Subgroups — C₂×C₄×#88102 #16797190

Order 3328.

1358 conjugacy classes of subgroups.

The subgroup lattice has 354 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#88102	C₂	1	2	yes	maximal
2	C₂×C₄×C₄⋊#261	C₂	1	2	yes	maximal
3	C₄×#88102	C₂	1	8	yes	maximal, direct product factor
4	C₂×#11718265	C₂	1	2	yes	maximal
5	C₂×C₄×C₈×D₁₃	C₂	1	1	yes	maximal, characteristic
6	C₂²×C₄⋊#261	C₂²	1	4	yes	—
7	C₂²×C₄×#261	—	2	2	no	—
8	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
9	C₂²×C₈×D₁₃	C₂²	1	1	yes	characteristic
10	C₂×C₄²×D₁₃	C₂²	1	1	yes	characteristic
11	C₂×(C₂×#261)⋊C₄	—	2	2	no	—
12	C₂×#88102	C₄	1	16	yes	direct product factor
13	C₂×#88102	C₂²	1	8	yes	—
14	C₄×C₄⋊#261	—	2	4	no	—
15	C₄×C₄⋊#261	C₂²	1	8	yes	—
16	C₂×C₄×C₈×C₁₃	C₄	1	1	yes	characteristic, complemented
17	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
18	C₂×C₈×Dic₁₃	C₄	1	1	yes	characteristic, complemented
19	C₂×C₄×#1055	C₄	1	1	yes	characteristic, complemented
20	C₄×C₈×D₁₃	C₄	1	4	yes	complemented
21	C₄×C₈×D₁₃	C₂²	1	4	yes	—
22	#11718265	C₂²	1	8	yes	—
23	C₂³×#261	—	2	4	no	—
24	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
25	C₂²×C₄×D₁₃	D₄	1	1	yes	characteristic
26	C₂²×C₄×D₁₃	C₂³	1	1	yes	characteristic
27	C₂×C₄⋊#261	—	2	4	no	—
28	C₂×C₄⋊#261	—	2	8	no	—
29	C₂×C₄⋊#261	C₂×C₄	1	16	yes	—
30	C₂×C₄⋊#261	C₂³	1	8	yes	—
31	C₂×C₄×#261	—	2	8	no	—
32	C₂×C₄×#261	—	4	8	no	—
33	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
34	C₂²×C₈×C₁₃	C₂×C₄	1	1	yes	characteristic
35	C₂×C₄²×C₁₃	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×Dic₁₃	C₂×C₄	1	1	yes	characteristic
37	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
38	C₂×C₄×Dic₁₃	Q₈	1	1	yes	characteristic
39	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
40	C₂²×#1055	C₂×C₄	1	1	yes	characteristic
41	C₂×C₈×D₁₃	—	2	4	no	—
42	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
43	C₂×C₈×D₁₃	C₂×C₄	1	2	yes	—
44	C₂×C₈×D₁₃	C₂×C₄	1	8	yes	—
45	C₂×C₈×D₁₃	C₂³	1	2	yes	—
46	C₂×C₈×D₁₃	C₂³	1	2	yes	—
47	C₄²×D₁₃	C₂×C₄	1	2	yes	—
48	C₄²×D₁₃	D₄	1	2	yes	—
49	C₄²×D₁₃	Q₈	1	2	yes	—
50	C₄²×D₁₃	C₂³	1	2	yes	—
51	(C₂×#261)⋊C₄	—	2	8	no	—
52	#88102	C₂×C₄	1	32	yes	direct product factor
53	C₄×C₈×C₁₃	C₂×C₄	1	4	yes	complemented
54	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
55	C₈×Dic₁₃	C₂×C₄	1	4	yes	complemented
56	C₄×#1055	C₂×C₄	1	4	yes	complemented
57	C₂×C₄×#107	—	13	1	no	maximal, Sylow
58	C₂³×D₁₃	C₂×D₄	1	1	yes	characteristic
59	C₂²×#261	—	2	16	no	—
60	C₂²×#261	—	2	8	no	—
61	C₂²×#261	—	4	8	no	—
62	C₂²×#261	—	4	8	no	—
63	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
64	C₂²×C₄×C₁₃	C₄⋊C₄	1	1	yes	characteristic
65	C₂²×C₄×C₁₃	C₂²×C₄	1	1	yes	characteristic
66	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
67	C₂²×Dic₁₃	C₄⋊C₄	1	1	yes	characteristic
68	C₂²×Dic₁₃	C₂×Q₈	1	1	yes	characteristic
69	C₂×C₄×D₁₃	—	2	4	no	—
70	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
71	C₂×C₄×D₁₃	C₄⋊C₄	1	2	yes	—
72	C₂×C₄×D₁₃	D₈	1	4	yes	—
73	C₂×C₄×D₁₃	Q₁₆	1	4	yes	—
74	C₂×C₄×D₁₃	C₂²×C₄	1	1	yes	characteristic
75	C₂×C₄×D₁₃	C₂²×C₄	1	4	yes	—
76	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
77	C₂×C₄×D₁₃	C₂×D₄	1	1	yes	characteristic
78	C₂×C₄×D₁₃	C₂×D₄	1	2	yes	—
79	C₂×C₄×D₁₃	C₂×Q₈	1	1	yes	characteristic
80	C₂×C₄×D₁₃	#41	1	4	yes	—
81	C₂×C₄×D₁₃	C₂⁴	1	1	yes	characteristic
82	C₄⋊#261	—	2	16	no	—
83	C₄⋊#261	—	2	8	no	—
84	C₄⋊#261	C₂²×C₄	1	16	yes	—
85	C₄×#261	—	4	16	no	—
86	C₂×C₈×C₁₃	—	2	2	no	—
87	C₂×C₈×C₁₃	C₄²	1	4	yes	complemented
88	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
89	C₂×C₈×C₁₃	C₂²×C₄	1	2	yes	—
90	C₄²×C₁₃	C₄⋊C₄	1	2	yes	—
91	C₄²×C₁₃	C₂²×C₄	1	2	yes	—
92	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
93	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
94	C₄×Dic₁₃	C₄⋊C₄	1	2	yes	—
95	C₄×Dic₁₃	C₂²×C₄	1	2	yes	—
96	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
97	C₄×Dic₁₃	C₂×Q₈	1	2	yes	—
98	C₂×#1055	—	2	2	no	—
99	C₂×#1055	C₄²	1	4	yes	complemented
100	C₂×#1055	C₂²×C₄	1	2	yes	—
101	C₂×#1055	C₂²×C₄	1	2	yes	—
102	C₈×D₁₃	—	2	4	no	—
103	C₈×D₁₃	—	2	4	no	—
104	C₈×D₁₃	C₄²	1	8	yes	complemented
105	C₈×D₁₃	C₂²×C₄	1	8	yes	—
106	C₂²×#107	—	13	2	no	—
107	C₂²×C₄×C₈	—	13	1	no	—
108	C₂×C₄×C₄⋊C₄	—	13	2	no	—
109	C₄×#107	—	13	8	no	—
110	C₂×#340	—	13	2	no	—
111	C₂³×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
112	C₂²×D₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
113	C₂²×D₁₃	C₄×D₄	1	4	yes	—
114	C₂²×D₁₃	C₂×D₈	1	2	yes	—
115	C₂²×D₁₃	C₂×Q₁₆	1	2	yes	—
116	C₂²×D₁₃	#135	1	4	yes	—
117	C₂²×D₁₃	C₂²×D₄	1	1	yes	characteristic
118	C₂×#261	—	2	16	no	—
119	C₂×#261	—	4	8	no	—
120	C₂×#261	—	4	8	no	—
121	C₂×#261	—	4	32	no	—
122	C₂×C₄×C₁₃	—	2	2	no	—
123	C₂×C₄×C₁₃	#107	1	4	yes	complemented
124	C₂×C₄×C₁₃	C₂×C₄²	1	2	yes	—
125	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
126	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
127	C₂×C₄×C₁₃	C₂×C₄⋊C₄	1	2	yes	—
128	C₂×C₄×C₁₃	#117	1	2	yes	—
129	C₂×C₄×C₁₃	C₂³×C₄	1	1	yes	characteristic
130	C₂×Dic₁₃	—	2	2	no	—
131	C₂×Dic₁₃	#107	1	4	yes	complemented
132	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
133	C₂×Dic₁₃	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂×Dic₁₃	C₂×C₄⋊C₄	1	2	yes	—
135	C₂×Dic₁₃	C₄×Q₈	1	4	yes	—
136	C₂×Dic₁₃	C₂²×Q₈	1	1	yes	characteristic
137	C₄×D₁₃	—	2	4	no	—
138	C₄×D₁₃	—	2	4	no	—
139	C₄×D₁₃	#107	1	8	yes	complemented
140	C₄×D₁₃	C₂×C₄²	1	2	yes	—
141	C₄×D₁₃	#117	1	2	yes	—
142	C₄×D₁₃	C₄×D₄	1	4	yes	—
143	C₄×D₁₃	C₄×Q₈	1	4	yes	—
144	C₄×D₁₃	C₂×D₈	1	4	yes	—
145	C₄×D₁₃	C₂×Q₁₆	1	4	yes	—
146	C₄×D₁₃	C₂³×C₄	1	2	yes	—
147	C₄×D₁₃	C₂×#41	1	2	yes	—
148	C₈×C₁₃	—	2	2	no	—
149	C₈×C₁₃	C₂×C₄²	1	4	yes	complemented
150	#1055	—	2	2	no	—
151	#1055	C₂×C₄²	1	4	yes	complemented
152	C₂³×C₈	—	13	1	no	—
153	C₂³×C₈	—	13	1	no	—
154	C₂²×C₄⋊C₄	—	13	4	no	—
155	C₂²×C₄²	—	13	1	no	—
156	C₂²×C₄²	—	26	2	no	—
157	C₂×#107	—	13	16	no	—
158	C₂×#107	—	13	8	no	—
159	C₂×C₄×C₈	—	13	1	no	—
160	C₂×C₄×C₈	—	13	1	no	—
161	C₂×C₄×C₈	—	13	1	no	—
162	C₂×C₄×C₈	—	13	4	no	—
163	C₂×C₄×C₈	—	13	4	no	—
164	C₂×C₄×C₈	#261	1	1	yes	characteristic, complemented
165	C₄×C₄⋊C₄	—	13	8	no	—
166	C₄×C₄⋊C₄	—	26	4	no	—
167	C₂×#95	—	26	2	no	—
168	#340	—	13	8	no	—
169	C₂²×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
170	C₂²×C₁₃	C₂×#107	1	2	yes	—
171	C₂²×C₁₃	#427	1	2	yes	—
172	C₂²×C₁₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
173	C₂×D₁₃	C₄×C₄⋊C₄	1	2	yes	—
174	C₂×D₁₃	C₂×#107	1	2	yes	—
175	C₂×D₁₃	#427	1	2	yes	—
176	C₂×D₁₃	C₄×D₈	1	8	yes	—
177	C₂×D₁₃	C₄×Q₁₆	1	8	yes	—
178	C₂×D₁₃	C₂×C₄×D₄	1	2	yes	—
179	C₂×D₁₃	C₂²×D₈	1	1	yes	characteristic
180	C₂×D₁₃	C₂²×Q₁₆	1	1	yes	characteristic
181	C₂×D₁₃	C₂×#135	1	2	yes	—
182	#261	—	4	16	no	—
183	C₄×C₁₃	—	2	2	no	—
184	C₄×C₁₃	C₄×C₄⋊C₄	1	2	yes	—
185	C₄×C₁₃	C₂×#107	1	4	yes	complemented
186	C₄×C₁₃	C₂²×C₄²	1	1	yes	characteristic
187	C₄×C₁₃	C₂×#117	1	1	yes	characteristic
188	Dic₁₃	—	2	2	no	—
189	Dic₁₃	C₄×C₄⋊C₄	1	2	yes	—
190	Dic₁₃	C₂×#107	1	4	yes	complemented
191	Dic₁₃	C₂×C₄×Q₈	1	2	yes	—
192	C₂³×C₄	—	13	1	no	—
193	C₂³×C₄	—	13	1	no	—
194	C₂³×C₄	—	13	1	no	—
195	C₂³×C₄	—	26	4	no	—
196	C₂²×C₈	—	13	1	no	—
197	C₂²×C₈	—	13	8	no	—
198	C₂²×C₈	—	13	2	no	—
199	C₂²×C₈	—	13	2	no	—
200	C₂²×C₈	—	13	1	no	—
201	C₂²×C₈	—	13	2	no	—
202	C₂²×C₈	—	13	2	no	—
203	C₂²×C₈	—	26	4	no	—
204	C₂²×C₈	C₂×#261	1	1	yes	characteristic
205	C₂²×C₈	C₂×#261	1	1	yes	characteristic
206	C₂×C₄⋊C₄	—	13	8	no	—
207	C₂×C₄⋊C₄	—	13	16	no	—
208	C₂×C₄⋊C₄	—	26	4	no	—
209	C₂×C₄⋊C₄	—	26	8	no	—
210	C₂×C₄²	—	13	1	no	—
211	C₂×C₄²	—	13	1	no	—
212	C₂×C₄²	—	13	1	no	—
213	C₂×C₄²	—	13	2	no	—
214	C₂×C₄²	—	13	2	no	—
215	C₂×C₄²	—	13	2	no	—
216	C₂×C₄²	—	13	2	no	—
217	C₂×C₄²	—	26	8	no	—
218	C₂×C₄²	—	52	8	no	—
219	C₂×C₄²	C₂×#261	1	1	yes	characteristic
220	#107	—	13	32	no	—
221	C₄×C₈	—	13	4	no	—
222	C₄×C₈	—	13	4	no	—
223	C₄×C₈	—	13	4	no	—
224	C₄×C₈	C₂×#261	1	4	yes	complemented
225	#95	—	26	8	no	—
226	C₂×C₁₃	C₄×#107	1	4	yes	complemented
227	C₂×C₁₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
228	C₂×C₁₃	C₂²×#107	1	1	yes	characteristic
229	C₂×C₁₃	C₂×#427	1	1	yes	characteristic
230	D₁₃	C₄×#107	1	4	yes	complemented
231	D₁₃	C₂×C₄×D₈	1	2	yes	—
232	D₁₃	C₂×C₄×Q₁₆	1	2	yes	—
233	C₂⁴	—	13	1	no	—
234	C₂²×C₄	—	13	1	no	—
235	C₂²×C₄	—	13	1	no	—
236	C₂²×C₄	—	13	4	no	—
237	C₂²×C₄	—	13	4	no	—
238	C₂²×C₄	—	13	4	no	—
239	C₂²×C₄	—	13	2	no	—
240	C₂²×C₄	—	13	1	no	—
241	C₂²×C₄	—	13	2	no	—
242	C₂²×C₄	—	13	1	no	—
243	C₂²×C₄	—	13	4	no	—
244	C₂²×C₄	—	13	1	no	—
245	C₂²×C₄	—	13	1	no	—
246	C₂²×C₄	—	13	1	no	—
247	C₂²×C₄	—	13	2	no	—
248	C₂²×C₄	—	13	2	no	—
249	C₂²×C₄	—	26	4	no	—
250	C₂²×C₄	—	26	8	no	—
251	C₂²×C₄	—	26	16	no	—
252	C₂²×C₄	—	52	8	no	—
253	C₂²×C₄	—	52	8	no	—
254	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
255	C₂²×C₄	C₄⋊#261	1	1	yes	characteristic
256	C₂²×C₄	C₂²×#261	1	1	yes	characteristic
257	C₂×C₈	—	2	2	no	—
258	C₂×C₈	—	13	4	no	—
259	C₂×C₈	—	13	2	no	—
260	C₂×C₈	—	13	8	no	—
261	C₂×C₈	—	13	8	no	—
262	C₂×C₈	—	13	2	no	—
263	C₂×C₈	—	26	4	no	—
264	C₂×C₈	—	26	4	no	—
265	C₂×C₈	—	26	2	no	—
266	C₂×C₈	C₄×#261	1	4	yes	complemented
267	C₂×C₈	C₂²×#261	1	2	yes	—
268	C₂×C₈	C₂²×#261	1	2	yes	—
269	C₄⋊C₄	—	13	16	no	—
270	C₄⋊C₄	—	26	16	no	—
271	C₄⋊C₄	—	26	8	no	—
272	C₄²	—	13	2	no	—
273	C₄²	—	13	2	no	—
274	C₄²	—	13	2	no	—
275	C₄²	—	13	2	no	—
276	C₄²	—	13	2	no	—
277	C₄²	—	13	2	no	—
278	C₄²	—	52	16	no	—
279	C₄²	C₄⋊#261	1	2	yes	—
280	C₄²	C₂²×#261	1	2	yes	—
281	C₁₃	C₂×C₄×#107	1	1	yes	characteristic, complemented, Sylow
282	C₂³	—	13	4	no	—
283	C₂³	—	13	2	no	—
284	C₂³	—	13	2	no	—
285	C₂³	—	13	4	no	—
286	C₂³	—	13	1	no	—
287	C₂³	—	13	1	no	—
288	C₂³	C₂×C₄⋊#261	1	1	yes	characteristic
289	C₂×C₄	—	2	2	no	—
290	C₂×C₄	—	13	4	no	—
291	C₂×C₄	—	13	4	no	—
292	C₂×C₄	—	13	1	no	—
293	C₂×C₄	—	13	2	no	—
294	C₂×C₄	—	13	1	no	—
295	C₂×C₄	—	13	4	no	—
296	C₂×C₄	—	13	4	no	—
297	C₂×C₄	—	13	4	no	—
298	C₂×C₄	—	13	8	no	—
299	C₂×C₄	—	13	4	no	—
300	C₂×C₄	—	13	2	no	—
301	C₂×C₄	—	13	2	no	—
302	C₂×C₄	—	13	2	no	—
303	C₂×C₄	—	13	2	no	—
304	C₂×C₄	—	13	2	no	—
305	C₂×C₄	—	26	4	no	—
306	C₂×C₄	—	26	4	no	—
307	C₂×C₄	—	26	2	no	—
308	C₂×C₄	—	26	16	no	—
309	C₂×C₄	—	52	8	no	—
310	C₂×C₄	—	52	32	no	—
311	C₂×C₄	—	52	8	no	—
312	C₂×C₄	#88102	1	4	yes	direct product factor
313	C₂×C₄	C₂×C₄×#261	1	2	yes	—
314	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
315	C₂×C₄	C₂×C₄⋊#261	1	1	yes	characteristic
316	C₂×C₄	C₂×C₄⋊#261	1	2	yes	—
317	C₂×C₄	#88237	1	2	yes	—
318	C₂×C₄	C₂³×#261	1	1	yes	characteristic
319	C₈	—	2	2	no	—
320	C₈	—	13	4	no	—
321	C₈	—	26	2	no	—
322	C₈	C₂×C₄×#261	1	4	yes	complemented
323	C₂²	—	13	2	no	—
324	C₂²	—	13	2	no	—
325	C₂²	—	13	8	no	—
326	C₂²	—	13	8	no	—
327	C₂²	—	13	1	no	—
328	C₂²	—	13	1	no	—
329	C₂²	—	13	2	no	—
330	C₂²	—	13	2	no	—
331	C₂²	—	13	2	no	—
332	C₂²	C₄×C₄⋊#261	1	2	yes	—
333	C₂²	C₂×#88102	1	2	yes	—
334	C₂²	#11719092	1	2	yes	—
335	C₂²	C₂²×C₄⋊#261	1	1	yes	characteristic
336	C₄	—	2	2	no	—
337	C₄	—	13	2	no	—
338	C₄	—	13	2	no	—
339	C₄	—	13	4	no	—
340	C₄	—	26	2	no	—
341	C₄	—	52	16	no	—
342	C₄	C₄×C₄⋊#261	1	2	yes	—
343	C₄	C₂×#88102	1	4	yes	direct product factor
344	C₄	C₂²×C₄×#261	1	1	yes	characteristic
345	C₄	C₂×#88237	1	1	yes	characteristic
346	C₂	—	13	2	no	—
347	C₂	—	13	2	no	—
348	C₂	—	13	4	no	—
349	C₂	C₄×#88102	1	4	yes	direct product factor
350	C₂	C₂×C₄×C₄⋊#261	1	1	yes	characteristic
351	C₂	C₂²×#88102	1	1	yes	characteristic
352	C₂	C₂×#11719092	1	1	yes	characteristic

	subgroup	G/H
center	C₂²×C₄	C₄⋊#261
commutator	C₄×C₁₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#261
Fitting	C₂×C₄×C₈×C₁₃	C₄
socle	C₂³×C₁₃	C₂×C₄⋊C₄
prime radical	C₂³×D₁₃	C₂×D₄
cosocle	C₂×C₄×D₁₃	C₂⁴
hypercenter	C₂×C₄×C₈	#261
hypocenter	C₁₃	C₂×C₄×#107
LCS	G ▷ C₄×C₁₃ ▷ C₂×C₁₃ ▷ C₁₃
UCS	C₁ ◁ C₂²×C₄ ◁ C₂×C₄² ◁ C₂×C₄×C₈

Complements

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

N	H ≅ G/N	type
3. C₄×#88102	C₂	direct (N × H)
12. C₂×#88102	C₄	direct (N × H)
16. C₂×C₄×C₈×C₁₃	C₄	semidirect
17. C₂×C₈×Dic₁₃	C₄	semidirect
18. C₂×C₈×Dic₁₃	C₄	semidirect
19. C₂×C₄×#1055	C₄	semidirect
20. C₄×C₈×D₁₃	C₄	semidirect
52. #88102	C₂×C₄	direct (N × H)
53. C₄×C₈×C₁₃	C₂×C₄	semidirect
54. C₈×Dic₁₃	C₂×C₄	semidirect
55. C₈×Dic₁₃	C₂×C₄	semidirect
56. C₄×#1055	C₂×C₄	semidirect
87. C₂×C₈×C₁₃	C₄²	semidirect
99. C₂×#1055	C₄²	semidirect
104. C₈×D₁₃	C₄²	semidirect
123. C₂×C₄×C₁₃	#107	semidirect
131. C₂×Dic₁₃	#107	semidirect
139. C₄×D₁₃	#107	semidirect
149. C₈×C₁₃	C₂×C₄²	semidirect
151. #1055	C₂×C₄²	semidirect
164. C₂×C₄×C₈	#261	semidirect
185. C₄×C₁₃	C₂×#107	semidirect
190. Dic₁₃	C₂×#107	semidirect
224. C₄×C₈	C₂×#261	semidirect
226. C₂×C₁₃	C₄×#107	semidirect
230. D₁₃	C₄×#107	semidirect
266. C₂×C₈	C₄×#261	semidirect
281. C₁₃	C₂×C₄×#107	semidirect
312. C₂×C₄	#88102	direct (N × H)
322. C₈	C₂×C₄×#261	semidirect
343. C₄	C₂×#88102	direct (N × H)
349. C₂	C₄×#88102	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#88102	2
C₂×C₄×C₄⋊#261	2
C₄×#88102	2
C₂×#11718265	2
C₂×C₄×C₈×D₁₃	2
C₂×C₄×#107	13

Subgroups — C2×C4×#88102 #16797190

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×C₄×#88102 #16797190