Subgroups — C₂×#3475 #62708

Order 256.

3977 conjugacy classes of subgroups.

The subgroup lattice has 460 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3475	C₂	1	32	yes	maximal, direct product factor
2	C₂×#556	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#555	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#554	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#553	C₂	1	2	yes	maximal, complemented
6	C₂×#552	C₂	1	2	yes	maximal, complemented
7	C₂×#552	C₂	1	2	yes	maximal, complemented
8	C₂×#551	C₂	1	4	yes	maximal, complemented
9	C₂×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#546	C₂	1	2	yes	maximal, complemented
11	C₂×#533	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#529	C₂	1	4	yes	maximal, complemented
13	C₂×#529	C₂	1	2	yes	maximal, complemented
14	C₂×#525	C₂	1	2	yes	maximal, complemented
15	C₂×C₄×#41	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×C₄×#41	C₂	1	2	yes	maximal, complemented
17	C₂²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂²×#117	C₂	1	2	yes	maximal, complemented
19	C₂²×#41	C₂²	1	1	yes	characteristic
20	C₂²×#41	C₂²	1	2	yes	—
21	C₂³×D₄	C₂²	1	1	yes	characteristic
22	C₂⁴×C₄	C₂²	1	2	yes	—
23	#556	C₂²	1	16	yes	complemented
24	#555	C₂²	1	16	yes	complemented
25	#554	C₂²	1	16	yes	complemented
26	#553	C₂²	1	32	yes	complemented
27	#552	C₂²	1	32	yes	complemented
28	#552	C₂²	1	32	yes	complemented
29	#551	C₂²	1	64	yes	complemented
30	#547	C₂²	1	16	yes	complemented
31	#546	C₂²	1	32	yes	complemented
32	#533	C₂²	1	16	yes	complemented
33	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
35	#529	C₂²	1	64	yes	complemented
36	#529	C₂²	1	32	yes	complemented
37	C₂×#126	C₂²	1	4	yes	complemented
38	C₂×#126	C₂²	1	4	yes	complemented
39	C₂×#126	C₂²	1	4	yes	complemented
40	C₂×#125	C₂²	1	4	yes	complemented
41	C₂×#125	C₂²	1	2	yes	complemented
42	C₂×#125	C₂²	1	2	yes	complemented
43	C₂×#124	C₂²	1	2	yes	—
44	C₂×#124	C₂²	1	4	yes	complemented
45	#525	C₂²	1	32	yes	complemented
46	C₂×#123	C₂²	1	4	yes	—
47	C₂×#123	C₂²	1	4	yes	—
48	C₂×#123	C₂²	1	4	yes	complemented
49	C₂×#123	C₂²	1	4	yes	complemented
50	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
51	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
52	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
53	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
54	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
55	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
56	C₂×#121	C₂²	1	4	yes	—
57	C₂×#121	C₂²	1	2	yes	—
58	C₂×#121	C₂²	1	2	yes	complemented
59	C₂×#121	C₂²	1	2	yes	complemented
60	C₂×#120	C₂²	1	4	yes	—
61	C₄×#41	C₂²	1	16	yes	complemented
62	C₄×#41	C₂²	1	32	yes	complemented
63	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
64	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
65	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
66	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
67	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
68	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
69	C₂×C₄×D₄	C₂²	1	2	yes	—
70	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
71	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
72	C₂×C₄×D₄	C₂²	1	2	yes	—
73	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
74	C₂×C₄×D₄	C₂²	1	2	yes	—
75	C₂×C₄×D₄	C₂²	1	2	yes	—
76	C₂×C₄×D₄	C₂²	1	2	yes	—
77	C₂×C₄×D₄	C₂²	1	16	yes	complemented
78	C₂×C₄×D₄	C₂²	1	4	yes	complemented
79	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
80	C₂×C₄×D₄	C₂²	1	4	yes	complemented
81	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
82	C₂×C₄×D₄	C₂²	1	4	yes	complemented
83	C₂×#117	C₂²	1	1	yes	characteristic
84	C₂×#117	C₂²	1	2	yes	—
85	C₂×#117	C₂²	1	4	yes	—
86	C₂×#117	C₂²	1	4	yes	complemented
87	C₂×#117	C₂²	1	2	yes	complemented
88	C₂×#117	C₂²	1	2	yes	complemented
89	C₂×#117	C₂²	1	2	yes	complemented
90	C₂×#117	C₂²	1	4	yes	complemented
91	C₂×#117	C₂²	1	2	yes	complemented
92	C₂×#117	C₂²	1	32	yes	complemented
93	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
94	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
95	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
96	C₂²×C₂²⋊C₄	C₂²	1	4	yes	—
97	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
98	C₂²×C₄²	C₂²	1	1	yes	characteristic
99	C₂²×C₄²	C₂²	1	4	yes	complemented
100	C₂²×C₄²	C₂²	1	2	yes	complemented
101	C₂⁵	C₂³	1	2	yes	—
102	C₂×#41	—	2	16	no	—
103	C₂×#41	—	2	8	no	—
104	C₂×#41	C₂³	1	8	yes	—
105	C₂×#41	C₂³	1	16	yes	—
106	C₂²×Q₈	C₂³	1	2	yes	—
107	C₂²×Q₈	C₂³	1	1	yes	characteristic
108	C₂²×Q₈	C₂³	1	2	yes	—
109	C₂²×D₄	—	2	8	no	—
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	4	yes	—
114	C₂²×D₄	C₂³	1	1	yes	characteristic
115	C₂²×D₄	C₂³	1	8	yes	—
116	C₂²×D₄	C₂³	1	4	yes	—
117	C₂²×D₄	C₂³	1	1	yes	characteristic
118	C₂³×C₄	—	2	16	no	—
119	C₂³×C₄	C₂³	1	2	yes	—
120	C₂³×C₄	C₂³	1	4	yes	—
121	C₂³×C₄	C₂³	1	1	yes	characteristic
122	C₂³×C₄	C₂³	1	2	yes	—
123	C₂³×C₄	C₂³	1	2	yes	—
124	C₂³×C₄	C₂³	1	16	yes	—
125	C₂³×C₄	C₂³	1	2	yes	—
126	C₂³×C₄	C₂³	1	2	yes	—
127	C₂³×C₄	C₂³	1	2	yes	—
128	C₂³×C₄	C₂³	1	2	yes	—
129	C₂³×C₄	C₂³	1	1	yes	characteristic
130	C₂³×C₄	C₂³	1	4	yes	—
131	C₂³×C₄	C₂³	1	2	yes	—
132	C₂³×C₄	C₂³	1	1	yes	characteristic
133	C₄⋊Q₈	C₂³	1	8	yes	complemented
134	C₄⋊Q₈	C₂³	1	8	yes	complemented
135	#126	C₂³	1	32	yes	complemented
136	#126	C₂³	1	32	yes	complemented
137	#126	C₂³	1	32	yes	complemented
138	#125	C₂³	1	32	yes	complemented
139	#125	C₂³	1	16	yes	complemented
140	#125	C₂³	1	16	yes	complemented
141	#124	C₂³	1	16	yes	—
142	#124	C₂³	1	32	yes	complemented
143	#123	C₂³	1	32	yes	—
144	#123	C₂³	1	32	yes	—
145	#123	C₂³	1	32	yes	complemented
146	#123	C₂³	1	32	yes	complemented
147	C₂²⋊Q₈	C₂³	1	16	yes	—
148	C₂²⋊Q₈	C₂³	1	16	yes	—
149	C₂²⋊Q₈	C₂³	1	16	yes	complemented
150	C₂²⋊Q₈	C₂³	1	16	yes	complemented
151	C₂²⋊Q₈	C₂³	1	16	yes	complemented
152	C₂²⋊Q₈	C₂³	1	32	yes	complemented
153	#121	C₂³	1	32	yes	—
154	#121	C₂³	1	16	yes	—
155	#121	C₂³	1	16	yes	complemented
156	#121	C₂³	1	16	yes	complemented
157	#120	C₂³	1	32	yes	—
158	C₄×Q₈	C₂³	1	16	yes	complemented
159	C₄×Q₈	C₂³	1	8	yes	complemented
160	C₄×Q₈	C₂³	1	16	yes	complemented
161	C₄×Q₈	C₂³	1	8	yes	complemented
162	C₄×Q₈	C₂³	1	16	yes	complemented
163	C₄×D₄	C₂³	1	8	yes	—
164	C₄×D₄	C₂³	1	8	yes	—
165	C₄×D₄	C₂³	1	16	yes	—
166	C₄×D₄	C₂³	1	8	yes	—
167	C₄×D₄	C₂³	1	16	yes	—
168	C₄×D₄	C₂³	1	8	yes	—
169	C₄×D₄	C₂³	1	16	yes	—
170	C₄×D₄	C₂³	1	16	yes	—
171	C₄×D₄	C₂³	1	16	yes	—
172	C₄×D₄	C₂³	1	32	yes	complemented
173	C₄×D₄	C₂³	1	8	yes	complemented
174	C₄×D₄	C₂³	1	32	yes	complemented
175	C₄×D₄	C₂³	1	8	yes	complemented
176	C₄×D₄	C₂³	1	32	yes	complemented
177	#117	C₂³	1	8	yes	—
178	#117	C₂³	1	16	yes	—
179	#117	C₂³	1	32	yes	—
180	#117	C₂³	1	32	yes	complemented
181	#117	C₂³	1	16	yes	complemented
182	#117	C₂³	1	16	yes	complemented
183	#117	C₂³	1	16	yes	complemented
184	#117	C₂³	1	32	yes	complemented
185	#117	C₂³	1	16	yes	complemented
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	1	yes	characteristic
191	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₂×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄	C₂³	1	2	yes	—
194	C₂×C₄⋊C₄	C₂³	1	4	yes	—
195	C₂×C₄⋊C₄	C₂³	1	4	yes	—
196	C₂×C₄⋊C₄	C₂³	1	2	yes	—
197	C₂×C₄⋊C₄	C₂³	1	2	yes	—
198	C₂×C₄⋊C₄	C₂³	1	2	yes	—
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	2	yes	—
204	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
205	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
206	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
208	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
210	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
211	C₂×C₂²⋊C₄	C₂³	1	32	yes	—
212	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
215	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
216	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
217	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
218	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
220	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
221	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
222	C₂×C₄²	C₂³	1	4	yes	—
223	C₂×C₄²	C₂³	1	4	yes	—
224	C₂×C₄²	C₂³	1	2	yes	—
225	C₂×C₄²	C₂³	1	1	yes	characteristic
226	C₂×C₄²	C₂³	1	1	yes	characteristic
227	C₂×C₄²	C₂³	1	2	yes	—
228	C₂×C₄²	C₂³	1	8	yes	—
229	C₂×C₄²	C₂³	1	2	yes	—
230	C₂×C₄²	C₂³	1	4	yes	—
231	C₂×C₄²	C₂³	1	1	yes	characteristic
232	C₂×C₄²	C₂³	1	1	yes	characteristic
233	C₂×C₄²	C₂³	1	32	yes	complemented
234	C₂×C₄²	C₂³	1	16	yes	complemented
235	C₂⁴	—	2	8	no	—
236	C₂⁴	—	2	8	no	—
237	C₂⁴	—	4	4	no	—
238	C₂⁴	C₂⁴	1	2	yes	—
239	C₂⁴	C₂⁴	1	2	yes	—
240	C₂⁴	C₂⁴	1	8	yes	—
241	C₂⁴	C₂⁴	1	1	yes	characteristic
242	C₂⁴	C₂⁴	1	2	yes	—
243	#41	—	2	64	no	—
244	#41	—	2	32	no	—
245	C₂×Q₈	—	2	4	no	—
246	C₂×Q₈	—	2	8	no	—
247	C₂×Q₈	—	4	4	no	—
248	C₂×Q₈	C₂⁴	1	8	yes	—
249	C₂×Q₈	C₂⁴	1	4	yes	—
250	C₂×Q₈	C₂⁴	1	8	yes	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	8	no	—
253	C₂×D₄	—	2	16	no	—
254	C₂×D₄	—	2	32	no	—
255	C₂×D₄	—	2	4	no	—
256	C₂×D₄	—	2	4	no	—
257	C₂×D₄	—	4	8	no	—
258	C₂×D₄	#41	1	8	yes	complemented
259	C₂×D₄	C₂⁴	1	8	yes	—
260	C₂×D₄	C₂⁴	1	8	yes	—
261	C₂×D₄	C₂⁴	1	4	yes	—
262	C₂×D₄	C₂⁴	1	16	yes	—
263	C₂×D₄	C₂⁴	1	4	yes	—
264	C₂×D₄	C₂⁴	1	16	yes	—
265	C₂×D₄	C₂⁴	1	4	yes	—
266	C₂²×C₄	—	2	8	no	—
267	C₂²×C₄	—	2	16	no	—
268	C₂²×C₄	—	2	8	no	—
269	C₂²×C₄	—	2	8	no	—
270	C₂²×C₄	—	2	8	no	—
271	C₂²×C₄	—	2	8	no	—
272	C₂²×C₄	—	2	4	no	—
273	C₂²×C₄	—	2	8	no	—
274	C₂²×C₄	—	2	8	no	—
275	C₂²×C₄	—	2	64	no	—
276	C₂²×C₄	—	4	4	no	—
277	C₂²×C₄	—	4	8	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	#41	1	8	yes	complemented
280	C₂²×C₄	C₂⁴	1	2	yes	—
281	C₂²×C₄	C₂⁴	1	2	yes	—
282	C₂²×C₄	C₂⁴	1	2	yes	—
283	C₂²×C₄	C₂⁴	1	1	yes	characteristic
284	C₂²×C₄	C₂⁴	1	1	yes	characteristic
285	C₂²×C₄	C₂⁴	1	4	yes	—
286	C₂²×C₄	C₂⁴	1	2	yes	—
287	C₂²×C₄	C₂⁴	1	4	yes	—
288	C₂²×C₄	C₂⁴	1	1	yes	characteristic
289	C₂²×C₄	C₂⁴	1	4	yes	—
290	C₂²×C₄	C₂⁴	1	8	yes	—
291	C₂²×C₄	C₂⁴	1	16	yes	—
292	C₂²×C₄	C₂⁴	1	8	yes	—
293	C₂²×C₄	C₂⁴	1	8	yes	—
294	C₂²×C₄	C₂⁴	1	2	yes	—
295	C₂²×C₄	C₂⁴	1	8	yes	—
296	C₂²×C₄	C₂⁴	1	8	yes	—
297	C₂²×C₄	C₂⁴	1	8	yes	—
298	C₂²×C₄	C₂⁴	1	8	yes	—
299	C₂²×C₄	C₂⁴	1	4	yes	—
300	C₂²×C₄	C₂⁴	1	16	yes	—
301	C₂²×C₄	C₂⁴	1	8	yes	—
302	C₂²×C₄	C₂⁴	1	1	yes	characteristic
303	C₂²×C₄	C₂⁴	1	1	yes	characteristic
304	C₂²×C₄	C₂⁴	1	4	yes	—
305	C₂²×C₄	C₂⁴	1	1	yes	characteristic
306	C₄⋊C₄	C₂⁴	1	4	yes	—
307	C₄⋊C₄	C₂⁴	1	4	yes	—
308	C₄⋊C₄	C₂⁴	1	8	yes	—
309	C₄⋊C₄	C₂⁴	1	4	yes	—
310	C₄⋊C₄	C₂⁴	1	4	yes	—
311	C₄⋊C₄	C₂⁴	1	8	yes	—
312	C₄⋊C₄	C₂⁴	1	8	yes	—
313	C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₄⋊C₄	C₂⁴	1	16	yes	—
315	C₄⋊C₄	C₂⁴	1	8	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	C₄⋊C₄	C₂⁴	1	16	yes	—
321	C₄⋊C₄	C₂⁴	1	16	yes	—
322	C₄⋊C₄	C₂⁴	1	8	yes	—
323	C₂²⋊C₄	C₂⁴	1	8	yes	—
324	C₂²⋊C₄	C₂⁴	1	16	yes	—
325	C₂²⋊C₄	C₂⁴	1	8	yes	—
326	C₂²⋊C₄	C₂⁴	1	16	yes	—
327	C₂²⋊C₄	C₂⁴	1	16	yes	—
328	C₂²⋊C₄	C₂⁴	1	8	yes	—
329	C₂²⋊C₄	C₂⁴	1	8	yes	—
330	C₂²⋊C₄	C₂⁴	1	8	yes	—
331	C₂²⋊C₄	C₂⁴	1	16	yes	—
332	C₂²⋊C₄	C₂⁴	1	8	yes	—
333	C₂²⋊C₄	C₂⁴	1	8	yes	—
334	C₂²⋊C₄	C₂⁴	1	16	yes	—
335	C₂²⋊C₄	C₂⁴	1	16	yes	—
336	C₂²⋊C₄	C₂⁴	1	16	yes	—
337	C₄²	C₂⁴	1	4	yes	—
338	C₄²	C₂⁴	1	4	yes	—
339	C₄²	C₂⁴	1	4	yes	—
340	C₄²	C₂⁴	1	4	yes	—
341	C₄²	C₂⁴	1	8	yes	—
342	C₄²	C₂⁴	1	16	yes	—
343	C₄²	C₂⁴	1	16	yes	—
344	C₄²	C₂⁴	1	16	yes	—
345	C₄²	C₂⁴	1	8	yes	—
346	C₄²	C₂⁴	1	8	yes	—
347	C₂³	—	2	4	no	—
348	C₂³	—	2	2	no	—
349	C₂³	—	2	4	no	—
350	C₂³	—	2	2	no	—
351	C₂³	—	2	16	no	—
352	C₂³	—	2	4	no	—
353	C₂³	—	2	4	no	—
354	C₂³	—	2	4	no	—
355	C₂³	—	2	16	no	—
356	C₂³	—	2	4	no	—
357	C₂³	—	2	4	no	—
358	C₂³	—	2	4	no	—
359	C₂³	—	4	8	no	—
360	C₂³	—	4	32	no	—
361	C₂³	C₂×#41	1	4	yes	—
362	C₂³	C₂×#41	1	8	yes	—
363	C₂³	C₂⁵	1	4	yes	—
364	C₂³	C₂⁵	1	4	yes	—
365	C₂³	C₂⁵	1	2	yes	—
366	C₂³	C₂⁵	1	4	yes	—
367	C₂³	C₂⁵	1	1	yes	characteristic
368	Q₈	—	2	8	no	—
369	Q₈	—	2	16	no	—
370	Q₈	—	4	8	no	—
371	D₄	—	2	16	no	—
372	D₄	—	2	16	no	—
373	D₄	—	2	32	no	—
374	D₄	—	2	8	no	—
375	D₄	—	2	8	no	—
376	D₄	—	4	16	no	—
377	D₄	C₂×#41	1	16	yes	complemented
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	2	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	4	no	—
382	C₂×C₄	—	2	2	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	4	no	—
385	C₂×C₄	—	2	32	no	—
386	C₂×C₄	—	2	2	no	—
387	C₂×C₄	—	2	4	no	—
388	C₂×C₄	—	2	8	no	—
389	C₂×C₄	—	2	2	no	—
390	C₂×C₄	—	2	16	no	—
391	C₂×C₄	—	2	16	no	—
392	C₂×C₄	—	2	16	no	—
393	C₂×C₄	—	2	16	no	—
394	C₂×C₄	—	2	8	no	—
395	C₂×C₄	—	2	16	no	—
396	C₂×C₄	—	2	16	no	—
397	C₂×C₄	—	4	8	no	—
398	C₂×C₄	—	4	16	no	—
399	C₂×C₄	—	4	4	no	—
400	C₂×C₄	C₂×#41	1	4	yes	—
401	C₂×C₄	C₂×#41	1	4	yes	—
402	C₂×C₄	C₂×#41	1	4	yes	—
403	C₂×C₄	C₂×#41	1	16	yes	complemented
404	C₂×C₄	C₂⁵	1	4	yes	—
405	C₂×C₄	C₂⁵	1	4	yes	—
406	C₂×C₄	C₂⁵	1	2	yes	—
407	C₂×C₄	C₂⁵	1	4	yes	—
408	C₂×C₄	C₂⁵	1	2	yes	—
409	C₂×C₄	C₂⁵	1	8	yes	—
410	C₂×C₄	C₂⁵	1	4	yes	—
411	C₂×C₄	C₂⁵	1	8	yes	—
412	C₂×C₄	C₂⁵	1	2	yes	—
413	C₂×C₄	C₂⁵	1	4	yes	—
414	C₂×C₄	C₂⁵	1	2	yes	—
415	C₂×C₄	C₂⁵	1	2	yes	—
416	C₂×C₄	C₂⁵	1	2	yes	—
417	C₂²	—	2	4	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	2	4	no	—
420	C₂²	—	2	2	no	—
421	C₂²	—	2	8	no	—
422	C₂²	—	2	16	no	—
423	C₂²	—	2	4	no	—
424	C₂²	—	2	4	no	—
425	C₂²	—	2	4	no	—
426	C₂²	—	2	4	no	—
427	C₂²	—	2	4	no	—
428	C₂²	—	2	4	no	—
429	C₂²	—	4	32	no	—
430	C₂²	—	4	8	no	—
431	C₂²	—	4	8	no	—
432	C₂²	C₂²×#41	1	4	yes	—
433	C₂²	C₂²×#41	1	8	yes	—
434	C₂²	C₂²×#41	1	2	yes	—
435	C₂²	C₂²×#41	1	2	yes	—
436	C₂²	#585	1	2	yes	—
437	C₂²	C₂⁶	1	1	yes	characteristic
438	C₄	—	2	4	no	—
439	C₄	—	2	4	no	—
440	C₄	—	2	4	no	—
441	C₄	—	2	2	no	—
442	C₄	—	2	8	no	—
443	C₄	—	2	4	no	—
444	C₄	—	2	2	no	—
445	C₄	—	2	4	no	—
446	C₄	—	2	8	no	—
447	C₄	—	2	2	no	—
448	C₄	C₂²×#41	1	4	yes	—
449	C₄	C₂²×#41	1	4	yes	—
450	C₄	C₂²×#41	1	4	yes	—
451	C₂	—	2	4	no	—
452	C₂	—	2	8	no	—
453	C₂	—	4	4	no	—
454	C₂	—	4	4	no	—
455	C₂	#3475	1	4	yes	direct product factor
456	C₂	C₂³×#41	1	1	yes	characteristic
457	C₂	C₂³×#41	1	1	yes	characteristic
458	C₂	C₂×#585	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₂⁴
commutator, Frattini, cosocle	C₂²	C₂⁶
socle	C₂³	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₄ ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #3475	C₂	direct (N × H)
2. C₂×#556	C₂	semidirect
3. C₂×#555	C₂	semidirect
4. C₂×#554	C₂	semidirect
5. C₂×#553	C₂	semidirect
6. C₂×#552	C₂	semidirect
7. C₂×#552	C₂	semidirect
8. C₂×#551	C₂	semidirect
9. C₂×#547	C₂	semidirect
10. C₂×#546	C₂	semidirect
11. C₂×#533	C₂	semidirect
12. C₂×#529	C₂	semidirect
13. C₂×#529	C₂	semidirect
14. C₂×#525	C₂	semidirect
15. C₂×C₄×#41	C₂	semidirect
16. C₂×C₄×#41	C₂	semidirect
17. C₂²×C₄×D₄	C₂	semidirect
18. C₂²×#117	C₂	semidirect
23. #556	C₂²	semidirect
24. #555	C₂²	semidirect
25. #554	C₂²	semidirect
26. #553	C₂²	semidirect
27. #552	C₂²	semidirect
28. #552	C₂²	semidirect
29. #551	C₂²	semidirect
30. #547	C₂²	semidirect
31. #546	C₂²	semidirect
32. #533	C₂²	semidirect
33. C₂×C₄⋊Q₈	C₂²	semidirect
34. C₂×C₄⋊Q₈	C₂²	semidirect
35. #529	C₂²	semidirect
36. #529	C₂²	semidirect
37. C₂×#126	C₂²	semidirect
38. C₂×#126	C₂²	semidirect
39. C₂×#126	C₂²	semidirect
40. C₂×#125	C₂²	semidirect
41. C₂×#125	C₂²	semidirect
42. C₂×#125	C₂²	semidirect
44. C₂×#124	C₂²	semidirect
45. #525	C₂²	semidirect
48. C₂×#123	C₂²	semidirect
49. C₂×#123	C₂²	semidirect
52. C₂×C₂²⋊Q₈	C₂²	semidirect
53. C₂×C₂²⋊Q₈	C₂²	semidirect
54. C₂×C₂²⋊Q₈	C₂²	semidirect
55. C₂×C₂²⋊Q₈	C₂²	semidirect
58. C₂×#121	C₂²	semidirect
59. C₂×#121	C₂²	semidirect
61. C₄×#41	C₂²	semidirect
62. C₄×#41	C₂²	semidirect
63. C₂×C₄×Q₈	C₂²	semidirect
64. C₂×C₄×Q₈	C₂²	semidirect
65. C₂×C₄×Q₈	C₂²	semidirect
66. C₂×C₄×Q₈	C₂²	semidirect
67. C₂×C₄×Q₈	C₂²	semidirect
77. C₂×C₄×D₄	C₂²	semidirect
78. C₂×C₄×D₄	C₂²	semidirect
79. C₂×C₄×D₄	C₂²	semidirect
80. C₂×C₄×D₄	C₂²	semidirect
81. C₂×C₄×D₄	C₂²	semidirect
82. C₂×C₄×D₄	C₂²	semidirect
86. C₂×#117	C₂²	semidirect
87. C₂×#117	C₂²	semidirect
88. C₂×#117	C₂²	semidirect
89. C₂×#117	C₂²	semidirect
90. C₂×#117	C₂²	semidirect
91. C₂×#117	C₂²	semidirect
92. C₂×#117	C₂²	semidirect
94. C₂²×C₄⋊C₄	C₂²	semidirect
95. C₂²×C₄⋊C₄	C₂²	semidirect
99. C₂²×C₄²	C₂²	semidirect
100. C₂²×C₄²	C₂²	semidirect
133. C₄⋊Q₈	C₂³	semidirect
134. C₄⋊Q₈	C₂³	semidirect
135. #126	C₂³	semidirect
136. #126	C₂³	semidirect
137. #126	C₂³	semidirect
138. #125	C₂³	semidirect
139. #125	C₂³	semidirect
140. #125	C₂³	semidirect
142. #124	C₂³	semidirect
145. #123	C₂³	semidirect
146. #123	C₂³	semidirect
149. C₂²⋊Q₈	C₂³	semidirect
150. C₂²⋊Q₈	C₂³	semidirect
151. C₂²⋊Q₈	C₂³	semidirect
152. C₂²⋊Q₈	C₂³	semidirect
155. #121	C₂³	semidirect
156. #121	C₂³	semidirect
158. C₄×Q₈	C₂³	semidirect
159. C₄×Q₈	C₂³	semidirect
160. C₄×Q₈	C₂³	semidirect
161. C₄×Q₈	C₂³	semidirect
162. C₄×Q₈	C₂³	semidirect
172. C₄×D₄	C₂³	semidirect
173. C₄×D₄	C₂³	semidirect
174. C₄×D₄	C₂³	semidirect
175. C₄×D₄	C₂³	semidirect
176. C₄×D₄	C₂³	semidirect
180. #117	C₂³	semidirect
181. #117	C₂³	semidirect
182. #117	C₂³	semidirect
183. #117	C₂³	semidirect
184. #117	C₂³	semidirect
185. #117	C₂³	semidirect
204. C₂×C₄⋊C₄	C₂³	semidirect
205. C₂×C₄⋊C₄	C₂³	semidirect
233. C₂×C₄²	C₂³	semidirect
234. C₂×C₄²	C₂³	semidirect
258. C₂×D₄	#41	semidirect
279. C₂²×C₄	#41	semidirect
377. D₄	C₂×#41	semidirect
403. C₂×C₄	C₂×#41	semidirect
455. C₂	#3475	direct (N × H)

Maximal subgroups

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

subgroup	index
#3475	2
C₂×#556	2
C₂×#555	2
C₂×#554	2
C₂×#553	2
C₂×#552	2
C₂×#551	2
C₂×#547	2
C₂×#546	2
C₂×#533	2
C₂×#529	2
C₂×#525	2
C₂×C₄×#41	2
C₂²×C₄×D₄	2
C₂²×#117	2

Subgroups — C2×#3475 #62708

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3475 #62708