Finite Group Databasebeta

← #29647660

Subgroups — #29647660

Order 15616.

1298 conjugacy classes of subgroups.

The subgroup lattice has 1066 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459495C211yesmaximal, characteristic
2#21454265C211yesmaximal, characteristic, complemented
3#21448646C211yesmaximal, characteristic, complemented
4#21444389C211yesmaximal, characteristic, complemented
5#21444376C211yesmaximal, characteristic, complemented
6#21444374C211yesmaximal, characteristic, complemented
7#21444361C211yesmaximal, characteristic, complemented
8#21444352C211yesmaximal, characteristic, complemented
9#21444350C211yesmaximal, characteristic, complemented
10#21444337C211yesmaximal, characteristic, complemented
11#21444322C211yesmaximal, characteristic, complemented
12#21444321C211yesmaximal, characteristic, complemented
13#21444309C211yesmaximal, characteristic, complemented
14#328×D61C211yesmaximal, characteristic, complemented
15C2×C61×#328C211yesmaximal, characteristic, complemented
16C2×#14519825C411yescharacteristic, complemented
17C22×#11758222C2211yescharacteristic
18C2×#14519783—21no—
19#16840425—21no—
20#16840422—21no—
21#16840414—21no—
22#16840413—21no—
23#16840413—21no—
24#16840403—21no—
25#16840402—21no—
26#16840402—21no—
27#16840343C411yescharacteristic, complemented
28#16840342C411yescharacteristic, complemented
29#16840342C411yescharacteristic, complemented
30#16840336C411yescharacteristic, complemented
31#16840335C411yescharacteristic, complemented
32#16840335C411yescharacteristic, complemented
33#16840275C2211yescharacteristic
34#16840275C2211yescharacteristic
35#16840273C2211yescharacteristic
36C22⋊Q8×D61C2211yescharacteristic
37C22⋊Q8×D61C2211yescharacteristic
38#16840243C411yescharacteristic, complemented
39C2×C4×C22⋊D61—21no—
40#16839728—21no—
41#16839727—21no—
42#16839727—21no—
43#16839726C2211yescharacteristic
44#16839724C2211yescharacteristic
45#16839724C2211yescharacteristic
46C22⋊C8×D61C2211yescharacteristic
47C22⋊C8×D61C2211yescharacteristic
48#16839666—21no—
49#16839641—21no—
50#16839640—21no—
51#16839625C2211yescharacteristic
52#16839624C2211yescharacteristic
53#16839621C2211yescharacteristic
54#16839609C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839499C2211yescharacteristic
59#16839499C2211yescharacteristic
60#16839499C2211yescharacteristic
61#16839499C2211yescharacteristic
62#16839498C2211yescharacteristic
63#16839498C2211yescharacteristic
64#16839497C2211yescharacteristic
65#16839497C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C2×C22⋊Q8×C61C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic
70C2×#95×C61C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#328C2211yescharacteristic
74C61×#328C2211yescharacteristic
75#14519825—44no—
76C2×#11758226—21no—
77C2×#11758226C2×C411yescharacteristic, complemented
78C2×#11758226C2×C411yescharacteristic, complemented
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222—44no—
82C2×#11758222C2×C411yescharacteristic
83C2×#11758222C2×C411yescharacteristic
84C2×#11758222C2×C411yescharacteristic
85C2×#11758222C2×C411yescharacteristic
86C2×#11758222C2×C411yescharacteristic, complemented
87C2×#11758222D411yescharacteristic
88C2×#11758222D411yescharacteristic
89C2×#11758222D411yescharacteristic
90C2×#11758222D411yescharacteristic
91C22×Dic122D411yescharacteristic
92C2×Q8×D61—21no—
93C2×Q8×D61C2×C411yescharacteristic, complemented
94C2×Q8×D61C2×C411yescharacteristic, complemented
95C22×D244D411yescharacteristic
96C22×C22⋊D61D411yescharacteristic
97C22×C22⋊D61D411yescharacteristic
98C22×C4×D61—21no—
99C22×C4×D61C2311yescharacteristic
100C22×C4×D61C2311yescharacteristic
101#14519783—44no—
102C2×#11758194—21no—
103C2×#11758189—21no—
104C2×#11758189—21no—
105C2×C8×D61—21no—
106C2×C8×D61—21no—
107#14519776—21no—
108#14519776—21no—
109#14519775—21no—
110#14519766—21no—
111#14519763—21no—
112#14519763—21no—
113#14519762—21no—
114#14519762—21no—
115#14519762—21no—
116#14519762—21no—
117#14519760—21no—
118#14519760—21no—
119#14519760—21no—
120#14519759—21no—
121#14519759—21no—
122#14519757—21no—
123#14519757C2×C411yescharacteristic, complemented
124#14519757C2×C411yescharacteristic, complemented
125#14519756C2×C411yescharacteristic, complemented
126#14519756C2311yescharacteristic
127#14519755—21no—
128#14519755—21no—
129#14519755—21no—
130#14519755—21no—
131#14519754—21no—
132#14519754—21no—
133#14519753C2×C411yescharacteristic, complemented
134#14519753C2×C411yescharacteristic, complemented
135#14519753C2×C411yescharacteristic, complemented
136#14519753C2×C411yescharacteristic, complemented
137#14519752—21no—
138#14519752—21no—
139#14519752—21no—
140#14519752C2×C411yescharacteristic, complemented
141#14519752C2×C411yescharacteristic, complemented
142#14519751—21no—
143#14519751—21no—
144#14519751C2×C411yescharacteristic, complemented
145#14519751C2311yescharacteristic
146#14519750—21no—
147#14519750—21no—
148#14519750—21no—
149#14519750—21no—
150#14519747—21no—
151#14519747—21no—
152#14519746—21no—
153#14519742—21no—
154#14519739—21no—
155#14519739—21no—
156#14519739—21no—
157C4×C22⋊D61—21no—
158C4×C22⋊D61—21no—
159C4×C22⋊D61—21no—
160C4×C22⋊D61—21no—
161C4×C22⋊D61—44no—
162#14519737—21no—
163#14519737—21no—
164#14519736C2×C411yescharacteristic, complemented
165#14519735C2×C411yescharacteristic, complemented
166#14519735C2×C411yescharacteristic, complemented
167C2×#11758196—21no—
168C4⋊C4×D61—21no—
169C4⋊C4×D61—21no—
170C4⋊C4×D61C2×C411yescharacteristic, complemented
171C4⋊C4×D61C2×C411yescharacteristic, complemented
172C2×C22⋊Dic61—21no—
173C2×#11758198—21no—
174C2×#11758198—21no—
175C2×#11758198—21no—
176C22⋊C4×D61—21no—
177C22⋊C4×D61—21no—
178C2×C4×Dic61—21no—
179C22⋊#92418—21no—
180C22⋊#92418C2311yescharacteristic
181C22⋊#92418C2311yescharacteristic
182#14519689—21no—
183#14519689—21no—
184#14519689—21no—
185#14519689—21no—
186#14519684—21no—
187#14519684—21no—
188#14519684—21no—
189#14519684C2311yescharacteristic
190#14519684C2311yescharacteristic
191C22×Q8×C61C2×C411yescharacteristic, complemented
192C23×C4×C61—21no—
193C23×C4×C61C2311yescharacteristic
194C22×C8×C61—21no—
195C22⋊Q8×C61—21no—
196C22⋊Q8×C61—21no—
197C22⋊Q8×C61C2×C411yescharacteristic, complemented
198C22⋊Q8×C61C2×C411yescharacteristic, complemented
199C22⋊Q8×C61C2311yescharacteristic
200C22⋊Q8×C61C2311yescharacteristic
201C2×C4⋊C4×C61—21no—
202C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
203C2×C22⋊C4×C61—21no—
204C22⋊C8×C61—21no—
205C22⋊C8×C61C2311yescharacteristic
206C22⋊C8×C61C2311yescharacteristic
207#95×C61—21no—
208#95×C61C2311yescharacteristic
209#95×C61C2311yescharacteristic
210C24×C61C2×D411yescharacteristic
211C23×D61C2×D411yescharacteristic
212C23×D61C2×D411yescharacteristic
213C2×Q8×C61—21no—
214C2×Q8×C61—42no—
215C2×Q8×C61C22×C411yescharacteristic
216C2×Q8×C61C22×C411yescharacteristic
217C22×C4×C61—21no—
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61—21no—
221C22×C4×C61—42no—
222C22×C4×C61—42no—
223C22×C4×C61—42no—
224C22×C4×C61—81no—
225C22×C4×C61C22×C411yescharacteristic
226C22×C4×C61C22×C411yescharacteristic
227C22×C4×C61C2×D411yescharacteristic
228C22×C4×C61C2×D411yescharacteristic
229C22×C4×C61C2×D411yescharacteristic
230C22×C4×C61C2411yescharacteristic
231C2×C22⋊D61—24no—
232C2×C22⋊D61—21no—
233C2×C22⋊D61—21no—
234C2×C22⋊D61—21no—
235C2×C22⋊D61—42no—
236C2×C22⋊D61C22⋊C411yescharacteristic
237C2×C22⋊D61C22⋊C411yescharacteristic
238C2×C22⋊D61C22⋊C411yescharacteristic
239C2×C22⋊D61C22⋊C411yescharacteristic
240C2×C22⋊D61C22⋊C411yescharacteristic
241C2×C22⋊D61C22⋊C411yescharacteristic
242C2×C22⋊D61C22⋊C411yescharacteristic
243C2×C22⋊D61C22⋊C411yescharacteristic
244C22×Dic61—21no—
245C22×Dic61—21no—
246C22×Dic61C2×D411yescharacteristic
247C22×Dic61C2×D411yescharacteristic
248#11758226—42no—
249#11758226—42no—
250#11758226—44no—
251Q8×D61—44no—
252Q8×D61—42no—
253Q8×D61—42no—
254#11758222—24no—
255#11758222—24no—
256#11758222—42no—
257#11758222—42no—
258#11758222—42no—
259#11758222—42no—
260#11758222—42no—
261#11758222—42no—
262#11758222—44no—
263#11758222—44no—
264#11758222—42no—
265C2×D244—21no—
266C2×D244—21no—
267C2×D244—21no—
268C2×D244—21no—
269C2×D244—42no—
270C2×D244C22⋊C411yescharacteristic
271C2×D244C22⋊C411yescharacteristic
272C2×D244C22⋊C411yescharacteristic
273C2×D244C22⋊C411yescharacteristic
274C2×D244C22×C411yescharacteristic
275C2×C4×D61—21no—
276C2×C4×D61—21no—
277C2×C4×D61—21no—
278C2×C4×D61—21no—
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—42no—
283C2×C4×D61—42no—
284C2×C4×D61—42no—
285C2×C4×D61—42no—
286C2×C4×D61—81no—
287C2×C4×D61C22×C411yescharacteristic
288C2×C4×D61C22×C411yescharacteristic
289C2×C4×D61C22×C411yescharacteristic
290C2×C4×D61C22×C411yescharacteristic
291C2×C4×D61C2×D411yescharacteristic
292C2×C4×D61C2×D411yescharacteristic
293C2×C4×D61C2×D411yescharacteristic
294C2×C4×D61C2×D411yescharacteristic
295C2×Dic122—21no—
296C2×Dic122—21no—
297C2×Dic122—42no—
298C2×Dic122C22⋊C411yescharacteristic
299C2×Dic122C22⋊C411yescharacteristic
300C2×Dic122C22⋊C411yescharacteristic
301C2×Dic122C22⋊C411yescharacteristic
302C2×Dic122C22×C411yescharacteristic
303C2×C8×C61—21no—
304C2×C8×C61—21no—
305C2×C8×C61—42no—
306C4⋊C4×C61—21no—
307C4⋊C4×C61—21no—
308C4⋊C4×C61—21no—
309C4⋊C4×C61—21no—
310C4⋊C4×C61—21no—
311C4⋊C4×C61C22×C411yescharacteristic
312C4⋊C4×C61C22×C411yescharacteristic
313C22⋊C4×C61—21no—
314C22⋊C4×C61—21no—
315C22⋊C4×C61—21no—
316C22⋊C4×C61—21no—
317C22⋊Dic61—21no—
318C22⋊Dic61—21no—
319C22⋊Dic61—21no—
320C22⋊Dic61—42no—
321#11758198—21no—
322#11758198—21no—
323#11758198—21no—
324#11758198—21no—
325#11758198—21no—
326#11758198—21no—
327#11758198—21no—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198—42no—
334#11758198—42no—
335#11758198—81no—
336C4⋊Dic61—21no—
337C4⋊Dic61—21no—
338C4⋊Dic61C22×C411yescharacteristic
339C4⋊Dic61C22×C411yescharacteristic
340#11758196—21no—
341#11758196—21no—
342#11758196—21no—
343#11758196—21no—
344#11758196—21no—
345#11758196—21no—
346#11758196—21no—
347#11758196—21no—
348#11758196—42no—
349C4×Dic61—21no—
350C4×Dic61—21no—
351C4×Dic61—21no—
352C4×Dic61—42no—
353#11758194—42no—
354C2×#92418—21no—
355C2×#92418—21no—
356#11758189—42no—
357#11758189—42no—
358C8×D61—42no—
359C8×D61—42no—
360C23×C61—21no—
361C23×C61—21no—
362C23×C61—22no—
363C23×C61—41no—
364C23×C61C2×C22⋊C411yescharacteristic
365C23×C61C2×C22⋊C411yescharacteristic
366C23×C61C22×D411yescharacteristic
367C22×D61—21no—
368C22×D61—21no—
369C22×D61—21no—
370C22×D61—21no—
371C22×D61—22no—
372C22×D61—21no—
373C22×D61—41no—
374C22×D61—41no—
375C22×D61—41no—
376C22×D61C2×C22⋊C411yescharacteristic
377C22×D61C2×C22⋊C411yescharacteristic
378C22×D61C2×C22⋊C411yescharacteristic
379C22×D61C2×C22⋊C411yescharacteristic
380Q8×C61—42no—
381Q8×C61—41no—
382Q8×C61—41no—
383C2×C4×C61—22no—
384C2×C4×C61—22no—
385C2×C4×C61—22no—
386C2×C4×C61—21no—
387C2×C4×C61—21no—
388C2×C4×C61—21no—
389C2×C4×C61—21no—
390C2×C4×C61—41no—
391C2×C4×C61—41no—
392C2×C4×C61—41no—
393C2×C4×C61—41no—
394C2×C4×C61—41no—
395C2×C4×C61—41no—
396C2×C4×C61—42no—
397C2×C4×C61—41no—
398C2×C4×C61—41no—
399C2×C4×C61—41no—
400C2×C4×C61—81no—
401C2×C4×C61—84no—
402C2×C4×C61C2×C22⋊C411yescharacteristic
403C2×C4×C61C2×C22⋊C411yescharacteristic
404C2×C4×C61C23×C411yescharacteristic
405C2×C4×C61C22×D411yescharacteristic
406C22⋊D61—22no—
407C22⋊D61—22no—
408C22⋊D61—22no—
409C22⋊D61—22no—
410C22⋊D61—22no—
411C22⋊D61—41no—
412C22⋊D61—41no—
413C22⋊D61—41no—
414C22⋊D61—41no—
415C22⋊D61—42no—
416C22⋊D61—81no—
417C22⋊D61#9914yes—
418C2×Dic61—22no—
419C2×Dic61—21no—
420C2×Dic61—21no—
421C2×Dic61—21no—
422C2×Dic61—41no—
423C2×Dic61—41no—
424C2×Dic61—41no—
425C2×Dic61—41no—
426C2×Dic61—41no—
427C2×Dic61—41no—
428C2×Dic61—41no—
429C2×Dic61C2×C22⋊C411yescharacteristic
430C2×Dic61C2×C22⋊C411yescharacteristic
431C2×Dic61C2×C22⋊C411yescharacteristic
432C2×Dic61C2×C22⋊C411yescharacteristic
433D244—22no—
434D244—22no—
435D244—41no—
436D244—41no—
437D244—41no—
438D244—42no—
439D244—42no—
440D244—81no—
441D244—81no—
442C4×D61—22no—
443C4×D61—22no—
444C4×D61—22no—
445C4×D61—22no—
446C4×D61—41no—
447C4×D61—41no—
448C4×D61—41no—
449C4×D61—41no—
450C4×D61—42no—
451C4×D61—42no—
452C4×D61—42no—
453C4×D61—42no—
454C4×D61—42no—
455C4×D61—81no—
456C4×D61—81no—
457C4×D61—84no—
458Dic122—22no—
459Dic122—22no—
460Dic122—41no—
461Dic122—41no—
462Dic122—42no—
463Dic122—42no—
464Dic122—41no—
465C8×C61—41no—
466C8×C61—41no—
467#92418—41no—
468#92418—41no—
469#17608—611nomaximal, Sylow
470C22×C61—21no—
471C22×C61—21no—
472C22×C61—21no—
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—42no—
478C22×C61—42no—
479C22×C61C2×#9912yes—
480C22×C61C22×C22⋊C411yescharacteristic
481C22×C61#57711yescharacteristic
482C22×C61#57811yescharacteristic
483C2×D61—21no—
484C2×D61—21no—
485C2×D61—21no—
486C2×D61—21no—
487C2×D61—21no—
488C2×D61—21no—
489C2×D61—21no—
490C2×D61—21no—
491C2×D61—21no—
492C2×D61—21no—
493C2×D61—21no—
494C2×D61—42no—
495C2×D61—42no—
496C2×D61—41no—
497C2×D61—41no—
498C2×D61—41no—
499C2×D61—81no—
500C2×D61—81no—
501C2×D61C2×#9912yes—
502C4×C61—21no—
503C4×C61—21no—
504C4×C61—21no—
505C4×C61—21no—
506C4×C61—42no—
507C4×C61—41no—
508C4×C61—41no—
509C4×C61—41no—
510C4×C61—41no—
511C4×C61—81no—
512Dic61—21no—
513Dic61—21no—
514Dic61—21no—
515Dic61—41no—
516Dic61—41no—
517Dic61—41no—
518Dic61—81no—
519Dic61—81no—
520Dic61C2×#9912yes—
521#3489—611no—
522#2880—611no—
523#2339—611no—
524#1520—611no—
525#1516—611no—
526#1516—611no—
527#1513—611no—
528#1511—611no—
529#1511—611no—
530#1508—611no—
531#1504—611no—
532#1504—611no—
533#1501—611no—
534C2×#328—611no—
535C2×#328D6111yescharacteristic, complemented
536C2×C61—21no—
537C2×C61—21no—
538C2×C61—22no—
539C2×C61—41no—
540C2×C61C22×#9911yescharacteristic
541C2×C61#289811yescharacteristic
542C2×C61#290111yescharacteristic
543D61—22no—
544D61—41no—
545D61—41no—
546D61—41no—
547D61—81no—
548C2×2−1+4—611no—
549C22×#41—611no—
550C2×#131—1221no—
551D4×Q8—1221no—
552#548—1221no—
553#547—1221no—
554#547—1221no—
555#547—1221no—
556#546—1221no—
557#546—1221no—
558#546—1221no—
559#537—611no—
560#537—611no—
561#537—611no—
562#536—611no—
563#536—611no—
564#536—611no—
565#525—611no—
566#525—611no—
567#525—611no—
568C2×C22⋊Q8—611no—
569C2×C22⋊Q8—611no—
570C2×C22⋊Q8C2×D6111yescharacteristic
571#520—611no—
572C2×C4×D4—1221no—
573#408—1221no—
574#408—1221no—
575#408—1221no—
576#407—611no—
577#407—611no—
578#407—611no—
579C2×C22⋊C8—611no—
580C2×C22⋊C8—611no—
581C2×C22⋊C8C2×D6111yescharacteristic
582#391—1221no—
583#386—1221no—
584#386—1221no—
585#381—611no—
586#381—611no—
587#380—611no—
588C4×C22⋊C4—611no—
589C2×#95—611no—
590C2×#95C2×D6111yescharacteristic
591#328—611no—
592#328—611no—
593#328—611no—
594#328—611no—
595#328—611no—
596#328—611no—
597#328—611no—
598#328—611no—
599#328C2×D6111yescharacteristic
600#328C2×D6111yescharacteristic
601#328C2×D6111yescharacteristic
602#328C2×D6111yescharacteristic
603#327—611no—
604#327—611no—
605#327—611no—
606#327—611no—
607C61#1760811yescharacteristic, complemented, Sylow
6082−1+4—2444no—
609C2×#41—611no—
610C2×#41—611no—
611C2×#41—611no—
612C2×#41—611no—
613C2×#41—611no—
614C2×#41—611no—
615C2×#41—611no—
616C2×#41—611no—
617C2×#41—611no—
618C2×#41—611no—
619C2×#41—611no—
620C2×#41—1221no—
621C2×#41—1221no—
622C2×#41—1221no—
623C2×#41—2444no—
624C22×Q8—611no—
625C22×Q8—611no—
626C22×Q8—611no—
627C22×Q8—1221no—
628C22×Q8C4×D6111yescharacteristic, complemented
629C22×D4—611no—
630C22×D4—611no—
631C22×D4—611no—
632C23×C4—21no—
633C23×C4—611no—
634C23×C4—611no—
635C23×C4—1221no—
636C23×C4C22×D6111yescharacteristic
637#131—2444no—
638C2×M16—1221no—
639C2×M16—1221no—
640C2×M16—1221no—
641C22×C8—21no—
642C22×C8—1221no—
643C22×C8—1221no—
644C4⋊Q8—1221no—
645C4⋊Q8—1221no—
646C4⋊Q8—1221no—
647#124—1221no—
648#124—1221no—
649#124—1221no—
650#123—1221no—
651#123—1221no—
652#123—1221no—
653#123—1221no—
654#123—1221no—
655#123—1221no—
656#123—1221no—
657#123—1221no—
658#123—1221no—
659C22⋊Q8—21no—
660C22⋊Q8—21no—
661C22⋊Q8—611no—
662C22⋊Q8—611no—
663C22⋊Q8—611no—
664C22⋊Q8—611no—
665C22⋊Q8—611no—
666C22⋊Q8—611no—
667C22⋊Q8—611no—
668C22⋊Q8—611no—
669C22⋊Q8—1221no—
670C22⋊Q8—1221no—
671C22⋊Q8—1221no—
672C22⋊Q8—1221no—
673C22⋊Q8—1221no—
674C22⋊Q8—1221no—
675C22⋊Q8—1221no—
676C22⋊Q8C4×D6111yescharacteristic, complemented
677C22⋊Q8C4×D6111yescharacteristic, complemented
678C22⋊Q8C22×D6111yescharacteristic
679C22⋊Q8C22×D6111yescharacteristic
680#121—611no—
681#121—611no—
682#121—611no—
683#121—611no—
684#121—1221no—
685#121—1221no—
686#121—1221no—
687#121—1221no—
688#121—1221no—
689#121—1221no—
690#121—1221no—
691#121—1221no—
692#121—1221no—
693#120—1221no—
694#120—1221no—
695#120—1221no—
696C4×Q8—1221no—
697C4×D4—1221no—
698C4×D4—1221no—
699C4×D4—1221no—
700C4×D4—1221no—
701C4×D4—1221no—
702C4×D4—1221no—
703C4×D4—1221no—
704C4×D4—1221no—
705C4×D4—1221no—
706C4×D4—2444no—
707#117—611no—
708#117—611no—
709#117—611no—
710C2×C4⋊C4—21no—
711C2×C4⋊C4—611no—
712C2×C4⋊C4—611no—
713C2×C4⋊C4—1221no—
714C2×C4⋊C4—1221no—
715C2×C4⋊C4—1221no—
716C2×C4⋊C4C4×D6111yescharacteristic, complemented
717C2×C22⋊C4—21no—
718C2×C22⋊C4—1221no—
719C2×C22⋊C4—1221no—
720C2×C22⋊C4—1221no—
721C2×C22⋊C4—1221no—
722C2×C22⋊C4—1221no—
723C2×C22⋊C4—1221no—
724C2×C42—1221no—
725C22⋊C8—21no—
726C22⋊C8—611no—
727C22⋊C8—611no—
728C22⋊C8—1221no—
729C22⋊C8—1221no—
730C22⋊C8—1221no—
731C22⋊C8—1221no—
732C22⋊C8—1221no—
733C22⋊C8C22×D6111yescharacteristic
734C22⋊C8C22×D6111yescharacteristic
735#95—21no—
736#95—611no—
737#95—611no—
738#95—1221no—
739#95—1221no—
740#95—1221no—
741#95C22×D6111yescharacteristic
742#95C22×D6111yescharacteristic
743C24—611no—
744C24—611no—
745C24D4×D6111yescharacteristic
746#41—1224no—
747#41—1224no—
748#41—2442no—
749#41—2442no—
750#41—2442no—
751#41—2442no—
752#41—2442no—
753#41—2442no—
754#41—2442no—
755#41—2444no—
756#41—2444no—
757#41—2442no—
758#41—2442no—
759#41—2444no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8—611no—
763C2×Q8—611no—
764C2×Q8—611no—
765C2×Q8—611no—
766C2×Q8—611no—
767C2×Q8—1221no—
768C2×Q8—1221no—
769C2×Q8—2442no—
770C2×Q8—2442no—
771C2×Q8—2442no—
772C2×Q8—2444no—
773C2×Q8C2×C4×D6111yescharacteristic
774C2×Q8C2×C4×D6111yescharacteristic
775C2×D4—611no—
776C2×D4—611no—
777C2×D4—611no—
778C2×D4—611no—
779C2×D4—611no—
780C2×D4—611no—
781C2×D4—611no—
782C2×D4—611no—
783C2×D4—611no—
784C2×D4—611no—
785C2×D4—611no—
786C2×D4—611no—
787C2×D4—611no—
788C2×D4—1221no—
789C2×D4—1221no—
790C2×D4—1221no—
791C2×D4—1221no—
792C2×D4—1224no—
793C2×D4—1221no—
794C2×D4—1221no—
795C2×D4—1221no—
796C2×D4—2442no—
797C2×D4—2442no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—42no—
803C22×C4—42no—
804C22×C4—42no—
805C22×C4—81no—
806C22×C4—611no—
807C22×C4—611no—
808C22×C4—611no—
809C22×C4—611no—
810C22×C4—611no—
811C22×C4—611no—
812C22×C4—611no—
813C22×C4—611no—
814C22×C4—611no—
815C22×C4—611no—
816C22×C4—1221no—
817C22×C4—1221no—
818C22×C4—1221no—
819C22×C4—1221no—
820C22×C4—1221no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—1221no—
825C22×C4—4881no—
826C22×C4—2442no—
827C22×C4—2442no—
828C22×C4—2442no—
829C22×C4—2442no—
830C22×C4C2×C4×D6111yescharacteristic
831C22×C4C2×C4×D6111yescharacteristic
832C22×C4D4×D6111yescharacteristic
833C22×C4D4×D6111yescharacteristic
834C22×C4D4×D6111yescharacteristic
835C22×C4C23×D6111yescharacteristic
836M16—2442no—
837M16—2442no—
838M16—2442no—
839C2×C8—21no—
840C2×C8—21no—
841C2×C8—42no—
842C2×C8—1221no—
843C2×C8—1221no—
844C2×C8—2442no—
845C2×C8—2442no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—611no—
852C4⋊C4—611no—
853C4⋊C4—1221no—
854C4⋊C4—1221no—
855C4⋊C4—1221no—
856C4⋊C4—1221no—
857C4⋊C4—1221no—
858C4⋊C4—1221no—
859C4⋊C4—1221no—
860C4⋊C4—1221no—
861C4⋊C4—1221no—
862C4⋊C4—1221no—
863C4⋊C4—2442no—
864C4⋊C4C2×C4×D6111yescharacteristic
865C4⋊C4C2×C4×D6111yescharacteristic
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—1221no—
871C22⋊C4—1221no—
872C22⋊C4—1221no—
873C22⋊C4—1221no—
874C22⋊C4—1221no—
875C22⋊C4—1221no—
876C22⋊C4—1221no—
877C22⋊C4—1221no—
878C22⋊C4—1221no—
879C22⋊C4—1221no—
880C22⋊C4—1221no—
881C22⋊C4—1221no—
882C22⋊C4—1221no—
883C22⋊C4—1221no—
884C22⋊C4—1221no—
885C22⋊C4—4881no—
886C22⋊C4—2442no—
887C22⋊C4—2442no—
888C22⋊C4—2442no—
889C42—1221no—
890C42—1221no—
891C42—1221no—
892C42—2442no—
893C23—22no—
894C23—21no—
895C23—21no—
896C23—41no—
897C23—611no—
898C23—611no—
899C23—611no—
900C23—611no—
901C23—1222no—
902C23—1221no—
903C23—1221no—
904C23—1221no—
905C23—1221no—
906C23—1221no—
907C23—2441no—
908C23—2441no—
909C23—2441no—
910C23C22⋊C4×D6111yescharacteristic
911C23C22⋊C4×D6111yescharacteristic
912C23C2×D4×D6111yescharacteristic
913Q8—41no—
914Q8—41no—
915Q8—42no—
916Q8—1222no—
917Q8—1222no—
918Q8—2441no—
919Q8—2441no—
920Q8—2441no—
921Q8—2442no—
922Q8—2442no—
923D4—614no—
924D4—1222no—
925D4—1222no—
926D4—1222no—
927D4—1222no—
928D4—1222no—
929D4—1222no—
930D4—1222no—
931D4—4881no—
932D4—4881no—
933D4—4881no—
934D4—2441no—
935D4—2441no—
936D4—2441no—
937D4—2442no—
938D4—2442no—
939D4—2441no—
940D4—2441no—
941D4—2442no—
942D4—2441no—
943D4—2441no—
944C2×C4—22no—
945C2×C4—22no—
946C2×C4—22no—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—41no—
952C2×C4—41no—
953C2×C4—41no—
954C2×C4—41no—
955C2×C4—41no—
956C2×C4—42no—
957C2×C4—41no—
958C2×C4—41no—
959C2×C4—41no—
960C2×C4—41no—
961C2×C4—81no—
962C2×C4—84no—
963C2×C4—611no—
964C2×C4—611no—
965C2×C4—611no—
966C2×C4—611no—
967C2×C4—1222no—
968C2×C4—1222no—
969C2×C4—1222no—
970C2×C4—1222no—
971C2×C4—1222no—
972C2×C4—1221no—
973C2×C4—1221no—
974C2×C4—1221no—
975C2×C4—4884no—
976C2×C4—4881no—
977C2×C4—4881no—
978C2×C4—2441no—
979C2×C4—2441no—
980C2×C4—2441no—
981C2×C4—2441no—
982C2×C4—2442no—
983C2×C4—2442no—
984C2×C4—2442no—
985C2×C4—2442no—
986C2×C4—2442no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4C22⋊C4×D6111yescharacteristic
995C2×C4C22⋊C4×D6111yescharacteristic
996C2×C4C22×C4×D6111yescharacteristic
997C2×C4C2×D4×D6111yescharacteristic
998C8—41no—
999C8—41no—
1000C8—2441no—
1001C8—2441no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—21no—
1008C22—21no—
1009C22—42no—
1010C22—42no—
1011C22—612no—
1012C22—1221no—
1013C22—1221no—
1014C22—1221no—
1015C22—1221no—
1016C22—1221no—
1017C22—1221no—
1018C22—1221no—
1019C22—1221no—
1020C22—1221no—
1021C22—1221no—
1022C22—1221no—
1023C22—4881no—
1024C22—4881no—
1025C22—2442no—
1026C22—2442no—
1027C22—2441no—
1028C22—2441no—
1029C22—2441no—
1030C22#99×D6112yes—
1031C22C2×C22⋊C4×D6111yescharacteristic
1032C22#1684056811yescharacteristic
1033C22#1684057511yescharacteristic
1034C4—21no—
1035C4—21no—
1036C4—21no—
1037C4—21no—
1038C4—42no—
1039C4—41no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—81no—
1044C4—612no—
1045C4—1221no—
1046C4—1221no—
1047C4—1221no—
1048C4—4881no—
1049C4—4881no—
1050C4—2441no—
1051C4—2441no—
1052C4—2441no—
1053C2—21no—
1054C2—21no—
1055C2—22no—
1056C2—41no—
1057C2—1222no—
1058C2—4881no—
1059C2—2441no—
1060C2—2441no—
1061C2—2441no—
1062C2C2×#99×D6111yescharacteristic
1063C2#2145434711yescharacteristic
1064C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC2×C61×#328C2
socleC22×C61C22×C22⋊C4
prime radical#21459495C2
cosocleC22×C4×C61C24
hypercenterC2×#328D61
hypocenterC61#17608
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#328

Complements

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

NH ≅ G/Ntype
2. #21454265C2semidirect
3. #21448646C2semidirect
4. #21444389C2semidirect
5. #21444376C2semidirect
6. #21444374C2semidirect
7. #21444361C2semidirect
8. #21444352C2semidirect
9. #21444350C2semidirect
10. #21444337C2semidirect
11. #21444322C2semidirect
12. #21444321C2semidirect
13. #21444309C2semidirect
14. #328×D61C2semidirect
15. C2×C61×#328C2semidirect
16. C2×#14519825C4semidirect
27. #16840343C4semidirect
28. #16840342C4semidirect
29. #16840342C4semidirect
30. #16840336C4semidirect
31. #16840335C4semidirect
32. #16840335C4semidirect
38. #16840243C4semidirect
77. C2×#11758226C2×C4semidirect
78. C2×#11758226C2×C4semidirect
86. C2×#11758222C2×C4semidirect
93. C2×Q8×D61C2×C4semidirect
94. C2×Q8×D61C2×C4semidirect
123. #14519757C2×C4semidirect
124. #14519757C2×C4semidirect
125. #14519756C2×C4semidirect
133. #14519753C2×C4semidirect
134. #14519753C2×C4semidirect
135. #14519753C2×C4semidirect
136. #14519753C2×C4semidirect
140. #14519752C2×C4semidirect
141. #14519752C2×C4semidirect
144. #14519751C2×C4semidirect
164. #14519736C2×C4semidirect
165. #14519735C2×C4semidirect
166. #14519735C2×C4semidirect
170. C4⋊C4×D61C2×C4semidirect
171. C4⋊C4×D61C2×C4semidirect
191. C22×Q8×C61C2×C4semidirect
197. C22⋊Q8×C61C2×C4semidirect
198. C22⋊Q8×C61C2×C4semidirect
202. C2×C4⋊C4×C61C2×C4semidirect
535. C2×#328D61semidirect
607. C61#17608semidirect
628. C22×Q8C4×D61semidirect
676. C22⋊Q8C4×D61semidirect
677. C22⋊Q8C4×D61semidirect
716. C2×C4⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214594952
#214542652
#214486462
#214443892
#214443762
#214443742
#214443612
#214443522
#214443502
#214443372
#214443222
#214443212
#214443092
#328×D612
C2×C61×#3282
#1760861