Finite Group Databasebeta

← #27198190

Subgroups — #27198190

Order 13184.

716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692996C211yesmaximal, characteristic
2C2×C4×D412C211yesmaximal, characteristic, complemented
3C2×#15692983C211yesmaximal, characteristic, complemented
4#20267683C211yesmaximal, characteristic, complemented
5#20267681C211yesmaximal, characteristic, complemented
6#20267677C211yesmaximal, characteristic, complemented
7#20267669C211yesmaximal, characteristic, complemented
8#20267669C211yesmaximal, characteristic, complemented
9#20267669C211yesmaximal, characteristic, complemented
10#20267669C211yesmaximal, characteristic, complemented
11C4×(C2×D103)⋊C4C211yesmaximal, characteristic, complemented
12#20267638C211yesmaximal, characteristic, complemented
13#20267638C211yesmaximal, characteristic, complemented
14#95×D103C211yesmaximal, characteristic, complemented
15#387×C103C211yesmaximal, characteristic, complemented
16C22×D412C2211yescharacteristic
17C22×D412C2211yescharacteristic
18C22×D412C2211yescharacteristic
19C22×C4×D103C2211yescharacteristic
20C22×C4×D103C2211yescharacteristic
21C22×C4×D103C2211yescharacteristic
22C22×C4×D103C2211yescharacteristic
23C22×C4×D103C2211yescharacteristic
24#15692996C418yescomplemented
25C4×D412—24no—
26#15692983—24no—
27C2×C4⋊Dic103C2211yescharacteristic
28C2×(C2×D103)⋊C4C2211yescharacteristic
29C2×(C2×D103)⋊C4C2211yescharacteristic
30C2×(C2×D103)⋊C4C2211yescharacteristic
31C2×(C2×D103)⋊C4C2211yescharacteristic
32C2×(C2×D103)⋊C4C2211yescharacteristic
33C2×(C2×D103)⋊C4C2211yescharacteristic
34C2×(C2×D103)⋊C4C2211yescharacteristic
35C2×(C2×D103)⋊C4C2211yescharacteristic
36C2×(C2×D103)⋊C4C2211yescharacteristic
37C2×(C2×D103)⋊C4C2211yescharacteristic
38C2×C4×Dic103C2211yescharacteristic
39C2×C4×Dic103C2211yescharacteristic
40C2×C4×Dic103C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C103⋊#95C2211yescharacteristic
46C103⋊#95C2211yescharacteristic
47C2×C4⋊C4×C103C2211yescharacteristic
48C2×C4⋊C4×C103C2211yescharacteristic
49C2×C42×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52#95×C103C2211yescharacteristic
53#95×C103C2211yescharacteristic
54C23×D103C2311yescharacteristic
55C23×D103C2311yescharacteristic
56C23×D103C2311yescharacteristic
57C2×D412—22no—
58C2×D412—22no—
59C2×D412—22no—
60C2×D412—22no—
61C2×D412—41no—
62C2×D412—41no—
63C2×D412C2×C414yescomplemented
64C2×D412C2×C414yescomplemented
65C2×D412C2×C414yescomplemented
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—22no—
76C2×C4×D103—22no—
77C2×C4×D103—22no—
78C2×C4×D103—22no—
79C2×C4×D103—41no—
80C2×C4×D103—41no—
81C2×C4×D103—41no—
82C2×C4×D103—41no—
83C2×C4×D103—41no—
84C2×C4×D103—41no—
85C2×C4×D103C2×C414yescomplemented
86C4⋊Dic103—22no—
87(C2×D103)⋊C4—22no—
88(C2×D103)⋊C4—22no—
89(C2×D103)⋊C4—22no—
90(C2×D103)⋊C4—22no—
91(C2×D103)⋊C4—22no—
92(C2×D103)⋊C4—41no—
93(C2×D103)⋊C4—41no—
94(C2×D103)⋊C4C2×C414yescomplemented
95(C2×D103)⋊C4C2×C414yescomplemented
96(C2×D103)⋊C4D414yescomplemented
97C4×Dic103—22no—
98C4×Dic103—41no—
99C4×Dic103—41no—
100C22×C4×C103C2311yescharacteristic
101C22×C4×C103C2311yescharacteristic
102C22×C4×C103C2311yescharacteristic
103C22×C4×C103C2311yescharacteristic
104C22×C4×C103C2311yescharacteristic
105C22×C4×C103C2311yescharacteristic
106C22×C4×C103C2311yescharacteristic
107C4⋊C4×C103—22no—
108C4⋊C4×C103C2×C414yescomplemented
109C42×C103—22no—
110C23×C103C2411yescharacteristic
111C22×D103—21no—
112C22×D103—21no—
113C22×D103—21no—
114C22×D103—21no—
115C22×D103—21no—
116C22×D103—21no—
117C22×D103—21no—
118C22×D103—21no—
119C22×D103—21no—
120C22×D103—21no—
121C22×D103—21no—
122C22×D103—21no—
123C22×D103—21no—
124C22×D103—21no—
125C22×D103—21no—
126C22×D103—21no—
127C22×D103C22×C412yes—
128C22×D103C22×C412yes—
129C22×D103C22×C412yes—
130C22×D103C2×D412yes—
131C22×D103#4112yes—
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—21no—
139C2×C4×C103—21no—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103—21no—
143C2×C4×C103—21no—
144C2×C4×C103—21no—
145C2×C4×C103—21no—
146C2×C4×C103—21no—
147C2×C4×C103—21no—
148C2×C4×C103C22×C412yes—
149C2×C4×C103C22×C412yes—
150C2×C4×C103C22×C412yes—
151C2×C4×C103C2×D412yes—
152C2×C4×C103#4112yes—
153C2×Dic103—21no—
154C2×Dic103—21no—
155C2×Dic103—21no—
156C2×Dic103—21no—
157C2×Dic103—21no—
158C2×Dic103—21no—
159C2×Dic103—21no—
160C2×Dic103—21no—
161C2×Dic103—21no—
162C2×Dic103—21no—
163C2×Dic103—21no—
164C2×Dic103—21no—
165C2×Dic103C22×C412yes—
166C2×Dic103C2×D412yes—
167C2×Dic103#4112yes—
168D412—28no—
169D412—28no—
170D412—44no—
171C4×D103—44no—
172C4×D103—44no—
173C4×D103—44no—
174C4×D103—44no—
175C4×D103—44no—
176C22×C103C23×C411yescharacteristic
177C22×C103C22×D411yescharacteristic
178C22×C103C2×#4111yescharacteristic
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×D103—22no—
190C2×D103—22no—
191C2×D103—22no—
192C2×D103—22no—
193C2×D103—22no—
194C2×D103—22no—
195C2×D103—41no—
196C2×D103—41no—
197C2×D103—41no—
198C2×D103—41no—
199C2×D103—41no—
200C2×D103—41no—
201C2×D103—41no—
202C2×D103—41no—
203C2×D103C4×D414yes—
204C4×C103—22no—
205C4×C103—22no—
206C4×C103—22no—
207C4×C103—22no—
208C4×C103—22no—
209C4×C103—41no—
210C4×C103—41no—
211Dic103—22no—
212Dic103—22no—
213Dic103—22no—
214Dic103—41no—
215Dic103—41no—
216C2×C103C2×C4×D411yescharacteristic
217C2×C103C4×#4111yescharacteristic
218C2×C103#51811yescharacteristic
219C2×C103#54611yescharacteristic
220C2×C103#54611yescharacteristic
221C2×C103#55311yescharacteristic
222C2×C103#55311yescharacteristic
223D103—24no—
224D103—42no—
225D103—42no—
226#2364—1031nomaximal, Sylow
227C103#236411yescharacteristic, complemented, Sylow
228C2×#121—1031no—
229C2×C4×D4—1031no—
230C2×C4×D4—1031no—
231#388—1031no—
232#388—1031no—
233#387—1031no—
234#387D10311yescharacteristic, complemented
235#386—1031no—
236#386—1031no—
237#386—1031no—
238#386—1031no—
239C4×C22⋊C4—1031no—
240C4×C22⋊C4—1031no—
241C4×C22⋊C4—1031no—
242C2×#95—1031no—
243C22×D4—1031no—
244C22×D4—1031no—
245C22×D4—1031no—
246C23×C4—1031no—
247C23×C4—1031no—
248C23×C4—1031no—
249C23×C4—1031no—
250C23×C4—1031no—
251#121—1038no—
252C4×D4—2064no—
253C4×D4—2064no—
254C2×C4⋊C4—1031no—
255C2×C4⋊C4C2×D10311yescharacteristic
256C2×C4⋊C4C2×D10311yescharacteristic
257C2×C22⋊C4—1031no—
258C2×C22⋊C4—1031no—
259C2×C22⋊C4—1031no—
260C2×C22⋊C4—1031no—
261C2×C22⋊C4—1031no—
262C2×C22⋊C4—1031no—
263C2×C22⋊C4—1031no—
264C2×C22⋊C4—1031no—
265C2×C22⋊C4—1031no—
266C2×C22⋊C4—1031no—
267C2×C42—1031no—
268C2×C42—1031no—
269C2×C42—1031no—
270C2×C42C2×D10311yescharacteristic
271#95—1031no—
272#95—1031no—
273#95—1031no—
274#95—1031no—
275#95—1031no—
276#95—1031no—
277#95C2×D10311yescharacteristic
278#95C2×D10311yescharacteristic
279#95C2×D10311yescharacteristic
280#95C2×D10311yescharacteristic
281C24—1031no—
282C24—1031no—
283C24—1031no—
284C2×D4—1034no—
285C2×D4—1034no—
286C2×D4—1034no—
287C2×D4—4121no—
288C2×D4—4121no—
289C2×D4—2062no—
290C2×D4—2062no—
291C2×D4—2062no—
292C2×D4—2062no—
293C22×C4—1031no—
294C22×C4—1031no—
295C22×C4—1031no—
296C22×C4—1034no—
297C22×C4—1031no—
298C22×C4—1031no—
299C22×C4—4121no—
300C22×C4—4121no—
301C22×C4—4121no—
302C22×C4—4121no—
303C22×C4—4121no—
304C22×C4—4121no—
305C22×C4—2062no—
306C22×C4—2062no—
307C22×C4—2062no—
308C22×C4—2062no—
309C22×C4—2062no—
310C22×C4—2062no—
311C22×C4—2062no—
312C22×C4—2062no—
313C22×C4C22×D10311yescharacteristic
314C22×C4C22×D10311yescharacteristic
315C22×C4C22×D10311yescharacteristic
316C22×C4C22×D10311yescharacteristic
317C22×C4C22×D10311yescharacteristic
318C22×C4C22×D10311yescharacteristic
319C22×C4C22×D10311yescharacteristic
320C4⋊C4—22no—
321C4⋊C4—2062no—
322C4⋊C4C4×D10314yescomplemented
323C22⋊C4—1034no—
324C22⋊C4—1034no—
325C22⋊C4—1034no—
326C22⋊C4—4121no—
327C22⋊C4—4121no—
328C22⋊C4—2062no—
329C22⋊C4—2062no—
330C22⋊C4—2062no—
331C22⋊C4—2062no—
332C22⋊C4—2062no—
333C42—22no—
334C42—4121no—
335C42—4121no—
336C42—2062no—
337C23—1032no—
338C23—1032no—
339C23—1032no—
340C23—1032no—
341C23—1032no—
342C23—2061no—
343C23—2061no—
344C23—2061no—
345C23—2061no—
346C23—2061no—
347C23—2061no—
348C23—2061no—
349C23—2061no—
350C23—2061no—
351C23—2061no—
352C23—2061no—
353C23—2061no—
354C23—2061no—
355C23—2061no—
356C23—2061no—
357C23—2061no—
358C23C23×D10311yescharacteristic
359D4—4124no—
360D4—2068no—
361D4—2068no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—21no—
365C2×C4—21no—
366C2×C4—21no—
367C2×C4—21no—
368C2×C4—21no—
369C2×C4—21no—
370C2×C4—21no—
371C2×C4—21no—
372C2×C4—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—21no—
376C2×C4—21no—
377C2×C4—21no—
378C2×C4—1032no—
379C2×C4—1032no—
380C2×C4—1032no—
381C2×C4—4124no—
382C2×C4—4124no—
383C2×C4—4124no—
384C2×C4—4124no—
385C2×C4—4124no—
386C2×C4—2061no—
387C2×C4—2061no—
388C2×C4—2061no—
389C2×C4—2061no—
390C2×C4—2061no—
391C2×C4—2061no—
392C2×C4—2061no—
393C2×C4—2061no—
394C2×C4—2061no—
395C2×C4—2061no—
396C2×C4—2061no—
397C2×C4—2061no—
398C2×C4C2×C4×D10312yes—
399C2×C4C2×C4×D10312yes—
400C2×C4C2×C4×D10312yes—
401C2×C4D4×D10312yes—
402C2×C4#1311010612yes—
403C22—1034no—
404C22—4121no—
405C22—4121no—
406C22—4121no—
407C22—4121no—
408C22—4121no—
409C22—4121no—
410C22—4121no—
411C22—4121no—
412C22—2062no—
413C22—2062no—
414C22—2062no—
415C22—2062no—
416C22—2062no—
417C22—2062no—
418C22—2062no—
419C22—2062no—
420C22—2062no—
421C22—2062no—
422C22—2062no—
423C22—2062no—
424C22C22×C4×D10311yescharacteristic
425C22C2×D4×D10311yescharacteristic
426C22#41×D10311yescharacteristic
427C22#41×D10311yescharacteristic
428C22C2×#1311010611yescharacteristic
429C22#1569306711yescharacteristic
430C22#1569306711yescharacteristic
431C4—22no—
432C4—22no—
433C4—22no—
434C4—22no—
435C4—22no—
436C4—41no—
437C4—41no—
438C4—4121no—
439C4—4121no—
440C4—2062no—
441C4—2062no—
442C4—2062no—
443C2—4122no—
444C2—4122no—
445C2—2064no—
446C2C4×D4×D10311yescharacteristic
447C2C4×#1311010611yescharacteristic
448C2#2026826511yescharacteristic
449C2#2026843211yescharacteristic
450C2#2026843311yescharacteristic
451C2#2026849211yescharacteristic
452C2#2026849411yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#387×C103C2
socle, cosocleC23×C103C24
prime radicalC2×#15692996C2
hypercenter#387D103
hypocenterC103#2364
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
2. C2×C4×D412C2semidirect
3. C2×#15692983C2semidirect
4. #20267683C2semidirect
5. #20267681C2semidirect
6. #20267677C2semidirect
7. #20267669C2semidirect
8. #20267669C2semidirect
9. #20267669C2semidirect
10. #20267669C2semidirect
11. C4×(C2×D103)⋊C4C2semidirect
12. #20267638C2semidirect
13. #20267638C2semidirect
14. #95×D103C2semidirect
15. #387×C103C2semidirect
24. #15692996C4semidirect
63. C2×D412C2×C4semidirect
64. C2×D412C2×C4semidirect
65. C2×D412C2×C4semidirect
85. C2×C4×D103C2×C4semidirect
94. (C2×D103)⋊C4C2×C4semidirect
95. (C2×D103)⋊C4C2×C4semidirect
96. (C2×D103)⋊C4D4semidirect
108. C4⋊C4×C103C2×C4semidirect
227. C103#2364semidirect
234. #387D103semidirect
322. C4⋊C4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929962
C2×C4×D4122
C2×#156929832
#202676832
#202676812
#202676772
#202676692
C4×(C2×D103)⋊C42
#202676382
#95×D1032
#387×C1032
#2364103