Finite Group Databasebeta

← #25112657

Subgroups — #25112657

Order 11008.

1202 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×#14582970C211yesmaximal, characteristic, complemented
3C2×C8×C22⋊D43C211yesmaximal, characteristic, complemented
4#19135533C211yesmaximal, characteristic, complemented
5#19135529C211yesmaximal, characteristic, complemented
6#19134891C211yesmaximal, characteristic, complemented
7#19134887C211yesmaximal, characteristic, complemented
8#19134887C211yesmaximal, characteristic, complemented
9#19134886C211yesmaximal, characteristic, complemented
10#19134665C211yesmaximal, characteristic, complemented
11#19134663C211yesmaximal, characteristic, complemented
12#19134578C211yesmaximal, characteristic, complemented
13#19134360C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C2×C43×#336C211yesmaximal, characteristic, complemented
16C22×#10621872C2211yescharacteristic
17C22×C8×D43C2211yescharacteristic
18#14583433—24no—
19#14583433—24no—
20C2×#13063319C411yescharacteristic
21C2×#13063319C411yescharacteristic
22C2×#13063317C411yescharacteristic
23C2×#13063313C411yescharacteristic
24C2×#13063308C411yescharacteristic
25C2×#13063308C411yescharacteristic
26C2×#13063304C411yescharacteristic
27C2×#13063299C411yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×D172C2211yescharacteristic
30C2×C4×C22⋊D43C2211yescharacteristic
31C2×C4×C22⋊D43C2211yescharacteristic
32C2×#13063282C2211yescharacteristic
33C2×#13063282C2211yescharacteristic
34#14582970—24no—
35C8×C22⋊D43—24no—
36C2×Dic43⋊C8C2211yescharacteristic
37C2×Dic43⋊C8C2211yescharacteristic
38C2×C22⋊(C43⋊C8)C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
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
56C23×C8×C43C2211yescharacteristic
57C23×C8×C43C2211yescharacteristic
58C22×C42×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×#10621872—22no—
70C2×#10621872—22no—
71C2×#10621872—41no—
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75C22×C43⋊C8C2311yescharacteristic
76C2×C8×D43—22no—
77C2×C8×D43—22no—
78C2×C8×D43—41no—
79#13063319—24no—
80#13063319—24no—
81#13063317—24no—
82#13063313—24no—
83#13063308—24no—
84#13063308—24no—
85#13063304—24no—
86#13063299—24no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×D172—22no—
90C4×D172—22no—
91C4×C22⋊D43—22no—
92C4×C22⋊D43—22no—
93C4×C22⋊D43D414yes—
94C4×C22⋊D43D414yes—
95#13063282—22no—
96#13063282—22no—
97#13063282—22no—
98#13063282—22no—
99C2×C4⋊Dic43C2×C411yescharacteristic
100C2×C4⋊Dic43C2×C411yescharacteristic
101C2×Dic43⋊C4C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2×C411yescharacteristic
105C2×Dic43⋊C4C2×C411yescharacteristic
106C2×Dic43⋊C4C2×C411yescharacteristic
107C2×Dic43⋊C4C2×C411yescharacteristic
108C2×Dic43⋊C4C2×C411yescharacteristic
109C2×C22⋊Dic43C2×C411yescharacteristic
110C2×C22⋊Dic43C2×C411yescharacteristic
111C2×(C2×D43)⋊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×C4×Dic43C2311yescharacteristic
120C2×C4×Dic43C2311yescharacteristic
121Dic43⋊C8—22no—
122Dic43⋊C8—22no—
123C22⋊(C43⋊C8)—22no—
124C22⋊(C43⋊C8)—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—22no—
127(C2×D43)⋊C8—22no—
128(C2×D43)⋊C8—22no—
129(C2×D43)⋊C8—41no—
130(C2×D43)⋊C8—41no—
131#13063235—22no—
132C8×Dic43—22no—
133C23×C4×C43C2×C411yescharacteristic
134C23×C4×C43C2×C411yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C22×C8×C43—22no—
137C22×C8×C43—22no—
138C22×C8×C43—22no—
139C22×C8×C43—22no—
140C22×C8×C43—41no—
141C22×C8×C43—41no—
142C22×C8×C43C2311yescharacteristic
143C22×C8×C43C2311yescharacteristic
144C22×C8×C43C2311yescharacteristic
145C22×C8×C43C2311yescharacteristic
146C2×C42×C43—22no—
147C2×C42×C43—22no—
148C2×C42×C43C2×C411yescharacteristic
149C2×C42×C43C2×C411yescharacteristic
150C2×C42×C43C2311yescharacteristic
151C2×C42×C43C2311yescharacteristic
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—22no—
163C22×C4×C43—22no—
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—22no—
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—22no—
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—44no—
214C2×C8×C43—44no—
215C2×C8×C43#4112yes—
216C2×C8×C43#4112yes—
217C42×C43—22no—
218C42×C43—22no—
219C42×C43—21no—
220C42×C43—21no—
221C42×C43—21no—
222C42×C43—21no—
223C22⋊Dic43—22no—
224C22⋊Dic43C22⋊C414yes—
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—
233C4⋊Dic43—22no—
234C4⋊Dic43—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4—22no—
238Dic43⋊C4—22no—
239Dic43⋊C4—22no—
240Dic43⋊C4—22no—
241Dic43⋊C4—22no—
242Dic43⋊C4C22⋊C414yes—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C4×Dic43C2×D412yes—
246C4×Dic43C2×D412yes—
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—21no—
258C2×C43⋊C8—21no—
259#10621872—44no—
260C8×D43—44no—
261C23×C43—21no—
262C23×C43—21no—
263C23×C43—21no—
264C23×C43—21no—
265C23×C43C2×C22⋊C412yes—
266C23×C43#13112yes—
267C23×C43#13112yes—
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—28no—
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—22no—
341C8×C43—22no—
342C8×C43—41no—
343C8×C43—41no—
344C43⋊C8—41no—
345C43⋊C8—41no—
346C43⋊C8—41no—
347C43⋊C8—41no—
348#22470—431nomaximal, Sylow
349C22×C43—22no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—22no—
355C22×C43#40814yes—
356C22×C43C22×C22⋊C411yescharacteristic
357C22×C43C4×#4111yescharacteristic
358C22×C43#52011yescharacteristic
359C22×C43C2×#13111yescharacteristic
360C22×C43C2×#13111yescharacteristic
361C22×C43C2×#13111yescharacteristic
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×#435—431no—
394C2×C8×D4—431no—
395#1985—431no—
396#1984—431no—
397#1870—431no—
398#1869—431no—
399#1869—431no—
400#1869—431no—
401#1818—431no—
402#1817—431no—
403#1798—431no—
404#1750—431no—
405#1729—431no—
406C2×#336D4311yescharacteristic, complemented
407C2×C43—24no—
408C2×C43#233911yescharacteristic
409C2×C43C2×#40811yescharacteristic
410C2×C43#288011yescharacteristic
411C2×C43#296611yescharacteristic
412C2×C43#296811yescharacteristic
413C2×C43#299211yescharacteristic
414C2×C43#299411yescharacteristic
415D43—42no—
416D43—81no—
417C22×M16—431no—
418C23×C8—431no—
419C23×C8C2×D4311yescharacteristic
420C23×C8C2×D4311yescharacteristic
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#435—864no—
439C8×D4—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⋊C8—431no—
449C2×C22⋊C8—431no—
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#2247011yescharacteristic, 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—1721no—
477C22×C8—22no—
478C22×C8—22no—
479C22×C8—22no—
480C22×C8—22no—
481C22×C8—41no—
482C22×C8—41no—
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—862no—
545C22⋊C8—862no—
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—862no—
565C2×D4—862no—
566C2×D4—862no—
567C2×D4—862no—
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—22no—
577C22×C4—22no—
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—
606C2×C8—21no—
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—44no—
617C2×C8—44no—
618C2×C8—861no—
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#1062189812yes—
632C2×C8#1062189812yes—
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—432no—
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—
681C23C22⋊C4×D4312yes—
682C23#1306333112yes—
683C23#1306333312yes—
684C23C22×C4×D4311yescharacteristic
685Q8—1724no—
686D4—868no—
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×C4C2×#1062189811yescharacteristic
739C2×C4C2×#1062189811yescharacteristic
740C2×C4#1306337011yescharacteristic
741C2×C4#1306337311yescharacteristic
742C8—22no—
743C8—22no—
744C8—41no—
745C8—41no—
746C8—1721no—
747C8—1721no—
748C8—1721no—
749C8—1721no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
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#1458286414yes—
771C22C2×C22⋊C4×D4311yescharacteristic
772C22C4×#1062189811yescharacteristic
773C22#1458338011yescharacteristic
774C22C2×#1306333111yescharacteristic
775C22C2×#1306333111yescharacteristic
776C22C2×#1306333311yescharacteristic
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#1458353911yescharacteristic
790C4#1458353911yescharacteristic
791C4#1458355011yescharacteristic
792C4#1458355011yescharacteristic
793C2—24no—
794C2—3441no—
795C2—1722no—
796C2#1913742211yescharacteristic
797C2C2×#1458286411yescharacteristic
798C2#1914304111yescharacteristic
799C2#1914357011yescharacteristic
800C2#1914358911yescharacteristic
801C2#1914373111yescharacteristic
802C2#1914375111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC2×C43×#336C2
prime radicalC2×#13063299C4
cosocleC22×C4×C43C24
hypercenterC2×#336D43
hypocenterC43#22470
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
2. C2×#14582970C2semidirect
3. C2×C8×C22⋊D43C2semidirect
4. #19135533C2semidirect
5. #19135529C2semidirect
6. #19134891C2semidirect
7. #19134887C2semidirect
8. #19134887C2semidirect
9. #19134886C2semidirect
10. #19134665C2semidirect
11. #19134663C2semidirect
12. #19134578C2semidirect
13. #19134360C2semidirect
14. #19134290C2semidirect
15. C2×C43×#336C2semidirect
406. C2×#336D43semidirect
464. C43#22470semidirect

Maximal subgroups

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

subgroupindex
C2×#145834332
C2×#145829702
C2×C8×C22⋊D432
#191355332
#191355292
#191348912
#191348872
#191348862
#191346652
#191346632
#191345782
#191343602
#191342902
C2×C43×#3362
#2247043