Finite Group Databasebeta

← C2×#19137768 #25259222

Subgroups — C2×#19137768 #25259222

Order 11008.

2934 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#19137768C2116yesmaximal, direct product factor
3C2×#14582804C211yesmaximal, characteristic, complemented
4C2×#14582803C211yesmaximal, characteristic, complemented
5C2×#14582793C211yesmaximal, characteristic, complemented
6C2×#14582792C211yesmaximal, characteristic, complemented
7C2×#14582791C211yesmaximal, characteristic, complemented
8C2×#14582788C211yesmaximal, characteristic, complemented
9C2×#14582778C211yesmaximal, characteristic
10C2×#14582775C211yesmaximal, characteristic
11C2×#14582772C211yesmaximal, characteristic, complemented
12C2×#14582770C211yesmaximal, characteristic, complemented
13C2×#14582770C211yesmaximal, characteristic, complemented
14C2×#14582764C211yesmaximal, characteristic, complemented
15C2×#14582763C211yesmaximal, 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×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#14582804C2218yescomplemented
38#14582803C2218yescomplemented
39#14582793C2218yescomplemented
40#14582792C2218yescomplemented
41#14582791C2218yescomplemented
42#14582788C2218yescomplemented
43#14582778C2218yes—
44#14582775C2218yes—
45#14582772C2218yescomplemented
46#14582770C2218yescomplemented
47#14582770C2218yescomplemented
48#14582764C2218yescomplemented
49#14582763C2218yescomplemented
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—42no—
85C22×C4×D43—42no—
86C22×C4×D43—42no—
87C22×C4×D43C2314yes—
88#13063311C2×C4164yescomplemented
89C2×C4⋊Dic43—42no—
90C2×C4⋊Dic43C2314yes—
91C2×Dic43⋊C4—42no—
92C2×Dic43⋊C4—42no—
93C2×Dic43⋊C4—42no—
94C2×Dic43⋊C4C2314yes—
95C2×Dic43⋊C4C2314yes—
96C2×Dic43⋊C4C2314yes—
97C2×C22⋊Dic43—42no—
98C2×C22⋊Dic43—42no—
99C2×C22⋊Dic43C2×C418yescomplemented
100C2×C22⋊Dic43C2314yes—
101C2×C22⋊Dic43C2314yes—
102C2×C22⋊Dic43C2314yes—
103C2×(C2×D43)⋊C4—42no—
104C2×(C2×D43)⋊C4—42no—
105C2×(C2×D43)⋊C4—42no—
106C2×(C2×D43)⋊C4C2×C418yescomplemented
107C2×(C2×D43)⋊C4C2×C418yescomplemented
108C2×(C2×D43)⋊C4C2314yes—
109C2×(C2×D43)⋊C4C2314yes—
110C2×(C2×D43)⋊C4C2314yes—
111C2×(C2×D43)⋊C4C2314yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×C4×Dic43—42no—
114C2×C4×Dic43—42no—
115C2×C4×Dic43C2×C418yescomplemented
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—42no—
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—42no—
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—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×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—44no—
186C22×C4×C43—416no—
187C22×C4×C43C22×C414yes—
188C22×C4×C43C22×C414yes—
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×Dic43—22no—
217C22×Dic43C22×C414yes—
218C22×Dic43C22×C414yes—
219C22×Dic43C22×C414yes—
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C2×C4×D43—44no—
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—44no—
236C4⋊C4×C43—44no—
237C22⋊C4×C43—44no—
238C22⋊C4×C43C22×C4116yescomplemented
239C22⋊Dic43—44no—
240C22⋊Dic43—44no—
241C22⋊Dic43C22×C4116yescomplemented
242(C2×D43)⋊C4—44no—
243(C2×D43)⋊C4—44no—
244(C2×D43)⋊C4—44no—
245(C2×D43)⋊C4C22×C4116yescomplemented
246(C2×D43)⋊C4C22×C4116yescomplemented
247C4⋊Dic43—44no—
248Dic43⋊C4—44no—
249Dic43⋊C4—44no—
250Dic43⋊C4—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×C43H(5,𝔽2)12yes—
270C23×C43H(5,𝔽2)12yes—
271C23×C43H(5,𝔽2)12yes—
272C23×C43H(5,𝔽2)12yes—
273C23×C432−1+412yes—
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—22no—
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×C43—44no—
313C2×C4×C43C23×C414yes—
314C2×C4×C43C23×C414yes—
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×Dic43C23×C414yes—
342C2×Dic43C23×C414yes—
343C2×Dic43C23×C414yes—
344C4×D43—416no—
345Dic86—416no—
346C2×#2379—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×C43#51814yes—
356C22×C43#52014yes—
357C22×C43#52014yes—
358C22×C43H(3,𝔽4)14yes—
359C22×C43#56214yes—
360C22×C43#56214yes—
361C22×C43#56314yes—
362C22×C43C24×C411yescharacteristic
363C22×C43C2×H(5,𝔽2)11yescharacteristic
364C22×C43C2×H(5,𝔽2)11yescharacteristic
365C22×C43C2×H(5,𝔽2)11yescharacteristic
366C22×C43C2×H(5,𝔽2)11yescharacteristic
367C22×C43C2×2−1+411yescharacteristic
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—42no—
380C4×C43—42no—
381C4×C43—42no—
382C4×C43—42no—
383Dic43—24no—
384Dic43—24no—
385Dic43—24no—
386Dic43—42no—
387Dic43—42no—
388Dic43—42no—
389Dic43—42no—
390C22×#124—431no—
391#2379—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×#385—431no—
402C2×#385—431no—
403C2×#385D4311yescharacteristic, complemented
404C2×#382—431no—
405C2×#382—431no—
406C2×C43—44no—
407C2×C43#237918yescomplemented
408C2×C43C2×#51811yescharacteristic
409C2×C43C2×#52011yescharacteristic
410C2×C43C2×#52011yescharacteristic
411C2×C43C2×H(3,𝔽4)11yescharacteristic
412C2×C43C2×#56211yescharacteristic
413C2×C43C2×#56211yescharacteristic
414C2×C43C2×#56311yescharacteristic
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⋊C4—431no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4C2×D4311yescharacteristic
427C22×C4⋊C4C2×D4311yescharacteristic
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⋊C4—431no—
435C22×C22⋊C4—431no—
436C22×C22⋊C4C2×D4311yescharacteristic
437C22×C22⋊C4C2×D4311yescharacteristic
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#385—438no—
451#385—438no—
452#385C2×D4318yescomplemented
453#382—438no—
454#382—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×#237911yescharacteristic, 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—42no—
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—1722no—
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—42no—
501C2×C4⋊C4—42no—
502C2×C4⋊C4—434no—
503C2×C4⋊C4—434no—
504C2×C4⋊C4—434no—
505C2×C4⋊C4—434no—
506C2×C4⋊C4—1722no—
507C2×C4⋊C4—1722no—
508C2×C4⋊C4—1722no—
509C2×C4⋊C4—1722no—
510C2×C4⋊C4C22×D4314yes—
511C2×C4⋊C4C22×D4314yes—
512C2×C22⋊C4—42no—
513C2×C22⋊C4—438no—
514C2×C22⋊C4—434no—
515C2×C22⋊C4—438no—
516C2×C22⋊C4—438no—
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—434no—
524C2×C22⋊C4—1722no—
525C2×C22⋊C4—1722no—
526C2×C22⋊C4—1722no—
527C2×C22⋊C4—1722no—
528C2×C22⋊C4—1722no—
529C2×C22⋊C4C4×D4318yescomplemented
530C2×C22⋊C4C22×D4314yes—
531C2×C22⋊C4C22×D4314yes—
532C2×C42—438no—
533C2×C42—434no—
534C2×C42—434no—
535C2×C42—434no—
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—22no—
591C22×C4—44no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—416no—
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—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—862no—
622C22×C4—862no—
623C22×C4—1724no—
624C22×C4—1724no—
625C22×C4—1724no—
626C22×C4—17216no—
627C22×C4C2×C4×D4314yes—
628C22×C4C2×C4×D4314yes—
629C22×C4C23×D4312yes—
630C22×C4C23×D4312yes—
631C22×C4C23×D4312yes—
632C22×C4C23×D4312yes—
633C22×C4C23×D4312yes—
634C22×C4C23×D4312yes—
635C4⋊C4—44no—
636C4⋊C4—44no—
637C4⋊C4—1724no—
638C4⋊C4—1724no—
639C4⋊C4—1724no—
640C4⋊C4—1724no—
641C22⋊C4—44no—
642C22⋊C4—4316no—
643C22⋊C4—4316no—
644C22⋊C4—4316no—
645C22⋊C4—1724no—
646C22⋊C4—1724no—
647C22⋊C4—1724no—
648C22⋊C4—1724no—
649C22⋊C4—1724no—
650C22⋊C4C2×C4×D43116yescomplemented
651C42—4316no—
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#1306337012yes—
684C23#1306337012yes—
685C23#1306337012yes—
686C23#1306337112yes—
687C23#1306337212yes—
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—22no—
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—44no—
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—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—862no—
739C2×C4—17216no—
740C2×C4—1724no—
741C2×C4—1724no—
742C2×C4—1724no—
743C2×C4—1724no—
744C2×C4C22×C4×D4314yes—
745C2×C4C22×C4×D4314yes—
746C22—24no—
747C22—24no—
748C22—24no—
749C22—42no—
750C22—42no—
751C22—42no—
752C22—42no—
753C22—416no—
754C22—864no—
755C22—864no—
756C22—864no—
757C22—1722no—
758C22—1722no—
759C22—1722no—
760C22—1722no—
761C22—17216no—
762C22#1458337114yes—
763C22#1458337814yes—
764C22#1458338014yes—
765C22#1458364214yes—
766C22#1458364514yes—
767C22#1458364614yes—
768C22#1458365014yes—
769C22C23×C4×D4311yescharacteristic
770C22C2×#1306337011yescharacteristic
771C22C2×#1306337011yescharacteristic
772C22C2×#1306337011yescharacteristic
773C22C2×#1306337111yescharacteristic
774C22C2×#1306337211yescharacteristic
775C22C2×#1306337311yescharacteristic
776C4—24no—
777C4—24no—
778C4—42no—
779C4—42no—
780C4—42no—
781C4—42no—
782C4—864no—
783C4—864no—
784C4—864no—
785C4—1722no—
786C4—1722no—
787C4—1722no—
788C4—1722no—
789C2—44no—
790C2—1724no—
791C2#1913776818yesdirect product factor
792C2C2×#1458337111yescharacteristic
793C2C2×#1458337811yescharacteristic
794C2C2×#1458338011yescharacteristic
795C2C2×#1458364211yescharacteristic
796C2C2×#1458364511yescharacteristic
797C2C2×#1458364611yescharacteristic
798C2C2×#1458365011yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#385C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#385D43
hypocenterC43C2×#2379
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. #19137768C2direct (N × H)
3. C2×#14582804C2semidirect
4. C2×#14582803C2semidirect
5. C2×#14582793C2semidirect
6. C2×#14582792C2semidirect
7. C2×#14582791C2semidirect
8. C2×#14582788C2semidirect
11. C2×#14582772C2semidirect
12. C2×#14582770C2semidirect
13. C2×#14582770C2semidirect
14. C2×#14582764C2semidirect
15. C2×#14582763C2semidirect
16. C2×C43×#385C2semidirect
20. C2×#13063311C4semidirect
37. #14582804C22semidirect
38. #14582803C22semidirect
39. #14582793C22semidirect
40. #14582792C22semidirect
41. #14582791C22semidirect
42. #14582788C22semidirect
45. #14582772C22semidirect
46. #14582770C22semidirect
47. #14582770C22semidirect
48. #14582764C22semidirect
49. #14582763C22semidirect
65. C43×#385C22semidirect
71. C22×Dic86C2×C4semidirect
88. #13063311C2×C4semidirect
99. C2×C22⋊Dic43C2×C4semidirect
106. C2×(C2×D43)⋊C4C2×C4semidirect
107. C2×(C2×D43)⋊C4C2×C4semidirect
115. 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
403. C2×#385D43semidirect
407. C2×C43#2379semidirect
452. #385C2×D43semidirect
467. C43C2×#2379semidirect
529. C2×C22⋊C4C4×D43semidirect
650. C22⋊C4C2×C4×D43semidirect
791. C2#19137768direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633112
#191377682
C2×#145828042
C2×#145828032
C2×#145827932
C2×#145827922
C2×#145827912
C2×#145827882
C2×#145827782
C2×#145827752
C2×#145827722
C2×#145827702
C2×#145827642
C2×#145827632
C2×C43×#3852
C2×#237943