Finite Group Databasebeta

← #34034107

Subgroups — #34034107

Order 18688.

474 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556688C211yesmaximal, characteristic
2C2×#17989684C211yesmaximal, characteristic
3C2×#17989681C211yesmaximal, characteristic, complemented
4C2×C4×#11924040C211yesmaximal, characteristic, complemented
5#22627001C211yesmaximal, characteristic, complemented
6#22627001C211yesmaximal, characteristic, complemented
7#22625665C211yesmaximal, characteristic
8C2×#14556688—22no—
9C2×#14556688—22no—
10C2×#14556688C414yescomplemented
11C22×#11924040C2211yescharacteristic
12C22×#11924040C2211yescharacteristic
13C22×#11924040C2211yescharacteristic
14C22×#11924040C2211yescharacteristic
15#17989684C414yescomplemented
16#17989681—22no—
17C4×#11924040—22no—
18C22×#11924036C2211yescharacteristic
19C2×#14556648C411yescharacteristic
20C2×C4×#10596833C2211yescharacteristic
21C2×C4×#10596833C2211yescharacteristic
22#17989453C411yescharacteristic
23#17989453C411yescharacteristic
24#17988434C411yescharacteristic
25#14556688—28no—
26C2×#11924040—21no—
27C2×#11924040—21no—
28C2×#11924040—21no—
29C2×#11924040—21no—
30C2×#11924040—21no—
31C2×#11924040—21no—
32C2×#11924040C2×C412yes—
33C2×#11924040C2×C412yes—
34C2×#11924040C2×C412yes—
35C2×#11924040C2×C412yes—
36C2×#11924040D412yes—
37C2×#11924040D412yes—
38C2×#11924036—21no—
39C2×#11924036—21no—
40C2×#11924036—21no—
41C2×#11924036—21no—
42C2×#11924036C2×C412yes—
43C2×#11924036C2×C412yes—
44C22×#10596833C2×C411yescharacteristic
45C22×#10596833C2×C411yescharacteristic
46C22×#10596833C2×C411yescharacteristic
47C22×#10596833C2311yescharacteristic
48#14556648C814yes—
49C4×#10596833—21no—
50C4×#10596833—21no—
51C4×#10596833—21no—
52C4×#10596833—21no—
53C22×C4×D73C2×C411yescharacteristic
54C2×#11924005C811yescharacteristic
55C2×#11924005C811yescharacteristic
56C2×C4×Dic73C2×C411yescharacteristic
57C2×C4×Dic73C2×C411yescharacteristic
58#14556498C811yescharacteristic
59#95×C73C811yescharacteristic
60#11924040—22no—
61#11924040—22no—
62#11924040—22no—
63#11924040C22⋊C414yescomplemented
64#11924036—22no—
65#11924036—22no—
66#11924036—22no—
67#11924036—22no—
68C2×#10596833—21no—
69C2×#10596833—21no—
70C2×#10596833—21no—
71C2×#10596833—21no—
72C2×#10596833—21no—
73C2×#10596833—21no—
74C2×#10596833C4212yes—
75C2×#10596833C2×C812yes—
76C2×#10596833C2×C812yes—
77C2×#10596833C22×C411yescharacteristic
78C2×#10596833C22×C411yescharacteristic
79C2×#10596833C2×D411yescharacteristic
80C2×#10596833C2×D411yescharacteristic
81C2×#10596833#4111yescharacteristic
82C2×#10596833#4111yescharacteristic
83C23×D73C2×C811yescharacteristic
84C22×Dic73C2×C811yescharacteristic
85C22×Dic73C2×C811yescharacteristic
86C22×Dic73C22×C411yescharacteristic
87C2×C4×D73—21no—
88C2×C4×D73—21no—
89C2×C4×D73—21no—
90C2×C4×D73—21no—
91C2×C4×D73C4212yes—
92C2×C4×D73C2×C812yes—
93#11924005—22no—
94#11924005—22no—
95C4×Dic73—21no—
96C4×Dic73—21no—
97C4×Dic73—21no—
98C4×Dic73—21no—
99C22×C4×C73C2×C811yescharacteristic
100C22×C4×C73C2×C811yescharacteristic
101C22×C4×C73C2×C811yescharacteristic
102C23×C73C22×C811yescharacteristic
103C22×D73—21no—
104C22×D73—21no—
105C22×D73—21no—
106C22×D73—21no—
107C22×D73—21no—
108C22×D73—21no—
109C22×D73C4×C812yes—
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×C73C4×C812yes—
118C2×C4×C73M3212yescomplemented
119C2×Dic73—21no—
120C2×Dic73—21no—
121C2×Dic73—21no—
122C2×Dic73—21no—
123C2×Dic73—21no—
124C2×Dic73M3212yescomplemented
125C2×Dic73C2×C4211yescharacteristic
126C2×Dic73C4×D411yescharacteristic
127C2×Dic73C4×D411yescharacteristic
128C2×Dic73C22×C811yescharacteristic
129C2×Dic73#13111yescharacteristic
130C2×Dic73#13111yescharacteristic
131C4×D73—22no—
132C4×D73—22no—
133C4×D73—22no—
134C4×D73—22no—
135#10596833—22no—
136#10596833—22no—
137#10596833—22no—
138#10596833C2×C22⋊C411yescharacteristic
139#10596833#11711yescharacteristic
140#10596833C4×D411yescharacteristic
141#10596833C4×D411yescharacteristic
142C22×C73C2×C4×C811yescharacteristic
143C22×C73C8×D411yescharacteristic
144C22×C73C8×D411yescharacteristic
145C22×C73C2×M3211yescharacteristic
146C22×C73C2×M3211yescharacteristic
147C22×C73#50411yescharacteristic
148C22×C73#50411yescharacteristic
149C2×D73—22no—
150C2×D73—22no—
151C2×D73—22no—
152C2×D73—41no—
153C2×D73—41no—
154C2×D73—41no—
155C2×D73—41no—
156C4×C73—22no—
157C4×C73—22no—
158C4×C73—41no—
159Dic73—22no—
160Dic73—41no—
161Dic73C4×C22⋊C411yescharacteristic
162Dic73#40511yescharacteristic
163Dic73C8×D411yescharacteristic
164Dic73C8×D411yescharacteristic
165#12612—731nomaximal, Sylow
166C2×C73C8×C22⋊C411yescharacteristic
167C2×C73C4×M3211yescharacteristic
168C2×C73#210811yescharacteristic
169C2×C73#216811yescharacteristic
170C2×C73#216811yescharacteristic
171C2×C73#216911yescharacteristic
172C2×C73#216911yescharacteristic
173D73—42no—
174C22×M32—731no—
175C2×C22⋊C16—731no—
176C2×#346—731no—
177C2×C4×C16—731no—
178C8×C22⋊C4—731no—
179#1374—731no—
180#1374—731no—
181C73#1261211yescharacteristic, complemented, Sylow
182C23×C8—731no—
183C2×M32—734no—
184C2×M32—1462no—
185C2×M32—1462no—
186C22×C16—731no—
187C22×C16—731no—
188C22×C16—731no—
189C22×C16—731no—
190C2×C22⋊C8—731no—
191C2×C4×C8—731no—
192C2×C4×C8—731no—
193C4×C22⋊C4—731no—
194C22⋊C16—734no—
195#346—1462no—
196C4×C16—1462no—
197#336—731no—
198#336—731no—
199C23×C4—731no—
200C22×C8—731no—
201C22×C8—731no—
202C22×C8—731no—
203C22×C8—731no—
204C22×C8—732no—
205C22×C8—732no—
206C22×C8—1461no—
207C22×C8—1461no—
208C22×C8—1461no—
209C22×C8—1461no—
210C2×C22⋊C4—731no—
211C2×C22⋊C4—731no—
212C2×C42—731no—
213C2×C42—731no—
214M32—1468no—
215C2×C16—732no—
216C2×C16—732no—
217C2×C16—732no—
218C2×C16—732no—
219C2×C16—732no—
220C2×C16—732no—
221C2×C16—1461no—
222C2×C16—1461no—
223C2×C16—1461no—
224C2×C16—1461no—
225C2×C16—1461no—
226C2×C16—1461no—
227C22⋊C8—734no—
228C4×C8—1461no—
229C4×C8—1461no—
230C4×C8—1461no—
231C4×C8—1461no—
232#95—731no—
233#95#1059684211yescharacteristic
234C24—731no—
235C22×C4—731no—
236C22×C4—731no—
237C22×C4—732no—
238C22×C4—732no—
239C22×C4—731no—
240C22×C4—1461no—
241C22×C4—1461no—
242C22×C4—1461no—
243C22×C4—1461no—
244C22×C4C2×#1059684211yescharacteristic
245C22×C4C2×#1059684211yescharacteristic
246C22×C4C2×#1059684211yescharacteristic
247C2×C8—731no—
248C2×C8—731no—
249C2×C8—731no—
250C2×C8—731no—
251C2×C8—731no—
252C2×C8—731no—
253C2×C8—732no—
254C2×C8—732no—
255C2×C8—732no—
256C2×C8—1462no—
257C2×C8—1462no—
258C2×C8—1462no—
259C2×C8—1462no—
260C2×C8—1461no—
261C2×C8—1461no—
262C2×C8—1461no—
263C2×C8—1461no—
264C2×C8—1461no—
265C2×C8—1461no—
266C22⋊C4—1462no—
267C22⋊C4—1462no—
268C42—1461no—
269C42—1461no—
270C42—1461no—
271C42—1461no—
272C16—734no—
273C16—1462no—
274C16—1462no—
275C16—1462no—
276C23—732no—
277C23—1461no—
278C23—1461no—
279C23—1461no—
280C23—1461no—
281C23—1461no—
282C23—1461no—
283C23C22×#1059684211yescharacteristic
284C2×C4—21no—
285C2×C4—21no—
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—731no—
292C2×C4—731no—
293C2×C4—731no—
294C2×C4—731no—
295C2×C4—731no—
296C2×C4—731no—
297C2×C4—732no—
298C2×C4—1462no—
299C2×C4—1462no—
300C2×C4—1462no—
301C2×C4—1462no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4—1461no—
305C2×C4—1461no—
306C2×C4—1461no—
307C2×C4C4×#1059684212yes—
308C2×C4#1455668812yescomplemented
309C8—731no—
310C8—731no—
311C8—731no—
312C8—731no—
313C8—1462no—
314C8—1462no—
315C8—1462no—
316C22—2921no—
317C22—2921no—
318C22—2921no—
319C22—2921no—
320C22—1462no—
321C22—1462no—
322C22—1462no—
323C22C2×C4×#1059684211yescharacteristic
324C22D4×#1059684211yescharacteristic
325C22D4×#1059684211yescharacteristic
326C22#1798970611yescharacteristic
327C22C2×#1455668811yescharacteristic
328C22#1798970811yescharacteristic
329C22#1798970911yescharacteristic
330C4—22no—
331C4—22no—
332C4—41no—
333C4—2921no—
334C4—731no—
335C4—731no—
336C4—731no—
337C4—731no—
338C4—1462no—
339C2—2922no—
340C2C22⋊C4×#1059684211yescharacteristic
341C2C4×#1455668811yescharacteristic
342C2#2262709311yescharacteristic
343C2#2262714111yescharacteristic
344C2#2262714211yescharacteristic
345C2#2262714511yescharacteristic
346C2#2262714611yescharacteristic
subgroupG/H
center, FrattiniC23C22×#10596842
commutatorC22×C73C2×C4×C8
Fitting#95×C73C8
socleC23×C73C22×C8
prime radicalC23×D73C2×C8
cosocleC22×#10596833C23
hypercenter#95#10596842
hypocenterC73#12612
LCSG ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
3. C2×#17989681C2semidirect
4. C2×C4×#11924040C2semidirect
5. #22627001C2semidirect
6. #22627001C2semidirect
10. C2×#14556688C4semidirect
15. #17989684C4semidirect
63. #11924040C22⋊C4semidirect
118. C2×C4×C73M32semidirect
124. C2×Dic73M32semidirect
181. C73#12612semidirect
308. C2×C4#14556688semidirect

Maximal subgroups

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

subgroupindex
C22×#145566882
C2×#179896842
C2×#179896812
C2×C4×#119240402
#226270012
#226256652
#1261273