Subgroups — C₂×#135×D₁₁₃ #28405298

Order 14464.

1504 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#41×D₁₁₃	C₂	1	2	yes	maximal, complemented
2	C₂×#16813645	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16813644	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#16813643	C₂	1	2	yes	maximal, complemented
5	C₂×#16813642	C₂	1	2	yes	maximal, complemented
6	C₂×#16813641	C₂	1	1	yes	maximal, characteristic, complemented
7	#135×D₁₁₃	C₂	1	16	yes	maximal, direct product factor
8	C₂×Q₁₆×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×SD₁₆×D₁₁₃	C₂	1	2	yes	maximal, complemented
10	C₂×D₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂²×C₈×D₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#135×C₁₁₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14268648	C₂²	1	2	yes	complemented
14	C₂×#14268647	—	2	2	no	—
15	C₂×#14268647	C₂²	1	2	yes	complemented
16	C₂×#14268646	—	2	2	no	—
17	C₂×#14268646	C₂²	1	2	yes	complemented
18	#41×D₁₁₃	—	2	8	no	—
19	#41×D₁₁₃	C₂²	1	16	yes	complemented
20	C₂×Q₈×D₁₁₃	C₂²	1	2	yes	—
21	C₂×D₄×D₁₁₃	—	2	2	no	—
22	C₂×D₄×D₁₁₃	C₂²	1	2	yes	—
23	C₂²×C₄×D₁₁₃	—	2	2	no	—
24	C₂²×C₄×D₁₁₃	C₂²	1	1	yes	characteristic
25	#16813645	C₂²	1	8	yes	complemented
26	#16813644	C₂²	1	8	yes	complemented
27	#16813643	C₂²	1	16	yes	complemented
28	#16813642	C₂²	1	16	yes	complemented
29	#16813641	C₂²	1	8	yes	complemented
30	C₂×Dic₄₅₂	C₂²	1	1	yes	characteristic, complemented
31	C₂×#14268637	C₂²	1	2	yes	complemented
32	Q₁₆×D₁₁₃	C₂²	1	8	yes	complemented
33	C₂×#14268636	C₂²	1	2	yes	complemented
34	C₂×#14268635	C₂²	1	2	yes	complemented
35	C₂×#14268634	C₂²	1	2	yes	complemented
36	SD₁₆×D₁₁₃	C₂²	1	16	yes	complemented
37	C₂×D₉₀₄	C₂²	1	1	yes	characteristic, complemented
38	C₂×#14268632	C₂²	1	2	yes	complemented
39	D₈×D₁₁₃	C₂²	1	8	yes	complemented
40	C₂²×#11744751	C₂²	1	1	yes	characteristic, complemented
41	C₂×C₈×D₁₁₃	C₂²	1	1	yes	characteristic
42	C₂×C₈×D₁₁₃	C₂²	1	1	yes	characteristic
43	C₂×C₈×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
44	C₂×C₈×D₁₁₃	C₂²	1	1	yes	characteristic, complemented
45	C₂×C₈×D₁₁₃	C₂²	1	8	yes	complemented
46	C₂×#41×C₁₁₃	C₂²	1	2	yes	complemented
47	#135×C₁₁₃	C₂²	1	8	yes	complemented
48	C₂×Q₁₆×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×SD₁₆×C₁₁₃	C₂²	1	2	yes	complemented
50	C₂×D₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
51	C₂²×C₈×C₁₁₃	C₂²	1	1	yes	characteristic, complemented
52	C₂³×D₁₁₃	—	2	2	no	—
53	C₂³×D₁₁₃	D₄	1	1	yes	characteristic
54	#14268648	—	2	4	no	—
55	#14268648	C₂³	1	8	yes	complemented
56	#14268647	—	2	4	no	—
57	#14268647	—	2	16	no	—
58	#14268647	C₂³	1	8	yes	complemented
59	#14268646	—	2	16	no	—
60	#14268646	—	2	4	no	—
61	#14268646	C₂³	1	8	yes	complemented
62	C₂×Dic₂₂₆	—	2	2	no	—
63	C₂×Dic₂₂₆	C₂³	1	2	yes	—
64	Q₈×D₁₁₃	—	2	4	no	—
65	Q₈×D₁₁₃	C₂³	1	8	yes	—
66	C₂×D₄₅₂	—	2	2	no	—
67	C₂×D₄₅₂	C₂³	1	2	yes	—
68	C₂×C₂²⋊D₁₁₃	—	2	2	no	—
69	C₂×C₂²⋊D₁₁₃	—	2	2	no	—
70	C₂×C₂²⋊D₁₁₃	—	2	2	no	—
71	D₄×D₁₁₃	—	2	16	no	—
72	D₄×D₁₁₃	—	2	4	no	—
73	D₄×D₁₁₃	C₂³	1	8	yes	—
74	C₂²×Dic₁₁₃	—	2	2	no	—
75	C₂²×Dic₁₁₃	D₄	1	1	yes	characteristic
76	C₂×C₄×D₁₁₃	—	2	2	no	—
77	C₂×C₄×D₁₁₃	—	2	2	no	—
78	C₂×C₄×D₁₁₃	—	2	2	no	—
79	C₂×C₄×D₁₁₃	—	2	16	no	—
80	C₂×C₄×D₁₁₃	D₄	1	1	yes	characteristic
81	C₂×C₄×D₁₁₃	D₄	1	4	yes	—
82	C₂×C₄×D₁₁₃	D₄	1	1	yes	characteristic
83	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₁₁₃	C₂³	1	4	yes	—
85	C₂×C₄×D₁₁₃	C₂³	1	1	yes	characteristic
86	Dic₄₅₂	C₂³	1	4	yes	complemented
87	#14268637	C₂³	1	8	yes	complemented
88	#14268636	C₂³	1	8	yes	complemented
89	#14268635	C₂³	1	8	yes	complemented
90	#14268634	C₂³	1	8	yes	complemented
91	D₉₀₄	C₂³	1	4	yes	complemented
92	#14268632	C₂³	1	8	yes	complemented
93	C₂×#11744751	C₂³	1	1	yes	characteristic
94	C₂×#11744751	C₂³	1	1	yes	characteristic
95	C₂×#11744751	C₂³	1	4	yes	complemented
96	C₈×D₁₁₃	C₂³	1	4	yes	—
97	C₈×D₁₁₃	C₂³	1	4	yes	—
98	C₈×D₁₁₃	C₂³	1	4	yes	complemented
99	C₈×D₁₁₃	C₂³	1	4	yes	complemented
100	#41×C₁₁₃	—	2	4	no	—
101	#41×C₁₁₃	C₂³	1	8	yes	complemented
102	C₂×Q₈×C₁₁₃	C₂³	1	2	yes	—
103	C₂×D₄×C₁₁₃	—	2	2	no	—
104	C₂×D₄×C₁₁₃	C₂³	1	2	yes	—
105	C₂²×C₄×C₁₁₃	—	2	2	no	—
106	C₂²×C₄×C₁₁₃	C₂³	1	1	yes	characteristic
107	Q₁₆×C₁₁₃	C₂³	1	4	yes	complemented
108	SD₁₆×C₁₁₃	C₂³	1	8	yes	complemented
109	D₈×C₁₁₃	C₂³	1	4	yes	complemented
110	C₂×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
111	C₂×C₈×C₁₁₃	C₂³	1	1	yes	characteristic
112	C₂×C₈×C₁₁₃	C₂³	1	4	yes	complemented
113	C₂³×C₁₁₃	—	2	2	no	—
114	C₂³×C₁₁₃	C₂×D₄	1	1	yes	characteristic
115	C₂²×D₁₁₃	—	2	4	no	—
116	C₂²×D₁₁₃	—	2	2	no	—
117	C₂²×D₁₁₃	—	2	8	no	—
118	C₂²×D₁₁₃	—	4	8	no	—
119	C₂²×D₁₁₃	C₂×D₄	1	4	yes	—
120	C₂²×D₁₁₃	C₂×D₄	1	1	yes	characteristic
121	C₂²×D₁₁₃	C₂×D₄	1	1	yes	characteristic
122	Q₈×C₁₁₃	—	2	2	no	—
123	Q₈×C₁₁₃	C₂⁴	1	4	yes	—
124	D₄×C₁₁₃	—	2	8	no	—
125	D₄×C₁₁₃	—	2	2	no	—
126	D₄×C₁₁₃	C₂⁴	1	4	yes	—
127	C₂×C₄×C₁₁₃	—	2	2	no	—
128	C₂×C₄×C₁₁₃	—	2	8	no	—
129	C₂×C₄×C₁₁₃	C₂×D₄	1	2	yes	—
130	C₂×C₄×C₁₁₃	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₁₃	C₂⁴	1	1	yes	characteristic
132	C₂×C₄×C₁₁₃	C₂⁴	1	2	yes	—
133	C₂²⋊D₁₁₃	—	2	8	no	—
134	C₂²⋊D₁₁₃	—	2	8	no	—
135	C₂²⋊D₁₁₃	—	2	8	no	—
136	C₂×Dic₁₁₃	—	2	2	no	—
137	C₂×Dic₁₁₃	—	2	8	no	—
138	C₂×Dic₁₁₃	C₂×D₄	1	1	yes	characteristic
139	C₂×Dic₁₁₃	C₂×D₄	1	1	yes	characteristic
140	C₂×Dic₁₁₃	C₂×D₄	1	4	yes	—
141	D₄₅₂	—	2	8	no	—
142	D₄₅₂	—	2	2	no	—
143	D₄₅₂	C₂⁴	1	4	yes	—
144	C₄×D₁₁₃	—	2	8	no	—
145	C₄×D₁₁₃	—	2	8	no	—
146	C₄×D₁₁₃	—	2	8	no	—
147	C₄×D₁₁₃	C₂×D₄	1	4	yes	—
148	C₄×D₁₁₃	C₂×D₄	1	2	yes	—
149	C₄×D₁₁₃	C₂×D₄	1	2	yes	—
150	C₄×D₁₁₃	C₂×D₄	1	4	yes	—
151	C₄×D₁₁₃	C₂⁴	1	2	yes	—
152	C₄×D₁₁₃	C₂⁴	1	2	yes	—
153	Dic₂₂₆	—	2	2	no	—
154	Dic₂₂₆	—	2	8	no	—
155	Dic₂₂₆	C₂⁴	1	4	yes	—
156	C₈×C₁₁₃	C₂⁴	1	2	yes	—
157	C₈×C₁₁₃	C₂⁴	1	2	yes	—
158	#11744751	C₂⁴	1	2	yes	—
159	#11744751	C₂⁴	1	2	yes	—
160	C₂²×C₁₁₃	—	2	2	no	—
161	C₂²×C₁₁₃	—	2	4	no	—
162	C₂²×C₁₁₃	—	4	4	no	—
163	C₂²×C₁₁₃	C₂²×D₄	1	2	yes	—
164	C₂²×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
165	C₂×D₁₁₃	—	2	2	no	—
166	C₂×D₁₁₃	—	2	8	no	—
167	C₂×D₁₁₃	—	2	4	no	—
168	C₂×D₁₁₃	—	4	4	no	—
169	C₂×D₁₁₃	—	4	16	no	—
170	C₂×D₁₁₃	#135	1	4	yes	direct product factor
171	C₂×D₁₁₃	C₂²×D₄	1	2	yes	—
172	C₂×D₁₁₃	C₂²×D₄	1	2	yes	—
173	C₄×C₁₁₃	—	2	4	no	—
174	C₄×C₁₁₃	C₂²×D₄	1	1	yes	characteristic
175	C₄×C₁₁₃	C₂²×D₄	1	2	yes	—
176	C₄×C₁₁₃	C₂⁵	1	1	yes	characteristic
177	Dic₁₁₃	—	2	4	no	—
178	Dic₁₁₃	C₂²×D₄	1	2	yes	—
179	Dic₁₁₃	C₂²×D₄	1	2	yes	—
180	C₂×C₁₁₃	—	2	2	no	—
181	C₂×C₁₁₃	—	4	4	no	—
182	C₂×C₁₁₃	C₂×#135	1	2	yes	complemented
183	C₂×C₁₁₃	C₂³×D₄	1	1	yes	characteristic
184	D₁₁₃	—	2	2	no	—
185	D₁₁₃	—	4	4	no	—
186	D₁₁₃	C₂×#135	1	4	yes	direct product factor
187	C₂²×#135	—	113	1	no	maximal, Sylow
188	C₁₁₃	C₂²×#135	1	1	yes	characteristic, complemented, Sylow
189	C₂²×#41	—	113	2	no	—
190	C₂×#135	—	113	2	no	—
191	C₂×#135	—	113	16	no	—
192	C₂×#135	—	113	1	no	—
193	C₂×#135	—	113	2	no	—
194	C₂×#135	—	113	1	no	—
195	C₂×#135	—	113	1	no	—
196	C₂×#135	D₁₁₃	1	1	yes	characteristic, direct product factor
197	C₂²×Q₁₆	—	113	1	no	—
198	C₂²×SD₁₆	—	113	2	no	—
199	C₂²×D₈	—	113	1	no	—
200	C₂³×C₈	—	113	1	no	—
201	C₂×#41	—	113	16	no	—
202	C₂×#41	—	113	2	no	—
203	C₂×#41	—	113	2	no	—
204	C₂×#41	—	113	2	no	—
205	C₂×#41	—	226	2	no	—
206	C₂×#41	—	226	2	no	—
207	C₂×#41	—	226	8	no	—
208	C₂×#41	C₂×D₁₁₃	1	2	yes	complemented
209	C₂²×Q₈	—	113	2	no	—
210	C₂²×D₄	—	113	2	no	—
211	C₂²×D₄	—	226	2	no	—
212	C₂³×C₄	—	113	1	no	—
213	C₂³×C₄	—	226	2	no	—
214	#135	—	113	16	no	—
215	#135	—	113	8	no	—
216	#135	—	113	16	no	—
217	#135	—	113	8	no	—
218	#135	—	113	8	no	—
219	#135	C₂×D₁₁₃	1	8	yes	direct product factor
220	C₂×Q₁₆	—	113	2	no	—
221	C₂×Q₁₆	—	113	8	no	—
222	C₂×Q₁₆	—	113	1	no	—
223	C₂×Q₁₆	C₂×D₁₁₃	1	1	yes	characteristic, complemented
224	C₂×SD₁₆	—	113	2	no	—
225	C₂×SD₁₆	—	113	2	no	—
226	C₂×SD₁₆	—	113	16	no	—
227	C₂×SD₁₆	—	113	2	no	—
228	C₂×SD₁₆	C₂×D₁₁₃	1	2	yes	complemented
229	C₂×D₈	—	113	2	no	—
230	C₂×D₈	—	113	8	no	—
231	C₂×D₈	—	113	1	no	—
232	C₂×D₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
233	C₂²×C₈	—	113	1	no	—
234	C₂²×C₈	—	113	1	no	—
235	C₂²×C₈	—	113	1	no	—
236	C₂²×C₈	—	113	1	no	—
237	C₂²×C₈	—	113	1	no	—
238	C₂²×C₈	—	113	8	no	—
239	C₂²×C₈	C₂×D₁₁₃	1	1	yes	characteristic, complemented
240	C₂⁴	—	113	1	no	—
241	C₂⁴	—	226	2	no	—
242	#41	—	2	4	no	—
243	#41	—	113	8	no	—
244	#41	—	113	8	no	—
245	#41	—	113	8	no	—
246	#41	—	226	16	no	—
247	#41	—	226	16	no	—
248	#41	—	226	4	no	—
249	#41	—	226	4	no	—
250	#41	—	226	4	no	—
251	#41	C₂²×D₁₁₃	1	8	yes	complemented
252	C₂×Q₈	—	113	8	no	—
253	C₂×Q₈	—	113	2	no	—
254	C₂×Q₈	—	226	2	no	—
255	C₂×Q₈	—	226	4	no	—
256	C₂×Q₈	C₂²×D₁₁₃	1	2	yes	—
257	C₂×D₄	—	2	2	no	—
258	C₂×D₄	—	113	8	no	—
259	C₂×D₄	—	113	2	no	—
260	C₂×D₄	—	226	2	no	—
261	C₂×D₄	—	226	4	no	—
262	C₂×D₄	—	226	2	no	—
263	C₂×D₄	—	226	16	no	—
264	C₂×D₄	—	226	2	no	—
265	C₂×D₄	—	226	2	no	—
266	C₂×D₄	C₂²×D₁₁₃	1	2	yes	—
267	C₂²×C₄	—	2	2	no	—
268	C₂²×C₄	—	113	1	no	—
269	C₂²×C₄	—	113	4	no	—
270	C₂²×C₄	—	113	1	no	—
271	C₂²×C₄	—	113	1	no	—
272	C₂²×C₄	—	113	1	no	—
273	C₂²×C₄	—	113	1	no	—
274	C₂²×C₄	—	113	4	no	—
275	C₂²×C₄	—	226	2	no	—
276	C₂²×C₄	—	226	16	no	—
277	C₂²×C₄	—	226	2	no	—
278	C₂²×C₄	—	226	2	no	—
279	C₂²×C₄	—	226	2	no	—
280	C₂²×C₄	C₂²×D₁₁₃	1	1	yes	characteristic
281	Q₁₆	—	113	8	no	—
282	Q₁₆	—	113	4	no	—
283	Q₁₆	C₂²×D₁₁₃	1	4	yes	complemented
284	SD₁₆	—	113	8	no	—
285	SD₁₆	—	113	8	no	—
286	SD₁₆	—	113	8	no	—
287	SD₁₆	C₂²×D₁₁₃	1	8	yes	complemented
288	D₈	—	113	8	no	—
289	D₈	—	113	4	no	—
290	D₈	C₂²×D₁₁₃	1	4	yes	complemented
291	C₂×C₈	—	113	1	no	—
292	C₂×C₈	—	113	1	no	—
293	C₂×C₈	—	113	4	no	—
294	C₂×C₈	—	113	4	no	—
295	C₂×C₈	—	113	4	no	—
296	C₂×C₈	—	113	4	no	—
297	C₂×C₈	—	113	4	no	—
298	C₂×C₈	C₂²×D₁₁₃	1	1	yes	characteristic
299	C₂×C₈	C₂²×D₁₁₃	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₁₁₃	1	4	yes	complemented
301	C₂³	—	2	2	no	—
302	C₂³	—	113	1	no	—
303	C₂³	—	113	4	no	—
304	C₂³	—	113	1	no	—
305	C₂³	—	452	8	no	—
306	C₂³	—	226	8	no	—
307	C₂³	—	226	4	no	—
308	C₂³	—	226	2	no	—
309	C₂³	D₄×D₁₁₃	1	1	yes	characteristic
310	Q₈	—	2	2	no	—
311	Q₈	—	113	4	no	—
312	Q₈	—	226	8	no	—
313	Q₈	—	226	2	no	—
314	Q₈	C₂³×D₁₁₃	1	4	yes	—
315	D₄	—	2	8	no	—
316	D₄	—	2	2	no	—
317	D₄	—	113	4	no	—
318	D₄	—	226	8	no	—
319	D₄	—	226	8	no	—
320	D₄	—	226	8	no	—
321	D₄	—	226	8	no	—
322	D₄	—	226	2	no	—
323	D₄	C₂³×D₁₁₃	1	4	yes	—
324	C₂×C₄	—	2	2	no	—
325	C₂×C₄	—	2	8	no	—
326	C₂×C₄	—	113	1	no	—
327	C₂×C₄	—	113	1	no	—
328	C₂×C₄	—	113	4	no	—
329	C₂×C₄	—	113	4	no	—
330	C₂×C₄	—	113	2	no	—
331	C₂×C₄	—	113	2	no	—
332	C₂×C₄	—	113	4	no	—
333	C₂×C₄	—	113	2	no	—
334	C₂×C₄	—	113	2	no	—
335	C₂×C₄	—	226	8	no	—
336	C₂×C₄	—	226	8	no	—
337	C₂×C₄	—	226	8	no	—
338	C₂×C₄	—	226	2	no	—
339	C₂×C₄	—	226	8	no	—
340	C₂×C₄	D₄×D₁₁₃	1	2	yes	—
341	C₂×C₄	D₄×D₁₁₃	1	1	yes	characteristic
342	C₂×C₄	C₂³×D₁₁₃	1	1	yes	characteristic
343	C₂×C₄	C₂³×D₁₁₃	1	2	yes	—
344	C₈	—	113	2	no	—
345	C₈	—	113	2	no	—
346	C₈	C₂³×D₁₁₃	1	2	yes	—
347	C₈	C₂³×D₁₁₃	1	2	yes	—
348	C₂²	—	2	2	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	4	4	no	—
351	C₂²	—	113	4	no	—
352	C₂²	—	113	2	no	—
353	C₂²	—	113	2	no	—
354	C₂²	—	452	16	no	—
355	C₂²	—	452	4	no	—
356	C₂²	—	226	8	no	—
357	C₂²	—	226	4	no	—
358	C₂²	—	226	2	no	—
359	C₂²	C₂×D₄×D₁₁₃	1	2	yes	—
360	C₂²	C₂×D₄×D₁₁₃	1	1	yes	characteristic
361	C₄	—	2	4	no	—
362	C₄	—	113	2	no	—
363	C₄	—	113	2	no	—
364	C₄	—	226	4	no	—
365	C₄	C₂×D₄×D₁₁₃	1	2	yes	—
366	C₄	C₂×D₄×D₁₁₃	1	1	yes	characteristic
367	C₄	C₂⁴×D₁₁₃	1	1	yes	characteristic
368	C₂	—	2	2	no	—
369	C₂	—	4	4	no	—
370	C₂	—	113	4	no	—
371	C₂	—	452	4	no	—
372	C₂	—	226	2	no	—
373	C₂	#135×D₁₁₃	1	2	yes	direct product factor
374	C₂	C₂²×D₄×D₁₁₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₁₃
commutator, cosocle	C₄×C₁₁₃	C₂⁵
Frattini	C₄	C₂⁴×D₁₁₃
Fitting	C₂×#135×C₁₁₃	C₂
socle	C₂²×C₁₁₃	C₂²×D₄
hypercenter	C₂×#135	D₁₁₃
hypocenter	C₁₁₃	C₂²×#135
LCS	G ▷ C₄×C₁₁₃ ▷ C₂×C₁₁₃ ▷ C₁₁₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×#135

Complements

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

N	H ≅ G/N	type
1. C₂×#41×D₁₁₃	C₂	semidirect
2. C₂×#16813645	C₂	semidirect
3. C₂×#16813644	C₂	semidirect
4. C₂×#16813643	C₂	semidirect
5. C₂×#16813642	C₂	semidirect
6. C₂×#16813641	C₂	semidirect
7. #135×D₁₁₃	C₂	direct (N × H)
8. C₂×Q₁₆×D₁₁₃	C₂	semidirect
9. C₂×SD₁₆×D₁₁₃	C₂	semidirect
10. C₂×D₈×D₁₁₃	C₂	semidirect
11. C₂²×C₈×D₁₁₃	C₂	semidirect
12. C₂×#135×C₁₁₃	C₂	semidirect
13. C₂×#14268648	C₂²	semidirect
15. C₂×#14268647	C₂²	semidirect
17. C₂×#14268646	C₂²	semidirect
19. #41×D₁₁₃	C₂²	semidirect
25. #16813645	C₂²	semidirect
26. #16813644	C₂²	semidirect
27. #16813643	C₂²	semidirect
28. #16813642	C₂²	semidirect
29. #16813641	C₂²	semidirect
30. C₂×Dic₄₅₂	C₂²	semidirect
31. C₂×#14268637	C₂²	semidirect
32. Q₁₆×D₁₁₃	C₂²	semidirect
33. C₂×#14268636	C₂²	semidirect
34. C₂×#14268635	C₂²	semidirect
35. C₂×#14268634	C₂²	semidirect
36. SD₁₆×D₁₁₃	C₂²	semidirect
37. C₂×D₉₀₄	C₂²	semidirect
38. C₂×#14268632	C₂²	semidirect
39. D₈×D₁₁₃	C₂²	semidirect
40. C₂²×#11744751	C₂²	semidirect
43. C₂×C₈×D₁₁₃	C₂²	semidirect
44. C₂×C₈×D₁₁₃	C₂²	semidirect
45. C₂×C₈×D₁₁₃	C₂²	semidirect
46. C₂×#41×C₁₁₃	C₂²	semidirect
47. #135×C₁₁₃	C₂²	semidirect
48. C₂×Q₁₆×C₁₁₃	C₂²	semidirect
49. C₂×SD₁₆×C₁₁₃	C₂²	semidirect
50. C₂×D₈×C₁₁₃	C₂²	semidirect
51. C₂²×C₈×C₁₁₃	C₂²	semidirect
55. #14268648	C₂³	semidirect
58. #14268647	C₂³	semidirect
61. #14268646	C₂³	semidirect
86. Dic₄₅₂	C₂³	semidirect
87. #14268637	C₂³	semidirect
88. #14268636	C₂³	semidirect
89. #14268635	C₂³	semidirect
90. #14268634	C₂³	semidirect
91. D₉₀₄	C₂³	semidirect
92. #14268632	C₂³	semidirect
95. C₂×#11744751	C₂³	semidirect
98. C₈×D₁₁₃	C₂³	semidirect
99. C₈×D₁₁₃	C₂³	semidirect
101. #41×C₁₁₃	C₂³	semidirect
107. Q₁₆×C₁₁₃	C₂³	semidirect
108. SD₁₆×C₁₁₃	C₂³	semidirect
109. D₈×C₁₁₃	C₂³	semidirect
112. C₂×C₈×C₁₁₃	C₂³	semidirect
170. C₂×D₁₁₃	#135	direct (N × H)
182. C₂×C₁₁₃	C₂×#135	semidirect
186. D₁₁₃	C₂×#135	direct (N × H)
188. C₁₁₃	C₂²×#135	semidirect
196. C₂×#135	D₁₁₃	direct (N × H)
208. C₂×#41	C₂×D₁₁₃	semidirect
219. #135	C₂×D₁₁₃	direct (N × H)
223. C₂×Q₁₆	C₂×D₁₁₃	semidirect
228. C₂×SD₁₆	C₂×D₁₁₃	semidirect
232. C₂×D₈	C₂×D₁₁₃	semidirect
239. C₂²×C₈	C₂×D₁₁₃	semidirect
251. #41	C₂²×D₁₁₃	semidirect
283. Q₁₆	C₂²×D₁₁₃	semidirect
287. SD₁₆	C₂²×D₁₁₃	semidirect
290. D₈	C₂²×D₁₁₃	semidirect
300. C₂×C₈	C₂²×D₁₁₃	semidirect
373. C₂	#135×D₁₁₃	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×#41×D₁₁₃	2
C₂×#16813645	2
C₂×#16813644	2
C₂×#16813643	2
C₂×#16813642	2
C₂×#16813641	2
#135×D₁₁₃	2
C₂×Q₁₆×D₁₁₃	2
C₂×SD₁₆×D₁₁₃	2
C₂×D₈×D₁₁₃	2
C₂²×C₈×D₁₁₃	2
C₂×#135×C₁₁₃	2
C₂²×#135	113

Subgroups — C2×#135×D113 #28405298

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#135×D₁₁₃ #28405298