Subgroups — C₄⋊C₄×#11761612 #30853825

Order 17152.

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×#16863420	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#11761612	C₂	1	2	yes	maximal
3	C₂×C₄×#11761612	C₂	1	1	yes	maximal, characteristic
4	#22560084	C₂	1	4	yes	maximal, complemented
5	#22560078	C₂	1	2	yes	maximal, complemented
6	C₄⋊C₄×C₆₇⋊C₈	C₂	1	2	yes	maximal, complemented
7	#22559903	C₂	1	2	yes	maximal
8	C₂×C₄×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂²×#11761612	C₂²	1	2	yes	—
10	C₂²×#11761612	C₂²	1	1	yes	characteristic
11	C₂²×#11761612	C₂²	1	1	yes	characteristic
12	#16863420	C₄	1	8	yes	complemented
13	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
14	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
15	C₄×#11761612	—	2	8	no	—
16	C₄×#11761612	C₄	1	8	yes	complemented
17	C₂×#14523954	C₂²	1	4	yes	—
18	C₂×#14523954	C₂²	1	2	yes	—
19	C₂×C₄×C₆₇⋊C₈	C₂²	1	4	yes	—
20	C₂×C₄×C₆₇⋊C₈	C₂²	1	2	yes	—
21	#16863151	C₂²	1	4	yes	—
22	#16863151	C₂²	1	4	yes	—
23	C₂²×C₄⋊C₄×C₆₇	C₄	1	2	yes	—
24	C₂²×C₄²×C₆₇	C₂²	1	2	yes	—
25	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
26	C₄×C₄⋊C₄×C₆₇	C₄	1	2	yes	—
27	C₄×C₄⋊C₄×C₆₇	C₄	1	2	yes	—
28	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
29	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
30	C₄×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
31	C₂×#95×C₆₇	C₄	1	2	yes	—
32	C₂×#11761612	—	2	4	no	—
33	C₂×#11761612	—	2	2	no	—
34	C₂×#11761612	—	2	2	no	—
35	C₂×#11761612	—	2	4	no	—
36	C₂×#11761612	C₂×C₄	1	4	yes	—
37	C₂×#11761612	C₂×C₄	1	8	yes	—
38	C₂×#11761612	C₂×C₄	1	4	yes	—
39	C₂×#11761612	D₄	1	4	yes	—
40	C₂×#11761612	Q₈	1	4	yes	—
41	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
42	C₂²×C₆₇⋊C₈	C₂³	1	4	yes	—
43	C₂²×C₆₇⋊C₈	C₂³	1	2	yes	—
44	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	8	yes	complemented
45	C₄⋊(C₆₇⋊C₈)	C₂×C₄	1	8	yes	complemented
46	#14523954	—	2	8	no	—
47	#14523954	C₂×C₄	1	8	yes	complemented
48	C₄×C₆₇⋊C₈	—	2	8	no	—
49	C₄×C₆₇⋊C₈	C₂×C₄	1	8	yes	complemented
50	C₂³×C₄×C₆₇	C₂×C₄	1	4	yes	—
51	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
54	C₂×C₄⋊C₄×C₆₇	—	2	8	no	—
55	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
56	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
57	C₂×C₄⋊C₄×C₆₇	C₂×C₄	1	2	yes	—
58	C₂×C₄²×C₆₇	—	2	4	no	—
59	C₂×C₄²×C₆₇	—	2	4	no	—
60	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
61	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
62	C₂×C₄²×C₆₇	C₂×C₄	1	4	yes	—
63	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
64	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
65	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
66	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
67	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
68	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
69	#95×C₆₇	C₂×C₄	1	2	yes	—
70	#95×C₆₇	C₂×C₄	1	4	yes	—
71	#95×C₆₇	C₂×C₄	1	2	yes	—
72	#11761612	—	2	8	no	—
73	#11761612	—	2	16	no	—
74	#11761612	C₄⋊C₄	1	16	yes	direct product factor
75	C₂×C₆₇⋊C₈	—	2	4	no	—
76	C₂×C₆₇⋊C₈	—	2	2	no	—
77	C₂×C₆₇⋊C₈	—	2	2	no	—
78	C₂×C₆₇⋊C₈	—	2	4	no	—
79	C₂×C₆₇⋊C₈	C₂²×C₄	1	4	yes	—
80	C₂×C₆₇⋊C₈	C₂²×C₄	1	8	yes	—
81	C₂×C₆₇⋊C₈	C₂²×C₄	1	4	yes	—
82	C₂×C₆₇⋊C₈	C₂×D₄	1	4	yes	—
83	C₂×C₆₇⋊C₈	C₂×Q₈	1	4	yes	—
84	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	—	2	4	no	—
86	C₂²×C₄×C₆₇	—	2	8	no	—
87	C₂²×C₄×C₆₇	—	2	8	no	—
88	C₂²×C₄×C₆₇	—	4	2	no	—
89	C₂²×C₄×C₆₇	—	4	4	no	—
90	C₂²×C₄×C₆₇	C₄²	1	4	yes	—
91	C₂²×C₄×C₆₇	C₄²	1	4	yes	—
92	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
93	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
94	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
95	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
96	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
97	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	C₂²×C₄	1	4	yes	—
99	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
100	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
101	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
103	C₂²×C₄×C₆₇	#41	1	2	yes	—
104	C₂²×C₄×C₆₇	#41	1	2	yes	—
105	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
106	C₄⋊C₄×C₆₇	—	2	8	no	—
107	C₄⋊C₄×C₆₇	—	2	4	no	—
108	C₄⋊C₄×C₆₇	M₁₆	1	8	yes	complemented
109	C₄²×C₆₇	—	2	8	no	—
110	C₄²×C₆₇	—	2	2	no	—
111	C₄²×C₆₇	—	2	2	no	—
112	C₄²×C₆₇	—	2	2	no	—
113	C₄²×C₆₇	—	2	2	no	—
114	C₄²×C₆₇	C₄²	1	4	yes	—
115	C₄²×C₆₇	C₄²	1	4	yes	—
116	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
117	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
118	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
119	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
120	C₂³×C₆₇	—	2	2	no	—
121	C₂³×C₆₇	—	2	2	no	—
122	C₂³×C₆₇	C₂×C₄²	1	2	yes	—
123	C₂³×C₆₇	C₄×D₄	1	2	yes	—
124	C₂³×C₆₇	C₄×Q₈	1	2	yes	—
125	C₂³×C₆₇	C₂³×C₄	1	1	yes	characteristic
126	C₂×C₄×C₆₇	—	2	4	no	—
127	C₂×C₄×C₆₇	—	2	2	no	—
128	C₂×C₄×C₆₇	—	2	2	no	—
129	C₂×C₄×C₆₇	—	2	2	no	—
130	C₂×C₄×C₆₇	—	2	4	no	—
131	C₂×C₄×C₆₇	—	2	8	no	—
132	C₂×C₄×C₆₇	—	2	4	no	—
133	C₂×C₄×C₆₇	—	2	4	no	—
134	C₂×C₄×C₆₇	—	2	4	no	—
135	C₂×C₄×C₆₇	—	4	4	no	—
136	C₂×C₄×C₆₇	—	4	16	no	—
137	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
138	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
139	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
140	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
141	C₂×C₄×C₆₇	C₂×C₄²	1	2	yes	—
142	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
143	C₂×C₄×C₆₇	#117	1	4	yes	—
144	C₂×C₄×C₆₇	C₄×D₄	1	4	yes	—
145	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₆₇	C₄×Q₈	1	4	yes	—
147	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
148	C₂×C₄×C₆₇	C₂×M₁₆	1	8	yes	—
149	C₂×C₄×C₆₇	C₂×M₁₆	1	4	yes	—
150	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
156	C₆₇⋊C₈	—	2	4	no	—
157	C₆₇⋊C₈	—	2	8	no	—
158	C₆₇⋊C₈	C₂×C₄⋊C₄	1	8	yes	complemented
159	C₂²×C₆₇	—	2	2	no	—
160	C₂²×C₆₇	—	2	2	no	—
161	C₂²×C₆₇	—	2	4	no	—
162	C₂²×C₆₇	—	2	4	no	—
163	C₂²×C₆₇	C₄×C₄⋊C₄	1	4	yes	—
164	C₂²×C₆₇	C₂²×C₄²	1	1	yes	characteristic
165	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
167	C₂²×C₆₇	C₂²×M₁₆	1	2	yes	—
168	C₂²×C₆₇	#568	1	2	yes	—
169	C₄×C₆₇	—	2	2	no	—
170	C₄×C₆₇	—	2	2	no	—
171	C₄×C₆₇	—	2	2	no	—
172	C₄×C₆₇	—	2	8	no	—
173	C₄×C₆₇	—	4	4	no	—
174	C₄×C₆₇	C₄×C₄⋊C₄	1	4	yes	—
175	C₄×C₆₇	C₄×M₁₆	1	4	yes	complemented
176	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
177	C₄×C₆₇	C₂×#117	1	1	yes	characteristic
178	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
179	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
180	C₄⋊C₄×M₁₆	—	67	1	no	maximal, Sylow
181	C₂×C₆₇	—	2	4	no	—
182	C₂×C₆₇	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
183	C₂×C₆₇	C₂×C₄×M₁₆	1	1	yes	characteristic
184	C₂×C₆₇	#2873	1	1	yes	characteristic
185	C₂×C₆₇	D₄×M₁₆	1	2	yes	—
186	C₂×C₆₇	Q₈×M₁₆	1	2	yes	—
187	C₂×#423	—	67	1	no	—
188	C₂×C₄×M₁₆	—	67	1	no	—
189	C₂×C₄×M₁₆	—	67	2	no	—
190	C₂×C₄×C₄⋊C₄	D₆₇	1	1	yes	characteristic
191	#1771	—	67	4	no	—
192	#1770	—	67	2	no	—
193	C₈×C₄⋊C₄	—	67	2	no	—
194	#1728	—	67	2	no	—
195	C₆₇	C₄⋊C₄×M₁₆	1	1	yes	characteristic, complemented, Sylow
196	C₂²×M₁₆	—	67	1	no	—
197	C₂²×M₁₆	—	67	2	no	—
198	C₂²×M₁₆	—	67	1	no	—
199	C₂²×C₄⋊C₄	Dic₆₇	1	2	yes	—
200	C₂²×C₄²	C₂×D₆₇	1	2	yes	—
201	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
202	#423	—	67	8	no	—
203	C₂×C₄⋊C₈	—	67	2	no	—
204	C₂×C₄⋊C₈	—	67	2	no	—
205	C₄×M₁₆	—	67	8	no	—
206	C₄×M₁₆	—	134	8	no	—
207	C₂×#97	—	67	2	no	—
208	C₂×#97	—	67	4	no	—
209	C₂×C₄×C₈	—	67	2	no	—
210	C₂×C₄×C₈	—	67	4	no	—
211	C₄×C₄⋊C₄	Dic₆₇	1	2	yes	—
212	C₄×C₄⋊C₄	Dic₆₇	1	2	yes	—
213	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
214	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
215	C₄×C₄⋊C₄	C₂×D₆₇	1	2	yes	—
216	C₂×#95	Dic₆₇	1	2	yes	—
217	#336	—	67	4	no	—
218	#336	—	67	4	no	—
219	C₂³×C₄	C₂×Dic₆₇	1	4	yes	—
220	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
221	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
222	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
223	C₂×M₁₆	—	67	4	no	—
224	C₂×M₁₆	—	67	4	no	—
225	C₂×M₁₆	—	67	4	no	—
226	C₂×M₁₆	—	67	4	no	—
227	C₂×M₁₆	—	67	8	no	—
228	C₂×M₁₆	—	134	4	no	—
229	C₂×M₁₆	—	134	2	no	—
230	C₂×M₁₆	—	134	2	no	—
231	C₂×M₁₆	—	134	4	no	—
232	C₂²×C₈	—	67	2	no	—
233	C₂²×C₈	—	67	2	no	—
234	C₂²×C₈	—	67	4	no	—
235	C₂×C₄⋊C₄	—	2	8	no	—
236	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
237	C₂×C₄⋊C₄	C₂×Dic₆₇	1	4	yes	—
238	C₂×C₄⋊C₄	C₂×Dic₆₇	1	2	yes	—
239	C₂×C₄²	—	2	4	no	—
240	C₂×C₄²	—	2	4	no	—
241	C₂×C₄²	C₄×D₆₇	1	4	yes	—
242	C₂×C₄²	C₄×D₆₇	1	4	yes	—
243	C₂×C₄²	C₂×Dic₆₇	1	4	yes	—
244	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
245	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
246	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
247	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
248	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
249	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
250	C₄⋊C₈	—	67	8	no	—
251	C₄⋊C₈	—	67	8	no	—
252	#97	—	67	8	no	—
253	#97	—	134	8	no	—
254	C₄×C₈	—	67	8	no	—
255	C₄×C₈	—	134	8	no	—
256	#95	C₂×Dic₆₇	1	2	yes	—
257	#95	C₂×Dic₆₇	1	4	yes	—
258	#95	C₂×Dic₆₇	1	2	yes	—
259	C₂⁴	C₂²×Dic₆₇	1	1	yes	characteristic
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	—	4	2	no	—
264	C₂²×C₄	—	4	4	no	—
265	C₂²×C₄	C₄×Dic₆₇	1	4	yes	—
266	C₂²×C₄	C₄×Dic₆₇	1	4	yes	—
267	C₂²×C₄	C₂×C₄×D₆₇	1	2	yes	—
268	C₂²×C₄	C₂×C₄×D₆₇	1	2	yes	—
269	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
270	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
271	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
272	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
273	C₂²×C₄	C₂²×Dic₆₇	1	4	yes	—
274	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂²×Dic₆₇	1	1	yes	characteristic
276	C₂²×C₄	D₄×D₆₇	1	2	yes	—
277	C₂²×C₄	Q₈×D₆₇	1	2	yes	—
278	C₂²×C₄	#11761627	1	2	yes	—
279	C₂²×C₄	#11761629	1	2	yes	—
280	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
281	M₁₆	—	67	16	no	—
282	M₁₆	—	134	8	no	—
283	M₁₆	—	134	16	no	—
284	C₂×C₈	—	67	4	no	—
285	C₂×C₈	—	67	4	no	—
286	C₂×C₈	—	67	4	no	—
287	C₂×C₈	—	67	4	no	—
288	C₂×C₈	—	67	8	no	—
289	C₂×C₈	—	134	4	no	—
290	C₂×C₈	—	134	2	no	—
291	C₂×C₈	—	134	2	no	—
292	C₂×C₈	—	134	4	no	—
293	C₄⋊C₄	—	2	8	no	—
294	C₄⋊C₄	—	2	4	no	—
295	C₄⋊C₄	#11761612	1	8	yes	direct product factor
296	C₄²	—	2	8	no	—
297	C₄²	—	2	2	no	—
298	C₄²	—	2	2	no	—
299	C₄²	—	2	2	no	—
300	C₄²	—	2	2	no	—
301	C₄²	C₄×Dic₆₇	1	4	yes	—
302	C₄²	C₄×Dic₆₇	1	4	yes	—
303	C₄²	C₂×C₄×D₆₇	1	2	yes	—
304	C₄²	C₂×C₄×D₆₇	1	2	yes	—
305	C₄²	C₂×C₄×D₆₇	1	2	yes	—
306	C₄²	C₂×C₄×D₆₇	1	2	yes	—
307	C₂³	—	2	2	no	—
308	C₂³	—	2	2	no	—
309	C₂³	C₂×C₄×Dic₆₇	1	2	yes	—
310	C₂³	D₄×Dic₆₇	1	2	yes	—
311	C₂³	Q₈×Dic₆₇	1	2	yes	—
312	C₂³	C₂³×Dic₆₇	1	1	yes	characteristic
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	2	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	C₂×C₄×Dic₆₇	1	2	yes	—
325	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
326	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
327	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
328	C₂×C₄	C₂×C₄×Dic₆₇	1	2	yes	—
329	C₂×C₄	C₄⋊C₄×D₆₇	1	4	yes	—
330	C₂×C₄	#14524001	1	4	yes	—
331	C₂×C₄	#14524005	1	4	yes	—
332	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
333	C₂×C₄	#14524008	1	4	yes	—
334	C₂×C₄	Q₈×Dic₆₇	1	2	yes	—
335	C₂×C₄	C₂×#11761612	1	8	yes	—
336	C₂×C₄	C₂×#11761612	1	4	yes	—
337	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
338	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
339	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
340	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
341	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
342	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
343	C₈	—	67	8	no	—
344	C₈	—	134	4	no	—
345	C₈	—	134	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×Dic₆₇	1	4	yes	—
351	C₂²	C₂²×C₄×Dic₆₇	1	1	yes	characteristic
352	C₂²	C₂×D₄×Dic₆₇	1	1	yes	characteristic
353	C₂²	C₂×Q₈×Dic₆₇	1	1	yes	characteristic
354	C₂²	C₂²×#11761612	1	2	yes	—
355	C₂²	#16864163	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⋊C₄×Dic₆₇	1	4	yes	—
362	C₄	C₄×#11761612	1	4	yes	complemented
363	C₄	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
364	C₄	C₂×#14524001	1	1	yes	characteristic
365	C₄	C₂×#14524005	1	1	yes	characteristic
366	C₄	C₂×#14524008	1	1	yes	characteristic
367	C₂	—	2	4	no	—
368	C₂	C₂×C₄⋊C₄×Dic₆₇	1	1	yes	characteristic
369	C₂	C₂×C₄×#11761612	1	1	yes	characteristic
370	C₂	#22568628	1	1	yes	characteristic
371	C₂	D₄×#11761612	1	2	yes	—
372	C₂	Q₈×#11761612	1	2	yes	—

	subgroup	G/H
center, Frattini	C₂²×C₄	C₂³×D₆₇
commutator	C₂²×C₆₇	C₂²×C₄²
Fitting	C₂×C₄×C₄⋊C₄×C₆₇	C₂
socle	C₂³×C₆₇	C₂³×C₄
prime radical	C₂⁴×C₆₇	C₂²×C₄
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂×C₄×C₄⋊C₄	D₆₇
hypocenter	C₆₇	C₄⋊C₄×M₁₆
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
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. #22560084	C₂	semidirect
5. #22560078	C₂	semidirect
6. C₄⋊C₄×C₆₇⋊C₈	C₂	semidirect
12. #16863420	C₄	semidirect
16. C₄×#11761612	C₄	semidirect
44. C₄⋊(C₆₇⋊C₈)	C₂×C₄	semidirect
45. C₄⋊(C₆₇⋊C₈)	C₂×C₄	semidirect
47. #14523954	C₂×C₄	semidirect
49. C₄×C₆₇⋊C₈	C₂×C₄	semidirect
74. #11761612	C₄⋊C₄	direct (N × H)
108. C₄⋊C₄×C₆₇	M₁₆	semidirect
158. C₆₇⋊C₈	C₂×C₄⋊C₄	semidirect
175. C₄×C₆₇	C₄×M₁₆	semidirect
195. C₆₇	C₄⋊C₄×M₁₆	semidirect
295. C₄⋊C₄	#11761612	direct (N × H)
362. C₄	C₄×#11761612	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863420	2
C₂×C₄×#11761612	2
#22560084	2
#22560078	2
C₄⋊C₄×C₆₇⋊C₈	2
#22559903	2
C₂×C₄×C₄⋊C₄×C₆₇	2
C₄⋊C₄×M₁₆	67

Subgroups — C4⋊C4×#11761612 #30853825

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄⋊C₄×#11761612 #30853825