Finite Group Databasebeta

← C2×D73⋊#365 #34030085

Subgroups — C2×D73⋊#365 #34030085

Order 18688.

702 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D73⋊#108C211yesmaximal, characteristic
2C22×#14556659C211yesmaximal, characteristic
3D73⋊#365C218yesmaximal, direct product factor
4C2×#17989512C212yesmaximal, complemented
5C2×#17989511C212yesmaximal, complemented
6C2×M32×D73C211yesmaximal, characteristic
7C2×D73⋊M16—21no—
8C22×C4⋊#64408—21no—
9C2×#14556662—21no—
10D73⋊#108—22no—
11D73⋊#108C2214yes—
12C2×#14556661C2211yescharacteristic
13C2×#14556661C2211yescharacteristic
14C2×#14556659—22no—
15C2×#14556659—21no—
16C2×#14556659C2212yes—
17C2×#14556659C2214yes—
18#17989512C2218yescomplemented
19#17989511C2218yescomplemented
20C22×C8×D73C2211yescharacteristic
21C2×#14556531C411yescharacteristic, complemented
22C2×#14556530C2212yes—
23M32×D73C414yescomplemented
24M32×D73C2214yes—
25C2×C16×D73C412yescomplemented
26C2×M32×C73C411yescharacteristic, complemented
27C23×#64408—41no—
28C2×#11924038—21no—
29C2×#11924038—21no—
30D73⋊M16—24no—
31D73⋊M16—42no—
32C2×#11924037—41no—
33C2×#11924036—41no—
34C2×C4⋊#64408—24no—
35C2×C4⋊#64408—22no—
36C2×C4⋊#64408—42no—
37C2×C4⋊#64408—41no—
38#14556662—24no—
39#14556661—21no—
40#14556661—21no—
41#14556661C2312yes—
42#14556661C2312yes—
43#14556659—22no—
44#14556659—24no—
45#14556659C2314yes—
46C22×C4×D73D411yescharacteristic
47C22×#10596831Q811yescharacteristic
48C2×C8×D73C2×C411yescharacteristic
49C2×C8×D73C2×C412yes—
50C2×C8×D73D412yes—
51C2×C8×D73D411yescharacteristic
52C2×C8×D73Q812yes—
53C2×C8×D73Q811yescharacteristic
54C2×C8×D73C2312yes—
55C2×C8×D73C2311yescharacteristic
56#14556531C2×C414yescomplemented
57#14556530C2×C414yescomplemented
58#14556530C2314yes—
59C2×#11924003C2×C412yescomplemented
60C16×D73C2×C418yescomplemented
61C22×C8×C73C2×C411yescharacteristic
62M32×C73C2×C414yescomplemented
63C2×C16×C73C2×C412yescomplemented
64C22×#64408—44no—
65C22×#64408—42no—
66C22×#64408—84no—
67#11924038—22no—
68#11924038—22no—
69#11924038—41no—
70#11924038—41no—
71#11924037—44no—
72#11924036—44no—
73C2×#10596833—41no—
74C2×#10596833—41no—
75C4⋊#64408—24no—
76C4⋊#64408—44no—
77C4⋊#64408—42no—
78C23×D73SD1611yescharacteristic
79C22×Dic73SD1611yescharacteristic
80C2×C4×D73C4⋊C412yes—
81C2×C4×D73C4⋊C411yescharacteristic
82C2×C4×D73SD1612yes—
83C2×C4×D73SD1611yescharacteristic
84C2×C4×D73SD1611yescharacteristic
85C2×C4×D73SD1612yes—
86C2×C4×D73C2×D412yes—
87C2×C4×D73C2×D411yescharacteristic
88C2×#10596831C4⋊C411yescharacteristic
89C2×#10596831C4⋊C412yes—
90C2×#10596831C2×Q812yes—
91C2×#10596831C2×Q811yescharacteristic
92C8×D73C4⋊C412yes—
93C8×D73C4⋊C412yes—
94C8×D73C4⋊C412yes—
95C8×D73C22×C412yes—
96C8×D73C22×C411yescharacteristic
97C8×D73C2×D411yescharacteristic
98C8×D73C2×D412yes—
99C8×D73C2×Q812yes—
100C8×D73C2×Q811yescharacteristic
101C8×D73C2411yescharacteristic
102#11924003C22×C414yescomplemented
103C22×C4×C73C4⋊C411yescharacteristic
104C2×C8×C73C4⋊C412yes—
105C2×C8×C73C4⋊C411yescharacteristic
106C2×C8×C73C22×C411yescharacteristic
107C2×C8×C73C22×C412yes—
108C16×C73C22×C414yescomplemented
109C23×C73#10611yescharacteristic
110C22×D73—24no—
111C22×D73#10612yes—
112C22×D73#10611yescharacteristic
113C22×D73C2×SD1612yes—
114C22×D73C2×SD1611yescharacteristic
115C2×#64408—44no—
116C2×#64408—84no—
117C2×#64408—88no—
118C2×C4×C73#10612yes—
119C2×C4×C73#10611yescharacteristic
120C2×C4×C73C2×C4⋊C412yes—
121C2×C4×C73C2×C4⋊C411yescharacteristic
122C2×Dic73#10612yes—
123C2×Dic73#10611yescharacteristic
124C2×Dic73C2×SD1611yescharacteristic
125C2×Dic73C2×SD1612yes—
126C4×D73#10612yes—
127C4×D73#10612yes—
128C4×D73#10612yes—
129C4×D73C2×C4⋊C411yescharacteristic
130C4×D73C2×C4⋊C412yes—
131C4×D73C2×SD1612yes—
132C4×D73C2×SD1611yescharacteristic
133C4×D73C2×SD1612yes—
134C4×D73C2×SD1611yescharacteristic
135C4×D73C22×D411yescharacteristic
136#10596833—42no—
137#10596833—42no—
138C8×C73C2×C4⋊C411yescharacteristic
139C8×C73C2×C4⋊C412yes—
140C8×C73C23×C411yescharacteristic
141#10596831C2×C4⋊C412yes—
142#10596831C2×C4⋊C411yescharacteristic
143#10596831C22×Q811yescharacteristic
144C22×C73—22no—
145C22×C73C2×#10612yes—
146C22×C73C2×#10611yescharacteristic
147C2×D73—22no—
148C2×D73—24no—
149C2×D73—24no—
150C2×D73#36514yescomplemented
151C2×D73C2×#10611yescharacteristic
152C2×D73C2×#10612yes—
153C2×D73C22×SD1611yescharacteristic
154#64408—84no—
155C4×C73C2×#10612yes—
156C4×C73C2×#10611yescharacteristic
157C4×C73C22×C4⋊C411yescharacteristic
158Dic73C2×#10611yescharacteristic
159Dic73C2×#10612yes—
160Dic73C22×SD1611yescharacteristic
161C22×#365—731nomaximal, Sylow
162C2×C73—22no—
163C2×C73C2×#36512yescomplemented
164C2×C73C22×#10611yescharacteristic
165D73—21no—
166D73—21no—
167D73C2×#36514yescomplemented
168C22×M32—731no—
169C22×#108—731no—
170C22×#106—731no—
171C2×#365—732no—
172C2×#365—732no—
173C2×#365—738no—
174C73C22×#36511yescharacteristic, complemented, Sylow
175C22×M16—1461no—
176C23×C8—731no—
177C22×C4⋊C4—1461no—
178C2×M32—731no—
179C2×M32—734no—
180C2×M32—734no—
181C2×M32—732no—
182C2×M32#6440811yescharacteristic, complemented
183C22×C16—732no—
184C2×#108—731no—
185C2×#108—731no—
186C2×#108—734no—
187C2×#108—1462no—
188C2×#108—1461no—
189C2×#106—732no—
190C2×#106—734no—
191C2×#106—1462no—
192C2×#106—1461no—
193#365—738no—
194#365—738no—
195C23×C4—2921no—
196C23×C4—731no—
197C2×M16—2921no—
198C2×M16—2922no—
199C2×M16—1464no—
200C2×M16—1461no—
201C2×M16—1461no—
202C22×C8—2921no—
203C22×C8—731no—
204C22×C8—732no—
205C22×C8—731no—
206C22×C8—732no—
207C22×C8—731no—
208C22×C8—732no—
209C22×C8—731no—
210C22×C8—731no—
211C22×C8—732no—
212C22×C8C2×#6440811yescharacteristic
213C2×C4⋊C4—2922no—
214C2×C4⋊C4—2921no—
215C2×C4⋊C4—1464no—
216C2×C4⋊C4—1462no—
217M32—734no—
218M32—734no—
219M32—734no—
220M32C2×#6440814yescomplemented
221C2×C16—732no—
222C2×C16—738no—
223C2×C16C2×#6440812yescomplemented
224#108—732no—
225#108—732no—
226#108—1461no—
227#108—1461no—
228#108—1464no—
229#106—734no—
230#106—1462no—
231#106—1464no—
232C24—731no—
233C22×C4—2924no—
234C22×C4—2922no—
235C22×C4—5844no—
236C22×C4—731no—
237C22×C4—732no—
238C22×C4—731no—
239C22×C4—731no—
240C22×C4—732no—
241C22×C4—732no—
242C22×C4—731no—
243C22×C4—732no—
244C22×C4—731no—
245C22×C4C4⋊#6440811yescharacteristic
246M16—2924no—
247M16—2921no—
248M16—2921no—
249M16—1462no—
250M16—1462no—
251C2×C8—2921no—
252C2×C8—2921no—
253C2×C8—2924no—
254C2×C8—732no—
255C2×C8—731no—
256C2×C8—732no—
257C2×C8—731no—
258C2×C8—732no—
259C2×C8—731no—
260C2×C8—731no—
261C2×C8—732no—
262C2×C8—732no—
263C2×C8—732no—
264C2×C8—731no—
265C2×C8—732no—
266C2×C8—731no—
267C2×C8—732no—
268C2×C8C4⋊#6440812yes—
269C2×C8C4⋊#6440811yescharacteristic
270C2×C8C22×#6440811yescharacteristic
271C2×C8C22×#6440812yes—
272C4⋊C4—2924no—
273C4⋊C4—2922no—
274C4⋊C4—1464no—
275C16—734no—
276C16C22×#6440814yescomplemented
277C23—731no—
278C23—732no—
279C23—732no—
280C23—731no—
281C23—1464no—
282C23#1455665911yescharacteristic
283C2×C4—2924no—
284C2×C4—5848no—
285C2×C4—5844no—
286C2×C4—732no—
287C2×C4—732no—
288C2×C4—731no—
289C2×C4—731no—
290C2×C4—731no—
291C2×C4—732no—
292C2×C4—731no—
293C2×C4—732no—
294C2×C4—731no—
295C2×C4—732no—
296C2×C4—731no—
297C2×C4—732no—
298C2×C4—732no—
299C2×C4—732no—
300C2×C4#1455665912yes—
301C2×C4#1455665911yescharacteristic
302C2×C4C2×C4⋊#6440812yes—
303C2×C4C2×C4⋊#6440811yescharacteristic
304C8—2922no—
305C8—2922no—
306C8—732no—
307C8—731no—
308C8—731no—
309C8C2×C4⋊#6440811yescharacteristic
310C8C2×C4⋊#6440812yes—
311C8C23×#6440811yescharacteristic
312C22—22no—
313C22—732no—
314C22—734no—
315C22—731no—
316C22—731no—
317C22—1464no—
318C22—1464no—
319C22—1462no—
320C22C2×#1455665912yes—
321C22C2×#1455665911yescharacteristic
322C4—5844no—
323C4—731no—
324C4—732no—
325C4—731no—
326C4C2×#1455665912yes—
327C4C2×#1455665911yescharacteristic
328C4C22×C4⋊#6440811yescharacteristic
329C2—22no—
330C2—734no—
331C2—1461no—
332C2—1461no—
333C2D73⋊#36512yesdirect product factor
334C2C22×#1455665911yescharacteristic
subgroupG/H
centerC22C2×#14556659
commutatorC8×C73C23×C4
FrattiniC8C23×#64408
FittingC2×M32×C73C4
socleC22×C73C2×#106
prime radicalC23×D73SD16
cosocleC8×D73C24
hypercenterC2×M32#64408
hypocenterC73C22×#365
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
3. D73⋊#365C2direct (N × H)
4. C2×#17989512C2semidirect
5. C2×#17989511C2semidirect
18. #17989512C22semidirect
19. #17989511C22semidirect
21. C2×#14556531C4semidirect
23. M32×D73C4semidirect
25. C2×C16×D73C4semidirect
26. C2×M32×C73C4semidirect
56. #14556531C2×C4semidirect
57. #14556530C2×C4semidirect
59. C2×#11924003C2×C4semidirect
60. C16×D73C2×C4semidirect
62. M32×C73C2×C4semidirect
63. C2×C16×C73C2×C4semidirect
102. #11924003C22×C4semidirect
108. C16×C73C22×C4semidirect
150. C2×D73#365semidirect
163. C2×C73C2×#365semidirect
167. D73C2×#365semidirect
174. C73C22×#365semidirect
182. C2×M32#64408semidirect
220. M32C2×#64408semidirect
223. C2×C16C2×#64408semidirect
276. C16C22×#64408semidirect
333. C2D73⋊#365direct (N × H)

Maximal subgroups

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

subgroupindex
C2×D73⋊#1082
C22×#145566592
D73⋊#3652
C2×#179895122
C2×#179895112
C2×M32×D732
C22×#36573