Finite Group Databasebeta

← #27207013

Subgroups — #27207013

Order 13184.

388 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20268499C211yesmaximal, characteristic
2Q8×C22⋊D103C211yesmaximal, characteristic
3#20268140C211yesmaximal, characteristic, complemented
4#20268127C211yesmaximal, characteristic, complemented
5#20268125C211yesmaximal, characteristic, complemented
6#20268084C211yesmaximal, characteristic, complemented
7#20268030C211yesmaximal, characteristic, complemented
8#20268029C211yesmaximal, characteristic, complemented
9#20267999C211yesmaximal, characteristic, complemented
10#20267945C211yesmaximal, characteristic, complemented
11Q16×Dic103C211yesmaximal, characteristic, complemented
12(C22⋊D103)⋊C8C211yesmaximal, characteristic
13C2×#15692945C211yesmaximal, characteristic, complemented
14#103×D103C211yesmaximal, characteristic, complemented
15#451×C103C211yesmaximal, characteristic, complemented
16C2×Q8×D103C2211yescharacteristic
17C2×#13110095C2211yescharacteristic
18C22×C103⋊C8C2211yescharacteristic
19C2×C8×D103C2211yescharacteristic
20#15693020C2211yescharacteristic
21#15693019—21no—
22#15693019C2211yescharacteristic
23#15693011—21no—
24#15693001—21no—
25#15693000—21no—
26#15693000C2211yescharacteristic
27#15692998—21no—
28#15692997—21no—
29#15692997C2211yescharacteristic
30#15692997C2211yescharacteristic
31Q8×Dic103C2211yescharacteristic
32Q8×Dic103C2211yescharacteristic
33C4×C22⋊D103—21no—
34C4×C22⋊D103C2211yescharacteristic
35(C22⋊D103)⋊C4—21no—
36C2×C4⋊Dic103C2211yescharacteristic
37C4⋊C4×D103C2211yescharacteristic
38#15692955C2211yescharacteristic
39#15692955C2211yescharacteristic
40#15692954C2211yescharacteristic
41Dic103⋊C8C2211yescharacteristic
42#15692946C2211yescharacteristic
43#15692946C2211yescharacteristic
44#15692945C2211yescharacteristic
45#15692945C2211yescharacteristic
46#15692945C2211yescharacteristic
47#15692945C2211yescharacteristic
48#15692945C2211yescharacteristic
49#15692944C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic
51C8×Dic103C2211yescharacteristic
52C22×Q8×C103C2211yescharacteristic
53C2×Q16×C103C2211yescharacteristic
54C2×Q16×C103C2211yescharacteristic
55C22⋊Q8×C103C2211yescharacteristic
56#103×C103C2211yescharacteristic
57#103×C103C2211yescharacteristic
58C22⋊C8×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×Dic206—21no—
61C2×Dic206C2311yescharacteristic
62Q8×D103—22no—
63Q8×D103—41no—
64C2×C22⋊D103D411yescharacteristic
65C22×Dic103—21no—
66C2×C4×D103—21no—
67C2×C4×D103—21no—
68C2×C4×D103C2311yescharacteristic
69#13110095—41no—
70C2×C103⋊C8—41no—
71C2×C103⋊C8C2311yescharacteristic
72C2×C103⋊C8C2311yescharacteristic
73C8×D103—41no—
74C4⋊Dic103—21no—
75C4⋊Dic103—21no—
76C4⋊Dic103—21no—
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79C4⋊Dic103C2311yescharacteristic
80Dic103⋊C4—21no—
81Dic103⋊C4—21no—
82Dic103⋊C4—21no—
83Dic103⋊C4—21no—
84Dic103⋊C4—21no—
85Dic103⋊C4—21no—
86Dic103⋊C4—21no—
87Dic103⋊C4D411yescharacteristic
88C22⋊Dic103—21no—
89C22⋊Dic103D411yescharacteristic
90(C2×D103)⋊C4—21no—
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4D411yescharacteristic
93C4×Dic103—21no—
94C4×Dic103—21no—
95C4×Dic103C2311yescharacteristic
96C2×Q8×C103—21no—
97C2×Q8×C103—22no—
98C2×Q8×C103—41no—
99C2×Q8×C103C2311yescharacteristic
100C2×Q8×C103C2311yescharacteristic
101C2×Q8×C103C2311yescharacteristic
102C22×C4×C103—21no—
103C22×C4×C103C2311yescharacteristic
104Q16×C103—22no—
105Q16×C103—41no—
106C2×C8×C103C2311yescharacteristic
107C2×C8×C103C2311yescharacteristic
108C4⋊C4×C103—21no—
109C4⋊C4×C103C2311yescharacteristic
110C22⋊C4×C103—21no—
111C23×C103C2×D411yescharacteristic
112C22×D103C2×D411yescharacteristic
113Q8×C103—21no—
114Q8×C103—21no—
115Q8×C103—21no—
116Q8×C103—21no—
117Q8×C103—21no—
118Q8×C103—42no—
119Q8×C103#4112yes—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—42no—
127C2×C4×C103C2×D411yescharacteristic
128C2×C4×C103C2411yescharacteristic
129C22⋊D103Q1614yescomplemented
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—81no—
135C2×Dic103C2×D411yescharacteristic
136C2×Dic103C2×D411yescharacteristic
137C2×Dic103C2×D411yescharacteristic
138C4×D103—21no—
139C4×D103—21no—
140C4×D103—42no—
141C4×D103—81no—
142Dic206—21no—
143Dic206—21no—
144Dic206—42no—
145Dic206—81no—
146C8×C103—21no—
147C8×C103—21no—
148C103⋊C8—21no—
149C103⋊C8—21no—
150C22×C103—21no—
151C22×C103—21no—
152C22×C103C2×Q1612yes—
153C22×C103C22×D411yescharacteristic
154C2×D103—21no—
155C2×D103—21no—
156C2×D103C2×Q1612yes—
157C4×C103—22no—
158C4×C103—21no—
159C4×C103—41no—
160C4×C103—41no—
161C4×C103—41no—
162C4×C103C2×#4111yescharacteristic
163C4×C103H(5,𝔽2)11yescharacteristic
164Dic103—21no—
165Dic103—21no—
166Dic103—41no—
167Dic103—41no—
168Dic103—41no—
169Dic103—41no—
170Dic103C2×Q1612yes—
171C2×C103—22no—
172C2×C103#54611yescharacteristic
173C2×C103C22×Q1611yescharacteristic
174C2×C103#57711yescharacteristic
175D103—22no—
176#3299—1031nomaximal, Sylow
177C103#329911yescharacteristic, complemented, Sylow
178#554—1031no—
179D4×Q8—1031no—
180#487—1031no—
181#484—1031no—
182#484—1031no—
183#477—1031no—
184#467—1031no—
185#467—1031no—
186#462—1031no—
187#451—1031no—
188#451D10311yescharacteristic, complemented
189C4×Q16—1031no—
190C8×D4—1031no—
191C2×#103—1031no—
192C2×#103—1031no—
193C22×Q8—1031no—
194C22×Q8C2×D10311yescharacteristic
195C2×Q16—1031no—
196C2×Q16C2×D10311yescharacteristic
197C2×Q16C2×D10311yescharacteristic
198C22×C8—1031no—
199C22×C8—1031no—
200C4⋊Q8—1031no—
201C4⋊Q8—1031no—
202C4⋊Q8—2061no—
203#125—2061no—
204C22⋊Q8—1031no—
205C22⋊Q8—1031no—
206C22⋊Q8—1031no—
207C22⋊Q8—2061no—
208C22⋊Q8—2061no—
209C22⋊Q8—2061no—
210C22⋊Q8—2061no—
211C22⋊Q8C2×D10311yescharacteristic
212C4×Q8—1031no—
213C4×Q8—1031no—
214C4×D4—1031no—
215C4×D4—2061no—
216C4×D4—2061no—
217C2×C4⋊C4—1031no—
218C2×C4⋊C4—1031no—
219#107—1031no—
220#107—1031no—
221#107—1031no—
222C4⋊C8—1031no—
223#103—1031no—
224#103—1031no—
225#103—1031no—
226#103—1031no—
227#103—1031no—
228#103—1031no—
229#103—1031no—
230#103—1031no—
231#103C2×D10311yescharacteristic
232#103C2×D10311yescharacteristic
233C22⋊C8—1031no—
234C22⋊C8C2×D10311yescharacteristic
235C4×C8—1031no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—1031no—
240C2×Q8—4121no—
241C2×Q8—2061no—
242C2×Q8—2061no—
243C2×Q8—2062no—
244C2×Q8C22×D10311yescharacteristic
245C2×Q8C22×D10311yescharacteristic
246C2×Q8C22×D10311yescharacteristic
247C2×D4—1031no—
248C22×C4—21no—
249C22×C4—1031no—
250C22×C4—2061no—
251C22×C4—2061no—
252C22×C4—2061no—
253C22×C4C22×D10311yescharacteristic
254Q16—22no—
255Q16—41no—
256Q16—4121no—
257C2×C8—1031no—
258C2×C8—1031no—
259C2×C8—4121no—
260C2×C8—4121no—
261C2×C8C22×D10311yescharacteristic
262C2×C8C22×D10311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—1031no—
265C4⋊C4—1031no—
266C4⋊C4—1031no—
267C4⋊C4—1031no—
268C4⋊C4—2061no—
269C4⋊C4—2061no—
270C4⋊C4—2061no—
271C4⋊C4—2061no—
272C4⋊C4—2061no—
273C4⋊C4—2061no—
274C4⋊C4—2061no—
275C4⋊C4—2061no—
276C4⋊C4—2061no—
277C4⋊C4—2061no—
278C4⋊C4C22×D10311yescharacteristic
279C22⋊C4—21no—
280C22⋊C4—1031no—
281C22⋊C4—1031no—
282C22⋊C4—2061no—
283C22⋊C4—2061no—
284C22⋊C4—2061no—
285C42—1031no—
286C42—2061no—
287C42—2061no—
288C23—1031no—
289C23D4×D10311yescharacteristic
290Q8—21no—
291Q8—21no—
292Q8—21no—
293Q8—21no—
294Q8—21no—
295Q8—42no—
296Q8—8241no—
297Q8—4122no—
298Q8—2061no—
299Q8—2061no—
300Q8#1311010412yes—
301D4—1034no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—42no—
309C2×C4—8241no—
310C2×C4—8241no—
311C2×C4—1031no—
312C2×C4—1031no—
313C2×C4—1031no—
314C2×C4—4122no—
315C2×C4—2061no—
316C2×C4—2061no—
317C2×C4—2061no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4—2061no—
321C2×C4D4×D10311yescharacteristic
322C2×C4C23×D10311yescharacteristic
323C8—21no—
324C8—21no—
325C8—2061no—
326C8—2061no—
327C22—21no—
328C22—21no—
329C22—1032no—
330C22—2061no—
331C22—2061no—
332C22Q16×D10312yes—
333C22C2×D4×D10311yescharacteristic
334C4—21no—
335C4—22no—
336C4—41no—
337C4—41no—
338C4—41no—
339C4—1032no—
340C4—4121no—
341C4—4121no—
342C4—4121no—
343C4—4121no—
344C4—2061no—
345C4—2061no—
346C4C2×#1311010411yescharacteristic
347C4#1569306611yescharacteristic
348C2—22no—
349C2—2062no—
350C2#2026842811yescharacteristic
351C2C2×Q16×D10311yescharacteristic
352C2#2026860011yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
Fitting#451×C103C2
socleC22×C103C22×D4
prime radicalC2×C22⋊D103D4
hypercenter#451D103
hypocenterC103#3299
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ #451

Complements

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

NH ≅ G/Ntype
3. #20268140C2semidirect
4. #20268127C2semidirect
5. #20268125C2semidirect
6. #20268084C2semidirect
7. #20268030C2semidirect
8. #20268029C2semidirect
9. #20267999C2semidirect
10. #20267945C2semidirect
11. Q16×Dic103C2semidirect
13. C2×#15692945C2semidirect
14. #103×D103C2semidirect
15. #451×C103C2semidirect
129. C22⋊D103Q16semidirect
177. C103#3299semidirect
188. #451D103semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
#202684992
Q8×C22⋊D1032
#202681402
#202681272
#202681252
#202680842
#202680302
#202680292
#202679992
#202679452
Q16×Dic1032
(C22⋊D103)⋊C82
C2×#156929452
#103×D1032
#451×C1032
#3299103