Finite Group Databasebeta

← #27171966

Subgroups — #27171966

Order 12928.

408 conjugacy classes of subgroups; only the 85 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 85 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15692227C211yesmaximal, characteristic
2C2×#15692170C211yesmaximal, characteristic, complemented
3C2×#15692169C211yesmaximal, characteristic, complemented
4C2×#15692169C211yesmaximal, characteristic, complemented
5#20265035C211yesmaximal, characteristic, complemented
6C22⋊C4×Dic101C211yesmaximal, characteristic, complemented
7C2×#99×C101C211yesmaximal, characteristic, complemented
8C22×C22⋊D101C411yescharacteristic, complemented
9C22×C22⋊D101C2211yescharacteristic
10C23×Dic101C2211yescharacteristic
11#15692227—21no—
12#15692227—21no—
13#15692227—21no—
14#15692227—21no—
15C2×#13108053—21no—
16C2×#13108053C411yescharacteristic, complemented
17C2×C22⋊Dic101C411yescharacteristic, complemented
18C2×C22⋊Dic101C2211yescharacteristic
19C2×C22⋊Dic101C2211yescharacteristic
20C2×#13108051C411yescharacteristic, complemented
21C2×C4×Dic101—21no—
22#15692170—22no—
23#15692169—22no—
24#15692169—22no—
25#15692162—21no—
26#15692162—21no—
27C22×D4×C101C2211yescharacteristic
28C2×C22⋊C4×C101C2211yescharacteristic
29C2×C22⋊C4×C101C2211yescharacteristic
30#99×C101—22no—
31C23×D101C2×C411yescharacteristic
32C2×C22⋊D101—21no—
33C2×C22⋊D101—21no—
34C2×C22⋊D101—21no—
35C2×C22⋊D101—21no—
36C2×C22⋊D101—21no—
37C2×C22⋊D101—21no—
38C2×C22⋊D101—21no—
39C2×C22⋊D101—21no—
40C2×C22⋊D101—42no—
41C22×Dic101—21no—
42C22×Dic101—21no—
43C22×Dic101—42no—
44C22×Dic101C2×C411yescharacteristic
45C22×Dic101C2×C411yescharacteristic
46C22×Dic101C2×C411yescharacteristic
47C22×Dic101D411yescharacteristic
48C22×Dic101D411yescharacteristic
49C22×Dic101D411yescharacteristic
50C22×Dic101D411yescharacteristic
51#13108053—21no—
52#13108053—21no—
53#13108053—42no—
54C22⋊Dic101—21no—
55C22⋊Dic101—21no—
56C22⋊Dic101—21no—
57C22⋊Dic101—21no—
58C22⋊Dic101—21no—
59C22⋊Dic101D412yescomplemented
60#13108051—21no—
61#13108051—21no—
62C4×Dic101—42no—
63C24×C101C2×C411yescharacteristic
64C24×C101C2311yescharacteristic
65C2×D4×C101—21no—
66C2×D4×C101—21no—
67C2×D4×C101—21no—
68C2×D4×C101—21no—
69C2×D4×C101—21no—
70C2×D4×C101—21no—
71C22×C4×C101—21no—
72C22×C4×C101—21no—
73C22×C4×C101C2×C411yescharacteristic
74C22⋊C4×C101—21no—
75C22⋊C4×C101—21no—
76C22⋊C4×C101—21no—
77C22⋊C4×C101D412yescomplemented
78C23×C101—21no—
79C23×C101—21no—
80C23×C101—21no—
81C23×C101—41no—
82C23×C101—41no—
83C23×C101—41no—
84C23×C101—41no—
85C23×C101C22×C411yescharacteristic
86C23×C101C2×D411yescharacteristic
87C23×C101C2×D411yescharacteristic
88C23×C101C2×D411yescharacteristic
89C23×C101C2×D411yescharacteristic
90C23×C101#4111yescharacteristic
91C23×C101#4111yescharacteristic
92C22×D101—21no—
93C22×D101—21no—
94C22×D101—21no—
95C22×D101—41no—
96C22×D101—41no—
97D4×C101—41no—
98D4×C101—41no—
99D4×C101—41no—
100D4×C101—41no—
101C2×C4×C101—21no—
102C2×C4×C101—21no—
103C2×C4×C101—21no—
104C2×C4×C101—22no—
105C2×C4×C101—41no—
106C2×C4×C101—41no—
107C2×C4×C101—41no—
108C2×C4×C101—41no—
109C2×C4×C101—41no—
110C22⋊D101—42no—
111C22⋊D101—41no—
112C22⋊D101—41no—
113C22⋊D101—41no—
114C22⋊D101—41no—
115C22⋊D101—42no—
116C2×Dic101—22no—
117C2×Dic101—22no—
118C2×Dic101—22no—
119C2×Dic101—21no—
120C2×Dic101—21no—
121C2×Dic101—21no—
122C2×Dic101—22no—
123C2×Dic101—41no—
124C2×Dic101—41no—
125C2×Dic101—41no—
126C2×Dic101—41no—
127C2×Dic101—41no—
128C2×Dic101—41no—
129C2×Dic101—41no—
130C2×Dic101—41no—
131C2×Dic101C22⋊C411yescharacteristic
132C2×Dic101C22⋊C411yescharacteristic
133C2×Dic101C22⋊C411yescharacteristic
134C2×Dic101C22⋊C411yescharacteristic
135C22×C101—21no—
136C22×C101—21no—
137C22×C101—21no—
138C22×C101—21no—
139C22×C101—21no—
140C22×C101—21no—
141C22×C101—41no—
142C22×C101—41no—
143C22×C101—41no—
144C22×C101—41no—
145C22×C101—41no—
146C22×C101—41no—
147C22×C101—41no—
148C22×C101—81no—
149C22×C101—81no—
150C22×C101C2×C22⋊C411yescharacteristic
151C22×C101C4×D411yescharacteristic
152C22×C101C4×D411yescharacteristic
153C22×C101#12111yescharacteristic
154C22×C101#12111yescharacteristic
155C22×C101#12411yescharacteristic
156C22×C101#12711yescharacteristic
157C2×D101—41no—
158C2×D101—41no—
159C2×D101—41no—
160C2×D101—81no—
161C2×D101—81no—
162C4×C101—42no—
163C4×C101—41no—
164C4×C101—81no—
165Dic101—21no—
166Dic101—21no—
167Dic101—21no—
168Dic101—42no—
169Dic101—41no—
170Dic101—81no—
171Dic101#9912yescomplemented
172C2×C101—21no—
173C2×C101—21no—
174C2×C101—21no—
175C2×C101—21no—
176C2×C101—21no—
177C2×C101—21no—
178C2×C101—81no—
179C2×C101#39011yescharacteristic
180C2×C101C2×#9911yescharacteristic
181C2×C101#41011yescharacteristic
182D101—81no—
183#1964—1011nomaximal, Sylow
184C101#196411yescharacteristic, complemented, Sylow
185C2×#121—1011no—
186C2×#99—1011no—
187C2×#99—1011no—
188C2×#99—1011no—
189C2×#99D10111yescharacteristic, complemented
190#380—1011no—
191C4×C22⋊C4—1011no—
192C22×D4—1011no—
193C22×D4—1011no—
194C22×D4C2×D10111yescharacteristic
195C23×C4—1011no—
196#121—2021no—
197#121—2021no—
198#121—2021no—
199#121—2021no—
200C2×C4⋊C4—1011no—
201C2×C4⋊C4—2021no—
202C2×C22⋊C4—1011no—
203C2×C22⋊C4—1011no—
204C2×C22⋊C4—1011no—
205C2×C22⋊C4—1011no—
206C2×C22⋊C4C2×D10111yescharacteristic
207C2×C22⋊C4C2×D10111yescharacteristic
208C2×C42—2021no—
209#99—22no—
210#99—2022no—
211#99—2022no—
212#99—2022no—
213#95—2021no—
214#95—2021no—
215C24—1011no—
216C24C4×D10111yescharacteristic
217C24C22×D10111yescharacteristic
218C2×D4—21no—
219C2×D4—21no—
220C2×D4—21no—
221C2×D4—21no—
222C2×D4—21no—
223C2×D4—21no—
224C2×D4—4042no—
225C2×D4—2021no—
226C2×D4—2021no—
227C2×D4—2021no—
228C2×D4—2021no—
229C2×D4—2021no—
230C2×D4—2021no—
231C2×D4—2021no—
232C2×D4—2021no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4—1011no—
236C22×C4—1011no—
237C22×C4—1011no—
238C22×C4—1011no—
239C22×C4—1011no—
240C22×C4—1011no—
241C22×C4—1011no—
242C22×C4—4042no—
243C22×C4—2021no—
244C22×C4—2021no—
245C22×C4C4×D10111yescharacteristic
246C4⋊C4—4042no—
247C4⋊C4—2021no—
248C4⋊C4—2021no—
249C22⋊C4—21no—
250C22⋊C4—21no—
251C22⋊C4—21no—
252C22⋊C4—1012no—
253C22⋊C4—2021no—
254C22⋊C4—2021no—
255C22⋊C4—2021no—
256C22⋊C4—2021no—
257C22⋊C4—2021no—
258C22⋊C4—2021no—
259C22⋊C4—2021no—
260C22⋊C4C22⋊D10112yescomplemented
261C42—4042no—
262C23—21no—
263C23—21no—
264C23—21no—
265C23—41no—
266C23—41no—
267C23—41no—
268C23—41no—
269C23—4041no—
270C23—4041no—
271C23—2021no—
272C23—2021no—
273C23—2021no—
274C23C2×C4×D10111yescharacteristic
275C23D4×D10111yescharacteristic
276C23D4×D10111yescharacteristic
277C23D4×D10111yescharacteristic
278C23C2×C22⋊D10111yescharacteristic
279C23#1310807311yescharacteristic
280C23#1310807411yescharacteristic
281D4—41no—
282D4—41no—
283D4—41no—
284D4—41no—
285D4—4042no—
286D4—4041no—
287D4—4041no—
288D4—4041no—
289D4—4041no—
290D4—4042no—
291C2×C4—21no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—22no—
295C2×C4—41no—
296C2×C4—41no—
297C2×C4—41no—
298C2×C4—41no—
299C2×C4—41no—
300C2×C4—1011no—
301C2×C4—1011no—
302C2×C4—1011no—
303C2×C4—1011no—
304C2×C4—4041no—
305C2×C4—4041no—
306C2×C4—4041no—
307C2×C4—4041no—
308C2×C4—4041no—
309C2×C4—4041no—
310C2×C4—4041no—
311C2×C4—4041no—
312C2×C4—2022no—
313C2×C4—2022no—
314C2×C4—2022no—
315C2×C4—2021no—
316C2×C4—2021no—
317C2×C4—2021no—
318C2×C4—2022no—
319C22—21no—
320C22—21no—
321C22—21no—
322C22—21no—
323C22—21no—
324C22—21no—
325C22—41no—
326C22—41no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—81no—
333C22—81no—
334C22—8081no—
335C22—8081no—
336C22—4041no—
337C22—4041no—
338C22—4041no—
339C22C22⋊C4×D10111yescharacteristic
340C22#1569221511yescharacteristic
341C22C4×C22⋊D10111yescharacteristic
342C22#1569222711yescharacteristic
343C22#1569222811yescharacteristic
344C22#1569224111yescharacteristic
345C22#1569225111yescharacteristic
346C4—42no—
347C4—41no—
348C4—81no—
349C4—8081no—
350C4—1012no—
351C4—4042no—
352C4—4041no—
353C4—2021no—
354C4—2021no—
355C4—2021no—
356C2—21no—
357C2—21no—
358C2—21no—
359C2—21no—
360C2—21no—
361C2—21no—
362C2—81no—
363C2—8081no—
364C2#2026507711yescharacteristic
365C2#99×D10111yescharacteristic
366C2#2026514911yescharacteristic
subgroupG/H
centerC22C22⋊C4×D101
commutatorC23×C101C22×C4
FrattiniC24C22×D101
FittingC2×#99×C101C2
socleC22×C101C2×C22⋊C4
prime radicalC2×#15692227C2
cosocleC24×C101C23
hypercenterC2×#99D101
hypocenterC101#1964
LCSG ▷ C23×C101 ▷ C2×C101 ▷ C101
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#15692170C2semidirect
3. C2×#15692169C2semidirect
4. C2×#15692169C2semidirect
5. #20265035C2semidirect
6. C22⋊C4×Dic101C2semidirect
7. C2×#99×C101C2semidirect
8. C22×C22⋊D101C4semidirect
16. C2×#13108053C4semidirect
17. C2×C22⋊Dic101C4semidirect
20. C2×#13108051C4semidirect
59. C22⋊Dic101D4semidirect
77. C22⋊C4×C101D4semidirect
171. Dic101#99semidirect
184. C101#1964semidirect
189. C2×#99D101semidirect
260. C22⋊C4C22⋊D101semidirect

Maximal subgroups

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

subgroupindex
C2×#156922272
C2×#156921702
C2×#156921692
#202650352
C22⋊C4×Dic1012
C2×#99×C1012
#1964101