Finite Group Databasebeta

← #29696149

Subgroups — #29696149

Order 15616.

1294 conjugacy classes of subgroups.

The subgroup lattice has 1190 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16840435C211yesmaximal, characteristic
2#21448669C211yesmaximal, characteristic, complemented
3#21448661C211yesmaximal, characteristic, complemented
4#21446802C211yesmaximal, characteristic, complemented
5#21446802C211yesmaximal, characteristic, complemented
6#21446278C211yesmaximal, characteristic, complemented
7#21446269C211yesmaximal, characteristic
8#21446269C211yesmaximal, characteristic
9#21445894C211yesmaximal, characteristic, complemented
10#21445892C211yesmaximal, characteristic, complemented
11#21445805C211yesmaximal, characteristic, complemented
12#99×Dic61C211yesmaximal, characteristic, complemented
13#21445551C211yesmaximal, characteristic, complemented
14#342×D61C211yesmaximal, characteristic, complemented
15C61×#1899C211yesmaximal, 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, complemented
25C2×#14519772C411yescharacteristic, complemented
26C2×#14519763C411yescharacteristic, complemented
27C2×#14519761C411yescharacteristic, complemented
28C2×#14519759C411yescharacteristic, complemented
29C2×#14519757C411yescharacteristic, complemented
30C2×#14519754C2211yescharacteristic
31C2×#14519745C2211yescharacteristic
32C2×D4×Dic61C2211yescharacteristic
33C2×#14519737C411yescharacteristic, complemented
34C2×#14519736C2211yescharacteristic
35C2×#14519736C2211yescharacteristic
36C2×#14519735C411yescharacteristic, complemented
37C22×#11758198C2211yescharacteristic
38C2×C22⋊C4×D61C2211yescharacteristic
39C2×C22⋊C4×D61C2211yescharacteristic
40C2×C22⋊C4×D61C2211yescharacteristic
41C2×#14519692C2211yescharacteristic
42C2×#14519692C2211yescharacteristic
43#16839654—21no—
44#16839653—21no—
45#16839652—21no—
46#16839651—21no—
47#16839636—21no—
48#16839633—21no—
49#16839625C2211yescharacteristic
50#16839620C2211yescharacteristic
51#16839620C2211yescharacteristic
52#16839617C2211yescharacteristic
53#16839617C2211yescharacteristic
54C22⋊C4×Dic61C2211yescharacteristic
55C22⋊C4×Dic61C2211yescharacteristic
56C4×#11758198—21no—
57#16839609—21no—
58#16839529C2211yescharacteristic
59#16839529C2211yescharacteristic
60#16839528C2211yescharacteristic
61#16839528C2211yescharacteristic
62#16839528C2211yescharacteristic
63#16839528C2211yescharacteristic
64#16839528C2211yescharacteristic
65#16839528C2211yescharacteristic
66#16839528C2211yescharacteristic
67#16839528C2211yescharacteristic
68C2×#123×C61C2211yescharacteristic
69C2×#117×C61C2211yescharacteristic
70C2×#99×C61C2211yescharacteristic
71C2×#99×C61C2211yescharacteristic
72C61×#381C2211yescharacteristic
73C61×#342C2211yescharacteristic
74C61×#342C2211yescharacteristic
75C24×D61C2311yescharacteristic
76C22×Dic122C2×C411yescharacteristic, complemented
77C22×C22⋊D61C2×C411yescharacteristic
78C22×C22⋊D61C2×C411yescharacteristic
79C23×Dic61C2×C411yescharacteristic, complemented
80C23×Dic61C2311yescharacteristic
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2×C411yescharacteristic
84C22×C4×D61C2×C411yescharacteristic
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#14519736—21no—
126#14519736—21no—
127#14519736—21no—
128#14519736—21no—
129#14519736—22no—
130#14519736—41no—
131#14519735—21no—
132#14519735—21no—
133#14519735—21no—
134#14519735—21no—
135C2×C4⋊Dic61—21no—
136C2×C4⋊Dic61C2×C411yescharacteristic, complemented
137C2×C4⋊Dic61C2×C411yescharacteristic, complemented
138C2×C4⋊Dic61C2×C411yescharacteristic, complemented
139C2×C4⋊Dic61C2×C411yescharacteristic, complemented
140C2×#11758196—21no—
141C2×#11758196—21no—
142C2×#11758196C2×C411yescharacteristic, complemented
143C2×#11758196C2×C411yescharacteristic, complemented
144C2×C22⋊Dic61C2×C411yescharacteristic, complemented
145C2×C22⋊Dic61C2311yescharacteristic
146C2×C22⋊Dic61C2311yescharacteristic
147C2×C22⋊Dic61C2311yescharacteristic
148C2×C22⋊Dic61C2311yescharacteristic
149C2×C22⋊Dic61C2311yescharacteristic
150C2×C22⋊Dic61C2311yescharacteristic
151C2×#11758198—21no—
152C2×#11758198—21no—
153C2×#11758198—21no—
154C2×#11758198—21no—
155C2×#11758198—21no—
156C2×#11758198—21no—
157C2×#11758198C2×C411yescharacteristic
158C2×#11758198C2×C411yescharacteristic
159C2×#11758198C2×C411yescharacteristic
160C2×#11758198C2×C411yescharacteristic
161C2×#11758198C2×C411yescharacteristic
162C2×#11758198C2×C411yescharacteristic
163C2×#11758198C2×C411yescharacteristic
164C2×#11758198C2×C411yescharacteristic
165C2×#11758198D411yescharacteristic
166C2×#11758198D411yescharacteristic
167C2×#11758198D411yescharacteristic
168C2×#11758198D411yescharacteristic
169C2×#11758198D411yescharacteristic
170C2×#11758198D411yescharacteristic
171C2×#11758198D411yescharacteristic
172C2×#11758198D411yescharacteristic
173C22⋊C4×D61—21no—
174C22⋊C4×D61—21no—
175C22⋊C4×D61—21no—
176C22⋊C4×D61—21no—
177C22⋊C4×D61—22no—
178C22⋊C4×D61—22no—
179C22⋊C4×D61—41no—
180C22⋊C4×D61—41no—
181C2×C4×Dic61—21no—
182C2×C4×Dic61—21no—
183C2×C4×Dic61—21no—
184C2×C4×Dic61C2×C411yescharacteristic, complemented
185C2×C4×Dic61C2×C411yescharacteristic, complemented
186C2×C4×Dic61C2×C411yescharacteristic, complemented
187#14519692—22no—
188#14519692—41no—
189#14519684—21no—
190#14519684—21no—
191#14519684—21no—
192#14519684—21no—
193#14519684—21no—
194#14519684—21no—
195C22×D4×C61C2311yescharacteristic
196C23×C4×C61C2311yescharacteristic
197#123×C61—21no—
198#123×C61—21no—
199#123×C61—21no—
200#123×C61—21no—
201#117×C61—22no—
202#117×C61—41no—
203C2×C4⋊C4×C61—21no—
204C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
205C2×C4⋊C4×C61C2×C411yescharacteristic, complemented
206C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
207C2×C22⋊C4×C61C2×C411yescharacteristic, complemented
208C2×C22⋊C4×C61C2311yescharacteristic
209C2×C22⋊C4×C61C2311yescharacteristic
210C2×C22⋊C4×C61C2311yescharacteristic
211C2×C22⋊C4×C61C2311yescharacteristic
212C2×C22⋊C4×C61C2311yescharacteristic
213C2×C42×C61—21no—
214#99×C61—22no—
215#99×C61—41no—
216#95×C61—21no—
217#95×C61—21no—
218C24×C61C22×C411yescharacteristic
219C24×C61C2411yescharacteristic
220C23×D61—21no—
221C23×D61—21no—
222C23×D61—21no—
223C23×D61—21no—
224C23×D61—42no—
225C23×D61—81no—
226C23×D61C22×C411yescharacteristic
227C23×D61C22×C411yescharacteristic
228C23×D61C2×D411yescharacteristic
229C23×D61C2×D411yescharacteristic
230C23×D61C2×D411yescharacteristic
231C23×D61C2×D411yescharacteristic
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C22×C4×C61—21no—
239C22×C4×C61—21no—
240C22×C4×C61—21no—
241C22×C4×C61—21no—
242C22×C4×C61—21no—
243C22×C4×C61—21no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61C22×C411yescharacteristic
247C22×C4×C61C22×C411yescharacteristic
248C22×C4×C61C22×C411yescharacteristic
249C22×C4×C61C22×C411yescharacteristic
250C22×C4×C61C22×C411yescharacteristic
251C22×C4×C61C2×D411yescharacteristic
252C22×C4×C61C2×D411yescharacteristic
253C22×C4×C61C2×D411yescharacteristic
254C22×C4×C61C2×D411yescharacteristic
255C2×C22⋊D61—21no—
256C2×C22⋊D61—21no—
257C2×C22⋊D61—21no—
258C2×C22⋊D61—21no—
259C2×C22⋊D61—42no—
260C2×C22⋊D61—81no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—81no—
268C22×Dic61—81no—
269C22×Dic61C22×C411yescharacteristic
270C22×Dic61C22×C411yescharacteristic
271C22×Dic61C22×C411yescharacteristic
272C22×Dic61C22×C411yescharacteristic
273C22×Dic61C22×C411yescharacteristic
274C22×Dic61C22×C411yescharacteristic
275C22×Dic61C2×D411yescharacteristic
276C22×Dic61C2×D411yescharacteristic
277C22×Dic61C2×D411yescharacteristic
278C22×Dic61C2×D411yescharacteristic
279C2×C4×D61—21no—
280C2×C4×D61—21no—
281C2×C4×D61—21no—
282C2×C4×D61—21no—
283C2×C4×D61—42no—
284C2×C4×D61—42no—
285C2×C4×D61—42no—
286C2×C4×D61—42no—
287C2×C4×D61—42no—
288C2×C4×D61—81no—
289C2×C4×D61—81no—
290C2×C4×D61—81no—
291C2×Dic122—21no—
292C2×Dic122—21no—
293C2×Dic122—81no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61—21no—
296C4⋊C4×C61—21no—
297C4⋊C4×C61—21no—
298C4⋊C4×C61—42no—
299C22⋊C4×C61—21no—
300C22⋊C4×C61—21no—
301C22⋊C4×C61—21no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—21no—
307C22⋊C4×C61—21no—
308C22⋊C4×C61—21no—
309C22⋊C4×C61—21no—
310C22⋊C4×C61—21no—
311C22⋊C4×C61—21no—
312C22⋊C4×C61#4112yes—
313C42×C61—42no—
314C22⋊Dic61—21no—
315C22⋊Dic61—21no—
316C22⋊Dic61—21no—
317C22⋊Dic61—21no—
318C22⋊Dic61—21no—
319C22⋊Dic61—21no—
320C22⋊Dic61—21no—
321C22⋊Dic61—21no—
322C22⋊Dic61—21no—
323C22⋊Dic61—21no—
324C22⋊Dic61—21no—
325C22⋊Dic61—21no—
326C22⋊Dic61—21no—
327C22⋊Dic61#4112yes—
328#11758198—21no—
329#11758198—21no—
330#11758198—21no—
331#11758198—21no—
332#11758198—21no—
333#11758198—21no—
334#11758198—21no—
335#11758198—21no—
336#11758198—42no—
337#11758198—42no—
338#11758198—42no—
339#11758198—42no—
340#11758198—81no—
341#11758198—81no—
342#11758198C22⋊C411yescharacteristic
343#11758198C22⋊C411yescharacteristic
344#11758198C22⋊C411yescharacteristic
345#11758198C22⋊C411yescharacteristic
346#11758198C22⋊C411yescharacteristic
347#11758198C22⋊C411yescharacteristic
348#11758198C22⋊C411yescharacteristic
349#11758198C22⋊C411yescharacteristic
350#11758198C22⋊C411yescharacteristic
351#11758198C22⋊C411yescharacteristic
352#11758198C22⋊C411yescharacteristic
353#11758198C22⋊C411yescharacteristic
354#11758198C22⋊C411yescharacteristic
355#11758198C22⋊C411yescharacteristic
356#11758198C22⋊C411yescharacteristic
357#11758198C22⋊C411yescharacteristic
358C4⋊Dic61—21no—
359C4⋊Dic61—21no—
360C4⋊Dic61—21no—
361C4⋊Dic61—21no—
362C4⋊Dic61—21no—
363C4⋊Dic61—21no—
364C4⋊Dic61—21no—
365C4⋊Dic61—21no—
366C4⋊Dic61—42no—
367#11758196—21no—
368#11758196—21no—
369#11758196—21no—
370#11758196—21no—
371#11758196—81no—
372#11758196—81no—
373C4×Dic61—21no—
374C4×Dic61—21no—
375C4×Dic61—21no—
376C4×Dic61—21no—
377C4×Dic61—21no—
378C4×Dic61—21no—
379C4×Dic61—42no—
380C4×Dic61—81no—
381C4×Dic61—81no—
382C23×C61—21no—
383C23×C61—21no—
384C23×C61—21no—
385C23×C61—41no—
386C23×C61—41no—
387C23×C61—41no—
388C23×C61—41no—
389C23×C61C23×C411yescharacteristic
390C23×C61C22×D411yescharacteristic
391C23×C61C22×D411yescharacteristic
392C23×C61C2×#4111yescharacteristic
393C23×C61C2×#4111yescharacteristic
394C23×C61H(5,𝔽2)11yescharacteristic
395C23×C612−1+411yescharacteristic
396C22×D61—21no—
397C22×D61—21no—
398C22×D61—21no—
399C22×D61—21no—
400C22×D61—21no—
401C22×D61—21no—
402C22×D61—21no—
403C22×D61—21no—
404C22×D61—21no—
405C22×D61—21no—
406C22×D61—21no—
407C22×D61—21no—
408C22×D61—22no—
409C22×D61—22no—
410C22×D61—22no—
411C22×D61—41no—
412C22×D61—41no—
413C22×D61—41no—
414C22×D61—41no—
415C22×D61—41no—
416C22×D61—41no—
417C22×D61—41no—
418C22×D61—41no—
419C22×D61—41no—
420C22×D61—82no—
421C22×D61—82no—
422C22×D61—82no—
423C22×D61—82no—
424C22×D61C2×C22⋊C411yescharacteristic
425C22×D61C2×C22⋊C411yescharacteristic
426C22×D61C2×C22⋊C411yescharacteristic
427C22×D61C2×C22⋊C411yescharacteristic
428D4×C61—41no—
429D4×C61—41no—
430D4×C61—41no—
431D4×C61—41no—
432C2×C4×C61—21no—
433C2×C4×C61—21no—
434C2×C4×C61—21no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×C4×C61—21no—
442C2×C4×C61—21no—
443C2×C4×C61—21no—
444C2×C4×C61—21no—
445C2×C4×C61—21no—
446C2×C4×C61—21no—
447C2×C4×C61—21no—
448C2×C4×C61—21no—
449C2×C4×C61—22no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—41no—
456C2×C4×C61—41no—
457C2×C4×C61—41no—
458C2×C4×C61—41no—
459C2×C4×C61—41no—
460C2×C4×C61—41no—
461C2×C4×C61—41no—
462C2×C4×C61—41no—
463C2×C4×C61C2×C22⋊C411yescharacteristic
464C2×C4×C61C2×C22⋊C411yescharacteristic
465C2×C4×C61C2×C22⋊C411yescharacteristic
466C2×C4×C61C2×C22⋊C411yescharacteristic
467C22⋊D61—42no—
468C22⋊D61—42no—
469C22⋊D61—81no—
470C22⋊D61—81no—
471C2×Dic61—21no—
472C2×Dic61—21no—
473C2×Dic61—21no—
474C2×Dic61—21no—
475C2×Dic61—22no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—41no—
482C2×Dic61—41no—
483C2×Dic61—41no—
484C2×Dic61—41no—
485C2×Dic61—41no—
486C2×Dic61—41no—
487C2×Dic61—41no—
488C2×Dic61—41no—
489C2×Dic61—41no—
490C2×Dic61—41no—
491C2×Dic61—41no—
492C2×Dic61—41no—
493C2×Dic61—41no—
494C2×Dic61—41no—
495C2×Dic61—41no—
496C2×Dic61—41no—
497C2×Dic61—81no—
498C2×Dic61—81no—
499C2×Dic61C2×C22⋊C411yescharacteristic
500C2×Dic61C2×C22⋊C411yescharacteristic
501C2×Dic61C2×C22⋊C411yescharacteristic
502C2×Dic61C2×C22⋊C411yescharacteristic
503C4×D61—42no—
504C4×D61—42no—
505C4×D61—81no—
506C4×D61—81no—
507C4×D61—84no—
508C4×D61—84no—
509Dic122—81no—
510Dic122—81no—
511#22477—611nomaximal, Sylow
512C22×C61—21no—
513C22×C61—21no—
514C22×C61—21no—
515C22×C61—21no—
516C22×C61—21no—
517C22×C61—21no—
518C22×C61—41no—
519C22×C61—41no—
520C22×C61—41no—
521C22×C61—41no—
522C22×C61—41no—
523C22×C61—41no—
524C22×C61—41no—
525C22×C61—81no—
526C22×C61—81no—
527C22×C61C22×C22⋊C411yescharacteristic
528C22×C61C4×#4111yescharacteristic
529C22×C61#52011yescharacteristic
530C22×C61#54611yescharacteristic
531C22×C61#54611yescharacteristic
532C22×C61#54711yescharacteristic
533C22×C61#54711yescharacteristic
534C2×D61—21no—
535C2×D61—21no—
536C2×D61—21no—
537C2×D61—21no—
538C2×D61—21no—
539C2×D61—21no—
540C2×D61—21no—
541C2×D61—21no—
542C2×D61—21no—
543C2×D61—21no—
544C2×D61—21no—
545C2×D61—42no—
546C2×D61—42no—
547C2×D61—42no—
548C2×D61—42no—
549C2×D61—42no—
550C2×D61—42no—
551C2×D61—81no—
552C2×D61—81no—
553C2×D61—81no—
554C2×D61—81no—
555C2×D61—81no—
556C2×D61—81no—
557C2×D61#41012yes—
558C4×C61—21no—
559C4×C61—21no—
560C4×C61—21no—
561C4×C61—21no—
562C4×C61—42no—
563C4×C61—41no—
564C4×C61—41no—
565C4×C61—41no—
566C4×C61—81no—
567C4×C61—81no—
568C4×C61—81no—
569Dic61—21no—
570Dic61—21no—
571Dic61—21no—
572Dic61—21no—
573Dic61—42no—
574Dic61—41no—
575Dic61—41no—
576Dic61—41no—
577Dic61—41no—
578Dic61—81no—
579Dic61—81no—
580Dic61—81no—
581C2×#551—611no—
582#2342—611no—
583#2342—611no—
584#1996—611no—
585#1996—611no—
586#1899—611no—
587#1899D6111yescharacteristic, complemented
588#1898—611no—
589#1898—611no—
590#1820—611no—
591#1819—611no—
592#1799—611no—
593C4×#99—611no—
594#1740—611no—
595C2×#342—611no—
596C2×C61—21no—
597C2×C61—21no—
598C2×C61—21no—
599C2×C61—21no—
600C2×C61—21no—
601C2×C61—21no—
602C2×C61—81no—
603C2×C61#233911yescharacteristic
604C2×C61C2×#41011yescharacteristic
605C2×C61#288311yescharacteristic
606D61—22no—
607D61—41no—
608D61—41no—
609D61—41no—
610#551—1221no—
611#551—1221no—
612#551—1221no—
613#551—1221no—
614#551—1221no—
615#551—1221no—
616#551—1221no—
617#551—1221no—
618C2×#126—611no—
619C2×#126—611no—
620C2×#124—611no—
621C2×#123—611no—
622C2×#123—611no—
623C2×#123C2×D6111yescharacteristic
624C2×C22⋊Q8—611no—
625C2×C22⋊Q8—611no—
626C2×#120—611no—
627C2×C4×D4—611no—
628C2×C4×D4—611no—
629C2×#117—611no—
630C2×#117—611no—
631C2×#117—611no—
632C2×#117C2×D6111yescharacteristic
633C22×C22⋊C4—611no—
634C22×C22⋊C4—611no—
635C22×C22⋊C4—611no—
636C22×C22⋊C4—611no—
637C2×#99—611no—
638C2×#99—611no—
639C2×#99C2×D6111yescharacteristic
640C2×#99C2×D6111yescharacteristic
641#388—1221no—
642#388—1221no—
643#388—1221no—
644#388—1221no—
645#385—1221no—
646#385—1221no—
647#381—611no—
648#381C2×D6111yescharacteristic
649#380—611no—
650#380—611no—
651#379—611no—
652#379—611no—
653C4×C22⋊C4—611no—
654C4×C22⋊C4—611no—
655C4×C22⋊C4—1221no—
656C4×C22⋊C4—1221no—
657#342—611no—
658#342—611no—
659#342—611no—
660#342—611no—
661#342—611no—
662#342—611no—
663#342—611no—
664#342—611no—
665#342—611no—
666#342—611no—
667#342C2×D6111yescharacteristic
668#342C2×D6111yescharacteristic
669C61#2247711yescharacteristic, complemented, Sylow
670C25—611no—
671C22×Q8—611no—
672C22×D4—611no—
673C22×D4—611no—
674C22×D4C22×D6111yescharacteristic
675C23×C4—611no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—1221no—
680C23×C4—1221no—
681C23×C4C22×D6111yescharacteristic
682#126—1221no—
683#126—1221no—
684#126—1221no—
685#126—1221no—
686#126—1221no—
687#126—1221no—
688#126—1221no—
689#126—1221no—
690#124—1221no—
691#124—1221no—
692#124—1221no—
693#124—1221no—
694#123—21no—
695#123—21no—
696#123—21no—
697#123—21no—
698#123—1221no—
699#123—1221no—
700#123—1221no—
701#123—1221no—
702#123—1221no—
703#123—1221no—
704#123—1221no—
705#123—1221no—
706C22⋊Q8—1221no—
707C22⋊Q8—1221no—
708C22⋊Q8—1221no—
709C22⋊Q8—1221no—
710C22⋊Q8—1221no—
711C22⋊Q8—1221no—
712C22⋊Q8—1221no—
713C22⋊Q8—1221no—
714#120—1221no—
715#120—1221no—
716#120—1221no—
717#120—1221no—
718C4×D4—1221no—
719C4×D4—1221no—
720C4×D4—1221no—
721C4×D4—1221no—
722C4×D4—1221no—
723C4×D4—1221no—
724C4×D4—1221no—
725C4×D4—1221no—
726#117—22no—
727#117—41no—
728#117—1221no—
729#117—1221no—
730#117—1221no—
731#117—1221no—
732#117—1221no—
733#117—1221no—
734#117—1221no—
735#117—1221no—
736#117—1222no—
737#117—2441no—
738C2×C4⋊C4—21no—
739C2×C4⋊C4—611no—
740C2×C4⋊C4—611no—
741C2×C4⋊C4—611no—
742C2×C4⋊C4—611no—
743C2×C4⋊C4—611no—
744C2×C4⋊C4—611no—
745C2×C4⋊C4—1221no—
746C2×C4⋊C4—1221no—
747C2×C4⋊C4—1221no—
748C2×C4⋊C4C4×D6111yescharacteristic, complemented
749C2×C4⋊C4C4×D6111yescharacteristic, complemented
750C2×C22⋊C4—611no—
751C2×C22⋊C4—611no—
752C2×C22⋊C4—611no—
753C2×C22⋊C4—611no—
754C2×C22⋊C4—611no—
755C2×C22⋊C4—611no—
756C2×C22⋊C4—611no—
757C2×C22⋊C4—611no—
758C2×C22⋊C4—611no—
759C2×C22⋊C4—611no—
760C2×C22⋊C4—611no—
761C2×C22⋊C4—611no—
762C2×C22⋊C4—611no—
763C2×C22⋊C4—611no—
764C2×C22⋊C4—611no—
765C2×C22⋊C4—611no—
766C2×C22⋊C4—611no—
767C2×C22⋊C4—611no—
768C2×C22⋊C4—611no—
769C2×C22⋊C4—611no—
770C2×C22⋊C4—611no—
771C2×C22⋊C4—611no—
772C2×C22⋊C4—611no—
773C2×C22⋊C4—1222no—
774C2×C22⋊C4—1221no—
775C2×C22⋊C4—1221no—
776C2×C22⋊C4—1221no—
777C2×C22⋊C4—1221no—
778C2×C22⋊C4—1222no—
779C2×C22⋊C4—1221no—
780C2×C22⋊C4—1221no—
781C2×C22⋊C4—1221no—
782C2×C22⋊C4—1221no—
783C2×C22⋊C4—1221no—
784C2×C22⋊C4—1221no—
785C2×C22⋊C4—2441no—
786C2×C22⋊C4—2441no—
787C2×C22⋊C4C4×D6111yescharacteristic, complemented
788C2×C22⋊C4C4×D6111yescharacteristic, complemented
789C2×C22⋊C4C22×D6111yescharacteristic
790C2×C22⋊C4C22×D6111yescharacteristic
791C2×C22⋊C4C22×D6111yescharacteristic
792C2×C22⋊C4C22×D6111yescharacteristic
793C2×C22⋊C4C22×D6111yescharacteristic
794C2×C42—21no—
795C2×C42—611no—
796C2×C42—611no—
797C2×C42—611no—
798C2×C42—1221no—
799C2×C42—1221no—
800C2×C42—1221no—
801#99—22no—
802#99—41no—
803#99—1222no—
804#99—2441no—
805#95—21no—
806#95—21no—
807#95—1221no—
808#95—1221no—
809#95—1221no—
810#95—1221no—
811#95—1221no—
812#95—1221no—
813C24—611no—
814C24—611no—
815C24—611no—
816C24—611no—
817C24—611no—
818C24—611no—
819C24—1221no—
820C24—1221no—
821C24—1221no—
822C24—1221no—
823C24—4881no—
824C24—2442no—
825C24C2×C4×D6111yescharacteristic
826C24C23×D6111yescharacteristic
827C2×Q8—1221no—
828C2×Q8—1221no—
829C2×Q8—4881no—
830C2×D4—21no—
831C2×D4—21no—
832C2×D4—21no—
833C2×D4—21no—
834C2×D4—21no—
835C2×D4—21no—
836C2×D4—1221no—
837C2×D4—1221no—
838C2×D4—1221no—
839C2×D4—1221no—
840C2×D4—4881no—
841C2×D4—2442no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—611no—
851C22×C4—611no—
852C22×C4—611no—
853C22×C4—611no—
854C22×C4—611no—
855C22×C4—611no—
856C22×C4—611no—
857C22×C4—611no—
858C22×C4—611no—
859C22×C4—611no—
860C22×C4—1221no—
861C22×C4—1221no—
862C22×C4—1221no—
863C22×C4—1221no—
864C22×C4—1221no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
870C22×C4—4881no—
871C22×C4—4881no—
872C22×C4—4881no—
873C22×C4—4881no—
874C22×C4—4881no—
875C22×C4—2442no—
876C22×C4—2442no—
877C22×C4—2442no—
878C22×C4—2442no—
879C22×C4—2442no—
880C22×C4C2×C4×D6111yescharacteristic
881C22×C4C2×C4×D6111yescharacteristic
882C22×C4C2×C4×D6111yescharacteristic
883C22×C4C2×C4×D6111yescharacteristic
884C22×C4C2×C4×D6111yescharacteristic
885C22×C4D4×D6111yescharacteristic
886C22×C4D4×D6111yescharacteristic
887C22×C4D4×D6111yescharacteristic
888C22×C4D4×D6111yescharacteristic
889C4⋊C4—21no—
890C4⋊C4—21no—
891C4⋊C4—21no—
892C4⋊C4—21no—
893C4⋊C4—42no—
894C4⋊C4—1221no—
895C4⋊C4—1221no—
896C4⋊C4—1221no—
897C4⋊C4—1221no—
898C4⋊C4—1221no—
899C4⋊C4—1221no—
900C4⋊C4—1221no—
901C4⋊C4—1221no—
902C4⋊C4—1221no—
903C4⋊C4—1221no—
904C4⋊C4—1221no—
905C4⋊C4—1221no—
906C4⋊C4—4881no—
907C4⋊C4—4881no—
908C4⋊C4—2442no—
909C22⋊C4—21no—
910C22⋊C4—21no—
911C22⋊C4—21no—
912C22⋊C4—21no—
913C22⋊C4—21no—
914C22⋊C4—21no—
915C22⋊C4—21no—
916C22⋊C4—21no—
917C22⋊C4—21no—
918C22⋊C4—21no—
919C22⋊C4—21no—
920C22⋊C4—21no—
921C22⋊C4—21no—
922C22⋊C4—611no—
923C22⋊C4—611no—
924C22⋊C4—611no—
925C22⋊C4—611no—
926C22⋊C4—611no—
927C22⋊C4—611no—
928C22⋊C4—611no—
929C22⋊C4—611no—
930C22⋊C4—611no—
931C22⋊C4—611no—
932C22⋊C4—611no—
933C22⋊C4—611no—
934C22⋊C4—611no—
935C22⋊C4—611no—
936C22⋊C4—611no—
937C22⋊C4—611no—
938C22⋊C4—612no—
939C22⋊C4—1221no—
940C22⋊C4—1221no—
941C22⋊C4—1221no—
942C22⋊C4—1221no—
943C22⋊C4—1221no—
944C22⋊C4—1221no—
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—4881no—
961C22⋊C4—4881no—
962C22⋊C4—2442no—
963C22⋊C4—2442no—
964C22⋊C4—2442no—
965C22⋊C4—2442no—
966C22⋊C4#1175822412yes—
967C42—42no—
968C42—1221no—
969C42—1221no—
970C42—1221no—
971C42—1221no—
972C42—1221no—
973C42—1221no—
974C42—4881no—
975C42—4881no—
976C42—2442no—
977C23—21no—
978C23—21no—
979C23—21no—
980C23—41no—
981C23—41no—
982C23—41no—
983C23—41no—
984C23—611no—
985C23—611no—
986C23—611no—
987C23—611no—
988C23—1222no—
989C23—1222no—
990C23—1222no—
991C23—1221no—
992C23—1221no—
993C23—1221no—
994C23—1221no—
995C23—1221no—
996C23—1221no—
997C23—1221no—
998C23—1221no—
999C23—1221no—
1000C23—1221no—
1001C23—1221no—
1002C23—1221no—
1003C23—4882no—
1004C23—4882no—
1005C23—4882no—
1006C23—4882no—
1007C23—2441no—
1008C23—2441no—
1009C23—2441no—
1010C23—2441no—
1011C23—2441no—
1012C23—2441no—
1013C23—2441no—
1014C23—2441no—
1015C23—2441no—
1016C23C22×C4×D6111yescharacteristic
1017C23C2×D4×D6111yescharacteristic
1018C23C2×D4×D6111yescharacteristic
1019C23#41×D6111yescharacteristic
1020C23C2×#1175822411yescharacteristic
1021C23#1451982211yescharacteristic
1022C23#1451982411yescharacteristic
1023Q8—4881no—
1024Q8—4881no—
1025D4—41no—
1026D4—41no—
1027D4—41no—
1028D4—41no—
1029D4—4881no—
1030D4—4881no—
1031D4—2442no—
1032D4—2442no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—21no—
1039C2×C4—21no—
1040C2×C4—21no—
1041C2×C4—21no—
1042C2×C4—21no—
1043C2×C4—21no—
1044C2×C4—21no—
1045C2×C4—21no—
1046C2×C4—21no—
1047C2×C4—21no—
1048C2×C4—21no—
1049C2×C4—21no—
1050C2×C4—22no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—611no—
1065C2×C4—611no—
1066C2×C4—611no—
1067C2×C4—611no—
1068C2×C4—1221no—
1069C2×C4—1221no—
1070C2×C4—1221no—
1071C2×C4—1221no—
1072C2×C4—1222no—
1073C2×C4—4884no—
1074C2×C4—4881no—
1075C2×C4—4881no—
1076C2×C4—4884no—
1077C2×C4—4881no—
1078C2×C4—4881no—
1079C2×C4—2442no—
1080C2×C4—2442no—
1081C2×C4—2441no—
1082C2×C4—2441no—
1083C2×C4—2441no—
1084C2×C4—2441no—
1085C2×C4—2441no—
1086C2×C4—2441no—
1087C2×C4—2441no—
1088C2×C4—2441no—
1089C2×C4—2441no—
1090C2×C4—2441no—
1091C2×C4—2441no—
1092C2×C4—2441no—
1093C2×C4—2441no—
1094C2×C4—2441no—
1095C2×C4—2441no—
1096C2×C4—2441no—
1097C2×C4—2441no—
1098C2×C4—2441no—
1099C2×C4—2441no—
1100C2×C4—2441no—
1101C2×C4—2441no—
1102C2×C4C22⋊C4×D6111yescharacteristic
1103C2×C4C22⋊C4×D6111yescharacteristic
1104C2×C4C22⋊C4×D6111yescharacteristic
1105C2×C4C22⋊C4×D6111yescharacteristic
1106C22—21no—
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—41no—
1113C22—41no—
1114C22—41no—
1115C22—41no—
1116C22—41no—
1117C22—41no—
1118C22—41no—
1119C22—81no—
1120C22—81no—
1121C22—612no—
1122C22—1221no—
1123C22—1221no—
1124C22—1221no—
1125C22—1221no—
1126C22—1221no—
1127C22—1221no—
1128C22—1221no—
1129C22—1221no—
1130C22—1221no—
1131C22—1221no—
1132C22—1221no—
1133C22—4881no—
1134C22—4881no—
1135C22—4881no—
1136C22—4881no—
1137C22—4881no—
1138C22—4881no—
1139C22—2442no—
1140C22—2442no—
1141C22—2442no—
1142C22—2442no—
1143C22—2442no—
1144C22—2442no—
1145C22C2×C22⋊C4×D6111yescharacteristic
1146C22C4×#1175822411yescharacteristic
1147C22#1684024111yescharacteristic
1148C22#1684039911yescharacteristic
1149C22#1684040111yescharacteristic
1150C22#1684041011yescharacteristic
1151C22#1684041211yescharacteristic
1152C4—21no—
1153C4—21no—
1154C4—21no—
1155C4—21no—
1156C4—42no—
1157C4—41no—
1158C4—41no—
1159C4—41no—
1160C4—81no—
1161C4—81no—
1162C4—81no—
1163C4—1221no—
1164C4—1221no—
1165C4—1221no—
1166C4—1221no—
1167C4—4881no—
1168C4—4881no—
1169C4—4881no—
1170C4—2442no—
1171C4—2441no—
1172C4—2441no—
1173C4—2441no—
1174C4—2441no—
1175C2—21no—
1176C2—21no—
1177C2—21no—
1178C2—21no—
1179C2—21no—
1180C2—21no—
1181C2—81no—
1182C2—1222no—
1183C2—2441no—
1184C2—2441no—
1185C2—2441no—
1186C2#2144864511yescharacteristic
1187C2#410×D6111yescharacteristic
1188C2#2145427811yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1899C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#14519745C22
cosocleC24×C61C24
hypercenter#1899D61
hypocenterC61#22477
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1899

Complements

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

NH ≅ G/Ntype
2. #21448669C2semidirect
3. #21448661C2semidirect
4. #21446802C2semidirect
5. #21446802C2semidirect
6. #21446278C2semidirect
9. #21445894C2semidirect
10. #21445892C2semidirect
11. #21445805C2semidirect
12. #99×Dic61C2semidirect
13. #21445551C2semidirect
14. #342×D61C2semidirect
15. C61×#1899C2semidirect
24. C2×#14519772C4semidirect
25. C2×#14519772C4semidirect
26. C2×#14519763C4semidirect
27. C2×#14519761C4semidirect
28. C2×#14519759C4semidirect
29. C2×#14519757C4semidirect
33. C2×#14519737C4semidirect
36. C2×#14519735C4semidirect
76. C22×Dic122C2×C4semidirect
79. C23×Dic61C2×C4semidirect
136. C2×C4⋊Dic61C2×C4semidirect
137. C2×C4⋊Dic61C2×C4semidirect
138. C2×C4⋊Dic61C2×C4semidirect
139. C2×C4⋊Dic61C2×C4semidirect
142. C2×#11758196C2×C4semidirect
143. C2×#11758196C2×C4semidirect
144. C2×C22⋊Dic61C2×C4semidirect
184. C2×C4×Dic61C2×C4semidirect
185. C2×C4×Dic61C2×C4semidirect
186. C2×C4×Dic61C2×C4semidirect
204. C2×C4⋊C4×C61C2×C4semidirect
205. C2×C4⋊C4×C61C2×C4semidirect
206. C2×C22⋊C4×C61C2×C4semidirect
207. C2×C22⋊C4×C61C2×C4semidirect
587. #1899D61semidirect
669. C61#22477semidirect
748. C2×C4⋊C4C4×D61semidirect
749. C2×C4⋊C4C4×D61semidirect
787. C2×C22⋊C4C4×D61semidirect
788. C2×C22⋊C4C4×D61semidirect

Maximal subgroups

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

subgroupindex
C2×#168404352
#214486692
#214486612
#214468022
#214462782
#214462692
#214458942
#214458922
#214458052
#99×Dic612
#214455512
#342×D612
C61×#18992
#2247761