Subgroups — C₂×#22574903 #31763260

Order 17152.

6726 conjugacy classes of subgroups.

The subgroup lattice has 404 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#22574903	C₂	1	32	yes	maximal, direct product factor
2	C₂×#16864146	C₂	1	3	yes	maximal, complemented
3	C₂×#16864115	C₂	1	6	yes	maximal, complemented
4	C₂×#16864077	C₂	1	6	yes	maximal, complemented
5	C₂×#16864010	C₂	1	6	yes	maximal, complemented
6	C₂×#16863981	C₂	1	6	yes	maximal, complemented
7	C₂×#16863925	C₂	1	3	yes	maximal, complemented
8	C₂×H(3,𝔽₄)×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	#16864146	C₂²	1	48	yes	complemented
10	#16864115	C₂²	1	96	yes	complemented
11	#16864077	C₂²	1	96	yes	complemented
12	#16864010	C₂²	1	96	yes	complemented
13	#16863981	C₂²	1	96	yes	complemented
14	C₂×#14524041	C₂²	1	6	yes	complemented
15	#16863925	C₂²	1	48	yes	complemented
16	C₂×#14524037	C₂²	1	2	yes	complemented
17	C₂×#14524036	C₂²	1	6	yes	complemented
18	C₂×#14524036	C₂²	1	6	yes	complemented
19	C₂×#14524036	C₂²	1	6	yes	complemented
20	C₂×#14524036	C₂²	1	6	yes	complemented
21	C₂×#14524035	C₂²	1	3	yes	complemented
22	C₂×#14524030	C₂²	1	6	yes	—
23	C₂×#14524029	C₂²	1	6	yes	complemented
24	C₂×#14524025	C₂²	1	6	yes	complemented
25	C₂×#14524024	C₂²	1	6	yes	—
26	C₂×#14524024	C₂²	1	6	yes	—
27	C₂×#14524020	C₂²	1	6	yes	complemented
28	C₂×#14524020	C₂²	1	6	yes	complemented
29	C₂×#14524020	C₂²	1	6	yes	complemented
30	C₂×#14524019	C₂²	1	3	yes	complemented
31	C₂×#14524015	C₂²	1	6	yes	—
32	C₂×#14524014	C₂²	1	3	yes	—
33	C₂×#14524012	C₂²	1	2	yes	complemented
34	C₂×Q₈×Dic₆₇	C₂²	1	3	yes	complemented
35	C₂×C₄×Dic₁₃₄	C₂²	1	6	yes	complemented
36	C₂×D₄×Dic₆₇	C₂²	1	3	yes	—
37	C₂×D₄×Dic₆₇	C₂²	1	6	yes	—
38	C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	1	6	yes	complemented
39	C₂×#14523999	C₂²	1	6	yes	complemented
40	C₂×#14523999	C₂²	1	6	yes	complemented
41	C₂²×C₂²⋊Dic₆₇	C₂²	1	6	yes	complemented
42	C₂×C₄²×D₆₇	C₂²	1	1	yes	characteristic, complemented
43	H(3,𝔽₄)×C₆₇	C₂²	1	16	yes	complemented
44	C₂×#124×C₆₇	C₂²	1	3	yes	—
45	C₂×#124×C₆₇	C₂²	1	6	yes	—
46	C₂×#120×C₆₇	C₂²	1	6	yes	—
47	C₂²×Dic₁₃₄	C₂³	1	6	yes	—
48	C₂²×C₂²⋊D₆₇	C₂³	1	6	yes	—
49	C₂³×Dic₆₇	C₂³	1	6	yes	—
50	C₂³×Dic₆₇	C₂³	1	6	yes	—
51	C₂²×C₄×D₆₇	C₂³	1	3	yes	—
52	#14524041	C₂³	1	48	yes	complemented
53	#14524037	C₂³	1	16	yes	complemented
54	#14524036	C₂³	1	48	yes	complemented
55	#14524036	C₂³	1	48	yes	complemented
56	#14524036	C₂³	1	48	yes	complemented
57	#14524036	C₂³	1	48	yes	complemented
58	#14524035	C₂³	1	24	yes	complemented
59	#14524030	C₂³	1	48	yes	—
60	#14524029	C₂³	1	48	yes	complemented
61	#14524025	C₂³	1	48	yes	complemented
62	#14524024	C₂³	1	48	yes	—
63	#14524024	C₂³	1	48	yes	—
64	#14524020	C₂³	1	48	yes	complemented
65	#14524020	C₂³	1	48	yes	complemented
66	#14524020	C₂³	1	48	yes	complemented
67	#14524019	C₂³	1	24	yes	complemented
68	#14524015	C₂³	1	48	yes	—
69	#14524014	C₂³	1	24	yes	—
70	#14524012	C₂³	1	16	yes	complemented
71	Q₈×Dic₆₇	C₂³	1	24	yes	complemented
72	C₄×Dic₁₃₄	C₂³	1	48	yes	complemented
73	D₄×Dic₆₇	C₂³	1	24	yes	—
74	D₄×Dic₆₇	C₂³	1	48	yes	—
75	(C₂²⋊D₆₇)⋊C₄	C₂³	1	48	yes	complemented
76	#14523999	C₂³	1	48	yes	complemented
77	#14523999	C₂³	1	48	yes	complemented
78	C₂×C₄⋊Dic₆₇	C₂³	1	6	yes	—
79	C₂×C₄⋊Dic₆₇	C₂³	1	3	yes	—
80	C₂×C₄⋊Dic₆₇	C₂³	1	3	yes	—
81	C₂×Dic₆₇⋊C₄	C₂³	1	6	yes	—
82	C₂×Dic₆₇⋊C₄	C₂³	1	6	yes	—
83	C₂×Dic₆₇⋊C₄	C₂³	1	6	yes	—
84	C₂×Dic₆₇⋊C₄	C₂³	1	6	yes	—
85	C₂×Dic₆₇⋊C₄	C₂³	1	6	yes	—
86	C₂×C₂²⋊Dic₆₇	C₂³	1	6	yes	—
87	C₂×C₂²⋊Dic₆₇	C₂³	1	6	yes	—
88	C₂×C₂²⋊Dic₆₇	C₂³	1	6	yes	—
89	C₂×C₂²⋊Dic₆₇	C₂³	1	6	yes	—
90	C₂×C₂²⋊Dic₆₇	C₂³	1	6	yes	—
91	C₂×C₂²⋊Dic₆₇	C₂³	1	48	yes	complemented
92	C₂×(C₂×D₆₇)⋊C₄	C₂³	1	6	yes	—
93	C₂×C₄×Dic₆₇	C₂³	1	3	yes	—
94	C₂×C₄×Dic₆₇	C₂³	1	6	yes	—
95	C₂×C₄×Dic₆₇	C₂³	1	6	yes	—
96	C₄²×D₆₇	C₂³	1	8	yes	complemented
97	C₂⁵×C₆₇	C₂³	1	2	yes	—
98	C₂²×Q₈×C₆₇	C₂³	1	3	yes	—
99	C₂²×D₄×C₆₇	C₂³	1	3	yes	—
100	C₂²×D₄×C₆₇	C₂³	1	6	yes	—
101	#124×C₆₇	C₂³	1	48	yes	—
102	#124×C₆₇	C₂³	1	24	yes	—
103	#120×C₆₇	C₂³	1	48	yes	—
104	C₂×C₂²⋊C₄×C₆₇	C₂³	1	6	yes	—
105	C₂×C₂²⋊C₄×C₆₇	C₂³	1	6	yes	—
106	C₂×C₂²⋊C₄×C₆₇	C₂³	1	6	yes	—
107	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
108	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
109	C₂³×D₆₇	C₂⁴	1	1	yes	characteristic
110	C₂×Dic₁₃₄	—	4	12	no	—
111	C₂×Dic₁₃₄	C₂⁴	1	24	yes	—
112	C₂×C₂²⋊D₆₇	—	4	12	no	—
113	C₂×C₂²⋊D₆₇	C₂⁴	1	24	yes	—
114	C₂²×Dic₆₇	—	4	12	no	—
115	C₂²×Dic₆₇	—	4	12	no	—
116	C₂²×Dic₆₇	C₂⁴	1	3	yes	—
117	C₂²×Dic₆₇	C₂⁴	1	6	yes	—
118	C₂²×Dic₆₇	C₂⁴	1	6	yes	—
119	C₂²×Dic₆₇	C₂⁴	1	24	yes	—
120	C₂²×Dic₆₇	C₂⁴	1	24	yes	—
121	C₂×C₄×D₆₇	—	4	6	no	—
122	C₂×C₄×D₆₇	C₂⁴	1	12	yes	—
123	C₄⋊Dic₆₇	C₂⁴	1	24	yes	—
124	C₄⋊Dic₆₇	C₂⁴	1	12	yes	—
125	C₄⋊Dic₆₇	C₂⁴	1	12	yes	—
126	Dic₆₇⋊C₄	C₂⁴	1	24	yes	—
127	Dic₆₇⋊C₄	C₂⁴	1	24	yes	—
128	Dic₆₇⋊C₄	C₂⁴	1	24	yes	—
129	Dic₆₇⋊C₄	C₂⁴	1	24	yes	—
130	Dic₆₇⋊C₄	C₂⁴	1	24	yes	—
131	C₂²⋊Dic₆₇	C₂⁴	1	24	yes	—
132	C₂²⋊Dic₆₇	C₂⁴	1	24	yes	—
133	C₂²⋊Dic₆₇	C₂⁴	1	24	yes	—
134	C₂²⋊Dic₆₇	C₂⁴	1	24	yes	—
135	C₂²⋊Dic₆₇	C₂⁴	1	24	yes	—
136	(C₂×D₆₇)⋊C₄	C₂⁴	1	24	yes	—
137	C₄×Dic₆₇	C₂⁴	1	12	yes	—
138	C₄×Dic₆₇	C₂⁴	1	24	yes	—
139	C₄×Dic₆₇	C₂⁴	1	24	yes	—
140	C₂⁴×C₆₇	—	4	12	no	—
141	C₂⁴×C₆₇	C₂⁴	1	6	yes	—
142	C₂⁴×C₆₇	C₂⁴	1	8	yes	—
143	C₂×Q₈×C₆₇	—	4	6	no	—
144	C₂×Q₈×C₆₇	C₂⁴	1	12	yes	—
145	C₂×D₄×C₆₇	—	4	6	no	—
146	C₂×D₄×C₆₇	—	4	12	no	—
147	C₂×D₄×C₆₇	C₂⁴	1	12	yes	—
148	C₂×D₄×C₆₇	C₂⁴	1	24	yes	—
149	C₂²×C₄×C₆₇	C₂⁴	1	6	yes	—
150	C₂²×C₄×C₆₇	C₂⁴	1	3	yes	—
151	C₂²⋊C₄×C₆₇	C₂⁴	1	24	yes	—
152	C₂²⋊C₄×C₆₇	C₂⁴	1	24	yes	—
153	C₂²⋊C₄×C₆₇	C₂⁴	1	24	yes	—
154	C₄²×C₆₇	C₂⁴	1	4	yes	—
155	C₄²×C₆₇	C₂⁴	1	8	yes	—
156	C₂³×C₆₇	—	2	12	no	—
157	C₂³×C₆₇	—	2	12	no	—
158	C₂³×C₆₇	—	2	12	no	—
159	C₂³×C₆₇	—	4	24	no	—
160	C₂³×C₆₇	—	8	16	no	—
161	C₂³×C₆₇	C₂⁵	1	12	yes	—
162	C₂³×C₆₇	C₂⁵	1	1	yes	characteristic
163	C₂²×D₆₇	—	2	6	no	—
164	C₂²×D₆₇	C₂⁵	1	2	yes	—
165	Q₈×C₆₇	—	4	12	no	—
166	D₄×C₆₇	—	4	24	no	—
167	D₄×C₆₇	—	4	12	no	—
168	C₂×C₄×C₆₇	—	2	6	no	—
169	C₂×C₄×C₆₇	—	2	12	no	—
170	C₂×C₄×C₆₇	C₂⁵	1	12	yes	—
171	C₂×C₄×C₆₇	C₂⁵	1	6	yes	—
172	C₂²⋊D₆₇	—	4	24	no	—
173	C₂×Dic₆₇	—	2	6	no	—
174	C₂×Dic₆₇	—	2	12	no	—
175	C₂×Dic₆₇	—	2	12	no	—
176	C₂×Dic₆₇	—	4	24	no	—
177	C₂×Dic₆₇	—	4	24	no	—
178	C₂×Dic₆₇	C₂⁵	1	6	yes	—
179	C₂×Dic₆₇	C₂⁵	1	12	yes	—
180	C₂×Dic₆₇	C₂⁵	1	12	yes	—
181	C₄×D₆₇	—	4	12	no	—
182	Dic₁₃₄	—	4	24	no	—
183	C₂²×C₆₇	—	2	12	no	—
184	C₂²×C₆₇	—	2	12	no	—
185	C₂²×C₆₇	—	2	12	no	—
186	C₂²×C₆₇	—	4	24	no	—
187	C₂²×C₆₇	—	8	16	no	—
188	C₂²×C₆₇	#585	1	6	yes	—
189	C₂²×C₆₇	C₂⁶	1	1	yes	characteristic
190	C₂×D₆₇	—	2	6	no	—
191	C₂×D₆₇	—	4	4	no	—
192	C₄×C₆₇	—	2	12	no	—
193	C₄×C₆₇	—	2	6	no	—
194	Dic₆₇	—	2	12	no	—
195	Dic₆₇	—	2	12	no	—
196	Dic₆₇	—	2	6	no	—
197	C₂×#3568	—	67	1	no	maximal, Sylow
198	C₂×C₆₇	—	4	12	no	—
199	C₂×C₆₇	#3568	1	4	yes	complemented
200	C₂×C₆₇	C₂×#585	1	3	yes	—
201	D₆₇	—	4	2	no	—
202	#3568	—	67	32	no	—
203	C₂×#563	—	67	3	no	—
204	C₂×H(3,𝔽₄)	D₆₇	1	1	yes	characteristic, complemented
205	C₂×#556	—	67	6	no	—
206	C₂×#551	—	67	6	no	—
207	C₂×#542	—	67	6	no	—
208	C₂×#538	—	67	6	no	—
209	C₂×#529	—	67	3	no	—
210	C₆₇	C₂×#3568	1	1	yes	characteristic, complemented, Sylow
211	#563	—	67	48	no	—
212	H(3,𝔽₄)	C₂×D₆₇	1	16	yes	complemented
213	#556	—	67	96	no	—
214	#551	—	67	96	no	—
215	#542	—	67	96	no	—
216	#538	—	67	96	no	—
217	C₂×C₄⋊Q₈	—	67	6	no	—
218	#529	—	67	48	no	—
219	C₂×#126	—	67	6	no	—
220	C₂×#126	—	67	6	no	—
221	C₂×#126	—	67	6	no	—
222	C₂×#126	—	67	6	no	—
223	C₂×#126	—	67	2	no	—
224	C₂×#125	—	67	3	no	—
225	C₂×#124	—	67	6	no	—
226	C₂×#124	—	67	6	no	—
227	C₂×#124	C₂×D₆₇	1	3	yes	—
228	C₂×#124	C₂×D₆₇	1	6	yes	—
229	C₂×#123	—	67	6	no	—
230	C₂×#123	—	67	6	no	—
231	C₂×#123	—	67	6	no	—
232	C₂×C₂²⋊Q₈	—	67	3	no	—
233	C₂×C₂²⋊Q₈	—	67	6	no	—
234	C₂×C₂²⋊Q₈	—	67	6	no	—
235	C₂×C₂²⋊Q₈	—	67	6	no	—
236	C₂×#121	—	67	3	no	—
237	C₂×#121	—	67	6	no	—
238	C₂×#120	—	67	2	no	—
239	C₂×#120	C₂×D₆₇	1	6	yes	—
240	C₂×C₄×Q₈	—	67	3	no	—
241	C₂×C₄×Q₈	—	67	6	no	—
242	C₂×C₄×D₄	—	67	3	no	—
243	C₂×C₄×D₄	—	67	6	no	—
244	C₂×C₄×D₄	—	67	6	no	—
245	C₂×#117	—	67	6	no	—
246	C₂×#117	—	67	6	no	—
247	C₂²×C₂²⋊C₄	—	67	6	no	—
248	C₂²×C₄²	—	67	1	no	—
249	C₂⁵	C₂²×D₆₇	1	2	yes	—
250	C₂²×Q₈	—	67	6	no	—
251	C₂²×Q₈	C₂²×D₆₇	1	3	yes	—
252	C₂²×D₄	—	67	6	no	—
253	C₂²×D₄	C₂²×D₆₇	1	3	yes	—
254	C₂²×D₄	C₂²×D₆₇	1	6	yes	—
255	C₂³×C₄	—	67	6	no	—
256	C₂³×C₄	—	67	6	no	—
257	C₂³×C₄	—	67	3	no	—
258	C₄⋊Q₈	—	67	48	no	—
259	#126	—	67	48	no	—
260	#126	—	67	48	no	—
261	#126	—	67	48	no	—
262	#126	—	67	48	no	—
263	#126	—	67	16	no	—
264	#125	—	67	24	no	—
265	#124	—	67	48	no	—
266	#124	—	67	48	no	—
267	#124	C₂²×D₆₇	1	24	yes	—
268	#124	C₂²×D₆₇	1	48	yes	—
269	#123	—	67	48	no	—
270	#123	—	67	48	no	—
271	#123	—	67	48	no	—
272	C₂²⋊Q₈	—	67	24	no	—
273	C₂²⋊Q₈	—	67	48	no	—
274	C₂²⋊Q₈	—	67	48	no	—
275	C₂²⋊Q₈	—	67	48	no	—
276	#121	—	67	24	no	—
277	#121	—	67	48	no	—
278	#120	—	67	16	no	—
279	#120	C₂²×D₆₇	1	48	yes	—
280	C₄×Q₈	—	67	24	no	—
281	C₄×Q₈	—	67	48	no	—
282	C₄×D₄	—	67	24	no	—
283	C₄×D₄	—	67	48	no	—
284	C₄×D₄	—	67	48	no	—
285	#117	—	67	48	no	—
286	#117	—	67	48	no	—
287	C₂×C₄⋊C₄	—	67	6	no	—
288	C₂×C₄⋊C₄	—	67	6	no	—
289	C₂×C₄⋊C₄	—	67	6	no	—
290	C₂×C₄⋊C₄	—	67	6	no	—
291	C₂×C₄⋊C₄	—	67	3	no	—
292	C₂×C₄⋊C₄	—	67	6	no	—
293	C₂×C₄⋊C₄	—	67	3	no	—
294	C₂×C₄⋊C₄	—	67	6	no	—
295	C₂×C₂²⋊C₄	—	67	6	no	—
296	C₂×C₂²⋊C₄	—	67	6	no	—
297	C₂×C₂²⋊C₄	—	67	6	no	—
298	C₂×C₂²⋊C₄	—	67	6	no	—
299	C₂×C₂²⋊C₄	—	67	48	no	—
300	C₂×C₂²⋊C₄	—	67	6	no	—
301	C₂×C₂²⋊C₄	—	67	6	no	—
302	C₂×C₂²⋊C₄	C₂²×D₆₇	1	6	yes	—
303	C₂×C₂²⋊C₄	C₂²×D₆₇	1	6	yes	—
304	C₂×C₂²⋊C₄	C₂²×D₆₇	1	6	yes	—
305	C₂×C₄²	—	67	6	no	—
306	C₂×C₄²	—	67	3	no	—
307	C₂×C₄²	—	67	6	no	—
308	C₂×C₄²	—	67	8	no	—
309	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
310	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
311	C₂⁴	—	4	12	no	—
312	C₂⁴	—	67	1	no	—
313	C₂⁴	C₂³×D₆₇	1	6	yes	—
314	C₂⁴	C₂³×D₆₇	1	8	yes	—
315	C₂×Q₈	—	4	6	no	—
316	C₂×Q₈	—	268	12	no	—
317	C₂×Q₈	—	67	24	no	—
318	C₂×Q₈	C₂³×D₆₇	1	12	yes	—
319	C₂×D₄	—	4	6	no	—
320	C₂×D₄	—	4	12	no	—
321	C₂×D₄	—	268	12	no	—
322	C₂×D₄	—	67	24	no	—
323	C₂×D₄	C₂³×D₆₇	1	12	yes	—
324	C₂×D₄	C₂³×D₆₇	1	24	yes	—
325	C₂²×C₄	—	268	6	no	—
326	C₂²×C₄	—	268	12	no	—
327	C₂²×C₄	—	268	12	no	—
328	C₂²×C₄	—	67	24	no	—
329	C₂²×C₄	—	67	24	no	—
330	C₂²×C₄	—	67	12	no	—
331	C₂²×C₄	—	67	3	no	—
332	C₂²×C₄	—	67	6	no	—
333	C₂²×C₄	—	67	6	no	—
334	C₂²×C₄	C₂³×D₆₇	1	6	yes	—
335	C₂²×C₄	C₂³×D₆₇	1	3	yes	—
336	C₄⋊C₄	—	67	24	no	—
337	C₄⋊C₄	—	67	24	no	—
338	C₄⋊C₄	—	67	24	no	—
339	C₄⋊C₄	—	67	24	no	—
340	C₄⋊C₄	—	67	12	no	—
341	C₄⋊C₄	—	67	24	no	—
342	C₄⋊C₄	—	67	12	no	—
343	C₄⋊C₄	—	67	24	no	—
344	C₂²⋊C₄	—	67	24	no	—
345	C₂²⋊C₄	—	67	24	no	—
346	C₂²⋊C₄	—	67	24	no	—
347	C₂²⋊C₄	—	67	24	no	—
348	C₂²⋊C₄	—	67	24	no	—
349	C₂²⋊C₄	—	67	24	no	—
350	C₂²⋊C₄	C₂³×D₆₇	1	24	yes	—
351	C₂²⋊C₄	C₂³×D₆₇	1	24	yes	—
352	C₂²⋊C₄	C₂³×D₆₇	1	24	yes	—
353	C₄²	—	67	12	no	—
354	C₄²	—	67	24	no	—
355	C₄²	—	67	24	no	—
356	C₄²	C₂³×D₆₇	1	4	yes	—
357	C₄²	C₂³×D₆₇	1	8	yes	—
358	C₂³	—	2	12	no	—
359	C₂³	—	2	12	no	—
360	C₂³	—	2	12	no	—
361	C₂³	—	4	24	no	—
362	C₂³	—	8	16	no	—
363	C₂³	—	67	2	no	—
364	C₂³	—	134	6	no	—
365	C₂³	C₂⁴×D₆₇	1	12	yes	—
366	C₂³	C₂⁴×D₆₇	1	1	yes	characteristic
367	Q₈	—	4	12	no	—
368	Q₈	—	268	24	no	—
369	D₄	—	4	12	no	—
370	D₄	—	4	24	no	—
371	D₄	—	268	24	no	—
372	C₂×C₄	—	2	6	no	—
373	C₂×C₄	—	2	12	no	—
374	C₂×C₄	—	268	12	no	—
375	C₂×C₄	—	268	24	no	—
376	C₂×C₄	—	268	24	no	—
377	C₂×C₄	—	67	6	no	—
378	C₂×C₄	—	67	12	no	—
379	C₂×C₄	—	67	12	no	—
380	C₂×C₄	—	134	6	no	—
381	C₂×C₄	—	134	12	no	—
382	C₂×C₄	—	134	12	no	—
383	C₂×C₄	C₂⁴×D₆₇	1	12	yes	—
384	C₂×C₄	C₂⁴×D₆₇	1	6	yes	—
385	C₂²	—	2	12	no	—
386	C₂²	—	2	12	no	—
387	C₂²	—	2	12	no	—
388	C₂²	—	4	24	no	—
389	C₂²	—	8	16	no	—
390	C₂²	—	268	4	no	—
391	C₂²	—	134	6	no	—
392	C₂²	#16864231	1	6	yes	—
393	C₂²	C₂⁵×D₆₇	1	1	yes	characteristic
394	C₄	—	2	6	no	—
395	C₄	—	2	12	no	—
396	C₄	—	134	6	no	—
397	C₄	—	134	12	no	—
398	C₄	—	134	12	no	—
399	C₂	—	4	12	no	—
400	C₂	—	268	2	no	—
401	C₂	#22574903	1	4	yes	direct product factor
402	C₂	C₂×#16864231	1	3	yes	—

	subgroup	G/H
center	C₂³	C₂⁴×D₆₇
commutator, cosocle	C₂²×C₆₇	C₂⁶
Frattini	C₂²	C₂⁵×D₆₇
Fitting	C₂×H(3,𝔽₄)×C₆₇	C₂
socle	C₂³×C₆₇	C₂⁵
hypercenter	C₂×H(3,𝔽₄)	D₆₇
hypocenter	C₆₇	C₂×#3568
LCS	G ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×H(3,𝔽₄)

Complements

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

N	H ≅ G/N	type
1. #22574903	C₂	direct (N × H)
2. C₂×#16864146	C₂	semidirect
3. C₂×#16864115	C₂	semidirect
4. C₂×#16864077	C₂	semidirect
5. C₂×#16864010	C₂	semidirect
6. C₂×#16863981	C₂	semidirect
7. C₂×#16863925	C₂	semidirect
8. C₂×H(3,𝔽₄)×C₆₇	C₂	semidirect
9. #16864146	C₂²	semidirect
10. #16864115	C₂²	semidirect
11. #16864077	C₂²	semidirect
12. #16864010	C₂²	semidirect
13. #16863981	C₂²	semidirect
14. C₂×#14524041	C₂²	semidirect
15. #16863925	C₂²	semidirect
16. C₂×#14524037	C₂²	semidirect
17. C₂×#14524036	C₂²	semidirect
18. C₂×#14524036	C₂²	semidirect
19. C₂×#14524036	C₂²	semidirect
20. C₂×#14524036	C₂²	semidirect
21. C₂×#14524035	C₂²	semidirect
23. C₂×#14524029	C₂²	semidirect
24. C₂×#14524025	C₂²	semidirect
27. C₂×#14524020	C₂²	semidirect
28. C₂×#14524020	C₂²	semidirect
29. C₂×#14524020	C₂²	semidirect
30. C₂×#14524019	C₂²	semidirect
33. C₂×#14524012	C₂²	semidirect
34. C₂×Q₈×Dic₆₇	C₂²	semidirect
35. C₂×C₄×Dic₁₃₄	C₂²	semidirect
38. C₂×(C₂²⋊D₆₇)⋊C₄	C₂²	semidirect
39. C₂×#14523999	C₂²	semidirect
40. C₂×#14523999	C₂²	semidirect
41. C₂²×C₂²⋊Dic₆₇	C₂²	semidirect
42. C₂×C₄²×D₆₇	C₂²	semidirect
43. H(3,𝔽₄)×C₆₇	C₂²	semidirect
52. #14524041	C₂³	semidirect
53. #14524037	C₂³	semidirect
54. #14524036	C₂³	semidirect
55. #14524036	C₂³	semidirect
56. #14524036	C₂³	semidirect
57. #14524036	C₂³	semidirect
58. #14524035	C₂³	semidirect
60. #14524029	C₂³	semidirect
61. #14524025	C₂³	semidirect
64. #14524020	C₂³	semidirect
65. #14524020	C₂³	semidirect
66. #14524020	C₂³	semidirect
67. #14524019	C₂³	semidirect
70. #14524012	C₂³	semidirect
71. Q₈×Dic₆₇	C₂³	semidirect
72. C₄×Dic₁₃₄	C₂³	semidirect
75. (C₂²⋊D₆₇)⋊C₄	C₂³	semidirect
76. #14523999	C₂³	semidirect
77. #14523999	C₂³	semidirect
91. C₂×C₂²⋊Dic₆₇	C₂³	semidirect
96. C₄²×D₆₇	C₂³	semidirect
199. C₂×C₆₇	#3568	semidirect
204. C₂×H(3,𝔽₄)	D₆₇	semidirect
210. C₆₇	C₂×#3568	semidirect
212. H(3,𝔽₄)	C₂×D₆₇	semidirect
401. C₂	#22574903	direct (N × H)

Maximal subgroups

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

subgroup	index
#22574903	2
C₂×#16864146	2
C₂×#16864115	2
C₂×#16864077	2
C₂×#16864010	2
C₂×#16863981	2
C₂×#16863925	2
C₂×H(3,𝔽₄)×C₆₇	2
C₂×#3568	67

Subgroups — C2×#22574903 #31763260

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22574903 #31763260