Subgroups — C₂²×#17989390 #33999794

Order 18688.

11462 conjugacy classes of subgroups.

The subgroup lattice has 382 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14556637	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#17989390	C₂	1	48	yes	maximal, direct product factor
3	C₂²×#14556617	C₂	1	3	yes	maximal, complemented
4	C₂²×#14556616	C₂	1	3	yes	maximal, complemented
5	C₂²×#14556611	C₂	1	3	yes	maximal, complemented
6	C₂³×#11924013	C₂	1	3	yes	maximal, complemented
7	C₂²×#14556598	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂²×H(5,𝔽₂)×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14556637	—	2	12	no	—
10	C₂×#14556637	C₂²	1	24	yes	complemented
11	C₂²×#11924029	—	2	1	no	—
12	C₂²×#11924028	C₂²	1	3	yes	complemented
13	C₂³×D₂₉₂	C₂²	1	3	yes	complemented
14	C₂²×D₄×D₇₃	—	2	3	no	—
15	#17989390	C₂²	1	256	yes	direct product factor
16	C₂×#14556617	C₂²	1	72	yes	complemented
17	C₂×#14556616	C₂²	1	72	yes	complemented
18	C₂×#14556611	C₂²	1	72	yes	complemented
19	C₂²×#11924018	C₂²	1	1	yes	characteristic, complemented
20	C₂²×#11924016	C₂²	1	3	yes	complemented
21	C₂²×#11924015	C₂²	1	3	yes	complemented
22	C₂²×#11924013	C₂²	1	3	yes	complemented
23	C₂²×#11924013	C₂²	1	6	yes	complemented
24	C₂²×#11924013	C₂²	1	72	yes	complemented
25	C₂×#14556598	C₂²	1	24	yes	complemented
26	C₂²×#11924012	C₂²	1	3	yes	complemented
27	C₂³×#10596831	C₂²	1	3	yes	complemented
28	C₂×H(5,𝔽₂)×C₇₃	—	2	12	no	—
29	C₂×H(5,𝔽₂)×C₇₃	C₂²	1	24	yes	complemented
30	C₂²×#41×C₇₃	—	2	1	no	—
31	C₂²×#41×C₇₃	C₂²	1	1	yes	characteristic
32	C₂²×#41×C₇₃	C₂²	1	3	yes	complemented
33	C₂³×D₄×C₇₃	—	2	3	no	—
34	C₂³×D₄×C₇₃	C₂²	1	3	yes	complemented
35	C₂⁴×D₇₃	—	2	3	no	—
36	#14556637	—	2	96	no	—
37	#14556637	C₂³	1	64	yes	complemented
38	C₂×#11924029	—	2	24	no	—
39	C₂×#11924028	—	2	18	no	—
40	C₂×#11924028	C₂³	1	36	yes	complemented
41	C₂²×Dic₁₄₆	C₂³	1	1	yes	characteristic
42	C₂²×D₂₉₂	—	2	3	no	—
43	C₂²×D₂₉₂	—	2	18	no	—
44	C₂²×D₂₉₂	C₂³	1	3	yes	—
45	C₂²×D₂₉₂	C₂³	1	36	yes	complemented
46	C₂²×C₂²⋊D₇₃	—	2	3	no	—
47	C₂×D₄×D₇₃	—	2	72	no	—
48	C₂²×C₄×D₇₃	—	2	3	no	—
49	#14556617	C₂³	1	192	yes	complemented
50	#14556616	C₂³	1	192	yes	complemented
51	#14556611	C₂³	1	192	yes	complemented
52	C₂×#11924018	C₂³	1	12	yes	complemented
53	C₂×#11924016	C₂³	1	36	yes	complemented
54	C₂×#11924015	C₂³	1	36	yes	complemented
55	C₂×#11924013	C₂³	1	36	yes	complemented
56	C₂×#11924013	C₂³	1	72	yes	complemented
57	C₂×#11924013	C₂³	1	192	yes	complemented
58	#14556598	C₂³	1	64	yes	complemented
59	C₂×#11924012	C₂³	1	36	yes	complemented
60	C₂²×#10596831	C₂³	1	1	yes	characteristic
61	C₂²×#10596831	C₂³	1	3	yes	—
62	C₂²×#10596831	C₂³	1	36	yes	complemented
63	C₂⁵×C₇₃	—	2	3	no	—
64	H(5,𝔽₂)×C₇₃	—	2	96	no	—
65	H(5,𝔽₂)×C₇₃	C₂³	1	64	yes	complemented
66	C₂×#41×C₇₃	—	2	24	no	—
67	C₂×#41×C₇₃	—	2	18	no	—
68	C₂×#41×C₇₃	D₄	1	12	yes	—
69	C₂×#41×C₇₃	C₂³	1	12	yes	—
70	C₂×#41×C₇₃	C₂³	1	36	yes	complemented
71	C₂²×Q₈×C₇₃	D₄	1	1	yes	characteristic
72	C₂²×Q₈×C₇₃	C₂³	1	1	yes	characteristic
73	C₂²×D₄×C₇₃	—	2	3	no	—
74	C₂²×D₄×C₇₃	—	2	72	no	—
75	C₂²×D₄×C₇₃	—	2	3	no	—
76	C₂²×D₄×C₇₃	—	2	18	no	—
77	C₂²×D₄×C₇₃	D₄	1	3	yes	—
78	C₂²×D₄×C₇₃	C₂³	1	3	yes	—
79	C₂²×D₄×C₇₃	C₂³	1	36	yes	complemented
80	C₂³×C₄×C₇₃	—	2	3	no	—
81	C₂³×C₄×C₇₃	C₂³	1	3	yes	—
82	C₂³×D₇₃	—	2	3	no	—
83	C₂³×D₇₃	—	2	36	no	—
84	C₂³×D₇₃	—	8	12	no	—
85	#11924029	—	2	64	no	—
86	#11924028	—	2	72	no	—
87	#11924028	C₂⁴	1	48	yes	complemented
88	C₂×Dic₁₄₆	—	2	3	no	—
89	C₂×Dic₁₄₆	C₂⁴	1	6	yes	—
90	C₂×D₂₉₂	—	2	36	no	—
91	C₂×D₂₉₂	—	2	9	no	—
92	C₂×D₂₉₂	—	2	72	no	—
93	C₂×D₂₉₂	C₂⁴	1	18	yes	—
94	C₂×D₂₉₂	C₂⁴	1	48	yes	complemented
95	C₂×C₂²⋊D₇₃	—	2	36	no	—
96	D₄×D₇₃	—	2	192	no	—
97	C₂²×Dic₇₃	—	2	1	no	—
98	C₂×C₄×D₇₃	—	2	36	no	—
99	#11924018	C₂⁴	1	16	yes	complemented
100	#11924016	C₂⁴	1	48	yes	complemented
101	#11924015	C₂⁴	1	48	yes	complemented
102	#11924013	C₂⁴	1	48	yes	complemented
103	#11924013	C₂⁴	1	96	yes	complemented
104	#11924012	C₂⁴	1	48	yes	complemented
105	C₂×#10596831	C₂⁴	1	6	yes	—
106	C₂×#10596831	C₂⁴	1	18	yes	—
107	C₂×#10596831	C₂⁴	1	48	yes	complemented
108	C₂⁴×C₇₃	—	2	3	no	—
109	C₂⁴×C₇₃	—	2	36	no	—
110	C₂⁴×C₇₃	—	8	12	no	—
111	C₂⁴×C₇₃	C₂×D₄	1	3	yes	—
112	#41×C₇₃	—	2	64	no	—
113	#41×C₇₃	—	2	72	no	—
114	#41×C₇₃	C₂×D₄	1	48	yes	—
115	#41×C₇₃	C₂⁴	1	16	yes	—
116	#41×C₇₃	C₂⁴	1	48	yes	complemented
117	C₂×Q₈×C₇₃	—	2	3	no	—
118	C₂×Q₈×C₇₃	C₂×D₄	1	12	yes	—
119	C₂×Q₈×C₇₃	C₂⁴	1	6	yes	—
120	C₂×D₄×C₇₃	—	2	36	no	—
121	C₂×D₄×C₇₃	—	2	192	no	—
122	C₂×D₄×C₇₃	—	2	9	no	—
123	C₂×D₄×C₇₃	—	2	36	no	—
124	C₂×D₄×C₇₃	—	2	72	no	—
125	C₂×D₄×C₇₃	C₂×D₄	1	36	yes	—
126	C₂×D₄×C₇₃	C₂⁴	1	18	yes	—
127	C₂×D₄×C₇₃	C₂⁴	1	48	yes	complemented
128	C₂²×C₄×C₇₃	—	2	1	no	—
129	C₂²×C₄×C₇₃	—	2	36	no	—
130	C₂²×C₄×C₇₃	C₂×D₄	1	3	yes	—
131	C₂²×C₄×C₇₃	C₂×D₄	1	18	yes	—
132	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
133	C₂²×C₄×C₇₃	C₂⁴	1	18	yes	—
134	C₂³×C₇₃	—	2	12	no	—
135	C₂³×C₇₃	—	2	18	no	—
136	C₂³×C₇₃	—	2	48	no	—
137	C₂³×C₇₃	—	4	12	no	—
138	C₂³×C₇₃	—	8	72	no	—
139	C₂³×C₇₃	C₂²×D₄	1	18	yes	—
140	C₂³×C₇₃	C₂²×D₄	1	1	yes	characteristic
141	C₂²×D₇₃	—	2	18	no	—
142	C₂²×D₇₃	—	2	48	no	—
143	C₂²×D₇₃	—	4	12	no	—
144	C₂²×D₇₃	—	8	72	no	—
145	Q₈×C₇₃	—	2	6	no	—
146	Q₈×C₇₃	C₂²×D₄	1	16	yes	—
147	Q₈×C₇₃	C₂⁵	1	4	yes	—
148	D₄×C₇₃	—	2	48	no	—
149	D₄×C₇₃	—	2	18	no	—
150	D₄×C₇₃	—	2	48	no	—
151	D₄×C₇₃	C₂²×D₄	1	48	yes	—
152	D₄×C₇₃	C₂⁵	1	12	yes	—
153	C₂×C₄×C₇₃	—	2	6	no	—
154	C₂×C₄×C₇₃	—	2	48	no	—
155	C₂×C₄×C₇₃	C₂²×D₄	1	18	yes	—
156	C₂×C₄×C₇₃	C₂²×D₄	1	3	yes	—
157	C₂×C₄×C₇₃	C₂²×D₄	1	36	yes	—
158	C₂×C₄×C₇₃	C₂⁵	1	3	yes	—
159	C₂×C₄×C₇₃	C₂⁵	1	12	yes	—
160	C₂²⋊D₇₃	—	2	48	no	—
161	C₂×Dic₇₃	—	2	6	no	—
162	D₂₉₂	—	2	48	no	—
163	D₂₉₂	—	2	18	no	—
164	D₂₉₂	C₂⁵	1	12	yes	—
165	C₄×D₇₃	—	2	48	no	—
166	Dic₁₄₆	—	2	6	no	—
167	Dic₁₄₆	C₂⁵	1	4	yes	—
168	#10596831	C₂⁵	1	4	yes	—
169	#10596831	C₂⁵	1	12	yes	—
170	C₂²×C₇₃	—	2	36	no	—
171	C₂²×C₇₃	—	2	12	no	—
172	C₂²×C₇₃	—	4	36	no	—
173	C₂²×C₇₃	—	8	48	no	—
174	C₂²×C₇₃	#576	1	4	yes	complemented
175	C₂²×C₇₃	C₂³×D₄	1	12	yes	—
176	C₂²×C₇₃	C₂³×D₄	1	3	yes	—
177	C₂×D₇₃	—	2	12	no	—
178	C₂×D₇₃	—	4	36	no	—
179	C₂×D₇₃	—	8	48	no	—
180	C₄×C₇₃	—	2	4	no	—
181	C₄×C₇₃	C₂³×D₄	1	3	yes	—
182	C₄×C₇₃	C₂³×D₄	1	12	yes	—
183	C₄×C₇₃	C₂⁶	1	1	yes	characteristic
184	Dic₇₃	—	2	4	no	—
185	C₂²×#576	—	73	1	no	maximal, Sylow
186	C₂×C₇₃	—	2	12	no	—
187	C₂×C₇₃	—	4	12	no	—
188	C₂×C₇₃	C₂×#576	1	6	yes	complemented
189	C₂×C₇₃	C₂⁴×D₄	1	1	yes	characteristic
190	D₇₃	—	4	12	no	—
191	C₂²×H(5,𝔽₂)	—	73	1	no	—
192	C₂²×H(5,𝔽₂)	D₇₃	1	1	yes	characteristic, complemented
193	C₂×#576	—	73	48	no	—
194	C₂²×AGL(1,ℤ/8)	—	73	3	no	—
195	C₂²×AGL(1,ℤ/8)	—	73	3	no	—
196	C₂²×#135	—	73	3	no	—
197	C₂³×D₈	—	73	3	no	—
198	C₂²×#131	—	73	1	no	—
199	C₇₃	C₂²×#576	1	1	yes	characteristic, complemented, Sylow
200	C₂×H(5,𝔽₂)	—	2	12	no	—
201	C₂×H(5,𝔽₂)	—	73	24	no	—
202	C₂×H(5,𝔽₂)	—	146	12	no	—
203	C₂×H(5,𝔽₂)	C₂×D₇₃	1	24	yes	complemented
204	C₂²×#41	—	2	1	no	—
205	C₂²×#41	—	73	3	no	—
206	C₂²×#41	—	146	1	no	—
207	C₂²×#41	C₂×D₇₃	1	1	yes	characteristic
208	C₂²×#41	C₂×D₇₃	1	3	yes	complemented
209	C₂³×D₄	—	2	3	no	—
210	C₂³×D₄	—	73	3	no	—
211	C₂³×D₄	—	146	3	no	—
212	C₂³×D₄	C₂×D₇₃	1	3	yes	complemented
213	#576	—	73	256	no	—
214	C₂×AGL(1,ℤ/8)	—	73	72	no	—
215	C₂×AGL(1,ℤ/8)	—	73	72	no	—
216	C₂×#135	—	73	72	no	—
217	C₂²×Q₁₆	—	73	1	no	—
218	C₂²×SD₁₆	—	73	3	no	—
219	C₂²×SD₁₆	—	73	3	no	—
220	C₂²×D₈	—	73	3	no	—
221	C₂²×D₈	—	73	6	no	—
222	C₂²×D₈	—	73	72	no	—
223	C₂×#131	—	73	24	no	—
224	C₂²×M₁₆	—	73	3	no	—
225	C₂³×C₈	—	73	3	no	—
226	C₂⁵	—	2	3	no	—
227	C₂⁵	—	146	3	no	—
228	H(5,𝔽₂)	—	2	96	no	—
229	H(5,𝔽₂)	—	73	64	no	—
230	H(5,𝔽₂)	—	146	96	no	—
231	H(5,𝔽₂)	C₂²×D₇₃	1	64	yes	complemented
232	C₂×#41	—	2	24	no	—
233	C₂×#41	—	2	18	no	—
234	C₂×#41	—	73	36	no	—
235	C₂×#41	—	146	24	no	—
236	C₂×#41	—	146	18	no	—
237	C₂×#41	C₂²⋊D₇₃	1	12	yes	—
238	C₂×#41	C₂²×D₇₃	1	12	yes	—
239	C₂×#41	C₂²×D₇₃	1	36	yes	complemented
240	C₂²×Q₈	—	73	1	no	—
241	C₂²×Q₈	C₂²⋊D₇₃	1	1	yes	characteristic
242	C₂²×Q₈	C₂²×D₇₃	1	1	yes	characteristic
243	C₂²×D₄	—	2	3	no	—
244	C₂²×D₄	—	2	72	no	—
245	C₂²×D₄	—	2	3	no	—
246	C₂²×D₄	—	2	18	no	—
247	C₂²×D₄	—	73	3	no	—
248	C₂²×D₄	—	73	36	no	—
249	C₂²×D₄	—	146	3	no	—
250	C₂²×D₄	—	146	72	no	—
251	C₂²×D₄	—	146	3	no	—
252	C₂²×D₄	—	146	18	no	—
253	C₂²×D₄	C₂²⋊D₇₃	1	3	yes	—
254	C₂²×D₄	C₂²×D₇₃	1	3	yes	—
255	C₂²×D₄	C₂²×D₇₃	1	36	yes	complemented
256	C₂³×C₄	—	2	3	no	—
257	C₂³×C₄	—	146	3	no	—
258	C₂³×C₄	C₂²×D₇₃	1	3	yes	—
259	AGL(1,ℤ/8)	—	73	192	no	—
260	AGL(1,ℤ/8)	—	73	192	no	—
261	#135	—	73	192	no	—
262	C₂×Q₁₆	—	73	12	no	—
263	C₂×SD₁₆	—	73	36	no	—
264	C₂×SD₁₆	—	73	36	no	—
265	C₂×D₈	—	73	36	no	—
266	C₂×D₈	—	73	72	no	—
267	C₂×D₈	—	73	192	no	—
268	#131	—	73	64	no	—
269	C₂×M₁₆	—	73	36	no	—
270	C₂²×C₈	—	73	1	no	—
271	C₂²×C₈	—	73	3	no	—
272	C₂²×C₈	—	73	36	no	—
273	C₂⁴	—	2	3	no	—
274	C₂⁴	—	2	36	no	—
275	C₂⁴	—	8	12	no	—
276	C₂⁴	—	584	12	no	—
277	C₂⁴	—	146	3	no	—
278	C₂⁴	—	146	36	no	—
279	C₂⁴	C₂×C₂²⋊D₇₃	1	3	yes	—
280	#41	—	2	64	no	—
281	#41	—	2	72	no	—
282	#41	—	73	48	no	—
283	#41	—	146	64	no	—
284	#41	—	146	72	no	—
285	#41	C₂×C₂²⋊D₇₃	1	48	yes	—
286	#41	C₂³×D₇₃	1	16	yes	—
287	#41	C₂³×D₇₃	1	48	yes	complemented
288	C₂×Q₈	—	2	3	no	—
289	C₂×Q₈	—	73	6	no	—
290	C₂×Q₈	—	146	3	no	—
291	C₂×Q₈	C₂×C₂²⋊D₇₃	1	12	yes	—
292	C₂×Q₈	C₂³×D₇₃	1	6	yes	—
293	C₂×D₄	—	2	36	no	—
294	C₂×D₄	—	2	192	no	—
295	C₂×D₄	—	2	9	no	—
296	C₂×D₄	—	2	36	no	—
297	C₂×D₄	—	2	72	no	—
298	C₂×D₄	—	73	18	no	—
299	C₂×D₄	—	73	48	no	—
300	C₂×D₄	—	146	36	no	—
301	C₂×D₄	—	146	192	no	—
302	C₂×D₄	—	146	36	no	—
303	C₂×D₄	—	146	9	no	—
304	C₂×D₄	—	146	72	no	—
305	C₂×D₄	C₂×C₂²⋊D₇₃	1	36	yes	—
306	C₂×D₄	C₂³×D₇₃	1	18	yes	—
307	C₂×D₄	C₂³×D₇₃	1	48	yes	complemented
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	2	36	no	—
310	C₂²×C₄	—	146	1	no	—
311	C₂²×C₄	—	146	36	no	—
312	C₂²×C₄	C₂×C₂²⋊D₇₃	1	18	yes	—
313	C₂²×C₄	C₂×C₂²⋊D₇₃	1	3	yes	—
314	C₂²×C₄	C₂³×D₇₃	1	18	yes	—
315	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
316	Q₁₆	—	73	16	no	—
317	SD₁₆	—	73	48	no	—
318	SD₁₆	—	73	48	no	—
319	D₈	—	73	48	no	—
320	D₈	—	73	96	no	—
321	M₁₆	—	73	48	no	—
322	C₂×C₈	—	73	6	no	—
323	C₂×C₈	—	73	18	no	—
324	C₂×C₈	—	73	48	no	—
325	C₂³	—	2	12	no	—
326	C₂³	—	2	18	no	—
327	C₂³	—	2	48	no	—
328	C₂³	—	4	12	no	—
329	C₂³	—	8	72	no	—
330	C₂³	—	292	12	no	—
331	C₂³	—	584	72	no	—
332	C₂³	—	146	18	no	—
333	C₂³	—	146	48	no	—
334	C₂³	C₂²×C₂²⋊D₇₃	1	18	yes	—
335	C₂³	C₂²×C₂²⋊D₇₃	1	1	yes	characteristic
336	Q₈	—	2	6	no	—
337	Q₈	—	73	4	no	—
338	Q₈	—	146	6	no	—
339	Q₈	C₂²×C₂²⋊D₇₃	1	16	yes	—
340	Q₈	C₂⁴×D₇₃	1	4	yes	—
341	D₄	—	2	48	no	—
342	D₄	—	2	18	no	—
343	D₄	—	2	48	no	—
344	D₄	—	73	12	no	—
345	D₄	—	146	48	no	—
346	D₄	—	146	48	no	—
347	D₄	—	146	18	no	—
348	D₄	C₂²×C₂²⋊D₇₃	1	48	yes	—
349	D₄	C₂⁴×D₇₃	1	12	yes	—
350	C₂×C₄	—	2	6	no	—
351	C₂×C₄	—	2	48	no	—
352	C₂×C₄	—	146	6	no	—
353	C₂×C₄	—	146	48	no	—
354	C₂×C₄	C₂²×C₂²⋊D₇₃	1	18	yes	—
355	C₂×C₄	C₂²×C₂²⋊D₇₃	1	3	yes	—
356	C₂×C₄	C₂²×C₂²⋊D₇₃	1	36	yes	—
357	C₂×C₄	C₂⁴×D₇₃	1	3	yes	—
358	C₂×C₄	C₂⁴×D₇₃	1	12	yes	—
359	C₈	—	73	4	no	—
360	C₈	—	73	12	no	—
361	C₂²	—	2	36	no	—
362	C₂²	—	2	12	no	—
363	C₂²	—	4	36	no	—
364	C₂²	—	8	48	no	—
365	C₂²	—	292	36	no	—
366	C₂²	—	584	48	no	—
367	C₂²	—	146	12	no	—
368	C₂²	#17989390	1	4	yes	direct product factor
369	C₂²	C₂³×C₂²⋊D₇₃	1	12	yes	—
370	C₂²	C₂³×C₂²⋊D₇₃	1	3	yes	—
371	C₄	—	2	4	no	—
372	C₄	—	146	4	no	—
373	C₄	C₂³×C₂²⋊D₇₃	1	12	yes	—
374	C₄	C₂³×C₂²⋊D₇₃	1	3	yes	—
375	C₄	C₂⁵×D₇₃	1	1	yes	characteristic
376	C₂	—	2	12	no	—
377	C₂	—	4	12	no	—
378	C₂	—	292	12	no	—
379	C₂	C₂×#17989390	1	6	yes	direct product factor
380	C₂	C₂⁴×C₂²⋊D₇₃	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	C₂²×C₂²⋊D₇₃
commutator, cosocle	C₄×C₇₃	C₂⁶
Frattini	C₄	C₂⁵×D₇₃
Fitting	C₂²×H(5,𝔽₂)×C₇₃	C₂
socle	C₂³×C₇₃	C₂²×D₄
hypercenter	C₂²×H(5,𝔽₂)	D₇₃
hypocenter	C₇₃	C₂²×#576
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂³ ◁ C₂²×#41 ◁ C₂²×H(5,𝔽₂)

Complements

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

N	H ≅ G/N	type
1. C₂²×#14556637	C₂	semidirect
2. C₂×#17989390	C₂	direct (N × H)
3. C₂²×#14556617	C₂	semidirect
4. C₂²×#14556616	C₂	semidirect
5. C₂²×#14556611	C₂	semidirect
6. C₂³×#11924013	C₂	semidirect
7. C₂²×#14556598	C₂	semidirect
8. C₂²×H(5,𝔽₂)×C₇₃	C₂	semidirect
10. C₂×#14556637	C₂²	semidirect
12. C₂²×#11924028	C₂²	semidirect
13. C₂³×D₂₉₂	C₂²	semidirect
15. #17989390	C₂²	direct (N × H)
16. C₂×#14556617	C₂²	semidirect
17. C₂×#14556616	C₂²	semidirect
18. C₂×#14556611	C₂²	semidirect
19. C₂²×#11924018	C₂²	semidirect
20. C₂²×#11924016	C₂²	semidirect
21. C₂²×#11924015	C₂²	semidirect
22. C₂²×#11924013	C₂²	semidirect
23. C₂²×#11924013	C₂²	semidirect
24. C₂²×#11924013	C₂²	semidirect
25. C₂×#14556598	C₂²	semidirect
26. C₂²×#11924012	C₂²	semidirect
27. C₂³×#10596831	C₂²	semidirect
29. C₂×H(5,𝔽₂)×C₇₃	C₂²	semidirect
32. C₂²×#41×C₇₃	C₂²	semidirect
34. C₂³×D₄×C₇₃	C₂²	semidirect
37. #14556637	C₂³	semidirect
40. C₂×#11924028	C₂³	semidirect
45. C₂²×D₂₉₂	C₂³	semidirect
49. #14556617	C₂³	semidirect
50. #14556616	C₂³	semidirect
51. #14556611	C₂³	semidirect
52. C₂×#11924018	C₂³	semidirect
53. C₂×#11924016	C₂³	semidirect
54. C₂×#11924015	C₂³	semidirect
55. C₂×#11924013	C₂³	semidirect
56. C₂×#11924013	C₂³	semidirect
57. C₂×#11924013	C₂³	semidirect
58. #14556598	C₂³	semidirect
59. C₂×#11924012	C₂³	semidirect
62. C₂²×#10596831	C₂³	semidirect
65. H(5,𝔽₂)×C₇₃	C₂³	semidirect
70. C₂×#41×C₇₃	C₂³	semidirect
79. C₂²×D₄×C₇₃	C₂³	semidirect
87. #11924028	C₂⁴	semidirect
94. C₂×D₂₉₂	C₂⁴	semidirect
99. #11924018	C₂⁴	semidirect
100. #11924016	C₂⁴	semidirect
101. #11924015	C₂⁴	semidirect
102. #11924013	C₂⁴	semidirect
103. #11924013	C₂⁴	semidirect
104. #11924012	C₂⁴	semidirect
107. C₂×#10596831	C₂⁴	semidirect
116. #41×C₇₃	C₂⁴	semidirect
127. C₂×D₄×C₇₃	C₂⁴	semidirect
174. C₂²×C₇₃	#576	semidirect
188. C₂×C₇₃	C₂×#576	semidirect
192. C₂²×H(5,𝔽₂)	D₇₃	semidirect
199. C₇₃	C₂²×#576	semidirect
203. C₂×H(5,𝔽₂)	C₂×D₇₃	semidirect
208. C₂²×#41	C₂×D₇₃	semidirect
212. C₂³×D₄	C₂×D₇₃	semidirect
231. H(5,𝔽₂)	C₂²×D₇₃	semidirect
239. C₂×#41	C₂²×D₇₃	semidirect
255. C₂²×D₄	C₂²×D₇₃	semidirect
287. #41	C₂³×D₇₃	semidirect
307. C₂×D₄	C₂³×D₇₃	semidirect
368. C₂²	#17989390	direct (N × H)
379. C₂	C₂×#17989390	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14556637	2
C₂×#17989390	2
C₂²×#14556617	2
C₂²×#14556616	2
C₂²×#14556611	2
C₂³×#11924013	2
C₂²×#14556598	2
C₂²×H(5,𝔽₂)×C₇₃	2
C₂²×#576	73

Subgroups — C22×#17989390 #33999794

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂²×#17989390 #33999794