Subgroups — C₂×#22626936 #34033228

Order 18688.

974 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989700	C₂	1	2	yes	maximal
2	#22626936	C₂	1	4	yes	maximal, direct product factor
3	C₂×C₄²×#64408	C₂	1	1	yes	maximal, characteristic
4	#17989700	—	2	2	no	—
5	#17989700	—	2	2	no	—
6	#17989700	C₄	1	4	yes	complemented
7	#17989700	C₂²	1	4	yes	—
8	C₂×C₄⋊#10596842	C₄	1	4	yes	complemented
9	C₂×C₂²⋊#10596842	—	2	2	no	—
10	C₂×C₄×#10596842	—	2	2	no	—
11	C₂²×C₄×#64408	—	2	2	no	—
12	C₂²×C₄×#64408	C₄	1	1	yes	characteristic
13	C₂²×C₄×#64408	C₂²	1	1	yes	characteristic
14	C₄²×#64408	—	2	2	no	—
15	C₄²×#64408	C₄	1	2	yes	—
16	C₄²×#64408	C₂²	1	2	yes	—
17	C₂×C₄²×D₇₃	C₄	1	1	yes	characteristic
18	C₂²×#10596842	—	2	4	no	—
19	C₄⋊#10596842	—	2	4	no	—
20	C₄⋊#10596842	C₂×C₄	1	8	yes	complemented
21	C₂²⋊#10596842	—	2	4	no	—
22	C₂²⋊#10596842	—	2	4	no	—
23	C₄×#10596842	—	2	4	no	—
24	C₄×#10596842	—	2	4	no	—
25	C₂³×#64408	—	2	1	no	—
26	C₂³×#64408	D₄	1	2	yes	—
27	C₂×C₄×#64408	—	2	16	no	—
28	C₂×C₄×#64408	—	2	4	no	—
29	C₂×C₄×#64408	—	2	4	no	—
30	C₂×C₄×#64408	—	2	1	no	—
31	C₂×C₄×#64408	—	2	1	no	—
32	C₂×C₄×#64408	—	2	1	no	—
33	C₂×C₄×#64408	C₈	1	2	yes	complemented
34	C₂×C₄×#64408	C₈	1	2	yes	complemented
35	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
36	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
37	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
38	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
39	C₂×C₄×#64408	D₄	1	2	yes	—
40	C₂×C₄×#64408	D₄	1	1	yes	characteristic
41	C₂×C₄×#64408	D₄	1	1	yes	characteristic
42	C₂×C₄×#64408	Q₈	1	1	yes	characteristic
43	C₂×C₄×#64408	Q₈	1	1	yes	characteristic
44	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
45	C₂²×C₄×D₇₃	—	2	1	no	—
46	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
47	C₂×C₄×Dic₇₃	—	2	1	no	—
48	C₂×C₄×Dic₇₃	C₈	1	1	yes	characteristic, complemented
49	C₄²×D₇₃	—	2	1	no	—
50	C₄²×D₇₃	—	2	1	no	—
51	C₄²×D₇₃	C₈	1	2	yes	complemented
52	C₄²×D₇₃	C₂×C₄	1	2	yes	—
53	C₂×C₄²×C₇₃	C₈	1	1	yes	characteristic, complemented
54	C₂×#10596842	—	2	8	no	—
55	C₂×#10596842	—	4	8	no	—
56	C₂²×#64408	—	2	8	no	—
57	C₂²×#64408	—	2	2	no	—
58	C₂²×#64408	—	2	2	no	—
59	C₂²×#64408	—	2	2	no	—
60	C₂²×#64408	—	2	8	no	—
61	C₂²×#64408	C₂²⋊C₄	1	2	yes	—
62	C₂²×#64408	C₂²⋊C₄	1	2	yes	—
63	C₂²×#64408	C₂²⋊C₄	1	2	yes	—
64	C₂²×#64408	C₄⋊C₄	1	2	yes	—
65	C₂²×#64408	C₄⋊C₄	1	2	yes	—
66	C₂²×#64408	C₂×D₄	1	2	yes	—
67	C₄×#64408	—	2	16	no	—
68	C₄×#64408	—	2	16	no	—
69	C₄×#64408	—	2	2	no	—
70	C₄×#64408	—	2	2	no	—
71	C₄×#64408	—	2	2	no	—
72	C₄×#64408	C₄²	1	2	yes	—
73	C₄×#64408	C₂²⋊C₄	1	2	yes	—
74	C₄×#64408	C₂²⋊C₄	1	2	yes	—
75	C₄×#64408	C₄⋊C₄	1	2	yes	—
76	C₄×#64408	C₄⋊C₄	1	2	yes	—
77	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
78	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
79	C₄×#64408	C₂×C₈	1	4	yes	complemented
80	C₄×#64408	C₂²×C₄	1	2	yes	—
81	C₄×#64408	C₂×D₄	1	1	yes	characteristic
82	C₄×#64408	C₂×Q₈	1	1	yes	characteristic
83	C₂³×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
84	C₂²×Dic₇₃	—	2	1	no	—
85	C₂²×Dic₇₃	M₁₆	1	1	yes	characteristic
86	C₂×C₄×D₇₃	—	2	8	no	—
87	C₂×C₄×D₇₃	—	2	2	no	—
88	C₂×C₄×D₇₃	—	2	2	no	—
89	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
90	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
91	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
94	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
95	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
96	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
97	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
98	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
99	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
100	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
101	C₄×Dic₇₃	—	2	1	no	—
102	C₄×Dic₇₃	—	2	2	no	—
103	C₄×Dic₇₃	—	2	2	no	—
104	C₄×Dic₇₃	C₂×C₈	1	2	yes	complemented
105	C₂²×C₄×C₇₃	—	2	1	no	—
106	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
107	C₄²×C₇₃	—	2	1	no	—
108	C₄²×C₇₃	C₂×C₈	1	2	yes	complemented
109	C₂³×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
110	C₂²×D₇₃	—	2	4	no	—
111	C₂²×D₇₃	#95	1	1	yes	characteristic
112	C₂²×D₇₃	#95	1	1	yes	characteristic
113	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
114	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
115	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
116	C₂²×D₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
117	C₂×#64408	—	2	8	no	—
118	C₂×#64408	—	2	8	no	—
119	C₂×#64408	—	2	8	no	—
120	C₂×#64408	—	2	4	no	—
121	C₂×#64408	—	2	4	no	—
122	C₂×#64408	—	2	4	no	—
123	C₂×#64408	—	2	4	no	—
124	C₂×#64408	—	2	4	no	—
125	C₂×#64408	—	2	4	no	—
126	C₂×#64408	#95	1	2	yes	—
127	C₂×#64408	#95	1	2	yes	—
128	C₂×#64408	#104	1	8	yes	—
129	C₂×#64408	C₂×C₂²⋊C₄	1	2	yes	—
130	C₂×#64408	C₂×C₄⋊C₄	1	2	yes	—
131	#10596842	—	4	8	no	—
132	C₂×C₄×C₇₃	—	2	4	no	—
133	C₂×C₄×C₇₃	—	2	2	no	—
134	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
135	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
136	C₂×C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
137	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
138	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
139	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
140	C₂×Dic₇₃	—	2	4	no	—
141	C₂×Dic₇₃	—	2	2	no	—
142	C₂×Dic₇₃	#97	1	1	yes	characteristic
143	C₂×Dic₇₃	#97	1	1	yes	characteristic
144	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
145	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
146	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
147	C₂×Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
148	C₄×D₇₃	—	2	8	no	—
149	C₄×D₇₃	—	2	8	no	—
150	C₄×D₇₃	#95	1	1	yes	characteristic
151	C₄×D₇₃	#95	1	1	yes	characteristic
152	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
153	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
154	C₄×D₇₃	#97	1	1	yes	characteristic
155	C₄×D₇₃	#97	1	1	yes	characteristic
156	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
157	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
158	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
159	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
160	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
161	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
162	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
163	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
164	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
165	C₄×D₇₃	C₂×M₁₆	1	1	yes	characteristic
166	C₂²×C₇₃	—	2	2	no	—
167	C₂²×C₇₃	#336	1	1	yes	characteristic
168	C₂²×C₇₃	#336	1	1	yes	characteristic
169	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
170	C₂×D₇₃	—	2	2	no	—
171	C₂×D₇₃	—	2	2	no	—
172	C₂×D₇₃	—	2	2	no	—
173	C₂×D₇₃	—	2	2	no	—
174	C₂×D₇₃	—	2	2	no	—
175	C₂×D₇₃	#336	1	1	yes	characteristic
176	C₂×D₇₃	#336	1	1	yes	characteristic
177	C₂×D₇₃	#339	1	4	yes	—
178	C₂×D₇₃	C₂×#95	1	1	yes	characteristic
179	C₂×D₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
180	#64408	—	2	8	no	—
181	#64408	—	2	2	no	—
182	#64408	—	2	2	no	—
183	#64408	#339	1	4	yes	—
184	#64408	C₂×#104	1	4	yes	—
185	C₄×C₇₃	—	2	4	no	—
186	C₄×C₇₃	#336	1	1	yes	characteristic
187	C₄×C₇₃	#336	1	1	yes	characteristic
188	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
189	C₄×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
190	Dic₇₃	—	2	4	no	—
191	Dic₇₃	#336	1	1	yes	characteristic
192	Dic₇₃	#336	1	1	yes	characteristic
193	Dic₇₃	C₂×#97	1	1	yes	characteristic
194	Dic₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
195	C₂×#1276	—	73	1	no	maximal, Sylow
196	C₂×C₇₃	—	2	1	no	—
197	C₂×C₇₃	—	2	1	no	—
198	C₂×C₇₃	#1276	1	2	yes	complemented
199	C₂×C₇₃	C₂×#336	1	1	yes	characteristic
200	D₇₃	—	2	1	no	—
201	D₇₃	—	2	1	no	—
202	D₇₃	#1276	1	2	yes	complemented
203	D₇₃	C₂×#339	1	2	yes	—
204	C₂×#431	—	73	2	no	—
205	C₂×C₄³	—	73	1	no	—
206	#1276	—	73	4	no	—
207	C₇₃	C₂×#1276	1	1	yes	characteristic, complemented, Sylow
208	C₂²×C₄²	—	73	1	no	—
209	C₂²×C₄²	—	73	1	no	—
210	C₂²×C₄²	—	73	1	no	—
211	C₂²×C₄²	—	146	2	no	—
212	#431	—	73	4	no	—
213	#431	—	73	4	no	—
214	#431	—	146	2	no	—
215	#431	—	146	2	no	—
216	C₂×C₄⋊C₈	—	73	4	no	—
217	C₂×C₂²⋊C₈	—	146	2	no	—
218	C₂×C₄×C₈	—	146	2	no	—
219	C₄³	—	73	2	no	—
220	C₄³	—	73	2	no	—
221	C₄³	—	146	2	no	—
222	C₂³×C₄	—	73	1	no	—
223	C₂³×C₄	—	73	2	no	—
224	C₂³×C₄	—	146	1	no	—
225	C₂³×C₄	—	146	1	no	—
226	C₂²×C₈	—	146	4	no	—
227	C₂×C₄²	—	73	1	no	—
228	C₂×C₄²	—	73	1	no	—
229	C₂×C₄²	—	73	2	no	—
230	C₂×C₄²	—	73	1	no	—
231	C₂×C₄²	—	73	2	no	—
232	C₂×C₄²	—	73	2	no	—
233	C₂×C₄²	—	73	1	no	—
234	C₂×C₄²	—	73	1	no	—
235	C₂×C₄²	—	73	1	no	—
236	C₂×C₄²	—	73	2	no	—
237	C₂×C₄²	—	73	2	no	—
238	C₂×C₄²	—	73	2	no	—
239	C₂×C₄²	—	73	1	no	—
240	C₂×C₄²	—	73	2	no	—
241	C₂×C₄²	—	73	2	no	—
242	C₂×C₄²	—	146	1	no	—
243	C₂×C₄²	—	146	1	no	—
244	C₂×C₄²	—	146	1	no	—
245	C₂×C₄²	—	146	4	no	—
246	C₂×C₄²	—	146	4	no	—
247	C₂×C₄²	—	146	1	no	—
248	C₂×C₄²	—	146	1	no	—
249	C₂×C₄²	—	146	1	no	—
250	C₂×C₄²	—	146	16	no	—
251	C₂×C₄²	#10596842	1	1	yes	characteristic, complemented
252	C₄⋊C₈	—	73	8	no	—
253	C₄⋊C₈	—	146	4	no	—
254	C₂²⋊C₈	—	146	4	no	—
255	C₂²⋊C₈	—	146	4	no	—
256	C₄×C₈	—	146	4	no	—
257	C₄×C₈	—	146	4	no	—
258	C₂⁴	—	73	1	no	—
259	C₂²×C₄	—	2	1	no	—
260	C₂²×C₄	—	73	2	no	—
261	C₂²×C₄	—	73	1	no	—
262	C₂²×C₄	—	73	1	no	—
263	C₂²×C₄	—	73	1	no	—
264	C₂²×C₄	—	73	1	no	—
265	C₂²×C₄	—	73	1	no	—
266	C₂²×C₄	—	73	1	no	—
267	C₂²×C₄	—	73	1	no	—
268	C₂²×C₄	—	73	1	no	—
269	C₂²×C₄	—	73	1	no	—
270	C₂²×C₄	—	73	1	no	—
271	C₂²×C₄	—	73	1	no	—
272	C₂²×C₄	—	73	1	no	—
273	C₂²×C₄	—	73	1	no	—
274	C₂²×C₄	—	73	2	no	—
275	C₂²×C₄	—	73	2	no	—
276	C₂²×C₄	—	73	2	no	—
277	C₂²×C₄	—	73	2	no	—
278	C₂²×C₄	—	73	2	no	—
279	C₂²×C₄	—	146	2	no	—
280	C₂²×C₄	—	146	2	no	—
281	C₂²×C₄	—	146	8	no	—
282	C₂²×C₄	—	146	8	no	—
283	C₂²×C₄	—	146	2	no	—
284	C₂²×C₄	—	146	2	no	—
285	C₂²×C₄	—	146	2	no	—
286	C₂²×C₄	—	146	8	no	—
287	C₂²×C₄	—	146	1	no	—
288	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
289	C₂×C₈	—	292	8	no	—
290	C₂×C₈	—	146	8	no	—
291	C₄²	—	2	1	no	—
292	C₄²	—	73	2	no	—
293	C₄²	—	73	2	no	—
294	C₄²	—	73	2	no	—
295	C₄²	—	73	1	no	—
296	C₄²	—	73	2	no	—
297	C₄²	—	73	2	no	—
298	C₄²	—	73	1	no	—
299	C₄²	—	73	2	no	—
300	C₄²	—	73	1	no	—
301	C₄²	—	73	1	no	—
302	C₄²	—	73	4	no	—
303	C₄²	—	73	2	no	—
304	C₄²	—	146	2	no	—
305	C₄²	—	146	2	no	—
306	C₄²	—	146	2	no	—
307	C₄²	—	146	2	no	—
308	C₄²	—	146	2	no	—
309	C₄²	—	146	16	no	—
310	C₄²	—	146	16	no	—
311	C₄²	—	146	1	no	—
312	C₄²	C₂×#10596842	1	2	yes	complemented
313	C₂³	—	73	1	no	—
314	C₂³	—	73	1	no	—
315	C₂³	—	73	1	no	—
316	C₂³	—	73	1	no	—
317	C₂³	—	73	1	no	—
318	C₂³	—	73	1	no	—
319	C₂³	—	146	4	no	—
320	C₂³	C₂²⋊#10596842	1	1	yes	characteristic
321	C₂×C₄	—	2	4	no	—
322	C₂×C₄	—	2	2	no	—
323	C₂×C₄	—	73	2	no	—
324	C₂×C₄	—	73	2	no	—
325	C₂×C₄	—	73	8	no	—
326	C₂×C₄	—	73	1	no	—
327	C₂×C₄	—	73	1	no	—
328	C₂×C₄	—	73	1	no	—
329	C₂×C₄	—	73	1	no	—
330	C₂×C₄	—	73	1	no	—
331	C₂×C₄	—	73	1	no	—
332	C₂×C₄	—	73	1	no	—
333	C₂×C₄	—	73	1	no	—
334	C₂×C₄	—	73	1	no	—
335	C₂×C₄	—	73	1	no	—
336	C₂×C₄	—	73	1	no	—
337	C₂×C₄	—	73	1	no	—
338	C₂×C₄	—	73	1	no	—
339	C₂×C₄	—	73	1	no	—
340	C₂×C₄	—	73	1	no	—
341	C₂×C₄	—	73	1	no	—
342	C₂×C₄	—	73	1	no	—
343	C₂×C₄	—	73	1	no	—
344	C₂×C₄	—	73	1	no	—
345	C₂×C₄	—	73	1	no	—
346	C₂×C₄	—	73	1	no	—
347	C₂×C₄	—	73	1	no	—
348	C₂×C₄	—	73	2	no	—
349	C₂×C₄	—	73	2	no	—
350	C₂×C₄	—	146	8	no	—
351	C₂×C₄	—	146	8	no	—
352	C₂×C₄	—	146	4	no	—
353	C₂×C₄	—	146	4	no	—
354	C₂×C₄	—	146	4	no	—
355	C₂×C₄	—	146	4	no	—
356	C₂×C₄	—	146	4	no	—
357	C₂×C₄	—	146	4	no	—
358	C₂×C₄	—	146	4	no	—
359	C₂×C₄	—	146	8	no	—
360	C₂×C₄	—	146	8	no	—
361	C₂×C₄	—	146	8	no	—
362	C₂×C₄	—	146	2	no	—
363	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
364	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
365	C₂×C₄	C₂²⋊#10596842	1	1	yes	characteristic
366	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
367	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
368	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
369	C₈	—	292	8	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	73	4	no	—
372	C₂²	—	73	1	no	—
373	C₂²	—	73	1	no	—
374	C₂²	—	73	1	no	—
375	C₂²	—	73	1	no	—
376	C₂²	—	146	2	no	—
377	C₂²	—	146	2	no	—
378	C₂²	—	146	2	no	—
379	C₂²	—	146	2	no	—
380	C₂²	—	146	2	no	—
381	C₂²	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
382	C₂²	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
383	C₂²	C₂×C₂²⋊#10596842	1	1	yes	characteristic
384	C₄	—	2	4	no	—
385	C₄	—	73	4	no	—
386	C₄	—	73	4	no	—
387	C₄	—	73	1	no	—
388	C₄	—	73	1	no	—
389	C₄	—	73	1	no	—
390	C₄	—	73	1	no	—
391	C₄	—	146	4	no	—
392	C₄	—	146	2	no	—
393	C₄	—	146	2	no	—
394	C₄	—	146	8	no	—
395	C₄	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
396	C₄	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
397	C₄	C₂×C₄×#10596842	1	1	yes	characteristic
398	C₄	C₂×C₄⋊#10596842	1	1	yes	characteristic
399	C₂	—	2	1	no	—
400	C₂	—	2	1	no	—
401	C₂	—	73	2	no	—
402	C₂	—	73	2	no	—
403	C₂	—	146	1	no	—
404	C₂	—	146	1	no	—
405	C₂	#22626936	1	2	yes	direct product factor
406	C₂	C₂×(C₂×#10596842)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄⋊#10596842
commutator	C₄×C₇₃	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#10596842
Fitting	C₂×C₄²×C₇₃	C₈
socle	C₂²×C₇₃	#336
prime radical	C₂³×D₇₃	C₂²⋊C₄
cosocle	C₂×C₄×#64408	C₂³
hypercenter	C₂×C₄²	#10596842
hypocenter	C₇₃	C₂×#1276
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #22626936	C₂	direct (N × H)
6. #17989700	C₄	semidirect
8. C₂×C₄⋊#10596842	C₄	semidirect
20. C₄⋊#10596842	C₂×C₄	semidirect
33. C₂×C₄×#64408	C₈	semidirect
34. C₂×C₄×#64408	C₈	semidirect
48. C₂×C₄×Dic₇₃	C₈	semidirect
51. C₄²×D₇₃	C₈	semidirect
53. C₂×C₄²×C₇₃	C₈	semidirect
79. C₄×#64408	C₂×C₈	semidirect
104. C₄×Dic₇₃	C₂×C₈	semidirect
108. C₄²×C₇₃	C₂×C₈	semidirect
198. C₂×C₇₃	#1276	semidirect
202. D₇₃	#1276	semidirect
207. C₇₃	C₂×#1276	semidirect
251. C₂×C₄²	#10596842	semidirect
312. C₄²	C₂×#10596842	semidirect
405. C₂	#22626936	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17989700	2
#22626936	2
C₂×C₄²×#64408	2
C₂×#1276	73

Subgroups — C2×#22626936 #34033228

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22626936 #34033228