Subgroups — C₂×#3495 #62803

Order 256.

3603 conjugacy classes of subgroups.

The subgroup lattice has 452 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3495	C₂	1	32	yes	maximal, direct product factor
2	C₂×#556	C₂	1	2	yes	maximal, complemented
3	C₂×#554	C₂	1	2	yes	maximal, complemented
4	C₂×#552	C₂	1	2	yes	maximal, complemented
5	C₂×#552	C₂	1	4	yes	maximal, complemented
6	C₂×#552	C₂	1	2	yes	maximal, complemented
7	C₂×#551	C₂	1	4	yes	maximal, complemented
8	C₂×#544	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#542	C₂	1	2	yes	maximal, complemented
10	C₂×#541	C₂	1	2	yes	maximal, complemented
11	C₂×#536	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#533	C₂	1	2	yes	maximal, complemented
13	C₂×#529	C₂	1	2	yes	maximal, complemented
14	C₂×#525	C₂	1	1	yes	maximal, characteristic
15	C₂²×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#520	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#519	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#117	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂²×#41	C₂²	1	1	yes	characteristic
20	C₂³×Q₈	C₂²	1	1	yes	characteristic
21	C₂⁴×C₄	C₂²	1	1	yes	characteristic
22	#556	C₂²	1	32	yes	complemented
23	#554	C₂²	1	32	yes	complemented
24	#552	C₂²	1	32	yes	complemented
25	#552	C₂²	1	64	yes	complemented
26	#552	C₂²	1	32	yes	complemented
27	#551	C₂²	1	64	yes	complemented
28	#544	C₂²	1	16	yes	complemented
29	#542	C₂²	1	32	yes	complemented
30	#541	C₂²	1	32	yes	complemented
31	#536	C₂²	1	16	yes	complemented
32	#533	C₂²	1	32	yes	complemented
33	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
34	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
35	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
36	#529	C₂²	1	32	yes	complemented
37	C₂×#126	C₂²	1	4	yes	—
38	C₂×#126	C₂²	1	4	yes	—
39	C₂×#126	C₂²	1	4	yes	complemented
40	C₂×#126	C₂²	1	4	yes	complemented
41	C₂×#125	C₂²	1	2	yes	complemented
42	C₂×#125	C₂²	1	4	yes	complemented
43	C₂×#125	C₂²	1	4	yes	complemented
44	C₂×#125	C₂²	1	4	yes	complemented
45	C₂×#125	C₂²	1	2	yes	complemented
46	C₂×#124	C₂²	1	4	yes	—
47	C₂×#124	C₂²	1	2	yes	complemented
48	#525	C₂²	1	16	yes	—
49	C₂×#123	C₂²	1	2	yes	—
50	C₂×#123	C₂²	1	4	yes	—
51	C₂×#123	C₂²	1	4	yes	—
52	C₂×#123	C₂²	1	4	yes	—
53	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
54	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
55	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
56	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
57	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
58	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
59	C₂×C₂²⋊Q₈	C₂²	1	4	yes	—
60	C₂×C₂²⋊Q₈	C₂²	1	4	yes	—
61	C₂×C₂²⋊Q₈	C₂²	1	16	yes	complemented
62	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
63	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
64	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
65	C₂×#121	C₂²	1	1	yes	characteristic
66	C₂×#121	C₂²	1	1	yes	characteristic
67	C₂×#120	C₂²	1	2	yes	—
68	#520	C₂²	1	16	yes	complemented
69	#519	C₂²	1	16	yes	complemented
70	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
71	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
72	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
73	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
74	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
75	C₂×C₄×Q₈	C₂²	1	4	yes	complemented
76	C₂×C₄×D₄	C₂²	1	4	yes	—
77	C₂×C₄×D₄	C₂²	1	2	yes	—
78	C₂×C₄×D₄	C₂²	1	2	yes	—
79	C₂×C₄×D₄	C₂²	1	4	yes	—
80	C₂×C₄×D₄	C₂²	1	2	yes	complemented
81	C₂×#117	C₂²	1	1	yes	characteristic
82	C₂×#117	C₂²	1	1	yes	characteristic
83	C₂×#117	C₂²	1	2	yes	—
84	C₂×#117	C₂²	1	1	yes	characteristic
85	C₂×#117	C₂²	1	2	yes	—
86	C₂×#117	C₂²	1	1	yes	characteristic
87	C₂×#117	C₂²	1	1	yes	characteristic
88	C₂×#117	C₂²	1	4	yes	—
89	C₂×#117	C₂²	1	4	yes	—
90	C₂×#117	C₂²	1	16	yes	complemented
91	C₂×#117	C₂²	1	2	yes	complemented
92	C₂×#117	C₂²	1	4	yes	complemented
93	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
95	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
96	C₂²×C₄⋊C₄	C₂²	1	2	yes	—
97	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
98	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
99	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
100	C₂²×C₄²	C₂²	1	2	yes	—
101	C₂⁵	C₂³	1	1	yes	characteristic
102	C₂×#41	—	2	8	no	—
103	C₂×#41	C₂³	1	8	yes	—
104	C₂²×Q₈	—	2	8	no	—
105	C₂²×Q₈	C₂³	1	2	yes	—
106	C₂²×Q₈	C₂³	1	2	yes	—
107	C₂²×Q₈	C₂³	1	1	yes	characteristic
108	C₂²×Q₈	C₂³	1	8	yes	—
109	C₂²×Q₈	C₂³	1	4	yes	—
110	C₂²×D₄	C₂³	1	2	yes	—
111	C₂²×D₄	C₂³	1	2	yes	—
112	C₂²×D₄	C₂³	1	1	yes	characteristic
113	C₂²×D₄	C₂³	1	2	yes	—
114	C₂³×C₄	—	2	8	no	—
115	C₂³×C₄	C₂³	1	2	yes	—
116	C₂³×C₄	C₂³	1	2	yes	—
117	C₂³×C₄	C₂³	1	1	yes	characteristic
118	C₂³×C₄	C₂³	1	1	yes	characteristic
119	C₂³×C₄	C₂³	1	2	yes	—
120	C₂³×C₄	C₂³	1	1	yes	characteristic
121	C₂³×C₄	C₂³	1	1	yes	characteristic
122	C₂³×C₄	C₂³	1	8	yes	—
123	C₂³×C₄	C₂³	1	1	yes	characteristic
124	C₂³×C₄	C₂³	1	2	yes	—
125	C₂³×C₄	C₂³	1	2	yes	—
126	C₂³×C₄	C₂³	1	4	yes	—
127	C₂³×C₄	C₂³	1	1	yes	characteristic
128	C₄⋊Q₈	C₂³	1	16	yes	complemented
129	C₄⋊Q₈	C₂³	1	16	yes	complemented
130	C₄⋊Q₈	C₂³	1	16	yes	complemented
131	#126	C₂³	1	32	yes	—
132	#126	C₂³	1	32	yes	—
133	#126	C₂³	1	32	yes	complemented
134	#126	C₂³	1	32	yes	complemented
135	#125	C₂³	1	16	yes	complemented
136	#125	C₂³	1	32	yes	complemented
137	#125	C₂³	1	32	yes	complemented
138	#125	C₂³	1	32	yes	complemented
139	#125	C₂³	1	16	yes	complemented
140	#124	C₂³	1	32	yes	—
141	#124	C₂³	1	16	yes	complemented
142	#123	C₂³	1	16	yes	—
143	#123	C₂³	1	32	yes	—
144	#123	C₂³	1	32	yes	—
145	#123	C₂³	1	32	yes	—
146	C₂²⋊Q₈	C₂³	1	16	yes	—
147	C₂²⋊Q₈	C₂³	1	16	yes	—
148	C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₂²⋊Q₈	C₂³	1	16	yes	—
150	C₂²⋊Q₈	C₂³	1	8	yes	—
151	C₂²⋊Q₈	C₂³	1	8	yes	—
152	C₂²⋊Q₈	C₂³	1	32	yes	—
153	C₂²⋊Q₈	C₂³	1	32	yes	—
154	C₂²⋊Q₈	C₂³	1	16	yes	complemented
155	C₂²⋊Q₈	C₂³	1	16	yes	complemented
156	C₂²⋊Q₈	C₂³	1	32	yes	complemented
157	#121	C₂³	1	8	yes	—
158	#121	C₂³	1	8	yes	—
159	#120	C₂³	1	16	yes	—
160	C₄×Q₈	C₂³	1	16	yes	complemented
161	C₄×Q₈	C₂³	1	16	yes	complemented
162	C₄×Q₈	C₂³	1	16	yes	complemented
163	C₄×Q₈	C₂³	1	16	yes	complemented
164	C₄×Q₈	C₂³	1	16	yes	complemented
165	C₄×Q₈	C₂³	1	32	yes	complemented
166	C₄×D₄	C₂³	1	32	yes	—
167	C₄×D₄	C₂³	1	16	yes	—
168	C₄×D₄	C₂³	1	16	yes	—
169	C₄×D₄	C₂³	1	32	yes	—
170	C₄×D₄	C₂³	1	16	yes	complemented
171	#117	C₂³	1	8	yes	—
172	#117	C₂³	1	8	yes	—
173	#117	C₂³	1	16	yes	—
174	#117	C₂³	1	8	yes	—
175	#117	C₂³	1	16	yes	—
176	#117	C₂³	1	8	yes	—
177	#117	C₂³	1	8	yes	—
178	#117	C₂³	1	32	yes	—
179	#117	C₂³	1	32	yes	—
180	#117	C₂³	1	16	yes	complemented
181	#117	C₂³	1	32	yes	complemented
182	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
183	C₂×C₄⋊C₄	C₂³	1	2	yes	—
184	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₂×C₄⋊C₄	C₂³	1	2	yes	—
186	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
187	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄	C₂³	1	2	yes	—
189	C₂×C₄⋊C₄	C₂³	1	8	yes	—
190	C₂×C₄⋊C₄	C₂³	1	8	yes	—
191	C₂×C₄⋊C₄	C₂³	1	4	yes	—
192	C₂×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄	C₂³	1	8	yes	—
194	C₂×C₄⋊C₄	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄	C₂³	1	16	yes	—
196	C₂×C₄⋊C₄	C₂³	1	4	yes	—
197	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
198	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
199	C₂×C₄⋊C₄	C₂³	1	4	yes	—
200	C₂×C₄⋊C₄	C₂³	1	4	yes	—
201	C₂×C₄⋊C₄	C₂³	1	4	yes	—
202	C₂×C₄⋊C₄	C₂³	1	4	yes	—
203	C₂×C₄⋊C₄	C₂³	1	4	yes	—
204	C₂×C₄⋊C₄	C₂³	1	2	yes	—
205	C₂×C₄⋊C₄	C₂³	1	2	yes	—
206	C₂×C₄⋊C₄	C₂³	1	4	yes	—
207	C₂×C₄⋊C₄	C₂³	1	4	yes	—
208	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
209	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
214	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
215	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
216	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
217	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
225	C₂×C₄²	C₂³	1	2	yes	—
226	C₂×C₄²	C₂³	1	2	yes	—
227	C₂×C₄²	C₂³	1	4	yes	—
228	C₂×C₄²	C₂³	1	2	yes	—
229	C₂×C₄²	C₂³	1	2	yes	—
230	C₂×C₄²	C₂³	1	4	yes	—
231	C₂×C₄²	C₂³	1	4	yes	—
232	C₂×C₄²	C₂³	1	2	yes	—
233	C₂×C₄²	C₂³	1	16	yes	—
234	C₂⁴	—	2	4	no	—
235	C₂⁴	—	2	4	no	—
236	C₂⁴	—	4	2	no	—
237	C₂⁴	C₂⁴	1	1	yes	characteristic
238	C₂⁴	C₂⁴	1	2	yes	—
239	C₂⁴	C₂⁴	1	4	yes	—
240	C₂⁴	C₂⁴	1	1	yes	characteristic
241	C₂⁴	C₂⁴	1	1	yes	characteristic
242	#41	—	2	32	no	—
243	C₂×Q₈	—	2	8	no	—
244	C₂×Q₈	—	2	8	no	—
245	C₂×Q₈	—	2	32	no	—
246	C₂×Q₈	—	2	4	no	—
247	C₂×Q₈	—	4	8	no	—
248	C₂×Q₈	C₂⁴	1	8	yes	—
249	C₂×Q₈	C₂⁴	1	8	yes	—
250	C₂×Q₈	C₂⁴	1	4	yes	—
251	C₂×Q₈	C₂⁴	1	16	yes	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	8	no	—
254	C₂×D₄	—	2	4	no	—
255	C₂×D₄	—	4	4	no	—
256	C₂×D₄	C₂⁴	1	8	yes	—
257	C₂×D₄	C₂⁴	1	8	yes	—
258	C₂×D₄	C₂⁴	1	4	yes	—
259	C₂×D₄	C₂⁴	1	8	yes	—
260	C₂²×C₄	—	2	4	no	—
261	C₂²×C₄	—	2	8	no	—
262	C₂²×C₄	—	2	8	no	—
263	C₂²×C₄	—	2	4	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	32	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	4	8	no	—
270	C₂²×C₄	—	4	4	no	—
271	C₂²×C₄	—	4	4	no	—
272	C₂²×C₄	#41	1	8	yes	—
273	C₂²×C₄	C₂⁴	1	4	yes	—
274	C₂²×C₄	C₂⁴	1	8	yes	—
275	C₂²×C₄	C₂⁴	1	8	yes	—
276	C₂²×C₄	C₂⁴	1	4	yes	—
277	C₂²×C₄	C₂⁴	1	4	yes	—
278	C₂²×C₄	C₂⁴	1	8	yes	—
279	C₂²×C₄	C₂⁴	1	4	yes	—
280	C₂²×C₄	C₂⁴	1	4	yes	—
281	C₂²×C₄	C₂⁴	1	2	yes	—
282	C₂²×C₄	C₂⁴	1	1	yes	characteristic
283	C₂²×C₄	C₂⁴	1	2	yes	—
284	C₂²×C₄	C₂⁴	1	2	yes	—
285	C₂²×C₄	C₂⁴	1	2	yes	—
286	C₂²×C₄	C₂⁴	1	2	yes	—
287	C₂²×C₄	C₂⁴	1	4	yes	—
288	C₂²×C₄	C₂⁴	1	2	yes	—
289	C₂²×C₄	C₂⁴	1	2	yes	—
290	C₂²×C₄	C₂⁴	1	4	yes	—
291	C₂²×C₄	C₂⁴	1	1	yes	characteristic
292	C₂²×C₄	C₂⁴	1	8	yes	—
293	C₂²×C₄	C₂⁴	1	8	yes	—
294	C₂²×C₄	C₂⁴	1	16	yes	—
295	C₂²×C₄	C₂⁴	1	4	yes	—
296	C₂²×C₄	C₂⁴	1	1	yes	characteristic
297	C₂²×C₄	C₂⁴	1	1	yes	characteristic
298	C₄⋊C₄	C₂⁴	1	4	yes	—
299	C₄⋊C₄	C₂⁴	1	8	yes	—
300	C₄⋊C₄	C₂⁴	1	4	yes	—
301	C₄⋊C₄	C₂⁴	1	8	yes	—
302	C₄⋊C₄	C₂⁴	1	4	yes	—
303	C₄⋊C₄	C₂⁴	1	4	yes	—
304	C₄⋊C₄	C₂⁴	1	8	yes	—
305	C₄⋊C₄	C₂⁴	1	16	yes	—
306	C₄⋊C₄	C₂⁴	1	8	yes	—
307	C₄⋊C₄	C₂⁴	1	16	yes	—
308	C₄⋊C₄	C₂⁴	1	16	yes	—
309	C₄⋊C₄	C₂⁴	1	4	yes	—
310	C₄⋊C₄	C₂⁴	1	4	yes	—
311	C₄⋊C₄	C₂⁴	1	16	yes	—
312	C₄⋊C₄	C₂⁴	1	16	yes	—
313	C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₄⋊C₄	C₂⁴	1	16	yes	—
315	C₄⋊C₄	C₂⁴	1	16	yes	—
316	C₄⋊C₄	C₂⁴	1	8	yes	—
317	C₄⋊C₄	C₂⁴	1	8	yes	—
318	C₄⋊C₄	C₂⁴	1	16	yes	—
319	C₄⋊C₄	C₂⁴	1	16	yes	—
320	C₂²⋊C₄	C₂⁴	1	8	yes	—
321	C₂²⋊C₄	C₂⁴	1	8	yes	—
322	C₂²⋊C₄	C₂⁴	1	8	yes	—
323	C₂²⋊C₄	C₂⁴	1	8	yes	—
324	C₂²⋊C₄	C₂⁴	1	16	yes	—
325	C₂²⋊C₄	C₂⁴	1	16	yes	—
326	C₂²⋊C₄	C₂⁴	1	8	yes	—
327	C₂²⋊C₄	C₂⁴	1	8	yes	—
328	C₂²⋊C₄	C₂⁴	1	8	yes	—
329	C₂²⋊C₄	C₂⁴	1	16	yes	—
330	C₂²⋊C₄	C₂⁴	1	16	yes	—
331	C₂²⋊C₄	C₂⁴	1	8	yes	—
332	C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₂²⋊C₄	C₂⁴	1	16	yes	—
334	C₄²	C₂⁴	1	8	yes	—
335	C₄²	C₂⁴	1	8	yes	—
336	C₄²	C₂⁴	1	8	yes	—
337	C₄²	C₂⁴	1	8	yes	—
338	C₄²	C₂⁴	1	16	yes	—
339	C₄²	C₂⁴	1	16	yes	—
340	C₄²	C₂⁴	1	16	yes	—
341	C₄²	C₂⁴	1	8	yes	—
342	C₂³	—	2	2	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	2	no	—
345	C₂³	—	2	2	no	—
346	C₂³	—	2	8	no	—
347	C₂³	—	2	2	no	—
348	C₂³	—	2	4	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	8	no	—
351	C₂³	—	2	2	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	2	no	—
354	C₂³	—	4	4	no	—
355	C₂³	—	4	16	no	—
356	C₂³	C₂×#41	1	4	yes	—
357	C₂³	2₋¹⁺⁴	1	4	yes	—
358	C₂³	C₂⁵	1	2	yes	—
359	C₂³	C₂⁵	1	4	yes	—
360	C₂³	C₂⁵	1	2	yes	—
361	C₂³	C₂⁵	1	2	yes	—
362	C₂³	C₂⁵	1	1	yes	characteristic
363	Q₈	—	2	16	no	—
364	Q₈	—	2	16	no	—
365	Q₈	—	2	8	no	—
366	Q₈	—	4	16	no	—
367	D₄	—	2	16	no	—
368	D₄	—	2	16	no	—
369	D₄	—	2	8	no	—
370	D₄	—	4	8	no	—
371	C₂×C₄	—	2	8	no	—
372	C₂×C₄	—	2	2	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	4	no	—
375	C₂×C₄	—	2	16	no	—
376	C₂×C₄	—	2	8	no	—
377	C₂×C₄	—	2	16	no	—
378	C₂×C₄	—	2	4	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	8	no	—
383	C₂×C₄	—	2	4	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	8	no	—
387	C₂×C₄	—	2	8	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	16	no	—
390	C₂×C₄	—	4	16	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	8	no	—
393	C₂×C₄	C₂×#41	1	4	yes	—
394	C₂×C₄	C₂×#41	1	4	yes	—
395	C₂×C₄	C₂×#41	1	16	yes	—
396	C₂×C₄	C₂⁵	1	4	yes	—
397	C₂×C₄	C₂⁵	1	2	yes	—
398	C₂×C₄	C₂⁵	1	4	yes	—
399	C₂×C₄	C₂⁵	1	4	yes	—
400	C₂×C₄	C₂⁵	1	4	yes	—
401	C₂×C₄	C₂⁵	1	4	yes	—
402	C₂×C₄	C₂⁵	1	8	yes	—
403	C₂×C₄	C₂⁵	1	4	yes	—
404	C₂×C₄	C₂⁵	1	4	yes	—
405	C₂×C₄	C₂⁵	1	8	yes	—
406	C₂×C₄	C₂⁵	1	2	yes	—
407	C₂×C₄	C₂⁵	1	2	yes	—
408	C₂×C₄	C₂⁵	1	2	yes	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	2	no	—
411	C₂²	—	2	2	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	8	no	—
414	C₂²	—	2	8	no	—
415	C₂²	—	2	2	no	—
416	C₂²	—	2	4	no	—
417	C₂²	—	2	4	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	4	16	no	—
422	C₂²	—	4	8	no	—
423	C₂²	—	4	4	no	—
424	C₂²	C₂²×#41	1	4	yes	—
425	C₂²	C₂²×#41	1	2	yes	—
426	C₂²	C₂×2₋¹⁺⁴	1	4	yes	—
427	C₂²	C₂×2₋¹⁺⁴	1	2	yes	—
428	C₂²	#585	1	2	yes	—
429	C₂²	C₂⁶	1	1	yes	characteristic
430	C₄	—	2	2	no	—
431	C₄	—	2	2	no	—
432	C₄	—	2	4	no	—
433	C₄	—	2	8	no	—
434	C₄	—	2	4	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	4	no	—
437	C₄	—	2	4	no	—
438	C₄	—	2	8	no	—
439	C₄	—	2	4	no	—
440	C₄	—	2	4	no	—
441	C₄	C₂²×#41	1	4	yes	—
442	C₄	C₂²×#41	1	4	yes	—
443	C₂	—	2	4	no	—
444	C₂	—	2	4	no	—
445	C₂	—	4	4	no	—
446	C₂	—	4	2	no	—
447	C₂	#3495	1	4	yes	direct product factor
448	C₂	C₂³×#41	1	1	yes	characteristic
449	C₂	C₂²×2₋¹⁺⁴	1	1	yes	characteristic
450	C₂	C₂×#585	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶
prime radical	C₂×#525	C₂
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂³ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3495	C₂	direct (N × H)
2. C₂×#556	C₂	semidirect
3. C₂×#554	C₂	semidirect
4. C₂×#552	C₂	semidirect
5. C₂×#552	C₂	semidirect
6. C₂×#552	C₂	semidirect
7. C₂×#551	C₂	semidirect
8. C₂×#544	C₂	semidirect
9. C₂×#542	C₂	semidirect
10. C₂×#541	C₂	semidirect
11. C₂×#536	C₂	semidirect
12. C₂×#533	C₂	semidirect
13. C₂×#529	C₂	semidirect
15. C₂²×C₂²⋊Q₈	C₂	semidirect
16. C₂×#520	C₂	semidirect
17. C₂×#519	C₂	semidirect
18. C₂²×#117	C₂	semidirect
22. #556	C₂²	semidirect
23. #554	C₂²	semidirect
24. #552	C₂²	semidirect
25. #552	C₂²	semidirect
26. #552	C₂²	semidirect
27. #551	C₂²	semidirect
28. #544	C₂²	semidirect
29. #542	C₂²	semidirect
30. #541	C₂²	semidirect
31. #536	C₂²	semidirect
32. #533	C₂²	semidirect
33. C₂×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₄⋊Q₈	C₂²	semidirect
35. C₂×C₄⋊Q₈	C₂²	semidirect
36. #529	C₂²	semidirect
39. C₂×#126	C₂²	semidirect
40. C₂×#126	C₂²	semidirect
41. C₂×#125	C₂²	semidirect
42. C₂×#125	C₂²	semidirect
43. C₂×#125	C₂²	semidirect
44. C₂×#125	C₂²	semidirect
45. C₂×#125	C₂²	semidirect
47. C₂×#124	C₂²	semidirect
61. C₂×C₂²⋊Q₈	C₂²	semidirect
62. C₂×C₂²⋊Q₈	C₂²	semidirect
63. C₂×C₂²⋊Q₈	C₂²	semidirect
64. C₂×C₂²⋊Q₈	C₂²	semidirect
68. #520	C₂²	semidirect
69. #519	C₂²	semidirect
70. C₂×C₄×Q₈	C₂²	semidirect
71. C₂×C₄×Q₈	C₂²	semidirect
72. C₂×C₄×Q₈	C₂²	semidirect
73. C₂×C₄×Q₈	C₂²	semidirect
74. C₂×C₄×Q₈	C₂²	semidirect
75. C₂×C₄×Q₈	C₂²	semidirect
80. C₂×C₄×D₄	C₂²	semidirect
90. C₂×#117	C₂²	semidirect
91. C₂×#117	C₂²	semidirect
92. C₂×#117	C₂²	semidirect
97. C₂²×C₄⋊C₄	C₂²	semidirect
128. C₄⋊Q₈	C₂³	semidirect
129. C₄⋊Q₈	C₂³	semidirect
130. C₄⋊Q₈	C₂³	semidirect
133. #126	C₂³	semidirect
134. #126	C₂³	semidirect
135. #125	C₂³	semidirect
136. #125	C₂³	semidirect
137. #125	C₂³	semidirect
138. #125	C₂³	semidirect
139. #125	C₂³	semidirect
141. #124	C₂³	semidirect
154. C₂²⋊Q₈	C₂³	semidirect
155. C₂²⋊Q₈	C₂³	semidirect
156. C₂²⋊Q₈	C₂³	semidirect
160. C₄×Q₈	C₂³	semidirect
161. C₄×Q₈	C₂³	semidirect
162. C₄×Q₈	C₂³	semidirect
163. C₄×Q₈	C₂³	semidirect
164. C₄×Q₈	C₂³	semidirect
165. C₄×Q₈	C₂³	semidirect
170. C₄×D₄	C₂³	semidirect
180. #117	C₂³	semidirect
181. #117	C₂³	semidirect
208. C₂×C₄⋊C₄	C₂³	semidirect
447. C₂	#3495	direct (N × H)

Maximal subgroups

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

subgroup	index
#3495	2
C₂×#556	2
C₂×#554	2
C₂×#552	2
C₂×#551	2
C₂×#544	2
C₂×#542	2
C₂×#541	2
C₂×#536	2
C₂×#533	2
C₂×#529	2
C₂×#525	2
C₂²×C₂²⋊Q₈	2
C₂×#520	2
C₂×#519	2
C₂²×#117	2

Subgroups — C2×#3495 #62803

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3495 #62803