Finite Group Databasebeta

← #27198050

Subgroups — #27198050

Order 13184.

704 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×C22⋊D103C211yesmaximal, characteristic
2C2×(C22⋊D103)⋊C4C211yesmaximal, characteristic
3C2×(C22⋊D103)⋊C4C211yesmaximal, characteristic
4#20267688C211yesmaximal, characteristic, complemented
5#20267686C211yesmaximal, characteristic, complemented
6#20267666C211yesmaximal, characteristic, complemented
7#20267665C211yesmaximal, characteristic, complemented
8#20267662C211yesmaximal, characteristic, complemented
9#20267655C211yesmaximal, characteristic, complemented
10#20267649C211yesmaximal, characteristic, complemented
11#20267648C211yesmaximal, characteristic, complemented
12C4⋊C4×Dic103C211yesmaximal, characteristic, complemented
13C2×C103⋊#95C211yesmaximal, characteristic, complemented
14#95×D103C211yesmaximal, characteristic, complemented
15#385×C103C211yesmaximal, characteristic, complemented
16C22×C22⋊D103C2211yescharacteristic
17C23×Dic103C2211yescharacteristic
18C23×Dic103C2211yescharacteristic
19C22×C4×D103C2211yescharacteristic
20C22×C4×D103C2211yescharacteristic
21C22×C4×D103C2211yescharacteristic
22C4×C22⋊D103—24no—
23(C22⋊D103)⋊C4—24no—
24(C22⋊D103)⋊C4C418yescomplemented
25C2×C4⋊Dic103C2211yescharacteristic
26C2×C4⋊Dic103C2211yescharacteristic
27C2×Dic103⋊C4C2211yescharacteristic
28C2×Dic103⋊C4C2211yescharacteristic
29C2×Dic103⋊C4C2211yescharacteristic
30C2×Dic103⋊C4C2211yescharacteristic
31C2×Dic103⋊C4C2211yescharacteristic
32C2×C22⋊Dic103C2211yescharacteristic
33C2×(C2×D103)⋊C4C2211yescharacteristic
34C2×(C2×D103)⋊C4C2211yescharacteristic
35C2×(C2×D103)⋊C4C2211yescharacteristic
36C2×C4×Dic103C2211yescharacteristic
37C2×C4×Dic103C2211yescharacteristic
38C2×C4×Dic103C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C103⋊#95C2211yescharacteristic
46C103⋊#95C2211yescharacteristic
47C23×C4×C103C2211yescharacteristic
48C2×C4⋊C4×C103C2211yescharacteristic
49C2×C4⋊C4×C103C2211yescharacteristic
50C2×C22⋊C4×C103C2211yescharacteristic
51C2×C22⋊C4×C103C2211yescharacteristic
52#95×C103C2211yescharacteristic
53#95×C103C2211yescharacteristic
54C23×D103C2311yescharacteristic
55C2×C22⋊D103C2×C414yes—
56C2×C22⋊D103D414yes—
57C2×C22⋊D103Q814yes—
58C22×Dic103—22no—
59C22×Dic103—22no—
60C22×Dic103—41no—
61C22×Dic103—41no—
62C22×Dic103—41no—
63C22×Dic103C2×C414yescomplemented
64C22×Dic103C2311yescharacteristic
65C22×Dic103C2311yescharacteristic
66C22×Dic103C2311yescharacteristic
67C22×Dic103C2311yescharacteristic
68C22×Dic103C2311yescharacteristic
69C22×Dic103C2311yescharacteristic
70C22×Dic103C2311yescharacteristic
71C2×C4×D103—22no—
72C2×C4×D103—22no—
73C2×C4×D103—22no—
74C2×C4×D103—22no—
75C2×C4×D103—41no—
76C2×C4×D103—41no—
77C2×C4×D103—41no—
78C2×C4×D103—41no—
79C2×C4×D103C2×C414yescomplemented
80C4⋊Dic103—22no—
81C4⋊Dic103—41no—
82Dic103⋊C4—22no—
83Dic103⋊C4—22no—
84Dic103⋊C4—41no—
85Dic103⋊C4—41no—
86Dic103⋊C4C2×C414yescomplemented
87C22⋊Dic103—22no—
88(C2×D103)⋊C4—22no—
89(C2×D103)⋊C4—22no—
90(C2×D103)⋊C4C2×C414yescomplemented
91C4×Dic103—22no—
92C4×Dic103—22no—
93C4×Dic103C2×C414yescomplemented
94C24×C103C2311yescharacteristic
95C22×C4×C103—22no—
96C22×C4×C103—22no—
97C22×C4×C103—41no—
98C22×C4×C103C2311yescharacteristic
99C22×C4×C103C2311yescharacteristic
100C22×C4×C103C2311yescharacteristic
101C22×C4×C103C2311yescharacteristic
102C22×C4×C103C2311yescharacteristic
103C22×C4×C103C2311yescharacteristic
104C4⋊C4×C103—22no—
105C4⋊C4×C103—41no—
106C22⋊C4×C103—22no—
107C22⋊C4×C103C2×C414yescomplemented
108C23×C103—21no—
109C23×C103—21no—
110C23×C103—21no—
111C23×C103—21no—
112C23×C103C22×C412yes—
113C23×C103C2×D412yes—
114C23×C103C2×Q812yes—
115C23×C103C2411yescharacteristic
116C22×D103—21no—
117C22×D103—21no—
118C22×D103—21no—
119C22×D103—21no—
120C22×D103C22×C412yes—
121C22×D103C2×D412yes—
122C22×D103C2×Q812yes—
123C2×C4×C103—21no—
124C2×C4×C103—21no—
125C2×C4×C103—21no—
126C2×C4×C103—21no—
127C2×C4×C103—21no—
128C2×C4×C103—21no—
129C2×C4×C103—21no—
130C2×C4×C103—21no—
131C2×C4×C103—21no—
132C2×C4×C103—21no—
133C2×C4×C103—21no—
134C2×C4×C103—21no—
135C2×C4×C103—21no—
136C2×C4×C103—21no—
137C2×C4×C103—21no—
138C2×C4×C103—44no—
139C2×C4×C103C22×C412yes—
140C2×C4×C103C22×C412yes—
141C2×C4×C103#4112yes—
142C22⋊D103C4⋊C4116yescomplemented
143C2×Dic103—21no—
144C2×Dic103—21no—
145C2×Dic103—21no—
146C2×Dic103—21no—
147C2×Dic103—21no—
148C2×Dic103—21no—
149C2×Dic103—21no—
150C2×Dic103—21no—
151C2×Dic103—21no—
152C2×Dic103—21no—
153C2×Dic103—21no—
154C2×Dic103—21no—
155C2×Dic103—21no—
156C2×Dic103—21no—
157C2×Dic103—21no—
158C2×Dic103—44no—
159C2×Dic103—44no—
160C2×Dic103C22×C412yes—
161C2×Dic103C22×C412yes—
162C2×Dic103C22×C412yes—
163C2×Dic103C2×D412yes—
164C2×Dic103C2×Q812yes—
165C2×Dic103#4112yes—
166C4×D103—44no—
167C4×D103—44no—
168C4×D103—44no—
169C22×C103—22no—
170C22×C103—22no—
171C22×C103—22no—
172C22×C103—22no—
173C22×C103—22no—
174C22×C103—22no—
175C22×C103C2×C4⋊C414yes—
176C22×C103C23×C411yescharacteristic
177C22×C103C22×D411yescharacteristic
178C22×C103C22×Q811yescharacteristic
179C22×C103C2×#4111yescharacteristic
180C22×C103C2×#4111yescharacteristic
181C22×C103H(5,𝔽2)11yescharacteristic
182C22×C103H(5,𝔽2)11yescharacteristic
183C2×D103—22no—
184C2×D103—22no—
185C2×D103—22no—
186C2×D103—22no—
187C2×D103—22no—
188C2×D103—22no—
189C2×D103C2×C4⋊C414yes—
190C4×C103—22no—
191C4×C103—22no—
192C4×C103—22no—
193C4×C103—41no—
194C4×C103—41no—
195C4×C103—41no—
196Dic103—22no—
197Dic103—22no—
198Dic103—22no—
199Dic103—41no—
200Dic103—41no—
201Dic103—41no—
202Dic103C2×C4⋊C414yes—
203C2×C103—24no—
204C2×C103C22×C4⋊C411yescharacteristic
205C2×C103C4×#4111yescharacteristic
206C2×C103#51811yescharacteristic
207C2×C103#54611yescharacteristic
208C2×C103#54611yescharacteristic
209C2×C103#55411yescharacteristic
210C2×C103#55411yescharacteristic
211D103—24no—
212#2349—1031nomaximal, Sylow
213C103#234911yescharacteristic, complemented, Sylow
214C2×C4×D4—1031no—
215C2×C4×D4—1031no—
216C2×C4×D4—1031no—
217#389—1031no—
218#389—1031no—
219#385—1031no—
220#385—1031no—
221#385—1031no—
222#385D10311yescharacteristic, complemented
223#382—1031no—
224#380—1031no—
225#380—1031no—
226C4×C4⋊C4—1031no—
227C2×#95—1031no—
228C2×#95—1031no—
229C22×D4—1031no—
230C23×C4—1031no—
231C23×C4—1031no—
232C23×C4—1031no—
233C23×C4—1031no—
234C23×C4—1031no—
235C23×C4C2×D10311yescharacteristic
236C4×D4—1038no—
237C4×D4—2064no—
238C4×D4—2064no—
239C2×C4⋊C4—1031no—
240C2×C4⋊C4—1031no—
241C2×C4⋊C4—1031no—
242C2×C4⋊C4—1031no—
243C2×C4⋊C4—1031no—
244C2×C4⋊C4—1031no—
245C2×C4⋊C4—1031no—
246C2×C4⋊C4C2×D10311yescharacteristic
247C2×C4⋊C4C2×D10311yescharacteristic
248C2×C22⋊C4—1031no—
249C2×C22⋊C4—1031no—
250C2×C22⋊C4—1031no—
251C2×C22⋊C4—1031no—
252C2×C22⋊C4C2×D10311yescharacteristic
253C2×C22⋊C4C2×D10311yescharacteristic
254C2×C42—1031no—
255C2×C42—1031no—
256C2×C42—1031no—
257#95—1031no—
258#95—1031no—
259#95—1031no—
260#95—1031no—
261#95—1031no—
262#95—1031no—
263#95—1031no—
264#95—1031no—
265#95C2×D10311yescharacteristic
266#95C2×D10311yescharacteristic
267C24—1031no—
268C24C22×D10311yescharacteristic
269C2×D4—1034no—
270C2×D4—1034no—
271C2×D4—1034no—
272C22×C4—22no—
273C22×C4—22no—
274C22×C4—41no—
275C22×C4—1031no—
276C22×C4—1034no—
277C22×C4—1031no—
278C22×C4—1031no—
279C22×C4—1031no—
280C22×C4—1034no—
281C22×C4—1031no—
282C22×C4—1031no—
283C22×C4—1031no—
284C22×C4—4121no—
285C22×C4—4121no—
286C22×C4—4121no—
287C22×C4—4121no—
288C22×C4—4121no—
289C22×C4—4121no—
290C22×C4—4121no—
291C22×C4—2062no—
292C22×C4—2062no—
293C22×C4—2062no—
294C22×C4—2062no—
295C22×C4—2062no—
296C22×C4—2062no—
297C22×C4C22×D10311yescharacteristic
298C22×C4C22×D10311yescharacteristic
299C22×C4C22×D10311yescharacteristic
300C22×C4C22×D10311yescharacteristic
301C22×C4C22×D10311yescharacteristic
302C22×C4C22×D10311yescharacteristic
303C4⋊C4—22no—
304C4⋊C4—41no—
305C4⋊C4—1034no—
306C4⋊C4—4121no—
307C4⋊C4—4121no—
308C4⋊C4—4121no—
309C4⋊C4—2062no—
310C4⋊C4—2062no—
311C4⋊C4—2062no—
312C22⋊C4—22no—
313C22⋊C4—1034no—
314C22⋊C4—2062no—
315C22⋊C4—2062no—
316C22⋊C4—2062no—
317C22⋊C4C4×D10314yescomplemented
318C42—1034no—
319C42—2062no—
320C42—2062no—
321C23—21no—
322C23—21no—
323C23—21no—
324C23—21no—
325C23—1032no—
326C23—1032no—
327C23—1032no—
328C23—2061no—
329C23—2061no—
330C23—2061no—
331C23—2061no—
332C23C2×C4×D10312yes—
333C23D4×D10312yes—
334C23Q8×D10312yes—
335C23C23×D10311yescharacteristic
336D4—10316no—
337C2×C4—21no—
338C2×C4—21no—
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—21no—
342C2×C4—21no—
343C2×C4—21no—
344C2×C4—21no—
345C2×C4—21no—
346C2×C4—21no—
347C2×C4—21no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—44no—
353C2×C4—1032no—
354C2×C4—1032no—
355C2×C4—1032no—
356C2×C4—1032no—
357C2×C4—1032no—
358C2×C4—1032no—
359C2×C4—4124no—
360C2×C4—4124no—
361C2×C4—4124no—
362C2×C4—4124no—
363C2×C4—4124no—
364C2×C4—2061no—
365C2×C4—2061no—
366C2×C4—2061no—
367C2×C4—2061no—
368C2×C4—2061no—
369C2×C4—2061no—
370C2×C4—2061no—
371C2×C4—2061no—
372C2×C4—2061no—
373C2×C4—2061no—
374C2×C4—2061no—
375C2×C4—2061no—
376C2×C4—2061no—
377C2×C4—2061no—
378C2×C4—2061no—
379C2×C4C2×C4×D10312yes—
380C2×C4C2×C4×D10312yes—
381C2×C4#1311010412yes—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—22no—
387C22—22no—
388C22—1034no—
389C22—2062no—
390C22—2062no—
391C22—2062no—
392C22—2062no—
393C22—2062no—
394C22—2062no—
395C22C4⋊C4×D10314yes—
396C22C22×C4×D10311yescharacteristic
397C22C2×D4×D10311yescharacteristic
398C22C2×Q8×D10311yescharacteristic
399C22#41×D10311yescharacteristic
400C22C2×#1311010411yescharacteristic
401C22#1569306611yescharacteristic
402C22#1569306711yescharacteristic
403C4—22no—
404C4—22no—
405C4—22no—
406C4—41no—
407C4—41no—
408C4—41no—
409C4—1034no—
410C4—4121no—
411C4—4121no—
412C4—4121no—
413C4—2062no—
414C4—2062no—
415C4—2062no—
416C2—24no—
417C2—2064no—
418C2C2×C4⋊C4×D10311yescharacteristic
419C2C4×#1311010411yescharacteristic
420C2#2026826311yescharacteristic
421C2#2026842811yescharacteristic
422C2#2026843311yescharacteristic
423C2#2026849511yescharacteristic
424C2#2026849911yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#385×C103C2
socle, cosocleC23×C103C24
prime radicalC22×C22⋊D103C22
hypercenter#385D103
hypocenterC103#2349
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #385

Complements

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

NH ≅ G/Ntype
4. #20267688C2semidirect
5. #20267686C2semidirect
6. #20267666C2semidirect
7. #20267665C2semidirect
8. #20267662C2semidirect
9. #20267655C2semidirect
10. #20267649C2semidirect
11. #20267648C2semidirect
12. C4⋊C4×Dic103C2semidirect
13. C2×C103⋊#95C2semidirect
14. #95×D103C2semidirect
15. #385×C103C2semidirect
24. (C22⋊D103)⋊C4C4semidirect
63. C22×Dic103C2×C4semidirect
79. C2×C4×D103C2×C4semidirect
86. Dic103⋊C4C2×C4semidirect
90. (C2×D103)⋊C4C2×C4semidirect
93. C4×Dic103C2×C4semidirect
107. C22⋊C4×C103C2×C4semidirect
142. C22⋊D103C4⋊C4semidirect
213. C103#2349semidirect
222. #385D103semidirect
317. C22⋊C4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×C4×C22⋊D1032
C2×(C22⋊D103)⋊C42
#202676882
#202676862
#202676662
#202676652
#202676622
#202676552
#202676492
#202676482
C4⋊C4×Dic1032
C2×C103⋊#952
#95×D1032
#385×C1032
#2349103