Finite Group Databasebeta

← #29722410

Subgroups — #29722410

Order 15616.

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×#16840018C211yesmaximal, characteristic, complemented
2C2×#16840018C211yesmaximal, characteristic, complemented
3C2×#16839840C211yesmaximal, characteristic
4C2×#16839802C211yesmaximal, characteristic, complemented
5#21449248C211yesmaximal, characteristic
6#21447211C211yesmaximal, characteristic, complemented
7#21447200C211yesmaximal, characteristic, complemented
8#21447019C211yesmaximal, characteristic, complemented
9#21447015C211yesmaximal, characteristic, complemented
10#21446679C211yesmaximal, characteristic, complemented
11#21446544C211yesmaximal, characteristic, complemented
12#21446132C211yesmaximal, characteristic, complemented
13#21446126C211yesmaximal, characteristic, complemented
14#21445850C211yesmaximal, characteristic, complemented
15C61×#2417C211yesmaximal, characteristic
16C22×#11758202C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C2×#14519756C2211yescharacteristic
20C2×#14519756C2211yescharacteristic
21C2×#14519736C2211yescharacteristic
22#16840018—24no—
23#16840018—24no—
24#16839840—24no—
25#16839802—24no—
26C2×#14519710C2211yescharacteristic
27C2×#14519710C2211yescharacteristic
28C2×#14519708C2211yescharacteristic
29C2×#14519708C2211yescharacteristic
30C2×#14519708C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×#14519701C2211yescharacteristic
33C2×#14519701C2211yescharacteristic
34C2×#14519701C2211yescharacteristic
35C2×#14519700C2211yescharacteristic
36C2×#14519700C2211yescharacteristic
37C2×#14519700C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×C4×#92418C2211yescharacteristic
41#16839690—21no—
42#16839676—21no—
43#16839668C2211yescharacteristic
44#16839660C2211yescharacteristic
45#16839657—21no—
46#16839656—21no—
47#16839622C2211yescharacteristic
48#16839524C2211yescharacteristic
49#16839524C2211yescharacteristic
50#16839524C2211yescharacteristic
51#16839524C2211yescharacteristic
52C2×C22⋊Q8×C61C2211yescharacteristic
53C2×C22⋊Q8×C61C2211yescharacteristic
54C2×C4×D4×C61C2211yescharacteristic
55C22×C4⋊C4×C61C2211yescharacteristic
56C61×#398—21no—
57C61×#396—21no—
58C61×#391C2211yescharacteristic
59C61×#389C2211yescharacteristic
60C61×#386—21no—
61C61×#380—21no—
62C61×#380C2211yescharacteristic
63C22×Dic122C2311yescharacteristic
64C2×#11758202—22no—
65C2×#11758202—22no—
66C2×#11758202—22no—
67C2×#11758194—22no—
68C2×#11758194—22no—
69C2×#11758194—22no—
70C2×#11758194—22no—
71C2×#11758194—22no—
72C2×#11758194D414yes—
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77#14519756—22no—
78#14519756—22no—
79#14519756—22no—
80#14519756—41no—
81#14519736—22no—
82#14519736—41no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×C4⋊Dic61C2311yescharacteristic
86C2×#11758196—21no—
87C2×#11758196—21no—
88C2×#11758196—21no—
89C2×C22⋊Dic61—21no—
90C2×C22⋊Dic61—21no—
91C2×C22⋊Dic61—21no—
92C2×C22⋊Dic61—21no—
93C2×C4×Dic61—21no—
94#14519710—22no—
95#14519710—22no—
96#14519708—22no—
97#14519708—22no—
98#14519708D414yescomplemented
99C4⋊#92418—22no—
100#14519701—22no—
101#14519701—22no—
102#14519701—41no—
103#14519700—22no—
104#14519700—22no—
105#14519700—41no—
106C22⋊#92418—22no—
107C22⋊#92418—22no—
108C4×#92418—22no—
109#14519684—21no—
110#14519684—21no—
111#14519684—21no—
112#14519684—21no—
113C22×Q8×C61C2311yescharacteristic
114C22×D4×C61D411yescharacteristic
115C23×C4×C61—21no—
116C23×C4×C61C2311yescharacteristic
117C23×C4×C61C2311yescharacteristic
118C22⋊Q8×C61—22no—
119C22⋊Q8×C61—22no—
120C22⋊Q8×C61—22no—
121C22⋊Q8×C61—41no—
122C4×D4×C61—22no—
123C4×D4×C61—22no—
124C2×C4⋊C4×C61—22no—
125C2×C4⋊C4×C61—21no—
126C2×C4⋊C4×C61—21no—
127C2×C4⋊C4×C61—21no—
128C2×C4⋊C4×C61—21no—
129C2×C4⋊C4×C61—41no—
130C2×C4⋊C4×C61D411yescharacteristic
131C2×C4⋊C4×C61C2311yescharacteristic
132C2×C4⋊C4×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2311yescharacteristic
134C2×C22⋊C4×C61—21no—
135C2×C22⋊C4×C61—21no—
136C2×C22⋊C4×C61—21no—
137C2×C22⋊C4×C61D411yescharacteristic
138C2×C22⋊C4×C61D411yescharacteristic
139C2×C42×C61C2311yescharacteristic
140#95×C61—21no—
141#95×C61—21no—
142#95×C61—21no—
143#95×C61—21no—
144C24×C61C2×D411yescharacteristic
145C24×C61C2×D411yescharacteristic
146C2×Q8×C61—21no—
147C2×Q8×C61—21no—
148C2×Q8×C61—21no—
149C2×Q8×C61—21no—
150C2×Q8×C61—21no—
151C2×Q8×C61—21no—
152C2×D4×C61—22no—
153C2×D4×C61—22no—
154C2×D4×C61—41no—
155C22×C4×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61—21no—
159C22×C4×C61—21no—
160C22×C4×C61—21no—
161C22×C4×C61—21no—
162C22×C4×C61—21no—
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61—21no—
166C22×C4×C61—21no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—42no—
170C22×C4×C61—42no—
171C22×C4×C61—81no—
172C22×C4×C61C2×D411yescharacteristic
173C22×C4×C61C2×D411yescharacteristic
174C22×C4×C61C2×D411yescharacteristic
175C22×C4×C61C2×D412yes—
176C22×C4×C61C2×D411yescharacteristic
177C22×C4×C61#4112yes—
178C22×C4×C61C2411yescharacteristic
179C22×Dic61—21no—
180C22×Dic61—21no—
181C22×Dic61—21no—
182C22×Dic61—21no—
183C2×Dic122—21no—
184C2×Dic122—21no—
185C2×Dic122—21no—
186C2×Dic122—21no—
187C2×Dic122—21no—
188C2×Dic122—21no—
189C4⋊C4×C61—22no—
190C4⋊C4×C61—21no—
191C4⋊C4×C61—21no—
192C4⋊C4×C61—21no—
193C4⋊C4×C61—21no—
194C4⋊C4×C61—21no—
195C4⋊C4×C61—42no—
196C4⋊C4×C61—42no—
197C4⋊C4×C61—42no—
198C4⋊C4×C61—81no—
199C4⋊C4×C61C2×D412yes—
200C22⋊C4×C61—22no—
201C22⋊C4×C61—22no—
202C22⋊C4×C61—42no—
203C22⋊C4×C61—42no—
204C22⋊C4×C61—81no—
205C42×C61—21no—
206C42×C61—21no—
207C22⋊Dic61—42no—
208C22⋊Dic61—42no—
209C22⋊Dic61—42no—
210C22⋊Dic61—42no—
211#11758202—44no—
212C4⋊Dic61—21no—
213C4⋊Dic61—21no—
214C4⋊Dic61—21no—
215C4⋊Dic61—21no—
216C4⋊Dic61—21no—
217C4⋊Dic61C2×D412yes—
218#11758196—42no—
219#11758196—42no—
220#11758196—42no—
221C4×Dic61—42no—
222#11758194—28no—
223#11758194—44no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418C2×D412yes—
233C2×#92418C2×D412yes—
234C2×#92418C2×D412yes—
235C2×#92418#4112yes—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61—21no—
244C23×C61—21no—
245C23×C61—21no—
246C23×C61—21no—
247C23×C61—21no—
248C23×C61—21no—
249C23×C61#12112yes—
250C23×C61C22×D411yescharacteristic
251Q8×C61—41no—
252Q8×C61—41no—
253Q8×C61—41no—
254Q8×C61—41no—
255D4×C61—44no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—22no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—22no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—41no—
272C2×C4×C61—41no—
273C2×C4×C61—41no—
274C2×C4×C61—41no—
275C2×C4×C61—41no—
276C2×C4×C61—41no—
277C2×C4×C61—41no—
278C2×C4×C61—41no—
279C2×C4×C61—41no—
280C2×C4×C61—41no—
281C2×C4×C61—41no—
282C2×C4×C61—41no—
283C2×C4×C61—41no—
284C2×C4×C61—41no—
285C2×C4×C61—41no—
286C2×C4×C61—84no—
287C2×C4×C61#12112yes—
288C2×C4×C61#13712yes—
289C2×C4×C61C22×D411yescharacteristic
290C2×C4×C61C22×D411yescharacteristic
291C2×C4×C61C2×#4111yescharacteristic
292C2×C4×C61C2×#4111yescharacteristic
293C2×C4×C61H(5,𝔽2)11yescharacteristic
294C2×C4×C612−1+411yescharacteristic
295C2×Dic61—22no—
296C2×Dic61—41no—
297C2×Dic61—41no—
298C2×Dic61—41no—
299C2×Dic61—41no—
300C2×Dic61—41no—
301C2×Dic61—41no—
302C2×Dic61—41no—
303C2×Dic61—41no—
304C2×Dic61—41no—
305C2×Dic61—41no—
306C2×Dic61—41no—
307Dic122—41no—
308Dic122—41no—
309Dic122—41no—
310Dic122—41no—
311#92418—22no—
312#92418—41no—
313#92418—41no—
314#92418#12114yes—
315#24793—611nomaximal, Sylow
316C22×C61—22no—
317C22×C61—22no—
318C22×C61—22no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61—41no—
323C22×C61—41no—
324C22×C61—41no—
325C22×C61—41no—
326C22×C61—41no—
327C22×C61—41no—
328C22×C61—41no—
329C22×C61—41no—
330C22×C61C2×#12111yescharacteristic
331C22×C61D4211yescharacteristic
332C22×C61#54711yescharacteristic
333C22×C61C2×#13711yescharacteristic
334C22×C61#57511yescharacteristic
335C22×C61#57711yescharacteristic
336C22×C61#57811yescharacteristic
337C4×C61—22no—
338C4×C61—22no—
339C4×C61—41no—
340C4×C61—42no—
341C4×C61—41no—
342C4×C61—81no—
343C4×C61—81no—
344C4×C61—81no—
345C4×C61C2×#12111yescharacteristic
346C4×C61#53711yescharacteristic
347C4×C61#54811yescharacteristic
348C4×C61#55311yescharacteristic
349Dic61—42no—
350Dic61—81no—
351Dic61—81no—
352Dic61—81no—
353C2×#470—611no—
354C2×#470—611no—
355C2×#436—611no—
356C2×#428—611no—
357#2417D6111yescharacteristic
358#2415—611no—
359#2068—611no—
360#2066—611no—
361#2036—611no—
362#2035—611no—
363#1969—611no—
364#1941—611no—
365#1873—611no—
366#1872—611no—
367#1809—611no—
368C2×C61—42no—
369C2×C61—81no—
370C2×C61#241611yescharacteristic
371C2×C61#305611yescharacteristic
372C2×C61#306311yescharacteristic
373C2×C61#327511yescharacteristic
374C2×C61#327611yescharacteristic
375C2×C61#335211yescharacteristic
376C2×C61#335611yescharacteristic
377C22×Q16—611no—
378C22×M16—611no—
379C22×M16—611no—
380C2×C22⋊Q8—611no—
381C2×C22⋊Q8—611no—
382C2×C22⋊Q8C2×D6111yescharacteristic
383C2×C22⋊Q8C2×D6111yescharacteristic
384C2×C4×D4C2×D6111yescharacteristic
385C2×#117—611no—
386C22×C4⋊C4C2×D6111yescharacteristic
387#470—1224no—
388#470—1224no—
389#436—1224no—
390#428—1224no—
391C2×#107—611no—
392C2×#107—611no—
393C2×#106—611no—
394C2×#106—611no—
395C2×#106—611no—
396C2×C4⋊C8—611no—
397C2×#103—611no—
398C2×#103—611no—
399C2×#103—611no—
400C2×#103—611no—
401C2×#103—611no—
402C2×#103—611no—
403C2×C22⋊C8—611no—
404C2×C22⋊C8—611no—
405C2×C4×C8—611no—
406#398—21no—
407#397—1221no—
408#396—21no—
409#394—1221no—
410#391—611no—
411#391C2×D6111yescharacteristic
412#389—611no—
413#389—1221no—
414#389C2×D6111yescharacteristic
415#388—1221no—
416#386—21no—
417#380—21no—
418#380—611no—
419#380C2×D6111yescharacteristic
420#340—611no—
421#340—611no—
422#340—611no—
423#340—611no—
424C61#2479311yescharacteristic, complemented, Sylow
425C22×Q8—611no—
426C22×Q8C22×D6111yescharacteristic
427C22×D4C22⋊D6111yescharacteristic
428C23×C4—21no—
429C23×C4C22×D6111yescharacteristic
430C23×C4C22×D6111yescharacteristic
431C2×Q16—1222no—
432C2×Q16—1222no—
433C2×Q16—1222no—
434C2×M16—614no—
435C2×M16—1222no—
436C2×M16—1222no—
437C2×M16—1222no—
438C2×M16—1222no—
439C2×M16—1222no—
440C22×C8—611no—
441C22×C8—611no—
442C22×C8—611no—
443C22×C8—611no—
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—41no—
448C22⋊Q8—1222no—
449C22⋊Q8—1222no—
450C22⋊Q8—1222no—
451C22⋊Q8—2441no—
452C4×D4—22no—
453C4×D4—22no—
454#117—1222no—
455#117—2441no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—41no—
462C2×C4⋊C4—611no—
463C2×C4⋊C4—611no—
464C2×C4⋊C4—611no—
465C2×C4⋊C4—1221no—
466C2×C4⋊C4—1221no—
467C2×C4⋊C4—1221no—
468C2×C4⋊C4C22⋊D6111yescharacteristic
469C2×C4⋊C4C22×D6111yescharacteristic
470C2×C4⋊C4C22×D6111yescharacteristic
471C2×C4⋊C4C22×D6111yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—1221no—
476C2×C22⋊C4—1221no—
477C2×C22⋊C4—1221no—
478C2×C22⋊C4—1221no—
479C2×C22⋊C4C22⋊D6111yescharacteristic
480C2×C22⋊C4C22⋊D6111yescharacteristic
481C2×C42—1221no—
482C2×C42C22×D6111yescharacteristic
483#107—1222no—
484#107—1222no—
485#106—614no—
486#106—1222no—
487#106—1222no—
488C4⋊C8—1222no—
489#103—1222no—
490#103—1222no—
491#103—1222no—
492#103—1222no—
493#103—2441no—
494#103—2441no—
495C22⋊C8—1222no—
496C22⋊C8—1222no—
497C4×C8—1222no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—1221no—
503#95—1221no—
504#95—1221no—
505#95—1221no—
506C24C2×C22⋊D6111yescharacteristic
507C24C2×C22⋊D6111yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—1221no—
515C2×Q8—1221no—
516C2×Q8—1221no—
517C2×Q8—1221no—
518C2×Q8—1221no—
519C2×Q8—1221no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
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—21no—
537C22×C4—42no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1221no—
543C22×C4—1221no—
544C22×C4D4×D6112yes—
545C22×C4#1175822412yes—
546C22×C4C2×C22⋊D6111yescharacteristic
547C22×C4C2×C22⋊D6111yescharacteristic
548C22×C4C2×C22⋊D6111yescharacteristic
549C22×C4C2×C22⋊D6111yescharacteristic
550C22×C4C23×D6111yescharacteristic
551Q16—2444no—
552M16—1228no—
553M16—2444no—
554C2×C8—612no—
555C2×C8—612no—
556C2×C8—612no—
557C2×C8—612no—
558C2×C8—1221no—
559C2×C8—1221no—
560C2×C8—1221no—
561C2×C8—1221no—
562C2×C8—1221no—
563C2×C8—1221no—
564C2×C8—1221no—
565C2×C8—1221no—
566C4⋊C4—21no—
567C4⋊C4—22no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—42no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—81no—
576C4⋊C4—612no—
577C4⋊C4—1221no—
578C4⋊C4—1221no—
579C4⋊C4—1221no—
580C4⋊C4—1221no—
581C4⋊C4—1221no—
582C4⋊C4—2442no—
583C4⋊C4—2442no—
584C4⋊C4—2442no—
585C4⋊C4D4×D6112yes—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—81no—
591C22⋊C4—2442no—
592C22⋊C4—2442no—
593C22⋊C4—2442no—
594C22⋊C4—2442no—
595C42—21no—
596C42—21no—
597C42—2442no—
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#1451974912yes—
612C23C22×C22⋊D6111yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—2441no—
618Q8—2441no—
619Q8—2441no—
620Q8—2441no—
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—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—22no—
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—1222no—
654C2×C4—2441no—
655C2×C4—2441no—
656C2×C4—2441no—
657C2×C4—2441no—
658C2×C4—2441no—
659C2×C4—2441no—
660C2×C4—2441no—
661C2×C4—2441no—
662C2×C4—2441no—
663C2×C4—2441no—
664C2×C4—2441no—
665C2×C4#1451974912yes—
666C2×C4#1451980812yes—
667C2×C4C2×D4×D6111yescharacteristic
668C2×C4C2×D4×D6111yescharacteristic
669C2×C4#41×D6111yescharacteristic
670C2×C4C2×#1175822411yescharacteristic
671C2×C4#1451982211yescharacteristic
672C2×C4#1451982411yescharacteristic
673C8—614no—
674C8—1222no—
675C8—2441no—
676C8—2441no—
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—
691C22C2×#1451974911yescharacteristic
692C22D4×C22⋊D6111yescharacteristic
693C22#1684041111yescharacteristic
694C22C2×#1451980811yescharacteristic
695C22#1684056011yescharacteristic
696C22#1684057311yescharacteristic
697C22#1684057711yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—41no—
702C4—41no—
703C4—81no—
704C4—81no—
705C4—81no—
706C4—4881no—
707C4—4881no—
708C4—4881no—
709C4—2442no—
710C4#121×D6111yescharacteristic
711C4#1684033911yescharacteristic
712C4#1684041811yescharacteristic
713C4#1684045511yescharacteristic
714C2—42no—
715C2—81no—
716C2#2144925611yescharacteristic
717C2#2145544511yescharacteristic
718C2#2145551211yescharacteristic
719C2#2145744611yescharacteristic
720C2#2145746511yescharacteristic
721C2#2145838811yescharacteristic
722C2#2145843411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D61
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#2417C2
socleC23×C61C22×D4
prime radicalC22×D4×C61D4
hypercenter#2417D61
hypocenterC61#24793
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ #2417

Complements

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

NH ≅ G/Ntype
1. C2×#16840018C2semidirect
2. C2×#16840018C2semidirect
4. C2×#16839802C2semidirect
6. #21447211C2semidirect
7. #21447200C2semidirect
8. #21447019C2semidirect
9. #21447015C2semidirect
10. #21446679C2semidirect
11. #21446544C2semidirect
12. #21446132C2semidirect
13. #21446126C2semidirect
14. #21445850C2semidirect
98. #14519708D4semidirect
424. C61#24793semidirect

Maximal subgroups

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

subgroupindex
C2×#168400182
C2×#168398402
C2×#168398022
#214492482
#214472112
#214472002
#214470192
#214470152
#214466792
#214465442
#214461322
#214461262
#214458502
C61×#24172
#2479361