Finite Group Databasebeta

← #25112691

Subgroups — #25112691

Order 11008.

1162 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×#14583433C211yesmaximal, characteristic
2C2×#14582974C211yesmaximal, characteristic, complemented
3C2×#14582973C211yesmaximal, characteristic, complemented
4#19135533C211yesmaximal, characteristic, complemented
5#19135529C211yesmaximal, characteristic, complemented
6#19134891C211yesmaximal, characteristic, complemented
7#19134890C211yesmaximal, characteristic, complemented
8#19134890C211yesmaximal, characteristic, complemented
9#19134886C211yesmaximal, characteristic, complemented
10#19134665C211yesmaximal, characteristic, complemented
11#19134578C211yesmaximal, characteristic, complemented
12#19134360C211yesmaximal, characteristic, complemented
13#19134290C211yesmaximal, characteristic, complemented
14#19134289C211yesmaximal, characteristic, complemented
15C43×#1817C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C22×#10621877C2211yescharacteristic
18C22×#10621872C2211yescharacteristic
19C22×C8×D43C2211yescharacteristic
20#14583433—24no—
21#14583433—24no—
22C2×#13063319C411yescharacteristic
23C2×#13063319C411yescharacteristic
24C2×#13063317C411yescharacteristic
25C2×#13063313C411yescharacteristic
26C2×#13063308C411yescharacteristic
27C2×#13063308C411yescharacteristic
28C2×#13063304C411yescharacteristic
29C2×#13063299C411yescharacteristic
30C2×C4×Dic86C2211yescharacteristic
31C2×C4×D172C2211yescharacteristic
32C2×C4×C22⋊D43C2211yescharacteristic
33C2×C4×C22⋊D43C2211yescharacteristic
34C2×#13063282C2211yescharacteristic
35C2×#13063282C2211yescharacteristic
36#14582974—24no—
37#14582973—24no—
38C2×Dic43⋊C8C2211yescharacteristic
39C2×Dic43⋊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×#13063235C2211yescharacteristic
47C2×C8×Dic43C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582654C2211yescharacteristic
51#14582654C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C22×C42×C43C2211yescharacteristic
57C2×C22⋊C8×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86C2×C411yescharacteristic
64C22×D172C2×C411yescharacteristic
65C22×C22⋊D43C2×C411yescharacteristic
66C22×C22⋊D43C2×C411yescharacteristic
67C22×C4×D43C2311yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C2×#10621877—22no—
70C2×#10621877—22no—
71C2×#10621877—22no—
72C2×#10621877—22no—
73C2×#10621877—41no—
74C2×#10621877—41no—
75C2×#10621872—22no—
76C2×#10621872—22no—
77C2×#10621872—41no—
78C22×C43⋊C8C2311yescharacteristic
79C22×C43⋊C8C2311yescharacteristic
80C22×C43⋊C8C2311yescharacteristic
81C22×C43⋊C8C2311yescharacteristic
82C2×C8×D43—22no—
83C2×C8×D43—22no—
84C2×C8×D43—41no—
85#13063319—24no—
86#13063319—24no—
87#13063317—24no—
88#13063313—24no—
89#13063308—24no—
90#13063308—24no—
91#13063304—24no—
92#13063299—24no—
93C4×Dic86—22no—
94C4×Dic86—22no—
95C4×D172—22no—
96C4×D172—22no—
97C4×C22⋊D43—22no—
98C4×C22⋊D43—22no—
99C4×C22⋊D43D414yes—
100C4×C22⋊D43D414yes—
101#13063282—22no—
102#13063282—22no—
103#13063282—22no—
104#13063282—22no—
105C2×C4⋊Dic43C2×C411yescharacteristic
106C2×C4⋊Dic43C2×C411yescharacteristic
107C2×Dic43⋊C4C2×C411yescharacteristic
108C2×Dic43⋊C4C2×C411yescharacteristic
109C2×Dic43⋊C4C2×C411yescharacteristic
110C2×Dic43⋊C4C2×C411yescharacteristic
111C2×Dic43⋊C4C2×C411yescharacteristic
112C2×Dic43⋊C4C2×C411yescharacteristic
113C2×Dic43⋊C4C2×C411yescharacteristic
114C2×Dic43⋊C4C2×C411yescharacteristic
115C2×C22⋊Dic43C2×C411yescharacteristic
116C2×C22⋊Dic43C2×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×(C2×D43)⋊C4C2×C411yescharacteristic
123C2×(C2×D43)⋊C4C2×C411yescharacteristic
124C2×(C2×D43)⋊C4C2×C411yescharacteristic
125C2×C4×Dic43C2311yescharacteristic
126C2×C4×Dic43C2311yescharacteristic
127Dic43⋊C8—22no—
128Dic43⋊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—41no—
134(C2×D43)⋊C8—41no—
135#13063235—22no—
136C8×Dic43—22no—
137C23×C4×C43C2×C411yescharacteristic
138C23×C4×C43C2×C411yescharacteristic
139C23×C4×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C2×C42×C43—22no—
145C2×C42×C43—22no—
146C2×C42×C43C2×C411yescharacteristic
147C2×C42×C43C2×C411yescharacteristic
148C2×C42×C43C2311yescharacteristic
149C2×C42×C43C2311yescharacteristic
150C22⋊C8×C43—22no—
151C22⋊C8×C43—22no—
152C24×C43C22×C411yescharacteristic
153C23×D43C22×C411yescharacteristic
154C23×D43C22×C411yescharacteristic
155C22×C4×C43—21no—
156C22×C4×C43—21no—
157C22×C4×C43—21no—
158C22×C4×C43—21no—
159C22×C4×C43—22no—
160C22×C4×C43—22no—
161C22×C4×C43—22no—
162C22×C4×C43—41no—
163C22×C4×C43—41no—
164C22×C4×C43—41no—
165C22×C4×C43C22×C411yescharacteristic
166C22×C4×C43C22×C411yescharacteristic
167C22×C4×C43C22×C411yescharacteristic
168C22×C4×C43C22×C411yescharacteristic
169C22×C4×C43C22×C411yescharacteristic
170C22×C4×C43C2×D412yes—
171C22×C4×C43C2×D412yes—
172C22×C4×C43C2411yescharacteristic
173C2×C22⋊D43—22no—
174C2×C22⋊D43—41no—
175C2×C22⋊D43—41no—
176C2×C22⋊D43—41no—
177C2×C22⋊D43—41no—
178C2×C22⋊D43C22⋊C414yes—
179C22×Dic43C22×C411yescharacteristic
180C22×Dic43C22×C411yescharacteristic
181C22×Dic43C22×C411yescharacteristic
182C22×Dic43C22×C411yescharacteristic
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C2×D172—22no—
186C2×D172—22no—
187C2×D172—41no—
188C2×C4×D43—21no—
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—21no—
196C2×C4×D43—21no—
197C2×C4×D43—21no—
198C2×C4×D43C2×D412yes—
199C2×C4×D43C2×D412yes—
200C2×Dic86—22no—
201C2×Dic86—22no—
202C2×Dic86—41no—
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—21no—
215C42×C43—22no—
216C42×C43—22no—
217C42×C43—21no—
218C42×C43—21no—
219C42×C43—21no—
220C42×C43—21no—
221C22⋊Dic43—22no—
222C22⋊Dic43C22⋊C414yes—
223(C2×D43)⋊C4—22no—
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)⋊C4C22⋊C414yes—
231C4⋊Dic43—22no—
232C4⋊Dic43—22no—
233Dic43⋊C4—22no—
234Dic43⋊C4—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4—22no—
238Dic43⋊C4—22no—
239Dic43⋊C4—22no—
240Dic43⋊C4C22⋊C414yes—
241C4×Dic43—21no—
242C4×Dic43—21no—
243C4×Dic43C2×D412yes—
244C4×Dic43C2×D412yes—
245#10621877—44no—
246#10621877—44no—
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—21no—
257C2×C43⋊C8#4112yes—
258C2×C43⋊C8#4112yes—
259#10621872—44no—
260C8×D43—44no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43—21no—
266C23×C43—21no—
267C23×C43C2×C22⋊C412yes—
268C23×C43C23×C411yescharacteristic
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×D43—21no—
281C22×D43—21no—
282C22×D43C2×C22⋊C412yes—
283C2×C4×C43—21no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—21no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
290C2×C4×C43—22no—
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×C43—44no—
301C2×C4×C43—44no—
302C2×C4×C43C2×C22⋊C412yes—
303C2×C4×C43#13112yes—
304C2×C4×C43C22×D411yescharacteristic
305C2×C4×C43C22×D411yescharacteristic
306C2×C4×C43C2×#4111yescharacteristic
307C2×C4×C43C2×#4111yescharacteristic
308C2×C4×C43H(5,𝔽2)11yescharacteristic
309C2×C4×C432−1+411yescharacteristic
310C22⋊D43—44no—
311C22⋊D43—44no—
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×Dic43—21no—
322C2×Dic43—21no—
323C2×Dic43—21no—
324C2×Dic43—21no—
325C2×Dic43—21no—
326C2×Dic43—21no—
327C2×Dic43C2×C22⋊C412yes—
328C2×Dic43C2×C22⋊C412yes—
329C2×Dic43C2×C22⋊C412yes—
330D172—44no—
331C4×D43—22no—
332C4×D43—22no—
333C4×D43—22no—
334C4×D43—22no—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
339Dic86—44no—
340C8×C43—41no—
341C8×C43—41no—
342C8×C43—41no—
343C8×C43—41no—
344C43⋊C8—22no—
345C43⋊C8—22no—
346C43⋊C8—41no—
347C43⋊C8—41no—
348#22472—431nomaximal, Sylow
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—41no—
353C22×C43—41no—
354C22×C43—41no—
355C22×C43—41no—
356C22×C43C22×C22⋊C411yescharacteristic
357C22×C43C4×#4111yescharacteristic
358C22×C43#52011yescharacteristic
359C22×C43C2×#13111yescharacteristic
360C22×C43#56811yescharacteristic
361C22×C43#56811yescharacteristic
362C22×C43#56811yescharacteristic
363C2×D43—22no—
364C2×D43—22no—
365C2×D43—22no—
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#54611yescharacteristic
383C4×C43#54611yescharacteristic
384C4×C43#54711yescharacteristic
385C4×C43#54711yescharacteristic
386Dic43—22no—
387Dic43—22no—
388Dic43—22no—
389Dic43—41no—
390Dic43—41no—
391Dic43—41no—
392C2×#529—431no—
393C2×#436—431no—
394C2×#435—431no—
395#1985—431no—
396#1984—431no—
397#1870—431no—
398#1870—431no—
399#1870—431no—
400#1869—431no—
401#1818—431no—
402#1817D4311yescharacteristic, complemented
403#1798—431no—
404#1750—431no—
405#1729—431no—
406#1728—431no—
407C2×C43—42no—
408C2×C43#233911yescharacteristic
409C2×C43#287911yescharacteristic
410C2×C43#288011yescharacteristic
411C2×C43#296711yescharacteristic
412C2×C43#296911yescharacteristic
413C2×C43#299311yescharacteristic
414C2×C43#299511yescharacteristic
415D43—42no—
416D43—81no—
417C22×M16—431no—
418C22×M16—431no—
419C22×M16—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×Q8—431no—
432C2×C4×D4—431no—
433C2×C4×D4—431no—
434C2×C4×D4—431no—
435C2×#117—431no—
436C2×#117—431no—
437C22×C42C2×D4311yescharacteristic
438#436—864no—
439#435—864no—
440C2×C4⋊C8—431no—
441C2×C4⋊C8—431no—
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⋊C8C2×D4311yescharacteristic
449C2×C22⋊C8C2×D4311yescharacteristic
450C2×#97—431no—
451C2×C4×C8—431no—
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#2247211yescharacteristic, complemented, Sylow
465C22×Q8—431no—
466C22×D4—431no—
467C22×D4—431no—
468C22×D4—431no—
469C23×C4—431no—
470C23×C4—431no—
471C23×C4C4×D4311yescharacteristic
472C23×C4C4×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C2×M16—862no—
475C2×M16—862no—
476C2×M16—862no—
477C2×M16—862no—
478C2×M16—862no—
479C2×M16—862no—
480C2×M16—1721no—
481C2×M16—1721no—
482C2×M16—1721no—
483C22×C8—431no—
484C22×C8—431no—
485C22×C8—431no—
486C22×C8—431no—
487C22×C8—862no—
488C22×C8—862no—
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—862no—
503C4×Q8—862no—
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⋊C4—431no—
522C2×C4⋊C4—431no—
523C2×C4⋊C4—431no—
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—22no—
535C2×C42—22no—
536C2×C42—431no—
537C2×C42—431no—
538C2×C42C4×D4311yescharacteristic
539C2×C42C4×D4311yescharacteristic
540C2×C42C22×D4311yescharacteristic
541C2×C42C22×D4311yescharacteristic
542C4⋊C8—862no—
543C4⋊C8—862no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—862no—
547C22⋊C8—862no—
548C22⋊C8—862no—
549C22⋊C8—862no—
550C22⋊C8—1721no—
551C22⋊C8—1721no—
552#97—862no—
553C4×C8—862no—
554C24—431no—
555C24—431no—
556C24C2×C4×D4311yescharacteristic
557C2×Q8—862no—
558C2×Q8—862no—
559C2×Q8—1721no—
560C2×D4—434no—
561C2×D4—862no—
562C2×D4—862no—
563C2×D4—862no—
564C2×D4—1721no—
565C2×D4—1721no—
566C2×D4—1721no—
567C2×D4—1721no—
568C2×D4—1721no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—41no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—432no—
583C22×C4—432no—
584C22×C4—431no—
585C22×C4—431no—
586C22×C4—431no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—861no—
595C22×C4—861no—
596C22×C4—861no—
597C22×C4C2×C4×D4311yescharacteristic
598C22×C4C2×C4×D4311yescharacteristic
599C22×C4C2×C4×D4311yescharacteristic
600C22×C4C2×C4×D4311yescharacteristic
601C22×C4C2×C4×D4311yescharacteristic
602C22×C4D4×D4312yes—
603C22×C4D4×D4312yes—
604C22×C4C23×D4311yescharacteristic
605M16—1724no—
606M16—1724no—
607M16—1724no—
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—21no—
619C2×C8—21no—
620C2×C8—432no—
621C2×C8—432no—
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—861no—
631C2×C8—861no—
632C2×C8—1724no—
633C4⋊C4—434no—
634C4⋊C4—862no—
635C4⋊C4—862no—
636C4⋊C4—862no—
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—22no—
654C42—22no—
655C42—21no—
656C42—21no—
657C42—21no—
658C42—21no—
659C42—432no—
660C42—432no—
661C42—861no—
662C42—861no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—432no—
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—
683C23C22⋊C4×D4312yes—
684C23C22×C4×D4311yescharacteristic
685Q8—1724no—
686D4—1724no—
687D4—1724no—
688D4—1724no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
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—21no—
706C2×C4—44no—
707C2×C4—44no—
708C2×C4—432no—
709C2×C4—432no—
710C2×C4—432no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—862no—
718C2×C4—862no—
719C2×C4—862no—
720C2×C4—862no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—861no—
727C2×C4—861no—
728C2×C4—861no—
729C2×C4—861no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4—1721no—
733C2×C4—1721no—
734C2×C4C22⋊C4×D4312yes—
735C2×C4#1306333112yes—
736C2×C4C2×D4×D4311yescharacteristic
737C2×C4C2×D4×D4311yescharacteristic
738C2×C4#41×D4311yescharacteristic
739C2×C4#41×D4311yescharacteristic
740C2×C4#1306337111yescharacteristic
741C2×C4#1306337211yescharacteristic
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—862no—
747C8—862no—
748C8—1721no—
749C8—1721no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—862no—
758C22—862no—
759C22—862no—
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
772C22#1458336711yescharacteristic
773C22#1458337911yescharacteristic
774C22C2×#1306333111yescharacteristic
775C22#1458366511yescharacteristic
776C22#1458366511yescharacteristic
777C22#1458366511yescharacteristic
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—862no—
784C4—862no—
785C4—862no—
786C4—1721no—
787C4—1721no—
788C4—1721no—
789C4#1458354111yescharacteristic
790C4#1458354111yescharacteristic
791C4#1458354711yescharacteristic
792C4#1458354711yescharacteristic
793C2—42no—
794C2—3441no—
795C2—1722no—
796C2#1913741911yescharacteristic
797C2#1914303811yescharacteristic
798C2#1914304111yescharacteristic
799C2#1914357511yescharacteristic
800C2#1914359311yescharacteristic
801C2#1914374611yescharacteristic
802C2#1914376711yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1817C2
prime radicalC2×#13063299C4
cosocleC22×C4×C43C24
hypercenter#1817D43
hypocenterC43#22472
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1817

Complements

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

NH ≅ G/Ntype
2. C2×#14582974C2semidirect
3. C2×#14582973C2semidirect
4. #19135533C2semidirect
5. #19135529C2semidirect
6. #19134891C2semidirect
7. #19134890C2semidirect
8. #19134890C2semidirect
9. #19134886C2semidirect
10. #19134665C2semidirect
11. #19134578C2semidirect
12. #19134360C2semidirect
13. #19134290C2semidirect
14. #19134289C2semidirect
15. C43×#1817C2semidirect
402. #1817D43semidirect
464. C43#22472semidirect

Maximal subgroups

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

subgroupindex
C2×#145834332
C2×#145829742
C2×#145829732
#191355332
#191355292
#191348912
#191348902
#191348862
#191346652
#191345782
#191343602
#191342902
#191342892
C43×#18172
#2247243