Finite Group Databasebeta

← #25113642

Subgroups — #25113642

Order 11008.

990 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14582959C211yesmaximal, characteristic, complemented
2C2×#14582864C211yesmaximal, characteristic
3#19137081C211yesmaximal, characteristic
4#19135211C211yesmaximal, characteristic, complemented
5#19135210C211yesmaximal, characteristic, complemented
6#19135198C211yesmaximal, characteristic, complemented
7#19134776C211yesmaximal, characteristic, complemented
8#19134774C211yesmaximal, characteristic, complemented
9#19134665C211yesmaximal, characteristic, complemented
10#19134574C211yesmaximal, characteristic, complemented
11#19134506C211yesmaximal, characteristic
12#19134380C211yesmaximal, characteristic, complemented
13#19134370C211yesmaximal, characteristic, complemented
14#19134358C211yesmaximal, characteristic, complemented
15C43×#1924C211yesmaximal, characteristic, complemented
16C22×#10621898C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19C2×#13063282C2211yescharacteristic
20C2×C42×D43C2211yescharacteristic
21#14582959—24no—
22C2×C4⋊(C43⋊C8)C2211yescharacteristic
23C2×Dic43⋊C8C2211yescharacteristic
24C2×Dic43⋊C8C2211yescharacteristic
25#14582864—24no—
26C2×C22⋊(C43⋊C8)C2211yescharacteristic
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×(C2×D43)⋊C8C2211yescharacteristic
29C2×(C2×D43)⋊C8C2211yescharacteristic
30C2×(C2×D43)⋊C8C2211yescharacteristic
31C2×(C2×D43)⋊C8C2211yescharacteristic
32C2×(C2×D43)⋊C8C2211yescharacteristic
33C2×(C2×D43)⋊C8C2211yescharacteristic
34C2×#13063236C2211yescharacteristic
35C2×#13063235C2211yescharacteristic
36C2×C8×Dic43C2211yescharacteristic
37#14582803C411yescharacteristic
38#14582803C411yescharacteristic
39#14582799C411yescharacteristic
40#14582799C411yescharacteristic
41#14582777C411yescharacteristic
42#14582777C411yescharacteristic
43#14582775C411yescharacteristic
44#14582775C411yescharacteristic
45C4×(C2×D43)⋊C4C2211yescharacteristic
46C4×(C2×D43)⋊C4C2211yescharacteristic
47C4×C22⋊Dic43C2211yescharacteristic
48#14582654C2211yescharacteristic
49#14582654C2211yescharacteristic
50#14582653C2211yescharacteristic
51#14582653C2211yescharacteristic
52#14582653C2211yescharacteristic
53#14582653C2211yescharacteristic
54C2×C4⋊C8×C43C2211yescharacteristic
55C2×C22⋊C8×C43C2211yescharacteristic
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×#97×C43C2211yescharacteristic
58C4×C22⋊C4×C43C2211yescharacteristic
59C43×#336C2211yescharacteristic
60C43×#336C2211yescharacteristic
61C2×#10621898—22no—
62C2×#10621898—22no—
63C2×#10621898—22no—
64C2×#10621898—22no—
65C2×#10621898—41no—
66C2×#10621898—41no—
67C22×Dic86C2×C411yescharacteristic
68C22×D172C2×C411yescharacteristic
69C22×C22⋊D43C2×C411yescharacteristic
70C22×C22⋊D43C2×C411yescharacteristic
71C22×C4×D43C2×C411yescharacteristic
72C22×C4×D43C2×C411yescharacteristic
73C22×C4×D43C2311yescharacteristic
74C22×C4×D43C2311yescharacteristic
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#13063282—22no—
86#13063282—22no—
87C2×Dic43⋊C4C2×C411yescharacteristic
88C2×Dic43⋊C4C2×C411yescharacteristic
89C2×C22⋊Dic43C2×C411yescharacteristic
90C2×C22⋊Dic43C2×C411yescharacteristic
91C2×(C2×D43)⋊C4C2×C411yescharacteristic
92C2×(C2×D43)⋊C4C2×C411yescharacteristic
93C2×(C2×D43)⋊C4C2×C411yescharacteristic
94C2×(C2×D43)⋊C4C2×C411yescharacteristic
95C2×(C2×D43)⋊C4C2×C411yescharacteristic
96C2×(C2×D43)⋊C4C2×C411yescharacteristic
97C2×C4×Dic43C2×C411yescharacteristic
98C2×C4×Dic43C2×C411yescharacteristic
99C2×C4×Dic43C2311yescharacteristic
100C2×C4×Dic43C2311yescharacteristic
101C42×D43—41no—
102C42×D43—41no—
103C4⋊(C43⋊C8)—22no—
104Dic43⋊C8—41no—
105Dic43⋊C8—41no—
106C22⋊(C43⋊C8)—22no—
107C22⋊(C43⋊C8)—41no—
108(C2×D43)⋊C8—22no—
109(C2×D43)⋊C8—22no—
110(C2×D43)⋊C8—22no—
111(C2×D43)⋊C8—22no—
112(C2×D43)⋊C8—22no—
113(C2×D43)⋊C8D414yes—
114#13063236—41no—
115#13063235—22no—
116C8×Dic43—22no—
117C43⋊#95C2×C411yescharacteristic
118C43⋊#95C2×C411yescharacteristic
119C43⋊#95C2×C411yescharacteristic
120C43⋊#95C2×C411yescharacteristic
121C43⋊#95C2×C411yescharacteristic
122C43⋊#95C2×C411yescharacteristic
123C23×C4×C43C2311yescharacteristic
124C22×C8×C43C2311yescharacteristic
125C22×C8×C43C2311yescharacteristic
126C22×C8×C43C2311yescharacteristic
127C22×C8×C43C2311yescharacteristic
128C2×C22⋊C4×C43C2×C411yescharacteristic
129C2×C22⋊C4×C43C2×C411yescharacteristic
130C2×C42×C43C2311yescharacteristic
131C2×C42×C43C2311yescharacteristic
132C4⋊C8×C43—22no—
133C22⋊C8×C43—22no—
134C22⋊C8×C43—41no—
135#97×C43—41no—
136#95×C43C2×C411yescharacteristic
137#95×C43C2×C411yescharacteristic
138C24×C43C22×C411yescharacteristic
139C23×D43C22×C411yescharacteristic
140C23×D43C22×C411yescharacteristic
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—21no—
144C22×C4×C43—21no—
145C22×C4×C43—21no—
146C22×C4×C43—21no—
147C22×C4×C43C22×C411yescharacteristic
148C22×C4×C43C22×C411yescharacteristic
149C22×C4×C43C22×C411yescharacteristic
150C22×C4×C43C22×C411yescharacteristic
151C22×C4×C43C22×C411yescharacteristic
152C22×C4×C43C2411yescharacteristic
153C2×C22⋊D43—22no—
154C2×C22⋊D43—22no—
155C2×C22⋊D43—22no—
156C2×C22⋊D43—22no—
157C2×C22⋊D43—41no—
158C2×C22⋊D43—41no—
159C22×Dic43C22×C411yescharacteristic
160C22×Dic43C22×C411yescharacteristic
161C22×Dic43C22×C411yescharacteristic
162C22×Dic43C22×C411yescharacteristic
163C22×Dic43C22×C411yescharacteristic
164C22×Dic43C22×C411yescharacteristic
165#10621898—44no—
166#10621898—44no—
167#10621898—44no—
168#10621898—44no—
169C2×D172—22no—
170C2×D172—22no—
171C2×D172—41no—
172C2×C4×D43—21no—
173C2×C4×D43—21no—
174C2×C4×D43—21no—
175C2×C4×D43—21no—
176C2×C4×D43—21no—
177C2×C4×D43—21no—
178C2×C4×D43—21no—
179C2×C4×D43—21no—
180C2×C4×D43—22no—
181C2×C4×D43—41no—
182C2×C4×D43—41no—
183C2×C4×D43—41no—
184C2×C4×D43—41no—
185C2×C4×D43—41no—
186C2×C4×D43C2×D412yes—
187C2×C4×D43#4112yes—
188C2×C4×D43#4112yes—
189C2×C4×D43#4112yes—
190C2×Dic86—22no—
191C2×Dic86—22no—
192C2×Dic86—41no—
193C2×C8×C43—21no—
194C2×C8×C43—21no—
195C2×C8×C43—21no—
196C2×C8×C43—21no—
197C2×C8×C43—21no—
198C2×C8×C43—21no—
199C2×C8×C43—21no—
200C2×C8×C43—21no—
201C2×C8×C43—21no—
202C2×C8×C43—21no—
203C2×C8×C43—21no—
204C2×C8×C43C2×D412yes—
205C22⋊C4×C43—41no—
206C22⋊C4×C43—41no—
207C42×C43—21no—
208C42×C43—21no—
209C42×C43—21no—
210C42×C43—21no—
211C22⋊Dic43—22no—
212C22⋊Dic43—41no—
213(C2×D43)⋊C4—22no—
214(C2×D43)⋊C4—22no—
215(C2×D43)⋊C4—22no—
216(C2×D43)⋊C4—41no—
217(C2×D43)⋊C4—41no—
218(C2×D43)⋊C4—41no—
219Dic43⋊C4—22no—
220Dic43⋊C4—22no—
221C4×Dic43—21no—
222C4×Dic43—21no—
223C4×Dic43—21no—
224C4×Dic43—21no—
225C4×Dic43—41no—
226C4×Dic43—41no—
227C2×C43⋊C8—21no—
228C2×C43⋊C8—21no—
229C2×C43⋊C8—21no—
230C2×C43⋊C8—21no—
231C2×C43⋊C8—21no—
232C2×C43⋊C8—21no—
233C2×C43⋊C8—21no—
234C2×C43⋊C8—21no—
235C2×C43⋊C8—21no—
236C2×C43⋊C8—21no—
237C2×C43⋊C8—21no—
238C2×C43⋊C8C2×D412yes—
239#10621872—44no—
240C8×D43—44no—
241C23×C43—21no—
242C23×C43—21no—
243C23×C43—21no—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43C23×C411yescharacteristic
249C22×D43—21no—
250C22×D43—21no—
251C22×D43—21no—
252C22×D43—21no—
253C22×D43—21no—
254C22×D43—21no—
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—21no—
260C22×D43—21no—
261C22×D43#11712yes—
262C22×D43C4×D412yes—
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—21no—
278C2×C4×C43—41no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43C22×D411yescharacteristic
283C2×C4×C43C2×#4111yescharacteristic
284C2×C4×C43C2×#4111yescharacteristic
285C2×C4×C43C2×#4111yescharacteristic
286C2×C4×C43H(5,𝔽2)11yescharacteristic
287C2×C4×C43H(5,𝔽2)11yescharacteristic
288C22⋊D43—44no—
289C22⋊D43—44no—
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—21no—
305C2×Dic43#11712yes—
306C2×Dic43C4×D412yes—
307C2×Dic43#13112yes—
308D172—44no—
309C4×D43—22no—
310C4×D43—22no—
311C4×D43—22no—
312C4×D43—22no—
313C4×D43—22no—
314C4×D43—22no—
315C4×D43—22no—
316C4×D43—22no—
317C4×D43—44no—
318C4×D43—44no—
319Dic86—44no—
320C8×C43—22no—
321C8×C43—41no—
322C8×C43—41no—
323C8×C43—41no—
324C43⋊C8—22no—
325C43⋊C8—41no—
326C43⋊C8—41no—
327C43⋊C8—41no—
328#22561—431nomaximal, Sylow
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43C2×#11711yescharacteristic
337C22×C43C2×C4×D411yescharacteristic
338C22×C43#51811yescharacteristic
339C22×C43C2×#13111yescharacteristic
340C22×C43#56811yescharacteristic
341C22×C43#56811yescharacteristic
342C22×C43#56811yescharacteristic
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—22no—
348C2×D43—22no—
349C2×D43—41no—
350C2×D43—41no—
351C2×D43—41no—
352C2×D43—41no—
353C2×D43—41no—
354C2×D43—41no—
355C2×D43—41no—
356C2×D43—41no—
357C4×C43—41no—
358C4×C43—41no—
359C4×C43—41no—
360C4×C43—41no—
361C4×C43—41no—
362C4×C43#54611yescharacteristic
363C4×C43#54611yescharacteristic
364C4×C43#55111yescharacteristic
365C4×C43#55111yescharacteristic
366Dic43—22no—
367Dic43—22no—
368Dic43—22no—
369Dic43—41no—
370Dic43—41no—
371Dic43—41no—
372C2×#433—431no—
373C2×#408—431no—
374#2297—431no—
375#1924—431no—
376#1924—431no—
377#1924D4311yescharacteristic, complemented
378#1923—431no—
379#1851—431no—
380#1850—431no—
381#1818—431no—
382#1797—431no—
383#1780—431no—
384#1753—431no—
385#1752—431no—
386#1749—431no—
387C2×C43—81no—
388C2×C43#234211yescharacteristic
389C2×C43#292311yescharacteristic
390C2×C43#292511yescharacteristic
391C2×C43#293211yescharacteristic
392C2×C43#293511yescharacteristic
393C2×C43#297611yescharacteristic
394C2×C43#297811yescharacteristic
395D43—42no—
396D43—42no—
397C22×#41—431no—
398C22×M16—431no—
399C23×C8—431no—
400C2×#117—431no—
401C22×C42—431no—
402#433—864no—
403C2×C4⋊C8—431no—
404C2×C4⋊C8—431no—
405C2×C4⋊C8—431no—
406C2×C4⋊C8C2×D4311yescharacteristic
407#408—864no—
408C2×C22⋊C8—431no—
409C2×C22⋊C8—431no—
410C2×C22⋊C8—431no—
411C2×C22⋊C8—431no—
412C2×C22⋊C8—431no—
413C2×C22⋊C8—431no—
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×C22⋊C8C2×D4311yescharacteristic
417C2×C22⋊C8C2×D4311yescharacteristic
418C2×#97—431no—
419C2×#97—431no—
420C2×#97C2×D4311yescharacteristic
421C2×C4×C8—431no—
422#391—431no—
423#391—431no—
424#390—431no—
425#390—431no—
426#386—431no—
427#386—431no—
428#386—431no—
429#386—431no—
430C4×C22⋊C4—431no—
431C4×C22⋊C4—431no—
432C4×C22⋊C4—431no—
433C4×C22⋊C4C2×D4311yescharacteristic
434#336—431no—
435#336—431no—
436#336—431no—
437#336—431no—
438#336—431no—
439#336—431no—
440#336C2×D4311yescharacteristic
441#336C2×D4311yescharacteristic
442C43#2256111yescharacteristic, complemented, Sylow
443C2×#41—862no—
444C2×#41—862no—
445C2×#41—862no—
446C2×#41—862no—
447C2×#41—1721no—
448C2×#41—1721no—
449C22×Q8—431no—
450C22×D4—431no—
451C22×D4—431no—
452C22×D4—431no—
453C23×C4—431no—
454C23×C4—431no—
455C23×C4—431no—
456C23×C4—431no—
457C23×C4C22×D4311yescharacteristic
458C2×M16—862no—
459C2×M16—862no—
460C2×M16—1721no—
461C22×C8—431no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—431no—
465C22×C8—862no—
466C22×C8—862no—
467C22×C8—1721no—
468C22×C8C22×D4311yescharacteristic
469C22×C8C22×D4311yescharacteristic
470C22×C8C22×D4311yescharacteristic
471C22×C8C22×D4311yescharacteristic
472#117—862no—
473#117—862no—
474C2×C4⋊C4—431no—
475C2×C4⋊C4—431no—
476C2×C22⋊C4—431no—
477C2×C22⋊C4—431no—
478C2×C22⋊C4—431no—
479C2×C22⋊C4—431no—
480C2×C22⋊C4—431no—
481C2×C22⋊C4—431no—
482C2×C22⋊C4—431no—
483C2×C22⋊C4—431no—
484C2×C22⋊C4C4×D4311yescharacteristic
485C2×C22⋊C4C4×D4311yescharacteristic
486C2×C42—431no—
487C2×C42—431no—
488C2×C42—431no—
489C2×C42—431no—
490C2×C42—1721no—
491C2×C42—1721no—
492C2×C42C22×D4311yescharacteristic
493C2×C42C22×D4311yescharacteristic
494C4⋊C8—22no—
495C4⋊C8—862no—
496C4⋊C8—1721no—
497C4⋊C8—1721no—
498C22⋊C8—22no—
499C22⋊C8—41no—
500C22⋊C8—434no—
501C22⋊C8—862no—
502C22⋊C8—862no—
503C22⋊C8—862no—
504C22⋊C8—862no—
505C22⋊C8—862no—
506C22⋊C8—862no—
507C22⋊C8—1721no—
508#97—41no—
509#97—862no—
510#97—1721no—
511C4×C8—862no—
512#95—431no—
513#95—431no—
514#95—431no—
515#95—431no—
516#95—431no—
517#95—431no—
518#95C4×D4311yescharacteristic
519#95C4×D4311yescharacteristic
520C24—431no—
521C24—431no—
522C24C2×C4×D4311yescharacteristic
523#41—1724no—
524#41—1724no—
525#41—1724no—
526#41—1724no—
527C2×Q8—862no—
528C2×Q8—862no—
529C2×Q8—1721no—
530C2×D4—862no—
531C2×D4—862no—
532C2×D4—862no—
533C2×D4—862no—
534C2×D4—862no—
535C2×D4—862no—
536C2×D4—1721no—
537C2×D4—1721no—
538C2×D4—1721no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—431no—
546C22×C4—431no—
547C22×C4—431no—
548C22×C4—432no—
549C22×C4—432no—
550C22×C4—432no—
551C22×C4—432no—
552C22×C4—431no—
553C22×C4—431no—
554C22×C4—431no—
555C22×C4—862no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4—861no—
559C22×C4—861no—
560C22×C4—861no—
561C22×C4—861no—
562C22×C4—861no—
563C22×C4—861no—
564C22×C4—1721no—
565C22×C4—1721no—
566C22×C4—1721no—
567C22×C4—1721no—
568C22×C4—1721no—
569C22×C4C2×C4×D4311yescharacteristic
570C22×C4C2×C4×D4311yescharacteristic
571C22×C4C2×C4×D4311yescharacteristic
572C22×C4C2×C4×D4311yescharacteristic
573C22×C4C2×C4×D4311yescharacteristic
574C22×C4C23×D4311yescharacteristic
575M16—1724no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—432no—
588C2×C8—861no—
589C2×C8—861no—
590C2×C8—861no—
591C2×C8—861no—
592C2×C8—861no—
593C2×C8—861no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8—861no—
599C2×C8—1724no—
600C2×C8D4×D4312yes—
601C4⋊C4—862no—
602C4⋊C4—862no—
603C22⋊C4—41no—
604C22⋊C4—41no—
605C22⋊C4—862no—
606C22⋊C4—862no—
607C22⋊C4—862no—
608C22⋊C4—862no—
609C22⋊C4—1721no—
610C22⋊C4—1721no—
611C22⋊C4—1721no—
612C22⋊C4—1721no—
613C42—21no—
614C42—21no—
615C42—21no—
616C42—21no—
617C42—861no—
618C42—861no—
619C42—861no—
620C42—861no—
621C42—1721no—
622C42—1721no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—432no—
631C23—432no—
632C23—861no—
633C23—861no—
634C23—861no—
635C23—861no—
636C23—861no—
637C23—861no—
638C23—861no—
639C23—861no—
640C23—861no—
641C23—861no—
642C23—861no—
643C23—861no—
644C23C22×C4×D4311yescharacteristic
645Q8—1724no—
646D4—1724no—
647D4—1724no—
648D4—1724no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—432no—
669C2×C4—432no—
670C2×C4—432no—
671C2×C4—861no—
672C2×C4—861no—
673C2×C4—861no—
674C2×C4—861no—
675C2×C4—861no—
676C2×C4—861no—
677C2×C4—862no—
678C2×C4—862no—
679C2×C4—862no—
680C2×C4—862no—
681C2×C4—862no—
682C2×C4—862no—
683C2×C4—862no—
684C2×C4—862no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—861no—
689C2×C4—861no—
690C2×C4—861no—
691C2×C4—861no—
692C2×C4—861no—
693C2×C4—861no—
694C2×C4—1724no—
695C2×C4—1724no—
696C2×C4C2×D4×D4311yescharacteristic
697C2×C4#41×D4311yescharacteristic
698C2×C4#41×D4311yescharacteristic
699C2×C4#41×D4311yescharacteristic
700C2×C4#1306337011yescharacteristic
701C2×C4#1306337111yescharacteristic
702C8—22no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—862no—
707C8—1721no—
708C8—1721no—
709C8—1721no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—862no—
718C22—862no—
719C22—862no—
720C22—862no—
721C22—862no—
722C22—862no—
723C22—1721no—
724C22—1721no—
725C22—1721no—
726C22—1721no—
727C22—1721no—
728C22—1721no—
729C22—1721no—
730C22—1721no—
731C22#117×D4311yescharacteristic
732C22C4×D4×D4311yescharacteristic
733C22#1458337111yescharacteristic
734C22#131×D4311yescharacteristic
735C22#1458366411yescharacteristic
736C22#1458366511yescharacteristic
737C22#1458366511yescharacteristic
738C4—41no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—862no—
744C4—862no—
745C4—862no—
746C4—1721no—
747C4—1721no—
748C4—1721no—
749C4#1458353811yescharacteristic
750C4#1458354211yescharacteristic
751C4#1458357411yescharacteristic
752C4#1458357711yescharacteristic
753C2—81no—
754C2—1722no—
755C2—1722no—
756C2#1913744311yescharacteristic
757C2#1914324111yescharacteristic
758C2#1914325811yescharacteristic
759C2#1914330911yescharacteristic
760C2#1914333611yescharacteristic
761C2#1914363911yescharacteristic
762C2#1914365411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D43
commutator, socleC23×C43C23×C4
FittingC43×#1924C2
prime radicalC22×#10621898C22
cosocleC22×C4×C43C24
hypercenter#1924D43
hypocenterC43#22561
LCSG ▷ C23×C43 ▷ C43
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#14582959C2semidirect
4. #19135211C2semidirect
5. #19135210C2semidirect
6. #19135198C2semidirect
7. #19134776C2semidirect
8. #19134774C2semidirect
9. #19134665C2semidirect
10. #19134574C2semidirect
12. #19134380C2semidirect
13. #19134370C2semidirect
14. #19134358C2semidirect
15. C43×#1924C2semidirect
377. #1924D43semidirect
442. C43#22561semidirect

Maximal subgroups

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

subgroupindex
C2×#145829592
C2×#145828642
#191370812
#191352112
#191352102
#191351982
#191347762
#191347742
#191346652
#191345742
#191345062
#191343802
#191343702
#191343582
C43×#19242
#2256143