Finite Group Databasebeta

← #29646286

Subgroups — #29646286

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×#16840439C211yesmaximal, characteristic
2#21454855C211yesmaximal, characteristic, complemented
3#21454850C211yesmaximal, characteristic, complemented
4#21444187C211yesmaximal, characteristic, complemented
5#21444187C211yesmaximal, characteristic, complemented
6#21444183C211yesmaximal, characteristic, complemented
7#21444166C211yesmaximal, characteristic, complemented
8#21444166C211yesmaximal, characteristic, complemented
9#21444156C211yesmaximal, characteristic, complemented
10#21444152C211yesmaximal, characteristic, complemented
11#21444145C211yesmaximal, characteristic, complemented
12#21444136C211yesmaximal, characteristic, complemented
13#21444132C211yesmaximal, characteristic, complemented
14C2×#16839485C211yesmaximal, characteristic, complemented
15C61×#1472C211yesmaximal, characteristic, complemented
16#16840439—21no—
17#16840439—21no—
18#16840439—21no—
19#16840439—21no—
20#16840439—21no—
21#16840439—21no—
22#16840439—21no—
23#16840439—21no—
24C2×#14519772C411yescharacteristic
25C2×#14519772C2211yescharacteristic
26C2×#14519766C411yescharacteristic
27C2×#14519762C411yescharacteristic
28C2×#14519762C2211yescharacteristic
29C2×#14519761C411yescharacteristic
30C2×#14519753C411yescharacteristic
31C2×#14519747C411yescharacteristic
32C2×#14519739C2211yescharacteristic
33C2×C4×C22⋊D61C2211yescharacteristic
34C2×#14519735C2211yescharacteristic
35C2×#14519733C411yescharacteristic
36C22×#11758198C2211yescharacteristic
37C2×C22⋊C4×D61C411yescharacteristic
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
51#16839724C2211yescharacteristic, complemented
52#16839724C2211yescharacteristic, complemented
53C2×C22⋊#92418C2211yescharacteristic
54C22⋊C8×D61C2211yescharacteristic, complemented
55C22⋊C8×D61C2211yescharacteristic, complemented
56#16839488C2211yescharacteristic, complemented
57#16839488C2211yescharacteristic, complemented
58#16839488C2211yescharacteristic, complemented
59#16839488C2211yescharacteristic, complemented
60#16839485C2211yescharacteristic
61#16839485C2211yescharacteristic
62#16839485C2211yescharacteristic
63#16839485C2211yescharacteristic
64#16839485C2211yescharacteristic
65#16839485C2211yescharacteristic
66#16839485C2211yescharacteristic
67#16839485C2211yescharacteristic
68C2×C22⋊Q8×C61C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C2×C22⋊C8×C61C2211yescharacteristic
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#324C2211yescharacteristic, complemented
74C61×#324C2211yescharacteristic, complemented
75C24×D61C2×C411yescharacteristic
76C22×D244C2×C411yescharacteristic
77C22×D244C2×C411yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic
79C23×Dic61C2×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#14519772—21no—
90#14519772—21no—
91#14519772—21no—
92#14519772—21no—
93#14519772—21no—
94#14519772—21no—
95#14519772—21no—
96#14519772—21no—
97#14519766—21no—
98#14519766—21no—
99#14519766—21no—
100#14519766—21no—
101#14519762—21no—
102#14519762—21no—
103#14519762—21no—
104#14519762—21no—
105#14519762—21no—
106#14519762—21no—
107#14519762—21no—
108#14519762—21no—
109#14519761—21no—
110#14519761—21no—
111#14519761—21no—
112#14519761—21no—
113#14519753—21no—
114#14519753—21no—
115#14519753—21no—
116#14519753—21no—
117#14519747—21no—
118#14519747—21no—
119#14519747—21no—
120#14519747—21no—
121#14519739—21no—
122#14519739—21no—
123#14519739—21no—
124#14519739—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#14519733—21no—
138#14519733—21no—
139#14519733—21no—
140#14519733—21no—
141C2×C4⋊Dic61C2×C411yescharacteristic
142C2×C4⋊Dic61C2×C411yescharacteristic
143C2×#11758196C2×C411yescharacteristic
144C2×#11758196C2×C411yescharacteristic
145C2×#11758196C2×C411yescharacteristic
146C2×C22⋊Dic61C2×C411yescharacteristic
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198—21no—
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2×C411yescharacteristic
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×#11758198C2311yescharacteristic
161C2×#11758198C2311yescharacteristic
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×Q8×C61C2×C411yescharacteristic
188C23×C4×C61C2311yescharacteristic
189C2×M16×C61—21no—
190C22×C8×C61—21no—
191C22⋊Q8×C61—21no—
192C22⋊Q8×C61—21no—
193C22⋊Q8×C61—21no—
194C22⋊Q8×C61—21no—
195C2×C4⋊C4×C61C2×C411yescharacteristic
196C2×C4⋊C4×C61C2311yescharacteristic
197C2×C4⋊C4×C61C2311yescharacteristic
198C2×C22⋊C4×C61C2×C411yescharacteristic
199C2×C22⋊C4×C61C2×C411yescharacteristic
200C22⋊C8×C61—21no—
201C22⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204C22⋊C8×C61C2311yescharacteristic
205C22⋊C8×C61C2311yescharacteristic
206C24×C61C22×C411yescharacteristic
207C23×D61—21no—
208C23×D61—21no—
209C23×D61—22no—
210C23×D61—41no—
211C23×D61—42no—
212C23×D61—81no—
213C23×D61C22×C411yescharacteristic
214C23×D61C22×C411yescharacteristic
215C23×D61C22×C411yescharacteristic
216C2×Q8×C61—21no—
217C2×Q8×C61—21no—
218C2×Q8×C61—81no—
219C22×C4×C61—81no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C22×C411yescharacteristic
224C22×C4×C61C22×C411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2411yescharacteristic
230C2×C22⋊D61—42no—
231C2×C22⋊D61C22⋊C411yescharacteristic
232C2×C22⋊D61C22⋊C411yescharacteristic
233C2×C22⋊D61C22⋊C411yescharacteristic
234C2×C22⋊D61C22⋊C411yescharacteristic
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61—42no—
238C22×Dic61C22×C411yescharacteristic
239C22×Dic61C22×C411yescharacteristic
240C22×Dic61C22×C411yescharacteristic
241C22×Dic61C22×C411yescharacteristic
242C22×Dic61C22×C411yescharacteristic
243C2×D244—21no—
244C2×D244—21no—
245C2×D244—22no—
246C2×D244—21no—
247C2×D244—21no—
248C2×D244—41no—
249C2×D244—81no—
250C2×C4×D61—22no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—21no—
254C2×C4×D61—21no—
255C2×C4×D61—41no—
256C2×C4×D61—81no—
257C2×C4×D61—81no—
258C2×C4×D61C2×D411yescharacteristic
259C2×C4×D61C2×D411yescharacteristic
260C2×C4×D61C2×D411yescharacteristic
261C2×C4×D61C2×D411yescharacteristic
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—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C22⋊C4×C61—21no—
275C22⋊C4×C61—21no—
276C22⋊C4×C61—21no—
277C22⋊C4×C61—21no—
278C22⋊Dic61C22⋊C411yescharacteristic
279C22⋊Dic61C22⋊C411yescharacteristic
280C22⋊Dic61C22⋊C411yescharacteristic
281C22⋊Dic61C22⋊C411yescharacteristic
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
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#11758198—21no—
301#11758198—21no—
302#11758198C22⋊C411yescharacteristic
303#11758198C22⋊C411yescharacteristic
304#11758198C22⋊C411yescharacteristic
305#11758198C22⋊C411yescharacteristic
306C4⋊Dic61—21no—
307C4⋊Dic61—21no—
308C4⋊Dic61—21no—
309C4⋊Dic61—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—22no—
339C23×C61—41no—
340C23×C61C2×C22⋊C411yescharacteristic
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C23×C411yescharacteristic
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—21no—
350C22×D61—41no—
351C22×D61—41no—
352C22×D61—42no—
353C22×D61—42no—
354C22×D61—41no—
355C22×D61—41no—
356C22×D61—42no—
357C22×D61—42no—
358C22×D61—41no—
359C22×D61—41no—
360C22×D61—81no—
361C22×D61—81no—
362C22×D61—84no—
363C22×D61—84no—
364C22×D61C2×C22⋊C411yescharacteristic
365C22×D61C2×C22⋊C411yescharacteristic
366C22×D61#13112yes—
367Q8×C61—81no—
368Q8×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—21no—
375C2×C4×C61—21no—
376C2×C4×C61—21no—
377C2×C4×C61—41no—
378C2×C4×C61—41no—
379C2×C4×C61—41no—
380C2×C4×C61—41no—
381C2×C4×C61—41no—
382C2×C4×C61—41no—
383C2×C4×C61—41no—
384C2×C4×C61—41no—
385C2×C4×C61C2×C22⋊C411yescharacteristic
386C2×C4×C61C2×C22⋊C411yescharacteristic
387C2×C4×C61C22×D411yescharacteristic
388C2×C4×C61C22×D411yescharacteristic
389C22⋊D61—22no—
390C22⋊D61—22no—
391C22⋊D61—41no—
392C22⋊D61—41no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—21no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—42no—
400C2×Dic61—42no—
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
409D244—42no—
410D244—42no—
411D244—81no—
412D244—81no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—42no—
418C4×D61—42no—
419C4×D61—81no—
420C4×D61—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—42no—
438C22×C61—42no—
439C22×C61#41312yes—
440C22×C61C22×C22⋊C411yescharacteristic
441C22×C61C2×#13111yescharacteristic
442C22×C61#56811yescharacteristic
443C2×D61—22no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—42no—
451C2×D61—41no—
452C2×D61—41no—
453C2×D61—42no—
454C2×D61—41no—
455C2×D61—41no—
456C2×D61—41no—
457C2×D61—81no—
458C2×D61—81no—
459C2×D61—84no—
460C2×D61—84no—
461C2×D61—81no—
462C2×D61—81no—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—41no—
468C4×C61—41no—
469C4×C61—41no—
470C4×C61—41no—
471Dic61—21no—
472Dic61—21no—
473Dic61—21no—
474Dic61—21no—
475Dic61—21no—
476Dic61—21no—
477Dic61—41no—
478Dic61—41no—
479C2×#551—611no—
480#2974—611no—
481#2974—611no—
482#1473—611no—
483#1473—611no—
484#1472—611no—
485#1472D6111yescharacteristic, complemented
486#1468—611no—
487#1468—611no—
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—22no—
497C2×C61—41no—
498C2×C61#288011yescharacteristic
499C2×C61#288311yescharacteristic
500C2×C61C2×#41311yescharacteristic
501D61—41no—
502D61—41no—
503D61—42no—
504D61—81no—
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×#123—611no—
519C2×C22⋊Q8—611no—
520C2×C22⋊Q8C2×D6111yescharacteristic
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
544C2×C22⋊C8—611no—
545C2×C22⋊C8—611no—
546C2×C22⋊C8—611no—
547C2×C22⋊C8C2×D6111yescharacteristic
548#324—611no—
549#324—611no—
550#324—611no—
551#324—611no—
552#324C2×D6111yescharacteristic, complemented
553#324C2×D6111yescharacteristic, complemented
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#323—611no—
563#323—611no—
564C61#1742211yescharacteristic, complemented, Sylow
565C25—611no—
566C22×Q8C4×D6111yescharacteristic
567C22×D4—611no—
568C22×D4—611no—
569C22×D4—611no—
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—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
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—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
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⋊C4C4×D6111yescharacteristic
645C2×C4⋊C4C22×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—611no—
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⋊C4—1221no—
667C2×C22⋊C4C4×D6111yescharacteristic
668C2×C22⋊C4C4×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—611no—
699C24—1222no—
700C24—1221no—
701C24—1221no—
702C24—4881no—
703C24—2441no—
704C24—2442no—
705C24C2×C4×D6111yescharacteristic
706C2×Q8—21no—
707C2×Q8—21no—
708C2×Q8—81no—
709C2×D4—611no—
710C2×D4—611no—
711C2×D4—611no—
712C2×D4—611no—
713C2×D4—1221no—
714C2×D4—1221no—
715C2×D4—1221no—
716C2×D4—1221no—
717C2×D4—1222no—
718C2×D4—4881no—
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—1221no—
732C22×C4—1221no—
733C22×C4—1221no—
734C22×C4—1221no—
735C22×C4—1222no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—4881no—
739C22×C4—4881no—
740C22×C4—2441no—
741C22×C4—2442no—
742C22×C4C2×C4×D6111yescharacteristic
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—21no—
773C4⋊C4—21no—
774C4⋊C4—611no—
775C4⋊C4—611no—
776C4⋊C4—611no—
777C4⋊C4—611no—
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—611no—
791C22⋊C4—611no—
792C22⋊C4—611no—
793C22⋊C4—611no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—611no—
797C22⋊C4—611no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
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—22no—
827C23—21no—
828C23—21no—
829C23—41no—
830C23—611no—
831C23—611no—
832C23—612no—
833C23—1221no—
834C23—1221no—
835C23—1221no—
836C23—1221no—
837C23—1221no—
838C23—1221no—
839C23—1221no—
840C23—4881no—
841C23—4881no—
842C23—4884no—
843C23—4884no—
844C23—2441no—
845C23—2441no—
846C23—2442no—
847C23—2442no—
848C23—2441no—
849C23—2441no—
850C23—2442no—
851C23—2441no—
852C23—2441no—
853C23—2442no—
854C23C22⋊C4×D6111yescharacteristic
855C23C22⋊C4×D6111yescharacteristic
856C23C22×C4×D6111yescharacteristic
857Q8—81no—
858Q8—81no—
859D4—1222no—
860D4—1222no—
861D4—4881no—
862D4—4881no—
863D4—2442no—
864D4—2442no—
865D4—2441no—
866D4—2441no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—611no—
884C2×C4—611no—
885C2×C4—611no—
886C2×C4—611no—
887C2×C4—611no—
888C2×C4—611no—
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—2441no—
902C2×C4—2441no—
903C2×C4—2442no—
904C2×C4—2442no—
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—42no—
927C22—42no—
928C22—1222no—
929C22—1221no—
930C22—1221no—
931C22—1221no—
932C22—1221no—
933C22—1221no—
934C22—1221no—
935C22—4881no—
936C22—4881no—
937C22—4884no—
938C22—4881no—
939C22—4881no—
940C22—4884no—
941C22—2442no—
942C22—2442no—
943C22—2441no—
944C22—2441no—
945C22—2441no—
946C22—2441no—
947C22—2441no—
948C22#1683974512yes—
949C22C2×C22⋊C4×D6111yescharacteristic
950C22#131×D6111yescharacteristic
951C22#1684052711yescharacteristic
952C4—21no—
953C4—21no—
954C4—21no—
955C4—21no—
956C4—41no—
957C4—41no—
958C4—41no—
959C4—41no—
960C4—1221no—
961C4—1221no—
962C4—1221no—
963C4—1221no—
964C4—1221no—
965C4—1221no—
966C4—2441no—
967C4—2441no—
968C2—21no—
969C2—21no—
970C2—22no—
971C2—41no—
972C2—4881no—
973C2—2441no—
974C2—2441no—
975C2—2442no—
976C2#2145426711yescharacteristic
977C2#2145427711yescharacteristic
978C2C2×#1683974511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1472C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519747C4
cosocleC22×C4×C61C24
hypercenter#1472D61
hypocenterC61#17422
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1472

Complements

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

NH ≅ G/Ntype
2. #21454855C2semidirect
3. #21454850C2semidirect
4. #21444187C2semidirect
5. #21444187C2semidirect
6. #21444183C2semidirect
7. #21444166C2semidirect
8. #21444166C2semidirect
9. #21444156C2semidirect
10. #21444152C2semidirect
11. #21444145C2semidirect
12. #21444136C2semidirect
13. #21444132C2semidirect
14. C2×#16839485C2semidirect
15. C61×#1472C2semidirect
46. #16839816C22semidirect
47. #16839816C22semidirect
48. #16839812C22semidirect
49. #16839812C22semidirect
51. #16839724C22semidirect
52. #16839724C22semidirect
54. C22⋊C8×D61C22semidirect
55. C22⋊C8×D61C22semidirect
56. #16839488C22semidirect
57. #16839488C22semidirect
58. #16839488C22semidirect
59. #16839488C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
73. C61×#324C22semidirect
74. C61×#324C22semidirect
485. #1472D61semidirect
552. #324C2×D61semidirect
553. #324C2×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×#168404392
#214548552
#214548502
#214441872
#214441832
#214441662
#214441562
#214441522
#214441452
#214441362
#214441322
C2×#168394852
C61×#14722
#1742261