Finite Group Databasebeta

← #27207016

Subgroups — #27207016

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#20268496C211yesmaximal, characteristic
2Q8×C22⋊D103C211yesmaximal, characteristic
3#20268140C211yesmaximal, characteristic, complemented
4#20268126C211yesmaximal, characteristic, complemented
5#20268125C211yesmaximal, characteristic, complemented
6#20268084C211yesmaximal, characteristic, complemented
7#20268032C211yesmaximal, characteristic, complemented
8#20268031C211yesmaximal, characteristic, complemented
9#20268000C211yesmaximal, characteristic, complemented
10#20267948C211yesmaximal, characteristic, complemented
11#20267947C211yesmaximal, characteristic, complemented
12#20267883C211yesmaximal, characteristic, complemented
13C8×C22⋊D103C211yesmaximal, characteristic
14#103×D103C211yesmaximal, characteristic, complemented
15C2×#103×C103C211yesmaximal, characteristic, complemented
16C2×Q8×D103C2211yescharacteristic
17C2×Dic412C2211yescharacteristic
18C2×#13110095C2211yescharacteristic
19C2×#13110095C2211yescharacteristic
20C2×C8×D103C2211yescharacteristic
21#15693020C2211yescharacteristic
22#15693019—21no—
23#15693019C2211yescharacteristic
24#15693011—21no—
25#15693001C2211yescharacteristic
26#15693000—21no—
27#15693000—21no—
28#15693000C2211yescharacteristic
29#15693000C2211yescharacteristic
30#15692999—21no—
31#15692997—21no—
32#15692997C2211yescharacteristic
33Q8×Dic103C2211yescharacteristic
34#15692986C2211yescharacteristic
35C4×C22⋊D103—21no—
36C4×C22⋊D103—21no—
37C4×C22⋊D103C2211yescharacteristic
38C4⋊C4×D103C2211yescharacteristic
39#15692955C2211yescharacteristic
40#15692954C2211yescharacteristic
41#15692954C2211yescharacteristic
42Dic103⋊C8C2211yescharacteristic
43#15692946C2211yescharacteristic
44#15692946C2211yescharacteristic
45#15692945C2211yescharacteristic
46#15692945C2211yescharacteristic
47#15692944C2211yescharacteristic
48#15692944C2211yescharacteristic
49C22⋊(C103⋊C8)C2211yescharacteristic
50(C2×D103)⋊C8C2211yescharacteristic
51C8×Dic103C2211yescharacteristic
52C22×Q8×C103C2211yescharacteristic
53C22×C8×C103C2211yescharacteristic
54C2×C4⋊C4×C103C2211yescharacteristic
55#103×C103C2211yescharacteristic
56#103×C103C2211yescharacteristic
57#103×C103C2211yescharacteristic
58#103×C103C2211yescharacteristic
59C2×Dic206—21no—
60C2×Dic206—21no—
61C2×Dic206C2311yescharacteristic
62C2×Dic206C2311yescharacteristic
63Q8×D103—22no—
64Q8×D103—41no—
65C2×C22⋊D103D411yescharacteristic
66C2×C4×D103—21no—
67C2×C4×D103—21no—
68C2×C4×D103C2311yescharacteristic
69Dic412—41no—
70#13110095—22no—
71#13110095—41no—
72C2×C103⋊C8C2311yescharacteristic
73C2×C103⋊C8C2311yescharacteristic
74C8×D103—41no—
75C4⋊Dic103—21no—
76C4⋊Dic103—21no—
77C4⋊Dic103C2311yescharacteristic
78C4⋊Dic103C2311yescharacteristic
79Dic103⋊C4—21no—
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⋊Dic103—21no—
90C22⋊Dic103D411yescharacteristic
91(C2×D103)⋊C4—21no—
92(C2×D103)⋊C4—21no—
93(C2×D103)⋊C4D411yescharacteristic
94C4×Dic103—21no—
95C4×Dic103—21no—
96C4×Dic103C2311yescharacteristic
97C2×Q8×C103—21no—
98C2×Q8×C103—22no—
99C2×Q8×C103—41no—
100C2×Q8×C103C2311yescharacteristic
101C2×Q8×C103C2311yescharacteristic
102C22×C4×C103—21no—
103C22×C4×C103—21no—
104C22×C4×C103C2311yescharacteristic
105C2×C8×C103—41no—
106C2×C8×C103C2311yescharacteristic
107C2×C8×C103C2311yescharacteristic
108C4⋊C4×C103—21no—
109C4⋊C4×C103C2311yescharacteristic
110C4⋊C4×C103C2311yescharacteristic
111C23×C103C2×D411yescharacteristic
112C22×D103C2×D411yescharacteristic
113Q8×C103—21no—
114Q8×C103—21no—
115Q8×C103—21no—
116Q8×C103—42no—
117Q8×C103#4112yes—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—21no—
121C2×C4×C103—21no—
122C2×C4×C103—21no—
123C2×C4×C103—21no—
124C2×C4×C103—42no—
125C2×C4×C103—81no—
126C2×C4×C103C2×D411yescharacteristic
127C2×C4×C103C2411yescharacteristic
128C22⋊D103Q1614yescomplemented
129C2×Dic103—21no—
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103C2×D411yescharacteristic
134C2×Dic103C2×D411yescharacteristic
135C2×Dic103C2×D411yescharacteristic
136C4×D103—21no—
137C4×D103—21no—
138C4×D103—42no—
139C4×D103—81no—
140Dic206—21no—
141Dic206—21no—
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#451—1031no—
189C4×Q16—1031no—
190C8×D4—1031no—
191C2×#103—1031no—
192C2×#103D10311yescharacteristic, complemented
193C22×Q8—1031no—
194C22×Q8C2×D10311yescharacteristic
195C2×Q16—1031no—
196C2×Q16—1031no—
197C2×Q16—1031no—
198C22×C8—1031no—
199C22×C8C2×D10311yescharacteristic
200C4⋊Q8—1031no—
201C4⋊Q8—1031no—
202C4⋊Q8—2061no—
203#125—2061no—
204C22⋊Q8—1031no—
205C22⋊Q8—1031no—
206C22⋊Q8—1031no—
207C22⋊Q8—1031no—
208C22⋊Q8—2061no—
209C22⋊Q8—2061no—
210C22⋊Q8—2061no—
211C22⋊Q8—2061no—
212C4×Q8—1031no—
213C4×Q8—1031no—
214C4×D4—1031no—
215C4×D4—2061no—
216C4×D4—2061no—
217C2×C4⋊C4—1031no—
218C2×C4⋊C4C2×D10311yescharacteristic
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#103C2×D10311yescharacteristic
230#103C2×D10311yescharacteristic
231#103C2×D10311yescharacteristic
232#103C2×D10311yescharacteristic
233C22⋊C8—1031no—
234C22⋊C8—1031no—
235C4×C8—1031no—
236C2×Q8—21no—
237C2×Q8—22no—
238C2×Q8—41no—
239C2×Q8—1031no—
240C2×Q8—1031no—
241C2×Q8—4121no—
242C2×Q8—2061no—
243C2×Q8—2061no—
244C2×Q8—2062no—
245C2×Q8C22×D10311yescharacteristic
246C2×Q8C22×D10311yescharacteristic
247C2×D4—1031no—
248C22×C4—21no—
249C22×C4—21no—
250C22×C4—1031no—
251C22×C4—2061no—
252C22×C4—2061no—
253C22×C4C22×D10311yescharacteristic
254Q16—4121no—
255Q16—4121no—
256Q16—2062no—
257C2×C8—41no—
258C2×C8—1031no—
259C2×C8—1031no—
260C2×C8—4121no—
261C2×C8C22×D10311yescharacteristic
262C2×C8C22×D10311yescharacteristic
263C4⋊C4—21no—
264C4⋊C4—1031no—
265C4⋊C4—1031no—
266C4⋊C4—1031no—
267C4⋊C4—2061no—
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⋊C4C22×D10311yescharacteristic
278C4⋊C4C22×D10311yescharacteristic
279C22⋊C4—1031no—
280C22⋊C4—1031no—
281C22⋊C4—2061no—
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—42no—
294Q8—8241no—
295Q8—4122no—
296Q8—2061no—
297Q8—2061no—
298Q8—2061no—
299Q8—2061no—
300Q8#1311010512yes—
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—81no—
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×#1311010511yescharacteristic
347C4#1569306611yescharacteristic
348C2—22no—
349C2—2062no—
350C2#2026843111yescharacteristic
351C2C2×Q16×D10311yescharacteristic
352C2#2026859711yescharacteristic
subgroupG/H
centerC22C2×D4×D103
commutator, cosocleC2×C4×C103C24
FrattiniC2×C4C23×D103
FittingC2×#103×C103C2
socleC22×C103C22×D4
prime radicalC2×C22⋊D103D4
hypercenterC2×#103D103
hypocenterC103#3299
LCSG ▷ C2×C4×C103 ▷ C2×C103 ▷ C103
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
3. #20268140C2semidirect
4. #20268126C2semidirect
5. #20268125C2semidirect
6. #20268084C2semidirect
7. #20268032C2semidirect
8. #20268031C2semidirect
9. #20268000C2semidirect
10. #20267948C2semidirect
11. #20267947C2semidirect
12. #20267883C2semidirect
14. #103×D103C2semidirect
15. C2×#103×C103C2semidirect
128. C22⋊D103Q16semidirect
177. C103#3299semidirect
192. C2×#103D103semidirect

Maximal subgroups

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

subgroupindex
#202684962
Q8×C22⋊D1032
#202681402
#202681262
#202681252
#202680842
#202680322
#202680312
#202680002
#202679482
#202679472
#202678832
C8×C22⋊D1032
#103×D1032
C2×#103×C1032
#3299103