Subgroups — C₂×C₆₇×#1953 #30700434

Order 17152.

858 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#430×C₆₇	C₂	1	2	yes	maximal
2	C₂²×#108×C₆₇	C₂	1	1	yes	maximal, characteristic
3	C₂²×#108×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#1953	C₂	1	8	yes	maximal, direct product factor
6	C₂×#344×C₆₇	C₂	1	2	yes	maximal
7	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
9	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
10	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
11	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
12	#430×C₆₇	—	2	4	no	—
13	#430×C₆₇	C₂²	1	8	yes	—
14	C₂×#108×C₆₇	—	2	4	no	—
15	C₂×#108×C₆₇	—	2	1	no	—
16	C₂×#108×C₆₇	—	2	1	no	—
17	C₂×#108×C₆₇	—	2	2	no	—
18	C₂×#108×C₆₇	C₄	1	4	yes	complemented
19	C₂×#108×C₆₇	C₄	1	4	yes	complemented
20	C₂×#108×C₆₇	C₂²	1	4	yes	—
21	C₂×#108×C₆₇	C₂²	1	4	yes	—
22	#405×C₆₇	—	2	2	no	—
23	#405×C₆₇	C₂²	1	4	yes	—
24	C₂×#97×C₆₇	—	2	1	no	—
25	C₂×C₄×C₈×C₆₇	—	2	1	no	—
26	#344×C₆₇	C₂²	1	8	yes	—
27	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
28	C₂×M₁₆×C₆₇	—	2	1	no	—
29	C₂×M₁₆×C₆₇	—	2	2	no	—
30	C₂×M₁₆×C₆₇	—	2	2	no	—
31	C₂×M₁₆×C₆₇	—	2	2	no	—
32	C₂×M₁₆×C₆₇	—	2	1	no	—
33	C₂×M₁₆×C₆₇	—	2	1	no	—
34	C₂×M₁₆×C₆₇	—	2	2	no	—
35	C₂×M₁₆×C₆₇	—	2	2	no	—
36	C₂×M₁₆×C₆₇	—	2	2	no	—
37	C₂×M₁₆×C₆₇	—	2	2	no	—
38	C₂×M₁₆×C₆₇	—	2	2	no	—
39	C₂×M₁₆×C₆₇	C₂×C₄	1	4	yes	—
40	C₂×M₁₆×C₆₇	C₂×C₄	1	4	yes	—
41	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
42	C₂×M₁₆×C₆₇	D₄	1	2	yes	—
43	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
44	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
45	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
46	C₂²×C₈×C₆₇	—	2	1	no	—
47	C₂²×C₈×C₆₇	—	2	2	no	—
48	C₂²×C₈×C₆₇	—	2	2	no	—
49	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
50	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
51	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
52	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
53	C₂²×C₈×C₆₇	D₄	1	2	yes	—
54	C₂²×C₈×C₆₇	Q₈	1	2	yes	—
55	C₂²×C₈×C₆₇	Q₈	1	2	yes	—
56	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
57	#117×C₆₇	—	2	1	no	—
58	#117×C₆₇	—	2	1	no	—
59	#117×C₆₇	Q₈	1	2	yes	—
60	#117×C₆₇	C₂³	1	2	yes	—
61	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
62	C₂×C₂²⋊C₄×C₆₇	Q₈	1	2	yes	—
63	C₂×C₄²×C₆₇	—	2	1	no	—
64	#108×C₆₇	—	2	16	no	—
65	#108×C₆₇	—	2	4	no	—
66	#108×C₆₇	—	2	4	no	—
67	#108×C₆₇	C₂×C₄	1	16	yes	complemented
68	#97×C₆₇	—	2	4	no	—
69	C₄×C₈×C₆₇	—	2	4	no	—
70	C₂⁴×C₆₇	C₂×Q₈	1	1	yes	characteristic
71	C₂²×C₄×C₆₇	—	2	2	no	—
72	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
73	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
74	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
75	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
76	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
77	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
78	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
79	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
80	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
81	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
83	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
84	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
85	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
86	M₁₆×C₆₇	—	2	4	no	—
87	M₁₆×C₆₇	—	2	4	no	—
88	M₁₆×C₆₇	—	2	2	no	—
89	M₁₆×C₆₇	—	2	2	no	—
90	M₁₆×C₆₇	—	2	4	no	—
91	M₁₆×C₆₇	—	2	2	no	—
92	M₁₆×C₆₇	—	2	4	no	—
93	M₁₆×C₆₇	—	2	4	no	—
94	M₁₆×C₆₇	—	4	2	no	—
95	M₁₆×C₆₇	—	4	2	no	—
96	M₁₆×C₆₇	C₂²×C₄	1	8	yes	—
97	M₁₆×C₆₇	C₂×D₄	1	4	yes	—
98	C₂×C₈×C₆₇	—	2	4	no	—
99	C₂×C₈×C₆₇	—	2	4	no	—
100	C₂×C₈×C₆₇	—	2	2	no	—
101	C₂×C₈×C₆₇	—	2	2	no	—
102	C₂×C₈×C₆₇	—	2	4	no	—
103	C₂×C₈×C₆₇	—	2	2	no	—
104	C₂×C₈×C₆₇	—	2	4	no	—
105	C₂×C₈×C₆₇	—	4	2	no	—
106	C₂×C₈×C₆₇	—	4	2	no	—
107	C₂×C₈×C₆₇	C₄⋊C₄	1	2	yes	—
108	C₂×C₈×C₆₇	C₄⋊C₄	1	2	yes	—
109	C₂×C₈×C₆₇	C₄⋊C₄	1	2	yes	—
110	C₂×C₈×C₆₇	C₄⋊C₄	1	2	yes	—
111	C₂×C₈×C₆₇	C₄⋊C₄	1	4	yes	—
112	C₂×C₈×C₆₇	C₄⋊C₄	1	4	yes	—
113	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
114	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
115	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
116	C₂×C₈×C₆₇	C₂×Q₈	1	4	yes	—
117	C₄⋊C₄×C₆₇	—	2	2	no	—
118	C₄⋊C₄×C₆₇	—	2	2	no	—
119	C₂²⋊C₄×C₆₇	—	2	2	no	—
120	C₂²⋊C₄×C₆₇	C₂×Q₈	1	4	yes	—
121	C₄²×C₆₇	—	2	2	no	—
122	C₄²×C₆₇	—	2	2	no	—
123	C₂³×C₆₇	—	4	2	no	—
124	C₂³×C₆₇	C₄×Q₈	1	1	yes	characteristic
125	C₂³×C₆₇	C₄×Q₈	1	1	yes	characteristic
126	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
127	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
128	C₂³×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
129	C₂³×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
130	C₂³×C₆₇	C₂²×Q₈	1	1	yes	characteristic
131	C₂×C₄×C₆₇	—	2	4	no	—
132	C₂×C₄×C₆₇	—	4	4	no	—
133	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
136	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
137	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
138	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
139	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
140	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
141	C₂×C₄×C₆₇	C₄×Q₈	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₄×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
144	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
145	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
146	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
149	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
150	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
151	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
152	C₂×C₄×C₆₇	#125	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₄⋊Q₈	1	1	yes	characteristic
155	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
157	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
158	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
161	C₈×C₆₇	—	2	8	no	—
162	C₈×C₆₇	—	2	4	no	—
163	C₈×C₆₇	—	4	4	no	—
164	C₈×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
165	C₈×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
166	C₂²×C₆₇	—	2	2	no	—
167	C₂²×C₆₇	—	2	2	no	—
168	C₂²×C₆₇	—	2	2	no	—
169	C₂²×C₆₇	—	4	1	no	—
170	C₂²×C₆₇	—	4	1	no	—
171	C₂²×C₆₇	—	4	1	no	—
172	C₂²×C₆₇	—	4	1	no	—
173	C₂²×C₆₇	#389	1	1	yes	characteristic
174	C₂²×C₆₇	#389	1	1	yes	characteristic
175	C₂²×C₆₇	#389	1	1	yes	characteristic
176	C₂²×C₆₇	#389	1	1	yes	characteristic
177	C₂²×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
178	C₂²×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
179	C₂²×C₆₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
180	C₄×C₆₇	—	4	4	no	—
181	C₄×C₆₇	#389	1	1	yes	characteristic
182	C₄×C₆₇	#389	1	1	yes	characteristic
183	C₄×C₆₇	#389	1	1	yes	characteristic
184	C₄×C₆₇	#389	1	1	yes	characteristic
185	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
187	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
188	C₄×C₆₇	C₂×#125	1	1	yes	characteristic
189	C₂×#1953	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₆₇	—	2	1	no	—
191	C₂×C₆₇	—	2	1	no	—
192	C₂×C₆₇	—	2	1	no	—
193	C₂×C₆₇	—	2	1	no	—
194	C₂×C₆₇	—	2	1	no	—
195	C₂×C₆₇	—	2	1	no	—
196	C₂×C₆₇	#1953	1	2	yes	direct product factor
197	C₂×C₆₇	C₂×#389	1	1	yes	characteristic
198	C₂×#430	C₂×C₆₇	1	2	yes	—
199	C₂²×#108	C₂×C₆₇	1	1	yes	characteristic
200	C₂²×#108	C₂×C₆₇	1	1	yes	characteristic
201	C₂×#405	C₂×C₆₇	1	1	yes	characteristic
202	#1953	C₂×C₆₇	1	8	yes	direct product factor
203	C₂×#344	C₂×C₆₇	1	2	yes	—
204	C₆₇	C₂×#1953	1	1	yes	characteristic, direct product factor, Sylow
205	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
206	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
207	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
208	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
209	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
210	#430	—	2	4	no	—
211	#430	C₂²×C₆₇	1	8	yes	—
212	C₂×#108	—	2	4	no	—
213	C₂×#108	—	2	1	no	—
214	C₂×#108	—	2	1	no	—
215	C₂×#108	—	2	2	no	—
216	C₂×#108	C₄×C₆₇	1	4	yes	complemented
217	C₂×#108	C₄×C₆₇	1	4	yes	complemented
218	C₂×#108	C₂²×C₆₇	1	4	yes	—
219	C₂×#108	C₂²×C₆₇	1	4	yes	—
220	#405	—	2	2	no	—
221	#405	C₂²×C₆₇	1	4	yes	—
222	C₂×#97	—	2	1	no	—
223	C₂×C₄×C₈	—	2	1	no	—
224	#344	C₂²×C₆₇	1	8	yes	—
225	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
226	C₂×M₁₆	—	2	1	no	—
227	C₂×M₁₆	—	2	2	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂×M₁₆	—	2	2	no	—
230	C₂×M₁₆	—	2	1	no	—
231	C₂×M₁₆	—	2	1	no	—
232	C₂×M₁₆	—	2	2	no	—
233	C₂×M₁₆	—	2	2	no	—
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	2	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	C₂×C₄×C₆₇	1	4	yes	—
238	C₂×M₁₆	C₂×C₄×C₆₇	1	4	yes	—
239	C₂×M₁₆	D₄×C₆₇	1	2	yes	—
240	C₂×M₁₆	D₄×C₆₇	1	2	yes	—
241	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
242	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
243	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
244	C₂²×C₈	—	2	1	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	2	no	—
247	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
248	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
249	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
250	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
251	C₂²×C₈	D₄×C₆₇	1	2	yes	—
252	C₂²×C₈	Q₈×C₆₇	1	2	yes	—
253	C₂²×C₈	Q₈×C₆₇	1	2	yes	—
254	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
255	#117	—	2	1	no	—
256	#117	—	2	1	no	—
257	#117	Q₈×C₆₇	1	2	yes	—
258	#117	C₂³×C₆₇	1	2	yes	—
259	C₂×C₄⋊C₄	—	2	1	no	—
260	C₂×C₂²⋊C₄	Q₈×C₆₇	1	2	yes	—
261	C₂×C₄²	—	2	1	no	—
262	#108	—	2	16	no	—
263	#108	—	2	4	no	—
264	#108	—	2	4	no	—
265	#108	C₂×C₄×C₆₇	1	16	yes	complemented
266	#97	—	2	4	no	—
267	C₄×C₈	—	2	4	no	—
268	C₂⁴	C₂×Q₈×C₆₇	1	1	yes	characteristic
269	C₂²×C₄	—	2	2	no	—
270	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
271	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
272	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
273	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
274	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
275	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
276	C₂²×C₄	C₂×Q₈×C₆₇	1	1	yes	characteristic
277	C₂²×C₄	C₂×Q₈×C₆₇	1	1	yes	characteristic
278	C₂²×C₄	C₂×Q₈×C₆₇	1	1	yes	characteristic
279	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
280	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
281	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
282	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
283	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
284	M₁₆	—	2	4	no	—
285	M₁₆	—	2	4	no	—
286	M₁₆	—	2	2	no	—
287	M₁₆	—	2	2	no	—
288	M₁₆	—	2	4	no	—
289	M₁₆	—	2	2	no	—
290	M₁₆	—	2	4	no	—
291	M₁₆	—	2	4	no	—
292	M₁₆	—	4	2	no	—
293	M₁₆	—	4	2	no	—
294	M₁₆	C₂²×C₄×C₆₇	1	8	yes	—
295	M₁₆	C₂×D₄×C₆₇	1	4	yes	—
296	C₂×C₈	—	2	4	no	—
297	C₂×C₈	—	2	4	no	—
298	C₂×C₈	—	2	2	no	—
299	C₂×C₈	—	2	2	no	—
300	C₂×C₈	—	2	2	no	—
301	C₂×C₈	—	2	4	no	—
302	C₂×C₈	—	2	4	no	—
303	C₂×C₈	—	4	2	no	—
304	C₂×C₈	—	4	2	no	—
305	C₂×C₈	C₄⋊C₄×C₆₇	1	2	yes	—
306	C₂×C₈	C₄⋊C₄×C₆₇	1	2	yes	—
307	C₂×C₈	C₄⋊C₄×C₆₇	1	2	yes	—
308	C₂×C₈	C₄⋊C₄×C₆₇	1	2	yes	—
309	C₂×C₈	C₄⋊C₄×C₆₇	1	4	yes	—
310	C₂×C₈	C₄⋊C₄×C₆₇	1	4	yes	—
311	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
312	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
313	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
314	C₂×C₈	C₂×Q₈×C₆₇	1	4	yes	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₂²⋊C₄	—	2	2	no	—
318	C₂²⋊C₄	C₂×Q₈×C₆₇	1	4	yes	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	C₄×Q₈×C₆₇	1	1	yes	characteristic
323	C₂³	C₄×Q₈×C₆₇	1	1	yes	characteristic
324	C₂³	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
325	C₂³	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
326	C₂³	C₄⋊Q₈×C₆₇	1	1	yes	characteristic
327	C₂³	C₄⋊Q₈×C₆₇	1	1	yes	characteristic
328	C₂³	C₂²×Q₈×C₆₇	1	1	yes	characteristic
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	4	4	no	—
331	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
332	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
333	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
334	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
335	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
336	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
337	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
338	C₂×C₄	C₄×D₄×C₆₇	1	1	yes	characteristic
339	C₂×C₄	C₄×Q₈×C₆₇	1	1	yes	characteristic
340	C₂×C₄	C₄×Q₈×C₆₇	1	1	yes	characteristic
341	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
342	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
343	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
344	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
345	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
346	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
347	C₂×C₄	#125×C₆₇	1	1	yes	characteristic
348	C₂×C₄	#125×C₆₇	1	1	yes	characteristic
349	C₂×C₄	#125×C₆₇	1	1	yes	characteristic
350	C₂×C₄	#125×C₆₇	1	1	yes	characteristic
351	C₂×C₄	C₄⋊Q₈×C₆₇	1	1	yes	characteristic
352	C₂×C₄	C₄⋊Q₈×C₆₇	1	1	yes	characteristic
353	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
354	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
355	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
356	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
358	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
359	C₈	—	2	8	no	—
360	C₈	—	2	4	no	—
361	C₈	—	4	4	no	—
362	C₈	C₂×C₄⋊C₄×C₆₇	1	4	yes	—
363	C₈	C₂×C₄⋊C₄×C₆₇	1	4	yes	—
364	C₂²	—	2	2	no	—
365	C₂²	—	2	2	no	—
366	C₂²	—	2	2	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	#389×C₆₇	1	1	yes	characteristic
372	C₂²	#389×C₆₇	1	1	yes	characteristic
373	C₂²	#389×C₆₇	1	1	yes	characteristic
374	C₂²	#389×C₆₇	1	1	yes	characteristic
375	C₂²	C₂×C₄×Q₈×C₆₇	1	1	yes	characteristic
376	C₂²	C₂×C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
377	C₂²	C₂×C₄⋊Q₈×C₆₇	1	1	yes	characteristic
378	C₄	—	4	4	no	—
379	C₄	#389×C₆₇	1	1	yes	characteristic
380	C₄	#389×C₆₇	1	1	yes	characteristic
381	C₄	#389×C₆₇	1	1	yes	characteristic
382	C₄	#389×C₆₇	1	1	yes	characteristic
383	C₄	C₂²×C₄⋊C₄×C₆₇	1	1	yes	characteristic
384	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
385	C₄	C₂×#121×C₆₇	1	1	yes	characteristic
386	C₄	C₂×#125×C₆₇	1	1	yes	characteristic
387	C₂	—	2	1	no	—
388	C₂	—	2	1	no	—
389	C₂	—	2	1	no	—
390	C₂	—	2	1	no	—
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	C₆₇×#1953	1	2	yes	direct product factor
394	C₂	C₂×#389×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄×C₆₇	#121
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
socle	C₂²×C₆₇	#389
prime radical	C₂⁴×C₆₇	C₂×Q₈
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₆₇×#1953	C₂	direct (N × H)
18. C₂×#108×C₆₇	C₄	semidirect
19. C₂×#108×C₆₇	C₄	semidirect
67. #108×C₆₇	C₂×C₄	semidirect
189. C₂×#1953	C₆₇	direct (N × H)
196. C₂×C₆₇	#1953	direct (N × H)
202. #1953	C₂×C₆₇	direct (N × H)
204. C₆₇	C₂×#1953	direct (N × H)
216. C₂×#108	C₄×C₆₇	semidirect
217. C₂×#108	C₄×C₆₇	semidirect
265. #108	C₂×C₄×C₆₇	semidirect
393. C₂	C₆₇×#1953	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#430×C₆₇	2
C₂²×#108×C₆₇	2
C₂×#405×C₆₇	2
C₆₇×#1953	2
C₂×#344×C₆₇	2
C₂×#1953	67

Subgroups — C2×C67×#1953 #30700434

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1953 #30700434