Subgroups — C₂×#3513 #62770

Order 256.

4041 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3513	C₂	1	32	yes	maximal, direct product factor
2	C₂×#559	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#554	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#553	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#553	C₂	1	2	yes	maximal, complemented
6	C₂×#552	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#551	C₂	1	2	yes	maximal, complemented
8	C₂×#551	C₂	1	2	yes	maximal, complemented
9	C₂×#547	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#546	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#546	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#546	C₂	1	2	yes	maximal, complemented
13	C₂×D₄²	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#542	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#540	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#539	C₂	1	2	yes	maximal, complemented
17	C₂×#538	C₂	1	2	yes	maximal, complemented
18	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
19	C₂×#529	C₂	1	1	yes	maximal, characteristic, complemented
20	C₂×#525	C₂	1	2	yes	maximal, complemented
21	C₂²×#123	C₂	1	2	yes	maximal, complemented
22	C₂×#520	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#518	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂²×C₄×D₄	C₂	1	1	yes	maximal, characteristic, complemented
25	C₂²×#41	C₂²	1	1	yes	characteristic
26	C₂²×#41	C₂²	1	2	yes	complemented
27	C₂³×D₄	C₂²	1	1	yes	characteristic
28	C₂³×D₄	C₂²	1	1	yes	characteristic
29	C₂³×D₄	C₂²	1	2	yes	—
30	C₂⁴×C₄	C₂²	1	2	yes	complemented
31	#559	C₂²	1	16	yes	complemented
32	#554	C₂²	1	16	yes	complemented
33	#553	C₂²	1	16	yes	complemented
34	#553	C₂²	1	32	yes	complemented
35	#552	C₂²	1	16	yes	complemented
36	#551	C₂²	1	32	yes	complemented
37	#551	C₂²	1	32	yes	complemented
38	#547	C₂²	1	16	yes	complemented
39	#546	C₂²	1	16	yes	complemented
40	#546	C₂²	1	16	yes	complemented
41	#546	C₂²	1	32	yes	complemented
42	D₄²	C₂²	1	16	yes	complemented
43	#542	C₂²	1	16	yes	complemented
44	#540	C₂²	1	16	yes	complemented
45	#539	C₂²	1	32	yes	complemented
46	#538	C₂²	1	32	yes	complemented
47	C₂×C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
48	C₂×#127	C₂²	1	1	yes	characteristic
49	#529	C₂²	1	16	yes	complemented
50	#529	C₂²	1	16	yes	complemented
51	C₂×#126	C₂²	1	2	yes	complemented
52	C₂×#126	C₂²	1	1	yes	characteristic, complemented
53	C₂×#126	C₂²	1	1	yes	characteristic, complemented
54	C₂×#126	C₂²	1	2	yes	complemented
55	C₂×#126	C₂²	1	2	yes	complemented
56	C₂×#126	C₂²	1	2	yes	complemented
57	C₂×#125	C₂²	1	1	yes	characteristic, complemented
58	C₂×#125	C₂²	1	1	yes	characteristic, complemented
59	C₂×#125	C₂²	1	2	yes	complemented
60	C₂×#125	C₂²	1	1	yes	characteristic, complemented
61	C₂×#124	C₂²	1	1	yes	characteristic, complemented
62	C₂×#124	C₂²	1	1	yes	characteristic, complemented
63	C₂×#124	C₂²	1	2	yes	complemented
64	C₂×#124	C₂²	1	2	yes	complemented
65	C₂×#124	C₂²	1	1	yes	characteristic, complemented
66	#525	C₂²	1	32	yes	complemented
67	C₂×#123	C₂²	1	1	yes	characteristic
68	C₂×#123	C₂²	1	2	yes	—
69	C₂×#123	C₂²	1	2	yes	complemented
70	C₂×#123	C₂²	1	2	yes	complemented
71	C₂×#123	C₂²	1	2	yes	complemented
72	C₂×#123	C₂²	1	2	yes	complemented
73	C₂×#123	C₂²	1	2	yes	complemented
74	C₂×#123	C₂²	1	2	yes	complemented
75	C₂×#123	C₂²	1	1	yes	characteristic, complemented
76	C₂×#123	C₂²	1	2	yes	complemented
77	C₂×#123	C₂²	1	2	yes	complemented
78	C₂×#123	C₂²	1	2	yes	complemented
79	C₂×#123	C₂²	1	2	yes	complemented
80	C₂×#123	C₂²	1	2	yes	complemented
81	C₂×#123	C₂²	1	32	yes	complemented
82	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
83	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
84	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
85	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
87	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
88	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
89	C₂×C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
90	C₂×#121	C₂²	1	1	yes	characteristic
91	C₂×#121	C₂²	1	1	yes	characteristic
92	C₂×#121	C₂²	1	2	yes	—
93	C₂×#121	C₂²	1	1	yes	characteristic
94	C₂×#121	C₂²	1	2	yes	complemented
95	C₂×#121	C₂²	1	2	yes	complemented
96	C₂×#121	C₂²	1	2	yes	complemented
97	C₂×#121	C₂²	1	2	yes	complemented
98	C₂×#121	C₂²	1	1	yes	characteristic, complemented
99	C₂×#121	C₂²	1	2	yes	complemented
100	C₂×#121	C₂²	1	1	yes	characteristic, complemented
101	C₂×#120	C₂²	1	2	yes	—
102	C₂×#120	C₂²	1	2	yes	—
103	C₂×#120	C₂²	1	2	yes	complemented
104	C₂×#120	C₂²	1	2	yes	complemented
105	#520	C₂²	1	16	yes	complemented
106	#518	C₂²	1	16	yes	complemented
107	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
108	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
109	C₂×C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
110	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
111	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
112	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
113	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
114	C₂×C₄×D₄	C₂²	1	1	yes	characteristic
115	C₂×C₄×D₄	C₂²	1	2	yes	complemented
116	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
117	C₂×C₄×D₄	C₂²	1	2	yes	complemented
118	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄×D₄	C₂²	1	2	yes	complemented
120	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
121	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
122	C₂×C₄×D₄	C₂²	1	2	yes	complemented
123	C₂×C₄×D₄	C₂²	1	2	yes	complemented
124	C₂×C₄×D₄	C₂²	1	2	yes	complemented
125	C₂×C₄×D₄	C₂²	1	2	yes	complemented
126	C₂×C₄×D₄	C₂²	1	2	yes	complemented
127	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
128	C₂×C₄×D₄	C₂²	1	2	yes	complemented
129	C₂×C₄×D₄	C₂²	1	1	yes	characteristic, complemented
130	C₂×C₄×D₄	C₂²	1	16	yes	complemented
131	C₂×#117	C₂²	1	1	yes	characteristic, complemented
132	C₂×#117	C₂²	1	1	yes	characteristic, complemented
133	C₂×#117	C₂²	1	1	yes	characteristic, complemented
134	C₂×#117	C₂²	1	2	yes	complemented
135	C₂×#117	C₂²	1	2	yes	complemented
136	C₂×#117	C₂²	1	2	yes	complemented
137	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
138	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
139	C₂²×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
140	C₂²×C₄⋊C₄	C₂²	1	2	yes	complemented
141	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
142	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
143	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
144	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
145	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
146	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
147	C₂⁵	C₂³	1	2	yes	—
148	C₂⁵	C₂³	1	2	yes	—
149	C₂×#41	—	2	8	no	—
150	C₂×#41	—	4	8	no	—
151	C₂×#41	C₂³	1	8	yes	—
152	C₂×#41	C₂³	1	16	yes	complemented
153	C₂²×Q₈	C₂³	1	1	yes	characteristic
154	C₂²×Q₈	C₂³	1	1	yes	characteristic
155	C₂²×Q₈	C₂³	1	2	yes	—
156	C₂²×D₄	—	2	8	no	—
157	C₂²×D₄	—	2	8	no	—
158	C₂²×D₄	—	4	8	no	—
159	C₂²×D₄	C₂³	1	1	yes	characteristic
160	C₂²×D₄	C₂³	1	2	yes	—
161	C₂²×D₄	C₂³	1	2	yes	—
162	C₂²×D₄	C₂³	1	2	yes	—
163	C₂²×D₄	C₂³	1	1	yes	characteristic
164	C₂²×D₄	C₂³	1	1	yes	characteristic
165	C₂²×D₄	C₂³	1	8	yes	—
166	C₂²×D₄	C₂³	1	2	yes	—
167	C₂²×D₄	C₂³	1	1	yes	characteristic
168	C₂²×D₄	C₂³	1	8	yes	—
169	C₂²×D₄	C₂³	1	2	yes	—
170	C₂²×D₄	C₂³	1	1	yes	characteristic
171	C₂²×D₄	C₂³	1	2	yes	—
172	C₂²×D₄	C₂³	1	2	yes	—
173	C₂²×D₄	C₂³	1	2	yes	—
174	C₂²×D₄	C₂³	1	2	yes	—
175	C₂²×D₄	C₂³	1	16	yes	—
176	C₂²×D₄	C₂³	1	1	yes	characteristic
177	C₂³×C₄	—	4	8	no	—
178	C₂³×C₄	C₂³	1	2	yes	—
179	C₂³×C₄	C₂³	1	2	yes	—
180	C₂³×C₄	C₂³	1	1	yes	characteristic
181	C₂³×C₄	C₂³	1	1	yes	characteristic
182	C₂³×C₄	C₂³	1	1	yes	characteristic
183	C₂³×C₄	C₂³	1	1	yes	characteristic
184	C₂³×C₄	C₂³	1	2	yes	—
185	C₂³×C₄	C₂³	1	1	yes	characteristic
186	C₂³×C₄	C₂³	1	2	yes	—
187	C₂³×C₄	C₂³	1	2	yes	—
188	C₂³×C₄	C₂³	1	2	yes	—
189	C₂³×C₄	C₂³	1	2	yes	—
190	C₂³×C₄	C₂³	1	2	yes	—
191	C₂³×C₄	C₂³	1	2	yes	—
192	C₂³×C₄	C₂³	1	2	yes	—
193	C₂³×C₄	C₂³	1	2	yes	—
194	C₂³×C₄	C₂³	1	16	yes	complemented
195	C₄⋊Q₈	C₂³	1	8	yes	complemented
196	#127	C₂³	1	8	yes	—
197	#126	C₂³	1	16	yes	complemented
198	#126	C₂³	1	8	yes	complemented
199	#126	C₂³	1	8	yes	complemented
200	#126	C₂³	1	16	yes	complemented
201	#126	C₂³	1	16	yes	complemented
202	#126	C₂³	1	16	yes	complemented
203	#125	C₂³	1	8	yes	complemented
204	#125	C₂³	1	8	yes	complemented
205	#125	C₂³	1	16	yes	complemented
206	#125	C₂³	1	8	yes	complemented
207	#124	C₂³	1	8	yes	complemented
208	#124	C₂³	1	8	yes	complemented
209	#124	C₂³	1	16	yes	complemented
210	#124	C₂³	1	16	yes	complemented
211	#124	C₂³	1	8	yes	complemented
212	#123	C₂³	1	8	yes	—
213	#123	C₂³	1	16	yes	—
214	#123	C₂³	1	16	yes	complemented
215	#123	C₂³	1	16	yes	complemented
216	#123	C₂³	1	16	yes	complemented
217	#123	C₂³	1	16	yes	complemented
218	#123	C₂³	1	16	yes	complemented
219	#123	C₂³	1	16	yes	complemented
220	#123	C₂³	1	8	yes	complemented
221	#123	C₂³	1	16	yes	complemented
222	#123	C₂³	1	16	yes	complemented
223	#123	C₂³	1	16	yes	complemented
224	#123	C₂³	1	16	yes	complemented
225	#123	C₂³	1	16	yes	complemented
226	C₂²⋊Q₈	C₂³	1	16	yes	complemented
227	C₂²⋊Q₈	C₂³	1	16	yes	complemented
228	C₂²⋊Q₈	C₂³	1	8	yes	complemented
229	C₂²⋊Q₈	C₂³	1	8	yes	complemented
230	C₂²⋊Q₈	C₂³	1	16	yes	complemented
231	C₂²⋊Q₈	C₂³	1	16	yes	complemented
232	C₂²⋊Q₈	C₂³	1	16	yes	complemented
233	C₂²⋊Q₈	C₂³	1	8	yes	complemented
234	#121	C₂³	1	8	yes	—
235	#121	C₂³	1	8	yes	—
236	#121	C₂³	1	16	yes	—
237	#121	C₂³	1	8	yes	—
238	#121	C₂³	1	16	yes	complemented
239	#121	C₂³	1	16	yes	complemented
240	#121	C₂³	1	16	yes	complemented
241	#121	C₂³	1	16	yes	complemented
242	#121	C₂³	1	8	yes	complemented
243	#121	C₂³	1	16	yes	complemented
244	#121	C₂³	1	8	yes	complemented
245	#120	C₂³	1	16	yes	—
246	#120	C₂³	1	16	yes	—
247	#120	C₂³	1	16	yes	complemented
248	#120	C₂³	1	16	yes	complemented
249	C₄×Q₈	C₂³	1	8	yes	complemented
250	C₄×Q₈	C₂³	1	8	yes	complemented
251	C₄×Q₈	C₂³	1	8	yes	complemented
252	C₄×D₄	C₂³	1	8	yes	—
253	C₄×D₄	C₂³	1	8	yes	—
254	C₄×D₄	C₂³	1	8	yes	—
255	C₄×D₄	C₂³	1	8	yes	—
256	C₄×D₄	C₂³	1	8	yes	—
257	C₄×D₄	C₂³	1	16	yes	complemented
258	C₄×D₄	C₂³	1	8	yes	complemented
259	C₄×D₄	C₂³	1	16	yes	complemented
260	C₄×D₄	C₂³	1	8	yes	complemented
261	C₄×D₄	C₂³	1	16	yes	complemented
262	C₄×D₄	C₂³	1	8	yes	complemented
263	C₄×D₄	C₂³	1	8	yes	complemented
264	C₄×D₄	C₂³	1	16	yes	complemented
265	C₄×D₄	C₂³	1	16	yes	complemented
266	C₄×D₄	C₂³	1	16	yes	complemented
267	C₄×D₄	C₂³	1	16	yes	complemented
268	C₄×D₄	C₂³	1	16	yes	complemented
269	C₄×D₄	C₂³	1	8	yes	complemented
270	C₄×D₄	C₂³	1	16	yes	complemented
271	C₄×D₄	C₂³	1	8	yes	complemented
272	#117	C₂³	1	8	yes	complemented
273	#117	C₂³	1	8	yes	complemented
274	#117	C₂³	1	8	yes	complemented
275	#117	C₂³	1	16	yes	complemented
276	#117	C₂³	1	16	yes	complemented
277	#117	C₂³	1	16	yes	complemented
278	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
279	C₂×C₄⋊C₄	C₂³	1	2	yes	—
280	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
281	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
282	C₂×C₄⋊C₄	C₂³	1	2	yes	—
283	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
284	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
285	C₂×C₄⋊C₄	C₂³	1	2	yes	—
286	C₂×C₄⋊C₄	C₂³	1	2	yes	—
287	C₂×C₄⋊C₄	C₂³	1	2	yes	—
288	C₂×C₄⋊C₄	C₂³	1	2	yes	—
289	C₂×C₄⋊C₄	C₂³	1	2	yes	—
290	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
291	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
292	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
293	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
294	C₂×C₄⋊C₄	C₂³	1	2	yes	—
295	C₂×C₄⋊C₄	C₂³	1	2	yes	—
296	C₂×C₄⋊C₄	C₂³	1	2	yes	—
297	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
298	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
299	C₂×C₄⋊C₄	C₂³	1	2	yes	—
300	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
301	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
302	C₂×C₄⋊C₄	C₂³	1	1	yes	characteristic
303	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
304	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
305	C₂×C₄⋊C₄	C₂³	1	8	yes	complemented
306	C₂×C₄⋊C₄	C₂³	1	16	yes	complemented
307	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
308	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
309	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
310	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
311	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
312	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
314	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
315	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
316	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
317	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
318	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
319	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
320	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
321	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
322	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
323	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
324	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
325	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
326	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
327	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
328	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
329	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
330	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
331	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
332	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
333	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
334	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
335	C₂×C₂²⋊C₄	C₂³	1	1	yes	characteristic
336	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
337	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
338	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
339	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
340	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
341	C₂×C₄²	C₂³	1	1	yes	characteristic
342	C₂×C₄²	C₂³	1	2	yes	—
343	C₂×C₄²	C₂³	1	2	yes	—
344	C₂×C₄²	C₂³	1	2	yes	—
345	C₂×C₄²	C₂³	1	1	yes	characteristic
346	C₂×C₄²	C₂³	1	1	yes	characteristic
347	C₂×C₄²	C₂³	1	1	yes	characteristic
348	C₂×C₄²	C₂³	1	1	yes	characteristic
349	C₂×C₄²	C₂³	1	1	yes	characteristic
350	C₂×C₄²	C₂³	1	8	yes	complemented
351	C₂⁴	—	2	8	no	—
352	C₂⁴	—	2	8	no	—
353	C₂⁴	—	2	8	no	—
354	C₂⁴	—	4	4	no	—
355	C₂⁴	—	4	4	no	—
356	C₂⁴	—	4	4	no	—
357	C₂⁴	C₂⁴	1	1	yes	characteristic
358	C₂⁴	C₂⁴	1	2	yes	—
359	C₂⁴	C₂⁴	1	2	yes	—
360	C₂⁴	C₂⁴	1	1	yes	characteristic
361	C₂⁴	C₂⁴	1	8	yes	—
362	C₂⁴	C₂⁴	1	2	yes	—
363	C₂⁴	C₂⁴	1	1	yes	characteristic
364	C₂⁴	C₂⁴	1	8	yes	—
365	#41	—	2	32	no	—
366	#41	—	4	32	no	—
367	C₂×Q₈	—	2	4	no	—
368	C₂×Q₈	—	4	2	no	—
369	C₂×Q₈	—	4	4	no	—
370	C₂×Q₈	C₂⁴	1	4	yes	—
371	C₂×Q₈	C₂⁴	1	4	yes	—
372	C₂×Q₈	C₂⁴	1	8	yes	—
373	C₂×D₄	—	2	8	no	—
374	C₂×D₄	—	2	8	no	—
375	C₂×D₄	—	2	8	no	—
376	C₂×D₄	—	2	4	no	—
377	C₂×D₄	—	2	8	no	—
378	C₂×D₄	—	2	4	no	—
379	C₂×D₄	—	2	32	no	—
380	C₂×D₄	—	2	32	no	—
381	C₂×D₄	—	2	4	no	—
382	C₂×D₄	—	2	4	no	—
383	C₂×D₄	—	4	4	no	—
384	C₂×D₄	—	4	4	no	—
385	C₂×D₄	—	4	4	no	—
386	C₂×D₄	—	4	2	no	—
387	C₂×D₄	—	4	4	no	—
388	C₂×D₄	—	4	4	no	—
389	C₂×D₄	—	4	32	no	—
390	C₂×D₄	#41	1	8	yes	complemented
391	C₂×D₄	C₂⁴	1	4	yes	—
392	C₂×D₄	C₂⁴	1	8	yes	—
393	C₂×D₄	C₂⁴	1	8	yes	—
394	C₂×D₄	C₂⁴	1	8	yes	—
395	C₂×D₄	C₂⁴	1	4	yes	—
396	C₂×D₄	C₂⁴	1	4	yes	—
397	C₂×D₄	C₂⁴	1	8	yes	—
398	C₂×D₄	C₂⁴	1	4	yes	—
399	C₂×D₄	C₂⁴	1	8	yes	—
400	C₂×D₄	C₂⁴	1	4	yes	—
401	C₂×D₄	C₂⁴	1	8	yes	—
402	C₂×D₄	C₂⁴	1	8	yes	—
403	C₂×D₄	C₂⁴	1	8	yes	—
404	C₂×D₄	C₂⁴	1	8	yes	—
405	C₂×D₄	C₂⁴	1	4	yes	—
406	C₂²×C₄	—	2	8	no	—
407	C₂²×C₄	—	2	4	no	—
408	C₂²×C₄	—	2	8	no	—
409	C₂²×C₄	—	2	4	no	—
410	C₂²×C₄	—	2	4	no	—
411	C₂²×C₄	—	2	4	no	—
412	C₂²×C₄	—	4	4	no	—
413	C₂²×C₄	—	4	4	no	—
414	C₂²×C₄	—	4	4	no	—
415	C₂²×C₄	—	4	4	no	—
416	C₂²×C₄	—	4	32	no	—
417	C₂²×C₄	—	4	4	no	—
418	C₂²×C₄	—	4	2	no	—
419	C₂²×C₄	—	4	4	no	—
420	C₂²×C₄	—	4	4	no	—
421	C₂²×C₄	—	4	4	no	—
422	C₂²×C₄	—	4	4	no	—
423	C₂²×C₄	C₂⁴	1	4	yes	—
424	C₂²×C₄	C₂⁴	1	4	yes	—
425	C₂²×C₄	C₂⁴	1	8	yes	—
426	C₂²×C₄	C₂⁴	1	8	yes	—
427	C₂²×C₄	C₂⁴	1	4	yes	—
428	C₂²×C₄	C₂⁴	1	4	yes	—
429	C₂²×C₄	C₂⁴	1	1	yes	characteristic
430	C₂²×C₄	C₂⁴	1	1	yes	characteristic
431	C₂²×C₄	C₂⁴	1	2	yes	—
432	C₂²×C₄	C₂⁴	1	1	yes	characteristic
433	C₂²×C₄	C₂⁴	1	1	yes	characteristic
434	C₂²×C₄	C₂⁴	1	1	yes	characteristic
435	C₂²×C₄	C₂⁴	1	1	yes	characteristic
436	C₂²×C₄	C₂⁴	1	2	yes	—
437	C₂²×C₄	C₂⁴	1	1	yes	characteristic
438	C₂²×C₄	C₂⁴	1	1	yes	characteristic
439	C₂²×C₄	C₂⁴	1	2	yes	—
440	C₂²×C₄	C₂⁴	1	1	yes	characteristic
441	C₂²×C₄	C₂⁴	1	2	yes	—
442	C₂²×C₄	C₂⁴	1	1	yes	characteristic
443	C₂²×C₄	C₂⁴	1	1	yes	characteristic
444	C₂²×C₄	C₂⁴	1	2	yes	—
445	C₂²×C₄	C₂⁴	1	4	yes	—
446	C₂²×C₄	C₂⁴	1	8	yes	—
447	C₂²×C₄	C₂⁴	1	8	yes	—
448	C₂²×C₄	C₂⁴	1	8	yes	—
449	C₂²×C₄	C₂⁴	1	8	yes	—
450	C₂²×C₄	C₂⁴	1	8	yes	—
451	C₂²×C₄	C₂⁴	1	8	yes	—
452	C₂²×C₄	C₂⁴	1	8	yes	—
453	C₂²×C₄	C₂⁴	1	8	yes	—
454	C₂²×C₄	C₂⁴	1	8	yes	—
455	C₂²×C₄	C₂⁴	1	1	yes	characteristic
456	C₄⋊C₄	C₂⁴	1	4	yes	—
457	C₄⋊C₄	C₂⁴	1	8	yes	—
458	C₄⋊C₄	C₂⁴	1	4	yes	—
459	C₄⋊C₄	C₂⁴	1	4	yes	—
460	C₄⋊C₄	C₂⁴	1	8	yes	—
461	C₄⋊C₄	C₂⁴	1	4	yes	—
462	C₄⋊C₄	C₂⁴	1	4	yes	—
463	C₄⋊C₄	C₂⁴	1	8	yes	—
464	C₄⋊C₄	C₂⁴	1	8	yes	—
465	C₄⋊C₄	C₂⁴	1	8	yes	—
466	C₄⋊C₄	C₂⁴	1	8	yes	—
467	C₄⋊C₄	C₂⁴	1	8	yes	—
468	C₄⋊C₄	C₂⁴	1	4	yes	—
469	C₄⋊C₄	C₂⁴	1	4	yes	—
470	C₄⋊C₄	C₂⁴	1	4	yes	—
471	C₄⋊C₄	C₂⁴	1	4	yes	—
472	C₄⋊C₄	C₂⁴	1	8	yes	—
473	C₄⋊C₄	C₂⁴	1	8	yes	—
474	C₄⋊C₄	C₂⁴	1	8	yes	—
475	C₄⋊C₄	C₂⁴	1	4	yes	—
476	C₄⋊C₄	C₂⁴	1	4	yes	—
477	C₄⋊C₄	C₂⁴	1	8	yes	—
478	C₄⋊C₄	C₂⁴	1	4	yes	—
479	C₄⋊C₄	C₂⁴	1	4	yes	—
480	C₄⋊C₄	C₂⁴	1	4	yes	—
481	C₂²⋊C₄	C₂⁴	1	8	yes	—
482	C₂²⋊C₄	C₂⁴	1	4	yes	—
483	C₂²⋊C₄	C₂⁴	1	8	yes	—
484	C₂²⋊C₄	C₂⁴	1	4	yes	—
485	C₂²⋊C₄	C₂⁴	1	4	yes	—
486	C₂²⋊C₄	C₂⁴	1	4	yes	—
487	C₂²⋊C₄	C₂⁴	1	8	yes	—
488	C₂²⋊C₄	C₂⁴	1	8	yes	—
489	C₂²⋊C₄	C₂⁴	1	8	yes	—
490	C₂²⋊C₄	C₂⁴	1	8	yes	—
491	C₂²⋊C₄	C₂⁴	1	8	yes	—
492	C₂²⋊C₄	C₂⁴	1	8	yes	—
493	C₂²⋊C₄	C₂⁴	1	8	yes	—
494	C₂²⋊C₄	C₂⁴	1	8	yes	—
495	C₂²⋊C₄	C₂⁴	1	8	yes	—
496	C₂²⋊C₄	C₂⁴	1	8	yes	—
497	C₂²⋊C₄	C₂⁴	1	8	yes	—
498	C₂²⋊C₄	C₂⁴	1	8	yes	—
499	C₂²⋊C₄	C₂⁴	1	4	yes	—
500	C₂²⋊C₄	C₂⁴	1	8	yes	—
501	C₂²⋊C₄	C₂⁴	1	4	yes	—
502	C₂²⋊C₄	C₂⁴	1	4	yes	—
503	C₂²⋊C₄	C₂⁴	1	8	yes	—
504	C₂²⋊C₄	C₂⁴	1	4	yes	—
505	C₂²⋊C₄	C₂⁴	1	4	yes	—
506	C₂²⋊C₄	C₂⁴	1	8	yes	—
507	C₂²⋊C₄	C₂⁴	1	8	yes	—
508	C₂²⋊C₄	C₂⁴	1	8	yes	—
509	C₂²⋊C₄	C₂⁴	1	4	yes	—
510	C₄²	C₂⁴	1	4	yes	—
511	C₄²	C₂⁴	1	4	yes	—
512	C₄²	C₂⁴	1	4	yes	—
513	C₄²	C₂⁴	1	4	yes	—
514	C₄²	C₂⁴	1	8	yes	—
515	C₄²	C₂⁴	1	8	yes	—
516	C₄²	C₂⁴	1	8	yes	—
517	C₄²	C₂⁴	1	4	yes	—
518	C₄²	C₂⁴	1	4	yes	—
519	C₂³	—	2	2	no	—
520	C₂³	—	2	4	no	—
521	C₂³	—	2	2	no	—
522	C₂³	—	2	4	no	—
523	C₂³	—	2	2	no	—
524	C₂³	—	2	2	no	—
525	C₂³	—	2	16	no	—
526	C₂³	—	2	4	no	—
527	C₂³	—	2	4	no	—
528	C₂³	—	2	2	no	—
529	C₂³	—	2	16	no	—
530	C₂³	—	2	4	no	—
531	C₂³	—	2	4	no	—
532	C₂³	—	2	2	no	—
533	C₂³	—	2	4	no	—
534	C₂³	—	2	2	no	—
535	C₂³	—	2	4	no	—
536	C₂³	—	2	2	no	—
537	C₂³	—	2	16	no	—
538	C₂³	—	4	8	no	—
539	C₂³	—	4	8	no	—
540	C₂³	—	4	8	no	—
541	C₂³	—	4	32	no	—
542	C₂³	—	8	16	no	—
543	C₂³	C₂×#41	1	8	yes	—
544	C₂³	H(5,𝔽₂)	1	4	yes	—
545	C₂³	C₂⁵	1	2	yes	—
546	C₂³	C₂⁵	1	4	yes	—
547	C₂³	C₂⁵	1	4	yes	—
548	C₂³	C₂⁵	1	2	yes	—
549	C₂³	C₂⁵	1	4	yes	—
550	C₂³	C₂⁵	1	2	yes	—
551	C₂³	C₂⁵	1	1	yes	characteristic
552	Q₈	—	2	8	no	—
553	Q₈	—	4	4	no	—
554	Q₈	—	4	8	no	—
555	D₄	—	2	16	no	—
556	D₄	—	2	16	no	—
557	D₄	—	2	16	no	—
558	D₄	—	2	8	no	—
559	D₄	—	2	16	no	—
560	D₄	—	2	8	no	—
561	D₄	—	2	8	no	—
562	D₄	—	2	8	no	—
563	D₄	—	4	8	no	—
564	D₄	—	4	8	no	—
565	D₄	—	4	8	no	—
566	D₄	—	4	4	no	—
567	D₄	—	4	8	no	—
568	D₄	—	4	8	no	—
569	D₄	C₂×#41	1	16	yes	complemented
570	C₂×C₄	—	2	2	no	—
571	C₂×C₄	—	2	2	no	—
572	C₂×C₄	—	2	2	no	—
573	C₂×C₄	—	2	4	no	—
574	C₂×C₄	—	2	16	no	—
575	C₂×C₄	—	2	8	no	—
576	C₂×C₄	—	2	2	no	—
577	C₂×C₄	—	2	2	no	—
578	C₂×C₄	—	2	4	no	—
579	C₂×C₄	—	2	4	no	—
580	C₂×C₄	—	2	16	no	—
581	C₂×C₄	—	2	2	no	—
582	C₂×C₄	—	2	4	no	—
583	C₂×C₄	—	2	2	no	—
584	C₂×C₄	—	2	2	no	—
585	C₂×C₄	—	2	4	no	—
586	C₂×C₄	—	2	2	no	—
587	C₂×C₄	—	2	2	no	—
588	C₂×C₄	—	2	2	no	—
589	C₂×C₄	—	2	8	no	—
590	C₂×C₄	—	2	8	no	—
591	C₂×C₄	—	2	8	no	—
592	C₂×C₄	—	4	8	no	—
593	C₂×C₄	—	4	8	no	—
594	C₂×C₄	—	4	8	no	—
595	C₂×C₄	—	4	8	no	—
596	C₂×C₄	—	4	8	no	—
597	C₂×C₄	—	4	4	no	—
598	C₂×C₄	—	4	8	no	—
599	C₂×C₄	—	4	8	no	—
600	C₂×C₄	—	4	8	no	—
601	C₂×C₄	—	4	8	no	—
602	C₂×C₄	C₂×#41	1	4	yes	—
603	C₂×C₄	C₂⁵	1	2	yes	—
604	C₂×C₄	C₂⁵	1	2	yes	—
605	C₂×C₄	C₂⁵	1	4	yes	—
606	C₂×C₄	C₂⁵	1	2	yes	—
607	C₂×C₄	C₂⁵	1	2	yes	—
608	C₂×C₄	C₂⁵	1	2	yes	—
609	C₂×C₄	C₂⁵	1	2	yes	—
610	C₂×C₄	C₂⁵	1	2	yes	—
611	C₂×C₄	C₂⁵	1	4	yes	—
612	C₂×C₄	C₂⁵	1	2	yes	—
613	C₂×C₄	C₂⁵	1	4	yes	—
614	C₂×C₄	C₂⁵	1	2	yes	—
615	C₂×C₄	C₂⁵	1	4	yes	—
616	C₂×C₄	C₂⁵	1	2	yes	—
617	C₂×C₄	C₂⁵	1	2	yes	—
618	C₂×C₄	C₂⁵	1	4	yes	—
619	C₂×C₄	C₂⁵	1	2	yes	—
620	C₂²	—	2	2	no	—
621	C₂²	—	2	4	no	—
622	C₂²	—	2	2	no	—
623	C₂²	—	2	4	no	—
624	C₂²	—	2	8	no	—
625	C₂²	—	2	16	no	—
626	C₂²	—	2	2	no	—
627	C₂²	—	2	2	no	—
628	C₂²	—	2	4	no	—
629	C₂²	—	2	4	no	—
630	C₂²	—	2	2	no	—
631	C₂²	—	2	4	no	—
632	C₂²	—	2	4	no	—
633	C₂²	—	2	2	no	—
634	C₂²	—	2	4	no	—
635	C₂²	—	2	2	no	—
636	C₂²	—	2	4	no	—
637	C₂²	—	2	2	no	—
638	C₂²	—	4	32	no	—
639	C₂²	—	4	4	no	—
640	C₂²	—	4	8	no	—
641	C₂²	—	4	8	no	—
642	C₂²	—	4	4	no	—
643	C₂²	—	8	16	no	—
644	C₂²	C₂²×#41	1	8	yes	—
645	C₂²	C₂²×#41	1	2	yes	—
646	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
647	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
648	C₂²	#585	1	2	yes	—
649	C₂²	C₂⁶	1	1	yes	characteristic
650	C₄	—	2	2	no	—
651	C₄	—	2	2	no	—
652	C₄	—	2	2	no	—
653	C₄	—	2	4	no	—
654	C₄	—	2	2	no	—
655	C₄	—	2	2	no	—
656	C₄	—	2	4	no	—
657	C₄	—	2	4	no	—
658	C₄	—	2	2	no	—
659	C₄	—	2	4	no	—
660	C₄	—	2	2	no	—
661	C₄	—	2	2	no	—
662	C₄	—	2	4	no	—
663	C₄	—	2	2	no	—
664	C₄	—	2	2	no	—
665	C₄	—	2	2	no	—
666	C₄	C₂²×#41	1	4	yes	—
667	C₂	—	2	4	no	—
668	C₂	—	2	8	no	—
669	C₂	—	4	2	no	—
670	C₂	—	4	4	no	—
671	C₂	—	4	4	no	—
672	C₂	—	4	2	no	—
673	C₂	#3513	1	4	yes	direct product factor
674	C₂	C₂³×#41	1	1	yes	characteristic
675	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
676	C₂	C₂×#585	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. #3513	C₂	direct (N × H)
2. C₂×#559	C₂	semidirect
3. C₂×#554	C₂	semidirect
4. C₂×#553	C₂	semidirect
5. C₂×#553	C₂	semidirect
6. C₂×#552	C₂	semidirect
7. C₂×#551	C₂	semidirect
8. C₂×#551	C₂	semidirect
9. C₂×#547	C₂	semidirect
10. C₂×#546	C₂	semidirect
11. C₂×#546	C₂	semidirect
12. C₂×#546	C₂	semidirect
13. C₂×D₄²	C₂	semidirect
14. C₂×#542	C₂	semidirect
15. C₂×#540	C₂	semidirect
16. C₂×#539	C₂	semidirect
17. C₂×#538	C₂	semidirect
18. C₂×#529	C₂	semidirect
19. C₂×#529	C₂	semidirect
20. C₂×#525	C₂	semidirect
21. C₂²×#123	C₂	semidirect
22. C₂×#520	C₂	semidirect
23. C₂×#518	C₂	semidirect
24. C₂²×C₄×D₄	C₂	semidirect
26. C₂²×#41	C₂²	semidirect
30. C₂⁴×C₄	C₂²	semidirect
31. #559	C₂²	semidirect
32. #554	C₂²	semidirect
33. #553	C₂²	semidirect
34. #553	C₂²	semidirect
35. #552	C₂²	semidirect
36. #551	C₂²	semidirect
37. #551	C₂²	semidirect
38. #547	C₂²	semidirect
39. #546	C₂²	semidirect
40. #546	C₂²	semidirect
41. #546	C₂²	semidirect
42. D₄²	C₂²	semidirect
43. #542	C₂²	semidirect
44. #540	C₂²	semidirect
45. #539	C₂²	semidirect
46. #538	C₂²	semidirect
47. C₂×C₄⋊Q₈	C₂²	semidirect
49. #529	C₂²	semidirect
50. #529	C₂²	semidirect
51. C₂×#126	C₂²	semidirect
52. C₂×#126	C₂²	semidirect
53. C₂×#126	C₂²	semidirect
54. C₂×#126	C₂²	semidirect
55. C₂×#126	C₂²	semidirect
56. C₂×#126	C₂²	semidirect
57. C₂×#125	C₂²	semidirect
58. C₂×#125	C₂²	semidirect
59. C₂×#125	C₂²	semidirect
60. C₂×#125	C₂²	semidirect
61. C₂×#124	C₂²	semidirect
62. C₂×#124	C₂²	semidirect
63. C₂×#124	C₂²	semidirect
64. C₂×#124	C₂²	semidirect
65. C₂×#124	C₂²	semidirect
66. #525	C₂²	semidirect
69. C₂×#123	C₂²	semidirect
70. C₂×#123	C₂²	semidirect
71. C₂×#123	C₂²	semidirect
72. C₂×#123	C₂²	semidirect
73. C₂×#123	C₂²	semidirect
74. C₂×#123	C₂²	semidirect
75. C₂×#123	C₂²	semidirect
76. C₂×#123	C₂²	semidirect
77. C₂×#123	C₂²	semidirect
78. C₂×#123	C₂²	semidirect
79. C₂×#123	C₂²	semidirect
80. C₂×#123	C₂²	semidirect
81. C₂×#123	C₂²	semidirect
82. C₂×C₂²⋊Q₈	C₂²	semidirect
83. C₂×C₂²⋊Q₈	C₂²	semidirect
84. C₂×C₂²⋊Q₈	C₂²	semidirect
85. C₂×C₂²⋊Q₈	C₂²	semidirect
86. C₂×C₂²⋊Q₈	C₂²	semidirect
87. C₂×C₂²⋊Q₈	C₂²	semidirect
88. C₂×C₂²⋊Q₈	C₂²	semidirect
89. C₂×C₂²⋊Q₈	C₂²	semidirect
94. C₂×#121	C₂²	semidirect
95. C₂×#121	C₂²	semidirect
96. C₂×#121	C₂²	semidirect
97. C₂×#121	C₂²	semidirect
98. C₂×#121	C₂²	semidirect
99. C₂×#121	C₂²	semidirect
100. C₂×#121	C₂²	semidirect
103. C₂×#120	C₂²	semidirect
104. C₂×#120	C₂²	semidirect
105. #520	C₂²	semidirect
106. #518	C₂²	semidirect
107. C₂×C₄×Q₈	C₂²	semidirect
108. C₂×C₄×Q₈	C₂²	semidirect
109. C₂×C₄×Q₈	C₂²	semidirect
115. C₂×C₄×D₄	C₂²	semidirect
116. C₂×C₄×D₄	C₂²	semidirect
117. C₂×C₄×D₄	C₂²	semidirect
118. C₂×C₄×D₄	C₂²	semidirect
119. C₂×C₄×D₄	C₂²	semidirect
120. C₂×C₄×D₄	C₂²	semidirect
121. C₂×C₄×D₄	C₂²	semidirect
122. C₂×C₄×D₄	C₂²	semidirect
123. C₂×C₄×D₄	C₂²	semidirect
124. C₂×C₄×D₄	C₂²	semidirect
125. C₂×C₄×D₄	C₂²	semidirect
126. C₂×C₄×D₄	C₂²	semidirect
127. C₂×C₄×D₄	C₂²	semidirect
128. C₂×C₄×D₄	C₂²	semidirect
129. C₂×C₄×D₄	C₂²	semidirect
130. C₂×C₄×D₄	C₂²	semidirect
131. C₂×#117	C₂²	semidirect
132. C₂×#117	C₂²	semidirect
133. C₂×#117	C₂²	semidirect
134. C₂×#117	C₂²	semidirect
135. C₂×#117	C₂²	semidirect
136. C₂×#117	C₂²	semidirect
137. C₂²×C₄⋊C₄	C₂²	semidirect
138. C₂²×C₄⋊C₄	C₂²	semidirect
139. C₂²×C₄⋊C₄	C₂²	semidirect
140. C₂²×C₄⋊C₄	C₂²	semidirect
141. C₂²×C₂²⋊C₄	C₂²	semidirect
142. C₂²×C₂²⋊C₄	C₂²	semidirect
143. C₂²×C₂²⋊C₄	C₂²	semidirect
144. C₂²×C₂²⋊C₄	C₂²	semidirect
145. C₂²×C₂²⋊C₄	C₂²	semidirect
146. C₂²×C₄²	C₂²	semidirect
152. C₂×#41	C₂³	semidirect
194. C₂³×C₄	C₂³	semidirect
195. C₄⋊Q₈	C₂³	semidirect
197. #126	C₂³	semidirect
198. #126	C₂³	semidirect
199. #126	C₂³	semidirect
200. #126	C₂³	semidirect
201. #126	C₂³	semidirect
202. #126	C₂³	semidirect
203. #125	C₂³	semidirect
204. #125	C₂³	semidirect
205. #125	C₂³	semidirect
206. #125	C₂³	semidirect
207. #124	C₂³	semidirect
208. #124	C₂³	semidirect
209. #124	C₂³	semidirect
210. #124	C₂³	semidirect
211. #124	C₂³	semidirect
214. #123	C₂³	semidirect
215. #123	C₂³	semidirect
216. #123	C₂³	semidirect
217. #123	C₂³	semidirect
218. #123	C₂³	semidirect
219. #123	C₂³	semidirect
220. #123	C₂³	semidirect
221. #123	C₂³	semidirect
222. #123	C₂³	semidirect
223. #123	C₂³	semidirect
224. #123	C₂³	semidirect
225. #123	C₂³	semidirect
226. C₂²⋊Q₈	C₂³	semidirect
227. C₂²⋊Q₈	C₂³	semidirect
228. C₂²⋊Q₈	C₂³	semidirect
229. C₂²⋊Q₈	C₂³	semidirect
230. C₂²⋊Q₈	C₂³	semidirect
231. C₂²⋊Q₈	C₂³	semidirect
232. C₂²⋊Q₈	C₂³	semidirect
233. C₂²⋊Q₈	C₂³	semidirect
238. #121	C₂³	semidirect
239. #121	C₂³	semidirect
240. #121	C₂³	semidirect
241. #121	C₂³	semidirect
242. #121	C₂³	semidirect
243. #121	C₂³	semidirect
244. #121	C₂³	semidirect
247. #120	C₂³	semidirect
248. #120	C₂³	semidirect
249. C₄×Q₈	C₂³	semidirect
250. C₄×Q₈	C₂³	semidirect
251. C₄×Q₈	C₂³	semidirect
257. C₄×D₄	C₂³	semidirect
258. C₄×D₄	C₂³	semidirect
259. C₄×D₄	C₂³	semidirect
260. C₄×D₄	C₂³	semidirect
261. C₄×D₄	C₂³	semidirect
262. C₄×D₄	C₂³	semidirect
263. C₄×D₄	C₂³	semidirect
264. C₄×D₄	C₂³	semidirect
265. C₄×D₄	C₂³	semidirect
266. C₄×D₄	C₂³	semidirect
267. C₄×D₄	C₂³	semidirect
268. C₄×D₄	C₂³	semidirect
269. C₄×D₄	C₂³	semidirect
270. C₄×D₄	C₂³	semidirect
271. C₄×D₄	C₂³	semidirect
272. #117	C₂³	semidirect
273. #117	C₂³	semidirect
274. #117	C₂³	semidirect
275. #117	C₂³	semidirect
276. #117	C₂³	semidirect
277. #117	C₂³	semidirect
303. C₂×C₄⋊C₄	C₂³	semidirect
304. C₂×C₄⋊C₄	C₂³	semidirect
305. C₂×C₄⋊C₄	C₂³	semidirect
306. C₂×C₄⋊C₄	C₂³	semidirect
336. C₂×C₂²⋊C₄	C₂³	semidirect
337. C₂×C₂²⋊C₄	C₂³	semidirect
338. C₂×C₂²⋊C₄	C₂³	semidirect
339. C₂×C₂²⋊C₄	C₂³	semidirect
340. C₂×C₂²⋊C₄	C₂³	semidirect
350. C₂×C₄²	C₂³	semidirect
390. C₂×D₄	#41	semidirect
569. D₄	C₂×#41	semidirect
673. C₂	#3513	direct (N × H)

Maximal subgroups

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

subgroup	index
#3513	2
C₂×#559	2
C₂×#554	2
C₂×#553	2
C₂×#552	2
C₂×#551	2
C₂×#547	2
C₂×#546	2
C₂×D₄²	2
C₂×#542	2
C₂×#540	2
C₂×#539	2
C₂×#538	2
C₂×#529	2
C₂×#525	2
C₂²×#123	2
C₂×#520	2
C₂×#518	2
C₂²×C₄×D₄	2

Subgroups — C2×#3513 #62770

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3513 #62770