Subgroups — C₂×#3545 #62753

Order 256.

3715 conjugacy classes of subgroups.

The subgroup lattice has 380 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#3545	C₂	1	32	yes	maximal, direct product factor
2	C₂×#563	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#562	C₂	1	2	yes	maximal, complemented
4	C₂×H(3,𝔽₄)	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#555	C₂	1	2	yes	maximal, complemented
6	C₂×#551	C₂	1	2	yes	maximal, complemented
7	C₂×#551	C₂	1	4	yes	maximal, complemented
8	C₂×#546	C₂	1	4	yes	maximal, complemented
9	C₂×#542	C₂	1	4	yes	maximal, complemented
10	C₂×#538	C₂	1	4	yes	maximal, complemented
11	C₂×#536	C₂	1	2	yes	maximal, complemented
12	C₂×#534	C₂	1	2	yes	maximal, complemented
13	C₂×#529	C₂	1	2	yes	maximal, complemented
14	C₂²×#124	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×#41	C₂²	1	2	yes	—
16	C₂³×Q₈	C₂²	1	1	yes	characteristic, complemented
17	C₂³×D₄	C₂²	1	1	yes	characteristic
18	C₂³×D₄	C₂²	1	2	yes	complemented
19	#563	C₂²	1	16	yes	complemented
20	#562	C₂²	1	32	yes	complemented
21	H(3,𝔽₄)	C₂²	1	16	yes	complemented
22	#555	C₂²	1	32	yes	complemented
23	#551	C₂²	1	32	yes	complemented
24	#551	C₂²	1	64	yes	complemented
25	#546	C₂²	1	64	yes	complemented
26	#542	C₂²	1	64	yes	complemented
27	#538	C₂²	1	64	yes	complemented
28	#536	C₂²	1	32	yes	complemented
29	#534	C₂²	1	32	yes	complemented
30	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
31	C₂×C₄⋊Q₈	C₂²	1	2	yes	complemented
32	#529	C₂²	1	32	yes	complemented
33	C₂×#126	C₂²	1	4	yes	complemented
34	C₂×#126	C₂²	1	4	yes	complemented
35	C₂×#126	C₂²	1	4	yes	complemented
36	C₂×#125	C₂²	1	2	yes	complemented
37	C₂×#124	C₂²	1	1	yes	characteristic
38	C₂×#124	C₂²	1	1	yes	characteristic
39	C₂×#124	C₂²	1	4	yes	complemented
40	C₂×#124	C₂²	1	1	yes	characteristic, complemented
41	C₂×#124	C₂²	1	1	yes	characteristic, complemented
42	C₂×#124	C₂²	1	2	yes	complemented
43	C₂×#124	C₂²	1	2	yes	complemented
44	C₂×#124	C₂²	1	2	yes	complemented
45	C₂×#124	C₂²	1	4	yes	complemented
46	C₂×#124	C₂²	1	4	yes	complemented
47	C₂×#124	C₂²	1	16	yes	complemented
48	C₂×#123	C₂²	1	2	yes	—
49	C₂×#123	C₂²	1	4	yes	complemented
50	C₂×#123	C₂²	1	2	yes	complemented
51	C₂×#123	C₂²	1	4	yes	complemented
52	C₂×#123	C₂²	1	4	yes	complemented
53	C₂×#123	C₂²	1	4	yes	complemented
54	C₂×#123	C₂²	1	4	yes	complemented
55	C₂×C₂²⋊Q₈	C₂²	1	2	yes	complemented
56	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
57	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
58	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
59	C₂×C₂²⋊Q₈	C₂²	1	4	yes	complemented
60	C₂×#121	C₂²	1	2	yes	—
61	C₂×#121	C₂²	1	4	yes	—
62	C₂×#121	C₂²	1	4	yes	complemented
63	C₂×#121	C₂²	1	4	yes	complemented
64	C₂×#121	C₂²	1	4	yes	complemented
65	C₂×#120	C₂²	1	4	yes	—
66	C₂×#120	C₂²	1	2	yes	—
67	C₂×#120	C₂²	1	2	yes	complemented
68	C₂×#120	C₂²	1	4	yes	complemented
69	C₂×C₄×Q₈	C₂²	1	2	yes	complemented
70	C₂×C₄×D₄	C₂²	1	2	yes	complemented
71	C₂×C₄×D₄	C₂²	1	4	yes	complemented
72	C₂×C₄×D₄	C₂²	1	4	yes	complemented
73	C₂×C₄×D₄	C₂²	1	4	yes	complemented
74	C₂×#117	C₂²	1	4	yes	complemented
75	C₂×#117	C₂²	1	2	yes	complemented
76	C₂×#117	C₂²	1	4	yes	complemented
77	C₂²×C₂²⋊C₄	C₂²	1	4	yes	complemented
78	C₂²×C₂²⋊C₄	C₂²	1	2	yes	complemented
79	C₂²×C₂²⋊C₄	C₂²	1	4	yes	complemented
80	C₂²×C₄²	C₂²	1	1	yes	characteristic, complemented
81	C₂⁵	C₂³	1	2	yes	—
82	C₂⁵	C₂³	1	2	yes	—
83	C₂×#41	—	4	8	no	—
84	C₂×#41	C₂³	1	16	yes	—
85	C₂²×Q₈	—	4	4	no	—
86	C₂²×Q₈	C₂³	1	2	yes	—
87	C₂²×Q₈	C₂³	1	1	yes	characteristic
88	C₂²×Q₈	C₂³	1	2	yes	—
89	C₂²×Q₈	C₂³	1	2	yes	—
90	C₂²×Q₈	C₂³	1	1	yes	characteristic
91	C₂²×Q₈	C₂³	1	8	yes	complemented
92	C₂²×D₄	—	4	4	no	—
93	C₂²×D₄	—	4	8	no	—
94	C₂²×D₄	C₂³	1	4	yes	—
95	C₂²×D₄	C₂³	1	4	yes	—
96	C₂²×D₄	C₂³	1	4	yes	—
97	C₂²×D₄	C₂³	1	2	yes	—
98	C₂²×D₄	C₂³	1	1	yes	characteristic
99	C₂²×D₄	C₂³	1	2	yes	—
100	C₂²×D₄	C₂³	1	2	yes	—
101	C₂²×D₄	C₂³	1	4	yes	—
102	C₂²×D₄	C₂³	1	1	yes	characteristic
103	C₂²×D₄	C₂³	1	8	yes	—
104	C₂²×D₄	C₂³	1	16	yes	complemented
105	C₂³×C₄	C₂³	1	2	yes	—
106	C₂³×C₄	C₂³	1	1	yes	characteristic
107	C₂³×C₄	C₂³	1	2	yes	—
108	C₂³×C₄	C₂³	1	4	yes	—
109	C₂³×C₄	C₂³	1	4	yes	—
110	C₂³×C₄	C₂³	1	4	yes	—
111	C₂³×C₄	C₂³	1	2	yes	—
112	C₄⋊Q₈	C₂³	1	16	yes	complemented
113	C₄⋊Q₈	C₂³	1	16	yes	complemented
114	#126	C₂³	1	32	yes	complemented
115	#126	C₂³	1	32	yes	complemented
116	#126	C₂³	1	32	yes	complemented
117	#125	C₂³	1	16	yes	complemented
118	#124	C₂³	1	8	yes	—
119	#124	C₂³	1	8	yes	—
120	#124	C₂³	1	32	yes	complemented
121	#124	C₂³	1	8	yes	complemented
122	#124	C₂³	1	8	yes	complemented
123	#124	C₂³	1	16	yes	complemented
124	#124	C₂³	1	16	yes	complemented
125	#124	C₂³	1	16	yes	complemented
126	#124	C₂³	1	32	yes	complemented
127	#124	C₂³	1	32	yes	complemented
128	#123	C₂³	1	16	yes	—
129	#123	C₂³	1	32	yes	complemented
130	#123	C₂³	1	16	yes	complemented
131	#123	C₂³	1	32	yes	complemented
132	#123	C₂³	1	32	yes	complemented
133	#123	C₂³	1	32	yes	complemented
134	#123	C₂³	1	32	yes	complemented
135	C₂²⋊Q₈	C₂³	1	16	yes	complemented
136	C₂²⋊Q₈	C₂³	1	32	yes	complemented
137	C₂²⋊Q₈	C₂³	1	32	yes	complemented
138	C₂²⋊Q₈	C₂³	1	32	yes	complemented
139	C₂²⋊Q₈	C₂³	1	32	yes	complemented
140	#121	C₂³	1	16	yes	—
141	#121	C₂³	1	32	yes	—
142	#121	C₂³	1	32	yes	complemented
143	#121	C₂³	1	32	yes	complemented
144	#121	C₂³	1	32	yes	complemented
145	#120	C₂³	1	32	yes	—
146	#120	C₂³	1	16	yes	—
147	#120	C₂³	1	16	yes	complemented
148	#120	C₂³	1	32	yes	complemented
149	C₄×Q₈	C₂³	1	16	yes	complemented
150	C₄×D₄	C₂³	1	16	yes	complemented
151	C₄×D₄	C₂³	1	32	yes	complemented
152	C₄×D₄	C₂³	1	32	yes	complemented
153	C₄×D₄	C₂³	1	32	yes	complemented
154	#117	C₂³	1	32	yes	complemented
155	#117	C₂³	1	16	yes	complemented
156	#117	C₂³	1	32	yes	complemented
157	C₂×C₄⋊C₄	C₂³	1	4	yes	—
158	C₂×C₄⋊C₄	C₂³	1	4	yes	—
159	C₂×C₄⋊C₄	C₂³	1	4	yes	—
160	C₂×C₄⋊C₄	C₂³	1	4	yes	—
161	C₂×C₄⋊C₄	C₂³	1	4	yes	—
162	C₂×C₄⋊C₄	C₂³	1	4	yes	—
163	C₂×C₄⋊C₄	C₂³	1	2	yes	—
164	C₂×C₄⋊C₄	C₂³	1	2	yes	—
165	C₂×C₄⋊C₄	C₂³	1	4	yes	—
166	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
167	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
168	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
169	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
170	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
171	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
172	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
173	C₂×C₂²⋊C₄	C₂³	1	2	yes	—
174	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
175	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
176	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
177	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
178	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
179	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
180	C₂×C₂²⋊C₄	C₂³	1	4	yes	—
181	C₂×C₂²⋊C₄	C₂³	1	32	yes	complemented
182	C₂×C₂²⋊C₄	C₂³	1	16	yes	complemented
183	C₂×C₂²⋊C₄	C₂³	1	32	yes	complemented
184	C₂×C₄²	C₂³	1	1	yes	characteristic
185	C₂×C₄²	C₂³	1	2	yes	—
186	C₂×C₄²	C₂³	1	4	yes	—
187	C₂×C₄²	C₂³	1	2	yes	—
188	C₂×C₄²	C₂³	1	2	yes	—
189	C₂×C₄²	C₂³	1	1	yes	characteristic
190	C₂×C₄²	C₂³	1	8	yes	complemented
191	C₂⁴	—	2	8	no	—
192	C₂⁴	—	4	4	no	—
193	C₂⁴	—	4	8	no	—
194	C₂⁴	—	4	8	no	—
195	C₂⁴	C₂⁴	1	2	yes	—
196	C₂⁴	C₂⁴	1	4	yes	—
197	C₂⁴	C₂⁴	1	2	yes	—
198	C₂⁴	C₂⁴	1	1	yes	characteristic
199	C₂⁴	C₂⁴	1	8	yes	—
200	C₂⁴	C₂⁴	1	8	yes	—
201	#41	—	4	32	no	—
202	C₂×Q₈	—	4	2	no	—
203	C₂×Q₈	—	4	4	no	—
204	C₂×Q₈	—	4	2	no	—
205	C₂×Q₈	—	4	16	no	—
206	C₂×Q₈	—	4	4	no	—
207	C₂×Q₈	—	4	4	no	—
208	C₂×Q₈	C₂⁴	1	8	yes	—
209	C₂×Q₈	C₂⁴	1	4	yes	—
210	C₂×Q₈	C₂⁴	1	8	yes	—
211	C₂×Q₈	C₂⁴	1	8	yes	—
212	C₂×Q₈	C₂⁴	1	4	yes	—
213	C₂×D₄	—	2	16	no	—
214	C₂×D₄	—	4	2	no	—
215	C₂×D₄	—	4	4	no	—
216	C₂×D₄	—	4	2	no	—
217	C₂×D₄	—	4	16	no	—
218	C₂×D₄	—	4	8	no	—
219	C₂×D₄	—	4	8	no	—
220	C₂×D₄	—	4	8	no	—
221	C₂×D₄	—	4	4	no	—
222	C₂×D₄	—	4	4	no	—
223	C₂×D₄	—	4	32	no	—
224	C₂×D₄	C₂⁴	1	16	yes	—
225	C₂×D₄	C₂⁴	1	16	yes	—
226	C₂×D₄	C₂⁴	1	16	yes	—
227	C₂×D₄	C₂⁴	1	8	yes	—
228	C₂×D₄	C₂⁴	1	4	yes	—
229	C₂×D₄	C₂⁴	1	8	yes	—
230	C₂×D₄	C₂⁴	1	8	yes	—
231	C₂×D₄	C₂⁴	1	16	yes	—
232	C₂×D₄	C₂⁴	1	4	yes	—
233	C₂²×C₄	—	2	4	no	—
234	C₂²×C₄	—	2	8	no	—
235	C₂²×C₄	—	4	8	no	—
236	C₂²×C₄	—	4	4	no	—
237	C₂²×C₄	—	4	8	no	—
238	C₂²×C₄	—	4	4	no	—
239	C₂²×C₄	—	4	8	no	—
240	C₂²×C₄	C₂⁴	1	4	yes	—
241	C₂²×C₄	C₂⁴	1	8	yes	—
242	C₂²×C₄	C₂⁴	1	2	yes	—
243	C₂²×C₄	C₂⁴	1	4	yes	—
244	C₂²×C₄	C₂⁴	1	2	yes	—
245	C₂²×C₄	C₂⁴	1	2	yes	—
246	C₂²×C₄	C₂⁴	1	1	yes	characteristic
247	C₂²×C₄	C₂⁴	1	1	yes	characteristic
248	C₂²×C₄	C₂⁴	1	4	yes	—
249	C₂²×C₄	C₂⁴	1	4	yes	—
250	C₂²×C₄	C₂⁴	1	2	yes	—
251	C₂²×C₄	C₂⁴	1	8	yes	—
252	C₂²×C₄	C₂⁴	1	16	yes	—
253	C₂²×C₄	C₂⁴	1	16	yes	—
254	C₂²×C₄	C₂⁴	1	16	yes	—
255	C₂²×C₄	C₂⁴	1	8	yes	—
256	C₄⋊C₄	C₂⁴	1	16	yes	—
257	C₄⋊C₄	C₂⁴	1	16	yes	—
258	C₄⋊C₄	C₂⁴	1	16	yes	—
259	C₄⋊C₄	C₂⁴	1	16	yes	—
260	C₄⋊C₄	C₂⁴	1	16	yes	—
261	C₄⋊C₄	C₂⁴	1	16	yes	—
262	C₄⋊C₄	C₂⁴	1	8	yes	—
263	C₄⋊C₄	C₂⁴	1	8	yes	—
264	C₄⋊C₄	C₂⁴	1	16	yes	—
265	C₂²⋊C₄	C₂⁴	1	16	yes	—
266	C₂²⋊C₄	C₂⁴	1	16	yes	—
267	C₂²⋊C₄	C₂⁴	1	16	yes	—
268	C₂²⋊C₄	C₂⁴	1	16	yes	—
269	C₂²⋊C₄	C₂⁴	1	16	yes	—
270	C₂²⋊C₄	C₂⁴	1	8	yes	—
271	C₂²⋊C₄	C₂⁴	1	16	yes	—
272	C₂²⋊C₄	C₂⁴	1	8	yes	—
273	C₂²⋊C₄	C₂⁴	1	16	yes	—
274	C₂²⋊C₄	C₂⁴	1	16	yes	—
275	C₂²⋊C₄	C₂⁴	1	16	yes	—
276	C₂²⋊C₄	C₂⁴	1	16	yes	—
277	C₂²⋊C₄	C₂⁴	1	16	yes	—
278	C₂²⋊C₄	C₂⁴	1	16	yes	—
279	C₂²⋊C₄	C₂⁴	1	16	yes	—
280	C₄²	C₂⁴	1	4	yes	—
281	C₄²	C₂⁴	1	8	yes	—
282	C₄²	C₂⁴	1	4	yes	—
283	C₄²	C₂⁴	1	8	yes	—
284	C₄²	C₂⁴	1	16	yes	—
285	C₄²	C₂⁴	1	8	yes	—
286	C₂³	—	2	4	no	—
287	C₂³	—	2	8	no	—
288	C₂³	—	2	4	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	2	8	no	—
291	C₂³	—	2	8	no	—
292	C₂³	—	2	8	no	—
293	C₂³	—	2	8	no	—
294	C₂³	—	2	16	no	—
295	C₂³	—	4	8	no	—
296	C₂³	—	4	16	no	—
297	C₂³	—	4	16	no	—
298	C₂³	—	8	16	no	—
299	C₂³	—	8	16	no	—
300	C₂³	H(5,𝔽₂)	1	4	yes	—
301	C₂³	C₂⁵	1	4	yes	—
302	C₂³	C₂⁵	1	8	yes	—
303	C₂³	C₂⁵	1	4	yes	—
304	C₂³	C₂⁵	1	2	yes	—
305	C₂³	C₂⁵	1	1	yes	characteristic
306	Q₈	—	4	4	no	—
307	Q₈	—	4	8	no	—
308	Q₈	—	4	4	no	—
309	Q₈	—	4	8	no	—
310	Q₈	—	4	8	no	—
311	D₄	—	2	32	no	—
312	D₄	—	4	4	no	—
313	D₄	—	4	8	no	—
314	D₄	—	4	4	no	—
315	D₄	—	4	16	no	—
316	D₄	—	4	16	no	—
317	D₄	—	4	16	no	—
318	D₄	—	4	8	no	—
319	D₄	—	4	8	no	—
320	C₂×C₄	—	2	4	no	—
321	C₂×C₄	—	2	8	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	16	no	—
326	C₂×C₄	—	2	8	no	—
327	C₂×C₄	—	2	4	no	—
328	C₂×C₄	—	2	8	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	8	no	—
331	C₂×C₄	—	4	16	no	—
332	C₂×C₄	—	4	8	no	—
333	C₂×C₄	—	4	16	no	—
334	C₂×C₄	—	4	8	no	—
335	C₂×C₄	—	4	16	no	—
336	C₂×C₄	C₂⁵	1	4	yes	—
337	C₂×C₄	C₂⁵	1	4	yes	—
338	C₂×C₄	C₂⁵	1	8	yes	—
339	C₂×C₄	C₂⁵	1	4	yes	—
340	C₂×C₄	C₂⁵	1	2	yes	—
341	C₂×C₄	C₂⁵	1	2	yes	—
342	C₂×C₄	C₂⁵	1	8	yes	—
343	C₂×C₄	C₂⁵	1	8	yes	—
344	C₂×C₄	C₂⁵	1	4	yes	—
345	C₂²	—	2	4	no	—
346	C₂²	—	2	8	no	—
347	C₂²	—	2	8	no	—
348	C₂²	—	2	4	no	—
349	C₂²	—	2	4	no	—
350	C₂²	—	2	8	no	—
351	C₂²	—	2	8	no	—
352	C₂²	—	2	8	no	—
353	C₂²	—	2	8	no	—
354	C₂²	—	4	16	no	—
355	C₂²	—	4	8	no	—
356	C₂²	—	4	8	no	—
357	C₂²	—	8	16	no	—
358	C₂²	—	8	16	no	—
359	C₂²	C₂×H(5,𝔽₂)	1	4	yes	—
360	C₂²	C₂×H(5,𝔽₂)	1	2	yes	—
361	C₂²	#585	1	4	yes	—
362	C₂²	C₂⁶	1	1	yes	characteristic
363	C₄	—	2	4	no	—
364	C₄	—	2	2	no	—
365	C₄	—	2	2	no	—
366	C₄	—	2	4	no	—
367	C₄	—	2	8	no	—
368	C₄	—	2	4	no	—
369	C₄	—	2	8	no	—
370	C₄	—	2	4	no	—
371	C₄	—	2	8	no	—
372	C₂	—	2	4	no	—
373	C₂	—	4	8	no	—
374	C₂	—	4	4	no	—
375	C₂	—	4	4	no	—
376	C₂	#3545	1	4	yes	direct product factor
377	C₂	C₂²×H(5,𝔽₂)	1	1	yes	characteristic
378	C₂	C₂×#585	1	2	yes	—

	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. #3545	C₂	direct (N × H)
2. C₂×#563	C₂	semidirect
3. C₂×#562	C₂	semidirect
4. C₂×H(3,𝔽₄)	C₂	semidirect
5. C₂×#555	C₂	semidirect
6. C₂×#551	C₂	semidirect
7. C₂×#551	C₂	semidirect
8. C₂×#546	C₂	semidirect
9. C₂×#542	C₂	semidirect
10. C₂×#538	C₂	semidirect
11. C₂×#536	C₂	semidirect
12. C₂×#534	C₂	semidirect
13. C₂×#529	C₂	semidirect
14. C₂²×#124	C₂	semidirect
16. C₂³×Q₈	C₂²	semidirect
18. C₂³×D₄	C₂²	semidirect
19. #563	C₂²	semidirect
20. #562	C₂²	semidirect
21. H(3,𝔽₄)	C₂²	semidirect
22. #555	C₂²	semidirect
23. #551	C₂²	semidirect
24. #551	C₂²	semidirect
25. #546	C₂²	semidirect
26. #542	C₂²	semidirect
27. #538	C₂²	semidirect
28. #536	C₂²	semidirect
29. #534	C₂²	semidirect
30. C₂×C₄⋊Q₈	C₂²	semidirect
31. C₂×C₄⋊Q₈	C₂²	semidirect
32. #529	C₂²	semidirect
33. C₂×#126	C₂²	semidirect
34. C₂×#126	C₂²	semidirect
35. C₂×#126	C₂²	semidirect
36. C₂×#125	C₂²	semidirect
39. C₂×#124	C₂²	semidirect
40. C₂×#124	C₂²	semidirect
41. C₂×#124	C₂²	semidirect
42. C₂×#124	C₂²	semidirect
43. C₂×#124	C₂²	semidirect
44. C₂×#124	C₂²	semidirect
45. C₂×#124	C₂²	semidirect
46. C₂×#124	C₂²	semidirect
47. C₂×#124	C₂²	semidirect
49. C₂×#123	C₂²	semidirect
50. C₂×#123	C₂²	semidirect
51. C₂×#123	C₂²	semidirect
52. C₂×#123	C₂²	semidirect
53. C₂×#123	C₂²	semidirect
54. C₂×#123	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
62. C₂×#121	C₂²	semidirect
63. C₂×#121	C₂²	semidirect
64. C₂×#121	C₂²	semidirect
67. C₂×#120	C₂²	semidirect
68. C₂×#120	C₂²	semidirect
69. C₂×C₄×Q₈	C₂²	semidirect
70. C₂×C₄×D₄	C₂²	semidirect
71. C₂×C₄×D₄	C₂²	semidirect
72. C₂×C₄×D₄	C₂²	semidirect
73. C₂×C₄×D₄	C₂²	semidirect
74. C₂×#117	C₂²	semidirect
75. C₂×#117	C₂²	semidirect
76. C₂×#117	C₂²	semidirect
77. C₂²×C₂²⋊C₄	C₂²	semidirect
78. C₂²×C₂²⋊C₄	C₂²	semidirect
79. C₂²×C₂²⋊C₄	C₂²	semidirect
80. C₂²×C₄²	C₂²	semidirect
91. C₂²×Q₈	C₂³	semidirect
104. C₂²×D₄	C₂³	semidirect
112. C₄⋊Q₈	C₂³	semidirect
113. C₄⋊Q₈	C₂³	semidirect
114. #126	C₂³	semidirect
115. #126	C₂³	semidirect
116. #126	C₂³	semidirect
117. #125	C₂³	semidirect
120. #124	C₂³	semidirect
121. #124	C₂³	semidirect
122. #124	C₂³	semidirect
123. #124	C₂³	semidirect
124. #124	C₂³	semidirect
125. #124	C₂³	semidirect
126. #124	C₂³	semidirect
127. #124	C₂³	semidirect
129. #123	C₂³	semidirect
130. #123	C₂³	semidirect
131. #123	C₂³	semidirect
132. #123	C₂³	semidirect
133. #123	C₂³	semidirect
134. #123	C₂³	semidirect
135. C₂²⋊Q₈	C₂³	semidirect
136. C₂²⋊Q₈	C₂³	semidirect
137. C₂²⋊Q₈	C₂³	semidirect
138. C₂²⋊Q₈	C₂³	semidirect
139. C₂²⋊Q₈	C₂³	semidirect
142. #121	C₂³	semidirect
143. #121	C₂³	semidirect
144. #121	C₂³	semidirect
147. #120	C₂³	semidirect
148. #120	C₂³	semidirect
149. C₄×Q₈	C₂³	semidirect
150. C₄×D₄	C₂³	semidirect
151. C₄×D₄	C₂³	semidirect
152. C₄×D₄	C₂³	semidirect
153. C₄×D₄	C₂³	semidirect
154. #117	C₂³	semidirect
155. #117	C₂³	semidirect
156. #117	C₂³	semidirect
181. C₂×C₂²⋊C₄	C₂³	semidirect
182. C₂×C₂²⋊C₄	C₂³	semidirect
183. C₂×C₂²⋊C₄	C₂³	semidirect
190. C₂×C₄²	C₂³	semidirect
376. C₂	#3545	direct (N × H)

Maximal subgroups

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

subgroup	index
#3545	2
C₂×#563	2
C₂×#562	2
C₂×H(3,𝔽₄)	2
C₂×#555	2
C₂×#551	2
C₂×#546	2
C₂×#542	2
C₂×#538	2
C₂×#536	2
C₂×#534	2
C₂×#529	2
C₂²×#124	2

Subgroups — C2×#3545 #62753

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#3545 #62753