Subgroups — C₄⋊C₄×#6099 #15860913

Order 3328.

1242 conjugacy classes of subgroups.

The subgroup lattice has 374 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6099	C₂	1	2	yes	maximal
3	C₂×C₄×#6099	C₂	1	1	yes	maximal, characteristic
4	#13114711	C₂	1	4	yes	maximal, complemented
5	#13114705	C₂	1	2	yes	maximal, complemented
6	C₄⋊C₄×#1055	C₂	1	2	yes	maximal, complemented
7	#13114530	C₂	1	2	yes	maximal
8	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
9	C₂²×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
10	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
11	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
12	C₂²×#6099	C₂²	1	2	yes	—
13	C₂²×#6099	C₂²	1	1	yes	characteristic
14	C₂²×#6099	C₂²	1	1	yes	characteristic
15	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
16	C₄×C₁₃×C₄⋊C₄	C₄	1	2	yes	—
17	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
18	C₄×C₁₃×C₄⋊C₄	C₂²	1	1	yes	characteristic
19	C₄×C₁₃×C₄⋊C₄	C₂²	1	2	yes	—
20	C₂×C₁₃×#95	C₄	1	2	yes	—
21	#11718585	C₄	1	8	yes	complemented
22	C₂×C₄⋊#1055	C₂²	1	2	yes	—
23	C₂×C₄⋊#1055	C₂²	1	2	yes	—
24	C₄×#6099	—	2	8	no	—
25	C₄×#6099	C₄	1	8	yes	complemented
26	C₂×#88043	C₂²	1	4	yes	—
27	C₂×#88043	C₂²	1	2	yes	—
28	C₂×C₄×#1055	C₂²	1	4	yes	—
29	C₂×C₄×#1055	C₂²	1	2	yes	—
30	#11718116	C₂²	1	4	yes	—
31	#11718116	C₂²	1	4	yes	—
32	C₂³×C₄×C₁₃	C₂×C₄	1	4	yes	—
33	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂³×C₄×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
36	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
37	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
38	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	4	yes	—
39	C₂×C₁₃×C₄⋊C₄	C₂×C₄	1	2	yes	—
40	C₂×C₄²×C₁₃	—	2	4	no	—
41	C₂×C₄²×C₁₃	—	2	4	no	—
42	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
43	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
44	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
45	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
48	C₂×C₄²×C₁₃	C₂³	1	2	yes	—
49	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
50	C₂×C₄²×C₁₃	C₂³	1	1	yes	characteristic
51	C₂×#6099	—	2	4	no	—
52	C₂×#6099	—	2	2	no	—
53	C₂×#6099	—	2	2	no	—
54	C₂×#6099	—	2	4	no	—
55	C₂×#6099	C₂×C₄	1	4	yes	—
56	C₂×#6099	C₂×C₄	1	8	yes	—
57	C₂×#6099	C₂×C₄	1	4	yes	—
58	C₂×#6099	D₄	1	4	yes	—
59	C₂×#6099	Q₈	1	4	yes	—
60	C₂²×#1055	C₂³	1	4	yes	—
61	C₂²×#1055	C₂³	1	2	yes	—
62	C₂²×#1055	C₂³	1	2	yes	—
63	C₁₃×#95	C₂×C₄	1	2	yes	—
64	C₁₃×#95	C₂×C₄	1	4	yes	—
65	C₁₃×#95	C₂×C₄	1	2	yes	—
66	C₄⋊#1055	C₂×C₄	1	8	yes	complemented
67	C₄⋊#1055	C₂×C₄	1	8	yes	complemented
68	#88043	—	2	8	no	—
69	#88043	C₂×C₄	1	8	yes	complemented
70	C₄×#1055	—	2	8	no	—
71	C₄×#1055	C₂×C₄	1	8	yes	complemented
72	C₄⋊C₄×M₁₆	—	13	1	no	maximal, Sylow
73	C₂⁴×C₁₃	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	—	2	4	no	—
75	C₂²×C₄×C₁₃	—	2	8	no	—
76	C₂²×C₄×C₁₃	—	2	8	no	—
77	C₂²×C₄×C₁₃	—	4	2	no	—
78	C₂²×C₄×C₁₃	—	4	4	no	—
79	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
80	C₂²×C₄×C₁₃	C₄²	1	4	yes	—
81	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂²×C₄	1	2	yes	—
83	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
84	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₁₃	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
89	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
91	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
92	C₂²×C₄×C₁₃	#41	1	2	yes	—
93	C₂²×C₄×C₁₃	#41	1	2	yes	—
94	C₂²×C₄×C₁₃	C₂⁴	1	1	yes	characteristic
95	C₁₃×C₄⋊C₄	—	2	8	no	—
96	C₁₃×C₄⋊C₄	—	2	4	no	—
97	C₁₃×C₄⋊C₄	M₁₆	1	8	yes	complemented
98	C₄²×C₁₃	—	2	8	no	—
99	C₄²×C₁₃	—	2	2	no	—
100	C₄²×C₁₃	—	2	2	no	—
101	C₄²×C₁₃	—	2	2	no	—
102	C₄²×C₁₃	—	2	2	no	—
103	C₄²×C₁₃	C₄²	1	4	yes	—
104	C₄²×C₁₃	C₄²	1	4	yes	—
105	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
106	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
107	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
108	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
109	#6099	—	2	8	no	—
110	#6099	—	2	16	no	—
111	#6099	C₄⋊C₄	1	16	yes	direct product factor
112	C₂×#1055	—	2	4	no	—
113	C₂×#1055	—	2	2	no	—
114	C₂×#1055	—	2	2	no	—
115	C₂×#1055	—	2	4	no	—
116	C₂×#1055	C₂²×C₄	1	4	yes	—
117	C₂×#1055	C₂²×C₄	1	8	yes	—
118	C₂×#1055	C₂²×C₄	1	4	yes	—
119	C₂×#1055	C₂×D₄	1	4	yes	—
120	C₂×#1055	C₂×Q₈	1	4	yes	—
121	C₂×#423	—	13	1	no	—
122	C₂×C₄×M₁₆	—	13	1	no	—
123	C₂×C₄×M₁₆	—	13	2	no	—
124	C₂×C₄×C₄⋊C₄	D₁₃	1	1	yes	characteristic
125	#1771	—	13	4	no	—
126	#1770	—	13	2	no	—
127	C₈×C₄⋊C₄	—	13	2	no	—
128	#1728	—	13	2	no	—
129	C₂³×C₁₃	—	2	2	no	—
130	C₂³×C₁₃	—	2	2	no	—
131	C₂³×C₁₃	C₂×C₄²	1	2	yes	—
132	C₂³×C₁₃	C₄×D₄	1	2	yes	—
133	C₂³×C₁₃	C₄×Q₈	1	2	yes	—
134	C₂³×C₁₃	C₂³×C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₃	—	2	4	no	—
136	C₂×C₄×C₁₃	—	2	2	no	—
137	C₂×C₄×C₁₃	—	2	2	no	—
138	C₂×C₄×C₁₃	—	2	2	no	—
139	C₂×C₄×C₁₃	—	2	4	no	—
140	C₂×C₄×C₁₃	—	2	8	no	—
141	C₂×C₄×C₁₃	—	2	4	no	—
142	C₂×C₄×C₁₃	—	2	4	no	—
143	C₂×C₄×C₁₃	—	2	4	no	—
144	C₂×C₄×C₁₃	—	4	4	no	—
145	C₂×C₄×C₁₃	—	4	16	no	—
146	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
147	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
148	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
149	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
150	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
151	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	4	yes	—
152	C₂×C₄×C₁₃	#117	1	4	yes	—
153	C₂×C₄×C₁₃	C₄×D₄	1	4	yes	—
154	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
155	C₂×C₄×C₁₃	C₄×Q₈	1	4	yes	—
156	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
157	C₂×C₄×C₁₃	C₂×M₁₆	1	8	yes	—
158	C₂×C₄×C₁₃	C₂×M₁₆	1	4	yes	—
159	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
160	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
161	C₂×C₄×C₁₃	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₃	C₂²×Q₈	1	1	yes	characteristic
163	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₃	C₂×#41	1	1	yes	characteristic
165	#1055	—	2	4	no	—
166	#1055	—	2	8	no	—
167	#1055	C₂×C₄⋊C₄	1	8	yes	complemented
168	C₂²×M₁₆	—	13	1	no	—
169	C₂²×M₁₆	—	13	2	no	—
170	C₂²×M₁₆	—	13	1	no	—
171	C₂²×C₄⋊C₄	Dic₁₃	1	2	yes	—
172	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
173	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
174	#423	—	13	8	no	—
175	C₂×C₄⋊C₈	—	13	2	no	—
176	C₂×C₄⋊C₈	—	13	2	no	—
177	C₄×M₁₆	—	13	8	no	—
178	C₄×M₁₆	—	26	8	no	—
179	C₂×#97	—	13	2	no	—
180	C₂×#97	—	13	4	no	—
181	C₂×C₄×C₈	—	13	2	no	—
182	C₂×C₄×C₈	—	13	4	no	—
183	C₄×C₄⋊C₄	Dic₁₃	1	2	yes	—
184	C₄×C₄⋊C₄	Dic₁₃	1	2	yes	—
185	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
186	C₄×C₄⋊C₄	C₂×D₁₃	1	1	yes	characteristic
187	C₄×C₄⋊C₄	C₂×D₁₃	1	2	yes	—
188	C₂×#95	Dic₁₃	1	2	yes	—
189	#336	—	13	4	no	—
190	#336	—	13	4	no	—
191	C₂²×C₁₃	—	2	2	no	—
192	C₂²×C₁₃	—	2	2	no	—
193	C₂²×C₁₃	—	2	4	no	—
194	C₂²×C₁₃	—	2	4	no	—
195	C₂²×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
196	C₂²×C₁₃	C₂²×C₄²	1	1	yes	characteristic
197	C₂²×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
198	C₂²×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
199	C₂²×C₁₃	C₂²×M₁₆	1	2	yes	—
200	C₂²×C₁₃	#568	1	2	yes	—
201	C₄×C₁₃	—	2	2	no	—
202	C₄×C₁₃	—	2	2	no	—
203	C₄×C₁₃	—	2	2	no	—
204	C₄×C₁₃	—	2	8	no	—
205	C₄×C₁₃	—	4	4	no	—
206	C₄×C₁₃	C₄×C₄⋊C₄	1	4	yes	—
207	C₄×C₁₃	C₄×M₁₆	1	4	yes	complemented
208	C₄×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
209	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
210	C₄×C₁₃	C₂×C₄×D₄	1	1	yes	characteristic
211	C₄×C₁₃	C₂×C₄×Q₈	1	1	yes	characteristic
212	C₂³×C₄	C₂×Dic₁₃	1	4	yes	—
213	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
214	C₂³×C₄	C₂×Dic₁₃	1	1	yes	characteristic
215	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
216	C₂×M₁₆	—	13	4	no	—
217	C₂×M₁₆	—	13	4	no	—
218	C₂×M₁₆	—	13	4	no	—
219	C₂×M₁₆	—	13	4	no	—
220	C₂×M₁₆	—	13	8	no	—
221	C₂×M₁₆	—	26	4	no	—
222	C₂×M₁₆	—	26	2	no	—
223	C₂×M₁₆	—	26	2	no	—
224	C₂×M₁₆	—	26	4	no	—
225	C₂²×C₈	—	13	2	no	—
226	C₂²×C₈	—	13	2	no	—
227	C₂²×C₈	—	13	4	no	—
228	C₂×C₄⋊C₄	—	2	8	no	—
229	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
230	C₂×C₄⋊C₄	C₂×Dic₁₃	1	4	yes	—
231	C₂×C₄⋊C₄	C₂×Dic₁₃	1	2	yes	—
232	C₂×C₄²	—	2	4	no	—
233	C₂×C₄²	—	2	4	no	—
234	C₂×C₄²	C₄×D₁₃	1	4	yes	—
235	C₂×C₄²	C₄×D₁₃	1	4	yes	—
236	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
237	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
238	C₂×C₄²	C₂×Dic₁₃	1	1	yes	characteristic
239	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
240	C₂×C₄²	C₂²×D₁₃	1	2	yes	—
241	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
242	C₂×C₄²	C₂²×D₁₃	1	1	yes	characteristic
243	C₄⋊C₈	—	13	8	no	—
244	C₄⋊C₈	—	13	8	no	—
245	#97	—	13	8	no	—
246	#97	—	26	8	no	—
247	C₄×C₈	—	13	8	no	—
248	C₄×C₈	—	26	8	no	—
249	#95	C₂×Dic₁₃	1	2	yes	—
250	#95	C₂×Dic₁₃	1	4	yes	—
251	#95	C₂×Dic₁₃	1	2	yes	—
252	C₂×C₁₃	—	2	4	no	—
253	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
254	C₂×C₁₃	C₂×C₄×M₁₆	1	1	yes	characteristic
255	C₂×C₁₃	#2873	1	1	yes	characteristic
256	C₂×C₁₃	D₄×M₁₆	1	2	yes	—
257	C₂×C₁₃	Q₈×M₁₆	1	2	yes	—
258	C₂⁴	C₂²×Dic₁₃	1	1	yes	characteristic
259	C₂²×C₄	—	2	4	no	—
260	C₂²×C₄	—	2	8	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	4	2	no	—
263	C₂²×C₄	—	4	4	no	—
264	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
265	C₂²×C₄	C₄×Dic₁₃	1	4	yes	—
266	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
267	C₂²×C₄	C₂×C₄×D₁₃	1	2	yes	—
268	C₂²×C₄	D₄×D₁₃	1	2	yes	—
269	C₂²×C₄	#6129	1	2	yes	—
270	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
271	C₂²×C₄	#6131	1	2	yes	—
272	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
273	C₂²×C₄	C₂²×Dic₁₃	1	4	yes	—
274	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
276	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
277	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
278	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
279	C₂²×C₄	C₂³×D₁₃	1	1	yes	characteristic
280	M₁₆	—	13	16	no	—
281	M₁₆	—	26	8	no	—
282	M₁₆	—	26	16	no	—
283	C₂×C₈	—	13	4	no	—
284	C₂×C₈	—	13	4	no	—
285	C₂×C₈	—	13	4	no	—
286	C₂×C₈	—	13	4	no	—
287	C₂×C₈	—	13	8	no	—
288	C₂×C₈	—	26	4	no	—
289	C₂×C₈	—	26	2	no	—
290	C₂×C₈	—	26	2	no	—
291	C₂×C₈	—	26	4	no	—
292	C₄⋊C₄	—	2	8	no	—
293	C₄⋊C₄	—	2	4	no	—
294	C₄⋊C₄	#6099	1	8	yes	direct product factor
295	C₄²	—	2	8	no	—
296	C₄²	—	2	2	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	C₄×Dic₁₃	1	4	yes	—
301	C₄²	C₄×Dic₁₃	1	4	yes	—
302	C₄²	C₂×C₄×D₁₃	1	2	yes	—
303	C₄²	C₂×C₄×D₁₃	1	2	yes	—
304	C₄²	C₂×C₄×D₁₃	1	2	yes	—
305	C₄²	C₂×C₄×D₁₃	1	2	yes	—
306	C₁₃	C₄⋊C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×C₄×Dic₁₃	1	2	yes	—
310	C₂³	D₄×Dic₁₃	1	2	yes	—
311	C₂³	Q₈×Dic₁₃	1	2	yes	—
312	C₂³	C₂³×Dic₁₃	1	1	yes	characteristic
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	4	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	2	no	—
317	C₂×C₄	—	2	4	no	—
318	C₂×C₄	—	2	8	no	—
319	C₂×C₄	—	2	4	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	4	4	no	—
323	C₂×C₄	—	4	16	no	—
324	C₂×C₄	#88141	1	4	yes	—
325	C₂×C₄	C₄⋊C₄×D₁₃	1	4	yes	—
326	C₂×C₄	#88146	1	4	yes	—
327	C₂×C₄	#88147	1	4	yes	—
328	C₂×C₄	C₂×#6099	1	8	yes	—
329	C₂×C₄	C₂×#6099	1	4	yes	—
330	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
331	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
332	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
333	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
334	C₂×C₄	C₂×C₄×Dic₁₃	1	2	yes	—
335	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
336	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
337	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₄×D₁₃	1	1	yes	characteristic
339	C₂×C₄	C₂×D₄×D₁₃	1	1	yes	characteristic
340	C₂×C₄	C₂×#6129	1	1	yes	characteristic
341	C₂×C₄	C₂×Q₈×D₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂×#6131	1	1	yes	characteristic
343	C₈	—	13	8	no	—
344	C₈	—	26	4	no	—
345	C₈	—	26	8	no	—
346	C₂²	—	2	2	no	—
347	C₂²	—	2	2	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	C₄⋊C₄×Dic₁₃	1	4	yes	—
351	C₂²	C₂²×#6099	1	2	yes	—
352	C₂²	C₂²×C₄×Dic₁₃	1	1	yes	characteristic
353	C₂²	C₂×D₄×Dic₁₃	1	1	yes	characteristic
354	C₂²	C₂×Q₈×Dic₁₃	1	1	yes	characteristic
355	C₂²	#11719524	1	2	yes	—
356	C₄	—	2	2	no	—
357	C₄	—	2	2	no	—
358	C₄	—	2	2	no	—
359	C₄	—	2	8	no	—
360	C₄	—	4	4	no	—
361	C₄	C₄×#6099	1	4	yes	complemented
362	C₄	C₄⋊C₄×Dic₁₃	1	4	yes	—
363	C₄	C₂×#88141	1	1	yes	characteristic
364	C₄	C₂×C₄⋊C₄×D₁₃	1	1	yes	characteristic
365	C₄	C₂×#88146	1	1	yes	characteristic
366	C₄	C₂×#88147	1	1	yes	characteristic
367	C₂	—	2	4	no	—
368	C₂	C₂×C₄⋊C₄×Dic₁₃	1	1	yes	characteristic
369	C₂	C₂×C₄×#6099	1	1	yes	characteristic
370	C₂	#13123255	1	1	yes	characteristic
371	C₂	D₄×#6099	1	2	yes	—
372	C₂	Q₈×#6099	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₁₃
commutator	C₂²×C₁₃	C₂²×C₄²
Fitting	C₂×C₄×C₁₃×C₄⋊C₄	C₂
socle	C₂³×C₁₃	C₂³×C₄
prime radical	C₂⁴×C₁₃	C₂²×C₄
cosocle	C₂²×C₄×C₁₃	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₁₃
hypocenter	C₁₃	C₄⋊C₄×M₁₆
LCS	G ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
4. #13114711	C₂	semidirect
5. #13114705	C₂	semidirect
6. C₄⋊C₄×#1055	C₂	semidirect
21. #11718585	C₄	semidirect
25. C₄×#6099	C₄	semidirect
66. C₄⋊#1055	C₂×C₄	semidirect
67. C₄⋊#1055	C₂×C₄	semidirect
69. #88043	C₂×C₄	semidirect
71. C₄×#1055	C₂×C₄	semidirect
97. C₁₃×C₄⋊C₄	M₁₆	semidirect
111. #6099	C₄⋊C₄	direct (N × H)
167. #1055	C₂×C₄⋊C₄	semidirect
207. C₄×C₁₃	C₄×M₁₆	semidirect
294. C₄⋊C₄	#6099	direct (N × H)
306. C₁₃	C₄⋊C₄×M₁₆	semidirect
361. C₄	C₄×#6099	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718585	2
C₂×C₄×#6099	2
#13114711	2
#13114705	2
C₄⋊C₄×#1055	2
#13114530	2
C₂×C₄×C₁₃×C₄⋊C₄	2
C₄⋊C₄×M₁₆	13

Subgroups — C4⋊C4×#6099 #15860913

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×#6099 #15860913