Finite Group Databasebeta

← C2×#19139737 #25266760

Subgroups — C2×#19139737 #25266760

Order 11008.

2898 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063303C211yesmaximal, characteristic, complemented
2#19139737C2116yesmaximal, direct product factor
3C2×#14582832C211yesmaximal, characteristic, complemented
4C2×#14582825C211yesmaximal, characteristic, complemented
5C2×#14582815C211yesmaximal, characteristic
6C2×#14582811C211yesmaximal, characteristic, complemented
7C2×#14582804C211yesmaximal, characteristic, complemented
8C2×#14582799C211yesmaximal, characteristic
9C2×#14582793C211yesmaximal, characteristic, complemented
10C2×#14582793C211yesmaximal, characteristic, complemented
11C2×#14582789C211yesmaximal, characteristic, complemented
12C2×#14582783C211yesmaximal, characteristic, complemented
13C2×#14582775C211yesmaximal, characteristic
14C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
15C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
16C22×#126×C43C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063303—28no—
21C2×#13063303C2218yescomplemented
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×Dic43⋊C4C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×C22⋊Dic43C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×(C2×D43)⋊C4C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582832C2218yescomplemented
38#14582825C2218yescomplemented
39#14582815C2218yes—
40#14582811C2218yescomplemented
41#14582804C2218yescomplemented
42#14582799C2218yes—
43#14582793C2218yescomplemented
44#14582793C2218yescomplemented
45#14582789C2218yescomplemented
46#14582783C2218yescomplemented
47#14582775C2218yes—
48C4⋊C4×Dic43C2218yescomplemented
49C4×(C2×D43)⋊C4C2218yescomplemented
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×#126×C43—28no—
61C2×#126×C43C2218yescomplemented
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C4⋊C4×C43C2211yescharacteristic
64C22×C4⋊C4×C43C2211yescharacteristic
65C22×C22⋊C4×C43C2211yescharacteristic
66C22×C22⋊C4×C43C2211yescharacteristic
67C22×C22⋊C4×C43C2211yescharacteristic
68C22×C42×C43C2211yescharacteristic
69C24×D43C2311yescharacteristic
70C22×Dic86—24no—
71C22×Dic86—24no—
72C22×Dic86—42no—
73C22×Dic86C2314yes—
74C22×C22⋊D43—24no—
75C22×C22⋊D43—24no—
76C22×C22⋊D43—42no—
77C22×C22⋊D43C2314yes—
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C23×Dic43C2311yescharacteristic
85C22×C4×D43—24no—
86C22×C4×D43—24no—
87C22×C4×D43—42no—
88C22×C4×D43C2314yes—
89#13063303—232no—
90C2×C4⋊Dic43—24no—
91C2×C4⋊Dic43C2314yes—
92C2×Dic43⋊C4—24no—
93C2×Dic43⋊C4—24no—
94C2×Dic43⋊C4—24no—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2314yes—
97C2×Dic43⋊C4C2314yes—
98C2×C22⋊Dic43—24no—
99C2×C22⋊Dic43—24no—
100C2×C22⋊Dic43—42no—
101C2×C22⋊Dic43C2314yes—
102C2×C22⋊Dic43C2314yes—
103C2×C22⋊Dic43C2314yes—
104C2×(C2×D43)⋊C4—24no—
105C2×(C2×D43)⋊C4—24no—
106C2×(C2×D43)⋊C4—24no—
107C2×(C2×D43)⋊C4—24no—
108C2×(C2×D43)⋊C4—24no—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×C4×Dic43—24no—
115C2×C4×Dic43—42no—
116C2×C4×Dic43—42no—
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
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137#126×C43—232no—
138C2×C4⋊C4×C43—24no—
139C2×C4⋊C4×C43—24no—
140C2×C4⋊C4×C43D418yescomplemented
141C2×C4⋊C4×C43C2314yes—
142C2×C4⋊C4×C43C2314yes—
143C2×C4⋊C4×C43C2314yes—
144C2×C22⋊C4×C43—24no—
145C2×C22⋊C4×C43—24no—
146C2×C22⋊C4×C43—24no—
147C2×C22⋊C4×C43C2314yes—
148C2×C22⋊C4×C43C2314yes—
149C2×C22⋊C4×C43C2314yes—
150C2×C42×C43—24no—
151C2×C42×C43C2314yes—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43—22no—
157C24×C43—22no—
158C24×C43—22no—
159C24×C43C2412yes—
160C24×C43C2411yescharacteristic
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43—22no—
166C23×D43—22no—
167C23×D43#4114yes—
168C23×D43C2412yes—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43—22no—
175C22×C4×C43—22no—
176C22×C4×C43—22no—
177C22×C4×C43—22no—
178C22×C4×C43—22no—
179C22×C4×C43—22no—
180C22×C4×C43—22no—
181C22×C4×C43—22no—
182C22×C4×C43—22no—
183C22×C4×C43—22no—
184C22×C4×C43C2×D414yes—
185C22×C4×C43C2×D414yes—
186C22×C4×C43C2×D414yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C2×C22⋊D43—28no—
194C2×C22⋊D43—28no—
195C2×C22⋊D43—44no—
196C2×C22⋊D43—416no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43—22no—
203C22×Dic43—22no—
204C22×Dic43—22no—
205C22×Dic43—22no—
206C22×Dic43—22no—
207C22×Dic43—22no—
208C22×Dic43—22no—
209C22×Dic43—22no—
210C22×Dic43—22no—
211C22×Dic43—22no—
212C22×Dic43—22no—
213C22×Dic43—22no—
214C22×Dic43—22no—
215C22×Dic43#4114yes—
216C22×Dic43#4114yes—
217C22×Dic43#4114yes—
218C22×Dic43C2412yes—
219C22×Dic43C2412yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C2×C4×D43—28no—
226C2×C4×D43—28no—
227C2×C4×D43—44no—
228C2×C4×D43—416no—
229C2×Dic86—28no—
230C2×Dic86—28no—
231C2×Dic86—44no—
232C2×Dic86—416no—
233C4⋊C4×C43—28no—
234C4⋊C4×C43—28no—
235C4⋊C4×C43C2×D4116yescomplemented
236C22⋊C4×C43—28no—
237C22⋊C4×C43—28no—
238C22⋊C4×C43—28no—
239C42×C43—28no—
240C22⋊Dic43—28no—
241C22⋊Dic43—28no—
242C22⋊Dic43—44no—
243(C2×D43)⋊C4—28no—
244(C2×D43)⋊C4—28no—
245(C2×D43)⋊C4—28no—
246(C2×D43)⋊C4—28no—
247(C2×D43)⋊C4—28no—
248C4⋊Dic43—28no—
249Dic43⋊C4—28no—
250Dic43⋊C4—28no—
251Dic43⋊C4—28no—
252C4×Dic43—28no—
253C4×Dic43—44no—
254C4×Dic43—44no—
255C23×C43—22no—
256C23×C43—22no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—44no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43—44no—
268C23×C43—44no—
269C23×C43C22×D412yes—
270C23×C43C2×#4112yes—
271C23×C43C2×#4112yes—
272C23×C43C2×#4112yes—
273C23×C43C2×#4112yes—
274C23×C43H(5,𝔽2)12yes—
275C23×C432−1+412yes—
276C23×C43C2511yescharacteristic
277C22×D43—28no—
278C22×D43—28no—
279C22×D43—28no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43—44no—
290C22×D43C2×#4114yes—
291C2×C4×C43—28no—
292C2×C4×C43—28no—
293C2×C4×C43—28no—
294C2×C4×C43—22no—
295C2×C4×C43—22no—
296C2×C4×C43—22no—
297C2×C4×C43—22no—
298C2×C4×C43—22no—
299C2×C4×C43—22no—
300C2×C4×C43—22no—
301C2×C4×C43—22no—
302C2×C4×C43—22no—
303C2×C4×C43—22no—
304C2×C4×C43—22no—
305C2×C4×C43—22no—
306C2×C4×C43—22no—
307C2×C4×C43—22no—
308C2×C4×C43—22no—
309C2×C4×C43—44no—
310C2×C4×C43—44no—
311C2×C4×C43—44no—
312C2×C4×C43C22×D414yes—
313C2×C4×C43C22×D414yes—
314C2×C4×C43C22×D414yes—
315C22⋊D43—416no—
316C2×Dic43—28no—
317C2×Dic43—28no—
318C2×Dic43—28no—
319C2×Dic43—22no—
320C2×Dic43—22no—
321C2×Dic43—22no—
322C2×Dic43—22no—
323C2×Dic43—22no—
324C2×Dic43—22no—
325C2×Dic43—22no—
326C2×Dic43—22no—
327C2×Dic43—22no—
328C2×Dic43—22no—
329C2×Dic43—22no—
330C2×Dic43—22no—
331C2×Dic43—22no—
332C2×Dic43—22no—
333C2×Dic43—22no—
334C2×Dic43—22no—
335C2×Dic43—22no—
336C2×Dic43—22no—
337C2×Dic43—44no—
338C2×Dic43—44no—
339C2×Dic43—44no—
340C2×Dic43—44no—
341C2×Dic43C2×#4114yes—
342C2×Dic43C2×#4114yes—
343C2×Dic43C2×#4114yes—
344C4×D43—416no—
345Dic86—416no—
346C2×#2560—431nomaximal, Sylow
347C22×C43—42no—
348C22×C43—42no—
349C22×C43—42no—
350C22×C43—42no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—88no—
355C22×C43#52914yes—
356C22×C43#53214yes—
357C22×C43#53914yes—
358C22×C43#54614yes—
359C22×C43#54814yes—
360C22×C43#55114yes—
361C22×C43#55614yes—
362C22×C43C23×D411yescharacteristic
363C22×C43C22×#4111yescharacteristic
364C22×C43C22×#4111yescharacteristic
365C22×C43C22×#4111yescharacteristic
366C22×C43C22×#4111yescharacteristic
367C22×C43C2×H(5,𝔽2)11yescharacteristic
368C22×C43C2×2−1+411yescharacteristic
369C2×D43—24no—
370C2×D43—24no—
371C2×D43—24no—
372C2×D43—416no—
373C2×D43—42no—
374C2×D43—42no—
375C2×D43—42no—
376C2×D43—42no—
377C4×C43—24no—
378C4×C43—24no—
379C4×C43—24no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43—42no—
383Dic43—24no—
384Dic43—24no—
385Dic43—24no—
386Dic43—42no—
387Dic43—42no—
388Dic43—42no—
389Dic43—42no—
390C22×#126D4311yescharacteristic, complemented
391C22×C22⋊Q8—431no—
392#2560—4316no—
393C2×#398—431no—
394C2×#397—431no—
395C2×#394—431no—
396C2×#393—431no—
397C2×#391—431no—
398C2×#390—431no—
399C2×#388—431no—
400C2×#388—431no—
401C2×#388—431no—
402C2×#387—431no—
403C2×#386—431no—
404C2×C4×C4⋊C4—431no—
405C2×C4×C22⋊C4—431no—
406C2×C43—82no—
407C2×C43#256018yescomplemented
408C2×C43C2×#52911yescharacteristic
409C2×C43C2×#53211yescharacteristic
410C2×C43C2×#53911yescharacteristic
411C2×C43C2×#54611yescharacteristic
412C2×C43C2×#54811yescharacteristic
413C2×C43C2×#55111yescharacteristic
414C2×C43C2×#55611yescharacteristic
415D43—44no—
416C23×Q8—431no—
417C23×D4—431no—
418C24×C4—431no—
419C2×#126—28no—
420C2×#126C2×D4318yescomplemented
421C2×C22⋊Q8—438no—
422C2×C22⋊Q8—868no—
423C22×C4⋊C4—431no—
424C22×C4⋊C4—431no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427C22×C4⋊C4C2×D4311yescharacteristic
428C22×C4⋊C4C2×D4311yescharacteristic
429C22×C4⋊C4C2×D4311yescharacteristic
430C22×C22⋊C4—431no—
431C22×C22⋊C4—431no—
432C22×C22⋊C4—431no—
433C22×C22⋊C4—431no—
434C22×C22⋊C4—431no—
435C22×C22⋊C4—431no—
436C22×C22⋊C4—431no—
437C22×C22⋊C4—431no—
438C22×C22⋊C4C2×D4311yescharacteristic
439C22×C22⋊C4C2×D4311yescharacteristic
440C22×C22⋊C4C2×D4311yescharacteristic
441C22×C42—431no—
442C22×C42—431no—
443C22×C42—431no—
444C22×C42C2×D4311yescharacteristic
445#398—438no—
446#397—438no—
447#394—438no—
448#393—438no—
449#391—438no—
450#390—438no—
451#388—438no—
452#388—438no—
453#388—438no—
454#387—438no—
455#386—438no—
456C4×C4⋊C4—438no—
457C4×C22⋊C4—438no—
458C2×#95—431no—
459C2×#95—431no—
460C2×#95—431no—
461C2×#95—431no—
462C2×#95—431no—
463C2×#95—431no—
464C2×#95—431no—
465C2×#95—431no—
466C2×#95—431no—
467C2×#95—431no—
468C43C2×#256011yescharacteristic, complemented, Sylow
469C25—431no—
470C25C22×D4311yescharacteristic
471C22×Q8—434no—
472C22×Q8—864no—
473C22×Q8—864no—
474C22×Q8—1722no—
475C22×D4—434no—
476C22×D4—864no—
477C22×D4—864no—
478C22×D4—1722no—
479C23×C4—431no—
480C23×C4—431no—
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—434no—
487C23×C4—864no—
488C23×C4—864no—
489C23×C4—1722no—
490C23×C4C22×D4311yescharacteristic
491C23×C4C22×D4311yescharacteristic
492C23×C4C22×D4311yescharacteristic
493C23×C4C22×D4311yescharacteristic
494C23×C4C22×D4311yescharacteristic
495C23×C4C22×D4311yescharacteristic
496#126—232no—
497C22⋊Q8—8632no—
498C2×C4⋊C4—24no—
499C2×C4⋊C4—24no—
500C2×C4⋊C4—434no—
501C2×C4⋊C4—434no—
502C2×C4⋊C4—434no—
503C2×C4⋊C4—434no—
504C2×C4⋊C4—864no—
505C2×C4⋊C4—864no—
506C2×C4⋊C4—864no—
507C2×C4⋊C4—864no—
508C2×C4⋊C4C22⋊D4318yescomplemented
509C2×C4⋊C4C22×D4314yes—
510C2×C4⋊C4C22×D4314yes—
511C2×C4⋊C4C22×D4314yes—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—434no—
516C2×C22⋊C4—434no—
517C2×C22⋊C4—434no—
518C2×C22⋊C4—434no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—434no—
521C2×C22⋊C4—434no—
522C2×C22⋊C4—434no—
523C2×C22⋊C4—864no—
524C2×C22⋊C4—864no—
525C2×C22⋊C4—864no—
526C2×C22⋊C4—864no—
527C2×C22⋊C4—864no—
528C2×C22⋊C4—864no—
529C2×C22⋊C4—864no—
530C2×C22⋊C4—1722no—
531C2×C22⋊C4C22×D4314yes—
532C2×C22⋊C4C22×D4314yes—
533C2×C22⋊C4C22×D4314yes—
534C2×C42—24no—
535C2×C42—434no—
536C2×C42—434no—
537C2×C42—434no—
538C2×C42—864no—
539C2×C42—1722no—
540C2×C42—1722no—
541C2×C42C22×D4314yes—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95—434no—
547#95—434no—
548#95—434no—
549#95—434no—
550#95—434no—
551#95—434no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—434no—
560C24—432no—
561C24—862no—
562C24—862no—
563C24—862no—
564C24—862no—
565C24—862no—
566C24—862no—
567C24C23×D4312yes—
568C24C23×D4311yescharacteristic
569C2×Q8—868no—
570C2×Q8—868no—
571C2×Q8—1724no—
572C2×Q8—17216no—
573C2×D4—868no—
574C2×D4—868no—
575C2×D4—1724no—
576C2×D4—17216no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—434no—
593C22×C4—434no—
594C22×C4—434no—
595C22×C4—432no—
596C22×C4—432no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—432no—
602C22×C4—868no—
603C22×C4—862no—
604C22×C4—862no—
605C22×C4—862no—
606C22×C4—862no—
607C22×C4—862no—
608C22×C4—862no—
609C22×C4—862no—
610C22×C4—862no—
611C22×C4—862no—
612C22×C4—862no—
613C22×C4—862no—
614C22×C4—862no—
615C22×C4—862no—
616C22×C4—862no—
617C22×C4—862no—
618C22×C4—862no—
619C22×C4—862no—
620C22×C4—862no—
621C22×C4—868no—
622C22×C4—1724no—
623C22×C4—17216no—
624C22×C4C2×C22⋊D4314yes—
625C22×C4C2×C22⋊D4314yes—
626C22×C4C2×C22⋊D4314yes—
627C22×C4C23×D4312yes—
628C22×C4C23×D4312yes—
629C22×C4C23×D4312yes—
630C22×C4C23×D4312yes—
631C22×C4C23×D4312yes—
632C22×C4C23×D4312yes—
633C4⋊C4—28no—
634C4⋊C4—28no—
635C4⋊C4—868no—
636C4⋊C4—868no—
637C4⋊C4—868no—
638C4⋊C4—868no—
639C4⋊C4C2×C22⋊D43116yescomplemented
640C22⋊C4—28no—
641C22⋊C4—28no—
642C22⋊C4—28no—
643C22⋊C4—868no—
644C22⋊C4—868no—
645C22⋊C4—868no—
646C22⋊C4—868no—
647C22⋊C4—868no—
648C22⋊C4—868no—
649C22⋊C4—868no—
650C22⋊C4—1724no—
651C42—28no—
652C42—868no—
653C42—1724no—
654C42—1724no—
655C23—22no—
656C23—22no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—44no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—434no—
670C23—868no—
671C23—868no—
672C23—868no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—1724no—
680C23—1724no—
681C23—1724no—
682C23—1724no—
683C23C22×C22⋊D4312yes—
684C23#41×D4312yes—
685C23#41×D4312yes—
686C23#41×D4312yes—
687C23#41×D4312yes—
688C23#1306337112yes—
689C23#1306337212yes—
690C23C24×D4311yescharacteristic
691Q8—17216no—
692D4—17216no—
693C2×C4—28no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—28no—
701C2×C4—28no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—434no—
715C2×C4—434no—
716C2×C4—434no—
717C2×C4—868no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—868no—
725C2×C4—868no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—862no—
730C2×C4—862no—
731C2×C4—862no—
732C2×C4—862no—
733C2×C4—862no—
734C2×C4—862no—
735C2×C4—862no—
736C2×C4—862no—
737C2×C4—862no—
738C2×C4—17216no—
739C2×C4—1724no—
740C2×C4—1724no—
741C2×C4—1724no—
742C2×C4—1724no—
743C2×C4C22×C22⋊D4314yes—
744C2×C4C22×C22⋊D4314yes—
745C2×C4C22×C22⋊D4314yes—
746C22—42no—
747C22—42no—
748C22—42no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—88no—
754C22—864no—
755C22—864no—
756C22—864no—
757C22—1722no—
758C22—1722no—
759C22—1722no—
760C22—17216no—
761C22—1722no—
762C22#1458343214yes—
763C22#1458344514yes—
764C22#1458349014yes—
765C22#1458353714yes—
766C22#1458355614yes—
767C22#1458357414yes—
768C22#1458361614yes—
769C22C23×C22⋊D4311yescharacteristic
770C22C2×#41×D4311yescharacteristic
771C22C2×#41×D4311yescharacteristic
772C22C2×#41×D4311yescharacteristic
773C22C2×#41×D4311yescharacteristic
774C22C2×#1306337111yescharacteristic
775C22C2×#1306337211yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—864no—
783C4—864no—
784C4—864no—
785C4—1722no—
786C4—1722no—
787C4—1722no—
788C4—1722no—
789C2—82no—
790C2—1724no—
791C2#1913973718yesdirect product factor
792C2C2×#1458343211yescharacteristic
793C2C2×#1458344511yescharacteristic
794C2C2×#1458349011yescharacteristic
795C2C2×#1458353711yescharacteristic
796C2C2×#1458355611yescharacteristic
797C2C2×#1458357411yescharacteristic
798C2C2×#1458361611yescharacteristic
subgroupG/H
centerC24C23×D43
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC22×#126×C43C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
hypercenterC22×#126D43
hypocenterC43C2×#2560
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×#13063303C2semidirect
2. #19139737C2direct (N × H)
3. C2×#14582832C2semidirect
4. C2×#14582825C2semidirect
6. C2×#14582811C2semidirect
7. C2×#14582804C2semidirect
9. C2×#14582793C2semidirect
10. C2×#14582793C2semidirect
11. C2×#14582789C2semidirect
12. C2×#14582783C2semidirect
14. C2×C4⋊C4×Dic43C2semidirect
15. C2×C4×(C2×D43)⋊C4C2semidirect
16. C22×#126×C43C2semidirect
21. C2×#13063303C22semidirect
37. #14582832C22semidirect
38. #14582825C22semidirect
40. #14582811C22semidirect
41. #14582804C22semidirect
43. #14582793C22semidirect
44. #14582793C22semidirect
45. #14582789C22semidirect
46. #14582783C22semidirect
48. C4⋊C4×Dic43C22semidirect
49. C4×(C2×D43)⋊C4C22semidirect
61. C2×#126×C43C22semidirect
140. C2×C4⋊C4×C43D4semidirect
235. C4⋊C4×C43C2×D4semidirect
390. C22×#126D43semidirect
407. C2×C43#2560semidirect
420. C2×#126C2×D43semidirect
468. C43C2×#2560semidirect
508. C2×C4⋊C4C22⋊D43semidirect
639. C4⋊C4C2×C22⋊D43semidirect
791. C2#19139737direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633032
#191397372
C2×#145828322
C2×#145828252
C2×#145828152
C2×#145828112
C2×#145828042
C2×#145827992
C2×#145827932
C2×#145827892
C2×#145827832
C2×#145827752
C2×C4⋊C4×Dic432
C2×C4×(C2×D43)⋊C42
C22×#126×C432
C2×#256043