Finite Group Databasebeta

← #29646326

Subgroups — #29646326

Order 15616.

1022 conjugacy classes of subgroups.

The subgroup lattice has 972 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840455C211yesmaximal, characteristic
2#21454855C211yesmaximal, characteristic, complemented
3#21454850C211yesmaximal, characteristic, complemented
4#21444185C211yesmaximal, characteristic, complemented
5#21444185C211yesmaximal, characteristic, complemented
6#21444179C211yesmaximal, characteristic, complemented
7#21444164C211yesmaximal, characteristic, complemented
8#21444164C211yesmaximal, characteristic, complemented
9#21444154C211yesmaximal, characteristic, complemented
10#21444150C211yesmaximal, characteristic, complemented
11#21444148C211yesmaximal, characteristic, complemented
12#21444134C211yesmaximal, characteristic, complemented
13#21444130C211yesmaximal, characteristic, complemented
14C2×#16839487C211yesmaximal, characteristic, complemented
15C61×#1471C211yesmaximal, characteristic, complemented
16#16840455—21no—
17#16840455—21no—
18#16840455—21no—
19#16840455—21no—
20#16840455—21no—
21#16840455—21no—
22#16840455—21no—
23#16840455—21no—
24C2×#14519772C411yescharacteristic
25C2×#14519770C2211yescharacteristic
26C2×#14519767C411yescharacteristic
27C2×#14519759C2211yescharacteristic
28C2×#14519758C411yescharacteristic
29C2×#14519749C411yescharacteristic
30C2×#14519749C411yescharacteristic
31C2×#14519749C411yescharacteristic
32C2×D4×Dic61C411yescharacteristic
33C2×D4×Dic61C411yescharacteristic
34C2×C4×C22⋊D61C2211yescharacteristic
35C2×#14519737C2211yescharacteristic
36C2×#14519733C2211yescharacteristic
37C22×#11758196C2211yescharacteristic
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
47#16839816C2211yescharacteristic
48#16839812C2211yescharacteristic
49#16839812C2211yescharacteristic
50#16839726C2211yescharacteristic
51#16839724C2211yescharacteristic
52#16839724C2211yescharacteristic
53C2×C22⋊#92418C2211yescharacteristic
54C22⋊C8×D61C2211yescharacteristic
55C22⋊C8×D61C2211yescharacteristic
56#16839487C2211yescharacteristic
57#16839487C2211yescharacteristic
58#16839487C2211yescharacteristic
59#16839487C2211yescharacteristic
60#16839487C2211yescharacteristic
61#16839487C2211yescharacteristic
62#16839487C2211yescharacteristic
63#16839487C2211yescharacteristic
64#16839486C2211yescharacteristic
65#16839486C2211yescharacteristic
66#16839486C2211yescharacteristic
67#16839486C2211yescharacteristic
68C2×#121×C61C2211yescharacteristic
69C61×#407C2211yescharacteristic
70C2×C22⋊C8×C61C2211yescharacteristic
71C61×#323C2211yescharacteristic
72C61×#323C2211yescharacteristic
73C61×#323C2211yescharacteristic
74C61×#323C2211yescharacteristic
75C22×C22⋊D61C2×C411yescharacteristic
76C22×C22⋊D61C2×C411yescharacteristic
77C22×C22⋊D61C2×C411yescharacteristic
78C23×Dic61C2×C411yescharacteristic
79C23×Dic61C2×C411yescharacteristic
80C23×Dic61C2×C411yescharacteristic
81C23×Dic61C2×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#14519770—21no—
94#14519770—21no—
95#14519770—21no—
96#14519770—21no—
97#14519767—21no—
98#14519767—21no—
99#14519767—21no—
100#14519767—21no—
101#14519759—21no—
102#14519759—21no—
103#14519759—21no—
104#14519759—21no—
105#14519758—21no—
106#14519758—21no—
107#14519758—21no—
108#14519758—21no—
109#14519749—21no—
110#14519749—21no—
111#14519749—21no—
112#14519749—21no—
113#14519749—21no—
114#14519749—21no—
115#14519749—21no—
116#14519749—21no—
117#14519749—21no—
118#14519749—21no—
119#14519749—21no—
120#14519749—21no—
121D4×Dic61—21no—
122D4×Dic61—21no—
123D4×Dic61—21no—
124D4×Dic61—21no—
125D4×Dic61—21no—
126D4×Dic61—21no—
127D4×Dic61—21no—
128D4×Dic61—21no—
129C4×C22⋊D61D411yescharacteristic
130C4×C22⋊D61D411yescharacteristic
131C4×C22⋊D61D411yescharacteristic
132C4×C22⋊D61D411yescharacteristic
133C4×C22⋊D61D411yescharacteristic
134C4×C22⋊D61D411yescharacteristic
135C4×C22⋊D61D411yescharacteristic
136C4×C22⋊D61D411yescharacteristic
137#14519737—21no—
138#14519737—21no—
139#14519737—21no—
140#14519737—21no—
141#14519733—21no—
142#14519733—21no—
143#14519733—21no—
144#14519733—21no—
145C2×C4⋊Dic61C2×C411yescharacteristic
146C2×C4⋊Dic61C2×C411yescharacteristic
147C2×#11758196—21no—
148C2×#11758196—21no—
149C2×#11758196—21no—
150C2×#11758196—21no—
151C2×#11758196C2×C411yescharacteristic
152C2×#11758196C2×C411yescharacteristic
153C2×#11758196C2×C411yescharacteristic
154C2×#11758196C2×C411yescharacteristic
155C2×#11758196C2×C411yescharacteristic
156C2×#11758196C2311yescharacteristic
157C2×#11758196C2311yescharacteristic
158C2×C22⋊Dic61C2×C411yescharacteristic
159C2×C22⋊Dic61C2×C411yescharacteristic
160C2×C22⋊Dic61C2×C411yescharacteristic
161C2×C22⋊Dic61C2×C411yescharacteristic
162C2×C22⋊Dic61C2×C411yescharacteristic
163C2×#11758198C2×C411yescharacteristic
164C2×#11758198C2×C411yescharacteristic
165C2×#11758198C2×C411yescharacteristic
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
188C22×D4×C61C2×C411yescharacteristic
189C22×D4×C61C2×C411yescharacteristic
190C23×C4×C61C2311yescharacteristic
191C2×M16×C61—21no—
192C22×C8×C61—21no—
193#121×C61—21no—
194#121×C61—21no—
195#121×C61—21no—
196#121×C61—21no—
197C2×C4⋊C4×C61C2×C411yescharacteristic
198C2×C22⋊C4×C61C2311yescharacteristic
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
208C24×C61C22×C411yescharacteristic
209C23×D61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61—42no—
217C2×D4×C61—42no—
218C2×D4×C61—81no—
219C22×C4×C61—81no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C22×C411yescharacteristic
222C22×C4×C61C22×C411yescharacteristic
223C22×C4×C61C2×D411yescharacteristic
224C22×C4×C61C2×D411yescharacteristic
225C22×C4×C61C2×D411yescharacteristic
226C22×C4×C61C2×D411yescharacteristic
227C22×C4×C61C2411yescharacteristic
228C2×C22⋊D61—21no—
229C2×C22⋊D61—21no—
230C2×C22⋊D61—21no—
231C2×C22⋊D61—21no—
232C2×C22⋊D61—22no—
233C2×C22⋊D61—41no—
234C2×C22⋊D61—42no—
235C2×C22⋊D61—81no—
236C2×C22⋊D61C22⋊C411yescharacteristic
237C2×C22⋊D61C22⋊C411yescharacteristic
238C2×C22⋊D61C22⋊C411yescharacteristic
239C2×C22⋊D61C22⋊C411yescharacteristic
240C22×Dic61—21no—
241C22×Dic61—21no—
242C22×Dic61—21no—
243C22×Dic61—21no—
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61—22no—
247C22×Dic61—22no—
248C22×Dic61—21no—
249C22×Dic61—21no—
250C22×Dic61—41no—
251C22×Dic61—41no—
252C22×Dic61—81no—
253C22×Dic61—81no—
254C22×Dic61C22×C411yescharacteristic
255C22×Dic61C22×C411yescharacteristic
256C22×Dic61C22×C411yescharacteristic
257C22×Dic61C22×C411yescharacteristic
258C22×Dic61C22×C411yescharacteristic
259C22×Dic61C22×C411yescharacteristic
260C22×Dic61C22×C411yescharacteristic
261C2×C4×D61—81no—
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266M16×C61—81no—
267C2×C8×C61—21no—
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C2×C8×C61—21no—
271C2×C8×C61—81no—
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⋊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#11758198C22⋊C411yescharacteristic
295#11758198C22⋊C411yescharacteristic
296#11758198C22⋊C411yescharacteristic
297#11758198C22⋊C411yescharacteristic
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—21no—
301C4⋊Dic61—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—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—22no—
339C23×C61—21no—
340C23×C61—21no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61—21no—
345C23×C61—41no—
346C23×C61—41no—
347C23×C61—41no—
348C23×C61—41no—
349C23×C61—41no—
350C23×C61C2×C22⋊C411yescharacteristic
351C23×C61C2×C22⋊C411yescharacteristic
352C23×C61C23×C411yescharacteristic
353C22×D61—21no—
354C22×D61—21no—
355C22×D61—41no—
356C22×D61—41no—
357C22×D61C2×C22⋊C411yescharacteristic
358C22×D61C2×C22⋊C411yescharacteristic
359D4×C61—42no—
360D4×C61—42no—
361D4×C61—42no—
362D4×C61—42no—
363D4×C61—81no—
364D4×C61—81no—
365C2×C4×C61—21no—
366C2×C4×C61—21no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61C2×C22⋊C411yescharacteristic
376C2×C4×C61C2×C22⋊C411yescharacteristic
377C2×C4×C61C22×D411yescharacteristic
378C2×C4×C61C22×D411yescharacteristic
379C22⋊D61—22no—
380C22⋊D61—22no—
381C22⋊D61—41no—
382C22⋊D61—41no—
383C22⋊D61—42no—
384C22⋊D61—42no—
385C22⋊D61—81no—
386C22⋊D61—81no—
387C2×Dic61—21no—
388C2×Dic61—21no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—21no—
393C2×Dic61—21no—
394C2×Dic61—21no—
395C2×Dic61—21no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—42no—
399C2×Dic61—42no—
400C2×Dic61—42no—
401C2×Dic61—42no—
402C2×Dic61—41no—
403C2×Dic61—41no—
404C2×Dic61—81no—
405C2×Dic61—81no—
406C2×Dic61—81no—
407C2×Dic61—81no—
408C2×Dic61C2×C22⋊C411yescharacteristic
409C2×Dic61C2×C22⋊C411yescharacteristic
410C2×Dic61C2×C22⋊C411yescharacteristic
411C2×Dic61C2×C22⋊C411yescharacteristic
412C2×Dic61C2×C22⋊C411yescharacteristic
413C2×Dic61C2×C22⋊C411yescharacteristic
414C2×Dic61#13112yes—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C8×C61—41no—
420C8×C61—41no—
421C8×C61—41no—
422C8×C61—41no—
423#92418—41no—
424#92418—41no—
425#92418—41no—
426#92418—41no—
427#17427—611nomaximal, Sylow
428C22×C61—21no—
429C22×C61—21no—
430C22×C61—21no—
431C22×C61—21no—
432C22×C61—21no—
433C22×C61—21no—
434C22×C61—21no—
435C22×C61—42no—
436C22×C61—42no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61—41no—
441C22×C61—41no—
442C22×C61—41no—
443C22×C61—81no—
444C22×C61—81no—
445C22×C61—81no—
446C22×C61—81no—
447C22×C61#41312yes—
448C22×C61C22×C22⋊C411yescharacteristic
449C22×C61C2×#13111yescharacteristic
450C22×C61#56811yescharacteristic
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—21no—
454C2×D61—21no—
455C2×D61—21no—
456C2×D61—21no—
457C2×D61—81no—
458C2×D61—81no—
459C4×C61—21no—
460C4×C61—21no—
461C4×C61—21no—
462C4×C61—21no—
463C4×C61—41no—
464C4×C61—41no—
465Dic61—22no—
466Dic61—21no—
467Dic61—21no—
468Dic61—21no—
469Dic61—21no—
470Dic61—21no—
471Dic61—21no—
472Dic61—41no—
473Dic61—41no—
474Dic61—41no—
475C2×#553—611no—
476#2974—611no—
477#2974—611no—
478#1473—611no—
479#1473—611no—
480#1471—611no—
481#1471D6111yescharacteristic, complemented
482#1468—611no—
483#1468—611no—
484#1465—611no—
485#1464—611no—
486#1463—611no—
487#1459—611no—
488#1458—611no—
489C2×#324—611no—
490C2×C61—21no—
491C2×C61—21no—
492C2×C61—22no—
493C2×C61—41no—
494C2×C61—81no—
495C2×C61—81no—
496C2×C61#288011yescharacteristic
497C2×C61#288311yescharacteristic
498C2×C61C2×#41311yescharacteristic
499D61—41no—
500D61—41no—
501#553—1221no—
502#553—1221no—
503#553—1221no—
504#553—1221no—
505#553—1221no—
506#553—1221no—
507#553—1221no—
508#553—1221no—
509C2×#126—611no—
510C2×#126—611no—
511C2×#125—611no—
512C2×#123—611no—
513C2×#123—611no—
514C2×#121—611no—
515C2×#121—611no—
516C2×#121—611no—
517C2×#121C2×D6111yescharacteristic
518C2×C4×D4—611no—
519C2×C4×D4—611no—
520C2×C4×D4—611no—
521C2×C4×D4—611no—
522C2×#117—611no—
523C22×C4⋊C4—611no—
524#436—1221no—
525#436—1221no—
526#435—1221no—
527#435—1221no—
528#435—1221no—
529#435—1221no—
530C8×D4—1221no—
531C8×D4—1221no—
532#432—611no—
533#432—611no—
534#431—611no—
535#431—611no—
536#407—611no—
537#407—611no—
538#407—611no—
539#407C2×D6111yescharacteristic
540C2×C22⋊C8—611no—
541C2×C22⋊C8—611no—
542C2×C22⋊C8—611no—
543C2×C22⋊C8C2×D6111yescharacteristic
544#324—611no—
545#324—611no—
546#324—611no—
547#324—611no—
548#324—611no—
549#324—611no—
550#324—611no—
551#324—611no—
552#323—611no—
553#323—611no—
554#323—611no—
555#323—611no—
556#323C2×D6111yescharacteristic
557#323C2×D6111yescharacteristic
558#323C2×D6111yescharacteristic
559#323C2×D6111yescharacteristic
560C61#1742711yescharacteristic, complemented, Sylow
561C22×D4—611no—
562C22×D4—611no—
563C22×D4—611no—
564C22×D4C4×D6111yescharacteristic
565C22×D4C4×D6111yescharacteristic
566C22×D4C4×D6111yescharacteristic
567C23×C4—611no—
568C23×C4—611no—
569C23×C4—611no—
570C23×C4—611no—
571C23×C4—611no—
572C23×C4C22×D6111yescharacteristic
573C2×M16—21no—
574C2×M16—1221no—
575C2×M16—1221no—
576C2×M16—1221no—
577C22×C8—21no—
578C22×C8—1221no—
579C22×C8—1221no—
580C22×C8—1221no—
581#126—1221no—
582#126—1221no—
583#126—1221no—
584#126—1221no—
585#126—1221no—
586#126—1221no—
587#126—1221no—
588#126—1221no—
589#125—1221no—
590#125—1221no—
591#125—1221no—
592#125—1221no—
593#123—1221no—
594#123—1221no—
595#123—1221no—
596#123—1221no—
597#123—1221no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—1221no—
606#121—1221no—
607#121—1221no—
608#121—1221no—
609#121—1221no—
610#121—1221no—
611#121—1221no—
612#121—1221no—
613#121—1221no—
614#121—1221no—
615#121—1221no—
616#121—1221no—
617C4×D4—611no—
618C4×D4—611no—
619C4×D4—611no—
620C4×D4—611no—
621C4×D4—611no—
622C4×D4—611no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—1221no—
626C4×D4—1221no—
627C4×D4—1221no—
628C4×D4—1221no—
629C4×D4—1221no—
630C4×D4—1221no—
631C4×D4—1221no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637#117—1221no—
638#117—1221no—
639#117—1221no—
640#117—1221no—
641C2×C4⋊C4—611no—
642C2×C4⋊C4—611no—
643C2×C4⋊C4—611no—
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—611no—
647C2×C4⋊C4—611no—
648C2×C4⋊C4—611no—
649C2×C4⋊C4—611no—
650C2×C4⋊C4—1221no—
651C2×C4⋊C4—1221no—
652C2×C4⋊C4—1221no—
653C2×C4⋊C4—1221no—
654C2×C4⋊C4C4×D6111yescharacteristic
655C2×C22⋊C4—611no—
656C2×C22⋊C4—611no—
657C2×C22⋊C4—611no—
658C2×C22⋊C4—611no—
659C2×C22⋊C4—611no—
660C2×C22⋊C4—611no—
661C2×C22⋊C4—611no—
662C2×C22⋊C4—611no—
663C2×C22⋊C4C22×D6111yescharacteristic
664C2×C22⋊C4C22×D6111yescharacteristic
665C2×C42—611no—
666C2×C42—611no—
667C2×C42—611no—
668C4⋊C8—1221no—
669C4⋊C8—1221no—
670C4⋊C8—1221no—
671C4⋊C8—1221no—
672C22⋊C8—21no—
673C22⋊C8—21no—
674C22⋊C8—611no—
675C22⋊C8—611no—
676C22⋊C8—611no—
677C22⋊C8—611no—
678C22⋊C8—1221no—
679C22⋊C8—1221no—
680C22⋊C8—1221no—
681C22⋊C8—1221no—
682C22⋊C8—1221no—
683C22⋊C8—1221no—
684C22⋊C8C22×D6111yescharacteristic
685C22⋊C8C22×D6111yescharacteristic
686C22⋊C8C22×D6111yescharacteristic
687C22⋊C8C22×D6111yescharacteristic
688#97—1221no—
689#97—1221no—
690C4×C8—1221no—
691C4×C8—1221no—
692C24—611no—
693C24C2×C4×D6111yescharacteristic
694C24C2×C4×D6111yescharacteristic
695C24C2×C4×D6111yescharacteristic
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—42no—
703C2×D4—42no—
704C2×D4—81no—
705C2×D4—611no—
706C2×D4—611no—
707C2×D4—611no—
708C2×D4—611no—
709C2×D4—1222no—
710C2×D4—1221no—
711C2×D4—1221no—
712C2×D4—1221no—
713C2×D4—1221no—
714C2×D4—4881no—
715C2×D4—2441no—
716C2×D4—2442no—
717C22×C4—81no—
718C22×C4—611no—
719C22×C4—611no—
720C22×C4—611no—
721C22×C4—611no—
722C22×C4—611no—
723C22×C4—611no—
724C22×C4—611no—
725C22×C4—611no—
726C22×C4—611no—
727C22×C4—611no—
728C22×C4—611no—
729C22×C4—1221no—
730C22×C4—1221no—
731C22×C4—1221no—
732C22×C4—1221no—
733C22×C4—1222no—
734C22×C4—1222no—
735C22×C4—1221no—
736C22×C4—1221no—
737C22×C4—1221no—
738C22×C4—1221no—
739C22×C4—4881no—
740C22×C4—4881no—
741C22×C4—4881no—
742C22×C4—2441no—
743C22×C4—2441no—
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—611no—
771C4⋊C4—611no—
772C4⋊C4—611no—
773C4⋊C4—611no—
774C4⋊C4—1221no—
775C4⋊C4—1221no—
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—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—611no—
795C22⋊C4—611no—
796C22⋊C4—611no—
797C22⋊C4—611no—
798C22⋊C4—611no—
799C22⋊C4—611no—
800C22⋊C4—611no—
801C22⋊C4—611no—
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—
814C42—611no—
815C42—611no—
816C42—611no—
817C42—611no—
818C42—1221no—
819C42—1221no—
820C42—1221no—
821C42—1221no—
822C23—22no—
823C23—21no—
824C23—21no—
825C23—21no—
826C23—21no—
827C23—21no—
828C23—21no—
829C23—21no—
830C23—21no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—611no—
837C23—611no—
838C23—1221no—
839C23—1221no—
840C23—2441no—
841C23—2441no—
842C23C22⋊C4×D6111yescharacteristic
843C23C22⋊C4×D6111yescharacteristic
844C23C22×C4×D6111yescharacteristic
845D4—42no—
846D4—42no—
847D4—42no—
848D4—42no—
849D4—81no—
850D4—81no—
851D4—1222no—
852D4—1222no—
853D4—4881no—
854D4—4881no—
855D4—2441no—
856D4—2441no—
857D4—2442no—
858D4—2442no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—611no—
870C2×C4—611no—
871C2×C4—611no—
872C2×C4—611no—
873C2×C4—611no—
874C2×C4—611no—
875C2×C4—612no—
876C2×C4—1221no—
877C2×C4—1221no—
878C2×C4—1221no—
879C2×C4—1221no—
880C2×C4—1221no—
881C2×C4—1221no—
882C2×C4—1221no—
883C2×C4—1221no—
884C2×C4—1221no—
885C2×C4—4881no—
886C2×C4—4881no—
887C2×C4—4881no—
888C2×C4—4881no—
889C2×C4—2441no—
890C2×C4—2441no—
891C2×C4—2441no—
892C2×C4—2441no—
893C2×C4—2441no—
894C2×C4—2441no—
895C2×C4—2442no—
896C2×C4—2442no—
897C2×C4—2442no—
898C2×C4—2442no—
899C2×C4—2441no—
900C2×C4—2441no—
901C2×C4C22⋊C4×D6111yescharacteristic
902C2×C4C22⋊C4×D6111yescharacteristic
903C2×C4C2×D4×D6111yescharacteristic
904C2×C4C2×D4×D6111yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C8—2441no—
910C8—2441no—
911C8—2441no—
912C8—2441no—
913C22—21no—
914C22—21no—
915C22—21no—
916C22—21no—
917C22—21no—
918C22—21no—
919C22—21no—
920C22—42no—
921C22—42no—
922C22—41no—
923C22—41no—
924C22—41no—
925C22—41no—
926C22—41no—
927C22—41no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—1221no—
933C22—1221no—
934C22—1221no—
935C22—1221no—
936C22—1221no—
937C22—1221no—
938C22—4881no—
939C22—4881no—
940C22#1683974312yes—
941C22C2×C22⋊C4×D6111yescharacteristic
942C22#131×D6111yescharacteristic
943C22#1684052711yescharacteristic
944C4—21no—
945C4—21no—
946C4—21no—
947C4—21no—
948C4—41no—
949C4—41no—
950C4—1221no—
951C4—1221no—
952C4—1222no—
953C4—1221no—
954C4—1221no—
955C4—1221no—
956C4—1221no—
957C4—2441no—
958C4—2441no—
959C4—2441no—
960C2—21no—
961C2—21no—
962C2—22no—
963C2—41no—
964C2—81no—
965C2—81no—
966C2—2441no—
967C2—2441no—
968C2#2145426711yescharacteristic
969C2#2145427711yescharacteristic
970C2C2×#1683974311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1471C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#16840455C2
cosocleC22×C4×C61C24
hypercenter#1471D61
hypocenterC61#17427
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1471

Complements

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

NH ≅ G/Ntype
2. #21454855C2semidirect
3. #21454850C2semidirect
4. #21444185C2semidirect
5. #21444185C2semidirect
6. #21444179C2semidirect
7. #21444164C2semidirect
8. #21444164C2semidirect
9. #21444154C2semidirect
10. #21444150C2semidirect
11. #21444148C2semidirect
12. #21444134C2semidirect
13. #21444130C2semidirect
14. C2×#16839487C2semidirect
15. C61×#1471C2semidirect
481. #1471D61semidirect
560. C61#17427semidirect

Maximal subgroups

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

subgroupindex
C2×#168404552
#214548552
#214548502
#214441852
#214441792
#214441642
#214441542
#214441502
#214441482
#214441342
#214441302
C2×#168394872
C61×#14712
#1742761