Finite Group Databasebeta

← #21452072

Subgroups — #21452072

Order 7808.

618 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14519763C211yesmaximal, characteristic, complemented
2C2×#14519758C211yesmaximal, characteristic, complemented
3C2×#14519754C211yesmaximal, characteristic, complemented
4C2×#14519749C211yesmaximal, characteristic
5#16839697C211yesmaximal, characteristic, complemented
6#16839686C211yesmaximal, characteristic, complemented
7#16839682C211yesmaximal, characteristic, complemented
8#16839678C211yesmaximal, characteristic, complemented
9#16839677C211yesmaximal, characteristic, complemented
10#16839659C211yesmaximal, characteristic, complemented
11#16839656C211yesmaximal, characteristic, complemented
12#16839639C211yesmaximal, characteristic, complemented
13#16839634C211yesmaximal, characteristic, complemented
14#16839620C211yesmaximal, characteristic, complemented
15C61×#394C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×C22⋊D61C2211yescharacteristic
18C22×C22⋊D61C2211yescharacteristic
19C23×Dic61C2211yescharacteristic
20C23×Dic61C2211yescharacteristic
21#14519763—24no—
22#14519758—24no—
23#14519754—24no—
24#14519749—24no—
25C2×C4⋊Dic61C2211yescharacteristic
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
31C2×#11758196C2211yescharacteristic
32C2×#11758196C2211yescharacteristic
33C2×C22⋊Dic61C2211yescharacteristic
34C2×C22⋊Dic61C2211yescharacteristic
35C2×C22⋊Dic61C2211yescharacteristic
36C2×C22⋊Dic61C2211yescharacteristic
37C2×#11758198C2211yescharacteristic
38C2×#11758198C2211yescharacteristic
39C2×#11758198C2211yescharacteristic
40C2×#11758198C2211yescharacteristic
41C2×#11758198C2211yescharacteristic
42C2×C4×Dic61C2211yescharacteristic
43#14519684C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48C22×D4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C22⋊C4×C61C2211yescharacteristic
51C2×C22⋊C4×C61C2211yescharacteristic
52C2×C22⋊C4×C61C2211yescharacteristic
53C2×C22⋊C4×C61C2211yescharacteristic
54#95×C61C2211yescharacteristic
55C24×C61C2311yescharacteristic
56C24×C61C2311yescharacteristic
57C23×D61C2311yescharacteristic
58C2×D4×C61—22no—
59C2×D4×C61—22no—
60C2×D4×C61—41no—
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×C4×C61C2311yescharacteristic
66C2×C22⋊D61—22no—
67C2×C22⋊D61—22no—
68C2×C22⋊D61—22no—
69C2×C22⋊D61—22no—
70C2×C22⋊D61—41no—
71C2×C22⋊D61—41no—
72C22×Dic61—22no—
73C22×Dic61—22no—
74C22×Dic61—22no—
75C22×Dic61—22no—
76C22×Dic61—41no—
77C22×Dic61—41no—
78C22×Dic61C2311yescharacteristic
79C22×Dic61C2311yescharacteristic
80C22×Dic61C2311yescharacteristic
81C22×Dic61C2311yescharacteristic
82C22×Dic61C2311yescharacteristic
83C22×Dic61C2311yescharacteristic
84C22×Dic61C2311yescharacteristic
85C2×Dic122—22no—
86C2×Dic122—22no—
87C2×Dic122—41no—
88C4⋊C4×C61—41no—
89C22⋊C4×C61—22no—
90C22⋊C4×C61—22no—
91C22⋊C4×C61—41no—
92C22⋊C4×C61—41no—
93C22⋊Dic61—22no—
94C22⋊Dic61—22no—
95C22⋊Dic61D414yes—
96C22⋊Dic61D414yescomplemented
97#11758198—22no—
98#11758198—22no—
99#11758198—22no—
100#11758198—41no—
101#11758198—41no—
102C4⋊Dic61—22no—
103#11758196—22no—
104#11758196—22no—
105#11758196—22no—
106#11758196—22no—
107#11758196—22no—
108#11758196—22no—
109#11758196—41no—
110C4×Dic61—22no—
111C23×C61—21no—
112C23×C61—21no—
113C23×C61—21no—
114C23×C61—21no—
115C23×C61—21no—
116C23×C61—21no—
117C23×C61—21no—
118C23×C61—21no—
119C23×C61—21no—
120C23×C61—21no—
121C23×C61—21no—
122C23×C61—21no—
123C23×C61C2×D412yes—
124C23×C61C2×D412yes—
125C23×C61C2411yescharacteristic
126C22×D61—21no—
127C22×D61—21no—
128C22×D61—21no—
129C22×D61—21no—
130C22×D61—21no—
131C22×D61—21no—
132C22×D61—21no—
133D4×C61—44no—
134C2×C4×C61—21no—
135C2×C4×C61—21no—
136C2×C4×C61—21no—
137C2×C4×C61—21no—
138C2×C4×C61—21no—
139C2×C4×C61—21no—
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—
149C22⋊D61—44no—
150C22⋊D61—44no—
151C2×Dic61—21no—
152C2×Dic61—21no—
153C2×Dic61—21no—
154C2×Dic61—21no—
155C2×Dic61—21no—
156C2×Dic61—21no—
157C2×Dic61—21no—
158C2×Dic61—21no—
159C2×Dic61—21no—
160C2×Dic61—21no—
161C2×Dic61—21no—
162C2×Dic61—21no—
163C2×Dic61—21no—
164C2×Dic61—21no—
165C2×Dic61—21no—
166C2×Dic61—21no—
167C2×Dic61—44no—
168C2×Dic61—44no—
169C2×Dic61C2×D412yes—
170C2×Dic61C2×D412yes—
171C2×Dic61C2×D412yes—
172C2×Dic61C2×D412yes—
173C2×Dic61#4112yes—
174Dic122—44no—
175C22×C61—22no—
176C22×C61—22no—
177C22×C61—22no—
178C22×C61—22no—
179C22×C61—22no—
180C22×C61—22no—
181C22×C61—41no—
182C22×C61—41no—
183C22×C61—41no—
184C22×C61—41no—
185C22×C61—41no—
186C22×C61—41no—
187C22×C61—41no—
188C22×C61—41no—
189C22×C61C22×D411yescharacteristic
190C22×C61C22×D411yescharacteristic
191C22×C61C2×#4111yescharacteristic
192C22×C61H(5,𝔽2)11yescharacteristic
193C22×C61H(5,𝔽2)11yescharacteristic
194C22×C612−1+411yescharacteristic
195C22×C612−1+411yescharacteristic
196C2×D61—41no—
197C2×D61—41no—
198C2×D61—41no—
199C2×D61—41no—
200C2×D61—41no—
201C2×D61—41no—
202C2×D61—41no—
203C4×C61—41no—
204C4×C61—41no—
205C4×C61—41no—
206C4×C61—41no—
207C4×C61—41no—
208Dic61—22no—
209Dic61—22no—
210Dic61—22no—
211Dic61—22no—
212Dic61—22no—
213Dic61—41no—
214Dic61—41no—
215#2672—611nomaximal, Sylow
216C2×C61—42no—
217C2×C61—42no—
218C2×C61#53611yescharacteristic
219C2×C61#53711yescharacteristic
220C2×C61#54211yescharacteristic
221C2×C61D4211yescharacteristic
222C2×C61#54611yescharacteristic
223C2×C61#54711yescharacteristic
224C2×C61#56211yescharacteristic
225D61—81no—
226C2×#124—611no—
227C2×#123—611no—
228C2×C22⋊Q8—611no—
229C2×#121—611no—
230#399—611no—
231#396—611no—
232#395—611no—
233#394—611no—
234#394—611no—
235#394D6111yescharacteristic, complemented
236#389—611no—
237#388—611no—
238#386—611no—
239#385—611no—
240#380—611no—
241C61#267211yescharacteristic, complemented, Sylow
242C22×Q8—611no—
243C22×D4—611no—
244C22×D4—611no—
245C22×D4C2×D6111yescharacteristic
246C23×C4—611no—
247C23×C4—611no—
248#124—1224no—
249#123—1224no—
250C22⋊Q8—1224no—
251#121—1224no—
252C2×C4⋊C4—611no—
253C2×C4⋊C4—611no—
254C2×C4⋊C4—611no—
255C2×C4⋊C4—611no—
256C2×C4⋊C4—611no—
257C2×C4⋊C4—611no—
258C2×C4⋊C4—611no—
259C2×C4⋊C4—611no—
260C2×C4⋊C4C2×D6111yescharacteristic
261C2×C22⋊C4—611no—
262C2×C22⋊C4—611no—
263C2×C22⋊C4—611no—
264C2×C22⋊C4—611no—
265C2×C22⋊C4—611no—
266C2×C22⋊C4—611no—
267C2×C22⋊C4—611no—
268C2×C22⋊C4—611no—
269C2×C22⋊C4—611no—
270C2×C22⋊C4C2×D6111yescharacteristic
271C2×C22⋊C4C2×D6111yescharacteristic
272C2×C22⋊C4C2×D6111yescharacteristic
273C2×C22⋊C4C2×D6111yescharacteristic
274C2×C42—611no—
275#95—611no—
276#95—611no—
277#95—611no—
278#95—611no—
279#95—611no—
280#95C2×D6111yescharacteristic
281C24—611no—
282C24C22×D6111yescharacteristic
283C24C22×D6111yescharacteristic
284C2×Q8—1222no—
285C2×Q8—1222no—
286C2×Q8—2441no—
287C2×D4—22no—
288C2×D4—22no—
289C2×D4—41no—
290C2×D4—1222no—
291C2×D4—1222no—
292C2×D4—1222no—
293C2×D4—1222no—
294C2×D4—2441no—
295C2×D4—2441no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—611no—
302C22×C4—611no—
303C22×C4—1222no—
304C22×C4—1222no—
305C22×C4—1222no—
306C22×C4—1222no—
307C22×C4—2441no—
308C22×C4—2441no—
309C22×C4C22×D6111yescharacteristic
310C22×C4C22×D6111yescharacteristic
311C22×C4C22×D6111yescharacteristic
312C22×C4C22×D6111yescharacteristic
313C22×C4C22×D6111yescharacteristic
314C4⋊C4—41no—
315C4⋊C4—1222no—
316C4⋊C4—1222no—
317C4⋊C4—1222no—
318C4⋊C4—1222no—
319C4⋊C4—1222no—
320C4⋊C4—1222no—
321C4⋊C4—1222no—
322C4⋊C4—2441no—
323C22⋊C4—22no—
324C22⋊C4—22no—
325C22⋊C4—41no—
326C22⋊C4—41no—
327C22⋊C4—614no—
328C22⋊C4—614no—
329C22⋊C4—1222no—
330C22⋊C4—1222no—
331C22⋊C4—1222no—
332C22⋊C4—1222no—
333C22⋊C4—1222no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42—1222no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—21no—
348C23—21no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23D4×D6112yes—
357C23D4×D6112yes—
358C23C23×D6111yescharacteristic
359Q8—2444no—
360D4—44no—
361D4—2444no—
362D4—2444no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—612no—
379C2×C4—612no—
380C2×C4—612no—
381C2×C4—612no—
382C2×C4—612no—
383C2×C4—1221no—
384C2×C4—1221no—
385C2×C4—1221no—
386C2×C4—1221no—
387C2×C4—1221no—
388C2×C4—1221no—
389C2×C4—1221no—
390C2×C4—1221no—
391C2×C4—1221no—
392C2×C4—1221no—
393C2×C4—1221no—
394C2×C4—1221no—
395C2×C4—1221no—
396C2×C4—1221no—
397C2×C4—1221no—
398C2×C4—1221no—
399C2×C4—2444no—
400C2×C4—2444no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—22no—
406C22—22no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—41no—
414C22—41no—
415C22—2441no—
416C22—2441no—
417C22—2441no—
418C22—2441no—
419C22—2441no—
420C22—2441no—
421C22—2441no—
422C22C2×D4×D6111yescharacteristic
423C22C2×D4×D6111yescharacteristic
424C22#41×D6111yescharacteristic
425C22#1451982211yescharacteristic
426C22#1451982211yescharacteristic
427C22#1451982411yescharacteristic
428C22#1451982411yescharacteristic
429C4—41no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—41no—
434C4—1222no—
435C4—1222no—
436C4—1222no—
437C4—1222no—
438C4—1222no—
439C4—2441no—
440C4—2441no—
441C2—42no—
442C2—42no—
443C2—4881no—
444C2#1684033411yescharacteristic
445C2#1684033911yescharacteristic
446C2#1684037611yescharacteristic
447C2#1684039411yescharacteristic
448C2#1684040111yescharacteristic
449C2#1684041011yescharacteristic
450C2#1684050711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#394C2
hypercenter#394D61
hypocenterC61#2672
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #394

Complements

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

NH ≅ G/Ntype
1. C2×#14519763C2semidirect
2. C2×#14519758C2semidirect
3. C2×#14519754C2semidirect
5. #16839697C2semidirect
6. #16839686C2semidirect
7. #16839682C2semidirect
8. #16839678C2semidirect
9. #16839677C2semidirect
10. #16839659C2semidirect
11. #16839656C2semidirect
12. #16839639C2semidirect
13. #16839634C2semidirect
14. #16839620C2semidirect
15. C61×#394C2semidirect
96. C22⋊Dic61D4semidirect
235. #394D61semidirect
241. C61#2672semidirect