Finite Group Databasebeta

← #27197875

Subgroups — #27197875

Order 13184.

528 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692998C211yesmaximal, characteristic
2#20267696C211yesmaximal, characteristic, complemented
3#20267695C211yesmaximal, characteristic, complemented
4#20267687C211yesmaximal, characteristic, complemented
5#20267686C211yesmaximal, characteristic, complemented
6#20267676C211yesmaximal, characteristic, complemented
7#20267673C211yesmaximal, characteristic, complemented
8#20267673C211yesmaximal, characteristic, complemented
9#20267672C211yesmaximal, characteristic, complemented
10#20267664C211yesmaximal, characteristic
11#20267649C211yesmaximal, characteristic
12C22⋊C4×Dic103C211yesmaximal, characteristic
13C22⋊C4×Dic103C211yesmaximal, characteristic
14C2×C103⋊#95C211yesmaximal, characteristic
15#385×C103C211yesmaximal, characteristic
16C22×Dic206C2211yescharacteristic
17C23×Dic103C2211yescharacteristic
18C23×Dic103C2211yescharacteristic
19#15692998C418yescomplemented
20C2×C4⋊Dic103C2211yescharacteristic
21C2×Dic103⋊C4C2211yescharacteristic
22C2×Dic103⋊C4C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×Dic103⋊C4C2211yescharacteristic
27C2×C22⋊Dic103C2211yescharacteristic
28C2×C22⋊Dic103C2211yescharacteristic
29C2×C4×Dic103C2211yescharacteristic
30C2×C4×Dic103C2211yescharacteristic
31C2×C4×Dic103C2211yescharacteristic
32C2×C4×Dic103C2211yescharacteristic
33C103⋊#95C2211yescharacteristic
34C103⋊#95C2211yescharacteristic
35C103⋊#95C2211yescharacteristic
36C103⋊#95C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C23×C4×C103C2211yescharacteristic
46C2×C4⋊C4×C103C2211yescharacteristic
47C2×C4⋊C4×C103C2211yescharacteristic
48C2×C22⋊C4×C103C2211yescharacteristic
49C2×C22⋊C4×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52C2×Dic206—41no—
53C2×Dic206—41no—
54C2×Dic206C2×C414yescomplemented
55C22×Dic103—41no—
56C22×Dic103—41no—
57C22×Dic103—41no—
58C22×Dic103—41no—
59C22×Dic103C2×C414yes—
60C22×Dic103Q814yescomplemented
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C22×Dic103C2311yescharacteristic
64C22×Dic103C2311yescharacteristic
65C22×Dic103C2311yescharacteristic
66C22×Dic103C2311yescharacteristic
67C22×Dic103C2311yescharacteristic
68C22×Dic103C2311yescharacteristic
69C4⋊Dic103C2×C414yescomplemented
70Dic103⋊C4—41no—
71Dic103⋊C4—41no—
72Dic103⋊C4—41no—
73Dic103⋊C4—41no—
74Dic103⋊C4C2×C414yescomplemented
75Dic103⋊C4C2×C414yescomplemented
76C22⋊Dic103—22no—
77C22⋊Dic103C2×C414yes—
78C4×Dic103—41no—
79C4×Dic103—41no—
80C4×Dic103—41no—
81C4×Dic103—41no—
82C24×C103C2311yescharacteristic
83C22×C4×C103—22no—
84C22×C4×C103—41no—
85C22×C4×C103—41no—
86C22×C4×C103C2311yescharacteristic
87C22×C4×C103C2311yescharacteristic
88C22×C4×C103C2311yescharacteristic
89C22×C4×C103C2311yescharacteristic
90C22×C4×C103C2311yescharacteristic
91C22×C4×C103C2311yescharacteristic
92C4⋊C4×C103—41no—
93C4⋊C4×C103—41no—
94C22⋊C4×C103—22no—
95C22⋊C4×C103C2×C414yes—
96C23×C103—21no—
97C23×C103—21no—
98C23×C103—21no—
99C23×C103—21no—
100C23×C103C22×C412yes—
101C23×C103C2×Q812yes—
102C23×C103#4112yes—
103C23×C103C2411yescharacteristic
104C2×C4×C103—21no—
105C2×C4×C103—21no—
106C2×C4×C103—21no—
107C2×C4×C103—21no—
108C2×C4×C103—21no—
109C2×C4×C103—21no—
110C2×C4×C103—21no—
111C2×C4×C103—21no—
112C2×C4×C103—21no—
113C2×C4×C103—21no—
114C2×C4×C103—21no—
115C2×C4×C103—21no—
116C2×C4×C103—21no—
117C2×C4×C103—21no—
118C2×C4×C103—21no—
119C2×C4×C103—21no—
120C2×C4×C103—44no—
121C2×C4×C103C22×C412yes—
122C2×C4×C103C22×C412yes—
123C2×Dic103—21no—
124C2×Dic103—21no—
125C2×Dic103—21no—
126C2×Dic103—21no—
127C2×Dic103—21no—
128C2×Dic103—21no—
129C2×Dic103—21no—
130C2×Dic103—21no—
131C2×Dic103—21no—
132C2×Dic103—21no—
133C2×Dic103—21no—
134C2×Dic103—21no—
135C2×Dic103—21no—
136C2×Dic103—21no—
137C2×Dic103—21no—
138C2×Dic103—21no—
139C2×Dic103—21no—
140C2×Dic103—21no—
141C2×Dic103—44no—
142C2×Dic103—44no—
143C2×Dic103C22×C412yes—
144C2×Dic103C22×C412yes—
145C2×Dic103C22×C412yes—
146C2×Dic103C22×C412yes—
147C2×Dic103C2×Q812yes—
148C2×Dic103C2×Q812yes—
149Dic206—44no—
150C22×C103—22no—
151C22×C103—22no—
152C22×C103—22no—
153C22×C103—22no—
154C22×C103—22no—
155C22×C103—22no—
156C22×C103C4×Q814yes—
157C22×C103C23×C411yescharacteristic
158C22×C103C22×Q811yescharacteristic
159C22×C103C2×#4111yescharacteristic
160C22×C103H(5,𝔽2)11yescharacteristic
161C22×C103H(5,𝔽2)11yescharacteristic
162C22×C103H(5,𝔽2)11yescharacteristic
163C22×C1032−1+411yescharacteristic
164C4×C103—22no—
165C4×C103—22no—
166C4×C103—41no—
167C4×C103—41no—
168C4×C103—41no—
169C4×C103—41no—
170Dic103—22no—
171Dic103—22no—
172Dic103—22no—
173Dic103—22no—
174Dic103—22no—
175Dic103—22no—
176Dic103—41no—
177Dic103—41no—
178C2×C103—24no—
179C2×C103C2×C4×Q811yescharacteristic
180C2×C103#51811yescharacteristic
181C2×C103#52011yescharacteristic
182C2×C103#53811yescharacteristic
183C2×C103#53911yescharacteristic
184C2×C103#54311yescharacteristic
185C2×C103#54411yescharacteristic
186#2329—1031nomaximal, Sylow
187C103#232911yescharacteristic, complemented, Sylow
188C2×C22⋊Q8—1031no—
189#391—1031no—
190#391—1031no—
191#389—1031no—
192#389—1031no—
193#387—1031no—
194#387—1031no—
195#387—1031no—
196#387—1031no—
197#385—1031no—
198#385D10311yescharacteristic
199#380—1031no—
200C4×C22⋊C4—1031no—
201C4×C22⋊C4—1031no—
202C2×#95—1031no—
203C22×Q8—1031no—
204C23×C4—1031no—
205C23×C4—1031no—
206C23×C4C2×D10311yescharacteristic
207C22⋊Q8—1038no—
208C2×C4⋊C4—1031no—
209C2×C4⋊C4—1031no—
210C2×C4⋊C4—1031no—
211C2×C4⋊C4—1031no—
212C2×C4⋊C4—1031no—
213C2×C4⋊C4—1031no—
214C2×C4⋊C4—1031no—
215C2×C4⋊C4C2×D10311yescharacteristic
216C2×C4⋊C4C2×D10311yescharacteristic
217C2×C22⋊C4—1031no—
218C2×C22⋊C4—1031no—
219C2×C22⋊C4C2×D10311yescharacteristic
220C2×C22⋊C4C2×D10311yescharacteristic
221C2×C42—1031no—
222C2×C42—1031no—
223C2×C42—1031no—
224C2×C42—1031no—
225#95—1031no—
226#95—1031no—
227#95—1031no—
228#95—1031no—
229#95—1031no—
230#95—1031no—
231#95—1031no—
232#95—1031no—
233#95—1031no—
234#95—1031no—
235#95—1031no—
236#95—1031no—
237#95C2×D10311yescharacteristic
238#95C2×D10311yescharacteristic
239C24C22×D10311yescharacteristic
240C2×Q8—1034no—
241C2×Q8—4121no—
242C2×Q8—4121no—
243C22×C4—22no—
244C22×C4—41no—
245C22×C4—41no—
246C22×C4—1034no—
247C22×C4—1034no—
248C22×C4—1031no—
249C22×C4—1031no—
250C22×C4—1031no—
251C22×C4—1031no—
252C22×C4—1031no—
253C22×C4—1031no—
254C22×C4—1031no—
255C22×C4—1031no—
256C22×C4—4121no—
257C22×C4—4121no—
258C22×C4—4121no—
259C22×C4—4121no—
260C22×C4C22×D10311yescharacteristic
261C22×C4C22×D10311yescharacteristic
262C22×C4C22×D10311yescharacteristic
263C22×C4C22×D10311yescharacteristic
264C22×C4C22×D10311yescharacteristic
265C22×C4C22×D10311yescharacteristic
266C4⋊C4—41no—
267C4⋊C4—41no—
268C4⋊C4—1034no—
269C4⋊C4—1034no—
270C4⋊C4—1034no—
271C4⋊C4—4121no—
272C4⋊C4—4121no—
273C4⋊C4—4121no—
274C4⋊C4—4121no—
275C22⋊C4—22no—
276C22⋊C4—1034no—
277C22⋊C4—2062no—
278C22⋊C4C4×D10314yes—
279C42—4121no—
280C42—4121no—
281C42—4121no—
282C42—4121no—
283C23—21no—
284C23—21no—
285C23—21no—
286C23—21no—
287C23C2×C4×D10312yes—
288C23Q8×D10312yes—
289C23#1311010412yes—
290C23C23×D10311yescharacteristic
291Q8—4124no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—21no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—44no—
309C2×C4—1032no—
310C2×C4—1032no—
311C2×C4—1032no—
312C2×C4—1032no—
313C2×C4—1032no—
314C2×C4—1032no—
315C2×C4—4124no—
316C2×C4—4124no—
317C2×C4—2061no—
318C2×C4—2061no—
319C2×C4—2061no—
320C2×C4—2061no—
321C2×C4—2061no—
322C2×C4—2061no—
323C2×C4—2061no—
324C2×C4—2061no—
325C2×C4—2061no—
326C2×C4—2061no—
327C2×C4—2061no—
328C2×C4—2061no—
329C2×C4—2061no—
330C2×C4—2061no—
331C2×C4—2061no—
332C2×C4—2061no—
333C2×C4—2061no—
334C2×C4—2061no—
335C2×C4C2×C4×D10312yes—
336C2×C4C2×C4×D10312yes—
337C22—22no—
338C22—22no—
339C22—22no—
340C22—22no—
341C22—22no—
342C22—22no—
343C22#1569298614yes—
344C22C22×C4×D10311yescharacteristic
345C22C2×Q8×D10311yescharacteristic
346C22C2×#1311010411yescharacteristic
347C22#1569306611yescharacteristic
348C22#1569306611yescharacteristic
349C22#1569306711yescharacteristic
350C22#1569306811yescharacteristic
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—41no—
357C4—4121no—
358C4—4121no—
359C4—2062no—
360C4—2062no—
361C4—2062no—
362C4—2062no—
363C4—2062no—
364C4—2062no—
365C2—24no—
366C2C2×#1569298611yescharacteristic
367C2#2026826311yescharacteristic
368C2#2026827011yescharacteristic
369C2#2026837611yescharacteristic
370C2#2026838511yescharacteristic
371C2#2026841611yescharacteristic
372C2#2026842011yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#385×C103C2
socle, cosocleC23×C103C24
prime radicalC24×C103C23
hypercenter#385D103
hypocenterC103#2329
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
2. #20267696C2semidirect
3. #20267695C2semidirect
4. #20267687C2semidirect
5. #20267686C2semidirect
6. #20267676C2semidirect
7. #20267673C2semidirect
8. #20267673C2semidirect
9. #20267672C2semidirect
19. #15692998C4semidirect
54. C2×Dic206C2×C4semidirect
60. C22×Dic103Q8semidirect
69. C4⋊Dic103C2×C4semidirect
74. Dic103⋊C4C2×C4semidirect
75. Dic103⋊C4C2×C4semidirect
187. C103#2329semidirect

Maximal subgroups

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

subgroupindex
C2×#156929982
#202676962
#202676952
#202676872
#202676862
#202676762
#202676732
#202676722
#202676642
#202676492
C22⋊C4×Dic1032
C2×C103⋊#952
#385×C1032
#2329103