Finite Group Databasebeta

← #29646287

Subgroups — #29646287

Order 15616.

1060 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840440C211yesmaximal, characteristic
2#21454855C211yesmaximal, characteristic, complemented
3#21454850C211yesmaximal, characteristic, complemented
4#21444185C211yesmaximal, characteristic, complemented
5#21444185C211yesmaximal, characteristic, complemented
6#21444181C211yesmaximal, characteristic, complemented
7#21444181C211yesmaximal, characteristic, complemented
8#21444167C211yesmaximal, characteristic, complemented
9#21444155C211yesmaximal, characteristic, complemented
10#21444152C211yesmaximal, characteristic, complemented
11#21444144C211yesmaximal, characteristic, complemented
12#21444135C211yesmaximal, characteristic, complemented
13#21444132C211yesmaximal, characteristic, complemented
14#323×D61C211yesmaximal, characteristic, complemented
15C61×#1468C211yesmaximal, characteristic, complemented
16#16840440—21no—
17#16840440—21no—
18#16840440—21no—
19#16840440—21no—
20#16840440—21no—
21#16840440—21no—
22#16840440—21no—
23#16840440—21no—
24C2×#14519770C411yescharacteristic
25C2×#14519770C2211yescharacteristic
26C2×#14519764C411yescharacteristic
27C2×#14519759C411yescharacteristic
28C2×#14519759C411yescharacteristic
29C2×#14519755C411yescharacteristic
30C2×#14519755C2211yescharacteristic
31C2×#14519745C411yescharacteristic
32C2×C4×C22⋊D61C2211yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519735C411yescharacteristic
35C2×#14519735C2211yescharacteristic
36C2×C22⋊C4×D61C411yescharacteristic
37C2×C22⋊C4×D61C2211yescharacteristic
38#16839838—21no—
39#16839837—21no—
40#16839836—21no—
41#16839833—21no—
42#16839831—21no—
43#16839830—21no—
44C8×C22⋊D61—21no—
45#16839825—21no—
46#16839816C2211yescharacteristic, complemented
47#16839816C2211yescharacteristic, complemented
48#16839812C2211yescharacteristic, complemented
49#16839812C2211yescharacteristic, complemented
50#16839726C2211yescharacteristic, complemented
51#16839724C2211yescharacteristic
52#16839724C2211yescharacteristic
53C2×C22⋊#92418C2211yescharacteristic, complemented
54C22⋊C8×D61C2211yescharacteristic
55C22⋊C8×D61C2211yescharacteristic
56#16839488C2211yescharacteristic, complemented
57#16839488C2211yescharacteristic, complemented
58#16839487C2211yescharacteristic, complemented
59#16839487C2211yescharacteristic, complemented
60#16839487C2211yescharacteristic, complemented
61#16839487C2211yescharacteristic, complemented
62#16839486C2211yescharacteristic
63#16839486C2211yescharacteristic
64#16839485C2211yescharacteristic
65#16839485C2211yescharacteristic
66#16839485C2211yescharacteristic
67#16839485C2211yescharacteristic
68C2×#123×C61C2211yescharacteristic
69C61×#407C2211yescharacteristic, complemented
70C2×C22⋊C8×C61C2211yescharacteristic, complemented
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C24×D61C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×C22⋊D61C2×C411yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic
79C22×C4×D61C2×C411yescharacteristic
80C22×C4×D61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2311yescharacteristic
83C2×#11758194—21no—
84C2×#11758189—21no—
85C2×#11758189—21no—
86C22×#92418—21no—
87C2×C8×D61—21no—
88C2×C8×D61—21no—
89#14519770—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519770—21no—
94#14519770—21no—
95#14519770—21no—
96#14519770—21no—
97#14519764—21no—
98#14519764—21no—
99#14519764—21no—
100#14519764—21no—
101#14519759—21no—
102#14519759—21no—
103#14519759—21no—
104#14519759—21no—
105#14519759—21no—
106#14519759—21no—
107#14519759—21no—
108#14519759—21no—
109#14519755—21no—
110#14519755—21no—
111#14519755—21no—
112#14519755—21no—
113#14519755—21no—
114#14519755—21no—
115#14519755—21no—
116#14519755—21no—
117#14519745—21no—
118#14519745—21no—
119#14519745—21no—
120#14519745—21no—
121C4×C22⋊D61—21no—
122C4×C22⋊D61—21no—
123C4×C22⋊D61—21no—
124C4×C22⋊D61—21no—
125C4×C22⋊D61D411yescharacteristic
126C4×C22⋊D61D411yescharacteristic
127C4×C22⋊D61D411yescharacteristic
128C4×C22⋊D61D411yescharacteristic
129C4×C22⋊D61D411yescharacteristic
130C4×C22⋊D61D411yescharacteristic
131C4×C22⋊D61D411yescharacteristic
132C4×C22⋊D61D411yescharacteristic
133#14519735—21no—
134#14519735—21no—
135#14519735—21no—
136#14519735—21no—
137#14519735—21no—
138#14519735—21no—
139#14519735—21no—
140#14519735—21no—
141C2×C4⋊Dic61C2×C411yescharacteristic
142C2×C4⋊Dic61C2×C411yescharacteristic
143C2×#11758196C2×C411yescharacteristic
144C2×#11758196C2×C411yescharacteristic
145C2×#11758196C2×C411yescharacteristic
146C2×#11758196C2311yescharacteristic
147C2×C22⋊Dic61C2×C411yescharacteristic
148C2×C22⋊Dic61C2×C411yescharacteristic
149C2×C22⋊Dic61C2×C411yescharacteristic
150C2×C22⋊Dic61C2×C411yescharacteristic
151C2×C22⋊Dic61C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2311yescharacteristic
158C22⋊C4×D61—21no—
159C22⋊C4×D61—21no—
160C22⋊C4×D61—21no—
161C22⋊C4×D61—21no—
162C22⋊C4×D61—21no—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—21no—
165C22⋊C4×D61—21no—
166C2×C4×Dic61C2×C411yescharacteristic
167C2×C4×Dic61C2×C411yescharacteristic
168C2×C4×Dic61C2311yescharacteristic
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174C22⋊#92418—21no—
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177C22⋊#92418C2311yescharacteristic
178C22⋊#92418C2311yescharacteristic
179#14519689—21no—
180#14519689—21no—
181#14519689—21no—
182#14519689—21no—
183#14519687—21no—
184#14519687—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C22×D4×C61C2×C411yescharacteristic
188C23×C4×C61C2311yescharacteristic
189C2×M16×C61—21no—
190C22×C8×C61—21no—
191#123×C61—21no—
192#123×C61—21no—
193#123×C61—21no—
194#123×C61—21no—
195C2×C4⋊C4×C61C2×C411yescharacteristic
196C2×C4⋊C4×C61C2311yescharacteristic
197C2×C22⋊C4×C61C2×C411yescharacteristic
198C2×C22⋊C4×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61C2311yescharacteristic
200C22⋊C8×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204C22⋊C8×C61C2311yescharacteristic
205C22⋊C8×C61C2311yescharacteristic
206C24×C61C22×C411yescharacteristic
207C24×C61C22×C411yescharacteristic
208C23×D61—21no—
209C23×D61—21no—
210C23×D61—22no—
211C23×D61—41no—
212C23×D61—42no—
213C23×D61—81no—
214C23×D61C22×C411yescharacteristic
215C23×D61C22×C411yescharacteristic
216C2×D4×C61—21no—
217C2×D4×C61—21no—
218C2×D4×C61—81no—
219C22×C4×C61—81no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2411yescharacteristic
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—22no—
232C2×C22⋊D61—41no—
233C2×C22⋊D61—42no—
234C2×C22⋊D61C22⋊C411yescharacteristic
235C2×C22⋊D61C22⋊C411yescharacteristic
236C2×C22⋊D61C22⋊C411yescharacteristic
237C2×C22⋊D61C22⋊C411yescharacteristic
238C22×Dic61C22×C411yescharacteristic
239C22×Dic61C22×C411yescharacteristic
240C22×Dic61C22×C411yescharacteristic
241C22×Dic61C22×C411yescharacteristic
242C22×Dic61C22×C411yescharacteristic
243C22×Dic61C22×C411yescharacteristic
244C2×C4×D61—21no—
245C2×C4×D61—21no—
246C2×C4×D61—22no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—41no—
252C2×C4×D61—42no—
253C2×C4×D61—81no—
254C2×C4×D61—81no—
255C2×C4×D61C2×D411yescharacteristic
256C2×C4×D61C2×D411yescharacteristic
257C2×C4×D61C2×D411yescharacteristic
258C2×C4×D61C2×D411yescharacteristic
259C2×Dic122—21no—
260C2×Dic122—21no—
261C2×Dic122—81no—
262M16×C61—81no—
263C2×C8×C61—21no—
264C2×C8×C61—21no—
265C2×C8×C61—21no—
266C2×C8×C61—21no—
267C2×C8×C61—81no—
268C4⋊C4×C61—21no—
269C4⋊C4×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—21no—
282C22⋊Dic61—21no—
283C22⋊Dic61—21no—
284C22⋊Dic61—21no—
285C22⋊Dic61—21no—
286C22⋊Dic61C22⋊C411yescharacteristic
287C22⋊Dic61C22⋊C411yescharacteristic
288C22⋊Dic61C22⋊C411yescharacteristic
289C22⋊Dic61C22⋊C411yescharacteristic
290#11758198—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198C22⋊C411yescharacteristic
301#11758198C22⋊C411yescharacteristic
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304C4⋊Dic61—21no—
305C4⋊Dic61—21no—
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196C22⋊C411yescharacteristic
315#11758196C22⋊C411yescharacteristic
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318C4×Dic61—21no—
319C4×Dic61—21no—
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326#11758194—81no—
327C2×#92418—21no—
328C2×#92418—21no—
329C2×#92418—21no—
330C2×#92418—21no—
331C2×#92418—81no—
332#11758189—81no—
333#11758189—81no—
334C8×D61—81no—
335C8×D61—81no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—21no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—41no—
342C23×C61—41no—
343C23×C61—41no—
344C23×C61—41no—
345C23×C61C2×C22⋊C411yescharacteristic
346C23×C61C2×C22⋊C411yescharacteristic
347C23×C61C23×C411yescharacteristic
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—21no—
351C22×D61—21no—
352C22×D61—22no—
353C22×D61—41no—
354C22×D61—42no—
355C22×D61—42no—
356C22×D61—42no—
357C22×D61—41no—
358C22×D61—41no—
359C22×D61—42no—
360C22×D61—81no—
361C22×D61—81no—
362C22×D61—84no—
363C22×D61—84no—
364C22×D61C2×C22⋊C411yescharacteristic
365C22×D61C2×C22⋊C411yescharacteristic
366C22×D61#13112yes—
367D4×C61—81no—
368D4×C61—81no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—21no—
372C2×C4×C61—21no—
373C2×C4×C61—21no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61C2×C22⋊C411yescharacteristic
383C2×C4×C61C2×C22⋊C411yescharacteristic
384C2×C4×C61C22×D411yescharacteristic
385C2×C4×C61C22×D411yescharacteristic
386C22⋊D61—22no—
387C22⋊D61—22no—
388C22⋊D61—41no—
389C22⋊D61—41no—
390C22⋊D61—42no—
391C22⋊D61—42no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—21no—
398C2×Dic61—21no—
399C2×Dic61—41no—
400C2×Dic61—41no—
401C2×Dic61—41no—
402C2×Dic61—41no—
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C2×Dic61C2×C22⋊C411yescharacteristic
408C2×Dic61C2×C22⋊C411yescharacteristic
409C4×D61—41no—
410C4×D61—41no—
411C4×D61—41no—
412C4×D61—41no—
413C4×D61—42no—
414C4×D61—42no—
415C4×D61—42no—
416C4×D61—42no—
417C4×D61—81no—
418C4×D61—81no—
419Dic122—81no—
420Dic122—81no—
421C8×C61—41no—
422C8×C61—41no—
423C8×C61—41no—
424C8×C61—41no—
425#92418—41no—
426#92418—41no—
427#92418—41no—
428#92418—41no—
429#17422—611nomaximal, Sylow
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—21no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—81no—
442C22×C61—81no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61C22×C22⋊C411yescharacteristic
446C22×C61C2×#13111yescharacteristic
447C22×C61#56811yescharacteristic
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—22no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—42no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—42no—
460C2×D61—84no—
461C2×D61—84no—
462C2×D61#41312yes—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61—41no—
470Dic61—21no—
471Dic61—21no—
472Dic61—21no—
473Dic61—21no—
474Dic61—21no—
475Dic61—21no—
476Dic61—41no—
477Dic61—41no—
478Dic61—41no—
479C2×#551—611no—
480#2974—611no—
481#2974—611no—
482#1473—611no—
483#1473—611no—
484#1472—611no—
485#1472—611no—
486#1468—611no—
487#1468D6111yescharacteristic, complemented
488#1465—611no—
489#1464—611no—
490#1462—611no—
491#1459—611no—
492#1458—611no—
493C2×#323—611no—
494C2×C61—21no—
495C2×C61—21no—
496C2×C61—41no—
497C2×C61—41no—
498C2×C61—81no—
499C2×C61#288011yescharacteristic
500C2×C61#288311yescharacteristic
501C2×C61C2×#41311yescharacteristic
502D61—22no—
503D61—41no—
504D61—42no—
505#551—1221no—
506#551—1221no—
507#551—1221no—
508#551—1221no—
509#551—1221no—
510#551—1221no—
511#551—1221no—
512#551—1221no—
513C2×#126—611no—
514C2×#126—611no—
515C2×#124—611no—
516C2×#123—611no—
517C2×#123—611no—
518C2×#123C2×D6111yescharacteristic
519C2×C22⋊Q8—611no—
520C2×C22⋊Q8—611no—
521C2×#120—611no—
522C2×C4×D4—611no—
523C2×C4×D4—611no—
524C2×#117—611no—
525C2×#117—611no—
526C22×C22⋊C4—611no—
527C22×C22⋊C4—611no—
528#436—1221no—
529#436—1221no—
530#435—1221no—
531#435—1221no—
532#435—1221no—
533#435—1221no—
534C8×D4—1221no—
535C8×D4—1221no—
536#432—611no—
537#432—611no—
538#431—611no—
539#431—611no—
540#407—611no—
541#407—611no—
542#407—611no—
543#407C2×D6111yescharacteristic, complemented
544C2×C22⋊C8—611no—
545C2×C22⋊C8—611no—
546C2×C22⋊C8—611no—
547C2×C22⋊C8C2×D6111yescharacteristic, complemented
548#324—611no—
549#324—611no—
550#324—611no—
551#324—611no—
552#324—611no—
553#324—611no—
554#324C2×D6111yescharacteristic, complemented
555#324C2×D6111yescharacteristic, complemented
556#323—611no—
557#323—611no—
558#323—611no—
559#323—611no—
560#323—611no—
561#323—611no—
562#323C2×D6111yescharacteristic
563#323C2×D6111yescharacteristic
564C61#1742211yescharacteristic, complemented, Sylow
565C25—611no—
566C22×Q8—611no—
567C22×D4—611no—
568C22×D4—611no—
569C22×D4C4×D6111yescharacteristic
570C23×C4—611no—
571C23×C4—611no—
572C23×C4—611no—
573C23×C4—611no—
574C23×C4C22×D6111yescharacteristic
575C2×M16—21no—
576C2×M16—1221no—
577C2×M16—1221no—
578C2×M16—1221no—
579C22×C8—21no—
580C22×C8—1221no—
581C22×C8—1221no—
582C22×C8—1221no—
583#126—1221no—
584#126—1221no—
585#126—1221no—
586#126—1221no—
587#126—1221no—
588#126—1221no—
589#126—1221no—
590#126—1221no—
591#124—1221no—
592#124—1221no—
593#124—1221no—
594#124—1221no—
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—1221no—
600#123—1221no—
601#123—1221no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605#123—1221no—
606#123—1221no—
607C22⋊Q8—1221no—
608C22⋊Q8—1221no—
609C22⋊Q8—1221no—
610C22⋊Q8—1221no—
611C22⋊Q8—1221no—
612C22⋊Q8—1221no—
613C22⋊Q8—1221no—
614C22⋊Q8—1221no—
615#120—1221no—
616#120—1221no—
617#120—1221no—
618#120—1221no—
619C4×D4—611no—
620C4×D4—611no—
621C4×D4—611no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—611no—
626C4×D4—611no—
627C4×D4—1221no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631#117—1221no—
632#117—1221no—
633#117—1221no—
634#117—1221no—
635#117—1221no—
636#117—1221no—
637#117—1221no—
638#117—1221no—
639C2×C4⋊C4—611no—
640C2×C4⋊C4—611no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4C4×D6111yescharacteristic
646C2×C4⋊C4C22×D6111yescharacteristic
647C2×C22⋊C4—611no—
648C2×C22⋊C4—611no—
649C2×C22⋊C4—611no—
650C2×C22⋊C4—611no—
651C2×C22⋊C4—611no—
652C2×C22⋊C4—611no—
653C2×C22⋊C4—611no—
654C2×C22⋊C4—611no—
655C2×C22⋊C4—611no—
656C2×C22⋊C4—611no—
657C2×C22⋊C4—611no—
658C2×C22⋊C4—1221no—
659C2×C22⋊C4—1221no—
660C2×C22⋊C4—1221no—
661C2×C22⋊C4—1221no—
662C2×C22⋊C4—1221no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1221no—
666C2×C22⋊C4C4×D6111yescharacteristic
667C2×C22⋊C4C4×D6111yescharacteristic
668C2×C22⋊C4C22×D6111yescharacteristic
669C2×C42—611no—
670C2×C42—611no—
671C2×C42—611no—
672C4⋊C8—1221no—
673C4⋊C8—1221no—
674C4⋊C8—1221no—
675C4⋊C8—1221no—
676C22⋊C8—21no—
677C22⋊C8—21no—
678C22⋊C8—611no—
679C22⋊C8—611no—
680C22⋊C8—611no—
681C22⋊C8—611no—
682C22⋊C8—1221no—
683C22⋊C8—1221no—
684C22⋊C8—1221no—
685C22⋊C8—1221no—
686C22⋊C8—1221no—
687C22⋊C8—1221no—
688C22⋊C8C22×D6111yescharacteristic
689C22⋊C8C22×D6111yescharacteristic
690C22⋊C8C22×D6111yescharacteristic
691C22⋊C8C22×D6111yescharacteristic
692#97—1221no—
693#97—1221no—
694C4×C8—1221no—
695C4×C8—1221no—
696C24—611no—
697C24—611no—
698C24—1222no—
699C24—1221no—
700C24—1221no—
701C24—4881no—
702C24—2441no—
703C24—2442no—
704C24C2×C4×D6111yescharacteristic
705C24C2×C4×D6111yescharacteristic
706C2×Q8—1221no—
707C2×Q8—1221no—
708C2×Q8—4881no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—81no—
712C2×D4—611no—
713C2×D4—611no—
714C2×D4—611no—
715C2×D4—611no—
716C2×D4—1222no—
717C2×D4—1221no—
718C2×D4—1221no—
719C2×D4—2441no—
720C2×D4—2442no—
721C22×C4—81no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—611no—
730C22×C4—611no—
731C22×C4—611no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1221no—
736C22×C4—1222no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—4881no—
740C22×C4—4881no—
741C22×C4—2441no—
742C22×C4—2442no—
743C22×C4C2×C4×D6111yescharacteristic
744C22×C4C2×C4×D6111yescharacteristic
745C22×C4C2×C4×D6111yescharacteristic
746C22×C4C2×C4×D6111yescharacteristic
747C22×C4D4×D6111yescharacteristic
748C22×C4D4×D6111yescharacteristic
749C22×C4D4×D6111yescharacteristic
750C22×C4D4×D6111yescharacteristic
751C22×C4C23×D6111yescharacteristic
752M16—81no—
753M16—4881no—
754M16—4881no—
755M16—4881no—
756C2×C8—21no—
757C2×C8—21no—
758C2×C8—21no—
759C2×C8—21no—
760C2×C8—81no—
761C2×C8—1221no—
762C2×C8—1221no—
763C2×C8—1221no—
764C2×C8—1221no—
765C2×C8—4881no—
766C2×C8—4881no—
767C2×C8—4881no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—611no—
773C4⋊C4—611no—
774C4⋊C4—611no—
775C4⋊C4—611no—
776C4⋊C4—1221no—
777C4⋊C4—1221no—
778C4⋊C4—1221no—
779C4⋊C4—1221no—
780C4⋊C4—1221no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—611no—
797C22⋊C4—611no—
798C22⋊C4—611no—
799C22⋊C4—611no—
800C22⋊C4—1221no—
801C22⋊C4—1221no—
802C22⋊C4—1221no—
803C22⋊C4—1221no—
804C22⋊C4—1221no—
805C22⋊C4—1221no—
806C22⋊C4—1221no—
807C22⋊C4—1221no—
808C22⋊C4—1221no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C42—611no—
819C42—611no—
820C42—611no—
821C42—611no—
822C42—1221no—
823C42—1221no—
824C42—1221no—
825C42—1221no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—611no—
836C23—611no—
837C23—612no—
838C23—1222no—
839C23—1221no—
840C23—1221no—
841C23—1221no—
842C23—1221no—
843C23—4881no—
844C23—4881no—
845C23—4884no—
846C23—4884no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2442no—
851C23—2442no—
852C23—2442no—
853C23—2442no—
854C23C22⋊C4×D6111yescharacteristic
855C23C22⋊C4×D6111yescharacteristic
856C23C22×C4×D6111yescharacteristic
857Q8—4881no—
858Q8—4881no—
859D4—81no—
860D4—81no—
861D4—1222no—
862D4—1222no—
863D4—2441no—
864D4—2441no—
865D4—2442no—
866D4—2442no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—611no—
881C2×C4—611no—
882C2×C4—611no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—611no—
886C2×C4—1221no—
887C2×C4—1221no—
888C2×C4—1221no—
889C2×C4—1221no—
890C2×C4—1221no—
891C2×C4—1221no—
892C2×C4—1221no—
893C2×C4—4881no—
894C2×C4—4881no—
895C2×C4—2441no—
896C2×C4—2441no—
897C2×C4—2441no—
898C2×C4—2441no—
899C2×C4—2442no—
900C2×C4—2442no—
901C2×C4—2442no—
902C2×C4—2442no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4C22⋊C4×D6111yescharacteristic
908C2×C4C22⋊C4×D6111yescharacteristic
909C2×C4C2×D4×D6111yescharacteristic
910C2×C4C2×D4×D6111yescharacteristic
911C8—41no—
912C8—41no—
913C8—41no—
914C8—41no—
915C8—2441no—
916C8—2441no—
917C8—2441no—
918C8—2441no—
919C22—21no—
920C22—21no—
921C22—21no—
922C22—21no—
923C22—21no—
924C22—21no—
925C22—21no—
926C22—21no—
927C22—41no—
928C22—41no—
929C22—41no—
930C22—81no—
931C22—81no—
932C22—81no—
933C22—81no—
934C22—612no—
935C22—1221no—
936C22—1221no—
937C22—1222no—
938C22—1221no—
939C22—1221no—
940C22—1221no—
941C22—4884no—
942C22—4884no—
943C22—2442no—
944C22—2442no—
945C22—2442no—
946C22—2442no—
947C22—2441no—
948C22—2441no—
949C22C2×C22⋊C4×D6111yescharacteristic
950C22#131×D6111yescharacteristic
951C22#1684052711yescharacteristic
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—41no—
957C4—41no—
958C4—41no—
959C4—1221no—
960C4—1221no—
961C4—1221no—
962C4—1221no—
963C4—1221no—
964C4—1221no—
965C4—2441no—
966C4—2441no—
967C4—2441no—
968C2—21no—
969C2—21no—
970C2—41no—
971C2—41no—
972C2—81no—
973C2—1222no—
974C2—2441no—
975C2—2442no—
976C2#2145426711yescharacteristic
977C2#2145427711yescharacteristic
978C2#413×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1468C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519745C4
cosocleC22×C4×C61C24
hypercenter#1468D61
hypocenterC61#17422
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1468

Complements

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

NH ≅ G/Ntype
2. #21454855C2semidirect
3. #21454850C2semidirect
4. #21444185C2semidirect
5. #21444185C2semidirect
6. #21444181C2semidirect
7. #21444181C2semidirect
8. #21444167C2semidirect
9. #21444155C2semidirect
10. #21444152C2semidirect
11. #21444144C2semidirect
12. #21444135C2semidirect
13. #21444132C2semidirect
14. #323×D61C2semidirect
15. C61×#1468C2semidirect
46. #16839816C22semidirect
47. #16839816C22semidirect
48. #16839812C22semidirect
49. #16839812C22semidirect
50. #16839726C22semidirect
53. C2×C22⋊#92418C22semidirect
56. #16839488C22semidirect
57. #16839488C22semidirect
58. #16839487C22semidirect
59. #16839487C22semidirect
60. #16839487C22semidirect
61. #16839487C22semidirect
69. C61×#407C22semidirect
70. C2×C22⋊C8×C61C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
487. #1468D61semidirect
543. #407C2×D61semidirect
547. C2×C22⋊C8C2×D61semidirect
554. #324C2×D61semidirect
555. #324C2×D61semidirect
564. C61#17422semidirect

Maximal subgroups

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

subgroupindex
C2×#168404402
#214548552
#214548502
#214441852
#214441812
#214441672
#214441552
#214441522
#214441442
#214441352
#214441322
#323×D612
C61×#14682
#1742261