Subgroups — #72314663

Order 2048.

At least 6916 conjugacy classes of subgroups; only the 662 normal subgroups are shown.

The subgroup lattice has 352 nodes (normal subgroups only) — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72314650	C₂	1	4	yes	maximal, complemented
2	#72314643	C₂	1	4	yes	maximal, complemented
3	#72314440	C₂	1	1	yes	maximal, characteristic, complemented
4	#72266864	C₂	1	1	yes	maximal, characteristic, complemented
5	#72266366	C₂	1	1	yes	maximal, characteristic, complemented
6	#72259125	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#144639	C₂	1	1	yes	maximal, characteristic, complemented
8	#72258225	C₂	1	4	yes	maximal, complemented
9	C₂×#139742	C₂	1	1	yes	maximal, characteristic, complemented
10	#72256043	C₂	1	1	yes	maximal, characteristic, complemented
11	#72255841	C₂	1	1	yes	maximal, characteristic, complemented
12	#72251471	C₂	1	1	yes	maximal, characteristic, complemented
13	#72237829	C₂	1	1	yes	maximal, characteristic, complemented
14	#72236631	C₂	1	1	yes	maximal, characteristic, complemented
15	#72235130	C₂	1	1	yes	maximal, characteristic, complemented
16	#72235130	C₂	1	1	yes	maximal, characteristic, complemented
17	C₂×#144364	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×#139743	C₂	1	1	yes	maximal, characteristic, complemented
19	#72216381	C₂	1	4	yes	maximal, complemented
20	#10586404	C₂²	1	1	yes	characteristic
21	#7266799	C₂²	1	4	yes	complemented
22	#7266798	C₂²	1	4	yes	complemented
23	C₂×#32873	C₂²	1	1	yes	characteristic, complemented
24	C₂×#23895	C₂²	1	1	yes	characteristic
25	C₂×#23895	C₂²	1	1	yes	characteristic
26	C₂×#23895	C₂²	1	1	yes	characteristic, complemented
27	#6437621	C₂²	1	1	yes	characteristic
28	#6437621	C₂²	1	1	yes	characteristic
29	C₂×#23897	C₂²	1	1	yes	characteristic
30	C₂×#23897	C₂²	1	1	yes	characteristic
31	C₂×#21776	C₂²	1	1	yes	characteristic, complemented
32	C₂×#21776	C₂²	1	1	yes	characteristic, complemented
33	#6374128	C₂²	1	1	yes	characteristic
34	#552670	C₂²	1	1	yes	characteristic
35	#511791	C₂²	1	4	yes	complemented
36	#511791	C₂²	1	4	yes	complemented
37	#511790	C₂²	1	4	yes	complemented
38	#511790	C₂²	1	4	yes	complemented
39	C₂×#12707	C₂²	1	1	yes	characteristic
40	C₂×#12707	C₂²	1	1	yes	characteristic
41	C₂×#12705	C₂²	1	1	yes	characteristic
42	C₂×#12705	C₂²	1	1	yes	characteristic
43	#493357	C₂²	1	1	yes	characteristic
44	#493357	C₂²	1	1	yes	characteristic
45	#187952	C₂²	1	2	yes	complemented
46	#187949	C₂²	1	2	yes	complemented
47	#187944	C₂²	1	1	yes	characteristic
48	#187944	C₂²	1	1	yes	characteristic
49	#187944	C₂²	1	1	yes	characteristic, complemented
50	#187943	C₂²	1	2	yes	complemented
51	#187940	C₂²	1	2	yes	complemented
52	C₂×#8534	C₂²	1	1	yes	characteristic
53	C₂×#8534	C₂²	1	1	yes	characteristic
54	C₂×#8534	C₂²	1	1	yes	characteristic, complemented
55	#186835	C₂²	1	1	yes	characteristic, complemented
56	C₂×#8453	C₂²	1	1	yes	characteristic, complemented
57	#144639	C₂²	1	4	yes	complemented
58	#144639	C₂²	1	4	yes	complemented
59	#144639	C₂²	1	4	yes	complemented
60	#144639	C₂²	1	4	yes	complemented
61	#144364	C₂²	1	4	yes	complemented
62	#144364	C₂²	1	4	yes	complemented
63	#144364	C₂²	1	4	yes	complemented
64	#144364	C₂²	1	4	yes	complemented
65	#139743	C₂²	1	4	yes	complemented
66	#139743	C₂²	1	4	yes	complemented
67	#139743	C₂²	1	4	yes	complemented
68	#139743	C₂²	1	4	yes	complemented
69	#139742	C₂²	1	4	yes	complemented
70	#139742	C₂²	1	4	yes	complemented
71	#139742	C₂²	1	4	yes	complemented
72	#139742	C₂²	1	4	yes	complemented
73	#139703	C₂²	1	2	yes	complemented
74	#139703	C₂²	1	2	yes	complemented
75	#139702	C₂²	1	2	yes	complemented
76	#139702	C₂²	1	2	yes	complemented
77	#139701	C₂²	1	2	yes	complemented
78	#139701	C₂²	1	2	yes	complemented
79	#139700	C₂²	1	2	yes	complemented
80	#139700	C₂²	1	2	yes	complemented
81	#135514	C₂²	1	4	yes	complemented
82	#135513	C₂²	1	4	yes	complemented
83	#128033	C₂²	1	1	yes	characteristic, complemented
84	C₂×#7304	C₂²	1	1	yes	characteristic, complemented
85	C₂×#7316	C₂²	1	1	yes	characteristic, complemented
86	C₂×#7316	C₂²	1	1	yes	characteristic, complemented
87	C₂×#7311	C₂²	1	1	yes	characteristic, complemented
88	C₂×#7310	C₂²	1	1	yes	characteristic, complemented
89	#128009	C₂²	1	1	yes	characteristic, complemented
90	C₂×#7307	C₂²	1	1	yes	characteristic, complemented
91	#62820	C₂³	1	2	yes	—
92	#62817	C₂³	1	2	yes	—
93	C₂×#3484	C₂³	1	1	yes	characteristic
94	C₂×#3484	C₂³	1	1	yes	characteristic
95	C₂×#3484	C₂³	1	1	yes	characteristic
96	C₂×#3484	C₂³	1	1	yes	characteristic
97	C₂²×#534	C₂³	1	1	yes	characteristic
98	C₂×#3026	D₄	1	2	yes	complemented
99	C₂×#3026	D₄	1	2	yes	complemented
100	#34171	D₄	1	2	yes	complemented
101	#32873	C₂³	1	4	yes	—
102	#23903	D₄	1	4	yes	complemented
103	#23903	D₄	1	4	yes	complemented
104	#23901	C₂³	1	2	yes	—
105	#23901	C₂³	1	2	yes	—
106	#23900	C₂³	1	2	yes	—
107	#23900	C₂³	1	2	yes	—
108	#23897	C₂³	1	4	yes	—
109	#23897	C₂³	1	4	yes	—
110	#23895	C₂³	1	4	yes	—
111	#23895	C₂³	1	4	yes	—
112	#23895	C₂³	1	4	yes	—
113	#21776	C₂³	1	4	yes	—
114	#21776	C₂³	1	4	yes	—
115	#21747	D₄	1	2	yes	complemented
116	#21747	C₂³	1	2	yes	—
117	#21746	D₄	1	2	yes	complemented
118	#21746	C₂³	1	2	yes	—
119	#20960	D₄	1	2	yes	complemented
120	#20960	D₄	1	2	yes	complemented
121	C₂×#1819	D₄	1	2	yes	complemented
122	C₂×#1783	C₂³	1	1	yes	characteristic
123	C₂×#1783	C₂³	1	1	yes	characteristic
124	C₂×#1781	C₂³	1	1	yes	characteristic
125	C₂×#1781	C₂³	1	1	yes	characteristic
126	C₂×#1781	C₂³	1	1	yes	characteristic
127	C₂×#1781	C₂³	1	1	yes	characteristic
128	C₂×#1781	C₂³	1	1	yes	characteristic
129	C₂×#1781	C₂³	1	1	yes	characteristic
130	#14658	C₂³	1	1	yes	characteristic
131	#14657	C₂³	1	1	yes	characteristic
132	#14335	C₂³	1	1	yes	characteristic
133	#14167	C₂³	1	1	yes	characteristic
134	#14134	C₂³	1	1	yes	characteristic
135	C₂×#1438	C₂³	1	1	yes	characteristic
136	#12707	C₂³	1	4	yes	—
137	#12707	C₂³	1	4	yes	—
138	#12705	C₂³	1	4	yes	—
139	#12705	C₂³	1	4	yes	—
140	#12688	C₂³	1	2	yes	—
141	#12688	C₂³	1	2	yes	—
142	#12687	C₂³	1	2	yes	—
143	#12687	C₂³	1	2	yes	—
144	#8534	C₂³	1	2	yes	—
145	#8534	C₂³	1	2	yes	—
146	#8534	C₂³	1	2	yes	—
147	#8534	C₂³	1	2	yes	—
148	#8534	C₂³	1	2	yes	—
149	#8534	C₂³	1	2	yes	—
150	#8534	C₂³	1	2	yes	—
151	#8534	C₂³	1	2	yes	—
152	#8534	C₂³	1	2	yes	—
153	#8534	C₂³	1	2	yes	—
154	#8534	C₂³	1	2	yes	—
155	#8534	C₂³	1	2	yes	—
156	#8453	C₂³	1	2	yes	—
157	#8453	C₂³	1	2	yes	—
158	#8453	C₂³	1	2	yes	—
159	#8453	C₂³	1	2	yes	—
160	#7316	C₂³	1	4	yes	—
161	#7316	C₂³	1	4	yes	—
162	#7311	C₂³	1	4	yes	—
163	#7310	C₂³	1	4	yes	—
164	#7307	C₂³	1	2	yes	—
165	#7307	C₂³	1	2	yes	—
166	#7307	C₂³	1	2	yes	—
167	#7307	C₂³	1	2	yes	—
168	#7304	C₂³	1	2	yes	—
169	#7304	C₂³	1	2	yes	—
170	#7304	C₂³	1	2	yes	—
171	#7304	C₂³	1	2	yes	—
172	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
173	C₂²×H(5,𝔽₂)	C₂×D₄	1	1	yes	characteristic
174	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
175	C₂²×H(5,𝔽₂)	#41	1	1	yes	characteristic, complemented
176	C₂⁴×D₄	C₂×D₄	1	1	yes	characteristic
177	C₂⁴×D₄	C₂⁴	1	1	yes	characteristic
178	#3484	C₂×D₄	1	2	yes	—
179	#3484	C₂×D₄	1	2	yes	—
180	#3484	#41	1	2	yes	complemented
181	#3484	#41	1	2	yes	complemented
182	#3484	C₂⁴	1	2	yes	—
183	#3484	C₂⁴	1	2	yes	—
184	#3484	C₂⁴	1	2	yes	—
185	#3484	C₂⁴	1	2	yes	—
186	C₂×#534	C₂×D₄	1	2	yes	—
187	C₂×#534	C₂×D₄	1	2	yes	—
188	C₂×#534	C₂×D₄	1	2	yes	—
189	C₂×#534	C₂×D₄	1	2	yes	—
190	C₂²×#123	C₂×D₄	1	1	yes	characteristic
191	C₂²×#123	C₂⁴	1	1	yes	characteristic
192	C₂²×#120	C₂×D₄	1	1	yes	characteristic
193	C₂²×#120	C₂⁴	1	1	yes	characteristic
194	C₂×#518	C₂×D₄	1	1	yes	characteristic
195	C₂×#518	C₂×D₄	1	1	yes	characteristic
196	C₂×#518	#41	1	1	yes	characteristic, complemented
197	C₂×#518	#41	1	1	yes	characteristic, complemented
198	C₂³×C₂²⋊C₄	C₂×D₄	1	1	yes	characteristic
199	C₂×#458	C₂×D₄	1	4	yes	complemented
200	C₂×#458	C₂×D₄	1	4	yes	complemented
201	C₂×B(4,𝔽₂)	C₂×D₄	1	4	yes	complemented
202	C₂×B(4,𝔽₂)	C₂×D₄	1	4	yes	complemented
203	C₂²×#99	C₂×D₄	1	2	yes	—
204	C₂²×#99	C₂×D₄	1	2	yes	—
205	#2280	C₂×D₄	1	4	yes	complemented
206	C₂×#379	C₂×D₄	1	2	yes	—
207	C₂×#379	C₂×D₄	1	2	yes	—
208	C₂×#379	C₂×D₄	1	4	yes	complemented
209	#1890	C₂×D₄	1	4	yes	complemented
210	#1890	C₂×D₄	1	4	yes	complemented
211	#1889	C₂×D₄	1	4	yes	complemented
212	#1889	C₂×D₄	1	4	yes	complemented
213	#1819	C₂×D₄	1	4	yes	complemented
214	#1819	C₂×D₄	1	4	yes	complemented
215	#1783	C₂⁴	1	2	yes	—
216	#1783	C₂⁴	1	2	yes	—
217	#1781	C₂×D₄	1	2	yes	—
218	#1781	C₂×D₄	1	2	yes	—
219	#1781	C₂×D₄	1	2	yes	—
220	#1781	C₂×D₄	1	2	yes	—
221	#1781	C₂⁴	1	2	yes	—
222	#1781	C₂⁴	1	2	yes	—
223	#1781	C₂⁴	1	2	yes	—
224	#1781	C₂⁴	1	2	yes	—
225	#1781	C₂⁴	1	2	yes	—
226	#1781	C₂⁴	1	2	yes	—
227	#1438	C₂⁴	1	1	yes	characteristic
228	#1438	C₂⁴	1	1	yes	characteristic
229	#1438	C₂⁴	1	1	yes	characteristic
230	#1438	C₂⁴	1	1	yes	characteristic
231	C₂⁶	C₂²×D₄	1	1	yes	characteristic
232	C₂⁶	C₂²×D₄	1	1	yes	characteristic
233	C₂⁶	H(5,𝔽₂)	1	1	yes	characteristic
234	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
235	C₂×H(5,𝔽₂)	C₂²×D₄	1	2	yes	—
236	C₂×H(5,𝔽₂)	C₂×#41	1	2	yes	—
237	C₂×H(5,𝔽₂)	C₂×#41	1	2	yes	—
238	C₂³×D₄	#120	1	2	yes	—
239	C₂³×D₄	#120	1	2	yes	—
240	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
241	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
242	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
243	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
244	C₂³×D₄	C₂²×D₄	1	1	yes	characteristic
245	C₂³×D₄	C₂×#41	1	1	yes	characteristic
246	C₂³×D₄	C₂×#41	1	1	yes	characteristic
247	C₂³×D₄	C₂×#41	1	1	yes	characteristic
248	C₂³×D₄	C₂×#41	1	1	yes	characteristic
249	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
250	C₂³×D₄	H(5,𝔽₂)	1	1	yes	characteristic
251	C₂³×D₄	C₂⁵	1	1	yes	characteristic
252	C₂⁴×C₄	C₂²×D₄	1	1	yes	characteristic
253	C₂⁴×C₄	H(5,𝔽₂)	1	1	yes	characteristic
254	C₂×#123	#120	1	2	yes	—
255	C₂×#123	#120	1	2	yes	—
256	C₂×#123	C₂²×D₄	1	2	yes	—
257	C₂×#123	C₂²×D₄	1	2	yes	—
258	C₂×#120	#120	1	2	yes	—
259	C₂×#120	#120	1	2	yes	—
260	C₂×#120	C₂²×D₄	1	2	yes	—
261	C₂×#120	C₂²×D₄	1	2	yes	—
262	#518	C₂²×D₄	1	2	yes	—
263	#518	C₂²×D₄	1	2	yes	—
264	#518	C₂×#41	1	2	yes	—
265	#518	C₂×#41	1	2	yes	—
266	C₂²×C₂²⋊C₄	#120	1	2	yes	—
267	C₂²×C₂²⋊C₄	#120	1	2	yes	—
268	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
269	C₂²×C₂²⋊C₄	C₂²×D₄	1	1	yes	characteristic
270	C₂×#99	C₂²×D₄	1	4	yes	—
271	C₂×#99	C₂²×D₄	1	4	yes	—
272	#379	C₂²×D₄	1	4	yes	—
273	#379	C₂²×D₄	1	4	yes	—
274	C₂⁵	C₂×#120	1	1	yes	characteristic
275	C₂⁵	C₂×#120	1	1	yes	characteristic
276	C₂⁵	C₂×#120	1	2	yes	—
277	C₂⁵	#525	1	1	yes	characteristic
278	C₂⁵	#525	1	1	yes	characteristic
279	C₂⁵	#535	1	1	yes	characteristic
280	C₂⁵	#535	1	1	yes	characteristic
281	C₂⁵	#535	1	1	yes	characteristic
282	C₂⁵	#546	1	1	yes	characteristic
283	C₂⁵	#546	1	1	yes	characteristic
284	C₂⁵	#546	1	1	yes	characteristic
285	C₂⁵	#546	1	1	yes	characteristic
286	C₂⁵	C₂³×D₄	1	1	yes	characteristic
287	C₂⁵	C₂×H(5,𝔽₂)	1	1	yes	characteristic
288	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
289	C₂²×D₄	B(4,𝔽₂)	1	4	yes	—
290	C₂²×D₄	C₂×#120	1	1	yes	characteristic
291	C₂²×D₄	C₂×#120	1	1	yes	characteristic
292	C₂²×D₄	#525	1	1	yes	characteristic
293	C₂²×D₄	#525	1	1	yes	characteristic
294	C₂²×D₄	#546	1	1	yes	characteristic
295	C₂²×D₄	#546	1	1	yes	characteristic
296	C₂²×D₄	#546	1	1	yes	characteristic
297	C₂²×D₄	#546	1	1	yes	characteristic
298	C₂²×D₄	#546	1	1	yes	characteristic
299	C₂²×D₄	#546	1	1	yes	characteristic
300	C₂²×D₄	#546	1	1	yes	characteristic
301	C₂²×D₄	#546	1	1	yes	characteristic
302	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
303	C₂²×D₄	C₂³×D₄	1	1	yes	characteristic
304	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
305	C₂²×D₄	C₂²×#41	1	1	yes	characteristic
306	C₂³×C₄	C₂×#120	1	2	yes	—
307	C₂³×C₄	#535	1	1	yes	characteristic
308	C₂³×C₄	#546	1	1	yes	characteristic
309	C₂³×C₄	#546	1	1	yes	characteristic
310	C₂³×C₄	#546	1	1	yes	characteristic
311	C₂³×C₄	#546	1	1	yes	characteristic
312	C₂³×C₄	C₂×H(5,𝔽₂)	1	1	yes	characteristic
313	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
314	C₂×C₂²⋊C₄	C₂×#120	1	2	yes	—
315	C₂⁴	#2404	1	1	yes	characteristic
316	C₂⁴	#2404	1	1	yes	characteristic
317	C₂⁴	#2404	1	1	yes	characteristic
318	C₂⁴	#2404	1	1	yes	characteristic
319	C₂⁴	#2404	1	1	yes	characteristic
320	C₂⁴	#2404	1	1	yes	characteristic
321	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
322	C₂⁴	C₂×B(4,𝔽₂)	1	2	yes	—
323	C₂⁴	C₂×B(4,𝔽₂)	1	4	yes	—
324	C₂⁴	C₂²×#120	1	1	yes	characteristic
325	C₂⁴	C₂×#525	1	1	yes	characteristic
326	C₂⁴	C₂×#535	1	1	yes	characteristic
327	C₂⁴	C₂×#546	1	1	yes	characteristic
328	C₂⁴	C₂×#546	1	1	yes	characteristic
329	C₂²×C₄	#2404	1	1	yes	characteristic
330	C₂²×C₄	#2404	1	1	yes	characteristic
331	C₂²×C₄	C₂×B(4,𝔽₂)	1	4	yes	—
332	C₂²×C₄	C₂×#546	1	1	yes	characteristic
333	C₂²×C₄	C₂×#546	1	1	yes	characteristic
334	C₂³	#23984	1	2	yes	—
335	C₂³	#23984	1	1	yes	characteristic
336	C₂³	#23984	1	1	yes	characteristic
337	C₂³	#23996	1	1	yes	characteristic
338	C₂³	#23996	1	1	yes	characteristic
339	C₂³	#23996	1	1	yes	characteristic
340	C₂³	#23996	1	1	yes	characteristic
341	C₂³	C₂×#2404	1	1	yes	characteristic
342	C₂³	C₂²×B(4,𝔽₂)	1	2	yes	—
343	C₂²	#251827	1	1	yes	characteristic
344	C₂²	#251827	1	1	yes	characteristic
345	C₂²	#251827	1	1	yes	characteristic
346	C₂²	#251827	1	1	yes	characteristic
347	C₂²	C₂×#23996	1	1	yes	characteristic
348	C₂²	C₂×#23996	1	1	yes	characteristic
349	C₂²	C₂×#23984	1	1	yes	characteristic
350	C₂	C₂×#251827	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂	C₂×#251827
commutator, Frattini, cosocle	C₂³×D₄	C₂⁵
LCS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂ ◁ C₂⁴ ◁ C₂⁴×D₄ ◁ G
LECS	G ▷ C₂³×D₄ ▷ C₂³ ▷ C₂ ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #72314650	C₂	semidirect
2. #72314643	C₂	semidirect
3. #72314440	C₂	semidirect
4. #72266864	C₂	semidirect
5. #72266366	C₂	semidirect
6. #72259125	C₂	semidirect
7. C₂×#144639	C₂	semidirect
8. #72258225	C₂	semidirect
9. C₂×#139742	C₂	semidirect
10. #72256043	C₂	semidirect
11. #72255841	C₂	semidirect
12. #72251471	C₂	semidirect
13. #72237829	C₂	semidirect
14. #72236631	C₂	semidirect
15. #72235130	C₂	semidirect
16. #72235130	C₂	semidirect
17. C₂×#144364	C₂	semidirect
18. C₂×#139743	C₂	semidirect
19. #72216381	C₂	semidirect
21. #7266799	C₂²	semidirect
22. #7266798	C₂²	semidirect
23. C₂×#32873	C₂²	semidirect
26. C₂×#23895	C₂²	semidirect
31. C₂×#21776	C₂²	semidirect
32. C₂×#21776	C₂²	semidirect
35. #511791	C₂²	semidirect
36. #511791	C₂²	semidirect
37. #511790	C₂²	semidirect
38. #511790	C₂²	semidirect
45. #187952	C₂²	semidirect
46. #187949	C₂²	semidirect
49. #187944	C₂²	semidirect
50. #187943	C₂²	semidirect
51. #187940	C₂²	semidirect
54. C₂×#8534	C₂²	semidirect
55. #186835	C₂²	semidirect
56. C₂×#8453	C₂²	semidirect
57. #144639	C₂²	semidirect
58. #144639	C₂²	semidirect
59. #144639	C₂²	semidirect
60. #144639	C₂²	semidirect
61. #144364	C₂²	semidirect
62. #144364	C₂²	semidirect
63. #144364	C₂²	semidirect
64. #144364	C₂²	semidirect
65. #139743	C₂²	semidirect
66. #139743	C₂²	semidirect
67. #139743	C₂²	semidirect
68. #139743	C₂²	semidirect
69. #139742	C₂²	semidirect
70. #139742	C₂²	semidirect
71. #139742	C₂²	semidirect
72. #139742	C₂²	semidirect
73. #139703	C₂²	semidirect
74. #139703	C₂²	semidirect
75. #139702	C₂²	semidirect
76. #139702	C₂²	semidirect
77. #139701	C₂²	semidirect
78. #139701	C₂²	semidirect
79. #139700	C₂²	semidirect
80. #139700	C₂²	semidirect
81. #135514	C₂²	semidirect
82. #135513	C₂²	semidirect
83. #128033	C₂²	semidirect
84. C₂×#7304	C₂²	semidirect
85. C₂×#7316	C₂²	semidirect
86. C₂×#7316	C₂²	semidirect
87. C₂×#7311	C₂²	semidirect
88. C₂×#7310	C₂²	semidirect
89. #128009	C₂²	semidirect
90. C₂×#7307	C₂²	semidirect
98. C₂×#3026	D₄	semidirect
99. C₂×#3026	D₄	semidirect
100. #34171	D₄	semidirect
102. #23903	D₄	semidirect
103. #23903	D₄	semidirect
115. #21747	D₄	semidirect
117. #21746	D₄	semidirect
119. #20960	D₄	semidirect
120. #20960	D₄	semidirect
121. C₂×#1819	D₄	semidirect
174. C₂²×H(5,𝔽₂)	#41	semidirect
175. C₂²×H(5,𝔽₂)	#41	semidirect
180. #3484	#41	semidirect
181. #3484	#41	semidirect
196. C₂×#518	#41	semidirect
197. C₂×#518	#41	semidirect
199. C₂×#458	C₂×D₄	semidirect
200. C₂×#458	C₂×D₄	semidirect
201. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
202. C₂×B(4,𝔽₂)	C₂×D₄	semidirect
205. #2280	C₂×D₄	semidirect
208. C₂×#379	C₂×D₄	semidirect
209. #1890	C₂×D₄	semidirect
210. #1890	C₂×D₄	semidirect
211. #1889	C₂×D₄	semidirect
212. #1889	C₂×D₄	semidirect
213. #1819	C₂×D₄	semidirect
214. #1819	C₂×D₄	semidirect

Maximal subgroups

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

subgroup	index
#72314650	2
#72314643	2
#72314440	2
#72266864	2
#72266366	2
#72259125	2
C₂×#144639	2
#72258225	2
C₂×#139742	2
#72256043	2
#72255841	2
#72251471	2
#72237829	2
#72236631	2
#72235130	2
C₂×#144364	2
C₂×#139743	2
#72216381	2