Finite Group Databasebeta

← #21455195

Subgroups — #21455195

Order 7808.

704 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 704 conjugacy classes of subgroups — too many to draw. Only its 145 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#16840598C211yesmaximal, characteristic
2C2×#14519808C211yesmaximal, characteristic, complemented
3#16840336C211yesmaximal, characteristic, complemented
4#16839943C214yesmaximal, complemented
5#16839938C214yesmaximal, complemented
6#16839779C211yesmaximal, characteristic, complemented
7#16839778C211yesmaximal, characteristic, complemented
8#16839744C211yesmaximal, characteristic, complemented
9C2×#137×C61C211yesmaximal, characteristic, complemented
10#14519825—21no—
11#14519824—21no—
12#14519824C2212yes—
13#14519823—21no—
14#14519823C2212yes—
15#14519822—21no—
16#14519822—22no—
17C2×#11758222—22no—
18C2×#11758222C2211yescharacteristic
19C2×#11758222C2211yescharacteristic
20#41×D61—22no—
21#41×D61—22no—
22#14519808—22no—
23#14519808C2214yescomplemented
24C2×#11758202—21no—
25C2×#11758201—21no—
26C2×#11758194C2211yescharacteristic, complemented
27#14519775C2212yescomplemented
28#14519766C2212yescomplemented
29#14519760—22no—
30#14519753—22no—
31#14519736C2211yescharacteristic, complemented
32#14519704C2214yescomplemented
33#14519703C2214yescomplemented
34#14519695C2212yescomplemented
35#14519693C2212yescomplemented
36C2×#41×C61C2211yescharacteristic
37C22×Q8×C61C2211yescharacteristic, complemented
38#137×C61—22no—
39#137×C61C2214yescomplemented
40C2×Q16×C61—21no—
41C2×SD16×C61—21no—
42C2×M16×C61C2211yescharacteristic, complemented
43#41×C61—21no—
44#41×C61—21no—
45#41×C61D412yes—
46#41×C61C2312yes—
47C2×Q8×C61—21no—
48C2×Q8×C61—21no—
49C2×Q8×C61—21no—
50C2×Q8×C61—21no—
51C2×Q8×C61—21no—
52C2×Q8×C61D411yescharacteristic
53C2×Q8×C61C2312yes—
54C2×D4×C61—21no—
55C2×D4×C61D411yescharacteristic
56C22×C4×C61—21no—
57C22×C4×C61—21no—
58C22×C4×C61C2311yescharacteristic
59C2×C22⋊D61—24no—
60C2×C22⋊D61—21no—
61C2×C22⋊D61D412yes—
62#11758226—22no—
63#11758226—22no—
64Q8×D61—22no—
65Q8×D61—22no—
66#11758224—24no—
67#11758224—22no—
68#11758224—22no—
69#11758224—24no—
70D4×D61—24no—
71D4×D61—22no—
72D4×D61—24no—
73D4×D61—22no—
74#11758222—24no—
75#11758222—24no—
76#11758222—21no—
77#11758222—21no—
78#11758222—21no—
79#11758222—21no—
80#11758222—21no—
81#11758222—21no—
82#11758222—22no—
83#11758222—22no—
84#11758222D412yes—
85#11758222C2312yes—
86C2×D244—22no—
87C2×D244D411yescharacteristic
88C2×D244C2311yescharacteristic
89C2×C4×D61—24no—
90C2×C4×D61—21no—
91C2×C4×D61D412yes—
92C2×Dic122—22no—
93C2×Dic122D411yescharacteristic
94C2×Dic122C2311yescharacteristic
95Q16×C61—24no—
96SD16×C61—24no—
97M16×C61—21no—
98M16×C61C2312yes—
99C2×C8×C61—21no—
100C22⋊Dic61—21no—
101#11758202—24no—
102#11758201—24no—
103#11758198—24no—
104C4⋊Dic61—21no—
105#11758196—24no—
106C4×Dic61C2312yes—
107#11758194—21no—
108#11758194C2312yes—
109C2×#92418—21no—
110C23×C61—21no—
111C23×C61C2×D411yescharacteristic
112C22×D61—24no—
113C22×D61—21no—
114C22×D61C2×D412yes—
115Q8×C61—21no—
116Q8×C61—22no—
117Q8×C61—22no—
118Q8×C61—41no—
119Q8×C61—41no—
120Q8×C61C2×D412yes—
121D4×C61—22no—
122D4×C61—22no—
123D4×C61—21no—
124D4×C61C2×D412yes—
125C2×C4×C61—21no—
126C2×C4×C61—22no—
127C2×C4×C61—22no—
128C2×C4×C61—22no—
129C2×C4×C61—41no—
130C2×C4×C61—41no—
131C2×C4×C61C2×D411yescharacteristic
132C2×C4×C61C2×D411yescharacteristic
133C2×C4×C61C2×D411yescharacteristic
134C2×C4×C61C2×D411yescharacteristic
135C2×C4×C61C2×D411yescharacteristic
136C2×C4×C61C2411yescharacteristic
137C22⋊D61—24no—
138C22⋊D61—24no—
139C22⋊D61—22no—
140C22⋊D61—22no—
141C22⋊D61—22no—
142C22⋊D61—22no—
143C2×Dic61—24no—
144C2×Dic61—21no—
145C2×Dic61—22no—
146C2×Dic61C2×D412yes—
147D244—24no—
148D244—21no—
149D244—21no—
150D244—21no—
151D244C2×D412yes—
152C4×D61—24no—
153C4×D61—24no—
154C4×D61—22no—
155C4×D61—22no—
156C4×D61—22no—
157C4×D61—22no—
158Dic122—24no—
159Dic122—21no—
160Dic122—21no—
161Dic122—21no—
162Dic122C2×D412yes—
163C8×C61—22no—
164#92418—22no—
165C22×C61—22no—
166C22×C61—41no—
167C22×C61—81no—
168C22×C61#12011yescharacteristic
169C22×C61#12011yescharacteristic
170C22×C61C22×D411yescharacteristic
171C2×D61—22no—
172C2×D61—22no—
173C2×D61—42no—
174C2×D61—81no—
175C2×D61—84no—
176C4×C61—22no—
177C4×C61—42no—
178C4×C61#12011yescharacteristic
179C4×C61#12011yescharacteristic
180C4×C61C22×D411yescharacteristic
181C4×C61C22×D411yescharacteristic
182Dic61—22no—
183Dic61—22no—
184Dic61—42no—
185#3022—611nomaximal, Sylow
186C2×C61—21no—
187C2×C61—21no—
188C2×C61—21no—
189C2×C61—42no—
190C2×C61C2×#12011yescharacteristic
191D61—42no—
192D61—42no—
193#585—611no—
194C2×#137—611no—
195C2×#137D6111yescharacteristic, complemented
196#536—611no—
197#456—614no—
198#455—614no—
199#421—611no—
200#421—611no—
201#413—611no—
202C61#302211yescharacteristic, complemented, Sylow
2032−1+4—612no—
2042−1+4—1221no—
2052−1+4—1221no—
206H(5,𝔽2)—612no—
207H(5,𝔽2)—1222no—
208H(5,𝔽2)—1221no—
209H(5,𝔽2)—1221no—
210C2×#41—611no—
211C2×#41—611no—
212C2×#41—1222no—
213C2×#41—1222no—
214C2×#41—1222no—
215C2×#41C2×D6111yescharacteristic
216C22×Q8C2×D6111yescharacteristic, complemented
217#137—22no—
218#137—614no—
219#137—1222no—
220#137C2×D6114yescomplemented
221C2×Q16—21no—
222C2×Q16—1221no—
223C2×SD16—21no—
224C2×SD16—1221no—
225C2×M16—611no—
226C2×M16C2×D6111yescharacteristic, complemented
227C4⋊Q8—612no—
228#124—612no—
229#123—1222no—
230C22⋊Q8—1222no—
231#117—611no—
232#104—614no—
233#104—614no—
234#101—612no—
235#100—612no—
236#41—21no—
237#41—21no—
238#41—612no—
239#41—612no—
240#41—1222no—
241#41—1222no—
242#41—1224no—
243#41—1224no—
244#41—1224no—
245#41—1224no—
246#41—1222no—
247#41—1222no—
248#41—1222no—
249#41—1222no—
250#41—1221no—
251#41—1221no—
252#41—1221no—
253#41—1221no—
254#41—1221no—
255#41—1221no—
256#41C22⋊D6112yes—
257#41C22×D6112yes—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—611no—
264C2×Q8—611no—
265C2×Q8—1222no—
266C2×Q8—1222no—
267C2×Q8—1222no—
268C2×Q8C22⋊D6111yescharacteristic
269C2×Q8C22×D6112yes—
270C2×D4—21no—
271C2×D4—612no—
272C2×D4—611no—
273C2×D4—611no—
274C2×D4—1222no—
275C2×D4—1224no—
276C2×D4—1224no—
277C2×D4—1222no—
278C2×D4—1224no—
279C2×D4—1221no—
280C2×D4—1222no—
281C2×D4C22⋊D6111yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—612no—
285C22×C4—1224no—
286C22×C4—1221no—
287C22×C4C22×D6111yescharacteristic
288Q16—24no—
289Q16—1224no—
290SD16—24no—
291SD16—1224no—
292M16—21no—
293M16—612no—
294M16—1221no—
295M16C22×D6112yes—
296C2×C8—21no—
297C2×C8—1221no—
298C4⋊C4—1224no—
299C4⋊C4—1221no—
300C22⋊C4—1224no—
301C22⋊C4—1221no—
302C42—612no—
303C23—21no—
304C23—612no—
305C23—1224no—
306C23—1221no—
307C23D4×D6111yescharacteristic
308Q8—21no—
309Q8—22no—
310Q8—22no—
311Q8—41no—
312Q8—41no—
313Q8—612no—
314Q8—1224no—
315Q8—1221no—
316Q8—1221no—
317Q8—1221no—
318Q8C2×C22⋊D6112yes—
319D4—22no—
320D4—22no—
321D4—21no—
322D4—612no—
323D4—1224no—
324D4—1224no—
325D4—1224no—
326D4—1222no—
327D4—1222no—
328D4—1222no—
329D4—1222no—
330D4—1221no—
331D4—1221no—
332D4—1221no—
333D4C2×C22⋊D6112yes—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—612no—
341C2×C4—1224no—
342C2×C4—1224no—
343C2×C4—1224no—
344C2×C4—1221no—
345C2×C4—1222no—
346C2×C4—1222no—
347C2×C4—1222no—
348C2×C4—1222no—
349C2×C4—1222no—
350C2×C4D4×D6111yescharacteristic
351C2×C4D4×D6111yescharacteristic
352C2×C4D4×D6111yescharacteristic
353C2×C4C2×C22⋊D6111yescharacteristic
354C2×C4C2×C22⋊D6111yescharacteristic
355C2×C4C23×D6111yescharacteristic
356C8—22no—
357C8—1222no—
358C22—22no—
359C22—41no—
360C22—81no—
361C22—1222no—
362C22—1222no—
363C22—4881no—
364C22—4884no—
365C22—2442no—
366C22#1451974511yescharacteristic
367C22#1451974511yescharacteristic
368C22C2×D4×D6111yescharacteristic
369C4—22no—
370C4—42no—
371C4—1222no—
372C4—1222no—
373C4—2442no—
374C4#1451974511yescharacteristic
375C4#1451974511yescharacteristic
376C4C2×D4×D6111yescharacteristic
377C4C22×C22⋊D6111yescharacteristic
378C2—21no—
379C2—21no—
380C2—21no—
381C2—42no—
382C2—2442no—
383C2—2442no—
384C2C2×#1451974511yescharacteristic
subgroupG/H
centerC2C2×#14519745
commutatorC2×C4×C61C24
FrattiniC2×C4C23×D61
FittingC2×#137×C61C2
socleC2×C61C2×#120
hypercenterC2×#137D61
hypocenterC61#3022
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#14519808C2semidirect
3. #16840336C2semidirect
4. #16839943C2semidirect
5. #16839938C2semidirect
6. #16839779C2semidirect
7. #16839778C2semidirect
8. #16839744C2semidirect
9. C2×#137×C61C2semidirect
23. #14519808C22semidirect
26. C2×#11758194C22semidirect
27. #14519775C22semidirect
28. #14519766C22semidirect
31. #14519736C22semidirect
32. #14519704C22semidirect
33. #14519703C22semidirect
34. #14519695C22semidirect
35. #14519693C22semidirect
37. C22×Q8×C61C22semidirect
39. #137×C61C22semidirect
42. C2×M16×C61C22semidirect
195. C2×#137D61semidirect
202. C61#3022semidirect
216. C22×Q8C2×D61semidirect
220. #137C2×D61semidirect
226. C2×M16C2×D61semidirect