Finite Group Databasebeta

← #34060533

Subgroups — #34060533

Order 19072.

618 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 618 conjugacy classes of subgroups — too many to draw. Only its 88 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×#18011976C212yesmaximal, complemented
2C2×#18011975C212yesmaximal, complemented
3#23750596C211yesmaximal, characteristic, complemented
4C4×C22⋊#10597010C211yesmaximal, characteristic, complemented
5C2×#41×D149C211yesmaximal, characteristic
6C2×#14558746C2212yescomplemented
7C2×C22⋊#10597010—21no—
8C2×C4×#10597010C2212yescomplemented
9#18011976—24no—
10#18011975—24no—
11#18011968—21no—
12C22⋊#11924753—21no—
13(C2×#10597010)⋊C4—21no—
14C2×#14558737C2211yescharacteristic
15C2×#14558736—21no—
16C2×#14558736C411yescharacteristic, complemented
17C2×#14558735—21no—
18C2×#14558735C2211yescharacteristic
19#41×D149—24no—
20#41×D149—24no—
21C2×Q8×D149C411yescharacteristic, complemented
22C2×D4×D149—21no—
23C2×D4×D149C411yescharacteristic, complemented
24C22×C4×D149—21no—
25C22×C4×D149C2211yescharacteristic
26C2×#41×C149C411yescharacteristic, complemented
27C22×#10597010—22no—
28#14558746—22no—
29#14558746—22no—
30C2×#11924753—22no—
31C22⋊#10597010—24no—
32C4×#10597010—22no—
33C4×#10597010—22no—
34C23×D149—21no—
35C23×D149D411yescharacteristic
36#14558737—22no—
37#14558737D414yes—
38#14558736—28no—
39#14558736—22no—
40#14558736—22no—
41#14558735—28no—
42#14558735—22no—
43#14558735D414yes—
44C2×Dic298—21no—
45C2×Dic298C2×C411yescharacteristic
46Q8×D149—22no—
47Q8×D149—22no—
48C2×D596—21no—
49C2×D596C2×C411yescharacteristic
50C2×C22⋊D149—21no—
51C2×C22⋊D149—21no—
52C2×C22⋊D149—21no—
53D4×D149—28no—
54D4×D149—22no—
55D4×D149—22no—
56C22×Dic149—21no—
57C22×Dic149D411yescharacteristic
58C2×C4×D149—28no—
59C2×C4×D149—21no—
60C2×C4×D149—21no—
61C2×C4×D149—22no—
62C2×C4×D149—22no—
63C2×C4×D149—21no—
64C2×C4×D149C2×C411yescharacteristic
65C2×C4×D149D411yescharacteristic
66C2×C4×D149D411yescharacteristic
67C2×C4×D149C2311yescharacteristic
68#41×C149—22no—
69#41×C149—22no—
70C2×Q8×C149C2×C411yescharacteristic
71C2×D4×C149—21no—
72C2×D4×C149C2×C411yescharacteristic
73C22×C4×C149—21no—
74C22×C4×C149C2×C411yescharacteristic
75C2×#10597010—24no—
76C2×#10597010—42no—
77C2×#10597010—42no—
78#11924753—42no—
79C22×D149—24no—
80C22×D149—21no—
81C22×D149—22no—
82C22×D149—22no—
83C22×D149—41no—
84C22×D149—42no—
85C22×D149—42no—
86C22×D149C22⋊C411yescharacteristic
87C22×D149C2×D411yescharacteristic
88Dic298—24no—
89Dic298—21no—
90Dic298C22⋊C412yescomplemented
91D596—24no—
92D596—21no—
93D596C22⋊C412yescomplemented
94C22⋊D149—24no—
95C22⋊D149—24no—
96C22⋊D149—24no—
97C2×Dic149—21no—
98C2×Dic149—24no—
99C2×Dic149—22no—
100C2×Dic149C22⋊C411yescharacteristic
101C2×Dic149C2×D411yescharacteristic
102C4×D149—24no—
103C4×D149—24no—
104C4×D149—22no—
105C4×D149—21no—
106C4×D149—21no—
107C4×D149—22no—
108C4×D149—24no—
109C4×D149C2×D412yes—
110C4×D149C2×D412yes—
111C23×C149—21no—
112C23×C149C22⋊C411yescharacteristic
113Q8×C149—21no—
114Q8×C149C22⋊C412yescomplemented
115D4×C149—24no—
116D4×C149—21no—
117D4×C149C22⋊C412yescomplemented
118C2×C4×C149—24no—
119C2×C4×C149—21no—
120C2×C4×C149—21no—
121C2×C4×C149—21no—
122C2×C4×C149C22⋊C411yescharacteristic
123C2×C4×C149C22×C411yescharacteristic
124C22×C149—21no—
125C22×C149—22no—
126C22×C149—21no—
127C22×C149—21no—
128C22×C149—41no—
129C22×C149—41no—
130C22×C149C2×C22⋊C411yescharacteristic
131C2×D149—21no—
132C2×D149—21no—
133C2×D149—21no—
134C2×D149—21no—
135C2×D149—22no—
136C2×D149—44no—
137C2×D149—48no—
138C2×D149—41no—
139C2×D149—41no—
140C2×D149#10412yescomplemented
141C2×D149#12012yes—
142#10597010—44no—
143C4×C149—21no—
144C4×C149—22no—
145C4×C149C2×C22⋊C411yescharacteristic
146C4×C149C2×C22⋊C411yescharacteristic
147Dic149—22no—
148Dic149—21no—
149Dic149#12012yes—
150C2×C149—41no—
151C2×C149—42no—
152C2×C149#37911yescharacteristic
153C2×C149C2×#10411yescharacteristic
154C2×C149#42111yescharacteristic
155D149—22no—
156D149—22no—
157D149—42no—
158C149#178911yescharacteristic, complemented, Sylow
159#1789—1491nomaximal, Sylow
160C22×#41—1491no—
161C2×#104—1492no—
162C2×#104—1492no—
163#407—1491no—
164C4×C22⋊C4—1491no—
165C2×#41—2981no—
166C2×#41—2984no—
167C2×#41—2984no—
168C2×#41—2981no—
169C2×#41—1491no—
170C2×#41—1491no—
171C2×#41—1491no—
172C2×#41#1059701011yescharacteristic, complemented
173C22×Q8—1491no—
174C22×D4—2981no—
175C22×D4—1491no—
176C23×C4—2981no—
177C23×C4—1491no—
178C2×M16—1492no—
179C2×C22⋊C4—2981no—
180C2×C42—1492no—
181#104—2984no—
182#104—2984no—
183C22⋊C8—2981no—
184C22⋊C8—2981no—
185#95—2981no—
186C24—2981no—
187C24—1491no—
188#41—22no—
189#41—22no—
190#41—2988no—
191#41—2982no—
192#41—2982no—
193#41—2988no—
194#41—2982no—
195#41—2982no—
196#41—1494no—
197#41—1494no—
198C2×Q8—2981no—
199C2×Q8—2982no—
200C2×Q8—2982no—
201C2×Q8—1491no—
202C2×Q8C2×#1059701011yescharacteristic
203C2×D4—21no—
204C2×D4—2981no—
205C2×D4—2988no—
206C2×D4—2982no—
207C2×D4—2981no—
208C2×D4—2981no—
209C2×D4—2982no—
210C2×D4—2981no—
211C2×D4—1491no—
212C2×D4C2×#1059701011yescharacteristic
213C22×C4—21no—
214C22×C4—2988no—
215C22×C4—2981no—
216C22×C4—2981no—
217C22×C4—2982no—
218C22×C4—2982no—
219C22×C4—2981no—
220C22×C4—2981no—
221C22×C4—2982no—
222C22×C4—1491no—
223C22×C4—1491no—
224C22×C4—1491no—
225C22×C4—1491no—
226C22×C4—1491no—
227C22×C4C2×#1059701011yescharacteristic
228M16—2982no—
229M16—2982no—
230C2×C8—2982no—
231C22⋊C4—2984no—
232C42—2982no—
233C42—2982no—
234C23—21no—
235C23—2984no—
236C23—2982no—
237C23—2982no—
238C23—2981no—
239C23—5961no—
240C23—5962no—
241C23—5962no—
242C23—1491no—
243C23—1491no—
244C23C22⋊#1059701011yescharacteristic
245Q8—21no—
246Q8—2984no—
247Q8—2981no—
248Q8—1492no—
249Q8C22⋊#1059701012yescomplemented
250D4—24no—
251D4—21no—
252D4—2984no—
253D4—2984no—
254D4—2984no—
255D4—2984no—
256D4—2981no—
257D4—1492no—
258D4C22⋊#1059701012yescomplemented
259C2×C4—24no—
260C2×C4—21no—
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—2984no—
264C2×C4—2984no—
265C2×C4—2982no—
266C2×C4—2982no—
267C2×C4—2984no—
268C2×C4—2981no—
269C2×C4—2984no—
270C2×C4—2982no—
271C2×C4—2981no—
272C2×C4—2981no—
273C2×C4—2984no—
274C2×C4—5962no—
275C2×C4—5962no—
276C2×C4—1491no—
277C2×C4—1491no—
278C2×C4—1492no—
279C2×C4—1492no—
280C2×C4C22⋊#1059701011yescharacteristic
281C2×C4C22×#1059701011yescharacteristic
282C8—5962no—
283C22—21no—
284C22—22no—
285C22—21no—
286C22—21no—
287C22—41no—
288C22—41no—
289C22—2981no—
290C22—2981no—
291C22—2981no—
292C22—2981no—
293C22—2982no—
294C22—5964no—
295C22—5968no—
296C22—5961no—
297C22—5961no—
298C22—1492no—
299C22—1492no—
300C22C2×C22⋊#1059701011yescharacteristic
301C4—21no—
302C4—22no—
303C4—2982no—
304C4—2981no—
305C4—5964no—
306C4—1492no—
307C4C2×C22⋊#1059701011yescharacteristic
308C4C2×C22⋊#1059701011yescharacteristic
309C2—41no—
310C2—42no—
311C2—2982no—
312C2—2982no—
313C2—5962no—
314C2#2375056611yescharacteristic
315C2D149⋊#10411yescharacteristic
316C2#2375062211yescharacteristic
subgroupG/H
centerC22C2×C22⋊#10597010
commutatorC2×C4×C149C22×C4
FrattiniC2×C4C22×#10597010
FittingC2×#41×C149C4
socleC22×C149C2×C22⋊C4
prime radicalC2×#41×D149C2
cosocleC2×C4×D149C23
hypercenterC2×#41#10597010
hypocenterC149#1789
LCSG ▷ C2×C4×C149 ▷ C2×C149 ▷ C149
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#41

Complements

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

NH ≅ G/Ntype
1. C2×#18011976C2semidirect
2. C2×#18011975C2semidirect
3. #23750596C2semidirect
4. C4×C22⋊#10597010C2semidirect
6. C2×#14558746C22semidirect
8. C2×C4×#10597010C22semidirect
16. C2×#14558736C4semidirect
21. C2×Q8×D149C4semidirect
23. C2×D4×D149C4semidirect
26. C2×#41×C149C4semidirect
90. Dic298C22⋊C4semidirect
93. D596C22⋊C4semidirect
114. Q8×C149C22⋊C4semidirect
117. D4×C149C22⋊C4semidirect
140. C2×D149#104semidirect
158. C149#1789semidirect
172. C2×#41#10597010semidirect
249. Q8C22⋊#10597010semidirect
258. D4C22⋊#10597010semidirect

Maximal subgroups

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

subgroupindex
C2×#180119762
C2×#180119752
#237505962
C4×C22⋊#105970102
C2×#41×D1492
#1789149