Subgroups — C₂×#13129722 #16779900

Order 3328.

674 conjugacy classes of subgroups.

The subgroup lattice has 412 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#11719052	C₂	1	1	yes	maximal, characteristic
2	C₂×C₄×#6118	C₂	1	1	yes	maximal, characteristic
3	#13129722	C₂	1	4	yes	maximal, direct product factor
4	C₂×#11718494	C₂	1	1	yes	maximal, characteristic
5	C₂²×#6118	—	2	1	no	—
6	C₂²×#6118	C₄	1	2	yes	—
7	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88110	C₄	1	2	yes	—
9	C₂×C₄⋊#1057	—	2	1	no	—
10	C₂×C₄⋊#1057	—	2	1	no	—
11	C₂×C₄×#1057	—	2	1	no	—
12	#11719052	—	2	1	no	—
13	#11719052	—	2	1	no	—
14	#11719052	C₄	1	2	yes	—
15	#11719052	C₂²	1	2	yes	—
16	C₄×#6118	—	2	1	no	—
17	C₄×#6118	—	2	1	no	—
18	C₄×#6118	C₄	1	2	yes	—
19	C₄×#6118	C₂²	1	2	yes	—
20	C₂×C₁₃×C₄⋊C₈	C₄	1	1	yes	characteristic
21	C₂×#88060	—	2	1	no	—
22	C₂×C₈×Dic₁₃	—	2	1	no	—
23	C₂×C₄⋊#1055	C₄	1	1	yes	characteristic
24	#11718494	—	2	1	no	—
25	#11718494	—	2	1	no	—
26	#11718494	C₄	1	2	yes	—
27	#11718494	C₂²	1	2	yes	—
28	C₂²×C₄×D₁₃	C₂×C₄	1	1	yes	characteristic
29	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
30	C₂²×C₄×D₁₃	Q₈	1	1	yes	characteristic
31	C₂²×#1057	—	2	2	no	—
32	C₂²×#1057	—	2	2	no	—
33	C₂×#6118	—	2	4	no	—
34	C₂×#6118	—	2	4	no	—
35	C₂×#6118	—	2	2	no	—
36	C₂×#6118	—	2	2	no	—
37	C₂×#6118	—	2	2	no	—
38	C₂×#6118	—	4	4	no	—
39	C₂×#6118	C₂×C₄	1	4	yes	—
40	C₂²×C₈×C₁₃	—	2	1	no	—
41	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
42	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
43	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
44	C₂×C₄×Dic₁₃	D₄	1	1	yes	characteristic
45	C₂²×#1055	—	2	1	no	—
46	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
47	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
48	C₄²×D₁₃	C₂×C₄	1	1	yes	characteristic
49	C₄²×D₁₃	D₄	1	1	yes	characteristic
50	C₄²×D₁₃	D₄	1	1	yes	characteristic
51	C₄²×D₁₃	D₄	1	1	yes	characteristic
52	C₄²×D₁₃	Q₈	1	1	yes	characteristic
53	C₄²×D₁₃	C₂³	1	1	yes	characteristic
54	#88110	—	2	2	no	—
55	#88110	C₂×C₄	1	4	yes	—
56	C₄⋊#1057	—	2	2	no	—
57	C₄⋊#1057	—	2	2	no	—
58	C₄⋊#1057	—	2	2	no	—
59	C₄⋊#1057	—	2	2	no	—
60	C₄×#1057	—	2	2	no	—
61	C₄×#1057	—	2	2	no	—
62	C₁₃×C₄⋊C₈	—	2	1	no	—
63	C₁₃×C₄⋊C₈	C₂×C₄	1	2	yes	—
64	#88060	—	2	2	no	—
65	#88060	—	2	2	no	—
66	C₈×Dic₁₃	—	2	2	no	—
67	C₈×Dic₁₃	—	2	2	no	—
68	C₄⋊#1055	—	2	1	no	—
69	C₄⋊#1055	C₂×C₄	1	2	yes	—
70	C₂×#1299	—	13	1	no	maximal, Sylow
71	C₂³×D₁₃	C₄⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₄²	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
74	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
75	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
76	C₂²×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
77	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
78	C₂×C₄×D₁₃	—	2	2	no	—
79	C₂×C₄×D₁₃	—	2	2	no	—
80	C₂×C₄×D₁₃	—	2	2	no	—
81	C₂×C₄×D₁₃	—	2	2	no	—
82	C₂×C₄×D₁₃	—	2	2	no	—
83	C₂×C₄×D₁₃	—	2	2	no	—
84	C₂×C₄×D₁₃	C₄²	1	1	yes	characteristic
85	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
86	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
87	C₂×C₄×D₁₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
92	C₂×C₄×D₁₃	C₄⋊C₄	1	1	yes	characteristic
93	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
94	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
95	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
96	C₂×#1057	—	2	8	no	—
97	C₂×#1057	—	2	4	no	—
98	C₂×#1057	—	2	4	no	—
99	C₂×#1057	—	4	4	no	—
100	#6118	—	2	8	no	—
101	#6118	—	2	4	no	—
102	#6118	—	2	4	no	—
103	#6118	—	4	4	no	—
104	#6118	—	4	4	no	—
105	C₂×C₈×C₁₃	—	2	2	no	—
106	C₂×C₈×C₁₃	—	4	2	no	—
107	C₄²×C₁₃	C₄²	1	1	yes	characteristic
108	C₄²×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
109	C₄²×C₁₃	C₄⋊C₄	1	1	yes	characteristic
110	C₄²×C₁₃	C₂²×C₄	1	1	yes	characteristic
111	C₄×Dic₁₃	C₄²	1	1	yes	characteristic
112	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
113	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
114	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
115	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
116	C₄×Dic₁₃	C₂²⋊C₄	1	1	yes	characteristic
117	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
118	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
119	C₄×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
120	C₄×Dic₁₃	C₂²×C₄	1	1	yes	characteristic
121	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
122	C₄×Dic₁₃	C₂×D₄	1	1	yes	characteristic
123	C₂×#1055	—	2	2	no	—
124	C₂×#1055	—	4	2	no	—
125	C₂×#431	—	13	1	no	—
126	C₂×#423	—	13	1	no	—
127	C₂×C₄×M₁₆	—	13	1	no	—
128	#1299	—	13	4	no	—
129	C₂³×C₁₃	#95	1	1	yes	characteristic
130	C₂²×D₁₃	—	2	2	no	—
131	C₂²×D₁₃	—	2	2	no	—
132	C₂²×D₁₃	—	2	2	no	—
133	C₂²×D₁₃	#95	1	1	yes	characteristic
134	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
135	C₂×C₄×C₁₃	—	2	2	no	—
136	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
137	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
138	C₂×C₄×C₁₃	#95	1	1	yes	characteristic
139	C₂×C₄×C₁₃	#104	1	2	yes	—
140	C₂×C₄×C₁₃	#104	1	2	yes	—
141	C₂×C₄×C₁₃	#108	1	2	yes	—
142	C₂×C₄×C₁₃	#108	1	2	yes	—
143	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×Dic₁₃	—	2	2	no	—
147	C₂×Dic₁₃	—	2	2	no	—
148	C₂×Dic₁₃	#95	1	1	yes	characteristic
149	C₂×Dic₁₃	#95	1	1	yes	characteristic
150	C₂×Dic₁₃	#95	1	1	yes	characteristic
151	C₂×Dic₁₃	#100	1	2	yes	—
152	C₂×Dic₁₃	#101	1	2	yes	—
153	C₂×Dic₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
154	C₂×Dic₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
155	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
156	C₄×D₁₃	—	2	2	no	—
157	C₄×D₁₃	—	2	2	no	—
158	C₄×D₁₃	—	2	2	no	—
159	C₄×D₁₃	—	2	2	no	—
160	C₄×D₁₃	—	2	1	no	—
161	C₄×D₁₃	—	2	1	no	—
162	C₄×D₁₃	—	2	1	no	—
163	C₄×D₁₃	—	2	1	no	—
164	C₄×D₁₃	—	2	1	no	—
165	C₄×D₁₃	—	2	1	no	—
166	C₄×D₁₃	—	2	1	no	—
167	C₄×D₁₃	—	2	1	no	—
168	C₄×D₁₃	—	2	2	no	—
169	C₄×D₁₃	—	2	2	no	—
170	C₄×D₁₃	—	2	1	no	—
171	C₄×D₁₃	—	2	1	no	—
172	C₄×D₁₃	—	2	1	no	—
173	C₄×D₁₃	—	2	1	no	—
174	#1057	—	2	8	no	—
175	#1057	—	4	4	no	—
176	C₈×C₁₃	—	4	2	no	—
177	#1055	—	4	2	no	—
178	C₂²×M₁₆	—	13	2	no	—
179	C₂²×M₁₆	—	26	1	no	—
180	C₂²×C₄²	—	13	1	no	—
181	#431	—	13	2	no	—
182	#431	—	13	2	no	—
183	#431	—	26	1	no	—
184	#431	—	26	1	no	—
185	#423	—	13	2	no	—
186	#423	—	13	2	no	—
187	#423	—	26	1	no	—
188	#423	—	26	1	no	—
189	C₂×C₄⋊C₈	—	13	1	no	—
190	C₂×C₄⋊C₈	—	26	1	no	—
191	C₂×C₄⋊C₈	—	26	1	no	—
192	C₂×C₄⋊C₈	#261	1	1	yes	characteristic
193	C₂×C₂²⋊C₈	—	26	1	no	—
194	C₄×M₁₆	—	13	2	no	—
195	C₄×M₁₆	—	13	2	no	—
196	C₄×M₁₆	—	26	1	no	—
197	C₄×M₁₆	—	26	1	no	—
198	C₂×#97	—	13	2	no	—
199	C₂×C₄×C₈	—	26	1	no	—
200	C₂×C₄×C₈	—	26	1	no	—
201	C₂²×C₁₃	#339	1	2	yes	—
202	C₂²×C₁₃	#341	1	2	yes	—
203	C₂²×C₁₃	#343	1	2	yes	—
204	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
205	C₂×D₁₃	—	2	1	no	—
206	C₂×D₁₃	—	2	1	no	—
207	C₂×D₁₃	—	2	1	no	—
208	C₂×D₁₃	—	2	1	no	—
209	C₂×D₁₃	—	2	1	no	—
210	C₂×D₁₃	—	2	1	no	—
211	C₂×D₁₃	—	4	4	no	—
212	C₄×C₁₃	—	2	1	no	—
213	C₄×C₁₃	—	2	1	no	—
214	C₄×C₁₃	#339	1	2	yes	—
215	C₄×C₁₃	#341	1	2	yes	—
216	C₄×C₁₃	C₂×#104	1	1	yes	characteristic
217	C₄×C₁₃	C₂×#104	1	1	yes	characteristic
218	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
219	C₄×C₁₃	C₂×#108	1	1	yes	characteristic
220	Dic₁₃	—	2	1	no	—
221	Dic₁₃	—	2	1	no	—
222	Dic₁₃	—	2	1	no	—
223	Dic₁₃	—	2	1	no	—
224	Dic₁₃	#343	1	2	yes	—
225	Dic₁₃	C₂×#100	1	1	yes	characteristic
226	Dic₁₃	C₂×#101	1	1	yes	characteristic
227	C₂³×C₄	—	13	1	no	—
228	C₂³×C₄	—	13	1	no	—
229	C₂³×C₄	—	13	1	no	—
230	C₂×M₁₆	—	13	4	no	—
231	C₂×M₁₆	—	26	2	no	—
232	C₂×M₁₆	—	26	2	no	—
233	C₂×M₁₆	—	26	4	no	—
234	C₂×M₁₆	—	26	4	no	—
235	C₂×M₁₆	—	26	2	no	—
236	C₂×M₁₆	—	52	4	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	26	2	no	—
239	C₂²×C₈	—	26	2	no	—
240	C₂²×C₈	—	26	1	no	—
241	C₂×C₄²	—	13	1	no	—
242	C₂×C₄²	—	13	1	no	—
243	C₂×C₄²	—	13	1	no	—
244	C₂×C₄²	—	13	1	no	—
245	C₂×C₄²	—	13	1	no	—
246	C₂×C₄²	—	13	1	no	—
247	C₂×C₄²	—	13	1	no	—
248	C₂×C₄²	—	13	1	no	—
249	C₂×C₄²	—	13	1	no	—
250	C₂×C₄²	—	13	1	no	—
251	C₂×C₄²	—	13	1	no	—
252	C₂×C₄²	C₂×#261	1	1	yes	characteristic
253	C₄⋊C₈	—	2	1	no	—
254	C₄⋊C₈	—	13	2	no	—
255	C₄⋊C₈	—	26	2	no	—
256	C₄⋊C₈	—	26	2	no	—
257	C₄⋊C₈	—	26	2	no	—
258	C₄⋊C₈	—	26	2	no	—
259	C₄⋊C₈	—	26	1	no	—
260	C₄⋊C₈	C₂×#261	1	2	yes	—
261	C₂²⋊C₈	—	26	2	no	—
262	C₂²⋊C₈	—	26	2	no	—
263	#97	—	13	4	no	—
264	#97	—	26	2	no	—
265	C₄×C₈	—	26	2	no	—
266	C₄×C₈	—	26	2	no	—
267	C₄×C₈	—	26	2	no	—
268	C₄×C₈	—	26	2	no	—
269	C₂×C₁₃	#1299	1	4	yes	complemented
270	C₂×C₁₃	C₂×#339	1	1	yes	characteristic
271	C₂×C₁₃	C₂×#341	1	1	yes	characteristic
272	C₂×C₁₃	C₂×#343	1	1	yes	characteristic
273	D₁₃	—	4	1	no	—
274	D₁₃	—	4	1	no	—
275	C₂⁴	—	13	1	no	—
276	C₂²×C₄	—	13	1	no	—
277	C₂²×C₄	—	13	1	no	—
278	C₂²×C₄	—	13	1	no	—
279	C₂²×C₄	—	13	1	no	—
280	C₂²×C₄	—	13	1	no	—
281	C₂²×C₄	—	13	1	no	—
282	C₂²×C₄	—	13	1	no	—
283	C₂²×C₄	—	13	1	no	—
284	C₂²×C₄	—	13	1	no	—
285	C₂²×C₄	—	13	1	no	—
286	C₂²×C₄	—	13	1	no	—
287	C₂²×C₄	—	13	1	no	—
288	C₂²×C₄	—	13	1	no	—
289	C₂²×C₄	—	13	1	no	—
290	C₂²×C₄	—	13	1	no	—
291	C₂²×C₄	—	26	2	no	—
292	C₂²×C₄	—	26	2	no	—
293	C₂²×C₄	—	26	2	no	—
294	C₂²×C₄	—	26	2	no	—
295	C₂²×C₄	—	26	2	no	—
296	C₂²×C₄	—	26	2	no	—
297	C₂²×C₄	C₄×#261	1	1	yes	characteristic
298	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
299	C₂²×C₄	C₂²⋊#261	1	1	yes	characteristic
300	M₁₆	—	26	8	no	—
301	M₁₆	—	26	4	no	—
302	M₁₆	—	26	4	no	—
303	M₁₆	—	52	4	no	—
304	M₁₆	—	52	4	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	4	2	no	—
307	C₂×C₈	—	26	4	no	—
308	C₂×C₈	—	26	8	no	—
309	C₂×C₈	—	26	4	no	—
310	C₂×C₈	—	26	2	no	—
311	C₂×C₈	—	52	4	no	—
312	C₂×C₈	—	52	2	no	—
313	C₄²	—	13	1	no	—
314	C₄²	—	13	1	no	—
315	C₄²	—	13	1	no	—
316	C₄²	—	13	1	no	—
317	C₄²	—	13	1	no	—
318	C₄²	—	13	1	no	—
319	C₄²	—	13	1	no	—
320	C₄²	—	13	1	no	—
321	C₄²	—	13	1	no	—
322	C₄²	—	13	1	no	—
323	C₄²	—	13	1	no	—
324	C₄²	—	13	1	no	—
325	C₄²	C₄×#261	1	1	yes	characteristic
326	C₄²	C₄⋊#261	1	1	yes	characteristic
327	C₄²	C₂²⋊#261	1	1	yes	characteristic
328	C₄²	C₂²×#261	1	1	yes	characteristic
329	C₁₃	C₂×#1299	1	1	yes	characteristic, complemented, Sylow
330	C₂³	—	13	1	no	—
331	C₂³	—	13	1	no	—
332	C₂³	—	26	2	no	—
333	C₂³	—	26	2	no	—
334	C₂³	—	26	2	no	—
335	C₂³	(C₂×#261)⋊C₄	1	1	yes	characteristic
336	C₂×C₄	—	2	2	no	—
337	C₂×C₄	—	13	2	no	—
338	C₂×C₄	—	13	2	no	—
339	C₂×C₄	—	13	1	no	—
340	C₂×C₄	—	13	1	no	—
341	C₂×C₄	—	13	1	no	—
342	C₂×C₄	—	13	1	no	—
343	C₂×C₄	—	13	1	no	—
344	C₂×C₄	—	13	1	no	—
345	C₂×C₄	—	26	1	no	—
346	C₂×C₄	—	26	1	no	—
347	C₂×C₄	—	26	2	no	—
348	C₂×C₄	—	26	1	no	—
349	C₂×C₄	—	26	2	no	—
350	C₂×C₄	—	26	1	no	—
351	C₂×C₄	—	26	2	no	—
352	C₂×C₄	—	26	2	no	—
353	C₂×C₄	—	26	2	no	—
354	C₂×C₄	—	26	2	no	—
355	C₂×C₄	—	26	2	no	—
356	C₂×C₄	—	26	2	no	—
357	C₂×C₄	—	26	1	no	—
358	C₂×C₄	—	26	1	no	—
359	C₂×C₄	—	26	1	no	—
360	C₂×C₄	—	26	1	no	—
361	C₂×C₄	—	26	1	no	—
362	C₂×C₄	—	26	1	no	—
363	C₂×C₄	—	26	1	no	—
364	C₂×C₄	—	26	1	no	—
365	C₂×C₄	#88103	1	2	yes	—
366	C₂×C₄	#88104	1	2	yes	—
367	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
368	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
369	C₂×C₄	(C₂×#261)⋊C₄	1	1	yes	characteristic
370	C₂×C₄	#88116	1	2	yes	—
371	C₂×C₄	#88118	1	2	yes	—
372	C₂×C₄	C₂×C₄×#261	1	1	yes	characteristic
373	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
374	C₂×C₄	C₂×C₂²⋊#261	1	1	yes	characteristic
375	C₈	—	4	2	no	—
376	C₈	—	26	8	no	—
377	C₈	—	52	4	no	—
378	C₈	—	52	2	no	—
379	C₂²	—	26	1	no	—
380	C₂²	—	26	1	no	—
381	C₂²	—	26	1	no	—
382	C₂²	—	26	1	no	—
383	C₂²	—	26	1	no	—
384	C₂²	—	26	1	no	—
385	C₂²	—	52	4	no	—
386	C₂²	#11718247	1	2	yes	—
387	C₂²	#11718268	1	2	yes	—
388	C₂²	#11718271	1	2	yes	—
389	C₂²	C₂×(C₂×#261)⋊C₄	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	13	2	no	—
393	C₄	—	13	1	no	—
394	C₄	—	13	1	no	—
395	C₄	—	26	1	no	—
396	C₄	—	26	1	no	—
397	C₄	—	26	1	no	—
398	C₄	—	26	1	no	—
399	C₄	#11718247	1	2	yes	—
400	C₄	#11718268	1	2	yes	—
401	C₄	C₂×#88103	1	1	yes	characteristic
402	C₄	C₂×#88104	1	1	yes	characteristic
403	C₄	C₂×#88116	1	1	yes	characteristic
404	C₄	C₂×#88118	1	1	yes	characteristic
405	C₂	—	52	1	no	—
406	C₂	—	52	1	no	—
407	C₂	#13129722	1	4	yes	direct product factor
408	C₂	C₂×#11718247	1	1	yes	characteristic
409	C₂	C₂×#11718268	1	1	yes	characteristic
410	C₂	C₂×#11718271	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	(C₂×#261)⋊C₄
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₄²	C₂²×#261
Fitting	C₂×C₁₃×C₄⋊C₈	C₄
socle	C₂³×C₁₃	#95
prime radical	C₂³×D₁₃	C₄⋊C₄
cosocle	C₄²×D₁₃	C₂³
hypercenter	C₂×C₄⋊C₈	#261
hypocenter	C₁₃	C₂×#1299
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂²×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄⋊C₈

Complements

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

N	H ≅ G/N	type
3. #13129722	C₂	direct (N × H)
269. C₂×C₁₃	#1299	semidirect
329. C₁₃	C₂×#1299	semidirect
407. C₂	#13129722	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×#11719052	2
C₂×C₄×#6118	2
#13129722	2
C₂×#11718494	2
C₂×#1299	13

Subgroups — C2×#13129722 #16779900

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#13129722 #16779900