Finite Group Databasebeta

← #27198297

Subgroups — #27198297

Order 13184.

576 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692994C211yesmaximal, characteristic
2#20267693C211yesmaximal, characteristic, complemented
3#20267691C211yesmaximal, characteristic, complemented
4#20267683C211yesmaximal, characteristic, complemented
5#20267678C211yesmaximal, characteristic, complemented
6#20267675C211yesmaximal, characteristic, complemented
7#20267669C211yesmaximal, characteristic, complemented
8#20267668C211yesmaximal, characteristic, complemented
9#20267668C211yesmaximal, characteristic, complemented
10#20267667C211yesmaximal, characteristic, complemented
11#20267666C211yesmaximal, characteristic, complemented
12#20267662C211yesmaximal, characteristic, complemented
13#20267653C211yesmaximal, characteristic, complemented
14#20267648C211yesmaximal, 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
23C2×C4⋊Dic103C2211yescharacteristic
24C2×C4⋊Dic103C2211yescharacteristic
25C2×Dic103⋊C4C2211yescharacteristic
26C2×Dic103⋊C4C2211yescharacteristic
27C2×C22⋊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×C4×Dic103C2211yescharacteristic
37C103⋊#95C2211yescharacteristic
38C103⋊#95C2211yescharacteristic
39C103⋊#95C2211yescharacteristic
40C103⋊#95C2211yescharacteristic
41C103⋊#95C2211yescharacteristic
42C103⋊#95C2211yescharacteristic
43C103⋊#95C2211yescharacteristic
44C103⋊#95C2211yescharacteristic
45C2×C4⋊C4×C103C2211yescharacteristic
46C2×C22⋊C4×C103C2211yescharacteristic
47C2×C22⋊C4×C103C2211yescharacteristic
48C2×C22⋊C4×C103C2211yescharacteristic
49C2×C42×C103C2211yescharacteristic
50#95×C103C2211yescharacteristic
51#95×C103C2211yescharacteristic
52C23×D103C2311yescharacteristic
53C23×D103C2311yescharacteristic
54C2×D412—41no—
55C2×D412—41no—
56C2×D412C2×C414yescomplemented
57C2×C22⋊D103—41no—
58C2×C22⋊D103—41no—
59C2×C22⋊D103—41no—
60C2×C22⋊D103—41no—
61C2×C22⋊D103C2×C414yes—
62C2×C22⋊D103C2×C414yescomplemented
63C22×Dic103—41no—
64C22×Dic103—41no—
65C22×Dic103—41no—
66C22×Dic103C2311yescharacteristic
67C22×Dic103C2311yescharacteristic
68C22×Dic103C2311yescharacteristic
69C22×Dic103C2311yescharacteristic
70C22×Dic103C2311yescharacteristic
71C22×Dic103C2311yescharacteristic
72C2×C4×D103—41no—
73C2×C4×D103—41no—
74C2×C4×D103—41no—
75C2×C4×D103—41no—
76C2×C4×D103—41no—
77C2×C4×D103C2×C414yescomplemented
78C4⋊Dic103—41no—
79C4⋊Dic103—41no—
80Dic103⋊C4—41no—
81Dic103⋊C4C2×C414yescomplemented
82C22⋊Dic103—41no—
83(C2×D103)⋊C4—41no—
84(C2×D103)⋊C4—41no—
85(C2×D103)⋊C4—41no—
86(C2×D103)⋊C4—41no—
87(C2×D103)⋊C4—41no—
88(C2×D103)⋊C4—41no—
89(C2×D103)⋊C4—41no—
90(C2×D103)⋊C4C2×C414yescomplemented
91C4×Dic103—41no—
92C24×C103C2311yescharacteristic
93C22×C4×C103C2311yescharacteristic
94C22×C4×C103C2311yescharacteristic
95C22×C4×C103C2311yescharacteristic
96C22×C4×C103C2311yescharacteristic
97C22×C4×C103C2311yescharacteristic
98C22×C4×C103C2311yescharacteristic
99C4⋊C4×C103—41no—
100C22⋊C4×C103—41no—
101C22⋊C4×C103—41no—
102C22⋊C4×C103C2×C414yescomplemented
103C42×C103—41no—
104C23×C103—21no—
105C23×C103—21no—
106C23×C103—21no—
107C23×C103—21no—
108C23×C103—21no—
109C23×C103—21no—
110C23×C103C22×C412yes—
111C23×C103C2411yescharacteristic
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×D103C22×C412yes—
125C22×D103C22×C412yes—
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—21no—
139C2×C4×C103—21no—
140C2×C4×C103—21no—
141C2×C4×C103—21no—
142C2×C4×C103C22×C412yes—
143C2×C4×C103C22×C412yes—
144C22⋊D103—44no—
145C22⋊D103—44no—
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—21no—
159C2×Dic103—21no—
160C2×Dic103—21no—
161C2×Dic103—21no—
162C2×Dic103—44no—
163C2×Dic103C22×C412yes—
164C2×Dic103C22×C412yes—
165D412—44no—
166C4×D103—44no—
167C4×D103—44no—
168C22×C103—22no—
169C22×C103—22no—
170C22×C103—22no—
171C22×C103—41no—
172C22×C103—41no—
173C22×C103—41no—
174C22×C103—41no—
175C22×C103C23×C411yescharacteristic
176C22×C103H(5,𝔽2)11yescharacteristic
177C22×C103H(5,𝔽2)11yescharacteristic
178C22×C103H(5,𝔽2)11yescharacteristic
179C22×C103H(5,𝔽2)11yescharacteristic
180C22×C103H(5,𝔽2)11yescharacteristic
181C22×C1032−1+411yescharacteristic
182C2×D103—22no—
183C2×D103—22no—
184C2×D103—22no—
185C2×D103—22no—
186C2×D103—22no—
187C2×D103—22no—
188C2×D103—41no—
189C2×D103—41no—
190C2×D103—41no—
191C2×D103—41no—
192C2×D103—41no—
193C2×D103—41no—
194C2×D103—41no—
195C2×D103—41no—
196C4×C103—22no—
197C4×C103—22no—
198C4×C103—41no—
199C4×C103—41no—
200C4×C103—41no—
201C4×C103—41no—
202Dic103—22no—
203Dic103—22no—
204Dic103—41no—
205Dic103—41no—
206Dic103—41no—
207Dic103—41no—
208C2×C103—42no—
209C2×C103#51811yescharacteristic
210C2×C103#51811yescharacteristic
211C2×C103#52011yescharacteristic
212C2×C103#56011yescharacteristic
213C2×C103#56011yescharacteristic
214C2×C103#56211yescharacteristic
215C2×C103#56211yescharacteristic
216D103—42no—
217D103—42no—
218#2377—1031nomaximal, Sylow
219C103#237711yescharacteristic, complemented, Sylow
220C2×#121—1031no—
221#390—1031no—
222#390—1031no—
223#388—1031no—
224#388D10311yescharacteristic, complemented
225#387—1031no—
226#387—1031no—
227#386—1031no—
228#386—1031no—
229#386—1031no—
230#386—1031no—
231#385—1031no—
232#385—1031no—
233#381—1031no—
234#380—1031no—
235C22×D4—1031no—
236C22×D4—1031no—
237C22×D4—1031no—
238C23×C4—1031no—
239C23×C4—1031no—
240C23×C4—1031no—
241#121—1038no—
242C2×C4⋊C4—1031no—
243C2×C4⋊C4—1031no—
244C2×C4⋊C4—1031no—
245C2×C4⋊C4—1031no—
246C2×C4⋊C4C2×D10311yescharacteristic
247C2×C22⋊C4—1031no—
248C2×C22⋊C4—1031no—
249C2×C22⋊C4—1031no—
250C2×C22⋊C4—1031no—
251C2×C22⋊C4—1031no—
252C2×C22⋊C4—1031no—
253C2×C22⋊C4—1031no—
254C2×C22⋊C4—1031no—
255C2×C22⋊C4—1031no—
256C2×C22⋊C4C2×D10311yescharacteristic
257C2×C22⋊C4C2×D10311yescharacteristic
258C2×C22⋊C4C2×D10311yescharacteristic
259C2×C42—1031no—
260C2×C42C2×D10311yescharacteristic
261#95—1031no—
262#95—1031no—
263#95—1031no—
264#95—1031no—
265#95—1031no—
266#95—1031no—
267#95—1031no—
268#95—1031no—
269#95C2×D10311yescharacteristic
270#95C2×D10311yescharacteristic
271C24—1031no—
272C24—1031no—
273C24C22×D10311yescharacteristic
274C2×D4—1034no—
275C2×D4—1034no—
276C2×D4—1034no—
277C2×D4—4121no—
278C2×D4—4121no—
279C2×D4—4121no—
280C2×D4—4121no—
281C2×D4—4121no—
282C2×D4—4121no—
283C22×C4—1031no—
284C22×C4—1031no—
285C22×C4—1034no—
286C22×C4—1031no—
287C22×C4—1031no—
288C22×C4—1031no—
289C22×C4—1031no—
290C22×C4—4121no—
291C22×C4—4121no—
292C22×C4—4121no—
293C22×C4—4121no—
294C22×C4—4121no—
295C22×C4—4121no—
296C22×C4—4121no—
297C22×C4—4121no—
298C22×C4C22×D10311yescharacteristic
299C22×C4C22×D10311yescharacteristic
300C22×C4C22×D10311yescharacteristic
301C22×C4C22×D10311yescharacteristic
302C22×C4C22×D10311yescharacteristic
303C22×C4C22×D10311yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—1034no—
306C4⋊C4—4121no—
307C4⋊C4—4121no—
308C4⋊C4—4121no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—1034no—
312C22⋊C4—4121no—
313C22⋊C4—4121no—
314C22⋊C4—4121no—
315C22⋊C4—4121no—
316C22⋊C4—4121no—
317C22⋊C4—4121no—
318C22⋊C4—4121no—
319C22⋊C4—4121no—
320C22⋊C4C4×D10314yescomplemented
321C42—41no—
322C42—4121no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—1032no—
330C23—1032no—
331C23—2061no—
332C23—2061no—
333C23—2061no—
334C23—2061no—
335C23—2061no—
336C23—2061no—
337C23—2061no—
338C23—2061no—
339C23—2061no—
340C23—2061no—
341C23—2061no—
342C23—2061no—
343C23C2×C4×D10312yes—
344C23C23×D10311yescharacteristic
345D4—4124no—
346D4—4124no—
347D4—4124no—
348C2×C4—21no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—21no—
353C2×C4—21no—
354C2×C4—21no—
355C2×C4—21no—
356C2×C4—21no—
357C2×C4—21no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—21no—
361C2×C4—21no—
362C2×C4—21no—
363C2×C4—21no—
364C2×C4—1032no—
365C2×C4—1032no—
366C2×C4—4124no—
367C2×C4—4124no—
368C2×C4—4124no—
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×C4—2061no—
380C2×C4—2061no—
381C2×C4—2061no—
382C2×C4—2061no—
383C2×C4—2061no—
384C2×C4—2061no—
385C2×C4C2×C4×D10312yes—
386C2×C4C2×C4×D10312yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—4121no—
395C22—4121no—
396C22—4121no—
397C22—4121no—
398C22—4121no—
399C22—4121no—
400C22—4121no—
401C22—4121no—
402C22—2062no—
403C22—2062no—
404C22—2062no—
405C22—2062no—
406C22—2062no—
407C22—2062no—
408C22C22×C4×D10311yescharacteristic
409C22#1569306611yescharacteristic
410C22#1569306611yescharacteristic
411C22#1569306711yescharacteristic
412C22#1569306711yescharacteristic
413C22#1569306711yescharacteristic
414C22#1569306811yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—4121no—
422C4—4121no—
423C4—4121no—
424C4—4121no—
425C4—2062no—
426C4—2062no—
427C2—42no—
428C2—4122no—
429C2—4122no—
430C2#2026826311yescharacteristic
431C2#2026826311yescharacteristic
432C2#2026827111yescharacteristic
433C2#2026852911yescharacteristic
434C2#2026853211yescharacteristic
435C2#2026853511yescharacteristic
436C2#2026853811yescharacteristic
subgroupG/H
center, FrattiniC23C23×D103
commutatorC22×C103C23×C4
Fitting#388×C103C2
socle, cosocleC23×C103C24
prime radicalC2×#15692994C2
hypercenter#388D103
hypocenterC103#2377
LCSG ▷ C22×C103 ▷ C103
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #20267693C2semidirect
3. #20267691C2semidirect
4. #20267683C2semidirect
5. #20267678C2semidirect
6. #20267675C2semidirect
7. #20267669C2semidirect
8. #20267668C2semidirect
9. #20267668C2semidirect
10. #20267667C2semidirect
11. #20267666C2semidirect
12. #20267662C2semidirect
13. #20267653C2semidirect
14. #20267648C2semidirect
15. #388×C103C2semidirect
22. #15692994C4semidirect
56. C2×D412C2×C4semidirect
62. C2×C22⋊D103C2×C4semidirect
77. C2×C4×D103C2×C4semidirect
81. Dic103⋊C4C2×C4semidirect
90. (C2×D103)⋊C4C2×C4semidirect
102. C22⋊C4×C103C2×C4semidirect
219. C103#2377semidirect
224. #388D103semidirect
320. 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
#202676932
#202676912
#202676832
#202676782
#202676752
#202676692
#202676682
#202676672
#202676662
#202676622
#202676532
#202676482
#388×C1032
#2377103