Finite Group Databasebeta

← #29685032

Subgroups — #29685032

Order 15616.

1184 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839823C211yesmaximal, characteristic, complemented
2C2×#16839718C211yesmaximal, characteristic, complemented
3#21446760C211yesmaximal, characteristic, complemented
4#21446756C211yesmaximal, characteristic, complemented
5#21446618C211yesmaximal, characteristic, complemented
6#21446614C211yesmaximal, characteristic, complemented
7#21446117C211yesmaximal, characteristic, complemented
8#21446117C211yesmaximal, characteristic, complemented
9#21446112C211yesmaximal, characteristic, complemented
10#21446112C211yesmaximal, characteristic, complemented
11#21445585C211yesmaximal, characteristic, complemented
12#21445585C211yesmaximal, characteristic, complemented
13#21445581C211yesmaximal, characteristic, complemented
14C4×C22⋊#92418C211yesmaximal, characteristic, complemented
15C2×C61×#529C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C23×#92418C2211yescharacteristic
18#16839823—24no—
19C2×C4⋊#92418C2211yescharacteristic
20C2×C4⋊#92418C2211yescharacteristic
21C2×C22⋊#92418C2211yescharacteristic
22C2×C22⋊#92418C2211yescharacteristic
23C2×C22⋊#92418C2211yescharacteristic
24C2×C22⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31#16839718—24no—
32C2×#14519688C2211yescharacteristic
33C2×#14519688C2211yescharacteristic
34C2×#14519688C2211yescharacteristic
35C2×C4×#92418C2211yescharacteristic
36C2×C4×#92418C2211yescharacteristic
37C2×C4×#92418C2211yescharacteristic
38#16839517C2211yescharacteristic
39#16839517C2211yescharacteristic
40#16839517C2211yescharacteristic
41#16839517C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46C61×#529—24no—
47C61×#529—24no—
48C2×#126×C61C411yescharacteristic
49C2×#126×C61C411yescharacteristic
50C2×#125×C61C411yescharacteristic
51C2×#124×C61C411yescharacteristic
52C2×#123×C61C411yescharacteristic
53C2×#123×C61C411yescharacteristic
54C2×C22⋊Q8×C61C411yescharacteristic
55C2×#121×C61C411yescharacteristic
56C2×C4×Q8×C61C2211yescharacteristic
57C2×C4×D4×C61C2211yescharacteristic
58C2×C4×D4×C61C2211yescharacteristic
59C2×C4×D4×C61C2211yescharacteristic
60C2×#117×C61C2211yescharacteristic
61C2×#117×C61C2211yescharacteristic
62C22×C42×C61C2211yescharacteristic
63C2×#11758194—22no—
64C2×#11758194—22no—
65C2×#11758194—22no—
66C22×#92418—22no—
67C22×#92418—22no—
68C22×#92418—22no—
69C22×#92418C2311yescharacteristic
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C4⋊#92418—22no—
78C4⋊#92418—22no—
79C22⋊#92418—22no—
80C22⋊#92418—22no—
81C22⋊#92418—22no—
82C22⋊#92418—22no—
83C22⋊#92418—22no—
84C22⋊#92418—22no—
85C22⋊#92418—22no—
86C22⋊#92418—22no—
87C22⋊#92418—22no—
88C22⋊#92418—22no—
89#14519688—22no—
90#14519688—22no—
91#14519688—22no—
92C4×#92418—22no—
93C4×#92418—22no—
94C4×#92418—22no—
95C22×Q8×C61C2×C411yescharacteristic
96C22×D4×C61C2×C411yescharacteristic
97C22×D4×C61C2×C411yescharacteristic
98C22×D4×C61C2×C411yescharacteristic
99C23×C4×C61C2×C411yescharacteristic
100C23×C4×C61C2×C411yescharacteristic
101C23×C4×C61C2311yescharacteristic
102C23×C4×C61C2311yescharacteristic
103C23×C4×C61C2311yescharacteristic
104#126×C61—24no—
105#126×C61—24no—
106#125×C61—24no—
107#124×C61—24no—
108#123×C61—24no—
109#123×C61—24no—
110C22⋊Q8×C61—24no—
111#121×C61—24no—
112C4×Q8×C61—22no—
113C4×Q8×C61—22no—
114C4×D4×C61—22no—
115C4×D4×C61—22no—
116C4×D4×C61—22no—
117C4×D4×C61—22no—
118C4×D4×C61—22no—
119C4×D4×C61—22no—
120#117×C61—22no—
121#117×C61—22no—
122#117×C61D414yes—
123#117×C61D414yes—
124C2×C4⋊C4×C61C2×C411yescharacteristic
125C2×C4⋊C4×C61C2×C411yescharacteristic
126C2×C4⋊C4×C61C2×C411yescharacteristic
127C2×C4⋊C4×C61C2×C411yescharacteristic
128C2×C4⋊C4×C61C2×C411yescharacteristic
129C2×C4⋊C4×C61C2×C411yescharacteristic
130C2×C4⋊C4×C61C2×C411yescharacteristic
131C2×C4⋊C4×C61C2×C411yescharacteristic
132C2×C4⋊C4×C61C2×C411yescharacteristic
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C22⋊C4×C61C2×C411yescharacteristic
136C2×C22⋊C4×C61C2×C411yescharacteristic
137C2×C22⋊C4×C61C2×C411yescharacteristic
138C2×C22⋊C4×C61C2×C411yescharacteristic
139C2×C22⋊C4×C61C2×C411yescharacteristic
140C2×C22⋊C4×C61C2×C411yescharacteristic
141C2×C22⋊C4×C61C2×C411yescharacteristic
142C2×C22⋊C4×C61C2×C411yescharacteristic
143C2×C22⋊C4×C61C2×C411yescharacteristic
144C2×C42×C61—22no—
145C2×C42×C61—22no—
146C2×C42×C61C2×C411yescharacteristic
147C2×C42×C61C2×C411yescharacteristic
148C2×C42×C61C2311yescharacteristic
149C2×C42×C61C2311yescharacteristic
150C2×C42×C61C2311yescharacteristic
151C2×C42×C61C2311yescharacteristic
152C24×C61C22×C411yescharacteristic
153C24×C61C22×C411yescharacteristic
154C24×C61C22×C411yescharacteristic
155C2×Q8×C61—22no—
156C2×Q8×C61—22no—
157C2×Q8×C61—41no—
158C2×D4×C61—22no—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—22no—
162C2×D4×C61—22no—
163C2×D4×C61—22no—
164C2×D4×C61—41no—
165C2×D4×C61—41no—
166C2×D4×C61—41no—
167C22×C4×C61—21no—
168C22×C4×C61—21no—
169C22×C4×C61—21no—
170C22×C4×C61—21no—
171C22×C4×C61—22no—
172C22×C4×C61—22no—
173C22×C4×C61—22no—
174C22×C4×C61—22no—
175C22×C4×C61—21no—
176C22×C4×C61—21no—
177C22×C4×C61—21no—
178C22×C4×C61—21no—
179C22×C4×C61—21no—
180C22×C4×C61—21no—
181C22×C4×C61—21no—
182C22×C4×C61—21no—
183C22×C4×C61—21no—
184C22×C4×C61—21no—
185C22×C4×C61—21no—
186C22×C4×C61—21no—
187C22×C4×C61—41no—
188C22×C4×C61—41no—
189C22×C4×C61C22×C411yescharacteristic
190C22×C4×C61C22×C411yescharacteristic
191C22×C4×C61C22×C411yescharacteristic
192C22×C4×C61C22×C411yescharacteristic
193C22×C4×C61C22×C411yescharacteristic
194C22×C4×C61C22×C411yescharacteristic
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C22×C411yescharacteristic
198C22×C4×C61C22×C411yescharacteristic
199C22×C4×C61C22×C411yescharacteristic
200C22×C4×C61C2×D412yes—
201C22×C4×C61C2×D412yes—
202C22×C4×C61C2411yescharacteristic
203C4⋊C4×C61—22no—
204C4⋊C4×C61—22no—
205C4⋊C4×C61—22no—
206C4⋊C4×C61—22no—
207C4⋊C4×C61—22no—
208C4⋊C4×C61—22no—
209C4⋊C4×C61—22no—
210C4⋊C4×C61—22no—
211C4⋊C4×C61C22⋊C414yes—
212C4⋊C4×C61C22⋊C414yes—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—22no—
218C22⋊C4×C61—22no—
219C22⋊C4×C61—22no—
220C22⋊C4×C61—22no—
221C22⋊C4×C61C22⋊C414yes—
222C22⋊C4×C61C22⋊C414yes—
223C42×C61—22no—
224C42×C61—22no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—21no—
229C42×C61C2×D412yes—
230C42×C61C2×D412yes—
231C42×C61C2×D412yes—
232C42×C61C2×D412yes—
233#11758194—28no—
234C2×#92418—28no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418—21no—
239C2×#92418—21no—
240C2×#92418—21no—
241C2×#92418—21no—
242C2×#92418—21no—
243C2×#92418—21no—
244C2×#92418—21no—
245C2×#92418—21no—
246C2×#92418—21no—
247C2×#92418—21no—
248C2×#92418—21no—
249C2×#92418—21no—
250C2×#92418—21no—
251C2×#92418—21no—
252C2×#92418—21no—
253C2×#92418—21no—
254C2×#92418—21no—
255C2×#92418#4112yes—
256C2×#92418#4112yes—
257C2×#92418#4112yes—
258C2×#92418#4112yes—
259C23×C61—21no—
260C23×C61—21no—
261C23×C61—21no—
262C23×C61—21no—
263C23×C61—21no—
264C23×C61—21no—
265C23×C61—21no—
266C23×C61—21no—
267C23×C61—21no—
268C23×C61—21no—
269C23×C61—21no—
270C23×C61—21no—
271C23×C61—21no—
272C23×C61—21no—
273C23×C61—21no—
274C23×C61—21no—
275C23×C61—21no—
276C23×C61—21no—
277C23×C61—21no—
278C23×C61C2×C22⋊C412yes—
279C23×C61#13112yes—
280C23×C61C23×C411yescharacteristic
281Q8×C61—44no—
282D4×C61—44no—
283D4×C61—44no—
284D4×C61—44no—
285C2×C4×C61—21no—
286C2×C4×C61—21no—
287C2×C4×C61—21no—
288C2×C4×C61—21no—
289C2×C4×C61—21no—
290C2×C4×C61—21no—
291C2×C4×C61—21no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—22no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—21no—
302C2×C4×C61—21no—
303C2×C4×C61—21no—
304C2×C4×C61—21no—
305C2×C4×C61—21no—
306C2×C4×C61—21no—
307C2×C4×C61—21no—
308C2×C4×C61—21no—
309C2×C4×C61—21no—
310C2×C4×C61—21no—
311C2×C4×C61—21no—
312C2×C4×C61—21no—
313C2×C4×C61—21no—
314C2×C4×C61—21no—
315C2×C4×C61—21no—
316C2×C4×C61—44no—
317C2×C4×C61—44no—
318C2×C4×C61—41no—
319C2×C4×C61—41no—
320C2×C4×C61—41no—
321C2×C4×C61—41no—
322C2×C4×C61—41no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61C2×C22⋊C412yes—
327C2×C4×C61C2×C22⋊C412yes—
328C2×C4×C61C2×C22⋊C412yes—
329C2×C4×C61C2×C22⋊C412yes—
330C2×C4×C61C2×C22⋊C412yes—
331C2×C4×C61#13112yes—
332C2×C4×C61C22×D411yescharacteristic
333C2×C4×C61C22×D411yescharacteristic
334C2×C4×C61C2×#4111yescharacteristic
335C2×C4×C61C2×#4111yescharacteristic
336C2×C4×C61C2×#4111yescharacteristic
337C2×C4×C61C2×#4111yescharacteristic
338#92418—22no—
339#92418—22no—
340#92418—22no—
341#92418—22no—
342#92418—41no—
343#92418—41no—
344#92418—41no—
345#92418—41no—
346#21381—611nomaximal, Sylow
347C22×C61—22no—
348C22×C61—22no—
349C22×C61—22no—
350C22×C61—22no—
351C22×C61—22no—
352C22×C61—22no—
353C22×C61—41no—
354C22×C61—41no—
355C22×C61—41no—
356C22×C61—41no—
357C22×C61—41no—
358C22×C61—41no—
359C22×C61—41no—
360C22×C61—41no—
361C22×C61—41no—
362C22×C61—41no—
363C22×C61—41no—
364C22×C61—41no—
365C22×C61—41no—
366C22×C61—41no—
367C22×C61—41no—
368C22×C61C22×C22⋊C411yescharacteristic
369C22×C61C4×#4111yescharacteristic
370C22×C61C4×#4111yescharacteristic
371C22×C61C2×#13111yescharacteristic
372C22×C61C2×#13111yescharacteristic
373C22×C61#56811yescharacteristic
374C22×C61#56811yescharacteristic
375C4×C61—22no—
376C4×C61—22no—
377C4×C61—22no—
378C4×C61—22no—
379C4×C61—22no—
380C4×C61—22no—
381C4×C61—41no—
382C4×C61—41no—
383C4×C61—41no—
384C4×C61—41no—
385C4×C61—41no—
386C4×C61#52511yescharacteristic
387C4×C61#52511yescharacteristic
388C4×C61#53211yescharacteristic
389C4×C61#53211yescharacteristic
390C2×#529D6111yescharacteristic
391C2×#433—611no—
392C2×#405—611no—
393#1985—611no—
394#1984—611no—
395#1955—611no—
396#1954—611no—
397#1870—611no—
398#1870—611no—
399#1869—611no—
400#1869—611no—
401#1750—611no—
402#1750—611no—
403#1749—611no—
404C4×C22⋊C8—611no—
405C2×C61—42no—
406C2×C61—42no—
407C2×C61—81no—
408C2×C61#229711yescharacteristic
409C2×C61#288011yescharacteristic
410C2×C61#288011yescharacteristic
411C2×C61#296611yescharacteristic
412C2×C61#296711yescharacteristic
413C2×C61#296811yescharacteristic
414C2×C61#296911yescharacteristic
415C22×M16—611no—
416C23×C8—611no—
417#529—24no—
418#529—24no—
419C2×#126Dic6111yescharacteristic
420C2×#126Dic6111yescharacteristic
421C2×#125Dic6111yescharacteristic
422C2×#124Dic6111yescharacteristic
423C2×#123Dic6111yescharacteristic
424C2×#123Dic6111yescharacteristic
425C2×C22⋊Q8Dic6111yescharacteristic
426C2×#121Dic6111yescharacteristic
427C2×C4×Q8C2×D6111yescharacteristic
428C2×C4×D4C2×D6111yescharacteristic
429C2×C4×D4C2×D6111yescharacteristic
430C2×C4×D4C2×D6111yescharacteristic
431C2×#117C2×D6111yescharacteristic
432C2×#117C2×D6111yescharacteristic
433C22×C42C2×D6111yescharacteristic
434#433—1224no—
435C2×C4⋊C8—611no—
436C2×C4⋊C8—611no—
437C2×C22⋊C8—611no—
438C2×C22⋊C8—611no—
439C2×C22⋊C8—611no—
440C2×C22⋊C8—611no—
441C2×C22⋊C8—611no—
442C2×C22⋊C8—611no—
443C2×C22⋊C8—611no—
444C2×C22⋊C8—611no—
445C2×C22⋊C8—611no—
446C2×C22⋊C8—611no—
447#405—1224no—
448C2×#97—611no—
449C2×#97—611no—
450C2×#97—611no—
451C2×C4×C8—611no—
452C2×C4×C8—611no—
453C2×C4×C8—611no—
454#336—611no—
455#336—611no—
456#336—611no—
457#336—611no—
458#336—611no—
459#336—611no—
460#336—611no—
461#336—611no—
462C61#2138111yescharacteristic, complemented, Sylow
463C22×Q8C2×Dic6111yescharacteristic
464C22×D4C2×Dic6111yescharacteristic
465C22×D4C2×Dic6111yescharacteristic
466C22×D4C2×Dic6111yescharacteristic
467C23×C4C2×Dic6111yescharacteristic
468C23×C4C2×Dic6111yescharacteristic
469C23×C4C22×D6111yescharacteristic
470C23×C4C22×D6111yescharacteristic
471C23×C4C22×D6111yescharacteristic
472C2×M16—1222no—
473C2×M16—1222no—
474C2×M16—1222no—
475C22×C8—611no—
476C22×C8—611no—
477C22×C8—611no—
478C22×C8—611no—
479C22×C8—611no—
480C22×C8—611no—
481C22×C8—611no—
482C22×C8—611no—
483C22×C8—1222no—
484C22×C8—1222no—
485C22×C8—1222no—
486#126—24no—
487#126—24no—
488#125—24no—
489#124—24no—
490#123—24no—
491#123—24no—
492C22⋊Q8—24no—
493#121—24no—
494C4×Q8—22no—
495C4×Q8—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—22no—
502#117—22no—
503#117—22no—
504#117C22⋊D6114yes—
505#117C22⋊D6114yes—
506C2×C4⋊C4C2×Dic6111yescharacteristic
507C2×C4⋊C4C2×Dic6111yescharacteristic
508C2×C4⋊C4C2×Dic6111yescharacteristic
509C2×C4⋊C4C2×Dic6111yescharacteristic
510C2×C4⋊C4C2×Dic6111yescharacteristic
511C2×C4⋊C4C2×Dic6111yescharacteristic
512C2×C4⋊C4C2×Dic6111yescharacteristic
513C2×C4⋊C4C2×Dic6111yescharacteristic
514C2×C4⋊C4C2×Dic6111yescharacteristic
515C2×C4⋊C4C2×Dic6111yescharacteristic
516C2×C22⋊C4C2×Dic6111yescharacteristic
517C2×C22⋊C4C2×Dic6111yescharacteristic
518C2×C22⋊C4C2×Dic6111yescharacteristic
519C2×C22⋊C4C2×Dic6111yescharacteristic
520C2×C22⋊C4C2×Dic6111yescharacteristic
521C2×C22⋊C4C2×Dic6111yescharacteristic
522C2×C22⋊C4C2×Dic6111yescharacteristic
523C2×C22⋊C4C2×Dic6111yescharacteristic
524C2×C22⋊C4C2×Dic6111yescharacteristic
525C2×C22⋊C4C2×Dic6111yescharacteristic
526C2×C42—22no—
527C2×C42—22no—
528C2×C42C2×Dic6111yescharacteristic
529C2×C42C2×Dic6111yescharacteristic
530C2×C42C22×D6111yescharacteristic
531C2×C42C22×D6111yescharacteristic
532C2×C42C22×D6111yescharacteristic
533C2×C42C22×D6111yescharacteristic
534C4⋊C8—1222no—
535C4⋊C8—1222no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542C22⋊C8—1222no—
543C22⋊C8—1222no—
544C22⋊C8—1222no—
545C22⋊C8—1222no—
546#97—1222no—
547#97—1222no—
548#97—1222no—
549C4×C8—1222no—
550C4×C8—1222no—
551C4×C8—1222no—
552C24C22×Dic6111yescharacteristic
553C24C22×Dic6111yescharacteristic
554C24C22×Dic6111yescharacteristic
555C2×Q8—22no—
556C2×Q8—22no—
557C2×Q8—41no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—41no—
565C2×D4—41no—
566C2×D4—41no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—22no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—22no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4C22×Dic6111yescharacteristic
590C22×C4C22×Dic6111yescharacteristic
591C22×C4C22×Dic6111yescharacteristic
592C22×C4C22×Dic6111yescharacteristic
593C22×C4C22×Dic6111yescharacteristic
594C22×C4C22×Dic6111yescharacteristic
595C22×C4C22×Dic6111yescharacteristic
596C22×C4C22×Dic6111yescharacteristic
597C22×C4C22×Dic6111yescharacteristic
598C22×C4C22×Dic6111yescharacteristic
599C22×C4C22×Dic6111yescharacteristic
600C22×C4C2×C22⋊D6112yes—
601C22×C4C2×C22⋊D6112yes—
602C22×C4C23×D6111yescharacteristic
603M16—1228no—
604C2×C8—612no—
605C2×C8—612no—
606C2×C8—612no—
607C2×C8—612no—
608C2×C8—1228no—
609C2×C8—1221no—
610C2×C8—1221no—
611C2×C8—1221no—
612C2×C8—1221no—
613C2×C8—1221no—
614C2×C8—1221no—
615C2×C8—1221no—
616C2×C8—1221no—
617C2×C8—1221no—
618C2×C8—1221no—
619C2×C8—1221no—
620C2×C8—1221no—
621C2×C8—1221no—
622C2×C8—1221no—
623C2×C8—1221no—
624C2×C8—1221no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C4⋊C4—22no—
630C4⋊C4—22no—
631C4⋊C4—22no—
632C4⋊C4—22no—
633C4⋊C4—22no—
634C4⋊C4—22no—
635C4⋊C4—22no—
636C4⋊C4—22no—
637C4⋊C4C22⋊Dic6114yes—
638C4⋊C4C22⋊Dic6114yes—
639C22⋊C4—22no—
640C22⋊C4—22no—
641C22⋊C4—22no—
642C22⋊C4—22no—
643C22⋊C4—22no—
644C22⋊C4—22no—
645C22⋊C4—22no—
646C22⋊C4—22no—
647C22⋊C4C22⋊Dic6114yes—
648C22⋊C4C22⋊Dic6114yes—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42—22no—
654C42—22no—
655C42C2×C22⋊D6112yes—
656C42C2×C22⋊D6112yes—
657C42C2×C22⋊D6112yes—
658C42C2×C22⋊D6112yes—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—21no—
666C23—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23C2×C22⋊Dic6112yes—
679C23#1451978412yes—
680C23C23×Dic6111yescharacteristic
681Q8—44no—
682D4—44no—
683D4—44no—
684D4—44no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—22no—
698C2×C4—22no—
699C2×C4—22no—
700C2×C4—22no—
701C2×C4—21no—
702C2×C4—21no—
703C2×C4—21no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—21no—
715C2×C4—21no—
716C2×C4—44no—
717C2×C4—44no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4C2×C22⋊Dic6112yes—
727C2×C4C2×C22⋊Dic6112yes—
728C2×C4C2×C22⋊Dic6112yes—
729C2×C4C2×C22⋊Dic6112yes—
730C2×C4C2×C22⋊Dic6112yes—
731C2×C4#1451978412yes—
732C2×C4C22×C22⋊D6111yescharacteristic
733C2×C4C22×C22⋊D6111yescharacteristic
734C2×C4#41×D6111yescharacteristic
735C2×C4#41×D6111yescharacteristic
736C2×C4#41×D6111yescharacteristic
737C2×C4#41×D6111yescharacteristic
738C8—1222no—
739C8—1222no—
740C8—1222no—
741C8—1222no—
742C8—2441no—
743C8—2441no—
744C8—2441no—
745C8—2441no—
746C22—22no—
747C22—22no—
748C22—22no—
749C22—22no—
750C22—22no—
751C22—22no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—41no—
767C22C22×C22⋊Dic6111yescharacteristic
768C22#41×Dic6111yescharacteristic
769C22#41×Dic6111yescharacteristic
770C22C2×#1451978411yescharacteristic
771C22C2×#1451978411yescharacteristic
772C22#1684052911yescharacteristic
773C22#1684052911yescharacteristic
774C4—22no—
775C4—22no—
776C4—22no—
777C4—22no—
778C4—22no—
779C4—22no—
780C4—41no—
781C4—41no—
782C4—41no—
783C4—41no—
784C4—41no—
785C4#1684026911yescharacteristic
786C4#1684026911yescharacteristic
787C4#1684030811yescharacteristic
788C4#1684030811yescharacteristic
789C2—42no—
790C2—42no—
791C2—81no—
792C2#2144831011yescharacteristic
793C2#2145426811yescharacteristic
794C2#2145426811yescharacteristic
795C2#2145479511yescharacteristic
796C2#2145480611yescharacteristic
797C2#2145481511yescharacteristic
798C2#2145482411yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC2×C61×#529C2
prime radicalC2×#121×C61C4
cosocleC22×C4×C61C24
hypercenterC2×#529D61
hypocenterC61#21381
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#16839823C2semidirect
2. C2×#16839718C2semidirect
3. #21446760C2semidirect
4. #21446756C2semidirect
5. #21446618C2semidirect
6. #21446614C2semidirect
7. #21446117C2semidirect
8. #21446117C2semidirect
9. #21446112C2semidirect
10. #21446112C2semidirect
11. #21445585C2semidirect
12. #21445585C2semidirect
13. #21445581C2semidirect
14. C4×C22⋊#92418C2semidirect
462. C61#21381semidirect

Maximal subgroups

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

subgroupindex
C2×#168398232
C2×#168397182
#214467602
#214467562
#214466182
#214466142
#214461172
#214461122
#214455852
#214455812
C4×C22⋊#924182
C2×C61×#5292
#2138161