Finite Group Databasebeta

← C2×#19137409 #25255517

Subgroups — C2×#19137409 #25255517

Order 11008.

3046 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×#13063311C211yesmaximal, characteristic
2#19137409C2116yesmaximal, direct product factor
3C2×#14582804C211yesmaximal, characteristic, complemented
4C2×#14582803C211yesmaximal, characteristic, complemented
5C2×#14582792C211yesmaximal, characteristic, complemented
6C2×#14582789C211yesmaximal, characteristic, complemented
7C2×#14582789C211yesmaximal, characteristic, complemented
8C2×#14582787C211yesmaximal, characteristic, complemented
9C2×#14582778C211yesmaximal, characteristic
10C2×#14582775C211yesmaximal, characteristic
11C2×#14582773C211yesmaximal, characteristic, complemented
12C2×#14582766C211yesmaximal, characteristic, complemented
13C2×C4⋊C4×Dic43C211yesmaximal, characteristic, complemented
14C2×C4×C22⋊Dic43C211yesmaximal, characteristic, complemented
15C2×#14582746C211yesmaximal, characteristic, complemented
16C2×C43×#385C211yesmaximal, characteristic, complemented
17C23×Dic86C2211yescharacteristic
18C23×C22⋊D43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C2×#13063311C4116yescomplemented
21C2×#13063311C2218yes—
22C22×C4⋊Dic43C2211yescharacteristic
23C22×Dic43⋊C4C2211yescharacteristic
24C22×C22⋊Dic43C2211yescharacteristic
25C22×C22⋊Dic43C2211yescharacteristic
26C22×C22⋊Dic43C2211yescharacteristic
27C22×(C2×D43)⋊C4C2211yescharacteristic
28C22×(C2×D43)⋊C4C2211yescharacteristic
29C22×(C2×D43)⋊C4C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×C4×Dic43C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35C22×C4×Dic43C2211yescharacteristic
36C22×C4×Dic43C2211yescharacteristic
37#14582804C2218yescomplemented
38#14582803C2218yescomplemented
39#14582792C2218yescomplemented
40#14582789C2218yescomplemented
41#14582789C2218yescomplemented
42#14582787C2218yescomplemented
43#14582778C2218yes—
44#14582775C2218yes—
45#14582773C2218yescomplemented
46#14582766C2218yescomplemented
47C4⋊C4×Dic43C2218yescomplemented
48C4×C22⋊Dic43C2218yescomplemented
49#14582746C2218yescomplemented
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
60C24×C4×C43C2211yescharacteristic
61C22×C4⋊C4×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C22⋊C4×C43C2211yescharacteristic
65C43×#385C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C22×Dic86—42no—
70C22×Dic86—42no—
71C22×Dic86C2×C418yescomplemented
72C22×Dic86C2314yes—
73C22×C22⋊D43—42no—
74C22×C22⋊D43—42no—
75C22×C22⋊D43C2×C418yes—
76C22×C22⋊D43C2314yes—
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2311yescharacteristic
84C22×C4×D43—24no—
85C22×C4×D43—42no—
86C22×C4×D43—42no—
87C22×C4×D43C2314yes—
88#13063311C2×C4164yescomplemented
89C2×C4⋊Dic43—24no—
90C2×C4⋊Dic43C2314yes—
91C2×Dic43⋊C4—42no—
92C2×Dic43⋊C4C2314yes—
93C2×C22⋊Dic43—24no—
94C2×C22⋊Dic43—42no—
95C2×C22⋊Dic43C2×C418yescomplemented
96C2×C22⋊Dic43C2314yes—
97C2×C22⋊Dic43C2314yes—
98C2×C22⋊Dic43C2314yes—
99C2×(C2×D43)⋊C4—24no—
100C2×(C2×D43)⋊C4—42no—
101C2×(C2×D43)⋊C4—42no—
102C2×(C2×D43)⋊C4C2×C418yescomplemented
103C2×(C2×D43)⋊C4C2×C418yescomplemented
104C2×(C2×D43)⋊C4C2314yes—
105C2×(C2×D43)⋊C4C2314yes—
106C2×(C2×D43)⋊C4C2314yes—
107C2×(C2×D43)⋊C4C2314yes—
108C2×(C2×D43)⋊C4C2314yes—
109C2×C4×Dic43—42no—
110C2×C4×Dic43—42no—
111C2×C4×Dic43—42no—
112C2×C4×Dic43—42no—
113C2×C4×Dic43C2×C418yescomplemented
114C2×C4×Dic43C2314yes—
115C2×C4×Dic43C2314yes—
116C2×C4×Dic43C2314yes—
117C2×C4×Dic43C2314yes—
118C2×C4×Dic43C2314yes—
119C43⋊#95C2314yes—
120C43⋊#95C2314yes—
121C43⋊#95C2314yes—
122C43⋊#95C2314yes—
123C43⋊#95C2314yes—
124C43⋊#95C2314yes—
125C43⋊#95C2314yes—
126C43⋊#95C2314yes—
127C43⋊#95C2314yes—
128C43⋊#95C2314yes—
129C25×C43C2311yescharacteristic
130C23×C4×C43—24no—
131C23×C4×C43—42no—
132C23×C4×C43—42no—
133C23×C4×C43C2311yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C23×C4×C43C2311yescharacteristic
137C23×C4×C43C2311yescharacteristic
138C23×C4×C43C2311yescharacteristic
139C23×C4×C43C2314yes—
140C2×C4⋊C4×C43—24no—
141C2×C4⋊C4×C43—42no—
142C2×C4⋊C4×C43C2314yes—
143C2×C4⋊C4×C43C2314yes—
144C2×C22⋊C4×C43—42no—
145C2×C22⋊C4×C43C2×C418yescomplemented
146C2×C22⋊C4×C43C2314yes—
147C2×C22⋊C4×C43C2314yes—
148#95×C43C2314yes—
149#95×C43C2314yes—
150C24×C43—22no—
151C24×C43—22no—
152C24×C43—22no—
153C24×C43—22no—
154C24×C43—22no—
155C24×C43—22no—
156C24×C43C22×C414yes—
157C24×C43C2412yes—
158C24×C43C2411yescharacteristic
159C23×D43—22no—
160C23×D43—22no—
161C23×D43—22no—
162C23×D43—22no—
163C23×D43—22no—
164C23×D43—22no—
165C23×D43C22×C414yes—
166C23×D43C2412yes—
167C22×C4×C43—28no—
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×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—44no—
184C22×C4×C43—44no—
185C22×C4×C43—416no—
186C22×C4×C43C22×C414yes—
187C22×C4×C43C22×C414yes—
188C22×C4×C43#4114yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C22×C4×C43C2412yes—
192C22×C4×C43C2412yes—
193C22×C4×C43C2412yes—
194C22×C4×C43C2412yes—
195C2×C22⋊D43—416no—
196C2×C22⋊D43—44no—
197C2×C22⋊D43—44no—
198C2×C22⋊D43C22×C4116yes—
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—22no—
216C22×Dic43C22×C414yes—
217C22×Dic43C22×C414yes—
218C22×Dic43C22×C414yes—
219C22×Dic43#4114yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C2×C4×D43—28no—
228C2×C4×D43—44no—
229C2×C4×D43—44no—
230C2×C4×D43—416no—
231C2×Dic86—416no—
232C2×Dic86—44no—
233C2×Dic86—44no—
234C2×Dic86C22×C4116yescomplemented
235C4⋊C4×C43—28no—
236C4⋊C4×C43—44no—
237C22⋊C4×C43—44no—
238C22⋊C4×C43C22×C4116yescomplemented
239C22⋊Dic43—28no—
240C22⋊Dic43—44no—
241C22⋊Dic43C22×C4116yescomplemented
242(C2×D43)⋊C4—28no—
243(C2×D43)⋊C4—44no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4C22×C4116yescomplemented
246(C2×D43)⋊C4C22×C4116yescomplemented
247C4⋊Dic43—28no—
248Dic43⋊C4—44no—
249C4×Dic43—44no—
250C4×Dic43—44no—
251C4×Dic43—44no—
252C4×Dic43—44no—
253C4×Dic43C22×C4116yescomplemented
254C23×C43—28no—
255C23×C43—28no—
256C23×C43—28no—
257C23×C43—22no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—44no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43C23×C414yes—
268C23×C43C23×C412yes—
269C23×C43C2×#4112yes—
270C23×C43C2×#4112yes—
271C23×C43H(5,𝔽2)12yes—
272C23×C43H(5,𝔽2)12yes—
273C23×C43H(5,𝔽2)12yes—
274C23×C432−1+412yes—
275C23×C43C2511yescharacteristic
276C22×D43—28no—
277C22×D43—28no—
278C22×D43—28no—
279C22×D43—22no—
280C22×D43—22no—
281C22×D43—22no—
282C22×D43—22no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—44no—
286C22×D43—44no—
287C22×D43—44no—
288C22×D43—44no—
289C22×D43C23×C414yes—
290C2×C4×C43—28no—
291C2×C4×C43—28no—
292C2×C4×C43—28no—
293C2×C4×C43—22no—
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—416no—
309C2×C4×C43—44no—
310C2×C4×C43—44no—
311C2×C4×C43—44no—
312C2×C4×C43C23×C414yes—
313C2×C4×C43C23×C414yes—
314C2×C4×C43C2×#4114yes—
315C22⋊D43—416no—
316C2×Dic43—28no—
317C2×Dic43—28no—
318C2×Dic43—28no—
319C2×Dic43—28no—
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×Dic43C23×C414yes—
341C2×Dic43C23×C414yes—
342C2×Dic43C23×C414yes—
343C2×Dic43C2×#4114yes—
344C4×D43—416no—
345Dic86—416no—
346C2×#2337—431nomaximal, Sylow
347C22×C43—24no—
348C22×C43—24no—
349C22×C43—24no—
350C22×C43—416no—
351C22×C43—42no—
352C22×C43—42no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43C4×#4114yes—
356C22×C43#51814yes—
357C22×C43#52014yes—
358C22×C43#53814yes—
359C22×C43#53814yes—
360C22×C43#54214yes—
361C22×C43#54214yes—
362C22×C43C24×C411yescharacteristic
363C22×C43C22×#4111yescharacteristic
364C22×C43C22×#4111yescharacteristic
365C22×C43C2×H(5,𝔽2)11yescharacteristic
366C22×C43C2×H(5,𝔽2)11yescharacteristic
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—24no—
387Dic43—42no—
388Dic43—42no—
389Dic43—42no—
390C22×#124—431no—
391#2337—4316no—
392C2×#391—431no—
393C2×#391—431no—
394C2×#388—431no—
395C2×#388—431no—
396C2×#388—431no—
397C2×#388—431no—
398C2×#386—431no—
399C2×#386—431no—
400C2×#385—431no—
401C2×#385D4311yescharacteristic, complemented
402C2×#383—431no—
403C2×C4×C4⋊C4—431no—
404C2×C4×C22⋊C4—431no—
405C2×C4×C22⋊C4—431no—
406C2×C43—44no—
407C2×C43#233718yescomplemented
408C2×C43C2×C4×#4111yescharacteristic
409C2×C43C2×#51811yescharacteristic
410C2×C43C2×#52011yescharacteristic
411C2×C43C2×#53811yescharacteristic
412C2×C43C2×#53811yescharacteristic
413C2×C43C2×#54211yescharacteristic
414C2×C43C2×#54211yescharacteristic
415D43—44no—
416C23×Q8—431no—
417C23×D4—431no—
418C24×C4—431no—
419C24×C4C2×D4311yescharacteristic
420C2×#124—438no—
421C2×#124—4316no—
422C22×C4⋊C4—431no—
423C22×C4⋊C4—431no—
424C22×C4⋊C4C2×D4311yescharacteristic
425C22×C4⋊C4C2×D4311yescharacteristic
426C22×C22⋊C4—431no—
427C22×C22⋊C4—431no—
428C22×C22⋊C4—431no—
429C22×C22⋊C4—431no—
430C22×C22⋊C4—431no—
431C22×C22⋊C4—431no—
432C22×C22⋊C4—431no—
433C22×C22⋊C4—431no—
434C22×C22⋊C4C2×D4311yescharacteristic
435C22×C22⋊C4C2×D4311yescharacteristic
436C22×C42—431no—
437C22×C42—431no—
438C22×C42—431no—
439C22×C42—431no—
440C22×C42—431no—
441#391—438no—
442#391—438no—
443#388—438no—
444#388—438no—
445#388—438no—
446#388—438no—
447#386—438no—
448#386—438no—
449#385—438no—
450#385C2×D4318yescomplemented
451#383—438no—
452C4×C4⋊C4—438no—
453C4×C22⋊C4—438no—
454C4×C22⋊C4—438no—
455C2×#95—431no—
456C2×#95—431no—
457C2×#95—431no—
458C2×#95—431no—
459C2×#95—431no—
460C2×#95—431no—
461C2×#95—431no—
462C2×#95—431no—
463C2×#95—431no—
464C2×#95—431no—
465C2×#95C2×D4311yescharacteristic
466C2×#95C2×D4311yescharacteristic
467C43C2×#233711yescharacteristic, complemented, Sylow
468C25—431no—
469C25C22×D4311yescharacteristic
470C22×Q8—438no—
471C22×Q8—434no—
472C22×Q8—1722no—
473C22×Q8—1722no—
474C22×D4—438no—
475C22×D4—434no—
476C22×D4—1722no—
477C22×D4—1722no—
478C23×C4—24no—
479C23×C4—42no—
480C23×C4—42no—
481C23×C4—431no—
482C23×C4—431no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—431no—
487C23×C4—431no—
488C23×C4—434no—
489C23×C4—864no—
490C23×C4—1722no—
491C23×C4—1722no—
492C23×C4C22×D4311yescharacteristic
493C23×C4C22×D4311yescharacteristic
494C23×C4C22×D4311yescharacteristic
495C23×C4C22×D4311yescharacteristic
496C23×C4C22×D4311yescharacteristic
497C23×C4C22×D4311yescharacteristic
498C23×C4C22×D4314yes—
499#124—4364no—
500C2×C4⋊C4—24no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—434no—
503C2×C4⋊C4—434no—
504C2×C4⋊C4—864no—
505C2×C4⋊C4—1722no—
506C2×C4⋊C4C22×D4314yes—
507C2×C4⋊C4C22×D4314yes—
508C2×C22⋊C4—42no—
509C2×C22⋊C4—438no—
510C2×C22⋊C4—434no—
511C2×C22⋊C4—438no—
512C2×C22⋊C4—438no—
513C2×C22⋊C4—434no—
514C2×C22⋊C4—434no—
515C2×C22⋊C4—434no—
516C2×C22⋊C4—434no—
517C2×C22⋊C4—434no—
518C2×C22⋊C4—434no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—864no—
521C2×C22⋊C4—864no—
522C2×C22⋊C4—1722no—
523C2×C22⋊C4—1722no—
524C2×C22⋊C4—1722no—
525C2×C22⋊C4C4×D4318yescomplemented
526C2×C22⋊C4C22×D4314yes—
527C2×C22⋊C4C22×D4314yes—
528C2×C42—438no—
529C2×C42—434no—
530C2×C42—434no—
531C2×C42—434no—
532C2×C42—434no—
533C2×C42—434no—
534C2×C42—1722no—
535C2×C42—1722no—
536C2×C42—1722no—
537C2×C42—1722no—
538#95—434no—
539#95—434no—
540#95—434no—
541#95—434no—
542#95—434no—
543#95—434no—
544#95—434no—
545#95—434no—
546#95—434no—
547#95—434no—
548#95C22×D4314yes—
549#95C22×D4314yes—
550C24—22no—
551C24—22no—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—434no—
557C24—432no—
558C24—862no—
559C24—862no—
560C24—862no—
561C24—862no—
562C24—862no—
563C24—862no—
564C24C2×C4×D4314yes—
565C24C23×D4312yes—
566C24C23×D4311yescharacteristic
567C2×Q8—4316no—
568C2×Q8—17216no—
569C2×Q8—1724no—
570C2×Q8—1724no—
571C2×D4—4316no—
572C2×D4—17216no—
573C2×D4—1724no—
574C2×D4—1724no—
575C22×C4—22no—
576C22×C4—22no—
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—28no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—416no—
594C22×C4—434no—
595C22×C4—434no—
596C22×C4—434no—
597C22×C4—434no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—432no—
602C22×C4—432no—
603C22×C4—432no—
604C22×C4—432no—
605C22×C4—868no—
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—862no—
622C22×C4—862no—
623C22×C4—1724no—
624C22×C4—1724no—
625C22×C4—17216no—
626C22×C4C2×C4×D4314yes—
627C22×C4C2×C4×D4314yes—
628C22×C4#1062190014yes—
629C22×C4C23×D4312yes—
630C22×C4C23×D4312yes—
631C22×C4C23×D4312yes—
632C22×C4C23×D4312yes—
633C22×C4C23×D4312yes—
634C22×C4C23×D4312yes—
635C4⋊C4—28no—
636C4⋊C4—44no—
637C4⋊C4—868no—
638C4⋊C4—1724no—
639C22⋊C4—44no—
640C22⋊C4—4316no—
641C22⋊C4—4316no—
642C22⋊C4—4316no—
643C22⋊C4—868no—
644C22⋊C4—868no—
645C22⋊C4—1724no—
646C22⋊C4—1724no—
647C22⋊C4—1724no—
648C22⋊C4C2×C4×D43116yescomplemented
649C42—4316no—
650C42—1724no—
651C42—1724no—
652C42—1724no—
653C42—1724no—
654C23—28no—
655C23—28no—
656C23—28no—
657C23—22no—
658C23—22no—
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—44no—
664C23—44no—
665C23—44no—
666C23—44no—
667C23—434no—
668C23—868no—
669C23—868no—
670C23—868no—
671C23—862no—
672C23—862no—
673C23—862no—
674C23—862no—
675C23—862no—
676C23—862no—
677C23—1724no—
678C23—1724no—
679C23—1724no—
680C23—1724no—
681C23C22×C4×D4314yes—
682C23C22×C4×D4312yes—
683C23#41×D4312yes—
684C23C2×#1062190012yes—
685C23#1306337012yes—
686C23#1306337012yes—
687C23#1306337112yes—
688C23#1306337312yes—
689C23C24×D4311yescharacteristic
690Q8—17216no—
691D4—17216no—
692C2×C4—28no—
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—22no—
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—416no—
711C2×C4—44no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—434no—
715C2×C4—434no—
716C2×C4—434no—
717C2×C4—434no—
718C2×C4—868no—
719C2×C4—868no—
720C2×C4—868no—
721C2×C4—862no—
722C2×C4—862no—
723C2×C4—862no—
724C2×C4—862no—
725C2×C4—862no—
726C2×C4—862no—
727C2×C4—862no—
728C2×C4—862no—
729C2×C4—868no—
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—862no—
739C2×C4—17216no—
740C2×C4—1724no—
741C2×C4—1724no—
742C2×C4—1724no—
743C2×C4C22×C4×D4314yes—
744C2×C4C22×C4×D4314yes—
745C2×C4C2×#1062190014yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—416no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—42no—
754C22—864no—
755C22—864no—
756C22—864no—
757C22—17216no—
758C22—1722no—
759C22—1722no—
760C22—1722no—
761C22—1722no—
762C22C4×#1062190014yes—
763C22#1458337114yes—
764C22#1458338014yes—
765C22#1458348414yes—
766C22#1458348514yes—
767C22#1458351914yes—
768C22#1458352214yes—
769C22C23×C4×D4311yescharacteristic
770C22C2×#41×D4311yescharacteristic
771C22C22×#1062190011yescharacteristic
772C22C2×#1306337011yescharacteristic
773C22C2×#1306337011yescharacteristic
774C22C2×#1306337111yescharacteristic
775C22C2×#1306337311yescharacteristic
776C4—24no—
777C4—24no—
778C4—24no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—864no—
783C4—864no—
784C4—864no—
785C4—864no—
786C4—1722no—
787C4—1722no—
788C4—1722no—
789C2—44no—
790C2—1724no—
791C2#1913740918yesdirect product factor
792C2C2×C4×#1062190011yescharacteristic
793C2C2×#1458337111yescharacteristic
794C2C2×#1458338011yescharacteristic
795C2C2×#1458348411yescharacteristic
796C2C2×#1458348511yescharacteristic
797C2C2×#1458351911yescharacteristic
798C2C2×#1458352211yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#385D43
hypocenterC43C2×#2337
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #19137409C2direct (N × H)
3. C2×#14582804C2semidirect
4. C2×#14582803C2semidirect
5. C2×#14582792C2semidirect
6. C2×#14582789C2semidirect
7. C2×#14582789C2semidirect
8. C2×#14582787C2semidirect
11. C2×#14582773C2semidirect
12. C2×#14582766C2semidirect
13. C2×C4⋊C4×Dic43C2semidirect
14. C2×C4×C22⋊Dic43C2semidirect
15. C2×#14582746C2semidirect
16. C2×C43×#385C2semidirect
20. C2×#13063311C4semidirect
37. #14582804C22semidirect
38. #14582803C22semidirect
39. #14582792C22semidirect
40. #14582789C22semidirect
41. #14582789C22semidirect
42. #14582787C22semidirect
45. #14582773C22semidirect
46. #14582766C22semidirect
47. C4⋊C4×Dic43C22semidirect
48. C4×C22⋊Dic43C22semidirect
49. #14582746C22semidirect
65. C43×#385C22semidirect
71. C22×Dic86C2×C4semidirect
88. #13063311C2×C4semidirect
95. C2×C22⋊Dic43C2×C4semidirect
102. C2×(C2×D43)⋊C4C2×C4semidirect
103. C2×(C2×D43)⋊C4C2×C4semidirect
113. C2×C4×Dic43C2×C4semidirect
145. C2×C22⋊C4×C43C2×C4semidirect
234. C2×Dic86C22×C4semidirect
238. C22⋊C4×C43C22×C4semidirect
241. C22⋊Dic43C22×C4semidirect
245. (C2×D43)⋊C4C22×C4semidirect
246. (C2×D43)⋊C4C22×C4semidirect
253. C4×Dic43C22×C4semidirect
401. C2×#385D43semidirect
407. C2×C43#2337semidirect
450. #385C2×D43semidirect
467. C43C2×#2337semidirect
525. C2×C22⋊C4C4×D43semidirect
648. C22⋊C4C2×C4×D43semidirect
791. C2#19137409direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633112
#191374092
C2×#145828042
C2×#145828032
C2×#145827922
C2×#145827892
C2×#145827872
C2×#145827782
C2×#145827752
C2×#145827732
C2×#145827662
C2×C4⋊C4×Dic432
C2×C4×C22⋊Dic432
C2×#145827462
C2×C43×#3852
C2×#233743