Finite Group Databasebeta

← #29696152

Subgroups — #29696152

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×#16840443C211yesmaximal, characteristic
2#21448670C211yesmaximal, characteristic, complemented
3#21448664C211yesmaximal, characteristic, complemented
4#21446802C211yesmaximal, characteristic, complemented
5#21446802C211yesmaximal, characteristic, complemented
6#21446274C211yesmaximal, characteristic, complemented
7#21446274C211yesmaximal, characteristic, complemented
8#21446273C211yesmaximal, characteristic
9#21445895C211yesmaximal, characteristic, complemented
10#21445891C211yesmaximal, characteristic, complemented
11#21445805C211yesmaximal, characteristic, complemented
12#99×Dic61C211yesmaximal, characteristic, complemented
13#21445550C211yesmaximal, characteristic, complemented
14C2×#16839528C211yesmaximal, characteristic, complemented
15C61×#1898C211yesmaximal, characteristic
16#16840443—21no—
17#16840443—21no—
18#16840443—21no—
19#16840443—21no—
20#16840443—21no—
21#16840443—21no—
22#16840443—21no—
23#16840443—21no—
24C2×#14519770C411yescharacteristic, complemented
25C2×#14519770C411yescharacteristic, complemented
26C2×#14519764C411yescharacteristic, complemented
27C2×#14519758C411yescharacteristic, complemented
28C2×#14519758C411yescharacteristic, complemented
29C2×#14519758C2211yescharacteristic
30C2×#14519754C411yescharacteristic, complemented
31C2×#14519754C2211yescharacteristic
32C2×D4×Dic61C411yescharacteristic, complemented
33C2×D4×Dic61C2211yescharacteristic
34C2×#14519733C411yescharacteristic, complemented
35C2×#14519733C2211yescharacteristic
36C2×#14519733C2211yescharacteristic
37C2×#14519733C2211yescharacteristic
38C22×C22⋊Dic61C2211yescharacteristic
39C22×C22⋊Dic61C2211yescharacteristic
40C22×C22⋊Dic61C2211yescharacteristic
41C2×#14519692C2211yescharacteristic
42C2×#14519692C2211yescharacteristic
43#16839656—21no—
44#16839656—21no—
45#16839650—21no—
46#16839650—21no—
47#16839635—21no—
48#16839634—21no—
49#16839623C2211yescharacteristic
50#16839623C2211yescharacteristic
51#16839620C2211yescharacteristic
52#16839620C2211yescharacteristic
53#16839618C2211yescharacteristic
54C22⋊C4×Dic61—21no—
55C22⋊C4×Dic61C2211yescharacteristic
56C22⋊C4×Dic61C2211yescharacteristic
57C4×C22⋊Dic61—21no—
58#16839529C2211yescharacteristic
59#16839529C2211yescharacteristic
60#16839528C2211yescharacteristic
61#16839528C2211yescharacteristic
62#16839528C2211yescharacteristic
63#16839528C2211yescharacteristic
64#16839528C2211yescharacteristic
65#16839528C2211yescharacteristic
66#16839528C2211yescharacteristic
67#16839528C2211yescharacteristic
68C2×#120×C61C2211yescharacteristic
69C22×C22⋊C4×C61C2211yescharacteristic
70C2×#99×C61C2211yescharacteristic
71C2×#99×C61C2211yescharacteristic
72C61×#379C2211yescharacteristic
73C61×#342C2211yescharacteristic
74C61×#342C2211yescharacteristic
75C22×Dic122C2×C411yescharacteristic, complemented
76C23×Dic61—21no—
77C23×Dic61C2×C411yescharacteristic
78C23×Dic61C2×C411yescharacteristic
79C23×Dic61C2×C411yescharacteristic, complemented
80C23×Dic61C2311yescharacteristic
81C23×Dic61C2311yescharacteristic
82#14519770—21no—
83#14519770—21no—
84#14519770—21no—
85#14519770—21no—
86#14519770—21no—
87#14519770—21no—
88#14519770—21no—
89#14519770—21no—
90#14519764—21no—
91#14519764—21no—
92#14519764—21no—
93#14519764—21no—
94#14519758—21no—
95#14519758—21no—
96#14519758—21no—
97#14519758—21no—
98#14519758—21no—
99#14519758—21no—
100#14519758—21no—
101#14519758—21no—
102#14519758—21no—
103#14519758—21no—
104#14519758—21no—
105#14519758—21no—
106#14519754—21no—
107#14519754—21no—
108#14519754—21no—
109#14519754—21no—
110#14519754—21no—
111#14519754—21no—
112#14519754—21no—
113#14519754—21no—
114D4×Dic61—21no—
115D4×Dic61—21no—
116D4×Dic61—21no—
117D4×Dic61—21no—
118D4×Dic61—21no—
119D4×Dic61—21no—
120D4×Dic61—21no—
121D4×Dic61—21no—
122#14519733—21no—
123#14519733—21no—
124#14519733—21no—
125#14519733—21no—
126#14519733—21no—
127#14519733—21no—
128#14519733—21no—
129#14519733—21no—
130#14519733—22no—
131#14519733—22no—
132#14519733—41no—
133#14519733—41no—
134C2×C4⋊Dic61C2×C411yescharacteristic, complemented
135C2×C4⋊Dic61C2×C411yescharacteristic, complemented
136C2×#11758196—21no—
137C2×#11758196—21no—
138C2×#11758196—21no—
139C2×#11758196—21no—
140C2×#11758196C2×C411yescharacteristic, complemented
141C2×#11758196C2×C411yescharacteristic, complemented
142C2×#11758196C2×C411yescharacteristic, complemented
143C2×#11758196C2×C411yescharacteristic, complemented
144C2×#11758196C2×C411yescharacteristic, complemented
145C2×#11758196C2×C411yescharacteristic, complemented
146C2×C22⋊Dic61—21no—
147C2×C22⋊Dic61—21no—
148C2×C22⋊Dic61—21no—
149C2×C22⋊Dic61—21no—
150C2×C22⋊Dic61—22no—
151C2×C22⋊Dic61—21no—
152C2×C22⋊Dic61—21no—
153C2×C22⋊Dic61—21no—
154C2×C22⋊Dic61—41no—
155C2×C22⋊Dic61C2×C411yescharacteristic
156C2×C22⋊Dic61C2×C411yescharacteristic
157C2×C22⋊Dic61C2×C411yescharacteristic
158C2×C22⋊Dic61C2×C411yescharacteristic
159C2×C22⋊Dic61C2×C411yescharacteristic
160C2×C22⋊Dic61C2×C411yescharacteristic
161C2×C22⋊Dic61C2×C411yescharacteristic, complemented
162C2×C22⋊Dic61C2×C411yescharacteristic, complemented
163C2×C22⋊Dic61C2×C411yescharacteristic, complemented
164C2×C22⋊Dic61D411yescharacteristic
165C2×C22⋊Dic61D411yescharacteristic
166C2×C22⋊Dic61D411yescharacteristic
167C2×C22⋊Dic61D411yescharacteristic
168C2×C22⋊Dic61D411yescharacteristic
169C2×C22⋊Dic61D411yescharacteristic
170C2×C22⋊Dic61D411yescharacteristic
171C2×C22⋊Dic61D411yescharacteristic
172C2×C22⋊Dic61C2311yescharacteristic
173C2×C22⋊Dic61C2311yescharacteristic
174C2×C22⋊Dic61C2311yescharacteristic
175C2×C22⋊Dic61C2311yescharacteristic
176C2×C22⋊Dic61C2311yescharacteristic
177C2×C22⋊Dic61C2311yescharacteristic
178C2×C4×Dic61—21no—
179C2×C4×Dic61—21no—
180C2×C4×Dic61—21no—
181C2×C4×Dic61—21no—
182C2×C4×Dic61C2×C411yescharacteristic, complemented
183C2×C4×Dic61C2×C411yescharacteristic, complemented
184C2×C4×Dic61C2×C411yescharacteristic, complemented
185#14519692—22no—
186#14519692—41no—
187#14519684—21no—
188#14519684—21no—
189#14519684—21no—
190#14519684—21no—
191#14519684—21no—
192#14519684—21no—
193#14519684—21no—
194#14519684—21no—
195C25×C61C2311yescharacteristic
196C22×D4×C61C2×C411yescharacteristic
197C22×D4×C61C2×C411yescharacteristic
198C22×D4×C61C2311yescharacteristic
199C23×C4×C61—21no—
200#120×C61—21no—
201#120×C61—21no—
202#120×C61—21no—
203#120×C61—21no—
204C2×C22⋊C4×C61—22no—
205C2×C22⋊C4×C61—21no—
206C2×C22⋊C4×C61—21no—
207C2×C22⋊C4×C61—21no—
208C2×C22⋊C4×C61—41no—
209C2×C22⋊C4×C61C2×C411yescharacteristic
210C2×C22⋊C4×C61C2×C411yescharacteristic
211C2×C22⋊C4×C61C2311yescharacteristic
212C2×C22⋊C4×C61C2311yescharacteristic
213C2×C22⋊C4×C61C2311yescharacteristic
214C2×C22⋊C4×C61C2311yescharacteristic
215C2×C22⋊C4×C61C2311yescharacteristic
216#99×C61—22no—
217#99×C61—41no—
218C24×C61—21no—
219C24×C61—21no—
220C24×C61—21no—
221C24×C61—21no—
222C24×C61—42no—
223C24×C61—81no—
224C24×C61C22×C411yescharacteristic
225C24×C61C22×C411yescharacteristic
226C24×C61C22×C411yescharacteristic
227C24×C61C2×D411yescharacteristic
228C24×C61C2×D411yescharacteristic
229C24×C61C2×D411yescharacteristic
230C24×C61C2×D411yescharacteristic
231C24×C61C2411yescharacteristic
232C2×D4×C61—21no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61—21no—
239C2×D4×C61—21no—
240C2×D4×C61—21no—
241C2×D4×C61—21no—
242C2×D4×C61—42no—
243C2×D4×C61—81no—
244C22×C4×C61—21no—
245C22×C4×C61—21no—
246C22×C4×C61—21no—
247C22×C4×C61—21no—
248C22×C4×C61—42no—
249C22×C4×C61—42no—
250C22×C4×C61—81no—
251C22×C4×C61C22×C411yescharacteristic
252C22×C4×C61C22×C411yescharacteristic
253C22×C4×C61C22×C411yescharacteristic
254C22×Dic61—21no—
255C22×Dic61—21no—
256C22×Dic61—21no—
257C22×Dic61—21no—
258C22×Dic61—21no—
259C22×Dic61—21no—
260C22×Dic61—21no—
261C22×Dic61—21no—
262C22×Dic61—21no—
263C22×Dic61—21no—
264C22×Dic61—21no—
265C22×Dic61—21no—
266C22×Dic61—21no—
267C22×Dic61—21no—
268C22×Dic61—42no—
269C22×Dic61—42no—
270C22×Dic61—42no—
271C22×Dic61—81no—
272C22×Dic61—81no—
273C22×Dic61—81no—
274C22×Dic61—81no—
275C22×Dic61C22×C411yescharacteristic
276C22×Dic61C22×C411yescharacteristic
277C22×Dic61C22×C411yescharacteristic
278C22×Dic61C22×C411yescharacteristic
279C22×Dic61C22×C411yescharacteristic
280C22×Dic61C22×C411yescharacteristic
281C22×Dic61C22×C411yescharacteristic
282C22×Dic61C22×C411yescharacteristic
283C22×Dic61C2×D411yescharacteristic
284C22×Dic61C2×D411yescharacteristic
285C22×Dic61C2×D411yescharacteristic
286C22×Dic61C2×D411yescharacteristic
287C22×Dic61C2×D411yescharacteristic
288C22×Dic61C2×D411yescharacteristic
289C22×Dic61C2×D411yescharacteristic
290C22×Dic61C2×D411yescharacteristic
291C2×Dic122—21no—
292C2×Dic122—21no—
293C2×Dic122—81no—
294C22⋊C4×C61—21no—
295C22⋊C4×C61—21no—
296C22⋊C4×C61—21no—
297C22⋊C4×C61—21no—
298C22⋊C4×C61—21no—
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—42no—
308C22⋊C4×C61—42no—
309C22⋊C4×C61—81no—
310C22⋊C4×C61#4112yes—
311C22⋊Dic61—21no—
312C22⋊Dic61—21no—
313C22⋊Dic61—21no—
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—21no—
328C22⋊Dic61—21no—
329C22⋊Dic61—21no—
330C22⋊Dic61—21no—
331C22⋊Dic61—21no—
332C22⋊Dic61—42no—
333C22⋊Dic61—42no—
334C22⋊Dic61—81no—
335C22⋊Dic61C22⋊C411yescharacteristic
336C22⋊Dic61C22⋊C411yescharacteristic
337C22⋊Dic61C22⋊C411yescharacteristic
338C22⋊Dic61C22⋊C411yescharacteristic
339C22⋊Dic61C22⋊C411yescharacteristic
340C22⋊Dic61C22⋊C411yescharacteristic
341C22⋊Dic61C22⋊C411yescharacteristic
342C22⋊Dic61C22⋊C411yescharacteristic
343C22⋊Dic61C22⋊C411yescharacteristic
344C22⋊Dic61C22⋊C411yescharacteristic
345C22⋊Dic61C22⋊C411yescharacteristic
346C22⋊Dic61C22⋊C411yescharacteristic
347C22⋊Dic61C22⋊C411yescharacteristic
348C22⋊Dic61C22⋊C411yescharacteristic
349C22⋊Dic61C22⋊C411yescharacteristic
350C22⋊Dic61C22⋊C411yescharacteristic
351C22⋊Dic61#4112yes—
352C4⋊Dic61—21no—
353C4⋊Dic61—21no—
354C4⋊Dic61—21no—
355C4⋊Dic61—21no—
356#11758196—21no—
357#11758196—21no—
358#11758196—21no—
359#11758196—21no—
360#11758196—21no—
361#11758196—21no—
362#11758196—21no—
363#11758196—21no—
364#11758196—21no—
365#11758196—21no—
366#11758196—21no—
367#11758196—21no—
368#11758196—42no—
369#11758196—42no—
370#11758196—81no—
371#11758196—81no—
372C4×Dic61—21no—
373C4×Dic61—21no—
374C4×Dic61—21no—
375C4×Dic61—21no—
376C4×Dic61—21no—
377C4×Dic61—21no—
378C4×Dic61—42no—
379C4×Dic61—42no—
380C4×Dic61—81no—
381C4×Dic61—81no—
382C23×C61—21no—
383C23×C61—21no—
384C23×C61—21no—
385C23×C61—21no—
386C23×C61—21no—
387C23×C61—21no—
388C23×C61—22no—
389C23×C61—22no—
390C23×C61—22no—
391C23×C61—21no—
392C23×C61—21no—
393C23×C61—21no—
394C23×C61—21no—
395C23×C61—21no—
396C23×C61—21no—
397C23×C61—21no—
398C23×C61—21no—
399C23×C61—21no—
400C23×C61—41no—
401C23×C61—41no—
402C23×C61—41no—
403C23×C61—41no—
404C23×C61—41no—
405C23×C61—41no—
406C23×C61—41no—
407C23×C61—41no—
408C23×C61—41no—
409C23×C61—41no—
410C23×C61—41no—
411C23×C61—41no—
412C23×C61—41no—
413C23×C61—82no—
414C23×C61—82no—
415C23×C61—82no—
416C23×C61—82no—
417C23×C61C2×C22⋊C411yescharacteristic
418C23×C61C2×C22⋊C411yescharacteristic
419C23×C61C2×C22⋊C411yescharacteristic
420C23×C61C2×C22⋊C411yescharacteristic
421C23×C61C23×C411yescharacteristic
422C23×C61C22×D411yescharacteristic
423C23×C61C22×D411yescharacteristic
424C23×C61C2×#4111yescharacteristic
425C23×C61C2×#4111yescharacteristic
426C23×C61H(5,𝔽2)11yescharacteristic
427C23×C612−1+411yescharacteristic
428D4×C61—42no—
429D4×C61—41no—
430D4×C61—41no—
431D4×C61—41no—
432D4×C61—41no—
433D4×C61—42no—
434D4×C61—81no—
435D4×C61—81no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—21no—
440C2×C4×C61—21no—
441C2×C4×C61—22no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—41no—
448C2×C4×C61—41no—
449C2×C4×C61—41no—
450C2×C4×C61—41no—
451C2×C4×C61—41no—
452C2×C4×C61—41no—
453C2×C4×C61—41no—
454C2×C4×C61—41no—
455C2×C4×C61—84no—
456C2×Dic61—21no—
457C2×Dic61—21no—
458C2×Dic61—21no—
459C2×Dic61—21no—
460C2×Dic61—21no—
461C2×Dic61—21no—
462C2×Dic61—21no—
463C2×Dic61—21no—
464C2×Dic61—21no—
465C2×Dic61—21no—
466C2×Dic61—21no—
467C2×Dic61—21no—
468C2×Dic61—21no—
469C2×Dic61—21no—
470C2×Dic61—21no—
471C2×Dic61—21no—
472C2×Dic61—22no—
473C2×Dic61—41no—
474C2×Dic61—41no—
475C2×Dic61—41no—
476C2×Dic61—41no—
477C2×Dic61—41no—
478C2×Dic61—41no—
479C2×Dic61—41no—
480C2×Dic61—41no—
481C2×Dic61—42no—
482C2×Dic61—42no—
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—81no—
497C2×Dic61—81no—
498C2×Dic61—81no—
499C2×Dic61—81no—
500C2×Dic61—84no—
501C2×Dic61C2×C22⋊C411yescharacteristic
502C2×Dic61C2×C22⋊C411yescharacteristic
503C2×Dic61C2×C22⋊C411yescharacteristic
504C2×Dic61C2×C22⋊C411yescharacteristic
505C2×Dic61C2×C22⋊C411yescharacteristic
506C2×Dic61C2×C22⋊C411yescharacteristic
507C2×Dic61C2×C22⋊C411yescharacteristic
508C2×Dic61C2×C22⋊C411yescharacteristic
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—21no—
519C22×C61—21no—
520C22×C61—21no—
521C22×C61—21no—
522C22×C61—21no—
523C22×C61—21no—
524C22×C61—21no—
525C22×C61—21no—
526C22×C61—21no—
527C22×C61—21no—
528C22×C61—21no—
529C22×C61—41no—
530C22×C61—41no—
531C22×C61—41no—
532C22×C61—41no—
533C22×C61—42no—
534C22×C61—42no—
535C22×C61—42no—
536C22×C61—42no—
537C22×C61—42no—
538C22×C61—42no—
539C22×C61—41no—
540C22×C61—41no—
541C22×C61—41no—
542C22×C61—81no—
543C22×C61—81no—
544C22×C61—81no—
545C22×C61—81no—
546C22×C61—81no—
547C22×C61—81no—
548C22×C61—81no—
549C22×C61—81no—
550C22×C61#41012yes—
551C22×C61C22×C22⋊C411yescharacteristic
552C22×C61C4×#4111yescharacteristic
553C22×C61#52011yescharacteristic
554C22×C61#54611yescharacteristic
555C22×C61#54611yescharacteristic
556C22×C61#54711yescharacteristic
557C22×C61#54711yescharacteristic
558C4×C61—42no—
559C4×C61—41no—
560C4×C61—41no—
561C4×C61—41no—
562C4×C61—81no—
563C4×C61—81no—
564C4×C61—81no—
565Dic61—21no—
566Dic61—21no—
567Dic61—21no—
568Dic61—21no—
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#1899—611no—
588#1898—611no—
589#1898D6111yescharacteristic
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—22no—
601C2×C61—21no—
602C2×C61—21no—
603C2×C61—41no—
604C2×C61—41no—
605C2×C61—41no—
606C2×C61—81no—
607C2×C61#233911yescharacteristic
608C2×C61C2×#41011yescharacteristic
609C2×C61#288311yescharacteristic
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×#123—611no—
624C2×C22⋊Q8—611no—
625C2×C22⋊Q8—611no—
626C2×#120C2×D6111yescharacteristic
627C2×C4×D4—611no—
628C2×C4×D4—611no—
629C2×#117—611no—
630C2×#117—611no—
631C2×#117—611no—
632C2×#117—611no—
633C22×C22⋊C4—611no—
634C22×C22⋊C4—611no—
635C22×C22⋊C4—611no—
636C22×C22⋊C4C2×D6111yescharacteristic
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#381—611no—
649#380—611no—
650#380—611no—
651#379—611no—
652#379C2×D6111yescharacteristic
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
670C25C22×D6111yescharacteristic
671C22×Q8—611no—
672C22×D4C4×D6111yescharacteristic
673C22×D4C4×D6111yescharacteristic
674C22×D4C22×D6111yescharacteristic
675C23×C4—21no—
676C23×C4—611no—
677C23×C4—611no—
678C23×C4—611no—
679C23×C4—611no—
680C23×C4—611no—
681C23×C4—1221no—
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—1221no—
695#123—1221no—
696#123—1221no—
697#123—1221no—
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—21no—
715#120—21no—
716#120—21no—
717#120—21no—
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—1221no—
727#117—1221no—
728#117—1221no—
729#117—1221no—
730#117—1221no—
731#117—1221no—
732#117—1221no—
733#117—1221no—
734#117—1222no—
735#117—1222no—
736#117—2441no—
737#117—2441no—
738C2×C4⋊C4—611no—
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—611no—
746C2×C4⋊C4—1221no—
747C2×C4⋊C4—1221no—
748C2×C4⋊C4—1221no—
749C2×C4⋊C4—1221no—
750C2×C22⋊C4—22no—
751C2×C22⋊C4—21no—
752C2×C22⋊C4—21no—
753C2×C22⋊C4—21no—
754C2×C22⋊C4—41no—
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—611no—
774C2×C22⋊C4—611no—
775C2×C22⋊C4—611no—
776C2×C22⋊C4—611no—
777C2×C22⋊C4—611no—
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—1221no—
786C2×C22⋊C4—2441no—
787C2×C22⋊C4C4×D6111yescharacteristic
788C2×C22⋊C4C4×D6111yescharacteristic
789C2×C22⋊C4C22×D6111yescharacteristic
790C2×C22⋊C4C22×D6111yescharacteristic
791C2×C22⋊C4C22×D6111yescharacteristic
792C2×C22⋊C4C22×D6111yescharacteristic
793C2×C22⋊C4C22×D6111yescharacteristic
794C2×C42—611no—
795C2×C42—611no—
796C2×C42—611no—
797C2×C42—1221no—
798C2×C42—1221no—
799C2×C42—1221no—
800C2×C42—1221no—
801#99—22no—
802#99—41no—
803#99—1222no—
804#99—2441no—
805#95—1221no—
806#95—1221no—
807#95—1221no—
808#95—1221no—
809#95—1221no—
810#95—1221no—
811#95—1221no—
812#95—1221no—
813C24—21no—
814C24—21no—
815C24—21no—
816C24—21no—
817C24—42no—
818C24—81no—
819C24C2×C4×D6111yescharacteristic
820C24C2×C4×D6111yescharacteristic
821C24C2×C4×D6111yescharacteristic
822C24D4×D6111yescharacteristic
823C24D4×D6111yescharacteristic
824C24D4×D6111yescharacteristic
825C24D4×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—21no—
837C2×D4—21no—
838C2×D4—21no—
839C2×D4—21no—
840C2×D4—42no—
841C2×D4—81no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—21no—
845C22×C4—21no—
846C22×C4—42no—
847C22×C4—42no—
848C22×C4—81no—
849C22×C4—611no—
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—611no—
861C22×C4—611no—
862C22×C4—611no—
863C22×C4—611no—
864C22×C4—611no—
865C22×C4—1221no—
866C22×C4—1221no—
867C22×C4—1221no—
868C22×C4—1221no—
869C22×C4—1221no—
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—4881no—
880C22×C4—4881no—
881C22×C4—4881no—
882C22×C4—4881no—
883C22×C4—2442no—
884C22×C4—2442no—
885C22×C4—2442no—
886C22×C4C2×C4×D6111yescharacteristic
887C22×C4C2×C4×D6111yescharacteristic
888C22×C4C2×C4×D6111yescharacteristic
889C4⋊C4—1221no—
890C4⋊C4—1221no—
891C4⋊C4—1221no—
892C4⋊C4—1221no—
893C4⋊C4—1221no—
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—4881no—
906C4⋊C4—4881no—
907C4⋊C4—2442no—
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—42no—
923C22⋊C4—42no—
924C22⋊C4—81no—
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—611no—
939C22⋊C4—611no—
940C22⋊C4—611no—
941C22⋊C4—612no—
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—1221no—
961C22⋊C4—1221no—
962C22⋊C4—1221no—
963C22⋊C4—4881no—
964C22⋊C4—2442no—
965C22⋊C4—2442no—
966C22⋊C4#1175822412yes—
967C42—1221no—
968C42—1221no—
969C42—1221no—
970C42—1221no—
971C42—1221no—
972C42—1221no—
973C42—4881no—
974C42—4881no—
975C42—2442no—
976C42—2442no—
977C23—21no—
978C23—21no—
979C23—22no—
980C23—22no—
981C23—22no—
982C23—21no—
983C23—21no—
984C23—21no—
985C23—21no—
986C23—21no—
987C23—21no—
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—21no—
995C23—41no—
996C23—41no—
997C23—41no—
998C23—41no—
999C23—41no—
1000C23—41no—
1001C23—41no—
1002C23—41no—
1003C23—41no—
1004C23—41no—
1005C23—41no—
1006C23—41no—
1007C23—41no—
1008C23—82no—
1009C23—82no—
1010C23—82no—
1011C23—82no—
1012C23C22⋊C4×D6111yescharacteristic
1013C23C22⋊C4×D6111yescharacteristic
1014C23C22⋊C4×D6111yescharacteristic
1015C23C22⋊C4×D6111yescharacteristic
1016C23C22×C4×D6111yescharacteristic
1017C23C2×D4×D6111yescharacteristic
1018C23C2×D4×D6111yescharacteristic
1019C23#41×D6111yescharacteristic
1020C23C2×#1175822411yescharacteristic
1021C23#1451982211yescharacteristic
1022C23#1451982411yescharacteristic
1023Q8—4881no—
1024Q8—4881no—
1025D4—42no—
1026D4—42no—
1027D4—41no—
1028D4—41no—
1029D4—41no—
1030D4—41no—
1031D4—81no—
1032D4—81no—
1033C2×C4—21no—
1034C2×C4—21no—
1035C2×C4—21no—
1036C2×C4—21no—
1037C2×C4—21no—
1038C2×C4—22no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—84no—
1053C2×C4—611no—
1054C2×C4—611no—
1055C2×C4—611no—
1056C2×C4—611no—
1057C2×C4—611no—
1058C2×C4—611no—
1059C2×C4—611no—
1060C2×C4—611no—
1061C2×C4—1221no—
1062C2×C4—1221no—
1063C2×C4—1221no—
1064C2×C4—1221no—
1065C2×C4—1221no—
1066C2×C4—1221no—
1067C2×C4—1221no—
1068C2×C4—1221no—
1069C2×C4—1221no—
1070C2×C4—1221no—
1071C2×C4—1221no—
1072C2×C4—1221no—
1073C2×C4—1221no—
1074C2×C4—1221no—
1075C2×C4—1221no—
1076C2×C4—1221no—
1077C2×C4—1222no—
1078C2×C4—4881no—
1079C2×C4—4881no—
1080C2×C4—4884no—
1081C2×C4—4881no—
1082C2×C4—4881no—
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—2442no—
1101C2×C4—2442no—
1102C2×C4—2441no—
1103C2×C4—2441no—
1104C2×C4—2441no—
1105C2×C4—2441no—
1106C22—21no—
1107C22—21no—
1108C22—21no—
1109C22—21no—
1110C22—21no—
1111C22—21no—
1112C22—21no—
1113C22—21no—
1114C22—21no—
1115C22—21no—
1116C22—21no—
1117C22—21no—
1118C22—21no—
1119C22—21no—
1120C22—21no—
1121C22—21no—
1122C22—21no—
1123C22—41no—
1124C22—41no—
1125C22—41no—
1126C22—41no—
1127C22—42no—
1128C22—42no—
1129C22—42no—
1130C22—42no—
1131C22—42no—
1132C22—42no—
1133C22—41no—
1134C22—41no—
1135C22—41no—
1136C22—81no—
1137C22—81no—
1138C22—81no—
1139C22—81no—
1140C22—81no—
1141C22—81no—
1142C22—81no—
1143C22—81no—
1144C22#1683973412yes—
1145C22C2×C22⋊C4×D6111yescharacteristic
1146C22C4×#1175822411yescharacteristic
1147C22#1684024111yescharacteristic
1148C22#1684039911yescharacteristic
1149C22#1684040111yescharacteristic
1150C22#1684041011yescharacteristic
1151C22#1684041211yescharacteristic
1152C4—42no—
1153C4—41no—
1154C4—41no—
1155C4—41no—
1156C4—81no—
1157C4—81no—
1158C4—81no—
1159C4—1221no—
1160C4—1221no—
1161C4—1221no—
1162C4—1221no—
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—22no—
1180C2—21no—
1181C2—21no—
1182C2—41no—
1183C2—41no—
1184C2—41no—
1185C2—81no—
1186C2#2144864511yescharacteristic
1187C2C2×#1683973411yescharacteristic
1188C2#2145427711yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC23×C61C23×C4
FrattiniC24C23×D61
FittingC61×#1898C2
socleC22×C61C22×C22⋊C4
prime radicalC2×#120×C61C22
cosocleC24×C61C24
hypercenter#1898D61
hypocenterC61#22477
LCSG ▷ C23×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C25 ◁ #1898

Complements

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

NH ≅ G/Ntype
2. #21448670C2semidirect
3. #21448664C2semidirect
4. #21446802C2semidirect
5. #21446802C2semidirect
6. #21446274C2semidirect
7. #21446274C2semidirect
9. #21445895C2semidirect
10. #21445891C2semidirect
11. #21445805C2semidirect
12. #99×Dic61C2semidirect
13. #21445550C2semidirect
14. C2×#16839528C2semidirect
24. C2×#14519770C4semidirect
25. C2×#14519770C4semidirect
26. C2×#14519764C4semidirect
27. C2×#14519758C4semidirect
28. C2×#14519758C4semidirect
30. C2×#14519754C4semidirect
32. C2×D4×Dic61C4semidirect
34. C2×#14519733C4semidirect
75. C22×Dic122C2×C4semidirect
79. C23×Dic61C2×C4semidirect
134. C2×C4⋊Dic61C2×C4semidirect
135. C2×C4⋊Dic61C2×C4semidirect
140. C2×#11758196C2×C4semidirect
141. C2×#11758196C2×C4semidirect
142. C2×#11758196C2×C4semidirect
143. C2×#11758196C2×C4semidirect
144. C2×#11758196C2×C4semidirect
145. C2×#11758196C2×C4semidirect
161. C2×C22⋊Dic61C2×C4semidirect
162. C2×C22⋊Dic61C2×C4semidirect
163. C2×C22⋊Dic61C2×C4semidirect
182. C2×C4×Dic61C2×C4semidirect
183. C2×C4×Dic61C2×C4semidirect
184. C2×C4×Dic61C2×C4semidirect
669. C61#22477semidirect

Maximal subgroups

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

subgroupindex
C2×#168404432
#214486702
#214486642
#214468022
#214462742
#214462732
#214458952
#214458912
#214458052
#99×Dic612
#214455502
C2×#168395282
C61×#18982
#2247761