Subgroups — #30745508

Order 17152.

666 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863453	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863453	C₂	1	1	yes	maximal, characteristic
3	#22558057	C₂	1	4	yes	maximal
4	C₄×#117×C₆₇	C₂	1	1	yes	maximal, characteristic
5	#16863453	—	2	1	no	—
6	#16863453	—	2	1	no	—
7	#16863453	—	2	1	no	—
8	#16863453	—	2	1	no	—
9	#16863453	—	2	1	no	—
10	#16863453	—	2	1	no	—
11	#16863453	C₄	1	2	yes	complemented
12	#16863453	C₄	1	2	yes	complemented
13	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
14	C₂×C₄⋊(C₆₇⋊C₈)	C₄	1	2	yes	complemented
15	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
16	C₂×C₂²⋊(C₆₇⋊C₈)	C₂²	1	2	yes	—
17	C₂×#14523954	—	2	1	no	—
18	C₂×#14523954	C₄	1	2	yes	complemented
19	C₂×#117×C₆₇	C₄	1	2	yes	—
20	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
21	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
22	C₄×C₄⋊C₄×C₆₇	—	2	1	no	—
23	C₄×C₂²⋊C₄×C₆₇	C₄	1	2	yes	—
24	C₄×C₂²⋊C₄×C₆₇	C₂²	1	2	yes	—
25	#376×C₆₇	—	2	1	no	—
26	C₄³×C₆₇	—	2	1	no	—
27	C₂²×C₆₇⋊C₈	—	2	2	no	—
28	C₂²×C₆₇⋊C₈	C₂×C₄	1	4	yes	—
29	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
30	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
31	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
32	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
33	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
34	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
35	C₂²⋊(C₆₇⋊C₈)	—	2	2	no	—
36	C₂²⋊(C₆₇⋊C₈)	C₂×C₄	1	4	yes	—
37	#14523954	—	2	2	no	—
38	#14523954	—	2	2	no	—
39	#14523954	—	2	2	no	—
40	#14523954	—	2	2	no	—
41	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
42	C₂³×C₄×C₆₇	C₂×C₄	1	1	yes	characteristic
43	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
44	#117×C₆₇	—	2	8	no	—
45	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
46	C₂×C₂²⋊C₄×C₆₇	C₂×C₄	1	4	yes	—
47	C₂×C₄²×C₆₇	—	2	2	no	—
48	C₂×C₄²×C₆₇	—	2	2	no	—
49	C₂×C₄²×C₆₇	—	2	2	no	—
50	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
51	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
52	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
53	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
54	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
55	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
57	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
58	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
59	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
61	C₂×C₄²×C₆₇	Q₈	1	1	yes	characteristic
62	#95×C₆₇	—	2	2	no	—
63	#95×C₆₇	—	2	2	no	—
64	C₂×C₆₇⋊C₈	—	2	4	no	—
65	C₂×C₆₇⋊C₈	—	2	4	no	—
66	C₂×C₆₇⋊C₈	—	4	4	no	—
67	C₂×C₆₇⋊C₈	—	4	4	no	—
68	C₂⁴×C₆₇	C₂²×C₄	1	1	yes	characteristic
69	C₂²×C₄×C₆₇	—	2	4	no	—
70	C₂²×C₄×C₆₇	—	2	4	no	—
71	C₂²×C₄×C₆₇	—	4	2	no	—
72	C₂²×C₄×C₆₇	—	4	2	no	—
73	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
74	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
75	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
76	C₂²×C₄×C₆₇	C₄²	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
79	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
80	C₂²×C₄×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
87	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
91	C₄⋊C₄×C₆₇	—	2	8	no	—
92	C₂²⋊C₄×C₆₇	—	2	4	no	—
93	C₂²⋊C₄×C₆₇	M₁₆	1	8	yes	—
94	C₄²×C₆₇	—	2	8	no	—
95	C₄²×C₆₇	—	4	4	no	—
96	C₄²×C₆₇	—	4	4	no	—
97	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
98	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
99	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
100	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
101	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
102	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
103	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
104	C₄²×C₆₇	C₂²⋊C₄	1	1	yes	characteristic
105	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
106	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
107	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
108	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
109	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
111	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
112	C₄²×C₆₇	C₄⋊C₄	1	1	yes	characteristic
113	C₂³×C₆₇	—	4	1	no	—
114	C₂³×C₆₇	—	4	1	no	—
115	C₂³×C₆₇	C₂×C₄²	1	1	yes	characteristic
116	C₂³×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂³×C₆₇	C₂×M₁₆	1	4	yes	—
119	C₂×C₄×C₆₇	—	2	2	no	—
120	C₂×C₄×C₆₇	—	2	2	no	—
121	C₂×C₄×C₆₇	—	2	2	no	—
122	C₂×C₄×C₆₇	—	2	2	no	—
123	C₂×C₄×C₆₇	—	2	2	no	—
124	C₂×C₄×C₆₇	—	2	2	no	—
125	C₂×C₄×C₆₇	—	2	2	no	—
126	C₂×C₄×C₆₇	—	2	2	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	2	no	—
131	C₂×C₄×C₆₇	—	2	8	no	—
132	C₂×C₄×C₆₇	—	4	1	no	—
133	C₂×C₄×C₆₇	—	4	1	no	—
134	C₂×C₄×C₆₇	—	4	1	no	—
135	C₂×C₄×C₆₇	—	4	1	no	—
136	C₂×C₄×C₆₇	—	4	1	no	—
137	C₂×C₄×C₆₇	—	4	1	no	—
138	C₂×C₄×C₆₇	—	4	4	no	—
139	C₂×C₄×C₆₇	—	4	4	no	—
140	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
141	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
142	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
143	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
144	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
146	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
147	C₂×C₄×C₆₇	#95	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
152	C₆₇⋊C₈	—	4	4	no	—
153	C₆₇⋊C₈	—	4	4	no	—
154	C₂²×C₆₇	—	2	1	no	—
155	C₂²×C₆₇	—	2	1	no	—
156	C₂²×C₆₇	—	2	1	no	—
157	C₂²×C₆₇	—	2	1	no	—
158	C₂²×C₆₇	—	2	1	no	—
159	C₂²×C₆₇	—	2	1	no	—
160	C₂²×C₆₇	—	4	4	no	—
161	C₂²×C₆₇	C₂×#95	1	1	yes	characteristic
162	C₂²×C₆₇	C₄×M₁₆	1	2	yes	—
163	C₂²×C₆₇	#407	1	2	yes	—
164	C₂²×C₆₇	#423	1	2	yes	—
165	C₄×C₆₇	—	2	1	no	—
166	C₄×C₆₇	—	2	1	no	—
167	C₄×C₆₇	—	2	1	no	—
168	C₄×C₆₇	—	2	1	no	—
169	C₄×C₆₇	—	2	1	no	—
170	C₄×C₆₇	—	2	1	no	—
171	C₄×C₆₇	—	2	1	no	—
172	C₄×C₆₇	—	2	1	no	—
173	C₄×C₆₇	—	2	1	no	—
174	C₄×C₆₇	—	2	1	no	—
175	C₄×C₆₇	—	4	8	no	—
176	C₄×C₆₇	#344	1	2	yes	—
177	C₄×C₆₇	#410	1	2	yes	—
178	#7930	—	67	1	no	maximal, Sylow
179	C₂×C₆₇	—	2	2	no	—
180	C₂×C₆₇	—	2	2	no	—
181	C₂×C₆₇	—	2	2	no	—
182	C₂×C₆₇	#1728	1	1	yes	characteristic
183	C₂×C₆₇	#1740	1	1	yes	characteristic
184	C₂×C₆₇	C₂×#344	1	1	yes	characteristic
185	C₂×#432	—	67	1	no	—
186	C₂×#432	—	67	1	no	—
187	C₄×#117	D₆₇	1	1	yes	characteristic
188	#1282	—	67	4	no	—
189	C₆₇	#7930	1	1	yes	characteristic, complemented, Sylow
190	C₂×#117	Dic₆₇	1	2	yes	—
191	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
192	#432	—	67	2	no	—
193	#432	—	67	2	no	—
194	#432	—	134	1	no	—
195	#432	—	134	1	no	—
196	#432	—	134	1	no	—
197	#432	—	134	1	no	—
198	#432	—	134	1	no	—
199	#432	—	134	1	no	—
200	C₂×C₄⋊C₈	—	67	2	no	—
201	C₂×C₄⋊C₈	—	134	1	no	—
202	C₂×C₂²⋊C₈	—	67	2	no	—
203	C₂×C₂²⋊C₈	—	67	2	no	—
204	C₂×#97	—	67	2	no	—
205	C₂×#97	—	134	1	no	—
206	C₄×C₄⋊C₄	—	2	1	no	—
207	C₄×C₄⋊C₄	—	2	1	no	—
208	C₄×C₂²⋊C₄	Dic₆₇	1	2	yes	—
209	C₄×C₂²⋊C₄	C₂×D₆₇	1	2	yes	—
210	#376	—	2	1	no	—
211	C₄³	—	2	1	no	—
212	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
213	C₂³×C₄	C₂×Dic₆₇	1	1	yes	characteristic
214	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
215	C₂²×C₈	—	67	4	no	—
216	C₂²×C₈	—	134	2	no	—
217	#117	—	2	8	no	—
218	C₂×C₄⋊C₄	—	2	2	no	—
219	C₂×C₂²⋊C₄	C₂×Dic₆₇	1	4	yes	—
220	C₂×C₄²	—	2	2	no	—
221	C₂×C₄²	—	2	2	no	—
222	C₂×C₄²	—	2	2	no	—
223	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
224	C₂×C₄²	Dic₁₃₄	1	1	yes	characteristic
225	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
226	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
227	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
228	C₂×C₄²	C₄×D₆₇	1	1	yes	characteristic
229	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
230	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
231	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
232	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
233	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
234	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
235	C₄⋊C₈	—	134	2	no	—
236	C₄⋊C₈	—	134	2	no	—
237	C₄⋊C₈	—	134	2	no	—
238	C₄⋊C₈	—	134	2	no	—
239	C₂²⋊C₈	—	67	4	no	—
240	C₂²⋊C₈	—	134	2	no	—
241	C₂²⋊C₈	—	134	2	no	—
242	C₂²⋊C₈	—	134	2	no	—
243	#97	—	134	2	no	—
244	#97	—	134	2	no	—
245	#97	—	134	2	no	—
246	#97	—	134	2	no	—
247	#95	—	2	2	no	—
248	#95	—	2	2	no	—
249	C₂⁴	C₂²×Dic₆₇	1	1	yes	characteristic
250	C₂²×C₄	—	2	4	no	—
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	4	2	no	—
253	C₂²×C₄	—	4	2	no	—
254	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
255	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
256	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
257	C₂²×C₄	C₄×Dic₆₇	1	1	yes	characteristic
258	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
259	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
260	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
261	C₂²×C₄	C₂²⋊Dic₆₇	1	1	yes	characteristic
262	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
263	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
264	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
265	C₂²×C₄	C₄⋊Dic₆₇	1	1	yes	characteristic
266	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×D₆₇	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
269	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
270	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
271	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
272	C₂×C₈	—	268	4	no	—
273	C₂×C₈	—	268	4	no	—
274	C₂×C₈	—	134	4	no	—
275	C₂×C₈	—	134	4	no	—
276	C₄⋊C₄	—	2	8	no	—
277	C₂²⋊C₄	—	2	4	no	—
278	C₂²⋊C₄	#11761612	1	8	yes	—
279	C₄²	—	2	8	no	—
280	C₄²	—	4	4	no	—
281	C₄²	—	4	4	no	—
282	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
283	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
284	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
285	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
286	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
287	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
288	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
289	C₄²	(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
290	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
291	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
292	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
293	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
294	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
295	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
296	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
297	C₄²	Dic₆₇⋊C₄	1	1	yes	characteristic
298	C₂³	—	4	1	no	—
299	C₂³	—	4	1	no	—
300	C₂³	C₂×C₄×Dic₆₇	1	1	yes	characteristic
301	C₂³	C₂×C₂²⋊Dic₆₇	1	1	yes	characteristic
302	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
303	C₂³	C₂×#11761612	1	4	yes	—
304	C₂×C₄	—	2	2	no	—
305	C₂×C₄	—	2	2	no	—
306	C₂×C₄	—	2	2	no	—
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	2	no	—
313	C₂×C₄	—	2	2	no	—
314	C₂×C₄	—	2	2	no	—
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	2	8	no	—
317	C₂×C₄	—	4	1	no	—
318	C₂×C₄	—	4	1	no	—
319	C₂×C₄	—	4	1	no	—
320	C₂×C₄	—	4	1	no	—
321	C₂×C₄	—	4	1	no	—
322	C₂×C₄	—	4	1	no	—
323	C₂×C₄	—	4	4	no	—
324	C₂×C₄	—	4	4	no	—
325	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
326	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
327	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
328	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
329	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
330	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
331	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
332	C₂×C₄	C₆₇⋊#95	1	1	yes	characteristic
333	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
334	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄	1	1	yes	characteristic
335	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
336	C₂×C₄	C₂×Dic₆₇⋊C₄	1	1	yes	characteristic
337	C₈	—	268	4	no	—
338	C₈	—	268	4	no	—
339	C₂²	—	2	1	no	—
340	C₂²	—	2	1	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	4	4	no	—
346	C₂²	C₂×C₆₇⋊#95	1	1	yes	characteristic
347	C₂²	C₄×#11761612	1	2	yes	—
348	C₂²	#16863360	1	2	yes	—
349	C₂²	#16863420	1	2	yes	—
350	C₄	—	2	1	no	—
351	C₄	—	2	1	no	—
352	C₄	—	2	1	no	—
353	C₄	—	2	1	no	—
354	C₄	—	2	1	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	2	1	no	—
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	4	8	no	—
361	C₄	#16863166	1	2	yes	—
362	C₄	#16863369	1	2	yes	—
363	C₂	—	2	2	no	—
364	C₂	—	2	2	no	—
365	C₂	—	2	2	no	—
366	C₂	#22559903	1	1	yes	characteristic
367	C₂	#22559941	1	1	yes	characteristic
368	C₂	C₂×#16863166	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×(C₂×D₆₇)⋊C₄
commutator	C₂³×C₆₇	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₆₇
Fitting	C₄×#117×C₆₇	C₂
socle	C₂²×C₆₇	C₂×#95
prime radical	C₂⁴×C₆₇	C₂²×C₄
cosocle	C₂³×C₄×C₆₇	C₂³
hypercenter	C₄×#117	D₆₇
hypocenter	C₆₇	#7930
LCS	G ▷ C₂³×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄² ◁ C₄×#117

Complements

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

N	H ≅ G/N	type
11. #16863453	C₄	semidirect
12. #16863453	C₄	semidirect
14. C₂×C₄⋊(C₆₇⋊C₈)	C₄	semidirect
18. C₂×#14523954	C₄	semidirect
189. C₆₇	#7930	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863453	2
#22558057	2
C₄×#117×C₆₇	2
#7930	67