Finite Group Databasebeta

← #25112719

Subgroups — #25112719

Order 11008.

1168 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
1C2×#14583436C211yesmaximal, characteristic
2C2×#14582972C211yesmaximal, characteristic, complemented
3C2×#14582969C211yesmaximal, characteristic, complemented
4#19135536C211yesmaximal, characteristic, complemented
5#19134891C211yesmaximal, characteristic, complemented
6#19134891C211yesmaximal, characteristic, complemented
7#19134886C211yesmaximal, characteristic, complemented
8#19134886C211yesmaximal, characteristic, complemented
9#19134665C211yesmaximal, characteristic, complemented
10#19134665C211yesmaximal, characteristic, complemented
11#19134572C211yesmaximal, characteristic, complemented
12#19134358C211yesmaximal, characteristic, complemented
13#19134290C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1985C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583436—24no—
21#14583436—24no—
22C2×#13063320C411yescharacteristic
23C2×#13063320C411yescharacteristic
24C2×#13063316C411yescharacteristic
25C2×#13063314C411yescharacteristic
26C2×#13063310C411yescharacteristic
27C2×#13063310C411yescharacteristic
28C2×#13063301C411yescharacteristic
29C2×#13063300C411yescharacteristic
30C2×C4×D172C2211yescharacteristic
31C2×C4×D172C2211yescharacteristic
32C2×C4×D172C2211yescharacteristic
33C2×#13063282C2211yescharacteristic
34C2×#13063282C2211yescharacteristic
35C2×C42×D43C2211yescharacteristic
36#14582972—24no—
37#14582969—24no—
38C2×C4⋊(C43⋊C8)C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×(C2×D43)⋊C8C2211yescharacteristic
45C2×(C2×D43)⋊C8C2211yescharacteristic
46C2×(C2×D43)⋊C8C2211yescharacteristic
47C2×#13063236C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C2×C4×Q8×C43C2211yescharacteristic
57C2×C4⋊C8×C43C2211yescharacteristic
58C2×#97×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×D172C2×C411yescharacteristic
64C22×D172C2×C411yescharacteristic
65C22×D172C2×C411yescharacteristic
66C22×C4×D43C2×C411yescharacteristic
67C22×C4×D43C2×C411yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C22×C4×D43C2311yescharacteristic
70C22×C4×D43C2311yescharacteristic
71C2×#10621872—22no—
72C2×#10621872—22no—
73C2×#10621872—22no—
74C2×#10621872—22no—
75C2×#10621872—41no—
76C2×#10621872—41no—
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C2×C8×D43—22no—
82C2×C8×D43—22no—
83C2×C8×D43—22no—
84C2×C8×D43—22no—
85C2×C8×D43—41no—
86C2×C8×D43—41no—
87#13063320—24no—
88#13063320—24no—
89#13063316—24no—
90#13063314—24no—
91#13063310—24no—
92#13063310—24no—
93#13063301—24no—
94#13063300—24no—
95C4×D172—22no—
96C4×D172—22no—
97C4×D172—22no—
98C4×D172—22no—
99C4×D172D414yes—
100C4×D172D414yes—
101#13063282—22no—
102#13063282—22no—
103#13063282—22no—
104#13063282—22no—
105C2×C4⋊Dic43C2×C411yescharacteristic
106C2×C4⋊Dic43C2×C411yescharacteristic
107C2×C4⋊Dic43C2×C411yescharacteristic
108C2×Dic43⋊C4C2×C411yescharacteristic
109C2×Dic43⋊C4C2×C411yescharacteristic
110C2×Dic43⋊C4C2×C411yescharacteristic
111C2×Dic43⋊C4C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic
114C2×(C2×D43)⋊C4C2×C411yescharacteristic
115C2×(C2×D43)⋊C4C2×C411yescharacteristic
116C2×(C2×D43)⋊C4C2×C411yescharacteristic
117C2×(C2×D43)⋊C4C2×C411yescharacteristic
118C2×(C2×D43)⋊C4C2×C411yescharacteristic
119C2×(C2×D43)⋊C4C2×C411yescharacteristic
120C2×(C2×D43)⋊C4C2×C411yescharacteristic
121C2×(C2×D43)⋊C4C2×C411yescharacteristic
122C2×C4×Dic43C2×C411yescharacteristic
123C2×C4×Dic43C2×C411yescharacteristic
124C2×C4×Dic43C2311yescharacteristic
125C42×D43—22no—
126C42×D43—22no—
127C4⋊(C43⋊C8)—22no—
128(C2×D43)⋊C8—22no—
129(C2×D43)⋊C8—22no—
130(C2×D43)⋊C8—22no—
131(C2×D43)⋊C8—22no—
132(C2×D43)⋊C8—22no—
133(C2×D43)⋊C8—22no—
134(C2×D43)⋊C8—41no—
135(C2×D43)⋊C8—41no—
136#13063236—22no—
137C22×Q8×C43C2×C411yescharacteristic
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C4×Q8×C43—22no—
143C4×Q8×C43—22no—
144C2×C4⋊C4×C43C2×C411yescharacteristic
145C2×C4⋊C4×C43C2×C411yescharacteristic
146C2×C4⋊C4×C43C2×C411yescharacteristic
147C2×C42×C43C2311yescharacteristic
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150C4⋊C8×C43—22no—
151#97×C43—22no—
152C23×D43C22×C411yescharacteristic
153C23×D43C22×C411yescharacteristic
154C23×D43C22×C411yescharacteristic
155C2×Q8×C43—22no—
156C2×Q8×C43—41no—
157C2×Q8×C43—41no—
158C22×C4×C43C22×C411yescharacteristic
159C22×C4×C43C22×C411yescharacteristic
160C22×C4×C43C22×C411yescharacteristic
161C22×C4×C43C22×C411yescharacteristic
162C22×C4×C43C22×C411yescharacteristic
163C22×C4×C43C22×C411yescharacteristic
164C22×C4×C43C2411yescharacteristic
165C22×Dic43C22×C411yescharacteristic
166C22×Dic43C22×C411yescharacteristic
167C22×Dic43C22×C411yescharacteristic
168C22×Dic43C22×C411yescharacteristic
169C22×Dic43C22×C411yescharacteristic
170C2×D172—22no—
171C2×D172—22no—
172C2×D172—22no—
173C2×D172—22no—
174C2×D172—41no—
175C2×D172—41no—
176C2×D172—41no—
177C2×D172—41no—
178C2×D172C22⋊C414yes—
179C2×C4×D43—21no—
180C2×C4×D43—21no—
181C2×C4×D43—21no—
182C2×C4×D43—21no—
183C2×C4×D43—21no—
184C2×C4×D43—21no—
185C2×C4×D43—21no—
186C2×C4×D43—21no—
187C2×C4×D43—22no—
188C2×C4×D43—22no—
189C2×C4×D43—21no—
190C2×C4×D43—21no—
191C2×C4×D43—21no—
192C2×C4×D43—21no—
193C2×C4×D43—21no—
194C2×C4×D43—21no—
195C2×C4×D43—22no—
196C2×C4×D43—41no—
197C2×C4×D43—41no—
198C2×C4×D43—41no—
199C2×C4×D43C2×D412yes—
200C2×C4×D43C2×D412yes—
201C2×C4×D43C2×D412yes—
202C2×C4×D43C2×D412yes—
203C2×C8×C43—21no—
204C2×C8×C43—21no—
205C2×C8×C43—21no—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43—21no—
211C2×C8×C43—21no—
212C2×C8×C43—21no—
213C2×C8×C43—21no—
214C2×C8×C43#4112yes—
215C4⋊C4×C43—22no—
216C4⋊C4×C43—22no—
217C4⋊C4×C43—22no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43C2×D412yes—
223C42×C43C2×D412yes—
224(C2×D43)⋊C4—22no—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230(C2×D43)⋊C4—22no—
231(C2×D43)⋊C4—22no—
232(C2×D43)⋊C4C22⋊C414yes—
233(C2×D43)⋊C4C22⋊C414yes—
234C4⋊Dic43—22no—
235C4⋊Dic43—22no—
236C4⋊Dic43C22⋊C414yes—
237Dic43⋊C4—22no—
238Dic43⋊C4—22no—
239Dic43⋊C4—22no—
240Dic43⋊C4—22no—
241C4×Dic43—22no—
242C4×Dic43—22no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C2×C43⋊C8—21no—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8—21no—
251C2×C43⋊C8—21no—
252C2×C43⋊C8—21no—
253C2×C43⋊C8—21no—
254C2×C43⋊C8—21no—
255C2×C43⋊C8—21no—
256C2×C43⋊C8#4112yes—
257#10621872—44no—
258#10621872—44no—
259C8×D43—44no—
260C8×D43—44no—
261C23×C43C23×C411yescharacteristic
262C22×D43—21no—
263C22×D43—21no—
264C22×D43—21no—
265C22×D43—21no—
266C22×D43—21no—
267C22×D43—21no—
268C22×D43—21no—
269C22×D43—21no—
270C22×D43—21no—
271C22×D43—21no—
272C22×D43—21no—
273C22×D43—21no—
274C22×D43—21no—
275C22×D43—21no—
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43C2×C22⋊C412yes—
281C22×D43C2×C22⋊C412yes—
282C22×D43#13112yes—
283Q8×C43—44no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—21no—
288C2×C4×C43—21no—
289C2×C4×C43—21no—
290C2×C4×C43—21no—
291C2×C4×C43—21no—
292C2×C4×C43—21no—
293C2×C4×C43—21no—
294C2×C4×C43—21no—
295C2×C4×C43—21no—
296C2×C4×C43—21no—
297C2×C4×C43—21no—
298C2×C4×C43—21no—
299C2×C4×C43—21no—
300C2×C4×C43C2×C22⋊C412yes—
301C2×C4×C43C2×C22⋊C412yes—
302C2×C4×C43C22×D411yescharacteristic
303C2×C4×C43C22×D411yescharacteristic
304C2×C4×C43C2×#4111yescharacteristic
305C2×C4×C43C2×#4111yescharacteristic
306C2×C4×C43H(5,𝔽2)11yescharacteristic
307C2×C4×C432−1+411yescharacteristic
308C2×Dic43—21no—
309C2×Dic43—21no—
310C2×Dic43—21no—
311C2×Dic43—21no—
312C2×Dic43—21no—
313C2×Dic43—21no—
314C2×Dic43—21no—
315C2×Dic43—21no—
316C2×Dic43—21no—
317C2×Dic43—21no—
318C2×Dic43—21no—
319C2×Dic43—21no—
320C2×Dic43—21no—
321C2×Dic43C2×C22⋊C412yes—
322C2×Dic43C2×C22⋊C412yes—
323D172—44no—
324D172—44no—
325D172—44no—
326C4×D43—22no—
327C4×D43—22no—
328C4×D43—22no—
329C4×D43—22no—
330C4×D43—22no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—44no—
335C4×D43—44no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
339C4×D43—41no—
340C8×C43—22no—
341C8×C43—41no—
342C8×C43—41no—
343C8×C43—41no—
344C43⋊C8—22no—
345C43⋊C8—41no—
346C43⋊C8—41no—
347C43⋊C8—41no—
348#22475—431nomaximal, Sylow
349C22×C43C22×C22⋊C411yescharacteristic
350C22×C43C4×#4111yescharacteristic
351C22×C43#52011yescharacteristic
352C22×C43C2×#13111yescharacteristic
353C22×C43#56811yescharacteristic
354C22×C43#56811yescharacteristic
355C22×C43#56811yescharacteristic
356C2×D43—22no—
357C2×D43—22no—
358C2×D43—22no—
359C2×D43—22no—
360C2×D43—22no—
361C2×D43—22no—
362C2×D43—22no—
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—41no—
366C2×D43—41no—
367C2×D43—41no—
368C2×D43—41no—
369C2×D43—41no—
370C2×D43—41no—
371C2×D43—41no—
372C2×D43—41no—
373C2×D43—41no—
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
377C4×C43—22no—
378C4×C43—22no—
379C4×C43—41no—
380C4×C43—41no—
381C4×C43—41no—
382C4×C43—41no—
383C4×C43#54611yescharacteristic
384C4×C43#54611yescharacteristic
385C4×C43#54711yescharacteristic
386C4×C43#54711yescharacteristic
387Dic43—22no—
388Dic43—22no—
389Dic43—41no—
390Dic43—41no—
391Dic43—41no—
392C2×#529—431no—
393C2×#435—431no—
394C2×#435—431no—
395#1985—431no—
396#1985D4311yescharacteristic, complemented
397#1870—431no—
398#1870—431no—
399#1869—431no—
400#1869—431no—
401#1818—431no—
402#1818—431no—
403#1797—431no—
404#1749—431no—
405#1729—431no—
406#1729—431no—
407C2×C43#233911yescharacteristic
408C2×C43#287911yescharacteristic
409C2×C43#288011yescharacteristic
410C2×C43#296711yescharacteristic
411C2×C43#296811yescharacteristic
412C2×C43#299211yescharacteristic
413C2×C43#299511yescharacteristic
414D43—42no—
415D43—42no—
416D43—42no—
417C22×M16—431no—
418C22×M16—431no—
419C23×C8—431no—
420C23×C8—431no—
421#529—864no—
422#529—864no—
423C2×#126—431no—
424C2×#126—431no—
425C2×#125—431no—
426C2×#124—431no—
427C2×#123—431no—
428C2×#123—431no—
429C2×C22⋊Q8—431no—
430C2×#121—431no—
431C2×C4×Q8C2×D4311yescharacteristic
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×#117—431no—
436C2×#117—431no—
437C22×C42—431no—
438#435—864no—
439#435—864no—
440C2×C4⋊C8—431no—
441C2×C4⋊C8C2×D4311yescharacteristic
442C2×C22⋊C8—431no—
443C2×C22⋊C8—431no—
444C2×C22⋊C8—431no—
445C2×C22⋊C8—431no—
446C2×C22⋊C8—431no—
447C2×C22⋊C8—431no—
448C2×C22⋊C8—431no—
449C2×C22⋊C8—431no—
450C2×#97—431no—
451C2×#97C2×D4311yescharacteristic
452#336—431no—
453#336—431no—
454#336—431no—
455#336—431no—
456#336—431no—
457#336—431no—
458#336—431no—
459#336—431no—
460#336C2×D4311yescharacteristic
461#336C2×D4311yescharacteristic
462#336C2×D4311yescharacteristic
463#336C2×D4311yescharacteristic
464C43#2247511yescharacteristic, complemented, Sylow
465C22×Q8C4×D4311yescharacteristic
466C22×D4—431no—
467C22×D4—431no—
468C22×D4—431no—
469C23×C4—431no—
470C23×C4—431no—
471C23×C4—431no—
472C23×C4—431no—
473C23×C4—431no—
474C2×M16—862no—
475C2×M16—862no—
476C2×M16—862no—
477C2×M16—862no—
478C2×M16—1721no—
479C2×M16—1721no—
480C22×C8—431no—
481C22×C8—431no—
482C22×C8—431no—
483C22×C8—431no—
484C22×C8—862no—
485C22×C8—862no—
486C22×C8—862no—
487C22×C8—862no—
488C22×C8—1721no—
489C22×C8—1721no—
490C22×C8C22×D4311yescharacteristic
491C22×C8C22×D4311yescharacteristic
492C22×C8C22×D4311yescharacteristic
493C22×C8C22×D4311yescharacteristic
494#126—864no—
495#126—864no—
496#125—864no—
497#124—864no—
498#123—864no—
499#123—864no—
500C22⋊Q8—864no—
501#121—864no—
502C4×Q8—22no—
503C4×Q8—22no—
504C4×D4—434no—
505C4×D4—434no—
506C4×D4—862no—
507C4×D4—862no—
508C4×D4—862no—
509C4×D4—862no—
510#117—862no—
511#117—862no—
512#117—862no—
513#117—862no—
514C2×C4⋊C4—431no—
515C2×C4⋊C4—431no—
516C2×C4⋊C4—431no—
517C2×C4⋊C4—431no—
518C2×C4⋊C4—431no—
519C2×C4⋊C4—431no—
520C2×C4⋊C4—431no—
521C2×C4⋊C4C4×D4311yescharacteristic
522C2×C4⋊C4C4×D4311yescharacteristic
523C2×C4⋊C4C4×D4311yescharacteristic
524C2×C22⋊C4—431no—
525C2×C22⋊C4—431no—
526C2×C22⋊C4—431no—
527C2×C22⋊C4—431no—
528C2×C22⋊C4—431no—
529C2×C22⋊C4—431no—
530C2×C22⋊C4—431no—
531C2×C22⋊C4—431no—
532C2×C22⋊C4—431no—
533C2×C22⋊C4—431no—
534C2×C42—431no—
535C2×C42—431no—
536C2×C42—431no—
537C2×C42—862no—
538C2×C42—862no—
539C2×C42C22×D4311yescharacteristic
540C2×C42C22×D4311yescharacteristic
541C2×C42C22×D4311yescharacteristic
542C4⋊C8—22no—
543C4⋊C8—862no—
544C22⋊C8—862no—
545C22⋊C8—862no—
546C22⋊C8—862no—
547C22⋊C8—862no—
548C22⋊C8—862no—
549C22⋊C8—862no—
550C22⋊C8—1721no—
551C22⋊C8—1721no—
552#97—22no—
553#97—862no—
554C24—431no—
555C24—431no—
556C24—431no—
557C2×Q8—22no—
558C2×Q8—41no—
559C2×Q8—41no—
560C2×D4—434no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—862no—
564C2×D4—862no—
565C2×D4—1721no—
566C2×D4—1721no—
567C2×D4—1721no—
568C2×D4—1721no—
569C22×C4—431no—
570C22×C4—431no—
571C22×C4—432no—
572C22×C4—432no—
573C22×C4—432no—
574C22×C4—432no—
575C22×C4—431no—
576C22×C4—431no—
577C22×C4—431no—
578C22×C4—862no—
579C22×C4—861no—
580C22×C4—861no—
581C22×C4—861no—
582C22×C4—861no—
583C22×C4—861no—
584C22×C4—861no—
585C22×C4—861no—
586C22×C4—861no—
587C22×C4—862no—
588C22×C4—862no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—1721no—
596C22×C4—1721no—
597C22×C4—1721no—
598C22×C4C2×C4×D4311yescharacteristic
599C22×C4C2×C4×D4311yescharacteristic
600C22×C4C2×C4×D4311yescharacteristic
601C22×C4C2×C4×D4311yescharacteristic
602C22×C4C2×C4×D4311yescharacteristic
603C22×C4C2×C4×D4311yescharacteristic
604C22×C4C23×D4311yescharacteristic
605M16—1724no—
606M16—1724no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—432no—
619C2×C8—861no—
620C2×C8—861no—
621C2×C8—861no—
622C2×C8—861no—
623C2×C8—861no—
624C2×C8—861no—
625C2×C8—861no—
626C2×C8—861no—
627C2×C8—861no—
628C2×C8—861no—
629C2×C8—861no—
630C2×C8—1724no—
631C2×C8—1724no—
632C2×C8#1062190212yes—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—434no—
637C4⋊C4—862no—
638C4⋊C4—862no—
639C4⋊C4—862no—
640C4⋊C4—862no—
641C4⋊C4—862no—
642C4⋊C4—862no—
643C22⋊C4—434no—
644C22⋊C4—434no—
645C22⋊C4—862no—
646C22⋊C4—862no—
647C22⋊C4—862no—
648C22⋊C4—862no—
649C22⋊C4—862no—
650C22⋊C4—862no—
651C22⋊C4—862no—
652C22⋊C4—862no—
653C42—21no—
654C42—21no—
655C42—21no—
656C42—21no—
657C42—862no—
658C42—862no—
659C42—861no—
660C42—861no—
661C42D4×D4312yes—
662C42D4×D4312yes—
663C23—432no—
664C23—432no—
665C23—432no—
666C23—861no—
667C23—861no—
668C23—861no—
669C23—861no—
670C23—861no—
671C23—861no—
672C23—861no—
673C23—861no—
674C23—861no—
675C23—861no—
676C23—861no—
677C23—861no—
678C23—861no—
679C23—861no—
680C23—861no—
681C23—861no—
682C23—861no—
683C23—861no—
684C23C22×C4×D4311yescharacteristic
685Q8—44no—
686D4—1724no—
687D4—1724no—
688D4—1724no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—432no—
706C2×C4—432no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—862no—
712C2×C4—862no—
713C2×C4—862no—
714C2×C4—862no—
715C2×C4—862no—
716C2×C4—862no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—1724no—
729C2×C4—1724no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4C22⋊C4×D4312yes—
735C2×C4C22⋊C4×D4312yes—
736C2×C4C2×D4×D4311yescharacteristic
737C2×C4C2×D4×D4311yescharacteristic
738C2×C4#41×D4311yescharacteristic
739C2×C4C2×#1062190211yescharacteristic
740C2×C4#1306337111yescharacteristic
741C2×C4#1306337311yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—862no—
747C8—1721no—
748C8—1721no—
749C8—1721no—
750C22—862no—
751C22—862no—
752C22—862no—
753C22—862no—
754C22—862no—
755C22—862no—
756C22—862no—
757C22—862no—
758C22—862no—
759C22—1721no—
760C22—1721no—
761C22—1721no—
762C22—1721no—
763C22—1721no—
764C22—1721no—
765C22—1721no—
766C22—1721no—
767C22—1721no—
768C22—1721no—
769C22—1721no—
770C22—1721no—
771C22C2×C22⋊C4×D4311yescharacteristic
772C22C4×#1062190211yescharacteristic
773C22#1458338111yescharacteristic
774C22#131×D4311yescharacteristic
775C22#1458366411yescharacteristic
776C22#1458366511yescharacteristic
777C22#1458366511yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—862no—
785C4—862no—
786C4—1721no—
787C4—1721no—
788C4—1721no—
789C4#1458354011yescharacteristic
790C4#1458354211yescharacteristic
791C4#1458355111yescharacteristic
792C4#1458355211yescharacteristic
793C2—1722no—
794C2—1722no—
795C2—1722no—
796C2#1913742411yescharacteristic
797C2#1914303811yescharacteristic
798C2#1914304311yescharacteristic
799C2#1914357911yescharacteristic
800C2#1914358811yescharacteristic
801C2#1914373311yescharacteristic
802C2#1914376411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1985C2
prime radicalC2×#13063300C4
cosocleC22×C4×C43C24
hypercenter#1985D43
hypocenterC43#22475
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1985

Complements

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

NH ≅ G/Ntype
2. C2×#14582972C2semidirect
3. C2×#14582969C2semidirect
4. #19135536C2semidirect
5. #19134891C2semidirect
6. #19134891C2semidirect
7. #19134886C2semidirect
8. #19134886C2semidirect
9. #19134665C2semidirect
10. #19134665C2semidirect
11. #19134572C2semidirect
12. #19134358C2semidirect
13. #19134290C2semidirect
14. #19134290C2semidirect
15. C43×#1985C2semidirect
396. #1985D43semidirect
464. C43#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#145834362
C2×#145829722
C2×#145829692
#191355362
#191348912
#191348862
#191346652
#191345722
#191343582
#191342902
C43×#19852
#2247543