Finite Group Databasebeta

← #27198018

Subgroups — #27198018

Order 13184.

548 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊C4×D103C211yesmaximal, characteristic
2#20267688C211yesmaximal, characteristic, complemented
3#20267686C211yesmaximal, characteristic, complemented
4#20267677C211yesmaximal, characteristic, complemented
5#20267676C211yesmaximal, characteristic, complemented
6#20267674C211yesmaximal, characteristic, complemented
7#20267650C211yesmaximal, characteristic
8#20267650C211yesmaximal, characteristic
9#20267648C211yesmaximal, characteristic
10C4×Dic103⋊C4C211yesmaximal, characteristic, complemented
11#20267642C211yesmaximal, characteristic, complemented
12C4×(C2×D103)⋊C4C211yesmaximal, characteristic
13#20267638C211yesmaximal, characteristic
14#20267638C211yesmaximal, characteristic
15#387×C103C211yesmaximal, characteristic, complemented
16C22×C4×D103C2211yescharacteristic
17C22×C4×D103C2211yescharacteristic
18C22×C4×D103C2211yescharacteristic
19C2×C4⋊Dic103C2211yescharacteristic
20C2×C4⋊Dic103C2211yescharacteristic
21C2×Dic103⋊C4C2211yescharacteristic
22C2×Dic103⋊C4C2211yescharacteristic
23C2×Dic103⋊C4C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×Dic103⋊C4C2211yescharacteristic
27C4⋊C4×D103C418yescomplemented
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
35C2×C4×Dic103C2211yescharacteristic
36C2×C4×Dic103C2211yescharacteristic
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
53C22×Dic103C2311yescharacteristic
54C22×Dic103C2311yescharacteristic
55C22×Dic103C2311yescharacteristic
56C22×Dic103C2311yescharacteristic
57C22×Dic103C2311yescharacteristic
58C22×Dic103C2311yescharacteristic
59C22×Dic103C2311yescharacteristic
60C2×C4×D103—22no—
61C2×C4×D103—22no—
62C2×C4×D103—41no—
63C2×C4×D103—41no—
64C2×C4×D103—41no—
65C2×C4×D103—41no—
66C2×C4×D103C2×C414yes—
67C2×C4×D103C2×C414yes—
68C2×C4×D103C2×C414yes—
69C4⋊Dic103—41no—
70C4⋊Dic103C2×C414yes—
71Dic103⋊C4—22no—
72Dic103⋊C4—22no—
73Dic103⋊C4—41no—
74Dic103⋊C4—41no—
75Dic103⋊C4C2×C414yes—
76Dic103⋊C4C2×C414yes—
77(C2×D103)⋊C4—22no—
78(C2×D103)⋊C4—22no—
79(C2×D103)⋊C4—22no—
80(C2×D103)⋊C4Q814yes—
81C4×Dic103—22no—
82C4×Dic103—22no—
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×C414yes—
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×Dic103C22×C412yes—
141C2×Dic103C22×C412yes—
142C2×Dic103C22×C412yes—
143C2×Dic103C2×Q812yes—
144C2×Dic103#4112yes—
145C2×Dic103#4112yes—
146C4×D103—28no—
147C4×D103—44no—
148C4×D103—44no—
149C22×C103C23×C411yescharacteristic
150C22×C103C22×Q811yescharacteristic
151C22×C103C2×#4111yescharacteristic
152C22×C103C2×#4111yescharacteristic
153C22×C103C2×#4111yescharacteristic
154C22×C103H(5,𝔽2)11yescharacteristic
155C22×C103H(5,𝔽2)11yescharacteristic
156C2×D103—22no—
157C2×D103—22no—
158C2×D103—22no—
159C2×D103—22no—
160C2×D103—22no—
161C2×D103—22no—
162C2×D103C4×Q814yes—
163C4×C103—22no—
164C4×C103—22no—
165C4×C103—22no—
166C4×C103—22no—
167C4×C103—41no—
168C4×C103—41no—
169C4×C103—41no—
170Dic103—22no—
171Dic103—22no—
172Dic103—22no—
173Dic103—41no—
174Dic103—41no—
175Dic103—41no—
176Dic103#11714yes—
177C2×C103C2×#11711yescharacteristic
178C2×C103C2×C4×Q811yescharacteristic
179C2×C103#51811yescharacteristic
180C2×C103#55311yescharacteristic
181C2×C103#55311yescharacteristic
182C2×C103#55411yescharacteristic
183C2×C103#55411yescharacteristic
184D103—24no—
185#2345—1031nomaximal, Sylow
186C103#234511yescharacteristic, complemented, Sylow
187C22×C4⋊C4—1031no—
188#389—1031no—
189#389—1031no—
190#387—1031no—
191#387—1031no—
192#387—1031no—
193#387D10311yescharacteristic, complemented
194#380—1031no—
195#380—1031no—
196#380—1031no—
197C4×C4⋊C4—1031no—
198C4×C4⋊C4—1031no—
199C4×C22⋊C4—1031no—
200C4×C22⋊C4—1031no—
201C4×C22⋊C4—1031no—
202C23×C4—1031no—
203C23×C4—1031no—
204C23×C4—1031no—
205C2×C4⋊C4—1031no—
206C2×C4⋊C4—1031no—
207C2×C4⋊C4—1031no—
208C2×C4⋊C4—1038no—
209C2×C4⋊C4—1031no—
210C2×C4⋊C4—1031no—
211C2×C4⋊C4—1031no—
212C2×C4⋊C4—1031no—
213C2×C4⋊C4—1031no—
214C2×C4⋊C4C2×D10311yescharacteristic
215C2×C4⋊C4C2×D10311yescharacteristic
216C2×C22⋊C4—1031no—
217C2×C22⋊C4—1031no—
218C2×C22⋊C4—1031no—
219C2×C22⋊C4—1031no—
220C2×C42—1031no—
221C2×C42—1031no—
222C2×C42—1031no—
223C2×C42—1031no—
224C2×C42—1031no—
225C2×C42C2×D10311yescharacteristic
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#95C2×D10311yescharacteristic
235#95C2×D10311yescharacteristic
236#95C2×D10311yescharacteristic
237#95C2×D10311yescharacteristic
238C24—1031no—
239C22×C4—1031no—
240C22×C4—1031no—
241C22×C4—1031no—
242C22×C4—1031no—
243C22×C4—1034no—
244C22×C4—1034no—
245C22×C4—1034no—
246C22×C4—1031no—
247C22×C4—1031no—
248C22×C4—1031no—
249C22×C4—4121no—
250C22×C4—4121no—
251C22×C4—4121no—
252C22×C4—4121no—
253C22×C4—2062no—
254C22×C4—2062no—
255C22×C4C22×D10311yescharacteristic
256C22×C4C22×D10311yescharacteristic
257C22×C4C22×D10311yescharacteristic
258C22×C4C22×D10311yescharacteristic
259C22×C4C22×D10311yescharacteristic
260C22×C4C22×D10311yescharacteristic
261C22×C4C22×D10311yescharacteristic
262C4⋊C4—41no—
263C4⋊C4—1034no—
264C4⋊C4—1034no—
265C4⋊C4—1034no—
266C4⋊C4—4121no—
267C4⋊C4—4121no—
268C4⋊C4—4121no—
269C4⋊C4—2062no—
270C4⋊C4—2062no—
271C4⋊C4C4×D10314yes—
272C22⋊C4—1034no—
273C22⋊C4—2062no—
274C22⋊C4—2062no—
275C22⋊C4—2062no—
276C42—41no—
277C42—4121no—
278C42—4121no—
279C42—4121no—
280C42—2062no—
281C42—2062no—
282C23—1032no—
283C23—1032no—
284C23—1032no—
285C23—2061no—
286C23—2061no—
287C23—2061no—
288C23—2061no—
289C23C23×D10311yescharacteristic
290C2×C4—21no—
291C2×C4—21no—
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—1032no—
308C2×C4—1032no—
309C2×C4—1032no—
310C2×C4—1032no—
311C2×C4—1032no—
312C2×C4—1032no—
313C2×C4—4124no—
314C2×C4—4124no—
315C2×C4—2068no—
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×C4C2×C4×D10312yes—
332C2×C4C2×C4×D10312yes—
333C2×C4C2×C4×D10312yes—
334C2×C4Q8×D10312yes—
335C22—1034no—
336C22—2062no—
337C22—2062no—
338C22—2062no—
339C22—2062no—
340C22—2062no—
341C22—2062no—
342C22C22×C4×D10311yescharacteristic
343C22C2×Q8×D10311yescharacteristic
344C22#41×D10311yescharacteristic
345C22#41×D10311yescharacteristic
346C22#41×D10311yescharacteristic
347C22#1569306611yescharacteristic
348C22#1569306711yescharacteristic
349C4—22no—
350C4—22no—
351C4—22no—
352C4—22no—
353C4—41no—
354C4—41no—
355C4—41no—
356C4—1034no—
357C4—4121no—
358C4—4121no—
359C4—4121no—
360C4—2062no—
361C4—2062no—
362C4—2062no—
363C2—2064no—
364C2#117×D10311yescharacteristic
365C2C4×Q8×D10311yescharacteristic
366C2#2026826311yescharacteristic
367C2#2026848611yescharacteristic
368C2#2026849211yescharacteristic
369C2#2026849511yescharacteristic
370C2#2026849711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#387×C103C2
socle, cosocleC23×C103C24
prime radicalC23×D103C23
hypercenter#387D103
hypocenterC103#2345
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. #20267688C2semidirect
3. #20267686C2semidirect
4. #20267677C2semidirect
5. #20267676C2semidirect
6. #20267674C2semidirect
10. C4×Dic103⋊C4C2semidirect
11. #20267642C2semidirect
15. #387×C103C2semidirect
27. C4⋊C4×D103C4semidirect
186. C103#2345semidirect
193. #387D103semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×D1032
#202676882
#202676862
#202676772
#202676762
#202676742
#202676502
#202676482
C4×Dic103⋊C42
#202676422
C4×(C2×D103)⋊C42
#202676382
#387×C1032
#2345103