Subgroups — C₂×#19152214 #26033625

Order 11392.

1132 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#19152214	C₂	1	16	yes	maximal, direct product factor
2	C₂×#15668011	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#15668007	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#15668000	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#15667998	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#15667998	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#15667997	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#15667996	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#15667992	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#15667990	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#15667989	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#15667985	C₂	1	1	yes	maximal, characteristic
13	C₂×C₄×Dic₁₇₈	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#15667972	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#15667970	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#126×C₈₉	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
18	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
19	C₂²×Dic₁₇₈	C₂²	1	1	yes	characteristic
20	C₂²×D₃₅₆	C₂²	1	1	yes	characteristic
21	C₂²×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
22	C₂²×C₂²⋊D₈₉	C₂²	1	1	yes	characteristic
23	C₂³×Dic₈₉	C₂²	1	1	yes	characteristic
24	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
25	C₂²×C₄×D₈₉	C₂²	1	1	yes	characteristic
26	#15668011	C₂²	1	8	yes	complemented
27	#15668007	C₂²	1	8	yes	complemented
28	#15668000	C₂²	1	8	yes	complemented
29	#15667998	C₂²	1	8	yes	complemented
30	#15667998	C₂²	1	8	yes	complemented
31	#15667997	C₂²	1	8	yes	complemented
32	#15667996	C₂²	1	8	yes	complemented
33	#15667992	C₂²	1	8	yes	complemented
34	#15667990	C₂²	1	8	yes	complemented
35	#15667989	C₂²	1	8	yes	complemented
36	#15667985	C₂²	1	8	yes	—
37	C₄×Dic₁₇₈	C₂²	1	8	yes	complemented
38	#15667972	C₂²	1	8	yes	complemented
39	#15667970	C₂²	1	8	yes	complemented
40	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
41	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
42	C₂×C₄⋊Dic₈₉	C₂²	1	1	yes	characteristic
43	C₂×#13083553	C₂²	1	1	yes	characteristic
44	C₂×#13083553	C₂²	1	1	yes	characteristic
45	C₂×#13083553	C₂²	1	1	yes	characteristic
46	C₂×#13083553	C₂²	1	1	yes	characteristic
47	C₂×C₂²⋊Dic₈₉	C₂²	1	1	yes	characteristic
48	C₂×#13083551	C₂²	1	1	yes	characteristic
49	C₂×#13083551	C₂²	1	1	yes	characteristic
50	C₂×#13083551	C₂²	1	1	yes	characteristic
51	C₂×#13083551	C₂²	1	1	yes	characteristic
52	C₂×#13083551	C₂²	1	1	yes	characteristic
53	C₂×#13083551	C₂²	1	1	yes	characteristic
54	C₂×#13083551	C₂²	1	1	yes	characteristic
55	C₂×#13083551	C₂²	1	1	yes	characteristic
56	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
57	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
58	C₂×C₄×Dic₈₉	C₂²	1	1	yes	characteristic
59	#126×C₈₉	C₂²	1	8	yes	complemented
60	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
61	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
62	C₂×C₄⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
63	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
64	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
65	C₂×C₂²⋊C₄×C₈₉	C₂²	1	1	yes	characteristic
66	C₂×C₄²×C₈₉	C₂²	1	1	yes	characteristic
67	C₂³×D₈₉	C₂³	1	1	yes	characteristic
68	C₂³×D₈₉	C₂³	1	1	yes	characteristic
69	C₂×Dic₁₇₈	—	2	4	no	—
70	C₂×Dic₁₇₈	—	4	2	no	—
71	C₂×Dic₁₇₈	—	4	2	no	—
72	C₂×Dic₁₇₈	C₂³	1	4	yes	—
73	C₂×Dic₁₇₈	C₂³	1	4	yes	—
74	C₂×Dic₁₇₈	C₂³	1	4	yes	—
75	C₂×D₃₅₆	—	4	2	no	—
76	C₂×D₃₅₆	C₂³	1	4	yes	—
77	C₂×C₂²⋊D₈₉	—	2	4	no	—
78	C₂×C₂²⋊D₈₉	—	4	2	no	—
79	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
80	C₂×C₂²⋊D₈₉	C₂³	1	4	yes	—
81	C₂²×Dic₈₉	—	4	2	no	—
82	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
83	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
84	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
85	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
86	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
87	C₂²×Dic₈₉	C₂³	1	4	yes	—
88	C₂²×Dic₈₉	C₂³	1	1	yes	characteristic
89	C₂×C₄×D₈₉	—	2	4	no	—
90	C₂×C₄×D₈₉	—	4	2	no	—
91	C₂×C₄×D₈₉	C₂³	1	4	yes	—
92	C₂×C₄×D₈₉	C₂³	1	4	yes	—
93	C₄⋊Dic₈₉	C₂³	1	4	yes	—
94	C₄⋊Dic₈₉	C₂³	1	4	yes	—
95	C₄⋊Dic₈₉	C₂³	1	4	yes	—
96	#13083553	C₂³	1	4	yes	—
97	#13083553	C₂³	1	4	yes	—
98	#13083553	C₂³	1	4	yes	—
99	#13083553	C₂³	1	4	yes	—
100	C₂²⋊Dic₈₉	C₂³	1	4	yes	—
101	#13083551	C₂³	1	4	yes	—
102	#13083551	C₂³	1	4	yes	—
103	#13083551	C₂³	1	4	yes	—
104	#13083551	C₂³	1	4	yes	—
105	#13083551	C₂³	1	4	yes	—
106	#13083551	C₂³	1	4	yes	—
107	#13083551	C₂³	1	4	yes	—
108	#13083551	C₂³	1	4	yes	—
109	C₄×Dic₈₉	C₂³	1	4	yes	—
110	C₄×Dic₈₉	C₂³	1	4	yes	—
111	C₄×Dic₈₉	C₂³	1	4	yes	—
112	C₂⁴×C₈₉	C₂³	1	1	yes	characteristic
113	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
114	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
116	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
117	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
118	C₂²×C₄×C₈₉	C₂³	1	1	yes	characteristic
119	C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
120	C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
121	C₄⋊C₄×C₈₉	C₂³	1	4	yes	—
122	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
123	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
124	C₂²⋊C₄×C₈₉	C₂³	1	4	yes	—
125	C₄²×C₈₉	C₂³	1	4	yes	—
126	C₂³×C₈₉	—	2	2	no	—
127	C₂³×C₈₉	—	2	2	no	—
128	C₂³×C₈₉	—	2	2	no	—
129	C₂³×C₈₉	C₂⁴	1	2	yes	—
130	C₂³×C₈₉	C₂⁴	1	1	yes	characteristic
131	C₂²×D₈₉	—	2	2	no	—
132	C₂²×D₈₉	—	2	2	no	—
133	C₂²×D₈₉	—	2	2	no	—
134	C₂²×D₈₉	—	2	2	no	—
135	C₂²×D₈₉	—	2	2	no	—
136	C₂²×D₈₉	—	2	2	no	—
137	C₂²×D₈₉	C₂⁴	1	2	yes	—
138	C₂²×D₈₉	C₂⁴	1	2	yes	—
139	C₂×C₄×C₈₉	—	2	2	no	—
140	C₂×C₄×C₈₉	—	2	2	no	—
141	C₂×C₄×C₈₉	—	2	2	no	—
142	C₂×C₄×C₈₉	—	2	2	no	—
143	C₂×C₄×C₈₉	—	2	2	no	—
144	C₂×C₄×C₈₉	—	2	2	no	—
145	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
146	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
147	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
148	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
149	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
150	C₂×C₄×C₈₉	C₂⁴	1	2	yes	—
151	C₂²⋊D₈₉	—	2	8	no	—
152	C₂²⋊D₈₉	—	4	4	no	—
153	C₂×Dic₈₉	—	2	2	no	—
154	C₂×Dic₈₉	—	2	2	no	—
155	C₂×Dic₈₉	—	2	2	no	—
156	C₂×Dic₈₉	—	2	2	no	—
157	C₂×Dic₈₉	—	2	2	no	—
158	C₂×Dic₈₉	—	4	4	no	—
159	C₂×Dic₈₉	#41	1	4	yes	—
160	C₂×Dic₈₉	C₂⁴	1	2	yes	—
161	C₂×Dic₈₉	C₂⁴	1	2	yes	—
162	C₂×Dic₈₉	C₂⁴	1	2	yes	—
163	C₂×Dic₈₉	C₂⁴	1	2	yes	—
164	C₂×Dic₈₉	C₂⁴	1	2	yes	—
165	C₂×Dic₈₉	C₂⁴	1	2	yes	—
166	D₃₅₆	—	4	4	no	—
167	C₄×D₈₉	—	2	8	no	—
168	C₄×D₈₉	—	4	4	no	—
169	Dic₁₇₈	—	2	8	no	—
170	Dic₁₇₈	—	4	4	no	—
171	Dic₁₇₈	—	4	4	no	—
172	C₂²×C₈₉	—	2	2	no	—
173	C₂²×C₈₉	—	2	2	no	—
174	C₂²×C₈₉	—	2	2	no	—
175	C₂²×C₈₉	—	4	4	no	—
176	C₂²×C₈₉	C₂×#41	1	2	yes	—
177	C₂²×C₈₉	H(5,𝔽₂)	1	2	yes	—
178	C₂²×C₈₉	2₋¹⁺⁴	1	2	yes	—
179	C₂²×C₈₉	C₂⁵	1	1	yes	characteristic
180	C₂×D₈₉	—	2	2	no	—
181	C₂×D₈₉	—	2	2	no	—
182	C₂×D₈₉	—	2	2	no	—
183	C₂×D₈₉	—	2	2	no	—
184	C₂×D₈₉	—	2	2	no	—
185	C₂×D₈₉	—	2	2	no	—
186	C₂×D₈₉	—	4	4	no	—
187	C₂×D₈₉	—	4	4	no	—
188	C₄×C₈₉	—	2	2	no	—
189	C₄×C₈₉	—	2	2	no	—
190	C₄×C₈₉	—	2	2	no	—
191	C₄×C₈₉	—	2	2	no	—
192	C₄×C₈₉	—	2	2	no	—
193	C₄×C₈₉	—	2	2	no	—
194	Dic₈₉	—	2	2	no	—
195	Dic₈₉	—	2	2	no	—
196	Dic₈₉	—	2	2	no	—
197	Dic₈₉	—	2	2	no	—
198	Dic₈₉	—	2	2	no	—
199	Dic₈₉	C₂×#41	1	4	yes	—
200	C₂×C₈₉	—	4	2	no	—
201	C₂×C₈₉	#542	1	4	yes	complemented
202	C₂×C₈₉	C₂²×#41	1	1	yes	characteristic
203	C₂×C₈₉	C₂×H(5,𝔽₂)	1	1	yes	characteristic
204	C₂×C₈₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
205	D₈₉	—	4	2	no	—
206	D₈₉	—	4	2	no	—
207	C₂×#542	—	89	1	no	maximal, Sylow
208	C₈₉	C₂×#542	1	1	yes	characteristic, complemented, Sylow
209	#542	—	89	16	no	—
210	C₂×C₄⋊Q₈	—	89	1	no	—
211	C₂×#126	—	89	1	no	—
212	C₂×#126	D₈₉	1	1	yes	characteristic, complemented
213	C₂×#124	—	89	1	no	—
214	C₂×#124	—	89	1	no	—
215	C₂×#124	—	89	1	no	—
216	C₂×#123	—	89	1	no	—
217	C₂×#123	—	89	1	no	—
218	C₂×C₂²⋊Q₈	—	89	1	no	—
219	C₂×C₂²⋊Q₈	—	89	1	no	—
220	C₂×C₂²⋊Q₈	—	89	1	no	—
221	C₂×#121	—	89	1	no	—
222	C₂×C₄×Q₈	—	89	1	no	—
223	C₂×C₄×D₄	—	89	1	no	—
224	C₂×#117	—	89	1	no	—
225	C₂²×Q₈	—	89	1	no	—
226	C₂²×Q₈	—	89	1	no	—
227	C₂²×Q₈	—	89	1	no	—
228	C₂²×D₄	—	89	1	no	—
229	C₂²×D₄	—	89	1	no	—
230	C₂²×D₄	—	89	1	no	—
231	C₂³×C₄	—	89	1	no	—
232	C₂³×C₄	—	89	1	no	—
233	C₂³×C₄	—	89	1	no	—
234	C₄⋊Q₈	—	89	8	no	—
235	#126	—	89	8	no	—
236	#126	C₂×D₈₉	1	8	yes	complemented
237	#124	—	89	8	no	—
238	#124	—	89	8	no	—
239	#124	—	89	8	no	—
240	#123	—	89	8	no	—
241	#123	—	89	8	no	—
242	C₂²⋊Q₈	—	89	8	no	—
243	C₂²⋊Q₈	—	89	8	no	—
244	C₂²⋊Q₈	—	89	8	no	—
245	#121	—	89	8	no	—
246	C₄×Q₈	—	89	8	no	—
247	C₄×D₄	—	89	8	no	—
248	#117	—	89	8	no	—
249	C₂×C₄⋊C₄	—	89	1	no	—
250	C₂×C₄⋊C₄	—	89	1	no	—
251	C₂×C₄⋊C₄	—	89	1	no	—
252	C₂×C₄⋊C₄	—	89	1	no	—
253	C₂×C₄⋊C₄	—	89	1	no	—
254	C₂×C₄⋊C₄	—	89	1	no	—
255	C₂×C₄⋊C₄	—	89	1	no	—
256	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
257	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
258	C₂×C₄⋊C₄	C₂×D₈₉	1	1	yes	characteristic
259	C₂×C₂²⋊C₄	—	89	1	no	—
260	C₂×C₂²⋊C₄	—	89	1	no	—
261	C₂×C₂²⋊C₄	—	89	1	no	—
262	C₂×C₂²⋊C₄	—	89	1	no	—
263	C₂×C₂²⋊C₄	—	89	1	no	—
264	C₂×C₂²⋊C₄	—	89	1	no	—
265	C₂×C₂²⋊C₄	—	89	1	no	—
266	C₂×C₂²⋊C₄	—	89	1	no	—
267	C₂×C₂²⋊C₄	—	89	1	no	—
268	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
269	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
270	C₂×C₂²⋊C₄	C₂×D₈₉	1	1	yes	characteristic
271	C₂×C₄²	—	89	1	no	—
272	C₂×C₄²	—	89	1	no	—
273	C₂×C₄²	—	89	1	no	—
274	C₂×C₄²	C₂×D₈₉	1	1	yes	characteristic
275	C₂⁴	—	89	1	no	—
276	C₂⁴	—	89	1	no	—
277	C₂⁴	C₂²×D₈₉	1	1	yes	characteristic
278	C₂×Q₈	—	89	4	no	—
279	C₂×Q₈	—	89	4	no	—
280	C₂×Q₈	—	89	4	no	—
281	C₂×Q₈	—	356	2	no	—
282	C₂×Q₈	—	356	2	no	—
283	C₂×Q₈	—	178	4	no	—
284	C₂×D₄	—	89	4	no	—
285	C₂×D₄	—	89	4	no	—
286	C₂×D₄	—	89	4	no	—
287	C₂×D₄	—	356	2	no	—
288	C₂×D₄	—	356	2	no	—
289	C₂×D₄	—	178	4	no	—
290	C₂²×C₄	—	89	1	no	—
291	C₂²×C₄	—	89	4	no	—
292	C₂²×C₄	—	89	1	no	—
293	C₂²×C₄	—	89	1	no	—
294	C₂²×C₄	—	89	1	no	—
295	C₂²×C₄	—	89	1	no	—
296	C₂²×C₄	—	89	1	no	—
297	C₂²×C₄	—	89	4	no	—
298	C₂²×C₄	—	89	4	no	—
299	C₂²×C₄	—	356	2	no	—
300	C₂²×C₄	—	356	2	no	—
301	C₂²×C₄	—	178	4	no	—
302	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
303	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
304	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
305	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
306	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
307	C₂²×C₄	C₂²×D₈₉	1	1	yes	characteristic
308	C₄⋊C₄	—	89	4	no	—
309	C₄⋊C₄	—	89	4	no	—
310	C₄⋊C₄	—	89	4	no	—
311	C₄⋊C₄	—	89	4	no	—
312	C₄⋊C₄	—	89	4	no	—
313	C₄⋊C₄	—	89	4	no	—
314	C₄⋊C₄	—	89	4	no	—
315	C₄⋊C₄	C₂²×D₈₉	1	4	yes	—
316	C₄⋊C₄	C₂²×D₈₉	1	4	yes	—
317	C₄⋊C₄	C₂²×D₈₉	1	4	yes	—
318	C₂²⋊C₄	—	89	4	no	—
319	C₂²⋊C₄	—	89	4	no	—
320	C₂²⋊C₄	—	89	4	no	—
321	C₂²⋊C₄	—	89	4	no	—
322	C₂²⋊C₄	—	89	4	no	—
323	C₂²⋊C₄	—	89	4	no	—
324	C₂²⋊C₄	—	89	4	no	—
325	C₂²⋊C₄	—	89	4	no	—
326	C₂²⋊C₄	—	89	4	no	—
327	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
328	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
329	C₂²⋊C₄	C₂²×D₈₉	1	4	yes	—
330	C₄²	—	89	4	no	—
331	C₄²	—	89	4	no	—
332	C₄²	—	89	4	no	—
333	C₄²	C₂²×D₈₉	1	4	yes	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	2	no	—
336	C₂³	—	2	2	no	—
337	C₂³	—	89	2	no	—
338	C₂³	—	89	2	no	—
339	C₂³	—	178	2	no	—
340	C₂³	—	178	2	no	—
341	C₂³	—	178	2	no	—
342	C₂³	—	178	2	no	—
343	C₂³	—	178	2	no	—
344	C₂³	—	178	2	no	—
345	C₂³	C₂³×D₈₉	1	2	yes	—
346	C₂³	C₂³×D₈₉	1	1	yes	characteristic
347	Q₈	—	356	4	no	—
348	Q₈	—	356	4	no	—
349	Q₈	—	178	8	no	—
350	D₄	—	356	4	no	—
351	D₄	—	356	4	no	—
352	D₄	—	178	8	no	—
353	C₂×C₄	—	2	2	no	—
354	C₂×C₄	—	2	2	no	—
355	C₂×C₄	—	2	2	no	—
356	C₂×C₄	—	2	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	89	4	no	—
360	C₂×C₄	—	89	2	no	—
361	C₂×C₄	—	89	2	no	—
362	C₂×C₄	—	89	2	no	—
363	C₂×C₄	—	89	2	no	—
364	C₂×C₄	—	89	2	no	—
365	C₂×C₄	—	89	2	no	—
366	C₂×C₄	—	356	4	no	—
367	C₂×C₄	—	356	4	no	—
368	C₂×C₄	—	178	8	no	—
369	C₂×C₄	—	178	2	no	—
370	C₂×C₄	—	178	2	no	—
371	C₂×C₄	—	178	2	no	—
372	C₂×C₄	—	178	2	no	—
373	C₂×C₄	—	178	2	no	—
374	C₂×C₄	C₂³×D₈₉	1	2	yes	—
375	C₂×C₄	C₂³×D₈₉	1	2	yes	—
376	C₂×C₄	C₂³×D₈₉	1	2	yes	—
377	C₂×C₄	C₂³×D₈₉	1	2	yes	—
378	C₂×C₄	C₂³×D₈₉	1	2	yes	—
379	C₂×C₄	C₂³×D₈₉	1	2	yes	—
380	C₂²	—	2	2	no	—
381	C₂²	—	2	2	no	—
382	C₂²	—	2	2	no	—
383	C₂²	—	4	4	no	—
384	C₂²	—	356	4	no	—
385	C₂²	—	356	4	no	—
386	C₂²	—	178	2	no	—
387	C₂²	—	178	2	no	—
388	C₂²	—	178	2	no	—
389	C₂²	—	178	2	no	—
390	C₂²	—	178	2	no	—
391	C₂²	—	178	2	no	—
392	C₂²	#41×D₈₉	1	2	yes	—
393	C₂²	#15668058	1	2	yes	—
394	C₂²	#15668059	1	2	yes	—
395	C₂²	C₂⁴×D₈₉	1	1	yes	characteristic
396	C₄	—	2	2	no	—
397	C₄	—	2	2	no	—
398	C₄	—	2	2	no	—
399	C₄	—	2	2	no	—
400	C₄	—	2	2	no	—
401	C₄	—	2	2	no	—
402	C₄	—	89	4	no	—
403	C₄	—	178	2	no	—
404	C₄	—	178	2	no	—
405	C₄	—	178	2	no	—
406	C₄	—	178	2	no	—
407	C₄	—	178	2	no	—
408	C₂	—	4	2	no	—
409	C₂	—	356	2	no	—
410	C₂	—	356	2	no	—
411	C₂	#19152214	1	4	yes	direct product factor
412	C₂	C₂×#41×D₈₉	1	1	yes	characteristic
413	C₂	C₂×#15668058	1	1	yes	characteristic
414	C₂	C₂×#15668059	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂³×D₈₉
commutator, cosocle	C₂²×C₈₉	C₂⁵
Frattini	C₂²	C₂⁴×D₈₉
Fitting	C₂×#126×C₈₉	C₂
socle	C₂³×C₈₉	C₂⁴
prime radical	C₂×#15667985	C₂
hypercenter	C₂×#126	D₈₉
hypocenter	C₈₉	C₂×#542
LCS	G ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×#126

Complements

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

N	H ≅ G/N	type
1. #19152214	C₂	direct (N × H)
2. C₂×#15668011	C₂	semidirect
3. C₂×#15668007	C₂	semidirect
4. C₂×#15668000	C₂	semidirect
5. C₂×#15667998	C₂	semidirect
6. C₂×#15667998	C₂	semidirect
7. C₂×#15667997	C₂	semidirect
8. C₂×#15667996	C₂	semidirect
9. C₂×#15667992	C₂	semidirect
10. C₂×#15667990	C₂	semidirect
11. C₂×#15667989	C₂	semidirect
13. C₂×C₄×Dic₁₇₈	C₂	semidirect
14. C₂×#15667972	C₂	semidirect
15. C₂×#15667970	C₂	semidirect
16. C₂×#126×C₈₉	C₂	semidirect
26. #15668011	C₂²	semidirect
27. #15668007	C₂²	semidirect
28. #15668000	C₂²	semidirect
29. #15667998	C₂²	semidirect
30. #15667998	C₂²	semidirect
31. #15667997	C₂²	semidirect
32. #15667996	C₂²	semidirect
33. #15667992	C₂²	semidirect
34. #15667990	C₂²	semidirect
35. #15667989	C₂²	semidirect
37. C₄×Dic₁₇₈	C₂²	semidirect
38. #15667972	C₂²	semidirect
39. #15667970	C₂²	semidirect
59. #126×C₈₉	C₂²	semidirect
201. C₂×C₈₉	#542	semidirect
208. C₈₉	C₂×#542	semidirect
212. C₂×#126	D₈₉	semidirect
236. #126	C₂×D₈₉	semidirect
411. C₂	#19152214	direct (N × H)

Maximal subgroups

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

subgroup	index
#19152214	2
C₂×#15668011	2
C₂×#15668007	2
C₂×#15668000	2
C₂×#15667998	2
C₂×#15667997	2
C₂×#15667996	2
C₂×#15667992	2
C₂×#15667990	2
C₂×#15667989	2
C₂×#15667985	2
C₂×C₄×Dic₁₇₈	2
C₂×#15667972	2
C₂×#15667970	2
C₂×#126×C₈₉	2
C₂×#542	89

Subgroups — C2×#19152214 #26033625

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#19152214 #26033625