Finite Group Databasebeta

← #34013776

Subgroups — #34013776

Order 18688.

394 conjugacy classes of subgroups.

The subgroup lattice has 342 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊#11924031C211yesmaximal, characteristic, complemented
2C2×C22⋊#11924031C211yesmaximal, characteristic
3C2×C22⋊#11924031C211yesmaximal, characteristic
4C2×C4×#11924031C211yesmaximal, characteristic, complemented
5#22624969C211yesmaximal, characteristic, complemented
6#22624969C211yesmaximal, characteristic, complemented
7C22⋊C4×#10596831C211yesmaximal, characteristic
8C22×#11924031C2211yescharacteristic
9C22×#11924031C2211yescharacteristic
10C22×#11924031C2211yescharacteristic
11C22×#11924031C2211yescharacteristic
12C4⋊#11924031—22no—
13C22⋊#11924031—22no—
14C22⋊#11924031—22no—
15C4×#11924031—22no—
16C23×#10596831C2211yescharacteristic
17C2×C22⋊#10596831C411yescharacteristic
18C2×C4×#10596831C2211yescharacteristic
19C2×C4×#10596831C2211yescharacteristic
20#17988342C411yescharacteristic
21#17988342C411yescharacteristic
22C4×C22⋊C4×C73C411yescharacteristic
23C2×#11924031—21no—
24C2×#11924031—21no—
25C2×#11924031—21no—
26C2×#11924031—21no—
27C2×#11924031—21no—
28C2×#11924031—21no—
29C2×#11924031—21no—
30C2×#11924031—21no—
31C2×#11924031—21no—
32C2×#11924031—21no—
33C2×#11924031D412yes—
34C2×#11924031D412yes—
35C22×#10596831—21no—
36C22×#10596831—21no—
37C22×#10596831—21no—
38C22×#10596831—21no—
39C22×#10596831—21no—
40C22×#10596831—21no—
41C22×#10596831C2×C411yescharacteristic
42C22×#10596831C2×C411yescharacteristic
43C22×#10596831C2×C411yescharacteristic
44C22×#10596831C2311yescharacteristic
45C22⋊#10596831—22no—
46C4×#10596831—21no—
47C4×#10596831—21no—
48C4×#10596831—21no—
49C4×#10596831—21no—
50C23×C4×C73C2×C411yescharacteristic
51C2×C22⋊C4×C73C811yescharacteristic
52C2×C22⋊C4×C73C811yescharacteristic
53C2×C42×C73C2×C411yescharacteristic
54C2×C42×C73C2×C411yescharacteristic
55#95×C73C811yescharacteristic
56#95×C73C811yescharacteristic
57#11924031—22no—
58#11924031—22no—
59#11924031—41no—
60#11924031—41no—
61C2×#10596831—21no—
62C2×#10596831—21no—
63C2×#10596831—21no—
64C2×#10596831—21no—
65C2×#10596831—21no—
66C2×#10596831—21no—
67C2×#10596831—21no—
68C2×#10596831—21no—
69C2×#10596831—41no—
70C2×#10596831—41no—
71C2×#10596831—41no—
72C2×#10596831—41no—
73C2×#10596831M1612yes—
74C2×#10596831C2×D411yescharacteristic
75C2×#10596831C2×D411yescharacteristic
76C2×#10596831#4111yescharacteristic
77C2×#10596831#4111yescharacteristic
78C2×#10596831#4111yescharacteristic
79C2×#10596831#4111yescharacteristic
80C24×C73C2×C811yescharacteristic
81C22×C4×C73—21no—
82C22×C4×C73—21no—
83C22×C4×C73—21no—
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73C2×C811yescharacteristic
88C22×C4×C73C2×C811yescharacteristic
89C22×C4×C73C2×C811yescharacteristic
90C22×C4×C73C2×C811yescharacteristic
91C22×C4×C73C2×C811yescharacteristic
92C22×C4×C73C22×C411yescharacteristic
93C22⋊C4×C73—22no—
94C22⋊C4×C73C1614yescomplemented
95C42×C73—21no—
96C42×C73—21no—
97C42×C73—21no—
98C42×C73—21no—
99C23×C73—21no—
100C23×C73—21no—
101C23×C73—21no—
102C23×C73—21no—
103C23×C73—21no—
104C23×C73—21no—
105C23×C73C2×C1612yes—
106C23×C73C22×C811yescharacteristic
107C2×C4×C73—21no—
108C2×C4×C73—21no—
109C2×C4×C73—21no—
110C2×C4×C73—21no—
111C2×C4×C73—21no—
112C2×C4×C73—21no—
113C2×C4×C73—21no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—21no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—41no—
120C2×C4×C73—41no—
121C2×C4×C73—41no—
122C2×C4×C73—41no—
123C2×C4×C73C2×C1612yes—
124C2×C4×C73C2×C1612yes—
125C2×C4×C73M3212yes—
126C2×C4×C73#11711yescharacteristic
127C2×C4×C73C4×D411yescharacteristic
128C2×C4×C73C4×D411yescharacteristic
129C2×C4×C73C2×M1611yescharacteristic
130C2×C4×C73#13111yescharacteristic
131C2×C4×C73#13111yescharacteristic
132#10596831—22no—
133#10596831—41no—
134#10596831—41no—
135#10596831#12111yescharacteristic
136#10596831#12311yescharacteristic
137#10596831#12411yescharacteristic
138#10596831#12611yescharacteristic
139C22×C73—22no—
140C22×C73—22no—
141C22×C73—22no—
142C22×C73—41no—
143C22×C73—41no—
144C22×C73—41no—
145C22×C73—41no—
146C22×C73#43111yescharacteristic
147C22×C73C8×D411yescharacteristic
148C22×C73C8×D411yescharacteristic
149C22×C73C22×C1611yescharacteristic
150C22×C73C2×M3211yescharacteristic
151C22×C73#50411yescharacteristic
152C22×C73#50411yescharacteristic
153C4×C73—22no—
154C4×C73—22no—
155C4×C73—22no—
156C4×C73—41no—
157C4×C73—41no—
158C4×C73#38811yescharacteristic
159C4×C73#43311yescharacteristic
160C4×C73#43511yescharacteristic
161C4×C73#43611yescharacteristic
162#13120—731nomaximal, Sylow
163C2×C73—42no—
164C2×C73#192311yescharacteristic
165C2×C73#216211yescharacteristic
166C2×C73#216411yescharacteristic
167C2×C73D4×C1611yescharacteristic
168C2×C73D4×C1611yescharacteristic
169C2×C73#216811yescharacteristic
170C2×C73#216911yescharacteristic
171C2×C4⋊C16—731no—
172C2×C22⋊C16—731no—
173C2×C22⋊C16—731no—
174C2×C4×C16—731no—
175C8×C22⋊C4—731no—
176#1374—731no—
177#1374—731no—
178C73#1312011yescharacteristic, complemented, Sylow
179C23×C8—731no—
180C22×C16—731no—
181C22×C16—731no—
182C22×C16—731no—
183C22×C16—731no—
184C2×C22⋊C8—731no—
185C2×C4×C8—731no—
186C2×C4×C8—731no—
187C4×C22⋊C4#6440811yescharacteristic
188C4⋊C16—1462no—
189C22⋊C16—1462no—
190C22⋊C16—1462no—
191C4×C16—1462no—
192#336—731no—
193#336—731no—
194C23×C4C2×#6440811yescharacteristic
195C22×C8—731no—
196C22×C8—731no—
197C22×C8—731no—
198C22×C8—731no—
199C22×C8—1461no—
200C22×C8—1461no—
201C22×C8—1461no—
202C22×C8—1461no—
203C22×C8—1461no—
204C22×C8—1461no—
205C2×C22⋊C4#1059683311yescharacteristic
206C2×C22⋊C4#1059683311yescharacteristic
207C2×C42C2×#6440811yescharacteristic
208C2×C42C2×#6440811yescharacteristic
209C2×C16—732no—
210C2×C16—732no—
211C2×C16—1461no—
212C2×C16—1461no—
213C2×C16—1461no—
214C2×C16—1461no—
215C2×C16—1461no—
216C2×C16—1461no—
217C2×C16—1461no—
218C2×C16—1461no—
219C2×C16—1461no—
220C2×C16—1461no—
221C22⋊C8—1462no—
222C4×C8—1461no—
223C4×C8—1461no—
224C4×C8—1461no—
225C4×C8—1461no—
226#95#1059683311yescharacteristic
227#95#1059683311yescharacteristic
228C24C2×#1059683311yescharacteristic
229C22×C4—21no—
230C22×C4—21no—
231C22×C4—21no—
232C22×C4—21no—
233C22×C4—21no—
234C22×C4—21no—
235C22×C4C2×#1059683311yescharacteristic
236C22×C4C2×#1059683311yescharacteristic
237C22×C4C2×#1059683311yescharacteristic
238C22×C4C2×#1059683311yescharacteristic
239C22×C4C2×#1059683311yescharacteristic
240C22×C4C22×#6440811yescharacteristic
241C2×C8—2921no—
242C2×C8—2921no—
243C2×C8—2921no—
244C2×C8—2921no—
245C2×C8—731no—
246C2×C8—731no—
247C2×C8—731no—
248C2×C8—731no—
249C2×C8—731no—
250C2×C8—731no—
251C2×C8—732no—
252C2×C8—1461no—
253C2×C8—1461no—
254C2×C8—1461no—
255C2×C8—1461no—
256C2×C8—1461no—
257C2×C8—1461no—
258C2×C8—1461no—
259C2×C8—1461no—
260C22⋊C4—22no—
261C22⋊C4#1192403114yescomplemented
262C42—21no—
263C42—21no—
264C42—21no—
265C42—21no—
266C16—2921no—
267C16—2921no—
268C16—1462no—
269C16—1462no—
270C23—21no—
271C23—21no—
272C23—21no—
273C23—21no—
274C23—21no—
275C23—21no—
276C23C2×#1192403112yes—
277C23C22×#1059683311yescharacteristic
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—21no—
281C2×C4—21no—
282C2×C4—21no—
283C2×C4—21no—
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—41no—
291C2×C4—41no—
292C2×C4—41no—
293C2×C4—41no—
294C2×C4C2×#1192403112yes—
295C2×C4C2×#1192403112yes—
296C2×C4#1455666512yes—
297C2×C4#1455667011yescharacteristic
298C2×C4D4×#6440811yescharacteristic
299C2×C4D4×#6440811yescharacteristic
300C2×C4D73⋊M1611yescharacteristic
301C2×C4#1455667811yescharacteristic
302C2×C4#1455667811yescharacteristic
303C8—2921no—
304C8—2921no—
305C8—731no—
306C8—731no—
307C8—731no—
308C8—731no—
309C8—1462no—
310C22—22no—
311C22—22no—
312C22—22no—
313C22—41no—
314C22—41no—
315C22—41no—
316C22—41no—
317C22#1798960311yescharacteristic
318C22D4×#1059683311yescharacteristic
319C22D4×#1059683311yescharacteristic
320C22C22×#1192403111yescharacteristic
321C22C2×#1455666511yescharacteristic
322C22#1798964511yescharacteristic
323C22#1798964511yescharacteristic
324C4—22no—
325C4—22no—
326C4—22no—
327C4—41no—
328C4—41no—
329C4#1798953711yescharacteristic
330C4#1798961111yescharacteristic
331C4#1798961911yescharacteristic
332C4#1798962011yescharacteristic
333C2—42no—
334C2#2262600011yescharacteristic
335C2#2262628811yescharacteristic
336C2#2262629611yescharacteristic
337C2D4×#1192403111yescharacteristic
338C2D4×#1192403111yescharacteristic
339C2#2262631111yescharacteristic
340C2#2262631511yescharacteristic
subgroupG/H
center, FrattiniC22×C4C22×#64408
commutatorC22×C73C22×C16
FittingC4×C22⋊C4×C73C4
socleC23×C73C22×C8
prime radicalC24×C73C2×C8
cosocleC22×#10596831C23
hypercenterC4×C22⋊C4#64408
hypocenterC73#13120
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C22×C4 ◁ C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C4⋊#11924031C2semidirect
4. C2×C4×#11924031C2semidirect
5. #22624969C2semidirect
6. #22624969C2semidirect
94. C22⋊C4×C73C16semidirect
178. C73#13120semidirect
261. C22⋊C4#11924031semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊#119240312
C2×C22⋊#119240312
C2×C4×#119240312
#226249692
C22⋊C4×#105968312
#1312073