—862no—
629C22×C4—862no—
630C22×C4—868no—
631C22×C4—862no—
632C22×C4—862no—
633C22×C4—862no—
634C22×C4—868no—
635C22×C4—862no—
636C22×C4—862no—
637C22×C4—862no—
638C22×C4—862no—
639C22×C4—862no—
640C22×C4—862no—
641C22×C4—862no—
642C22×C4—862no—
643C22×C4—862no—
644C22×C4—862no—
645C22×C4—868no—
646C22×C4—862no—
647C22×C4—862no—
648C22×C4—862no—
649C22×C4—862no—
650C22×C4—1724no—
651C22×C4—17216no—
652C22×C4C2×C4×D4314yes—
653C22×C4#1062190014yes—
654C22×C4C2×C22⋊D4314yes—
655C22×C4C2×C22⋊D4314yes—
656C22×C4C23×D4312yes—
657C22×C4C23×D4312yes—
658C22×C4C23×D4312yes—
659C22×C4C23×D4312yes—
660C22×C4C23×D4312yes—
661C4⋊C4—28no—
662C4⋊C4—4316no—
663C4⋊C4—4316no—
664C4⋊C4—868no—
665C4⋊C4—868no—
666C4⋊C4—868no—
667C4⋊C4—1724no—
668C22⋊C4—28no—
669C22⋊C4—4316no—
670C22⋊C4—4316no—
671C22⋊C4—4316no—
672C22⋊C4—868no—
673C22⋊C4—868no—
674C22⋊C4—1724no—
675C22⋊C4C2×C22⋊D43116yes—
676C42—28no—
677C42—868no—
678C42—868no—
679C42—868no—
680C42—1724no—
681C23—28no—
682C23—28no—
683C23—28no—
684C23—28no—
685C23—22no—
686C23—22no—
687C23—22no—
688C23—22no—
689C23—28no—
690C23—28no—
691C23—28no—
692C23—28no—
693C23—28no—
694C23—22no—
695C23—22no—
696C23—22no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—44no—
701C23—44no—
702C23—44no—
703C23—44no—
704C23C4×C22⋊D43116yes—
705C23C22×C4×D4314yes—
706C23C22×C4×D4314yes—
707C23C22×C4×D4312yes—
708C23C22×C22⋊D4314yes—
709C23C22×C22⋊D4312yes—
710C23#41×D4312yes—
711C23C2×#1062190012yes—
712C23C2×#1062189814yes—
713C23C2×#1062189812yes—
714C23#1306337012yes—
715C23#1306337212yes—
716C23C24×D4311yescharacteristic
717D4—232no—
718C2×C4—28no—
719C2×C4—22no—
720C2×C4—22no—
721C2×C4—22no—
722C2×C4—22no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—28no—
728C2×C4—28no—
729C2×C4—28no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—416no—
734C2×C4—416no—
735C2×C4—44no—
736C2×C4—434no—
737C2×C4—434no—
738C2×C4—434no—
739C2×C4—434no—
740C2×C4—434no—
741C2×C4—868no—
742C2×C4—8632no—
743C2×C4—868no—
744C2×C4—868no—
745C2×C4—868no—
746C2×C4—868no—
747C2×C4—862no—
748C2×C4—862no—
749C2×C4—862no—
750C2×C4—862no—
751C2×C4—862no—
752C2×C4—862no—
753C2×C4—862no—
754C2×C4—862no—
755C2×C4—862no—
756C2×C4—862no—
757C2×C4—862no—
758C2×C4—862no—
759C2×C4—862no—
760C2×C4—862no—
761C2×C4—862no—
762C2×C4—862no—
763C2×C4—862no—
764C2×C4—862no—
765C2×C4—862no—
766C2×C4—17216no—
767C2×C4—1724no—
768C2×C4—1724no—
769C2×C4—1724no—
770C2×C4C22×C4×D4314yes—
771C2×C4C22×C22⋊D4314yes—
772C2×C4C22×C22⋊D4314yes—
773C2×C4C2×#1062190014yes—
774C22—24no—
775C22—24no—
776C22—24no—
777C22—232no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—24no—
782C22—24no—
783C22—24no—
784C22—42no—
785C22—42no—
786C22—416no—
787C22—42no—
788C22—42no—
789C22C2×C4×C22⋊D4318yes—
790C22C2×C4×C22⋊D4314yes—
791C22C4×#1062190014yes—
792C22#1458337814yes—
793C22#1458354314yes—
794C22#1458354814yes—
795C22#1458357814yes—
796C22#1458358914yes—
797C22C23×C4×D4311yescharacteristic
798C22C23×C22⋊D4311yescharacteristic
799C22C2×#41×D4311yescharacteristic
800C22C22×#1062190011yescharacteristic
801C22C22×#1062189811yescharacteristic
802C22C2×#1306337011yescharacteristic
803C22C2×#1306337211yescharacteristic
804C4—24no—
805C4—24no—
806C4—24no—
807C4—24no—
808C4—42no—
809C4—864no—
810C4—864no—
811C4—864no—
812C4—864no—
813C4—864no—
814C4—1722no—
815C4—1722no—
816C4—1722no—
817C2—28no—
818C2—44no—
819C2#1913758118yesdirect product factor
820C2C22×C4×C22⋊D4311yescharacteristic
821C2C2×C4×#1062190011yescharacteristic
822C2C2×#1458337811yescharacteristic
823C2C2×#1458354311yescharacteristic
824C2C2×#1458354811yescharacteristic
825C2C2×#1458357811yescharacteristic
826C2C2×#1458358911yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC22×C4×D4×C43C2
socleC24×C43C24
prime radicalC23×D4×C43C22
cosocleC23×C43C25
hypercenterC22×C4×D4D43
hypocenterC43C2×#2359
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C22×#13063281C2semidirect
3. #19137581C2direct (N × H)
4. C2×#14582794C2semidirect
5. C2×#14582793C2semidirect
6. C2×#14582787C2semidirect
7. C2×#14582783C2semidirect
8. C2×#14582780C2semidirect
10. C2×#14582772C2semidirect
11. C2×#14582772C2semidirect
12. C2×C4×Dic43⋊C4C2semidirect
13. C2×C22⋊C4×Dic43C2semidirect
14. C2×C4×C22⋊Dic43C2semidirect
15. C22×C43⋊#95C2semidirect
19. C2×#13063306C4semidirect
22. C2×#13063281C22semidirect
39. #14582794C22semidirect
40. #14582793C22semidirect
41. #14582787C22semidirect
42. #14582783C22semidirect
43. #14582780C22semidirect
45. #14582772C22semidirect
46. #14582772C22semidirect
47. C4×Dic43⋊C4C22semidirect
48. C22⋊C4×Dic43C22semidirect
49. C4×C22⋊Dic43C22semidirect
60. C2×C43⋊#95C22semidirect
75. C23×Dic43C2×C4semidirect
86. #13063306C2×C4semidirect
92. C2×Dic43⋊C4C2×C4semidirect
93. C2×Dic43⋊C4C2×C4semidirect
103. C2×C22⋊Dic43C2×C4semidirect
104. C2×C22⋊Dic43C2×C4semidirect
105. C2×C22⋊Dic43C2×C4semidirect
237. C22×Dic43C22×C4semidirect
254. C22⋊Dic43C22×C4semidirect
255. C22⋊Dic43C22×C4semidirect
256. C22⋊Dic43C22×C4semidirect
261. Dic43⋊C4C22×C4semidirect
262. Dic43⋊C4C22×C4semidirect
422. C2×C43#2359semidirect
483. C43C2×#2359semidirect
819. C2#19137581direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633062
C22×#130632812
#191375812
C2×#145827942
C2×#145827932
C2×#145827872
C2×#145827832
C2×#145827802
C2×#145827792
C2×#145827722
C2×C4×Dic43⋊C42
C2×C22⋊C4×Dic432
C2×C4×C22⋊Dic432
C22×C43⋊#952
C22×C4×D4×C432
C2×#235943