Finite Group Databasebeta

← #25130765

Subgroups — #25130765

Order 11008.

1090 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583203C211yesmaximal, characteristic, complemented
2C2×#14583004C211yesmaximal, characteristic, complemented
3#19139517C211yesmaximal, characteristic
4#19135795C211yesmaximal, characteristic, complemented
5#19135788C211yesmaximal, characteristic, complemented
6#19135603C211yesmaximal, characteristic, complemented
7#19135603C211yesmaximal, characteristic, complemented
8#19135565C211yesmaximal, characteristic, complemented
9#19135394C211yesmaximal, characteristic
10#19134907C211yesmaximal, characteristic, complemented
11#19134902C211yesmaximal, characteristic, complemented
12#19134794C211yesmaximal, characteristic, complemented
13#19134788C211yesmaximal, characteristic, complemented
14#19134600C211yesmaximal, characteristic, complemented
15C2×C43×#552C211yesmaximal, characteristic
16C22×#10621885C2211yescharacteristic
17C2×#13063304C2211yescharacteristic
18C2×#13063304C2211yescharacteristic
19C2×C4×Dic86C2211yescharacteristic
20#14583203—24no—
21#14583004—24no—
22C2×#13063258C2211yescharacteristic
23C2×#13063256C2211yescharacteristic
24C2×#13063256C2211yescharacteristic
25C2×C4⋊(C43⋊C8)C2211yescharacteristic
26C2×#13063249C2211yescharacteristic
27C2×#13063249C2211yescharacteristic
28C2×#13063249C2211yescharacteristic
29C2×#13063248C2211yescharacteristic
30C2×#13063248C2211yescharacteristic
31C2×#13063248C2211yescharacteristic
32C2×C22⋊(C43⋊C8)C2211yescharacteristic
33C2×C22⋊(C43⋊C8)C2211yescharacteristic
34C2×C22⋊(C43⋊C8)C2211yescharacteristic
35C2×C22⋊(C43⋊C8)C2211yescharacteristic
36C2×#13063236C2211yescharacteristic
37#14582822—21no—
38#14582822—21no—
39#14582802—21no—
40#14582795—21no—
41#14582769C2211yescharacteristic
42#14582759C2211yescharacteristic
43#14582759C2211yescharacteristic
44#14582661C2211yescharacteristic
45#14582661C2211yescharacteristic
46#14582661C2211yescharacteristic
47#14582661C2211yescharacteristic
48#14582661C2211yescharacteristic
49#14582661C2211yescharacteristic
50C43×#552—24no—
51C43×#552—24no—
52C2×#126×C43—21no—
53C2×#125×C43—21no—
54C2×#125×C43C2211yescharacteristic
55C2×#123×C43—21no—
56C2×C22⋊Q8×C43C2211yescharacteristic
57C2×C22⋊Q8×C43C2211yescharacteristic
58C2×C4×Q8×C43C2211yescharacteristic
59C2×C4×D4×C43C2211yescharacteristic
60C2×#117×C43—21no—
61C2×#117×C43C2211yescharacteristic
62C22×C4⋊C4×C43C2211yescharacteristic
63C22×Dic86C2311yescharacteristic
64C2×#10621885—22no—
65C2×#10621885—22no—
66C2×#10621885—22no—
67C22×C43⋊C8C2311yescharacteristic
68C22×C43⋊C8C2311yescharacteristic
69C22×C43⋊C8C2311yescharacteristic
70C22×C43⋊C8C2311yescharacteristic
71#13063304—22no—
72#13063304—22no—
73#13063304—41no—
74#13063304—41no—
75C4×Dic86—22no—
76C4×Dic86—22no—
77C2×C4⋊Dic43—21no—
78C2×C4⋊Dic43—21no—
79C2×C4⋊Dic43C2311yescharacteristic
80C2×C4⋊Dic43C2311yescharacteristic
81C2×C4⋊Dic43C2311yescharacteristic
82C2×Dic43⋊C4—21no—
83C2×Dic43⋊C4—21no—
84C2×Dic43⋊C4—21no—
85C2×C22⋊Dic43—21no—
86C2×C22⋊Dic43—21no—
87C2×C22⋊Dic43—21no—
88C2×C22⋊Dic43—21no—
89C2×C4×Dic43—21no—
90#13063258—22no—
91#13063256—22no—
92#13063256—22no—
93C4⋊(C43⋊C8)—22no—
94#13063249—22no—
95#13063249—41no—
96#13063249—41no—
97#13063248—22no—
98#13063248—22no—
99#13063248—22no—
100C22⋊(C43⋊C8)—22no—
101C22⋊(C43⋊C8)—22no—
102C22⋊(C43⋊C8)—41no—
103C22⋊(C43⋊C8)—41no—
104#13063236—22no—
105C43⋊#95—21no—
106C43⋊#95—21no—
107C22×Q8×C43C2311yescharacteristic
108C22×D4×C43D411yescharacteristic
109C23×C4×C43—21no—
110C23×C4×C43C2311yescharacteristic
111C23×C4×C43C2311yescharacteristic
112#126×C43—28no—
113#125×C43—28no—
114#125×C43—22no—
115#125×C43D414yes—
116#123×C43—28no—
117C22⋊Q8×C43—22no—
118C22⋊Q8×C43—22no—
119C22⋊Q8×C43—22no—
120C22⋊Q8×C43—22no—
121C4×Q8×C43—22no—
122C4×Q8×C43D414yes—
123C4×D4×C43—22no—
124C4×D4×C43—22no—
125#117×C43—28no—
126#117×C43—22no—
127#117×C43—22no—
128C2×C4⋊C4×C43—21no—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—21no—
131C2×C4⋊C4×C43—21no—
132C2×C4⋊C4×C43—21no—
133C2×C4⋊C4×C43—21no—
134C2×C4⋊C4×C43—22no—
135C2×C4⋊C4×C43—22no—
136C2×C4⋊C4×C43D411yescharacteristic
137C2×C4⋊C4×C43C2311yescharacteristic
138C2×C4⋊C4×C43C2311yescharacteristic
139C2×C4⋊C4×C43C2311yescharacteristic
140C2×C22⋊C4×C43—21no—
141C2×C22⋊C4×C43—21no—
142C2×C22⋊C4×C43—21no—
143C2×C22⋊C4×C43D411yescharacteristic
144C2×C22⋊C4×C43D411yescharacteristic
145C2×C42×C43—21no—
146C2×C42×C43—21no—
147C2×C42×C43C2311yescharacteristic
148C24×C43C2×D411yescharacteristic
149C24×C43C2×D411yescharacteristic
150C2×Q8×C43—21no—
151C2×Q8×C43—21no—
152C2×Q8×C43—21no—
153C2×Q8×C43—21no—
154C2×Q8×C43—21no—
155C2×Q8×C43C2×D412yes—
156C2×D4×C43—22no—
157C2×D4×C43—22no—
158C2×D4×C43—41no—
159C22×C4×C43—24no—
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×C43—21no—
169C22×C4×C43—21no—
170C22×C4×C43—21no—
171C22×C4×C43—21no—
172C22×C4×C43—21no—
173C22×C4×C43—21no—
174C22×C4×C43—21no—
175C22×C4×C43—21no—
176C22×C4×C43—42no—
177C22×C4×C43—42no—
178C22×C4×C43C2×D411yescharacteristic
179C22×C4×C43C2×D411yescharacteristic
180C22×C4×C43C2×D411yescharacteristic
181C22×C4×C43C2×D411yescharacteristic
182C22×C4×C43C2411yescharacteristic
183C22×Dic43—21no—
184C22×Dic43—21no—
185C22×Dic43—21no—
186C22×Dic43—21no—
187C2×Dic86—21no—
188C2×Dic86—21no—
189C2×Dic86—21no—
190C2×Dic86—21no—
191C2×Dic86—21no—
192C2×Dic86#4112yes—
193C4⋊C4×C43—24no—
194C4⋊C4×C43—24no—
195C4⋊C4×C43—24no—
196C4⋊C4×C43—24no—
197C4⋊C4×C43—24no—
198C4⋊C4×C43—24no—
199C4⋊C4×C43—22no—
200C4⋊C4×C43—21no—
201C4⋊C4×C43—21no—
202C4⋊C4×C43—21no—
203C4⋊C4×C43C2×D412yes—
204C4⋊C4×C43C2×D412yes—
205C4⋊C4×C43C2×D412yes—
206C22⋊C4×C43—24no—
207C22⋊C4×C43—24no—
208C22⋊C4×C43—24no—
209C22⋊C4×C43—22no—
210C22⋊C4×C43—22no—
211C42×C43—24no—
212C42×C43—24no—
213C42×C43C2×D412yes—
214C42×C43C2×D412yes—
215C22⋊Dic43—42no—
216C22⋊Dic43—42no—
217C22⋊Dic43—81no—
218C22⋊Dic43—81no—
219#10621885—28no—
220C4⋊Dic43—21no—
221C4⋊Dic43—21no—
222C4⋊Dic43—21no—
223C4⋊Dic43—21no—
224C4⋊Dic43—21no—
225C4⋊Dic43—21no—
226C4⋊Dic43—42no—
227C4⋊Dic43—81no—
228Dic43⋊C4—42no—
229Dic43⋊C4—42no—
230Dic43⋊C4—42no—
231C4×Dic43—42no—
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⋊C8—21no—
239C2×C43⋊C8—21no—
240C2×C43⋊C8—21no—
241C2×C43⋊C8—21no—
242C2×C43⋊C8—21no—
243C2×C43⋊C8#4112yes—
244C23×C43—21no—
245C23×C43—21no—
246C23×C43—21no—
247C23×C43—21no—
248C23×C43—21no—
249C23×C43—21no—
250C23×C43—21no—
251C23×C43—21no—
252C23×C43—21no—
253C23×C43—21no—
254C23×C43—21no—
255C23×C43—21no—
256C23×C43—21no—
257C23×C43#13712yes—
258C23×C43C22×D411yescharacteristic
259Q8×C43—22no—
260Q8×C43—22no—
261Q8×C43—41no—
262Q8×C43—41no—
263D4×C43—44no—
264C2×C4×C43—21no—
265C2×C4×C43—21no—
266C2×C4×C43—21no—
267C2×C4×C43—21no—
268C2×C4×C43—21no—
269C2×C4×C43—22no—
270C2×C4×C43—22no—
271C2×C4×C43—22no—
272C2×C4×C43—21no—
273C2×C4×C43—22no—
274C2×C4×C43—21no—
275C2×C4×C43—21no—
276C2×C4×C43—21no—
277C2×C4×C43—21no—
278C2×C4×C43—48no—
279C2×C4×C43—41no—
280C2×C4×C43—41no—
281C2×C4×C43—41no—
282C2×C4×C43—41no—
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×C43—41no—
290C2×C4×C43—41no—
291C2×C4×C43—41no—
292C2×C4×C43—41no—
293C2×C4×C43—41no—
294C2×C4×C43—41no—
295C2×C4×C43#12012yes—
296C2×C4×C43#12012yes—
297C2×C4×C43C22×D411yescharacteristic
298C2×C4×C43C22×D411yescharacteristic
299C2×C4×C43C2×#4111yescharacteristic
300C2×C4×C43C2×#4111yescharacteristic
301C2×C4×C43H(5,𝔽2)11yescharacteristic
302C2×C4×C432−1+411yescharacteristic
303C2×Dic43—22no—
304C2×Dic43—41no—
305C2×Dic43—41no—
306C2×Dic43—41no—
307C2×Dic43—41no—
308C2×Dic43—41no—
309C2×Dic43—41no—
310C2×Dic43—41no—
311C2×Dic43—41no—
312C2×Dic43—41no—
313C2×Dic43—41no—
314C2×Dic43—41no—
315Dic86—22no—
316Dic86—22no—
317Dic86—41no—
318Dic86—41no—
319C43⋊C8—22no—
320C43⋊C8—41no—
321C43⋊C8—41no—
322C43⋊C8—41no—
323#24139—431nomaximal, Sylow
324C22×C43—22no—
325C22×C43—22no—
326C22×C43—22no—
327C22×C43—41no—
328C22×C43—41no—
329C22×C43—41no—
330C22×C43—41no—
331C22×C43—41no—
332C22×C43—41no—
333C22×C43—41no—
334C22×C43—41no—
335C22×C43—41no—
336C22×C43—41no—
337C22×C43—41no—
338C22×C43C2×#12011yescharacteristic
339C22×C43#54611yescharacteristic
340C22×C43#54711yescharacteristic
341C22×C43C2×#13711yescharacteristic
342C22×C43#57511yescharacteristic
343C22×C43#57711yescharacteristic
344C22×C43#57811yescharacteristic
345C4×C43—22no—
346C4×C43—22no—
347C4×C43—41no—
348C4×C43—41no—
349C4×C43—42no—
350C4×C43—42no—
351C4×C43—42no—
352C4×C43—42no—
353C4×C43#52511yescharacteristic
354C4×C43#53711yescharacteristic
355C4×C43#54811yescharacteristic
356C4×C43#55011yescharacteristic
357Dic43—42no—
358Dic43—81no—
359Dic43—81no—
360Dic43—81no—
361C2×#552D4311yescharacteristic
362C2×#479—431no—
363C2×#441—431no—
364#2538—431no—
365#2036—431no—
366#2035—431no—
367#2001—431no—
368#2001—431no—
369#1992—431no—
370#1955—431no—
371#1873—431no—
372#1872—431no—
373#1854—431no—
374#1853—431no—
375#1803—431no—
376C2×C43—42no—
377C2×C43—81no—
378C2×C43#240711yescharacteristic
379C2×C43#300711yescharacteristic
380C2×C43#301311yescharacteristic
381C2×C43#331211yescharacteristic
382C2×C43#331711yescharacteristic
383C2×C43#334411yescharacteristic
384C2×C43#334911yescharacteristic
385C22×Q16—431no—
386#552—24no—
387#552—24no—
388C2×#126—21no—
389C2×#125—21no—
390C2×#125C2×D4311yescharacteristic
391C2×#123—21no—
392C2×C22⋊Q8—431no—
393C2×C22⋊Q8—431no—
394C2×C22⋊Q8C2×D4311yescharacteristic
395C2×C22⋊Q8C2×D4311yescharacteristic
396C2×C4×Q8—431no—
397C2×C4×Q8C2×D4311yescharacteristic
398C2×C4×D4C2×D4311yescharacteristic
399C2×#117—21no—
400C2×#117C2×D4311yescharacteristic
401C22×C4⋊C4C2×D4311yescharacteristic
402#479—864no—
403#441—864no—
404C2×#107—431no—
405C2×#106—431no—
406C2×#106—431no—
407C2×C4⋊C8—431no—
408C2×#103—431no—
409C2×#103—431no—
410C2×#103—431no—
411C2×#103—431no—
412C2×#103—431no—
413C2×#103—431no—
414C2×C22⋊C8—431no—
415C2×C22⋊C8—431no—
416C2×C22⋊C8—431no—
417C2×C22⋊C8—431no—
418C2×#97—431no—
419#396—861no—
420#396—861no—
421#390—861no—
422#389—861no—
423#384—431no—
424#380—431no—
425#380—431no—
426#340—431no—
427#340—431no—
428#340—431no—
429#340—431no—
430#340—431no—
431#340—431no—
432C43#2413911yescharacteristic, complemented, Sylow
433C22×Q8—431no—
434C22×Q8C22×D4311yescharacteristic
435C22×D4C22⋊D4311yescharacteristic
436C23×C4—21no—
437C23×C4C22×D4311yescharacteristic
438C23×C4C22×D4311yescharacteristic
439C2×Q16—862no—
440C2×Q16—862no—
441C2×Q16—862no—
442C22×C8—431no—
443C22×C8—431no—
444C22×C8—431no—
445C22×C8—431no—
446#126—28no—
447#125—28no—
448#125—22no—
449#125C22⋊D4314yes—
450#123—28no—
451C22⋊Q8—22no—
452C22⋊Q8—22no—
453C22⋊Q8—22no—
454C22⋊Q8—22no—
455C22⋊Q8—862no—
456C22⋊Q8—862no—
457C22⋊Q8—1721no—
458C22⋊Q8—1721no—
459C4×Q8—22no—
460C4×Q8—862no—
461C4×Q8—862no—
462C4×Q8C22⋊D4314yes—
463C4×D4—22no—
464C4×D4—22no—
465#117—28no—
466#117—22no—
467#117—22no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—22no—
475C2×C4⋊C4—22no—
476C2×C4⋊C4—431no—
477C2×C4⋊C4—431no—
478C2×C4⋊C4—431no—
479C2×C4⋊C4—861no—
480C2×C4⋊C4—861no—
481C2×C4⋊C4—861no—
482C2×C4⋊C4—861no—
483C2×C4⋊C4—861no—
484C2×C4⋊C4C22⋊D4311yescharacteristic
485C2×C4⋊C4C22×D4311yescharacteristic
486C2×C4⋊C4C22×D4311yescharacteristic
487C2×C4⋊C4C22×D4311yescharacteristic
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—861no—
492C2×C22⋊C4—861no—
493C2×C22⋊C4—861no—
494C2×C22⋊C4—861no—
495C2×C22⋊C4C22⋊D4311yescharacteristic
496C2×C22⋊C4C22⋊D4311yescharacteristic
497C2×C42—21no—
498C2×C42—21no—
499C2×C42—861no—
500C2×C42C22×D4311yescharacteristic
501#107—862no—
502#106—862no—
503#106—862no—
504C4⋊C8—862no—
505#103—862no—
506#103—862no—
507#103—862no—
508#103—862no—
509#103—1721no—
510#103—1721no—
511C22⋊C8—862no—
512C22⋊C8—862no—
513C22⋊C8—1721no—
514C22⋊C8—1721no—
515#97—862no—
516#95—861no—
517#95—861no—
518C24C2×C22⋊D4311yescharacteristic
519C24C2×C22⋊D4311yescharacteristic
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—432no—
526C2×Q8—861no—
527C2×Q8—861no—
528C2×Q8—861no—
529C2×Q8—861no—
530C2×Q8—861no—
531C2×Q8C2×C22⋊D4312yes—
532C2×D4—22no—
533C2×D4—22no—
534C2×D4—41no—
535C22×C4—24no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—42no—
553C22×C4—42no—
554C22×C4—861no—
555C22×C4—861no—
556C22×C4—861no—
557C22×C4—861no—
558C22×C4C2×C22⋊D4311yescharacteristic
559C22×C4C2×C22⋊D4311yescharacteristic
560C22×C4C2×C22⋊D4311yescharacteristic
561C22×C4C2×C22⋊D4311yescharacteristic
562C22×C4C23×D4311yescharacteristic
563Q16—868no—
564C2×C8—432no—
565C2×C8—861no—
566C2×C8—861no—
567C2×C8—861no—
568C2×C8—861no—
569C2×C8—861no—
570C2×C8—861no—
571C2×C8—861no—
572C2×C8—861no—
573C2×C8—861no—
574C2×C8—861no—
575C2×C8—861no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—24no—
581C4⋊C4—24no—
582C4⋊C4—22no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—861no—
587C4⋊C4—861no—
588C4⋊C4—861no—
589C4⋊C4—861no—
590C4⋊C4—861no—
591C4⋊C4—861no—
592C4⋊C4—3441no—
593C4⋊C4—1722no—
594C4⋊C4—1722no—
595C4⋊C4—1722no—
596C4⋊C4—1722no—
597C4⋊C4C2×C22⋊D4312yes—
598C4⋊C4C2×C22⋊D4312yes—
599C4⋊C4C2×C22⋊D4312yes—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—22no—
604C22⋊C4—22no—
605C22⋊C4—3441no—
606C22⋊C4—3441no—
607C22⋊C4—1722no—
608C22⋊C4—1722no—
609C42—24no—
610C42—24no—
611C42—1722no—
612C42C2×C22⋊D4312yes—
613C42C2×C22⋊D4312yes—
614C23—21no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—21no—
627C23#1306335512yes—
628C23C22×C22⋊D4311yescharacteristic
629Q8—22no—
630Q8—22no—
631Q8—41no—
632Q8—41no—
633Q8—862no—
634Q8—862no—
635Q8—1721no—
636Q8—1721no—
637D4—44no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—48no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—862no—
670C2×C4—1721no—
671C2×C4—1721no—
672C2×C4—1721no—
673C2×C4—1721no—
674C2×C4—1721no—
675C2×C4—1721no—
676C2×C4—1721no—
677C2×C4—1721no—
678C2×C4—1721no—
679C2×C4—1721no—
680C2×C4—1721no—
681C2×C4#1306329412yes—
682C2×C4#1306329412yes—
683C2×C4C22×C22⋊D4311yescharacteristic
684C2×C4C22×C22⋊D4311yescharacteristic
685C2×C4#41×D4311yescharacteristic
686C2×C4#41×D4311yescharacteristic
687C2×C4#1306337111yescharacteristic
688C2×C4#1306337211yescharacteristic
689C8—862no—
690C8—1721no—
691C8—1721no—
692C8—1721no—
693C22—22no—
694C22—22no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—41no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22C2×#1306329411yescharacteristic
708C22#1458353711yescharacteristic
709C22#1458354811yescharacteristic
710C22C2×#1306335511yescharacteristic
711C22#1458369711yescharacteristic
712C22#1458370711yescharacteristic
713C22#1458371411yescharacteristic
714C4—22no—
715C4—22no—
716C4—41no—
717C4—41no—
718C4—42no—
719C4—42no—
720C4—42no—
721C4—42no—
722C4—3441no—
723C4—3441no—
724C4—3441no—
725C4—1722no—
726C4#1458340611yescharacteristic
727C4#1458347711yescharacteristic
728C4#1458355611yescharacteristic
729C4#1458356811yescharacteristic
730C2—42no—
731C2—81no—
732C2#1913793411yescharacteristic
733C2#1914385511yescharacteristic
734C2#1914391011yescharacteristic
735C2#1914664011yescharacteristic
736C2#1914671511yescharacteristic
737C2#1914705011yescharacteristic
738C2#1914712511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D43
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#552C2
socleC23×C43C22×D4
prime radicalC22×D4×C43D4
hypercenterC2×#552D43
hypocenterC43#24139
LCSG ▷ C22×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#552

Complements

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

NH ≅ G/Ntype
1. C2×#14583203C2semidirect
2. C2×#14583004C2semidirect
4. #19135795C2semidirect
5. #19135788C2semidirect
6. #19135603C2semidirect
7. #19135603C2semidirect
8. #19135565C2semidirect
10. #19134907C2semidirect
11. #19134902C2semidirect
12. #19134794C2semidirect
13. #19134788C2semidirect
14. #19134600C2semidirect
432. C43#24139semidirect

Maximal subgroups

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

subgroupindex
C2×#145832032
C2×#145830042
#191395172
#191357952
#191357882
#191356032
#191355652
#191353942
#191349072
#191349022
#191347942
#191347882
#191346002
C2×C43×#5522
#2413943