Finite Group Databasebeta

← #21455075

Subgroups — #21455075

Order 7808.

754 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#41×D61C211yesmaximal, characteristic
2C2×#14519808C211yesmaximal, characteristic, complemented
3C2×#14519753C211yesmaximal, characteristic, complemented
4#16839923C212yesmaximal, complemented
5#16839921C212yesmaximal, complemented
6#16839916C212yesmaximal, complemented
7#16839911C212yesmaximal, complemented
8#16839764C211yesmaximal, characteristic, complemented
9#16839763C211yesmaximal, characteristic, complemented
10#16839725C211yesmaximal, characteristic, complemented
11C2×#137×C61C211yesmaximal, characteristic, complemented
12C2×#11758226C2211yescharacteristic
13C2×#11758222—21no—
14C2×#11758222C2211yescharacteristic
15C2×#11758224—21no—
16C2×#11758224C2211yescharacteristic
17#41×D61—24no—
18#41×D61—24no—
19C2×Q8×D61C2211yescharacteristic
20C2×D4×D61—21no—
21C2×D4×D61C2211yescharacteristic
22C22×C4×D61—21no—
23C22×C4×D61C2211yescharacteristic
24#14519808—24no—
25C2×#11758202C2212yescomplemented
26C2×#11758201C2212yescomplemented
27C2×#11758194C2211yescharacteristic, complemented
28#14519753—21no—
29#14519753—21no—
30#14519753C2212yes—
31#14519753C2212yescomplemented
32C2×C4⋊Dic61C2211yescharacteristic, complemented
33C2×#11758196—21no—
34C2×#11758198—21no—
35#14519702C2212yescomplemented
36#14519701C2212yescomplemented
37#14519699C2212yescomplemented
38#14519698C2212yescomplemented
39#14519689C2212yes—
40#14519689C2212yescomplemented
41C2×#41×C61C2211yescharacteristic
42C22×Q8×C61C2211yescharacteristic, complemented
43#137×C61—24no—
44C2×Q16×C61C2212yescomplemented
45C2×SD16×C61C2212yescomplemented
46C2×M16×C61C2211yescharacteristic, complemented
47C23×D61—21no—
48C23×D61D411yescharacteristic
49#41×C61—22no—
50#41×C61D414yes—
51C2×Q8×C61—21no—
52C2×Q8×C61—22no—
53C2×Q8×C61—22no—
54C2×Q8×C61C2312yes—
55C2×Q8×C61C2311yescharacteristic
56C2×D4×C61—21no—
57C2×D4×C61C2311yescharacteristic
58C22×C4×C61—21no—
59C22×C4×C61—21no—
60C22×C4×C61C2311yescharacteristic
61C2×C22⋊D61—21no—
62C2×C22⋊D61—21no—
63C2×C22⋊D61—21no—
64C22×Dic61—21no—
65C22×Dic61—21no—
66C22×Dic61D411yescharacteristic
67#11758226—22no—
68#11758226—22no—
69Q8×D61—22no—
70Q8×D61—22no—
71#11758224—28no—
72#11758224—22no—
73#11758224—22no—
74D4×D61—28no—
75D4×D61—22no—
76D4×D61—22no—
77#11758222—28no—
78#11758222—22no—
79#11758222D414yes—
80C2×D244—21no—
81C2×D244C2311yescharacteristic
82C2×C4×D61—28no—
83C2×C4×D61—21no—
84C2×C4×D61—21no—
85C2×C4×D61—22no—
86C2×C4×D61—22no—
87C2×C4×D61—21no—
88C2×C4×D61D411yescharacteristic
89C2×C4×D61D411yescharacteristic
90C2×C4×D61C2311yescharacteristic
91C2×C4×D61C2311yescharacteristic
92C2×Dic122—21no—
93C2×Dic122C2311yescharacteristic
94Q16×C61—24no—
95SD16×C61—24no—
96M16×C61—22no—
97C2×C8×C61C2312yes—
98#11758202—24no—
99#11758201—24no—
100#11758198—22no—
101#11758198—22no—
102C4⋊Dic61—21no—
103C4⋊Dic61C2312yes—
104#11758196—22no—
105#11758196—22no—
106#11758194—22no—
107C2×#92418C2312yes—
108C23×C61—21no—
109C23×C61C2×D411yescharacteristic
110C22×D61—24no—
111C22×D61—22no—
112C22×D61—21no—
113C22×D61—22no—
114C22×D61—41no—
115C22×D61—42no—
116C22×D61—42no—
117C22×D61C2×D411yescharacteristic
118C22×D61C2×D411yescharacteristic
119Q8×C61—21no—
120Q8×C61—22no—
121Q8×C61—22no—
122Q8×C61—42no—
123Q8×C61C2×D412yes—
124D4×C61—24no—
125D4×C61—21no—
126D4×C61C2×D412yes—
127C2×C4×C61—21no—
128C2×C4×C61—24no—
129C2×C4×C61—22no—
130C2×C4×C61—42no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D412yes—
133C2×C4×C61C2×D412yes—
134C2×C4×C61C2411yescharacteristic
135C22⋊D61—24no—
136C22⋊D61—24no—
137C22⋊D61—24no—
138C2×Dic61—24no—
139C2×Dic61—22no—
140C2×Dic61—21no—
141C2×Dic61—22no—
142C2×Dic61—42no—
143C2×Dic61C2×D411yescharacteristic
144C2×Dic61C2×D411yescharacteristic
145D244—24no—
146D244—21no—
147D244C2×D412yes—
148C4×D61—24no—
149C4×D61—24no—
150C4×D61—22no—
151C4×D61—24no—
152C4×D61—22no—
153C4×D61—21no—
154C4×D61—21no—
155C4×D61—21no—
156C4×D61—21no—
157Dic122—24no—
158Dic122—21no—
159Dic122C2×D412yes—
160C8×C61—22no—
161#92418—22no—
162C22×C61—21no—
163C22×C61—21no—
164C22×C61—22no—
165C22×C61—41no—
166C22×C61—41no—
167C22×C61#12012yes—
168C22×C61C22×D411yescharacteristic
169C2×D61—21no—
170C2×D61—21no—
171C2×D61—21no—
172C2×D61—22no—
173C2×D61—21no—
174C2×D61—21no—
175C2×D61—44no—
176C2×D61—48no—
177C2×D61—41no—
178C2×D61—41no—
179C2×D61#13712yescomplemented
180C4×C61—22no—
181C4×C61—42no—
182C4×C61#12012yes—
183C4×C61C22×D411yescharacteristic
184C4×C61C22×D411yescharacteristic
185Dic61—21no—
186Dic61—22no—
187Dic61—21no—
188Dic61—42no—
189#3007—611nomaximal, Sylow
190C2×C61—22no—
191C2×C61—42no—
192C2×C61C2×#12011yescharacteristic
193C2×C61C2×#13711yescharacteristic
194C2×C61#57511yescharacteristic
195D61—22no—
196D61—41no—
197D61—42no—
198C22×#41—611no—
199C2×#137—611no—
200C2×#137D6111yescharacteristic, complemented
201C2×C22⋊Q8—611no—
202#452—612no—
203#452—612no—
204#451—612no—
205#450—612no—
206#417—611no—
207#417—611no—
208#407—611no—
209C61#300711yescharacteristic, complemented, Sylow
210C2×#41—611no—
211C2×#41—611no—
212C2×#41—611no—
213C2×#41—1221no—
214C2×#41—1221no—
215C2×#41—1224no—
216C2×#41—1224no—
217C2×#41C2×D6111yescharacteristic
218C22×Q8—611no—
219C22×Q8C2×D6111yescharacteristic, complemented
220C22×D4—611no—
221C22×D4—1221no—
222C23×C4—611no—
223C23×C4—1221no—
224#137—24no—
225#137—1224no—
226C2×Q16—612no—
227C2×Q16C2×D6112yescomplemented
228C2×SD16—612no—
229C2×SD16C2×D6112yescomplemented
230C2×M16—611no—
231C2×M16C2×D6111yescharacteristic, complemented
232C22⋊Q8—612no—
233C22⋊Q8—612no—
234C22⋊Q8—1221no—
235C22⋊Q8—1221no—
236C2×C4⋊C4—611no—
237C2×C4⋊C4—1221no—
238C2×C22⋊C4—1221no—
239#103—612no—
240#103—612no—
241#102—612no—
242#102—612no—
243C22⋊C8—612no—
244C22⋊C8—612no—
245C24—611no—
246C24—1221no—
247#41—22no—
248#41—614no—
249#41—1228no—
250#41—1222no—
251#41—1228no—
252#41—1222no—
253#41—1222no—
254#41—1222no—
255#41—1222no—
256#41C22⋊D6114yes—
257C2×Q8—21no—
258C2×Q8—22no—
259C2×Q8—22no—
260C2×Q8—611no—
261C2×Q8—1221no—
262C2×Q8—1222no—
263C2×Q8—1222no—
264C2×Q8C22×D6112yes—
265C2×Q8C22×D6111yescharacteristic
266C2×D4—21no—
267C2×D4—611no—
268C2×D4—1221no—
269C2×D4—1221no—
270C2×D4—1222no—
271C2×D4—1228no—
272C2×D4—1221no—
273C2×D4—1221no—
274C2×D4—1222no—
275C2×D4C22×D6111yescharacteristic
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—611no—
279C22×C4—611no—
280C22×C4—611no—
281C22×C4—611no—
282C22×C4—611no—
283C22×C4—1221no—
284C22×C4—1221no—
285C22×C4—1228no—
286C22×C4—1221no—
287C22×C4—1222no—
288C22×C4—1221no—
289C22×C4—1222no—
290C22×C4—1221no—
291C22×C4C22×D6111yescharacteristic
292Q16—24no—
293Q16—1224no—
294SD16—24no—
295SD16—1224no—
296M16—22no—
297M16—1222no—
298C2×C8—612no—
299C2×C8C22×D6112yes—
300C4⋊C4—612no—
301C4⋊C4—1222no—
302C4⋊C4—1222no—
303C4⋊C4—1221no—
304C22⋊C4—1222no—
305C22⋊C4—1222no—
306C23—21no—
307C23—611no—
308C23—611no—
309C23—1222no—
310C23—1224no—
311C23—1221no—
312C23—1222no—
313C23—2441no—
314C23—2442no—
315C23—2442no—
316C23D4×D6111yescharacteristic
317Q8—21no—
318Q8—22no—
319Q8—22no—
320Q8—42no—
321Q8—612no—
322Q8—1224no—
323Q8—1221no—
324Q8C2×C22⋊D6112yes—
325D4—24no—
326D4—21no—
327D4—612no—
328D4—1224no—
329D4—1224no—
330D4—1224no—
331D4—1224no—
332D4—1221no—
333D4C2×C22⋊D6112yes—
334C2×C4—21no—
335C2×C4—24no—
336C2×C4—22no—
337C2×C4—42no—
338C2×C4—611no—
339C2×C4—611no—
340C2×C4—1224no—
341C2×C4—1224no—
342C2×C4—1224no—
343C2×C4—1221no—
344C2×C4—1222no—
345C2×C4—1221no—
346C2×C4—1221no—
347C2×C4—1221no—
348C2×C4—1221no—
349C2×C4—1222no—
350C2×C4—1222no—
351C2×C4—1224no—
352C2×C4—1222no—
353C2×C4—2442no—
354C2×C4D4×D6112yes—
355C2×C4D4×D6111yescharacteristic
356C2×C4C2×C22⋊D6112yes—
357C2×C4C23×D6111yescharacteristic
358C8—22no—
359C8—1222no—
360C22—21no—
361C22—21no—
362C22—22no—
363C22—41no—
364C22—41no—
365C22—612no—
366C22—1221no—
367C22—1221no—
368C22—1222no—
369C22—1221no—
370C22—1221no—
371C22—1221no—
372C22—2444no—
373C22—2448no—
374C22—2441no—
375C22—2441no—
376C22#1451974512yes—
377C22C2×D4×D6111yescharacteristic
378C4—22no—
379C4—42no—
380C4—1221no—
381C4—1221no—
382C4—1222no—
383C4—2442no—
384C4#1451974512yes—
385C4C2×D4×D6111yescharacteristic
386C4C22×C22⋊D6111yescharacteristic
387C2—22no—
388C2—42no—
389C2—1222no—
390C2—2441no—
391C2—2442no—
392C2C2×#1451974511yescharacteristic
393C2#137×D6111yescharacteristic
394C2#1684056111yescharacteristic
subgroupG/H
centerC22C2×D4×D61
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC22×C61C22×D4
hypercenterC2×#137D61
hypocenterC61#3007
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#14519808C2semidirect
3. C2×#14519753C2semidirect
4. #16839923C2semidirect
5. #16839921C2semidirect
6. #16839916C2semidirect
7. #16839911C2semidirect
8. #16839764C2semidirect
9. #16839763C2semidirect
10. #16839725C2semidirect
11. C2×#137×C61C2semidirect
25. C2×#11758202C22semidirect
26. C2×#11758201C22semidirect
27. C2×#11758194C22semidirect
31. #14519753C22semidirect
32. C2×C4⋊Dic61C22semidirect
35. #14519702C22semidirect
36. #14519701C22semidirect
37. #14519699C22semidirect
38. #14519698C22semidirect
40. #14519689C22semidirect
42. C22×Q8×C61C22semidirect
44. C2×Q16×C61C22semidirect
45. C2×SD16×C61C22semidirect
46. C2×M16×C61C22semidirect
179. C2×D61#137semidirect
200. C2×#137D61semidirect
209. C61#3007semidirect
219. C22×Q8C2×D61semidirect
227. C2×Q16C2×D61semidirect
229. C2×SD16C2×D61semidirect
231. C2×M16C2×D61semidirect