Finite Group Databasebeta

← #25112715

Subgroups — #25112715

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×#14583431C211yesmaximal, characteristic
2C2×#14582971C211yesmaximal, characteristic, complemented
3#19135535C211yesmaximal, characteristic, complemented
4#19135534C211yesmaximal, characteristic, complemented
5#19134892C211yesmaximal, characteristic, complemented
6#19134890C211yesmaximal, characteristic, complemented
7#19134887C211yesmaximal, characteristic, complemented
8#19134885C211yesmaximal, characteristic, complemented
9#19134664C211yesmaximal, characteristic, complemented
10#19134664C211yesmaximal, characteristic, complemented
11#19134572C211yesmaximal, characteristic, complemented
12#19134358C211yesmaximal, characteristic, complemented
13#19134293C211yesmaximal, characteristic, complemented
14#19134291C211yesmaximal, characteristic, complemented
15C2×C43×#435C211yesmaximal, characteristic, complemented
16C22×#10621877C2211yescharacteristic
17C23×C43⋊C8C2211yescharacteristic
18#14583431—24no—
19#14583431—24no—
20C2×#13063318C411yescharacteristic
21C2×#13063318C411yescharacteristic
22C2×#13063316C411yescharacteristic
23C2×#13063312C411yescharacteristic
24C2×#13063307C411yescharacteristic
25C2×#13063307C411yescharacteristic
26C2×#13063305C411yescharacteristic
27C2×#13063296C411yescharacteristic
28C2×C4×Dic86C2211yescharacteristic
29C2×C4×C22⋊D43C2211yescharacteristic
30C2×C4×C22⋊D43C2211yescharacteristic
31C2×#13063284C2211yescharacteristic
32C2×#13063284C2211yescharacteristic
33C2×C42×D43C2211yescharacteristic
34#14582971—24no—
35C2×C4⋊(C43⋊C8)C2211yescharacteristic
36C2×C22⋊(C43⋊C8)C2211yescharacteristic
37C2×C22⋊(C43⋊C8)C2211yescharacteristic
38C2×(C2×D43)⋊C8C2211yescharacteristic
39C2×(C2×D43)⋊C8C2211yescharacteristic
40C2×(C2×D43)⋊C8C2211yescharacteristic
41C2×(C2×D43)⋊C8C2211yescharacteristic
42C2×#13063236C2211yescharacteristic
43#14582653C2211yescharacteristic
44#14582653C2211yescharacteristic
45#14582653C2211yescharacteristic
46#14582653C2211yescharacteristic
47#14582653C2211yescharacteristic
48#14582653C2211yescharacteristic
49#14582653C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54#14582653C2211yescharacteristic
55C22×M16×C43C2211yescharacteristic
56C23×C8×C43C2211yescharacteristic
57C2×C4×D4×C43C2211yescharacteristic
58C43×#435—24no—
59C2×C4⋊C8×C43C2211yescharacteristic
60C2×C22⋊C8×C43C2211yescharacteristic
61C2×C22⋊C8×C43C2211yescharacteristic
62C2×#97×C43C2211yescharacteristic
63C22×Dic86C2×C411yescharacteristic
64C22×C22⋊D43C2×C411yescharacteristic
65C22×C22⋊D43C2×C411yescharacteristic
66C22×C4×D43C2×C411yescharacteristic
67C22×C4×D43C2×C411yescharacteristic
68C22×C4×D43C2311yescharacteristic
69C2×#10621877—22no—
70C2×#10621877—22no—
71C2×#10621877—41no—
72C22×C43⋊C8—22no—
73C22×C43⋊C8—22no—
74C22×C43⋊C8—41no—
75C22×C43⋊C8C2311yescharacteristic
76C22×C43⋊C8C2311yescharacteristic
77C22×C43⋊C8C2311yescharacteristic
78C22×C43⋊C8C2311yescharacteristic
79#13063318—24no—
80#13063318—24no—
81#13063316—24no—
82#13063312—24no—
83#13063307—24no—
84#13063307—24no—
85#13063305—24no—
86#13063296—24no—
87C4×Dic86—22no—
88C4×Dic86—22no—
89C4×C22⋊D43—22no—
90C4×C22⋊D43—22no—
91C4×C22⋊D43—22no—
92C4×C22⋊D43—22no—
93#13063284—22no—
94#13063284—22no—
95#13063284—22no—
96#13063284—22no—
97C2×C4⋊Dic43C2×C411yescharacteristic
98C2×C4⋊Dic43C2×C411yescharacteristic
99C2×C4⋊Dic43C2×C411yescharacteristic
100C2×C4⋊Dic43C2×C411yescharacteristic
101C2×C4⋊Dic43C2×C411yescharacteristic
102C2×Dic43⋊C4C2×C411yescharacteristic
103C2×Dic43⋊C4C2×C411yescharacteristic
104C2×Dic43⋊C4C2×C411yescharacteristic
105C2×Dic43⋊C4C2×C411yescharacteristic
106C2×C22⋊Dic43C2×C411yescharacteristic
107C2×C22⋊Dic43C2×C411yescharacteristic
108C2×C22⋊Dic43C2×C411yescharacteristic
109C2×C22⋊Dic43C2×C411yescharacteristic
110C2×C22⋊Dic43C2×C411yescharacteristic
111C2×C22⋊Dic43C2×C411yescharacteristic
112C2×(C2×D43)⋊C4C2×C411yescharacteristic
113C2×(C2×D43)⋊C4C2×C411yescharacteristic
114C2×C4×Dic43C2×C411yescharacteristic
115C2×C4×Dic43C2×C411yescharacteristic
116C2×C4×Dic43C2311yescharacteristic
117C2×C4×Dic43C2311yescharacteristic
118C2×C4×Dic43C2311yescharacteristic
119C42×D43—22no—
120C42×D43—22no—
121C4⋊(C43⋊C8)—22no—
122C22⋊(C43⋊C8)—22no—
123C22⋊(C43⋊C8)—22no—
124(C2×D43)⋊C8—22no—
125(C2×D43)⋊C8—22no—
126(C2×D43)⋊C8—41no—
127(C2×D43)⋊C8—41no—
128#13063236—22no—
129C22×D4×C43C2×C411yescharacteristic
130C23×C4×C43C2311yescharacteristic
131C23×C4×C43C2311yescharacteristic
132C2×M16×C43—22no—
133C2×M16×C43—22no—
134C2×M16×C43—41no—
135C22×C8×C43—22no—
136C22×C8×C43—22no—
137C22×C8×C43—41no—
138C22×C8×C43C2311yescharacteristic
139C22×C8×C43C2311yescharacteristic
140C22×C8×C43C2311yescharacteristic
141C22×C8×C43C2311yescharacteristic
142C4×D4×C43D414yes—
143C4×D4×C43D414yes—
144C2×C4⋊C4×C43C2×C411yescharacteristic
145C2×C22⋊C4×C43C2×C411yescharacteristic
146C2×C22⋊C4×C43C2×C411yescharacteristic
147C2×C42×C43C2311yescharacteristic
148C4⋊C8×C43—22no—
149C22⋊C8×C43—22no—
150C22⋊C8×C43—22no—
151#97×C43—22no—
152C24×C43C22×C411yescharacteristic
153C24×C43C22×C411yescharacteristic
154C23×D43C22×C411yescharacteristic
155C2×D4×C43—41no—
156C2×D4×C43—41no—
157C2×D4×C43C22⋊C414yes—
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×C43C22×C411yescharacteristic
167C22×C4×C43C22×C411yescharacteristic
168C22×C4×C43C22×C411yescharacteristic
169C22×C4×C43C22×C411yescharacteristic
170C22×C4×C43C2×D412yes—
171C22×C4×C43C2×D412yes—
172C22×C4×C43C2×D412yes—
173C22×C4×C43C2×D412yes—
174C22×C4×C43C2411yescharacteristic
175C2×C22⋊D43—22no—
176C2×C22⋊D43—22no—
177C2×C22⋊D43—22no—
178C2×C22⋊D43—22no—
179C2×C22⋊D43—41no—
180C2×C22⋊D43—41no—
181C22×Dic43C22×C411yescharacteristic
182C22×Dic43C22×C411yescharacteristic
183C22×Dic43C22×C411yescharacteristic
184C22×Dic43C22×C411yescharacteristic
185C22×Dic43C22×C411yescharacteristic
186C22×Dic43C22×C411yescharacteristic
187C22×Dic43C22×C411yescharacteristic
188C2×C4×D43—22no—
189C2×C4×D43—22no—
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—22no—
197C2×C4×D43—41no—
198C2×C4×D43—41no—
199C2×C4×D43—41no—
200C2×Dic86—22no—
201C2×Dic86—41no—
202C2×Dic86—41no—
203M16×C43—44no—
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—
215C2×C8×C43—44no—
216C2×C8×C43#4112yes—
217C4⋊C4×C43C22⋊C414yes—
218C22⋊C4×C43C22⋊C414yes—
219C22⋊C4×C43C22⋊C414yes—
220C42×C43C2×D412yes—
221C42×C43C2×D412yes—
222C22⋊Dic43—22no—
223C22⋊Dic43—22no—
224C22⋊Dic43—22no—
225C22⋊Dic43—22no—
226C22⋊Dic43—22no—
227C22⋊Dic43—22no—
228(C2×D43)⋊C4—22no—
229(C2×D43)⋊C4—22no—
230C4⋊Dic43—22no—
231C4⋊Dic43—22no—
232C4⋊Dic43—22no—
233C4⋊Dic43—22no—
234C4⋊Dic43—22no—
235Dic43⋊C4—22no—
236Dic43⋊C4—22no—
237Dic43⋊C4—22no—
238Dic43⋊C4—22no—
239C4×Dic43—22no—
240C4×Dic43—22no—
241C4×Dic43—21no—
242C4×Dic43—21no—
243C4×Dic43—21no—
244C4×Dic43—21no—
245C4×Dic43—21no—
246C4×Dic43—21no—
247#10621877—44no—
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—
259C2×C43⋊C8—44no—
260C2×C43⋊C8#4112yes—
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×C43C2×C22⋊C412yes—
275C23×C43C23×C411yescharacteristic
276C22×D43—21no—
277C22×D43—21no—
278C22×D43—21no—
279C22×D43—21no—
280C22×D43—21no—
281C22×D43—21no—
282C22×D43#13112yes—
283D4×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—22no—
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×C43C2×C22⋊C412yes—
301C2×C4×C43C2×C22⋊C412yes—
302C2×C4×C43C2×C22⋊C412yes—
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—21no—
331C2×Dic43—21no—
332C2×Dic43—21no—
333C4×D43—44no—
334C4×D43—44no—
335C4×D43—41no—
336C4×D43—41no—
337C4×D43—41no—
338C4×D43—41no—
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—22no—
379C4×C43—22no—
380C4×C43—22no—
381C4×C43#54611yescharacteristic
382C4×C43#54611yescharacteristic
383C4×C43#54711yescharacteristic
384C4×C43#54711yescharacteristic
385Dic43—41no—
386Dic43—41no—
387Dic43—41no—
388Dic43—41no—
389Dic43—41no—
390Dic43—41no—
391Dic43—41no—
392C2×#529—431no—
393C2×#435—431no—
394C2×#435D4311yescharacteristic, complemented
395#1985—431no—
396#1985—431no—
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—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×M16C2×D4311yescharacteristic
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—24no—
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⋊C8C2×D4311yescharacteristic
449C2×C22⋊C8C2×D4311yescharacteristic
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#336—431no—
461#336—431no—
462#336—431no—
463#336—431no—
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—22no—
475C2×M16—22no—
476C2×M16—41no—
477C2×M16—862no—
478C2×M16—862no—
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—862no—
505C4×D4—862no—
506C4×D4—862no—
507C4×D4—862no—
508C4×D4D17214yes—
509C4×D4C22⋊D4314yes—
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—22no—
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—22no—
553#97—862no—
554C24—431no—
555C24C2×C4×D4311yescharacteristic
556C24C2×C4×D4311yescharacteristic
557C2×Q8—862no—
558C2×Q8—1721no—
559C2×Q8—1721no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—862no—
563C2×D4—862no—
564C2×D4—862no—
565C2×D4—862no—
566C2×D4—1721no—
567C2×D4—1721no—
568C2×D4(C2×D43)⋊C414yes—
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—431no—
578C22×C4—431no—
579C22×C4—431no—
580C22×C4—431no—
581C22×C4—431no—
582C22×C4—431no—
583C22×C4—431no—
584C22×C4—862no—
585C22×C4—862no—
586C22×C4—862no—
587C22×C4—861no—
588C22×C4—861no—
589C22×C4—861no—
590C22×C4—861no—
591C22×C4—861no—
592C22×C4—861no—
593C22×C4—1721no—
594C22×C4—1721no—
595C22×C4—1721no—
596C22×C4C2×C4×D4311yescharacteristic
597C22×C4C2×C4×D4311yescharacteristic
598C22×C4C2×C4×D4311yescharacteristic
599C22×C4C2×C4×D4311yescharacteristic
600C22×C4C2×D17212yes—
601C22×C4C2×D17212yes—
602C22×C4C2×C22⋊D4312yes—
603C22×C4C2×C22⋊D4312yes—
604C22×C4C23×D4311yescharacteristic
605M16—44no—
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—862no—
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(C2×D43)⋊C414yes—
643C22⋊C4—862no—
644C22⋊C4—862no—
645C22⋊C4—862no—
646C22⋊C4—862no—
647C22⋊C4—862no—
648C22⋊C4—862no—
649C22⋊C4—862no—
650C22⋊C4—862no—
651C22⋊C4(C2×D43)⋊C414yes—
652C22⋊C4(C2×D43)⋊C414yes—
653C42—862no—
654C42—862no—
655C42—861no—
656C42—861no—
657C42—861no—
658C42—861no—
659C42—861no—
660C42—861no—
661C42C2×D17212yes—
662C42C2×C22⋊D4312yes—
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—
682C23C2×(C2×D43)⋊C412yes—
683C23C2×(C2×D43)⋊C412yes—
684C23C22×C4×D4311yescharacteristic
685Q8—1724no—
686D4—44no—
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—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—22no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—22no—
705C2×C4—861no—
706C2×C4—861no—
707C2×C4—861no—
708C2×C4—861no—
709C2×C4—861no—
710C2×C4—861no—
711C2×C4—861no—
712C2×C4—861no—
713C2×C4—861no—
714C2×C4—861no—
715C2×C4—861no—
716C2×C4—861no—
717C2×C4—861no—
718C2×C4—861no—
719C2×C4—861no—
720C2×C4—861no—
721C2×C4—861no—
722C2×C4—861no—
723C2×C4—861no—
724C2×C4—861no—
725C2×C4—861no—
726C2×C4—1724no—
727C2×C4—1724no—
728C2×C4—1721no—
729C2×C4—1721no—
730C2×C4—1721no—
731C2×C4—1721no—
732C2×C4C2×(C2×D43)⋊C412yes—
733C2×C4C2×(C2×D43)⋊C412yes—
734C2×C4C2×(C2×D43)⋊C412yes—
735C2×C4C2×(C2×D43)⋊C412yes—
736C2×C4C22×C22⋊D4311yescharacteristic
737C2×C4C22×D17211yescharacteristic
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—
771C22C22×(C2×D43)⋊C411yescharacteristic
772C22C4×#1062190011yescharacteristic
773C22#1458337811yescharacteristic
774C22#131×D4311yescharacteristic
775C22#1458366411yescharacteristic
776C22#1458366511yescharacteristic
777C22#1458366511yescharacteristic
778C4—22no—
779C4—22no—
780C4—22no—
781C4—22no—
782C4—1721no—
783C4—1721no—
784C4—1721no—
785C4—1721no—
786C4—1721no—
787C4—1721no—
788C4—1721no—
789C4#1458354311yescharacteristic
790C4#1458354411yescharacteristic
791C4#1458354811yescharacteristic
792C4#1458355311yescharacteristic
793C2—42no—
794C2—42no—
795C2—1722no—
796C2#1913742011yescharacteristic
797C2#1914303911yescharacteristic
798C2#1914304211yescharacteristic
799C2#1914357711yescharacteristic
800C2#1914358611yescharacteristic
801C2#1914373011yescharacteristic
802C2#1914376111yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC2×C43×#435C2
prime radicalC2×#13063296C4
cosocleC22×C4×C43C24
hypercenterC2×#435D43
hypocenterC43#22475
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
2. C2×#14582971C2semidirect
3. #19135535C2semidirect
4. #19135534C2semidirect
5. #19134892C2semidirect
6. #19134890C2semidirect
7. #19134887C2semidirect
8. #19134885C2semidirect
9. #19134664C2semidirect
10. #19134664C2semidirect
11. #19134572C2semidirect
12. #19134358C2semidirect
13. #19134293C2semidirect
14. #19134291C2semidirect
15. C2×C43×#435C2semidirect
394. C2×#435D43semidirect
464. C43#22475semidirect

Maximal subgroups

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

subgroupindex
C2×#145834312
C2×#145829712
#191355352
#191355342
#191348922
#191348902
#191348872
#191348852
#191346642
#191345722
#191343582
#191342932
#191342912
C2×C43×#4352
#2247543