Subgroups — #15768777

Order 3328.

986 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	C₂×#11718585	C₂	1	1	yes	maximal, characteristic
2	C₄×#88180	C₂	1	1	yes	maximal, characteristic
3	C₂×#11718115	C₂	1	4	yes	maximal
4	C₂×C₄×C₁₃×C₄⋊C₄	C₂	1	1	yes	maximal, characteristic
5	C₂²×C₁₃×C₄⋊C₄	—	2	1	no	—
6	C₂²×C₄²×C₁₃	C₂²	1	2	yes	—
7	C₂²×C₄²×C₁₃	C₂²	1	1	yes	characteristic
8	C₂×#88180	C₂²	1	2	yes	—
9	C₂²×#6099	C₂²	1	2	yes	—
10	C₄×C₁₃×C₄⋊C₄	—	2	2	no	—
11	C₄×C₁₃×C₄⋊C₄	C₄	1	4	yes	complemented
12	C₂×C₁₃×#95	—	2	1	no	—
13	C₄×C₂²⋊Dic₁₃	—	2	1	no	—
14	C₄×C₂²⋊Dic₁₃	—	2	1	no	—
15	C₄×C₄⋊Dic₁₃	C₄	1	2	yes	complemented
16	C₄×C₄⋊Dic₁₃	C₄	1	2	yes	complemented
17	#11718593	—	2	1	no	—
18	C₄²×Dic₁₃	—	2	1	no	—
19	#11718585	—	2	2	no	—
20	#11718585	C₄	1	4	yes	complemented
21	C₂×C₄⋊#1055	—	2	1	no	—
22	C₂×C₄⋊#1055	—	2	1	no	—
23	#11718115	—	2	8	no	—
24	C₂³×C₄×C₁₃	—	2	2	no	—
25	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
26	C₂³×C₄×C₁₃	D₄	1	1	yes	characteristic
27	C₂³×C₄×C₁₃	C₂³	1	1	yes	characteristic
28	C₂×C₁₃×C₄⋊C₄	—	2	8	no	—
29	C₂×C₁₃×C₄⋊C₄	—	2	4	no	—
30	C₂×C₄²×C₁₃	—	2	4	no	—
31	C₂×C₄²×C₁₃	—	2	4	no	—
32	C₂×C₄²×C₁₃	—	2	2	no	—
33	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
34	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄²×C₁₃	C₂×C₄	1	4	yes	—
37	C₂×C₄²×C₁₃	C₂×C₄	1	2	yes	—
38	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
39	C₂×C₄²×C₁₃	D₄	1	1	yes	characteristic
40	C₂×C₄²×C₁₃	D₄	1	2	yes	—
41	C₂×C₄²×C₁₃	Q₈	1	2	yes	—
42	C₂×C₂²⋊Dic₁₃	—	2	2	no	—
43	#88180	—	2	2	no	—
44	#88180	—	2	2	no	—
45	#88180	D₄	1	4	yes	—
46	#88180	Q₈	1	4	yes	—
47	C₂×C₄⋊Dic₁₃	C₂×C₄	1	4	yes	—
48	C₂×C₄×Dic₁₃	—	2	2	no	—
49	C₂×C₄×Dic₁₃	—	2	2	no	—
50	C₂×C₄×Dic₁₃	—	2	2	no	—
51	C₂×#6099	—	2	2	no	—
52	C₂×#6099	—	2	4	no	—
53	C₂×#6099	—	2	4	no	—
54	C₂×#6099	C₂×C₄	1	4	yes	—
55	C₂²×#1055	—	2	2	no	—
56	C₁₃×#95	—	2	4	no	—
57	#88071	—	2	2	no	—
58	#88071	—	2	2	no	—
59	C₄⋊#1055	—	2	4	no	—
60	C₄⋊#1055	—	2	4	no	—
61	#10852	—	13	1	no	maximal, Sylow
62	C₂⁴×C₁₃	C₂×D₄	1	1	yes	characteristic
63	C₂²×C₄×C₁₃	—	2	4	no	—
64	C₂²×C₄×C₁₃	—	2	8	no	—
65	C₂²×C₄×C₁₃	—	2	4	no	—
66	C₂²×C₄×C₁₃	—	4	2	no	—
67	C₂²×C₄×C₁₃	—	4	4	no	—
68	C₂²×C₄×C₁₃	—	4	4	no	—
69	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
70	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
71	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
72	C₂²×C₄×C₁₃	C₂²⋊C₄	1	1	yes	characteristic
73	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
74	C₂²×C₄×C₁₃	C₂²⋊C₄	1	2	yes	—
75	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
76	C₂²×C₄×C₁₃	C₄⋊C₄	1	2	yes	—
77	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
78	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
79	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
80	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
81	C₂²×C₄×C₁₃	C₂×D₄	1	2	yes	—
82	C₂²×C₄×C₁₃	C₂×D₄	1	1	yes	characteristic
83	C₂²×C₄×C₁₃	C₂×Q₈	1	1	yes	characteristic
84	C₂²×C₄×C₁₃	C₂×Q₈	1	2	yes	—
85	C₂²×C₄×C₁₃	#41	1	2	yes	—
86	C₂²×C₄×C₁₃	#41	1	2	yes	—
87	C₂²×Dic₁₃	—	2	4	no	—
88	C₁₃×C₄⋊C₄	—	2	16	no	—
89	C₄²×C₁₃	—	2	8	no	—
90	C₄²×C₁₃	—	4	2	no	—
91	C₄²×C₁₃	—	4	2	no	—
92	C₄²×C₁₃	C₄²	1	2	yes	—
93	C₄²×C₁₃	C₄²	1	2	yes	—
94	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
95	C₄²×C₁₃	C₂²⋊C₄	1	2	yes	—
96	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
97	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
98	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
99	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
100	C₂²⋊Dic₁₃	—	2	4	no	—
101	C₂²⋊Dic₁₃	—	2	4	no	—
102	C₄⋊Dic₁₃	—	2	4	no	—
103	C₄⋊Dic₁₃	C₄⋊C₄	1	8	yes	complemented
104	C₄×Dic₁₃	—	2	4	no	—
105	C₄×Dic₁₃	—	2	4	no	—
106	C₄×Dic₁₃	—	4	4	no	—
107	C₄×Dic₁₃	—	4	4	no	—
108	#6099	—	2	8	no	—
109	#6099	—	4	2	no	—
110	#6099	—	4	2	no	—
111	C₂×#1055	—	2	4	no	—
112	C₂×#1055	—	4	4	no	—
113	C₂×#423	—	13	1	no	—
114	C₄×#117	—	13	1	no	—
115	C₂×C₄×C₄⋊C₄	D₁₃	1	1	yes	characteristic
116	C₂×#339	—	13	4	no	—
117	C₂³×C₁₃	—	2	2	no	—
118	C₂³×C₁₃	—	2	2	no	—
119	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
120	C₂³×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
121	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
122	C₂³×C₁₃	#121	1	2	yes	—
123	C₂³×C₁₃	C₂²⋊Q₈	1	2	yes	—
124	C₂×C₄×C₁₃	—	2	2	no	—
125	C₂×C₄×C₁₃	—	2	2	no	—
126	C₂×C₄×C₁₃	—	2	2	no	—
127	C₂×C₄×C₁₃	—	2	4	no	—
128	C₂×C₄×C₁₃	—	2	4	no	—
129	C₂×C₄×C₁₃	—	2	8	no	—
130	C₂×C₄×C₁₃	—	4	2	no	—
131	C₂×C₄×C₁₃	—	4	2	no	—
132	C₂×C₄×C₁₃	—	4	16	no	—
133	C₂×C₄×C₁₃	—	4	4	no	—
134	C₂×C₄×C₁₃	—	4	4	no	—
135	C₂×C₄×C₁₃	#95	1	2	yes	—
136	C₂×C₄×C₁₃	#95	1	2	yes	—
137	C₂×C₄×C₁₃	#95	1	2	yes	—
138	C₂×C₄×C₁₃	#95	1	2	yes	—
139	C₂×C₄×C₁₃	#104	1	4	yes	—
140	C₂×C₄×C₁₃	C₂×C₄²	1	1	yes	characteristic
141	C₂×C₄×C₁₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
143	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
144	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
145	C₂×C₄×C₁₃	#117	1	2	yes	—
146	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
147	C₂×C₄×C₁₃	C₄×D₄	1	2	yes	—
148	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
149	C₂×C₄×C₁₃	C₄×Q₈	1	2	yes	—
150	C₂×C₄×C₁₃	#121	1	2	yes	—
151	C₂×C₄×C₁₃	C₂²⋊Q₈	1	2	yes	—
152	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
153	C₂×C₄×C₁₃	#124	1	1	yes	characteristic
154	C₂×C₄×C₁₃	#125	1	2	yes	—
155	C₂×C₄×C₁₃	#127	1	1	yes	characteristic
156	C₂×C₄×C₁₃	C₄⋊Q₈	1	2	yes	—
157	C₂×C₄×C₁₃	C₄⋊Q₈	1	1	yes	characteristic
158	C₂×Dic₁₃	—	2	8	no	—
159	C₂×Dic₁₃	—	4	4	no	—
160	C₂×Dic₁₃	—	4	4	no	—
161	#1055	—	4	4	no	—
162	C₂²×M₁₆	—	13	2	no	—
163	C₂×#117	—	13	2	no	—
164	C₂²×C₄⋊C₄	—	2	1	no	—
165	C₂²×C₄²	C₂×D₁₃	1	2	yes	—
166	C₂²×C₄²	C₂×D₁₃	1	1	yes	characteristic
167	#423	—	13	4	no	—
168	#423	—	26	2	no	—
169	C₂×C₄⋊C₈	—	26	1	no	—
170	C₂×C₄⋊C₈	—	26	1	no	—
171	C₄×C₄⋊C₄	—	2	2	no	—
172	C₄×C₄⋊C₄	—	13	2	no	—
173	C₄×C₄⋊C₄	—	13	2	no	—
174	C₄×C₄⋊C₄	Dic₁₃	1	4	yes	complemented
175	C₄×C₂²⋊C₄	—	26	1	no	—
176	C₄×C₂²⋊C₄	—	26	1	no	—
177	#376	—	26	1	no	—
178	C₂×#95	—	2	1	no	—
179	C₄³	—	26	1	no	—
180	#339	—	26	8	no	—
181	C₂²×C₁₃	—	2	4	no	—
182	C₂²×C₁₃	—	2	4	no	—
183	C₂²×C₁₃	—	2	1	no	—
184	C₂²×C₁₃	—	2	1	no	—
185	C₂²×C₁₃	—	2	1	no	—
186	C₂²×C₁₃	—	2	1	no	—
187	C₂²×C₁₃	C₂×#95	1	1	yes	characteristic
188	C₂²×C₁₃	#380	1	2	yes	—
189	C₂²×C₁₃	#389	1	2	yes	—
190	C₂²×C₁₃	#390	1	1	yes	characteristic
191	C₂²×C₁₃	#391	1	1	yes	characteristic
192	C₂²×C₁₃	C₂×#104	1	2	yes	—
193	C₂²×C₁₃	#421	1	2	yes	—
194	C₄×C₁₃	—	2	2	no	—
195	C₄×C₁₃	—	2	2	no	—
196	C₄×C₁₃	—	2	2	no	—
197	C₄×C₁₃	—	4	8	no	—
198	C₄×C₁₃	#339	1	4	yes	complemented
199	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
200	C₄×C₁₃	#382	1	1	yes	characteristic
201	C₄×C₁₃	#384	1	1	yes	characteristic
202	C₄×C₁₃	#389	1	2	yes	—
203	C₄×C₁₃	#390	1	1	yes	characteristic
204	C₄×C₁₃	#391	1	1	yes	characteristic
205	Dic₁₃	—	4	8	no	—
206	C₂³×C₄	—	2	2	no	—
207	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
208	C₂³×C₄	C₂²⋊D₁₃	1	1	yes	characteristic
209	C₂³×C₄	C₂²×D₁₃	1	1	yes	characteristic
210	C₂×M₁₆	—	13	4	no	—
211	C₂×M₁₆	—	26	2	no	—
212	C₂×M₁₆	—	26	4	no	—
213	C₂×M₁₆	—	26	4	no	—
214	C₂²×C₈	—	26	2	no	—
215	#117	—	13	4	no	—
216	#117	—	13	4	no	—
217	#117	—	26	2	no	—
218	#117	—	26	2	no	—
219	C₂×C₄⋊C₄	—	2	8	no	—
220	C₂×C₄⋊C₄	—	2	4	no	—
221	C₂×C₄⋊C₄	—	13	4	no	—
222	C₂×C₂²⋊C₄	—	26	2	no	—
223	C₂×C₄²	—	2	4	no	—
224	C₂×C₄²	—	2	4	no	—
225	C₂×C₄²	—	2	2	no	—
226	C₂×C₄²	—	26	2	no	—
227	C₂×C₄²	—	26	2	no	—
228	C₂×C₄²	—	26	2	no	—
229	C₂×C₄²	Dic₂₆	1	2	yes	—
230	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
231	C₂×C₄²	C₄×D₁₃	1	1	yes	characteristic
232	C₂×C₄²	C₄×D₁₃	1	2	yes	—
233	C₂×C₄²	D₅₂	1	1	yes	characteristic
234	C₂×C₄²	D₅₂	1	1	yes	characteristic
235	C₂×C₄²	C₂×Dic₁₃	1	4	yes	—
236	C₂×C₄²	C₂×Dic₁₃	1	2	yes	—
237	C₂×C₄²	C₂²⋊D₁₃	1	2	yes	—
238	C₄⋊C₈	—	26	4	no	—
239	C₄⋊C₈	—	26	4	no	—
240	#95	—	2	4	no	—
241	#95	—	26	2	no	—
242	#95	—	26	2	no	—
243	C₂×C₁₃	—	2	1	no	—
244	C₂×C₁₃	—	2	2	no	—
245	C₂×C₁₃	—	2	1	no	—
246	C₂×C₁₃	C₄⋊#95	1	1	yes	characteristic
247	C₂×C₁₃	C₂×#339	1	1	yes	characteristic
248	C₂×C₁₃	#1733	1	1	yes	characteristic
249	C₂×C₁₃	#1806	1	4	yes	—
250	C₂⁴	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
251	C₂²×C₄	—	2	4	no	—
252	C₂²×C₄	—	2	8	no	—
253	C₂²×C₄	—	2	4	no	—
254	C₂²×C₄	—	4	2	no	—
255	C₂²×C₄	—	4	4	no	—
256	C₂²×C₄	—	4	4	no	—
257	C₂²×C₄	—	26	4	no	—
258	C₂²×C₄	#6101	1	2	yes	—
259	C₂²×C₄	#6101	1	2	yes	—
260	C₂²×C₄	#6103	1	1	yes	characteristic
261	C₂²×C₄	#6103	1	1	yes	characteristic
262	C₂²×C₄	#6103	1	1	yes	characteristic
263	C₂²×C₄	#6103	1	1	yes	characteristic
264	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
265	C₂²×C₄	C₂²⋊Dic₁₃	1	2	yes	—
266	C₂²×C₄	C₂×Dic₂₆	1	1	yes	characteristic
267	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
268	C₂²×C₄	C₂×C₄×D₁₃	1	1	yes	characteristic
269	C₂²×C₄	C₂×D₅₂	1	1	yes	characteristic
270	C₂²×C₄	D₄×D₁₃	1	2	yes	—
271	C₂²×C₄	#6129	1	2	yes	—
272	C₂²×C₄	Q₈×D₁₃	1	2	yes	—
273	C₂²×C₄	#6131	1	2	yes	—
274	C₂²×C₄	C₂²×Dic₁₃	1	1	yes	characteristic
275	C₂²×C₄	C₂×C₂²⋊D₁₃	1	1	yes	characteristic
276	M₁₆	—	26	8	no	—
277	M₁₆	—	52	2	no	—
278	M₁₆	—	52	2	no	—
279	C₂×C₈	—	26	4	no	—
280	C₂×C₈	—	52	4	no	—
281	C₄⋊C₄	—	2	16	no	—
282	C₄⋊C₄	—	13	8	no	—
283	C₄⋊C₄	—	26	4	no	—
284	C₂²⋊C₄	—	26	4	no	—
285	C₂²⋊C₄	—	26	4	no	—
286	C₄²	—	2	8	no	—
287	C₄²	—	4	2	no	—
288	C₄²	—	4	2	no	—
289	C₄²	—	26	4	no	—
290	C₄²	—	26	4	no	—
291	C₄²	—	52	4	no	—
292	C₄²	—	52	4	no	—
293	C₄²	C₄×Dic₁₃	1	2	yes	—
294	C₄²	C₄×Dic₁₃	1	2	yes	—
295	C₄²	#6101	1	2	yes	—
296	C₄²	#6101	1	2	yes	—
297	C₄²	C₄⋊Dic₁₃	1	2	yes	—
298	C₄²	C₄⋊Dic₁₃	1	2	yes	—
299	C₄²	#6103	1	2	yes	—
300	C₄²	#6103	1	2	yes	—
301	C₁₃	#10852	1	1	yes	characteristic, complemented, Sylow
302	C₂³	—	2	2	no	—
303	C₂³	—	2	2	no	—
304	C₂³	C₂×#6101	1	1	yes	characteristic
305	C₂³	C₂×#6103	1	1	yes	characteristic
306	C₂³	#88192	1	2	yes	—
307	C₂³	#88200	1	2	yes	—
308	C₂³	C₂×C₂²⋊Dic₁₃	1	1	yes	characteristic
309	C₂×C₄	—	2	2	no	—
310	C₂×C₄	—	2	2	no	—
311	C₂×C₄	—	2	2	no	—
312	C₂×C₄	—	2	4	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	4	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	4	4	no	—
318	C₂×C₄	—	4	16	no	—
319	C₂×C₄	—	4	4	no	—
320	C₂×C₄	—	26	8	no	—
321	C₂×C₄	—	52	4	no	—
322	C₂×C₄	—	52	4	no	—
323	C₂×C₄	#88045	1	4	yes	—
324	C₂×C₄	#88071	1	2	yes	—
325	C₂×C₄	#88071	1	2	yes	—
326	C₂×C₄	#88071	1	2	yes	—
327	C₂×C₄	#88071	1	2	yes	—
328	C₂×C₄	#88141	1	2	yes	—
329	C₂×C₄	#88142	1	2	yes	—
330	C₂×C₄	#88144	1	2	yes	—
331	C₂×C₄	C₄⋊C₄×D₁₃	1	2	yes	—
332	C₂×C₄	#88146	1	2	yes	—
333	C₂×C₄	#88147	1	2	yes	—
334	C₂×C₄	#88149	1	2	yes	—
335	C₂×C₄	#88151	1	2	yes	—
336	C₂×C₄	C₂×C₄×Dic₁₃	1	1	yes	characteristic
337	C₂×C₄	C₂×#6101	1	1	yes	characteristic
338	C₂×C₄	C₂×C₄⋊Dic₁₃	1	1	yes	characteristic
339	C₂×C₄	C₂×#6103	1	1	yes	characteristic
340	C₂×C₄	D₄×Dic₁₃	1	2	yes	—
341	C₂×C₄	#88190	1	1	yes	characteristic
342	C₂×C₄	#88194	1	1	yes	characteristic
343	C₂×C₄	#88198	1	1	yes	characteristic
344	C₂×C₄	Q₈×Dic₁₃	1	2	yes	—
345	C₂×C₄	#88201	1	1	yes	characteristic
346	C₈	—	52	4	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	2	1	no	—
349	C₂²	—	2	1	no	—
350	C₂²	—	2	1	no	—
351	C₂²	—	2	4	no	—
352	C₂²	—	2	4	no	—
353	C₂²	C₂×#88045	1	2	yes	—
354	C₂²	#11718634	1	2	yes	—
355	C₂²	#11718648	1	2	yes	—
356	C₂²	#11718666	1	2	yes	—
357	C₂²	C₂×#88071	1	1	yes	characteristic
358	C₂²	#11718882	1	1	yes	characteristic
359	C₂²	#11718891	1	1	yes	characteristic
360	C₄	—	2	2	no	—
361	C₄	—	2	2	no	—
362	C₄	—	2	2	no	—
363	C₄	—	4	8	no	—
364	C₄	—	52	8	no	—
365	C₄	#11718115	1	4	yes	complemented
366	C₄	#11718635	1	1	yes	characteristic
367	C₄	C₄⋊C₄×Dic₁₃	1	2	yes	—
368	C₄	#11718637	1	1	yes	characteristic
369	C₄	#11718638	1	1	yes	characteristic
370	C₄	#11718646	1	2	yes	—
371	C₄	#11718649	1	1	yes	characteristic
372	C₂	—	2	1	no	—
373	C₂	—	2	2	no	—
374	C₂	—	2	1	no	—
375	C₂	#13113065	1	1	yes	characteristic
376	C₂	C₂×#11718115	1	1	yes	characteristic
377	C₂	#13114546	1	1	yes	characteristic
378	C₂	#13114857	1	4	yes	—

	subgroup	G/H
center	C₂²×C₄	C₂×D₅₂
commutator	C₂×C₄×C₁₃	C₂×C₄²
Frattini	C₂³×C₄	C₂²×D₁₃
Fitting	C₂×C₄×C₁₃×C₄⋊C₄	C₂
socle	C₂³×C₁₃	C₂×C₂²⋊C₄
prime radical	C₂⁴×C₁₃	C₂×D₄
cosocle	C₂³×C₄×C₁₃	C₂³
hypercenter	C₂×C₄×C₄⋊C₄	D₁₃
hypocenter	C₁₃	#10852
LCS	G ▷ C₂×C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂²×C₄² ◁ C₂×C₄×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
11. C₄×C₁₃×C₄⋊C₄	C₄	semidirect
15. C₄×C₄⋊Dic₁₃	C₄	semidirect
16. C₄×C₄⋊Dic₁₃	C₄	semidirect
20. #11718585	C₄	semidirect
103. C₄⋊Dic₁₃	C₄⋊C₄	semidirect
174. C₄×C₄⋊C₄	Dic₁₃	semidirect
198. C₄×C₁₃	#339	semidirect
301. C₁₃	#10852	semidirect
365. C₄	#11718115	semidirect

Maximal subgroups

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

subgroup	index
C₂×#11718585	2
C₄×#88180	2
C₂×#11718115	2
C₂×C₄×C₁₃×C₄⋊C₄	2
#10852	13