Subgroups — C₂×#11797877 #72269713

Order 2304.

1962 conjugacy classes of subgroups.

The subgroup lattice has 399 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#10592603	C₂	1	1	yes	maximal, characteristic
2	C₂×#10592399	C₂	1	2	yes	maximal, complemented
3	#11797877	C₂	1	8	yes	maximal, direct product factor
4	C₂×#10589372	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#10589376	C₂	1	2	yes	maximal, complemented
6	C₂×C₃²×#346	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#69085	—	3	4	no	maximal
8	C₂×#64113	C₂²	1	2	yes	—
9	C₂×#64110	—	2	2	no	—
10	C₂²×C₃²×C₁₆	C₂²	1	1	yes	characteristic
11	C₂²×C₃²×C₁₆	C₂²	1	1	yes	characteristic
12	C₂×C₃²×C₄×C₈	C₂²	1	1	yes	characteristic
13	C₂×#63646	C₂²	1	2	yes	—
14	C₂×#63632	—	2	2	no	—
15	C₂×#63628	C₄	1	1	yes	characteristic, complemented
16	#10592603	C₄	1	4	yes	complemented
17	#10592603	C₂²	1	4	yes	—
18	C₂×#63627	C₄	1	2	yes	complemented
19	C₂×#63626	C₄	1	1	yes	characteristic, complemented
20	#10592399	—	2	4	no	—
21	#10592399	C₂²	1	8	yes	complemented
22	C₃²×#346	C₂²	1	4	yes	complemented
23	#10589376	C₂²	1	8	yes	complemented
24	#10589372	C₂²	1	4	yes	complemented
25	C₂×#4904	—	3	4	no	—
26	C₂×#4700	—	3	8	no	—
27	C₂×C₃×#346	D₃	1	4	yes	complemented
28	C₂×#4510	—	3	8	no	—
29	C₂×#4506	—	3	4	no	—
30	#69085	—	3	32	no	—
31	C₂×#3828	—	2	2	no	—
32	C₂²×C₃²×C₈	D₄	1	1	yes	characteristic
33	C₂²×C₃²×C₈	C₂³	1	1	yes	characteristic
34	C₂×C₃²×C₄²	D₄	1	1	yes	characteristic
35	C₂×#3748	—	2	2	no	—
36	C₂×#3746	C₂×C₄	1	2	yes	—
37	#64113	—	2	2	no	—
38	#64113	—	2	2	no	—
39	#64113	C₂×C₄	1	4	yes	—
40	#64113	C₂³	1	4	yes	—
41	C₂×#3745	C₂×C₄	1	2	yes	—
42	C₂×#3744	—	2	2	no	—
43	#64110	—	2	8	no	—
44	#64110	—	4	4	no	—
45	C₂×#3743	—	4	2	no	—
46	C₂×C₈×C₃⋊D₃	—	4	2	no	—
47	C₂×C₃²×C₁₆	—	2	1	no	—
48	C₂×C₃²×C₁₆	—	2	1	no	—
49	C₂×C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
50	C₂×C₃²×C₁₆	C₂×C₄	1	1	yes	characteristic
51	C₂×C₃²×C₁₆	C₂×C₄	1	2	yes	—
52	C₂×C₃²×C₁₆	C₂³	1	2	yes	—
53	C₂×C₃²×C₁₆	C₂³	1	2	yes	—
54	C₃²×C₄×C₈	D₄	1	2	yes	—
55	C₃²×C₄×C₈	C₂³	1	2	yes	—
56	#63646	—	2	2	no	—
57	#63646	C₂³	1	4	yes	—
58	#63632	—	2	8	no	—
59	#63628	C₂×C₄	1	4	yes	complemented
60	#63627	C₂×C₄	1	8	yes	complemented
61	#63626	C₂×C₄	1	4	yes	complemented
62	C₂×#2179	—	9	1	no	Sylow
63	C₂×#904	—	3	8	no	—
64	C₂×#901	—	6	8	no	—
65	C₂²×C₃×C₁₆	C₂×D₃	1	4	yes	—
66	C₂²×C₃×C₁₆	C₂×D₃	1	4	yes	—
67	C₂×C₃×C₄×C₈	C₂×D₃	1	4	yes	—
68	C₂×#819	—	3	8	no	—
69	C₂×#805	—	6	8	no	—
70	C₂×Dic₂₄	—	3	4	no	—
71	#4904	—	3	16	no	—
72	#4904	—	3	16	no	—
73	C₂×#800	—	3	8	no	—
74	C₂×D₄₈	—	3	4	no	—
75	#4700	—	3	32	no	—
76	#4700	—	6	16	no	—
77	C₃×#346	C₂×D₃	1	16	yes	complemented
78	#4510	—	3	32	no	—
79	#4506	—	3	16	no	—
80	C₂²×C₃²×C₄	—	2	1	no	—
81	C₂²×C₃²×C₄	C₂×D₄	1	1	yes	characteristic
82	C₂×#638	—	4	2	no	—
83	#3828	—	2	4	no	—
84	#3828	—	2	4	no	—
85	#3828	—	4	2	no	—
86	#3828	—	4	2	no	—
87	C₂×C₄⋊(C₃⋊D₃)	—	2	2	no	—
88	C₂×C₄×C₃⋊D₃	—	4	2	no	—
89	C₂×#634	—	2	2	no	—
90	C₂×C₃²×C₈	D₈	1	2	yes	—
91	C₂×C₃²×C₈	D₈	1	2	yes	—
92	C₂×C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₃²×C₈	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₃²×C₈	C₂×D₄	1	1	yes	characteristic
95	C₂×C₃²×C₈	C₂×D₄	1	2	yes	—
96	C₂×C₃²×C₈	#41	1	1	yes	characteristic
97	C₂×C₃²×C₈	#41	1	1	yes	characteristic
98	C₂×C₃²×C₈	C₂⁴	1	1	yes	characteristic
99	C₃²×C₄²	—	2	1	no	—
100	C₃²×C₄²	C₂×D₄	1	2	yes	—
101	#3748	—	2	4	no	—
102	#3748	—	4	2	no	—
103	C₂×C₃⋊(C₃⋊C₈)	—	4	2	no	—
104	#3746	—	2	2	no	—
105	#3746	C₂²×C₄	1	4	yes	—
106	#3745	—	2	2	no	—
107	#3745	C₂²×C₄	1	4	yes	—
108	#3744	—	2	4	no	—
109	#3744	—	2	4	no	—
110	#3743	—	4	8	no	—
111	C₈×C₃⋊D₃	—	4	8	no	—
112	C₃²×C₁₆	—	2	2	no	—
113	C₃²×C₁₆	C₂²×C₄	1	2	yes	—
114	C₃²×C₁₆	C₂²×C₄	1	2	yes	—
115	C₂×#508	—	9	1	no	—
116	C₂×#443	—	9	2	no	—
117	#2179	—	9	8	no	—
118	C₂×#368	—	9	1	no	—
119	C₂×#359	—	9	2	no	—
120	C₂×#346	C₃⋊D₃	1	1	yes	characteristic, complemented
121	C₂×#235	—	6	8	no	—
122	C₂²×C₃×C₈	D₁₂	1	4	yes	—
123	C₂²×C₃×C₈	C₂²×D₃	1	4	yes	—
124	C₂×C₃×C₄²	D₁₂	1	4	yes	—
125	C₂×#208	—	6	8	no	—
126	C₂×Dic₁₂	—	3	8	no	—
127	#904	—	3	16	no	—
128	#904	—	3	16	no	—
129	#904	—	6	8	no	—
130	#904	—	6	8	no	—
131	C₂×D₂₄	—	3	8	no	—
132	C₂×#204	—	6	8	no	—
133	#901	—	6	32	no	—
134	#901	—	12	16	no	—
135	C₂×ΓL(1,𝔽₂₅)	—	12	8	no	—
136	C₂×D₃×C₈	—	12	8	no	—
137	C₂×C₃×C₁₆	—	2	4	no	—
138	C₂×C₃×C₁₆	—	2	4	no	—
139	C₂×C₃×C₁₆	C₄×D₃	1	4	yes	—
140	C₂×C₃×C₁₆	C₄×D₃	1	4	yes	—
141	C₂×C₃×C₁₆	C₄×D₃	1	8	yes	—
142	C₂×C₃×C₁₆	C₂²×D₃	1	8	yes	—
143	C₂×C₃×C₁₆	C₂²×D₃	1	8	yes	—
144	C₃×C₄×C₈	D₁₂	1	8	yes	—
145	C₃×C₄×C₈	C₂²×D₃	1	8	yes	—
146	#819	—	3	16	no	—
147	#819	—	6	8	no	—
148	#805	—	6	32	no	—
149	Dic₂₄	—	3	16	no	—
150	#800	—	3	32	no	—
151	D₄₈	—	3	16	no	—
152	C₂³×C₃²	#135	1	1	yes	characteristic
153	C₂²×C₃⋊D₃	—	4	2	no	—
154	C₂×C₃²×C₄	—	2	2	no	—
155	C₂×C₃²×C₄	—	4	2	no	—
156	C₂×C₃²×C₄	C₄×D₄	1	1	yes	characteristic
157	C₂×C₃²×C₄	C₄×D₄	1	1	yes	characteristic
158	C₂×C₃²×C₄	C₂×D₈	1	1	yes	characteristic
159	C₂×C₃²×C₄	C₂×D₈	1	1	yes	characteristic
160	C₂×C₃²×C₄	#135	1	1	yes	characteristic
161	C₂×C₃²×C₄	C₂²×D₄	1	1	yes	characteristic
162	#638	—	4	4	no	—
163	#638	—	4	4	no	—
164	C₂×C₃⋊Dic₃	—	4	2	no	—
165	C₄⋊(C₃⋊D₃)	—	2	4	no	—
166	C₄⋊(C₃⋊D₃)	—	4	2	no	—
167	C₄×C₃⋊D₃	—	4	4	no	—
168	C₄×C₃⋊D₃	—	4	4	no	—
169	#634	—	2	4	no	—
170	#634	—	4	2	no	—
171	C₃²×C₈	C₄×D₄	1	1	yes	characteristic
172	C₃²×C₈	C₄×D₄	1	1	yes	characteristic
173	C₃²×C₈	C₂×D₈	1	4	yes	—
174	C₃²×C₈	C₂³×C₄	1	1	yes	characteristic
175	C₃²×C₈	C₂×#41	1	1	yes	characteristic
176	C₃⋊(C₃⋊C₈)	—	4	4	no	—
177	C₂×#135	—	9	2	no	—
178	C₂×#131	—	18	2	no	—
179	#508	—	9	4	no	—
180	#508	—	9	4	no	—
181	C₂×Q₃₂	—	9	1	no	—
182	C₂×SD₃₂	—	9	2	no	—
183	C₂×D₁₆	—	9	1	no	—
184	C₂²×C₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic
185	C₂²×C₁₆	C₂×C₃⋊D₃	1	1	yes	characteristic
186	#443	—	9	8	no	—
187	#443	—	18	4	no	—
188	C₂×#108	—	9	2	no	—
189	C₂×#104	—	18	2	no	—
190	C₂×C₄×C₈	C₂×C₃⋊D₃	1	1	yes	characteristic
191	#368	—	9	4	no	—
192	#359	—	9	8	no	—
193	#346	C₂×C₃⋊D₃	1	4	yes	complemented
194	C₂²×C₃×C₄	—	2	4	no	—
195	C₂²×C₃×C₄	C₂×D₁₂	1	4	yes	—
196	C₂×#67	—	12	8	no	—
197	#235	—	6	16	no	—
198	#235	—	6	16	no	—
199	#235	—	12	8	no	—
200	#235	—	12	8	no	—
201	C₂×D₁₂	—	6	8	no	—
202	C₂×C₄×D₃	—	12	8	no	—
203	C₂×Dic₆	—	6	8	no	—
204	C₂×C₃×C₈	D₂₄	1	8	yes	—
205	C₂×C₃×C₈	D₂₄	1	8	yes	—
206	C₂×C₃×C₈	C₂×C₄×D₃	1	4	yes	—
207	C₂×C₃×C₈	C₂×C₄×D₃	1	4	yes	—
208	C₂×C₃×C₈	C₂×D₁₂	1	4	yes	—
209	C₂×C₃×C₈	C₂×D₁₂	1	8	yes	—
210	C₂×C₃×C₈	#235	1	4	yes	—
211	C₂×C₃×C₈	#235	1	4	yes	—
212	C₂×C₃×C₈	C₂³×D₃	1	4	yes	—
213	C₃×C₄²	—	2	4	no	—
214	C₃×C₄²	C₂×D₁₂	1	8	yes	—
215	#208	—	6	16	no	—
216	#208	—	12	8	no	—
217	C₂×C₃⋊C₈	—	12	8	no	—
218	Dic₁₂	—	3	16	no	—
219	Dic₁₂	—	6	8	no	—
220	D₂₄	—	3	16	no	—
221	D₂₄	—	6	8	no	—
222	#204	—	6	16	no	—
223	#204	—	6	16	no	—
224	ΓL(1,𝔽₂₅)	—	12	32	no	—
225	D₃×C₈	—	12	32	no	—
226	C₃×C₁₆	—	2	8	no	—
227	C₃×C₁₆	C₂×C₄×D₃	1	8	yes	—
228	C₃×C₁₆	C₂×C₄×D₃	1	8	yes	—
229	C₂²×C₃²	—	2	2	no	—
230	C₂²×C₃²	C₄×D₈	1	1	yes	characteristic
231	C₂²×C₃²	C₄×D₈	1	1	yes	characteristic
232	C₂²×C₃²	C₂×#135	1	1	yes	characteristic
233	C₂×C₃⋊D₃	—	4	4	no	—
234	C₂×C₃⋊D₃	—	8	4	no	—
235	C₃²×C₄	—	4	2	no	—
236	C₃²×C₄	C₄×D₈	1	1	yes	characteristic
237	C₃²×C₄	C₄×D₈	1	1	yes	characteristic
238	C₃²×C₄	C₂×C₄×D₄	1	1	yes	characteristic
239	C₃²×C₄	C₂²×D₈	1	1	yes	characteristic
240	C₃⋊Dic₃	—	4	4	no	—
241	C₂×#41	—	18	2	no	—
242	#135	—	9	4	no	—
243	#135	—	9	4	no	—
244	#135	—	18	2	no	—
245	#135	—	18	2	no	—
246	C₂×Q₁₆	—	9	2	no	—
247	C₂×SD₁₆	—	18	2	no	—
248	C₂×D₈	—	9	2	no	—
249	#131	—	18	8	no	—
250	#131	—	36	4	no	—
251	C₂×M₁₆	—	18	2	no	—
252	C₂×M₁₆	—	36	2	no	—
253	C₂²×C₈	—	36	2	no	—
254	C₂²×C₈	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
255	C₂²×C₈	C₂²×C₃⋊D₃	1	1	yes	characteristic
256	C₂×C₄²	C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
257	Q₃₂	—	9	4	no	—
258	SD₃₂	—	9	8	no	—
259	D₁₆	—	9	4	no	—
260	C₂×C₁₆	—	2	1	no	—
261	C₂×C₁₆	—	2	1	no	—
262	C₂×C₁₆	C₄×C₃⋊D₃	1	1	yes	characteristic
263	C₂×C₁₆	C₄×C₃⋊D₃	1	1	yes	characteristic
264	C₂×C₁₆	C₄×C₃⋊D₃	1	2	yes	—
265	C₂×C₁₆	C₂²×C₃⋊D₃	1	2	yes	—
266	C₂×C₁₆	C₂²×C₃⋊D₃	1	2	yes	—
267	#108	—	9	4	no	—
268	#108	—	18	2	no	—
269	#104	—	18	8	no	—
270	C₄×C₈	C₄⋊(C₃⋊D₃)	1	2	yes	—
271	C₄×C₈	C₂²×C₃⋊D₃	1	2	yes	—
272	C₂³×C₃	#904	1	4	yes	—
273	C₂²×D₃	—	12	8	no	—
274	C₂×C₃×C₄	—	2	8	no	—
275	C₂×C₃×C₄	—	4	8	no	—
276	C₂×C₃×C₄	C₄×D₁₂	1	4	yes	—
277	C₂×C₃×C₄	C₄×D₁₂	1	4	yes	—
278	C₂×C₃×C₄	C₂×D₂₄	1	4	yes	—
279	C₂×C₃×C₄	C₂×D₂₄	1	4	yes	—
280	C₂×C₃×C₄	#904	1	4	yes	—
281	C₂×C₃×C₄	C₂²×D₁₂	1	4	yes	—
282	#67	—	12	16	no	—
283	#67	—	12	16	no	—
284	C₂×Dic₃	—	12	8	no	—
285	D₁₂	—	6	16	no	—
286	D₁₂	—	12	8	no	—
287	C₄×D₃	—	12	16	no	—
288	C₄×D₃	—	12	16	no	—
289	Dic₆	—	6	16	no	—
290	Dic₆	—	12	8	no	—
291	C₃×C₈	C₄×D₁₂	1	4	yes	—
292	C₃×C₈	C₄×D₁₂	1	4	yes	—
293	C₃×C₈	C₂×D₂₄	1	16	yes	—
294	C₃×C₈	C₂²×C₄×D₃	1	4	yes	—
295	C₃×C₈	C₂×#235	1	4	yes	—
296	C₃⋊C₈	—	12	16	no	—
297	C₂×C₃²	—	2	1	no	—
298	C₂×C₃²	—	2	1	no	—
299	C₂×C₃²	#2179	1	2	yes	complemented
300	C₂×C₃²	C₂×C₄×D₈	1	1	yes	characteristic
301	C₃⋊D₃	—	8	4	no	—
302	#41	—	18	4	no	—
303	#41	—	18	4	no	—
304	#41	—	36	2	no	—
305	#41	—	36	2	no	—
306	C₂×Q₈	—	18	2	no	—
307	C₂×D₄	—	18	2	no	—
308	C₂×D₄	—	36	2	no	—
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	36	2	no	—
311	C₂²×C₄	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
312	Q₁₆	—	9	4	no	—
313	Q₁₆	—	18	2	no	—
314	SD₁₆	—	18	4	no	—
315	SD₁₆	—	18	4	no	—
316	D₈	—	9	4	no	—
317	D₈	—	18	2	no	—
318	M₁₆	—	18	4	no	—
319	M₁₆	—	36	2	no	—
320	M₁₆	—	36	8	no	—
321	C₂×C₈	—	36	2	no	—
322	C₂×C₈	—	36	8	no	—
323	C₂×C₈	#3745	1	2	yes	—
324	C₂×C₈	#3745	1	2	yes	—
325	C₂×C₈	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
326	C₂×C₈	C₂×C₄×C₃⋊D₃	1	1	yes	characteristic
327	C₂×C₈	C₂×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
328	C₂×C₈	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
329	C₂×C₈	#3828	1	1	yes	characteristic
330	C₂×C₈	#3828	1	1	yes	characteristic
331	C₂×C₈	C₂³×C₃⋊D₃	1	1	yes	characteristic
332	C₄²	—	2	1	no	—
333	C₄²	C₂×C₄⋊(C₃⋊D₃)	1	2	yes	—
334	C₁₆	—	2	2	no	—
335	C₁₆	C₂×C₄×C₃⋊D₃	1	2	yes	—
336	C₁₆	C₂×C₄×C₃⋊D₃	1	2	yes	—
337	C₂²×C₃	—	2	8	no	—
338	C₂²×C₃	C₄×D₂₄	1	4	yes	—
339	C₂²×C₃	C₄×D₂₄	1	4	yes	—
340	C₂²×C₃	C₂×#904	1	4	yes	—
341	C₂×D₃	—	12	16	no	—
342	C₂×D₃	—	24	16	no	—
343	C₃×C₄	—	4	8	no	—
344	C₃×C₄	C₄×D₂₄	1	4	yes	—
345	C₃×C₄	C₄×D₂₄	1	4	yes	—
346	C₃×C₄	C₂×C₄×D₁₂	1	4	yes	—
347	C₃×C₄	C₂²×D₂₄	1	4	yes	—
348	Dic₃	—	12	16	no	—
349	C₃²	C₂×#2179	1	1	yes	characteristic, complemented, Sylow
350	C₂³	—	36	2	no	—
351	C₂³	#64113	1	1	yes	characteristic
352	Q₈	—	18	4	no	—
353	Q₈	—	36	2	no	—
354	D₄	—	18	4	no	—
355	D₄	—	36	4	no	—
356	D₄	—	36	4	no	—
357	D₄	—	36	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	4	2	no	—
360	C₂×C₄	—	36	2	no	—
361	C₂×C₄	—	36	4	no	—
362	C₂×C₄	—	36	4	no	—
363	C₂×C₄	C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
364	C₂×C₄	C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
365	C₂×C₄	C₂×#3745	1	1	yes	characteristic
366	C₂×C₄	C₂×#3745	1	1	yes	characteristic
367	C₂×C₄	#64113	1	1	yes	characteristic
368	C₂×C₄	C₂²×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
369	C₈	—	36	4	no	—
370	C₈	C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
371	C₈	C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
372	C₈	C₂×#3745	1	4	yes	—
373	C₈	C₂²×C₄×C₃⋊D₃	1	1	yes	characteristic
374	C₈	C₂×#3828	1	1	yes	characteristic
375	C₂×C₃	—	2	4	no	—
376	C₂×C₃	—	2	4	no	—
377	C₂×C₃	#69085	1	8	yes	complemented
378	C₂×C₃	C₂×C₄×D₂₄	1	4	yes	—
379	D₃	—	24	16	no	—
380	C₂²	—	2	2	no	—
381	C₂²	—	36	4	no	—
382	C₂²	—	72	4	no	—
383	C₂²	C₄×#3745	1	1	yes	characteristic
384	C₂²	C₄×#3745	1	1	yes	characteristic
385	C₂²	C₂×#64113	1	1	yes	characteristic
386	C₄	—	4	2	no	—
387	C₄	—	36	4	no	—
388	C₄	C₄×#3745	1	1	yes	characteristic
389	C₄	C₄×#3745	1	1	yes	characteristic
390	C₄	C₂×C₄×C₄⋊(C₃⋊D₃)	1	1	yes	characteristic
391	C₄	C₂²×#3745	1	1	yes	characteristic
392	C₃	C₂×#69085	1	4	yes	complemented
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	72	4	no	—
396	C₂	#11797877	1	2	yes	direct product factor
397	C₂	C₂×C₄×#3745	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂×#3745
commutator	C₃²×C₈	C₂³×C₄
Frattini	C₂×C₈	C₂³×C₃⋊D₃
Fitting	C₂×C₃²×#346	C₂
socle	C₂²×C₃²	C₄×D₈
prime radical	C₂×#10592603	C₂
cosocle	C₂×C₃²×C₈	C₂⁴
hypercenter	C₂×#346	C₃⋊D₃
hypocenter	C₃²	C₂×#2179
LCS	G ▷ C₃²×C₈ ▷ C₃²×C₄ ▷ C₂×C₃² ▷ C₃²
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#346

Complements

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

N	H ≅ G/N	type
2. C₂×#10592399	C₂	semidirect
3. #11797877	C₂	direct (N × H)
4. C₂×#10589372	C₂	semidirect
5. C₂×#10589376	C₂	semidirect
6. C₂×C₃²×#346	C₂	semidirect
15. C₂×#63628	C₄	semidirect
16. #10592603	C₄	semidirect
18. C₂×#63627	C₄	semidirect
19. C₂×#63626	C₄	semidirect
21. #10592399	C₂²	semidirect
22. C₃²×#346	C₂²	semidirect
23. #10589376	C₂²	semidirect
24. #10589372	C₂²	semidirect
27. C₂×C₃×#346	D₃	semidirect
59. #63628	C₂×C₄	semidirect
60. #63627	C₂×C₄	semidirect
61. #63626	C₂×C₄	semidirect
77. C₃×#346	C₂×D₃	semidirect
120. C₂×#346	C₃⋊D₃	semidirect
193. #346	C₂×C₃⋊D₃	semidirect
299. C₂×C₃²	#2179	semidirect
349. C₃²	C₂×#2179	semidirect
377. C₂×C₃	#69085	semidirect
392. C₃	C₂×#69085	semidirect
396. C₂	#11797877	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×#10592603	2
C₂×#10592399	2
#11797877	2
C₂×#10589372	2
C₂×#10589376	2
C₂×C₃²×#346	2
C₂×#69085	3

Subgroups — C2×#11797877 #72269713

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#11797877 #72269713