Finite Group Databasebeta

← #29695697

Subgroups — #29695697

Order 15616.

1494 conjugacy classes of subgroups.

The subgroup lattice has 1244 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459305C211yesmaximal, characteristic
2#21454554C211yesmaximal, characteristic, complemented
3C2×#16839777C211yesmaximal, characteristic, complemented
4C2×#104×D61C211yesmaximal, characteristic, complemented
5#21448263C211yesmaximal, characteristic, complemented
6#21446739C211yesmaximal, characteristic, complemented
7#21446264C211yesmaximal, characteristic, complemented
8#21446259C211yesmaximal, characteristic, complemented
9#21446118C211yesmaximal, characteristic, complemented
10#21446118C211yesmaximal, characteristic, complemented
11#21445836C211yesmaximal, characteristic, complemented
12#21445761C211yesmaximal, characteristic, complemented
13#21445761C211yesmaximal, characteristic, complemented
14#21445630C211yesmaximal, characteristic, complemented
15C61×#1963C211yesmaximal, characteristic, complemented
16C2×#41×D61C2211yescharacteristic
17C2×#41×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic, complemented
19C2×M16×D61C2211yescharacteristic, complemented
20#16840432C411yescharacteristic, complemented
21#16840427C411yescharacteristic, complemented
22#16840420C411yescharacteristic, complemented
23#16840420C411yescharacteristic, complemented
24#16840415C411yescharacteristic, complemented
25#16840412—21no—
26#16840405C411yescharacteristic, complemented
27#16840405C411yescharacteristic, complemented
28#16840401—21no—
29#16840401—21no—
30#16840397C411yescharacteristic, complemented
31#16840396—21no—
32#16840309—21no—
33#16840271—21no—
34#16840271—21no—
35#16840269C2211yescharacteristic
36#16840269C2211yescharacteristic
37C4×#11758222C2211yescharacteristic
38C2×C4×D244C2211yescharacteristic
39C4×D4×D61—21no—
40C2×#14519734C2211yescharacteristic, complemented
41C2×C42×D61C2211yescharacteristic, complemented
42#16839839—21no—
43#16839832—21no—
44#16839832—21no—
45#16839827—21no—
46#16839777—24no—
47C2×#14519705C2211yescharacteristic
48C2×#14519705C2211yescharacteristic
49C2×#14519704C2211yescharacteristic, complemented
50C2×#14519704C2211yescharacteristic, complemented
51C2×#14519704C2211yescharacteristic, complemented
52C2×#14519704C2211yescharacteristic, complemented
53C2×#14519703C2211yescharacteristic
54C2×#14519703C2211yescharacteristic
55#104×D61—24no—
56#16839725C2211yescharacteristic, complemented
57#16839725C2211yescharacteristic, complemented
58C4×#11758194C2211yescharacteristic, complemented
59#16839654—21no—
60#16839647—21no—
61#16839640—21no—
62#16839636—21no—
63C4×C4⋊Dic61C2211yescharacteristic, complemented
64C4×#11758198C2211yescharacteristic, complemented
65C4×#11758198C2211yescharacteristic, complemented
66#16839523C2211yescharacteristic, complemented
67#16839523C2211yescharacteristic, complemented
68#16839522C2211yescharacteristic, complemented
69#16839522C2211yescharacteristic, complemented
70C61×#532C2211yescharacteristic
71C61×#423C2211yescharacteristic, complemented
72C2×#104×C61C2211yescharacteristic, complemented
73C2×#104×C61C2211yescharacteristic, complemented
74C2×#104×C61C2211yescharacteristic, complemented
75C2×#104×C61C2211yescharacteristic, complemented
76C61×#376C2211yescharacteristic, complemented
77C2×#11758226C2×C411yescharacteristic
78C2×#11758226C2×C411yescharacteristic, complemented
79C2×#11758222—21no—
80C2×#11758222—21no—
81C2×#11758222C2311yescharacteristic
82C2×#11758224—21no—
83C2×#11758224—21no—
84C2×#11758224C2×C411yescharacteristic
85C2×#11758224C2×C411yescharacteristic, complemented
86#41×D61—22no—
87#41×D61—22no—
88#41×D61—22no—
89#41×D61—22no—
90#41×D61—41no—
91#41×D61—41no—
92#41×D61—41no—
93#41×D61—41no—
94C2×Q8×D61C2×C411yescharacteristic
95C2×Q8×D61C2×C411yescharacteristic, complemented
96C22×D244D411yescharacteristic
97C2×D4×D61—21no—
98C2×D4×D61—21no—
99C2×D4×D61—21no—
100C2×D4×D61C2×C411yescharacteristic
101C2×D4×D61C2×C411yescharacteristic, complemented
102C22×C4×D61—21no—
103C22×C4×D61—21no—
104C22×C4×D61—21no—
105C22×C4×D61C2311yescharacteristic
106C22×C4×D61C2311yescharacteristic
107C2×#11758194C2311yescharacteristic
108C2×#11758194C2311yescharacteristic
109C2×#11758189—21no—
110C2×#11758189—21no—
111M16×D61—22no—
112M16×D61—22no—
113M16×D61—41no—
114M16×D61—41no—
115C2×C8×D61—21no—
116C2×C8×D61—21no—
117#14519776—21no—
118#14519773—21no—
119#14519763—21no—
120#14519763—21no—
121#14519762—21no—
122#14519762—21no—
123#14519759—21no—
124#14519759—21no—
125#14519758—21no—
126#14519758—21no—
127#14519755—21no—
128#14519755—21no—
129#14519754—21no—
130#14519754—21no—
131#14519753C2×C411yescharacteristic
132#14519753C2×C411yescharacteristic
133#14519753C2×C411yescharacteristic, complemented
134#14519753C2×C411yescharacteristic, complemented
135#14519752—21no—
136#14519750—21no—
137#14519750—21no—
138#14519750—21no—
139#14519750—21no—
140#14519749—21no—
141#14519749—21no—
142#14519748—21no—
143#14519748C2×C411yescharacteristic
144#14519748C2×C411yescharacteristic
145#14519748C2×C411yescharacteristic, complemented
146#14519748C2×C411yescharacteristic, complemented
147#14519747—21no—
148#14519747—21no—
149#14519745—21no—
150#14519745—21no—
151#14519745—21no—
152#14519745—21no—
153C4×Dic122C2×C411yescharacteristic, complemented
154C4×Dic122C2×C411yescharacteristic, complemented
155C4×D244C2×C411yescharacteristic
156C4×D244C2×C411yescharacteristic
157C4×D244C2×C411yescharacteristic
158C4×D244C2×C411yescharacteristic
159C4×D244C2×C411yescharacteristic, complemented
160C4×D244C2×C411yescharacteristic, complemented
161C4×D244D411yescharacteristic
162C4×D244D411yescharacteristic
163C4×D244D411yescharacteristic
164C4×D244D411yescharacteristic
165D4×Dic61—21no—
166#14519739—21no—
167C4×C22⋊D61—21no—
168C4×C22⋊D61—21no—
169C4×C22⋊D61—21no—
170C4×C22⋊D61—21no—
171C4×C22⋊D61—21no—
172C4×C22⋊D61—21no—
173#14519737—21no—
174#14519737—21no—
175#14519736C2311yescharacteristic
176#14519734—21no—
177#14519734—22no—
178#14519734—41no—
179C2×C4⋊Dic61—21no—
180C2×C4⋊Dic61D411yescharacteristic
181C2×#11758196—21no—
182C4⋊C4×D61—21no—
183C2×#11758198—21no—
184C2×#11758198—21no—
185C2×#11758198—21no—
186C2×#11758198D411yescharacteristic
187C2×#11758198D411yescharacteristic
188C22⋊C4×D61—21no—
189C22⋊C4×D61—21no—
190C2×C4×Dic61—21no—
191C2×C4×Dic61C2311yescharacteristic
192C2×C4×Dic61C2311yescharacteristic
193C42×D61—21no—
194C42×D61—22no—
195C42×D61—41no—
196#14519705—22no—
197#14519705D414yescomplemented
198#14519704—22no—
199#14519704—22no—
200#14519704—41no—
201#14519704—41no—
202#14519703—22no—
203#14519703—22no—
204#14519689—21no—
205#14519689—21no—
206#14519689—21no—
207#14519689—21no—
208#14519688—21no—
209C4×#92418—21no—
210#14519684—21no—
211#14519684—21no—
212#14519684—21no—
213C2×#41×C61C2311yescharacteristic
214C2×#41×C61C2311yescharacteristic
215C2×M16×C61C2311yescharacteristic
216C2×M16×C61C2311yescharacteristic
217C4⋊Q8×C61C2×C411yescharacteristic, complemented
218#127×C61C2×C411yescharacteristic, complemented
219#124×C61C2×C411yescharacteristic, complemented
220#124×C61C2×C411yescharacteristic, complemented
221#121×C61—21no—
222#121×C61—21no—
223C4×D4×C61—21no—
224C4×D4×C61—21no—
225C2×C42×C61C2311yescharacteristic
226C2×C42×C61C2311yescharacteristic
227C2×C42×C61C2311yescharacteristic
228C4⋊C8×C61—21no—
229C4⋊C8×C61—21no—
230#104×C61—22no—
231#104×C61—22no—
232#104×C61—41no—
233#104×C61—41no—
234#95×C61—21no—
235#95×C61—21no—
236C23×D61—21no—
237C23×D61—21no—
238C23×D61C2×D411yescharacteristic
239C23×D61C2×D411yescharacteristic
240#41×C61—21no—
241#41×C61—21no—
242#41×C61—21no—
243#41×C61—21no—
244#41×C61—21no—
245#41×C61—21no—
246#41×C61—21no—
247#41×C61—21no—
248C2×Q8×C61C22×C411yescharacteristic
249C2×Q8×C61C22×C411yescharacteristic
250C2×D4×C61—21no—
251C2×D4×C61—21no—
252C2×D4×C61—21no—
253C2×D4×C61—21no—
254C2×D4×C61C22×C411yescharacteristic
255C2×D4×C61C22×C411yescharacteristic
256C22×C4×C61—21no—
257C22×C4×C61—21no—
258C22×C4×C61—21no—
259C22×C4×C61—21no—
260C22×C4×C61C2×D411yescharacteristic
261C22×C4×C61C2×D411yescharacteristic
262C22×C4×C61C2411yescharacteristic
263C2×C22⋊D61—21no—
264C2×C22⋊D61—21no—
265C2×C22⋊D61—21no—
266C2×C22⋊D61—21no—
267C2×C22⋊D61—21no—
268C2×C22⋊D61—21no—
269C2×C22⋊D61—21no—
270C2×C22⋊D61—21no—
271C2×C22⋊D61—21no—
272C22×Dic61—21no—
273C22×Dic61—21no—
274C22×Dic61—21no—
275C22×Dic61—21no—
276C22×Dic61C2×D411yescharacteristic
277C22×Dic61C2×D411yescharacteristic
278#11758226—22no—
279#11758226—22no—
280#11758226—41no—
281#11758226—41no—
282Q8×D61—22no—
283Q8×D61—22no—
284Q8×D61—41no—
285Q8×D61—41no—
286#11758224—22no—
287#11758224—22no—
288#11758224—41no—
289#11758224—41no—
290#11758224—42no—
291#11758224—42no—
292#11758224—42no—
293#11758224—42no—
294D4×D61—22no—
295D4×D61—22no—
296D4×D61—41no—
297D4×D61—41no—
298D4×D61—44no—
299D4×D61—42no—
300D4×D61—42no—
301D4×D61—42no—
302D4×D61—42no—
303#11758222—21no—
304#11758222—21no—
305#11758222—42no—
306#11758222—42no—
307#11758222—42no—
308#11758222—42no—
309#11758222C2×D412yes—
310#11758222#4112yes—
311C2×D244—21no—
312C2×D244—21no—
313C2×D244—42no—
314C2×D244C22⋊C411yescharacteristic
315C2×D244C22⋊C411yescharacteristic
316C2×D244C22⋊C411yescharacteristic
317C2×D244C22⋊C411yescharacteristic
318C2×D244C22×C411yescharacteristic
319C2×C4×D61—21no—
320C2×C4×D61—21no—
321C2×C4×D61—21no—
322C2×C4×D61—21no—
323C2×C4×D61—21no—
324C2×C4×D61—21no—
325C2×C4×D61—21no—
326C2×C4×D61—21no—
327C2×C4×D61—21no—
328C2×C4×D61—21no—
329C2×C4×D61—21no—
330C2×C4×D61—21no—
331C2×C4×D61—21no—
332C2×C4×D61—21no—
333C2×C4×D61—21no—
334C2×C4×D61—42no—
335C2×C4×D61—42no—
336C2×C4×D61—42no—
337C2×C4×D61—42no—
338C2×C4×D61—42no—
339C2×C4×D61—42no—
340C2×C4×D61—42no—
341C2×C4×D61C22×C411yescharacteristic
342C2×C4×D61C22×C411yescharacteristic
343C2×C4×D61C22×C411yescharacteristic
344C2×C4×D61C22×C411yescharacteristic
345C2×C4×D61C2×D411yescharacteristic
346C2×C4×D61C2×D411yescharacteristic
347C2×C4×D61C2×D411yescharacteristic
348C2×C4×D61C2×D411yescharacteristic
349C2×Dic122—21no—
350C2×Dic122—21no—
351C2×Dic122C22×C411yescharacteristic
352M16×C61—21no—
353M16×C61—21no—
354M16×C61—21no—
355M16×C61—21no—
356C2×C8×C61—21no—
357C2×C8×C61—21no—
358C4⋊C4×C61—21no—
359C4⋊C4×C61—21no—
360C22⋊C4×C61—21no—
361C22⋊C4×C61—21no—
362C22⋊C4×C61—21no—
363C22⋊C4×C61—21no—
364C42×C61—21no—
365C42×C61—21no—
366C42×C61—21no—
367C42×C61C22×C411yescharacteristic
368C42×C61C22×C411yescharacteristic
369C42×C61C2×D411yescharacteristic
370C42×C61C2×D411yescharacteristic
371C42×C61C2×D412yescomplemented
372C22⋊Dic61—21no—
373C22⋊Dic61—21no—
374C22⋊Dic61—21no—
375C22⋊Dic61—21no—
376C22⋊Dic61—21no—
377#11758198—21no—
378#11758198—21no—
379#11758198—21no—
380#11758198—21no—
381#11758198—21no—
382#11758198—21no—
383#11758198—42no—
384#11758198—42no—
385#11758198—42no—
386#11758198C22⋊C411yescharacteristic
387#11758198C22⋊C411yescharacteristic
388#11758198C22⋊C411yescharacteristic
389#11758198C22⋊C411yescharacteristic
390#11758198C22⋊C411yescharacteristic
391#11758198C22⋊C411yescharacteristic
392#11758198C22⋊C411yescharacteristic
393#11758198C22⋊C411yescharacteristic
394C4⋊Dic61—42no—
395C4⋊Dic61C22⋊C411yescharacteristic
396C4⋊Dic61C22⋊C411yescharacteristic
397C4⋊Dic61C22⋊C411yescharacteristic
398C4⋊Dic61C22⋊C411yescharacteristic
399C4⋊Dic61C22×C411yescharacteristic
400C4⋊Dic61C22×C411yescharacteristic
401#11758196—21no—
402#11758196—21no—
403#11758196—21no—
404#11758196—21no—
405#11758196—21no—
406#11758196—21no—
407#11758196—42no—
408C4×Dic61—21no—
409C4×Dic61—21no—
410C4×Dic61—21no—
411C4×Dic61—21no—
412C4×Dic61—21no—
413C4×Dic61—21no—
414C4×Dic61—21no—
415C4×Dic61—42no—
416#11758194—21no—
417#11758194—21no—
418#11758194—21no—
419#11758194C2×D412yescomplemented
420C2×#92418—21no—
421C2×#92418—21no—
422#11758189—42no—
423#11758189—42no—
424C8×D61—42no—
425C8×D61—42no—
426C23×C61—21no—
427C23×C61—21no—
428C23×C61C22×D411yescharacteristic
429C22×D61—21no—
430C22×D61—21no—
431C22×D61—21no—
432C22×D61—21no—
433C22×D61—21no—
434C22×D61—22no—
435C22×D61—41no—
436C22×D61—41no—
437C22×D61—41no—
438C22×D61—42no—
439C22×D61—42no—
440C22×D61—42no—
441C22×D61—42no—
442C22×D61—81no—
443C22×D61—81no—
444C22×D61C2×C22⋊C411yescharacteristic
445C22×D61C2×C22⋊C411yescharacteristic
446C22×D61C2×C22⋊C411yescharacteristic
447C22×D61C2×C22⋊C411yescharacteristic
448Q8×C61—21no—
449Q8×C61—21no—
450Q8×C61—21no—
451Q8×C61—21no—
452D4×C61—21no—
453D4×C61—21no—
454D4×C61—21no—
455D4×C61—21no—
456D4×C61—42no—
457D4×C61—41no—
458D4×C61—41no—
459D4×C61—41no—
460D4×C61—41no—
461D4×C61—81no—
462C2×C4×C61—21no—
463C2×C4×C61—21no—
464C2×C4×C61—22no—
465C2×C4×C61—41no—
466C2×C4×C61—41no—
467C2×C4×C61—41no—
468C2×C4×C61—41no—
469C2×C4×C61—41no—
470C2×C4×C61—41no—
471C2×C4×C61—41no—
472C2×C4×C61—41no—
473C2×C4×C61—41no—
474C2×C4×C61—41no—
475C2×C4×C61—41no—
476C2×C4×C61C2×C22⋊C411yescharacteristic
477C2×C4×C61C2×C22⋊C411yescharacteristic
478C2×C4×C61C2×C22⋊C411yescharacteristic
479C2×C4×C61C2×C22⋊C411yescharacteristic
480C2×C4×C61C23×C411yescharacteristic
481C2×C4×C61C22×D411yescharacteristic
482C2×C4×C61C22×D411yescharacteristic
483C2×C4×C61C2×#4111yescharacteristic
484C2×C4×C61H(5,𝔽2)11yescharacteristic
485C2×C4×C61H(5,𝔽2)11yescharacteristic
486C22⋊D61—22no—
487C22⋊D61—22no—
488C22⋊D61—42no—
489C22⋊D61—42no—
490C22⋊D61—42no—
491C22⋊D61—42no—
492C22⋊D61—42no—
493C22⋊D61—42no—
494C22⋊D61—81no—
495C22⋊D61—81no—
496C2×Dic61—21no—
497C2×Dic61—21no—
498C2×Dic61—21no—
499C2×Dic61—21no—
500C2×Dic61—21no—
501C2×Dic61—22no—
502C2×Dic61—21no—
503C2×Dic61—21no—
504C2×Dic61—42no—
505C2×Dic61—42no—
506C2×Dic61—41no—
507C2×Dic61—41no—
508C2×Dic61—41no—
509C2×Dic61—41no—
510C2×Dic61—41no—
511C2×Dic61C2×C22⋊C411yescharacteristic
512C2×Dic61C2×C22⋊C411yescharacteristic
513C2×Dic61C2×C22⋊C411yescharacteristic
514C2×Dic61C2×C22⋊C411yescharacteristic
515D244—22no—
516D244—22no—
517D244—21no—
518D244—41no—
519D244—41no—
520D244—42no—
521D244—42no—
522D244C4×D412yes—
523C4×D61—21no—
524C4×D61—21no—
525C4×D61—21no—
526C4×D61—21no—
527C4×D61—21no—
528C4×D61—21no—
529C4×D61—21no—
530C4×D61—21no—
531C4×D61—21no—
532C4×D61—21no—
533C4×D61—21no—
534C4×D61—21no—
535C4×D61—22no—
536C4×D61—21no—
537C4×D61—21no—
538C4×D61—21no—
539C4×D61—21no—
540C4×D61—22no—
541C4×D61—42no—
542C4×D61—42no—
543C4×D61—42no—
544C4×D61—42no—
545C4×D61—42no—
546C4×D61—48no—
547C4×D61—81no—
548Dic122—21no—
549Dic122—42no—
550Dic122—42no—
551Dic122C4×D412yes—
552C8×C61—41no—
553C8×C61—41no—
554#92418—22no—
555#92418—41no—
556#22434—611nomaximal, Sylow
557C22×C61—21no—
558C22×C61—21no—
559C22×C61—41no—
560C22×C61—41no—
561C22×C61—41no—
562C22×C61—41no—
563C22×C61—41no—
564C22×C61—41no—
565C22×C61C22×C22⋊C411yescharacteristic
566C22×C61D4211yescharacteristic
567C22×C61#54611yescharacteristic
568C2×D61—21no—
569C2×D61—21no—
570C2×D61—21no—
571C2×D61—21no—
572C2×D61—21no—
573C2×D61—22no—
574C2×D61—21no—
575C2×D61—21no—
576C2×D61—21no—
577C2×D61—21no—
578C2×D61—21no—
579C2×D61—21no—
580C2×D61—42no—
581C2×D61—42no—
582C2×D61—41no—
583C2×D61—41no—
584C2×D61—84no—
585C2×D61—81no—
586C2×D61—81no—
587C2×D61—84no—
588C2×D61#42112yescomplemented
589C4×C61—21no—
590C4×C61—21no—
591C4×C61—21no—
592C4×C61—21no—
593C4×C61—42no—
594C4×C61—41no—
595C4×C61—41no—
596C4×C61—81no—
597C4×C61C2×C4×D411yescharacteristic
598C4×C61#51811yescharacteristic
599C4×C61D4211yescharacteristic
600C4×C61#54611yescharacteristic
601Dic61—22no—
602Dic61—21no—
603Dic61—21no—
604Dic61—21no—
605Dic61—21no—
606Dic61—42no—
607Dic61—41no—
608Dic61—41no—
609Dic61—81no—
610D4×#41—611no—
611D4×M16—611no—
612C2×#421—611no—
613C22×#104—611no—
614#2290—611no—
615#1980—611no—
616#1963D6111yescharacteristic, complemented
617#1897—611no—
618#1896—611no—
619#1871—611no—
620#1871—611no—
621#1806—611no—
622#1789—611no—
623#1789—611no—
624#1759—611no—
625C2×C61—21no—
626C2×C61—21no—
627C2×C61—81no—
628C2×C61—81no—
629C2×C61D4×C22⋊C411yescharacteristic
630C2×C61C2×#42111yescharacteristic
631C2×C61#290111yescharacteristic
632D61—22no—
633D61—41no—
634D61—41no—
635D61—41no—
636D61—42no—
637C22×#41—611no—
638C22×#41—611no—
639C22×M16—611no—
640C22×M16—611no—
641#550—611no—
642D4×Q8—611no—
643#548—611no—
644#548—611no—
645#547—611no—
646#547—1221no—
647#546—611no—
648#546—611no—
649#546—1221no—
650#546—1221no—
651D42—611no—
652D42—1221no—
653#532—1221no—
654#532C2×D6111yescharacteristic
655#525—611no—
656#525—611no—
657#525—1221no—
658#525—1221no—
659C4×#41—611no—
660C2×C4×D4—611no—
661C2×C4×D4—1221no—
662C2×#117—611no—
663C22×C42—611no—
664#436—1221no—
665#435—1221no—
666#435—1221no—
667C8×D4—1221no—
668#423C2×D6111yescharacteristic, complemented
669#421—1224no—
670C2×#104—611no—
671C2×#104—611no—
672C2×#104—611no—
673C2×#104—611no—
674C2×#104—611no—
675C2×#104—611no—
676C2×#104—611no—
677C2×#104—611no—
678C2×#104—1224no—
679C2×#104C2×D6111yescharacteristic, complemented
680C2×#104C2×D6111yescharacteristic, complemented
681C2×#104C2×D6111yescharacteristic, complemented
682C2×#104C2×D6111yescharacteristic, complemented
683#407—611no—
684#407—611no—
685C4×M16—611no—
686#388—1221no—
687#387—1221no—
688#386—1221no—
689#385—1221no—
690C4×C4⋊C4—611no—
691C4×C22⋊C4—611no—
692C4×C22⋊C4—611no—
693#376C2×D6111yescharacteristic, complemented
694#339—611no—
695#339—611no—
696#339—611no—
697#339—611no—
698C61#2243411yescharacteristic, complemented, Sylow
699C2×#41—611no—
700C2×#41—611no—
701C2×#41—611no—
702C2×#41—611no—
703C2×#41—611no—
704C2×#41—1221no—
705C2×#41—1221no—
706C2×#41—1221no—
707C2×#41—1221no—
708C2×#41—1222no—
709C2×#41—1222no—
710C2×#41—1222no—
711C2×#41—1222no—
712C2×#41—2441no—
713C2×#41—2441no—
714C2×#41—2441no—
715C2×#41—2441no—
716C2×#41C22×D6111yescharacteristic
717C2×#41C22×D6111yescharacteristic
718C22×Q8—611no—
719C22×Q8—611no—
720C22×D4—611no—
721C22×D4—611no—
722C22×D4—611no—
723C22×D4—1221no—
724C22×D4—1221no—
725C22×D4—1221no—
726C23×C4—611no—
727C23×C4—611no—
728C23×C4—1221no—
729C23×C4—1221no—
730C23×C4—1221no—
731C2×M16—611no—
732C2×M16—611no—
733C2×M16—1221no—
734C2×M16—1221no—
735C2×M16—1222no—
736C2×M16—1222no—
737C2×M16—2441no—
738C2×M16—2441no—
739C2×M16C22×D6111yescharacteristic
740C2×M16C22×D6111yescharacteristic
741C22×C8—1221no—
742C22×C8—1221no—
743C4⋊Q8—1221no—
744C4⋊Q8C4×D6111yescharacteristic, complemented
745#127—1221no—
746#127C4×D6111yescharacteristic, complemented
747#124—1221no—
748#124—1221no—
749#124C4×D6111yescharacteristic, complemented
750#124C4×D6111yescharacteristic, complemented
751#123—1221no—
752#123—1221no—
753#123—1221no—
754#123—1221no—
755#123—1221no—
756#123—1221no—
757C22⋊Q8—611no—
758C22⋊Q8—611no—
759C22⋊Q8—611no—
760C22⋊Q8—611no—
761C22⋊Q8—1221no—
762C22⋊Q8—1221no—
763C22⋊Q8—1221no—
764C22⋊Q8—1221no—
765#121—21no—
766#121—21no—
767#121—611no—
768#121—611no—
769#121—611no—
770#121—611no—
771#121—1221no—
772#121—1221no—
773#121—1221no—
774#121—1221no—
775#121—1221no—
776#121—1221no—
777#121—1221no—
778#121—1221no—
779#120—1221no—
780#120—1221no—
781#120—1221no—
782#120—1221no—
783#120—1221no—
784#120—1221no—
785C4×Q8—611no—
786C4×Q8—611no—
787C4×D4—21no—
788C4×D4—21no—
789C4×D4—611no—
790C4×D4—611no—
791C4×D4—611no—
792C4×D4—611no—
793C4×D4—611no—
794C4×D4—611no—
795C4×D4—611no—
796C4×D4—611no—
797C4×D4—611no—
798C4×D4—611no—
799C4×D4—1221no—
800C4×D4—1221no—
801C4×D4—1221no—
802C4×D4—1221no—
803C4×D4—1221no—
804C4×D4—1221no—
805C4×D4—1221no—
806C4×D4—1221no—
807C4×D4—1221no—
808C4×D4—1221no—
809#117—611no—
810#117—1221no—
811#117—1222no—
812#117—2441no—
813C2×C4⋊C4—611no—
814C2×C4⋊C4—1221no—
815C2×C4⋊C4—1221no—
816C2×C4⋊C4—1221no—
817C2×C22⋊C4—611no—
818C2×C22⋊C4—611no—
819C2×C22⋊C4—1221no—
820C2×C22⋊C4—1221no—
821C2×C22⋊C4—1221no—
822C2×C22⋊C4—1221no—
823C2×C22⋊C4—1221no—
824C2×C42—611no—
825C2×C42—611no—
826C2×C42—1221no—
827C2×C42—1222no—
828C2×C42—1221no—
829C2×C42—2441no—
830C2×C42C22×D6111yescharacteristic
831C2×C42C22×D6111yescharacteristic
832C2×C42C22×D6111yescharacteristic
833C4⋊C8—21no—
834C4⋊C8—21no—
835#104—22no—
836#104—22no—
837#104—41no—
838#104—41no—
839#104—614no—
840#104—1222no—
841#104—1222no—
842#104—1222no—
843#104—1222no—
844#104—1222no—
845#104—2441no—
846#104—2441no—
847C22⋊C8—1221no—
848C22⋊C8—1221no—
849C22⋊C8—1221no—
850C22⋊C8—1221no—
851#97—1221no—
852C4×C8—1221no—
853#95—21no—
854#95—21no—
855#95—1221no—
856#95—1221no—
857#95—1221no—
858C24—611no—
859C24—611no—
860C24—1221no—
861C24—1221no—
862#41—21no—
863#41—21no—
864#41—21no—
865#41—21no—
866#41—21no—
867#41—21no—
868#41—21no—
869#41—21no—
870#41—612no—
871#41—612no—
872#41—1221no—
873#41—1221no—
874#41—1222no—
875#41—1222no—
876#41—1222no—
877#41—1222no—
878#41—2442no—
879#41—2442no—
880#41—2442no—
881#41—2442no—
882#41—2441no—
883#41—2441no—
884#41—2442no—
885#41—2442no—
886#41—2442no—
887#41—2442no—
888#41—2441no—
889#41—2441no—
890C2×Q8—611no—
891C2×Q8—1221no—
892C2×Q8—1221no—
893C2×Q8—1222no—
894C2×Q8—1222no—
895C2×Q8—2441no—
896C2×Q8—2441no—
897C2×Q8C2×C4×D6111yescharacteristic
898C2×Q8C2×C4×D6111yescharacteristic
899C2×D4—21no—
900C2×D4—21no—
901C2×D4—21no—
902C2×D4—21no—
903C2×D4—611no—
904C2×D4—611no—
905C2×D4—611no—
906C2×D4—611no—
907C2×D4—611no—
908C2×D4—1221no—
909C2×D4—1221no—
910C2×D4—1221no—
911C2×D4—1221no—
912C2×D4—1222no—
913C2×D4—1222no—
914C2×D4—1221no—
915C2×D4—1221no—
916C2×D4—1221no—
917C2×D4—1221no—
918C2×D4—1221no—
919C2×D4—1221no—
920C2×D4—1221no—
921C2×D4—2442no—
922C2×D4—2441no—
923C2×D4—2441no—
924C2×D4—2442no—
925C2×D4—2442no—
926C2×D4—2442no—
927C2×D4—2442no—
928C2×D4—2444no—
929C2×D4C2×C4×D6111yescharacteristic
930C2×D4C2×C4×D6111yescharacteristic
931C22×C4—21no—
932C22×C4—21no—
933C22×C4—21no—
934C22×C4—21no—
935C22×C4—611no—
936C22×C4—611no—
937C22×C4—611no—
938C22×C4—611no—
939C22×C4—611no—
940C22×C4—611no—
941C22×C4—611no—
942C22×C4—611no—
943C22×C4—611no—
944C22×C4—611no—
945C22×C4—1221no—
946C22×C4—1221no—
947C22×C4—1221no—
948C22×C4—1221no—
949C22×C4—1221no—
950C22×C4—1221no—
951C22×C4—1221no—
952C22×C4—1221no—
953C22×C4—1221no—
954C22×C4—1221no—
955C22×C4—1221no—
956C22×C4—1221no—
957C22×C4—1221no—
958C22×C4—1221no—
959C22×C4—1221no—
960C22×C4—1221no—
961C22×C4—1221no—
962C22×C4—1221no—
963C22×C4—1221no—
964C22×C4—2442no—
965C22×C4—2442no—
966C22×C4—2442no—
967C22×C4—2442no—
968C22×C4—2442no—
969C22×C4—2442no—
970C22×C4—2442no—
971C22×C4D4×D6111yescharacteristic
972C22×C4D4×D6111yescharacteristic
973C22×C4C23×D6111yescharacteristic
974M16—21no—
975M16—21no—
976M16—21no—
977M16—21no—
978M16—612no—
979M16—1221no—
980M16—1221no—
981M16—1221no—
982M16—2442no—
983M16—2442no—
984C2×C8—21no—
985C2×C8—21no—
986C2×C8—1221no—
987C2×C8—1221no—
988C2×C8—2442no—
989C2×C8—2442no—
990C4⋊C4—21no—
991C4⋊C4—21no—
992C4⋊C4—611no—
993C4⋊C4—611no—
994C4⋊C4—611no—
995C4⋊C4—611no—
996C4⋊C4—611no—
997C4⋊C4—611no—
998C4⋊C4—1221no—
999C4⋊C4—1221no—
1000C4⋊C4—1221no—
1001C4⋊C4—1221no—
1002C4⋊C4—1221no—
1003C4⋊C4—1221no—
1004C4⋊C4—2442no—
1005C4⋊C4—2442no—
1006C22⋊C4—21no—
1007C22⋊C4—21no—
1008C22⋊C4—21no—
1009C22⋊C4—21no—
1010C22⋊C4—611no—
1011C22⋊C4—611no—
1012C22⋊C4—611no—
1013C22⋊C4—611no—
1014C22⋊C4—611no—
1015C22⋊C4—611no—
1016C22⋊C4—611no—
1017C22⋊C4—611no—
1018C22⋊C4—1221no—
1019C22⋊C4—1221no—
1020C22⋊C4—1221no—
1021C22⋊C4—1221no—
1022C22⋊C4—1221no—
1023C22⋊C4—1221no—
1024C22⋊C4—1221no—
1025C22⋊C4—1221no—
1026C22⋊C4—1221no—
1027C22⋊C4—1221no—
1028C22⋊C4—1221no—
1029C22⋊C4—2442no—
1030C22⋊C4—2442no—
1031C22⋊C4—2442no—
1032C42—21no—
1033C42—21no—
1034C42—21no—
1035C42—1221no—
1036C42—1221no—
1037C42—1221no—
1038C42—1221no—
1039C42—1221no—
1040C42—1221no—
1041C42—1221no—
1042C42—2442no—
1043C42C2×C4×D6111yescharacteristic
1044C42C2×C4×D6111yescharacteristic
1045C42D4×D6111yescharacteristic
1046C42D4×D6111yescharacteristic
1047C42D4×D6112yescomplemented
1048C23—21no—
1049C23—21no—
1050C23—611no—
1051C23—611no—
1052C23—611no—
1053C23—611no—
1054C23—1222no—
1055C23—1221no—
1056C23—1221no—
1057C23—1221no—
1058C23—1221no—
1059C23—1221no—
1060C23—4881no—
1061C23—4881no—
1062C23—2441no—
1063C23—2441no—
1064C23—2441no—
1065C23—2442no—
1066C23—2442no—
1067C23—2442no—
1068C23—2442no—
1069C23C2×D4×D6111yescharacteristic
1070Q8—21no—
1071Q8—21no—
1072Q8—21no—
1073Q8—21no—
1074Q8—612no—
1075Q8—1221no—
1076Q8—2442no—
1077Q8—2442no—
1078D4—21no—
1079D4—21no—
1080D4—21no—
1081D4—21no—
1082D4—42no—
1083D4—41no—
1084D4—41no—
1085D4—41no—
1086D4—41no—
1087D4—81no—
1088D4—612no—
1089D4—1222no—
1090D4—1222no—
1091D4—1222no—
1092D4—1222no—
1093D4—1221no—
1094D4—4881no—
1095D4—4881no—
1096D4—2441no—
1097D4—2441no—
1098D4—2442no—
1099D4—2442no—
1100D4—2442no—
1101D4—2442no—
1102D4—2442no—
1103D4—2442no—
1104D4—2442no—
1105D4—2442no—
1106C2×C4—21no—
1107C2×C4—21no—
1108C2×C4—22no—
1109C2×C4—41no—
1110C2×C4—41no—
1111C2×C4—41no—
1112C2×C4—41no—
1113C2×C4—41no—
1114C2×C4—41no—
1115C2×C4—41no—
1116C2×C4—41no—
1117C2×C4—41no—
1118C2×C4—41no—
1119C2×C4—41no—
1120C2×C4—611no—
1121C2×C4—611no—
1122C2×C4—611no—
1123C2×C4—611no—
1124C2×C4—1221no—
1125C2×C4—1221no—
1126C2×C4—1221no—
1127C2×C4—1221no—
1128C2×C4—1221no—
1129C2×C4—1221no—
1130C2×C4—1221no—
1131C2×C4—1221no—
1132C2×C4—1221no—
1133C2×C4—1221no—
1134C2×C4—1221no—
1135C2×C4—1221no—
1136C2×C4—1221no—
1137C2×C4—1221no—
1138C2×C4—1221no—
1139C2×C4—1221no—
1140C2×C4—1221no—
1141C2×C4—1222no—
1142C2×C4—1221no—
1143C2×C4—1221no—
1144C2×C4—1221no—
1145C2×C4—1221no—
1146C2×C4—1222no—
1147C2×C4—1222no—
1148C2×C4—1221no—
1149C2×C4—1221no—
1150C2×C4—4881no—
1151C2×C4—2442no—
1152C2×C4—2442no—
1153C2×C4—2442no—
1154C2×C4—2442no—
1155C2×C4—2442no—
1156C2×C4—2448no—
1157C2×C4—2442no—
1158C2×C4—2442no—
1159C2×C4—2441no—
1160C2×C4—2441no—
1161C2×C4—2441no—
1162C2×C4—2441no—
1163C2×C4—2441no—
1164C2×C4C22⋊C4×D6111yescharacteristic
1165C2×C4C22⋊C4×D6111yescharacteristic
1166C2×C4C22⋊C4×D6111yescharacteristic
1167C2×C4C22⋊C4×D6111yescharacteristic
1168C2×C4C22×C4×D6111yescharacteristic
1169C2×C4C2×D4×D6111yescharacteristic
1170C2×C4C2×D4×D6111yescharacteristic
1171C2×C4#41×D6111yescharacteristic
1172C2×C4#1451982211yescharacteristic
1173C2×C4#1451982311yescharacteristic
1174C8—41no—
1175C8—41no—
1176C8—1222no—
1177C8—2441no—
1178C22—21no—
1179C22—21no—
1180C22—41no—
1181C22—41no—
1182C22—41no—
1183C22—41no—
1184C22—41no—
1185C22—41no—
1186C22—612no—
1187C22—1221no—
1188C22—1221no—
1189C22—1221no—
1190C22—1221no—
1191C22—1221no—
1192C22—1221no—
1193C22—1221no—
1194C22—1221no—
1195C22—1221no—
1196C22—1221no—
1197C22—1221no—
1198C22—1222no—
1199C22—4881no—
1200C22—4881no—
1201C22—4884no—
1202C22—4884no—
1203C22—2442no—
1204C22—2442no—
1205C22—2441no—
1206C22—2441no—
1207C22C2×C22⋊C4×D6111yescharacteristic
1208C22#1684039611yescharacteristic
1209C22#1684040911yescharacteristic
1210C4—21no—
1211C4—21no—
1212C4—21no—
1213C4—21no—
1214C4—42no—
1215C4—41no—
1216C4—41no—
1217C4—81no—
1218C4—1221no—
1219C4—1221no—
1220C4—1221no—
1221C4—1221no—
1222C4—1222no—
1223C4—4881no—
1224C4—2442no—
1225C4—2441no—
1226C4—2441no—
1227C4C4×D4×D6111yescharacteristic
1228C4#1684023411yescharacteristic
1229C4#1684039711yescharacteristic
1230C4#1684040511yescharacteristic
1231C2—21no—
1232C2—21no—
1233C2—81no—
1234C2—81no—
1235C2—1222no—
1236C2—2441no—
1237C2—2441no—
1238C2—2441no—
1239C2—2442no—
1240C2#2144864011yescharacteristic
1241C2#421×D6111yescharacteristic
1242C2#2145436511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1963C2
socleC22×C61C22×C22⋊C4
prime radical#21459305C2
cosocleC22×C4×C61C24
hypercenter#1963D61
hypocenterC61#22434
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #21454554C2semidirect
3. C2×#16839777C2semidirect
4. C2×#104×D61C2semidirect
5. #21448263C2semidirect
6. #21446739C2semidirect
7. #21446264C2semidirect
8. #21446259C2semidirect
9. #21446118C2semidirect
10. #21446118C2semidirect
11. #21445836C2semidirect
12. #21445761C2semidirect
13. #21445761C2semidirect
14. #21445630C2semidirect
15. C61×#1963C2semidirect
18. C2×M16×D61C22semidirect
19. C2×M16×D61C22semidirect
20. #16840432C4semidirect
21. #16840427C4semidirect
22. #16840420C4semidirect
23. #16840420C4semidirect
24. #16840415C4semidirect
26. #16840405C4semidirect
27. #16840405C4semidirect
30. #16840397C4semidirect
40. C2×#14519734C22semidirect
41. C2×C42×D61C22semidirect
49. C2×#14519704C22semidirect
50. C2×#14519704C22semidirect
51. C2×#14519704C22semidirect
52. C2×#14519704C22semidirect
56. #16839725C22semidirect
57. #16839725C22semidirect
58. C4×#11758194C22semidirect
63. C4×C4⋊Dic61C22semidirect
64. C4×#11758198C22semidirect
65. C4×#11758198C22semidirect
66. #16839523C22semidirect
67. #16839523C22semidirect
68. #16839522C22semidirect
69. #16839522C22semidirect
71. C61×#423C22semidirect
72. C2×#104×C61C22semidirect
73. C2×#104×C61C22semidirect
74. C2×#104×C61C22semidirect
75. C2×#104×C61C22semidirect
76. C61×#376C22semidirect
78. C2×#11758226C2×C4semidirect
85. C2×#11758224C2×C4semidirect
95. C2×Q8×D61C2×C4semidirect
101. C2×D4×D61C2×C4semidirect
133. #14519753C2×C4semidirect
134. #14519753C2×C4semidirect
145. #14519748C2×C4semidirect
146. #14519748C2×C4semidirect
153. C4×Dic122C2×C4semidirect
154. C4×Dic122C2×C4semidirect
159. C4×D244C2×C4semidirect
160. C4×D244C2×C4semidirect
197. #14519705D4semidirect
217. C4⋊Q8×C61C2×C4semidirect
218. #127×C61C2×C4semidirect
219. #124×C61C2×C4semidirect
220. #124×C61C2×C4semidirect
371. C42×C61C2×D4semidirect
419. #11758194C2×D4semidirect
588. C2×D61#421semidirect
616. #1963D61semidirect
668. #423C2×D61semidirect
679. C2×#104C2×D61semidirect
680. C2×#104C2×D61semidirect
681. C2×#104C2×D61semidirect
682. C2×#104C2×D61semidirect
693. #376C2×D61semidirect
698. C61#22434semidirect
744. C4⋊Q8C4×D61semidirect
746. #127C4×D61semidirect
749. #124C4×D61semidirect
750. #124C4×D61semidirect
1047. C42D4×D61semidirect

Maximal subgroups

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

subgroupindex
#214593052
#214545542
C2×#168397772
C2×#104×D612
#214482632
#214467392
#214462642
#214462592
#214461182
#214458362
#214457612
#214456302
C61×#19632
#2243461