Finite Group Databasebeta

← C2×#19137324 #25255415

Subgroups — C2×#19137324 #25255415

Order 11008.

2982 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063305C211yesmaximal, characteristic
2#19137324C2116yesmaximal, direct product factor
3C2×#14582803C211yesmaximal, characteristic, complemented
4C2×#14582803C211yesmaximal, characteristic, complemented
5C2×#14582797C211yesmaximal, characteristic, complemented
6C2×#14582795C211yesmaximal, characteristic, complemented
7C2×#14582785C211yesmaximal, characteristic, complemented
8C2×#14582784C211yesmaximal, characteristic, complemented
9C2×#14582782C211yesmaximal, characteristic, complemented
10C2×#14582773C211yesmaximal, characteristic
11C2×#14582770C211yesmaximal, characteristic
12C2×#14582758C211yesmaximal, characteristic
13C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic
14C2×#14582746C211yesmaximal, characteristic
15C2×#95×D43C211yesmaximal, characteristic
16C2×C43×#387C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C4×D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C2×#13063305C4116yescomplemented
22C2×#13063305C2218yes—
23C22×C4⋊Dic43C2211yescharacteristic
24C22×C4⋊Dic43C2211yescharacteristic
25C22×C4⋊Dic43C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×Dic43⋊C4C2211yescharacteristic
29C22×Dic43⋊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#14582803C2218yescomplemented
38#14582803C2218yescomplemented
39#14582797C2218yescomplemented
40#14582795C2218yescomplemented
41#14582785C2218yescomplemented
42#14582784C2218yescomplemented
43#14582782C2218yescomplemented
44#14582773C2218yes—
45#14582770C2218yes—
46#14582758C2218yes—
47C4×(C2×D43)⋊C4C2218yes—
48#14582746C2218yes—
49C2×C43⋊#95C2211yescharacteristic
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
59#95×D43C2218yes—
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C42×C43C2211yescharacteristic
63C43×#387C2218yescomplemented
64C2×#95×C43C2211yescharacteristic
65C2×#95×C43C2211yescharacteristic
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C22×Dic86—42no—
70C22×Dic86—42no—
71C22×Dic86C2×C418yescomplemented
72C22×Dic86C2314yes—
73C23×Dic43C2311yescharacteristic
74C23×Dic43C2311yescharacteristic
75C23×Dic43C2311yescharacteristic
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C22×C4×D43—24no—
81C22×C4×D43—42no—
82C22×C4×D43—42no—
83C22×C4×D43—42no—
84C22×C4×D43—42no—
85C22×C4×D43—42no—
86C22×C4×D43—42no—
87C22×C4×D43C2×C418yes—
88C22×C4×D43Q818yescomplemented
89C22×C4×D43C2314yes—
90C22×C4×D43C2314yes—
91C22×C4×D43C2314yes—
92#13063305C2×C4164yescomplemented
93C2×C4⋊Dic43—42no—
94C2×C4⋊Dic43C2×C418yescomplemented
95C2×C4⋊Dic43C2×C418yescomplemented
96C2×C4⋊Dic43C2314yes—
97C2×C4⋊Dic43C2314yes—
98C2×C4⋊Dic43C2314yes—
99C2×Dic43⋊C4—42no—
100C2×Dic43⋊C4—42no—
101C2×Dic43⋊C4—42no—
102C2×Dic43⋊C4—42no—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×Dic43⋊C4C2314yes—
106C2×Dic43⋊C4C2314yes—
107C2×(C2×D43)⋊C4—24no—
108C2×(C2×D43)⋊C4—24no—
109C2×(C2×D43)⋊C4C2×C418yes—
110C2×(C2×D43)⋊C4C2×C418yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×C4×Dic43—42no—
116C2×C4×Dic43—42no—
117C2×C4×Dic43—42no—
118C2×C4×Dic43C2314yes—
119C2×C4×Dic43C2314yes—
120C2×C4×Dic43C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C23×C4×C43C2311yescharacteristic
132C23×C4×C43C2311yescharacteristic
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43—42no—
139C2×C4⋊C4×C43C2×C418yescomplemented
140C2×C4⋊C4×C43C2314yes—
141C2×C4⋊C4×C43C2314yes—
142C2×C42×C43—42no—
143C2×C42×C43C2314yes—
144#95×C43C2314yes—
145#95×C43C2314yes—
146#95×C43C2314yes—
147#95×C43C2314yes—
148C24×C43C2411yescharacteristic
149C23×D43—22no—
150C23×D43—22no—
151C23×D43—22no—
152C23×D43—22no—
153C23×D43C22×C414yes—
154C23×D43C2×Q814yes—
155C23×D43#4114yes—
156C23×D43C2412yes—
157C22×C4×C43—22no—
158C22×C4×C43—22no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—22no—
163C22×C4×C43—22no—
164C22×C4×C43—22no—
165C22×C4×C43—22no—
166C22×C4×C43—22no—
167C22×C4×C43—22no—
168C22×C4×C43—22no—
169C22×C4×C43—22no—
170C22×C4×C43—22no—
171C22×C4×C43—22no—
172C22×C4×C43—22no—
173C22×C4×C43—22no—
174C22×C4×C43C22×C414yes—
175C22×C4×C43C22×C414yes—
176C22×C4×C43C22×C414yes—
177C22×C4×C43C2×Q814yes—
178C22×C4×C43C2412yes—
179C22×C4×C43C2412yes—
180C22×C4×C43C2412yes—
181C22×C4×C43C2412yes—
182C22×C4×C43C2412yes—
183C22×C4×C43C2412yes—
184C22×C4×C43C2412yes—
185C22×Dic43—22no—
186C22×Dic43—22no—
187C22×Dic43—22no—
188C22×Dic43—22no—
189C22×Dic43—22no—
190C22×Dic43—22no—
191C22×Dic43—22no—
192C22×Dic43—22no—
193C22×Dic43—22no—
194C22×Dic43—22no—
195C22×Dic43—22no—
196C22×Dic43—22no—
197C22×Dic43—22no—
198C22×Dic43—22no—
199C22×Dic43—22no—
200C22×Dic43—22no—
201C22×Dic43—22no—
202C22×Dic43C22×C414yes—
203C22×Dic43C22×C414yes—
204C22×Dic43C22×C414yes—
205C22×Dic43C2×Q814yes—
206C22×Dic43C2412yes—
207C22×Dic43C2412yes—
208C22×Dic43C2412yes—
209C22×Dic43C2412yes—
210C22×Dic43C2412yes—
211C22×Dic43C2412yes—
212C22×Dic43C2412yes—
213C2×C4×D43—28no—
214C2×C4×D43—416no—
215C2×C4×D43—416no—
216C2×C4×D43—44no—
217C2×C4×D43—44no—
218C2×C4×D43—44no—
219C2×C4×D43—44no—
220C2×C4×D43—44no—
221C2×C4×D43—44no—
222C2×C4×D43—416no—
223C2×C4×D43C22×C4116yes—
224C2×C4×D43C2×Q8116yescomplemented
225C2×Dic86—416no—
226C2×Dic86—44no—
227C2×Dic86—44no—
228C2×Dic86C22×C4116yescomplemented
229C4⋊C4×C43—44no—
230C4⋊C4×C43C22×C4116yescomplemented
231C42×C43—44no—
232(C2×D43)⋊C4—28no—
233(C2×D43)⋊C4—28no—
234(C2×D43)⋊C4C22×C4116yes—
235(C2×D43)⋊C4C22×C4116yes—
236C4⋊Dic43—44no—
237C4⋊Dic43C22×C4116yescomplemented
238C4⋊Dic43C22×C4116yescomplemented
239Dic43⋊C4—44no—
240Dic43⋊C4—44no—
241Dic43⋊C4—44no—
242Dic43⋊C4—44no—
243C4×Dic43—44no—
244C4×Dic43—44no—
245C4×Dic43—44no—
246C23×C43C23×C412yes—
247C23×C43C22×Q812yes—
248C23×C43C2×#4112yes—
249C23×C43H(5,𝔽2)12yes—
250C23×C43H(5,𝔽2)12yes—
251C23×C43H(5,𝔽2)12yes—
252C23×C432−1+412yes—
253C23×C43C2511yescharacteristic
254C22×D43—28no—
255C22×D43—28no—
256C22×D43—28no—
257C22×D43—28no—
258C22×D43—28no—
259C22×D43—28no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—22no—
263C22×D43—22no—
264C22×D43C4×Q8116yes—
265C22×D43C23×C414yes—
266C22×D43C22×Q814yes—
267C22×D43C2×#4114yes—
268C2×C4×C43—28no—
269C2×C4×C43—28no—
270C2×C4×C43—28no—
271C2×C4×C43—28no—
272C2×C4×C43—22no—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—22no—
277C2×C4×C43—22no—
278C2×C4×C43—22no—
279C2×C4×C43—22no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—22no—
284C2×C4×C43—22no—
285C2×C4×C43—22no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—44no—
290C2×C4×C43—44no—
291C2×C4×C43—44no—
292C2×C4×C43C23×C414yes—
293C2×C4×C43C23×C414yes—
294C2×C4×C43C23×C414yes—
295C2×C4×C43C22×Q814yes—
296C2×Dic43—28no—
297C2×Dic43—28no—
298C2×Dic43—28no—
299C2×Dic43—28no—
300C2×Dic43—22no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—22no—
305C2×Dic43—22no—
306C2×Dic43—22no—
307C2×Dic43—22no—
308C2×Dic43—22no—
309C2×Dic43—22no—
310C2×Dic43—22no—
311C2×Dic43—22no—
312C2×Dic43—22no—
313C2×Dic43—22no—
314C2×Dic43—22no—
315C2×Dic43—22no—
316C2×Dic43—22no—
317C2×Dic43—44no—
318C2×Dic43—44no—
319C2×Dic43—44no—
320C2×Dic43C23×C414yes—
321C2×Dic43C23×C414yes—
322C2×Dic43C23×C414yes—
323C2×Dic43C22×Q814yes—
324C4×D43—416no—
325C4×D43—416no—
326C4×D43—416no—
327Dic86—416no—
328C2×#2329—431nomaximal, Sylow
329C22×C43C2×C4×Q814yes—
330C22×C43#51814yes—
331C22×C43#52014yes—
332C22×C43#53814yes—
333C22×C43#53914yes—
334C22×C43#54314yes—
335C22×C43#54414yes—
336C22×C43C24×C411yescharacteristic
337C22×C43C23×Q811yescharacteristic
338C22×C43C22×#4111yescharacteristic
339C22×C43C2×H(5,𝔽2)11yescharacteristic
340C22×C43C2×H(5,𝔽2)11yescharacteristic
341C22×C43C2×H(5,𝔽2)11yescharacteristic
342C22×C43C2×2−1+411yescharacteristic
343C2×D43—232no—
344C2×D43—24no—
345C2×D43—24no—
346C2×D43—24no—
347C2×D43—24no—
348C2×D43—24no—
349C2×D43—24no—
350C2×D43C2×C4×Q818yes—
351C4×C43—24no—
352C4×C43—24no—
353C4×C43—24no—
354C4×C43—24no—
355C4×C43—42no—
356C4×C43—42no—
357C4×C43—42no—
358Dic43—24no—
359Dic43—24no—
360Dic43—24no—
361Dic43—24no—
362Dic43—42no—
363Dic43—42no—
364Dic43—42no—
365C22×C22⋊Q8—431no—
366#2329—4316no—
367C2×#391—431no—
368C2×#391—431no—
369C2×#389—431no—
370C2×#389—431no—
371C2×#387—431no—
372C2×#387—431no—
373C2×#387—431no—
374C2×#387D4311yescharacteristic, complemented
375C2×#385—431no—
376C2×#385—431no—
377C2×#380—431no—
378C2×C4×C22⋊C4—431no—
379C2×C4×C22⋊C4—431no—
380C22×#95—431no—
381C2×C43#232918yescomplemented
382C2×C43C22×C4×Q811yescharacteristic
383C2×C43C2×#51811yescharacteristic
384C2×C43C2×#52011yescharacteristic
385C2×C43C2×#53811yescharacteristic
386C2×C43C2×#53911yescharacteristic
387C2×C43C2×#54311yescharacteristic
388C2×C43C2×#54411yescharacteristic
389D43—28no—
390C23×Q8—431no—
391C24×C4—431no—
392C24×C4—431no—
393C24×C4—431no—
394C2×C22⋊Q8—438no—
395C2×C22⋊Q8—4316no—
396C22×C4⋊C4—431no—
397C22×C4⋊C4—431no—
398C22×C4⋊C4—431no—
399C22×C4⋊C4—431no—
400C22×C4⋊C4—431no—
401C22×C4⋊C4—431no—
402C22×C4⋊C4—431no—
403C22×C4⋊C4C2×D4311yescharacteristic
404C22×C4⋊C4C2×D4311yescharacteristic
405C22×C22⋊C4—431no—
406C22×C22⋊C4—431no—
407C22×C22⋊C4—431no—
408C22×C22⋊C4—431no—
409C22×C42—431no—
410C22×C42—431no—
411C22×C42—431no—
412C22×C42C2×D4311yescharacteristic
413#391—438no—
414#391—438no—
415#389—438no—
416#389—438no—
417#387—438no—
418#387—438no—
419#387—438no—
420#387C2×D4318yescomplemented
421#385—438no—
422#385—438no—
423#380—438no—
424C4×C22⋊C4—438no—
425C4×C22⋊C4—438no—
426C2×#95—431no—
427C2×#95—431no—
428C2×#95—431no—
429C2×#95—431no—
430C2×#95—431no—
431C2×#95—431no—
432C2×#95—431no—
433C2×#95—431no—
434C2×#95—431no—
435C2×#95—431no—
436C2×#95—438no—
437C2×#95C2×D4311yescharacteristic
438C2×#95C2×D4311yescharacteristic
439C2×#95C2×D4311yescharacteristic
440C2×#95C2×D4311yescharacteristic
441C43C2×#232911yescharacteristic, complemented, Sylow
442C25—431no—
443C22×Q8—438no—
444C22×Q8—434no—
445C22×Q8—1722no—
446C22×Q8—1722no—
447C23×C4—431no—
448C23×C4—431no—
449C23×C4—431no—
450C23×C4—431no—
451C23×C4—438no—
452C23×C4—438no—
453C23×C4—434no—
454C23×C4—434no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4—431no—
458C23×C4—434no—
459C23×C4—864no—
460C23×C4—1722no—
461C23×C4—1722no—
462C23×C4—1722no—
463C23×C4—1722no—
464C23×C4—1722no—
465C23×C4—1722no—
466C23×C4C22×D4311yescharacteristic
467C23×C4C22×D4311yescharacteristic
468C23×C4C22×D4311yescharacteristic
469C23×C4C22×D4311yescharacteristic
470C23×C4C22×D4311yescharacteristic
471C23×C4C22×D4311yescharacteristic
472C23×C4C22×D4311yescharacteristic
473C22⋊Q8—4364no—
474C2×C4⋊C4—42no—
475C2×C4⋊C4—438no—
476C2×C4⋊C4—438no—
477C2×C4⋊C4—434no—
478C2×C4⋊C4—434no—
479C2×C4⋊C4—434no—
480C2×C4⋊C4—434no—
481C2×C4⋊C4—434no—
482C2×C4⋊C4—434no—
483C2×C4⋊C4—434no—
484C2×C4⋊C4—1722no—
485C2×C4⋊C4—1722no—
486C2×C4⋊C4—1722no—
487C2×C4⋊C4—1722no—
488C2×C4⋊C4—1722no—
489C2×C4⋊C4C4×D4318yescomplemented
490C2×C4⋊C4C22×D4314yes—
491C2×C4⋊C4C22×D4314yes—
492C2×C22⋊C4—438no—
493C2×C22⋊C4—438no—
494C2×C22⋊C4—434no—
495C2×C22⋊C4—434no—
496C2×C22⋊C4—434no—
497C2×C22⋊C4—434no—
498C2×C22⋊C4—864no—
499C2×C22⋊C4—864no—
500C2×C42—42no—
501C2×C42—434no—
502C2×C42—434no—
503C2×C42—434no—
504C2×C42—1722no—
505C2×C42—1722no—
506C2×C42—1722no—
507C2×C42C22×D4314yes—
508#95—434no—
509#95—434no—
510#95—434no—
511#95—434no—
512#95—434no—
513#95—434no—
514#95—434no—
515#95—434no—
516#95—434no—
517#95—434no—
518#95C22×D4314yes—
519#95C22×D4314yes—
520#95C22×D4314yes—
521#95C22×D4314yes—
522C24—434no—
523C24—434no—
524C24—434no—
525C24—432no—
526C24—862no—
527C24—862no—
528C24—862no—
529C24—862no—
530C24C23×D4311yescharacteristic
531C2×Q8—4316no—
532C2×Q8—17216no—
533C2×Q8—1724no—
534C2×Q8—1724no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—22no—
543C22×C4—22no—
544C22×C4—22no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—22no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—434no—
553C22×C4—434no—
554C22×C4—434no—
555C22×C4—434no—
556C22×C4—432no—
557C22×C4—432no—
558C22×C4—432no—
559C22×C4—432no—
560C22×C4—4316no—
561C22×C4—4316no—
562C22×C4—432no—
563C22×C4—432no—
564C22×C4—432no—
565C22×C4—868no—
566C22×C4—862no—
567C22×C4—862no—
568C22×C4—862no—
569C22×C4—862no—
570C22×C4—862no—
571C22×C4—862no—
572C22×C4—862no—
573C22×C4—862no—
574C22×C4—862no—
575C22×C4—862no—
576C22×C4—862no—
577C22×C4—862no—
578C22×C4—862no—
579C22×C4—862no—
580C22×C4—862no—
581C22×C4—862no—
582C22×C4—862no—
583C22×C4—17216no—
584C22×C4—1724no—
585C22×C4—1724no—
586C22×C4—1724no—
587C22×C4—1724no—
588C22×C4—17216no—
589C22×C4—1724no—
590C22×C4—1724no—
591C22×C4—17216no—
592C22×C4C2×C4×D4314yes—
593C22×C4C2×C4×D4314yes—
594C22×C4C2×C4×D4314yes—
595C22×C4Q8×D4314yes—
596C22×C4C23×D4312yes—
597C22×C4C23×D4312yes—
598C22×C4C23×D4312yes—
599C22×C4C23×D4312yes—
600C22×C4C23×D4312yes—
601C22×C4C23×D4312yes—
602C22×C4C23×D4312yes—
603C4⋊C4—44no—
604C4⋊C4—4316no—
605C4⋊C4—4316no—
606C4⋊C4—1724no—
607C4⋊C4—1724no—
608C4⋊C4—1724no—
609C4⋊C4—1724no—
610C4⋊C4—1724no—
611C4⋊C4C2×C4×D43116yescomplemented
612C22⋊C4—4316no—
613C22⋊C4—4316no—
614C22⋊C4—868no—
615C22⋊C4—868no—
616C42—44no—
617C42—1724no—
618C42—1724no—
619C42—1724no—
620C23—4316no—
621C23—434no—
622C23—434no—
623C23—434no—
624C23—868no—
625C23—868no—
626C23—862no—
627C23—862no—
628C23—862no—
629C23—862no—
630C23—868no—
631C23—868no—
632C23—868no—
633C23—868no—
634C23C22×C4×D4312yes—
635C23C2×Q8×D4312yes—
636C23#41×D4312yes—
637C23#1306337012yes—
638C23#1306337112yes—
639C23#1306337112yes—
640C23#1306337212yes—
641C23C24×D4311yescharacteristic
642Q8—17216no—
643C2×C4—28no—
644C2×C4—28no—
645C2×C4—28no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—28no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—44no—
665C2×C4—44no—
666C2×C4—44no—
667C2×C4—434no—
668C2×C4—434no—
669C2×C4—434no—
670C2×C4—434no—
671C2×C4—868no—
672C2×C4—868no—
673C2×C4—868no—
674C2×C4—862no—
675C2×C4—862no—
676C2×C4—862no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—868no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—862no—
686C2×C4—862no—
687C2×C4—862no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—862no—
692C2×C4—17216no—
693C2×C4—17216no—
694C2×C4—17216no—
695C2×C4—1724no—
696C2×C4—1724no—
697C2×C4—1724no—
698C2×C4C22×C4×D4314yes—
699C2×C4C22×C4×D4314yes—
700C2×C4C22×C4×D4314yes—
701C2×C4C2×Q8×D4314yes—
702C22—438no—
703C22—864no—
704C22—864no—
705C22—8632no—
706C22—864no—
707C22—864no—
708C22—864no—
709C22—864no—
710C22C4×Q8×D4314yes—
711C22#1458337314yes—
712C22#1458337814yes—
713C22#1458348514yes—
714C22#1458349014yes—
715C22#1458352414yes—
716C22#1458352914yes—
717C22C23×C4×D4311yescharacteristic
718C22C22×Q8×D4311yescharacteristic
719C22C2×#41×D4311yescharacteristic
720C22C2×#1306337011yescharacteristic
721C22C2×#1306337111yescharacteristic
722C22C2×#1306337111yescharacteristic
723C22C2×#1306337211yescharacteristic
724C4—24no—
725C4—24no—
726C4—24no—
727C4—24no—
728C4—42no—
729C4—42no—
730C4—42no—
731C4—864no—
732C4—864no—
733C4—864no—
734C4—864no—
735C4—1722no—
736C4—1722no—
737C4—1722no—
738C2—868no—
739C2#1913732418yesdirect product factor
740C2C2×C4×Q8×D4311yescharacteristic
741C2C2×#1458337311yescharacteristic
742C2C2×#1458337811yescharacteristic
743C2C2×#1458348511yescharacteristic
744C2C2×#1458349011yescharacteristic
745C2C2×#1458352411yescharacteristic
746C2C2×#1458352911yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#387C2
socleC24×C43C24
prime radicalC24×D43C23
cosocleC23×C43C25
hypercenterC2×#387D43
hypocenterC43C2×#2329
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#387

Complements

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

NH ≅ G/Ntype
2. #19137324C2direct (N × H)
3. C2×#14582803C2semidirect
4. C2×#14582803C2semidirect
5. C2×#14582797C2semidirect
6. C2×#14582795C2semidirect
7. C2×#14582785C2semidirect
8. C2×#14582784C2semidirect
9. C2×#14582782C2semidirect
16. C2×C43×#387C2semidirect
21. C2×#13063305C4semidirect
37. #14582803C22semidirect
38. #14582803C22semidirect
39. #14582797C22semidirect
40. #14582795C22semidirect
41. #14582785C22semidirect
42. #14582784C22semidirect
43. #14582782C22semidirect
63. C43×#387C22semidirect
71. C22×Dic86C2×C4semidirect
88. C22×C4×D43Q8semidirect
92. #13063305C2×C4semidirect
94. C2×C4⋊Dic43C2×C4semidirect
95. C2×C4⋊Dic43C2×C4semidirect
139. C2×C4⋊C4×C43C2×C4semidirect
224. C2×C4×D43C2×Q8semidirect
228. C2×Dic86C22×C4semidirect
230. C4⋊C4×C43C22×C4semidirect
237. C4⋊Dic43C22×C4semidirect
238. C4⋊Dic43C22×C4semidirect
374. C2×#387D43semidirect
381. C2×C43#2329semidirect
420. #387C2×D43semidirect
441. C43C2×#2329semidirect
489. C2×C4⋊C4C4×D43semidirect
611. C4⋊C4C2×C4×D43semidirect
739. C2#19137324direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633052
#191373242
C2×#145828032
C2×#145827972
C2×#145827952
C2×#145827852
C2×#145827842
C2×#145827822
C2×#145827732
C2×#145827702
C2×#145827582
C2×C4×(C2×D43)⋊C42
C2×#145827462
C2×#95×D432
C2×C43×#3872
C2×#232943