Finite Group Databasebeta

← #21452613

Subgroups — #21452613

Order 7808.

598 conjugacy classes of subgroups.

The subgroup lattice has 476 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519772C211yesmaximal, characteristic, complemented
2C2×#14519752C211yesmaximal, characteristic, complemented
3#16839689C211yesmaximal, characteristic, complemented
4#16839680C211yesmaximal, characteristic, complemented
5#16839679C211yesmaximal, characteristic, complemented
6#16839672C211yesmaximal, characteristic, complemented
7#16839672C211yesmaximal, characteristic, complemented
8#16839672C211yesmaximal, characteristic, complemented
9#16839664C211yesmaximal, characteristic, complemented
10#16839664C211yesmaximal, characteristic, complemented
11#16839663C211yesmaximal, characteristic, complemented
12#16839654C211yesmaximal, characteristic, complemented
13#16839640C211yesmaximal, characteristic, complemented
14#16839636C211yesmaximal, characteristic, complemented
15C61×#387C211yesmaximal, characteristic, complemented
16C22×D244C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×D244C2211yescharacteristic
20C22×D244C2211yescharacteristic
21C22×D244C2211yescharacteristic
22C22×C4×D61C2211yescharacteristic
23#14519772—24no—
24#14519752—24no—
25C2×C4⋊Dic61C2211yescharacteristic
26C2×C4⋊Dic61C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758198C2211yescharacteristic
29C2×#11758198C2211yescharacteristic
30C2×#11758198C2211yescharacteristic
31C2×#11758198C2211yescharacteristic
32C2×#11758198C2211yescharacteristic
33C2×#11758198C2211yescharacteristic
34C2×#11758198C2211yescharacteristic
35C2×#11758198C2211yescharacteristic
36C2×#11758198C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×#11758198C2211yescharacteristic
43C2×C4×Dic61C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46C2×C4⋊C4×C61C2211yescharacteristic
47C2×C4⋊C4×C61C2211yescharacteristic
48C2×C42×C61C2211yescharacteristic
49#95×C61C2211yescharacteristic
50#95×C61C2211yescharacteristic
51#95×C61C2211yescharacteristic
52#95×C61C2211yescharacteristic
53C23×D61C2311yescharacteristic
54C23×D61C2311yescharacteristic
55C23×D61C2311yescharacteristic
56C23×D61C2311yescharacteristic
57C22×C4×C61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×Dic61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C2×D244—22no—
69C2×D244—22no—
70C2×D244—22no—
71C2×D244—22no—
72C2×D244—22no—
73C2×D244—22no—
74C2×D244—22no—
75C2×D244—41no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×D244—41no—
80C2×D244—41no—
81C2×D244—41no—
82C2×D244—41no—
83C2×D244—41no—
84C2×D244—41no—
85C2×D244—41no—
86C2×C4×D61—22no—
87C2×C4×D61—41no—
88C2×C4×D61—41no—
89C4⋊C4×C61—41no—
90C4⋊C4×C61D414yescomplemented
91C42×C61—41no—
92#11758198—22no—
93#11758198—22no—
94#11758198—22no—
95#11758198—22no—
96#11758198—22no—
97#11758198—22no—
98#11758198—22no—
99#11758198—41no—
100#11758198—41no—
101#11758198—41no—
102#11758198—41no—
103#11758198—41no—
104#11758198—41no—
105#11758198—41no—
106#11758198—41no—
107C4⋊Dic61—22no—
108C4⋊Dic61—41no—
109#11758196—22no—
110C4×Dic61—22no—
111C23×C61C2411yescharacteristic
112C22×D61—21no—
113C22×D61—21no—
114C22×D61—21no—
115C22×D61—21no—
116C22×D61—21no—
117C22×D61—21no—
118C22×D61—21no—
119C22×D61—21no—
120C22×D61—21no—
121C22×D61—21no—
122C22×D61—21no—
123C22×D61—21no—
124C22×D61—21no—
125C22×D61—21no—
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133C22×D61—21no—
134C22×D61—21no—
135C22×D61—21no—
136C22×D61—21no—
137C22×D61—21no—
138C22×D61—21no—
139C22×D61#4112yes—
140C2×C4×C61—21no—
141C2×C4×C61—21no—
142C2×C4×C61—21no—
143C2×C4×C61—21no—
144C2×C4×C61—21no—
145C2×C4×C61—21no—
146C2×C4×C61—21no—
147C2×C4×C61—21no—
148C2×C4×C61—21no—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61—21no—
152C2×C4×C61—21no—
153C2×C4×C61—21no—
154C2×C4×C61—21no—
155C2×C4×C61—21no—
156C2×C4×C61—21no—
157C2×C4×C61C2×D412yes—
158C2×C4×C61C2×D412yes—
159C2×C4×C61C2×D412yes—
160C2×C4×C61#4112yes—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—21no—
168C2×Dic61—21no—
169C2×Dic61—21no—
170C2×Dic61—21no—
171C2×Dic61—21no—
172C2×Dic61—21no—
173D244—44no—
174D244—44no—
175D244—44no—
176D244—44no—
177D244—44no—
178D244—44no—
179C4×D61—44no—
180C22×C61C22×D411yescharacteristic
181C22×C61C2×#4111yescharacteristic
182C22×C61C2×#4111yescharacteristic
183C22×C61H(5,𝔽2)11yescharacteristic
184C22×C61H(5,𝔽2)11yescharacteristic
185C22×C61H(5,𝔽2)11yescharacteristic
186C22×C61H(5,𝔽2)11yescharacteristic
187C2×D61—22no—
188C2×D61—22no—
189C2×D61—22no—
190C2×D61—41no—
191C2×D61—41no—
192C2×D61—41no—
193C2×D61—41no—
194C2×D61—41no—
195C2×D61—41no—
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C2×D61—41no—
204C2×D61—41no—
205C2×D61—41no—
206C2×D61—41no—
207C2×D61—41no—
208C2×D61—41no—
209C2×D61—41no—
210C2×D61—41no—
211C2×D61—41no—
212C2×D61—41no—
213C2×D61—41no—
214C2×D61—41no—
215C4×C61—22no—
216C4×C61—22no—
217C4×C61—22no—
218C4×C61—22no—
219C4×C61—41no—
220C4×C61—41no—
221C4×C61—41no—
222Dic61—41no—
223Dic61—41no—
224Dic61—41no—
225Dic61—41no—
226#2714—611nomaximal, Sylow
227C2×C61#53511yescharacteristic
228C2×C61#53811yescharacteristic
229C2×C61#53811yescharacteristic
230C2×C61#54611yescharacteristic
231C2×C61#55011yescharacteristic
232C2×C61#55311yescharacteristic
233C2×C61#56011yescharacteristic
234D61—42no—
235D61—81no—
236D61—81no—
237D61—81no—
238C2×#126—611no—
239C2×#121—611no—
240#397—611no—
241#394—611no—
242#394—611no—
243#392—611no—
244#392—611no—
245#392—611no—
246#390—611no—
247#390—611no—
248#390—611no—
249#388—611no—
250#387D6111yescharacteristic, complemented
251#386—611no—
252#385—611no—
253C61#271411yescharacteristic, complemented, Sylow
254C22×D4—611no—
255C22×D4—611no—
256C22×D4—611no—
257C22×D4—611no—
258C22×D4—611no—
259C22×D4—611no—
260C23×C4—611no—
261#126—1224no—
262#121—1224no—
263C2×C4⋊C4—611no—
264C2×C4⋊C4—611no—
265C2×C4⋊C4—611no—
266C2×C4⋊C4C2×D6111yescharacteristic
267C2×C4⋊C4C2×D6111yescharacteristic
268C2×C22⋊C4—611no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4—611no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—611no—
274C2×C22⋊C4—611no—
275C2×C22⋊C4—611no—
276C2×C22⋊C4—611no—
277C2×C22⋊C4—611no—
278C2×C22⋊C4—611no—
279C2×C22⋊C4—611no—
280C2×C22⋊C4—611no—
281C2×C22⋊C4—611no—
282C2×C22⋊C4—611no—
283C2×C42—611no—
284C2×C42C2×D6111yescharacteristic
285#95—611no—
286#95—611no—
287#95C2×D6111yescharacteristic
288#95C2×D6111yescharacteristic
289#95C2×D6111yescharacteristic
290#95C2×D6111yescharacteristic
291C24—611no—
292C24—611no—
293C24—611no—
294C24—611no—
295C2×D4—1222no—
296C2×D4—1222no—
297C2×D4—1222no—
298C2×D4—1222no—
299C2×D4—1222no—
300C2×D4—1222no—
301C2×D4—1222no—
302C2×D4—2441no—
303C2×D4—2441no—
304C2×D4—2441no—
305C2×D4—2441no—
306C2×D4—2441no—
307C2×D4—2441no—
308C2×D4—2441no—
309C2×D4—2441no—
310C2×D4—2441no—
311C2×D4—2441no—
312C2×D4—2441no—
313C22×C4—611no—
314C22×C4—611no—
315C22×C4—611no—
316C22×C4—611no—
317C22×C4—1222no—
318C22×C4—2441no—
319C22×C4—2441no—
320C22×C4C22×D6111yescharacteristic
321C22×C4C22×D6111yescharacteristic
322C22×C4C22×D6111yescharacteristic
323C22×C4C22×D6111yescharacteristic
324C22×C4C22×D6111yescharacteristic
325C22×C4C22×D6111yescharacteristic
326C22×C4C22×D6111yescharacteristic
327C4⋊C4—41no—
328C4⋊C4—1222no—
329C4⋊C4—1222no—
330C4⋊C4—2441no—
331C4⋊C4D24414yescomplemented
332C22⋊C4—1222no—
333C22⋊C4—1222no—
334C22⋊C4—1222no—
335C22⋊C4—1222no—
336C22⋊C4—1222no—
337C22⋊C4—1222no—
338C22⋊C4—1222no—
339C22⋊C4—2441no—
340C22⋊C4—2441no—
341C22⋊C4—2441no—
342C22⋊C4—2441no—
343C22⋊C4—2441no—
344C22⋊C4—2441no—
345C22⋊C4—2441no—
346C22⋊C4—2441no—
347C42—41no—
348C42—1222no—
349C23—612no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—1221no—
357C23—1221no—
358C23—1221no—
359C23—1221no—
360C23—1221no—
361C23—1221no—
362C23—1221no—
363C23—1221no—
364C23—1221no—
365C23—1221no—
366C23—1221no—
367C23—1221no—
368C23—1221no—
369C23—1221no—
370C23—1221no—
371C23—1221no—
372C23—1221no—
373C23—1221no—
374C23—1221no—
375C23—1221no—
376C23—1221no—
377C23C23×D6111yescharacteristic
378D4—2444no—
379D4—2444no—
380D4—2444no—
381D4—2444no—
382D4—2444no—
383D4—2444no—
384C2×C4—21no—
385C2×C4—21no—
386C2×C4—21no—
387C2×C4—21no—
388C2×C4—21no—
389C2×C4—21no—
390C2×C4—21no—
391C2×C4—21no—
392C2×C4—21no—
393C2×C4—21no—
394C2×C4—21no—
395C2×C4—21no—
396C2×C4—21no—
397C2×C4—21no—
398C2×C4—21no—
399C2×C4—21no—
400C2×C4—21no—
401C2×C4—1221no—
402C2×C4—1221no—
403C2×C4—1221no—
404C2×C4—1221no—
405C2×C4—1221no—
406C2×C4—1221no—
407C2×C4—1221no—
408C2×C4—1221no—
409C2×C4—1221no—
410C2×C4—1221no—
411C2×C4—1221no—
412C2×C4—1221no—
413C2×C4—2444no—
414C2×C4C2×D24412yes—
415C2×C4C2×D24412yes—
416C2×C4C2×D24412yes—
417C2×C4#1175822612yes—
418C22—1222no—
419C22—1222no—
420C22—1222no—
421C22—2441no—
422C22—2441no—
423C22—2441no—
424C22—2441no—
425C22—2441no—
426C22—2441no—
427C22—2441no—
428C22—2441no—
429C22—2441no—
430C22—2441no—
431C22—2441no—
432C22—2441no—
433C22—2441no—
434C22—2441no—
435C22—2441no—
436C22—2441no—
437C22—2441no—
438C22—2441no—
439C22—2441no—
440C22—2441no—
441C22—2441no—
442C22—2441no—
443C22—2441no—
444C22—2441no—
445C22—2441no—
446C22C22×D24411yescharacteristic
447C22#41×D6111yescharacteristic
448C22C2×#1175822611yescharacteristic
449C22#1451982211yescharacteristic
450C22#1451982311yescharacteristic
451C22#1451982311yescharacteristic
452C22#1451982311yescharacteristic
453C4—22no—
454C4—22no—
455C4—22no—
456C4—22no—
457C4—41no—
458C4—41no—
459C4—41no—
460C4—2441no—
461C4—2441no—
462C4—2441no—
463C4—2441no—
464C2—4881no—
465C2—4881no—
466C2—4881no—
467C2—2442no—
468C2#1684033111yescharacteristic
469C2#1684035111yescharacteristic
470C2#1684035211yescharacteristic
471C2#1684040711yescharacteristic
472C2#1684043411yescharacteristic
473C2#1684046511yescharacteristic
474C2#1684050211yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#387C2
hypercenter#387D61
hypocenterC61#2714
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
1. C2×#14519772C2semidirect
2. C2×#14519752C2semidirect
3. #16839689C2semidirect
4. #16839680C2semidirect
5. #16839679C2semidirect
6. #16839672C2semidirect
7. #16839672C2semidirect
8. #16839672C2semidirect
9. #16839664C2semidirect
10. #16839664C2semidirect
11. #16839663C2semidirect
12. #16839654C2semidirect
13. #16839640C2semidirect
14. #16839636C2semidirect
15. C61×#387C2semidirect
90. C4⋊C4×C61D4semidirect
250. #387D61semidirect
253. C61#2714semidirect
331. C4⋊C4D244semidirect