Subgroups — C₂²×#15689838 #27123300

Order 12032.

8710 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#15689838	C₂	1	48	yes	maximal, direct product factor
2	C₂²×#13094024	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂²×#13094010	C₂	1	4	yes	maximal, complemented
4	C₂²×#13093998	C₂	1	2	yes	maximal, complemented
5	C₂²×#13093995	C₂	1	2	yes	maximal, complemented
6	C₂²×C₄×D₁₈₈	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂²×#13093983	C₂	1	2	yes	maximal, complemented
8	C₂²×#13093982	C₂	1	2	yes	maximal, complemented
9	C₂²×C₄×D₄×C₄₇	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂³×Dic₉₄	C₂²	1	2	yes	—
11	C₂³×D₁₈₈	C₂²	1	1	yes	characteristic
12	C₂³×C₂²⋊D₄₇	C₂²	1	4	yes	—
13	C₂³×C₄×D₄₇	C₂²	1	2	yes	—
14	#15689838	C₂²	1	256	yes	direct product factor
15	C₂×#13094024	C₂²	1	24	yes	complemented
16	C₂×#13094010	C₂²	1	96	yes	complemented
17	C₂×#13093998	C₂²	1	48	yes	complemented
18	C₂×#13093995	C₂²	1	48	yes	complemented
19	C₂×C₄×D₁₈₈	C₂²	1	24	yes	complemented
20	C₂×#13093983	C₂²	1	48	yes	complemented
21	C₂×#13093982	C₂²	1	48	yes	complemented
22	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
23	C₂²×C₄⋊Dic₄₇	C₂²	1	1	yes	characteristic
24	C₂²×C₄⋊Dic₄₇	C₂²	1	2	yes	—
25	C₂²×C₂²⋊Dic₄₇	C₂²	1	4	yes	—
26	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	4	yes	—
27	C₂²×(C₂×D₄₇)⋊C₄	C₂²	1	2	yes	—
28	C₂²×C₄×Dic₄₇	C₂²	1	4	yes	—
29	C₂³×D₄×C₄₇	C₂²	1	1	yes	characteristic
30	C₂⁴×C₄×C₄₇	C₂²	1	2	yes	—
31	C₂×C₄×D₄×C₄₇	C₂²	1	24	yes	complemented
32	C₂²×C₄⋊C₄×C₄₇	C₂²	1	1	yes	characteristic
33	C₂²×C₂²⋊C₄×C₄₇	C₂²	1	2	yes	—
34	C₂²×C₄²×C₄₇	C₂²	1	1	yes	characteristic
35	C₂⁴×D₄₇	C₂³	1	2	yes	—
36	C₂²×Dic₉₄	—	4	8	no	—
37	C₂²×Dic₉₄	C₂³	1	24	yes	—
38	C₂²×D₁₈₈	—	2	8	no	—
39	C₂²×D₁₈₈	C₂³	1	12	yes	—
40	C₂²×C₂²⋊D₄₇	—	4	16	no	—
41	C₂²×C₂²⋊D₄₇	C₂³	1	48	yes	—
42	C₂³×Dic₄₇	C₂³	1	2	yes	—
43	C₂³×Dic₄₇	C₂³	1	4	yes	—
44	C₂²×C₄×D₄₇	—	2	16	no	—
45	C₂²×C₄×D₄₇	C₂³	1	24	yes	—
46	#13094024	C₂³	1	64	yes	complemented
47	#13094010	C₂³	1	256	yes	complemented
48	#13093998	C₂³	1	128	yes	complemented
49	#13093995	C₂³	1	128	yes	complemented
50	C₄×D₁₈₈	C₂³	1	64	yes	complemented
51	#13093983	C₂³	1	128	yes	complemented
52	#13093982	C₂³	1	128	yes	complemented
53	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	—
54	C₂×C₄⋊Dic₄₇	C₂³	1	12	yes	—
55	C₂×C₄⋊Dic₄₇	C₂³	1	24	yes	—
56	C₂×C₂²⋊Dic₄₇	C₂³	1	48	yes	—
57	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	48	yes	—
58	C₂×(C₂×D₄₇)⋊C₄	C₂³	1	24	yes	—
59	C₂×C₄×Dic₄₇	C₂³	1	48	yes	—
60	C₂⁵×C₄₇	C₂³	1	2	yes	—
61	C₂²×D₄×C₄₇	—	2	8	no	—
62	C₂²×D₄×C₄₇	C₂³	1	12	yes	—
63	C₂³×C₄×C₄₇	—	2	16	no	—
64	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
65	C₂³×C₄×C₄₇	C₂³	1	2	yes	—
66	C₂³×C₄×C₄₇	C₂³	1	24	yes	—
67	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
68	C₂³×C₄×C₄₇	C₂³	1	1	yes	characteristic
69	C₄×D₄×C₄₇	C₂³	1	64	yes	complemented
70	C₂×C₄⋊C₄×C₄₇	C₂³	1	12	yes	—
71	C₂×C₂²⋊C₄×C₄₇	C₂³	1	24	yes	—
72	C₂×C₄²×C₄₇	C₂³	1	12	yes	—
73	C₂⁴×C₄₇	—	2	8	no	—
74	C₂⁴×C₄₇	—	2	8	no	—
75	C₂⁴×C₄₇	—	2	8	no	—
76	C₂⁴×C₄₇	C₂⁴	1	12	yes	—
77	C₂⁴×C₄₇	C₂⁴	1	1	yes	characteristic
78	C₂³×D₄₇	—	2	8	no	—
79	C₂³×D₄₇	—	2	8	no	—
80	C₂³×D₄₇	—	2	8	no	—
81	C₂³×D₄₇	C₂⁴	1	12	yes	—
82	C₂×D₄×C₄₇	—	2	48	no	—
83	C₂×D₄×C₄₇	C₂⁴	1	16	yes	—
84	C₂²×C₄×C₄₇	—	2	8	no	—
85	C₂²×C₄×C₄₇	—	2	4	no	—
86	C₂²×C₄×C₄₇	—	2	96	no	—
87	C₂²×C₄×C₄₇	#41	1	8	yes	—
88	C₂²×C₄×C₄₇	#41	1	8	yes	—
89	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
90	C₂²×C₄×C₄₇	C₂⁴	1	12	yes	—
91	C₂²×C₄×C₄₇	C₂⁴	1	32	yes	—
92	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
93	C₂²×C₄×C₄₇	C₂⁴	1	6	yes	—
94	C₂×C₂²⋊D₄₇	—	4	96	no	—
95	C₂×C₂²⋊D₄₇	C₂⁴	1	64	yes	—
96	C₂²×Dic₄₇	—	2	8	no	—
97	C₂²×Dic₄₇	—	2	16	no	—
98	C₂²×Dic₄₇	C₂⁴	1	12	yes	—
99	C₂²×Dic₄₇	C₂⁴	1	24	yes	—
100	C₂×D₁₈₈	—	2	48	no	—
101	C₂×D₁₈₈	C₂⁴	1	16	yes	—
102	C₂×C₄×D₄₇	—	2	96	no	—
103	C₂×C₄×D₄₇	C₂⁴	1	32	yes	—
104	C₂×Dic₉₄	—	4	48	no	—
105	C₂×Dic₉₄	C₂⁴	1	32	yes	—
106	C₄⋊C₄×C₄₇	C₂⁴	1	16	yes	—
107	C₂²⋊C₄×C₄₇	C₂⁴	1	32	yes	—
108	C₄²×C₄₇	C₂⁴	1	16	yes	—
109	C₂²⋊Dic₄₇	C₂⁴	1	64	yes	—
110	(C₂×D₄₇)⋊C₄	C₂⁴	1	64	yes	—
111	(C₂×D₄₇)⋊C₄	C₂⁴	1	32	yes	—
112	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
113	C₄⋊Dic₄₇	C₂⁴	1	16	yes	—
114	C₄⋊Dic₄₇	C₂⁴	1	32	yes	—
115	C₄×Dic₄₇	C₂⁴	1	64	yes	—
116	C₂³×C₄₇	—	2	24	no	—
117	C₂³×C₄₇	—	2	24	no	—
118	C₂³×C₄₇	—	2	24	no	—
119	C₂³×C₄₇	—	4	32	no	—
120	C₂³×C₄₇	C₂×#41	1	4	yes	—
121	C₂³×C₄₇	C₂×#41	1	4	yes	—
122	C₂³×C₄₇	H(5,𝔽₂)	1	4	yes	—
123	C₂³×C₄₇	C₂⁵	1	8	yes	—
124	C₂³×C₄₇	C₂⁵	1	3	yes	—
125	C₂²×D₄₇	—	2	24	no	—
126	C₂²×D₄₇	—	2	24	no	—
127	C₂²×D₄₇	—	2	24	no	—
128	C₂²×D₄₇	—	4	32	no	—
129	C₂²×D₄₇	C₂⁵	1	8	yes	—
130	D₄×C₄₇	—	2	32	no	—
131	C₂×C₄×C₄₇	—	2	24	no	—
132	C₂×C₄×C₄₇	—	2	12	no	—
133	C₂×C₄×C₄₇	—	2	64	no	—
134	C₂×C₄×C₄₇	C₂×#41	1	24	yes	—
135	C₂×C₄×C₄₇	C₂×#41	1	24	yes	—
136	C₂×C₄×C₄₇	C₂⁵	1	8	yes	—
137	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
138	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
139	C₂×C₄×C₄₇	C₂⁵	1	4	yes	—
140	C₂²⋊D₄₇	—	4	64	no	—
141	C₂×Dic₄₇	—	2	24	no	—
142	C₂×Dic₄₇	—	2	48	no	—
143	C₂×Dic₄₇	C₂⁵	1	8	yes	—
144	C₂×Dic₄₇	C₂⁵	1	16	yes	—
145	D₁₈₈	—	2	32	no	—
146	C₄×D₄₇	—	2	64	no	—
147	Dic₉₄	—	4	32	no	—
148	C₂²×#555	—	47	1	no	maximal, Sylow
149	C₂²×C₄₇	—	2	8	no	—
150	C₂²×C₄₇	—	2	8	no	—
151	C₂²×C₄₇	—	2	8	no	—
152	C₂²×C₄₇	—	4	48	no	—
153	C₂²×C₄₇	#555	1	16	yes	complemented
154	C₂²×C₄₇	C₂²×#41	1	6	yes	—
155	C₂²×C₄₇	C₂²×#41	1	6	yes	—
156	C₂²×C₄₇	C₂×H(5,𝔽₂)	1	6	yes	—
157	C₂²×C₄₇	C₂⁶	1	1	yes	characteristic
158	C₂×D₄₇	—	2	8	no	—
159	C₂×D₄₇	—	2	8	no	—
160	C₂×D₄₇	—	2	8	no	—
161	C₂×D₄₇	—	4	48	no	—
162	C₄×C₄₇	—	2	8	no	—
163	C₄×C₄₇	—	2	4	no	—
164	C₄×C₄₇	C₂²×#41	1	8	yes	—
165	C₄×C₄₇	C₂²×#41	1	8	yes	—
166	Dic₄₇	—	2	8	no	—
167	Dic₄₇	—	2	16	no	—
168	C₂×#555	—	47	48	no	—
169	C₂²×C₄⋊Q₈	—	47	1	no	—
170	C₂²×#124	—	47	4	no	—
171	C₂²×#121	—	47	2	no	—
172	C₂²×#121	—	47	2	no	—
173	C₂²×C₄×D₄	—	47	1	no	—
174	C₂²×C₄×D₄	D₄₇	1	1	yes	characteristic, complemented
175	C₂²×#117	—	47	2	no	—
176	C₂²×#117	—	47	2	no	—
177	C₂×C₄₇	—	4	8	no	—
178	C₂×C₄₇	C₂×#555	1	12	yes	complemented
179	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
180	C₂×C₄₇	C₂³×#41	1	1	yes	characteristic
181	C₂×C₄₇	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
182	D₄₇	—	4	8	no	—
183	C₂³×Q₈	—	47	2	no	—
184	C₂³×D₄	—	47	4	no	—
185	C₂³×D₄	—	47	1	no	—
186	C₂³×D₄	C₂×D₄₇	1	1	yes	characteristic
187	C₂⁴×C₄	—	47	2	no	—
188	C₂⁴×C₄	C₂×D₄₇	1	2	yes	—
189	#555	—	47	256	no	—
190	C₂×C₄⋊Q₈	—	47	24	no	—
191	C₂×#124	—	47	96	no	—
192	C₂×#121	—	47	48	no	—
193	C₂×#121	—	47	48	no	—
194	C₂×C₄×D₄	—	47	24	no	—
195	C₂×C₄×D₄	C₂×D₄₇	1	24	yes	complemented
196	C₂×#117	—	47	48	no	—
197	C₂×#117	—	47	48	no	—
198	C₂²×C₄⋊C₄	—	47	1	no	—
199	C₂²×C₄⋊C₄	—	47	2	no	—
200	C₂²×C₄⋊C₄	—	47	2	no	—
201	C₂²×C₄⋊C₄	C₂×D₄₇	1	1	yes	characteristic
202	C₂²×C₂²⋊C₄	—	47	4	no	—
203	C₂²×C₂²⋊C₄	—	47	4	no	—
204	C₂²×C₂²⋊C₄	—	47	2	no	—
205	C₂²×C₂²⋊C₄	C₂×D₄₇	1	2	yes	—
206	C₂²×C₄²	—	47	4	no	—
207	C₂²×C₄²	C₂×D₄₇	1	1	yes	characteristic
208	C₄₇	C₂²×#555	1	1	yes	characteristic, complemented, Sylow
209	C₂⁵	—	47	2	no	—
210	C₂⁵	C₂²×D₄₇	1	2	yes	—
211	C₂²×Q₈	—	47	24	no	—
212	C₂²×Q₈	—	188	8	no	—
213	C₂²×D₄	—	2	8	no	—
214	C₂²×D₄	—	47	48	no	—
215	C₂²×D₄	—	47	12	no	—
216	C₂²×D₄	—	94	8	no	—
217	C₂²×D₄	—	188	16	no	—
218	C₂²×D₄	C₂²×D₄₇	1	12	yes	—
219	C₂³×C₄	—	2	16	no	—
220	C₂³×C₄	—	47	2	no	—
221	C₂³×C₄	—	47	4	no	—
222	C₂³×C₄	—	47	24	no	—
223	C₂³×C₄	—	94	16	no	—
224	C₂³×C₄	C₂²×D₄₇	1	24	yes	—
225	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
226	C₂³×C₄	C₂²×D₄₇	1	2	yes	—
227	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
228	C₂³×C₄	C₂²×D₄₇	1	1	yes	characteristic
229	C₄⋊Q₈	—	47	64	no	—
230	#124	—	47	256	no	—
231	#121	—	47	128	no	—
232	#121	—	47	128	no	—
233	C₄×D₄	—	47	64	no	—
234	C₄×D₄	C₂²×D₄₇	1	64	yes	complemented
235	#117	—	47	128	no	—
236	#117	—	47	128	no	—
237	C₂×C₄⋊C₄	—	47	12	no	—
238	C₂×C₄⋊C₄	—	47	24	no	—
239	C₂×C₄⋊C₄	—	47	24	no	—
240	C₂×C₄⋊C₄	C₂²×D₄₇	1	12	yes	—
241	C₂×C₂²⋊C₄	—	47	48	no	—
242	C₂×C₂²⋊C₄	—	47	48	no	—
243	C₂×C₂²⋊C₄	—	47	24	no	—
244	C₂×C₂²⋊C₄	C₂²×D₄₇	1	24	yes	—
245	C₂×C₄²	—	47	48	no	—
246	C₂×C₄²	C₂²×D₄₇	1	12	yes	—
247	C₂⁴	—	2	8	no	—
248	C₂⁴	—	2	8	no	—
249	C₂⁴	—	2	8	no	—
250	C₂⁴	—	47	12	no	—
251	C₂⁴	—	94	8	no	—
252	C₂⁴	—	94	8	no	—
253	C₂⁴	—	94	8	no	—
254	C₂⁴	C₂³×D₄₇	1	12	yes	—
255	C₂⁴	C₂³×D₄₇	1	1	yes	characteristic
256	C₂×Q₈	—	47	32	no	—
257	C₂×Q₈	—	188	48	no	—
258	C₂×D₄	—	2	48	no	—
259	C₂×D₄	—	47	64	no	—
260	C₂×D₄	—	47	16	no	—
261	C₂×D₄	—	94	48	no	—
262	C₂×D₄	—	188	96	no	—
263	C₂×D₄	C₂³×D₄₇	1	16	yes	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	96	no	—
267	C₂²×C₄	—	47	12	no	—
268	C₂²×C₄	—	47	24	no	—
269	C₂²×C₄	—	47	32	no	—
270	C₂²×C₄	—	94	8	no	—
271	C₂²×C₄	—	94	16	no	—
272	C₂²×C₄	—	94	96	no	—
273	C₂²×C₄	#10625350	1	8	yes	—
274	C₂²×C₄	#10625352	1	8	yes	—
275	C₂²×C₄	C₂³×D₄₇	1	12	yes	—
276	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
277	C₂²×C₄	C₂³×D₄₇	1	32	yes	—
278	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
279	C₂²×C₄	C₂³×D₄₇	1	6	yes	—
280	C₄⋊C₄	—	47	16	no	—
281	C₄⋊C₄	—	47	32	no	—
282	C₄⋊C₄	—	47	32	no	—
283	C₄⋊C₄	C₂³×D₄₇	1	16	yes	—
284	C₂²⋊C₄	—	47	64	no	—
285	C₂²⋊C₄	—	47	64	no	—
286	C₂²⋊C₄	—	47	32	no	—
287	C₂²⋊C₄	C₂³×D₄₇	1	32	yes	—
288	C₄²	—	47	64	no	—
289	C₄²	C₂³×D₄₇	1	16	yes	—
290	C₂³	—	2	24	no	—
291	C₂³	—	2	24	no	—
292	C₂³	—	2	24	no	—
293	C₂³	—	4	32	no	—
294	C₂³	—	47	8	no	—
295	C₂³	—	94	24	no	—
296	C₂³	—	94	24	no	—
297	C₂³	—	94	24	no	—
298	C₂³	—	188	32	no	—
299	C₂³	C₂×#10625352	1	4	yes	—
300	C₂³	C₂×#10625350	1	4	yes	—
301	C₂³	#13094070	1	4	yes	—
302	C₂³	C₂⁴×D₄₇	1	8	yes	—
303	C₂³	C₂⁴×D₄₇	1	3	yes	—
304	Q₈	—	188	32	no	—
305	D₄	—	2	32	no	—
306	D₄	—	94	32	no	—
307	D₄	—	188	64	no	—
308	C₂×C₄	—	2	24	no	—
309	C₂×C₄	—	2	12	no	—
310	C₂×C₄	—	2	64	no	—
311	C₂×C₄	—	47	8	no	—
312	C₂×C₄	—	47	16	no	—
313	C₂×C₄	—	94	24	no	—
314	C₂×C₄	—	94	48	no	—
315	C₂×C₄	—	94	64	no	—
316	C₂×C₄	C₂×#10625352	1	24	yes	—
317	C₂×C₄	C₂×#10625350	1	24	yes	—
318	C₂×C₄	C₂⁴×D₄₇	1	8	yes	—
319	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
320	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
321	C₂×C₄	C₂⁴×D₄₇	1	4	yes	—
322	C₂²	—	2	8	no	—
323	C₂²	—	2	8	no	—
324	C₂²	—	2	8	no	—
325	C₂²	—	4	48	no	—
326	C₂²	—	94	8	no	—
327	C₂²	—	94	8	no	—
328	C₂²	—	94	8	no	—
329	C₂²	—	188	48	no	—
330	C₂²	#15689838	1	16	yes	direct product factor
331	C₂²	C₂²×#10625352	1	6	yes	—
332	C₂²	C₂²×#10625350	1	6	yes	—
333	C₂²	C₂×#13094070	1	6	yes	—
334	C₂²	C₂⁵×D₄₇	1	1	yes	characteristic
335	C₄	—	2	8	no	—
336	C₄	—	2	4	no	—
337	C₄	—	94	8	no	—
338	C₄	—	94	16	no	—
339	C₄	C₂²×#10625352	1	8	yes	—
340	C₄	C₂²×#10625350	1	8	yes	—
341	C₂	—	4	8	no	—
342	C₂	—	188	8	no	—
343	C₂	C₂×#15689838	1	12	yes	direct product factor
344	C₂	C₂³×#10625352	1	1	yes	characteristic
345	C₂	C₂³×#10625350	1	1	yes	characteristic
346	C₂	C₂²×#13094070	1	1	yes	characteristic

	subgroup	G/H
center	C₂⁴	C₂³×D₄₇
commutator, cosocle	C₂²×C₄₇	C₂⁶
Frattini	C₂²	C₂⁵×D₄₇
Fitting	C₂²×C₄×D₄×C₄₇	C₂
socle	C₂⁴×C₄₇	C₂⁴
hypercenter	C₂²×C₄×D₄	D₄₇
hypocenter	C₄₇	C₂²×#555
LCS	G ▷ C₂²×C₄₇ ▷ C₄₇
UCS	C₁ ◁ C₂⁴ ◁ C₂²×C₄×D₄

Complements

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

N	H ≅ G/N	type
1. C₂×#15689838	C₂	direct (N × H)
2. C₂²×#13094024	C₂	semidirect
3. C₂²×#13094010	C₂	semidirect
4. C₂²×#13093998	C₂	semidirect
5. C₂²×#13093995	C₂	semidirect
6. C₂²×C₄×D₁₈₈	C₂	semidirect
7. C₂²×#13093983	C₂	semidirect
8. C₂²×#13093982	C₂	semidirect
9. C₂²×C₄×D₄×C₄₇	C₂	semidirect
14. #15689838	C₂²	direct (N × H)
15. C₂×#13094024	C₂²	semidirect
16. C₂×#13094010	C₂²	semidirect
17. C₂×#13093998	C₂²	semidirect
18. C₂×#13093995	C₂²	semidirect
19. C₂×C₄×D₁₈₈	C₂²	semidirect
20. C₂×#13093983	C₂²	semidirect
21. C₂×#13093982	C₂²	semidirect
31. C₂×C₄×D₄×C₄₇	C₂²	semidirect
46. #13094024	C₂³	semidirect
47. #13094010	C₂³	semidirect
48. #13093998	C₂³	semidirect
49. #13093995	C₂³	semidirect
50. C₄×D₁₈₈	C₂³	semidirect
51. #13093983	C₂³	semidirect
52. #13093982	C₂³	semidirect
69. C₄×D₄×C₄₇	C₂³	semidirect
153. C₂²×C₄₇	#555	semidirect
174. C₂²×C₄×D₄	D₄₇	semidirect
178. C₂×C₄₇	C₂×#555	semidirect
195. C₂×C₄×D₄	C₂×D₄₇	semidirect
208. C₄₇	C₂²×#555	semidirect
234. C₄×D₄	C₂²×D₄₇	semidirect
330. C₂²	#15689838	direct (N × H)
343. C₂	C₂×#15689838	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×#15689838	2
C₂²×#13094024	2
C₂²×#13094010	2
C₂²×#13093998	2
C₂²×#13093995	2
C₂²×C₄×D₁₈₈	2
C₂²×#13093983	2
C₂²×#13093982	2
C₂²×C₄×D₄×C₄₇	2
C₂²×#555	47

Subgroups — C22×#15689838 #27123300

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#15689838 #27123300