Subgroups — C₂²×C₄×#10625335 #27080284

Order 12032.

3262 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂³×#10625335	C₂	1	1	yes	maximal, characteristic
2	C₂²×C₄×Dic₉₄	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×C₄×#10625335	C₂	1	24	yes	maximal, direct product factor
4	C₂²×#13093955	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂²×#13093947	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#13093945	C₂	1	1	yes	maximal, characteristic
7	C₂²×C₄×C₄₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic
9	C₂³×Dic₉₄	C₂²	1	1	yes	characteristic
10	C₂²×#10625335	C₄	1	16	yes	direct product factor
11	C₂²×#10625335	C₂²	1	12	yes	—
12	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
13	C₂³×C₄₇⋊C₈	C₂²	1	1	yes	characteristic
14	C₂×C₄×Dic₉₄	—	2	6	no	—
15	C₂×C₄×Dic₉₄	C₂²	1	12	yes	complemented
16	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
17	C₂²×Dic₄₇⋊C₄	—	2	1	no	—
18	C₂²×C₄×Dic₄₇	—	2	1	no	—
19	C₄×#10625335	C₂²	1	64	yes	direct product factor
20	C₂×#13093955	C₂²	1	12	yes	complemented
21	C₂×#13093947	C₂²	1	12	yes	complemented
22	C₂×#13093945	C₂²	1	12	yes	—
23	C₂×C₄×C₄₇⋊C₈	C₂²	1	12	yes	complemented
24	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
25	C₂⁴×C₄×C₄₇	—	2	1	no	—
26	C₂×C₄×D₄×C₄₇	—	2	6	no	—
27	C₂×C₄×D₄×C₄₇	C₂²	1	12	yes	—
28	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
29	C₂²×C₂²⋊C₄×C₄₇	—	2	1	no	—
30	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
31	C₂²×Dic₉₄	—	2	3	no	—
32	C₂²×Dic₉₄	—	2	4	no	—
33	C₂²×Dic₉₄	C₂×C₄	1	8	yes	complemented
34	C₂²×Dic₉₄	C₂³	1	6	yes	—
35	C₂³×Dic₄₇	—	2	1	no	—
36	C₂³×Dic₄₇	—	2	1	no	—
37	C₂×#10625335	C₂×C₄	1	96	yes	direct product factor
38	C₂×#10625335	C₂³	1	16	yes	—
39	C₂²×C₄₇⋊C₈	—	2	4	no	—
40	C₂²×C₄₇⋊C₈	C₂×C₄	1	8	yes	complemented
41	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
42	C₂²×C₄₇⋊C₈	C₂³	1	6	yes	—
43	C₄×Dic₉₄	—	2	24	no	—
44	C₄×Dic₉₄	C₂³	1	16	yes	complemented
45	C₂×C₄⋊Dic₄₇	—	2	3	no	—
46	C₂×C₄⋊Dic₄₇	C₂³	1	6	yes	—
47	C₂×Dic₄₇⋊C₄	—	2	12	no	—
48	C₂×C₄×Dic₄₇	—	2	12	no	—
49	#13093955	C₂³	1	16	yes	complemented
50	#13093947	C₂³	1	16	yes	complemented
51	#13093945	C₂³	1	16	yes	—
52	C₄×C₄₇⋊C₈	C₂³	1	16	yes	complemented
53	C₂⁵×C₄₇	—	2	1	no	—
54	C₂²×D₄×C₄₇	—	2	3	no	—
55	C₂²×D₄×C₄₇	—	2	4	no	—
56	C₂²×D₄×C₄₇	C₂×C₄	1	8	yes	—
57	C₂²×D₄×C₄₇	C₂³	1	6	yes	—
58	C₂³×C₄×C₄₇	—	2	1	no	—
59	C₂³×C₄×C₄₇	—	2	12	no	—
60	C₂³×C₄×C₄₇	—	4	8	no	—
61	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
62	C₂³×C₄×C₄₇	D₄	1	1	yes	characteristic
63	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
64	C₄×D₄×C₄₇	—	2	24	no	—
65	C₄×D₄×C₄₇	C₂³	1	16	yes	—
66	C₂×C₄⋊C₄×C₄₇	—	2	3	no	—
67	C₂×C₄⋊C₄×C₄₇	C₂³	1	6	yes	—
68	C₂×C₂²⋊C₄×C₄₇	—	2	12	no	—
69	C₂×C₄²×C₄₇	D₄	1	6	yes	—
70	C₂×C₄²×C₄₇	C₂³	1	6	yes	—
71	C₂⁴×C₄₇	—	2	8	no	—
72	C₂⁴×C₄₇	—	2	6	no	—
73	C₂⁴×C₄₇	—	4	4	no	—
74	C₂⁴×C₄₇	—	4	4	no	—
75	C₂⁴×C₄₇	C₂×D₄	1	1	yes	characteristic
76	C₂×D₄×C₄₇	—	2	24	no	—
77	C₂×D₄×C₄₇	—	2	6	no	—
78	C₂×D₄×C₄₇	—	2	12	no	—
79	C₂×D₄×C₄₇	C₂²×C₄	1	24	yes	—
80	C₂×D₄×C₄₇	C₂⁴	1	4	yes	—
81	C₂²×C₄×C₄₇	—	2	4	no	—
82	C₂²×C₄×C₄₇	—	2	6	no	—
83	C₂²×C₄×C₄₇	—	2	16	no	—
84	C₂²×C₄×C₄₇	—	4	4	no	—
85	C₂²×C₄×C₄₇	—	4	48	no	—
86	C₂²×C₄×C₄₇	SD₁₆	1	8	yes	complemented
87	C₂²×C₄×C₄₇	C₂²×C₄	1	4	yes	—
88	C₂²×C₄×C₄₇	C₂×D₄	1	6	yes	—
89	C₂²×C₄×C₄₇	C₂×D₄	1	3	yes	—
90	C₂²×C₄×C₄₇	C₂×D₄	1	6	yes	—
91	C₂²×C₄×C₄₇	#41	1	4	yes	—
92	C₂²×C₄×C₄₇	C₂⁴	1	3	yes	—
93	C₂²×Dic₄₇	—	2	8	no	—
94	C₂²×Dic₄₇	—	2	6	no	—
95	C₂²×Dic₄₇	—	2	6	no	—
96	C₂²×Dic₄₇	—	4	4	no	—
97	C₂×Dic₉₄	—	2	24	no	—
98	C₂×Dic₉₄	—	2	6	no	—
99	C₂×Dic₉₄	—	2	12	no	—
100	C₂×Dic₉₄	C₂²×C₄	1	24	yes	complemented
101	C₂×Dic₉₄	C₂⁴	1	4	yes	—
102	C₄⋊C₄×C₄₇	—	2	6	no	—
103	C₄⋊C₄×C₄₇	C₂⁴	1	4	yes	—
104	C₂²⋊C₄×C₄₇	—	2	16	no	—
105	C₄²×C₄₇	C₂×D₄	1	12	yes	—
106	C₄²×C₄₇	C₂⁴	1	4	yes	—
107	#10625335	C₂²×C₄	1	64	yes	direct product factor
108	C₄⋊Dic₄₇	—	2	6	no	—
109	C₄⋊Dic₄₇	C₂⁴	1	4	yes	—
110	Dic₄₇⋊C₄	—	2	16	no	—
111	C₄×Dic₄₇	—	2	16	no	—
112	C₂×C₄₇⋊C₈	—	2	12	no	—
113	C₂×C₄₇⋊C₈	C₂²×C₄	1	24	yes	complemented
114	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
115	C₂×C₄₇⋊C₈	C₂⁴	1	4	yes	—
116	C₂³×C₄₇	—	2	24	no	—
117	C₂³×C₄₇	—	2	4	no	—
118	C₂³×C₄₇	—	4	12	no	—
119	C₂³×C₄₇	—	4	12	no	—
120	C₂³×C₄₇	—	4	32	no	—
121	C₂³×C₄₇	C₄×D₄	1	4	yes	—
122	C₂³×C₄₇	C₂×SD₁₆	1	4	yes	—
123	C₂³×C₄₇	#135	1	4	yes	—
124	C₂³×C₄₇	C₂²×D₄	1	3	yes	—
125	D₄×C₄₇	—	2	24	no	—
126	D₄×C₄₇	—	2	4	no	—
127	D₄×C₄₇	C₂³×C₄	1	8	yes	—
128	C₂×C₄×C₄₇	—	2	12	no	—
129	C₂×C₄×C₄₇	—	2	4	no	—
130	C₂×C₄×C₄₇	—	4	12	no	—
131	C₂×C₄×C₄₇	—	4	32	no	—
132	C₂×C₄×C₄₇	C₄×D₄	1	12	yes	—
133	C₂×C₄×C₄₇	C₂×SD₁₆	1	24	yes	complemented
134	C₂×C₄×C₄₇	C₂³×C₄	1	6	yes	—
135	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
136	C₂×C₄×C₄₇	C₂²×D₄	1	3	yes	—
137	C₂×C₄×C₄₇	C₂²×D₄	1	4	yes	—
138	C₂×C₄×C₄₇	C₂×#41	1	6	yes	—
139	C₂×C₄×C₄₇	C₂⁵	1	1	yes	characteristic
140	C₂×Dic₄₇	—	2	24	no	—
141	C₂×Dic₄₇	—	2	4	no	—
142	C₂×Dic₄₇	—	2	4	no	—
143	C₂×Dic₄₇	—	4	12	no	—
144	Dic₉₄	—	2	24	no	—
145	Dic₉₄	—	2	4	no	—
146	Dic₉₄	C₂³×C₄	1	8	yes	complemented
147	C₄₇⋊C₈	—	2	4	no	—
148	C₄₇⋊C₈	C₂³×C₄	1	8	yes	complemented
149	C₂²×C₄×SD₁₆	—	47	1	no	maximal, Sylow
150	C₂²×C₄₇	—	2	8	no	—
151	C₂²×C₄₇	—	4	48	no	—
152	C₂²×C₄₇	—	4	4	no	—
153	C₂²×C₄₇	—	4	4	no	—
154	C₂²×C₄₇	C₄×SD₁₆	1	16	yes	complemented
155	C₂²×C₄₇	C₂×C₄×D₄	1	6	yes	—
156	C₂²×C₄₇	C₂²×SD₁₆	1	6	yes	—
157	C₂²×C₄₇	C₂×#135	1	6	yes	—
158	C₂²×C₄₇	C₂³×D₄	1	1	yes	characteristic
159	C₄×C₄₇	—	2	4	no	—
160	C₄×C₄₇	—	4	4	no	—
161	C₄×C₄₇	C₂×C₄×D₄	1	6	yes	—
162	C₄×C₄₇	C₂²×SD₁₆	1	8	yes	complemented
163	C₄×C₄₇	C₂⁴×C₄	1	1	yes	characteristic
164	C₄×C₄₇	C₂²×#41	1	1	yes	characteristic
165	Dic₄₇	—	2	8	no	—
166	Dic₄₇	—	4	4	no	—
167	C₂³×SD₁₆	—	47	1	no	—
168	C₂²×C₄×Q₈	—	47	1	no	—
169	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic
170	C₂×C₄×SD₁₆	—	47	24	no	—
171	C₂²×#106	—	47	1	no	—
172	C₂²×#103	—	47	1	no	—
173	C₂²×#102	—	47	1	no	—
174	C₂²×C₄×C₈	—	47	1	no	—
175	C₂×C₄₇	—	4	8	no	—
176	C₂×C₄₇	C₂×C₄×SD₁₆	1	12	yes	complemented
177	C₂×C₄₇	C₂²×C₄×D₄	1	1	yes	characteristic
178	C₂×C₄₇	C₂³×SD₁₆	1	1	yes	characteristic
179	C₂×C₄₇	C₂²×#135	1	1	yes	characteristic
180	C₂³×Q₈	—	47	1	no	—
181	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
182	C₂⁴×C₄	—	2	1	no	—
183	C₂²×SD₁₆	—	47	16	no	—
184	C₂²×SD₁₆	—	47	12	no	—
185	C₂³×C₈	—	47	1	no	—
186	C₂³×C₈	—	47	1	no	—
187	C₂×C₄×Q₈	—	47	12	no	—
188	C₂×C₄×Q₈	—	94	6	no	—
189	C₂×C₄×D₄	—	2	6	no	—
190	C₂×C₄×D₄	C₂×D₄₇	1	12	yes	—
191	C₂²×C₄⋊C₄	—	47	1	no	—
192	C₂²×C₄⋊C₄	—	94	1	no	—
193	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
194	C₂²×C₂²⋊C₄	—	2	1	no	—
195	C₂²×C₄²	—	94	1	no	—
196	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
197	C₄×SD₁₆	—	47	64	no	—
198	C₂×#106	—	47	12	no	—
199	C₂×#103	—	47	12	no	—
200	C₂×#102	—	47	12	no	—
201	C₂×C₄×C₈	—	47	12	no	—
202	C₄₇	C₂²×C₄×SD₁₆	1	1	yes	characteristic, complemented, Sylow
203	C₂⁵	—	2	1	no	—
204	C₂²×Q₈	—	47	8	no	—
205	C₂²×Q₈	—	47	6	no	—
206	C₂²×Q₈	—	94	4	no	—
207	C₂²×Q₈	—	94	3	no	—
208	C₂²×D₄	—	2	4	no	—
209	C₂²×D₄	—	2	3	no	—
210	C₂²×D₄	C₄×D₄₇	1	8	yes	—
211	C₂²×D₄	C₂²×D₄₇	1	6	yes	—
212	C₂³×C₄	—	2	1	no	—
213	C₂³×C₄	—	2	12	no	—
214	C₂³×C₄	—	4	8	no	—
215	C₂³×C₄	—	94	1	no	—
216	C₂³×C₄	—	94	1	no	—
217	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
218	C₂³×C₄	C₂²⋊D₄₇	1	1	yes	characteristic
219	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
220	C₂×SD₁₆	—	47	96	no	—
221	C₂×SD₁₆	—	47	16	no	—
222	C₂²×C₈	—	47	8	no	—
223	C₂²×C₈	—	47	6	no	—
224	C₂²×C₈	—	47	6	no	—
225	C₂²×C₈	—	94	4	no	—
226	C₄×Q₈	—	47	16	no	—
227	C₄×Q₈	—	94	24	no	—
228	C₄×D₄	—	2	24	no	—
229	C₄×D₄	C₂²×D₄₇	1	16	yes	—
230	C₂×C₄⋊C₄	—	2	3	no	—
231	C₂×C₄⋊C₄	—	47	6	no	—
232	C₂×C₄⋊C₄	—	94	3	no	—
233	C₂×C₄⋊C₄	—	94	12	no	—
234	C₂×C₄⋊C₄	C₂²×D₄₇	1	6	yes	—
235	C₂×C₂²⋊C₄	—	2	12	no	—
236	C₂×C₄²	—	94	12	no	—
237	C₂×C₄²	C₂²⋊D₄₇	1	6	yes	—
238	C₂×C₄²	C₂²×D₄₇	1	6	yes	—
239	#106	—	47	16	no	—
240	#103	—	47	16	no	—
241	#102	—	47	16	no	—
242	C₄×C₈	—	47	16	no	—
243	C₂⁴	—	2	8	no	—
244	C₂⁴	—	2	6	no	—
245	C₂⁴	—	4	4	no	—
246	C₂⁴	—	4	4	no	—
247	C₂⁴	C₂×C₂²⋊D₄₇	1	1	yes	characteristic
248	C₂×Q₈	—	47	24	no	—
249	C₂×Q₈	—	47	4	no	—
250	C₂×Q₈	—	94	24	no	—
251	C₂×Q₈	—	94	6	no	—
252	C₂×Q₈	—	94	12	no	—
253	C₂×D₄	—	2	24	no	—
254	C₂×D₄	—	2	6	no	—
255	C₂×D₄	—	2	12	no	—
256	C₂×D₄	C₂×C₄×D₄₇	1	24	yes	—
257	C₂×D₄	C₂³×D₄₇	1	4	yes	—
258	C₂²×C₄	—	2	4	no	—
259	C₂²×C₄	—	2	6	no	—
260	C₂²×C₄	—	2	16	no	—
261	C₂²×C₄	—	4	4	no	—
262	C₂²×C₄	—	4	48	no	—
263	C₂²×C₄	—	94	8	no	—
264	C₂²×C₄	—	94	6	no	—
265	C₂²×C₄	—	94	6	no	—
266	C₂²×C₄	—	188	4	no	—
267	C₂²×C₄	#10625335	1	8	yes	direct product factor
268	C₂²×C₄	C₂×C₄×D₄₇	1	4	yes	—
269	C₂²×C₄	#10625350	1	4	yes	—
270	C₂²×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
271	C₂²×C₄	C₂×C₂²⋊D₄₇	1	3	yes	—
272	C₂²×C₄	C₂×C₂²⋊D₄₇	1	6	yes	—
273	C₂²×C₄	C₂³×D₄₇	1	3	yes	—
274	SD₁₆	—	47	64	no	—
275	C₂×C₈	—	47	24	no	—
276	C₂×C₈	—	47	4	no	—
277	C₂×C₈	—	47	4	no	—
278	C₂×C₈	—	94	12	no	—
279	C₄⋊C₄	—	2	6	no	—
280	C₄⋊C₄	—	47	4	no	—
281	C₄⋊C₄	—	94	16	no	—
282	C₄⋊C₄	—	94	6	no	—
283	C₄⋊C₄	C₂³×D₄₇	1	4	yes	—
284	C₂²⋊C₄	—	2	16	no	—
285	C₄²	—	94	16	no	—
286	C₄²	C₂×C₂²⋊D₄₇	1	12	yes	—
287	C₄²	C₂³×D₄₇	1	4	yes	—
288	C₂³	—	2	24	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	4	12	no	—
291	C₂³	—	4	12	no	—
292	C₂³	—	4	32	no	—
293	C₂³	C₄×C₂²⋊D₄₇	1	4	yes	—
294	C₂³	C₂×#10625335	1	4	yes	—
295	C₂³	#13094044	1	4	yes	—
296	C₂³	C₂²×C₂²⋊D₄₇	1	3	yes	—
297	Q₈	—	47	8	no	—
298	Q₈	—	94	24	no	—
299	Q₈	—	94	4	no	—
300	D₄	—	2	24	no	—
301	D₄	—	2	4	no	—
302	D₄	C₂²×C₄×D₄₇	1	8	yes	—
303	C₂×C₄	—	2	12	no	—
304	C₂×C₄	—	2	4	no	—
305	C₂×C₄	—	4	12	no	—
306	C₂×C₄	—	4	32	no	—
307	C₂×C₄	—	94	24	no	—
308	C₂×C₄	—	94	4	no	—
309	C₂×C₄	—	94	4	no	—
310	C₂×C₄	—	188	12	no	—
311	C₂×C₄	C₄×C₂²⋊D₄₇	1	12	yes	—
312	C₂×C₄	C₂×#10625335	1	24	yes	direct product factor
313	C₂×C₄	C₂²×C₄×D₄₇	1	6	yes	—
314	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
315	C₂×C₄	C₂²×C₂²⋊D₄₇	1	3	yes	—
316	C₂×C₄	C₂²×C₂²⋊D₄₇	1	4	yes	—
317	C₂×C₄	C₂×#10625350	1	6	yes	—
318	C₂×C₄	C₂⁴×D₄₇	1	1	yes	characteristic
319	C₈	—	47	8	no	—
320	C₈	—	94	4	no	—
321	C₂²	—	2	8	no	—
322	C₂²	—	4	4	no	—
323	C₂²	—	4	4	no	—
324	C₂²	—	4	48	no	—
325	C₂²	C₄×#10625335	1	16	yes	direct product factor
326	C₂²	C₂×C₄×C₂²⋊D₄₇	1	6	yes	—
327	C₂²	C₂²×#10625335	1	6	yes	—
328	C₂²	C₂×#13094044	1	6	yes	—
329	C₂²	C₂³×C₂²⋊D₄₇	1	1	yes	characteristic
330	C₄	—	2	4	no	—
331	C₄	—	4	4	no	—
332	C₄	—	94	8	no	—
333	C₄	—	188	4	no	—
334	C₄	C₂×C₄×C₂²⋊D₄₇	1	6	yes	—
335	C₄	C₂²×#10625335	1	8	yes	direct product factor
336	C₄	C₂³×C₄×D₄₇	1	1	yes	characteristic
337	C₄	C₂²×#10625350	1	1	yes	characteristic
338	C₂	—	4	8	no	—
339	C₂	C₂×C₄×#10625335	1	12	yes	direct product factor
340	C₂	C₂²×C₄×C₂²⋊D₄₇	1	1	yes	characteristic
341	C₂	C₂³×#10625335	1	1	yes	characteristic
342	C₂	C₂²×#13094044	1	1	yes	characteristic

	subgroup	G/H
center	C₂³×C₄	C₂²⋊D₄₇
commutator	C₄×C₄₇	C₂⁴×C₄
Frattini	C₂×C₄	C₂⁴×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂×D₄
prime radical	C₂³×D₄×C₄₇	C₂²
cosocle	C₂×C₄×C₄₇	C₂⁵
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂²×C₄×SD₁₆
LCS	G ▷ C₄×C₄₇ ▷ C₂×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂³×C₄ ◁ C₂²×C₄² ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. C₂²×C₄×Dic₉₄	C₂	semidirect
3. C₂×C₄×#10625335	C₂	direct (N × H)
4. C₂²×#13093955	C₂	semidirect
5. C₂²×#13093947	C₂	semidirect
7. C₂²×C₄×C₄₇⋊C₈	C₂	semidirect
10. C₂²×#10625335	C₄	direct (N × H)
15. C₂×C₄×Dic₉₄	C₂²	semidirect
19. C₄×#10625335	C₂²	direct (N × H)
20. C₂×#13093955	C₂²	semidirect
21. C₂×#13093947	C₂²	semidirect
23. C₂×C₄×C₄₇⋊C₈	C₂²	semidirect
33. C₂²×Dic₉₄	C₂×C₄	semidirect
37. C₂×#10625335	C₂×C₄	direct (N × H)
40. C₂²×C₄₇⋊C₈	C₂×C₄	semidirect
44. C₄×Dic₉₄	C₂³	semidirect
49. #13093955	C₂³	semidirect
50. #13093947	C₂³	semidirect
52. C₄×C₄₇⋊C₈	C₂³	semidirect
86. C₂²×C₄×C₄₇	SD₁₆	semidirect
100. C₂×Dic₉₄	C₂²×C₄	semidirect
107. #10625335	C₂²×C₄	direct (N × H)
113. C₂×C₄₇⋊C₈	C₂²×C₄	semidirect
133. C₂×C₄×C₄₇	C₂×SD₁₆	semidirect
146. Dic₉₄	C₂³×C₄	semidirect
148. C₄₇⋊C₈	C₂³×C₄	semidirect
154. C₂²×C₄₇	C₄×SD₁₆	semidirect
162. C₄×C₄₇	C₂²×SD₁₆	semidirect
176. C₂×C₄₇	C₂×C₄×SD₁₆	semidirect
202. C₄₇	C₂²×C₄×SD₁₆	semidirect
267. C₂²×C₄	#10625335	direct (N × H)
312. C₂×C₄	C₂×#10625335	direct (N × H)
325. C₂²	C₄×#10625335	direct (N × H)
335. C₄	C₂²×#10625335	direct (N × H)
339. C₂	C₂×C₄×#10625335	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂³×#10625335	2
C₂²×C₄×Dic₉₄	2
C₂×C₄×#10625335	2
C₂²×#13093955	2
C₂²×#13093947	2
C₂²×#13093945	2
C₂²×C₄×C₄₇⋊C₈	2
C₂²×C₄×D₄×C₄₇	2
C₂²×C₄×SD₁₆	47

Subgroups — C22×C4×#10625335 #27080284

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×C₄×#10625335 #27080284