Subgroups — #25110383

Order 11008.

886 conjugacy classes of subgroups.

The subgroup lattice has 388 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#14583278	C₂	1	1	yes	maximal, characteristic
2	C₄×#13063325	C₂	1	1	yes	maximal, characteristic
3	#19135398	C₂	1	1	yes	maximal, characteristic
4	#19135396	C₂	1	1	yes	maximal, characteristic
5	#19134939	C₂	1	4	yes	maximal
6	#19134936	C₂	1	4	yes	maximal
7	#19134722	C₂	1	1	yes	maximal, characteristic
8	#19134341	C₂	1	1	yes	maximal, characteristic
9	C₄×C₄⋊Q₈×C₄₃	C₂	1	1	yes	maximal, characteristic
10	C₂²×#10621885	C₂²	1	4	yes	—
11	C₂×#13063325	C₂²	1	1	yes	characteristic
12	C₂×C₄×Dic₈₆	C₂²	1	2	yes	—
13	#14583278	C₄	1	8	yes	complemented
14	C₂×#13063249	C₂²	1	4	yes	—
15	C₂×#13063248	C₂²	1	4	yes	—
16	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
17	C₂×C₄×C₄₃⋊C₈	C₂²	1	1	yes	characteristic
18	#14582805	C₂²	1	2	yes	—
19	#14582797	—	2	1	no	—
20	#14582797	—	2	1	no	—
21	#14582769	C₂²	1	1	yes	characteristic
22	C₄×C₄⋊Dic₄₃	—	2	1	no	—
23	C₄×C₄⋊Dic₄₃	—	2	1	no	—
24	#14582661	C₂²	1	4	yes	—
25	#14582654	C₂²	1	2	yes	—
26	#14582654	C₂²	1	2	yes	—
27	C₂×C₄⋊Q₈×C₄₃	C₂²	1	1	yes	characteristic
28	C₂×C₄×Q₈×C₄₃	C₂²	1	2	yes	—
29	C₄₃×#391	C₂²	1	2	yes	—
30	C₄₃×#389	—	2	1	no	—
31	C₄₃×#389	—	2	1	no	—
32	C₄₃×#384	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
34	C₄×C₄⋊C₄×C₄₃	—	2	1	no	—
35	C₄³×C₄₃	C₂²	1	1	yes	characteristic
36	C₂²×Dic₈₆	C₂³	1	2	yes	—
37	C₂×#10621885	—	4	4	no	—
38	C₂×#10621885	—	4	4	no	—
39	C₂×#10621885	C₂×C₄	1	16	yes	—
40	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
41	C₂²×C₄₃⋊C₈	C₂³	1	2	yes	—
42	#13063325	—	2	2	no	—
43	#13063325	C₂×C₄	1	4	yes	—
44	C₄×Dic₈₆	—	4	4	no	—
45	C₂×C₄⋊Dic₄₃	—	2	1	no	—
46	C₂×C₄⋊Dic₄₃	—	2	1	no	—
47	C₂×C₄⋊Dic₄₃	—	2	1	no	—
48	C₂×C₄⋊Dic₄₃	—	2	1	no	—
49	C₂×C₄⋊Dic₄₃	C₂³	1	2	yes	—
50	C₂×Dic₄₃⋊C₄	—	2	2	no	—
51	C₂×C₄×Dic₄₃	—	2	2	no	—
52	#13063249	—	4	4	no	—
53	#13063248	—	4	4	no	—
54	C₄×C₄₃⋊C₈	—	2	2	no	—
55	C₄×C₄₃⋊C₈	C₂×C₄	1	4	yes	—
56	C₄₃⋊#95	—	2	2	no	—
57	C₄₃⋊#95	—	2	2	no	—
58	C₂²×Q₈×C₄₃	C₂³	1	2	yes	—
59	C₄⋊Q₈×C₄₃	—	2	2	no	—
60	C₄⋊Q₈×C₄₃	C₂×C₄	1	4	yes	—
61	C₄×Q₈×C₄₃	—	4	4	no	—
62	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
63	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
64	C₂×C₄⋊C₄×C₄₃	—	2	2	no	—
65	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
66	C₂×C₄⋊C₄×C₄₃	—	2	1	no	—
67	C₂×C₄⋊C₄×C₄₃	C₂³	1	2	yes	—
68	C₂×C₄²×C₄₃	—	2	2	no	—
69	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
70	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
71	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
72	C₂×C₄²×C₄₃	D₄	1	1	yes	characteristic
73	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
74	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
75	C₂×C₄²×C₄₃	C₂³	1	1	yes	characteristic
76	#95×C₄₃	—	2	2	no	—
77	#95×C₄₃	—	2	2	no	—
78	C₂×Q₈×C₄₃	—	2	2	no	—
79	C₂×Q₈×C₄₃	—	2	4	no	—
80	C₂×Q₈×C₄₃	—	2	4	no	—
81	C₂×Q₈×C₄₃	C₂²×C₄	1	4	yes	—
82	C₂²×C₄×C₄₃	—	2	2	no	—
83	C₂²×C₄×C₄₃	—	2	2	no	—
84	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
85	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
86	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
87	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
88	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
89	C₂²×C₄×C₄₃	C₂×D₄	1	1	yes	characteristic
90	C₂²×C₄×C₄₃	C₂⁴	1	1	yes	characteristic
91	C₂²×Dic₄₃	—	2	2	no	—
92	C₂²×Dic₄₃	—	2	2	no	—
93	C₂×Dic₈₆	—	2	4	no	—
94	C₂×Dic₈₆	—	2	4	no	—
95	C₂×Dic₈₆	—	2	2	no	—
96	C₂×Dic₈₆	C₂²×C₄	1	4	yes	—
97	C₄⋊C₄×C₄₃	—	2	4	no	—
98	C₄⋊C₄×C₄₃	—	2	4	no	—
99	C₄⋊C₄×C₄₃	—	2	4	no	—
100	C₄⋊C₄×C₄₃	—	4	4	no	—
101	C₄⋊C₄×C₄₃	—	4	2	no	—
102	C₄⋊C₄×C₄₃	—	4	2	no	—
103	C₄²×C₄₃	—	2	2	no	—
104	C₄²×C₄₃	—	2	2	no	—
105	C₄²×C₄₃	—	2	2	no	—
106	C₄²×C₄₃	—	2	2	no	—
107	C₄²×C₄₃	—	2	2	no	—
108	C₄²×C₄₃	—	4	4	no	—
109	C₄²×C₄₃	Q₁₆	1	4	yes	complemented
110	C₄²×C₄₃	C₂²×C₄	1	2	yes	—
111	C₄²×C₄₃	#41	1	2	yes	—
112	#10621885	—	4	16	no	—
113	C₄⋊Dic₄₃	—	2	4	no	—
114	C₄⋊Dic₄₃	—	2	4	no	—
115	C₄⋊Dic₄₃	—	2	4	no	—
116	C₄⋊Dic₄₃	—	4	2	no	—
117	C₄⋊Dic₄₃	—	4	2	no	—
118	Dic₄₃⋊C₄	—	4	4	no	—
119	C₄×Dic₄₃	—	4	4	no	—
120	C₂×C₄₃⋊C₈	—	2	2	no	—
121	C₂×C₄₃⋊C₈	—	2	2	no	—
122	C₂×C₄₃⋊C₈	—	2	2	no	—
123	C₂×C₄₃⋊C₈	—	2	2	no	—
124	C₂×C₄₃⋊C₈	—	2	2	no	—
125	C₂×C₄₃⋊C₈	C₂²×C₄	1	4	yes	—
126	C₂³×C₄₃	C₂²×D₄	1	1	yes	characteristic
127	Q₈×C₄₃	—	2	8	no	—
128	Q₈×C₄₃	—	4	4	no	—
129	C₂×C₄×C₄₃	—	2	1	no	—
130	C₂×C₄×C₄₃	—	2	1	no	—
131	C₂×C₄×C₄₃	—	2	1	no	—
132	C₂×C₄×C₄₃	—	2	1	no	—
133	C₂×C₄×C₄₃	—	2	4	no	—
134	C₂×C₄×C₄₃	—	2	1	no	—
135	C₂×C₄×C₄₃	—	2	1	no	—
136	C₂×C₄×C₄₃	—	2	1	no	—
137	C₂×C₄×C₄₃	—	2	1	no	—
138	C₂×C₄×C₄₃	—	2	1	no	—
139	C₂×C₄×C₄₃	—	2	1	no	—
140	C₂×C₄×C₄₃	—	4	2	no	—
141	C₂×C₄×C₄₃	—	4	2	no	—
142	C₂×C₄×C₄₃	—	4	2	no	—
143	C₂×C₄×C₄₃	—	4	2	no	—
144	C₂×C₄×C₄₃	—	4	2	no	—
145	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
146	C₂×C₄×C₄₃	C₄×D₄	1	2	yes	—
147	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
148	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
149	C₂×C₄×C₄₃	C₂×Q₁₆	1	2	yes	—
150	C₂×C₄×C₄₃	#135	1	2	yes	—
151	C₂×C₄×C₄₃	#137	1	2	yes	—
152	C₂×C₄×C₄₃	#137	1	2	yes	—
153	C₂×C₄×C₄₃	C₂³×C₄	1	1	yes	characteristic
154	C₂×C₄×C₄₃	C₂×#41	1	1	yes	characteristic
155	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
156	C₂×C₄×C₄₃	H(5,𝔽₂)	1	2	yes	—
157	C₂×Dic₄₃	—	2	4	no	—
158	C₂×Dic₄₃	—	4	2	no	—
159	C₂×Dic₄₃	—	4	2	no	—
160	C₂×Dic₄₃	—	4	2	no	—
161	C₂×Dic₄₃	—	4	2	no	—
162	C₂×Dic₄₃	—	4	2	no	—
163	Dic₈₆	—	2	8	no	—
164	Dic₈₆	—	4	4	no	—
165	C₄₃⋊C₈	—	2	4	no	—
166	C₄₃⋊C₈	—	4	2	no	—
167	#22270	—	43	1	no	maximal, Sylow
168	C₂²×C₄₃	C₂×C₄×D₄	1	1	yes	characteristic
169	C₂²×C₄₃	#535	1	1	yes	characteristic
170	C₂²×C₄₃	#535	1	1	yes	characteristic
171	C₂²×C₄₃	C₂²×Q₁₆	1	1	yes	characteristic
172	C₂²×C₄₃	C₂×#135	1	1	yes	characteristic
173	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
174	C₂²×C₄₃	C₂×#137	1	1	yes	characteristic
175	C₄×C₄₃	—	2	2	no	—
176	C₄×C₄₃	—	2	2	no	—
177	C₄×C₄₃	—	4	4	no	—
178	C₄×C₄₃	—	4	1	no	—
179	C₄×C₄₃	—	4	1	no	—
180	C₄×C₄₃	—	8	2	no	—
181	C₄×C₄₃	C₄×Q₁₆	1	4	yes	—
182	C₄×C₄₃	#441	1	4	yes	—
183	C₄×C₄₃	#518	1	2	yes	—
184	C₄×C₄₃	#540	1	2	yes	—
185	Dic₄₃	—	4	4	no	—
186	Dic₄₃	—	8	2	no	—
187	C₂×#494	—	43	1	no	—
188	C₄×C₄⋊Q₈	—	43	1	no	—
189	C₄×C₄⋊Q₈	D₄₃	1	1	yes	characteristic
190	#1956	—	43	1	no	—
191	#1956	—	43	1	no	—
192	#1878	—	43	4	no	—
193	#1878	—	43	4	no	—
194	#1834	—	43	1	no	—
195	#1744	—	43	1	no	—
196	C₂×C₄₃	#2328	1	1	yes	characteristic
197	C₂×C₄₃	C₂×C₄×Q₁₆	1	1	yes	characteristic
198	C₂×C₄₃	C₂×#441	1	1	yes	characteristic
199	C₂×C₄₃	#3209	1	1	yes	characteristic
200	C₂×C₄₃	#3209	1	1	yes	characteristic
201	C₂×C₄₃	#3210	1	1	yes	characteristic
202	C₂×C₄₃	#3210	1	1	yes	characteristic
203	C₂²×Q₁₆	—	43	4	no	—
204	C₂×C₄⋊Q₈	—	43	1	no	—
205	C₂×C₄⋊Q₈	C₂×D₄₃	1	1	yes	characteristic
206	C₂×C₄×Q₈	—	43	2	no	—
207	C₂×C₄×Q₈	C₂×D₄₃	1	2	yes	—
208	#494	—	43	8	no	—
209	C₂×#103	—	43	4	no	—
210	C₂×#103	—	43	4	no	—
211	C₂×C₄×C₈	—	43	1	no	—
212	C₂×C₄×C₈	—	43	1	no	—
213	#391	—	43	2	no	—
214	#391	C₂×D₄₃	1	2	yes	—
215	#389	—	2	1	no	—
216	#389	—	2	1	no	—
217	#389	—	86	1	no	—
218	#389	—	86	1	no	—
219	#384	—	43	1	no	—
220	#384	C₂×D₄₃	1	1	yes	characteristic
221	C₄×C₄⋊C₄	—	2	1	no	—
222	C₄×C₄⋊C₄	—	2	1	no	—
223	C₄×C₄⋊C₄	—	86	1	no	—
224	C₄×C₄⋊C₄	—	86	1	no	—
225	C₄³	C₂×D₄₃	1	1	yes	characteristic
226	#340	—	43	4	no	—
227	#336	—	43	2	no	—
228	#336	—	43	2	no	—
229	C₄₃	#22270	1	1	yes	characteristic, complemented, Sylow
230	C₂²×Q₈	—	43	2	no	—
231	C₂²×Q₈	C₂²×D₄₃	1	2	yes	—
232	C₂×Q₁₆	—	43	16	no	—
233	C₂×Q₁₆	—	172	4	no	—
234	C₂×Q₁₆	—	172	4	no	—
235	C₂²×C₈	—	43	2	no	—
236	C₂²×C₈	—	43	2	no	—
237	C₄⋊Q₈	—	2	2	no	—
238	C₄⋊Q₈	—	43	4	no	—
239	C₄⋊Q₈	—	86	2	no	—
240	C₄⋊Q₈	C₄×D₄₃	1	4	yes	—
241	C₄×Q₈	—	4	4	no	—
242	C₄×Q₈	—	172	4	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	—	2	1	no	—
245	C₂×C₄⋊C₄	—	2	2	no	—
246	C₂×C₄⋊C₄	—	2	1	no	—
247	C₂×C₄⋊C₄	—	2	1	no	—
248	C₂×C₄⋊C₄	—	43	2	no	—
249	C₂×C₄⋊C₄	—	86	1	no	—
250	C₂×C₄⋊C₄	—	86	1	no	—
251	C₂×C₄⋊C₄	—	86	2	no	—
252	C₂×C₄⋊C₄	—	86	1	no	—
253	C₂×C₄⋊C₄	—	86	1	no	—
254	C₂×C₄⋊C₄	C₂²×D₄₃	1	2	yes	—
255	C₂×C₄²	—	2	2	no	—
256	C₂×C₄²	—	86	2	no	—
257	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
259	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
260	C₂×C₄²	C₂²⋊D₄₃	1	1	yes	characteristic
261	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
262	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
263	C₂×C₄²	C₂²×D₄₃	1	1	yes	characteristic
264	#103	—	172	4	no	—
265	#103	—	172	4	no	—
266	C₄×C₈	—	43	4	no	—
267	C₄×C₈	—	86	2	no	—
268	#95	—	2	2	no	—
269	#95	—	2	2	no	—
270	#95	—	86	2	no	—
271	#95	—	86	2	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	4	no	—
274	C₂×Q₈	—	2	4	no	—
275	C₂×Q₈	—	43	4	no	—
276	C₂×Q₈	—	86	2	no	—
277	C₂×Q₈	—	86	4	no	—
278	C₂×Q₈	—	86	4	no	—
279	C₂×Q₈	C₂×C₄×D₄₃	1	4	yes	—
280	C₂²×C₄	—	2	2	no	—
281	C₂²×C₄	—	2	2	no	—
282	C₂²×C₄	—	86	2	no	—
283	C₂²×C₄	—	86	2	no	—
284	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
285	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
286	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
287	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
288	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
289	C₂²×C₄	C₂×C₂²⋊D₄₃	1	1	yes	characteristic
290	C₂²×C₄	C₂³×D₄₃	1	1	yes	characteristic
291	Q₁₆	—	172	16	no	—
292	C₂×C₈	—	43	4	no	—
293	C₂×C₈	—	86	2	no	—
294	C₂×C₈	—	86	2	no	—
295	C₂×C₈	—	86	2	no	—
296	C₂×C₈	—	86	2	no	—
297	C₂×C₈	—	86	2	no	—
298	C₄⋊C₄	—	2	4	no	—
299	C₄⋊C₄	—	2	4	no	—
300	C₄⋊C₄	—	2	4	no	—
301	C₄⋊C₄	—	4	4	no	—
302	C₄⋊C₄	—	4	2	no	—
303	C₄⋊C₄	—	4	2	no	—
304	C₄⋊C₄	—	86	4	no	—
305	C₄⋊C₄	—	86	4	no	—
306	C₄⋊C₄	—	86	4	no	—
307	C₄⋊C₄	—	172	4	no	—
308	C₄⋊C₄	—	172	2	no	—
309	C₄⋊C₄	—	172	2	no	—
310	C₄²	—	2	2	no	—
311	C₄²	—	2	2	no	—
312	C₄²	—	2	2	no	—
313	C₄²	—	2	2	no	—
314	C₄²	—	2	2	no	—
315	C₄²	—	4	4	no	—
316	C₄²	—	172	4	no	—
317	C₄²	#10621885	1	4	yes	complemented
318	C₄²	C₂×C₄×D₄₃	1	2	yes	—
319	C₄²	#10621898	1	2	yes	—
320	C₂³	C₂²×C₂²⋊D₄₃	1	1	yes	characteristic
321	Q₈	—	2	8	no	—
322	Q₈	—	4	4	no	—
323	Q₈	—	86	8	no	—
324	Q₈	—	172	4	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	1	no	—
328	C₂×C₄	—	2	1	no	—
329	C₂×C₄	—	2	4	no	—
330	C₂×C₄	—	2	1	no	—
331	C₂×C₄	—	2	1	no	—
332	C₂×C₄	—	2	1	no	—
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	2	1	no	—
335	C₂×C₄	—	2	1	no	—
336	C₂×C₄	—	4	2	no	—
337	C₂×C₄	—	4	2	no	—
338	C₂×C₄	—	4	2	no	—
339	C₂×C₄	—	4	2	no	—
340	C₂×C₄	—	4	2	no	—
341	C₂×C₄	—	86	4	no	—
342	C₂×C₄	—	172	2	no	—
343	C₂×C₄	—	172	2	no	—
344	C₂×C₄	—	172	2	no	—
345	C₂×C₄	—	172	2	no	—
346	C₂×C₄	—	172	2	no	—
347	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
348	C₂×C₄	C₄×C₂²⋊D₄₃	1	2	yes	—
349	C₂×C₄	C₂×#10621885	1	2	yes	—
350	C₂×C₄	C₂×#10621885	1	2	yes	—
351	C₂×C₄	C₂×#10621885	1	2	yes	—
352	C₂×C₄	#13063345	1	2	yes	—
353	C₂×C₄	#13063355	1	2	yes	—
354	C₂×C₄	#13063356	1	2	yes	—
355	C₂×C₄	C₂²×C₄×D₄₃	1	1	yes	characteristic
356	C₂×C₄	C₂×#10621898	1	1	yes	characteristic
357	C₂×C₄	#13063370	1	2	yes	—
358	C₂×C₄	#13063371	1	2	yes	—
359	C₈	—	86	4	no	—
360	C₈	—	172	2	no	—
361	C₂²	C₂×C₄×C₂²⋊D₄₃	1	1	yes	characteristic
362	C₂²	#14583463	1	1	yes	characteristic
363	C₂²	#14583466	1	1	yes	characteristic
364	C₂²	C₂²×#10621885	1	1	yes	characteristic
365	C₂²	C₂×#13063345	1	1	yes	characteristic
366	C₂²	C₂×#13063355	1	1	yes	characteristic
367	C₂²	C₂×#13063356	1	1	yes	characteristic
368	C₄	—	2	2	no	—
369	C₄	—	2	2	no	—
370	C₄	—	4	4	no	—
371	C₄	—	4	1	no	—
372	C₄	—	4	1	no	—
373	C₄	—	8	2	no	—
374	C₄	—	344	2	no	—
375	C₄	—	172	4	no	—
376	C₄	C₄×#10621885	1	4	yes	—
377	C₄	#14583004	1	4	yes	—
378	C₄	#14583371	1	2	yes	—
379	C₄	#14583500	1	2	yes	—
380	C₂	#19137317	1	1	yes	characteristic
381	C₂	C₂×C₄×#10621885	1	1	yes	characteristic
382	C₂	C₂×#14583004	1	1	yes	characteristic
383	C₂	#19145540	1	1	yes	characteristic
384	C₂	#19145543	1	1	yes	characteristic
385	C₂	#19145547	1	1	yes	characteristic
386	C₂	#19145551	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₄₃
commutator	C₂×C₄×C₄₃	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₄₃
Fitting	C₄×C₄⋊Q₈×C₄₃	C₂
socle, prime radical	C₂³×C₄₃	C₂²×D₄
cosocle	C₂²×C₄×C₄₃	C₂⁴
hypercenter	C₄×C₄⋊Q₈	D₄₃
hypocenter	C₄₃	#22270
LCS	G ▷ C₂×C₄×C₄₃ ▷ C₂×C₄₃ ▷ C₄₃
UCS	C₁ ◁ C₂³ ◁ C₄³ ◁ C₄×C₄⋊Q₈

Complements

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

N	H ≅ G/N	type
13. #14583278	C₄	semidirect
109. C₄²×C₄₃	Q₁₆	semidirect
229. C₄₃	#22270	semidirect
317. C₄²	#10621885	semidirect

Maximal subgroups

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

subgroup	index
C₂×#14583278	2
C₄×#13063325	2
#19135398	2
#19135396	2
#19134939	2
#19134936	2
#19134722	2
#19134341	2
C₄×C₄⋊Q₈×C₄₃	2
#22270	43