Finite Group Databasebeta

← #21452067

Subgroups — #21452067

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×#14519765C211yesmaximal, characteristic, complemented
2C2×#14519762C211yesmaximal, characteristic, complemented
3C2×#14519755C211yesmaximal, characteristic, complemented
4C2×#14519752C211yesmaximal, characteristic
5#16839697C211yesmaximal, characteristic, complemented
6#16839686C211yesmaximal, characteristic, complemented
7#16839682C211yesmaximal, characteristic, complemented
8#16839680C211yesmaximal, characteristic, complemented
9#16839679C211yesmaximal, characteristic, complemented
10#16839679C211yesmaximal, characteristic, complemented
11#16839653C211yesmaximal, characteristic, complemented
12#16839640C211yesmaximal, characteristic, complemented
13#16839633C211yesmaximal, characteristic, complemented
14#16839621C211yesmaximal, characteristic, complemented
15C61×#389C211yesmaximal, characteristic, complemented
16C22×Dic122C2211yescharacteristic
17C22×D244C2211yescharacteristic
18C22×D244C2211yescharacteristic
19C22×D244C2211yescharacteristic
20C22×C4×D61C2211yescharacteristic
21C22×C4×D61C2211yescharacteristic
22#14519765—24no—
23#14519762—24no—
24#14519755—24no—
25#14519752—24no—
26C2×#11758196C2211yescharacteristic
27C2×#11758196C2211yescharacteristic
28C2×#11758196C2211yescharacteristic
29C2×#11758196C2211yescharacteristic
30C2×#11758196C2211yescharacteristic
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×#11758198C2211yescharacteristic
44#14519684C2211yescharacteristic
45#14519684C2211yescharacteristic
46#14519684C2211yescharacteristic
47#14519684C2211yescharacteristic
48C2×C4⋊C4×C61C2211yescharacteristic
49C2×C4⋊C4×C61C2211yescharacteristic
50C2×C4⋊C4×C61C2211yescharacteristic
51C2×C4⋊C4×C61C2211yescharacteristic
52C2×C42×C61C2211yescharacteristic
53#95×C61C2211yescharacteristic
54#95×C61C2211yescharacteristic
55C23×D61C2311yescharacteristic
56C23×D61C2311yescharacteristic
57C23×D61C2311yescharacteristic
58C22×C4×C61C2311yescharacteristic
59C22×C4×C61C2311yescharacteristic
60C22×C4×C61C2311yescharacteristic
61C22×C4×C61C2311yescharacteristic
62C22×C4×C61C2311yescharacteristic
63C22×C4×C61C2311yescharacteristic
64C22×C4×C61C2311yescharacteristic
65C22×Dic61C2311yescharacteristic
66C22×Dic61C2311yescharacteristic
67C22×Dic61C2311yescharacteristic
68C22×Dic61C2311yescharacteristic
69C22×Dic61C2311yescharacteristic
70C2×D244—22no—
71C2×D244—22no—
72C2×D244—22no—
73C2×D244—22no—
74C2×D244—22no—
75C2×D244—22no—
76C2×D244—41no—
77C2×D244—41no—
78C2×D244—41no—
79C2×C4×D61—22no—
80C2×C4×D61—22no—
81C2×C4×D61—22no—
82C2×C4×D61—22no—
83C2×C4×D61—41no—
84C2×C4×D61—41no—
85C2×Dic122—22no—
86C2×Dic122—22no—
87C2×Dic122—41no—
88C4⋊C4×C61—22no—
89C4⋊C4×C61—22no—
90C4⋊C4×C61—22no—
91C4⋊C4×C61—22no—
92C42×C61—22no—
93#11758198—22no—
94#11758198—22no—
95#11758198—22no—
96#11758198—22no—
97#11758198—22no—
98#11758198—22no—
99#11758198—22no—
100#11758198—41no—
101#11758198—41no—
102#11758198—41no—
103#11758198—41no—
104#11758198D414yes—
105#11758198D414yescomplemented
106#11758196—22no—
107#11758196—22no—
108#11758196—22no—
109#11758196—41no—
110#11758196—41no—
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×D61C2×D412yes—
132C22×D61C2×D412yes—
133C2×C4×C61—21no—
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—
149C2×C4×C61—21no—
150C2×C4×C61—21no—
151C2×C4×C61C2×D412yes—
152C2×C4×C61C2×D412yes—
153C2×C4×C61#4112yes—
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×Dic61C2×D412yes—
168C2×Dic61C2×D412yes—
169D244—44no—
170D244—44no—
171D244—44no—
172C4×D61—44no—
173C4×D61—44no—
174Dic122—44no—
175C22×C61C22×D411yescharacteristic
176C22×C61C22×D411yescharacteristic
177C22×C61C2×#4111yescharacteristic
178C22×C61H(5,𝔽2)11yescharacteristic
179C22×C61H(5,𝔽2)11yescharacteristic
180C22×C612−1+411yescharacteristic
181C22×C612−1+411yescharacteristic
182C2×D61—22no—
183C2×D61—22no—
184C2×D61—22no—
185C2×D61—22no—
186C2×D61—22no—
187C2×D61—22no—
188C2×D61—41no—
189C2×D61—41no—
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—
203C4×C61—22no—
204C4×C61—22no—
205C4×C61—22no—
206C4×C61—41no—
207C4×C61—41no—
208C4×C61—41no—
209C4×C61—41no—
210Dic61—22no—
211Dic61—22no—
212Dic61—41no—
213Dic61—41no—
214Dic61—41no—
215#2672—611nomaximal, Sylow
216C2×C61#53611yescharacteristic
217C2×C61#53711yescharacteristic
218C2×C61#54211yescharacteristic
219C2×C61D4211yescharacteristic
220C2×C61#54611yescharacteristic
221C2×C61#54711yescharacteristic
222C2×C61#56211yescharacteristic
223D61—42no—
224D61—42no—
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#394—611no—
236#389D6111yescharacteristic, complemented
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×D4—611no—
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⋊C4C2×D6111yescharacteristic
258C2×C4⋊C4C2×D6111yescharacteristic
259C2×C4⋊C4C2×D6111yescharacteristic
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⋊C4—611no—
271C2×C22⋊C4—611no—
272C2×C22⋊C4—611no—
273C2×C22⋊C4—611no—
274C2×C42C2×D6111yescharacteristic
275#95—611no—
276#95—611no—
277#95—611no—
278#95—611no—
279#95C2×D6111yescharacteristic
280#95C2×D6111yescharacteristic
281C24—611no—
282C24—611no—
283C24—611no—
284C2×Q8—1222no—
285C2×Q8—1222no—
286C2×Q8—2441no—
287C2×D4—1222no—
288C2×D4—1222no—
289C2×D4—1222no—
290C2×D4—1222no—
291C2×D4—1222no—
292C2×D4—1222no—
293C2×D4—2441no—
294C2×D4—2441no—
295C2×D4—2441no—
296C22×C4—611no—
297C22×C4—611no—
298C22×C4—611no—
299C22×C4—611no—
300C22×C4—611no—
301C22×C4—1222no—
302C22×C4—1222no—
303C22×C4—1222no—
304C22×C4—1222no—
305C22×C4—2441no—
306C22×C4—2441no—
307C22×C4C22×D6111yescharacteristic
308C22×C4C22×D6111yescharacteristic
309C22×C4C22×D6111yescharacteristic
310C22×C4C22×D6111yescharacteristic
311C22×C4C22×D6111yescharacteristic
312C22×C4C22×D6111yescharacteristic
313C22×C4C22×D6111yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—22no—
316C4⋊C4—22no—
317C4⋊C4—22no—
318C4⋊C4—1222no—
319C4⋊C4—1222no—
320C4⋊C4—1222no—
321C4⋊C4—2441no—
322C4⋊C4—2441no—
323C22⋊C4—614no—
324C22⋊C4—614no—
325C22⋊C4—1222no—
326C22⋊C4—1222no—
327C22⋊C4—1222no—
328C22⋊C4—1222no—
329C22⋊C4—1222no—
330C22⋊C4—1222no—
331C22⋊C4—1222no—
332C22⋊C4—2441no—
333C22⋊C4—2441no—
334C22⋊C4—2441no—
335C22⋊C4—2441no—
336C42—22no—
337C23—612no—
338C23—612no—
339C23—1221no—
340C23—1221no—
341C23—1221no—
342C23—1221no—
343C23—1221no—
344C23—1221no—
345C23—1221no—
346C23—1221no—
347C23—1221no—
348C23—1221no—
349C23—1221no—
350C23—1221no—
351C23—1221no—
352C23—1221no—
353C23—1221no—
354C23—1221no—
355C23—1221no—
356C23—1221no—
357C23—1221no—
358C23C23×D6111yescharacteristic
359Q8—2444no—
360D4—2444no—
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—21no—
379C2×C4—21no—
380C2×C4—21no—
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—2444no—
397C2×C4—2444no—
398C2×C4#1175822212yes—
399C2×C4D4×D6112yes—
400C2×C4D4×D6112yes—
401C22—1222no—
402C22—1222no—
403C22—1222no—
404C22—1222no—
405C22—1222no—
406C22—1222no—
407C22—2441no—
408C22—2441no—
409C22—2441no—
410C22—2441no—
411C22—2441no—
412C22—2441no—
413C22—2441no—
414C22—2441no—
415C22—2441no—
416C22—2441no—
417C22—2441no—
418C22—2441no—
419C22—2441no—
420C22—2441no—
421C22—2441no—
422C22C2×D4×D6111yescharacteristic
423C22C2×D4×D6111yescharacteristic
424C22C2×#1175822211yescharacteristic
425C22#1451982311yescharacteristic
426C22#1451982311yescharacteristic
427C22#1451982511yescharacteristic
428C22#1451982511yescharacteristic
429C4—22no—
430C4—22no—
431C4—22no—
432C4—41no—
433C4—41no—
434C4—41no—
435C4—41no—
436C4—1222no—
437C4—1222no—
438C4—2441no—
439C4—2441no—
440C4—2441no—
441C2—4881no—
442C2—2442no—
443C2—2442no—
444C2#1684033711yescharacteristic
445C2#1684034211yescharacteristic
446C2#1684038411yescharacteristic
447C2#1684039611yescharacteristic
448C2#1684040811yescharacteristic
449C2#1684041311yescharacteristic
450C2#1684051011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D61
commutator, socleC23×C61C24
FittingC61×#389C2
hypercenter#389D61
hypocenterC61#2672
LCSG ▷ C23×C61 ▷ C61
UCSC1 ◁ C23 ◁ #389

Complements

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

NH ≅ G/Ntype
1. C2×#14519765C2semidirect
2. C2×#14519762C2semidirect
3. C2×#14519755C2semidirect
5. #16839697C2semidirect
6. #16839686C2semidirect
7. #16839682C2semidirect
8. #16839680C2semidirect
9. #16839679C2semidirect
10. #16839679C2semidirect
11. #16839653C2semidirect
12. #16839640C2semidirect
13. #16839633C2semidirect
14. #16839621C2semidirect
15. C61×#389C2semidirect
105. #11758198D4semidirect
236. #389D61semidirect
241. C61#2672semidirect