Finite Group Databasebeta

← #25106653

Subgroups — #25106653

Order 11008.

950 conjugacy classes of subgroups.

The subgroup lattice has 758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#19136976C211yesmaximal, characteristic
2#19135211C211yesmaximal, characteristic, complemented
3#19135210C211yesmaximal, characteristic, complemented
4#19135209C211yesmaximal, characteristic, complemented
5#19135206C211yesmaximal, characteristic, complemented
6#19135201C211yesmaximal, characteristic, complemented
7#19135200C211yesmaximal, characteristic, complemented
8#19135198C211yesmaximal, characteristic, complemented
9#19134578C211yesmaximal, characteristic, complemented
10#19134576C211yesmaximal, characteristic, complemented
11#19134504C211yesmaximal, characteristic
12#19134504C211yesmaximal, characteristic
13#19134362C211yesmaximal, characteristic, complemented
14#19134360C211yesmaximal, characteristic, complemented
15C43×#1923C211yesmaximal, characteristic, complemented
16C23×C4×D43C2211yescharacteristic
17C2×#13063282C2211yescharacteristic
18C2×#13063282C2211yescharacteristic
19C2×C4⋊(C43⋊C8)C2211yescharacteristic, complemented
20C2×Dic43⋊C8C2211yescharacteristic, complemented
21C2×Dic43⋊C8C2211yescharacteristic, complemented
22C2×C22⋊(C43⋊C8)C2211yescharacteristic
23C2×C22⋊(C43⋊C8)C2211yescharacteristic
24C2×(C2×D43)⋊C8C2211yescharacteristic
25C2×(C2×D43)⋊C8C2211yescharacteristic
26C2×(C2×D43)⋊C8C2211yescharacteristic
27C2×(C2×D43)⋊C8C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×#13063236C2211yescharacteristic, complemented
33C2×#13063235C2211yescharacteristic, complemented
34C2×C8×Dic43C2211yescharacteristic, complemented
35#14582761C411yescharacteristic
36#14582761C411yescharacteristic
37#14582758C411yescharacteristic
38#14582758C411yescharacteristic
39#14582757C411yescharacteristic
40#14582757C411yescharacteristic
41#14582754C411yescharacteristic
42#14582754C411yescharacteristic
43C4×(C2×D43)⋊C4C2211yescharacteristic
44C4×(C2×D43)⋊C4C2211yescharacteristic
45C4×C22⋊Dic43C2211yescharacteristic
46#14582654C2211yescharacteristic, complemented
47#14582654C2211yescharacteristic, complemented
48#14582653C2211yescharacteristic, complemented
49#14582653C2211yescharacteristic, complemented
50#14582653C2211yescharacteristic, complemented
51#14582653C2211yescharacteristic, complemented
52C2×C4⋊C8×C43C2211yescharacteristic, complemented
53C2×C22⋊C8×C43C2211yescharacteristic
54C2×C22⋊C8×C43C2211yescharacteristic
55C2×C4×C8×C43C2211yescharacteristic, complemented
56C4×C22⋊C4×C43C2211yescharacteristic
57C43×#336C2211yescharacteristic, complemented
58C43×#336C2211yescharacteristic, complemented
59C24×D43C2×C411yescharacteristic
60C23×Dic43C2×C411yescharacteristic
61C22×C4×D43—22no—
62C22×C4×D43—22no—
63C22×C4×D43—41no—
64C22×C4×D43—41no—
65C22×C4×D43—41no—
66C22×C4×D43—41no—
67C22×C4×D43C2×C411yescharacteristic
68C22×C4×D43C2×C411yescharacteristic
69C22×C4×D43C2311yescharacteristic
70C22×C4×D43C2311yescharacteristic
71C22×C43⋊C8C2311yescharacteristic
72C22×C43⋊C8C2311yescharacteristic
73C22×C43⋊C8C2311yescharacteristic
74C22×C43⋊C8C2311yescharacteristic
75#13063282—41no—
76#13063282—41no—
77#13063282—41no—
78#13063282—41no—
79C2×Dic43⋊C4C2×C411yescharacteristic
80C2×Dic43⋊C4C2×C411yescharacteristic
81C2×Dic43⋊C4C2×C411yescharacteristic
82C2×Dic43⋊C4C2×C411yescharacteristic
83C2×C22⋊Dic43C2×C411yescharacteristic
84C2×C22⋊Dic43C2×C411yescharacteristic
85C2×(C2×D43)⋊C4C2×C411yescharacteristic
86C2×(C2×D43)⋊C4C2×C411yescharacteristic
87C2×(C2×D43)⋊C4C2×C411yescharacteristic
88C2×(C2×D43)⋊C4C2×C411yescharacteristic
89C2×(C2×D43)⋊C4C2×C411yescharacteristic
90C2×(C2×D43)⋊C4C2×C411yescharacteristic
91C2×(C2×D43)⋊C4C2×C411yescharacteristic
92C2×(C2×D43)⋊C4C2×C411yescharacteristic
93C2×C4×Dic43C2311yescharacteristic
94C2×C4×Dic43C2311yescharacteristic
95C4⋊(C43⋊C8)—41no—
96Dic43⋊C8—41no—
97Dic43⋊C8—41no—
98C22⋊(C43⋊C8)—41no—
99C22⋊(C43⋊C8)—41no—
100(C2×D43)⋊C8—22no—
101(C2×D43)⋊C8—22no—
102(C2×D43)⋊C8—22no—
103(C2×D43)⋊C8—22no—
104(C2×D43)⋊C8—41no—
105(C2×D43)⋊C8—41no—
106(C2×D43)⋊C8—41no—
107(C2×D43)⋊C8—41no—
108#13063236—41no—
109#13063235—41no—
110C8×Dic43—41no—
111C43⋊#95C2×C411yescharacteristic
112C43⋊#95C2×C411yescharacteristic
113C43⋊#95C2×C411yescharacteristic
114C43⋊#95C2×C411yescharacteristic
115C43⋊#95C2×C411yescharacteristic
116C43⋊#95C2×C411yescharacteristic
117C23×C4×C43C2311yescharacteristic
118C22×C8×C43C2311yescharacteristic
119C22×C8×C43C2311yescharacteristic
120C22×C8×C43C2311yescharacteristic
121C22×C8×C43C2311yescharacteristic
122C2×C22⋊C4×C43C2×C411yescharacteristic
123C2×C22⋊C4×C43C2×C411yescharacteristic
124C2×C42×C43C2311yescharacteristic
125C2×C42×C43C2311yescharacteristic
126C4⋊C8×C43—41no—
127C22⋊C8×C43—41no—
128C22⋊C8×C43—41no—
129C4×C8×C43—41no—
130#95×C43C2×C411yescharacteristic
131#95×C43C2×C411yescharacteristic
132C24×C43C22×C411yescharacteristic
133C23×D43—22no—
134C23×D43—22no—
135C23×D43—22no—
136C23×D43—41no—
137C23×D43—41no—
138C23×D43—41no—
139C23×D43—41no—
140C23×D43C22×C411yescharacteristic
141C23×D43C22×C411yescharacteristic
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43—21no—
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C22×C411yescharacteristic
153C22×C4×C43C2411yescharacteristic
154C22×Dic43—22no—
155C22×Dic43—41no—
156C22×Dic43—41no—
157C22×Dic43C22×C411yescharacteristic
158C22×Dic43C22×C411yescharacteristic
159C22×Dic43C22×C411yescharacteristic
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C411yescharacteristic
163C2×C4×D43—21no—
164C2×C4×D43—21no—
165C2×C4×D43—21no—
166C2×C4×D43—21no—
167C2×C4×D43—21no—
168C2×C4×D43—21no—
169C2×C4×D43—21no—
170C2×C4×D43—21no—
171C2×C4×D43—21no—
172C2×C4×D43—21no—
173C2×C4×D43—22no—
174C2×C4×D43—22no—
175C2×C4×D43—41no—
176C2×C4×D43—41no—
177C2×C4×D43—41no—
178C2×C4×D43—41no—
179C2×C4×D43—44no—
180C2×C4×D43—44no—
181C2×C4×D43—44no—
182C2×C4×D43—44no—
183C2×C4×D43#4112yes—
184C2×C4×D43#4112yes—
185C2×C8×C43—21no—
186C2×C8×C43—21no—
187C2×C8×C43—21no—
188C2×C8×C43—21no—
189C2×C8×C43—21no—
190C2×C8×C43—21no—
191C2×C8×C43—21no—
192C2×C8×C43—21no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C22⋊C4×C43—22no—
198C22⋊C4×C43—41no—
199C42×C43—21no—
200C42×C43—21no—
201C42×C43—21no—
202C42×C43—21no—
203C22⋊Dic43—22no—
204C22⋊Dic43—41no—
205(C2×D43)⋊C4—22no—
206(C2×D43)⋊C4—22no—
207(C2×D43)⋊C4—41no—
208(C2×D43)⋊C4—41no—
209(C2×D43)⋊C4—41no—
210(C2×D43)⋊C4—41no—
211(C2×D43)⋊C4—41no—
212(C2×D43)⋊C4—41no—
213Dic43⋊C4—41no—
214Dic43⋊C4—41no—
215Dic43⋊C4—41no—
216Dic43⋊C4—41no—
217C4×Dic43—21no—
218C4×Dic43—21no—
219C4×Dic43—21no—
220C4×Dic43—21no—
221C2×C43⋊C8—21no—
222C2×C43⋊C8—21no—
223C2×C43⋊C8—21no—
224C2×C43⋊C8—21no—
225C2×C43⋊C8—21no—
226C2×C43⋊C8—21no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C23×C43—21no—
234C23×C43—21no—
235C23×C43—21no—
236C23×C43—21no—
237C23×C43—21no—
238C23×C43—21no—
239C23×C43#13112yes—
240C23×C43C23×C411yescharacteristic
241C22×D43—21no—
242C22×D43—21no—
243C22×D43—21no—
244C22×D43—21no—
245C22×D43—21no—
246C22×D43—21no—
247C22×D43—21no—
248C22×D43—21no—
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—44no—
254C22×D43—44no—
255C22×D43—44no—
256C22×D43—44no—
257C22×D43—44no—
258C22×D43—44no—
259C22×D43—44no—
260C22×D43#11712yes—
261C22×D43#13112yes—
262C2×C4×C43—21no—
263C2×C4×C43—21no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—21no—
270C2×C4×C43—21no—
271C2×C4×C43—21no—
272C2×C4×C43—21no—
273C2×C4×C43—21no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—41no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43C2×#4111yescharacteristic
282C2×C4×C43C2×#4111yescharacteristic
283C2×C4×C43H(5,𝔽2)11yescharacteristic
284C2×C4×C43H(5,𝔽2)11yescharacteristic
285C2×C4×C43H(5,𝔽2)11yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×Dic43—21no—
288C2×Dic43—21no—
289C2×Dic43—21no—
290C2×Dic43—21no—
291C2×Dic43—21no—
292C2×Dic43—21no—
293C2×Dic43—21no—
294C2×Dic43—21no—
295C2×Dic43—21no—
296C2×Dic43—21no—
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—21no—
302C2×Dic43—21no—
303C2×Dic43—21no—
304C2×Dic43—44no—
305C2×Dic43#11712yes—
306C4×D43—22no—
307C4×D43—22no—
308C4×D43—22no—
309C4×D43—22no—
310C4×D43—44no—
311C4×D43—44no—
312C4×D43—41no—
313C4×D43—41no—
314C4×D43—41no—
315C4×D43—41no—
316C8×C43—41no—
317C8×C43—41no—
318C8×C43—41no—
319C8×C43—41no—
320C43⋊C8—41no—
321C43⋊C8—41no—
322C43⋊C8—41no—
323C43⋊C8—41no—
324#21908—431nomaximal, Sylow
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—22no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43C2×#11711yescharacteristic
333C22×C43#51811yescharacteristic
334C22×C43#51811yescharacteristic
335C22×C43C2×#13111yescharacteristic
336C22×C43C2×#13111yescharacteristic
337C22×C43#56811yescharacteristic
338C22×C43#56811yescharacteristic
339C2×D43—22no—
340C2×D43—22no—
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—416no—
346C2×D43—41no—
347C2×D43—41no—
348C2×D43—41no—
349C2×D43—41no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—41no—
353C2×D43—41no—
354C4×C43—41no—
355C4×C43—41no—
356C4×C43—41no—
357C4×C43—41no—
358C4×C43—41no—
359C4×C43#53811yescharacteristic
360C4×C43#53811yescharacteristic
361C4×C43#53811yescharacteristic
362C4×C43#53811yescharacteristic
363Dic43—22no—
364Dic43—41no—
365Dic43—41no—
366Dic43—41no—
367Dic43—41no—
368Dic43—41no—
369#2280—431no—
370#1924—431no—
371#1924—431no—
372#1924—431no—
373#1924—431no—
374#1923—431no—
375#1923—431no—
376#1923—431no—
377#1923D4311yescharacteristic, complemented
378#1798—431no—
379#1798—431no—
380#1779—431no—
381#1779—431no—
382#1750—431no—
383#1750—431no—
384C2×C43—42no—
385C2×C43#231211yescharacteristic
386C2×C43#292411yescharacteristic
387C2×C43#292411yescharacteristic
388C2×C43#297611yescharacteristic
389C2×C43#297611yescharacteristic
390C2×C43#297711yescharacteristic
391C2×C43#297811yescharacteristic
392D43—42no—
393D43—42no—
394C24×C4—431no—
395C2×#117—431no—
396C2×#117—431no—
397C2×C4⋊C8—431no—
398C2×C4⋊C8—431no—
399C2×C4⋊C8—431no—
400C2×C4⋊C8C2×D4311yescharacteristic, complemented
401C2×C22⋊C8—431no—
402C2×C22⋊C8—431no—
403C2×C22⋊C8—431no—
404C2×C22⋊C8—431no—
405C2×C22⋊C8—431no—
406C2×C22⋊C8—431no—
407C2×C22⋊C8—431no—
408C2×C22⋊C8—431no—
409C2×C22⋊C8—431no—
410C2×C22⋊C8—431no—
411C2×C22⋊C8C2×D4311yescharacteristic
412C2×C22⋊C8C2×D4311yescharacteristic
413C2×#97—431no—
414C2×#97—431no—
415C2×C4×C8—431no—
416C2×C4×C8C2×D4311yescharacteristic, complemented
417#381—431no—
418#381—431no—
419#380—431no—
420#380—431no—
421#380—431no—
422#380—431no—
423#379—431no—
424#379—431no—
425C4×C22⋊C4—431no—
426C4×C22⋊C4—431no—
427C4×C22⋊C4—431no—
428C4×C22⋊C4C2×D4311yescharacteristic
429#336—431no—
430#336—431no—
431#336—431no—
432#336—431no—
433#336—431no—
434#336—431no—
435#336C2×D4311yescharacteristic, complemented
436#336C2×D4311yescharacteristic, complemented
437C43#2190811yescharacteristic, complemented, Sylow
438C25—431no—
439C23×C4—431no—
440C23×C4—431no—
441C23×C4—431no—
442C23×C4—431no—
443C23×C4—431no—
444C23×C4—862no—
445C23×C4—862no—
446C23×C4—1721no—
447C23×C4—1721no—
448C23×C4—1721no—
449C23×C4—1721no—
450C23×C4C22×D4311yescharacteristic
451C22×C8—431no—
452C22×C8—431no—
453C22×C8—431no—
454C22×C8—431no—
455C22×C8C22×D4311yescharacteristic
456C22×C8C22×D4311yescharacteristic
457C22×C8C22×D4311yescharacteristic
458C22×C8C22×D4311yescharacteristic
459#117—1721no—
460#117—1721no—
461#117—1721no—
462#117—1721no—
463C2×C4⋊C4—431no—
464C2×C4⋊C4—431no—
465C2×C4⋊C4—431no—
466C2×C4⋊C4—431no—
467C2×C22⋊C4—431no—
468C2×C22⋊C4—431no—
469C2×C22⋊C4—431no—
470C2×C22⋊C4—431no—
471C2×C22⋊C4—431no—
472C2×C22⋊C4—431no—
473C2×C22⋊C4—431no—
474C2×C22⋊C4—431no—
475C2×C22⋊C4—431no—
476C2×C22⋊C4—431no—
477C2×C22⋊C4C4×D4311yescharacteristic
478C2×C22⋊C4C4×D4311yescharacteristic
479C2×C42—431no—
480C2×C42—431no—
481C2×C42C22×D4311yescharacteristic
482C2×C42C22×D4311yescharacteristic
483C4⋊C8—41no—
484C4⋊C8—1721no—
485C4⋊C8—1721no—
486C4⋊C8—1721no—
487C22⋊C8—41no—
488C22⋊C8—41no—
489C22⋊C8—862no—
490C22⋊C8—862no—
491C22⋊C8—862no—
492C22⋊C8—862no—
493C22⋊C8—1721no—
494C22⋊C8—1721no—
495C22⋊C8—1721no—
496C22⋊C8—1721no—
497C22⋊C8—1721no—
498C22⋊C8—1721no—
499#97—1721no—
500#97—1721no—
501C4×C8—41no—
502C4×C8—1721no—
503#95—431no—
504#95—431no—
505#95—431no—
506#95—431no—
507#95—431no—
508#95—431no—
509#95C4×D4311yescharacteristic
510#95C4×D4311yescharacteristic
511C24—431no—
512C24—431no—
513C24—862no—
514C24—862no—
515C24—862no—
516C24—1721no—
517C24—1721no—
518C24—1721no—
519C24—1721no—
520C24C2×C4×D4311yescharacteristic
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—431no—
528C22×C4—432no—
529C22×C4—432no—
530C22×C4—431no—
531C22×C4—431no—
532C22×C4—431no—
533C22×C4—431no—
534C22×C4—431no—
535C22×C4—862no—
536C22×C4—862no—
537C22×C4—862no—
538C22×C4—861no—
539C22×C4—861no—
540C22×C4—861no—
541C22×C4—861no—
542C22×C4—861no—
543C22×C4—861no—
544C22×C4—861no—
545C22×C4—861no—
546C22×C4—861no—
547C22×C4—861no—
548C22×C4—1721no—
549C22×C4—1721no—
550C22×C4—1721no—
551C22×C4—1721no—
552C22×C4—1724no—
553C22×C4—1724no—
554C22×C4—1724no—
555C22×C4—1724no—
556C22×C4—1721no—
557C22×C4—1721no—
558C22×C4C2×C4×D4311yescharacteristic
559C22×C4C2×C4×D4311yescharacteristic
560C22×C4C2×C4×D4311yescharacteristic
561C22×C4C2×C4×D4311yescharacteristic
562C22×C4C2×C4×D4311yescharacteristic
563C22×C4C23×D4311yescharacteristic
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—861no—
577C2×C8—861no—
578C2×C8—861no—
579C2×C8—861no—
580C2×C8—861no—
581C2×C8—861no—
582C2×C8—861no—
583C2×C8—861no—
584C2×C8—861no—
585C2×C8—861no—
586C2×C8—861no—
587C2×C8—861no—
588C4⋊C4—1721no—
589C4⋊C4—1721no—
590C4⋊C4—1721no—
591C4⋊C4—1721no—
592C22⋊C4—22no—
593C22⋊C4—41no—
594C22⋊C4—862no—
595C22⋊C4—862no—
596C22⋊C4—862no—
597C22⋊C4—1721no—
598C22⋊C4—1721no—
599C22⋊C4—1721no—
600C22⋊C4—1721no—
601C22⋊C4—1721no—
602C22⋊C4—1721no—
603C22⋊C4—1721no—
604C42—21no—
605C42—21no—
606C42—21no—
607C42—21no—
608C42—861no—
609C42—861no—
610C42—861no—
611C42—861no—
612C23—21no—
613C23—21no—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—432no—
619C23—432no—
620C23—861no—
621C23—861no—
622C23—861no—
623C23—861no—
624C23—861no—
625C23—861no—
626C23—861no—
627C23—861no—
628C23—861no—
629C23—861no—
630C23—861no—
631C23—861no—
632C23—1724no—
633C23—1724no—
634C23—1724no—
635C23—1724no—
636C23—1724no—
637C23—1724no—
638C23—1724no—
639C23#1306333112yes—
640C23C22×C4×D4311yescharacteristic
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—432no—
661C2×C4—861no—
662C2×C4—861no—
663C2×C4—862no—
664C2×C4—862no—
665C2×C4—862no—
666C2×C4—862no—
667C2×C4—861no—
668C2×C4—861no—
669C2×C4—861no—
670C2×C4—861no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—861no—
678C2×C4—861no—
679C2×C4—861no—
680C2×C4—861no—
681C2×C4—861no—
682C2×C4—1724no—
683C2×C4—1724no—
684C2×C4—1724no—
685C2×C4—1721no—
686C2×C4—1721no—
687C2×C4—1721no—
688C2×C4—1721no—
689C2×C4#41×D4311yescharacteristic
690C2×C4#41×D4311yescharacteristic
691C2×C4#1306337011yescharacteristic
692C2×C4#1306337011yescharacteristic
693C2×C4#1306337111yescharacteristic
694C2×C4#1306337111yescharacteristic
695C8—41no—
696C8—41no—
697C8—41no—
698C8—41no—
699C8—1721no—
700C8—1721no—
701C8—1721no—
702C8—1721no—
703C22—22no—
704C22—22no—
705C22—22no—
706C22—41no—
707C22—41no—
708C22—41no—
709C22—41no—
710C22—862no—
711C22—862no—
712C22—862no—
713C22—862no—
714C22—862no—
715C22—862no—
716C22—17216no—
717C22—1721no—
718C22—1721no—
719C22—1721no—
720C22—1721no—
721C22—1721no—
722C22—1721no—
723C22—1721no—
724C22—1721no—
725C22#117×D4311yescharacteristic
726C22#1458337111yescharacteristic
727C22#1458337111yescharacteristic
728C22#131×D4311yescharacteristic
729C22C2×#1306333111yescharacteristic
730C22#1458366411yescharacteristic
731C22#1458366511yescharacteristic
732C4—41no—
733C4—41no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—862no—
738C4—1721no—
739C4—1721no—
740C4—1721no—
741C4—1721no—
742C4—1721no—
743C4#1458348111yescharacteristic
744C4#1458348311yescharacteristic
745C4#1458348511yescharacteristic
746C4#1458348811yescharacteristic
747C2—42no—
748C2—1722no—
749C2—1722no—
750C2#1913718911yescharacteristic
751C2#1914324811yescharacteristic
752C2#1914325111yescharacteristic
753C2#1914363711yescharacteristic
754C2#1914364211yescharacteristic
755C2#1914364811yescharacteristic
756C2#1914365211yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1923C2
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenter#1923D43
hypocenterC43#21908
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1923

Complements

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

NH ≅ G/Ntype
2. #19135211C2semidirect
3. #19135210C2semidirect
4. #19135209C2semidirect
5. #19135206C2semidirect
6. #19135201C2semidirect
7. #19135200C2semidirect
8. #19135198C2semidirect
9. #19134578C2semidirect
10. #19134576C2semidirect
13. #19134362C2semidirect
14. #19134360C2semidirect
15. C43×#1923C2semidirect
19. C2×C4⋊(C43⋊C8)C22semidirect
20. C2×Dic43⋊C8C22semidirect
21. C2×Dic43⋊C8C22semidirect
32. C2×#13063236C22semidirect
33. C2×#13063235C22semidirect
34. C2×C8×Dic43C22semidirect
46. #14582654C22semidirect
47. #14582654C22semidirect
48. #14582653C22semidirect
49. #14582653C22semidirect
50. #14582653C22semidirect
51. #14582653C22semidirect
52. C2×C4⋊C8×C43C22semidirect
55. C2×C4×C8×C43C22semidirect
57. C43×#336C22semidirect
58. C43×#336C22semidirect
377. #1923D43semidirect
400. C2×C4⋊C8C2×D43semidirect
416. C2×C4×C8C2×D43semidirect
435. #336C2×D43semidirect
436. #336C2×D43semidirect
437. C43#21908semidirect

Maximal subgroups

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

subgroupindex
#191369762
#191352112
#191352102
#191352092
#191352062
#191352012
#191352002
#191351982
#191345782
#191345762
#191345042
#191343622
#191343602
C43×#19232
#2190843