Finite Group Databasebeta

← #27198185

Subgroups — #27198185

Order 13184.

688 conjugacy classes of subgroups.

The subgroup lattice has 450 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692993C211yesmaximal, characteristic
2C2×C4×C22⋊D103C211yesmaximal, characteristic, complemented
3C2×#15692977C211yesmaximal, characteristic, complemented
4#20267694C211yesmaximal, characteristic, complemented
5#20267691C211yesmaximal, characteristic, complemented
6#20267691C211yesmaximal, characteristic, complemented
7#20267688C211yesmaximal, characteristic, complemented
8#20267685C211yesmaximal, characteristic, complemented
9#20267683C211yesmaximal, characteristic, complemented
10#20267667C211yesmaximal, characteristic, complemented
11#20267642C211yesmaximal, characteristic, complemented
12C22⋊C4×Dic103C211yesmaximal, characteristic, complemented
13C4×C22⋊Dic103C211yesmaximal, characteristic, complemented
14#20267638C211yesmaximal, characteristic, complemented
15#386×C103C211yesmaximal, characteristic, complemented
16C22×C22⋊D103C2211yescharacteristic
17C22×C22⋊D103C2211yescharacteristic
18C23×Dic103C2211yescharacteristic
19C22×C4×D103C2211yescharacteristic
20#15692993C418yescomplemented
21C4×C22⋊D103—24no—
22#15692977—24no—
23C2×C4⋊Dic103C2211yescharacteristic
24C2×Dic103⋊C4C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×Dic103⋊C4C2211yescharacteristic
27C2×Dic103⋊C4C2211yescharacteristic
28C2×C22⋊Dic103C2211yescharacteristic
29C2×C22⋊Dic103C2211yescharacteristic
30C2×C22⋊Dic103C2211yescharacteristic
31C2×C22⋊Dic103C2211yescharacteristic
32C2×C22⋊Dic103C2211yescharacteristic
33C2×(C2×D103)⋊C4C2211yescharacteristic
34C2×(C2×D103)⋊C4C2211yescharacteristic
35C2×(C2×D103)⋊C4C2211yescharacteristic
36C2×(C2×D103)⋊C4C2211yescharacteristic
37C2×C4×Dic103C2211yescharacteristic
38C2×C4×Dic103C2211yescharacteristic
39C2×C4×Dic103C2211yescharacteristic
40C2×C4×Dic103C2211yescharacteristic
41C2×C4×Dic103C2211yescharacteristic
42C2×C4×Dic103C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C103⋊#95C2211yescharacteristic
46C103⋊#95C2211yescharacteristic
47C22×D4×C103C2211yescharacteristic
48C23×C4×C103C2211yescharacteristic
49C2×C22⋊C4×C103C2211yescharacteristic
50C2×C22⋊C4×C103C2211yescharacteristic
51C2×C22⋊C4×C103C2211yescharacteristic
52#95×C103C2211yescharacteristic
53#95×C103C2211yescharacteristic
54C23×D103C2311yescharacteristic
55C2×C22⋊D103—22no—
56C2×C22⋊D103—22no—
57C2×C22⋊D103—41no—
58C2×C22⋊D103—41no—
59C2×C22⋊D103C2×C414yes—
60C2×C22⋊D103C2×C414yescomplemented
61C22×Dic103—22no—
62C22×Dic103—22no—
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—41no—
74C4⋊Dic103—41no—
75Dic103⋊C4—22no—
76Dic103⋊C4—41no—
77Dic103⋊C4C2×C414yescomplemented
78Dic103⋊C4D414yescomplemented
79C22⋊Dic103—22no—
80C22⋊Dic103—22no—
81C22⋊Dic103—22no—
82C22⋊Dic103—22no—
83C22⋊Dic103C2×C414yescomplemented
84(C2×D103)⋊C4—22no—
85(C2×D103)⋊C4—22no—
86(C2×D103)⋊C4—41no—
87(C2×D103)⋊C4C2×C414yescomplemented
88C4×Dic103—22no—
89C4×Dic103—22no—
90C4×Dic103—22no—
91C4×Dic103—22no—
92C4×Dic103—41no—
93C4×Dic103—41no—
94C24×C103C2311yescharacteristic
95C24×C103C2311yescharacteristic
96C2×D4×C103—41no—
97C2×D4×C103—41no—
98C2×D4×C103C2×C414yescomplemented
99C22×C4×C103—22no—
100C22×C4×C103—22no—
101C22×C4×C103—41no—
102C22×C4×C103C2311yescharacteristic
103C22×C4×C103C2311yescharacteristic
104C22×C4×C103C2311yescharacteristic
105C22×C4×C103C2311yescharacteristic
106C22×C4×C103C2311yescharacteristic
107C22⋊C4×C103—22no—
108C22⋊C4×C103—22no—
109C22⋊C4×C103—41no—
110C23×C103—21no—
111C23×C103—21no—
112C23×C103—21no—
113C23×C103—21no—
114C23×C103—21no—
115C23×C103—21no—
116C23×C103—21no—
117C23×C103—21no—
118C23×C103—21no—
119C23×C103—21no—
120C23×C103—21no—
121C23×C103—21no—
122C23×C103C22×C412yes—
123C23×C103C22×C412yes—
124C23×C103C2411yescharacteristic
125C22×D103—21no—
126C22×D103—21no—
127C22×D103—21no—
128C22×D103—21no—
129C22×D103—21no—
130C22×D103—21no—
131C22×D103C22×C412yes—
132D4×C103—44no—
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—44no—
146C2×C4×C103C22×C412yes—
147C2×C4×C103C2×D412yes—
148C2×C4×C103#4112yes—
149C22⋊D103—28no—
150C22⋊D103—44no—
151C2×Dic103—21no—
152C2×Dic103—21no—
153C2×Dic103—21no—
154C2×Dic103—21no—
155C2×Dic103—21no—
156C2×Dic103—21no—
157C2×Dic103—21no—
158C2×Dic103—21no—
159C2×Dic103—28no—
160C2×Dic103—21no—
161C2×Dic103—21no—
162C2×Dic103—21no—
163C2×Dic103—21no—
164C2×Dic103—21no—
165C2×Dic103—21no—
166C2×Dic103C22×C412yes—
167C2×Dic103C22×C412yes—
168C2×Dic103C22×C412yes—
169C2×Dic103C2×D412yes—
170C2×Dic103C2×D412yes—
171C2×Dic103#4112yes—
172C2×Dic103#4112yes—
173C4×D103—44no—
174C22×C103—22no—
175C22×C103—22no—
176C22×C103—22no—
177C22×C103—22no—
178C22×C103—22no—
179C22×C103—22no—
180C22×C103—41no—
181C22×C103—41no—
182C22×C103—41no—
183C22×C103—41no—
184C22×C103—41no—
185C22×C103—41no—
186C22×C103—41no—
187C22×C103—41no—
188C22×C103C23×C411yescharacteristic
189C22×C103C22×D411yescharacteristic
190C22×C103C2×#4111yescharacteristic
191C22×C103C2×#4111yescharacteristic
192C22×C103C2×#4111yescharacteristic
193C22×C103H(5,𝔽2)11yescharacteristic
194C22×C103H(5,𝔽2)11yescharacteristic
195C2×D103—22no—
196C2×D103—22no—
197C2×D103—22no—
198C2×D103—41no—
199C2×D103—41no—
200C2×D103—41no—
201C2×D103—41no—
202C4×C103—22no—
203C4×C103—22no—
204C4×C103—22no—
205C4×C103—41no—
206C4×C103—41no—
207Dic103—22no—
208Dic103—22no—
209Dic103—22no—
210Dic103—22no—
211Dic103—41no—
212Dic103—41no—
213Dic103C4×D414yes—
214C2×C103—42no—
215C2×C103—42no—
216C2×C103C2×C4×D411yescharacteristic
217C2×C103C4×#4111yescharacteristic
218C2×C103#51811yescharacteristic
219C2×C103#54611yescharacteristic
220C2×C103#55011yescharacteristic
221C2×C103#55311yescharacteristic
222C2×C103#55511yescharacteristic
223D103—42no—
224#2363—1031nomaximal, Sylow
225C103#236311yescharacteristic, complemented, Sylow
226C2×#121—1031no—
227C2×C4×D4—1031no—
228C2×#117—1031no—
229#390—1031no—
230#390—1031no—
231#390—1031no—
232#389—1031no—
233#388—1031no—
234#388—1031no—
235#386—1031no—
236#386D10311yescharacteristic, complemented
237C4×C4⋊C4—1031no—
238C4×C22⋊C4—1031no—
239C4×C22⋊C4—1031no—
240C4×C22⋊C4—1031no—
241C22×D4—1031no—
242C22×D4—1031no—
243C22×D4C2×D10311yescharacteristic
244C23×C4—1031no—
245C23×C4—1031no—
246C23×C4C2×D10311yescharacteristic
247#121—1038no—
248C4×D4—2064no—
249#117—2064no—
250C2×C4⋊C4—1031no—
251C2×C4⋊C4—1031no—
252C2×C4⋊C4—1031no—
253C2×C4⋊C4—1031no—
254C2×C4⋊C4—1031no—
255C2×C22⋊C4—1031no—
256C2×C22⋊C4—1031no—
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⋊C4C2×D10311yescharacteristic
265C2×C22⋊C4C2×D10311yescharacteristic
266C2×C22⋊C4C2×D10311yescharacteristic
267C2×C42—1031no—
268C2×C42—1031no—
269C2×C42—1031no—
270C2×C42—1031no—
271C2×C42—1031no—
272C2×C42—1031no—
273#95—1031no—
274#95—1031no—
275#95—1031no—
276#95—1031no—
277#95C2×D10311yescharacteristic
278#95C2×D10311yescharacteristic
279C24—1031no—
280C24C22×D10311yescharacteristic
281C24C22×D10311yescharacteristic
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—1034no—
285C2×D4—1034no—
286C2×D4—4121no—
287C2×D4—4121no—
288C2×D4—2062no—
289C2×D4—2062no—
290C2×D4C4×D10314yescomplemented
291C22×C4—22no—
292C22×C4—22no—
293C22×C4—41no—
294C22×C4—1031no—
295C22×C4—1034no—
296C22×C4—1031no—
297C22×C4—1031no—
298C22×C4—1031no—
299C22×C4—1031no—
300C22×C4—1031no—
301C22×C4—1031no—
302C22×C4—4121no—
303C22×C4—2062no—
304C22×C4—2062no—
305C22×C4—2062no—
306C22×C4—2062no—
307C22×C4C22×D10311yescharacteristic
308C22×C4C22×D10311yescharacteristic
309C22×C4C22×D10311yescharacteristic
310C22×C4C22×D10311yescharacteristic
311C22×C4C22×D10311yescharacteristic
312C4⋊C4—1034no—
313C4⋊C4—1034no—
314C4⋊C4—4121no—
315C4⋊C4—4121no—
316C4⋊C4—2062no—
317C22⋊C4—22no—
318C22⋊C4—22no—
319C22⋊C4—41no—
320C22⋊C4—1034no—
321C22⋊C4—1034no—
322C22⋊C4—4121no—
323C22⋊C4—2062no—
324C22⋊C4—2062no—
325C22⋊C4—2062no—
326C22⋊C4—2062no—
327C22⋊C4—2062no—
328C22⋊C4—2062no—
329C42—4121no—
330C42—4121no—
331C42—2062no—
332C42—2062no—
333C42—2062no—
334C42—2062no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—21no—
342C23—21no—
343C23—21no—
344C23—21no—
345C23—21no—
346C23—21no—
347C23—1032no—
348C23—2061no—
349C23—2061no—
350C23—2061no—
351C23—2061no—
352C23—2061no—
353C23—2061no—
354C23C2×C4×D10312yes—
355C23C2×C4×D10312yes—
356C23C23×D10311yescharacteristic
357D4—44no—
358D4—4124no—
359D4—2068no—
360C2×C4—21no—
361C2×C4—21no—
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—44no—
373C2×C4—1032no—
374C2×C4—1032no—
375C2×C4—1032no—
376C2×C4—1032no—
377C2×C4—1032no—
378C2×C4—1032no—
379C2×C4—1032no—
380C2×C4—4124no—
381C2×C4—2068no—
382C2×C4—2061no—
383C2×C4—2061no—
384C2×C4—2061no—
385C2×C4—2061no—
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×C4C2×C4×D10312yes—
397C2×C4D4×D10312yes—
398C2×C4#1311010412yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—22no—
403C22—22no—
404C22—22no—
405C22—41no—
406C22—41no—
407C22—41no—
408C22—41no—
409C22—41no—
410C22—41no—
411C22—41no—
412C22—41no—
413C22—4121no—
414C22—4121no—
415C22—4121no—
416C22—4121no—
417C22—2062no—
418C22—2062no—
419C22—2062no—
420C22C22×C4×D10311yescharacteristic
421C22C2×D4×D10311yescharacteristic
422C22#41×D10311yescharacteristic
423C22#41×D10311yescharacteristic
424C22C2×#1311010411yescharacteristic
425C22#1569306611yescharacteristic
426C22#1569306611yescharacteristic
427C4—22no—
428C4—22no—
429C4—22no—
430C4—41no—
431C4—41no—
432C4—1034no—
433C4—4121no—
434C4—4121no—
435C4—2062no—
436C4—2062no—
437C4—2062no—
438C4—2062no—
439C2—42no—
440C2—42no—
441C2—4122no—
442C2C4×D4×D10311yescharacteristic
443C2C4×#1311010411yescharacteristic
444C2#2026826411yescharacteristic
445C2#2026842811yescharacteristic
446C2#2026845911yescharacteristic
447C2#2026848611yescharacteristic
448C2#2026850511yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#386×C103C2
socle, cosocleC23×C103C24
prime radicalC2×#15692993C2
hypercenter#386D103
hypocenterC103#2363
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #386

Complements

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

NH ≅ G/Ntype
2. C2×C4×C22⋊D103C2semidirect
3. C2×#15692977C2semidirect
4. #20267694C2semidirect
5. #20267691C2semidirect
6. #20267691C2semidirect
7. #20267688C2semidirect
8. #20267685C2semidirect
9. #20267683C2semidirect
10. #20267667C2semidirect
11. #20267642C2semidirect
12. C22⋊C4×Dic103C2semidirect
13. C4×C22⋊Dic103C2semidirect
14. #20267638C2semidirect
15. #386×C103C2semidirect
20. #15692993C4semidirect
60. C2×C22⋊D103C2×C4semidirect
63. C22×Dic103C2×C4semidirect
77. Dic103⋊C4C2×C4semidirect
78. Dic103⋊C4D4semidirect
83. C22⋊Dic103C2×C4semidirect
87. (C2×D103)⋊C4C2×C4semidirect
98. C2×D4×C103C2×C4semidirect
225. C103#2363semidirect
236. #386D103semidirect
290. C2×D4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929932
C2×C4×C22⋊D1032
C2×#156929772
#202676942
#202676912
#202676882
#202676852
#202676832
#202676672
#202676422
C22⋊C4×Dic1032
C4×C22⋊Dic1032
#202676382
#386×C1032
#2363103