Subgroups — C₂×#3536 #62723

Order 256.

3981 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	#3536	C₂	1	32	yes	maximal, direct product factor
2	C₂×#562	C₂	1	4	yes	maximal, complemented
3	C₂×#554	C₂	1	2	yes	maximal, complemented
4	C₂×#548	C₂	1	2	yes	maximal, complemented
5	C₂×#547	C₂	1	2	yes	maximal, complemented
6	C₂×#546	C₂	1	4	yes	maximal, complemented
7	C₂×#546	C₂	1	2	yes	maximal, complemented
8	C₂×#543	C₂	1	2	yes	maximal, complemented
9	C₂×#542	C₂	1	2	yes	maximal, complemented
10	C₂×#539	C₂	1	2	yes	maximal, complemented
11	C₂×#538	C₂	1	2	yes	maximal, complemented
12	C₂×#537	C₂	1	2	yes	maximal, complemented
13	C₂×#537	C₂	1	2	yes	maximal, complemented
14	C₂×#525	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×C₂²⋊Q₈	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂²×#121	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂²×#41	C₂²	1	1	yes	characteristic, complemented
18	C₂²×#41	C₂²	1	4	yes	complemented
19	C₂²×#41	C₂²	1	2	yes	complemented
20	C₂³×Q₈	C₂²	1	1	yes	characteristic, complemented
21	C₂³×D₄	C₂²	1	1	yes	characteristic
22	C₂³×D₄	C₂²	1	2	yes	—
23	C₂⁴×C₄	C₂²	1	1	yes	characteristic
24	#562	C₂²	1	64	yes	complemented
25	#554	C₂²	1	32	yes	complemented
26	#548	C₂²	1	32	yes	complemented
27	#547	C₂²	1	32	yes	complemented
28	#546	C₂²	1	64	yes	complemented
29	#546	C₂²	1	32	yes	complemented
30	#543	C₂²	1	32	yes	complemented
31	#542	C₂²	1	32	yes	complemented
32	#539	C₂²	1	32	yes	complemented
33	#538	C₂²	1	32	yes	complemented
34	#537	C₂²	1	32	yes	complemented
35	#537	C₂²	1	32	yes	complemented
36	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
37	C₂×#126	C₂²	1	4	yes	complemented
38	C₂×#125	C₂²	1	4	yes	complemented
39	C₂×#124	C₂²	1	4	yes	complemented
40	C₂×#124	C₂²	1	2	yes	complemented
41	C₂×#124	C₂²	1	4	yes	complemented
42	#525	C₂²	1	16	yes	complemented
43	C₂×#123	C₂²	1	2	yes	complemented
44	C₂×#123	C₂²	1	4	yes	complemented
45	C₂×#123	C₂²	1	4	yes	complemented
46	C₂×#123	C₂²	1	4	yes	complemented
47	C₂×#123	C₂²	1	4	yes	complemented
48	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
49	C₂×C₂²⋊Q₈	C₂²	1	2	yes	—
50	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic
51	C₂×C₂²⋊Q₈	C₂²	1	4	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	1	yes	characteristic, complemented
55	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
56	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
58	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
59	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
61	C₂×C₂²⋊Q₈	C₂²	1	16	yes	complemented
62	C₂×#121	C₂²	1	2	yes	—
63	C₂×#121	C₂²	1	2	yes	—
64	C₂×#121	C₂²	1	2	yes	—
65	C₂×#121	C₂²	1	2	yes	—
66	C₂×#121	C₂²	1	1	yes	characteristic
67	C₂×#121	C₂²	1	16	yes	complemented
68	C₂×#121	C₂²	1	1	yes	characteristic, complemented
69	C₂×#121	C₂²	1	4	yes	complemented
70	C₂×#121	C₂²	1	2	yes	complemented
71	C₂×#121	C₂²	1	4	yes	complemented
72	C₂×#121	C₂²	1	4	yes	complemented
73	C₂×#121	C₂²	1	4	yes	complemented
74	C₂×#121	C₂²	1	4	yes	complemented
75	C₂×#120	C₂²	1	2	yes	—
76	C₂×#120	C₂²	1	4	yes	—
77	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
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×C₄×D₄	C₂²	1	4	yes	complemented
82	C₂×C₄×D₄	C₂²	1	2	yes	complemented
83	C₂×#117	C₂²	1	1	yes	characteristic, complemented
84	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic
85	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
86	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
87	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
88	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
89	C₂²×C₂²⋊C₄	C₂²	1	2	yes	—
90	C₂²×C₂²⋊C₄	C₂²	1	4	yes	—
91	C₂⁵	C₂³	1	1	yes	characteristic
92	C₂⁵	C₂³	1	2	yes	—
93	C₂×#41	—	4	4	no	—
94	C₂×#41	—	4	16	no	—
95	C₂×#41	—	4	8	no	—
96	C₂×#41	C₂³	1	8	yes	complemented
97	C₂×#41	C₂³	1	32	yes	complemented
98	C₂×#41	C₂³	1	16	yes	complemented
99	C₂²×Q₈	—	4	4	no	—
100	C₂²×Q₈	C₂³	1	2	yes	—
101	C₂²×Q₈	C₂³	1	1	yes	characteristic
102	C₂²×Q₈	C₂³	1	2	yes	—
103	C₂²×Q₈	C₂³	1	4	yes	—
104	C₂²×Q₈	C₂³	1	8	yes	complemented
105	C₂²×D₄	—	4	4	no	—
106	C₂²×D₄	—	4	8	no	—
107	C₂²×D₄	C₂³	1	2	yes	—
108	C₂²×D₄	C₂³	1	2	yes	—
109	C₂²×D₄	C₂³	1	4	yes	—
110	C₂²×D₄	C₂³	1	2	yes	—
111	C₂²×D₄	C₂³	1	2	yes	—
112	C₂²×D₄	C₂³	1	4	yes	—
113	C₂²×D₄	C₂³	1	4	yes	—
114	C₂²×D₄	C₂³	1	2	yes	—
115	C₂²×D₄	C₂³	1	4	yes	—
116	C₂²×D₄	C₂³	1	1	yes	characteristic
117	C₂²×D₄	C₂³	1	8	yes	—
118	C₂²×D₄	C₂³	1	16	yes	—
119	C₂³×C₄	—	4	4	no	—
120	C₂³×C₄	C₂³	1	2	yes	—
121	C₂³×C₄	C₂³	1	1	yes	characteristic
122	C₂³×C₄	C₂³	1	2	yes	—
123	C₂³×C₄	C₂³	1	1	yes	characteristic
124	C₂³×C₄	C₂³	1	1	yes	characteristic
125	C₂³×C₄	C₂³	1	1	yes	characteristic
126	C₂³×C₄	C₂³	1	2	yes	—
127	C₂³×C₄	C₂³	1	2	yes	—
128	C₂³×C₄	C₂³	1	4	yes	—
129	C₂³×C₄	C₂³	1	4	yes	—
130	C₂³×C₄	C₂³	1	1	yes	characteristic
131	C₂³×C₄	C₂³	1	4	yes	—
132	C₂³×C₄	C₂³	1	1	yes	characteristic
133	C₂³×C₄	C₂³	1	8	yes	—
134	C₄⋊Q₈	C₂³	1	16	yes	complemented
135	#126	C₂³	1	32	yes	complemented
136	#125	C₂³	1	32	yes	complemented
137	#124	C₂³	1	32	yes	complemented
138	#124	C₂³	1	16	yes	complemented
139	#124	C₂³	1	32	yes	complemented
140	#123	C₂³	1	16	yes	complemented
141	#123	C₂³	1	32	yes	complemented
142	#123	C₂³	1	32	yes	complemented
143	#123	C₂³	1	32	yes	complemented
144	#123	C₂³	1	32	yes	complemented
145	C₂²⋊Q₈	C₂³	1	16	yes	—
146	C₂²⋊Q₈	C₂³	1	16	yes	—
147	C₂²⋊Q₈	C₂³	1	8	yes	—
148	C₂²⋊Q₈	C₂³	1	32	yes	—
149	C₂²⋊Q₈	C₂³	1	16	yes	complemented
150	C₂²⋊Q₈	C₂³	1	16	yes	complemented
151	C₂²⋊Q₈	C₂³	1	8	yes	complemented
152	C₂²⋊Q₈	C₂³	1	32	yes	complemented
153	C₂²⋊Q₈	C₂³	1	32	yes	complemented
154	C₂²⋊Q₈	C₂³	1	16	yes	complemented
155	C₂²⋊Q₈	C₂³	1	32	yes	complemented
156	C₂²⋊Q₈	C₂³	1	32	yes	complemented
157	C₂²⋊Q₈	C₂³	1	32	yes	complemented
158	#121	C₂³	1	16	yes	—
159	#121	C₂³	1	16	yes	—
160	#121	C₂³	1	16	yes	—
161	#121	C₂³	1	16	yes	—
162	#121	C₂³	1	8	yes	—
163	#121	C₂³	1	8	yes	complemented
164	#121	C₂³	1	32	yes	complemented
165	#121	C₂³	1	16	yes	complemented
166	#121	C₂³	1	32	yes	complemented
167	#121	C₂³	1	32	yes	complemented
168	#121	C₂³	1	32	yes	complemented
169	#121	C₂³	1	32	yes	complemented
170	#120	C₂³	1	16	yes	—
171	#120	C₂³	1	32	yes	—
172	C₄×Q₈	C₂³	1	16	yes	complemented
173	C₄×D₄	C₂³	1	16	yes	—
174	C₄×D₄	C₂³	1	32	yes	—
175	C₄×D₄	C₂³	1	16	yes	complemented
176	C₄×D₄	C₂³	1	32	yes	complemented
177	C₄×D₄	C₂³	1	16	yes	complemented
178	#117	C₂³	1	8	yes	complemented
179	C₂×C₄⋊C₄	C₂³	1	2	yes	—
180	C₂×C₄⋊C₄	C₂³	1	2	yes	—
181	C₂×C₄⋊C₄	C₂³	1	8	yes	—
182	C₂×C₄⋊C₄	C₂³	1	2	yes	—
183	C₂×C₄⋊C₄	C₂³	1	4	yes	—
184	C₂×C₄⋊C₄	C₂³	1	4	yes	—
185	C₂×C₄⋊C₄	C₂³	1	4	yes	—
186	C₂×C₄⋊C₄	C₂³	1	2	yes	—
187	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
188	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₂×C₄⋊C₄	C₂³	1	2	yes	—
190	C₂×C₄⋊C₄	C₂³	1	4	yes	—
191	C₂×C₄⋊C₄	C₂³	1	4	yes	—
192	C₂×C₄⋊C₄	C₂³	1	2	yes	—
193	C₂×C₄⋊C₄	C₂³	1	4	yes	—
194	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
195	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
196	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
197	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
198	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
200	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
201	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
202	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
203	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
204	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
205	C₂×C₂²⋊C₄	C₂³	1	16	yes	—
206	C₂×C₂²⋊C₄	C₂³	1	32	yes	—
207	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
209	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
210	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
211	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
212	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
213	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
214	C₂×C₄²	C₂³	1	2	yes	—
215	C₂×C₄²	C₂³	1	4	yes	—
216	C₂⁴	—	2	4	no	—
217	C₂⁴	—	2	4	no	—
218	C₂⁴	—	2	8	no	—
219	C₂⁴	—	4	2	no	—
220	C₂⁴	—	4	4	no	—
221	C₂⁴	—	4	4	no	—
222	C₂⁴	C₂⁴	1	1	yes	characteristic
223	C₂⁴	C₂⁴	1	4	yes	—
224	C₂⁴	C₂⁴	1	2	yes	—
225	C₂⁴	C₂⁴	1	4	yes	—
226	C₂⁴	C₂⁴	1	1	yes	characteristic
227	C₂⁴	C₂⁴	1	1	yes	characteristic
228	C₂⁴	C₂⁴	1	8	yes	—
229	#41	—	4	16	no	—
230	#41	—	4	64	no	—
231	#41	—	4	32	no	—
232	C₂×Q₈	—	2	8	no	—
233	C₂×Q₈	—	4	4	no	—
234	C₂×Q₈	—	4	2	no	—
235	C₂×Q₈	—	4	8	no	—
236	C₂×Q₈	—	4	16	no	—
237	C₂×Q₈	C₂⁴	1	8	yes	—
238	C₂×Q₈	C₂⁴	1	4	yes	—
239	C₂×Q₈	C₂⁴	1	8	yes	—
240	C₂×Q₈	C₂⁴	1	16	yes	—
241	C₂×D₄	—	2	16	no	—
242	C₂×D₄	—	2	8	no	—
243	C₂×D₄	—	2	8	no	—
244	C₂×D₄	—	2	8	no	—
245	C₂×D₄	—	4	16	no	—
246	C₂×D₄	—	4	4	no	—
247	C₂×D₄	—	4	8	no	—
248	C₂×D₄	—	4	4	no	—
249	C₂×D₄	—	4	2	no	—
250	C₂×D₄	—	4	8	no	—
251	C₂×D₄	—	4	8	no	—
252	C₂×D₄	—	4	32	no	—
253	C₂×D₄	C₂⁴	1	8	yes	—
254	C₂×D₄	C₂⁴	1	8	yes	—
255	C₂×D₄	C₂⁴	1	16	yes	—
256	C₂×D₄	C₂⁴	1	8	yes	—
257	C₂×D₄	C₂⁴	1	8	yes	—
258	C₂×D₄	C₂⁴	1	16	yes	—
259	C₂×D₄	C₂⁴	1	16	yes	—
260	C₂×D₄	C₂⁴	1	8	yes	—
261	C₂×D₄	C₂⁴	1	16	yes	—
262	C₂×D₄	C₂⁴	1	4	yes	—
263	C₂²×C₄	—	2	8	no	—
264	C₂²×C₄	—	2	4	no	—
265	C₂²×C₄	—	2	4	no	—
266	C₂²×C₄	—	2	4	no	—
267	C₂²×C₄	—	2	8	no	—
268	C₂²×C₄	—	4	16	no	—
269	C₂²×C₄	—	4	2	no	—
270	C₂²×C₄	—	4	2	no	—
271	C₂²×C₄	—	4	2	no	—
272	C₂²×C₄	—	4	4	no	—
273	C₂²×C₄	—	4	4	no	—
274	C₂²×C₄	—	4	8	no	—
275	C₂²×C₄	—	4	8	no	—
276	C₂²×C₄	—	4	8	no	—
277	C₂²×C₄	C₂⁴	1	8	yes	—
278	C₂²×C₄	C₂⁴	1	4	yes	—
279	C₂²×C₄	C₂⁴	1	8	yes	—
280	C₂²×C₄	C₂⁴	1	4	yes	—
281	C₂²×C₄	C₂⁴	1	4	yes	—
282	C₂²×C₄	C₂⁴	1	2	yes	—
283	C₂²×C₄	C₂⁴	1	2	yes	—
284	C₂²×C₄	C₂⁴	1	4	yes	—
285	C₂²×C₄	C₂⁴	1	4	yes	—
286	C₂²×C₄	C₂⁴	1	1	yes	characteristic
287	C₂²×C₄	C₂⁴	1	2	yes	—
288	C₂²×C₄	C₂⁴	1	4	yes	—
289	C₂²×C₄	C₂⁴	1	1	yes	characteristic
290	C₂²×C₄	C₂⁴	1	1	yes	characteristic
291	C₂²×C₄	C₂⁴	1	4	yes	—
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	16	yes	—
296	C₂²×C₄	C₂⁴	1	4	yes	—
297	C₂²×C₄	C₂⁴	1	16	yes	—
298	C₂²×C₄	C₂⁴	1	4	yes	—
299	C₂²×C₄	C₂⁴	1	1	yes	characteristic
300	C₄⋊C₄	C₂⁴	1	8	yes	—
301	C₄⋊C₄	C₂⁴	1	8	yes	—
302	C₄⋊C₄	C₂⁴	1	8	yes	—
303	C₄⋊C₄	C₂⁴	1	16	yes	—
304	C₄⋊C₄	C₂⁴	1	16	yes	—
305	C₄⋊C₄	C₂⁴	1	16	yes	—
306	C₄⋊C₄	C₂⁴	1	8	yes	—
307	C₄⋊C₄	C₂⁴	1	4	yes	—
308	C₄⋊C₄	C₂⁴	1	4	yes	—
309	C₄⋊C₄	C₂⁴	1	8	yes	—
310	C₄⋊C₄	C₂⁴	1	16	yes	—
311	C₄⋊C₄	C₂⁴	1	16	yes	—
312	C₄⋊C₄	C₂⁴	1	8	yes	—
313	C₄⋊C₄	C₂⁴	1	16	yes	—
314	C₂²⋊C₄	C₂⁴	1	16	yes	—
315	C₂²⋊C₄	C₂⁴	1	8	yes	—
316	C₂²⋊C₄	C₂⁴	1	16	yes	—
317	C₂²⋊C₄	C₂⁴	1	16	yes	—
318	C₂²⋊C₄	C₂⁴	1	16	yes	—
319	C₂²⋊C₄	C₂⁴	1	16	yes	—
320	C₂²⋊C₄	C₂⁴	1	16	yes	—
321	C₂²⋊C₄	C₂⁴	1	8	yes	—
322	C₂²⋊C₄	C₂⁴	1	8	yes	—
323	C₂²⋊C₄	C₂⁴	1	16	yes	—
324	C₂²⋊C₄	C₂⁴	1	8	yes	—
325	C₂²⋊C₄	C₂⁴	1	16	yes	—
326	C₂²⋊C₄	C₂⁴	1	16	yes	—
327	C₂²⋊C₄	C₂⁴	1	8	yes	—
328	C₄²	C₂⁴	1	8	yes	—
329	C₄²	C₂⁴	1	16	yes	—
330	C₂³	—	2	2	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	2	2	no	—
334	C₂³	—	2	2	no	—
335	C₂³	—	2	4	no	—
336	C₂³	—	2	4	no	—
337	C₂³	—	2	8	no	—
338	C₂³	—	2	8	no	—
339	C₂³	—	2	8	no	—
340	C₂³	—	2	2	no	—
341	C₂³	—	2	4	no	—
342	C₂³	—	2	8	no	—
343	C₂³	—	2	2	no	—
344	C₂³	—	2	8	no	—
345	C₂³	—	2	16	no	—
346	C₂³	—	4	4	no	—
347	C₂³	—	4	8	no	—
348	C₂³	—	4	8	no	—
349	C₂³	—	4	16	no	—
350	C₂³	—	8	16	no	—
351	C₂³	H(5,𝔽₂)	1	4	yes	—
352	C₂³	2₋¹⁺⁴	1	4	yes	—
353	C₂³	C₂⁵	1	2	yes	—
354	C₂³	C₂⁵	1	8	yes	—
355	C₂³	C₂⁵	1	4	yes	—
356	C₂³	C₂⁵	1	2	yes	—
357	C₂³	C₂⁵	1	2	yes	—
358	C₂³	C₂⁵	1	1	yes	characteristic
359	Q₈	—	2	16	no	—
360	Q₈	—	4	8	no	—
361	Q₈	—	4	4	no	—
362	Q₈	—	4	16	no	—
363	D₄	—	2	32	no	—
364	D₄	—	2	16	no	—
365	D₄	—	2	16	no	—
366	D₄	—	2	16	no	—
367	D₄	—	4	8	no	—
368	D₄	—	4	16	no	—
369	D₄	—	4	8	no	—
370	D₄	—	4	4	no	—
371	D₄	—	4	16	no	—
372	D₄	—	4	16	no	—
373	C₂×C₄	—	2	2	no	—
374	C₂×C₄	—	2	8	no	—
375	C₂×C₄	—	2	2	no	—
376	C₂×C₄	—	2	4	no	—
377	C₂×C₄	—	2	2	no	—
378	C₂×C₄	—	2	16	no	—
379	C₂×C₄	—	2	8	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	8	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	2	8	no	—
384	C₂×C₄	—	2	8	no	—
385	C₂×C₄	—	2	8	no	—
386	C₂×C₄	—	2	16	no	—
387	C₂×C₄	—	4	4	no	—
388	C₂×C₄	—	4	4	no	—
389	C₂×C₄	—	4	4	no	—
390	C₂×C₄	—	4	8	no	—
391	C₂×C₄	—	4	8	no	—
392	C₂×C₄	—	4	16	no	—
393	C₂×C₄	—	4	16	no	—
394	C₂×C₄	—	4	16	no	—
395	C₂×C₄	H(5,𝔽₂)	1	4	yes	—
396	C₂×C₄	C₂⁵	1	4	yes	—
397	C₂×C₄	C₂⁵	1	4	yes	—
398	C₂×C₄	C₂⁵	1	8	yes	—
399	C₂×C₄	C₂⁵	1	8	yes	—
400	C₂×C₄	C₂⁵	1	2	yes	—
401	C₂×C₄	C₂⁵	1	4	yes	—
402	C₂×C₄	C₂⁵	1	8	yes	—
403	C₂×C₄	C₂⁵	1	2	yes	—
404	C₂×C₄	C₂⁵	1	2	yes	—
405	C₂×C₄	C₂⁵	1	2	yes	—
406	C₂²	—	2	2	no	—
407	C₂²	—	2	2	no	—
408	C₂²	—	2	2	no	—
409	C₂²	—	2	2	no	—
410	C₂²	—	2	8	no	—
411	C₂²	—	2	8	no	—
412	C₂²	—	2	2	no	—
413	C₂²	—	2	4	no	—
414	C₂²	—	2	4	no	—
415	C₂²	—	2	8	no	—
416	C₂²	—	2	8	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	4	no	—
419	C₂²	—	2	2	no	—
420	C₂²	—	2	8	no	—
421	C₂²	—	4	16	no	—
422	C₂²	—	4	8	no	—
423	C₂²	—	4	4	no	—
424	C₂²	—	4	16	no	—
425	C₂²	—	8	16	no	—
426	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
427	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
428	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
429	C₂²	C₂×2₋¹⁺⁴	1	4	yes	—
430	C₂²	C₂×2₋¹⁺⁴	1	2	yes	—
431	C₂²	C₂⁶	1	1	yes	characteristic
432	C₄	—	2	2	no	—
433	C₄	—	2	8	no	—
434	C₄	—	2	2	no	—
435	C₄	—	2	4	no	—
436	C₄	—	2	2	no	—
437	C₄	—	2	8	no	—
438	C₄	—	2	4	no	—
439	C₄	—	2	8	no	—
440	C₄	—	2	4	no	—
441	C₄	C₂×H(5,𝔽₂)	1	4	yes	—
442	C₂	—	2	4	no	—
443	C₂	—	2	4	no	—
444	C₂	—	4	4	no	—
445	C₂	—	4	2	no	—
446	C₂	—	4	8	no	—
447	C₂	#3536	1	4	yes	direct product factor
448	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
449	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
450	C₂	C₂²×2₋¹⁺⁴	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂³	C₂⁵
commutator, Frattini, cosocle	C₂²	C₂⁶
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. #3536	C₂	direct (N × H)
2. C₂×#562	C₂	semidirect
3. C₂×#554	C₂	semidirect
4. C₂×#548	C₂	semidirect
5. C₂×#547	C₂	semidirect
6. C₂×#546	C₂	semidirect
7. C₂×#546	C₂	semidirect
8. C₂×#543	C₂	semidirect
9. C₂×#542	C₂	semidirect
10. C₂×#539	C₂	semidirect
11. C₂×#538	C₂	semidirect
12. C₂×#537	C₂	semidirect
13. C₂×#537	C₂	semidirect
14. C₂×#525	C₂	semidirect
15. C₂²×C₂²⋊Q₈	C₂	semidirect
16. C₂²×#121	C₂	semidirect
17. C₂²×#41	C₂²	semidirect
18. C₂²×#41	C₂²	semidirect
19. C₂²×#41	C₂²	semidirect
20. C₂³×Q₈	C₂²	semidirect
24. #562	C₂²	semidirect
25. #554	C₂²	semidirect
26. #548	C₂²	semidirect
27. #547	C₂²	semidirect
28. #546	C₂²	semidirect
29. #546	C₂²	semidirect
30. #543	C₂²	semidirect
31. #542	C₂²	semidirect
32. #539	C₂²	semidirect
33. #538	C₂²	semidirect
34. #537	C₂²	semidirect
35. #537	C₂²	semidirect
36. C₂×C₄⋊Q₈	C₂²	semidirect
37. C₂×#126	C₂²	semidirect
38. C₂×#125	C₂²	semidirect
39. C₂×#124	C₂²	semidirect
40. C₂×#124	C₂²	semidirect
41. C₂×#124	C₂²	semidirect
42. #525	C₂²	semidirect
43. C₂×#123	C₂²	semidirect
44. C₂×#123	C₂²	semidirect
45. C₂×#123	C₂²	semidirect
46. C₂×#123	C₂²	semidirect
47. 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
56. C₂×C₂²⋊Q₈	C₂²	semidirect
57. C₂×C₂²⋊Q₈	C₂²	semidirect
58. C₂×C₂²⋊Q₈	C₂²	semidirect
59. C₂×C₂²⋊Q₈	C₂²	semidirect
60. C₂×C₂²⋊Q₈	C₂²	semidirect
61. C₂×C₂²⋊Q₈	C₂²	semidirect
67. C₂×#121	C₂²	semidirect
68. C₂×#121	C₂²	semidirect
69. C₂×#121	C₂²	semidirect
70. C₂×#121	C₂²	semidirect
71. C₂×#121	C₂²	semidirect
72. C₂×#121	C₂²	semidirect
73. C₂×#121	C₂²	semidirect
74. C₂×#121	C₂²	semidirect
77. C₂×C₄×Q₈	C₂²	semidirect
80. C₂×C₄×D₄	C₂²	semidirect
81. C₂×C₄×D₄	C₂²	semidirect
82. C₂×C₄×D₄	C₂²	semidirect
83. C₂×#117	C₂²	semidirect
85. C₂²×C₄⋊C₄	C₂²	semidirect
86. C₂²×C₄⋊C₄	C₂²	semidirect
87. C₂²×C₄⋊C₄	C₂²	semidirect
96. C₂×#41	C₂³	semidirect
97. C₂×#41	C₂³	semidirect
98. C₂×#41	C₂³	semidirect
104. C₂²×Q₈	C₂³	semidirect
134. C₄⋊Q₈	C₂³	semidirect
135. #126	C₂³	semidirect
136. #125	C₂³	semidirect
137. #124	C₂³	semidirect
138. #124	C₂³	semidirect
139. #124	C₂³	semidirect
140. #123	C₂³	semidirect
141. #123	C₂³	semidirect
142. #123	C₂³	semidirect
143. #123	C₂³	semidirect
144. #123	C₂³	semidirect
149. C₂²⋊Q₈	C₂³	semidirect
150. C₂²⋊Q₈	C₂³	semidirect
151. C₂²⋊Q₈	C₂³	semidirect
152. C₂²⋊Q₈	C₂³	semidirect
153. C₂²⋊Q₈	C₂³	semidirect
154. C₂²⋊Q₈	C₂³	semidirect
155. C₂²⋊Q₈	C₂³	semidirect
156. C₂²⋊Q₈	C₂³	semidirect
157. C₂²⋊Q₈	C₂³	semidirect
163. #121	C₂³	semidirect
164. #121	C₂³	semidirect
165. #121	C₂³	semidirect
166. #121	C₂³	semidirect
167. #121	C₂³	semidirect
168. #121	C₂³	semidirect
169. #121	C₂³	semidirect
172. C₄×Q₈	C₂³	semidirect
175. C₄×D₄	C₂³	semidirect
176. C₄×D₄	C₂³	semidirect
177. C₄×D₄	C₂³	semidirect
178. #117	C₂³	semidirect
194. C₂×C₄⋊C₄	C₂³	semidirect
195. C₂×C₄⋊C₄	C₂³	semidirect
196. C₂×C₄⋊C₄	C₂³	semidirect
447. C₂	#3536	direct (N × H)

Maximal subgroups

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

subgroup	index
#3536	2
C₂×#562	2
C₂×#554	2
C₂×#548	2
C₂×#547	2
C₂×#546	2
C₂×#543	2
C₂×#542	2
C₂×#539	2
C₂×#538	2
C₂×#537	2
C₂×#525	2
C₂²×C₂²⋊Q₈	2
C₂²×#121	2

Subgroups — C2×#3536 #62723

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3536 #62723