Subgroups — #72311383

Order 2048.

Only the 830 normal subgroups are shown; non-normal subgroups are omitted.

The subgroup lattice has 356 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72311172	C₂	1	2	yes	maximal, complemented
2	#72311150	C₂	1	4	yes	maximal, complemented
3	C₂×#128079	C₂	1	2	yes	maximal, complemented
4	C₂×#392136	C₂	1	1	yes	maximal, characteristic, complemented
5	#72240597	C₂	1	1	yes	maximal, characteristic
6	C₂×#392135	C₂	1	1	yes	maximal, characteristic, complemented
7	#72236925	C₂	1	4	yes	maximal, complemented
8	C₂²×H(7,𝔽₂)	C₂²	1	1	yes	characteristic
9	#7630442	C₄	1	2	yes	complemented
10	#7630442	C₂²	1	1	yes	characteristic
11	#6628897	C₄	1	2	yes	complemented
12	#6628897	C₂²	1	2	yes	—
13	#6628896	C₄	1	2	yes	complemented
14	#6628896	C₂²	1	2	yes	—
15	C₂×#20592	C₂²	1	2	yes	—
16	C₂×#20585	C₄	1	2	yes	complemented
17	C₂×#20585	C₂²	1	1	yes	characteristic
18	C₂×#20585	C₂²	1	2	yes	—
19	#496241	C₂²	1	4	yes	complemented
20	#496240	C₂²	1	4	yes	complemented
21	#392136	C₂²	1	4	yes	—
22	#392135	C₂²	1	4	yes	—
23	#128079	C₂²	1	8	yes	complemented
24	C₂×H(7,𝔽₂)	C₂×C₄	1	2	yes	—
25	C₂×H(7,𝔽₂)	D₄	1	2	yes	—
26	C₂×H(7,𝔽₂)	D₄	1	2	yes	—
27	C₂×H(7,𝔽₂)	C₂³	1	2	yes	—
28	C₂³×H(5,𝔽₂)	C₂×C₄	1	2	yes	—
29	C₂³×H(5,𝔽₂)	D₄	1	2	yes	—
30	C₂³×H(5,𝔽₂)	D₄	1	2	yes	—
31	C₂³×H(5,𝔽₂)	C₂³	1	1	yes	characteristic
32	C₂²×#534	C₂×C₄	1	1	yes	characteristic
33	C₂²×#534	D₄	1	2	yes	—
34	C₂²×#413	D₄	1	4	yes	complemented
35	C₂³×#99	D₄	1	4	yes	complemented
36	#35446	C₂×C₄	1	1	yes	characteristic
37	#35446	C₂×C₄	1	4	yes	complemented
38	#35446	D₄	1	2	yes	—
39	#35446	C₂³	1	1	yes	characteristic
40	#35346	C₂×C₄	1	1	yes	characteristic
41	#35346	C₂×C₄	1	4	yes	complemented
42	#35346	D₄	1	2	yes	—
43	#35346	C₂³	1	1	yes	characteristic
44	C₂×#2308	C₂×C₄	1	1	yes	characteristic
45	C₂×#2308	C₂×C₄	1	2	yes	—
46	C₂×#2308	D₄	1	2	yes	—
47	#20592	D₄	1	4	yes	complemented
48	#20592	C₂³	1	4	yes	—
49	#20585	C₂×C₄	1	2	yes	—
50	#20585	C₂×C₄	1	4	yes	complemented
51	#20585	C₂×C₄	1	4	yes	complemented
52	#20585	D₄	1	4	yes	—
53	#20585	D₄	1	4	yes	complemented
54	#20585	C₂³	1	2	yes	—
55	#20585	C₂³	1	4	yes	—
56	C₂×#1782	D₄	1	4	yes	—
57	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	4	yes	—
58	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	4	yes	—
59	C₂²×H(5,𝔽₂)	C₂²⋊C₄	1	4	yes	—
60	C₂²×H(5,𝔽₂)	C₂²×C₄	1	1	yes	characteristic
61	C₂²×H(5,𝔽₂)	C₂²×C₄	1	4	yes	—
62	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
63	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
64	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
65	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
66	C₂²×H(5,𝔽₂)	C₂×D₄	1	4	yes	—
67	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
68	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
69	C₂²×H(5,𝔽₂)	C₂×D₄	1	2	yes	—
70	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
71	C₂²×H(5,𝔽₂)	#41	1	2	yes	—
72	C₂²×H(5,𝔽₂)	C₂⁴	1	1	yes	characteristic
73	C₂³×#41	C₂×D₄	1	2	yes	—
74	C₂³×#41	C₂×D₄	1	2	yes	—
75	C₂³×#41	#41	1	2	yes	—
76	C₂⁴×D₄	C₂²⋊C₄	1	4	yes	—
77	C₂⁴×D₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
78	C₂⁴×D₄	C₂²×C₄	1	1	yes	characteristic
79	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
80	C₂⁴×D₄	C₂×D₄	1	2	yes	—
81	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
82	C₂⁴×D₄	C₂×D₄	1	2	yes	—
83	C₂⁴×D₄	#41	1	2	yes	—
84	C₂²×#123	C₂²⋊C₄	1	2	yes	complemented
85	C₂²×#123	C₂²⋊C₄	1	1	yes	characteristic, complemented
86	C₂²×#123	C₂²×C₄	1	1	yes	characteristic
87	C₂²×#123	C₂×D₄	1	2	yes	—
88	C₂²×#120	C₂²⋊C₄	1	2	yes	complemented
89	C₂²×#120	C₂²⋊C₄	1	1	yes	characteristic, complemented
90	C₂²×#120	C₂²×C₄	1	1	yes	characteristic
91	C₂²×#120	C₂×D₄	1	2	yes	—
92	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	1	yes	characteristic, complemented
93	C₂³×C₂²⋊C₄	C₂²⋊C₄	1	2	yes	complemented
94	C₂×#413	C₂×D₄	1	8	yes	—
95	C₂²×#99	C₂×D₄	1	8	yes	—
96	#2308	C₂²⋊C₄	1	2	yes	complemented
97	#2308	C₂²⋊C₄	1	2	yes	complemented
98	#2308	C₂²⋊C₄	1	2	yes	complemented
99	#2308	C₂²⋊C₄	1	4	yes	complemented
100	#2308	C₂²×C₄	1	1	yes	characteristic
101	#2308	C₂²×C₄	1	1	yes	characteristic
102	#2308	C₂²×C₄	1	4	yes	—
103	#2308	C₂×D₄	1	2	yes	—
104	#2308	C₂×D₄	1	2	yes	—
105	C₂×#381	C₂²⋊C₄	1	4	yes	complemented
106	#1782	C₂²⋊C₄	1	8	yes	complemented
107	#1782	C₂×D₄	1	8	yes	—
108	C₂⁶	#99	1	4	yes	—
109	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
110	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic
111	C₂⁶	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
112	C₂⁶	#120	1	1	yes	characteristic
113	C₂⁶	#121	1	2	yes	—
114	C₂⁶	#123	1	1	yes	characteristic
115	C₂²×#41	C₂×C₂²⋊C₄	1	2	yes	—
116	C₂²×#41	C₄×D₄	1	2	yes	—
117	C₂²×#41	C₄×D₄	1	2	yes	—
118	C₂²×#41	#120	1	2	yes	—
119	C₂²×#41	#120	1	2	yes	—
120	C₂²×#41	#120	1	2	yes	—
121	C₂²×#41	#120	1	2	yes	—
122	C₂²×#41	#121	1	2	yes	—
123	C₂²×#41	#121	1	2	yes	—
124	C₂²×#41	#121	1	2	yes	—
125	C₂²×#41	#121	1	2	yes	—
126	C₂²×#41	#121	1	2	yes	—
127	C₂²×#41	#121	1	2	yes	—
128	C₂²×#41	#121	1	2	yes	—
129	C₂²×#41	#121	1	2	yes	—
130	C₂²×#41	#123	1	2	yes	—
131	C₂²×#41	#123	1	2	yes	—
132	C₂²×#41	#124	1	2	yes	—
133	C₂²×#41	#124	1	2	yes	—
134	C₂²×#41	#127	1	2	yes	—
135	C₂²×#41	#127	1	2	yes	—
136	C₂²×#41	C₂²×D₄	1	2	yes	—
137	C₂²×#41	C₂²×D₄	1	2	yes	—
138	C₂²×#41	C₂×#41	1	2	yes	—
139	C₂³×Q₈	#121	1	2	yes	—
140	C₂³×D₄	#99	1	8	yes	—
141	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
142	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
143	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
144	C₂³×D₄	C₂×C₂²⋊C₄	1	2	yes	—
145	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
146	C₂³×D₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
147	C₂³×D₄	C₂×C₂²⋊C₄	1	8	yes	—
148	C₂³×D₄	C₄×D₄	1	2	yes	—
149	C₂³×D₄	C₄×D₄	1	2	yes	—
150	C₂³×D₄	C₄×D₄	1	2	yes	—
151	C₂³×D₄	C₄×D₄	1	2	yes	—
152	C₂³×D₄	C₄×D₄	1	2	yes	—
153	C₂³×D₄	C₄×D₄	1	2	yes	—
154	C₂³×D₄	#120	1	1	yes	characteristic
155	C₂³×D₄	#120	1	1	yes	characteristic
156	C₂³×D₄	#120	1	2	yes	—
157	C₂³×D₄	#120	1	2	yes	—
158	C₂³×D₄	#120	1	2	yes	—
159	C₂³×D₄	#120	1	2	yes	—
160	C₂³×D₄	#120	1	2	yes	—
161	C₂³×D₄	#120	1	2	yes	—
162	C₂³×D₄	#120	1	2	yes	—
163	C₂³×D₄	#120	1	2	yes	—
164	C₂³×D₄	#120	1	2	yes	—
165	C₂³×D₄	#120	1	2	yes	—
166	C₂³×D₄	#121	1	2	yes	—
167	C₂³×D₄	#121	1	2	yes	—
168	C₂³×D₄	#121	1	2	yes	—
169	C₂³×D₄	#121	1	2	yes	—
170	C₂³×D₄	#121	1	2	yes	—
171	C₂³×D₄	#121	1	2	yes	—
172	C₂³×D₄	#121	1	2	yes	—
173	C₂³×D₄	#121	1	2	yes	—
174	C₂³×D₄	#121	1	2	yes	—
175	C₂³×D₄	#121	1	2	yes	—
176	C₂³×D₄	#121	1	2	yes	—
177	C₂³×D₄	#121	1	2	yes	—
178	C₂³×D₄	#121	1	2	yes	—
179	C₂³×D₄	#123	1	1	yes	characteristic
180	C₂³×D₄	#123	1	1	yes	characteristic
181	C₂³×D₄	#123	1	2	yes	—
182	C₂³×D₄	#123	1	2	yes	—
183	C₂³×D₄	#123	1	2	yes	—
184	C₂³×D₄	#123	1	2	yes	—
185	C₂³×D₄	#124	1	2	yes	—
186	C₂³×D₄	#127	1	2	yes	—
187	C₂³×D₄	C₂³×C₄	1	1	yes	characteristic
188	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
189	C₂³×D₄	C₂²×D₄	1	2	yes	—
190	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
191	C₂³×D₄	C₂²×D₄	1	2	yes	—
192	C₂³×D₄	C₂×#41	1	2	yes	—
193	C₂⁴×C₄	#99	1	4	yes	—
194	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic
195	C₂⁴×C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
196	C₂⁴×C₄	#120	1	1	yes	characteristic
197	C₂⁴×C₄	#121	1	2	yes	—
198	C₂⁴×C₄	#123	1	1	yes	characteristic
199	C₂⁴×C₄	#124	1	2	yes	—
200	C₂⁴×C₄	#127	1	2	yes	—
201	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	complemented
202	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	2	yes	complemented
203	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
204	C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	1	1	yes	characteristic, complemented
205	#381	C₂×C₂²⋊C₄	1	8	yes	complemented
206	C₂⁵	#379	1	1	yes	characteristic
207	C₂⁵	#379	1	1	yes	characteristic
208	C₂⁵	#379	1	1	yes	characteristic
209	C₂⁵	#386	1	2	yes	—
210	C₂⁵	#386	1	1	yes	characteristic
211	C₂⁵	#386	1	1	yes	characteristic
212	C₂⁵	#386	1	1	yes	characteristic
213	C₂⁵	#386	1	1	yes	characteristic
214	C₂⁵	#386	1	1	yes	characteristic
215	C₂⁵	#386	1	2	yes	—
216	C₂⁵	#386	1	1	yes	characteristic
217	C₂⁵	#386	1	2	yes	—
218	C₂⁵	#392	1	2	yes	—
219	C₂⁵	#392	1	2	yes	—
220	C₂⁵	#392	1	2	yes	—
221	C₂⁵	#394	1	2	yes	—
222	C₂⁵	#394	1	2	yes	—
223	C₂⁵	#394	1	2	yes	—
224	C₂⁵	C₂×#99	1	8	yes	—
225	C₂⁵	C₂×#99	1	4	yes	—
226	C₂⁵	C₂×#99	1	4	yes	—
227	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
228	C₂⁵	C₂²×C₂²⋊C₄	1	1	yes	characteristic
229	C₂⁵	C₂×#120	1	1	yes	characteristic
230	C₂⁵	C₂×#121	1	2	yes	—
231	C₂⁵	C₂×#123	1	1	yes	characteristic
232	C₂²×Q₈	#390	1	2	yes	—
233	C₂²×Q₈	#392	1	2	yes	—
234	C₂²×Q₈	#394	1	2	yes	—
235	C₂²×Q₈	C₂×#121	1	2	yes	—
236	C₂²×D₄	#379	1	2	yes	—
237	C₂²×D₄	#379	1	2	yes	—
238	C₂²×D₄	#386	1	2	yes	—
239	C₂²×D₄	#386	1	2	yes	—
240	C₂²×D₄	#386	1	2	yes	—
241	C₂²×D₄	#386	1	2	yes	—
242	C₂²×D₄	#386	1	2	yes	—
243	C₂²×D₄	#386	1	2	yes	—
244	C₂²×D₄	#386	1	2	yes	—
245	C₂²×D₄	#386	1	2	yes	—
246	C₂²×D₄	#390	1	2	yes	—
247	C₂²×D₄	#390	1	2	yes	—
248	C₂²×D₄	#390	1	2	yes	—
249	C₂²×D₄	#392	1	2	yes	—
250	C₂²×D₄	#392	1	2	yes	—
251	C₂²×D₄	#392	1	2	yes	—
252	C₂²×D₄	#392	1	2	yes	—
253	C₂²×D₄	#392	1	2	yes	—
254	C₂²×D₄	#392	1	2	yes	—
255	C₂²×D₄	#392	1	2	yes	—
256	C₂²×D₄	#394	1	2	yes	—
257	C₂²×D₄	#394	1	2	yes	—
258	C₂²×D₄	#394	1	2	yes	—
259	C₂²×D₄	#394	1	2	yes	—
260	C₂²×D₄	#394	1	2	yes	—
261	C₂²×D₄	#394	1	2	yes	—
262	C₂²×D₄	#394	1	2	yes	—
263	C₂²×D₄	B(4,𝔽₂)	1	16	yes	—
264	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
265	C₂²×D₄	C₂×C₄×D₄	1	2	yes	—
266	C₂²×D₄	C₂×#120	1	2	yes	—
267	C₂²×D₄	C₂×#120	1	2	yes	—
268	C₂²×D₄	C₂×#120	1	2	yes	—
269	C₂²×D₄	C₂×#121	1	2	yes	—
270	C₂²×D₄	C₂×#121	1	2	yes	—
271	C₂²×D₄	C₂×#121	1	2	yes	—
272	C₂²×D₄	C₂×#123	1	2	yes	—
273	C₂³×C₄	#379	1	1	yes	characteristic
274	C₂³×C₄	#386	1	1	yes	characteristic
275	C₂³×C₄	#386	1	2	yes	—
276	C₂³×C₄	#386	1	1	yes	characteristic
277	C₂³×C₄	#390	1	2	yes	—
278	C₂³×C₄	#390	1	2	yes	—
279	C₂³×C₄	#390	1	2	yes	—
280	C₂³×C₄	#390	1	2	yes	—
281	C₂³×C₄	#392	1	2	yes	—
282	C₂³×C₄	#392	1	2	yes	—
283	C₂³×C₄	#392	1	2	yes	—
284	C₂³×C₄	#392	1	2	yes	—
285	C₂³×C₄	#392	1	2	yes	—
286	C₂³×C₄	#394	1	2	yes	—
287	C₂³×C₄	#394	1	2	yes	—
288	C₂³×C₄	#394	1	2	yes	—
289	C₂³×C₄	#394	1	2	yes	—
290	C₂³×C₄	#394	1	2	yes	—
291	C₂³×C₄	C₂×#99	1	8	yes	—
292	C₂³×C₄	C₂²×C₂²⋊C₄	1	1	yes	characteristic
293	C₂³×C₄	C₂×#120	1	1	yes	characteristic
294	C₂³×C₄	C₂×#121	1	2	yes	—
295	C₂³×C₄	C₂×#123	1	1	yes	characteristic
296	C₂³×C₄	C₂×#124	1	2	yes	—
297	C₂³×C₄	C₂×#127	1	2	yes	—
298	C₂⁴	#1438	1	2	yes	—
299	C₂⁴	#1438	1	1	yes	characteristic
300	C₂⁴	#1438	1	1	yes	characteristic
301	C₂⁴	#1438	1	1	yes	characteristic
302	C₂⁴	#1438	1	2	yes	—
303	C₂⁴	#1438	1	2	yes	—
304	C₂⁴	#1438	1	1	yes	characteristic
305	C₂⁴	#1781	1	4	yes	—
306	C₂⁴	#1781	1	2	yes	—
307	C₂⁴	#1781	1	2	yes	—
308	C₂⁴	#1889	1	8	yes	—
309	C₂⁴	#1898	1	4	yes	—
310	C₂⁴	#1898	1	4	yes	—
311	C₂⁴	#1898	1	2	yes	—
312	C₂⁴	#1898	1	2	yes	—
313	C₂⁴	#1898	1	2	yes	—
314	C₂⁴	#1898	1	2	yes	—
315	C₂⁴	#2021	1	8	yes	—
316	C₂⁴	C₂×#379	1	1	yes	characteristic
317	C₂⁴	C₂×#386	1	2	yes	—
318	C₂⁴	C₂×#386	1	1	yes	characteristic
319	C₂⁴	C₂×#386	1	1	yes	characteristic
320	C₂⁴	C₂×#392	1	2	yes	—
321	C₂⁴	C₂×#394	1	2	yes	—
322	C₂⁴	C₂²×#99	1	4	yes	—
323	C₂×D₄	#1889	1	8	yes	—
324	C₂×D₄	#2021	1	8	yes	—
325	C₂×D₄	#2021	1	8	yes	—
326	C₂×D₄	C₂×B(4,𝔽₂)	1	8	yes	—
327	C₂²×C₄	#1438	1	2	yes	—
328	C₂²×C₄	#1438	1	2	yes	—
329	C₂²×C₄	#1438	1	2	yes	—
330	C₂²×C₄	#2021	1	8	yes	—
331	C₂²×C₄	C₂×#390	1	2	yes	—
332	C₂²×C₄	C₂×#392	1	2	yes	—
333	C₂²×C₄	C₂×#394	1	2	yes	—
334	C₂³	#10965	1	2	yes	—
335	C₂³	#10965	1	2	yes	—
336	C₂³	#10965	1	2	yes	—
337	C₂³	#10965	1	1	yes	characteristic
338	C₂³	#10965	1	1	yes	characteristic
339	C₂³	#10991	1	4	yes	—
340	C₂³	#10991	1	4	yes	—
341	C₂³	#10991	1	4	yes	—
342	C₂³	C₂×#1438	1	1	yes	characteristic
343	C₂³	C₂×#1781	1	2	yes	—
344	C₂³	C₂×#1889	1	4	yes	—
345	C₂³	C₂×#1898	1	2	yes	—
346	C₂³	C₂×#1898	1	2	yes	—
347	C₂³	C₂×#2021	1	4	yes	—
348	C₂×C₄	#10991	1	4	yes	—
349	C₂×C₄	C₂×#2021	1	4	yes	—
350	C₂²	#115690	1	2	yes	—
351	C₂²	#115690	1	2	yes	—
352	C₂²	C₂×#10965	1	1	yes	characteristic
353	C₂²	C₂×#10991	1	2	yes	—
354	C₂	C₂×#115690	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#115690
commutator	C₂³×D₄	C₂³×C₄
Frattini, cosocle	C₂²×H(5,𝔽₂)	C₂⁴
prime radical	#72240597	C₂
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂³×H(5,𝔽₂) ◁ G
LECS	G ▷ C₂²×H(5,𝔽₂) ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72311172	C₂	semidirect
2. #72311150	C₂	semidirect
3. C₂×#128079	C₂	semidirect
4. C₂×#392136	C₂	semidirect
6. C₂×#392135	C₂	semidirect
7. #72236925	C₂	semidirect
9. #7630442	C₄	semidirect
11. #6628897	C₄	semidirect
13. #6628896	C₄	semidirect
16. C₂×#20585	C₄	semidirect
19. #496241	C₂²	semidirect
20. #496240	C₂²	semidirect
23. #128079	C₂²	semidirect
34. C₂²×#413	D₄	semidirect
35. C₂³×#99	D₄	semidirect
37. #35446	C₂×C₄	semidirect
41. #35346	C₂×C₄	semidirect
47. #20592	D₄	semidirect
50. #20585	C₂×C₄	semidirect
51. #20585	C₂×C₄	semidirect
53. #20585	D₄	semidirect
77. C₂⁴×D₄	C₂²⋊C₄	semidirect
84. C₂²×#123	C₂²⋊C₄	semidirect
85. C₂²×#123	C₂²⋊C₄	semidirect
88. C₂²×#120	C₂²⋊C₄	semidirect
89. C₂²×#120	C₂²⋊C₄	semidirect
92. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
93. C₂³×C₂²⋊C₄	C₂²⋊C₄	semidirect
96. #2308	C₂²⋊C₄	semidirect
97. #2308	C₂²⋊C₄	semidirect
98. #2308	C₂²⋊C₄	semidirect
99. #2308	C₂²⋊C₄	semidirect
105. C₂×#381	C₂²⋊C₄	semidirect
106. #1782	C₂²⋊C₄	semidirect
111. C₂⁶	C₂×C₂²⋊C₄	semidirect
195. C₂⁴×C₄	C₂×C₂²⋊C₄	semidirect
201. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
202. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
203. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
204. C₂²×C₂²⋊C₄	C₂×C₂²⋊C₄	semidirect
205. #381	C₂×C₂²⋊C₄	semidirect

Maximal subgroups

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

subgroup	index
#72311172	2
#72311150	2
C₂×#128079	2
C₂×#392136	2
#72240597	2
C₂×#392135	2
#72236925	2