Subgroups — C₂×C₆₇×#1952 #30700431

Order 17152.

918 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#108×C₆₇	C₂	1	1	yes	maximal, characteristic
2	C₂×#428×C₆₇	C₂	1	2	yes	maximal
3	C₂²×#107×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#405×C₆₇	C₂	1	1	yes	maximal, characteristic
5	C₆₇×#1952	C₂	1	8	yes	maximal, direct product factor
6	C₂×#343×C₆₇	C₂	1	2	yes	maximal
7	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
8	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
9	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂×#117×C₆₇	C₂²	1	1	yes	characteristic
11	C₂²×C₄⋊C₄×C₆₇	C₂²	1	2	yes	—
12	C₂×#108×C₆₇	C₄	1	8	yes	complemented
13	C₂×#108×C₆₇	C₂²	1	4	yes	—
14	#428×C₆₇	—	2	4	no	—
15	#428×C₆₇	C₂²	1	8	yes	—
16	C₂×#107×C₆₇	—	2	1	no	—
17	C₂×#107×C₆₇	—	2	1	no	—
18	C₂×#107×C₆₇	—	2	2	no	—
19	C₂×#107×C₆₇	—	2	2	no	—
20	C₂×#107×C₆₇	C₂²	1	4	yes	—
21	C₂×#106×C₆₇	—	2	2	no	—
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	#343×C₆₇	C₂²	1	8	yes	—
27	C₂³×C₄×C₆₇	—	2	2	no	—
28	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
29	C₂×M₁₆×C₆₇	—	2	1	no	—
30	C₂×M₁₆×C₆₇	—	2	2	no	—
31	C₂×M₁₆×C₆₇	—	2	4	no	—
32	C₂×M₁₆×C₆₇	—	2	2	no	—
33	C₂×M₁₆×C₆₇	C₂×C₄	1	8	yes	—
34	C₂×M₁₆×C₆₇	Q₈	1	4	yes	—
35	C₂×M₁₆×C₆₇	C₂³	1	4	yes	—
36	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
37	C₂²×C₈×C₆₇	—	2	1	no	—
38	C₂²×C₈×C₆₇	—	2	2	no	—
39	C₂²×C₈×C₆₇	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
41	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
42	C₂²×C₈×C₆₇	D₄	1	2	yes	—
43	C₂²×C₈×C₆₇	Q₈	1	4	yes	—
44	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
45	#117×C₆₇	—	2	1	no	—
46	#117×C₆₇	—	2	1	no	—
47	#117×C₆₇	D₄	1	2	yes	—
48	#117×C₆₇	C₂³	1	2	yes	—
49	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
50	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
51	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
52	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
53	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
54	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
55	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
56	C₂×C₄⋊C₄×C₆₇	C₂³	1	4	yes	—
57	C₂×C₂²⋊C₄×C₆₇	—	2	1	no	—
58	C₂×C₄²×C₆₇	—	2	1	no	—
59	#108×C₆₇	C₂×C₄	1	16	yes	complemented
60	#107×C₆₇	—	2	4	no	—
61	#107×C₆₇	—	2	4	no	—
62	#107×C₆₇	—	2	8	no	—
63	#106×C₆₇	—	2	8	no	—
64	#97×C₆₇	—	2	4	no	—
65	C₄×C₈×C₆₇	—	2	4	no	—
66	C₂⁴×C₆₇	#41	1	1	yes	characteristic
67	C₂²×C₄×C₆₇	—	2	1	no	—
68	C₂²×C₄×C₆₇	—	2	1	no	—
69	C₂²×C₄×C₆₇	—	2	4	no	—
70	C₂²×C₄×C₆₇	—	4	2	no	—
71	C₂²×C₄×C₆₇	—	4	2	no	—
72	C₂²×C₄×C₆₇	—	8	4	no	—
73	C₂²×C₄×C₆₇	C₂²×C₄	1	2	yes	—
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	2	yes	—
79	C₂²×C₄×C₆₇	C₂×Q₈	1	2	yes	—
80	C₂²×C₄×C₆₇	#41	1	2	yes	—
81	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
82	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
83	M₁₆×C₆₇	—	2	8	no	—
84	M₁₆×C₆₇	—	2	4	no	—
85	M₁₆×C₆₇	—	2	4	no	—
86	M₁₆×C₆₇	—	2	2	no	—
87	M₁₆×C₆₇	C₂²×C₄	1	8	yes	—
88	M₁₆×C₆₇	C₂×Q₈	1	4	yes	—
89	C₂×C₈×C₆₇	—	2	8	no	—
90	C₂×C₈×C₆₇	—	2	4	no	—
91	C₂×C₈×C₆₇	—	2	4	no	—
92	C₂×C₈×C₆₇	—	2	2	no	—
93	C₂×C₈×C₆₇	C₄⋊C₄	1	4	yes	—
94	C₂×C₈×C₆₇	C₄⋊C₄	1	4	yes	—
95	C₂×C₈×C₆₇	C₄⋊C₄	1	8	yes	—
96	C₂×C₈×C₆₇	C₂²×C₄	1	4	yes	—
97	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
98	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
99	C₂×C₈×C₆₇	C₂×Q₈	1	4	yes	—
100	C₄⋊C₄×C₆₇	—	2	1	no	—
101	C₄⋊C₄×C₆₇	—	2	1	no	—
102	C₄⋊C₄×C₆₇	—	2	4	no	—
103	C₄⋊C₄×C₆₇	—	2	4	no	—
104	C₄⋊C₄×C₆₇	—	4	2	no	—
105	C₄⋊C₄×C₆₇	—	4	2	no	—
106	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
107	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
108	C₂²⋊C₄×C₆₇	—	2	2	no	—
109	C₂²⋊C₄×C₆₇	—	2	2	no	—
110	C₄²×C₆₇	—	2	2	no	—
111	C₄²×C₆₇	—	2	2	no	—
112	C₂³×C₆₇	—	2	2	no	—
113	C₂³×C₆₇	—	2	2	no	—
114	C₂³×C₆₇	C₄×Q₈	1	2	yes	—
115	C₂³×C₆₇	#121	1	1	yes	characteristic
116	C₂³×C₆₇	#121	1	1	yes	characteristic
117	C₂³×C₆₇	#125	1	2	yes	—
118	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
119	C₂×C₄×C₆₇	—	2	2	no	—
120	C₂×C₄×C₆₇	—	2	2	no	—
121	C₂×C₄×C₆₇	—	4	2	no	—
122	C₂×C₄×C₆₇	—	4	2	no	—
123	C₂×C₄×C₆₇	—	4	4	no	—
124	C₂×C₄×C₆₇	—	8	4	no	—
125	C₂×C₄×C₆₇	—	8	4	no	—
126	C₂×C₄×C₆₇	—	8	4	no	—
127	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
129	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
130	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
131	C₂×C₄×C₆₇	C₄×Q₈	1	2	yes	—
132	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
133	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
134	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
135	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
136	C₂×C₄×C₆₇	#125	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	C₂³×C₄	1	1	yes	characteristic
140	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
141	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
142	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
145	C₈×C₆₇	—	2	8	no	—
146	C₈×C₆₇	—	2	4	no	—
147	C₈×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
148	C₈×C₆₇	C₂×C₄⋊C₄	1	4	yes	—
149	C₂²×C₆₇	—	2	4	no	—
150	C₂²×C₆₇	—	2	4	no	—
151	C₂²×C₆₇	—	2	1	no	—
152	C₂²×C₆₇	—	2	1	no	—
153	C₂²×C₆₇	—	2	1	no	—
154	C₂²×C₆₇	—	2	1	no	—
155	C₂²×C₆₇	#389	1	2	yes	—
156	C₂²×C₆₇	#389	1	2	yes	—
157	C₂²×C₆₇	#472	1	2	yes	—
158	C₂²×C₆₇	#473	1	2	yes	—
159	C₂²×C₆₇	C₂×C₄×Q₈	1	1	yes	characteristic
160	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
161	C₂²×C₆₇	C₂×#125	1	1	yes	characteristic
162	C₄×C₆₇	—	4	2	no	—
163	C₄×C₆₇	—	4	2	no	—
164	C₄×C₆₇	—	8	4	no	—
165	C₄×C₆₇	#389	1	2	yes	—
166	C₄×C₆₇	#389	1	2	yes	—
167	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
168	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
169	C₄×C₆₇	C₂×C₂²⋊Q₈	1	1	yes	characteristic
170	C₄×C₆₇	C₂×C₄⋊Q₈	1	1	yes	characteristic
171	C₂×#1952	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
172	C₂×C₆₇	—	2	1	no	—
173	C₂×C₆₇	—	2	1	no	—
174	C₂×C₆₇	—	2	2	no	—
175	C₂×C₆₇	#1952	1	4	yes	direct product factor
176	C₂×C₆₇	C₂×#389	1	1	yes	characteristic
177	C₂×C₆₇	C₂×#472	1	1	yes	characteristic
178	C₂×C₆₇	C₂×#473	1	1	yes	characteristic
179	C₂²×#108	C₂×C₆₇	1	1	yes	characteristic
180	C₂×#428	C₂×C₆₇	1	2	yes	—
181	C₂²×#107	C₂×C₆₇	1	1	yes	characteristic
182	C₂×#405	C₂×C₆₇	1	1	yes	characteristic
183	#1952	C₂×C₆₇	1	8	yes	direct product factor
184	C₂×#343	C₂×C₆₇	1	2	yes	—
185	C₆₇	C₂×#1952	1	1	yes	characteristic, direct product factor, Sylow
186	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
187	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
188	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
189	C₂×#117	C₂²×C₆₇	1	1	yes	characteristic
190	C₂²×C₄⋊C₄	C₂²×C₆₇	1	2	yes	—
191	C₂×#108	C₄×C₆₇	1	8	yes	complemented
192	C₂×#108	C₂²×C₆₇	1	4	yes	—
193	#428	—	2	4	no	—
194	#428	C₂²×C₆₇	1	8	yes	—
195	C₂×#107	—	2	1	no	—
196	C₂×#107	—	2	1	no	—
197	C₂×#107	—	2	2	no	—
198	C₂×#107	—	2	2	no	—
199	C₂×#107	C₂²×C₆₇	1	4	yes	—
200	C₂×#106	—	2	2	no	—
201	#405	—	2	2	no	—
202	#405	C₂²×C₆₇	1	4	yes	—
203	C₂×#97	—	2	1	no	—
204	C₂×C₄×C₈	—	2	1	no	—
205	#343	C₂²×C₆₇	1	8	yes	—
206	C₂³×C₄	—	2	2	no	—
207	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
208	C₂×M₁₆	—	2	1	no	—
209	C₂×M₁₆	—	2	2	no	—
210	C₂×M₁₆	—	2	4	no	—
211	C₂×M₁₆	—	2	2	no	—
212	C₂×M₁₆	C₂×C₄×C₆₇	1	8	yes	—
213	C₂×M₁₆	Q₈×C₆₇	1	4	yes	—
214	C₂×M₁₆	C₂³×C₆₇	1	4	yes	—
215	C₂×M₁₆	C₂³×C₆₇	1	2	yes	—
216	C₂²×C₈	—	2	1	no	—
217	C₂²×C₈	—	2	2	no	—
218	C₂²×C₈	C₂×C₄×C₆₇	1	4	yes	—
219	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
220	C₂²×C₈	D₄×C₆₇	1	1	yes	characteristic
221	C₂²×C₈	D₄×C₆₇	1	2	yes	—
222	C₂²×C₈	Q₈×C₆₇	1	4	yes	—
223	C₂²×C₈	C₂³×C₆₇	1	2	yes	—
224	#117	—	2	1	no	—
225	#117	—	2	1	no	—
226	#117	D₄×C₆₇	1	2	yes	—
227	#117	C₂³×C₆₇	1	2	yes	—
228	C₂×C₄⋊C₄	—	2	2	no	—
229	C₂×C₄⋊C₄	—	2	2	no	—
230	C₂×C₄⋊C₄	—	2	2	no	—
231	C₂×C₄⋊C₄	—	2	2	no	—
232	C₂×C₄⋊C₄	—	2	2	no	—
233	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
234	C₂×C₄⋊C₄	D₄×C₆₇	1	1	yes	characteristic
235	C₂×C₄⋊C₄	C₂³×C₆₇	1	4	yes	—
236	C₂×C₂²⋊C₄	—	2	1	no	—
237	C₂×C₄²	—	2	1	no	—
238	#108	C₂×C₄×C₆₇	1	16	yes	complemented
239	#107	—	2	4	no	—
240	#107	—	2	4	no	—
241	#107	—	2	8	no	—
242	#106	—	2	8	no	—
243	#97	—	2	4	no	—
244	C₄×C₈	—	2	4	no	—
245	C₂⁴	#41×C₆₇	1	1	yes	characteristic
246	C₂²×C₄	—	2	1	no	—
247	C₂²×C₄	—	2	1	no	—
248	C₂²×C₄	—	2	4	no	—
249	C₂²×C₄	—	4	2	no	—
250	C₂²×C₄	—	4	2	no	—
251	C₂²×C₄	—	8	4	no	—
252	C₂²×C₄	C₂²×C₄×C₆₇	1	2	yes	—
253	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
254	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
255	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
256	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
257	C₂²×C₄	C₂×Q₈×C₆₇	1	2	yes	—
258	C₂²×C₄	C₂×Q₈×C₆₇	1	2	yes	—
259	C₂²×C₄	#41×C₆₇	1	2	yes	—
260	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
261	C₂²×C₄	C₂⁴×C₆₇	1	1	yes	characteristic
262	M₁₆	—	2	8	no	—
263	M₁₆	—	2	4	no	—
264	M₁₆	—	2	4	no	—
265	M₁₆	—	2	2	no	—
266	M₁₆	C₂²×C₄×C₆₇	1	8	yes	—
267	M₁₆	C₂×Q₈×C₆₇	1	4	yes	—
268	C₂×C₈	—	2	8	no	—
269	C₂×C₈	—	2	4	no	—
270	C₂×C₈	—	2	2	no	—
271	C₂×C₈	—	2	4	no	—
272	C₂×C₈	C₄⋊C₄×C₆₇	1	4	yes	—
273	C₂×C₈	C₄⋊C₄×C₆₇	1	4	yes	—
274	C₂×C₈	C₄⋊C₄×C₆₇	1	8	yes	—
275	C₂×C₈	C₂²×C₄×C₆₇	1	4	yes	—
276	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
277	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
278	C₂×C₈	C₂×Q₈×C₆₇	1	4	yes	—
279	C₄⋊C₄	—	2	1	no	—
280	C₄⋊C₄	—	2	1	no	—
281	C₄⋊C₄	—	2	4	no	—
282	C₄⋊C₄	—	2	4	no	—
283	C₄⋊C₄	—	4	2	no	—
284	C₄⋊C₄	—	4	2	no	—
285	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
286	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
287	C₂²⋊C₄	—	2	2	no	—
288	C₂²⋊C₄	—	2	2	no	—
289	C₄²	—	2	2	no	—
290	C₄²	—	2	2	no	—
291	C₂³	—	2	2	no	—
292	C₂³	—	2	2	no	—
293	C₂³	C₄×Q₈×C₆₇	1	2	yes	—
294	C₂³	#121×C₆₇	1	1	yes	characteristic
295	C₂³	#121×C₆₇	1	1	yes	characteristic
296	C₂³	#125×C₆₇	1	2	yes	—
297	C₂³	C₂×#41×C₆₇	1	1	yes	characteristic
298	C₂×C₄	—	2	2	no	—
299	C₂×C₄	—	2	2	no	—
300	C₂×C₄	—	4	2	no	—
301	C₂×C₄	—	4	2	no	—
302	C₂×C₄	—	4	4	no	—
303	C₂×C₄	—	8	4	no	—
304	C₂×C₄	—	8	4	no	—
305	C₂×C₄	—	8	4	no	—
306	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	2	yes	—
307	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	2	yes	—
308	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
309	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
310	C₂×C₄	C₄×Q₈×C₆₇	1	2	yes	—
311	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
312	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
313	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
314	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
315	C₂×C₄	#125×C₆₇	1	2	yes	—
316	C₂×C₄	C₄⋊Q₈×C₆₇	1	2	yes	—
317	C₂×C₄	C₄⋊Q₈×C₆₇	1	2	yes	—
318	C₂×C₄	C₂³×C₄×C₆₇	1	1	yes	characteristic
319	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
320	C₂×C₄	C₂²×D₄×C₆₇	1	1	yes	characteristic
321	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
322	C₂×C₄	C₂²×Q₈×C₆₇	1	1	yes	characteristic
323	C₂×C₄	C₂×#41×C₆₇	1	1	yes	characteristic
324	C₈	—	2	8	no	—
325	C₈	—	2	4	no	—
326	C₈	C₂×C₄⋊C₄×C₆₇	1	4	yes	—
327	C₈	C₂×C₄⋊C₄×C₆₇	1	4	yes	—
328	C₂²	—	2	1	no	—
329	C₂²	—	2	1	no	—
330	C₂²	—	2	1	no	—
331	C₂²	—	2	1	no	—
332	C₂²	—	2	4	no	—
333	C₂²	—	2	4	no	—
334	C₂²	#389×C₆₇	1	2	yes	—
335	C₂²	#389×C₆₇	1	2	yes	—
336	C₂²	#472×C₆₇	1	2	yes	—
337	C₂²	#473×C₆₇	1	2	yes	—
338	C₂²	C₂×C₄×Q₈×C₆₇	1	1	yes	characteristic
339	C₂²	C₂×#121×C₆₇	1	1	yes	characteristic
340	C₂²	C₂×#125×C₆₇	1	1	yes	characteristic
341	C₄	—	4	2	no	—
342	C₄	—	4	2	no	—
343	C₄	—	8	4	no	—
344	C₄	#389×C₆₇	1	2	yes	—
345	C₄	#389×C₆₇	1	2	yes	—
346	C₄	C₂²×C₄⋊C₄×C₆₇	1	1	yes	characteristic
347	C₄	C₂×C₄×D₄×C₆₇	1	1	yes	characteristic
348	C₄	C₂×C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
349	C₄	C₂×C₄⋊Q₈×C₆₇	1	1	yes	characteristic
350	C₂	—	2	1	no	—
351	C₂	—	2	1	no	—
352	C₂	—	2	2	no	—
353	C₂	C₆₇×#1952	1	4	yes	direct product factor
354	C₂	C₂×#389×C₆₇	1	1	yes	characteristic
355	C₂	C₂×#472×C₆₇	1	1	yes	characteristic
356	C₂	C₂×#473×C₆₇	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³×C₆₇	#121
commutator	C₂×C₄	C₂³×C₄×C₆₇
Frattini, cosocle	C₂²×C₄	C₂⁴×C₆₇
prime radical	C₂⁴×C₆₇	#41
LCS	G ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂³×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
5. C₆₇×#1952	C₂	direct (N × H)
12. C₂×#108×C₆₇	C₄	semidirect
59. #108×C₆₇	C₂×C₄	semidirect
171. C₂×#1952	C₆₇	direct (N × H)
175. C₂×C₆₇	#1952	direct (N × H)
183. #1952	C₂×C₆₇	direct (N × H)
185. C₆₇	C₂×#1952	direct (N × H)
191. C₂×#108	C₄×C₆₇	semidirect
238. #108	C₂×C₄×C₆₇	semidirect
353. C₂	C₆₇×#1952	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×#108×C₆₇	2
C₂×#428×C₆₇	2
C₂²×#107×C₆₇	2
C₂×#405×C₆₇	2
C₆₇×#1952	2
C₂×#343×C₆₇	2
C₂×#1952	67

Subgroups — C2×C67×#1952 #30700431

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₆₇×#1952 #30700431