Finite Group Databasebeta

← #29698070

Subgroups — #29698070

Order 15616.

980 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839840C211yesmaximal, characteristic
2C2×#16839834C211yesmaximal, characteristic
3C2×#16839789C211yesmaximal, characteristic, complemented
4C2×#16839786C211yesmaximal, characteristic, complemented
5#21446543C211yesmaximal, characteristic, complemented
6#21446538C211yesmaximal, characteristic, complemented
7#21446004C211yesmaximal, characteristic, complemented
8#21446004C211yesmaximal, characteristic, complemented
9#21446004C211yesmaximal, characteristic, complemented
10#21445999C211yesmaximal, characteristic, complemented
11#21445973C211yesmaximal, characteristic, complemented
12#21445803C211yesmaximal, characteristic, complemented
13#21445799C211yesmaximal, characteristic, complemented
14#21445676C211yesmaximal, characteristic, complemented
15C61×#2290C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic
17C22×#11758194C2211yescharacteristic
18C22×#11758194C2211yescharacteristic
19C23×#92418C2211yescharacteristic
20#16839840—24no—
21#16839834—24no—
22#16839789—24no—
23#16839786—24no—
24C2×C4⋊#92418C2211yescharacteristic
25C2×C4⋊#92418C2211yescharacteristic
26C2×C4⋊#92418C2211yescharacteristic
27C2×C4⋊#92418C2211yescharacteristic
28C2×C4⋊#92418C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×C4⋊#92418C2211yescharacteristic
32C2×C4⋊#92418C2211yescharacteristic
33C2×C4⋊#92418C2211yescharacteristic
34C2×C4⋊#92418C2211yescharacteristic
35C2×C4⋊#92418C2211yescharacteristic
36C2×C22⋊#92418C2211yescharacteristic
37C2×C22⋊#92418C2211yescharacteristic
38C2×C22⋊#92418C2211yescharacteristic
39C2×C22⋊#92418C2211yescharacteristic
40C2×#14519688C2211yescharacteristic
41C2×C4×#92418C2211yescharacteristic
42#16839517C2211yescharacteristic
43#16839517C2211yescharacteristic
44#16839517C2211yescharacteristic
45#16839517C2211yescharacteristic
46#16839517C2211yescharacteristic
47#16839517C2211yescharacteristic
48C2×C4×D4×C61C2211yescharacteristic
49C2×#117×C61C2211yescharacteristic
50C22×C42×C61C2211yescharacteristic
51C61×#388C411yescharacteristic
52C61×#388C411yescharacteristic
53C61×#387C411yescharacteristic
54C61×#387C411yescharacteristic
55C61×#386C411yescharacteristic
56C61×#386C411yescharacteristic
57C61×#385C411yescharacteristic
58C61×#385C411yescharacteristic
59C4×C4⋊C4×C61C2211yescharacteristic
60C4×C22⋊C4×C61C2211yescharacteristic
61C4×C22⋊C4×C61C2211yescharacteristic
62C61×#376C2211yescharacteristic
63C2×#11758194—22no—
64C2×#11758194—22no—
65C2×#11758194—22no—
66C2×#11758194—22no—
67C2×#11758194—22no—
68C2×#11758194—22no—
69C2×#11758194—41no—
70C2×#11758194—41no—
71C2×#11758194—41no—
72C22×#92418—22no—
73C22×#92418—22no—
74C22×#92418—41no—
75C22×#92418C2311yescharacteristic
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C22×#92418C2311yescharacteristic
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C4⋊#92418—22no—
84C4⋊#92418—22no—
85C4⋊#92418—22no—
86C4⋊#92418—22no—
87C4⋊#92418—22no—
88C4⋊#92418—22no—
89C4⋊#92418—22no—
90C4⋊#92418—22no—
91C4⋊#92418—22no—
92C4⋊#92418—41no—
93C4⋊#92418—41no—
94C4⋊#92418D414yescomplemented
95C22⋊#92418—22no—
96C22⋊#92418—22no—
97C22⋊#92418—22no—
98C22⋊#92418—22no—
99#14519688—22no—
100C4×#92418—22no—
101C22×D4×C61C2×C411yescharacteristic
102C23×C4×C61C2×C411yescharacteristic
103C23×C4×C61C2×C411yescharacteristic
104C23×C4×C61C2311yescharacteristic
105C23×C4×C61C2311yescharacteristic
106C4×D4×C61D414yes—
107C4×D4×C61Q814yes—
108#117×C61—22no—
109#117×C61—22no—
110C2×C4⋊C4×C61C2×C411yescharacteristic
111C2×C4⋊C4×C61C2×C411yescharacteristic
112C2×C4⋊C4×C61C2×C411yescharacteristic
113C2×C4⋊C4×C61C2×C411yescharacteristic
114C2×C4⋊C4×C61C2×C411yescharacteristic
115C2×C22⋊C4×C61C2×C411yescharacteristic
116C2×C22⋊C4×C61C2×C411yescharacteristic
117C2×C22⋊C4×C61C2×C411yescharacteristic
118C2×C22⋊C4×C61C2×C411yescharacteristic
119C2×C22⋊C4×C61C2×C411yescharacteristic
120C2×C22⋊C4×C61C2×C411yescharacteristic
121C2×C22⋊C4×C61C2×C411yescharacteristic
122C2×C22⋊C4×C61C2×C411yescharacteristic
123C2×C42×C61—22no—
124C2×C42×C61—22no—
125C2×C42×C61C2×C411yescharacteristic
126C2×C42×C61C2×C411yescharacteristic
127C2×C42×C61C2311yescharacteristic
128C2×C42×C61C2311yescharacteristic
129C2×C42×C61C2311yescharacteristic
130C2×C42×C61C2311yescharacteristic
131C2×C42×C61C2311yescharacteristic
132#95×C61C2×C411yescharacteristic
133#95×C61C2×C411yescharacteristic
134#95×C61C2×C411yescharacteristic
135#95×C61C2×C411yescharacteristic
136#95×C61C2×C411yescharacteristic
137#95×C61C2×C411yescharacteristic
138#95×C61C2×C411yescharacteristic
139#95×C61C2×C411yescharacteristic
140#95×C61C2×C411yescharacteristic
141#95×C61C2×C411yescharacteristic
142C24×C61C22×C411yescharacteristic
143C24×C61C22×C411yescharacteristic
144C2×D4×C61—41no—
145C2×D4×C61—41no—
146C2×D4×C61C4⋊C414yes—
147C22×C4×C61—21no—
148C22×C4×C61—21no—
149C22×C4×C61—21no—
150C22×C4×C61—21no—
151C22×C4×C61—21no—
152C22×C4×C61—21no—
153C22×C4×C61—21no—
154C22×C4×C61—21no—
155C22×C4×C61—22no—
156C22×C4×C61—22no—
157C22×C4×C61—22no—
158C22×C4×C61—41no—
159C22×C4×C61—41no—
160C22×C4×C61—41no—
161C22×C4×C61C22×C411yescharacteristic
162C22×C4×C61C22×C411yescharacteristic
163C22×C4×C61C22×C411yescharacteristic
164C22×C4×C61C22×C411yescharacteristic
165C22×C4×C61C22×C411yescharacteristic
166C22×C4×C61C22×C411yescharacteristic
167C22×C4×C61C22×C411yescharacteristic
168C22×C4×C61C22×C411yescharacteristic
169C22×C4×C61C22×C411yescharacteristic
170C22×C4×C61C22×C411yescharacteristic
171C22×C4×C61C22×C411yescharacteristic
172C22×C4×C61C22×C411yescharacteristic
173C22×C4×C61C2×D412yes—
174C22×C4×C61C2×D412yes—
175C22×C4×C61C2×Q812yes—
176C22×C4×C61C2×Q812yes—
177C22×C4×C61C2411yescharacteristic
178C4⋊C4×C61—22no—
179C4⋊C4×C61—22no—
180C4⋊C4×C61—22no—
181C4⋊C4×C61—41no—
182C4⋊C4×C61C4⋊C414yes—
183C22⋊C4×C61—22no—
184C22⋊C4×C61—22no—
185C22⋊C4×C61—22no—
186C22⋊C4×C61—41no—
187C22⋊C4×C61—41no—
188C22⋊C4×C61—41no—
189C22⋊C4×C61C4⋊C414yes—
190C22⋊C4×C61C4⋊C414yes—
191C42×C61—22no—
192C42×C61—22no—
193C42×C61—21no—
194C42×C61—21no—
195C42×C61—21no—
196C42×C61—21no—
197C42×C61—21no—
198C42×C61—21no—
199C42×C61C2×D412yes—
200C42×C61C2×D412yes—
201C42×C61C2×Q812yes—
202C42×C61#4112yes—
203#11758194—44no—
204#11758194—44no—
205#11758194—44no—
206C2×#92418—21no—
207C2×#92418—21no—
208C2×#92418—21no—
209C2×#92418—21no—
210C2×#92418—21no—
211C2×#92418—21no—
212C2×#92418—21no—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—44no—
229C2×#92418C2×D412yes—
230C2×#92418C2×D412yes—
231C23×C61—21no—
232C23×C61—21no—
233C23×C61—21no—
234C23×C61—21no—
235C23×C61—21no—
236C23×C61—21no—
237C23×C61—21no—
238C23×C61—21no—
239C23×C61—21no—
240C23×C61—21no—
241C23×C61—21no—
242C23×C61—21no—
243C23×C61C2×C4⋊C412yes—
244C23×C61C2×C4⋊C412yes—
245C23×C61C23×C411yescharacteristic
246D4×C61—44no—
247C2×C4×C61—21no—
248C2×C4×C61—21no—
249C2×C4×C61—21no—
250C2×C4×C61—21no—
251C2×C4×C61—21no—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—22no—
262C2×C4×C61—22no—
263C2×C4×C61—22no—
264C2×C4×C61—22no—
265C2×C4×C61—22no—
266C2×C4×C61—22no—
267C2×C4×C61—22no—
268C2×C4×C61—22no—
269C2×C4×C61—21no—
270C2×C4×C61—21no—
271C2×C4×C61—21no—
272C2×C4×C61—21no—
273C2×C4×C61—21no—
274C2×C4×C61—21no—
275C2×C4×C61—21no—
276C2×C4×C61—21no—
277C2×C4×C61—21no—
278C2×C4×C61—21no—
279C2×C4×C61—21no—
280C2×C4×C61—21no—
281C2×C4×C61—21no—
282C2×C4×C61—21no—
283C2×C4×C61—21no—
284C2×C4×C61—44no—
285C2×C4×C61—44no—
286C2×C4×C61C2×C4⋊C412yes—
287C2×C4×C61C2×C4⋊C412yes—
288C2×C4×C61C2×C4⋊C412yes—
289C2×C4×C61C2×C4⋊C412yes—
290C2×C4×C61C4×D412yes—
291C2×C4×C61C4×D412yes—
292C2×C4×C61#13112yes—
293C2×C4×C61C22×D411yescharacteristic
294C2×C4×C61C22×D411yescharacteristic
295C2×C4×C61C22×Q811yescharacteristic
296C2×C4×C61C2×#4111yescharacteristic
297C2×C4×C61H(5,𝔽2)11yescharacteristic
298C2×C4×C612−1+411yescharacteristic
299#92418—22no—
300#92418—22no—
301#92418—41no—
302#92418—41no—
303#92418—41no—
304#92418—41no—
305#92418—41no—
306#92418—41no—
307#22649—611nomaximal, Sylow
308C22×C61—22no—
309C22×C61—22no—
310C22×C61—22no—
311C22×C61—22no—
312C22×C61—22no—
313C22×C61—22no—
314C22×C61—41no—
315C22×C61—41no—
316C22×C61—41no—
317C22×C61—41no—
318C22×C61—41no—
319C22×C61—41no—
320C22×C61—41no—
321C22×C61—41no—
322C22×C61C22×C4⋊C411yescharacteristic
323C22×C61C2×C4×D411yescharacteristic
324C22×C61#52011yescharacteristic
325C22×C61C2×#13111yescharacteristic
326C22×C61#56811yescharacteristic
327C22×C61#56811yescharacteristic
328C22×C61#56811yescharacteristic
329C4×C61—22no—
330C4×C61—22no—
331C4×C61—22no—
332C4×C61—22no—
333C4×C61—22no—
334C4×C61—22no—
335C4×C61—22no—
336C4×C61—41no—
337C4×C61—41no—
338C4×C61—41no—
339C4×C61—41no—
340C4×C61—41no—
341C4×C61D4211yescharacteristic
342C4×C61#54711yescharacteristic
343C4×C61D4×Q811yescharacteristic
344C4×C61#55411yescharacteristic
345C2×#436—611no—
346C2×#435—611no—
347C2×#424—611no—
348C2×#423—611no—
349#2290D6111yescharacteristic
350#1940—611no—
351#1939—611no—
352#1851—611no—
353#1851—611no—
354#1851—611no—
355#1850—611no—
356#1843—611no—
357#1798—611no—
358#1797—611no—
359#1768—611no—
360C2×C61—42no—
361C2×C61—42no—
362C2×C61D4×C4⋊C411yescharacteristic
363C2×C61#290511yescharacteristic
364C2×C61#290611yescharacteristic
365C2×C61#293011yescharacteristic
366C2×C61#293311yescharacteristic
367C2×C61#299311yescharacteristic
368C2×C61#299511yescharacteristic
369C22×M16—611no—
370C22×M16—611no—
371C22×M16—611no—
372C23×C8—611no—
373C2×C4×D4C2×D6111yescharacteristic
374C2×#117C2×D6111yescharacteristic
375C22×C42C2×D6111yescharacteristic
376#436—1224no—
377#435—1224no—
378#424—1224no—
379#423—1224no—
380C2×C4⋊C8—611no—
381C2×C4⋊C8—611no—
382C2×C4⋊C8—611no—
383C2×C4⋊C8—611no—
384C2×C4⋊C8—611no—
385C2×C4⋊C8—611no—
386C2×C4⋊C8—611no—
387C2×C4⋊C8—611no—
388C2×C4⋊C8—611no—
389C2×C4⋊C8—611no—
390C2×C4⋊C8—611no—
391C2×C4⋊C8—611no—
392C2×C22⋊C8—611no—
393C2×C22⋊C8—611no—
394C2×C22⋊C8—611no—
395C2×C22⋊C8—611no—
396C2×#97—611no—
397C2×C4×C8—611no—
398#388Dic6111yescharacteristic
399#388Dic6111yescharacteristic
400#387Dic6111yescharacteristic
401#387Dic6111yescharacteristic
402#386Dic6111yescharacteristic
403#386Dic6111yescharacteristic
404#385Dic6111yescharacteristic
405#385Dic6111yescharacteristic
406C4×C4⋊C4C2×D6111yescharacteristic
407C4×C22⋊C4C2×D6111yescharacteristic
408C4×C22⋊C4C2×D6111yescharacteristic
409#376C2×D6111yescharacteristic
410#336—611no—
411#336—611no—
412#336—611no—
413#336—611no—
414#336—611no—
415#336—611no—
416C61#2264911yescharacteristic, complemented, Sylow
417C22×D4C2×Dic6111yescharacteristic
418C23×C4C2×Dic6111yescharacteristic
419C23×C4C2×Dic6111yescharacteristic
420C23×C4C22×D6111yescharacteristic
421C23×C4C22×D6111yescharacteristic
422C2×M16—1222no—
423C2×M16—1222no—
424C2×M16—1222no—
425C2×M16—1222no—
426C2×M16—1222no—
427C2×M16—1222no—
428C2×M16—2441no—
429C2×M16—2441no—
430C2×M16—2441no—
431C22×C8—611no—
432C22×C8—611no—
433C22×C8—611no—
434C22×C8—611no—
435C22×C8—611no—
436C22×C8—611no—
437C22×C8—611no—
438C22×C8—611no—
439C22×C8—1222no—
440C22×C8—1222no—
441C22×C8—2441no—
442C4×D4Dic12214yes—
443C4×D4D24414yes—
444#117—22no—
445#117—22no—
446C2×C4⋊C4C2×Dic6111yescharacteristic
447C2×C4⋊C4C2×Dic6111yescharacteristic
448C2×C4⋊C4C2×Dic6111yescharacteristic
449C2×C4⋊C4C2×Dic6111yescharacteristic
450C2×C4⋊C4C2×Dic6111yescharacteristic
451C2×C22⋊C4C2×Dic6111yescharacteristic
452C2×C22⋊C4C2×Dic6111yescharacteristic
453C2×C22⋊C4C2×Dic6111yescharacteristic
454C2×C22⋊C4C2×Dic6111yescharacteristic
455C2×C22⋊C4C2×Dic6111yescharacteristic
456C2×C22⋊C4C2×Dic6111yescharacteristic
457C2×C22⋊C4C2×Dic6111yescharacteristic
458C2×C22⋊C4C2×Dic6111yescharacteristic
459C2×C42—22no—
460C2×C42—22no—
461C2×C42C2×Dic6111yescharacteristic
462C2×C42C2×Dic6111yescharacteristic
463C2×C42C22×D6111yescharacteristic
464C2×C42C22×D6111yescharacteristic
465C2×C42C22×D6111yescharacteristic
466C2×C42C22×D6111yescharacteristic
467C2×C42C22×D6111yescharacteristic
468C4⋊C8—614no—
469C4⋊C8—1222no—
470C4⋊C8—1222no—
471C4⋊C8—1222no—
472C4⋊C8—1222no—
473C4⋊C8—1222no—
474C4⋊C8—1222no—
475C4⋊C8—1222no—
476C4⋊C8—1222no—
477C4⋊C8—1222no—
478C4⋊C8—2441no—
479C4⋊C8—2441no—
480C22⋊C8—1222no—
481C22⋊C8—1222no—
482C22⋊C8—1222no—
483C22⋊C8—1222no—
484#97—1222no—
485C4×C8—1222no—
486#95C2×Dic6111yescharacteristic
487#95C2×Dic6111yescharacteristic
488#95C2×Dic6111yescharacteristic
489#95C2×Dic6111yescharacteristic
490#95C2×Dic6111yescharacteristic
491#95C2×Dic6111yescharacteristic
492#95C2×Dic6111yescharacteristic
493#95C2×Dic6111yescharacteristic
494#95C2×Dic6111yescharacteristic
495#95C2×Dic6111yescharacteristic
496C24C22×Dic6111yescharacteristic
497C24C22×Dic6111yescharacteristic
498C2×D4—41no—
499C2×D4—41no—
500C2×D4C4⋊Dic6114yes—
501C22×C4—21no—
502C22×C4—21no—
503C22×C4—21no—
504C22×C4—21no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—22no—
510C22×C4—22no—
511C22×C4—22no—
512C22×C4—41no—
513C22×C4—41no—
514C22×C4—41no—
515C22×C4C2×Dic12212yes—
516C22×C4C2×Dic12212yes—
517C22×C4C2×D24412yes—
518C22×C4C2×D24412yes—
519C22×C4C22×Dic6111yescharacteristic
520C22×C4C22×Dic6111yescharacteristic
521C22×C4C22×Dic6111yescharacteristic
522C22×C4C22×Dic6111yescharacteristic
523C22×C4C22×Dic6111yescharacteristic
524C22×C4C22×Dic6111yescharacteristic
525C22×C4C22×Dic6111yescharacteristic
526C22×C4C22×Dic6111yescharacteristic
527C22×C4C22×Dic6111yescharacteristic
528C22×C4C22×Dic6111yescharacteristic
529C22×C4C22×Dic6111yescharacteristic
530C22×C4C22×Dic6111yescharacteristic
531C22×C4C23×D6111yescharacteristic
532M16—2444no—
533M16—2444no—
534M16—2444no—
535C2×C8—612no—
536C2×C8—612no—
537C2×C8—1221no—
538C2×C8—1221no—
539C2×C8—1221no—
540C2×C8—1221no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—1221no—
552C2×C8—1221no—
553C2×C8—1221no—
554C2×C8—1221no—
555C2×C8—1221no—
556C2×C8—1221no—
557C2×C8—1221no—
558C2×C8—1221no—
559C2×C8—2444no—
560C4⋊C4—22no—
561C4⋊C4—22no—
562C4⋊C4—22no—
563C4⋊C4—41no—
564C4⋊C4C4⋊Dic6114yes—
565C22⋊C4—22no—
566C22⋊C4—22no—
567C22⋊C4—22no—
568C22⋊C4—41no—
569C22⋊C4—41no—
570C22⋊C4—41no—
571C22⋊C4C4⋊Dic6114yes—
572C22⋊C4C4⋊Dic6114yes—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—22no—
580C42—22no—
581C42C2×Dic12212yes—
582C42C2×D24412yes—
583C42D4×D6112yes—
584C42#1175822412yes—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—21no—
591C23—21no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23—21no—
597C23C2×C4⋊Dic6112yes—
598C23C2×C4⋊Dic6112yes—
599C23C23×Dic6111yescharacteristic
600D4—44no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—21no—
605C2×C4—21no—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—44no—
639C2×C4—44no—
640C2×C4C2×C4⋊Dic6112yes—
641C2×C4C2×C4⋊Dic6112yes—
642C2×C4C2×C4⋊Dic6112yes—
643C2×C4C2×C4⋊Dic6112yes—
644C2×C4D4×Dic6112yes—
645C2×C4D4×Dic6112yes—
646C2×C4#1451978412yes—
647C2×C4C2×D4×D6111yescharacteristic
648C2×C4C22×D24411yescharacteristic
649C2×C4C22×Dic12211yescharacteristic
650C2×C4C2×#1175822411yescharacteristic
651C2×C4#1451982311yescharacteristic
652C2×C4#1451982411yescharacteristic
653C8—1222no—
654C8—1222no—
655C8—2441no—
656C8—2441no—
657C8—2441no—
658C8—2441no—
659C8—2441no—
660C8—2441no—
661C22—22no—
662C22—22no—
663C22—22no—
664C22—22no—
665C22—22no—
666C22—22no—
667C22—41no—
668C22—41no—
669C22—41no—
670C22—41no—
671C22—41no—
672C22—41no—
673C22—41no—
674C22—41no—
675C22C22×C4⋊Dic6111yescharacteristic
676C22C2×D4×Dic6111yescharacteristic
677C22#1684024511yescharacteristic
678C22C2×#1451978411yescharacteristic
679C22#1684052911yescharacteristic
680C22#1684052911yescharacteristic
681C22#1684052911yescharacteristic
682C4—22no—
683C4—22no—
684C4—22no—
685C4—22no—
686C4—22no—
687C4—22no—
688C4—22no—
689C4—41no—
690C4—41no—
691C4—41no—
692C4—41no—
693C4—41no—
694C4D4×D24411yescharacteristic
695C4#1684041611yescharacteristic
696C4D4×Dic12211yescharacteristic
697C4#1684046911yescharacteristic
698C2—42no—
699C2—42no—
700C2D4×C4⋊Dic6111yescharacteristic
701C2#2145438311yescharacteristic
702C2#2145438711yescharacteristic
703C2#2145452311yescharacteristic
704C2#2145454611yescharacteristic
705C2#2145496811yescharacteristic
706C2#2145498911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#2290C2
prime radicalC22×D4×C61C2×C4
cosocleC22×C4×C61C24
hypercenter#2290D61
hypocenterC61#22649
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #2290

Complements

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

NH ≅ G/Ntype
3. C2×#16839789C2semidirect
4. C2×#16839786C2semidirect
5. #21446543C2semidirect
6. #21446538C2semidirect
7. #21446004C2semidirect
8. #21446004C2semidirect
9. #21446004C2semidirect
10. #21445999C2semidirect
11. #21445973C2semidirect
12. #21445803C2semidirect
13. #21445799C2semidirect
14. #21445676C2semidirect
94. C4⋊#92418D4semidirect
416. C61#22649semidirect

Maximal subgroups

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

subgroupindex
C2×#168398402
C2×#168398342
C2×#168397892
C2×#168397862
#214465432
#214465382
#214460042
#214459992
#214459732
#214458032
#214457992
#214456762
C61×#22902
#2264961