Finite Group Databasebeta

← #14796170

Subgroups — #14796170

Order 2816.

956 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622665C211yesmaximal, characteristic, complemented
2C2×#10622665C211yesmaximal, characteristic, complemented
3C2×#10622625C211yesmaximal, characteristic
4C2×#10622577C211yesmaximal, characteristic, complemented
5#13072045C211yesmaximal, characteristic
6#13070008C211yesmaximal, characteristic, complemented
7#13069997C211yesmaximal, characteristic, complemented
8#13069816C211yesmaximal, characteristic, complemented
9#13069812C211yesmaximal, characteristic, complemented
10#13069476C211yesmaximal, characteristic, complemented
11#13069341C211yesmaximal, characteristic, complemented
12#13068929C211yesmaximal, characteristic, complemented
13#13068923C211yesmaximal, characteristic, complemented
14#13068647C211yesmaximal, characteristic, complemented
15C11×#2417C211yesmaximal, characteristic
16C2×C11×C22⋊Q8C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×#4326C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23C2×#66977C2211yescharacteristic
24C22×#4318C2211yescharacteristic
25C22×#4318C2211yescharacteristic
26C11×#398—21no—
27C11×#396—21no—
28C11×#391C2211yescharacteristic
29C11×#389C2211yescharacteristic
30C11×#386—21no—
31C11×#380—21no—
32C11×#380C2211yescharacteristic
33C2×#66899C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36#10622835—21no—
37#10622825C2211yescharacteristic
38C2×C22⋊(C11⋊C8)C2211yescharacteristic
39C2×C22⋊(C11⋊C8)C2211yescharacteristic
40#10622665—24no—
41#10622665—24no—
42#10622625—24no—
43#10622585—21no—
44C2×#66874C2211yescharacteristic
45C2×#66874C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47#10622577—24no—
48C2×#66872C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C2×#66871C2211yescharacteristic
52C2×#66871C2211yescharacteristic
53#10622565—21no—
54#10622558—21no—
55#10622542C2211yescharacteristic
56#10622541C2211yescharacteristic
57C2×C4⋊(C11⋊C8)C2211yescharacteristic
58C2×C4×C11⋊C8C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62#10622167C2211yescharacteristic
63C22×Q8×C11C2311yescharacteristic
64C22×D4×C11D411yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×Dic22C2311yescharacteristic
69C11×C22⋊Q8—22no—
70C11×C22⋊Q8—22no—
71C11×C22⋊Q8—22no—
72C11×C22⋊Q8—41no—
73C4×D4×C11—22no—
74C4×D4×C11—22no—
75C2×C11×C4⋊C4—22no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4—41no—
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C11×C22⋊C4D411yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×#4326—22no—
96C2×#4326—22no—
97C2×#4326—22no—
98#66979—22no—
99#66979—41no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103#66977—22no—
104#66977—22no—
105#66977—22no—
106#66977—41no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×C4×Dic11—21no—
111C2×#4318—22no—
112C2×#4318—22no—
113C2×#4318—22no—
114C2×#4318—22no—
115C2×#4318—22no—
116C2×#4318D414yes—
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120C22×C11⋊C8C2311yescharacteristic
121C11×#95—21no—
122C11×#95—21no—
123C11×#95—21no—
124C11×#95—21no—
125#66899—22no—
126#66899—22no—
127#66899—41no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C22⋊(C11⋊C8)—22no—
133C22⋊(C11⋊C8)—22no—
134#66874—22no—
135#66874—22no—
136#66874—41no—
137#66872—22no—
138#66872—22no—
139#66872D414yescomplemented
140#66871—22no—
141#66871—22no—
142C4⋊(C11⋊C8)—22no—
143C4×C11⋊C8—22no—
144#24793—111nomaximal, Sylow
145C24×C11C2×D411yescharacteristic
146C24×C11C2×D411yescharacteristic
147C2×Q8×C11—21no—
148C2×Q8×C11—21no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×D4×C11—22no—
154C2×D4×C11—22no—
155C2×D4×C11—41no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—42no—
171C22×C4×C11—42no—
172C22×C4×C11—81no—
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D412yes—
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11#4112yes—
179C22×C4×C11C2411yescharacteristic
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C11×C4⋊C4—22no—
191C11×C4⋊C4—21no—
192C11×C4⋊C4—21no—
193C11×C4⋊C4—21no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—42no—
197C11×C4⋊C4—42no—
198C11×C4⋊C4—42no—
199C11×C4⋊C4—81no—
200C11×C4⋊C4C2×D412yes—
201C11×C22⋊C4—22no—
202C11×C22⋊C4—22no—
203C11×C22⋊C4—42no—
204C11×C22⋊C4—42no—
205C11×C22⋊C4—81no—
206C42×C11—21no—
207C42×C11—21no—
208C22⋊Dic11—42no—
209C22⋊Dic11—42no—
210C22⋊Dic11—42no—
211C22⋊Dic11—42no—
212#4326—44no—
213C4⋊Dic11—21no—
214C4⋊Dic11—21no—
215C4⋊Dic11—21no—
216C4⋊Dic11—21no—
217C4⋊Dic11—21no—
218C4⋊Dic11C2×D412yes—
219Dic11⋊C4—42no—
220Dic11⋊C4—42no—
221Dic11⋊C4—42no—
222C4×Dic11—42no—
223#4318—28no—
224#4318—44no—
225C2×C11⋊C8—21no—
226C2×C11⋊C8—21no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8C2×D412yes—
234C2×C11⋊C8C2×D412yes—
235C2×C11⋊C8C2×D412yes—
236C2×C11⋊C8#4112yes—
237C2×#470—111no—
238C2×#470—111no—
239C2×#436—111no—
240C2×#428—111no—
241#2417D1111yescharacteristic
242#2415—111no—
243#2068—111no—
244#2066—111no—
245#2036—111no—
246#2035—111no—
247#1969—111no—
248#1941—111no—
249#1873—111no—
250#1872—111no—
251#1809—111no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—21no—
261C23×C11—21no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11#12112yes—
266C23×C11C22×D411yescharacteristic
267Q8×C11—41no—
268Q8×C11—41no—
269Q8×C11—41no—
270Q8×C11—41no—
271D4×C11—44no—
272C2×C4×C11—21no—
273C2×C4×C11—21no—
274C2×C4×C11—21no—
275C2×C4×C11—21no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—22no—
279C2×C4×C11—22no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—22no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—84no—
303C2×C4×C11#12112yes—
304C2×C4×C11#13712yes—
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C22×D411yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×C4×C11H(5,𝔽2)11yescharacteristic
310C2×C4×C112−1+411yescharacteristic
311C2×Dic11—22no—
312C2×Dic11—41no—
313C2×Dic11—41no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323Dic22—41no—
324Dic22—41no—
325Dic22—41no—
326Dic22—41no—
327C11⋊C8—22no—
328C11⋊C8—41no—
329C11⋊C8—41no—
330C11⋊C8#12114yes—
331C22×Q16—111no—
332C22×M16—111no—
333C22×M16—111no—
334C2×C22⋊Q8—111no—
335C2×C22⋊Q8—111no—
336C2×C22⋊Q8C2×D1111yescharacteristic
337C2×C22⋊Q8C2×D1111yescharacteristic
338C2×C4×D4C2×D1111yescharacteristic
339C2×#117—111no—
340C22×C4⋊C4C2×D1111yescharacteristic
341#470—224no—
342#470—224no—
343#436—224no—
344#428—224no—
345C2×#107—111no—
346C2×#107—111no—
347C2×#106—111no—
348C2×#106—111no—
349C2×#106—111no—
350C2×C4⋊C8—111no—
351C2×#103—111no—
352C2×#103—111no—
353C2×#103—111no—
354C2×#103—111no—
355C2×#103—111no—
356C2×#103—111no—
357C2×C22⋊C8—111no—
358C2×C22⋊C8—111no—
359C2×C4×C8—111no—
360#398—21no—
361#397—221no—
362#396—21no—
363#394—221no—
364#391—111no—
365#391C2×D1111yescharacteristic
366#389—111no—
367#389—221no—
368#389C2×D1111yescharacteristic
369#388—221no—
370#386—21no—
371#380—21no—
372#380—111no—
373#380C2×D1111yescharacteristic
374#340—111no—
375#340—111no—
376#340—111no—
377#340—111no—
378C22×C11—22no—
379C22×C11—22no—
380C22×C11—22no—
381C22×C11—41no—
382C22×C11—41no—
383C22×C11—41no—
384C22×C11—41no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—41no—
390C22×C11—41no—
391C22×C11—41no—
392C22×C11C2×#12111yescharacteristic
393C22×C11D4211yescharacteristic
394C22×C11#54711yescharacteristic
395C22×C11C2×#13711yescharacteristic
396C22×C11#57511yescharacteristic
397C22×C11#57711yescharacteristic
398C22×C11#57811yescharacteristic
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—41no—
402C4×C11—42no—
403C4×C11—41no—
404C4×C11—81no—
405C4×C11—81no—
406C4×C11—81no—
407C4×C11C2×#12111yescharacteristic
408C4×C11#53711yescharacteristic
409C4×C11#54811yescharacteristic
410C4×C11#55311yescharacteristic
411Dic11—42no—
412Dic11—81no—
413Dic11—81no—
414Dic11—81no—
415C22×Q8—111no—
416C22×Q8C22×D1111yescharacteristic
417C22×D4C22⋊D1111yescharacteristic
418C23×C4—21no—
419C23×C4C22×D1111yescharacteristic
420C23×C4C22×D1111yescharacteristic
421C2×Q16—222no—
422C2×Q16—222no—
423C2×Q16—222no—
424C2×M16—114no—
425C2×M16—222no—
426C2×M16—222no—
427C2×M16—222no—
428C2×M16—222no—
429C2×M16—222no—
430C22×C8—111no—
431C22×C8—111no—
432C22×C8—111no—
433C22×C8—111no—
434C22⋊Q8—22no—
435C22⋊Q8—22no—
436C22⋊Q8—22no—
437C22⋊Q8—41no—
438C22⋊Q8—222no—
439C22⋊Q8—222no—
440C22⋊Q8—222no—
441C22⋊Q8—441no—
442C4×D4—22no—
443C4×D4—22no—
444#117—222no—
445#117—441no—
446C2×C4⋊C4—22no—
447C2×C4⋊C4—21no—
448C2×C4⋊C4—21no—
449C2×C4⋊C4—21no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—41no—
452C2×C4⋊C4—111no—
453C2×C4⋊C4—111no—
454C2×C4⋊C4—111no—
455C2×C4⋊C4—221no—
456C2×C4⋊C4—221no—
457C2×C4⋊C4—221no—
458C2×C4⋊C4C22⋊D1111yescharacteristic
459C2×C4⋊C4C22×D1111yescharacteristic
460C2×C4⋊C4C22×D1111yescharacteristic
461C2×C4⋊C4C22×D1111yescharacteristic
462C2×C22⋊C4—21no—
463C2×C22⋊C4—21no—
464C2×C22⋊C4—21no—
465C2×C22⋊C4—221no—
466C2×C22⋊C4—221no—
467C2×C22⋊C4—221no—
468C2×C22⋊C4—221no—
469C2×C22⋊C4C22⋊D1111yescharacteristic
470C2×C22⋊C4C22⋊D1111yescharacteristic
471C2×C42—221no—
472C2×C42C22×D1111yescharacteristic
473#107—222no—
474#107—222no—
475#106—114no—
476#106—222no—
477#106—222no—
478C4⋊C8—222no—
479#103—222no—
480#103—222no—
481#103—222no—
482#103—222no—
483#103—441no—
484#103—441no—
485C22⋊C8—222no—
486C22⋊C8—222no—
487C4×C8—222no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—21no—
492#95—221no—
493#95—221no—
494#95—221no—
495#95—221no—
496C2×C11—42no—
497C2×C11—81no—
498C2×C11#241611yescharacteristic
499C2×C11#305611yescharacteristic
500C2×C11#306311yescharacteristic
501C2×C11#327511yescharacteristic
502C2×C11#327611yescharacteristic
503C2×C11#335211yescharacteristic
504C2×C11#335611yescharacteristic
505C24C2×C22⋊D1111yescharacteristic
506C24C2×C22⋊D1111yescharacteristic
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—221no—
514C2×Q8—221no—
515C2×Q8—221no—
516C2×Q8—221no—
517C2×Q8—221no—
518C2×Q8—221no—
519C2×D4—22no—
520C2×D4—22no—
521C2×D4—41no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—42no—
537C22×C4—42no—
538C22×C4—81no—
539C22×C4—221no—
540C22×C4—221no—
541C22×C4—221no—
542C22×C4—221no—
543C22×C4D4×D1112yes—
544C22×C4#434112yes—
545C22×C4C2×C22⋊D1111yescharacteristic
546C22×C4C2×C22⋊D1111yescharacteristic
547C22×C4C2×C22⋊D1111yescharacteristic
548C22×C4C2×C22⋊D1111yescharacteristic
549C22×C4C23×D1111yescharacteristic
550Q16—444no—
551M16—228no—
552M16—444no—
553C2×C8—112no—
554C2×C8—112no—
555C2×C8—112no—
556C2×C8—112no—
557C2×C8—221no—
558C2×C8—221no—
559C2×C8—221no—
560C2×C8—221no—
561C2×C8—221no—
562C2×C8—221no—
563C2×C8—221no—
564C2×C8—221no—
565C4⋊C4—22no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—42no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—81no—
575C4⋊C4—112no—
576C4⋊C4—221no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—221no—
580C4⋊C4—221no—
581C4⋊C4—442no—
582C4⋊C4—442no—
583C4⋊C4—442no—
584C4⋊C4D4×D1112yes—
585C22⋊C4—22no—
586C22⋊C4—22no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—81no—
590C22⋊C4—442no—
591C22⋊C4—442no—
592C22⋊C4—442no—
593C22⋊C4—442no—
594C42—21no—
595C42—21no—
596C42—442no—
597C11#2479311yescharacteristic, complemented, Sylow
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23#6699212yes—
612C23C22×C22⋊D1111yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—441no—
618Q8—441no—
619Q8—441no—
620Q8—441no—
621D4—44no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—22no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—84no—
653C2×C4—222no—
654C2×C4—441no—
655C2×C4—441no—
656C2×C4—441no—
657C2×C4—441no—
658C2×C4—441no—
659C2×C4—441no—
660C2×C4—441no—
661C2×C4—441no—
662C2×C4—441no—
663C2×C4—441no—
664C2×C4—441no—
665C2×C4#6699212yes—
666C2×C4#6699512yes—
667C2×C4C2×D4×D1111yescharacteristic
668C2×C4C2×D4×D1111yescharacteristic
669C2×C4C2×#434111yescharacteristic
670C2×C4#6703711yescharacteristic
671C2×C4#41×D1111yescharacteristic
672C2×C4#6704311yescharacteristic
673C8—114no—
674C8—222no—
675C8—441no—
676C8—441no—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22D4×C22⋊D1111yescharacteristic
692C22C2×#6699211yescharacteristic
693C22C2×#6699511yescharacteristic
694C22#1062335311yescharacteristic
695C22#1062335511yescharacteristic
696C22#1062336711yescharacteristic
697C22#1062336911yescharacteristic
698C4—22no—
699C4—22no—
700C4—41no—
701C4—42no—
702C4—41no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—442no—
707C4—881no—
708C4—881no—
709C4—881no—
710C4#1062312811yescharacteristic
711C4#1062312911yescharacteristic
712C4#1062313211yescharacteristic
713C4D11×#12111yescharacteristic
714C2—42no—
715C2—81no—
716C2#1307205311yescharacteristic
717C2#1307824211yescharacteristic
718C2#1307830911yescharacteristic
719C2#1308024311yescharacteristic
720C2#1308026211yescharacteristic
721C2#1308118511yescharacteristic
722C2#1308123111yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2417C2
socleC23×C11C22×D4
prime radicalC22×D4×C11D4
hypercenter#2417D11
hypocenterC11#24793
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

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

NH ≅ G/Ntype
1. C2×#10622665C2semidirect
2. C2×#10622665C2semidirect
4. C2×#10622577C2semidirect
6. #13070008C2semidirect
7. #13069997C2semidirect
8. #13069816C2semidirect
9. #13069812C2semidirect
10. #13069476C2semidirect
11. #13069341C2semidirect
12. #13068929C2semidirect
13. #13068923C2semidirect
14. #13068647C2semidirect
139. #66872D4semidirect
597. C11#24793semidirect

Maximal subgroups

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

subgroupindex
C2×#106226652
C2×#106226252
C2×#106225772
#130720452
#130700082
#130699972
#130698162
#130698122
#130694762
#130693412
#130689292
#130689232
#130686472
C11×#24172
#2479311