Finite Group Databasebeta

← #25112721

Subgroups — #25112721

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×#14583429C211yesmaximal, characteristic
2C2×#14582973C211yesmaximal, characteristic, complemented
3C2×#14582970C211yesmaximal, characteristic, complemented
4#19135533C211yesmaximal, characteristic, complemented
5#19135533C211yesmaximal, characteristic, complemented
6#19134893C211yesmaximal, characteristic, complemented
7#19134889C211yesmaximal, characteristic, complemented
8#19134884C211yesmaximal, characteristic, complemented
9#19134665C211yesmaximal, characteristic, complemented
10#19134664C211yesmaximal, characteristic, complemented
11#19134573C211yesmaximal, characteristic, complemented
12#19134359C211yesmaximal, characteristic, complemented
13#19134291C211yesmaximal, characteristic, complemented
14#19134290C211yesmaximal, characteristic, complemented
15C43×#1869C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583429—24no—
20#14583429—24no—
21C2×#13063320C411yescharacteristic
22C2×#13063318C411yescharacteristic
23C2×#13063315C411yescharacteristic
24C2×#13063311C411yescharacteristic
25C2×#13063309C411yescharacteristic
26C2×#13063306C411yescharacteristic
27C2×#13063302C411yescharacteristic
28C2×#13063297C411yescharacteristic
29C2×C4×Dic86C2211yescharacteristic
30C2×C4×C22⋊D43C2211yescharacteristic
31C2×C4×C22⋊D43C2211yescharacteristic
32C2×#13063284C2211yescharacteristic
33C2×#13063282C2211yescharacteristic
34C22×C4×Dic43C2211yescharacteristic
35#14582973—24no—
36#14582970—24no—
37C2×Dic43⋊C8C2211yescharacteristic
38C2×Dic43⋊C8C2211yescharacteristic
39C2×C22⋊(C43⋊C8)C2211yescharacteristic
40C2×C22⋊(C43⋊C8)C2211yescharacteristic
41C2×C22⋊(C43⋊C8)C2211yescharacteristic
42C2×(C2×D43)⋊C8C2211yescharacteristic
43C2×(C2×D43)⋊C8C2211yescharacteristic
44C2×#13063235C2211yescharacteristic
45C2×#13063235C2211yescharacteristic
46#14582654C2211yescharacteristic
47#14582654C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55#14582653C2211yescharacteristic
56C23×C8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C2×C22⋊C8×C43C2211yescharacteristic
59C2×C22⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C43×#336C2211yescharacteristic
62C43×#336C2211yescharacteristic
63C22×Dic86C2×C411yescharacteristic
64C22×C22⋊D43C2×C411yescharacteristic
65C22×C22⋊D43C2×C411yescharacteristic
66C23×Dic43C2×C411yescharacteristic
67C23×Dic43C2×C411yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C2×#10621877—22no—
70C2×#10621877—22no—
71C2×#10621877—41no—
72C2×#10621872—22no—
73C2×#10621872—22no—
74C2×#10621872—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79C2×C8×D43—22no—
80C2×C8×D43—22no—
81C2×C8×D43—41no—
82#13063320—24no—
83#13063318—24no—
84#13063315—24no—
85#13063311—24no—
86#13063309—24no—
87#13063306—24no—
88#13063302—24no—
89#13063297—24no—
90C4×Dic86—22no—
91C4×Dic86—22no—
92C4×C22⋊D43—22no—
93C4×C22⋊D43—22no—
94C4×C22⋊D43D414yes—
95C4×C22⋊D43D414yes—
96#13063284—22no—
97#13063284—22no—
98#13063282—22no—
99#13063282—22no—
100C2×C4⋊Dic43C2×C411yescharacteristic
101C2×C4⋊Dic43C2×C411yescharacteristic
102C2×C4⋊Dic43C2×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×C22⋊Dic43C2×C411yescharacteristic
112C2×C22⋊Dic43C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic
114C2×(C2×D43)⋊C4C2×C411yescharacteristic
115C2×(C2×D43)⋊C4C2×C411yescharacteristic
116C2×(C2×D43)⋊C4C2×C411yescharacteristic
117C2×C4×Dic43—22no—
118C2×C4×Dic43—22no—
119C2×C4×Dic43C2×C411yescharacteristic
120C2×C4×Dic43C2×C411yescharacteristic
121C2×C4×Dic43C2311yescharacteristic
122C2×C4×Dic43C2311yescharacteristic
123C2×C4×Dic43C2311yescharacteristic
124Dic43⋊C8—22no—
125Dic43⋊C8—22no—
126C22⋊(C43⋊C8)—22no—
127C22⋊(C43⋊C8)—22no—
128C22⋊(C43⋊C8)—41no—
129(C2×D43)⋊C8—22no—
130(C2×D43)⋊C8—22no—
131#13063235—22no—
132#13063235—22no—
133C22×D4×C43C2×C411yescharacteristic
134C23×C4×C43C2311yescharacteristic
135C23×C4×C43C2311yescharacteristic
136C22×C8×C43—22no—
137C22×C8×C43—22no—
138C22×C8×C43—41no—
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C22×C8×C43C2311yescharacteristic
143C4×D4×C43—22no—
144C4×D4×C43—22no—
145C2×C4⋊C4×C43C2×C411yescharacteristic
146C2×C22⋊C4×C43C2×C411yescharacteristic
147C2×C22⋊C4×C43C2×C411yescharacteristic
148C2×C42×C43C2311yescharacteristic
149C22⋊C8×C43—22no—
150C22⋊C8×C43—22no—
151C22⋊C8×C43—41no—
152C24×C43C22×C411yescharacteristic
153C24×C43C22×C411yescharacteristic
154C23×D43C22×C411yescharacteristic
155C2×D4×C43—22no—
156C2×D4×C43—22no—
157C2×D4×C43—41no—
158C22×C4×C43—21no—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43—21no—
164C22×C4×C43—21no—
165C22×C4×C43—21no—
166C22×C4×C43—21no—
167C22×C4×C43—21no—
168C22×C4×C43C22×C411yescharacteristic
169C22×C4×C43C22×C411yescharacteristic
170C22×C4×C43C22×C411yescharacteristic
171C22×C4×C43C22×C411yescharacteristic
172C22×C4×C43C2×D412yes—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—41no—
178C2×C22⋊D43—41no—
179C2×C22⋊D43—41no—
180C2×C22⋊D43C22⋊C414yes—
181C22×Dic43—22no—
182C22×Dic43—22no—
183C22×Dic43—22no—
184C22×Dic43—41no—
185C22×Dic43—41no—
186C22×Dic43—41no—
187C22×Dic43C22×C411yescharacteristic
188C22×Dic43C22×C411yescharacteristic
189C22×Dic43C22×C411yescharacteristic
190C22×Dic43C22×C411yescharacteristic
191C22×Dic43C22×C411yescharacteristic
192C22×Dic43C22×C411yescharacteristic
193C22×Dic43C22×C411yescharacteristic
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—41no—
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—44no—
215C2×C8×C43#4112yes—
216C4⋊C4×C43—22no—
217C22⋊C4×C43—22no—
218C22⋊C4×C43—22no—
219C42×C43—21no—
220C42×C43—21no—
221C22⋊Dic43—22no—
222C22⋊Dic43—22no—
223C22⋊Dic43—22no—
224C22⋊Dic43C22⋊C414yes—
225(C2×D43)⋊C4—22no—
226(C2×D43)⋊C4—22no—
227(C2×D43)⋊C4—22no—
228(C2×D43)⋊C4C22⋊C414yes—
229C4⋊Dic43—22no—
230C4⋊Dic43—22no—
231C4⋊Dic43—22no—
232Dic43⋊C4—22no—
233Dic43⋊C4—22no—
234Dic43⋊C4—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4C22⋊C414yes—
238C4×Dic43—21no—
239C4×Dic43—21no—
240C4×Dic43—21no—
241C4×Dic43—21no—
242C4×Dic43—22no—
243C4×Dic43—22no—
244C4×Dic43C2×D412yes—
245C4×Dic43C2×D412yes—
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—21no—
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×C43—21no—
268C23×C43—21no—
269C23×C43—21no—
270C23×C43—21no—
271C23×C43—21no—
272C23×C43—21no—
273C23×C43C2×C22⋊C412yes—
274C23×C43#13112yes—
275C23×C43C23×C411yescharacteristic
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43C2×C22⋊C412yes—
283D4×C43—44no—
284C2×C4×C43—21no—
285C2×C4×C43—21no—
286C2×C4×C43—22no—
287C2×C4×C43—22no—
288C2×C4×C43—22no—
289C2×C4×C43—22no—
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—41no—
300C2×C4×C43—41no—
301C2×C4×C43—41no—
302C2×C4×C43—41no—
303C2×C4×C43C2×C22⋊C412yes—
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×Dic43—21no—
328C2×Dic43—21no—
329C2×Dic43—21no—
330C2×Dic43—44no—
331C2×Dic43—44no—
332C2×Dic43C2×C22⋊C412yes—
333C2×Dic43C2×C22⋊C412yes—
334C2×Dic43C2×C22⋊C412yes—
335C4×D43—22no—
336C4×D43—22no—
337C4×D43—22no—
338C4×D43—22no—
339Dic86—44no—
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×C43—22no—
350C22×C43—22no—
351C22×C43—22no—
352C22×C43—22no—
353C22×C43—22no—
354C22×C43—22no—
355C22×C43—41no—
356C22×C43—41no—
357C22×C43—41no—
358C22×C43—41no—
359C22×C43—41no—
360C22×C43—41no—
361C22×C43—41no—
362C22×C43—41no—
363C22×C43C22×C22⋊C411yescharacteristic
364C22×C43C4×#4111yescharacteristic
365C22×C43#52011yescharacteristic
366C22×C43C2×#13111yescharacteristic
367C22×C43#56811yescharacteristic
368C22×C43#56811yescharacteristic
369C22×C43#56811yescharacteristic
370C2×D43—22no—
371C2×D43—22no—
372C2×D43—22no—
373C2×D43—41no—
374C2×D43—41no—
375C2×D43—41no—
376C2×D43—41no—
377C4×C43—22no—
378C4×C43—41no—
379C4×C43—41no—
380C4×C43—41no—
381C4×C43#54611yescharacteristic
382C4×C43#54611yescharacteristic
383C4×C43#54711yescharacteristic
384C4×C43#54711yescharacteristic
385Dic43—22no—
386Dic43—22no—
387Dic43—22no—
388Dic43—41no—
389Dic43—41no—
390Dic43—41no—
391Dic43—41no—
392C2×#529—431no—
393C2×#435—431no—
394C2×#435—431no—
395#1985—431no—
396#1985—431no—
397#1870—431no—
398#1870—431no—
399#1869—431no—
400#1869D4311yescharacteristic, complemented
401#1818—431no—
402#1818—431no—
403#1797—431no—
404#1749—431no—
405#1729—431no—
406#1729—431no—
407C2×C43—42no—
408C2×C43—42no—
409C2×C43#233911yescharacteristic
410C2×C43#287911yescharacteristic
411C2×C43#288011yescharacteristic
412C2×C43#296711yescharacteristic
413C2×C43#296811yescharacteristic
414C2×C43#299211yescharacteristic
415C2×C43#299511yescharacteristic
416D43—42no—
417C22×M16—431no—
418C22×M16—431no—
419C23×C8—431no—
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×D4C2×D4311yescharacteristic
435C2×#117—431no—
436C2×#117—431no—
437C22×C42—431no—
438#435—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⋊C8C2×D4311yescharacteristic
448C2×C22⋊C8C2×D4311yescharacteristic
449C2×C22⋊C8C2×D4311yescharacteristic
450C2×#97—431no—
451C2×#97—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#336—431no—
461#336—431no—
462#336C2×D4311yescharacteristic
463#336C2×D4311yescharacteristic
464C43#2247511yescharacteristic, complemented, Sylow
465C22×Q8—431no—
466C22×D4—431no—
467C22×D4—431no—
468C22×D4C4×D4311yescharacteristic
469C23×C4—431no—
470C23×C4—431no—
471C23×C4—431no—
472C23×C4C22×D4311yescharacteristic
473C23×C4C22×D4311yescharacteristic
474C2×M16—862no—
475C2×M16—862no—
476C2×M16—862no—
477C2×M16—862no—
478C2×M16—1721no—
479C2×M16—1721no—
480C22×C8—22no—
481C22×C8—22no—
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—22no—
505C4×D4—22no—
506C4×D4—434no—
507C4×D4—434no—
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⋊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⋊C4C4×D4311yescharacteristic
533C2×C22⋊C4C4×D4311yescharacteristic
534C2×C42—431no—
535C2×C42—431no—
536C2×C42—431no—
537C2×C42—431no—
538C2×C42—431no—
539C2×C42—862no—
540C2×C42—862no—
541C2×C42C22×D4311yescharacteristic
542C4⋊C8—862no—
543C4⋊C8—862no—
544C22⋊C8—22no—
545C22⋊C8—22no—
546C22⋊C8—41no—
547C22⋊C8—862no—
548C22⋊C8—862no—
549C22⋊C8—862no—
550C22⋊C8—862no—
551C22⋊C8—1721no—
552#97—862no—
553#97—862no—
554C24—431no—
555C24C2×C4×D4311yescharacteristic
556C24C2×C4×D4311yescharacteristic
557C2×Q8—862no—
558C2×Q8—1721no—
559C2×Q8—1721no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—41no—
563C2×D4—434no—
564C2×D4—862no—
565C2×D4—862no—
566C2×D4—1721no—
567C2×D4—1721no—
568C2×D4—1721no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
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—431no—
588C22×C4—862no—
589C22×C4—862no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—861no—
594C22×C4—862no—
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×C4D4×D4312yes—
603C22×C4D4×D4312yes—
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—44no—
619C2×C8—432no—
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—861no—
631C2×C8—1724no—
632C2×C8#1062190012yes—
633C4⋊C4—22no—
634C4⋊C4—434no—
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—22no—
644C22⋊C4—22no—
645C22⋊C4—434no—
646C22⋊C4—434no—
647C22⋊C4—862no—
648C22⋊C4—862no—
649C22⋊C4—862no—
650C22⋊C4—862no—
651C22⋊C4—862no—
652C22⋊C4—862no—
653C42—21no—
654C42—21no—
655C42—432no—
656C42—432no—
657C42—862no—
658C42—862no—
659C42—861no—
660C42—861no—
661C42—861no—
662C42—861no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—432no—
676C23—861no—
677C23—861no—
678C23—861no—
679C23—861no—
680C23—861no—
681C23—861no—
682C23C22⋊C4×D4312yes—
683C23#1306333112yes—
684C23C22×C4×D4311yescharacteristic
685Q8—1724no—
686D4—44no—
687D4—1724no—
688D4—1724no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
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—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
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—861no—
731C2×C4—861no—
732C2×C4—861no—
733C2×C4—1724no—
734C2×C4—1724no—
735C2×C4C22⋊C4×D4312yes—
736C2×C4C2×D4×D4311yescharacteristic
737C2×C4C2×D4×D4311yescharacteristic
738C2×C4#41×D4311yescharacteristic
739C2×C4C2×#1062190011yescharacteristic
740C2×C4#1306337011yescharacteristic
741C2×C4#1306337211yescharacteristic
742C8—22no—
743C8—41no—
744C8—41no—
745C8—41no—
746C8—862no—
747C8—1721no—
748C8—1721no—
749C8—1721no—
750C22—22no—
751C22—22no—
752C22—22no—
753C22—22no—
754C22—22no—
755C22—22no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—862no—
765C22—862no—
766C22—862no—
767C22—1721no—
768C22—1721no—
769C22—1721no—
770C22—1721no—
771C22C2×C22⋊C4×D4311yescharacteristic
772C22C4×#1062190011yescharacteristic
773C22#1458337811yescharacteristic
774C22C2×#1306333111yescharacteristic
775C22#1458366411yescharacteristic
776C22#1458366411yescharacteristic
777C22#1458366511yescharacteristic
778C4—22no—
779C4—41no—
780C4—41no—
781C4—41no—
782C4—862no—
783C4—862no—
784C4—862no—
785C4—1721no—
786C4—1721no—
787C4—1721no—
788C4—1721no—
789C4#1458353611yescharacteristic
790C4#1458353811yescharacteristic
791C4#1458354711yescharacteristic
792C4#1458354911yescharacteristic
793C2—42no—
794C2—42no—
795C2—1722no—
796C2#1913742111yescharacteristic
797C2#1914303711yescharacteristic
798C2#1914304111yescharacteristic
799C2#1914357411yescharacteristic
800C2#1914358311yescharacteristic
801C2#1914372811yescharacteristic
802C2#1914376611yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1869C2
prime radicalC2×#13063297C4
cosocleC22×C4×C43C24
hypercenter#1869D43
hypocenterC43#22475
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1869

Complements

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

NH ≅ G/Ntype
2. C2×#14582973C2semidirect
3. C2×#14582970C2semidirect
4. #19135533C2semidirect
5. #19135533C2semidirect
6. #19134893C2semidirect
7. #19134889C2semidirect
8. #19134884C2semidirect
9. #19134665C2semidirect
10. #19134664C2semidirect
11. #19134573C2semidirect
12. #19134359C2semidirect
13. #19134291C2semidirect
14. #19134290C2semidirect
15. C43×#1869C2semidirect
400. #1869D43semidirect
464. C43#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#145834292
C2×#145829732
C2×#145829702
#191355332
#191348932
#191348892
#191348842
#191346652
#191346642
#191345732
#191343592
#191342912
#191342902
C43×#18692
#2247543