Finite Group Databasebeta

← #27197832

Subgroups — #27197832

Order 13184.

668 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×#15692994C211yesmaximal, characteristic
2C2×(C22⋊D103)⋊C4C211yesmaximal, characteristic, complemented
3C2×#15692979C211yesmaximal, characteristic, complemented
4#20267693C211yesmaximal, characteristic, complemented
5#20267691C211yesmaximal, characteristic, complemented
6#20267691C211yesmaximal, characteristic, complemented
7#20267688C211yesmaximal, characteristic, complemented
8#20267681C211yesmaximal, characteristic, complemented
9#20267669C211yesmaximal, characteristic, complemented
10#20267668C211yesmaximal, characteristic, complemented
11#20267666C211yesmaximal, characteristic, complemented
12#20267665C211yesmaximal, characteristic, complemented
13#20267650C211yesmaximal, characteristic, complemented
14C4×Dic103⋊C4C211yesmaximal, characteristic, complemented
15#388×C103C211yesmaximal, characteristic, complemented
16C22×D412C2211yescharacteristic
17C22×C22⋊D103C2211yescharacteristic
18C22×C22⋊D103C2211yescharacteristic
19C23×Dic103C2211yescharacteristic
20C22×C4×D103C2211yescharacteristic
21C22×C4×D103C2211yescharacteristic
22#15692994C418yescomplemented
23(C22⋊D103)⋊C4—24no—
24#15692979—24no—
25C2×C4⋊Dic103C2211yescharacteristic
26C2×C4⋊Dic103C2211yescharacteristic
27C2×Dic103⋊C4C2211yescharacteristic
28C2×Dic103⋊C4C2211yescharacteristic
29C2×Dic103⋊C4C2211yescharacteristic
30C2×Dic103⋊C4C2211yescharacteristic
31C2×C22⋊Dic103C2211yescharacteristic
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×(C2×D103)⋊C4C2211yescharacteristic
39C2×(C2×D103)⋊C4C2211yescharacteristic
40C2×C4×Dic103C2211yescharacteristic
41C2×C4×Dic103C2211yescharacteristic
42C2×C4×Dic103C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C103⋊#95C2211yescharacteristic
46C103⋊#95C2211yescharacteristic
47C2×C4⋊C4×C103C2211yescharacteristic
48C2×C22⋊C4×C103C2211yescharacteristic
49C2×C22⋊C4×C103C2211yescharacteristic
50C2×C22⋊C4×C103C2211yescharacteristic
51C2×C42×C103C2211yescharacteristic
52#95×C103C2211yescharacteristic
53#95×C103C2211yescharacteristic
54C23×D103C2311yescharacteristic
55C23×D103C2311yescharacteristic
56C2×D412—41no—
57C2×D412—41no—
58C2×D412C2×C414yescomplemented
59C2×C22⋊D103—22no—
60C2×C22⋊D103—22no—
61C2×C22⋊D103—41no—
62C2×C22⋊D103—41no—
63C2×C22⋊D103C2×C414yes—
64C2×C22⋊D103C2×C414yescomplemented
65C22×Dic103—22no—
66C22×Dic103—41no—
67C22×Dic103—41no—
68C22×Dic103C2311yescharacteristic
69C22×Dic103C2311yescharacteristic
70C22×Dic103C2311yescharacteristic
71C22×Dic103C2311yescharacteristic
72C22×Dic103C2311yescharacteristic
73C22×Dic103C2311yescharacteristic
74C2×C4×D103—22no—
75C2×C4×D103—22no—
76C2×C4×D103—22no—
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⋊C4C2×C414yescomplemented
86C22⋊Dic103—41no—
87(C2×D103)⋊C4—22no—
88(C2×D103)⋊C4—22no—
89(C2×D103)⋊C4—22no—
90(C2×D103)⋊C4—41no—
91(C2×D103)⋊C4—41no—
92(C2×D103)⋊C4—41no—
93(C2×D103)⋊C4—41no—
94(C2×D103)⋊C4C2×C414yescomplemented
95C4×Dic103—22no—
96C4×Dic103—41no—
97C4×Dic103D414yescomplemented
98C24×C103C2311yescharacteristic
99C22×C4×C103C2311yescharacteristic
100C22×C4×C103C2311yescharacteristic
101C22×C4×C103C2311yescharacteristic
102C22×C4×C103C2311yescharacteristic
103C22×C4×C103C2311yescharacteristic
104C22×C4×C103C2311yescharacteristic
105C4⋊C4×C103—22no—
106C22⋊C4×C103—22no—
107C22⋊C4×C103—41no—
108C22⋊C4×C103C2×C414yescomplemented
109C42×C103—41no—
110C23×C103—21no—
111C23×C103—21no—
112C23×C103—21no—
113C23×C103—21no—
114C23×C103—21no—
115C23×C103—21no—
116C23×C103C22×C412yes—
117C23×C103C2411yescharacteristic
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×D103—21no—
128C22×D103—21no—
129C22×D103—21no—
130C22×D103C22×C412yes—
131C22×D103C22×C412yes—
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×C103C22×C412yes—
148C2×C4×C103C22×C412yes—
149C2×C4×C103C2×D412yes—
150C22⋊D103—28no—
151C22⋊D103—44no—
152C2×Dic103—21no—
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×Dic103—44no—
166C2×Dic103C22×C412yes—
167C2×Dic103C22×C412yes—
168C2×Dic103C2×D412yes—
169C2×Dic103C2×D412yes—
170C2×Dic103#4112yes—
171D412—44no—
172C4×D103—28no—
173C4×D103—44no—
174C22×C103—22no—
175C22×C103—22no—
176C22×C103—22no—
177C22×C103—41no—
178C22×C103—41no—
179C22×C103—41no—
180C22×C103—41no—
181C22×C103C23×C411yescharacteristic
182C22×C103C22×D411yescharacteristic
183C22×C103C2×#4111yescharacteristic
184C22×C103H(5,𝔽2)11yescharacteristic
185C22×C103H(5,𝔽2)11yescharacteristic
186C22×C103H(5,𝔽2)11yescharacteristic
187C22×C1032−1+411yescharacteristic
188C2×D103—22no—
189C2×D103—22no—
190C2×D103—22no—
191C2×D103—22no—
192C2×D103—22no—
193C2×D103—22no—
194C2×D103—41no—
195C2×D103—41no—
196C2×D103—41no—
197C2×D103—41no—
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—
207C4×C103—41no—
208Dic103—22no—
209Dic103—22no—
210Dic103—41no—
211Dic103—41no—
212Dic103—41no—
213Dic103C4×D414yes—
214C2×C103—42no—
215C2×C103C2×C4×D411yescharacteristic
216C2×C103#51811yescharacteristic
217C2×C103#52011yescharacteristic
218C2×C103#53511yescharacteristic
219C2×C103#53711yescharacteristic
220C2×C103#54011yescharacteristic
221C2×C103#54211yescharacteristic
222D103—42no—
223D103—42no—
224#2324—1031nomaximal, Sylow
225C103#232411yescharacteristic, 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#388D10311yescharacteristic, complemented
235#386—1031no—
236#386—1031no—
237#385—1031no—
238#385—1031no—
239#380—1031no—
240C4×C4⋊C4—1031no—
241C22×D4—1031no—
242C22×D4—1031no—
243C22×D4—1031no—
244C23×C4—1031no—
245C23×C4—1031no—
246C23×C4—1031no—
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×C4⋊C4—1031no—
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⋊C4C2×D10311yescharacteristic
267C2×C22⋊C4C2×D10311yescharacteristic
268C2×C22⋊C4C2×D10311yescharacteristic
269C2×C42—1031no—
270C2×C42—1031no—
271C2×C42—1031no—
272C2×C42C2×D10311yescharacteristic
273#95—1031no—
274#95—1031no—
275#95—1031no—
276#95—1031no—
277#95C2×D10311yescharacteristic
278#95C2×D10311yescharacteristic
279C24—1031no—
280C24—1031no—
281C24C22×D10311yescharacteristic
282C2×D4—1034no—
283C2×D4—1034no—
284C2×D4—1034no—
285C2×D4—4121no—
286C2×D4—4121no—
287C2×D4—4121no—
288C2×D4—4121no—
289C2×D4—2062no—
290C2×D4—2062no—
291C22×C4—1031no—
292C22×C4—1031no—
293C22×C4—1031no—
294C22×C4—1034no—
295C22×C4—1031no—
296C22×C4—1031no—
297C22×C4—1031no—
298C22×C4—4121no—
299C22×C4—4121no—
300C22×C4—4121no—
301C22×C4—4121no—
302C22×C4—2062no—
303C22×C4—2062no—
304C22×C4—2062no—
305C22×C4—2062no—
306C22×C4C22×D10311yescharacteristic
307C22×C4C22×D10311yescharacteristic
308C22×C4C22×D10311yescharacteristic
309C22×C4C22×D10311yescharacteristic
310C22×C4C22×D10311yescharacteristic
311C22×C4C22×D10311yescharacteristic
312C4⋊C4—22no—
313C4⋊C4—1034no—
314C4⋊C4—4121no—
315C4⋊C4—4121no—
316C4⋊C4—2062no—
317C4⋊C4—2062no—
318C4⋊C4—2062no—
319C22⋊C4—22no—
320C22⋊C4—41no—
321C22⋊C4—1034no—
322C22⋊C4—4121no—
323C22⋊C4—4121no—
324C22⋊C4—4121no—
325C22⋊C4—4121no—
326C22⋊C4—4121no—
327C22⋊C4—2062no—
328C22⋊C4—2062no—
329C22⋊C4—2062no—
330C22⋊C4C4×D10314yescomplemented
331C42—41no—
332C42—1034no—
333C42—4121no—
334C42—2062no—
335C23—21no—
336C23—21no—
337C23—21no—
338C23—21no—
339C23—21no—
340C23—21no—
341C23—1032no—
342C23—1032no—
343C23—2061no—
344C23—2061no—
345C23—2061no—
346C23—2061no—
347C23—2061no—
348C23—2061no—
349C23—2061no—
350C23—2061no—
351C23—2061no—
352C23—2061no—
353C23—2061no—
354C23—2061no—
355C23C2×C4×D10312yes—
356C23C23×D10311yescharacteristic
357D4—4124no—
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—21no—
373C2×C4—21no—
374C2×C4—21no—
375C2×C4—1032no—
376C2×C4—1032no—
377C2×C4—1032no—
378C2×C4—1032no—
379C2×C4—1032no—
380C2×C4—4124no—
381C2×C4—4124no—
382C2×C4—2068no—
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×C4C2×C4×D10312yes—
398C2×C4D4×D10312yes—
399C22—22no—
400C22—22no—
401C22—22no—
402C22—41no—
403C22—41no—
404C22—41no—
405C22—41no—
406C22—4121no—
407C22—4121no—
408C22—4121no—
409C22—4121no—
410C22—4121no—
411C22—4121no—
412C22—4121no—
413C22—4121no—
414C22—2062no—
415C22—2062no—
416C22—2062no—
417C22—2062no—
418C22—2062no—
419C22—2062no—
420C22C22×C4×D10311yescharacteristic
421C22C2×D4×D10311yescharacteristic
422C22#41×D10311yescharacteristic
423C22#1569306611yescharacteristic
424C22#1569306711yescharacteristic
425C22#1569306711yescharacteristic
426C22#1569306811yescharacteristic
427C4—22no—
428C4—22no—
429C4—22no—
430C4—41no—
431C4—41no—
432C4—41no—
433C4—1034no—
434C4—4121no—
435C4—4121no—
436C4—4121no—
437C4—2062no—
438C4—2062no—
439C2—42no—
440C2—4122no—
441C2—4122no—
442C2C4×D4×D10311yescharacteristic
443C2#2026826311yescharacteristic
444C2#2026827111yescharacteristic
445C2#2026835911yescharacteristic
446C2#2026836811yescharacteristic
447C2#2026839311yescharacteristic
448C2#2026840711yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#388×C103C2
socle, cosocleC23×C103C24
prime radicalC2×#15692994C2
hypercenter#388D103
hypocenterC103#2324
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. C2×(C22⋊D103)⋊C4C2semidirect
3. C2×#15692979C2semidirect
4. #20267693C2semidirect
5. #20267691C2semidirect
6. #20267691C2semidirect
7. #20267688C2semidirect
8. #20267681C2semidirect
9. #20267669C2semidirect
10. #20267668C2semidirect
11. #20267666C2semidirect
12. #20267665C2semidirect
13. #20267650C2semidirect
14. C4×Dic103⋊C4C2semidirect
15. #388×C103C2semidirect
22. #15692994C4semidirect
58. C2×D412C2×C4semidirect
64. C2×C22⋊D103C2×C4semidirect
79. C2×C4×D103C2×C4semidirect
85. Dic103⋊C4C2×C4semidirect
94. (C2×D103)⋊C4C2×C4semidirect
97. C4×Dic103D4semidirect
108. C22⋊C4×C103C2×C4semidirect
225. C103#2324semidirect
234. #388D103semidirect
330. C22⋊C4C4×D103semidirect

Maximal subgroups

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

subgroupindex
C2×#156929942
C2×(C22⋊D103)⋊C42
C2×#156929792
#202676932
#202676912
#202676882
#202676812
#202676692
#202676682
#202676662
#202676652
#202676502
C4×Dic103⋊C42
#388×C1032
#2324103