Finite Group Databasebeta

← #29646206

Subgroups — #29646206

Order 15616.

1046 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840435C211yesmaximal, characteristic
2#21454479C211yesmaximal, characteristic, complemented
3#21454473C211yesmaximal, characteristic, complemented
4#21444187C211yesmaximal, characteristic, complemented
5#21444187C211yesmaximal, characteristic, complemented
6#21444169C211yesmaximal, characteristic, complemented
7#21444169C211yesmaximal, characteristic, complemented
8#21444167C211yesmaximal, characteristic, complemented
9#21444158C211yesmaximal, characteristic, complemented
10#21444152C211yesmaximal, characteristic, complemented
11#21444145C211yesmaximal, characteristic, complemented
12#21444138C211yesmaximal, characteristic, complemented
13#21444132C211yesmaximal, characteristic, complemented
14C2×#16839485C211yesmaximal, characteristic, complemented
15C61×#1468C211yesmaximal, characteristic, complemented
16#16840435—21no—
17#16840435—21no—
18#16840435—21no—
19#16840435—21no—
20#16840435—21no—
21#16840435—21no—
22#16840435—21no—
23#16840435—21no—
24C2×#14519772C411yescharacteristic
25C2×#14519772C2211yescharacteristic
26C2×#14519763C2211yescharacteristic
27C2×#14519761C411yescharacteristic
28C2×#14519759C411yescharacteristic
29C2×#14519757C411yescharacteristic
30C2×#14519754C411yescharacteristic
31C2×#14519745C411yescharacteristic
32C2×D4×Dic61C411yescharacteristic
33C2×#14519737C2211yescharacteristic
34C2×#14519736C2211yescharacteristic
35C2×#14519735C2211yescharacteristic
36C22×#11758198C2211yescharacteristic
37C2×C22⋊C4×D61C411yescharacteristic
38#16839820—21no—
39#16839820—21no—
40#16839820—21no—
41#16839820—21no—
42#16839816C2211yescharacteristic, complemented
43#16839816C2211yescharacteristic, complemented
44#16839816C2211yescharacteristic, complemented
45#16839816C2211yescharacteristic, complemented
46#16839812C2211yescharacteristic, complemented
47#16839812C2211yescharacteristic, complemented
48#16839812C2211yescharacteristic, complemented
49#16839812C2211yescharacteristic, complemented
50#16839790—21no—
51#16839788—21no—
52#16839726C2211yescharacteristic
53C2×C22⋊#92418C2211yescharacteristic
54#16839720—21no—
55#16839717—21no—
56#16839488C2211yescharacteristic, complemented
57#16839488C2211yescharacteristic, complemented
58#16839486C2211yescharacteristic, complemented
59#16839486C2211yescharacteristic, complemented
60#16839485C2211yescharacteristic
61#16839485C2211yescharacteristic
62#16839485C2211yescharacteristic
63#16839485C2211yescharacteristic
64#16839485C2211yescharacteristic
65#16839485C2211yescharacteristic
66#16839485C2211yescharacteristic
67#16839485C2211yescharacteristic
68C2×#123×C61C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C2×C22⋊C8×C61C2211yescharacteristic
71C61×#324C2211yescharacteristic, complemented
72C61×#324C2211yescharacteristic, complemented
73C61×#323C2211yescharacteristic, complemented
74C61×#323C2211yescharacteristic, complemented
75C24×D61C2×C411yescharacteristic
76C22×Dic122C2×C411yescharacteristic
77C22×C22⋊D61C2×C411yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic
79C23×Dic61C2×C411yescharacteristic
80C23×Dic61C2×C411yescharacteristic
81C22×C4×D61C2×C411yescharacteristic
82C22×C4×D61C2×C411yescharacteristic
83C2×#11758194—21no—
84C22×#92418—21no—
85#14519772—21no—
86#14519772—21no—
87#14519772—21no—
88#14519772—21no—
89#14519772—21no—
90#14519772—21no—
91#14519772—21no—
92#14519772—21no—
93#14519763—21no—
94#14519763—21no—
95#14519763—21no—
96#14519763—21no—
97#14519761—21no—
98#14519761—21no—
99#14519761—21no—
100#14519761—21no—
101#14519759—21no—
102#14519759—21no—
103#14519759—21no—
104#14519759—21no—
105#14519757—21no—
106#14519757—21no—
107#14519757—21no—
108#14519757—21no—
109#14519754—21no—
110#14519754—21no—
111#14519754—21no—
112#14519754—21no—
113#14519745—21no—
114#14519745—21no—
115#14519745—21no—
116#14519745—21no—
117D4×Dic61—21no—
118D4×Dic61—21no—
119D4×Dic61—21no—
120D4×Dic61—21no—
121#14519737—21no—
122#14519737—21no—
123#14519737—21no—
124#14519737—21no—
125#14519736D411yescharacteristic
126#14519736D411yescharacteristic
127#14519736D411yescharacteristic
128#14519736D411yescharacteristic
129#14519736D411yescharacteristic
130#14519736D411yescharacteristic
131#14519736D411yescharacteristic
132#14519736D411yescharacteristic
133#14519735—21no—
134#14519735—21no—
135#14519735—21no—
136#14519735—21no—
137C2×C4⋊Dic61C2×C411yescharacteristic
138C2×C4⋊Dic61C2×C411yescharacteristic
139C2×C4⋊Dic61C2×C411yescharacteristic
140C2×C4⋊Dic61C2×C411yescharacteristic
141C2×#11758196C2×C411yescharacteristic
142C2×#11758196C2×C411yescharacteristic
143C2×C22⋊Dic61C2×C411yescharacteristic
144C2×C22⋊Dic61C2×C411yescharacteristic
145C2×C22⋊Dic61C2×C411yescharacteristic
146C2×#11758198—21no—
147C2×#11758198—21no—
148C2×#11758198—21no—
149C2×#11758198—21no—
150C2×#11758198C2×C411yescharacteristic
151C2×#11758198C2×C411yescharacteristic
152C2×#11758198C2×C411yescharacteristic
153C2×#11758198C2×C411yescharacteristic
154C2×#11758198C2×C411yescharacteristic
155C2×#11758198C2×C411yescharacteristic
156C2×#11758198C2311yescharacteristic
157C2×#11758198C2311yescharacteristic
158C22⋊C4×D61—21no—
159C22⋊C4×D61—21no—
160C22⋊C4×D61—21no—
161C22⋊C4×D61—21no—
162C2×C4×Dic61C2×C411yescharacteristic
163C2×C4×Dic61C2311yescharacteristic
164C2×C4×Dic61C2311yescharacteristic
165#14519706—21no—
166#14519706—21no—
167#14519706—21no—
168#14519706—21no—
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#14519687—21no—
180#14519687—21no—
181#14519687—21no—
182#14519687—21no—
183C8×Dic61—21no—
184C8×Dic61—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—42no—
219C22×C4×C61—42no—
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—22no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—41no—
235C2×C22⋊D61—81no—
236C22×Dic61—21no—
237C22×Dic61—21no—
238C22×Dic61—21no—
239C22×Dic61—21no—
240C22×Dic61—81no—
241C22×Dic61—81no—
242C22×Dic61C22×C411yescharacteristic
243C22×Dic61C22×C411yescharacteristic
244C22×Dic61C22×C411yescharacteristic
245C22×Dic61C22×C411yescharacteristic
246C22×Dic61C22×C411yescharacteristic
247C22×Dic61C22×C411yescharacteristic
248C2×C4×D61—22no—
249C2×C4×D61—21no—
250C2×C4×D61—21no—
251C2×C4×D61—21no—
252C2×C4×D61—21no—
253C2×C4×D61—41no—
254C2×C4×D61—81no—
255C2×Dic122—21no—
256C2×Dic122—21no—
257C2×Dic122—81no—
258M16×C61—42no—
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—21no—
262C2×C8×C61—21no—
263C2×C8×C61—42no—
264C4⋊C4×C61—21no—
265C4⋊C4×C61—21no—
266C4⋊C4×C61—21no—
267C4⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—21no—
272C22⋊C4×C61—21no—
273C22⋊C4×C61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61C22⋊C411yescharacteristic
277C22⋊Dic61C22⋊C411yescharacteristic
278C22⋊Dic61C22⋊C411yescharacteristic
279C22⋊Dic61C22⋊C411yescharacteristic
280C22⋊Dic61C22⋊C411yescharacteristic
281C22⋊Dic61C22⋊C411yescharacteristic
282C22⋊Dic61C22⋊C411yescharacteristic
283C22⋊Dic61C22⋊C411yescharacteristic
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—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302C4⋊Dic61—21no—
303C4⋊Dic61—21no—
304C4⋊Dic61C22⋊C411yescharacteristic
305C4⋊Dic61C22⋊C411yescharacteristic
306C4⋊Dic61C22⋊C411yescharacteristic
307C4⋊Dic61C22⋊C411yescharacteristic
308C4⋊Dic61C22⋊C411yescharacteristic
309C4⋊Dic61C22⋊C411yescharacteristic
310C4⋊Dic61C22⋊C411yescharacteristic
311C4⋊Dic61C22⋊C411yescharacteristic
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—21no—
316C4×Dic61—21no—
317C4×Dic61—21no—
318C4×Dic61C2×D411yescharacteristic
319C4×Dic61C2×D411yescharacteristic
320C4×Dic61C2×D411yescharacteristic
321C4×Dic61C2×D411yescharacteristic
322C4×Dic61C2×D411yescharacteristic
323C4×Dic61C2×D411yescharacteristic
324C4×Dic61C2×D411yescharacteristic
325C4×Dic61C2×D411yescharacteristic
326#11758194—42no—
327C2×#92418—21no—
328C2×#92418—21no—
329C2×#92418—21no—
330C2×#92418—21no—
331C2×#92418—42no—
332C23×C61—21no—
333C23×C61—21no—
334C23×C61—22no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—21no—
338C23×C61—41no—
339C23×C61—41no—
340C23×C61—41no—
341C23×C61C2×C22⋊C411yescharacteristic
342C23×C61C2×C22⋊C411yescharacteristic
343C23×C61C23×C411yescharacteristic
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—21no—
347C22×D61—21no—
348C22×D61—21no—
349C22×D61—42no—
350C22×D61—42no—
351C22×D61—41no—
352C22×D61—41no—
353C22×D61—42no—
354C22×D61—42no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61—81no—
358C22×D61—81no—
359C22×D61—84no—
360C22×D61—84no—
361C22×D61#13112yes—
362D4×C61—42no—
363D4×C61—42no—
364C2×C4×C61—22no—
365C2×C4×C61—22no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—21no—
370C2×C4×C61—21no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—41no—
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C22×D411yescharacteristic
380C2×C4×C61C22×D411yescharacteristic
381C22⋊D61—42no—
382C22⋊D61—42no—
383C22⋊D61—81no—
384C22⋊D61—81no—
385C2×Dic61—21no—
386C2×Dic61—21no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—81no—
396C2×Dic61—81no—
397C2×Dic61—81no—
398C2×Dic61—81no—
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405C2×Dic61C2×C22⋊C411yescharacteristic
406C2×Dic61C2×C22⋊C411yescharacteristic
407C4×D61—42no—
408C4×D61—42no—
409C4×D61—81no—
410C4×D61—81no—
411Dic122—81no—
412Dic122—81no—
413C8×C61—41no—
414C8×C61—41no—
415C8×C61—41no—
416C8×C61—41no—
417#92418—41no—
418#92418—41no—
419#92418—41no—
420#92418—41no—
421#17412—611nomaximal, Sylow
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—42no—
430C22×C61—42no—
431C22×C61—41no—
432C22×C61—41no—
433C22×C61—41no—
434C22×C61—81no—
435C22×C61—81no—
436C22×C61#41012yes—
437C22×C61C22×C22⋊C411yescharacteristic
438C22×C61C2×#13111yescharacteristic
439C22×C61#56811yescharacteristic
440C2×D61—22no—
441C2×D61—42no—
442C2×D61—41no—
443C2×D61—41no—
444C2×D61—42no—
445C2×D61—41no—
446C2×D61—41no—
447C2×D61—41no—
448C2×D61—84no—
449C2×D61—84no—
450C2×D61—81no—
451C2×D61—81no—
452C4×C61—21no—
453C4×C61—21no—
454C4×C61—21no—
455C4×C61—21no—
456C4×C61—41no—
457C4×C61—41no—
458C4×C61—41no—
459Dic61—21no—
460Dic61—21no—
461Dic61—21no—
462Dic61—21no—
463Dic61—21no—
464Dic61—21no—
465Dic61—21no—
466Dic61—21no—
467Dic61—41no—
468Dic61—41no—
469C2×#551—611no—
470#2924—611no—
471#2924—611no—
472#1473—611no—
473#1473—611no—
474#1469—611no—
475#1469—611no—
476#1468—611no—
477#1468D6111yescharacteristic, complemented
478#1466—611no—
479#1464—611no—
480#1462—611no—
481#1460—611no—
482#1458—611no—
483C2×#323—611no—
484C2×C61—21no—
485C2×C61—21no—
486C2×C61—22no—
487C2×C61—41no—
488C2×C61—81no—
489C2×C61#288011yescharacteristic
490C2×C61C2×#41011yescharacteristic
491C2×C61#288811yescharacteristic
492D61—42no—
493D61—81no—
494#551—1221no—
495#551—1221no—
496#551—1221no—
497#551—1221no—
498#551—1221no—
499#551—1221no—
500#551—1221no—
501#551—1221no—
502C2×#126—611no—
503C2×#126—611no—
504C2×#124—611no—
505C2×#123—611no—
506C2×#123—611no—
507C2×#123C2×D6111yescharacteristic
508C2×C22⋊Q8—611no—
509C2×C22⋊Q8—611no—
510C2×#120—611no—
511C2×C4×D4—611no—
512C2×C4×D4—611no—
513C2×#117—611no—
514C2×#117—611no—
515C22×C22⋊C4—611no—
516C22×C22⋊C4—611no—
517#433—1221no—
518#433—1221no—
519#433—1221no—
520#433—1221no—
521#432—611no—
522#432—611no—
523#432—611no—
524#432—611no—
525#431—611no—
526#431—611no—
527#431—611no—
528#431—611no—
529#424—1221no—
530#424—1221no—
531#407—611no—
532#407C2×D6111yescharacteristic
533C2×C22⋊C8—611no—
534C2×C22⋊C8C2×D6111yescharacteristic
535#405—1221no—
536#405—1221no—
537#324—611no—
538#324—611no—
539#324C2×D6111yescharacteristic, complemented
540#324C2×D6111yescharacteristic, complemented
541#323—611no—
542#323—611no—
543#323—611no—
544#323—611no—
545#323—611no—
546#323—611no—
547#323—611no—
548#323—611no—
549#323—611no—
550#323—611no—
551#323C2×D6111yescharacteristic, complemented
552#323C2×D6111yescharacteristic, complemented
553C61#1741211yescharacteristic, complemented, Sylow
554C25—611no—
555C22×Q8—611no—
556C22×D4—611no—
557C22×D4—611no—
558C22×D4C4×D6111yescharacteristic
559C23×C4—611no—
560C23×C4—611no—
561C23×C4—611no—
562C23×C4—611no—
563C23×C4C22×D6111yescharacteristic
564C2×M16—21no—
565C2×M16—1221no—
566C22×C8—21no—
567C22×C8—1221no—
568#126—1221no—
569#126—1221no—
570#126—1221no—
571#126—1221no—
572#126—1221no—
573#126—1221no—
574#126—1221no—
575#126—1221no—
576#124—1221no—
577#124—1221no—
578#124—1221no—
579#124—1221no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—1221no—
585#123—1221no—
586#123—1221no—
587#123—1221no—
588#123—1221no—
589#123—1221no—
590#123—1221no—
591#123—1221no—
592C22⋊Q8—1221no—
593C22⋊Q8—1221no—
594C22⋊Q8—1221no—
595C22⋊Q8—1221no—
596C22⋊Q8—1221no—
597C22⋊Q8—1221no—
598C22⋊Q8—1221no—
599C22⋊Q8—1221no—
600#120—1221no—
601#120—1221no—
602#120—1221no—
603#120—1221no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611C4×D4—1221no—
612#117—611no—
613#117—611no—
614#117—611no—
615#117—611no—
616#117—611no—
617#117—611no—
618#117—611no—
619#117—611no—
620#117—1221no—
621#117—1221no—
622#117—1221no—
623#117—1221no—
624C2×C4⋊C4—611no—
625C2×C4⋊C4—611no—
626C2×C4⋊C4—611no—
627C2×C4⋊C4—611no—
628C2×C4⋊C4—611no—
629C2×C4⋊C4—611no—
630C2×C4⋊C4C4×D6111yescharacteristic
631C2×C4⋊C4C22×D6111yescharacteristic
632C2×C22⋊C4—611no—
633C2×C22⋊C4—611no—
634C2×C22⋊C4—611no—
635C2×C22⋊C4—611no—
636C2×C22⋊C4—611no—
637C2×C22⋊C4—611no—
638C2×C22⋊C4—611no—
639C2×C22⋊C4—611no—
640C2×C22⋊C4—611no—
641C2×C22⋊C4—611no—
642C2×C22⋊C4—611no—
643C2×C22⋊C4—1221no—
644C2×C22⋊C4—1221no—
645C2×C22⋊C4—1221no—
646C2×C22⋊C4—1221no—
647C2×C22⋊C4—1221no—
648C2×C22⋊C4—1221no—
649C2×C22⋊C4—1221no—
650C2×C22⋊C4—1221no—
651C2×C22⋊C4C4×D6111yescharacteristic
652C2×C22⋊C4C4×D6111yescharacteristic
653C2×C22⋊C4C22×D6111yescharacteristic
654C2×C42—611no—
655C2×C42—611no—
656C2×C42—611no—
657C4⋊C8—1221no—
658C4⋊C8—1221no—
659C4⋊C8—1221no—
660C4⋊C8—1221no—
661C4⋊C8—1221no—
662C4⋊C8—1221no—
663C4⋊C8—1221no—
664C4⋊C8—1221no—
665C22⋊C8—21no—
666C22⋊C8—21no—
667C22⋊C8—611no—
668C22⋊C8—611no—
669C22⋊C8—611no—
670C22⋊C8—611no—
671C22⋊C8—1221no—
672C22⋊C8—1221no—
673C22⋊C8C22×D6111yescharacteristic
674C22⋊C8C22×D6111yescharacteristic
675C22⋊C8C22×D6111yescharacteristic
676C22⋊C8C22×D6111yescharacteristic
677#97—1221no—
678#97—1221no—
679#97—1221no—
680#97—1221no—
681C4×C8—1221no—
682C4×C8—1221no—
683C4×C8—1221no—
684C4×C8—1221no—
685C24—611no—
686C24—611no—
687C24—1222no—
688C24—1221no—
689C24—1221no—
690C24—4881no—
691C24—2441no—
692C24—2442no—
693C24C2×C4×D6111yescharacteristic
694C24C2×C4×D6111yescharacteristic
695C2×Q8—1221no—
696C2×Q8—1221no—
697C2×Q8—4881no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—42no—
701C2×D4—1221no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—1221no—
705C2×D4—1222no—
706C2×D4—4881no—
707C2×D4—2441no—
708C22×C4—42no—
709C22×C4—611no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—1221no—
716C22×C4—1221no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1222no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—4881no—
725C22×C4—4881no—
726C22×C4—4881no—
727C22×C4—2441no—
728C22×C4C2×C4×D6111yescharacteristic
729C22×C4C2×C4×D6111yescharacteristic
730C22×C4C2×C4×D6111yescharacteristic
731C22×C4C2×C4×D6111yescharacteristic
732C22×C4D4×D6111yescharacteristic
733C22×C4D4×D6111yescharacteristic
734C22×C4D4×D6111yescharacteristic
735C22×C4D4×D6111yescharacteristic
736C22×C4C23×D6111yescharacteristic
737M16—42no—
738M16—2442no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—42no—
744C2×C8—1221no—
745C2×C8—1221no—
746C2×C8—1221no—
747C2×C8—1221no—
748C2×C8—2442no—
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—611no—
754C4⋊C4—611no—
755C4⋊C4—611no—
756C4⋊C4—611no—
757C4⋊C4—611no—
758C4⋊C4—611no—
759C4⋊C4—611no—
760C4⋊C4—611no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—1221no—
769C22⋊C4—21no—
770C22⋊C4—21no—
771C22⋊C4—21no—
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—611no—
776C22⋊C4—611no—
777C22⋊C4—611no—
778C22⋊C4—611no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—1221no—
784C22⋊C4—1221no—
785C22⋊C4—1221no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—1221no—
799C22⋊C4—1221no—
800C22⋊C4—1221no—
801C42—611no—
802C42—611no—
803C42—611no—
804C42—611no—
805C42—611no—
806C42—611no—
807C42—611no—
808C42—611no—
809C42—1221no—
810C42—1221no—
811C23—22no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—21no—
817C23—41no—
818C23—41no—
819C23—41no—
820C23—612no—
821C23—1221no—
822C23—1221no—
823C23—1221no—
824C23—1221no—
825C23—1221no—
826C23—4881no—
827C23—4881no—
828C23—4884no—
829C23—4884no—
830C23—2442no—
831C23—2442no—
832C23—2441no—
833C23—2441no—
834C23—2442no—
835C23—2441no—
836C23—2441no—
837C23—2442no—
838C23C22⋊C4×D6111yescharacteristic
839C23C22⋊C4×D6111yescharacteristic
840C23C22×C4×D6111yescharacteristic
841Q8—4881no—
842Q8—4881no—
843D4—42no—
844D4—42no—
845D4—4881no—
846D4—4881no—
847D4—2442no—
848D4—2442no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—21no—
855C2×C4—21no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—611no—
863C2×C4—611no—
864C2×C4—611no—
865C2×C4—611no—
866C2×C4—611no—
867C2×C4—611no—
868C2×C4—611no—
869C2×C4—611no—
870C2×C4—1221no—
871C2×C4—1221no—
872C2×C4—1221no—
873C2×C4—1221no—
874C2×C4—1221no—
875C2×C4—1221no—
876C2×C4—4881no—
877C2×C4—4881no—
878C2×C4—4881no—
879C2×C4—4881no—
880C2×C4—4881no—
881C2×C4—4881no—
882C2×C4—2442no—
883C2×C4—2442no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2441no—
888C2×C4C22⋊C4×D6111yescharacteristic
889C2×C4C22⋊C4×D6111yescharacteristic
890C2×C4C2×D4×D6111yescharacteristic
891C2×C4C2×D4×D6111yescharacteristic
892C8—41no—
893C8—41no—
894C8—41no—
895C8—41no—
896C8—2441no—
897C8—2441no—
898C8—2441no—
899C8—2441no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—21no—
907C22—42no—
908C22—42no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—81no—
913C22—81no—
914C22—1222no—
915C22—4881no—
916C22—4881no—
917C22—4884no—
918C22—4884no—
919C22—2442no—
920C22—2442no—
921C22—2441no—
922C22—2441no—
923C22—2441no—
924C22—2441no—
925C22—2441no—
926C22#1683973412yes—
927C22C2×C22⋊C4×D6111yescharacteristic
928C22#131×D6111yescharacteristic
929C22#1684052711yescharacteristic
930C4—21no—
931C4—21no—
932C4—21no—
933C4—21no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—1221no—
938C4—1221no—
939C4—1221no—
940C4—1221no—
941C4—1221no—
942C4—1221no—
943C4—1221no—
944C4—1221no—
945C4—2441no—
946C4—2441no—
947C2—21no—
948C2—21no—
949C2—22no—
950C2—41no—
951C2—81no—
952C2—4881no—
953C2—2442no—
954C2#2145426711yescharacteristic
955C2C2×#1683973411yescharacteristic
956C2#2145429611yescharacteristic
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#17412
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. #21454479C2semidirect
3. #21454473C2semidirect
4. #21444187C2semidirect
5. #21444187C2semidirect
6. #21444169C2semidirect
7. #21444169C2semidirect
8. #21444167C2semidirect
9. #21444158C2semidirect
10. #21444152C2semidirect
11. #21444145C2semidirect
12. #21444138C2semidirect
13. #21444132C2semidirect
14. C2×#16839485C2semidirect
15. C61×#1468C2semidirect
42. #16839816C22semidirect
43. #16839816C22semidirect
44. #16839816C22semidirect
45. #16839816C22semidirect
46. #16839812C22semidirect
47. #16839812C22semidirect
48. #16839812C22semidirect
49. #16839812C22semidirect
56. #16839488C22semidirect
57. #16839488C22semidirect
58. #16839486C22semidirect
59. #16839486C22semidirect
71. C61×#324C22semidirect
72. C61×#324C22semidirect
73. C61×#323C22semidirect
74. C61×#323C22semidirect
477. #1468D61semidirect
539. #324C2×D61semidirect
540. #324C2×D61semidirect
551. #323C2×D61semidirect
552. #323C2×D61semidirect
553. C61#17412semidirect

Maximal subgroups

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

subgroupindex
C2×#168404352
#214544792
#214544732
#214441872
#214441692
#214441672
#214441582
#214441522
#214441452
#214441382
#214441322
C2×#168394852
C61×#14682
#1741261