Subgroups — #72257265

Order 2048.

At least 6447 conjugacy classes of subgroups; only the 396 normal subgroups are shown.

The subgroup lattice has 361 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72257190	C₂	1	1	yes	maximal, characteristic
2	C₂×#130296	C₂	1	1	yes	maximal, characteristic, complemented
3	#72250955	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×#486701	C₂	1	1	yes	maximal, characteristic, complemented
5	#72250881	C₂	1	1	yes	maximal, characteristic, complemented
6	#72250850	C₂	1	1	yes	maximal, characteristic, complemented
7	#72250688	C₂	1	1	yes	maximal, characteristic, complemented
8	#72250377	C₂	1	1	yes	maximal, characteristic, complemented
9	#72250320	C₂	1	1	yes	maximal, characteristic, complemented
10	C₂×#130854	C₂	1	1	yes	maximal, characteristic, complemented
11	#72249883	C₂	1	1	yes	maximal, characteristic, complemented
12	#72240706	C₂	1	1	yes	maximal, characteristic, complemented
13	#72239959	C₂	1	1	yes	maximal, characteristic, complemented
14	C₂×#500351	C₂	1	1	yes	maximal, characteristic, complemented
15	#72237227	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#62334	C₂²	1	1	yes	characteristic
17	C₂×#61259	C₂²	1	1	yes	characteristic
18	C₂×#33659	C₂²	1	1	yes	characteristic
19	C₂×#33657	C₂²	1	1	yes	characteristic
20	C₂×#33404	C₂²	1	1	yes	characteristic, complemented
21	#6473006	C₂²	1	1	yes	characteristic
22	C₂×#27694	C₂²	1	1	yes	characteristic
23	C₂×#27691	C₂²	1	1	yes	characteristic, complemented
24	#6457372	C₂²	1	1	yes	characteristic
25	#6457186	C₂²	1	1	yes	characteristic
26	#6389178	C₂²	1	1	yes	characteristic
27	#6377581	C₂²	1	1	yes	characteristic
28	C₂×#13079	C₂²	1	1	yes	characteristic
29	C₂×#13076	C₂²	1	1	yes	characteristic
30	C₂×#12988	C₂²	1	1	yes	characteristic
31	C₂×#12981	C₂²	1	1	yes	characteristic, complemented
32	#493921	C₂²	1	1	yes	characteristic, complemented
33	C₂×#12874	C₂²	1	1	yes	characteristic, complemented
34	C₂×#12874	C₂²	1	1	yes	characteristic, complemented
35	C₂×#12873	C₂²	1	1	yes	characteristic, complemented
36	C₂×#12810	C₂²	1	1	yes	characteristic
37	C₂×#12805	C₂²	1	1	yes	characteristic, complemented
38	C₂×#11872	C₂²	1	1	yes	characteristic
39	C₂×#11870	C₂²	1	1	yes	characteristic
40	C₂×#11867	C₂²	1	1	yes	characteristic
41	C₂×#11868	C₂²	1	1	yes	characteristic
42	C₂×#11486	C₂²	1	1	yes	characteristic
43	C₂×#11483	C₂²	1	1	yes	characteristic, complemented
44	#362876	C₂²	1	1	yes	characteristic, complemented
45	#147021	C₂²	1	1	yes	characteristic, complemented
46	#146445	C₂²	1	1	yes	characteristic, complemented
47	#146410	C₂²	1	1	yes	characteristic, complemented
48	#127629	C₂²	1	1	yes	characteristic, complemented
49	#127629	C₂²	1	1	yes	characteristic, complemented
50	#126958	C₂²	1	1	yes	characteristic, complemented
51	C₂×#3407	C₂³	1	1	yes	characteristic
52	C₂×#3256	D₄	1	1	yes	characteristic
53	C₂×#3253	D₄	1	1	yes	characteristic
54	C₂×#3204	D₄	1	1	yes	characteristic
55	C₂×#3199	D₄	1	1	yes	characteristic
56	C₂×#3163	D₄	1	1	yes	characteristic
57	C₂×#3060	C₂³	1	1	yes	characteristic
58	C₂×#3058	C₂³	1	1	yes	characteristic
59	C₂×#3050	D₄	1	1	yes	characteristic
60	C₂×#2952	D₄	1	1	yes	characteristic
61	C₂×#2932	C₂³	1	1	yes	characteristic
62	C₂×#2929	C₂³	1	1	yes	characteristic
63	C₂×#2916	C₂³	1	1	yes	characteristic
64	C₂×#2912	C₂³	1	1	yes	characteristic
65	C₂³×#106	D₄	1	1	yes	characteristic
66	#52165	D₄	1	1	yes	characteristic
67	#33659	D₄	1	4	yes	complemented
68	C₂×#2115	C₂³	1	1	yes	characteristic
69	C₂×#2115	C₂³	1	1	yes	characteristic
70	C₂×#2115	C₂³	1	1	yes	characteristic
71	#29785	D₄	1	1	yes	characteristic
72	#29785	D₄	1	1	yes	characteristic
73	#29742	D₄	1	1	yes	characteristic
74	#29742	D₄	1	1	yes	characteristic
75	#22199	D₄	1	1	yes	characteristic
76	#22198	D₄	1	1	yes	characteristic
77	#22188	D₄	1	1	yes	characteristic
78	#22187	D₄	1	1	yes	characteristic
79	#21937	D₄	1	1	yes	characteristic
80	#21745	D₄	1	1	yes	characteristic
81	#21744	D₄	1	1	yes	characteristic
82	#21233	D₄	1	1	yes	characteristic
83	C₂×#1972	D₄	1	1	yes	characteristic
84	#21154	D₄	1	1	yes	characteristic
85	C₂×#1943	D₄	1	1	yes	characteristic
86	#20802	D₄	1	1	yes	characteristic
87	#20799	D₄	1	1	yes	characteristic
88	C₂×#1813	C₂³	1	1	yes	characteristic
89	C₂×#1813	C₂³	1	1	yes	characteristic
90	C₂×#1812	C₂³	1	1	yes	characteristic
91	#20663	D₄	1	1	yes	characteristic
92	#20663	C₂³	1	1	yes	characteristic
93	#20662	D₄	1	1	yes	characteristic
94	#20384	C₂³	1	1	yes	characteristic
95	#13076	D₄	1	4	yes	complemented
96	#11867	D₄	1	4	yes	complemented
97	C₂²×#135	C₂×D₄	1	1	yes	characteristic
98	C₂³×D₈	C₂×D₄	1	1	yes	characteristic
99	C₂²×#131	C₂×D₄	1	1	yes	characteristic
100	C₂²×#131	C₂⁴	1	1	yes	characteristic
101	C₂⁴×C₈	C₂×D₄	1	1	yes	characteristic
102	C₂×#532	C₂×D₄	1	1	yes	characteristic
103	C₂×#525	C₂×D₄	1	1	yes	characteristic
104	#3407	C₂×D₄	1	2	yes	—
105	#3060	C₂×D₄	1	2	yes	—
106	#3060	C₂×D₄	1	2	yes	—
107	#3060	C₂×D₄	1	2	yes	—
108	#3060	#41	1	2	yes	—
109	C₂×#470	C₂×D₄	1	1	yes	characteristic
110	C₂×#470	C₂×D₄	1	1	yes	characteristic
111	C₂×#469	C₂×D₄	1	1	yes	characteristic
112	C₂×#469	C₂×D₄	1	1	yes	characteristic
113	C₂×#469	C₂×D₄	1	1	yes	characteristic
114	C₂×#469	C₂×D₄	1	1	yes	characteristic
115	C₂×#469	C₂×D₄	1	1	yes	characteristic
116	C₂×#469	C₂×D₄	1	1	yes	characteristic
117	#2916	C₂×D₄	1	2	yes	—
118	C₂×#427	C₂×D₄	1	1	yes	characteristic
119	C₂×#427	C₂×D₄	1	1	yes	characteristic
120	C₂×#427	C₂×D₄	1	1	yes	characteristic
121	C₂×#427	C₂×D₄	1	1	yes	characteristic
122	C₂×#427	C₂×D₄	1	1	yes	characteristic
123	C₂²×#107	C₂×D₄	1	1	yes	characteristic
124	C₂²×#106	C₂×D₄	1	1	yes	characteristic
125	C₂²×#106	C₂×D₄	1	1	yes	characteristic
126	C₂²×#106	C₂×D₄	1	1	yes	characteristic
127	C₂²×#106	C₂×D₄	1	1	yes	characteristic
128	C₂×#424	C₂×D₄	1	1	yes	characteristic
129	C₂×#423	C₂×D₄	1	1	yes	characteristic
130	C₂×#408	C₂×D₄	1	1	yes	characteristic
131	C₂×#408	C₂×D₄	1	1	yes	characteristic
132	C₂×#408	C₂×D₄	1	1	yes	characteristic
133	C₂×#408	C₂×D₄	1	1	yes	characteristic
134	C₂×#407	C₂×D₄	1	1	yes	characteristic
135	C₂×#405	C₂×D₄	1	1	yes	characteristic
136	C₂×#405	C₂×D₄	1	1	yes	characteristic
137	C₂²×#97	C₂×D₄	1	1	yes	characteristic
138	C₂²×#97	C₂×D₄	1	1	yes	characteristic
139	#2717	SD₁₆	1	1	yes	characteristic
140	#2709	SD₁₆	1	1	yes	characteristic
141	#2684	SD₁₆	1	1	yes	characteristic
142	#2669	SD₁₆	1	1	yes	characteristic
143	#2297	C₂×D₄	1	1	yes	characteristic
144	#2115	C₂×D₄	1	2	yes	—
145	#2115	C₂×D₄	1	2	yes	—
146	#1813	C₂×D₄	1	2	yes	—
147	#1812	C₂×D₄	1	2	yes	—
148	#1809	C₂×D₄	1	1	yes	characteristic
149	#1809	C₂×D₄	1	1	yes	characteristic
150	#1809	C₂×D₄	1	1	yes	characteristic
151	#1809	C₂×D₄	1	1	yes	characteristic
152	#1729	C₂×D₄	1	1	yes	characteristic
153	#1728	C₂×D₄	1	1	yes	characteristic
154	C₂²×#41	#120	1	1	yes	characteristic
155	C₂²×#41	C₂²×D₄	1	1	yes	characteristic
156	C₂⁴×C₄	#120	1	1	yes	characteristic
157	C₂×#135	#120	1	2	yes	—
158	C₂×#135	#121	1	2	yes	—
159	C₂²×Q₁₆	#120	1	1	yes	characteristic
160	C₂²×D₈	#120	1	1	yes	characteristic
161	C₂²×D₈	#120	1	1	yes	characteristic
162	C₂²×D₈	#120	1	1	yes	characteristic
163	C₂×#131	C₂²×D₄	1	1	yes	characteristic
164	C₂×#131	C₂²×D₄	1	1	yes	characteristic
165	C₂×#131	C₂²×D₄	1	1	yes	characteristic
166	C₂×#131	C₂×#41	1	1	yes	characteristic
167	C₂×#131	H(5,𝔽₂)	1	1	yes	characteristic
168	C₂×#131	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×#131	H(5,𝔽₂)	1	1	yes	characteristic
170	C₂×#131	H(5,𝔽₂)	1	1	yes	characteristic
171	C₂²×M₁₆	#120	1	1	yes	characteristic
172	C₂²×M₁₆	#120	1	1	yes	characteristic
173	C₂²×M₁₆	#120	1	1	yes	characteristic
174	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
175	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
176	C₂²×M₁₆	C₂²×D₄	1	1	yes	characteristic
177	C₂³×C₈	#120	1	1	yes	characteristic
178	C₂³×C₈	#120	1	1	yes	characteristic
179	C₂³×C₈	#120	1	1	yes	characteristic
180	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
181	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
182	C₂³×C₈	C₂²×D₄	1	1	yes	characteristic
183	C₂×C₄⋊Q₈	AGL(1,ℤ/8)	1	1	yes	characteristic
184	C₂×#127	C₂×SD₁₆	1	1	yes	characteristic
185	C₂×#124	C₂×SD₁₆	1	1	yes	characteristic
186	C₂×#124	AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×#123	C₂×SD₁₆	1	1	yes	characteristic
188	C₂×#123	AGL(1,ℤ/8)	1	1	yes	characteristic
189	C₂×#120	C₂×SD₁₆	1	1	yes	characteristic
190	C₂×#120	AGL(1,ℤ/8)	1	1	yes	characteristic
191	C₂×#117	#120	1	1	yes	characteristic
192	C₂×#117	#120	1	1	yes	characteristic
193	C₂²×C₄²	#120	1	1	yes	characteristic
194	C₂²×C₄²	#120	1	1	yes	characteristic
195	#470	#120	1	2	yes	—
196	#470	#121	1	2	yes	—
197	#470	#121	1	2	yes	—
198	#470	#127	1	2	yes	—
199	#469	#120	1	2	yes	—
200	#469	#121	1	2	yes	—
201	#469	#121	1	2	yes	—
202	#469	#127	1	2	yes	—
203	C₂×#107	#120	1	1	yes	characteristic
204	C₂×#107	#120	1	1	yes	characteristic
205	C₂×#106	#120	1	1	yes	characteristic
206	C₂×#106	#120	1	1	yes	characteristic
207	C₂×#106	#120	1	1	yes	characteristic
208	C₂×#106	#120	1	1	yes	characteristic
209	C₂×#106	#120	1	1	yes	characteristic
210	C₂×#106	#120	1	1	yes	characteristic
211	C₂×#106	#120	1	1	yes	characteristic
212	C₂×#106	#120	1	1	yes	characteristic
213	C₂×#106	#120	1	2	yes	—
214	C₂×#106	#120	1	1	yes	characteristic
215	C₂×#106	#120	1	1	yes	characteristic
216	C₂×#106	#121	1	2	yes	—
217	#386	C₂×SD₁₆	1	1	yes	characteristic
218	#386	C₂×SD₁₆	1	1	yes	characteristic
219	#386	AGL(1,ℤ/8)	1	1	yes	characteristic
220	#386	AGL(1,ℤ/8)	1	1	yes	characteristic
221	C₂⁵	#450	1	1	yes	characteristic
222	C₂×#41	D₄²	1	1	yes	characteristic
223	C₂×#41	D₄²	1	1	yes	characteristic
224	C₂×#41	D₄²	1	1	yes	characteristic
225	C₂×#41	#546	1	1	yes	characteristic
226	C₂×#41	#576	1	1	yes	characteristic
227	C₂×#41	#577	1	1	yes	characteristic
228	C₂×#41	#577	1	1	yes	characteristic
229	C₂×#41	#577	1	1	yes	characteristic
230	C₂²×Q₈	#450	1	1	yes	characteristic
231	C₂²×Q₈	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
232	C₂²×D₄	#450	1	1	yes	characteristic
233	C₂²×D₄	C₂²×SD₁₆	1	1	yes	characteristic
234	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
235	C₂²×D₄	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
236	C₂³×C₄	#450	1	1	yes	characteristic
237	C₂³×C₄	#450	1	1	yes	characteristic
238	C₂³×C₄	#450	1	1	yes	characteristic
239	C₂³×C₄	C₂×#120	1	1	yes	characteristic
240	C₂³×C₄	C₂×#120	1	1	yes	characteristic
241	C₂³×C₄	C₂×#120	1	1	yes	characteristic
242	C₂×Q₁₆	#392	1	2	yes	—
243	C₂×D₈	#392	1	2	yes	—
244	C₂×M₁₆	C₂×#120	1	1	yes	characteristic
245	C₂×M₁₆	C₂×#121	1	1	yes	characteristic
246	C₂×M₁₆	C₂×#121	1	1	yes	characteristic
247	C₂×M₁₆	C₂×#127	1	1	yes	characteristic
248	C₂×M₁₆	#534	1	1	yes	characteristic
249	C₂×M₁₆	#534	1	1	yes	characteristic
250	C₂×M₁₆	#535	1	1	yes	characteristic
251	C₂×M₁₆	#535	1	1	yes	characteristic
252	C₂×M₁₆	D₄²	1	1	yes	characteristic
253	C₂×M₁₆	D₄²	1	1	yes	characteristic
254	C₂×M₁₆	D₄²	1	1	yes	characteristic
255	C₂×M₁₆	#546	1	1	yes	characteristic
256	C₂²×C₈	C₂×#120	1	1	yes	characteristic
257	C₂²×C₈	C₂×#120	1	1	yes	characteristic
258	C₂²×C₈	C₂×#120	1	1	yes	characteristic
259	C₂²×C₈	C₂×#120	1	1	yes	characteristic
260	C₂²×C₈	C₂×#120	1	1	yes	characteristic
261	C₂²×C₈	C₂×#121	1	1	yes	characteristic
262	C₂²×C₈	#534	1	1	yes	characteristic
263	C₂²×C₈	#534	1	1	yes	characteristic
264	C₂²×C₈	D₄²	1	1	yes	characteristic
265	C₂²×C₈	D₄²	1	1	yes	characteristic
266	C₂²×C₈	D₄²	1	1	yes	characteristic
267	C₂²×C₈	D₄²	1	1	yes	characteristic
268	C₂²×C₈	D₄²	1	1	yes	characteristic
269	C₂²×C₈	D₄²	1	1	yes	characteristic
270	C₂²×C₈	#546	1	1	yes	characteristic
271	C₂²×C₈	#546	1	1	yes	characteristic
272	C₂×C₂²⋊C₄	#450	1	1	yes	characteristic
273	C₂×C₂²⋊C₄	#450	1	1	yes	characteristic
274	C₂×C₂²⋊C₄	#450	1	1	yes	characteristic
275	C₂×C₂²⋊C₄	#450	1	1	yes	characteristic
276	C₂×C₄²	#450	1	1	yes	characteristic
277	C₂×C₄²	#450	1	1	yes	characteristic
278	#106	#392	1	2	yes	—
279	#106	#392	1	2	yes	—
280	C₂⁴	C₂×#450	1	1	yes	characteristic
281	C₂⁴	C₂×#450	1	1	yes	characteristic
282	C₂⁴	#3003	1	1	yes	characteristic
283	C₂×Q₈	#3264	1	1	yes	characteristic
284	C₂×Q₈	#3265	1	1	yes	characteristic
285	C₂×Q₈	#3265	1	1	yes	characteristic
286	C₂×Q₈	#3310	1	1	yes	characteristic
287	C₂×D₄	#3264	1	1	yes	characteristic
288	C₂×D₄	#3265	1	1	yes	characteristic
289	C₂×D₄	#3265	1	1	yes	characteristic
290	C₂×D₄	#3272	1	1	yes	characteristic
291	C₂×D₄	#3272	1	1	yes	characteristic
292	C₂×D₄	#3274	1	1	yes	characteristic
293	C₂×D₄	D₄×SD₁₆	1	1	yes	characteristic
294	C₂×D₄	D₄×SD₁₆	1	1	yes	characteristic
295	C₂×D₄	D₄×SD₁₆	1	1	yes	characteristic
296	C₂×D₄	#3295	1	1	yes	characteristic
297	C₂×D₄	#3310	1	1	yes	characteristic
298	C₂×D₄	#3324	1	1	yes	characteristic
299	C₂²×C₄	#2403	1	1	yes	characteristic
300	C₂²×C₄	#2403	1	1	yes	characteristic
301	C₂²×C₄	#2408	1	1	yes	characteristic
302	C₂²×C₄	#2410	1	1	yes	characteristic
303	C₂²×C₄	#2410	1	1	yes	characteristic
304	C₂²×C₄	#2433	1	1	yes	characteristic
305	C₂²×C₄	#2846	1	1	yes	characteristic
306	C₂²×C₄	C₂×#450	1	1	yes	characteristic
307	C₂²×C₄	#3003	1	1	yes	characteristic
308	C₂²×C₄	#3003	1	1	yes	characteristic
309	C₂²×C₄	#3009	1	1	yes	characteristic
310	C₂²×C₄	#3009	1	1	yes	characteristic
311	C₂²×C₄	#3009	1	1	yes	characteristic
312	C₂²×C₄	#3012	1	1	yes	characteristic
313	C₂²×C₄	#3012	1	1	yes	characteristic
314	C₂²×C₄	#3012	1	1	yes	characteristic
315	C₂×C₈	C₂×#392	1	1	yes	characteristic
316	C₂×C₈	#2403	1	1	yes	characteristic
317	C₂×C₈	#2403	1	1	yes	characteristic
318	C₂×C₈	#2408	1	1	yes	characteristic
319	C₂×C₈	#2410	1	1	yes	characteristic
320	C₂×C₈	#2410	1	1	yes	characteristic
321	C₂×C₈	#2433	1	1	yes	characteristic
322	C₂×C₈	#2613	1	1	yes	characteristic
323	C₂×C₈	#3025	1	1	yes	characteristic
324	C₂×C₈	#3025	1	1	yes	characteristic
325	C₂×C₈	#3028	1	1	yes	characteristic
326	C₂×C₈	#3028	1	1	yes	characteristic
327	C₂³	#23849	1	1	yes	characteristic
328	C₂³	#23860	1	1	yes	characteristic
329	C₂³	#24240	1	1	yes	characteristic
330	C₂³	#24432	1	1	yes	characteristic
331	C₂³	#24448	1	1	yes	characteristic
332	C₂³	#25753	1	1	yes	characteristic
333	C₂³	#32881	1	1	yes	characteristic
334	C₂×C₄	#14715	1	1	yes	characteristic
335	C₂×C₄	#23849	1	1	yes	characteristic
336	C₂×C₄	#23860	1	1	yes	characteristic
337	C₂×C₄	#24252	1	1	yes	characteristic
338	C₂×C₄	#24432	1	1	yes	characteristic
339	C₂×C₄	#24448	1	1	yes	characteristic
340	C₂×C₄	#25763	1	1	yes	characteristic
341	C₂×C₄	#32886	1	1	yes	characteristic
342	C₂×C₄	#32895	1	1	yes	characteristic
343	C₂×C₄	#32895	1	1	yes	characteristic
344	C₂×C₄	#32901	1	1	yes	characteristic
345	C₂×C₄	#32901	1	1	yes	characteristic
346	C₈	#23902	1	1	yes	characteristic
347	C₈	#23905	1	1	yes	characteristic
348	C₈	#24407	1	1	yes	characteristic
349	C₈	#24407	1	1	yes	characteristic
350	C₂²	#346546	1	1	yes	characteristic
351	C₂²	#346546	1	1	yes	characteristic
352	C₂²	#393915	1	1	yes	characteristic
353	C₄	#346578	1	1	yes	characteristic
354	C₄	#346578	1	1	yes	characteristic
355	C₄	#394069	1	1	yes	characteristic
356	C₄	#394110	1	1	yes	characteristic
357	C₂	#72231596	1	1	yes	characteristic
358	C₂	#72250407	1	1	yes	characteristic
359	C₂	#72250762	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²	#346546
commutator, Frattini, cosocle	C₂²×#131	C₂⁴
prime radical	#72257190	C₂
LCS	G ▷ C₂²×#131 ▷ C₂×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×#131 ◁ G
LECS	G ▷ C₂²×#131 ▷ C₂×C₄ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
2. C₂×#130296	C₂	semidirect
3. #72250955	C₂	semidirect
4. C₂×#486701	C₂	semidirect
5. #72250881	C₂	semidirect
6. #72250850	C₂	semidirect
7. #72250688	C₂	semidirect
8. #72250377	C₂	semidirect
9. #72250320	C₂	semidirect
10. C₂×#130854	C₂	semidirect
11. #72249883	C₂	semidirect
12. #72240706	C₂	semidirect
13. #72239959	C₂	semidirect
14. C₂×#500351	C₂	semidirect
15. #72237227	C₂	semidirect
20. C₂×#33404	C₂²	semidirect
23. C₂×#27691	C₂²	semidirect
31. C₂×#12981	C₂²	semidirect
32. #493921	C₂²	semidirect
33. C₂×#12874	C₂²	semidirect
34. C₂×#12874	C₂²	semidirect
35. C₂×#12873	C₂²	semidirect
37. C₂×#12805	C₂²	semidirect
43. C₂×#11483	C₂²	semidirect
44. #362876	C₂²	semidirect
45. #147021	C₂²	semidirect
46. #146445	C₂²	semidirect
47. #146410	C₂²	semidirect
48. #127629	C₂²	semidirect
49. #127629	C₂²	semidirect
50. #126958	C₂²	semidirect
67. #33659	D₄	semidirect
95. #13076	D₄	semidirect
96. #11867	D₄	semidirect

Maximal subgroups

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

subgroup	index
#72257190	2
C₂×#130296	2
#72250955	2
C₂×#486701	2
#72250881	2
#72250850	2
#72250688	2
#72250377	2
#72250320	2
C₂×#130854	2
#72249883	2
#72240706	2
#72239959	2
C₂×#500351	2
#72237227	2