Finite Group Databasebeta

← #28366185

Subgroups — #28366185

Order 13952.

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×#16812672C211yesmaximal, characteristic
2#20294928C211yesmaximal, characteristic, complemented
3#20294926C211yesmaximal, characteristic, complemented
4#20294918C211yesmaximal, characteristic, complemented
5#20294913C211yesmaximal, characteristic, complemented
6#20294910C211yesmaximal, characteristic, complemented
7#20294904C211yesmaximal, characteristic, complemented
8#20294903C211yesmaximal, characteristic, complemented
9#20294903C211yesmaximal, characteristic, complemented
10#20294902C211yesmaximal, characteristic, complemented
11#20294901C211yesmaximal, characteristic, complemented
12#20294897C211yesmaximal, characteristic, complemented
13#20294888C211yesmaximal, characteristic, complemented
14#20294883C211yesmaximal, characteristic, complemented
15#388×C109C211yesmaximal, characteristic, complemented
16C22×D436C2211yescharacteristic
17C22×C22⋊D109C2211yescharacteristic
18C22×C22⋊D109C2211yescharacteristic
19C23×Dic109C2211yescharacteristic
20C22×C4×D109C2211yescharacteristic
21C22×C4×D109C2211yescharacteristic
22#16812672C418yescomplemented
23C2×C4⋊Dic109C2211yescharacteristic
24C2×C4⋊Dic109C2211yescharacteristic
25C2×#13182008C2211yescharacteristic
26C2×#13182008C2211yescharacteristic
27C2×C22⋊Dic109C2211yescharacteristic
28C2×#13182006C2211yescharacteristic
29C2×#13182006C2211yescharacteristic
30C2×#13182006C2211yescharacteristic
31C2×#13182006C2211yescharacteristic
32C2×#13182006C2211yescharacteristic
33C2×#13182006C2211yescharacteristic
34C2×#13182006C2211yescharacteristic
35C2×#13182006C2211yescharacteristic
36C2×C4×Dic109C2211yescharacteristic
37#16812606C2211yescharacteristic
38#16812606C2211yescharacteristic
39#16812606C2211yescharacteristic
40#16812606C2211yescharacteristic
41#16812606C2211yescharacteristic
42#16812606C2211yescharacteristic
43#16812606C2211yescharacteristic
44#16812606C2211yescharacteristic
45C2×C4⋊C4×C109C2211yescharacteristic
46C2×C22⋊C4×C109C2211yescharacteristic
47C2×C22⋊C4×C109C2211yescharacteristic
48C2×C22⋊C4×C109C2211yescharacteristic
49C2×C42×C109C2211yescharacteristic
50#95×C109C2211yescharacteristic
51#95×C109C2211yescharacteristic
52C23×D109C2311yescharacteristic
53C23×D109C2311yescharacteristic
54C2×D436—41no—
55C2×D436—41no—
56C2×D436C2×C414yescomplemented
57C2×C22⋊D109—41no—
58C2×C22⋊D109—41no—
59C2×C22⋊D109—41no—
60C2×C22⋊D109—41no—
61C2×C22⋊D109C2×C414yes—
62C2×C22⋊D109C2×C414yescomplemented
63C22×Dic109—41no—
64C22×Dic109—41no—
65C22×Dic109—41no—
66C22×Dic109C2311yescharacteristic
67C22×Dic109C2311yescharacteristic
68C22×Dic109C2311yescharacteristic
69C22×Dic109C2311yescharacteristic
70C22×Dic109C2311yescharacteristic
71C22×Dic109C2311yescharacteristic
72C2×C4×D109—41no—
73C2×C4×D109—41no—
74C2×C4×D109—41no—
75C2×C4×D109—41no—
76C2×C4×D109—41no—
77C2×C4×D109C2×C414yescomplemented
78C4⋊Dic109—41no—
79C4⋊Dic109—41no—
80#13182008—41no—
81#13182008C2×C414yescomplemented
82C22⋊Dic109—41no—
83#13182006—41no—
84#13182006—41no—
85#13182006—41no—
86#13182006—41no—
87#13182006—41no—
88#13182006—41no—
89#13182006—41no—
90#13182006C2×C414yescomplemented
91C4×Dic109—41no—
92C24×C109C2311yescharacteristic
93C22×C4×C109C2311yescharacteristic
94C22×C4×C109C2311yescharacteristic
95C22×C4×C109C2311yescharacteristic
96C22×C4×C109C2311yescharacteristic
97C22×C4×C109C2311yescharacteristic
98C22×C4×C109C2311yescharacteristic
99C4⋊C4×C109—41no—
100C22⋊C4×C109—41no—
101C22⋊C4×C109—41no—
102C22⋊C4×C109C2×C414yescomplemented
103C42×C109—41no—
104C23×C109—21no—
105C23×C109—21no—
106C23×C109—21no—
107C23×C109—21no—
108C23×C109—21no—
109C23×C109—21no—
110C23×C109C22×C412yes—
111C23×C109C2411yescharacteristic
112C22×D109—21no—
113C22×D109—21no—
114C22×D109—21no—
115C22×D109—21no—
116C22×D109—21no—
117C22×D109—21no—
118C22×D109—21no—
119C22×D109—21no—
120C22×D109—21no—
121C22×D109—21no—
122C22×D109—21no—
123C22×D109—21no—
124C22×D109C22×C412yes—
125C22×D109C22×C412yes—
126C2×C4×C109—21no—
127C2×C4×C109—21no—
128C2×C4×C109—21no—
129C2×C4×C109—21no—
130C2×C4×C109—21no—
131C2×C4×C109—21no—
132C2×C4×C109—21no—
133C2×C4×C109—21no—
134C2×C4×C109—21no—
135C2×C4×C109—21no—
136C2×C4×C109—21no—
137C2×C4×C109—21no—
138C2×C4×C109—21no—
139C2×C4×C109—21no—
140C2×C4×C109—21no—
141C2×C4×C109—21no—
142C2×C4×C109C22×C412yes—
143C2×C4×C109C22×C412yes—
144C22⋊D109—44no—
145C22⋊D109—44no—
146C2×Dic109—21no—
147C2×Dic109—21no—
148C2×Dic109—21no—
149C2×Dic109—21no—
150C2×Dic109—21no—
151C2×Dic109—21no—
152C2×Dic109—21no—
153C2×Dic109—21no—
154C2×Dic109—21no—
155C2×Dic109—21no—
156C2×Dic109—21no—
157C2×Dic109—21no—
158C2×Dic109—21no—
159C2×Dic109—21no—
160C2×Dic109—21no—
161C2×Dic109—21no—
162C2×Dic109—44no—
163C2×Dic109C22×C412yes—
164C2×Dic109C22×C412yes—
165D436—44no—
166C4×D109—44no—
167C4×D109—44no—
168C22×C109—22no—
169C22×C109—22no—
170C22×C109—22no—
171C22×C109—41no—
172C22×C109—41no—
173C22×C109—41no—
174C22×C109—41no—
175C22×C109C23×C411yescharacteristic
176C22×C109H(5,𝔽2)11yescharacteristic
177C22×C109H(5,𝔽2)11yescharacteristic
178C22×C109H(5,𝔽2)11yescharacteristic
179C22×C109H(5,𝔽2)11yescharacteristic
180C22×C109H(5,𝔽2)11yescharacteristic
181C22×C1092−1+411yescharacteristic
182C2×D109—22no—
183C2×D109—22no—
184C2×D109—22no—
185C2×D109—22no—
186C2×D109—22no—
187C2×D109—22no—
188C2×D109—41no—
189C2×D109—41no—
190C2×D109—41no—
191C2×D109—41no—
192C2×D109—41no—
193C2×D109—41no—
194C2×D109—41no—
195C2×D109—41no—
196C4×C109—22no—
197C4×C109—22no—
198C4×C109—41no—
199C4×C109—41no—
200C4×C109—41no—
201C4×C109—41no—
202Dic109—22no—
203Dic109—22no—
204Dic109—41no—
205Dic109—41no—
206Dic109—41no—
207Dic109—41no—
208C2×C109—42no—
209C2×C109#51811yescharacteristic
210C2×C109#51811yescharacteristic
211C2×C109#52011yescharacteristic
212C2×C109#56011yescharacteristic
213C2×C109#56011yescharacteristic
214C2×C109#56211yescharacteristic
215C2×C109#56211yescharacteristic
216D109—42no—
217D109—42no—
218#2377—1091nomaximal, Sylow
219C109#237711yescharacteristic, complemented, Sylow
220C2×#121—1091no—
221#390—1091no—
222#390—1091no—
223#388—1091no—
224#388D10911yescharacteristic, complemented
225#387—1091no—
226#387—1091no—
227#386—1091no—
228#386—1091no—
229#386—1091no—
230#386—1091no—
231#385—1091no—
232#385—1091no—
233#381—1091no—
234#380—1091no—
235C22×D4—1091no—
236C22×D4—1091no—
237C22×D4—1091no—
238C23×C4—1091no—
239C23×C4—1091no—
240C23×C4—1091no—
241#121—1098no—
242C2×C4⋊C4—1091no—
243C2×C4⋊C4—1091no—
244C2×C4⋊C4—1091no—
245C2×C4⋊C4—1091no—
246C2×C4⋊C4C2×D10911yescharacteristic
247C2×C22⋊C4—1091no—
248C2×C22⋊C4—1091no—
249C2×C22⋊C4—1091no—
250C2×C22⋊C4—1091no—
251C2×C22⋊C4—1091no—
252C2×C22⋊C4—1091no—
253C2×C22⋊C4—1091no—
254C2×C22⋊C4—1091no—
255C2×C22⋊C4—1091no—
256C2×C22⋊C4C2×D10911yescharacteristic
257C2×C22⋊C4C2×D10911yescharacteristic
258C2×C22⋊C4C2×D10911yescharacteristic
259C2×C42—1091no—
260C2×C42C2×D10911yescharacteristic
261#95—1091no—
262#95—1091no—
263#95—1091no—
264#95—1091no—
265#95—1091no—
266#95—1091no—
267#95—1091no—
268#95—1091no—
269#95C2×D10911yescharacteristic
270#95C2×D10911yescharacteristic
271C24—1091no—
272C24—1091no—
273C24C22×D10911yescharacteristic
274C2×D4—1094no—
275C2×D4—1094no—
276C2×D4—1094no—
277C2×D4—4361no—
278C2×D4—4361no—
279C2×D4—4361no—
280C2×D4—4361no—
281C2×D4—4361no—
282C2×D4—4361no—
283C22×C4—1091no—
284C22×C4—1091no—
285C22×C4—1094no—
286C22×C4—1091no—
287C22×C4—1091no—
288C22×C4—1091no—
289C22×C4—1091no—
290C22×C4—4361no—
291C22×C4—4361no—
292C22×C4—4361no—
293C22×C4—4361no—
294C22×C4—4361no—
295C22×C4—4361no—
296C22×C4—4361no—
297C22×C4—4361no—
298C22×C4C22×D10911yescharacteristic
299C22×C4C22×D10911yescharacteristic
300C22×C4C22×D10911yescharacteristic
301C22×C4C22×D10911yescharacteristic
302C22×C4C22×D10911yescharacteristic
303C22×C4C22×D10911yescharacteristic
304C4⋊C4—41no—
305C4⋊C4—1094no—
306C4⋊C4—4361no—
307C4⋊C4—4361no—
308C4⋊C4—4361no—
309C22⋊C4—41no—
310C22⋊C4—41no—
311C22⋊C4—1094no—
312C22⋊C4—4361no—
313C22⋊C4—4361no—
314C22⋊C4—4361no—
315C22⋊C4—4361no—
316C22⋊C4—4361no—
317C22⋊C4—4361no—
318C22⋊C4—4361no—
319C22⋊C4—4361no—
320C22⋊C4C4×D10914yescomplemented
321C42—41no—
322C42—4361no—
323C23—21no—
324C23—21no—
325C23—21no—
326C23—21no—
327C23—21no—
328C23—21no—
329C23—1092no—
330C23—1092no—
331C23—2181no—
332C23—2181no—
333C23—2181no—
334C23—2181no—
335C23—2181no—
336C23—2181no—
337C23—2181no—
338C23—2181no—
339C23—2181no—
340C23—2181no—
341C23—2181no—
342C23—2181no—
343C23C2×C4×D10912yes—
344C23C23×D10911yescharacteristic
345D4—4364no—
346D4—4364no—
347D4—4364no—
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—1092no—
365C2×C4—1092no—
366C2×C4—4364no—
367C2×C4—4364no—
368C2×C4—4364no—
369C2×C4—2181no—
370C2×C4—2181no—
371C2×C4—2181no—
372C2×C4—2181no—
373C2×C4—2181no—
374C2×C4—2181no—
375C2×C4—2181no—
376C2×C4—2181no—
377C2×C4—2181no—
378C2×C4—2181no—
379C2×C4—2181no—
380C2×C4—2181no—
381C2×C4—2181no—
382C2×C4—2181no—
383C2×C4—2181no—
384C2×C4—2181no—
385C2×C4C2×C4×D10912yes—
386C2×C4C2×C4×D10912yes—
387C22—22no—
388C22—22no—
389C22—22no—
390C22—41no—
391C22—41no—
392C22—41no—
393C22—41no—
394C22—4361no—
395C22—4361no—
396C22—4361no—
397C22—4361no—
398C22—4361no—
399C22—4361no—
400C22—4361no—
401C22—4361no—
402C22—2182no—
403C22—2182no—
404C22—2182no—
405C22—2182no—
406C22—2182no—
407C22—2182no—
408C22C22×C4×D10911yescharacteristic
409C22#1681274411yescharacteristic
410C22#1681274411yescharacteristic
411C22#1681274511yescharacteristic
412C22#1681274511yescharacteristic
413C22#1681274511yescharacteristic
414C22#1681274611yescharacteristic
415C4—22no—
416C4—22no—
417C4—41no—
418C4—41no—
419C4—41no—
420C4—41no—
421C4—4361no—
422C4—4361no—
423C4—4361no—
424C4—4361no—
425C4—2182no—
426C4—2182no—
427C2—42no—
428C2—4362no—
429C2—4362no—
430C2#2029549811yescharacteristic
431C2#2029549811yescharacteristic
432C2#2029550611yescharacteristic
433C2#2029576411yescharacteristic
434C2#2029576711yescharacteristic
435C2#2029577011yescharacteristic
436C2#2029577311yescharacteristic
subgroupG/H
center, FrattiniC23C23×D109
commutatorC22×C109C23×C4
Fitting#388×C109C2
socle, cosocleC23×C109C24
prime radicalC2×#16812672C2
hypercenter#388D109
hypocenterC109#2377
LCSG ▷ C22×C109 ▷ C109
UCSC1 ◁ C23 ◁ #388

Complements

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

NH ≅ G/Ntype
2. #20294928C2semidirect
3. #20294926C2semidirect
4. #20294918C2semidirect
5. #20294913C2semidirect
6. #20294910C2semidirect
7. #20294904C2semidirect
8. #20294903C2semidirect
9. #20294903C2semidirect
10. #20294902C2semidirect
11. #20294901C2semidirect
12. #20294897C2semidirect
13. #20294888C2semidirect
14. #20294883C2semidirect
15. #388×C109C2semidirect
22. #16812672C4semidirect
56. C2×D436C2×C4semidirect
62. C2×C22⋊D109C2×C4semidirect
77. C2×C4×D109C2×C4semidirect
81. #13182008C2×C4semidirect
90. #13182006C2×C4semidirect
102. C22⋊C4×C109C2×C4semidirect
219. C109#2377semidirect
224. #388D109semidirect
320. C22⋊C4C4×D109semidirect

Maximal subgroups

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

subgroupindex
C2×#168126722
#202949282
#202949262
#202949182
#202949132
#202949102
#202949042
#202949032
#202949022
#202949012
#202948972
#202948882
#202948832
#388×C1092
#2377109