Finite Group Databasebeta

← #28374915

Subgroups — #28374915

Order 13952.

386 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20295711C211yesmaximal, characteristic, complemented
2#20295687C211yesmaximal, characteristic
3#20295382C211yesmaximal, characteristic, complemented
4#20295365C211yesmaximal, characteristic, complemented
5#20295339C211yesmaximal, characteristic, complemented
6#20295331C211yesmaximal, characteristic, complemented
7#20295266C211yesmaximal, characteristic, complemented
8#20295255C211yesmaximal, characteristic, complemented
9#20295251C211yesmaximal, characteristic, complemented
10#20295191C211yesmaximal, characteristic, complemented
11#20295182C211yesmaximal, characteristic, complemented
12#20295118C211yesmaximal, characteristic, complemented
13C8×C22⋊D109C211yesmaximal, characteristic, complemented
14#20295021C211yesmaximal, characteristic, complemented
15C2×#103×C109C211yesmaximal, characteristic, complemented
16C2×#13182030C2211yescharacteristic
17C2×#13182019C2211yescharacteristic
18C2×#13182019C2211yescharacteristic
19C2×#13182018C2211yescharacteristic
20C2×C8×D109C2211yescharacteristic
21#16812694—21no—
22#16812690C2211yescharacteristic
23#16812689—21no—
24#16812688—21no—
25#16812688C2211yescharacteristic
26#16812682—21no—
27#16812679C2211yescharacteristic
28#16812678C2211yescharacteristic
29#16812675—21no—
30#16812675C2211yescharacteristic
31#16812673—21no—
32#16812673C2211yescharacteristic
33Q8×Dic109C2211yescharacteristic
34#16812664C2211yescharacteristic
35C4×C22⋊D109—21no—
36C4×C22⋊D109C2211yescharacteristic
37#16812658—21no—
38#16812657C2211yescharacteristic
39#16812632C2211yescharacteristic
40#16812632C2211yescharacteristic
41#16812631C2211yescharacteristic
42#16812628C2211yescharacteristic
43#16812624C2211yescharacteristic
44#16812623C2211yescharacteristic
45#16812623C2211yescharacteristic
46#16812621C2211yescharacteristic
47#16812619C2211yescharacteristic
48#16812619C2211yescharacteristic
49C22⋊#11724784C2211yescharacteristic
50#16812611C2211yescharacteristic
51C8×Dic109C2211yescharacteristic
52C22×Q8×C109C2211yescharacteristic
53C22×C8×C109C2211yescharacteristic
54C2×C4⋊C4×C109C2211yescharacteristic
55#103×C109C2211yescharacteristic
56#103×C109C2211yescharacteristic
57#103×C109C2211yescharacteristic
58#103×C109C2211yescharacteristic
59#13182030—22no—
60#13182030—41no—
61C2×Dic218C2311yescharacteristic
62C2×D436—21no—
63C2×D436C2311yescharacteristic
64C2×C22⋊D109—21no—
65C2×C22⋊D109D411yescharacteristic
66C2×C4×D109—21no—
67C2×C4×D109C2311yescharacteristic
68#13182019—22no—
69#13182019—41no—
70#13182018—41no—
71C2×#11724784C2311yescharacteristic
72C2×#11724784C2311yescharacteristic
73C8×D109—41no—
74C4⋊Dic109—21no—
75C4⋊Dic109—21no—
76C4⋊Dic109—21no—
77C4⋊Dic109C2311yescharacteristic
78C4⋊Dic109C2311yescharacteristic
79#13182008—21no—
80#13182008—21no—
81#13182008—21no—
82#13182008—21no—
83#13182008D411yescharacteristic
84C22⋊Dic109—21no—
85C22⋊Dic109D411yescharacteristic
86#13182006—21no—
87#13182006—21no—
88#13182006—21no—
89#13182006—21no—
90#13182006—21no—
91#13182006—21no—
92#13182006D411yescharacteristic
93C4×Dic109—21no—
94C4×Dic109—21no—
95C4×Dic109—21no—
96C4×Dic109C2311yescharacteristic
97C2×Q8×C109—21no—
98C2×Q8×C109—22no—
99C2×Q8×C109—41no—
100C2×Q8×C109C2311yescharacteristic
101C2×Q8×C109C2311yescharacteristic
102C22×C4×C109—21no—
103C22×C4×C109—21no—
104C22×C4×C109C2311yescharacteristic
105C2×C8×C109—41no—
106C2×C8×C109C2311yescharacteristic
107C2×C8×C109C2311yescharacteristic
108C4⋊C4×C109—21no—
109C4⋊C4×C109C2311yescharacteristic
110C4⋊C4×C109C2311yescharacteristic
111C23×C109C2×D411yescharacteristic
112C22×D109—21no—
113C22×D109C2×D411yescharacteristic
114Q8×C109—21no—
115Q8×C109—21no—
116Q8×C109—21no—
117Q8×C109—42no—
118Q8×C109#4112yes—
119C2×C4×C109—21no—
120C2×C4×C109—21no—
121C2×C4×C109—21no—
122C2×C4×C109—21no—
123C2×C4×C109—21no—
124C2×C4×C109—21no—
125C2×C4×C109—42no—
126C2×C4×C109—42no—
127C2×C4×C109C2×D411yescharacteristic
128C2×C4×C109C2411yescharacteristic
129C22⋊D109—22no—
130C22⋊D109—42no—
131C2×Dic109—21no—
132C2×Dic109—21no—
133C2×Dic109—21no—
134C2×Dic109C2×D411yescharacteristic
135C2×Dic109C2×D411yescharacteristic
136C2×Dic109C2×D411yescharacteristic
137D436—21no—
138D436—21no—
139D436—42no—
140C4×D109—21no—
141C4×D109—21no—
142C4×D109—42no—
143Dic218—21no—
144Dic218—21no—
145C8×C109—21no—
146C8×C109—21no—
147#11724784—21no—
148#11724784—21no—
149C22×C109—21no—
150C22×C109—21no—
151C22×C109#13512yes—
152C22×C109C22×D411yescharacteristic
153C2×D109—21no—
154C2×D109—21no—
155C2×D109—21no—
156C2×D109—41no—
157C2×D109—41no—
158C2×D109—41no—
159C4×C109—22no—
160C4×C109—21no—
161C4×C109—41no—
162C4×C109—41no—
163C4×C109—41no—
164C4×C109C2×#4111yescharacteristic
165C4×C109H(5,𝔽2)11yescharacteristic
166Dic109—21no—
167Dic109—21no—
168Dic109—21no—
169Dic109—41no—
170Dic109—41no—
171Dic109—41no—
172C2×C109—22no—
173C2×C109#54611yescharacteristic
174C2×C109C2×#13511yescharacteristic
175C2×C109#57811yescharacteristic
176D109—41no—
177D109—81no—
178#3300—1091nomaximal, Sylow
179C109#330011yescharacteristic, complemented, Sylow
180#552—1091no—
181#548—1091no—
182#488—1091no—
183#485—1091no—
184#480—1091no—
185#479—1091no—
186#467—1091no—
187#465—1091no—
188#464—1091no—
189#452—1091no—
190#451—1091no—
191C4×Q16—1091no—
192C8×D4—1091no—
193#416—1091no—
194C2×#103D10911yescharacteristic, complemented
195C2×#41—1091no—
196C22×Q8C2×D10911yescharacteristic
197C2×Q16—1091no—
198C2×Q16—1091no—
199C2×SD16—1091no—
200C22×C8—1091no—
201C22×C8C2×D10911yescharacteristic
202#126—2181no—
203#125—1091no—
204#125—2181no—
205#124—1091no—
206#124—2181no—
207#123—2181no—
208C22⋊Q8—1091no—
209C22⋊Q8—1091no—
210C22⋊Q8—1091no—
211C22⋊Q8—2181no—
212#121—1091no—
213#121—2181no—
214C4×Q8—1091no—
215C4×Q8—1091no—
216C4×D4—1091no—
217C4×D4—2181no—
218#117—1091no—
219#117—2181no—
220C2×C4⋊C4C2×D10911yescharacteristic
221#107—1091no—
222#107—1091no—
223#106—1091no—
224C4⋊C8—1091no—
225#103—1091no—
226#103—1091no—
227#103—1091no—
228#103C2×D10911yescharacteristic
229#103C2×D10911yescharacteristic
230#103C2×D10911yescharacteristic
231#103C2×D10911yescharacteristic
232#102—1091no—
233#102—1091no—
234#102—1091no—
235C22⋊C8—1091no—
236C22⋊C8—1091no—
237C4×C8—1091no—
238#41—4361no—
239#41—2182no—
240C2×Q8—21no—
241C2×Q8—22no—
242C2×Q8—41no—
243C2×Q8—1091no—
244C2×Q8C22×D10911yescharacteristic
245C2×Q8C22×D10911yescharacteristic
246C2×D4—1091no—
247C2×D4—1091no—
248C2×D4—2181no—
249C2×D4—2181no—
250C22×C4—21no—
251C22×C4—21no—
252C22×C4—1091no—
253C22×C4—2181no—
254C22×C4C22×D10911yescharacteristic
255Q16—4361no—
256Q16—2182no—
257SD16—4361no—
258C2×C8—41no—
259C2×C8—1091no—
260C2×C8—1091no—
261C2×C8—4361no—
262C2×C8C22×D10911yescharacteristic
263C2×C8C22×D10911yescharacteristic
264C4⋊C4—21no—
265C4⋊C4—1091no—
266C4⋊C4—1091no—
267C4⋊C4—1091no—
268C4⋊C4—2181no—
269C4⋊C4—2181no—
270C4⋊C4—2181no—
271C4⋊C4—2181no—
272C4⋊C4—2181no—
273C4⋊C4—2181no—
274C4⋊C4—2181no—
275C4⋊C4C22×D10911yescharacteristic
276C4⋊C4C22×D10911yescharacteristic
277C22⋊C4—1091no—
278C22⋊C4—1091no—
279C22⋊C4—2181no—
280C22⋊C4—2181no—
281C22⋊C4—2181no—
282C22⋊C4—2181no—
283C22⋊C4—2181no—
284C22⋊C4—2181no—
285C22⋊C4—2181no—
286C42—1091no—
287C42—2181no—
288C42—2181no—
289C42—2181no—
290C23—1091no—
291C23—2181no—
292C23D4×D10911yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—21no—
296Q8—42no—
297Q8—2181no—
298Q8—2181no—
299Q8#1318202912yes—
300D4—4362no—
301D4—4362no—
302D4—2182no—
303D4—2181no—
304D4—2181no—
305C2×C4—21no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—1091no—
314C2×C4—1091no—
315C2×C4—1091no—
316C2×C4—4362no—
317C2×C4—2181no—
318C2×C4—2181no—
319C2×C4—2181no—
320C2×C4—2181no—
321C2×C4—2181no—
322C2×C4D4×D10911yescharacteristic
323C2×C4C23×D10911yescharacteristic
324C8—21no—
325C8—21no—
326C8—2181no—
327C8—2181no—
328C22—21no—
329C22—21no—
330C22—4361no—
331C22—4361no—
332C22—4361no—
333C22—2181no—
334C22—2181no—
335C22—2181no—
336C22#1681272012yes—
337C22C2×D4×D10911yescharacteristic
338C4—21no—
339C4—22no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—4361no—
344C4—4361no—
345C4—4361no—
346C4—2181no—
347C4—2181no—
348C4—2181no—
349C4C2×#1318202911yescharacteristic
350C4#1681274411yescharacteristic
351C2—22no—
352C2—8721no—
353C2—4361no—
354C2#2029566611yescharacteristic
355C2C2×#1681272011yescharacteristic
356C2#2029583911yescharacteristic
subgroupG/H
centerC22C2×D4×D109
commutator, cosocleC2×C4×C109C24
FrattiniC2×C4C23×D109
FittingC2×#103×C109C2
socleC22×C109C22×D4
prime radical#20295687C2
hypercenterC2×#103D109
hypocenterC109#3300
LCSG ▷ C2×C4×C109 ▷ C2×C109 ▷ C109
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
1. #20295711C2semidirect
3. #20295382C2semidirect
4. #20295365C2semidirect
5. #20295339C2semidirect
6. #20295331C2semidirect
7. #20295266C2semidirect
8. #20295255C2semidirect
9. #20295251C2semidirect
10. #20295191C2semidirect
11. #20295182C2semidirect
12. #20295118C2semidirect
13. C8×C22⋊D109C2semidirect
14. #20295021C2semidirect
15. C2×#103×C109C2semidirect
179. C109#3300semidirect
194. C2×#103D109semidirect

Maximal subgroups

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

subgroupindex
#202957112
#202956872
#202953822
#202953652
#202953392
#202953312
#202952662
#202952552
#202952512
#202951912
#202951822
#202951182
C8×C22⋊D1092
#202950212
C2×#103×C1092
#3300109