Finite Group Databasebeta

← #29698058

Subgroups — #29698058

Order 15616.

1116 conjugacy classes of subgroups.

The subgroup lattice has 732 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16839835C211yesmaximal, characteristic
2C2×#16839832C211yesmaximal, characteristic
3C2×#16839784C211yesmaximal, characteristic, complemented
4C2×C4⋊C8×D61C211yesmaximal, characteristic, complemented
5C4×#14519739C211yesmaximal, characteristic
6#21446543C211yesmaximal, characteristic, complemented
7#21446003C211yesmaximal, characteristic, complemented
8#21446000C211yesmaximal, characteristic, complemented
9#21445998C211yesmaximal, characteristic, complemented
10#21445995C211yesmaximal, characteristic, complemented
11#21445970C211yesmaximal, characteristic, complemented
12#21445798C211yesmaximal, characteristic, complemented
13#21445798C211yesmaximal, characteristic, complemented
14#21445673C211yesmaximal, characteristic, complemented
15C61×#1940C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C22×C8×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×C4×D244C2211yescharacteristic
21C2×#14519739C411yescharacteristic
22C2×#14519739C411yescharacteristic
23C2×C42×D61C2211yescharacteristic
24C2×C42×D61C2211yescharacteristic
25#16839835—24no—
26#16839832—24no—
27#16839784—24no—
28C2×C4⋊#92418C2211yescharacteristic
29C2×C4⋊#92418C2211yescharacteristic
30C2×C4⋊#92418C2211yescharacteristic
31C2×#14519706C2211yescharacteristic
32C2×#14519706C2211yescharacteristic
33C2×#14519706C2211yescharacteristic
34C2×#14519706C2211yescharacteristic
35C2×#14519706C2211yescharacteristic
36C2×#14519706C2211yescharacteristic
37C4⋊C8×D61—24no—
38C2×#14519689C2211yescharacteristic
39C2×#14519689C2211yescharacteristic
40C2×#14519689C2211yescharacteristic
41C2×#14519689C2211yescharacteristic
42C2×#14519688C2211yescharacteristic
43C4⋊C4×Dic61C411yescharacteristic
44C4⋊C4×Dic61C411yescharacteristic
45C4×#11758198C2211yescharacteristic
46C4×#11758198C2211yescharacteristic
47#16839609C411yescharacteristic
48#16839609C411yescharacteristic
49#16839609C411yescharacteristic
50#16839609C411yescharacteristic
51C42×Dic61C2211yescharacteristic
52#16839517C2211yescharacteristic
53#16839517C2211yescharacteristic
54#16839516C2211yescharacteristic
55#16839516C2211yescharacteristic
56C2×C4⋊C8×C61C2211yescharacteristic
57C2×C4⋊C8×C61C2211yescharacteristic
58C2×C4⋊C8×C61C2211yescharacteristic
59C2×#97×C61C2211yescharacteristic
60C4×C4⋊C4×C61C2211yescharacteristic
61C61×#336C2211yescharacteristic
62C61×#336C2211yescharacteristic
63C22×D244C2×C411yescharacteristic
64C22×C4×D61C2×C411yescharacteristic
65C22×C4×D61C2×C411yescharacteristic
66C22×C4×D61C2×C411yescharacteristic
67C22×C4×D61C2×C411yescharacteristic
68C22×C4×D61C2311yescharacteristic
69C22×C4×D61C2311yescharacteristic
70C2×#11758189—22no—
71C2×#11758189—22no—
72C2×#11758189—22no—
73C2×#11758189—22no—
74C2×#11758189—41no—
75C2×#11758189—41no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—22no—
81C2×C8×D61—22no—
82C2×C8×D61—22no—
83C2×C8×D61—22no—
84C2×C8×D61—41no—
85C2×C8×D61—41no—
86C4×D244D414yes—
87C4×D244Q814yes—
88#14519739—24no—
89#14519739—24no—
90C2×C4⋊Dic61C2×C411yescharacteristic
91C2×#11758198C2×C411yescharacteristic
92C2×#11758198C2×C411yescharacteristic
93C2×#11758198C2×C411yescharacteristic
94C2×#11758198C2×C411yescharacteristic
95C2×#11758198C2×C411yescharacteristic
96C2×#11758198C2×C411yescharacteristic
97C2×C4×Dic61C2×C411yescharacteristic
98C2×C4×Dic61C2×C411yescharacteristic
99C2×C4×Dic61C2×C411yescharacteristic
100C2×C4×Dic61C2×C411yescharacteristic
101C2×C4×Dic61C2×C411yescharacteristic
102C2×C4×Dic61C2×C411yescharacteristic
103C2×C4×Dic61C2×C411yescharacteristic
104C2×C4×Dic61C2×C411yescharacteristic
105C2×C4×Dic61C2311yescharacteristic
106C2×C4×Dic61C2311yescharacteristic
107C42×D61—22no—
108C42×D61—22no—
109C42×D61—22no—
110C42×D61—22no—
111C4⋊#92418—22no—
112C4⋊#92418—22no—
113C4⋊#92418—22no—
114#14519706—22no—
115#14519706—22no—
116#14519706—22no—
117#14519706—41no—
118#14519706—41no—
119#14519706D414yescomplemented
120#14519689—22no—
121#14519689—22no—
122#14519689—22no—
123#14519689—22no—
124#14519688—22no—
125#14519684C2×C411yescharacteristic
126#14519684C2×C411yescharacteristic
127#14519684C2×C411yescharacteristic
128#14519684C2×C411yescharacteristic
129C22×C8×C61C2311yescharacteristic
130C22×C8×C61C2311yescharacteristic
131C22×C8×C61C2311yescharacteristic
132C22×C8×C61C2311yescharacteristic
133C2×C4⋊C4×C61C2×C411yescharacteristic
134C2×C4⋊C4×C61C2×C411yescharacteristic
135C2×C42×C61C2311yescharacteristic
136C2×C42×C61C2311yescharacteristic
137C2×C42×C61C2311yescharacteristic
138C4⋊C8×C61—22no—
139C4⋊C8×C61—22no—
140C4⋊C8×C61—22no—
141#97×C61—22no—
142#95×C61C2×C411yescharacteristic
143#95×C61C2×C411yescharacteristic
144C23×D61C22×C411yescharacteristic
145C23×D61C22×C411yescharacteristic
146C22×C4×C61C22×C411yescharacteristic
147C22×C4×C61C22×C411yescharacteristic
148C22×C4×C61C22×C411yescharacteristic
149C22×C4×C61C22×C411yescharacteristic
150C22×C4×C61C22×C411yescharacteristic
151C22×C4×C61C22×C411yescharacteristic
152C22×C4×C61C2411yescharacteristic
153C22×Dic61C22×C411yescharacteristic
154C22×Dic61C22×C411yescharacteristic
155C22×Dic61C22×C411yescharacteristic
156C22×Dic61C22×C411yescharacteristic
157C22×Dic61C22×C411yescharacteristic
158C22×Dic61C22×C411yescharacteristic
159C2×D244—22no—
160C2×D244—22no—
161C2×D244C4⋊C414yes—
162C2×C4×D61—21no—
163C2×C4×D61—21no—
164C2×C4×D61—21no—
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×C4×D61—22no—
171C2×C4×D61—22no—
172C2×C4×D61—22no—
173C2×C4×D61—22no—
174C2×C4×D61—22no—
175C2×C4×D61—22no—
176C2×C4×D61—22no—
177C2×C4×D61—22no—
178C2×C4×D61—22no—
179C2×C4×D61—41no—
180C2×C4×D61—41no—
181C2×C4×D61M1614yescomplemented
182C2×C4×D61C2×D412yes—
183C2×C4×D61C2×D412yes—
184C2×C4×D61C2×Q812yes—
185C2×C4×D61C2×Q812yes—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61C2×D412yes—
198C4⋊C4×C61—22no—
199C4⋊C4×C61—22no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61—21no—
203C42×C61—21no—
204C42×C61C2×D412yes—
205C42×C61C2×Q812yes—
206#11758198—22no—
207#11758198—22no—
208#11758198—22no—
209#11758198C4⋊C414yes—
210#11758198C4⋊C414yes—
211#11758198M1614yescomplemented
212C4⋊Dic61C4⋊C414yes—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—22no—
216C4×Dic61—22no—
217C4×Dic61—22no—
218C4×Dic61—22no—
219C4×Dic61—22no—
220C4×Dic61—22no—
221C4×Dic61—22no—
222C4×Dic61—41no—
223C4×Dic61C2×D412yes—
224C4×Dic61#4112yes—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418C2×D412yes—
237#11758189—44no—
238#11758189—44no—
239C8×D61—44no—
240C8×D61—44no—
241C23×C61C23×C411yescharacteristic
242C22×D61—21no—
243C22×D61—21no—
244C22×D61—21no—
245C22×D61—21no—
246C22×D61—21no—
247C22×D61—21no—
248C22×D61—21no—
249C22×D61—21no—
250C22×D61—21no—
251C22×D61—21no—
252C22×D61C2×C4⋊C412yes—
253C22×D61C2×C4⋊C412yes—
254C22×D61C2×M1612yes—
255C22×D61C2×M1612yes—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—21no—
260C2×C4×C61—21no—
261C2×C4×C61—21no—
262C2×C4×C61—21no—
263C2×C4×C61—21no—
264C2×C4×C61—21no—
265C2×C4×C61—21no—
266C2×C4×C61—21no—
267C2×C4×C61—21no—
268C2×C4×C61—21no—
269C2×C4×C61—21no—
270C2×C4×C61C2×C4⋊C412yes—
271C2×C4×C61C2×C4⋊C412yes—
272C2×C4×C61C2×M1612yes—
273C2×C4×C61C2×M1612yes—
274C2×C4×C61C22×D411yescharacteristic
275C2×C4×C61C22×D411yescharacteristic
276C2×C4×C61C22×Q811yescharacteristic
277C2×C4×C61C2×#4111yescharacteristic
278C2×C4×C61H(5,𝔽2)11yescharacteristic
279C2×C4×C612−1+411yescharacteristic
280C2×Dic61—21no—
281C2×Dic61—21no—
282C2×Dic61—21no—
283C2×Dic61—21no—
284C2×Dic61—21no—
285C2×Dic61—21no—
286C2×Dic61—21no—
287C2×Dic61—21no—
288C2×Dic61—21no—
289C2×Dic61—21no—
290C2×Dic61—21no—
291C2×Dic61C2×C4⋊C412yes—
292C2×Dic61C2×C4⋊C412yes—
293C2×Dic61C4×D412yes—
294C2×Dic61C4×D412yes—
295C2×Dic61C2×M1612yes—
296C2×Dic61C2×M1612yes—
297C2×Dic61#13112yes—
298D244—28no—
299C4×D61—22no—
300C4×D61—22no—
301C4×D61—22no—
302C4×D61—22no—
303C4×D61—22no—
304C4×D61—22no—
305C4×D61—22no—
306C4×D61—22no—
307C4×D61—28no—
308C4×D61—44no—
309C4×D61—44no—
310C4×D61—44no—
311C8×C61—22no—
312C8×C61—41no—
313C8×C61—41no—
314C8×C61—41no—
315#92418—22no—
316#92418—41no—
317#92418—41no—
318#92418—41no—
319#22648—611nomaximal, Sylow
320C22×C61C22×C4⋊C411yescharacteristic
321C22×C61C2×C4×D411yescharacteristic
322C22×C61#52011yescharacteristic
323C22×C61C22×M1611yescharacteristic
324C22×C61C22×M1611yescharacteristic
325C22×C61C2×#13111yescharacteristic
326C22×C61#56811yescharacteristic
327C2×D61—22no—
328C2×D61—22no—
329C2×D61—22no—
330C2×D61—22no—
331C2×D61—22no—
332C2×D61—22no—
333C2×D61—22no—
334C2×D61—22no—
335C2×D61—22no—
336C2×D61—41no—
337C2×D61—41no—
338C2×D61—41no—
339C2×D61—41no—
340C2×D61#42314yescomplemented
341C4×C61—22no—
342C4×C61—22no—
343C4×C61—22no—
344C4×C61—22no—
345C4×C61—41no—
346C4×C61—41no—
347C4×C61D4211yescharacteristic
348C4×C61#54711yescharacteristic
349C4×C61D4×Q811yescharacteristic
350C4×C61#55411yescharacteristic
351Dic61—22no—
352Dic61—22no—
353Dic61—22no—
354Dic61—22no—
355Dic61—41no—
356Dic61#43514yescomplemented
357C2×#435—611no—
358C2×#435—611no—
359C2×#423—611no—
360C22×C4⋊C8—611no—
361C42×D4—611no—
362#1940—611no—
363#1940D6111yescharacteristic, complemented
364#1851—611no—
365#1851—611no—
366#1850—611no—
367#1850—611no—
368#1842—611no—
369#1797—611no—
370#1797—611no—
371#1767—611no—
372C2×C61D4×C4⋊C411yescharacteristic
373C2×C61C2×#42311yescharacteristic
374C2×C61#290611yescharacteristic
375C2×C61C2×#43511yescharacteristic
376C2×C61D4×M1611yescharacteristic
377C2×C61#298911yescharacteristic
378C2×C61#299011yescharacteristic
379D61—24no—
380D61—42no—
381C22×M16—611no—
382C22×M16—611no—
383C23×C8—611no—
384C23×C8—611no—
385C2×C4×D4—611no—
386C2×C4×D4—611no—
387C2×C4×D4—611no—
388C22×C42—611no—
389C22×C42—611no—
390#435—1224no—
391#435—1224no—
392#423—1224no—
393C2×C4⋊C8—611no—
394C2×C4⋊C8—611no—
395C2×C4⋊C8—611no—
396C2×C4⋊C8—611no—
397C2×C4⋊C8—611no—
398C2×C4⋊C8—611no—
399C2×C4⋊C8—611no—
400C2×C4⋊C8—611no—
401C2×C4⋊C8—611no—
402C2×C4⋊C8—1224no—
403C2×C4⋊C8C2×D6111yescharacteristic
404C2×C4⋊C8C2×D6111yescharacteristic
405C2×C4⋊C8C2×D6111yescharacteristic
406C2×C22⋊C8—611no—
407C2×C22⋊C8—611no—
408C2×C22⋊C8—611no—
409C2×C22⋊C8—611no—
410C2×#97—611no—
411C2×#97C2×D6111yescharacteristic
412C4×C4⋊C4—611no—
413C4×C4⋊C4—611no—
414C4×C4⋊C4C2×D6111yescharacteristic
415C4×C22⋊C4—611no—
416C4×C22⋊C4—611no—
417C4×C22⋊C4—611no—
418C4×C22⋊C4—611no—
419C4×C22⋊C4—611no—
420C4×C22⋊C4—611no—
421C43—611no—
422#336—611no—
423#336—611no—
424#336—611no—
425#336—611no—
426#336C2×D6111yescharacteristic
427#336C2×D6111yescharacteristic
428C61#2264811yescharacteristic, complemented, Sylow
429C22×D4—611no—
430C23×C4—611no—
431C23×C4—611no—
432C23×C4—611no—
433C23×C4—611no—
434C23×C4—611no—
435C23×C4—611no—
436C2×M16—1222no—
437C2×M16—1222no—
438C2×M16—1222no—
439C2×M16—1222no—
440C2×M16—2441no—
441C2×M16—2441no—
442C22×C8—611no—
443C22×C8—611no—
444C22×C8—611no—
445C22×C8—611no—
446C22×C8—1222no—
447C22×C8—1222no—
448C22×C8—1222no—
449C22×C8—1222no—
450C22×C8—2441no—
451C22×C8—2441no—
452C22×C8C22×D6111yescharacteristic
453C22×C8C22×D6111yescharacteristic
454C22×C8C22×D6111yescharacteristic
455C22×C8C22×D6111yescharacteristic
456C4×D4—614no—
457C4×D4—614no—
458C4×D4—1224no—
459C4×D4—1224no—
460C2×C4⋊C4—611no—
461C2×C4⋊C4C4×D6111yescharacteristic
462C2×C4⋊C4C4×D6111yescharacteristic
463C2×C22⋊C4—611no—
464C2×C22⋊C4—611no—
465C2×C22⋊C4—611no—
466C2×C22⋊C4—611no—
467C2×C22⋊C4—611no—
468C2×C22⋊C4—611no—
469C2×C42—611no—
470C2×C42—611no—
471C2×C42—611no—
472C2×C42—611no—
473C2×C42—611no—
474C2×C42—611no—
475C2×C42—611no—
476C2×C42—611no—
477C2×C42—611no—
478C2×C42—611no—
479C2×C42—1222no—
480C2×C42—1222no—
481C2×C42—1222no—
482C2×C42—1222no—
483C2×C42C22×D6111yescharacteristic
484C2×C42C22×D6111yescharacteristic
485C2×C42C22×D6111yescharacteristic
486C4⋊C8—22no—
487C4⋊C8—22no—
488C4⋊C8—22no—
489C4⋊C8—614no—
490C4⋊C8—1222no—
491C4⋊C8—1222no—
492C4⋊C8—1222no—
493C4⋊C8—1222no—
494C4⋊C8—1222no—
495C4⋊C8—1222no—
496C4⋊C8—2441no—
497C4⋊C8—2441no—
498C22⋊C8—1222no—
499C22⋊C8—1222no—
500C22⋊C8—1222no—
501C22⋊C8—1222no—
502#97—22no—
503#97—1222no—
504#95—611no—
505#95—611no—
506#95—611no—
507#95—611no—
508#95C4×D6111yescharacteristic
509#95C4×D6111yescharacteristic
510C24—611no—
511C24—611no—
512C2×D4—614no—
513C2×D4—1222no—
514C2×D4—1222no—
515C22×C4—611no—
516C22×C4—611no—
517C22×C4—611no—
518C22×C4—611no—
519C22×C4—611no—
520C22×C4—612no—
521C22×C4—612no—
522C22×C4—612no—
523C22×C4—612no—
524C22×C4—614no—
525C22×C4—611no—
526C22×C4—1222no—
527C22×C4—1222no—
528C22×C4—1222no—
529C22×C4—1222no—
530C22×C4—1222no—
531C22×C4—1222no—
532C22×C4—1222no—
533C22×C4—1222no—
534C22×C4—1221no—
535C22×C4—1221no—
536C22×C4—1221no—
537C22×C4—1221no—
538C22×C4—1221no—
539C22×C4—1221no—
540C22×C4—1221no—
541C22×C4—1221no—
542C22×C4—1222no—
543C22×C4—2441no—
544C22×C4—2441no—
545C22×C4C2×C4×D6111yescharacteristic
546C22×C4C2×C4×D6111yescharacteristic
547C22×C4C2×C4×D6111yescharacteristic
548C22×C4C2×C4×D6111yescharacteristic
549C22×C4C2×C4×D6111yescharacteristic
550C22×C4C2×C4×D6111yescharacteristic
551C22×C4C23×D6111yescharacteristic
552M16—2444no—
553M16—2444no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—612no—
566C2×C8—1221no—
567C2×C8—1221no—
568C2×C8—1221no—
569C2×C8—1221no—
570C2×C8—1221no—
571C2×C8—1221no—
572C2×C8—1221no—
573C2×C8—1221no—
574C2×C8—1221no—
575C2×C8—1221no—
576C2×C8—1221no—
577C2×C8—2444no—
578C2×C8—2444no—
579C2×C8D4×D6112yes—
580C4⋊C4—22no—
581C4⋊C4—22no—
582C4⋊C4—614no—
583C22⋊C4—614no—
584C22⋊C4—614no—
585C22⋊C4—614no—
586C22⋊C4—1222no—
587C22⋊C4—1222no—
588C22⋊C4—1222no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—612no—
594C42—612no—
595C42—1222no—
596C42—1222no—
597C42—1222no—
598C42—1222no—
599C42—1222no—
600C42—1222no—
601C42—1222no—
602C42—1221no—
603C42—1221no—
604C42—2441no—
605C42D4×D6112yes—
606C42Q8×D6112yes—
607C23—612no—
608C23—612no—
609C23—612no—
610C23—612no—
611C23—1221no—
612C23—1221no—
613C23—1221no—
614C23—1221no—
615C23—1221no—
616C23—1221no—
617C23—1221no—
618C23—1221no—
619C23—1221no—
620C23—1221no—
621C23C22×C4×D6111yescharacteristic
622D4—1228no—
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—612no—
638C2×C4—612no—
639C2×C4—612no—
640C2×C4—612no—
641C2×C4—612no—
642C2×C4—612no—
643C2×C4—612no—
644C2×C4—1228no—
645C2×C4—1221no—
646C2×C4—1221no—
647C2×C4—1221no—
648C2×C4—1221no—
649C2×C4—1221no—
650C2×C4—1221no—
651C2×C4—1221no—
652C2×C4—1221no—
653C2×C4—1222no—
654C2×C4—1222no—
655C2×C4—1222no—
656C2×C4—1222no—
657C2×C4—1222no—
658C2×C4—1222no—
659C2×C4—1222no—
660C2×C4—1222no—
661C2×C4—1221no—
662C2×C4—1221no—
663C2×C4—1221no—
664C2×C4—2444no—
665C2×C4—2444no—
666C2×C4—2444no—
667C2×C4C4⋊C4×D6112yes—
668C2×C4C4⋊C4×D6112yes—
669C2×C4M16×D6112yes—
670C2×C4M16×D6112yes—
671C2×C4C2×D4×D6111yescharacteristic
672C2×C4C2×D4×D6111yescharacteristic
673C2×C4C2×Q8×D6111yescharacteristic
674C2×C4#41×D6111yescharacteristic
675C2×C4#1451982311yescharacteristic
676C2×C4#1451982511yescharacteristic
677C8—22no—
678C8—41no—
679C8—41no—
680C8—41no—
681C8—1222no—
682C8—2441no—
683C8—2441no—
684C8—2441no—
685C22—614no—
686C22—1222no—
687C22—1222no—
688C22—1222no—
689C22—1222no—
690C22—1222no—
691C22—1222no—
692C22—1222no—
693C22—1222no—
694C22—1222no—
695C22—2441no—
696C22—2441no—
697C22—2441no—
698C22—2441no—
699C22C2×C4⋊C4×D6111yescharacteristic
700C22C4×D4×D6111yescharacteristic
701C22#1684024411yescharacteristic
702C22C2×M16×D6111yescharacteristic
703C22C2×M16×D6111yescharacteristic
704C22#131×D6111yescharacteristic
705C22#1684052711yescharacteristic
706C4—22no—
707C4—22no—
708C4—22no—
709C4—22no—
710C4—41no—
711C4—41no—
712C4—614no—
713C4—1222no—
714C4—1222no—
715C4—1222no—
716C4—1222no—
717C4—2441no—
718C4#1684039611yescharacteristic
719C4#1684041411yescharacteristic
720C4#1684042711yescharacteristic
721C4#1684046811yescharacteristic
722C2—1224no—
723C2—2442no—
724C2#2144872011yescharacteristic
725C2#423×D6111yescharacteristic
726C2#2145438611yescharacteristic
727C2#435×D6111yescharacteristic
728C2#2145455211yescharacteristic
729C2#2145493511yescharacteristic
730C2#2145494311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D61
commutator, socleC23×C61C23×C4
FittingC61×#1940C2
prime radicalC22×D244C2×C4
cosocleC22×C4×C61C24
hypercenter#1940D61
hypocenterC61#22648
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C22×C4 ◁ #1940

Complements

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

NH ≅ G/Ntype
3. C2×#16839784C2semidirect
4. C2×C4⋊C8×D61C2semidirect
6. #21446543C2semidirect
7. #21446003C2semidirect
8. #21446000C2semidirect
9. #21445998C2semidirect
10. #21445995C2semidirect
11. #21445970C2semidirect
12. #21445798C2semidirect
13. #21445798C2semidirect
14. #21445673C2semidirect
15. C61×#1940C2semidirect
119. #14519706D4semidirect
181. C2×C4×D61M16semidirect
211. #11758198M16semidirect
340. C2×D61#423semidirect
356. Dic61#435semidirect
363. #1940D61semidirect
428. C61#22648semidirect

Maximal subgroups

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

subgroupindex
C2×#168398352
C2×#168398322
C2×#168397842
C2×C4⋊C8×D612
C4×#145197392
#214465432
#214460032
#214460002
#214459982
#214459952
#214459702
#214457982
#214456732
C61×#19402
#2264861