Subgroups — C₂×#22560985 #30859352

Order 17152.

938 conjugacy classes of subgroups.

The subgroup lattice has 372 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523979	C₂	1	2	yes	maximal
2	C₂×#16863420	C₂	1	1	yes	maximal, characteristic
3	C₂×C₄×#11761612	C₂	1	1	yes	maximal, characteristic
4	#22560985	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863161	C₂	1	2	yes	maximal
6	C₂²×C₄⋊C₈×C₆₇	C₂	1	1	yes	maximal, characteristic
7	C₂²×#11761612	C₂²	1	2	yes	—
8	C₂²×#11761612	C₂²	1	1	yes	characteristic
9	C₂²×#11761612	C₂²	1	1	yes	characteristic
10	C₂×#14523979	—	2	8	no	—
11	C₂×#14523979	C₂²	1	8	yes	—
12	#16863420	—	2	2	no	—
13	#16863420	C₂²	1	4	yes	—
14	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
15	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
16	C₄×#11761612	—	2	2	no	—
17	C₄×#11761612	C₂²	1	4	yes	—
18	C₂×#14523954	—	2	1	no	—
19	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
20	#16863161	C₂²	1	8	yes	—
21	C₂³×C₈×C₆₇	C₂²	1	2	yes	—
22	C₂²×C₄²×C₆₇	C₂²	1	1	yes	characteristic
23	C₂×C₄⋊C₈×C₆₇	C₄	1	2	yes	—
24	C₂×C₄⋊C₈×C₆₇	C₄	1	4	yes	—
25	C₂×C₄⋊C₈×C₆₇	C₄	1	2	yes	—
26	C₂×C₄⋊C₈×C₆₇	C₂²	1	4	yes	—
27	C₂×#11761612	—	2	1	no	—
28	C₂×#11761612	—	2	1	no	—
29	C₂×#11761612	—	2	2	no	—
30	C₂×#11761612	—	2	4	no	—
31	C₂×#11761612	—	2	2	no	—
32	C₂×#11761612	—	2	2	no	—
33	C₂×#11761612	—	2	4	no	—
34	C₂×#11761612	D₄	1	4	yes	—
35	C₂×#11761612	Q₈	1	4	yes	—
36	C₂×#11761612	C₂³	1	4	yes	—
37	C₂×#11761612	C₂³	1	2	yes	—
38	C₂×#11761612	C₂³	1	2	yes	—
39	C₂²×C₆₇⋊C₈	—	2	1	no	—
40	C₂²×C₆₇⋊C₈	—	2	1	no	—
41	C₂²×C₆₇⋊C₈	—	2	2	no	—
42	#14523979	—	2	16	no	—
43	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
44	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
45	#14523954	—	2	4	no	—
46	C₄×C₆₇⋊C₈	—	2	4	no	—
47	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
48	C₂³×C₄×C₆₇	Q₈	1	1	yes	characteristic
49	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
50	C₂²×C₈×C₆₇	—	2	4	no	—
51	C₂²×C₈×C₆₇	—	2	4	no	—
52	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
53	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
54	C₂²×C₈×C₆₇	C₂³	1	4	yes	—
55	C₂×C₄²×C₆₇	C₂×C₄	1	1	yes	characteristic
56	C₂×C₄²×C₆₇	C₂×C₄	1	2	yes	—
57	C₂×C₄²×C₆₇	C₂×C₄	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	D₄	1	2	yes	—
61	C₂×C₄²×C₆₇	Q₈	1	2	yes	—
62	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
63	C₄⋊C₈×C₆₇	C₂×C₄	1	8	yes	—
64	C₄⋊C₈×C₆₇	C₂×C₄	1	8	yes	—
65	#11761612	—	2	4	no	—
66	#11761612	—	2	4	no	—
67	#11761612	—	2	2	no	—
68	#11761612	—	2	2	no	—
69	#11761612	—	2	4	no	—
70	#11761612	—	2	4	no	—
71	#11761612	—	4	4	no	—
72	#11761612	C₂×D₄	1	4	yes	—
73	#11761612	C₂×Q₈	1	4	yes	—
74	C₂×C₆₇⋊C₈	—	2	4	no	—
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	—	4	4	no	—
80	C₂⁴×C₆₇	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₆₇	—	2	4	no	—
82	C₂²×C₄×C₆₇	—	4	2	no	—
83	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
86	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
87	C₂²×C₄×C₆₇	C₄⋊C₄	1	2	yes	—
88	C₂²×C₄×C₆₇	C₄⋊C₄	1	1	yes	characteristic
89	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
90	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
91	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
92	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
95	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
96	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	#41	1	2	yes	—
99	C₂²×C₄×C₆₇	#41	1	2	yes	—
100	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
101	C₂×C₈×C₆₇	—	2	8	no	—
102	C₂×C₈×C₆₇	—	2	8	no	—
103	C₂×C₈×C₆₇	—	2	4	no	—
104	C₂×C₈×C₆₇	—	2	4	no	—
105	C₂×C₈×C₆₇	C₂²×C₄	1	8	yes	—
106	C₄²×C₆₇	C₄⋊C₄	1	2	yes	—
107	C₄²×C₆₇	C₄⋊C₄	1	2	yes	—
108	C₄²×C₆₇	C₄⋊C₄	1	2	yes	—
109	C₄²×C₆₇	C₄⋊C₄	1	2	yes	—
110	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
111	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
112	C₄²×C₆₇	C₂×D₄	1	2	yes	—
113	C₄²×C₆₇	C₂×D₄	1	2	yes	—
114	C₂³×C₆₇	—	2	2	no	—
115	C₂³×C₆₇	—	2	2	no	—
116	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
117	C₂³×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
118	C₂³×C₆₇	#125	1	2	yes	—
119	C₂³×C₆₇	C₄⋊Q₈	1	2	yes	—
120	C₂³×C₆₇	C₂²×Q₈	1	1	yes	characteristic
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	4	no	—
125	C₂×C₄×C₆₇	—	2	4	no	—
126	C₂×C₄×C₆₇	—	4	2	no	—
127	C₂×C₄×C₆₇	—	4	2	no	—
128	C₂×C₄×C₆₇	#108	1	4	yes	complemented
129	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
130	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
131	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
132	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
133	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
136	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
137	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
138	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
139	C₂×C₄×C₆₇	#121	1	2	yes	—
140	C₂×C₄×C₆₇	#121	1	2	yes	—
141	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
142	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
143	C₂×C₄×C₆₇	#125	1	2	yes	—
144	C₂×C₄×C₆₇	C₄⋊Q₈	1	2	yes	—
145	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
151	C₈×C₆₇	—	2	8	no	—
152	C₆₇⋊C₈	—	2	4	no	—
153	C₆₇⋊C₈	—	2	4	no	—
154	C₆₇⋊C₈	—	4	4	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	4	no	—
160	C₂²×C₆₇	—	2	4	no	—
161	C₂²×C₆₇	#389	1	2	yes	—
162	C₂²×C₆₇	#389	1	2	yes	—
163	C₂²×C₆₇	C₂×#108	1	2	yes	—
164	C₂²×C₆₇	#430	1	2	yes	—
165	C₂²×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
166	C₂²×C₆₇	C₂×#125	1	1	yes	characteristic
167	C₂²×C₆₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
168	C₄×C₆₇	—	2	2	no	—
169	C₄×C₆₇	—	2	2	no	—
170	C₄×C₆₇	—	2	2	no	—
171	C₄×C₆₇	#389	1	2	yes	—
172	C₄×C₆₇	#389	1	2	yes	—
173	C₄×C₆₇	C₂×#108	1	4	yes	complemented
174	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
175	C₄×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
176	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
177	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
178	C₂×#1950	—	67	1	no	maximal, Sylow
179	C₂×C₆₇	—	2	1	no	—
180	C₂×C₆₇	—	2	1	no	—
181	C₂×C₆₇	—	2	2	no	—
182	C₂×C₆₇	#1950	1	4	yes	complemented
183	C₂×C₆₇	C₂×#389	1	1	yes	characteristic
184	C₂×C₆₇	C₂²×#108	1	1	yes	characteristic
185	C₂×C₆₇	C₂×#430	1	1	yes	characteristic
186	C₂²×#108	—	67	2	no	—
187	C₂×#423	—	67	1	no	—
188	C₂²×C₄⋊C₈	D₆₇	1	1	yes	characteristic
189	C₂×C₄×M₁₆	—	67	1	no	—
190	#1950	—	67	8	no	—
191	C₂×#341	—	67	2	no	—
192	C₆₇	C₂×#1950	1	1	yes	characteristic, complemented, Sylow
193	C₂²×M₁₆	—	67	1	no	—
194	C₂²×M₁₆	—	67	1	no	—
195	C₂²×M₁₆	—	67	2	no	—
196	C₂³×C₈	C₂×D₆₇	1	2	yes	—
197	C₂²×C₄²	C₂×D₆₇	1	1	yes	characteristic
198	C₂×#108	—	67	8	no	—
199	C₂×#108	—	134	8	no	—
200	#423	—	67	4	no	—
201	#423	—	134	2	no	—
202	C₂×C₄⋊C₈	—	134	1	no	—
203	C₂×C₄⋊C₈	—	134	1	no	—
204	C₂×C₄⋊C₈	Dic₆₇	1	2	yes	—
205	C₂×C₄⋊C₈	Dic₆₇	1	4	yes	—
206	C₂×C₄⋊C₈	Dic₆₇	1	2	yes	—
207	C₂×C₄⋊C₈	C₂×D₆₇	1	4	yes	—
208	C₄×M₁₆	—	67	4	no	—
209	C₄×M₁₆	—	134	2	no	—
210	C₂×#97	—	134	1	no	—
211	C₂×C₄×C₈	—	134	1	no	—
212	#341	—	67	8	no	—
213	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
214	C₂³×C₄	Dic₁₃₄	1	1	yes	characteristic
215	C₂³×C₄	C₂²×D₆₇	1	1	yes	characteristic
216	C₂×M₁₆	—	67	4	no	—
217	C₂×M₁₆	—	67	4	no	—
218	C₂×M₁₆	—	67	2	no	—
219	C₂×M₁₆	—	67	2	no	—
220	C₂×M₁₆	—	67	4	no	—
221	C₂×M₁₆	—	134	4	no	—
222	C₂×M₁₆	—	134	4	no	—
223	C₂×M₁₆	—	134	2	no	—
224	C₂×M₁₆	—	134	1	no	—
225	C₂×M₁₆	—	134	1	no	—
226	C₂×M₁₆	—	134	2	no	—
227	C₂×M₁₆	—	134	2	no	—
228	C₂²×C₈	—	2	4	no	—
229	C₂²×C₈	—	2	4	no	—
230	C₂²×C₈	—	134	2	no	—
231	C₂²×C₈	—	134	1	no	—
232	C₂²×C₈	—	134	1	no	—
233	C₂²×C₈	C₂×Dic₆₇	1	4	yes	—
234	C₂²×C₈	C₂×Dic₆₇	1	4	yes	—
235	C₂²×C₈	C₂²×D₆₇	1	4	yes	—
236	C₂×C₄²	Dic₁₃₄	1	2	yes	—
237	C₂×C₄²	D₂₆₈	1	2	yes	—
238	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
239	C₂×C₄²	D₂₆₈	1	1	yes	characteristic
240	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
241	C₂×C₄²	C₂×Dic₆₇	1	2	yes	—
242	C₂×C₄²	C₂×Dic₆₇	1	1	yes	characteristic
243	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
244	#108	—	134	16	no	—
245	C₄⋊C₈	—	134	4	no	—
246	C₄⋊C₈	—	134	4	no	—
247	C₄⋊C₈	C₂×Dic₆₇	1	8	yes	—
248	C₄⋊C₈	C₂×Dic₆₇	1	8	yes	—
249	#97	—	134	4	no	—
250	C₄×C₈	—	134	4	no	—
251	C₂⁴	C₂×Dic₁₃₄	1	1	yes	characteristic
252	C₂²×C₄	—	2	4	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	2	yes	—
258	C₂²×C₄	C₄⋊Dic₆₇	1	2	yes	—
259	C₂²×C₄	C₄⋊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	D₄×D₆₇	1	2	yes	—
263	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
264	C₂²×C₄	C₂×D₂₆₈	1	1	yes	characteristic
265	C₂²×C₄	Q₈×D₆₇	1	2	yes	—
266	C₂²×C₄	C₂×Dic₁₃₄	1	2	yes	—
267	C₂²×C₄	C₂×Dic₁₃₄	1	2	yes	—
268	C₂²×C₄	C₂×Dic₁₃₄	1	1	yes	characteristic
269	C₂²×C₄	#11761627	1	2	yes	—
270	C₂²×C₄	#11761629	1	2	yes	—
271	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
272	M₁₆	—	268	4	no	—
273	M₁₆	—	67	4	no	—
274	M₁₆	—	67	4	no	—
275	M₁₆	—	134	4	no	—
276	M₁₆	—	134	4	no	—
277	M₁₆	—	134	4	no	—
278	M₁₆	—	134	4	no	—
279	M₁₆	—	134	2	no	—
280	M₁₆	—	134	2	no	—
281	C₂×C₈	—	2	8	no	—
282	C₂×C₈	—	2	8	no	—
283	C₂×C₈	—	2	4	no	—
284	C₂×C₈	—	2	4	no	—
285	C₂×C₈	—	268	4	no	—
286	C₂×C₈	—	134	4	no	—
287	C₂×C₈	—	134	4	no	—
288	C₂×C₈	—	134	4	no	—
289	C₂×C₈	—	134	2	no	—
290	C₂×C₈	—	134	2	no	—
291	C₂×C₈	C₂²×Dic₆₇	1	8	yes	—
292	C₄²	C₄⋊Dic₆₇	1	2	yes	—
293	C₄²	C₄⋊Dic₆₇	1	2	yes	—
294	C₄²	C₄⋊Dic₆₇	1	2	yes	—
295	C₄²	C₄⋊Dic₆₇	1	2	yes	—
296	C₄²	C₂²×Dic₆₇	1	2	yes	—
297	C₄²	C₂²×Dic₆₇	1	2	yes	—
298	C₄²	C₂×D₂₆₈	1	2	yes	—
299	C₄²	C₂×D₂₆₈	1	2	yes	—
300	C₂³	—	2	2	no	—
301	C₂³	—	2	2	no	—
302	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
303	C₂³	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
304	C₂³	#14524034	1	2	yes	—
305	C₂³	#14524042	1	2	yes	—
306	C₂³	C₂²×Dic₁₃₄	1	1	yes	characteristic
307	C₂×C₄	—	2	2	no	—
308	C₂×C₄	—	2	2	no	—
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	4	no	—
311	C₂×C₄	—	2	4	no	—
312	C₂×C₄	—	4	2	no	—
313	C₂×C₄	—	4	2	no	—
314	C₂×C₄	#14523979	1	4	yes	complemented
315	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
316	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
317	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
318	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
319	C₂×C₄	C₂×C₄⋊Dic₆₇	1	1	yes	characteristic
320	C₂×C₄	C₂×C₄⋊Dic₆₇	1	2	yes	—
321	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
322	C₂×C₄	D₄×Dic₆₇	1	2	yes	—
323	C₂×C₄	Q₈×Dic₆₇	1	2	yes	—
324	C₂×C₄	Q₈×Dic₆₇	1	2	yes	—
325	C₂×C₄	#14524018	1	2	yes	—
326	C₂×C₄	#14524018	1	2	yes	—
327	C₂×C₄	#14524023	1	2	yes	—
328	C₂×C₄	#14524023	1	2	yes	—
329	C₂×C₄	#14524034	1	2	yes	—
330	C₂×C₄	#14524042	1	2	yes	—
331	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
332	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
333	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
334	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
335	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
336	C₂×C₄	C₂×#11761629	1	1	yes	characteristic
337	C₈	—	2	8	no	—
338	C₈	—	268	4	no	—
339	C₈	—	134	4	no	—
340	C₈	—	134	4	no	—
341	C₂²	—	2	1	no	—
342	C₂²	—	2	1	no	—
343	C₂²	—	2	1	no	—
344	C₂²	—	2	1	no	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	4	no	—
347	C₂²	#16863295	1	2	yes	—
348	C₂²	#16863295	1	2	yes	—
349	C₂²	C₂×#14523979	1	2	yes	—
350	C₂²	#16863445	1	2	yes	—
351	C₂²	C₂²×C₄⋊Dic₆₇	1	1	yes	characteristic
352	C₂²	C₂×#14524034	1	1	yes	characteristic
353	C₂²	C₂×#14524042	1	1	yes	characteristic
354	C₄	—	2	2	no	—
355	C₄	—	2	2	no	—
356	C₄	—	2	2	no	—
357	C₄	#16863295	1	2	yes	—
358	C₄	#16863295	1	2	yes	—
359	C₄	C₂×#14523979	1	4	yes	complemented
360	C₄	C₂×D₄×Dic₆₇	1	1	yes	characteristic
361	C₄	C₂×Q₈×Dic₆₇	1	1	yes	characteristic
362	C₄	C₂×#14524018	1	1	yes	characteristic
363	C₄	C₂×#14524023	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	2	1	no	—
366	C₂	—	2	1	no	—
367	C₂	#22560985	1	4	yes	direct product factor
368	C₂	C₂×#16863295	1	1	yes	characteristic
369	C₂	C₂²×#14523979	1	1	yes	characteristic
370	C₂	C₂×#16863445	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂²×C₄⋊C₈×C₆₇	C₂
socle	C₂³×C₆₇	C₂×C₄⋊C₄
prime radical	C₂⁴×C₆₇	C₂×Q₈
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂²×C₄⋊C₈	D₆₇
hypocenter	C₆₇	C₂×#1950
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
4. #22560985	C₂	direct (N × H)
128. C₂×C₄×C₆₇	#108	semidirect
173. C₄×C₆₇	C₂×#108	semidirect
182. C₂×C₆₇	#1950	semidirect
192. C₆₇	C₂×#1950	semidirect
314. C₂×C₄	#14523979	semidirect
359. C₄	C₂×#14523979	semidirect
367. C₂	#22560985	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14523979	2
C₂×#16863420	2
C₂×C₄×#11761612	2
#22560985	2
C₂×#16863161	2
C₂²×C₄⋊C₈×C₆₇	2
C₂×#1950	67

Subgroups — C2×#22560985 #30859352

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22560985 #30859352