Finite Group Databasebeta

← #30617023

Subgroups — #30617023

Order 15616.

1120 conjugacy classes of subgroups.

The subgroup lattice has 932 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840803C211yesmaximal, characteristic, complemented
2C2×D8×#6923C211yesmaximal, characteristic, complemented
3#21462311C211yesmaximal, characteristic, complemented
4#21462258C211yesmaximal, characteristic, complemented
5#21461986C211yesmaximal, characteristic, complemented
6#21461932C211yesmaximal, characteristic, complemented
7#21461897C211yesmaximal, characteristic, complemented
8#21461896C211yesmaximal, characteristic, complemented
9#21461814C211yesmaximal, characteristic, complemented
10#21461814C211yesmaximal, characteristic, complemented
11#21461689C211yesmaximal, characteristic, complemented
12#21461608C211yesmaximal, characteristic, complemented
13#21461590C211yesmaximal, characteristic, complemented
14#102×#6923C211yesmaximal, characteristic, complemented
15#459×D61C211yesmaximal, characteristic
16C2×D4×#6923C2211yescharacteristic
17C2×D4×#6923C2211yescharacteristic
18C2×D4×#6923C2211yescharacteristic
19C2×D4×#6923C2211yescharacteristic
20#16840803—24no—
21D8×#6923—24no—
22C2×#14519846C2211yescharacteristic
23C2×#14519845C2211yescharacteristic
24D61⋊(C4⋊C8)C2211yescharacteristic
25C2×#14519839C2211yescharacteristic
26C2×#14519839C2211yescharacteristic
27C2×#14519839C2211yescharacteristic
28C2×#14519839C2211yescharacteristic
29C2×#14519839C2211yescharacteristic
30C2×#14519839C2211yescharacteristic
31C2×#14519831C2211yescharacteristic
32C2×C8×#6923C2211yescharacteristic
33#16840714C2211yescharacteristic
34#16840714C2211yescharacteristic
35#16840710—21no—
36#16840710—21no—
37#16840710—21no—
38#16840710—21no—
39#16840706C2211yescharacteristic
40C4⋊C4×#6923C2211yescharacteristic
41C4⋊C4×#6923C2211yescharacteristic
42C4×C4⋊#6923C2211yescharacteristic
43C22⋊C4×#6923—21no—
44C22⋊C4×#6923—21no—
45C4×C22⋊#6923—21no—
46#16840698C2211yescharacteristic
47C2×(C2×#6923)⋊C4—21no—
48#16840636C2211yescharacteristic
49#16840636C2211yescharacteristic
50#16840635C2211yescharacteristic
51#16840635C2211yescharacteristic
52(C2×#6923)⋊C8C2211yescharacteristic
53(C2×#6923)⋊C8C2211yescharacteristic
54C2×D8×D61C2211yescharacteristic
55C2×D8×D61C2211yescharacteristic
56#127×D61C2211yescharacteristic
57C4×D4×D61C2211yescharacteristic
58#16839958C411yescharacteristic, complemented
59#16839957C411yescharacteristic, complemented
60#16839956C411yescharacteristic, complemented
61#16839956C411yescharacteristic, complemented
62#16839955C411yescharacteristic, complemented
63#16839955C411yescharacteristic, complemented
64#16839954C411yescharacteristic, complemented
65C4⋊C8×D61C2211yescharacteristic
66#102×D61C2211yescharacteristic
67#102×D61C2211yescharacteristic
68C61×#459C411yescharacteristic, complemented
69C23×#6923—21no—
70C23×#6923—21no—
71C23×#6923—21no—
72C23×#6923—21no—
73C2×D61⋊C8C2311yescharacteristic
74C2×D61⋊C8C2311yescharacteristic
75D4×#6923—22no—
76D4×#6923—22no—
77D4×#6923—22no—
78D4×#6923—22no—
79D4×#6923—22no—
80D4×#6923—22no—
81D4×#6923—22no—
82D4×#6923D414yescomplemented
83C2×C4⋊#6923C2311yescharacteristic
84C2×C4⋊#6923C2311yescharacteristic
85C2×C4⋊#6923C2311yescharacteristic
86C2×C4⋊#6923C2311yescharacteristic
87C2×C22⋊#6923—21no—
88C2×C22⋊#6923—21no—
89C2×C22⋊#6923—21no—
90C2×C22⋊#6923—21no—
91C2×C22⋊#6923—21no—
92C2×C22⋊#6923—21no—
93C2×C22⋊#6923—21no—
94C2×C22⋊#6923—21no—
95C2×C4×#6923—21no—
96C2×C4×#6923—21no—
97C2×C4×#6923—21no—
98C2×C4×#6923C2311yescharacteristic
99C2×C4×#6923C2311yescharacteristic
100#14519846—22no—
101#14519845—22no—
102#14519844—21no—
103C4⋊#92420—21no—
104#14519839—22no—
105#14519839—22no—
106#14519839—22no—
107#14519839—22no—
108#14519839—22no—
109#14519839—22no—
110#14519831—22no—
111C8×#6923—22no—
112(C2×#6923)⋊C4—21no—
113(C2×#6923)⋊C4—21no—
114(C2×#6923)⋊C4—21no—
115(C2×#6923)⋊C4—21no—
116(C2×#6923)⋊C4—21no—
117(C2×#6923)⋊C4D411yescharacteristic
118(C2×#6923)⋊C4D411yescharacteristic
119(C2×#6923)⋊C4D411yescharacteristic
120(C2×#6923)⋊C4D411yescharacteristic
121C2×D4×D61—21no—
122C2×D4×D61—21no—
123C2×D4×D61C2311yescharacteristic
124C2×D4×D61C2311yescharacteristic
125C2×D4×D61C2311yescharacteristic
126C22×C4×D61—21no—
127C2×D488C2×C411yescharacteristic, complemented
128C2×D488C2×C411yescharacteristic, complemented
129C2×#11758199C2×C411yescharacteristic, complemented
130C2×#11758199C2×C411yescharacteristic, complemented
131C2×#11758199C2×C411yescharacteristic, complemented
132C2×#11758199C2×C411yescharacteristic, complemented
133D8×D61—22no—
134D8×D61—22no—
135D8×D61—22no—
136D8×D61—22no—
137C2×C8×D61C2311yescharacteristic
138C2×C8×D61C2311yescharacteristic
139#14519774C2×C411yescharacteristic, complemented
140#14519773—21no—
141#14519773—21no—
142#14519773C2×C411yescharacteristic, complemented
143#14519773C2×C411yescharacteristic, complemented
144C4×D244C2×C411yescharacteristic, complemented
145D4×Dic61C2×C411yescharacteristic, complemented
146#14519739C2×C411yescharacteristic, complemented
147C4×C22⋊D61—21no—
148#14519737—21no—
149C4⋊C4×D61C2311yescharacteristic
150C22⋊C4×D61—21no—
151C42×D61C2311yescharacteristic
152C4⋊#92418C2×C411yescharacteristic, complemented
153#14519706C2×C411yescharacteristic, complemented
154#14519706C2×C411yescharacteristic, complemented
155#14519699C2×C411yescharacteristic, complemented
156#14519699C2×C411yescharacteristic, complemented
157#14519698C2×C411yescharacteristic, complemented
158#14519698C2×C411yescharacteristic, complemented
159#14519697C2×C411yescharacteristic, complemented
160#14519697C2×C411yescharacteristic, complemented
161C2×D8×C61C2×C411yescharacteristic, complemented
162C2×D8×C61C2×C411yescharacteristic, complemented
163#127×C61C2×C411yescharacteristic, complemented
164C4×D4×C61C2×C411yescharacteristic, complemented
165C4⋊C8×C61C2×C411yescharacteristic, complemented
166#102×C61C2×C411yescharacteristic, complemented
167#102×C61C2×C411yescharacteristic, complemented
168C23×D61—21no—
169C23×D61—21no—
170C23×D61—21no—
171C22×#6923—21no—
172C22×#6923—21no—
173C22×#6923—24no—
174C22×#6923—24no—
175C22×#6923—21no—
176C22×#6923—21no—
177C22×#6923—42no—
178C22×#6923—42no—
179C22×#6923—81no—
180C22×#6923—81no—
181C22×#6923—81no—
182C22×#6923—81no—
183C22×#6923—81no—
184C22×#6923—81no—
185C22×#6923—81no—
186C22×#6923—81no—
187C22×#6923C2×D411yescharacteristic
188C22×#6923C2×D411yescharacteristic
189C22×#6923C2×D411yescharacteristic
190C22×#6923C2×D411yescharacteristic
191C2×D4×C61—21no—
192C2×D4×C61—21no—
193C2×D4×C61C22×C411yescharacteristic
194C2×D4×C61C22×C411yescharacteristic
195C2×D4×C61C22×C411yescharacteristic
196C22×C4×C61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C2×C22⋊D61—21no—
201C2×C22⋊D61—21no—
202C2×C22⋊D61—21no—
203C2×C22⋊D61—21no—
204C22×Dic61—21no—
205D4×D61—21no—
206D4×D61—21no—
207D4×D61—21no—
208D4×D61—21no—
209D4×D61—21no—
210D4×D61—21no—
211D4×D61—21no—
212D4×D61—21no—
213D4×D61—21no—
214D4×D61—21no—
215D4×D61—81no—
216D4×D61—81no—
217D4×D61—81no—
218D4×D61—81no—
219D4×D61C2×D412yes—
220D4×D61#4112yes—
221C2×D244—21no—
222C2×D244—21no—
223C2×D244C22×C411yescharacteristic
224C2×D244C22×C411yescharacteristic
225C2×D244C22×C411yescharacteristic
226C2×C4×D61—21no—
227C2×C4×D61—21no—
228C2×C4×D61—21no—
229C2×C4×D61—81no—
230C2×C4×D61—81no—
231C2×C4×D61C2×D411yescharacteristic
232C2×C4×D61C2×D411yescharacteristic
233C2×C4×D61C2411yescharacteristic
234C22⋊#6923—24no—
235C22⋊#6923—24no—
236C22⋊#6923—42no—
237C22⋊#6923—42no—
238C22⋊#6923—81no—
239C22⋊#6923—81no—
240C22⋊#6923—81no—
241C22⋊#6923—81no—
242C2×#92420—21no—
243C2×#92420—21no—
244C4⋊#6923—21no—
245C4⋊#6923—21no—
246C4⋊#6923—21no—
247C4⋊#6923—21no—
248C4⋊#6923—21no—
249C4⋊#6923—21no—
250C4⋊#6923C2×D412yes—
251C4⋊#6923#4112yes—
252C4×#6923—21no—
253C4×#6923—21no—
254C4×#6923—81no—
255C4×#6923—81no—
256C4×#6923—81no—
257C4×#6923C2×D412yes—
258C4×#6923#4112yes—
259D61⋊C8—21no—
260D61⋊C8—21no—
261D61⋊C8—21no—
262D61⋊C8—21no—
263D8×C61—22no—
264D8×C61—22no—
265C2×C8×C61C22×C411yescharacteristic
266C2×C8×C61C22×C411yescharacteristic
267C4⋊C4×C61C22×C411yescharacteristic
268C22⋊C4×C61—21no—
269C42×C61C22×C411yescharacteristic
270C22⋊Dic61—21no—
271#11758199—22no—
272#11758199—22no—
273#11758199—22no—
274#11758199—22no—
275#11758198—21no—
276#11758198—21no—
277C4⋊Dic61C22×C411yescharacteristic
278#11758196—21no—
279C4×Dic61C22×C411yescharacteristic
280C4×Dic61#4111yescharacteristic
281C4×Dic61#4111yescharacteristic
282C2×#92418C22×C411yescharacteristic
283C2×#92418C22×C411yescharacteristic
284D488—22no—
285D488—22no—
286C8×D61—21no—
287C8×D61—21no—
288C8×D61—21no—
289C8×D61—21no—
290C23×C61—21no—
291C23×C61—21no—
292C23×C61—21no—
293C22×D61—21no—
294C22×D61—22no—
295C22×D61—22no—
296C22×D61—21no—
297C22×D61—21no—
298C22×D61—41no—
299C22×D61—41no—
300C22×D61—41no—
301C22×D61—41no—
302C22×D61—41no—
303C22×D61—41no—
304C22×D61—41no—
305C22×D61—41no—
306C22×D61—41no—
307C22×D61—41no—
308C22×D61—41no—
309C22×D61—41no—
310C22×D61—41no—
311C22×D61—41no—
312C22×D61—41no—
313C22×D61—41no—
314C22×D61C22×D411yescharacteristic
315C2×#6923—21no—
316C2×#6923—21no—
317C2×#6923—21no—
318C2×#6923—21no—
319C2×#6923—22no—
320C2×#6923—21no—
321C2×#6923—21no—
322C2×#6923—22no—
323C2×#6923—21no—
324C2×#6923—21no—
325C2×#6923—21no—
326C2×#6923—21no—
327C2×#6923—41no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333C2×#6923—41no—
334C2×#6923—41no—
335C2×#6923—41no—
336C2×#6923—41no—
337C2×#6923—84no—
338C2×#6923—84no—
339C2×#6923—84no—
340C2×#6923—84no—
341C2×#6923#12112yes—
342C2×#6923#12112yes—
343D4×C61—21no—
344D4×C61—21no—
345D4×C61—21no—
346D4×C61—21no—
347D4×C61—21no—
348D4×C61—81no—
349D4×C61—81no—
350D4×C61C4×D412yes—
351C2×C4×C61—21no—
352C2×C4×C61—81no—
353C2×C4×C61C4×D411yescharacteristic
354C2×C4×C61C4×D411yescharacteristic
355C2×C4×C61C23×C411yescharacteristic
356C22⋊D61—22no—
357C22⋊D61—22no—
358C22⋊D61—41no—
359C22⋊D61—41no—
360C22⋊D61—41no—
361C22⋊D61—41no—
362C22⋊D61—81no—
363C22⋊D61—81no—
364C22⋊D61—81no—
365C22⋊D61—81no—
366C2×Dic61—21no—
367C2×Dic61—81no—
368C2×Dic61C4×D411yescharacteristic
369C2×Dic61C4×D411yescharacteristic
370C2×Dic61C2×#4111yescharacteristic
371D244—21no—
372D244—21no—
373D244—21no—
374D244—21no—
375D244—21no—
376D244—81no—
377D244—81no—
378D244C4×D412yes—
379C4×D61—21no—
380C4×D61—21no—
381C4×D61—21no—
382C4×D61—21no—
383C4×D61—41no—
384C4×D61—41no—
385C4×D61—81no—
386C4×D61—81no—
387C4×D61C22×D411yescharacteristic
388C4×D61C2×#4111yescharacteristic
389C4×D61C2×#4111yescharacteristic
390C4×D61C2×#4111yescharacteristic
391#92420—41no—
392#92420—41no—
393C8×C61—21no—
394C8×C61—21no—
395#92418—21no—
396#92418—21no—
397#21513—611nomaximal, Sylow
398C22×C61—22no—
399C22×C61—41no—
400C22×C61—41no—
401C22×C61—41no—
402C22×C61—41no—
403C22×C61—41no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61C2×C4×D411yescharacteristic
408C2×D61—22no—
409C2×D61—41no—
410C2×D61—41no—
411C2×D61—42no—
412C2×D61—42no—
413C2×D61—42no—
414C2×D61—42no—
415C2×D61—41no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—81no—
422C2×D61—81no—
423C2×D61—81no—
424C2×D61—81no—
425C2×D61—81no—
426C2×D61—81no—
427C2×D61—81no—
428C2×D61—81no—
429C2×D61C2×#12111yescharacteristic
430C2×D61#52511yescharacteristic
431C2×D61#57611yescharacteristic
432C2×D61#57611yescharacteristic
433C2×D61#57611yescharacteristic
434C2×D61#57711yescharacteristic
435#6923—22no—
436#6923—22no—
437#6923—41no—
438#6923—41no—
439#6923—42no—
440#6923—42no—
441#6923—81no—
442#6923—81no—
443C4×C61—21no—
444C4×C61—21no—
445C4×C61—41no—
446C4×C61C2×C4×D411yescharacteristic
447C4×C61C4×#4111yescharacteristic
448Dic61—21no—
449Dic61—21no—
450Dic61—41no—
451Dic61#52911yescharacteristic
452Dic61#53211yescharacteristic
453C2×#459—611no—
454C2×#442—611no—
455C2×C4×D8—611no—
456#2328—611no—
457#2275—611no—
458#1982—611no—
459#1949—611no—
460#1926—611no—
461#1925—611no—
462#1879—611no—
463#1879—611no—
464#1804—611no—
465#1768—611no—
466#1762—611no—
467C4×#102—611no—
468C2×C61—42no—
469C2×C61—81no—
470C2×C61—81no—
471C2×C61C4×#12111yescharacteristic
472C2×C61#294611yescharacteristic
473C2×C61#294811yescharacteristic
474D61—42no—
475D61—81no—
476D61—81no—
477D61#304111yescharacteristic
478D61#304511yescharacteristic
479D61#311911yescharacteristic
480D61#312211yescharacteristic
481C22×D8—611no—
482C22×D8—611no—
483C2×#127—611no—
484C2×C4×D4—611no—
485C2×C4×D4—611no—
486C2×C4×D4—611no—
487C2×C4×D4—611no—
488C2×C4×D4—611no—
489#459—611no—
490#459—611no—
491#459—611no—
492#459—611no—
493#459—611no—
494#459—611no—
495#459—611no—
496#459#692311yescharacteristic, complemented
497#442—1224no—
498C4×D8—1224no—
499C2×#107—611no—
500C2×#106—611no—
501C2×C4⋊C8—611no—
502C2×C4⋊C8—611no—
503C2×#102—611no—
504C2×#102—611no—
505C2×#102—611no—
506C2×#102—611no—
507C2×#102—611no—
508C2×#102—611no—
509C2×#102—611no—
510C2×#102—611no—
511C2×#97—611no—
512C2×C4×C8—611no—
513#390—611no—
514#390—611no—
515#386—1221no—
516#386—1221no—
517#386—1221no—
518#386—1221no—
519#382—611no—
520C4×C4⋊C4—611no—
521C4×C4⋊C4—611no—
522C4×C4⋊C4—611no—
523C4×C22⋊C4—1221no—
524C4×C22⋊C4—1221no—
525C4×C22⋊C4—1221no—
526#376—611no—
527C2×#95—1221no—
528#340—611no—
529#340—611no—
530#340—611no—
531#340—611no—
532#336—611no—
533#336—611no—
534C61#2151311yescharacteristic, complemented, Sylow
535C22×D4—611no—
536C22×D4—611no—
537C22×D4—611no—
538C22×D4—1221no—
539C22×D4—1221no—
540C23×C4—1221no—
541C23×C4—1221no—
542C23×C4—1221no—
543C23×C4—1221no—
544C23×C4—1221no—
545C2×D8—611no—
546C2×D8—611no—
547C2×D8—611no—
548C2×D8—611no—
549C2×D8—611no—
550C2×D8—611no—
551C2×D8—1222no—
552C2×D8—1222no—
553C2×D8—1222no—
554C2×D8—1222no—
555C2×D8C2×#692311yescharacteristic, complemented
556C2×D8C2×#692311yescharacteristic, complemented
557C22×C8—611no—
558C22×C8—611no—
559C22×C8—611no—
560C22×C8—611no—
561#127—611no—
562#127—611no—
563#127—611no—
564#127—1221no—
565#127—1221no—
566#127C2×#692311yescharacteristic, complemented
567C4×D4—614no—
568C4×D4—611no—
569C4×D4—611no—
570C4×D4—611no—
571C4×D4—1221no—
572C4×D4—1221no—
573C4×D4—1222no—
574C4×D4—1222no—
575C4×D4—1222no—
576C4×D4—1222no—
577C4×D4—1222no—
578C4×D4—1222no—
579C4×D4—1222no—
580C4×D4C2×#692311yescharacteristic, complemented
581C2×C4⋊C4—611no—
582C2×C4⋊C4—611no—
583C2×C4⋊C4—611no—
584C2×C4⋊C4—611no—
585C2×C4⋊C4—611no—
586C2×C22⋊C4—1221no—
587C2×C22⋊C4—1221no—
588C2×C22⋊C4—1221no—
589C2×C22⋊C4—1221no—
590C2×C22⋊C4—1221no—
591C2×C22⋊C4—1221no—
592C2×C22⋊C4—1221no—
593C2×C22⋊C4—1221no—
594C2×C22⋊C4—1221no—
595C2×C42—611no—
596C2×C42—611no—
597C2×C42—611no—
598C2×C42—1221no—
599C2×C42—1221no—
600C2×C42—1221no—
601#107—1222no—
602#106—1222no—
603C4⋊C8—611no—
604C4⋊C8—611no—
605C4⋊C8—611no—
606C4⋊C8—1221no—
607C4⋊C8—1221no—
608C4⋊C8C2×#692311yescharacteristic, complemented
609#102—611no—
610#102—611no—
611#102—611no—
612#102—611no—
613#102—611no—
614#102—611no—
615#102—1222no—
616#102—1222no—
617#102—1222no—
618#102—1222no—
619#102—1222no—
620#102—1222no—
621#102C2×#692311yescharacteristic, complemented
622#102C2×#692311yescharacteristic, complemented
623#97—1222no—
624C4×C8—1222no—
625#95—611no—
626#95—611no—
627#95—611no—
628#95—611no—
629#95—1221no—
630#95—1221no—
631#95—1221no—
632#95—1221no—
633#95—1221no—
634C24—1221no—
635C24—1221no—
636C24—1221no—
637C2×D4—21no—
638C2×D4—21no—
639C2×D4—612no—
640C2×D4—612no—
641C2×D4—611no—
642C2×D4—611no—
643C2×D4—611no—
644C2×D4—1221no—
645C2×D4—1221no—
646C2×D4—1221no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—1221no—
653C2×D4—1221no—
654C2×D4—1221no—
655C2×D4—1221no—
656C2×D4—1221no—
657C2×D4—1221no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1221no—
661C2×D4—1221no—
662C2×D4—1221no—
663C2×D4—4881no—
664C2×D4—4881no—
665C2×D4—4881no—
666C2×D4—4881no—
667C2×D4C22×#692311yescharacteristic
668C2×D4C22×#692311yescharacteristic
669C2×D4C22×#692311yescharacteristic
670C22×C4—21no—
671C22×C4—611no—
672C22×C4—611no—
673C22×C4—611no—
674C22×C4—611no—
675C22×C4—611no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—1221no—
679C22×C4—1221no—
680C22×C4—1221no—
681C22×C4—1224no—
682C22×C4—1224no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—4881no—
689C22×C4—4881no—
690C22×C4—4881no—
691C22×C4—4881no—
692C22×C4—4881no—
693C22×C4—4881no—
694C22×C4—4881no—
695C22×C4—4881no—
696C22×C4—4881no—
697C22×C4—4881no—
698C22×C4—2442no—
699C22×C4—2442no—
700D8—22no—
701D8—22no—
702D8—1222no—
703D8—1222no—
704D8—1222no—
705D8—1222no—
706D8—1222no—
707D8—1222no—
708C2×C8—611no—
709C2×C8—611no—
710C2×C8—1221no—
711C2×C8—1221no—
712C2×C8—1221no—
713C2×C8—1221no—
714C2×C8—1221no—
715C2×C8—1221no—
716C2×C8—1221no—
717C2×C8—1221no—
718C2×C8—1221no—
719C2×C8—1221no—
720C2×C8C22×#692311yescharacteristic
721C2×C8C22×#692311yescharacteristic
722C4⋊C4—612no—
723C4⋊C4—612no—
724C4⋊C4—611no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C4⋊C4C22×#692311yescharacteristic
733C22⋊C4—21no—
734C22⋊C4—1221no—
735C22⋊C4—1221no—
736C22⋊C4—1224no—
737C22⋊C4—1224no—
738C22⋊C4—1221no—
739C22⋊C4—4881no—
740C22⋊C4—4881no—
741C22⋊C4—4881no—
742C22⋊C4—4881no—
743C22⋊C4—2442no—
744C22⋊C4—2442no—
745C42—612no—
746C42—612no—
747C42—611no—
748C42—611no—
749C42—611no—
750C42—1221no—
751C42—1221no—
752C42—4881no—
753C42—4881no—
754C42—4881no—
755C42C22×#692311yescharacteristic
756C23—21no—
757C23—21no—
758C23—21no—
759C23—611no—
760C23—1222no—
761C23—1222no—
762C23—1221no—
763C23—1221no—
764C23—1221no—
765C23—2441no—
766C23—2441no—
767C23—2441no—
768C23—2441no—
769C23—2441no—
770C23—2441no—
771C23—2441no—
772C23—2441no—
773C23—2441no—
774C23—2441no—
775C23—2441no—
776C23—2441no—
777C23—2441no—
778C23—2441no—
779C23—2441no—
780C23—2441no—
781D4—21no—
782D4—21no—
783D4—21no—
784D4—21no—
785D4—21no—
786D4—81no—
787D4—81no—
788D4—612no—
789D4—1222no—
790D4—1222no—
791D4—1221no—
792D4—1221no—
793D4—1221no—
794D4—1221no—
795D4—1221no—
796D4—4881no—
797D4—4881no—
798D4—4881no—
799D4—4881no—
800D4—4881no—
801D4—4881no—
802D4—2441no—
803D4—2441no—
804D4—2441no—
805D4—2441no—
806D4D4×#692312yes—
807C2×C4—21no—
808C2×C4—81no—
809C2×C4—611no—
810C2×C4—611no—
811C2×C4—611no—
812C2×C4—611no—
813C2×C4—611no—
814C2×C4—612no—
815C2×C4—612no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—1221no—
819C2×C4—1221no—
820C2×C4—1221no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—1221no—
828C2×C4—1221no—
829C2×C4—1222no—
830C2×C4—1222no—
831C2×C4—1221no—
832C2×C4—1221no—
833C2×C4—1221no—
834C2×C4—1221no—
835C2×C4—4881no—
836C2×C4—4881no—
837C2×C4—4884no—
838C2×C4—4884no—
839C2×C4—4881no—
840C2×C4—4884no—
841C2×C4—4884no—
842C2×C4—2441no—
843C2×C4—2441no—
844C2×C4—2441no—
845C2×C4—2441no—
846C2×C4—2441no—
847C2×C4—2441no—
848C2×C4—2441no—
849C2×C4—2441no—
850C2×C4—2441no—
851C2×C4—2441no—
852C2×C4—2441no—
853C2×C4—2441no—
854C2×C4D4×#692311yescharacteristic
855C2×C4D4×#692311yescharacteristic
856C2×C4C23×#692311yescharacteristic
857C8—21no—
858C8—21no—
859C8—1221no—
860C8—1221no—
861C8—2441no—
862C8—2441no—
863C22—22no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—611no—
873C22—611no—
874C22—611no—
875C22—611no—
876C22—611no—
877C22—611no—
878C22—1222no—
879C22—4881no—
880C22—4881no—
881C22—4881no—
882C22—4881no—
883C22—4881no—
884C22—4881no—
885C22—4881no—
886C22—4881no—
887C22—2442no—
888C22—2442no—
889C22—2442no—
890C22—2442no—
891C22—2441no—
892C22—2441no—
893C22—2441no—
894C22—2441no—
895C22—2441no—
896C22—2441no—
897C22—2441no—
898C22—2441no—
899C22C2×D4×#692311yescharacteristic
900C4—21no—
901C4—21no—
902C4—41no—
903C4—611no—
904C4—611no—
905C4—1222no—
906C4—1222no—
907C4—1221no—
908C4—1221no—
909C4—4881no—
910C4—4881no—
911C4—2441no—
912C4—2441no—
913C4—2442no—
914C4—2442no—
915C4—2441no—
916C4C2×D4×#692311yescharacteristic
917C4#41×#692311yescharacteristic
918C2—42no—
919C2—81no—
920C2—81no—
921C2—611no—
922C2—611no—
923C2—611no—
924C2—611no—
925C2—4881no—
926C2—4881no—
927C2—2442no—
928C2#121×#692311yescharacteristic
929C2#2146257611yescharacteristic
930C2#2146257811yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#459C4
socleC22×C61C2×C4×D4
prime radical#459×D61C2
cosocleC2×C4×D61C24
hypercenter#459#6923
hypocenterC61#21513
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. C2×#16840803C2semidirect
2. C2×D8×#6923C2semidirect
3. #21462311C2semidirect
4. #21462258C2semidirect
5. #21461986C2semidirect
6. #21461932C2semidirect
7. #21461897C2semidirect
8. #21461896C2semidirect
9. #21461814C2semidirect
10. #21461814C2semidirect
11. #21461689C2semidirect
12. #21461608C2semidirect
13. #21461590C2semidirect
14. #102×#6923C2semidirect
58. #16839958C4semidirect
59. #16839957C4semidirect
60. #16839956C4semidirect
61. #16839956C4semidirect
62. #16839955C4semidirect
63. #16839955C4semidirect
64. #16839954C4semidirect
68. C61×#459C4semidirect
82. D4×#6923D4semidirect
127. C2×D488C2×C4semidirect
128. C2×D488C2×C4semidirect
129. C2×#11758199C2×C4semidirect
130. C2×#11758199C2×C4semidirect
131. C2×#11758199C2×C4semidirect
132. C2×#11758199C2×C4semidirect
139. #14519774C2×C4semidirect
142. #14519773C2×C4semidirect
143. #14519773C2×C4semidirect
144. C4×D244C2×C4semidirect
145. D4×Dic61C2×C4semidirect
146. #14519739C2×C4semidirect
152. C4⋊#92418C2×C4semidirect
153. #14519706C2×C4semidirect
154. #14519706C2×C4semidirect
155. #14519699C2×C4semidirect
156. #14519699C2×C4semidirect
157. #14519698C2×C4semidirect
158. #14519698C2×C4semidirect
159. #14519697C2×C4semidirect
160. #14519697C2×C4semidirect
161. C2×D8×C61C2×C4semidirect
162. C2×D8×C61C2×C4semidirect
163. #127×C61C2×C4semidirect
164. C4×D4×C61C2×C4semidirect
165. C4⋊C8×C61C2×C4semidirect
166. #102×C61C2×C4semidirect
167. #102×C61C2×C4semidirect
496. #459#6923semidirect
534. C61#21513semidirect
555. C2×D8C2×#6923semidirect
556. C2×D8C2×#6923semidirect
566. #127C2×#6923semidirect
580. C4×D4C2×#6923semidirect
608. C4⋊C8C2×#6923semidirect
621. #102C2×#6923semidirect
622. #102C2×#6923semidirect

Maximal subgroups

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

subgroupindex
C2×#168408032
C2×D8×#69232
#214623112
#214622582
#214619862
#214619322
#214618972
#214618962
#214618142
#214616892
#214616082
#214615902
#102×#69232
#459×D612
#2151361