Group #27179428 — subgroups

Subgroups — #27179428

Order 12928.

696 conjugacy classes of subgroups; only the 169 normal subgroups are shown.

normal subgroups only

This group has 696 conjugacy classes of subgroups — too many to draw. Only its 169 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15692231	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#15692226	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄²×D₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
4	#20265084	C₂	1	1	yes	maximal, characteristic, complemented
5	#20265080	C₂	1	1	yes	maximal, characteristic, complemented
6	#20265065	C₂	1	4	yes	maximal, complemented
7	#20265053	C₂	1	4	yes	maximal, complemented
8	#20265043	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#124×C₁₀₁	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂²×C₂²⋊D₁₀₁	C₂²	1	2	yes	—
11	C₂²×C₄×D₁₀₁	C₂²	1	2	yes	—
12	C₂²×C₄×D₁₀₁	C₂²	1	1	yes	characteristic
13	#15692231	—	2	4	no	—
14	#15692226	—	2	4	no	—
15	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Dic₁₀₁	C₂²	1	1	yes	characteristic
17	C₂×#13108053	C₂²	1	2	yes	—
18	C₂×C₂²⋊Dic₁₀₁	C₂²	1	4	yes	—
19	C₂×C₂²⋊Dic₁₀₁	C₂²	1	2	yes	—
20	C₂×#13108051	C₂²	1	2	yes	—
21	C₂×C₄×Dic₁₀₁	C₂²	1	2	yes	—
22	C₂×C₄×Dic₁₀₁	C₂²	1	1	yes	characteristic
23	C₄²×D₁₀₁	—	2	4	no	—
24	#15692162	C₂²	1	4	yes	—
25	#15692162	C₂²	1	4	yes	—
26	C₂²×Q₈×C₁₀₁	C₂²	1	1	yes	characteristic
27	C₂²×D₄×C₁₀₁	C₂²	1	1	yes	characteristic
28	#124×C₁₀₁	—	2	4	no	—
29	C₂×C₂²⋊C₄×C₁₀₁	C₂²	1	4	yes	—
30	C₂×C₄²×C₁₀₁	C₂²	1	1	yes	characteristic
31	C₂³×D₁₀₁	C₂³	1	1	yes	characteristic
32	C₂×C₂²⋊D₁₀₁	—	2	4	no	—
33	C₂×C₂²⋊D₁₀₁	—	2	8	no	—
34	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
35	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
36	C₂²×Dic₁₀₁	C₂³	1	1	yes	characteristic
37	C₂²×Dic₁₀₁	C₂³	1	2	yes	—
38	C₂×C₄×D₁₀₁	—	2	4	no	—
39	C₂×C₄×D₁₀₁	—	2	4	no	—
40	C₂×C₄×D₁₀₁	—	2	2	no	—
41	C₂×C₄×D₁₀₁	—	2	2	no	—
42	C₂×C₄×D₁₀₁	—	2	4	no	—
43	C₂×C₄×D₁₀₁	D₄	1	4	yes	—
44	C₄⋊Dic₁₀₁	—	2	2	no	—
45	C₄⋊Dic₁₀₁	—	2	2	no	—
46	#13108053	—	2	4	no	—
47	C₂²⋊Dic₁₀₁	—	2	4	no	—
48	C₂²⋊Dic₁₀₁	—	2	8	no	—
49	#13108051	—	2	4	no	—
50	C₄×Dic₁₀₁	—	2	4	no	—
51	C₄×Dic₁₀₁	—	2	2	no	—
52	C₂⁴×C₁₀₁	C₂³	1	2	yes	—
53	C₂×Q₈×C₁₀₁	—	2	2	no	—
54	C₂×Q₈×C₁₀₁	—	2	2	no	—
55	C₂×Q₈×C₁₀₁	—	2	2	no	—
56	C₂×D₄×C₁₀₁	—	2	2	no	—
57	C₂×D₄×C₁₀₁	—	2	2	no	—
58	C₂×D₄×C₁₀₁	—	2	2	no	—
59	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
60	C₂²×C₄×C₁₀₁	C₂³	1	2	yes	—
61	C₂²×C₄×C₁₀₁	C₂³	1	1	yes	characteristic
62	C₂²⋊C₄×C₁₀₁	—	2	8	no	—
63	C₄²×C₁₀₁	D₄	1	4	yes	complemented
64	C₂³×C₁₀₁	—	2	2	no	—
65	C₂³×C₁₀₁	—	2	2	no	—
66	C₂³×C₁₀₁	—	2	2	no	—
67	C₂³×C₁₀₁	—	2	4	no	—
68	C₂³×C₁₀₁	—	2	4	no	—
69	C₂³×C₁₀₁	C₂⁴	1	1	yes	characteristic
70	C₂²×D₁₀₁	—	2	1	no	—
71	C₂²×D₁₀₁	—	2	2	no	—
72	C₂²×D₁₀₁	—	2	1	no	—
73	C₂²×D₁₀₁	C₂×D₄	1	2	yes	—
74	C₂²×D₁₀₁	#41	1	4	yes	—
75	Q₈×C₁₀₁	—	4	4	no	—
76	D₄×C₁₀₁	—	4	4	no	—
77	C₂×C₄×C₁₀₁	—	2	2	no	—
78	C₂×C₄×C₁₀₁	—	2	2	no	—
79	C₂×C₄×C₁₀₁	—	2	2	no	—
80	C₂×C₄×C₁₀₁	—	2	2	no	—
81	C₂×C₄×C₁₀₁	—	2	2	no	—
82	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
83	C₂×C₄×C₁₀₁	C₂×D₄	1	4	yes	—
84	C₂×C₄×C₁₀₁	C₂×D₄	1	2	yes	—
85	C₂×C₄×C₁₀₁	#41	1	2	yes	—
86	C₂²⋊D₁₀₁	—	4	8	no	—
87	C₂×Dic₁₀₁	—	2	1	no	—
88	C₂×Dic₁₀₁	—	2	2	no	—
89	C₂×Dic₁₀₁	—	2	2	no	—
90	C₂×Dic₁₀₁	—	2	1	no	—
91	C₂×Dic₁₀₁	—	2	2	no	—
92	C₂×Dic₁₀₁	—	2	2	no	—
93	C₂×Dic₁₀₁	—	2	4	no	—
94	C₂×Dic₁₀₁	—	2	4	no	—
95	C₂×Dic₁₀₁	C₂×D₄	1	2	yes	—
96	C₂×Dic₁₀₁	#41	1	4	yes	—
97	C₄×D₁₀₁	—	2	16	no	—
98	C₄×D₁₀₁	—	2	8	no	—
99	C₂²×C₁₀₁	—	4	2	no	—
100	C₂²×C₁₀₁	—	4	4	no	—
101	C₂²×C₁₀₁	—	4	2	no	—
102	C₂²×C₁₀₁	—	4	4	no	—
103	C₂²×C₁₀₁	—	4	2	no	—
104	C₂²×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
105	C₂²×C₁₀₁	C₂²×D₄	1	1	yes	characteristic
106	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
107	C₂²×C₁₀₁	C₂×#41	1	2	yes	—
108	C₂²×C₁₀₁	C₂×#41	1	1	yes	characteristic
109	C₂×D₁₀₁	—	2	2	no	—
110	C₂×D₁₀₁	—	2	4	no	—
111	C₂×D₁₀₁	—	2	4	no	—
112	C₂×D₁₀₁	—	2	2	no	—
113	C₂×D₁₀₁	#124	1	4	yes	complemented
114	C₄×C₁₀₁	—	2	4	no	—
115	C₄×C₁₀₁	—	4	2	no	—
116	C₄×C₁₀₁	#121	1	4	yes	—
117	Dic₁₀₁	—	2	2	no	—
118	Dic₁₀₁	—	2	4	no	—
119	Dic₁₀₁	—	4	2	no	—
120	Dic₁₀₁	—	4	2	no	—
121	C₂×C₁₀₁	—	8	2	no	—
122	C₂×C₁₀₁	C₂×#121	1	1	yes	characteristic
123	C₂×C₁₀₁	#525	1	2	yes	—
124	C₂×C₁₀₁	C₂×#124	1	1	yes	characteristic
125	C₂×C₁₀₁	#529	1	2	yes	—
126	C₂×C₁₀₁	#532	1	1	yes	characteristic
127	D₁₀₁	—	2	4	no	—
128	#2850	—	101	1	no	maximal, Sylow
129	C₁₀₁	#2850	1	1	yes	characteristic, complemented, Sylow
130	C₂×#124	D₁₀₁	1	1	yes	characteristic, complemented
131	C₂×C₂²⋊Q₈	—	101	1	no	—
132	C₂×#121	—	101	1	no	—
133	C₂²×C₄²	—	101	1	no	—
134	#391	—	101	1	no	—
135	#390	—	101	1	no	—
136	#388	—	101	4	no	—
137	#386	—	101	4	no	—
138	#382	—	101	1	no	—
139	C₂²×Q₈	C₂×D₁₀₁	1	1	yes	characteristic
140	C₂²×D₄	—	101	2	no	—
141	C₂²×D₄	C₂×D₁₀₁	1	1	yes	characteristic
142	C₂³×C₄	—	101	1	no	—
143	C₂³×C₄	—	101	2	no	—
144	#124	—	2	4	no	—
145	C₂²⋊Q₈	—	202	4	no	—
146	#121	—	202	4	no	—
147	C₂×C₄⋊C₄	—	101	1	no	—
148	C₂×C₄⋊C₄	—	101	1	no	—
149	C₂×C₄⋊C₄	—	101	2	no	—
150	C₂×C₂²⋊C₄	—	101	2	no	—
151	C₂×C₂²⋊C₄	—	101	4	no	—
152	C₂×C₂²⋊C₄	—	101	2	no	—
153	C₂×C₂²⋊C₄	C₂×D₁₀₁	1	4	yes	—
154	C₂×C₄²	—	101	2	no	—
155	C₂×C₄²	—	101	1	no	—
156	C₂×C₄²	—	202	4	no	—
157	C₂×C₄²	C₂×D₁₀₁	1	1	yes	characteristic
158	#95	—	101	4	no	—
159	#95	—	101	4	no	—
160	C₂⁴	—	101	1	no	—
161	C₂⁴	C₂²×D₁₀₁	1	2	yes	—
162	C₂×Q₈	—	2	2	no	—
163	C₂×Q₈	—	2	2	no	—
164	C₂×Q₈	—	2	2	no	—
165	C₂×D₄	—	2	2	no	—
166	C₂×D₄	—	2	2	no	—
167	C₂×D₄	—	2	2	no	—
168	C₂×D₄	—	202	4	no	—
169	C₂×D₄	—	202	8	no	—
170	C₂²×C₄	—	101	2	no	—
171	C₂²×C₄	—	101	1	no	—
172	C₂²×C₄	—	101	4	no	—
173	C₂²×C₄	—	101	2	no	—
174	C₂²×C₄	—	101	2	no	—
175	C₂²×C₄	—	202	4	no	—
176	C₂²×C₄	—	202	4	no	—
177	C₂²×C₄	—	202	4	no	—
178	C₂²×C₄	—	202	2	no	—
179	C₂²×C₄	—	202	2	no	—
180	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
181	C₂²×C₄	C₂²×D₁₀₁	1	2	yes	—
182	C₂²×C₄	C₂²×D₁₀₁	1	1	yes	characteristic
183	C₄⋊C₄	—	202	4	no	—
184	C₄⋊C₄	—	202	2	no	—
185	C₄⋊C₄	—	202	2	no	—
186	C₂²⋊C₄	—	2	8	no	—
187	C₂²⋊C₄	—	202	4	no	—
188	C₂²⋊C₄	—	202	8	no	—
189	C₂²⋊C₄	—	202	4	no	—
190	C₄²	—	202	4	no	—
191	C₄²	—	202	2	no	—
192	C₄²	C₂²⋊D₁₀₁	1	4	yes	complemented
193	C₂³	—	2	2	no	—
194	C₂³	—	2	2	no	—
195	C₂³	—	2	4	no	—
196	C₂³	—	2	4	no	—
197	C₂³	—	2	2	no	—
198	C₂³	—	101	2	no	—
199	C₂³	—	101	4	no	—
200	C₂³	—	202	1	no	—
201	C₂³	—	202	2	no	—
202	C₂³	—	202	1	no	—
203	C₂³	C₂³×D₁₀₁	1	1	yes	characteristic
204	Q₈	—	4	4	no	—
205	D₄	—	4	4	no	—
206	D₄	—	404	8	no	—
207	C₂×C₄	—	2	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	2	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	101	2	no	—
213	C₂×C₄	—	101	4	no	—
214	C₂×C₄	—	202	16	no	—
215	C₂×C₄	—	202	2	no	—
216	C₂×C₄	—	202	2	no	—
217	C₂×C₄	—	202	4	no	—
218	C₂×C₄	—	202	4	no	—
219	C₂×C₄	—	202	1	no	—
220	C₂×C₄	—	202	2	no	—
221	C₂×C₄	—	202	2	no	—
222	C₂×C₄	—	202	1	no	—
223	C₂×C₄	—	202	8	no	—
224	C₂×C₄	D₄×D₁₀₁	1	2	yes	—
225	C₂×C₄	C₂×C₂²⋊D₁₀₁	1	4	yes	—
226	C₂×C₄	C₂×C₂²⋊D₁₀₁	1	2	yes	—
227	C₂×C₄	#13108073	1	2	yes	—
228	C₂²	—	4	2	no	—
229	C₂²	—	4	4	no	—
230	C₂²	—	4	2	no	—
231	C₂²	—	4	4	no	—
232	C₂²	—	4	2	no	—
233	C₂²	—	101	4	no	—
234	C₂²	—	202	2	no	—
235	C₂²	—	202	4	no	—
236	C₂²	—	202	4	no	—
237	C₂²	—	202	2	no	—
238	C₂²	C₂×D₄×D₁₀₁	1	1	yes	characteristic
239	C₂²	C₂²×C₂²⋊D₁₀₁	1	1	yes	characteristic
240	C₂²	#41×D₁₀₁	1	2	yes	—
241	C₂²	#41×D₁₀₁	1	2	yes	—
242	C₂²	C₂×#13108073	1	1	yes	characteristic
243	C₄	—	2	4	no	—
244	C₄	—	4	2	no	—
245	C₄	—	404	2	no	—
246	C₄	—	404	2	no	—
247	C₄	—	202	2	no	—
248	C₄	—	202	4	no	—
249	C₄	#15692226	1	4	yes	—
250	C₂	—	8	2	no	—
251	C₂	—	202	4	no	—
252	C₂	C₂×#15692226	1	1	yes	characteristic
253	C₂	#20265684	1	2	yes	—
254	C₂	#124×D₁₀₁	1	1	yes	characteristic
255	C₂	#20265706	1	2	yes	—
256	C₂	#20265726	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#15692231

C₂

yes

maximal, characteristic, complemented

C₂×#15692226

C₂

yes

maximal, characteristic

C₂×C₄²×D₁₀₁

C₂

yes

maximal, characteristic, complemented

#20265084

C₂

yes

maximal, characteristic, complemented

#20265080

C₂

yes

maximal, characteristic, complemented

#20265065

C₂

yes

maximal, complemented

#20265053

C₂

yes

maximal, complemented

#20265043

C₂

yes

maximal, characteristic, complemented

C₂×#124×C₁₀₁

C₂

yes

maximal, characteristic, complemented

C₂²×C₂²⋊D₁₀₁

C₂²

yes

—

C₂²×C₄×D₁₀₁

C₂²

yes

—

C₂²×C₄×D₁₀₁

C₂²

yes

characteristic

#15692231

—

#15692226

—

C₂×C₄⋊Dic₁₀₁

C₂²

yes

characteristic

C₂×C₄⋊Dic₁₀₁

C₂²

yes

characteristic

C₂×#13108053

C₂²

yes

—

C₂×C₂²⋊Dic₁₀₁

C₂²

yes

—

C₂×C₂²⋊Dic₁₀₁

C₂²

yes

—

C₂×#13108051

C₂²

yes

—

C₂×C₄×Dic₁₀₁

C₂²

yes

—

C₂×C₄×Dic₁₀₁

C₂²

yes

characteristic

C₄²×D₁₀₁

—

#15692162

C₂²

yes

—

#15692162

C₂²

yes

—

C₂²×Q₈×C₁₀₁

C₂²

yes

characteristic

C₂²×D₄×C₁₀₁

C₂²

yes

characteristic

#124×C₁₀₁

—

C₂×C₂²⋊C₄×C₁₀₁

C₂²

yes

—

C₂×C₄²×C₁₀₁

C₂²

yes

characteristic

C₂³×D₁₀₁

C₂³

yes

characteristic

C₂×C₂²⋊D₁₀₁

—

C₂×C₂²⋊D₁₀₁

—

C₂²×Dic₁₀₁

C₂³

yes

—

C₂²×Dic₁₀₁

C₂³

yes

—

C₂²×Dic₁₀₁

C₂³

yes

characteristic

C₂²×Dic₁₀₁

C₂³

yes

—

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

—

C₂×C₄×D₁₀₁

D₄

yes

—

C₄⋊Dic₁₀₁

—

C₄⋊Dic₁₀₁

—

#13108053

—

C₂²⋊Dic₁₀₁

—

C₂²⋊Dic₁₀₁

—

#13108051

—

C₄×Dic₁₀₁

—

C₄×Dic₁₀₁

—

C₂⁴×C₁₀₁

C₂³

yes

—

C₂×Q₈×C₁₀₁

—

C₂×Q₈×C₁₀₁

—

C₂×Q₈×C₁₀₁

—

C₂×D₄×C₁₀₁

—

C₂×D₄×C₁₀₁

—

C₂×D₄×C₁₀₁

—

C₂²×C₄×C₁₀₁

C₂³

yes

—

C₂²×C₄×C₁₀₁

C₂³

yes

—

C₂²×C₄×C₁₀₁

C₂³

yes

characteristic

C₂²⋊C₄×C₁₀₁

—

C₄²×C₁₀₁

D₄

yes

complemented

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

—

C₂³×C₁₀₁

C₂⁴

yes

characteristic

C₂²×D₁₀₁

—

C₂²×D₁₀₁

—

C₂²×D₁₀₁

—

C₂²×D₁₀₁

C₂×D₄

yes

—

C₂²×D₁₀₁

#41

yes

—

Q₈×C₁₀₁

—

D₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

—

C₂×C₄×C₁₀₁

C₂×D₄

yes

—

C₂×C₄×C₁₀₁

C₂×D₄

yes

—

C₂×C₄×C₁₀₁

C₂×D₄

yes

—

C₂×C₄×C₁₀₁

#41

yes

—

C₂²⋊D₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

—

C₂×Dic₁₀₁

C₂×D₄

yes

—

C₂×Dic₁₀₁

#41

yes

—

C₄×D₁₀₁

—

C₄×D₁₀₁

—

C₂²×C₁₀₁

—

100

C₂²×C₁₀₁

—

101

C₂²×C₁₀₁

—

102

C₂²×C₁₀₁

—

103

C₂²×C₁₀₁

—

104

C₂²×C₁₀₁

C₂²×D₄

yes

characteristic

105

C₂²×C₁₀₁

C₂²×D₄

yes

characteristic

106

C₂²×C₁₀₁

C₂×#41

yes

—

107

C₂²×C₁₀₁

C₂×#41

yes

—

108

C₂²×C₁₀₁

C₂×#41

yes

characteristic

109

C₂×D₁₀₁

—

110

C₂×D₁₀₁

—

111

C₂×D₁₀₁

—

112

C₂×D₁₀₁

—

113

C₂×D₁₀₁

#124

yes

complemented

114

C₄×C₁₀₁

—

115

C₄×C₁₀₁

—

116

C₄×C₁₀₁

#121

yes

—

117

Dic₁₀₁

—

118

Dic₁₀₁

—

119

Dic₁₀₁

—

120

Dic₁₀₁

—

121

C₂×C₁₀₁

—

122

C₂×C₁₀₁

C₂×#121

yes

characteristic

123

C₂×C₁₀₁

#525

yes

—

124

C₂×C₁₀₁

C₂×#124

yes

characteristic

125

C₂×C₁₀₁

#529

yes

—

126

C₂×C₁₀₁

#532

yes

characteristic

127

D₁₀₁

—

128

#2850

—

101

maximal, Sylow

129

C₁₀₁

#2850

yes

characteristic, complemented, Sylow

130

C₂×#124

D₁₀₁

yes

characteristic, complemented

131

C₂×C₂²⋊Q₈

—

101

—

132

C₂×#121

—

101

—

133

C₂²×C₄²

—

101

—

134

#391

—

101

—

135

#390

—

101

—

136

#388

—

101

—

137

#386

—

101

—

138

#382

—

101

—

139

C₂²×Q₈

C₂×D₁₀₁

yes

characteristic

140

C₂²×D₄

—

101

—

141

C₂²×D₄

C₂×D₁₀₁

yes

characteristic

142

C₂³×C₄

—

101

—

143

C₂³×C₄

—

101

—

144

#124

—

145

C₂²⋊Q₈

—

202

—

146

#121

—

202

—

147

C₂×C₄⋊C₄

—

101

—

148

C₂×C₄⋊C₄

—

101

—

149

C₂×C₄⋊C₄

—

101

—

150

C₂×C₂²⋊C₄

—

101

—

151

C₂×C₂²⋊C₄

—

101

—

152

C₂×C₂²⋊C₄

—

101

—

153

C₂×C₂²⋊C₄

C₂×D₁₀₁

yes

—

154

C₂×C₄²

—

101

—

155

C₂×C₄²

—

101

—

156

C₂×C₄²

—

202

—

157

C₂×C₄²

C₂×D₁₀₁

yes

characteristic

158

#95

—

101

—

159

#95

—

101

—

160

C₂⁴

—

101

—

161

C₂⁴

C₂²×D₁₀₁

yes

—

162

C₂×Q₈

—

163

C₂×Q₈

—

164

C₂×Q₈

—

165

C₂×D₄

—

166

C₂×D₄

—

167

C₂×D₄

—

168

C₂×D₄

—

202

—

169

C₂×D₄

—

202

—

170

C₂²×C₄

—

101

—

171

C₂²×C₄

—

101

—

172

C₂²×C₄

—

101

—

173

C₂²×C₄

—

101

—

174

C₂²×C₄

—

101

—

175

C₂²×C₄

—

202

—

176

C₂²×C₄

—

202

—

177

C₂²×C₄

—

202

—

178

C₂²×C₄

—

202

—

179

C₂²×C₄

—

202

—

180

C₂²×C₄

C₂²×D₁₀₁

yes

—

181

C₂²×C₄

C₂²×D₁₀₁

yes

—

182

C₂²×C₄

C₂²×D₁₀₁

yes

characteristic

183

C₄⋊C₄

—

202

—

184

C₄⋊C₄

—

202

—

185

C₄⋊C₄

—

202

—

186

C₂²⋊C₄

—

187

C₂²⋊C₄

—

202

—

188

C₂²⋊C₄

—

202

—

189

C₂²⋊C₄

—

202

—

190

C₄²

—

202

—

191

C₄²

—

202

—

192

C₄²

C₂²⋊D₁₀₁

yes

complemented

193

C₂³

—

194

C₂³

—

195

C₂³

—

196

C₂³

—

197

C₂³

—

198

C₂³

—

101

—

199

C₂³

—

101

—

200

C₂³

—

202

—

201

C₂³

—

202

—

202

C₂³

—

202

—

203

C₂³

C₂³×D₁₀₁

yes

characteristic

204

Q₈

—

205

D₄

—

206

D₄

—

404

—

207

C₂×C₄

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

101

—

213

C₂×C₄

—

101

—

214

C₂×C₄

—

202

—

215

C₂×C₄

—

202

—

216

C₂×C₄

—

202

—

217

C₂×C₄

—

202

—

218

C₂×C₄

—

202

—

219

C₂×C₄

—

202

—

220

C₂×C₄

—

202

—

221

C₂×C₄

—

202

—

222

C₂×C₄

—

202

—

223

C₂×C₄

—

202

—

224

C₂×C₄

D₄×D₁₀₁

yes

—

225

C₂×C₄

C₂×C₂²⋊D₁₀₁

yes

—

226

C₂×C₄

C₂×C₂²⋊D₁₀₁

yes

—

227

C₂×C₄

#13108073

yes

—

228

C₂²

—

229

C₂²

—

230

C₂²

—

231

C₂²

—

232

C₂²

—

233

C₂²

—

101

—

234

C₂²

—

202

—

235

C₂²

—

202

—

236

C₂²

—

202

—

237

C₂²

—

202

—

238

C₂²

C₂×D₄×D₁₀₁

yes

characteristic

239

C₂²

C₂²×C₂²⋊D₁₀₁

yes

characteristic

240

C₂²

#41×D₁₀₁

yes

—

241

C₂²

#41×D₁₀₁

yes

—

242

C₂²

C₂×#13108073

yes

characteristic

243

C₄

—

244

C₄

—

245

C₄

—

404

—

246

C₄

—

404

—

247

C₄

—

202

—

248

C₄

—

202

—

249

C₄

#15692226

yes

—

250

C₂

—

251

C₂

—

202

—

252

C₂

C₂×#15692226

yes

characteristic

253

C₂

#20265684

yes

—

254

C₂

#124×D₁₀₁

yes

characteristic

255

C₂

#20265706

yes

—

256

C₂

#20265726

yes

characteristic

	subgroup	G/H
center, Frattini	C₂³	C₂³×D₁₀₁
commutator, socle, cosocle	C₂³×C₁₀₁	C₂⁴
Fitting	C₂×#124×C₁₀₁	C₂
prime radical	C₂×#15692226	C₂
hypercenter	C₂×#124	D₁₀₁
hypocenter	C₁₀₁	#2850
LCS	G ▷ C₂³×C₁₀₁ ▷ C₁₀₁
UCS	C₁ ◁ C₂³ ◁ C₂×#124

subgroup

G/H

center, Frattini

C₂³

C₂³×D₁₀₁

commutator, socle, cosocle

C₂³×C₁₀₁

C₂⁴

Fitting

C₂×#124×C₁₀₁

C₂

C₂

D₁₀₁

C₁₀₁

G ▷ C₂³×C₁₀₁ ▷ C₁₀₁

C₁ ◁ C₂³ ◁ C₂×#124

N	H ≅ G/N	type
1. C₂×#15692231	C₂	semidirect
3. C₂×C₄²×D₁₀₁	C₂	semidirect
4. #20265084	C₂	semidirect
5. #20265080	C₂	semidirect
6. #20265065	C₂	semidirect
7. #20265053	C₂	semidirect
8. #20265043	C₂	semidirect
9. C₂×#124×C₁₀₁	C₂	semidirect
63. C₄²×C₁₀₁	D₄	semidirect
113. C₂×D₁₀₁	#124	semidirect
129. C₁₀₁	#2850	semidirect
130. C₂×#124	D₁₀₁	semidirect
192. C₄²	C₂²⋊D₁₀₁	semidirect

H ≅ G/N

type

1. C₂×#15692231

C₂

semidirect

3. C₂×C₄²×D₁₀₁

C₂

semidirect

4. #20265084

C₂

semidirect

5. #20265080

C₂

semidirect

6. #20265065

C₂

semidirect

7. #20265053

C₂

semidirect

8. #20265043

C₂

semidirect

9. C₂×#124×C₁₀₁

C₂

semidirect

63. C₄²×C₁₀₁

D₄

semidirect

113. C₂×D₁₀₁

#124

semidirect

129. C₁₀₁

#2850

semidirect

130. C₂×#124

D₁₀₁

semidirect

192. C₄²

C₂²⋊D₁₀₁

semidirect

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

subgroup	index
C₂×#15692231	2
C₂×#15692226	2
C₂×C₄²×D₁₀₁	2
#20265084	2
#20265080	2
#20265065	2
#20265053	2
#20265043	2
C₂×#124×C₁₀₁	2
#2850	101

subgroup

index

C₂×C₄²×D₁₀₁

C₂×#124×C₁₀₁

101

Subgroups — #27179428

Conjugacy classes of subgroups

Complements

Maximal subgroups