Subgroups — #107×#3633 #17981633

Order 4352.

446 conjugacy classes of subgroups.

The subgroup lattice has 272 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₄⋊C₄×#3633	C₂	1	2	yes	maximal
2	C₂×#11763899	C₂	1	1	yes	maximal, characteristic
3	C₂×C₈×#3633	C₂	1	1	yes	maximal, characteristic
4	#14545792	C₂	1	2	yes	maximal
5	#107×#595	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#3633	C₂²	1	2	yes	—
7	C₂×C₄×#3633	—	2	2	no	—
8	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
9	C₂×C₄×#3633	C₂²	1	1	yes	characteristic
10	(C₂×#3633)⋊C₄	—	2	2	no	—
11	#11763899	C₄	1	4	yes	complemented
12	C₈×#3633	C₄	1	4	yes	complemented
13	C₂×#10587534	C₄	1	1	yes	characteristic
14	C₂×C₈×#595	C₂²	1	1	yes	characteristic
15	C₄⋊C₄×#595	C₂²	1	2	yes	—
16	#11763682	C₄	1	2	yes	—
17	#107×D₁₇	C₄	1	1	yes	characteristic
18	C₂²×#3633	—	2	1	no	—
19	C₂²×#3633	—	2	2	no	—
20	C₂²×#3633	D₄	1	1	yes	characteristic
21	C₂²×#3633	D₄	1	1	yes	characteristic
22	C₂×C₄⋊#595	C₂×C₄	1	2	yes	—
23	C₂×C₄×#595	—	2	2	no	—
24	C₂×C₄×#595	C₂³	1	1	yes	characteristic
25	C₂×#63242	C₂×C₄	1	1	yes	characteristic
26	C₄⋊#3633	—	2	2	no	—
27	C₄⋊#3633	C₂×C₄	1	4	yes	—
28	C₄×#3633	—	2	1	no	—
29	C₄×#3633	—	4	4	no	—
30	C₄×#3633	C₂×C₄	1	2	yes	—
31	C₄×#3633	C₂×C₄	1	2	yes	—
32	C₄×#3633	Q₈	1	2	yes	—
33	C₂×C₈×D₁₇	C₂×C₄	1	1	yes	characteristic
34	C₄⋊C₄×D₁₇	C₂×C₄	1	2	yes	—
35	(C₂×#595)⋊C₄	—	2	2	no	—
36	#10587534	C₈	1	4	yes	complemented
37	C₈×#595	C₂×C₄	1	2	yes	—
38	C₈×#595	C₂×C₄	1	2	yes	—
39	C₁₇×#107	C₈	1	1	yes	characteristic, complemented
40	#10587489	C₈	1	1	yes	characteristic, complemented
41	#10587478	C₈	1	2	yes	complemented
42	C₂²×#595	—	2	2	no	—
43	C₂²×#595	C₂×D₄	1	1	yes	characteristic
44	C₂²×#595	#41	1	1	yes	characteristic
45	C₂×#3633	—	2	2	no	—
46	C₂×#3633	—	2	2	no	—
47	C₂×#3633	—	2	2	no	—
48	C₂×#3633	—	2	1	no	—
49	C₂×#3633	—	2	1	no	—
50	C₂×#3633	—	2	4	no	—
51	C₂×#3633	—	4	2	no	—
52	C₂×#3633	—	4	2	no	—
53	C₂×#3633	C₄⋊C₄	1	2	yes	—
54	C₂×#3633	C₄⋊C₄	1	2	yes	—
55	C₂×#3633	D₈	1	2	yes	—
56	C₂×#3633	Q₁₆	1	2	yes	—
57	C₂×C₄×D₁₇	—	2	2	no	—
58	C₂×C₄×D₁₇	C₂²×C₄	1	1	yes	characteristic
59	C₂×#3624	—	2	1	no	—
60	C₄⋊#595	—	2	2	no	—
61	C₄⋊#595	C₂×C₈	1	4	yes	—
62	C₄×#595	—	4	2	no	—
63	C₄×#595	—	4	2	no	—
64	C₄×#595	C₂²×C₄	1	1	yes	characteristic
65	C₄×#595	C₂²×C₄	1	1	yes	characteristic
66	C₄×#595	C₂×Q₈	1	1	yes	characteristic
67	C₄×#595	#41	1	1	yes	characteristic
68	#63242	—	2	1	no	—
69	#63242	C₄²	1	2	yes	—
70	C₂×C₈×C₁₇	C₂×C₈	1	1	yes	characteristic
71	C₄⋊C₄×C₁₇	C₂×C₈	1	2	yes	—
72	C₄⋊Dic₁₇	C₂×C₈	1	2	yes	—
73	#63225	—	2	2	no	—
74	C₂×#3622	C₂×C₈	1	1	yes	characteristic
75	C₈×D₁₇	C₄²	1	2	yes	—
76	C₈×D₁₇	C₂×C₈	1	2	yes	—
77	C₈×#107	—	17	1	no	maximal, Sylow
78	C₂²×D₁₇	C₄×D₄	1	1	yes	characteristic
79	C₂×#595	—	2	1	no	—
80	C₂×#595	—	2	1	no	—
81	C₂×#595	—	2	4	no	—
82	C₂×#595	—	4	2	no	—
83	C₂×#595	—	4	2	no	—
84	C₂×#595	C₂×C₄⋊C₄	1	1	yes	characteristic
85	C₂×#595	#117	1	1	yes	characteristic
86	C₂×#595	C₄×D₄	1	1	yes	characteristic
87	C₂×#595	C₄×Q₈	1	1	yes	characteristic
88	C₂×#595	C₂×D₈	1	1	yes	characteristic
89	C₂×#595	C₂×Q₁₆	1	1	yes	characteristic
90	C₂×#595	#135	1	1	yes	characteristic
91	C₂×#595	#135	1	1	yes	characteristic
92	#3633	—	2	4	no	—
93	#3633	—	2	2	no	—
94	#3633	—	4	4	no	—
95	#3633	#107	1	4	yes	direct product factor
96	C₂×C₄×C₁₇	—	2	2	no	—
97	C₂×C₄×C₁₇	C₂²×C₈	1	1	yes	characteristic
98	C₂×Dic₁₇	—	2	2	no	—
99	C₂×Dic₁₇	#131	1	1	yes	characteristic
100	C₄×D₁₇	—	4	2	no	—
101	C₄×D₁₇	—	4	2	no	—
102	C₄×D₁₇	C₂×C₄²	1	1	yes	characteristic
103	C₄×D₁₇	C₄×Q₈	1	1	yes	characteristic
104	C₄×D₁₇	C₂²×C₈	1	1	yes	characteristic
105	C₄×D₁₇	#131	1	1	yes	characteristic
106	#3624	—	2	2	no	—
107	C₈×C₁₇	C₄×C₈	1	2	yes	complemented
108	#3622	C₄×C₈	1	2	yes	complemented
109	C₄×#107	—	17	1	no	—
110	C₈×C₄⋊C₄	—	17	2	no	—
111	C₂×#335	—	17	1	no	—
112	C₂×C₈²	—	17	1	no	—
113	#1279	—	17	2	no	—
114	C₂²×C₁₇	C₈×D₄	1	1	yes	characteristic
115	C₂×D₁₇	C₄×C₄⋊C₄	1	1	yes	characteristic
116	C₂×D₁₇	C₈×D₄	1	1	yes	characteristic
117	C₂×D₁₇	C₄×D₈	1	1	yes	characteristic
118	C₂×D₁₇	C₄×Q₁₆	1	1	yes	characteristic
119	C₂×D₁₇	#443	1	1	yes	characteristic
120	C₂×D₁₇	#443	1	1	yes	characteristic
121	#595	—	2	1	no	—
122	#595	—	2	1	no	—
123	#595	—	4	4	no	—
124	#595	C₂×#107	1	1	yes	characteristic
125	#595	#427	1	1	yes	characteristic
126	#595	C₄×D₈	1	1	yes	characteristic
127	#595	C₄×Q₁₆	1	1	yes	characteristic
128	C₄×C₁₇	—	4	2	no	—
129	C₄×C₁₇	C₂×C₄×C₈	1	1	yes	characteristic
130	C₄×C₁₇	C₈×Q₈	1	1	yes	characteristic
131	Dic₁₇	—	4	2	no	—
132	Dic₁₇	#405	1	1	yes	characteristic
133	Dic₁₇	C₈×Q₈	1	1	yes	characteristic
134	C₂×#107	—	17	1	no	—
135	C₂×#107	—	17	1	no	—
136	C₂×C₄⋊C₈	—	17	2	no	—
137	C₂×C₄×C₈	—	17	1	no	—
138	C₂×C₄×C₈	—	17	1	no	—
139	C₂×C₄×C₈	—	17	1	no	—
140	C₂×C₄×C₈	—	34	2	no	—
141	C₄×C₄⋊C₄	—	17	2	no	—
142	#340	—	17	2	no	—
143	#336	—	34	2	no	—
144	#335	—	17	4	no	—
145	C₈²	—	17	4	no	—
146	C₂×C₁₇	C₈×D₈	1	1	yes	characteristic
147	C₂×C₁₇	C₈×Q₁₆	1	1	yes	characteristic
148	C₂×C₁₇	C₈×C₄⋊C₄	1	1	yes	characteristic
149	D₁₇	C₈×D₈	1	1	yes	characteristic
150	D₁₇	C₈×Q₁₆	1	1	yes	characteristic
151	D₁₇	#1772	1	1	yes	characteristic
152	D₁₇	C₄×#107	1	1	yes	characteristic
153	C₂²×C₈	—	17	1	no	—
154	C₂²×C₈	—	17	1	no	—
155	C₂²×C₈	—	17	1	no	—
156	C₂²×C₈	—	17	1	no	—
157	C₂²×C₈	—	34	1	no	—
158	C₂²×C₈	—	34	2	no	—
159	C₂×C₄⋊C₄	—	17	2	no	—
160	C₂×C₄⋊C₄	—	17	2	no	—
161	C₂×C₄²	—	17	1	no	—
162	C₂×C₄²	—	34	2	no	—
163	#107	—	17	4	no	—
164	#107	—	17	1	no	—
165	#107	—	17	2	no	—
166	#107	#3633	1	1	yes	characteristic, direct product factor
167	C₄⋊C₈	—	17	4	no	—
168	C₄⋊C₈	—	34	2	no	—
169	C₄×C₈	—	17	2	no	—
170	C₄×C₈	—	17	2	no	—
171	C₄×C₈	—	17	2	no	—
172	C₄×C₈	—	17	2	no	—
173	C₄×C₈	—	17	2	no	—
174	C₄×C₈	—	34	1	no	—
175	C₄×C₈	—	68	4	no	—
176	#95	—	34	2	no	—
177	C₁₇	C₈×#107	1	1	yes	characteristic, complemented, Sylow
178	C₂²×C₄	—	17	1	no	—
179	C₂²×C₄	—	17	1	no	—
180	C₂²×C₄	—	17	1	no	—
181	C₂²×C₄	—	34	2	no	—
182	C₂²×C₄	—	34	2	no	—
183	C₂×C₈	—	17	2	no	—
184	C₂×C₈	—	17	2	no	—
185	C₂×C₈	—	17	2	no	—
186	C₂×C₈	—	17	1	no	—
187	C₂×C₈	—	17	2	no	—
188	C₂×C₈	—	17	2	no	—
189	C₂×C₈	—	17	2	no	—
190	C₂×C₈	—	17	2	no	—
191	C₂×C₈	—	34	1	no	—
192	C₂×C₈	—	34	1	no	—
193	C₂×C₈	—	34	2	no	—
194	C₂×C₈	—	34	1	no	—
195	C₂×C₈	—	34	1	no	—
196	C₂×C₈	—	34	2	no	—
197	C₂×C₈	—	34	2	no	—
198	C₂×C₈	—	34	4	no	—
199	C₂×C₈	—	68	2	no	—
200	C₂×C₈	—	68	2	no	—
201	C₂×C₈	C₂×#3633	1	1	yes	characteristic
202	C₄⋊C₄	—	17	4	no	—
203	C₄⋊C₄	—	17	2	no	—
204	C₄⋊C₄	—	34	2	no	—
205	C₄⋊C₄	—	34	2	no	—
206	C₄⋊C₄	C₂×#3633	1	2	yes	—
207	C₄²	—	17	1	no	—
208	C₄²	—	17	1	no	—
209	C₄²	—	17	1	no	—
210	C₄²	—	17	1	no	—
211	C₄²	—	68	2	no	—
212	C₄²	—	68	2	no	—
213	C₂³	—	17	1	no	—
214	C₂×C₄	—	2	2	no	—
215	C₂×C₄	—	17	1	no	—
216	C₂×C₄	—	17	1	no	—
217	C₂×C₄	—	17	1	no	—
218	C₂×C₄	—	17	1	no	—
219	C₂×C₄	—	17	1	no	—
220	C₂×C₄	—	17	1	no	—
221	C₂×C₄	—	17	1	no	—
222	C₂×C₄	—	17	1	no	—
223	C₂×C₄	—	17	1	no	—
224	C₂×C₄	—	17	1	no	—
225	C₂×C₄	—	17	1	no	—
226	C₂×C₄	—	17	1	no	—
227	C₂×C₄	—	17	1	no	—
228	C₂×C₄	—	34	1	no	—
229	C₂×C₄	—	34	1	no	—
230	C₂×C₄	—	34	4	no	—
231	C₂×C₄	—	34	2	no	—
232	C₂×C₄	—	68	2	no	—
233	C₂×C₄	—	68	2	no	—
234	C₂×C₄	—	68	2	no	—
235	C₂×C₄	—	68	2	no	—
236	C₂×C₄	C₂²×#3633	1	1	yes	characteristic
237	C₈	—	17	4	no	—
238	C₈	—	17	2	no	—
239	C₈	—	34	2	no	—
240	C₈	—	34	2	no	—
241	C₈	—	34	4	no	—
242	C₈	—	68	4	no	—
243	C₈	C₄×#3633	1	2	yes	complemented
244	C₂²	—	17	1	no	—
245	C₂²	—	17	1	no	—
246	C₂²	—	17	1	no	—
247	C₂²	—	17	1	no	—
248	C₂²	—	17	1	no	—
249	C₂²	—	17	1	no	—
250	C₂²	D₄×#3633	1	1	yes	characteristic
251	C₄	—	4	2	no	—
252	C₄	—	17	1	no	—
253	C₄	—	17	1	no	—
254	C₄	—	17	1	no	—
255	C₄	—	17	1	no	—
256	C₄	—	17	1	no	—
257	C₄	—	17	1	no	—
258	C₄	—	34	1	no	—
259	C₄	—	34	1	no	—
260	C₄	—	68	4	no	—
261	C₄	—	68	2	no	—
262	C₄	C₂×C₄×#3633	1	1	yes	characteristic
263	C₄	Q₈×#3633	1	1	yes	characteristic
264	C₂	—	17	1	no	—
265	C₂	—	17	1	no	—
266	C₂	—	17	1	no	—
267	C₂	—	17	1	no	—
268	C₂	D₈×#3633	1	1	yes	characteristic
269	C₂	Q₁₆×#3633	1	1	yes	characteristic
270	C₂	C₄⋊C₄×#3633	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	D₄×#3633
commutator	C₄×C₁₇	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#3633
Fitting	C₁₇×#107	C₈
socle	C₂²×C₁₇	C₈×D₄
prime radical	C₂²×D₁₇	C₄×D₄
cosocle	C₂×C₄×#595	C₂³
hypercenter	#107	#3633
hypocenter	C₁₇	C₈×#107
LCS	G ▷ C₄×C₁₇ ▷ C₂×C₁₇ ▷ C₁₇
UCS	C₁ ◁ C₂² ◁ C₂×C₄ ◁ #107

Complements

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

N	H ≅ G/N	type
11. #11763899	C₄	semidirect
12. C₈×#3633	C₄	semidirect
36. #10587534	C₈	semidirect
39. C₁₇×#107	C₈	semidirect
40. #10587489	C₈	semidirect
41. #10587478	C₈	semidirect
95. #3633	#107	direct (N × H)
107. C₈×C₁₇	C₄×C₈	semidirect
108. #3622	C₄×C₈	semidirect
166. #107	#3633	direct (N × H)
177. C₁₇	C₈×#107	semidirect
243. C₈	C₄×#3633	semidirect

Maximal subgroups

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

subgroup	index
C₄⋊C₄×#3633	2
C₂×#11763899	2
C₂×C₈×#3633	2
#14545792	2
#107×#595	2
C₈×#107	17