Finite Group Databasebeta

← #29691135

Subgroups — #29691135

Order 15616.

1028 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839840C211yesmaximal, characteristic, complemented
2C2×#16839729C211yesmaximal, characteristic, complemented
3#21446618C211yesmaximal, characteristic, complemented
4#21446614C211yesmaximal, characteristic, complemented
5#21446434C211yesmaximal, characteristic, complemented
6#21446427C211yesmaximal, characteristic, complemented
7#21446427C211yesmaximal, characteristic, complemented
8#21446427C211yesmaximal, characteristic, complemented
9#21446117C211yesmaximal, characteristic, complemented
10#21446117C211yesmaximal, characteristic, complemented
11#21446112C211yesmaximal, characteristic, complemented
12#21445999C211yesmaximal, characteristic, complemented
13#21445731C211yesmaximal, characteristic, complemented
14#21445603C211yesmaximal, characteristic, complemented
15C61×#2388C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C23×#92418C2211yescharacteristic
19#16839840—24no—
20C2×C4⋊#92418C2211yescharacteristic
21C2×C4⋊#92418C2211yescharacteristic
22C2×C4⋊#92418C2211yescharacteristic
23#16839729—24no—
24C2×C22⋊#92418C2211yescharacteristic
25C2×C22⋊#92418C2211yescharacteristic
26C2×C22⋊#92418C2211yescharacteristic
27C2×C22⋊#92418C2211yescharacteristic
28C2×C22⋊#92418C2211yescharacteristic
29C2×C22⋊#92418C2211yescharacteristic
30C2×C22⋊#92418C2211yescharacteristic
31C2×C22⋊#92418C2211yescharacteristic
32C2×C22⋊#92418C2211yescharacteristic
33C2×C22⋊#92418C2211yescharacteristic
34C2×C22⋊#92418C2211yescharacteristic
35C2×C22⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×#14519688C2211yescharacteristic
38C2×C4×#92418C2211yescharacteristic
39C2×C4×#92418C2211yescharacteristic
40#16839517C2211yescharacteristic
41#16839517C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46C22×#41×C61C2211yescharacteristic
47C2×C4×D4×C61C2211yescharacteristic
48C2×C4×D4×C61C2211yescharacteristic
49C2×C4×D4×C61C2211yescharacteristic
50C61×#395C411yescharacteristic
51C61×#394C411yescharacteristic
52C61×#394C411yescharacteristic
53C61×#394C411yescharacteristic
54C61×#393C411yescharacteristic
55C61×#392C411yescharacteristic
56C61×#392C411yescharacteristic
57C61×#392C411yescharacteristic
58C4×C22⋊C4×C61C2211yescharacteristic
59C4×C22⋊C4×C61C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C2×#11758194—22no—
62C2×#11758194—41no—
63C2×#11758194—41no—
64C2×#11758194—41no—
65C2×#11758194—41no—
66C2×#11758194D414yescomplemented
67C22×#92418—22no—
68C22×#92418—41no—
69C22×#92418—41no—
70C22×#92418C2311yescharacteristic
71C22×#92418C2311yescharacteristic
72C22×#92418C2311yescharacteristic
73C22×#92418C2311yescharacteristic
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C4⋊#92418—22no—
79C4⋊#92418—41no—
80C4⋊#92418—41no—
81C22⋊#92418—22no—
82C22⋊#92418—22no—
83C22⋊#92418—22no—
84C22⋊#92418—22no—
85C22⋊#92418—22no—
86C22⋊#92418—22no—
87C22⋊#92418—22no—
88C22⋊#92418—41no—
89C22⋊#92418—41no—
90C22⋊#92418—41no—
91C22⋊#92418—41no—
92C22⋊#92418—41no—
93C22⋊#92418—41no—
94#14519688—41no—
95C4×#92418—22no—
96C4×#92418—41no—
97C2×#41×C61—22no—
98C2×#41×C61—22no—
99C2×#41×C61—41no—
100C2×#41×C61—41no—
101C2×#41×C61—41no—
102C2×#41×C61—41no—
103C22×Q8×C61C2×C411yescharacteristic
104C22×D4×C61C2×C411yescharacteristic
105C22×D4×C61C2×C411yescharacteristic
106C22×D4×C61C2×C411yescharacteristic
107C22×D4×C61C2×C411yescharacteristic
108C22×D4×C61C2×C411yescharacteristic
109C22×D4×C61C2×C411yescharacteristic
110C23×C4×C61C2311yescharacteristic
111C23×C4×C61C2311yescharacteristic
112C23×C4×C61C2311yescharacteristic
113C23×C4×C61C2311yescharacteristic
114C4×D4×C61—22no—
115C4×D4×C61—22no—
116C4×D4×C61—41no—
117C4×D4×C61—41no—
118C4×D4×C61—41no—
119C4×D4×C61—41no—
120C2×C4⋊C4×C61C2×C411yescharacteristic
121C2×C4⋊C4×C61C2×C411yescharacteristic
122C2×C4⋊C4×C61C2×C411yescharacteristic
123C2×C22⋊C4×C61C2×C411yescharacteristic
124C2×C22⋊C4×C61C2×C411yescharacteristic
125C2×C22⋊C4×C61C2×C411yescharacteristic
126C2×C22⋊C4×C61C2×C411yescharacteristic
127C2×C22⋊C4×C61C2×C411yescharacteristic
128C2×C22⋊C4×C61C2×C411yescharacteristic
129C2×C22⋊C4×C61C2×C411yescharacteristic
130C2×C22⋊C4×C61C2×C411yescharacteristic
131C2×C22⋊C4×C61C2×C411yescharacteristic
132C2×C22⋊C4×C61C2×C411yescharacteristic
133C2×C22⋊C4×C61C2×C411yescharacteristic
134C2×C22⋊C4×C61C2×C411yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138#95×C61C2×C411yescharacteristic
139#95×C61C2×C411yescharacteristic
140#95×C61C2×C411yescharacteristic
141#95×C61C2×C411yescharacteristic
142#95×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144C24×C61C22×C411yescharacteristic
145C24×C61C22×C411yescharacteristic
146C24×C61C22×C411yescharacteristic
147C24×C61C22×C411yescharacteristic
148#41×C61—44no—
149#41×C61—44no—
150#41×C61—44no—
151#41×C61—44no—
152C2×Q8×C61—22no—
153C2×Q8×C61—41no—
154C2×Q8×C61—41no—
155C2×D4×C61—22no—
156C2×D4×C61—22no—
157C2×D4×C61—22no—
158C2×D4×C61—22no—
159C2×D4×C61—22no—
160C2×D4×C61—22no—
161C2×D4×C61—41no—
162C2×D4×C61—41no—
163C2×D4×C61—41no—
164C2×D4×C61—41no—
165C2×D4×C61—41no—
166C2×D4×C61—41no—
167C2×D4×C61—41no—
168C2×D4×C61—41no—
169C2×D4×C61—41no—
170C2×D4×C61—41no—
171C2×D4×C61—41no—
172C2×D4×C61—41no—
173C22×C4×C61—21no—
174C22×C4×C61—21no—
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—21no—
188C22×C4×C61—21no—
189C22×C4×C61—21no—
190C22×C4×C61—21no—
191C22×C4×C61—21no—
192C22×C4×C61—21no—
193C22×C4×C61—21no—
194C22×C4×C61—21no—
195C22×C4×C61C22×C411yescharacteristic
196C22×C4×C61C22×C411yescharacteristic
197C22×C4×C61C22×C411yescharacteristic
198C22×C4×C61C22×C411yescharacteristic
199C22×C4×C61C22×C411yescharacteristic
200C22×C4×C61C22×C411yescharacteristic
201C22×C4×C61C22×C411yescharacteristic
202C22×C4×C61C22×C411yescharacteristic
203C22×C4×C61C22×C411yescharacteristic
204C22×C4×C61C22×C411yescharacteristic
205C22×C4×C61C2×D412yes—
206C22×C4×C61#4112yes—
207C22×C4×C61C2411yescharacteristic
208C4⋊C4×C61—22no—
209C4⋊C4×C61—41no—
210C4⋊C4×C61—41no—
211C22⋊C4×C61—22no—
212C22⋊C4×C61—22no—
213C22⋊C4×C61—22no—
214C22⋊C4×C61—22no—
215C22⋊C4×C61—22no—
216C22⋊C4×C61—22no—
217C22⋊C4×C61—41no—
218C22⋊C4×C61—41no—
219C22⋊C4×C61—41no—
220C22⋊C4×C61—41no—
221C22⋊C4×C61—41no—
222C22⋊C4×C61—41no—
223C42×C61—21no—
224C42×C61—21no—
225C42×C61—21no—
226C42×C61—21no—
227C42×C61—21no—
228C42×C61—21no—
229#11758194—44no—
230#11758194—44no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
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—44no—
254C2×#92418C2×D412yes—
255C2×#92418C2×D412yes—
256C23×C61—21no—
257C23×C61—21no—
258C23×C61—21no—
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×C61—21no—
279C23×C61—21no—
280C23×C61—21no—
281C23×C61—21no—
282C23×C61—21no—
283C23×C61C4×D412yes—
284C23×C61C23×C411yescharacteristic
285Q8×C61—44no—
286D4×C61—44no—
287D4×C61—44no—
288D4×C61—44no—
289D4×C61—44no—
290D4×C61—44no—
291D4×C61—44no—
292C2×C4×C61—21no—
293C2×C4×C61—21no—
294C2×C4×C61—21no—
295C2×C4×C61—21no—
296C2×C4×C61—21no—
297C2×C4×C61—21no—
298C2×C4×C61—22no—
299C2×C4×C61—22no—
300C2×C4×C61—22no—
301C2×C4×C61—22no—
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—21no—
317C2×C4×C61—21no—
318C2×C4×C61—21no—
319C2×C4×C61—21no—
320C2×C4×C61—21no—
321C2×C4×C61—21no—
322C2×C4×C61—21no—
323C2×C4×C61—41no—
324C2×C4×C61—41no—
325C2×C4×C61—41no—
326C2×C4×C61—41no—
327C2×C4×C61—41no—
328C2×C4×C61—41no—
329C2×C4×C61—41no—
330C2×C4×C61—41no—
331C2×C4×C61—41no—
332C2×C4×C61—41no—
333C2×C4×C61—41no—
334C2×C4×C61—41no—
335C2×C4×C61C4×D412yes—
336C2×C4×C61#13112yes—
337C2×C4×C61#13112yes—
338C2×C4×C61C22×D411yescharacteristic
339C2×C4×C61C2×#4111yescharacteristic
340C2×C4×C61H(5,𝔽2)11yescharacteristic
341C2×C4×C61H(5,𝔽2)11yescharacteristic
342C2×C4×C61H(5,𝔽2)11yescharacteristic
343C2×C4×C61H(5,𝔽2)11yescharacteristic
344#92418—22no—
345#92418—22no—
346#92418—41no—
347#92418—41no—
348#92418—41no—
349#92418—41no—
350#92418—41no—
351#92418—41no—
352#22039—611nomaximal, Sylow
353C22×C61—22no—
354C22×C61—22no—
355C22×C61—22no—
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×C61—41no—
369C22×C61—41no—
370C22×C61—41no—
371C22×C61—41no—
372C22×C61—41no—
373C22×C61—41no—
374C22×C61—41no—
375C22×C61—41no—
376C22×C61—41no—
377C22×C61—41no—
378C22×C61—41no—
379C22×C61—41no—
380C22×C61—41no—
381C22×C61C2×C4×D411yescharacteristic
382C22×C61#51811yescharacteristic
383C22×C61#51811yescharacteristic
384C22×C61C2×#13111yescharacteristic
385C22×C61C2×#13111yescharacteristic
386C22×C61#56811yescharacteristic
387C22×C61#56811yescharacteristic
388C4×C61—22no—
389C4×C61—22no—
390C4×C61—22no—
391C4×C61—41no—
392C4×C61—41no—
393C4×C61—41no—
394C4×C61—41no—
395C4×C61—41no—
396C4×C61—41no—
397C4×C61—41no—
398C4×C61#53411yescharacteristic
399C4×C61#53511yescharacteristic
400C4×C61#53811yescharacteristic
401C4×C61#53811yescharacteristic
402C2×#436—611no—
403C2×#408—611no—
404#2388D6111yescharacteristic
405#1955—611no—
406#1954—611no—
407#1924—611no—
408#1923—611no—
409#1923—611no—
410#1923—611no—
411#1870—611no—
412#1870—611no—
413#1869—611no—
414#1850—611no—
415#1780—611no—
416#1753—611no—
417C2×C61—42no—
418C2×C61—81no—
419C2×C61—81no—
420C2×C61—81no—
421C2×C61#232111yescharacteristic
422C2×C61#293311yescharacteristic
423C2×C61#293511yescharacteristic
424C2×C61#297611yescharacteristic
425C2×C61#297811yescharacteristic
426C2×C61#297911yescharacteristic
427C2×C61#298111yescharacteristic
428C22×#41C2×D6111yescharacteristic
429C22×M16—611no—
430C22×M16—611no—
431C23×C8—611no—
432C2×C4×D4C2×D6111yescharacteristic
433C2×C4×D4C2×D6111yescharacteristic
434C2×C4×D4C2×D6111yescharacteristic
435#436—1224no—
436C2×C4⋊C8—611no—
437C2×C4⋊C8—611no—
438C2×C4⋊C8—611no—
439#408—1224no—
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—
447C2×C22⋊C8—611no—
448C2×C22⋊C8—611no—
449C2×C22⋊C8—611no—
450C2×C22⋊C8—611no—
451C2×C22⋊C8—611no—
452C2×C22⋊C8—611no—
453C2×#97—611no—
454C2×C4×C8—611no—
455C2×C4×C8—611no—
456#395Dic6111yescharacteristic
457#394Dic6111yescharacteristic
458#394Dic6111yescharacteristic
459#394Dic6111yescharacteristic
460#393Dic6111yescharacteristic
461#392Dic6111yescharacteristic
462#392Dic6111yescharacteristic
463#392Dic6111yescharacteristic
464C4×C22⋊C4C2×D6111yescharacteristic
465C4×C22⋊C4C2×D6111yescharacteristic
466C4×C22⋊C4C2×D6111yescharacteristic
467#336—611no—
468#336—611no—
469#336—611no—
470#336—611no—
471#336—611no—
472#336—611no—
473C61#2203911yescharacteristic, complemented, Sylow
474C2×#41—22no—
475C2×#41—22no—
476C2×#41—41no—
477C2×#41—41no—
478C2×#41—41no—
479C2×#41—41no—
480C22×Q8C2×Dic6111yescharacteristic
481C22×D4C2×Dic6111yescharacteristic
482C22×D4C2×Dic6111yescharacteristic
483C22×D4C2×Dic6111yescharacteristic
484C22×D4C2×Dic6111yescharacteristic
485C22×D4C2×Dic6111yescharacteristic
486C22×D4C2×Dic6111yescharacteristic
487C23×C4C22×D6111yescharacteristic
488C23×C4C22×D6111yescharacteristic
489C23×C4C22×D6111yescharacteristic
490C23×C4C22×D6111yescharacteristic
491C2×M16—614no—
492C2×M16—1222no—
493C2×M16—2441no—
494C2×M16—2441no—
495C2×M16—2441no—
496C2×M16—2441no—
497C22×C8—611no—
498C22×C8—611no—
499C22×C8—611no—
500C22×C8—611no—
501C22×C8—611no—
502C22×C8—611no—
503C22×C8—611no—
504C22×C8—611no—
505C22×C8—1222no—
506C22×C8—2441no—
507C22×C8—2441no—
508C4×D4—22no—
509C4×D4—22no—
510C4×D4—41no—
511C4×D4—41no—
512C4×D4—41no—
513C4×D4—41no—
514C2×C4⋊C4C2×Dic6111yescharacteristic
515C2×C4⋊C4C2×Dic6111yescharacteristic
516C2×C4⋊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×C22⋊C4C2×Dic6111yescharacteristic
527C2×C22⋊C4C2×Dic6111yescharacteristic
528C2×C22⋊C4C2×Dic6111yescharacteristic
529C2×C42C22×D6111yescharacteristic
530C2×C42C22×D6111yescharacteristic
531C2×C42C22×D6111yescharacteristic
532C4⋊C8—1222no—
533C4⋊C8—2441no—
534C4⋊C8—2441no—
535C22⋊C8—1222no—
536C22⋊C8—1222no—
537C22⋊C8—1222no—
538C22⋊C8—1222no—
539C22⋊C8—1222no—
540C22⋊C8—1222no—
541C22⋊C8—1222no—
542C22⋊C8—2441no—
543C22⋊C8—2441no—
544C22⋊C8—2441no—
545C22⋊C8—2441no—
546C22⋊C8—2441no—
547C22⋊C8—2441no—
548#97—2441no—
549C4×C8—1222no—
550C4×C8—2441no—
551#95C2×Dic6111yescharacteristic
552#95C2×Dic6111yescharacteristic
553#95C2×Dic6111yescharacteristic
554#95C2×Dic6111yescharacteristic
555#95C2×Dic6111yescharacteristic
556#95C2×Dic6111yescharacteristic
557C24C22×Dic6111yescharacteristic
558C24C22×Dic6111yescharacteristic
559C24C22×Dic6111yescharacteristic
560C24C22×Dic6111yescharacteristic
561#41—44no—
562#41—44no—
563#41—44no—
564#41—44no—
565C2×Q8—22no—
566C2×Q8—41no—
567C2×Q8—41no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—22no—
572C2×D4—22no—
573C2×D4—22no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—41no—
582C2×D4—41no—
583C2×D4—41no—
584C2×D4—41no—
585C2×D4—41no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—21no—
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4D4×D6112yes—
609C22×C4#1175822412yes—
610C22×C4C22×Dic6111yescharacteristic
611C22×C4C22×Dic6111yescharacteristic
612C22×C4C22×Dic6111yescharacteristic
613C22×C4C22×Dic6111yescharacteristic
614C22×C4C22×Dic6111yescharacteristic
615C22×C4C22×Dic6111yescharacteristic
616C22×C4C22×Dic6111yescharacteristic
617C22×C4C22×Dic6111yescharacteristic
618C22×C4C22×Dic6111yescharacteristic
619C22×C4C22×Dic6111yescharacteristic
620C22×C4C23×D6111yescharacteristic
621M16—2444no—
622M16—2444no—
623C2×C8—612no—
624C2×C8—612no—
625C2×C8—1221no—
626C2×C8—1221no—
627C2×C8—1221no—
628C2×C8—1221no—
629C2×C8—1221no—
630C2×C8—1221no—
631C2×C8—1221no—
632C2×C8—1221no—
633C2×C8—1221no—
634C2×C8—1221no—
635C2×C8—1221no—
636C2×C8—1221no—
637C2×C8—1221no—
638C2×C8—1221no—
639C2×C8—1221no—
640C2×C8—1221no—
641C2×C8—1221no—
642C2×C8—1221no—
643C2×C8—1221no—
644C2×C8—1221no—
645C2×C8—1221no—
646C2×C8—1221no—
647C2×C8—2444no—
648C4⋊C4—22no—
649C4⋊C4—41no—
650C4⋊C4—41no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—41no—
658C22⋊C4—41no—
659C22⋊C4—41no—
660C22⋊C4—41no—
661C22⋊C4—41no—
662C22⋊C4—41no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C42—21no—
668C42—21no—
669C23—21no—
670C23—21no—
671C23—21no—
672C23—21no—
673C23—21no—
674C23—21no—
675C23—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—21no—
682C23—21no—
683C23—21no—
684C23—21no—
685C23—21no—
686C23—21no—
687C23—21no—
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23D4×Dic6112yes—
697C23C23×Dic6111yescharacteristic
698Q8—44no—
699D4—44no—
700D4—44no—
701D4—44no—
702D4—44no—
703D4—44no—
704D4—44no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—21no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—22no—
714C2×C4—22no—
715C2×C4—21no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—21no—
724C2×C4—21no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—21no—
731C2×C4—21no—
732C2×C4—21no—
733C2×C4—21no—
734C2×C4—21no—
735C2×C4—21no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—41no—
739C2×C4—41no—
740C2×C4—41no—
741C2×C4—41no—
742C2×C4—41no—
743C2×C4—41no—
744C2×C4—41no—
745C2×C4—41no—
746C2×C4—41no—
747C2×C4—41no—
748C2×C4D4×Dic6112yes—
749C2×C4#1451978412yes—
750C2×C4#1451978412yes—
751C2×C4C2×D4×D6111yescharacteristic
752C2×C4C2×#1175822411yescharacteristic
753C2×C4#1451982211yescharacteristic
754C2×C4#1451982211yescharacteristic
755C2×C4#1451982211yescharacteristic
756C2×C4#1451982211yescharacteristic
757C8—1222no—
758C8—1222no—
759C8—2441no—
760C8—2441no—
761C8—2441no—
762C8—2441no—
763C8—2441no—
764C8—2441no—
765C22—22no—
766C22—22no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—41no—
774C22—41no—
775C22—41no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—41no—
784C22—41no—
785C22—41no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22C2×D4×Dic6111yescharacteristic
794C22#1684023711yescharacteristic
795C22#1684023711yescharacteristic
796C22C2×#1451978411yescharacteristic
797C22C2×#1451978411yescharacteristic
798C22#1684052911yescharacteristic
799C22#1684052911yescharacteristic
800C4—22no—
801C4—22no—
802C4—22no—
803C4—41no—
804C4—41no—
805C4—41no—
806C4—41no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4#1684032211yescharacteristic
811C4#1684032711yescharacteristic
812C4#1684034711yescharacteristic
813C4#1684034711yescharacteristic
814C2—42no—
815C2—81no—
816C2—81no—
817C2—81no—
818C2#2144848011yescharacteristic
819C2#2145454611yescharacteristic
820C2#2145456311yescharacteristic
821C2#2145486711yescharacteristic
822C2#2145488111yescharacteristic
823C2#2145488611yescharacteristic
824C2#2145489511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
Fitting, prime radicalC61×#2388C2
cosocleC22×C4×C61C24
hypercenter#2388D61
hypocenterC61#22039
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #2388

Complements

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

NH ≅ G/Ntype
1. C2×#16839840C2semidirect
2. C2×#16839729C2semidirect
3. #21446618C2semidirect
4. #21446614C2semidirect
5. #21446434C2semidirect
6. #21446427C2semidirect
7. #21446427C2semidirect
8. #21446427C2semidirect
9. #21446117C2semidirect
10. #21446117C2semidirect
11. #21446112C2semidirect
12. #21445999C2semidirect
13. #21445731C2semidirect
14. #21445603C2semidirect
66. C2×#11758194D4semidirect
473. C61#22039semidirect

Maximal subgroups

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

subgroupindex
C2×#168398402
C2×#168397292
#214466182
#214466142
#214464342
#214464272
#214461172
#214461122
#214459992
#214457312
#214456032
C61×#23882
#2203961