Finite Group Databasebeta

← #25094396

Subgroups — #25094396

Order 11008.

1598 conjugacy classes of subgroups.

The subgroup lattice has 760 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583381C211yesmaximal, characteristic
2C2×#14582899C211yesmaximal, characteristic
3C2×#14582894C211yesmaximal, characteristic
4C2×#14582853C211yesmaximal, characteristic, complemented
5#19136949C211yesmaximal, characteristic, complemented
6#19134427C211yesmaximal, characteristic, complemented
7#19134425C211yesmaximal, characteristic, complemented
8#19134423C211yesmaximal, characteristic, complemented
9#19134419C211yesmaximal, characteristic, complemented
10#103×Dic43C211yesmaximal, characteristic, complemented
11C4×#13063247C211yesmaximal, characteristic, complemented
12#19134409C211yesmaximal, characteristic, complemented
13#19134313C211yesmaximal, characteristic, complemented
14#340×D43C211yesmaximal, characteristic, complemented
15C4×#103×C43C211yesmaximal, characteristic, complemented
16C22×#10621902C2211yescharacteristic
17C22×#10621872C2211yescharacteristic
18C22×C8×D43C2211yescharacteristic
19#14583381—24no—
20#14583381C418yescomplemented
21C2×Q8×Dic43C2211yescharacteristic
22C2×C4×D172—21no—
23C2×C4×D172C2211yescharacteristic
24C2×#13063287—21no—
25C2×#13063287C2211yescharacteristic
26C2×#13063283C2211yescharacteristic
27C2×#13063282—21no—
28C2×#13063282C2211yescharacteristic
29C2×C4⋊C4×D43—21no—
30C2×C4⋊C4×D43C2211yescharacteristic
31C2×C4⋊C4×D43C2211yescharacteristic
32#14582899C418yescomplemented
33#14582894C418yescomplemented
34C2×#13063249C2211yescharacteristic
35C2×#13063249C2211yescharacteristic
36C2×#13063247C2211yescharacteristic
37C2×#13063247C2211yescharacteristic
38C2×#13063245C2211yescharacteristic
39C2×#13063245C2211yescharacteristic
40#14582853—24no—
41C2×#13063236C2211yescharacteristic
42C2×#13063235C2211yescharacteristic
43C2×C8×Dic43C2211yescharacteristic
44C4⋊C4×Dic43C2211yescharacteristic
45C4⋊C4×Dic43C2211yescharacteristic
46C4×Dic43⋊C4—21no—
47C4×C4⋊Dic43C2211yescharacteristic
48#14582750—21no—
49C4×(C2×D43)⋊C4—21no—
50#14582746—21no—
51#14582662C2211yescharacteristic
52#14582662C2211yescharacteristic
53#14582661C2211yescharacteristic
54#14582661C2211yescharacteristic
55#14582661C2211yescharacteristic
56#14582661C2211yescharacteristic
57C2×C4×Q8×C43C2211yescharacteristic
58C2×#103×C43C2211yescharacteristic
59C2×#103×C43C2211yescharacteristic
60C2×C4×C8×C43C2211yescharacteristic
61C4×C4⋊C4×C43C2211yescharacteristic
62C43×#340C2211yescharacteristic
63C43×#340C2211yescharacteristic
64C2×#10621902—22no—
65C2×#10621902—22no—
66C2×#10621902—22no—
67C2×#10621902C2×C414yes—
68C2×#10621902C2×C414yes—
69C2×#10621902C2×C414yes—
70C22×D172—21no—
71C22×D172C2311yescharacteristic
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C22×C4×D43—21no—
75C22×C4×D43—21no—
76C22×C4×D43—21no—
77C22×C4×D43C2311yescharacteristic
78C2×#10621872—22no—
79C2×#10621872—22no—
80C2×#10621872C2×C414yescomplemented
81C22×C43⋊C8C2311yescharacteristic
82C22×C43⋊C8C2311yescharacteristic
83C2×C8×D43—22no—
84C2×C8×D43—22no—
85C2×C8×D43C2×C414yescomplemented
86Q8×Dic43—22no—
87Q8×Dic43C2×C414yescomplemented
88C4×D172—22no—
89C4×D172—28no—
90C4×D172C2×C414yescomplemented
91#13063287—28no—
92#13063287—22no—
93#13063287C2×C414yescomplemented
94#13063283—22no—
95#13063283C2×C414yescomplemented
96#13063282—28no—
97#13063282C2×C414yes—
98#13063282D414yes—
99C2×C4⋊Dic43—21no—
100C2×C4⋊Dic43C2311yescharacteristic
101C2×C4⋊Dic43C2311yescharacteristic
102C2×C4⋊Dic43C2311yescharacteristic
103C2×Dic43⋊C4—21no—
104C2×Dic43⋊C4—21no—
105C2×Dic43⋊C4D411yescharacteristic
106C2×Dic43⋊C4D411yescharacteristic
107C4⋊C4×D43—22no—
108C4⋊C4×D43—22no—
109C4⋊C4×D43—28no—
110C4⋊C4×D43C2×C414yes—
111C4⋊C4×D43C2×C414yescomplemented
112C2×(C2×D43)⋊C4—21no—
113C2×(C2×D43)⋊C4—21no—
114C2×(C2×D43)⋊C4—21no—
115C2×(C2×D43)⋊C4D411yescharacteristic
116C2×(C2×D43)⋊C4D411yescharacteristic
117C2×C4×Dic43—21no—
118C2×C4×Dic43—21no—
119C2×C4×Dic43—21no—
120C2×C4×Dic43—21no—
121C2×C4×Dic43—21no—
122C2×C4×Dic43C2311yescharacteristic
123#13063249C2×C414yescomplemented
124#13063249C2×C414yescomplemented
125#13063247C2×C414yescomplemented
126#13063247C2×C414yescomplemented
127#13063245C2×C414yescomplemented
128#13063245C2×C414yescomplemented
129#13063236—22no—
130#13063235—22no—
131C8×Dic43—22no—
132C43⋊#95—21no—
133C43⋊#95—21no—
134C43⋊#95—21no—
135C22×Q8×C43C2311yescharacteristic
136C22×C8×C43C2311yescharacteristic
137C22×C8×C43C2311yescharacteristic
138C4×Q8×C43—22no—
139C4×Q8×C43C2×C414yescomplemented
140C2×C4⋊C4×C43—21no—
141C2×C4⋊C4×C43C2311yescharacteristic
142C2×C4⋊C4×C43C2311yescharacteristic
143C2×C4⋊C4×C43C2311yescharacteristic
144C2×C42×C43—21no—
145C2×C42×C43—21no—
146C2×C42×C43C2311yescharacteristic
147#103×C43C2×C414yescomplemented
148#103×C43C2×C414yescomplemented
149C4×C8×C43—22no—
150#95×C43—21no—
151C23×D43—21no—
152C23×D43C2×D411yescharacteristic
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43—21no—
156C2×Q8×C43C22×C412yes—
157C2×Q8×C43C22×C412yes—
158C2×Q8×C43C22×C412yes—
159C22×C4×C43—21no—
160C22×C4×C43—21no—
161C22×C4×C43—21no—
162C22×C4×C43—21no—
163C22×C4×C43C2×D411yescharacteristic
164C22×C4×C43C2×D411yescharacteristic
165C22×C4×C43C2411yescharacteristic
166C22×Dic43—21no—
167C22×Dic43—21no—
168C22×Dic43—21no—
169C22×Dic43C2×D411yescharacteristic
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D411yescharacteristic
172#10621902—28no—
173#10621902—28no—
174#10621902—28no—
175#10621902C42116yescomplemented
176C2×D172—21no—
177C2×D172—21no—
178C2×D172—21no—
179C2×D172—24no—
180C2×D172—24no—
181C2×D172—24no—
182C2×D172C22×C412yes—
183C2×D172C22×C412yes—
184C2×D172C22×C412yes—
185C2×C4×D43—24no—
186C2×C4×D43—24no—
187C2×C4×D43—24no—
188C2×C4×D43—24no—
189C2×C4×D43—24no—
190C2×C4×D43—24no—
191C2×C4×D43—24no—
192C2×C4×D43—81no—
193C2×C4×D43—81no—
194C2×C4×D43—81no—
195C2×C4×D43—81no—
196C2×C4×D43—81no—
197C2×C4×D43—81no—
198C2×C4×D43—81no—
199C2×C4×D43—81no—
200C2×C4×D43C22×C412yes—
201C2×C4×D43C22×C412yes—
202C2×C4×D43C22×C412yes—
203C2×C4×D43C2×D412yes—
204C2×C4×D43#4112yes—
205C2×C4×D43#4112yes—
206C2×C8×C43—21no—
207C2×C8×C43—21no—
208C2×C8×C43—21no—
209C2×C8×C43—21no—
210C2×C8×C43C22×C412yes—
211C2×C8×C43C22×C412yes—
212C4⋊C4×C43—24no—
213C4⋊C4×C43—21no—
214C4⋊C4×C43—21no—
215C4⋊C4×C43—21no—
216C4⋊C4×C43C22×C412yes—
217C4⋊C4×C43C22×C412yes—
218C4⋊C4×C43C22×C412yes—
219C42×C43—24no—
220C42×C43—81no—
221C42×C43C22×C412yes—
222C42×C43C2×D412yes—
223(C2×D43)⋊C4—24no—
224(C2×D43)⋊C4—24no—
225(C2×D43)⋊C4—24no—
226(C2×D43)⋊C4C22⋊C414yes—
227(C2×D43)⋊C4C22⋊C414yes—
228C4⋊Dic43—21no—
229C4⋊Dic43—21no—
230C4⋊Dic43—21no—
231C4⋊Dic43—24no—
232C4⋊Dic43C22×C412yes—
233C4⋊Dic43C22×C412yes—
234C4⋊Dic43C22×C412yes—
235Dic43⋊C4—24no—
236Dic43⋊C4—24no—
237Dic43⋊C4C22⋊C414yes—
238Dic43⋊C4C22⋊C414yes—
239C4×Dic43—24no—
240C4×Dic43—24no—
241C4×Dic43—81no—
242C4×Dic43—81no—
243C4×Dic43—81no—
244C4×Dic43C22×C412yes—
245C4×Dic43C2×D412yes—
246C2×C43⋊C8—21no—
247C2×C43⋊C8—21no—
248C2×C43⋊C8—21no—
249C2×C43⋊C8—21no—
250C2×C43⋊C8C22×C412yes—
251C2×C43⋊C8C22×C412yes—
252#10621872—28no—
253C8×D43—28no—
254C23×C43C22×D411yescharacteristic
255C22×D43—21no—
256C22×D43—21no—
257C22×D43—21no—
258C22×D43—21no—
259C22×D43—22no—
260C22×D43—22no—
261C22×D43—22no—
262C22×D43—41no—
263C22×D43—41no—
264C22×D43—41no—
265C22×D43—41no—
266C22×D43C2×C22⋊C412yes—
267C22×D43C4×D412yes—
268C22×D43C4×D412yes—
269Q8×C43—22no—
270Q8×C43—22no—
271Q8×C43—22no—
272Q8×C43C2×C4214yes—
273C2×C4×C43—22no—
274C2×C4×C43—22no—
275C2×C4×C43—22no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—21no—
279C2×C4×C43—21no—
280C2×C4×C43—22no—
281C2×C4×C43—22no—
282C2×C4×C43—22no—
283C2×C4×C43—41no—
284C2×C4×C43—41no—
285C2×C4×C43—41no—
286C2×C4×C43—41no—
287C2×C4×C43—41no—
288C2×C4×C43—41no—
289C2×C4×C43C2×C22⋊C412yes—
290C2×C4×C43C2×C22⋊C412yes—
291C2×C4×C43C23×C411yescharacteristic
292C2×C4×C43C23×C411yescharacteristic
293C2×C4×C43C23×C411yescharacteristic
294C2×C4×C43C22×D411yescharacteristic
295C2×C4×C43C2×#4111yescharacteristic
296C2×C4×C43C2×#4111yescharacteristic
297C2×Dic43—21no—
298C2×Dic43—21no—
299C2×Dic43—21no—
300C2×Dic43—21no—
301C2×Dic43—22no—
302C2×Dic43—22no—
303C2×Dic43—22no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43C2×C22⋊C412yes—
311C2×Dic43C2×C22⋊C412yes—
312C2×Dic43C2×C22⋊C412yes—
313C2×Dic43C4×D412yes—
314C2×Dic43C4×D412yes—
315D172—216no—
316D172—22no—
317D172—22no—
318D172—22no—
319D172C2×C4214yes—
320C4×D43—216no—
321C4×D43—84no—
322C4×D43—84no—
323C4×D43—84no—
324C4×D43—84no—
325C4×D43C2×C4214yes—
326C4×D43#11714yes—
327C4×D43C4×D414yes—
328C4×D43C4×D414yes—
329C8×C43—22no—
330C8×C43—22no—
331C43⋊C8—22no—
332C43⋊C8—22no—
333#20415—431nomaximal, Sylow
334C22×C43C22×C22⋊C411yescharacteristic
335C22×C43C2×C4×D411yescharacteristic
336C22×C43C2×C4×D411yescharacteristic
337C22×C43#57611yescharacteristic
338C22×C43#57711yescharacteristic
339C22×C43#57711yescharacteristic
340C22×C43#57811yescharacteristic
341C2×D43—22no—
342C2×D43—22no—
343C2×D43—22no—
344C2×D43—22no—
345C2×D43—22no—
346C2×D43—22no—
347C2×D43—24no—
348C2×D43—42no—
349C2×D43—42no—
350C2×D43—42no—
351C2×D43—42no—
352C2×D43—42no—
353C2×D43—42no—
354C2×D43C4×C22⋊C414yes—
355C4×C43—22no—
356C4×C43—22no—
357C4×C43—24no—
358C4×C43—42no—
359C4×C43—42no—
360C4×C43—42no—
361C4×C43C22×C4211yescharacteristic
362C4×C43C2×#11711yescharacteristic
363C4×C43C2×C4×D411yescharacteristic
364C4×C43C2×C4×D411yescharacteristic
365Dic43—22no—
366Dic43—22no—
367Dic43—42no—
368Dic43—42no—
369Dic43—42no—
370Dic43C4×C22⋊C414yes—
371C2×#520—431no—
372C2×#417—431no—
373C2×#416—431no—
374C2×#405—431no—
375#2274—431no—
376#1763—431no—
377#1763—431no—
378#1762—431no—
379#1762—431no—
380C4×#103—431no—
381C4×#103D4311yescharacteristic, complemented
382C4×#102—431no—
383C4×#102—431no—
384#1736—431no—
385C2×#340—431no—
386C2×C43C2×C4×C22⋊C411yescharacteristic
387C2×C43#289711yescharacteristic
388C2×C43#289811yescharacteristic
389C2×C43#294611yescharacteristic
390C2×C43#294711yescharacteristic
391C2×C43#295111yescharacteristic
392C2×C43#295211yescharacteristic
393D43—24no—
394D43—44no—
395C22×#41—431no—
396C22×M16—431no—
397C23×C8—431no—
398#520—438no—
399#520—864no—
400C2×C4×Q8—431no—
401C2×C4×Q8C2×D4311yescharacteristic
402C2×C4×D4—431no—
403C2×C4×D4—431no—
404C2×C4×D4—861no—
405C2×C4×D4—861no—
406C2×#117—431no—
407C2×#117—431no—
408C2×#117—861no—
409C22×C4⋊C4—431no—
410C22×C4⋊C4—431no—
411C22×C4⋊C4—861no—
412#417—438no—
413#416—438no—
414C2×#103—431no—
415C2×#103—431no—
416C2×#103C2×D4311yescharacteristic
417C2×#103C2×D4311yescharacteristic
418C2×#102—431no—
419C2×#102—431no—
420C2×#102—431no—
421C2×#102—431no—
422#405—864no—
423C2×#97—431no—
424C2×#97—431no—
425C2×C4×C8—431no—
426C2×C4×C8C2×D4311yescharacteristic
427C4×C4⋊C4—431no—
428C4×C4⋊C4—431no—
429C4×C4⋊C4—431no—
430C4×C4⋊C4—861no—
431C4×C4⋊C4—861no—
432C4×C4⋊C4C2×D4311yescharacteristic
433C4×C22⋊C4—861no—
434C4×C22⋊C4—861no—
435#340—431no—
436#340—431no—
437#340—431no—
438#340—431no—
439#340—431no—
440#340—431no—
441#340C2×D4311yescharacteristic
442#340C2×D4311yescharacteristic
443C43#2041511yescharacteristic, complemented, Sylow
444C2×#41—434no—
445C2×#41—434no—
446C2×#41—434no—
447C2×#41—862no—
448C2×#41—862no—
449C2×#41—862no—
450C22×Q8C22×D4311yescharacteristic
451C22×D4—431no—
452C22×D4—861no—
453C23×C4—431no—
454C23×C4—861no—
455C23×C4—861no—
456C23×C4—861no—
457C23×C4—861no—
458C23×C4—861no—
459C2×M16—434no—
460C2×M16—862no—
461C2×M16—862no—
462C22×C8—431no—
463C22×C8—431no—
464C22×C8—434no—
465C22×C8—862no—
466C22×C8—862no—
467C22×C8C22×D4311yescharacteristic
468C22×C8C22×D4311yescharacteristic
469C4×Q8—22no—
470C4×Q8—434no—
471C4×Q8—862no—
472C4×Q8C4×D4314yescomplemented
473C4×D4—434no—
474C4×D4—434no—
475C4×D4—868no—
476C4×D4—862no—
477C4×D4—868no—
478C4×D4—862no—
479#117—434no—
480#117—434no—
481#117—434no—
482#117—868no—
483#117—862no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—431no—
486C2×C4⋊C4—431no—
487C2×C4⋊C4—431no—
488C2×C4⋊C4—431no—
489C2×C4⋊C4—431no—
490C2×C4⋊C4—434no—
491C2×C4⋊C4—434no—
492C2×C4⋊C4—868no—
493C2×C4⋊C4—862no—
494C2×C4⋊C4—862no—
495C2×C4⋊C4—861no—
496C2×C4⋊C4—861no—
497C2×C4⋊C4—861no—
498C2×C4⋊C4C22×D4311yescharacteristic
499C2×C4⋊C4C22×D4311yescharacteristic
500C2×C4⋊C4C22×D4311yescharacteristic
501C2×C22⋊C4—431no—
502C2×C22⋊C4—431no—
503C2×C22⋊C4—861no—
504C2×C22⋊C4—861no—
505C2×C22⋊C4—861no—
506C2×C42—21no—
507C2×C42—21no—
508C2×C42—431no—
509C2×C42—861no—
510C2×C42—861no—
511C2×C42—861no—
512C2×C42—861no—
513C2×C42—861no—
514C2×C42C22×D4311yescharacteristic
515#103—434no—
516#103—434no—
517#103C4×D4314yescomplemented
518#103C4×D4314yescomplemented
519#102—434no—
520#102—434no—
521#102—434no—
522#102—434no—
523#97—862no—
524#97—862no—
525C4×C8—22no—
526C4×C8—862no—
527#95—21no—
528#95—861no—
529#95—861no—
530#95—861no—
531C24—431no—
532C24—861no—
533#41—4316no—
534#41—868no—
535#41—868no—
536#41—868no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8C2×C4×D4312yes—
541C2×Q8C2×C4×D4312yes—
542C2×Q8C2×C4×D4312yes—
543C2×D4—432no—
544C2×D4—432no—
545C2×D4—432no—
546C2×D4—864no—
547C2×D4—864no—
548C2×D4—864no—
549C2×D4—861no—
550C2×D4—861no—
551C2×D4—861no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—431no—
557C22×C4—432no—
558C22×C4—432no—
559C22×C4—432no—
560C22×C4—432no—
561C22×C4—432no—
562C22×C4—432no—
563C22×C4—431no—
564C22×C4—431no—
565C22×C4—864no—
566C22×C4—864no—
567C22×C4—864no—
568C22×C4—864no—
569C22×C4—864no—
570C22×C4—864no—
571C22×C4—861no—
572C22×C4—861no—
573C22×C4—861no—
574C22×C4—864no—
575C22×C4—3441no—
576C22×C4—3441no—
577C22×C4—3441no—
578C22×C4—3441no—
579C22×C4—3441no—
580C22×C4—3441no—
581C22×C4—3441no—
582C22×C4—3441no—
583C22×C4D4×D4311yescharacteristic
584C22×C4D4×D4311yescharacteristic
585C22×C4C23×D4311yescharacteristic
586M16—868no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—432no—
592C2×C8—432no—
593C2×C8—868no—
594C2×C8—861no—
595C2×C8—861no—
596C2×C8—861no—
597C2×C8—861no—
598C2×C8C2×C4×D4312yes—
599C2×C8C2×C4×D4312yes—
600C4⋊C4—24no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—434no—
605C4⋊C4—434no—
606C4⋊C4—432no—
607C4⋊C4—432no—
608C4⋊C4—432no—
609C4⋊C4—864no—
610C4⋊C4—864no—
611C4⋊C4—864no—
612C4⋊C4—861no—
613C4⋊C4—861no—
614C4⋊C4—861no—
615C4⋊C4C2×C4×D4312yes—
616C4⋊C4C2×C4×D4312yes—
617C4⋊C4C2×C4×D4312yes—
618C22⋊C4—434no—
619C22⋊C4—434no—
620C22⋊C4—864no—
621C22⋊C4—864no—
622C22⋊C4—864no—
623C42—24no—
624C42—81no—
625C42—432no—
626C42—432no—
627C42—864no—
628C42—864no—
629C42—3441no—
630C42—3441no—
631C42—3441no—
632C42C2×C4×D4312yes—
633C42D4×D4312yes—
634C23—432no—
635C23—432no—
636C23—432no—
637C23—861no—
638C23—861no—
639C23—861no—
640C23—861no—
641C23—862no—
642C23—862no—
643C23—862no—
644C23—1721no—
645C23—1721no—
646C23—1721no—
647C23—1721no—
648C23C2×D4×D4311yescharacteristic
649Q8—22no—
650Q8—22no—
651Q8—22no—
652Q8C42×D4314yes—
653D4—434no—
654D4—8616no—
655D4—862no—
656D4—862no—
657D4—862no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—432no—
675C2×C4—432no—
676C2×C4—432no—
677C2×C4—434no—
678C2×C4—434no—
679C2×C4—434no—
680C2×C4—434no—
681C2×C4—432no—
682C2×C4—432no—
683C2×C4—8616no—
684C2×C4—861no—
685C2×C4—861no—
686C2×C4—861no—
687C2×C4—861no—
688C2×C4—862no—
689C2×C4—862no—
690C2×C4—862no—
691C2×C4—3444no—
692C2×C4—3444no—
693C2×C4—3444no—
694C2×C4—3444no—
695C2×C4—1721no—
696C2×C4—1721no—
697C2×C4—1721no—
698C2×C4—1721no—
699C2×C4—1721no—
700C2×C4—1721no—
701C2×C4C22⋊C4×D4312yes—
702C2×C4C22⋊C4×D4312yes—
703C2×C4C22×C4×D4311yescharacteristic
704C2×C4C22×C4×D4311yescharacteristic
705C2×C4C22×C4×D4311yescharacteristic
706C2×C4C2×D4×D4311yescharacteristic
707C2×C4#41×D4311yescharacteristic
708C2×C4#41×D4311yescharacteristic
709C8—22no—
710C8—22no—
711C8—862no—
712C8—862no—
713C22—434no—
714C22—862no—
715C22—862no—
716C22—862no—
717C22—862no—
718C22—862no—
719C22—862no—
720C22—864no—
721C22—1722no—
722C22—1722no—
723C22—1722no—
724C22—1722no—
725C22—1722no—
726C22—1722no—
727C22C2×C22⋊C4×D4311yescharacteristic
728C22C4×D4×D4311yescharacteristic
729C22C4×D4×D4311yescharacteristic
730C22#1458370111yescharacteristic
731C22#1458370511yescharacteristic
732C22#1458370611yescharacteristic
733C22#1458371211yescharacteristic
734C4—24no—
735C4—22no—
736C4—22no—
737C4—42no—
738C4—42no—
739C4—42no—
740C4—434no—
741C4—862no—
742C4—862no—
743C4—1722no—
744C4—1722no—
745C4—1722no—
746C4C2×C42×D4311yescharacteristic
747C4#117×D4311yescharacteristic
748C4C4×D4×D4311yescharacteristic
749C4C4×D4×D4311yescharacteristic
750C2—864no—
751C2—1724no—
752C2C4×C22⋊C4×D4311yescharacteristic
753C2#1914311711yescharacteristic
754C2#1914312311yescharacteristic
755C2#1914342211yescharacteristic
756C2#1914343311yescharacteristic
757C2#1914347011yescharacteristic
758C2#1914347311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutatorC4×C43C22×C42
FrattiniC22×C4C23×D43
FittingC4×#103×C43C2
socleC23×C43C22×D4
prime radicalC22×#10621902C22
cosocleC22×C4×C43C24
hypercenterC4×#103D43
hypocenterC43#20415
LCSG ▷ C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C42 ◁ C4×#103

Complements

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

NH ≅ G/Ntype
4. C2×#14582853C2semidirect
5. #19136949C2semidirect
6. #19134427C2semidirect
7. #19134425C2semidirect
8. #19134423C2semidirect
9. #19134419C2semidirect
10. #103×Dic43C2semidirect
11. C4×#13063247C2semidirect
12. #19134409C2semidirect
13. #19134313C2semidirect
14. #340×D43C2semidirect
15. C4×#103×C43C2semidirect
20. #14583381C4semidirect
32. #14582899C4semidirect
33. #14582894C4semidirect
80. C2×#10621872C2×C4semidirect
85. C2×C8×D43C2×C4semidirect
87. Q8×Dic43C2×C4semidirect
90. C4×D172C2×C4semidirect
93. #13063287C2×C4semidirect
95. #13063283C2×C4semidirect
111. C4⋊C4×D43C2×C4semidirect
123. #13063249C2×C4semidirect
124. #13063249C2×C4semidirect
125. #13063247C2×C4semidirect
126. #13063247C2×C4semidirect
127. #13063245C2×C4semidirect
128. #13063245C2×C4semidirect
139. C4×Q8×C43C2×C4semidirect
147. #103×C43C2×C4semidirect
148. #103×C43C2×C4semidirect
175. #10621902C42semidirect
381. C4×#103D43semidirect
443. C43#20415semidirect
472. C4×Q8C4×D43semidirect
517. #103C4×D43semidirect
518. #103C4×D43semidirect

Maximal subgroups

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

subgroupindex
C2×#145833812
C2×#145828992
C2×#145828942
C2×#145828532
#191369492
#191344272
#191344252
#191344232
#191344192
#103×Dic432
C4×#130632472
#191344092
#191343132
#340×D432
C4×#103×C432
#2041543