Finite Group Databasebeta

← #28373231

Subgroups — #28373231

Order 13952.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295631C211yesmaximal, characteristic, complemented
2#20295344C211yesmaximal, characteristic, complemented
3#20295339C211yesmaximal, characteristic, complemented
4#20295333C211yesmaximal, characteristic, complemented
5#20295326C211yesmaximal, characteristic, complemented
6#20295226C211yesmaximal, characteristic, complemented
7#20295221C211yesmaximal, characteristic, complemented
8#20295171C211yesmaximal, characteristic, complemented
9#20295171C211yesmaximal, characteristic, complemented
10#20295136C211yesmaximal, characteristic, complemented
11#20295124C211yesmaximal, characteristic, complemented
12C4×#13182016C211yesmaximal, characteristic, complemented
13C4×#13182014C211yesmaximal, characteristic, complemented
14#20295087C211yesmaximal, characteristic, complemented
15#520×C109C211yesmaximal, characteristic, complemented
16C2×#13182016C2211yescharacteristic
17C2×#13182016C2211yescharacteristic
18C2×#13182014C2211yescharacteristic
19C2×#13182014C2211yescharacteristic
20#16812696C2211yescharacteristic
21#16812691C2211yescharacteristic
22#16812684—21no—
23#16812684—21no—
24#16812673C2211yescharacteristic
25#16812673C2211yescharacteristic
26#16812672—21no—
27#16812672—21no—
28C4×D436C2211yescharacteristic
29C4×D436C2211yescharacteristic
30#16812632C2211yescharacteristic
31#16812632C2211yescharacteristic
32#16812630C2211yescharacteristic
33#16812630C2211yescharacteristic
34C4⋊#11724784C2211yescharacteristic
35C4⋊#11724784C2211yescharacteristic
36#16812623C2211yescharacteristic
37#16812623C2211yescharacteristic
38#16812620C2211yescharacteristic
39#16812620C2211yescharacteristic
40#16812619C2211yescharacteristic
41#16812619C2211yescharacteristic
42#16812619C2211yescharacteristic
43#16812619C2211yescharacteristic
44C22⋊#11724784C2211yescharacteristic
45C22⋊#11724784C2211yescharacteristic
46#16812610C2211yescharacteristic
47C4×#11724784C2211yescharacteristic
48C2×#41×C109C2211yescharacteristic
49C4×Q8×C109C2211yescharacteristic
50C4×Q8×C109C2211yescharacteristic
51C4×D4×C109—21no—
52C4×D4×C109—21no—
53C4×D4×C109C2211yescharacteristic
54C4×D4×C109C2211yescharacteristic
55#117×C109—21no—
56#117×C109C2211yescharacteristic
57C2×C4⋊C4×C109—21no—
58C2×C4⋊C4×C109C2211yescharacteristic
59C2×D436—21no—
60C2×D436—21no—
61C2×D436C2311yescharacteristic
62C2×D436C2311yescharacteristic
63C2×C22⋊D109—21no—
64C2×C22⋊D109—21no—
65C2×C4×D109—21no—
66C2×C4×D109—21no—
67#13182016—22no—
68#13182016—22no—
69#13182014—22no—
70#13182014—22no—
71C2×#11724784C2311yescharacteristic
72C2×#11724784C2311yescharacteristic
73C2×#11724784C2311yescharacteristic
74C2×#11724784C2311yescharacteristic
75C4⋊Dic109C2311yescharacteristic
76C4⋊Dic109C2311yescharacteristic
77#13182008—21no—
78#13182008—21no—
79#13182006—21no—
80#13182006—21no—
81#13182006—21no—
82#13182006—21no—
83#41×C109—22no—
84#41×C109—22no—
85C2×Q8×C109C2311yescharacteristic
86C2×D4×C109—21no—
87C2×D4×C109C2311yescharacteristic
88C22×C4×C109—21no—
89C22×C4×C109—21no—
90C22×C4×C109—21no—
91C22×C4×C109—21no—
92C22×C4×C109C2311yescharacteristic
93C4⋊C4×C109—21no—
94C4⋊C4×C109—21no—
95C4⋊C4×C109—21no—
96C4⋊C4×C109D411yescharacteristic
97C4⋊C4×C109D411yescharacteristic
98C4⋊C4×C109C2311yescharacteristic
99C4⋊C4×C109C2311yescharacteristic
100C22⋊C4×C109—21no—
101C22⋊C4×C109—21no—
102C22⋊C4×C109D411yescharacteristic
103C22⋊C4×C109D411yescharacteristic
104C42×C109—21no—
105C42×C109—21no—
106C42×C109C2311yescharacteristic
107C42×C109C2311yescharacteristic
108C23×C109—21no—
109C23×C109C2×D411yescharacteristic
110C22×D109—21no—
111C22×D109—21no—
112Q8×C109—21no—
113Q8×C109#4112yes—
114D4×C109—24no—
115D4×C109—21no—
116D4×C109#4112yes—
117C2×C4×C109—24no—
118C2×C4×C109—21no—
119C2×C4×C109—21no—
120C2×C4×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—21no—
123C2×C4×C109—81no—
124C2×C4×C109—81no—
125C2×C4×C109—81no—
126C2×C4×C109C2×D411yescharacteristic
127C2×C4×C109C2×D411yescharacteristic
128C2×C4×C109C2×D411yescharacteristic
129C2×C4×C109C2×D411yescharacteristic
130C2×C4×C109C2×D411yescharacteristic
131C2×C4×C109C2411yescharacteristic
132C22⋊D109—81no—
133C22⋊D109—81no—
134C2×Dic109—21no—
135C2×Dic109—21no—
136D436—21no—
137D436—21no—
138D436—21no—
139D436—21no—
140D436—81no—
141D436—81no—
142C4×D109—81no—
143C4×D109—81no—
144#11724784—21no—
145#11724784—21no—
146#11724784—21no—
147#11724784—21no—
148C22×C109—21no—
149C22×C109—22no—
150C22×C109—21no—
151C22×C109—21no—
152C22×C109—41no—
153C22×C109—41no—
154C22×C109C22×D411yescharacteristic
155C2×D109—41no—
156C2×D109—41no—
157C2×D109—41no—
158C2×D109—41no—
159C2×D109—41no—
160C2×D109—41no—
161C4×C109—21no—
162C4×C109—22no—
163C4×C109—21no—
164C4×C109—21no—
165C4×C109—21no—
166C4×C109—21no—
167C4×C109—41no—
168C4×C109—41no—
169C4×C109C2×#4111yescharacteristic
170C4×C109C2×#4111yescharacteristic
171Dic109—41no—
172Dic109—41no—
173C2×C109—41no—
174C2×C109—42no—
175C2×C109#52511yescharacteristic
176C2×C109#57611yescharacteristic
177C2×C109#57711yescharacteristic
178D109—81no—
179D109—81no—
180#3119—1091nomaximal, Sylow
181C109#311911yescharacteristic, complemented, Sylow
182#540—1091no—
183#520D10911yescharacteristic, complemented
184#481—1091no—
185#480—1091no—
186#479—1091no—
187#478—1091no—
188#460—1091no—
189#459—1091no—
190#449—1091no—
191#449—1091no—
192#442—1091no—
193#440—1091no—
194C4×SD16—1091no—
195C4×D8—1091no—
196#433—1091no—
197C2×#41C2×D10911yescharacteristic
198C2×SD16—1091no—
199C2×SD16—1091no—
200C2×D8—1091no—
201C2×D8—1091no—
202#127—1091no—
203#125—1091no—
204#123—2181no—
205#123—2181no—
206#121—1091no—
207#121—1091no—
208#121—2181no—
209#121—2181no—
210C4×Q8C2×D10911yescharacteristic
211C4×Q8C2×D10911yescharacteristic
212C4×D4—21no—
213C4×D4—21no—
214C4×D4—1091no—
215C4×D4—1091no—
216C4×D4C2×D10911yescharacteristic
217C4×D4C2×D10911yescharacteristic
218#117—21no—
219#117C2×D10911yescharacteristic
220C2×C4⋊C4—21no—
221C2×C4⋊C4C2×D10911yescharacteristic
222#107—1091no—
223#107—1091no—
224#106—1091no—
225#106—1091no—
226C4⋊C8—1091no—
227C4⋊C8—1091no—
228#103—1091no—
229#103—1091no—
230#102—1091no—
231#102—1091no—
232#102—1091no—
233#102—1091no—
234#102—1091no—
235#102—1091no—
236C22⋊C8—1091no—
237C22⋊C8—1091no—
238#97—1091no—
239C4×C8—1091no—
240#41—22no—
241#41—22no—
242C2×Q8C22×D10911yescharacteristic
243C2×D4—21no—
244C2×D4—1091no—
245C2×D4—1091no—
246C2×D4—2181no—
247C2×D4—2181no—
248C2×D4—2181no—
249C2×D4—2181no—
250C2×D4C22×D10911yescharacteristic
251C22×C4—21no—
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—21no—
255C22×C4—2181no—
256C22×C4—2181no—
257C22×C4C22×D10911yescharacteristic
258SD16—2182no—
259SD16—2182no—
260D8—2182no—
261D8—2182no—
262C2×C8—1091no—
263C2×C8—1091no—
264C2×C8—1091no—
265C2×C8—1091no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—1091no—
270C4⋊C4—1091no—
271C4⋊C4—2181no—
272C4⋊C4—2181no—
273C4⋊C4C22⋊D10911yescharacteristic
274C4⋊C4C22⋊D10911yescharacteristic
275C4⋊C4C22×D10911yescharacteristic
276C4⋊C4C22×D10911yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—2181no—
280C22⋊C4—2181no—
281C22⋊C4—2181no—
282C22⋊C4—2181no—
283C22⋊C4C22⋊D10911yescharacteristic
284C22⋊C4C22⋊D10911yescharacteristic
285C42—21no—
286C42—21no—
287C42C22×D10911yescharacteristic
288C42C22×D10911yescharacteristic
289C23—21no—
290C23—2181no—
291C23—2181no—
292C23C2×C22⋊D10911yescharacteristic
293Q8—21no—
294Q8#1318202912yes—
295D4—24no—
296D4—21no—
297D4—8721no—
298D4—8721no—
299D4—8721no—
300D4—8721no—
301D4—2181no—
302D4—2181no—
303D4—2181no—
304D4—2181no—
305D4#1318202912yes—
306C2×C4—24no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—81no—
313C2×C4—81no—
314C2×C4—81no—
315C2×C4—8721no—
316C2×C4—8721no—
317C2×C4—2181no—
318C2×C4—2181no—
319C2×C4C2×C22⋊D10911yescharacteristic
320C2×C4C2×C22⋊D10911yescharacteristic
321C2×C4C2×C22⋊D10911yescharacteristic
322C2×C4C2×C22⋊D10911yescharacteristic
323C2×C4C2×C22⋊D10911yescharacteristic
324C2×C4C23×D10911yescharacteristic
325C8—2181no—
326C8—2181no—
327C8—2181no—
328C8—2181no—
329C22—21no—
330C22—22no—
331C22—21no—
332C22—21no—
333C22—41no—
334C22—41no—
335C22—4361no—
336C22—4361no—
337C22—4361no—
338C22—4361no—
339C22—4361no—
340C22—4361no—
341C22C22×C22⋊D10911yescharacteristic
342C4—21no—
343C4—22no—
344C4—21no—
345C4—21no—
346C4—21no—
347C4—21no—
348C4—41no—
349C4—41no—
350C4—4361no—
351C4—4361no—
352C4C2×#1318202911yescharacteristic
353C4C2×#1318202911yescharacteristic
354C2—41no—
355C2—42no—
356C2—8721no—
357C2—8721no—
358C2#2029553711yescharacteristic
359C2#2029582911yescharacteristic
360C2#2029583411yescharacteristic
subgroupG/H
centerC22C22×C22⋊D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
Fitting#520×C109C2
socleC22×C109C22×D4
hypercenter#520D109
hypocenterC109#3119
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ #117 ◁ #520

Complements

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

NH ≅ G/Ntype
1. #20295631C2semidirect
2. #20295344C2semidirect
3. #20295339C2semidirect
4. #20295333C2semidirect
5. #20295326C2semidirect
6. #20295226C2semidirect
7. #20295221C2semidirect
8. #20295171C2semidirect
9. #20295171C2semidirect
10. #20295136C2semidirect
11. #20295124C2semidirect
12. C4×#13182016C2semidirect
13. C4×#13182014C2semidirect
14. #20295087C2semidirect
15. #520×C109C2semidirect
181. C109#3119semidirect
183. #520D109semidirect

Maximal subgroups

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

subgroupindex
#202956312
#202953442
#202953392
#202953332
#202953262
#202952262
#202952212
#202951712
#202951362
#202951242
C4×#131820162
C4×#131820142
#202950872
#520×C1092
#3119109