Subgroups — #72251565

Order 2048.

At least 8469 conjugacy classes of subgroups; only the 554 normal subgroups are shown.

The subgroup lattice has 329 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72251552	C₂	1	2	yes	maximal, complemented
2	#72251550	C₂	1	2	yes	maximal, complemented
3	#72240419	C₂	1	2	yes	maximal, complemented
4	#72237398	C₂	1	1	yes	maximal, characteristic, complemented
5	#72236948	C₂	1	2	yes	maximal, complemented
6	#72218455	C₂	1	1	yes	maximal, characteristic, complemented
7	#72218306	C₂	1	1	yes	maximal, characteristic, complemented
8	#72218180	C₂	1	1	yes	maximal, characteristic, complemented
9	#72218069	C₂	1	1	yes	maximal, characteristic, complemented
10	#72218057	C₂	1	1	yes	maximal, characteristic, complemented
11	#72216064	C₂	1	1	yes	maximal, characteristic
12	#10586066	C₄	1	1	yes	characteristic, complemented
13	C₂²×#3484	C₂²	1	1	yes	characteristic
14	C₂×#60399	C₄	1	1	yes	characteristic, complemented
15	C₂×#60399	C₂²	1	1	yes	characteristic
16	#7630939	C₂²	1	1	yes	characteristic
17	#7630939	C₂²	1	1	yes	characteristic
18	#6431795	C₄	1	1	yes	characteristic, complemented
19	#6431795	C₄	1	1	yes	characteristic, complemented
20	#6431795	C₂²	1	1	yes	characteristic
21	#6431795	C₂²	1	1	yes	characteristic
22	#6371558	C₄	1	1	yes	characteristic, complemented
23	#6371558	C₂²	1	1	yes	characteristic
24	#6371504	C₄	1	1	yes	characteristic, complemented
25	#6371504	C₄	1	1	yes	characteristic, complemented
26	#6370693	C₄	1	1	yes	characteristic, complemented
27	C₂²×#1781	C₂²	1	1	yes	characteristic, complemented
28	#517411	C₂²	1	1	yes	characteristic, complemented
29	C₂×#12707	C₂²	1	2	yes	complemented
30	C₂×#12705	C₂²	1	2	yes	—
31	C₂×#12705	C₂²	1	2	yes	complemented
32	C₂×#12705	C₂²	1	2	yes	complemented
33	#392113	C₂²	1	1	yes	characteristic, complemented
34	#392109	C₂²	1	1	yes	characteristic, complemented
35	#187944	C₂²	1	2	yes	—
36	#187944	C₂²	1	2	yes	complemented
37	#187944	C₂²	1	2	yes	complemented
38	#186835	C₂²	1	2	yes	complemented
39	#146479	C₂²	1	2	yes	complemented
40	#146475	C₂²	1	2	yes	complemented
41	#108238	C₂²	1	2	yes	complemented
42	#107114	C₂²	1	2	yes	complemented
43	C₂×H(7,𝔽₂)	C₂×C₄	1	1	yes	characteristic, complemented
44	C₂³×H(5,𝔽₂)	C₂×C₄	1	1	yes	characteristic
45	C₂⁵×D₄	C₂³	1	1	yes	characteristic
46	#62842	C₂×C₄	1	1	yes	characteristic, complemented
47	#62842	C₂×C₄	1	1	yes	characteristic, complemented
48	C₂×#3484	C₂×C₄	1	1	yes	characteristic
49	C₂×#3484	C₂×C₄	1	1	yes	characteristic
50	C₂×#3484	C₂×C₄	1	1	yes	characteristic
51	C₂×#3484	C₂×C₄	1	1	yes	characteristic
52	C₂×#3484	C₂×C₄	1	1	yes	characteristic
53	C₂×#3484	C₂×C₄	1	1	yes	characteristic
54	C₂×#3484	D₄	1	2	yes	—
55	C₂×#3484	D₄	1	2	yes	—
56	C₂×#3484	C₂³	1	1	yes	characteristic
57	C₂×#3484	C₂³	1	1	yes	characteristic
58	C₂×#3484	C₂³	1	1	yes	characteristic
59	C₂×#3484	C₂³	1	1	yes	characteristic
60	C₂²×#534	D₄	1	2	yes	—
61	C₂³×#120	D₄	1	2	yes	—
62	#62652	C₂×C₄	1	1	yes	characteristic, complemented
63	C₂²×#518	C₂×C₄	1	1	yes	characteristic
64	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
65	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
66	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
67	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
68	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
69	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
70	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
71	C₂×#2883	C₂×C₄	1	1	yes	characteristic, complemented
72	#36614	D₄	1	2	yes	—
73	C₂×#2846	D₄	1	2	yes	—
74	#35222	D₄	1	2	yes	—
75	#35222	D₄	1	2	yes	—
76	#35222	D₄	1	2	yes	—
77	#34980	D₄	1	2	yes	—
78	#34980	D₄	1	2	yes	—
79	#34980	D₄	1	2	yes	—
80	#34171	C₂×C₄	1	1	yes	characteristic
81	#34171	C₂×C₄	1	1	yes	characteristic
82	#34171	C₂×C₄	1	1	yes	characteristic
83	#34171	C₂×C₄	1	1	yes	characteristic
84	#34171	C₂³	1	1	yes	characteristic
85	#34171	C₂³	1	1	yes	characteristic
86	C₂×#1783	C₂³	1	2	yes	—
87	C₂×#1781	C₂³	1	2	yes	—
88	C₂×#1781	C₂³	1	2	yes	—
89	#20354	C₂×C₄	1	1	yes	characteristic, complemented
90	#20354	C₂×C₄	1	1	yes	characteristic, complemented
91	#20354	C₂×C₄	1	1	yes	characteristic, complemented
92	#20354	C₂×C₄	1	1	yes	characteristic, complemented
93	#14335	C₂³	1	2	yes	—
94	#8534	D₄	1	8	yes	complemented
95	C₂⁷	C₂×D₄	1	1	yes	characteristic
96	C₂⁷	C₂×D₄	1	1	yes	characteristic
97	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	2	yes	—
98	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
99	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
100	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
101	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
102	C₂⁴×D₄	C₂²⋊C₄	1	2	yes	—
103	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
104	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
105	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
106	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
107	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
108	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
109	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
110	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
111	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
112	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
113	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
114	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
115	C₂⁵×C₄	C₂×D₄	1	1	yes	characteristic
116	#3484	C₂×D₄	1	4	yes	—
117	#3484	#41	1	4	yes	—
118	C₂×#535	C₂²⋊C₄	1	2	yes	—
119	C₂×#535	C₂²⋊C₄	1	2	yes	—
120	C₂×#535	C₂×D₄	1	2	yes	—
121	C₂×#534	C₂²⋊C₄	1	2	yes	—
122	C₂×#534	C₂²⋊C₄	1	2	yes	—
123	C₂×#534	C₂²⋊C₄	1	2	yes	—
124	C₂×#534	C₂²⋊C₄	1	2	yes	—
125	C₂×#534	C₂×D₄	1	2	yes	—
126	C₂×#534	C₂×D₄	1	2	yes	—
127	C₂×#534	C₂×D₄	1	2	yes	—
128	C₂×#525	C₂²⋊C₄	1	2	yes	—
129	C₂×#525	C₂²⋊C₄	1	2	yes	—
130	C₂×#525	C₂×D₄	1	2	yes	—
131	C₂²×#120	C₂²⋊C₄	1	2	yes	—
132	C₂²×#120	C₂²⋊C₄	1	2	yes	—
133	C₂²×#120	C₂²⋊C₄	1	2	yes	—
134	C₂²×#120	C₂²⋊C₄	1	2	yes	—
135	C₂²×#120	C₂×D₄	1	2	yes	—
136	C₂²×#120	C₂×D₄	1	2	yes	—
137	C₂²×#120	C₂×D₄	1	2	yes	—
138	C₂×#518	C₂²⋊C₄	1	2	yes	—
139	C₂×#518	C₂²×C₄	1	1	yes	characteristic
140	C₂×#518	C₂²×C₄	1	1	yes	characteristic
141	C₂×#518	C₂²×C₄	1	1	yes	characteristic
142	C₂×#518	C₂²×C₄	1	1	yes	characteristic
143	C₂×#518	C₂²×C₄	1	1	yes	characteristic
144	C₂×#518	C₂²×C₄	1	1	yes	characteristic
145	C₂×#518	C₂²×C₄	1	1	yes	characteristic
146	C₂×#518	C₂²×C₄	1	1	yes	characteristic
147	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	—
148	#2309	C₂²⋊C₄	1	2	yes	—
149	#2309	C₂²⋊C₄	1	2	yes	—
150	#2309	C₂×D₄	1	2	yes	—
151	#2308	C₂²⋊C₄	1	2	yes	—
152	#2308	C₂²⋊C₄	1	2	yes	—
153	#2308	C₂×D₄	1	2	yes	—
154	#2280	C₂²⋊C₄	1	2	yes	—
155	#2280	C₂²⋊C₄	1	2	yes	—
156	#2280	C₂×D₄	1	2	yes	—
157	C₂×#379	C₂²⋊C₄	1	2	yes	—
158	C₂×#379	C₂²⋊C₄	1	2	yes	—
159	C₂×#379	C₂×D₄	1	2	yes	—
160	#1781	C₂×D₄	1	4	yes	complemented
161	#1438	C₂×D₄	1	4	yes	complemented
162	C₂⁶	#99	1	2	yes	complemented
163	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
164	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
165	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
166	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
167	C₂⁶	#120	1	1	yes	characteristic
168	C₂⁶	#120	1	1	yes	characteristic
169	C₂⁶	#120	1	1	yes	characteristic
170	C₂⁶	#120	1	1	yes	characteristic
171	C₂⁶	#120	1	1	yes	characteristic
172	C₂⁶	#120	1	1	yes	characteristic
173	C₂⁶	#120	1	1	yes	characteristic
174	C₂⁶	C₂²×D₄	1	1	yes	characteristic
175	C₂⁶	C₂²×D₄	1	1	yes	characteristic
176	C₂×H(5,𝔽₂)	C₄×D₄	1	4	yes	—
177	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
178	C₂³×D₄	#99	1	2	yes	complemented
179	C₂³×D₄	#99	1	2	yes	complemented
180	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
183	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
187	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
188	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
189	C₂³×D₄	#120	1	1	yes	characteristic
190	C₂³×D₄	#120	1	1	yes	characteristic
191	C₂³×D₄	#120	1	1	yes	characteristic
192	C₂³×D₄	#120	1	1	yes	characteristic
193	C₂³×D₄	#120	1	1	yes	characteristic
194	C₂³×D₄	#120	1	1	yes	characteristic
195	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
196	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
197	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
198	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
199	C₂³×D₄	C₂²×D₄	1	2	yes	—
200	C₂³×D₄	C₂×#41	1	2	yes	—
201	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
202	C₂³×D₄	H(5,𝔽₂)	1	2	yes	—
203	C₂⁴×C₄	#99	1	2	yes	complemented
204	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
205	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂⁴×C₄	#120	1	1	yes	characteristic
207	C₂⁴×C₄	#120	1	1	yes	characteristic
208	C₂⁴×C₄	#120	1	1	yes	characteristic
209	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
210	#534	#121	1	8	yes	—
211	C₂×#127	#99	1	4	yes	complemented
212	C₂×#124	#99	1	4	yes	complemented
213	C₂×#123	#99	1	4	yes	complemented
214	C₂×#120	#99	1	4	yes	complemented
215	C₂×#120	#99	1	4	yes	complemented
216	C₂×#120	#99	1	4	yes	complemented
217	C₂×#120	#120	1	4	yes	—
218	C₂×#120	#123	1	4	yes	—
219	#518	C₄×D₄	1	4	yes	—
220	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
221	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
222	C₂×#117	C₂×C₂²⋊C₄	1	2	yes	—
223	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
224	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
225	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
226	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
227	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	—
228	C₂⁵	#379	1	1	yes	characteristic
229	C₂⁵	#379	1	1	yes	characteristic
230	C₂⁵	#379	1	1	yes	characteristic
231	C₂⁵	#379	1	1	yes	characteristic
232	C₂⁵	#379	1	1	yes	characteristic
233	C₂⁵	#379	1	1	yes	characteristic
234	C₂⁵	C₂×#99	1	2	yes	—
235	C₂⁵	C₂×#99	1	2	yes	—
236	C₂⁵	C₂×#99	1	2	yes	—
237	C₂⁵	C₂×#99	1	2	yes	—
238	C₂⁵	C₂×#99	1	2	yes	—
239	C₂⁵	C₂×#99	1	2	yes	—
240	C₂⁵	C₂×#99	1	2	yes	complemented
241	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
242	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
243	C₂⁵	C₂×#120	1	1	yes	characteristic
244	C₂⁵	C₂×#120	1	1	yes	characteristic
245	C₂⁵	C₂×#120	1	1	yes	characteristic
246	C₂⁵	C₂×#120	1	1	yes	characteristic
247	C₂⁵	C₂×#123	1	1	yes	characteristic
248	C₂⁵	#534	1	1	yes	characteristic
249	C₂⁵	#534	1	1	yes	characteristic
250	C₂⁵	D₄²	1	2	yes	—
251	C₂⁵	#546	1	2	yes	—
252	C₂²×Q₈	C₂×#99	1	2	yes	complemented
253	C₂²×D₄	#386	1	4	yes	—
254	C₂²×D₄	C₂×#99	1	4	yes	—
255	C₂²×D₄	C₂×#99	1	4	yes	—
256	C₂²×D₄	C₂×#99	1	4	yes	—
257	C₂²×D₄	C₂×#99	1	2	yes	complemented
258	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
259	C₂²×D₄	#518	1	2	yes	—
260	C₂²×D₄	C₂×#121	1	2	yes	—
261	C₂²×D₄	#534	1	2	yes	—
262	C₂²×D₄	D₄²	1	2	yes	—
263	C₂²×D₄	D₄²	1	2	yes	—
264	C₂²×D₄	#546	1	2	yes	—
265	C₂²×D₄	#546	1	2	yes	—
266	C₂³×C₄	#379	1	1	yes	characteristic
267	C₂³×C₄	#379	1	1	yes	characteristic
268	C₂³×C₄	C₂×#99	1	2	yes	—
269	C₂³×C₄	C₂×#99	1	2	yes	—
270	C₂³×C₄	C₂×#99	1	2	yes	complemented
271	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
272	C₂³×C₄	C₂×#120	1	1	yes	characteristic
273	C₂³×C₄	D₄²	1	2	yes	—
274	C₂³×C₄	#546	1	2	yes	—
275	C₂×C₂²⋊C₄	#386	1	4	yes	—
276	C₂×C₂²⋊C₄	C₂×#99	1	4	yes	—
277	C₂×C₂²⋊C₄	C₂×#99	1	4	yes	complemented
278	C₂×C₄²	C₂×#99	1	4	yes	complemented
279	C₂⁴	#1781	1	1	yes	characteristic
280	C₂⁴	#1781	1	1	yes	characteristic
281	C₂⁴	#1781	1	2	yes	—
282	C₂⁴	#1781	1	1	yes	characteristic
283	C₂⁴	#1781	1	1	yes	characteristic
284	C₂⁴	#1781	1	2	yes	—
285	C₂⁴	#1781	1	2	yes	—
286	C₂⁴	#1781	1	2	yes	—
287	C₂⁴	#1781	1	2	yes	—
288	C₂⁴	#1898	1	4	yes	—
289	C₂⁴	C₂×#379	1	1	yes	characteristic
290	C₂⁴	C₂×#386	1	1	yes	characteristic
291	C₂⁴	#2308	1	1	yes	characteristic
292	C₂⁴	D₄×C₂²⋊C₄	1	2	yes	—
293	C₂⁴	#2403	1	1	yes	characteristic
294	C₂⁴	#2403	1	1	yes	characteristic
295	C₂⁴	#2405	1	1	yes	characteristic
296	C₂⁴	#2405	1	1	yes	characteristic
297	C₂⁴	#2410	1	2	yes	—
298	C₂⁴	C₂²×#99	1	2	yes	—
299	C₂⁴	C₂²×#99	1	2	yes	—
300	C₂⁴	C₂²×#99	1	2	yes	—
301	C₂⁴	#2883	1	2	yes	—
302	C₂²×C₄	#1781	1	2	yes	—
303	C₂²×C₄	#1898	1	4	yes	—
304	C₂²×C₄	D₄×C₂²⋊C₄	1	2	yes	—
305	C₂²×C₄	#2410	1	2	yes	—
306	C₂²×C₄	C₂²×#99	1	2	yes	—
307	C₂²×C₄	#2883	1	2	yes	—
308	C₂³	#8541	1	4	yes	—
309	C₂³	#13867	1	1	yes	characteristic
310	C₂³	C₂×#1781	1	1	yes	characteristic
311	C₂³	C₂×#1781	1	1	yes	characteristic
312	C₂³	C₂×#1781	1	1	yes	characteristic
313	C₂³	C₂×#1781	1	1	yes	characteristic
314	C₂³	#20585	1	1	yes	characteristic
315	C₂³	#20585	1	1	yes	characteristic
316	C₂³	C₂×#1898	1	2	yes	—
317	C₂³	#21746	1	2	yes	—
318	C₂³	D₄×#99	1	4	yes	—
319	C₂×C₄	D₄×#99	1	4	yes	—
320	C₂²	C₂×#8541	1	1	yes	characteristic
321	C₂²	#188035	1	1	yes	characteristic
322	C₂²	#188035	1	1	yes	characteristic
323	C₂²	#188049	1	1	yes	characteristic
324	C₂²	#359428	1	1	yes	characteristic
325	C₂²	#359579	1	1	yes	characteristic
326	C₂²	#359579	1	1	yes	characteristic
327	C₂	#72219457	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	#72219457
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂⁴×D₄	C₂⁴
prime radical	#72216064	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁵×D₄ ◁ G
LECS	G ▷ C₂⁴×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72251552	C₂	semidirect
2. #72251550	C₂	semidirect
3. #72240419	C₂	semidirect
4. #72237398	C₂	semidirect
5. #72236948	C₂	semidirect
6. #72218455	C₂	semidirect
7. #72218306	C₂	semidirect
8. #72218180	C₂	semidirect
9. #72218069	C₂	semidirect
10. #72218057	C₂	semidirect
12. #10586066	C₄	semidirect
14. C₂×#60399	C₄	semidirect
18. #6431795	C₄	semidirect
19. #6431795	C₄	semidirect
22. #6371558	C₄	semidirect
24. #6371504	C₄	semidirect
25. #6371504	C₄	semidirect
26. #6370693	C₄	semidirect
27. C₂²×#1781	C₂²	semidirect
28. #517411	C₂²	semidirect
29. C₂×#12707	C₂²	semidirect
31. C₂×#12705	C₂²	semidirect
32. C₂×#12705	C₂²	semidirect
33. #392113	C₂²	semidirect
34. #392109	C₂²	semidirect
36. #187944	C₂²	semidirect
37. #187944	C₂²	semidirect
38. #186835	C₂²	semidirect
39. #146479	C₂²	semidirect
40. #146475	C₂²	semidirect
41. #108238	C₂²	semidirect
42. #107114	C₂²	semidirect
43. C₂×H(7,𝔽₂)	C₂×C₄	semidirect
46. #62842	C₂×C₄	semidirect
47. #62842	C₂×C₄	semidirect
62. #62652	C₂×C₄	semidirect
64. C₂×#2883	C₂×C₄	semidirect
65. C₂×#2883	C₂×C₄	semidirect
66. C₂×#2883	C₂×C₄	semidirect
67. C₂×#2883	C₂×C₄	semidirect
68. C₂×#2883	C₂×C₄	semidirect
69. C₂×#2883	C₂×C₄	semidirect
70. C₂×#2883	C₂×C₄	semidirect
71. C₂×#2883	C₂×C₄	semidirect
89. #20354	C₂×C₄	semidirect
90. #20354	C₂×C₄	semidirect
91. #20354	C₂×C₄	semidirect
92. #20354	C₂×C₄	semidirect
94. #8534	D₄	semidirect
160. #1781	C₂×D₄	semidirect
161. #1438	C₂×D₄	semidirect
162. C₂⁶	#99	semidirect
178. C₂³×D₄	#99	semidirect
179. C₂³×D₄	#99	semidirect
203. C₂⁴×C₄	#99	semidirect
211. C₂×#127	#99	semidirect
212. C₂×#124	#99	semidirect
213. C₂×#123	#99	semidirect
214. C₂×#120	#99	semidirect
215. C₂×#120	#99	semidirect
216. C₂×#120	#99	semidirect
240. C₂⁵	C₂×#99	semidirect
252. C₂²×Q₈	C₂×#99	semidirect
257. C₂²×D₄	C₂×#99	semidirect
270. C₂³×C₄	C₂×#99	semidirect
277. C₂×C₂²⋊C₄	C₂×#99	semidirect
278. C₂×C₄²	C₂×#99	semidirect

Maximal subgroups

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

subgroup	index
#72251552	2
#72251550	2
#72240419	2
#72237398	2
#72236948	2
#72218455	2
#72218306	2
#72218180	2
#72218069	2
#72218057	2
#72216064	2