Finite Group Databasebeta

← #27197871

Subgroups — #27197871

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×#15692999C211yesmaximal, characteristic
2#20267697C211yesmaximal, characteristic, complemented
3#20267695C211yesmaximal, characteristic, complemented
4#20267690C211yesmaximal, characteristic, complemented
5#20267688C211yesmaximal, characteristic, complemented
6#20267678C211yesmaximal, characteristic, complemented
7#20267673C211yesmaximal, characteristic, complemented
8#20267672C211yesmaximal, characteristic, complemented
9#20267665C211yesmaximal, characteristic
10#20267665C211yesmaximal, characteristic
11#20267648C211yesmaximal, characteristic
12C4×(C2×D103)⋊C4C211yesmaximal, characteristic
13#20267638C211yesmaximal, characteristic
14#95×D103C211yesmaximal, characteristic
15#387×C103C211yesmaximal, characteristic, complemented
16C22×Dic206C2211yescharacteristic
17C22×C4×D103C2211yescharacteristic
18C22×C4×D103C2211yescharacteristic
19C22×C4×D103C2211yescharacteristic
20#15692999C418yescomplemented
21C2×C4⋊Dic103C2211yescharacteristic
22C2×C4⋊Dic103C2211yescharacteristic
23C2×C4⋊Dic103C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×Dic103⋊C4C2211yescharacteristic
27C2×Dic103⋊C4C2211yescharacteristic
28C2×(C2×D103)⋊C4C2211yescharacteristic
29C2×(C2×D103)⋊C4C2211yescharacteristic
30C2×(C2×D103)⋊C4C2211yescharacteristic
31C2×(C2×D103)⋊C4C2211yescharacteristic
32C2×C4×Dic103C2211yescharacteristic
33C2×C4×Dic103C2211yescharacteristic
34C2×C4×Dic103C2211yescharacteristic
35C103⋊#95C2211yescharacteristic
36C103⋊#95C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C2×C4⋊C4×C103C2211yescharacteristic
46C2×C4⋊C4×C103C2211yescharacteristic
47C2×C42×C103C2211yescharacteristic
48#95×C103C2211yescharacteristic
49#95×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52C23×D103C2311yescharacteristic
53C2×Dic206—41no—
54C2×Dic206—41no—
55C2×Dic206C2×C414yescomplemented
56C22×Dic103C2311yescharacteristic
57C22×Dic103C2311yescharacteristic
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C22×Dic103C2311yescharacteristic
61C22×Dic103C2311yescharacteristic
62C22×Dic103C2311yescharacteristic
63C2×C4×D103—22no—
64C2×C4×D103—41no—
65C2×C4×D103—41no—
66C2×C4×D103—41no—
67C2×C4×D103—41no—
68C2×C4×D103—41no—
69C2×C4×D103—41no—
70C2×C4×D103C2×C414yes—
71C2×C4×D103Q814yescomplemented
72C4⋊Dic103—41no—
73C4⋊Dic103—41no—
74C4⋊Dic103—41no—
75Dic103⋊C4—41no—
76Dic103⋊C4—41no—
77Dic103⋊C4C2×C414yescomplemented
78Dic103⋊C4C2×C414yescomplemented
79(C2×D103)⋊C4—22no—
80(C2×D103)⋊C4—22no—
81(C2×D103)⋊C4C2×C414yes—
82(C2×D103)⋊C4C2×C414yes—
83C4×Dic103—41no—
84C4×Dic103—41no—
85C4×Dic103—41no—
86C22×C4×C103C2311yescharacteristic
87C22×C4×C103C2311yescharacteristic
88C22×C4×C103C2311yescharacteristic
89C22×C4×C103C2311yescharacteristic
90C22×C4×C103C2311yescharacteristic
91C22×C4×C103C2311yescharacteristic
92C22×C4×C103C2311yescharacteristic
93C4⋊C4×C103—41no—
94C4⋊C4×C103C2×C414yescomplemented
95C42×C103—41no—
96C23×C103C2411yescharacteristic
97C22×D103—21no—
98C22×D103—21no—
99C22×D103—21no—
100C22×D103—21no—
101C22×D103C22×C412yes—
102C22×D103C2×Q812yes—
103C22×D103#4112yes—
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—21no—
121C2×C4×C103C22×C412yes—
122C2×C4×C103C22×C412yes—
123C2×C4×C103C22×C412yes—
124C2×C4×C103C2×Q812yes—
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—21no—
142C2×Dic103C22×C412yes—
143C2×Dic103C22×C412yes—
144C2×Dic103C22×C412yes—
145C2×Dic103C2×Q812yes—
146C4×D103—44no—
147C4×D103—44no—
148C4×D103—44no—
149Dic206—44no—
150C22×C103C23×C411yescharacteristic
151C22×C103C22×Q811yescharacteristic
152C22×C103C2×#4111yescharacteristic
153C22×C103H(5,𝔽2)11yescharacteristic
154C22×C103H(5,𝔽2)11yescharacteristic
155C22×C103H(5,𝔽2)11yescharacteristic
156C22×C1032−1+411yescharacteristic
157C2×D103—22no—
158C2×D103—22no—
159C2×D103—22no—
160C2×D103—22no—
161C2×D103—22no—
162C2×D103—22no—
163C2×D103C4×Q814yes—
164C4×C103—22no—
165C4×C103—22no—
166C4×C103—22no—
167C4×C103—22no—
168C4×C103—41no—
169C4×C103—41no—
170C4×C103—41no—
171Dic103—22no—
172Dic103—22no—
173Dic103—22no—
174Dic103—22no—
175Dic103—41no—
176Dic103—41no—
177Dic103—41no—
178C2×C103C2×C4×Q811yescharacteristic
179C2×C103#51811yescharacteristic
180C2×C103#52011yescharacteristic
181C2×C103#53811yescharacteristic
182C2×C103#53911yescharacteristic
183C2×C103#54311yescharacteristic
184C2×C103#54411yescharacteristic
185D103—24no—
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#387D10311yescharacteristic, complemented
197#385—1031no—
198#385—1031no—
199#380—1031no—
200C4×C22⋊C4—1031no—
201C4×C22⋊C4—1031no—
202C2×#95—1031no—
203C22×Q8—1031no—
204C23×C4—1031no—
205C23×C4—1031no—
206C23×C4—1031no—
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⋊C4—1031no—
220C2×C22⋊C4—1031no—
221C2×C42—1031no—
222C2×C42—1031no—
223C2×C42—1031no—
224C2×C42C2×D10311yescharacteristic
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#95C2×D10311yescharacteristic
236#95C2×D10311yescharacteristic
237#95C2×D10311yescharacteristic
238#95C2×D10311yescharacteristic
239C24—1031no—
240C2×Q8—1034no—
241C2×Q8—4121no—
242C2×Q8—4121no—
243C22×C4—1031no—
244C22×C4—1031no—
245C22×C4—1031no—
246C22×C4—1031no—
247C22×C4—1034no—
248C22×C4—1034no—
249C22×C4—1031no—
250C22×C4—1031no—
251C22×C4—1031no—
252C22×C4—4121no—
253C22×C4—4121no—
254C22×C4—4121no—
255C22×C4—4121no—
256C22×C4—4121no—
257C22×C4—4121no—
258C22×C4—2062no—
259C22×C4C22×D10311yescharacteristic
260C22×C4C22×D10311yescharacteristic
261C22×C4C22×D10311yescharacteristic
262C22×C4C22×D10311yescharacteristic
263C22×C4C22×D10311yescharacteristic
264C22×C4C22×D10311yescharacteristic
265C22×C4C22×D10311yescharacteristic
266C4⋊C4—41no—
267C4⋊C4—1034no—
268C4⋊C4—1034no—
269C4⋊C4—4121no—
270C4⋊C4—4121no—
271C4⋊C4—4121no—
272C4⋊C4—4121no—
273C4⋊C4—4121no—
274C4⋊C4C4×D10314yescomplemented
275C22⋊C4—1034no—
276C22⋊C4—1034no—
277C22⋊C4—2062no—
278C22⋊C4—2062no—
279C42—41no—
280C42—4121no—
281C42—4121no—
282C42—4121no—
283C23—1032no—
284C23—1032no—
285C23—1032no—
286C23—2061no—
287C23—2061no—
288C23—2061no—
289C23—2061no—
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—21no—
309C2×C4—1032no—
310C2×C4—1032no—
311C2×C4—1032no—
312C2×C4—1032no—
313C2×C4—4124no—
314C2×C4—4124no—
315C2×C4—4124no—
316C2×C4—2061no—
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×C4C2×C4×D10312yes—
334C2×C4C2×C4×D10312yes—
335C2×C4C2×C4×D10312yes—
336C2×C4Q8×D10312yes—
337C22—1034no—
338C22—2062no—
339C22—2062no—
340C22—2062no—
341C22—2062no—
342C22—2062no—
343C22—2062no—
344C22C22×C4×D10311yescharacteristic
345C22C2×Q8×D10311yescharacteristic
346C22#41×D10311yescharacteristic
347C22#1569306611yescharacteristic
348C22#1569306711yescharacteristic
349C22#1569306711yescharacteristic
350C22#1569306811yescharacteristic
351C4—22no—
352C4—22no—
353C4—22no—
354C4—22no—
355C4—41no—
356C4—41no—
357C4—41no—
358C4—4121no—
359C4—4121no—
360C4—4121no—
361C4—2062no—
362C4—2062no—
363C4—2062no—
364C4—2062no—
365C2—2064no—
366C2C4×Q8×D10311yescharacteristic
367C2#2026826311yescharacteristic
368C2#2026827111yescharacteristic
369C2#2026838011yescharacteristic
370C2#2026838411yescharacteristic
371C2#2026841611yescharacteristic
372C2#2026842111yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#387×C103C2
socle, cosocleC23×C103C24
prime radicalC23×D103C23
hypercenter#387D103
hypocenterC103#2329
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #20267697C2semidirect
3. #20267695C2semidirect
4. #20267690C2semidirect
5. #20267688C2semidirect
6. #20267678C2semidirect
7. #20267673C2semidirect
8. #20267672C2semidirect
15. #387×C103C2semidirect
20. #15692999C4semidirect
55. C2×Dic206C2×C4semidirect
71. C2×C4×D103Q8semidirect
77. Dic103⋊C4C2×C4semidirect
78. Dic103⋊C4C2×C4semidirect
94. C4⋊C4×C103C2×C4semidirect
187. C103#2329semidirect
196. #387D103semidirect
274. C4⋊C4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929992
#202676972
#202676952
#202676902
#202676882
#202676782
#202676732
#202676722
#202676652
#202676482
C4×(C2×D103)⋊C42
#202676382
#95×D1032
#387×C1032
#2329103