Subgroups — #72337739

Order 4096.

At least 15128 conjugacy classes of subgroups; only the 487 normal subgroups are shown.

The subgroup lattice has 317 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72337738	C₂	1	2	yes	maximal, complemented
2	#72337737	C₂	1	2	yes	maximal, complemented
3	#72337736	C₂	1	2	yes	maximal, complemented
4	#72334279	C₂	1	1	yes	maximal, characteristic, complemented
5	#72327288	C₂	1	1	yes	maximal, characteristic
6	#72327248	C₄	1	1	yes	characteristic, complemented
7	#72327244	C₄	1	1	yes	characteristic, complemented
8	#72327231	C₄	1	1	yes	characteristic, complemented
9	#72326786	C₄	1	1	yes	characteristic, complemented
10	#72318215	C₄	1	1	yes	characteristic, complemented
11	#72317049	C₂²	1	2	yes	complemented
12	#72310532	C₂	1	1	yes	maximal, characteristic, complemented
13	#72310531	C₂²	1	2	yes	complemented
14	#72309392	C₂	1	1	yes	maximal, characteristic, complemented
15	#72309335	C₂²	1	1	yes	characteristic
16	#72303878	C₂	1	1	yes	maximal, characteristic, complemented
17	#72283093	C₂²	1	1	yes	characteristic
18	#72247345	C₂	1	2	yes	maximal, complemented
19	#72247315	C₂²	1	2	yes	complemented
20	#72247307	C₂²	1	2	yes	—
21	#72237782	C₂	1	1	yes	maximal, characteristic, complemented
22	#72237781	C₂²	1	2	yes	complemented
23	#72237780	C₂²	1	2	yes	complemented
24	#72236977	C₂²	1	2	yes	—
25	#72236977	C₂²	1	2	yes	complemented
26	C₂×#97550	C₂²	1	1	yes	characteristic, complemented
27	#72234670	C₂²	1	1	yes	characteristic, complemented
28	#72226357	C₂	1	1	yes	maximal, characteristic, complemented
29	#72226348	C₂²	1	2	yes	complemented
30	#72225873	C₂²	1	1	yes	characteristic, complemented
31	#72225777	C₂²	1	1	yes	characteristic, complemented
32	#72225733	C₂²	1	1	yes	characteristic
33	#72225660	C₄	1	1	yes	characteristic, complemented
34	#72225655	C₂²	1	1	yes	characteristic
35	#72221174	C₂²	1	2	yes	complemented
36	#72219035	C₂²	1	2	yes	complemented
37	#72218920	C₂²	1	1	yes	characteristic
38	C₂×#134033	C₂²	1	2	yes	complemented
39	#72217730	C₂²	1	1	yes	characteristic
40	C₂×#449475	C₂²	1	1	yes	characteristic
41	#72216646	C₄	1	1	yes	characteristic, complemented
42	#72210024	C₄	1	1	yes	characteristic, complemented
43	#10586066	D₄	1	1	yes	characteristic
44	#8093108	C₂×C₄	1	1	yes	characteristic, complemented
45	#8093107	C₂×C₄	1	1	yes	characteristic, complemented
46	#7670230	C₂×C₄	1	1	yes	characteristic, complemented
47	#7670203	C₂×C₄	1	1	yes	characteristic, complemented
48	#7642273	C₂³	1	1	yes	characteristic
49	#7642244	C₂³	1	1	yes	characteristic
50	#7642244	C₂³	1	1	yes	characteristic
51	C₂²×#2846	D₄	1	2	yes	—
52	C₂²×#2846	C₂³	1	1	yes	characteristic
53	C₂×#35346	C₂³	1	1	yes	characteristic
54	#6629262	C₂×C₄	1	1	yes	characteristic
55	#6629262	D₄	1	1	yes	characteristic
56	#6628896	C₂×C₄	1	1	yes	characteristic
57	#6628896	D₄	1	1	yes	characteristic
58	#6451874	D₄	1	2	yes	—
59	#6432953	C₂×C₄	1	1	yes	characteristic
60	#6432953	C₂×C₄	1	1	yes	characteristic
61	#6432953	D₄	1	1	yes	characteristic
62	#6432953	D₄	1	1	yes	characteristic
63	#6374210	D₄	1	1	yes	characteristic
64	#6374210	D₄	1	1	yes	characteristic
65	#6370693	D₄	1	1	yes	characteristic
66	#515326	C₂³	1	2	yes	—
67	#449521	C₂×C₄	1	1	yes	characteristic, complemented
68	#449521	C₂×C₄	1	1	yes	characteristic, complemented
69	#449475	C₂×C₄	1	1	yes	characteristic
70	#449475	C₂×C₄	1	1	yes	characteristic
71	#449475	C₂×C₄	1	1	yes	characteristic
72	#449475	C₂×C₄	1	1	yes	characteristic
73	#449475	C₂×C₄	1	1	yes	characteristic, complemented
74	#449475	C₂×C₄	1	1	yes	characteristic, complemented
75	#449475	D₄	1	2	yes	—
76	#449475	D₄	1	2	yes	—
77	#418213	C₂×C₄	1	1	yes	characteristic, complemented
78	#418132	C₂×C₄	1	1	yes	characteristic, complemented
79	#417896	C₂×C₄	1	1	yes	characteristic
80	#417896	C₂×C₄	1	1	yes	characteristic
81	#417896	C₂×C₄	1	1	yes	characteristic, complemented
82	#417896	D₄	1	2	yes	—
83	#417824	C₂×C₄	1	1	yes	characteristic
84	#417824	C₂×C₄	1	1	yes	characteristic
85	#417824	C₂×C₄	1	1	yes	characteristic, complemented
86	#417824	D₄	1	2	yes	—
87	#391735	C₂×C₄	1	1	yes	characteristic, complemented
88	#391709	C₂×C₄	1	1	yes	characteristic, complemented
89	#382422	C₂³	1	1	yes	characteristic
90	#375666	C₂×C₄	1	1	yes	characteristic, complemented
91	#374004	C₂×C₄	1	1	yes	characteristic, complemented
92	#359705	D₄	1	2	yes	—
93	C₂×#10965	D₄	1	2	yes	—
94	C₂×#10965	C₂³	1	2	yes	—
95	C₂×#10965	C₂³	1	1	yes	characteristic
96	#200656	D₄	1	4	yes	complemented
97	#197526	D₄	1	4	yes	complemented
98	C₂×#8547	C₂³	1	2	yes	—
99	C₂×#8547	C₂³	1	2	yes	—
100	C₂⁸	C₂×D₄	1	1	yes	characteristic
101	C₂×H(7,𝔽₂)	C₂²⋊C₄	1	1	yes	characteristic, complemented
102	C₂³×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
103	#62842	C₂²⋊C₄	1	1	yes	characteristic, complemented
104	#62842	C₂²⋊C₄	1	1	yes	characteristic, complemented
105	C₂×#3490	C₂×D₄	1	1	yes	characteristic
106	C₂×#3484	C₂×D₄	1	1	yes	characteristic
107	C₂×#3484	C₂×D₄	1	1	yes	characteristic
108	C₂³×#120	C₂×D₄	1	2	yes	—
109	C₂³×#120	C₂⁴	1	1	yes	characteristic
110	#62652	C₂²⋊C₄	1	1	yes	characteristic, complemented
111	#36702	#41	1	4	yes	—
112	C₂×#2846	C₂²⋊C₄	1	2	yes	—
113	C₂×#2846	C₂²⋊C₄	1	2	yes	—
114	C₂×#2846	C₂²⋊C₄	1	2	yes	—
115	C₂×#2846	C₂²⋊C₄	1	2	yes	—
116	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
117	C₂×#2846	C₂²×C₄	1	1	yes	characteristic
118	C₂×#2846	C₂×D₄	1	1	yes	characteristic
119	C₂×#2846	C₂×D₄	1	1	yes	characteristic
120	#35390	C₂²×C₄	1	1	yes	characteristic
121	#35390	C₂×D₄	1	1	yes	characteristic
122	#35367	C₂²×C₄	1	1	yes	characteristic
123	#35367	C₂×D₄	1	1	yes	characteristic
124	#35350	C₂²×C₄	1	1	yes	characteristic
125	#35350	C₂²×C₄	1	1	yes	characteristic
126	#35350	C₂×D₄	1	1	yes	characteristic
127	#35350	C₂×D₄	1	1	yes	characteristic
128	#35346	C₂²×C₄	1	1	yes	characteristic
129	#35346	C₂²×C₄	1	1	yes	characteristic
130	#35346	C₂²×C₄	1	1	yes	characteristic
131	#35346	C₂²×C₄	1	1	yes	characteristic
132	#35346	C₂×D₄	1	1	yes	characteristic
133	#35346	C₂×D₄	1	1	yes	characteristic
134	#35346	C₂×D₄	1	2	yes	—
135	#35346	C₂×D₄	1	1	yes	characteristic
136	#35346	C₂×D₄	1	1	yes	characteristic
137	#35346	C₂×D₄	1	2	yes	—
138	#35050	C₂×D₄	1	4	yes	—
139	#34176	C₂×D₄	1	1	yes	characteristic
140	#34171	C₂×D₄	1	1	yes	characteristic
141	#34171	C₂×D₄	1	1	yes	characteristic
142	C₂×#2315	C₂×D₄	1	2	yes	complemented
143	C₂×#2308	C₂×D₄	1	2	yes	—
144	C₂×#2308	C₂×D₄	1	1	yes	characteristic
145	C₂²×#379	C₂×D₄	1	1	yes	characteristic
146	C₂²×#379	C₂×D₄	1	2	yes	—
147	C₂×#2273	C₂×D₄	1	2	yes	complemented
148	#23468	C₂²⋊C₄	1	2	yes	complemented
149	#23468	C₂²⋊C₄	1	2	yes	complemented
150	#23444	C₂²⋊C₄	1	2	yes	complemented
151	#23444	C₂²⋊C₄	1	2	yes	complemented
152	#20689	C₂²⋊C₄	1	1	yes	characteristic, complemented
153	#20689	C₂²⋊C₄	1	1	yes	characteristic, complemented
154	#20689	C₂²⋊C₄	1	1	yes	characteristic, complemented
155	#20689	C₂²⋊C₄	1	1	yes	characteristic, complemented
156	C₂×#1819	C₂×D₄	1	2	yes	—
157	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
158	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
159	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
160	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
161	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
162	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
163	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
164	#20585	C₂²⋊C₄	1	1	yes	characteristic, complemented
165	C₂×#1462	C₂×D₄	1	4	yes	complemented
166	#10965	C₂²⋊C₄	1	2	yes	—
167	#10965	C₂²⋊C₄	1	2	yes	—
168	#10965	C₂²⋊C₄	1	2	yes	—
169	#10965	C₂²⋊C₄	1	2	yes	—
170	#10965	C₂²×C₄	1	1	yes	characteristic
171	#10965	C₂²×C₄	1	1	yes	characteristic
172	#10965	C₂²×C₄	1	1	yes	characteristic
173	#10965	C₂²×C₄	1	1	yes	characteristic
174	#10965	C₂×D₄	1	2	yes	—
175	#10965	C₂×D₄	1	2	yes	—
176	#10938	C₂²⋊C₄	1	2	yes	complemented
177	#10938	C₂²⋊C₄	1	2	yes	complemented
178	#10938	C₂²⋊C₄	1	2	yes	complemented
179	#10938	C₂²⋊C₄	1	2	yes	complemented
180	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
181	C₂⁷	C₂×C₂²⋊C₄	1	1	yes	characteristic
182	C₂⁷	C₂²×D₄	1	1	yes	characteristic
183	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
184	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
185	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
186	C₂²×H(5,𝔽₂)	C₂×C₂²⋊C₄	1	1	yes	characteristic
187	C₂²×H(5,𝔽₂)	#120	1	2	yes	—
188	C₂⁴×D₄	#120	1	2	yes	—
189	C₂⁴×D₄	C₂²×D₄	1	1	yes	characteristic
190	C₂⁴×D₄	H(5,𝔽₂)	1	2	yes	—
191	C₂×#543	C₂×C₂²⋊C₄	1	1	yes	characteristic
192	C₂×#535	#123	1	2	yes	—
193	C₂×#534	C₂×C₂²⋊C₄	1	1	yes	characteristic
194	C₂×#525	#120	1	2	yes	—
195	C₂²×#120	C₂×C₂²⋊C₄	1	2	yes	—
196	C₂²×#120	C₂×C₂²⋊C₄	1	2	yes	—
197	C₂²×#120	#120	1	2	yes	—
198	C₂²×#120	#120	1	2	yes	—
199	C₂²×#120	C₂³×C₄	1	1	yes	characteristic
200	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
201	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
202	C₂²×#120	C₂²×D₄	1	1	yes	characteristic
203	C₂²×#120	C₂×#41	1	2	yes	—
204	C₂²×#120	H(5,𝔽₂)	1	2	yes	—
205	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
206	C₂×#518	C₂×C₂²⋊C₄	1	1	yes	characteristic
207	C₂³×C₂²⋊C₄	#120	1	2	yes	—
208	C₂³×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
209	C₂³×C₂²⋊C₄	C₂²×D₄	1	2	yes	—
210	#2482	C₄×D₄	1	4	yes	—
211	#2482	#121	1	4	yes	—
212	#2404	C₄×D₄	1	4	yes	—
213	#2404	#121	1	4	yes	—
214	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
215	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
216	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
217	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
218	#2308	C₂×C₂²⋊C₄	1	2	yes	—
219	#2308	C₂×C₂²⋊C₄	1	2	yes	—
220	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
221	#2308	C₂×C₂²⋊C₄	1	1	yes	characteristic
222	#2308	#120	1	2	yes	—
223	#2308	#120	1	2	yes	—
224	#2308	#120	1	2	yes	—
225	#2308	#123	1	2	yes	—
226	#2280	#120	1	2	yes	—
227	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
228	C₂×#379	C₂×C₂²⋊C₄	1	1	yes	characteristic
229	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
230	C₂×#379	C₂×C₂²⋊C₄	1	2	yes	—
231	#2273	C₂×C₂²⋊C₄	1	1	yes	characteristic
232	#2273	C₂×C₂²⋊C₄	1	1	yes	characteristic
233	C₂×#342	C₂×C₂²⋊C₄	1	2	yes	—
234	C₂×#342	C₂×C₂²⋊C₄	1	2	yes	—
235	C₂⁶	B(4,𝔽₂)	1	2	yes	—
236	C₂⁶	C₂²×C₂²⋊C₄	1	1	yes	characteristic
237	C₂⁶	C₂×#120	1	1	yes	characteristic
238	C₂⁶	C₂×#120	1	1	yes	characteristic
239	C₂⁶	#534	1	1	yes	characteristic
240	C₂⁶	D₄²	1	2	yes	—
241	C₂⁶	#546	1	2	yes	—
242	C₂²×#41	#386	1	2	yes	—
243	C₂³×D₄	#379	1	2	yes	—
244	C₂³×D₄	#379	1	2	yes	—
245	C₂³×D₄	#458	1	2	yes	—
246	C₂³×D₄	#458	1	2	yes	—
247	C₂³×D₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
248	C₂³×D₄	#518	1	2	yes	—
249	C₂³×D₄	C₂×#120	1	1	yes	characteristic
250	C₂³×D₄	C₂×#123	1	1	yes	characteristic
251	C₂³×D₄	#534	1	1	yes	characteristic
252	C₂³×D₄	#534	1	2	yes	—
253	C₂³×D₄	#546	1	2	yes	—
254	C₂³×D₄	#546	1	2	yes	—
255	C₂⁴×C₄	B(4,𝔽₂)	1	2	yes	—
256	C₂⁴×C₄	C₂×#120	1	1	yes	characteristic
257	C₂⁴×C₄	D₄²	1	2	yes	—
258	C₂×C₂²⋊Q₈	B(4,𝔽₂)	1	4	yes	—
259	C₂×#121	B(4,𝔽₂)	1	4	yes	—
260	C₂×#117	#386	1	2	yes	—
261	C₂²×C₂²⋊C₄	#379	1	2	yes	—
262	C₂²×C₂²⋊C₄	#379	1	2	yes	—
263	C₂²×C₂²⋊C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
264	C₂²×C₂²⋊C₄	C₂×C₄×D₄	1	2	yes	—
265	C₂²×C₂²⋊C₄	C₂×#120	1	1	yes	characteristic
266	C₂²×C₂²⋊C₄	C₂×#121	1	2	yes	—
267	C₂²×C₂²⋊C₄	D₄²	1	2	yes	—
268	C₂²×C₂²⋊C₄	D₄²	1	2	yes	—
269	C₂²×C₂²⋊C₄	#546	1	2	yes	—
270	#381	#386	1	2	yes	—
271	#381	#386	1	2	yes	—
272	C₂⁵	#1790	1	2	yes	—
273	C₂⁵	#1790	1	2	yes	—
274	C₂⁵	C₂×#379	1	1	yes	characteristic
275	C₂⁵	#2308	1	1	yes	characteristic
276	C₂⁵	D₄×C₂²⋊C₄	1	2	yes	—
277	C₂⁵	#2403	1	1	yes	characteristic
278	C₂⁵	#2405	1	1	yes	characteristic
279	C₂⁵	#2405	1	1	yes	characteristic
280	C₂⁵	#2410	1	2	yes	—
281	C₂⁵	C₂×B(4,𝔽₂)	1	2	yes	—
282	C₂⁵	C₂×#458	1	2	yes	—
283	C₂²×Q₈	#1889	1	2	yes	complemented
284	C₂²×D₄	#1889	1	2	yes	complemented
285	C₂³×C₄	#1790	1	2	yes	—
286	C₂³×C₄	#1790	1	2	yes	—
287	C₂³×C₄	C₂×#386	1	1	yes	characteristic
288	C₂³×C₄	D₄×C₂²⋊C₄	1	2	yes	—
289	C₂³×C₄	#2403	1	1	yes	characteristic
290	C₂³×C₄	#2410	1	2	yes	—
291	C₂³×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
292	C₂×C₄⋊C₄	#1889	1	4	yes	complemented
293	C₂⁴	#12753	1	4	yes	—
294	C₂⁴	#13867	1	1	yes	characteristic
295	C₂⁴	C₂×#1790	1	2	yes	—
296	C₂⁴	#23895	1	2	yes	—
297	C₂⁴	#23900	1	1	yes	characteristic
298	C₂⁴	#23900	1	2	yes	—
299	C₂⁴	#23901	1	1	yes	characteristic
300	C₂⁴	#24056	1	2	yes	—
301	C₂²×C₄	C₂×#1889	1	2	yes	—
302	C₂²×C₄	#23900	1	2	yes	—
303	C₂³	#245225	1	2	yes	—
304	C₂³	#245226	1	2	yes	—
305	C₂³	#359501	1	1	yes	characteristic
306	C₂³	#359549	1	1	yes	characteristic
307	C₂³	#359552	1	1	yes	characteristic
308	C₂³	C₂×#12753	1	2	yes	—
309	C₂³	#493562	1	2	yes	—
310	C₂²	#72210342	1	2	yes	—
311	C₂²	#72235131	1	2	yes	—
312	C₂²	#72236754	1	1	yes	characteristic
313	C₂²	#72251567	1	2	yes	—
314	C₂	#72258465	1	2	yes	—
315	C₂	#72266446	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#72236754
commutator	C₂²×#120	C₂³×C₄
Frattini, cosocle	C₂³×#120	C₂⁴
prime radical	#72327288	C₂
LCS	G ▷ C₂²×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂⁵ ◁ C₂³×#120 ◁ G
LECS	G ▷ C₂³×#120 ▷ C₂⁴ ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72337738	C₂	semidirect
2. #72337737	C₂	semidirect
3. #72337736	C₂	semidirect
4. #72334279	C₂	semidirect
6. #72327248	C₄	semidirect
7. #72327244	C₄	semidirect
8. #72327231	C₄	semidirect
9. #72326786	C₄	semidirect
10. #72318215	C₄	semidirect
11. #72317049	C₂²	semidirect
12. #72310532	C₂	semidirect
13. #72310531	C₂²	semidirect
14. #72309392	C₂	semidirect
16. #72303878	C₂	semidirect
18. #72247345	C₂	semidirect
19. #72247315	C₂²	semidirect
21. #72237782	C₂	semidirect
22. #72237781	C₂²	semidirect
23. #72237780	C₂²	semidirect
25. #72236977	C₂²	semidirect
26. C₂×#97550	C₂²	semidirect
27. #72234670	C₂²	semidirect
28. #72226357	C₂	semidirect
29. #72226348	C₂²	semidirect
30. #72225873	C₂²	semidirect
31. #72225777	C₂²	semidirect
33. #72225660	C₄	semidirect
35. #72221174	C₂²	semidirect
36. #72219035	C₂²	semidirect
38. C₂×#134033	C₂²	semidirect
41. #72216646	C₄	semidirect
42. #72210024	C₄	semidirect
44. #8093108	C₂×C₄	semidirect
45. #8093107	C₂×C₄	semidirect
46. #7670230	C₂×C₄	semidirect
47. #7670203	C₂×C₄	semidirect
67. #449521	C₂×C₄	semidirect
68. #449521	C₂×C₄	semidirect
73. #449475	C₂×C₄	semidirect
74. #449475	C₂×C₄	semidirect
77. #418213	C₂×C₄	semidirect
78. #418132	C₂×C₄	semidirect
81. #417896	C₂×C₄	semidirect
85. #417824	C₂×C₄	semidirect
87. #391735	C₂×C₄	semidirect
88. #391709	C₂×C₄	semidirect
90. #375666	C₂×C₄	semidirect
91. #374004	C₂×C₄	semidirect
96. #200656	D₄	semidirect
97. #197526	D₄	semidirect
101. C₂×H(7,𝔽₂)	C₂²⋊C₄	semidirect
103. #62842	C₂²⋊C₄	semidirect
104. #62842	C₂²⋊C₄	semidirect
110. #62652	C₂²⋊C₄	semidirect
142. C₂×#2315	C₂×D₄	semidirect
147. C₂×#2273	C₂×D₄	semidirect
148. #23468	C₂²⋊C₄	semidirect
149. #23468	C₂²⋊C₄	semidirect
150. #23444	C₂²⋊C₄	semidirect
151. #23444	C₂²⋊C₄	semidirect
152. #20689	C₂²⋊C₄	semidirect
153. #20689	C₂²⋊C₄	semidirect
154. #20689	C₂²⋊C₄	semidirect
155. #20689	C₂²⋊C₄	semidirect
157. #20585	C₂²⋊C₄	semidirect
158. #20585	C₂²⋊C₄	semidirect
159. #20585	C₂²⋊C₄	semidirect
160. #20585	C₂²⋊C₄	semidirect
161. #20585	C₂²⋊C₄	semidirect
162. #20585	C₂²⋊C₄	semidirect
163. #20585	C₂²⋊C₄	semidirect
164. #20585	C₂²⋊C₄	semidirect
165. C₂×#1462	C₂×D₄	semidirect
176. #10938	C₂²⋊C₄	semidirect
177. #10938	C₂²⋊C₄	semidirect
178. #10938	C₂²⋊C₄	semidirect
179. #10938	C₂²⋊C₄	semidirect
283. C₂²×Q₈	#1889	semidirect
284. C₂²×D₄	#1889	semidirect
292. C₂×C₄⋊C₄	#1889	semidirect

Maximal subgroups

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

subgroup	index
#72337738	2
#72337737	2
#72337736	2
#72334279	2
#72327288	2
#72310532	2
#72309392	2
#72303878	2
#72247345	2
#72237782	2
#72226357	2