Finite Group Databasebeta

← #2982×D73 #33950920

Subgroups — #2982×D73 #33950920

Order 18688.

2234 conjugacy classes of subgroups.

The subgroup lattice has 332 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D73C211yesmaximal, characteristic
2#22619012C211yesmaximal, characteristic, complemented
3#22619011C216yesmaximal, complemented
4#22619010C218yesmaximal, complemented
5C8×Q8×D73C218yesmaximal, complemented
6#431×D73C216yesmaximal
7C73×#2982C211yesmaximal, characteristic, complemented
8C22×Q8×D73C411yescharacteristic
9C2×Q8×Dic73C411yescharacteristic
10C2×C4×Dic146C2213yes—
11C2×#14556556C413yes—
12C4×Q8×D73C414yes—
13C4×Q8×D73C414yes—
14C4×Q8×D73C2214yes—
15C4×Q8×D73C2214yes—
16C2×C4⋊C4×D73C413yes—
17C2×C42×D73C2213yes—
18Q8×#10596831C2218yescomplemented
19C8×Dic146C22124yescomplemented
20#17988711C22124yescomplemented
21#17988640C2216yes—
22#17988639C22112yes—
23#17988638C22112yes—
24#17988637C22112yes—
25C4⋊C8×D73C22112yes—
26C22⋊C8×D73C2214yes—
27C4×C8×D73C22112yes—
28C2×C4×Q8×C73C2211yescharacteristic
29C8×Q8×C73C2218yescomplemented
30#431×C73C2216yes—
31C22×Dic146C2×C413yes—
32C2×Q8×D73C8116yescomplemented
33C2×Q8×D73C2×C414yes—
34C2×Q8×D73C2×C414yes—
35C22×C4×D73C2×C413yes—
36C22×C4×D73C2×C413yes—
37C22×C4×D73C2311yescharacteristic
38C2×C8×D73C2318yes—
39Q8×Dic73C2×C414yes—
40Q8×Dic73C2×C414yes—
41C4×Dic146C2×C4112yes—
42C4×Dic146C23112yes—
43#14556556C2×C4112yes—
44#14556556C2×C4112yes—
45C2×C4⋊Dic73C2×C413yes—
46C2×#11924007C2×C416yes—
47C4⋊C4×D73C2×C4112yes—
48C4⋊C4×D73C2×C4112yes—
49C2×C4×Dic73C2×C413yes—
50C2×C4×Dic73C2×C413yes—
51C2×C4×Dic73C2313yes—
52C42×D73C2×C416yes—
53C42×D73C2×C416yes—
54C42×D73C2316yes—
55C42×D73C2316yes—
56C4⋊#10596831C23112yes—
57#14556520C23124yes—
58C22⋊#10596831C2314yes—
59#14556503C2318yes—
60C4×#10596831C23112yes—
61C8×Dic73C23124yes—
62C22×Q8×C73C2×C411yescharacteristic
63C4×Q8×C73C2×C414yes—
64C4×Q8×C73C2314yes—
65C2×C4⋊C4×C73C2×C413yes—
66C2×C42×C73C2313yes—
67C4⋊C8×C73C23112yes—
68C22⋊C8×C73C2314yes—
69C4×C8×C73C23112yes—
70C23×D73C22×C411yescharacteristic
71C2×Dic146C2×C8124yescomplemented
72C2×Dic146C22×C4112yes—
73Q8×D73C2×C8132yes—
74Q8×D73C2×C8132yescomplemented
75C22×Dic73C22×C411yescharacteristic
76C22×Dic73C22×C413yes—
77C22×Dic73C22×C413yes—
78C2×C4×D73—24no—
79C2×C4×D73—46no—
80C2×C4×D73C2×C8124yes—
81C2×C4×D73C22×C411yescharacteristic
82C2×C4×D73C22×C411yescharacteristic
83C2×C4×D73C22×C416yes—
84C2×C4×D73C22×C416yes—
85C2×C4×D73C22×C416yes—
86C2×C4×D73C22×C416yes—
87C2×C4×D73C2411yescharacteristic
88C2×C4×D73C2411yescharacteristic
89C2×#10596831C2418yes—
90C8×D73—216no—
91C4⋊Dic73C22×C4112yes—
92#11924007C22×C4124yes—
93C4×Dic73C22×C416yes—
94C4×Dic73C22×C416yes—
95C4×Dic73C22×C416yes—
96C4×Dic73C22×C416yes—
97C4×Dic73C22×C416yes—
98C4×Dic73C2416yes—
99C2×Q8×C73C2×C818yescomplemented
100C2×Q8×C73C22×C414yes—
101C22×C4×C73C22×C413yes—
102C22×C4×C73C22×C413yes—
103C22×C4×C73C2411yescharacteristic
104C2×C8×C73C2418yes—
105C4⋊C4×C73C22×C4112yes—
106C42×C73C22×C416yes—
107C42×C73C2416yes—
108C23×C73C23×C411yescharacteristic
109C22×D73—22no—
110C22×D73—22no—
111C22×D73C22×C814yes—
112C22×D73C23×C411yescharacteristic
113C22×D73C23×C411yescharacteristic
114Q8×C73C22×C8116yes—
115C2×C4×C73—22no—
116C2×C4×C73—43no—
117C2×C4×C73C22×C8112yes—
118C2×C4×C73C23×C411yescharacteristic
119C2×C4×C73C23×C416yes—
120C2×C4×C73C23×C416yes—
121C2×C4×C73C2511yescharacteristic
122C2×Dic73—22no—
123C2×Dic73—43no—
124C2×Dic73C22×C8112yes—
125C2×Dic73C23×C411yescharacteristic
126C2×Dic73C23×C416yes—
127C2×Dic73C23×C411yescharacteristic
128C2×Dic73C23×C416yes—
129C4×D73—22no—
130C4×D73—212no—
131C4×D73—22no—
132C4×D73—22no—
133C4×D73—46no—
134C4×D73C22×C8124yes—
135C4×D73C22×C8124yes—
136C4×D732−1+414yes—
137Dic146C22×C8148yes—
138C8×C73—28no—
139#10596831—28no—
140C22×C73—21no—
141C22×C73—21no—
142C22×C73C23×C812yes—
143C22×C73C24×C411yescharacteristic
144C2×D73—21no—
145C2×D73—21no—
146C2×D73—28no—
147C2×D73#51912yes—
148C2×D73C23×C812yes—
149C2×D73C23×C812yes—
150C2×D73#56812yes—
151C4×C73—21no—
152C4×C73—26no—
153C4×C73C23×C8112yes—
154C4×C73C2×2−1+412yes—
155Dic73—21no—
156Dic73—26no—
157Dic73#51912yes—
158Dic73C23×C8112yes—
159C2×#2982—731nomaximal, Sylow
160C2×C73—22no—
161C2×C73C2×#51911yescharacteristic
162C2×C73C24×C811yescharacteristic
163C2×C73C2×#56811yescharacteristic
164D73—22no—
165D73#298214yesdirect product factor
166C22×C4×Q8—731no—
167#2982—738no—
168#2982—736no—
169#2982—731no—
170#2982D7311yescharacteristic, direct product factor
171C2×C8×Q8—738no—
172C2×#431—736no—
173C73C2×#298211yescharacteristic, complemented, Sylow
174C23×Q8—731no—
175C2×C4×Q8—731no—
176C2×C4×Q8—734no—
177C2×C4×Q8—734no—
178C2×C4×Q8—734no—
179C2×C4×Q8—734no—
180C2×C4×Q8—733no—
181C2×C4×Q8—733no—
182C2×C4×Q8C2×D7311yescharacteristic
183C22×C4⋊C4—733no—
184C22×C42—733no—
185C8×Q8—738no—
186C8×Q8—7324no—
187C8×Q8—7324no—
188C8×Q8C2×D7318yescomplemented
189#431—736no—
190#431—7312no—
191#431—7312no—
192#431—7312no—
193#431C2×D7316yes—
194C2×C4⋊C8—7312no—
195C2×C22⋊C8—734no—
196C2×C4×C8—7312no—
197C22×Q8—7316no—
198C22×Q8—734no—
199C22×Q8—734no—
200C22×Q8—733no—
201C22×Q8C4×D7311yescharacteristic
202C23×C4—733no—
203C23×C4—733no—
204C23×C4—731no—
205C22×C8—738no—
206C4×Q8—734no—
207C4×Q8—734no—
208C4×Q8—7312no—
209C4×Q8—7312no—
210C4×Q8—7312no—
211C4×Q8—7312no—
212C4×Q8C4×D7314yes—
213C4×Q8C22×D7314yes—
214C2×C4⋊C4—736no—
215C2×C4⋊C4—733no—
216C2×C4⋊C4—7312no—
217C2×C4⋊C4—7312no—
218C2×C4⋊C4C4×D7313yes—
219C2×C42—733no—
220C2×C42—733no—
221C2×C42—733no—
222C2×C42—736no—
223C2×C42—736no—
224C2×C42—736no—
225C2×C42—736no—
226C2×C42C22×D7313yes—
227C4⋊C8—7324no—
228C4⋊C8—7312no—
229C4⋊C8C22×D73112yes—
230C22⋊C8—734no—
231C22⋊C8—738no—
232C22⋊C8C22×D7314yes—
233C4×C8—7324no—
234C4×C8—7312no—
235C4×C8C22×D73112yes—
236C24—731no—
237C2×Q8—7332no—
238C2×Q8—7332no—
239C2×Q8—7324no—
240C2×Q8—7312no—
241C2×Q8C8×D7318yescomplemented
242C2×Q8C2×C4×D7314yes—
243C22×C4—2926no—
244C22×C4—733no—
245C22×C4—736no—
246C22×C4—733no—
247C22×C4—7324no—
248C22×C4—736no—
249C22×C4—736no—
250C22×C4—731no—
251C22×C4—731no—
252C22×C4—731no—
253C22×C4—731no—
254C22×C4—736no—
255C22×C4—731no—
256C22×C4—1464no—
257C22×C4C2×C4×D7313yes—
258C22×C4C2×C4×D7313yes—
259C22×C4C23×D7311yescharacteristic
260C2×C8—738no—
261C2×C8—14616no—
262C2×C8C23×D7318yes—
263C4⋊C4—7324no—
264C4⋊C4—7312no—
265C4⋊C4C2×C4×D73112yes—
266C42—736no—
267C42—736no—
268C42—736no—
269C42—736no—
270C42—736no—
271C42—736no—
272C42C2×C4×D7316yes—
273C42C23×D7316yes—
274C23—731no—
275C23—731no—
276C23—734no—
277C23—1462no—
278C23—1462no—
279C23C22×C4×D7311yescharacteristic
280Q8—7348no—
281Q8C2×C8×D73116yes—
282C2×C4—22no—
283C2×C4—43no—
284C2×C4—2926no—
285C2×C4—2923no—
286C2×C4—731no—
287C2×C4—736no—
288C2×C4—7312no—
289C2×C4—734no—
290C2×C4—7324no—
291C2×C4—7324no—
292C2×C4—731no—
293C2×C4—736no—
294C2×C4—1462no—
295C2×C4—14612no—
296C2×C4—1462no—
297C2×C4—1462no—
298C2×C4—1462no—
299C2×C4C2×C8×D73112yes—
300C2×C4C22×C4×D7311yescharacteristic
301C2×C4C22×C4×D7316yes—
302C2×C4C22×C4×D7316yes—
303C2×C4C24×D7311yescharacteristic
304C8—28no—
305C8—1468no—
306C22—21no—
307C22—21no—
308C22—732no—
309C22—732no—
310C22—732no—
311C22—732no—
312C22—1468no—
313C22—1461no—
314C22—1461no—
315C22C22×C8×D7312yes—
316C22C23×C4×D7311yescharacteristic
317C4—26no—
318C4—21no—
319C4—7312no—
320C4—732no—
321C4—1466no—
322C4—1461no—
323C4C22×C8×D73112yes—
324C42−1+4×D7312yes—
325C2—22no—
326C2—734no—
327C2—1462no—
328C2#519×D7311yescharacteristic
329C2C23×C8×D7311yescharacteristic
330C2#568×D7311yescharacteristic
subgroupG/H
center, FrattiniC2×C4C24×D73
commutatorC2×C73C24×C8
FittingC73×#2982C2
socleC22×C73C24×C4
prime radicalC23×D73C22×C4
cosocleC2×C4×C73C25
hypercenter#2982D73
hypocenterC73C2×#2982
LCSG ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ #2982

Complements

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

NH ≅ G/Ntype
2. #22619012C2semidirect
3. #22619011C2semidirect
4. #22619010C2semidirect
5. C8×Q8×D73C2semidirect
7. C73×#2982C2semidirect
18. Q8×#10596831C22semidirect
19. C8×Dic146C22semidirect
20. #17988711C22semidirect
29. C8×Q8×C73C22semidirect
32. C2×Q8×D73C8semidirect
71. C2×Dic146C2×C8semidirect
74. Q8×D73C2×C8semidirect
99. C2×Q8×C73C2×C8semidirect
165. D73#2982direct (N × H)
170. #2982D73direct (N × H)
173. C73C2×#2982semidirect
188. C8×Q8C2×D73semidirect
241. C2×Q8C8×D73semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D732
#226190122
#226190112
#226190102
C8×Q8×D732
#431×D732
C73×#29822
C2×#298273