Finite Group Databasebeta

← C2×#19137225 #25255232

Subgroups — C2×#19137225 #25255232

Order 11008.

3262 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2#19137225C2116yesmaximal, direct product factor
3C2×#14582792C211yesmaximal, characteristic, complemented
4C2×#14582783C211yesmaximal, characteristic, complemented
5C2×#14582781C211yesmaximal, characteristic, complemented
6C2×#14582775C211yesmaximal, characteristic
7C2×#14582775C211yesmaximal, characteristic
8C2×#14582773C211yesmaximal, characteristic, complemented
9C2×#14582770C211yesmaximal, characteristic, complemented
10C2×#14582766C211yesmaximal, characteristic, complemented
11C2×#14582764C211yesmaximal, characteristic, complemented
12C2×#14582760C211yesmaximal, characteristic, complemented
13C2×#14582757C211yesmaximal, characteristic, complemented
14C2×C4×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
15C2×#95×D43C211yesmaximal, characteristic, complemented
16C2×C43×#388C211yesmaximal, characteristic, complemented
17C23×C22⋊D43C2211yescharacteristic
18C24×Dic43C2211yescharacteristic
19C23×C4×D43C2211yescharacteristic
20C23×C4×D43C2211yescharacteristic
21C23×C4×D43C2211yescharacteristic
22C2×(C22⋊D43)⋊C4C4116yescomplemented
23C2×(C22⋊D43)⋊C4C2218yes—
24C22×C4⋊Dic43C2211yescharacteristic
25C22×Dic43⋊C4C2211yescharacteristic
26C22×Dic43⋊C4C2211yescharacteristic
27C22×Dic43⋊C4C2211yescharacteristic
28C22×C22⋊Dic43C2211yescharacteristic
29C22×C22⋊Dic43C2211yescharacteristic
30C22×(C2×D43)⋊C4C2211yescharacteristic
31C22×(C2×D43)⋊C4C2211yescharacteristic
32C22×(C2×D43)⋊C4C2211yescharacteristic
33C22×C4×Dic43C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582792C2218yescomplemented
36#14582783C2218yescomplemented
37#14582781C2218yescomplemented
38#14582775C2218yes—
39#14582775C2218yes—
40#14582773C2218yescomplemented
41#14582770C2218yescomplemented
42#14582766C2218yescomplemented
43#14582764C2218yescomplemented
44#14582760C2218yescomplemented
45#14582757C2218yescomplemented
46C4×(C2×D43)⋊C4C2218yescomplemented
47C2×C43⋊#95C2211yescharacteristic
48C2×C43⋊#95C2211yescharacteristic
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×D43C2218yescomplemented
60C22×C4⋊C4×C43C2211yescharacteristic
61C22×C22⋊C4×C43C2211yescharacteristic
62C22×C22⋊C4×C43C2211yescharacteristic
63C22×C22⋊C4×C43C2211yescharacteristic
64C22×C42×C43C2211yescharacteristic
65C43×#388C2218yescomplemented
66C2×#95×C43C2211yescharacteristic
67C2×#95×C43C2211yescharacteristic
68C24×D43C2311yescharacteristic
69C22×C22⋊D43—24no—
70C22×C22⋊D43—24no—
71C22×C22⋊D43C2×C418yes—
72C22×C22⋊D43C2314yes—
73C23×Dic43—42no—
74C23×Dic43—42no—
75C23×Dic43C2×C418yescomplemented
76C23×Dic43C2311yescharacteristic
77C23×Dic43C2311yescharacteristic
78C23×Dic43C2311yescharacteristic
79C23×Dic43C2311yescharacteristic
80C23×Dic43C2311yescharacteristic
81C23×Dic43C2311yescharacteristic
82C23×Dic43C2311yescharacteristic
83C23×Dic43C2314yes—
84C22×C4×D43—24no—
85C22×C4×D43—24no—
86C22×C4×D43—42no—
87C22×C4×D43—42no—
88C22×C4×D43—42no—
89C22×C4×D43—42no—
90C22×C4×D43—42no—
91C22×C4×D43—42no—
92C22×C4×D43C2×C418yes—
93C22×C4×D43C2314yes—
94C22×C4×D43C2314yes—
95C22×C4×D43C2314yes—
96(C22⋊D43)⋊C4C2×C4164yescomplemented
97C2×C4⋊Dic43—42no—
98C2×C4⋊Dic43C2314yes—
99C2×Dic43⋊C4—42no—
100C2×Dic43⋊C4—42no—
101C2×Dic43⋊C4C2×C418yescomplemented
102C2×Dic43⋊C4C2314yes—
103C2×Dic43⋊C4C2314yes—
104C2×Dic43⋊C4C2314yes—
105C2×C22⋊Dic43—42no—
106C2×C22⋊Dic43—42no—
107C2×C22⋊Dic43C2314yes—
108C2×C22⋊Dic43C2314yes—
109C2×(C2×D43)⋊C4—24no—
110C2×(C2×D43)⋊C4—24no—
111C2×(C2×D43)⋊C4C2×C418yes—
112C2×(C2×D43)⋊C4C2314yes—
113C2×(C2×D43)⋊C4C2314yes—
114C2×(C2×D43)⋊C4C2314yes—
115C2×C4×Dic43—42no—
116C2×C4×Dic43C2×C418yescomplemented
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—
129C43⋊#95C2314yes—
130C43⋊#95C2314yes—
131C25×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×C43C2314yes—
140C2×C22⋊C4×C43—42no—
141C2×C22⋊C4×C43—42no—
142C2×C22⋊C4×C43C2×C418yescomplemented
143C2×C22⋊C4×C43C2314yes—
144C2×C22⋊C4×C43C2314yes—
145C2×C22⋊C4×C43C2314yes—
146C2×C42×C43—42no—
147C2×C42×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×D43C22×C414yes—
164C23×D43#4114yes—
165C23×D43#4114yes—
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×C43C22×C414yes—
184C22×C4×C43C22×C414yes—
185C22×C4×C43C2412yes—
186C22×C4×C43C2412yes—
187C22×C4×C43C2412yes—
188C22×C4×C43C2412yes—
189C22×C4×C43C2412yes—
190C22×C4×C43C2412yes—
191C2×C22⋊D43—232no—
192C2×C22⋊D43—28no—
193C2×C22⋊D43—28no—
194C2×C22⋊D43C22×C4116yes—
195C22×Dic43—22no—
196C22×Dic43—22no—
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—416no—
214C22×Dic43—44no—
215C22×Dic43—44no—
216C22×Dic43C22×C414yes—
217C22×Dic43C22×C414yes—
218C22×Dic43C22×C414yes—
219C22×Dic43C22×C4116yescomplemented
220C22×Dic43C2412yes—
221C22×Dic43C2412yes—
222C22×Dic43C2412yes—
223C22×Dic43C2412yes—
224C22×Dic43C2412yes—
225C22×Dic43C2412yes—
226C22×Dic43C2412yes—
227C2×C4×D43—28no—
228C2×C4×D43—28no—
229C2×C4×D43—416no—
230C2×C4×D43—44no—
231C2×C4×D43—44no—
232C2×C4×D43—44no—
233C2×C4×D43—44no—
234C2×C4×D43—44no—
235C2×C4×D43—44no—
236C2×C4×D43—416no—
237C2×C4×D43—416no—
238C2×C4×D43C22×C4116yes—
239C4⋊C4×C43—44no—
240C22⋊C4×C43—44no—
241C22⋊C4×C43—44no—
242C22⋊C4×C43C22×C4116yescomplemented
243C42×C43—44no—
244C22⋊Dic43—44no—
245C22⋊Dic43—44no—
246(C2×D43)⋊C4—28no—
247(C2×D43)⋊C4—28no—
248(C2×D43)⋊C4C22×C4116yes—
249C4⋊Dic43—44no—
250Dic43⋊C4—44no—
251Dic43⋊C4—44no—
252Dic43⋊C4C22×C4116yescomplemented
253C4×Dic43—44no—
254C4×Dic43C22×C4116yescomplemented
255C23×C43—28no—
256C23×C43—28no—
257C23×C43—28no—
258C23×C43—22no—
259C23×C43—22no—
260C23×C43—22no—
261C23×C43—22no—
262C23×C43—22no—
263C23×C43—22no—
264C23×C43—44no—
265C23×C43—44no—
266C23×C43—44no—
267C23×C43—44no—
268C23×C43C23×C414yes—
269C23×C43C23×C412yes—
270C23×C43C2×#4112yes—
271C23×C43C2×#4112yes—
272C23×C43H(5,𝔽2)12yes—
273C23×C43H(5,𝔽2)12yes—
274C23×C43H(5,𝔽2)12yes—
275C23×C432−1+412yes—
276C23×C43C2511yescharacteristic
277C22×D43—28no—
278C22×D43—28no—
279C22×D43—28no—
280C22×D43—28no—
281C22×D43—28no—
282C22×D43—28no—
283C22×D43—22no—
284C22×D43—22no—
285C22×D43—22no—
286C22×D43—22no—
287C22×D43#117116yes—
288C22×D43C23×C414yes—
289C22×D43C2×#4114yes—
290C22×D43C2×#4114yes—
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—22no—
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—232no—
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—416no—
338C2×Dic43—44no—
339C2×Dic43—44no—
340C2×Dic43—44no—
341C2×Dic43—44no—
342C2×Dic43C23×C414yes—
343C2×Dic43C23×C414yes—
344C2×Dic43C23×C414yes—
345C4×D43—416no—
346C4×D43—416no—
347C4×D43—416no—
348C2×#2318—431nomaximal, Sylow
349C22×C43—24no—
350C22×C43—24no—
351C22×C43—24no—
352C22×C43—416no—
353C22×C43—42no—
354C22×C43—42no—
355C22×C43—42no—
356C22×C43—42no—
357C22×C43C2×#11714yes—
358C22×C43#51814yes—
359C22×C43#52014yes—
360C22×C43#53814yes—
361C22×C43#53814yes—
362C22×C43#53914yes—
363C22×C43#53914yes—
364C22×C43C24×C411yescharacteristic
365C22×C43C22×#4111yescharacteristic
366C22×C43C22×#4111yescharacteristic
367C22×C43C2×H(5,𝔽2)11yescharacteristic
368C22×C43C2×H(5,𝔽2)11yescharacteristic
369C22×C43C2×H(5,𝔽2)11yescharacteristic
370C22×C43C2×2−1+411yescharacteristic
371C2×D43—232no—
372C2×D43—24no—
373C2×D43—24no—
374C2×D43—24no—
375C2×D43—24no—
376C2×D43—24no—
377C2×D43—24no—
378C2×D43C2×#11718yes—
379C4×C43—24no—
380C4×C43—24no—
381C4×C43—42no—
382C4×C43—42no—
383C4×C43—42no—
384C4×C43—42no—
385Dic43—24no—
386Dic43—24no—
387Dic43—24no—
388Dic43—42no—
389Dic43—42no—
390Dic43—42no—
391Dic43—42no—
392C22×C4×D4—431no—
393#2318—4316no—
394C2×#388—431no—
395C2×#388D4311yescharacteristic, complemented
396C2×#387—431no—
397C2×#387—431no—
398C2×#386—431no—
399C2×#386—431no—
400C2×#385—431no—
401C2×#385—431no—
402C2×#383—431no—
403C2×#382—431no—
404C2×#381—431no—
405C2×#380—431no—
406C2×C4×C22⋊C4—431no—
407C22×#95—431no—
408C2×C43—44no—
409C2×C43#231818yescomplemented
410C2×C43C22×#11711yescharacteristic
411C2×C43C2×#51811yescharacteristic
412C2×C43C2×#52011yescharacteristic
413C2×C43C2×#53811yescharacteristic
414C2×C43C2×#53811yescharacteristic
415C2×C43C2×#53911yescharacteristic
416C2×C43C2×#53911yescharacteristic
417D43—28no—
418C23×D4—431no—
419C24×C4—431no—
420C24×C4—431no—
421C24×C4—431no—
422C24×C4—431no—
423C2×C4×D4—438no—
424C2×C4×D4—4316no—
425C22×C4⋊C4—431no—
426C22×C4⋊C4—431no—
427C22×C4⋊C4—431no—
428C22×C4⋊C4—431no—
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⋊C4C2×D4311yescharacteristic
436C22×C22⋊C4C2×D4311yescharacteristic
437C22×C22⋊C4C2×D4311yescharacteristic
438C22×C42—431no—
439C22×C42—431no—
440C22×C42C2×D4311yescharacteristic
441#388—438no—
442#388C2×D4318yescomplemented
443#387—438no—
444#387—438no—
445#386—438no—
446#386—438no—
447#385—438no—
448#385—438no—
449#383—438no—
450#382—438no—
451#381—438no—
452#380—438no—
453C4×C22⋊C4—438no—
454C2×#95—431no—
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×#95—431no—
466C2×#95—438no—
467C2×#95C2×D4311yescharacteristic
468C2×#95C2×D4311yescharacteristic
469C43C2×#231811yescharacteristic, complemented, Sylow
470C25—431no—
471C25C22×D4311yescharacteristic
472C22×D4—438no—
473C22×D4—434no—
474C22×D4—864no—
475C22×D4—864no—
476C23×C4—431no—
477C23×C4—431no—
478C23×C4—431no—
479C23×C4—438no—
480C23×C4—434no—
481C23×C4—438no—
482C23×C4—434no—
483C23×C4—431no—
484C23×C4—431no—
485C23×C4—431no—
486C23×C4—431no—
487C23×C4—434no—
488C23×C4—434no—
489C23×C4—864no—
490C23×C4—864no—
491C23×C4—1722no—
492C23×C4—1722no—
493C23×C4—1722no—
494C23×C4—1722no—
495C23×C4—1722no—
496C23×C4—1722no—
497C23×C4—1722no—
498C23×C4—1722no—
499C23×C4C22×D4311yescharacteristic
500C23×C4C22×D4311yescharacteristic
501C23×C4C22×D4311yescharacteristic
502C23×C4C22×D4311yescharacteristic
503C23×C4C22×D4311yescharacteristic
504C23×C4C22×D4311yescharacteristic
505C4×D4—4364no—
506C2×C4⋊C4—42no—
507C2×C4⋊C4—438no—
508C2×C4⋊C4—434no—
509C2×C4⋊C4—434no—
510C2×C4⋊C4—434no—
511C2×C4⋊C4—434no—
512C2×C4⋊C4—1722no—
513C2×C4⋊C4—1722no—
514C2×C4⋊C4—1722no—
515C2×C4⋊C4C22×D4314yes—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—42no—
518C2×C22⋊C4—438no—
519C2×C22⋊C4—434no—
520C2×C22⋊C4—434no—
521C2×C22⋊C4—434no—
522C2×C22⋊C4—434no—
523C2×C22⋊C4—434no—
524C2×C22⋊C4—864no—
525C2×C22⋊C4—864no—
526C2×C22⋊C4—1722no—
527C2×C22⋊C4—1722no—
528C2×C22⋊C4C4×D4318yescomplemented
529C2×C22⋊C4C22×D4314yes—
530C2×C22⋊C4C22×D4314yes—
531C2×C22⋊C4C22×D4314yes—
532C2×C42—42no—
533C2×C42—438no—
534C2×C42—434no—
535C2×C42—434no—
536C2×C42—1722no—
537C2×C42C22×D4314yes—
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#95—434no—
549#95—434no—
550#95C22×D4314yes—
551#95C22×D4314yes—
552C24—22no—
553C24—22no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—434no—
559C24—434no—
560C24—434no—
561C24—432no—
562C24—862no—
563C24—862no—
564C24—862no—
565C24—862no—
566C24C2×C4×D4314yes—
567C24C23×D4312yes—
568C24C23×D4311yescharacteristic
569C2×D4—4316no—
570C2×D4—8632no—
571C2×D4—868no—
572C2×D4—868no—
573C22×C4—22no—
574C22×C4—22no—
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—434no—
590C22×C4—434no—
591C22×C4—434no—
592C22×C4—432no—
593C22×C4—432no—
594C22×C4—432no—
595C22×C4—4316no—
596C22×C4—4316no—
597C22×C4—432no—
598C22×C4—432no—
599C22×C4—432no—
600C22×C4—432no—
601C22×C4—868no—
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—17216no—
622C22×C4—1724no—
623C22×C4—1724no—
624C22×C4—1724no—
625C22×C4—1724no—
626C22×C4—1724no—
627C22×C4—1724no—
628C22×C4—17216no—
629C22×C4—17216no—
630C22×C4—17216no—
631C22×C4—1724no—
632C22×C4—1724no—
633C22×C4C2×C4×D4314yes—
634C22×C4C2×C4×D4314yes—
635C22×C4C23×D4312yes—
636C22×C4C23×D4312yes—
637C22×C4C23×D4312yes—
638C22×C4C23×D4312yes—
639C22×C4C23×D4312yes—
640C22×C4C23×D4312yes—
641C4⋊C4—44no—
642C4⋊C4—4316no—
643C4⋊C4—1724no—
644C4⋊C4—1724no—
645C4⋊C4—1724no—
646C22⋊C4—44no—
647C22⋊C4—44no—
648C22⋊C4—4316no—
649C22⋊C4—868no—
650C22⋊C4—868no—
651C22⋊C4—1724no—
652C22⋊C4—1724no—
653C22⋊C4C2×C4×D43116yescomplemented
654C42—44no—
655C42—4316no—
656C42—1724no—
657C23—28no—
658C23—28no—
659C23—28no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—44no—
667C23—44no—
668C23—44no—
669C23—44no—
670C23—4316no—
671C23—434no—
672C23—434no—
673C23—434no—
674C23—868no—
675C23—868no—
676C23—862no—
677C23—862no—
678C23—862no—
679C23—862no—
680C23—868no—
681C23—868no—
682C23—868no—
683C23—868no—
684C23C22×C4×D4314yes—
685C23C22×C4×D4312yes—
686C23#41×D4312yes—
687C23#41×D4312yes—
688C23#1306337012yes—
689C23#1306337012yes—
690C23#1306337112yes—
691C23#1306337212yes—
692C23C24×D4311yescharacteristic
693D4—8632no—
694C2×C4—28no—
695C2×C4—28no—
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—22no—
711C2×C4—22no—
712C2×C4—44no—
713C2×C4—44no—
714C2×C4—44no—
715C2×C4—44no—
716C2×C4—434no—
717C2×C4—434no—
718C2×C4—434no—
719C2×C4—868no—
720C2×C4—868no—
721C2×C4—868no—
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—862no—
740C2×C4—17216no—
741C2×C4—17216no—
742C2×C4—17216no—
743C2×C4—17216no—
744C2×C4—1724no—
745C2×C4—1724no—
746C2×C4—1724no—
747C2×C4—1724no—
748C2×C4C22×C4×D4314yes—
749C2×C4C22×C4×D4314yes—
750C22—24no—
751C22—24no—
752C22—24no—
753C22—42no—
754C22—42no—
755C22—42no—
756C22—42no—
757C22—416no—
758C22—438no—
759C22—864no—
760C22—864no—
761C22—864no—
762C22—864no—
763C22—864no—
764C22—864no—
765C22—8632no—
766C22#117×D4314yes—
767C22#1458337114yes—
768C22#1458337814yes—
769C22#1458348114yes—
770C22#1458348314yes—
771C22#1458349014yes—
772C22#1458349214yes—
773C22C23×C4×D4311yescharacteristic
774C22C2×#41×D4311yescharacteristic
775C22C2×#41×D4311yescharacteristic
776C22C2×#1306337011yescharacteristic
777C22C2×#1306337011yescharacteristic
778C22C2×#1306337111yescharacteristic
779C22C2×#1306337211yescharacteristic
780C4—24no—
781C4—24no—
782C4—42no—
783C4—42no—
784C4—42no—
785C4—42no—
786C4—864no—
787C4—864no—
788C4—864no—
789C4—1722no—
790C4—1722no—
791C4—1722no—
792C4—1722no—
793C2—44no—
794C2—868no—
795C2#1913722518yesdirect product factor
796C2C2×#117×D4311yescharacteristic
797C2C2×#1458337111yescharacteristic
798C2C2×#1458337811yescharacteristic
799C2C2×#1458348111yescharacteristic
800C2C2×#1458348311yescharacteristic
801C2C2×#1458349011yescharacteristic
802C2C2×#1458349211yescharacteristic
subgroupG/H
centerC24C23×D43
commutatorC22×C43C24×C4
FrattiniC23C24×D43
FittingC2×C43×#388C2
socleC24×C43C24
prime radicalC23×C22⋊D43C22
cosocleC23×C43C25
hypercenterC2×#388D43
hypocenterC43C2×#2318
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. #19137225C2direct (N × H)
3. C2×#14582792C2semidirect
4. C2×#14582783C2semidirect
5. C2×#14582781C2semidirect
8. C2×#14582773C2semidirect
9. C2×#14582770C2semidirect
10. C2×#14582766C2semidirect
11. C2×#14582764C2semidirect
12. C2×#14582760C2semidirect
13. C2×#14582757C2semidirect
14. C2×C4×(C2×D43)⋊C4C2semidirect
15. C2×#95×D43C2semidirect
16. C2×C43×#388C2semidirect
22. C2×(C22⋊D43)⋊C4C4semidirect
35. #14582792C22semidirect
36. #14582783C22semidirect
37. #14582781C22semidirect
40. #14582773C22semidirect
41. #14582770C22semidirect
42. #14582766C22semidirect
43. #14582764C22semidirect
44. #14582760C22semidirect
45. #14582757C22semidirect
46. C4×(C2×D43)⋊C4C22semidirect
59. #95×D43C22semidirect
65. C43×#388C22semidirect
75. C23×Dic43C2×C4semidirect
96. (C22⋊D43)⋊C4C2×C4semidirect
101. C2×Dic43⋊C4C2×C4semidirect
116. C2×C4×Dic43C2×C4semidirect
142. C2×C22⋊C4×C43C2×C4semidirect
219. C22×Dic43C22×C4semidirect
242. C22⋊C4×C43C22×C4semidirect
252. Dic43⋊C4C22×C4semidirect
254. C4×Dic43C22×C4semidirect
395. C2×#388D43semidirect
409. C2×C43#2318semidirect
442. #388C2×D43semidirect
469. C43C2×#2318semidirect
528. C2×C22⋊C4C4×D43semidirect
653. C22⋊C4C2×C4×D43semidirect
795. C2#19137225direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
#191372252
C2×#145827922
C2×#145827832
C2×#145827812
C2×#145827752
C2×#145827732
C2×#145827702
C2×#145827662
C2×#145827642
C2×#145827602
C2×#145827572
C2×C4×(C2×D43)⋊C42
C2×#95×D432
C2×C43×#3882
C2×#231843