Subgroups — C₂×#22626934 #34033224

Order 18688.

758 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989700	C₂	1	2	yes	maximal
2	#22626934	C₂	1	4	yes	maximal, direct product factor
3	C₂×#17989523	C₂	1	1	yes	maximal, characteristic
4	#17989700	—	2	2	no	—
5	#17989700	—	2	2	no	—
6	#17989700	C₄	1	4	yes	complemented
7	#17989700	C₂²	1	4	yes	—
8	C₂×C₄⋊#10596842	—	2	2	no	—
9	C₂×C₂²⋊#10596842	—	2	2	no	—
10	C₂×C₄×#10596842	C₄	1	4	yes	complemented
11	C₂²×C₄×#64408	C₄	1	1	yes	characteristic
12	C₂²×C₄×#64408	C₂²	1	1	yes	characteristic
13	#17989523	—	2	2	no	—
14	#17989523	C₄	1	2	yes	—
15	#17989523	C₂²	1	2	yes	—
16	C₂×(C₂×#64408)⋊C₄	—	2	2	no	—
17	C₂×C₄²×D₇₃	C₄	1	1	yes	characteristic
18	C₂²×#10596842	—	2	4	no	—
19	C₄⋊#10596842	—	2	4	no	—
20	C₄⋊#10596842	—	2	4	no	—
21	C₂²⋊#10596842	—	2	4	no	—
22	C₂²⋊#10596842	—	2	4	no	—
23	C₄×#10596842	—	2	4	no	—
24	C₄×#10596842	C₂×C₄	1	8	yes	complemented
25	C₂³×#64408	—	2	1	no	—
26	C₂³×#64408	D₄	1	2	yes	—
27	C₂×C₄×#64408	—	2	1	no	—
28	C₂×C₄×#64408	—	2	1	no	—
29	C₂×C₄×#64408	—	2	1	no	—
30	C₂×C₄×#64408	C₈	1	2	yes	complemented
31	C₂×C₄×#64408	C₈	1	2	yes	complemented
32	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
33	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
34	C₂×C₄×#64408	C₂×C₄	1	2	yes	—
35	C₂×C₄×#64408	C₂×C₄	1	1	yes	characteristic
36	C₂×C₄×#64408	D₄	1	2	yes	—
37	C₂×C₄×#64408	D₄	1	1	yes	characteristic
38	C₂×C₄×#64408	D₄	1	1	yes	characteristic
39	C₂×C₄×#64408	Q₈	1	1	yes	characteristic
40	C₂×C₄×#64408	Q₈	1	1	yes	characteristic
41	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
42	(C₂×#64408)⋊C₄	—	2	4	no	—
43	(C₂×#64408)⋊C₄	—	2	4	no	—
44	C₂²×C₄×D₇₃	—	2	1	no	—
45	C₂²×C₄×D₇₃	C₂×C₄	1	1	yes	characteristic
46	C₂×C₄×Dic₇₃	—	2	1	no	—
47	C₂×C₄×Dic₇₃	C₈	1	1	yes	characteristic, complemented
48	C₄²×D₇₃	—	2	1	no	—
49	C₄²×D₇₃	—	2	1	no	—
50	C₄²×D₇₃	C₈	1	2	yes	complemented
51	C₄²×D₇₃	C₂×C₄	1	2	yes	—
52	C₂×C₄²×C₇₃	C₈	1	1	yes	characteristic, complemented
53	C₂×#10596842	—	2	8	no	—
54	C₂×#10596842	—	4	8	no	—
55	C₂²×#64408	—	2	2	no	—
56	C₂²×#64408	—	2	2	no	—
57	C₂²×#64408	—	2	2	no	—
58	C₂²×#64408	—	4	4	no	—
59	C₂²×#64408	—	4	4	no	—
60	C₂²×#64408	C₂²⋊C₄	1	2	yes	—
61	C₂²×#64408	C₂²⋊C₄	1	2	yes	—
62	C₂²×#64408	C₂²⋊C₄	1	2	yes	—
63	C₂²×#64408	C₄⋊C₄	1	2	yes	—
64	C₂²×#64408	C₄⋊C₄	1	2	yes	—
65	C₂²×#64408	C₂×D₄	1	2	yes	—
66	C₄×#64408	—	2	2	no	—
67	C₄×#64408	—	2	2	no	—
68	C₄×#64408	—	2	2	no	—
69	C₄×#64408	C₄²	1	2	yes	—
70	C₄×#64408	C₂²⋊C₄	1	2	yes	—
71	C₄×#64408	C₂²⋊C₄	1	2	yes	—
72	C₄×#64408	C₄⋊C₄	1	2	yes	—
73	C₄×#64408	C₄⋊C₄	1	2	yes	—
74	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
75	C₄×#64408	C₄⋊C₄	1	1	yes	characteristic
76	C₄×#64408	C₂×C₈	1	4	yes	complemented
77	C₄×#64408	C₂²×C₄	1	2	yes	—
78	C₄×#64408	C₂×D₄	1	1	yes	characteristic
79	C₄×#64408	C₂×Q₈	1	1	yes	characteristic
80	C₂³×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
81	C₂²×Dic₇₃	—	2	1	no	—
82	C₂²×Dic₇₃	M₁₆	1	1	yes	characteristic
83	C₂×C₄×D₇₃	—	2	2	no	—
84	C₂×C₄×D₇₃	—	2	2	no	—
85	C₂×C₄×D₇₃	—	4	4	no	—
86	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
87	C₂×C₄×D₇₃	C₄²	1	1	yes	characteristic
88	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
90	C₂×C₄×D₇₃	C₄⋊C₄	1	1	yes	characteristic
91	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
92	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
93	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
94	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
95	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
96	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
98	C₄×Dic₇₃	—	2	1	no	—
99	C₄×Dic₇₃	—	2	2	no	—
100	C₄×Dic₇₃	—	2	2	no	—
101	C₄×Dic₇₃	C₂×C₈	1	2	yes	complemented
102	C₂²×C₄×C₇₃	—	2	1	no	—
103	C₂²×C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
104	C₄²×C₇₃	—	2	1	no	—
105	C₄²×C₇₃	C₂×C₈	1	2	yes	complemented
106	C₂³×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
107	C₂²×D₇₃	—	2	4	no	—
108	C₂²×D₇₃	#95	1	1	yes	characteristic
109	C₂²×D₇₃	#95	1	1	yes	characteristic
110	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
111	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
112	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
113	C₂²×D₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
114	C₂×#64408	—	2	4	no	—
115	C₂×#64408	—	2	4	no	—
116	C₂×#64408	—	2	4	no	—
117	C₂×#64408	—	4	2	no	—
118	C₂×#64408	—	4	2	no	—
119	C₂×#64408	—	4	2	no	—
120	C₂×#64408	—	4	2	no	—
121	C₂×#64408	—	4	4	no	—
122	C₂×#64408	—	4	4	no	—
123	C₂×#64408	—	4	4	no	—
124	C₂×#64408	#95	1	2	yes	—
125	C₂×#64408	#95	1	2	yes	—
126	C₂×#64408	C₂×C₂²⋊C₄	1	2	yes	—
127	C₂×#64408	C₂×C₄⋊C₄	1	2	yes	—
128	#10596842	—	4	8	no	—
129	C₂×C₄×C₇₃	—	2	2	no	—
130	C₂×C₄×C₇₃	—	4	2	no	—
131	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
132	C₂×C₄×C₇₃	C₄×C₈	1	1	yes	characteristic
133	C₂×C₄×C₇₃	C₂²⋊C₈	1	1	yes	characteristic
134	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
135	C₂×C₄×C₇₃	C₄⋊C₈	1	1	yes	characteristic
136	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
137	C₂×Dic₇₃	—	2	2	no	—
138	C₂×Dic₇₃	—	4	2	no	—
139	C₂×Dic₇₃	#97	1	1	yes	characteristic
140	C₂×Dic₇₃	#97	1	1	yes	characteristic
141	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
142	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
143	C₂×Dic₇₃	C₄⋊C₈	1	1	yes	characteristic
144	C₂×Dic₇₃	C₂×M₁₆	1	1	yes	characteristic
145	C₄×D₇₃	—	4	4	no	—
146	C₄×D₇₃	—	4	4	no	—
147	C₄×D₇₃	#95	1	1	yes	characteristic
148	C₄×D₇₃	#95	1	1	yes	characteristic
149	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
150	C₄×D₇₃	C₄×C₈	1	1	yes	characteristic
151	C₄×D₇₃	#97	1	1	yes	characteristic
152	C₄×D₇₃	#97	1	1	yes	characteristic
153	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
154	C₄×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
155	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
156	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
157	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
158	C₄×D₇₃	C₄⋊C₈	1	1	yes	characteristic
159	C₄×D₇₃	C₂×C₄²	1	1	yes	characteristic
160	C₄×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
161	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
162	C₄×D₇₃	C₂×M₁₆	1	1	yes	characteristic
163	C₂²×C₇₃	—	2	2	no	—
164	C₂²×C₇₃	#336	1	1	yes	characteristic
165	C₂²×C₇₃	#336	1	1	yes	characteristic
166	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
167	C₂×D₇₃	—	2	2	no	—
168	C₂×D₇₃	—	2	2	no	—
169	C₂×D₇₃	—	2	2	no	—
170	C₂×D₇₃	—	2	2	no	—
171	C₂×D₇₃	—	2	2	no	—
172	C₂×D₇₃	#336	1	1	yes	characteristic
173	C₂×D₇₃	#336	1	1	yes	characteristic
174	C₂×D₇₃	H(3,ℤ/4)	1	4	yes	—
175	C₂×D₇₃	C₂×#95	1	1	yes	characteristic
176	C₂×D₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
177	#64408	—	2	2	no	—
178	#64408	—	2	2	no	—
179	#64408	—	2	2	no	—
180	#64408	—	2	2	no	—
181	#64408	—	4	4	no	—
182	C₄×C₇₃	—	4	2	no	—
183	C₄×C₇₃	#336	1	1	yes	characteristic
184	C₄×C₇₃	#336	1	1	yes	characteristic
185	C₄×C₇₃	C₂×C₄×C₈	1	1	yes	characteristic
186	C₄×C₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
187	Dic₇₃	—	4	2	no	—
188	Dic₇₃	#336	1	1	yes	characteristic
189	Dic₇₃	#336	1	1	yes	characteristic
190	Dic₇₃	C₂×#97	1	1	yes	characteristic
191	Dic₇₃	C₂×C₄⋊C₈	1	1	yes	characteristic
192	C₂×#1274	—	73	1	no	maximal, Sylow
193	C₂×C₇₃	—	2	1	no	—
194	C₂×C₇₃	—	2	1	no	—
195	C₂×C₇₃	#1274	1	2	yes	complemented
196	C₂×C₇₃	C₂×#336	1	1	yes	characteristic
197	D₇₃	—	2	1	no	—
198	D₇₃	—	2	1	no	—
199	D₇₃	#1274	1	2	yes	complemented
200	D₇₃	C₂×H(3,ℤ/4)	1	2	yes	—
201	C₂×#431	—	73	2	no	—
202	C₂×#376	—	73	1	no	—
203	#1274	—	73	4	no	—
204	C₇₃	C₂×#1274	1	1	yes	characteristic, complemented, Sylow
205	C₂²×C₄²	—	73	1	no	—
206	C₂²×C₄²	—	73	1	no	—
207	C₂²×C₄²	—	73	1	no	—
208	#431	—	73	4	no	—
209	#431	—	73	4	no	—
210	#431	—	146	2	no	—
211	#431	—	146	2	no	—
212	C₂×C₄⋊C₈	—	146	2	no	—
213	C₂×C₂²⋊C₈	—	146	2	no	—
214	C₂×C₄×C₈	—	73	4	no	—
215	#376	—	73	2	no	—
216	#376	—	73	2	no	—
217	#376	—	146	2	no	—
218	C₂×#95	—	146	2	no	—
219	C₂³×C₄	—	73	2	no	—
220	C₂³×C₄	—	73	1	no	—
221	C₂³×C₄	—	146	1	no	—
222	C₂³×C₄	—	146	1	no	—
223	C₂²×C₈	—	146	4	no	—
224	C₂×C₄²	—	73	1	no	—
225	C₂×C₄²	—	73	1	no	—
226	C₂×C₄²	—	73	2	no	—
227	C₂×C₄²	—	73	2	no	—
228	C₂×C₄²	—	73	1	no	—
229	C₂×C₄²	—	73	2	no	—
230	C₂×C₄²	—	73	1	no	—
231	C₂×C₄²	—	73	1	no	—
232	C₂×C₄²	—	73	1	no	—
233	C₂×C₄²	—	73	2	no	—
234	C₂×C₄²	—	73	2	no	—
235	C₂×C₄²	—	73	2	no	—
236	C₂×C₄²	—	73	1	no	—
237	C₂×C₄²	—	73	2	no	—
238	C₂×C₄²	—	73	2	no	—
239	C₂×C₄²	—	146	1	no	—
240	C₂×C₄²	—	146	1	no	—
241	C₂×C₄²	—	146	1	no	—
242	C₂×C₄²	—	146	1	no	—
243	C₂×C₄²	—	146	1	no	—
244	C₂×C₄²	—	146	1	no	—
245	C₂×C₄²	#10596842	1	1	yes	characteristic, complemented
246	C₄⋊C₈	—	146	4	no	—
247	C₄⋊C₈	—	146	4	no	—
248	C₂²⋊C₈	—	146	4	no	—
249	C₂²⋊C₈	—	146	4	no	—
250	C₄×C₈	—	73	8	no	—
251	C₄×C₈	—	146	4	no	—
252	#95	—	146	4	no	—
253	#95	—	146	4	no	—
254	C₂⁴	—	73	1	no	—
255	C₂²×C₄	—	2	1	no	—
256	C₂²×C₄	—	292	4	no	—
257	C₂²×C₄	—	292	4	no	—
258	C₂²×C₄	—	292	4	no	—
259	C₂²×C₄	—	73	2	no	—
260	C₂²×C₄	—	73	2	no	—
261	C₂²×C₄	—	73	2	no	—
262	C₂²×C₄	—	73	2	no	—
263	C₂²×C₄	—	73	1	no	—
264	C₂²×C₄	—	73	1	no	—
265	C₂²×C₄	—	73	1	no	—
266	C₂²×C₄	—	73	1	no	—
267	C₂²×C₄	—	73	1	no	—
268	C₂²×C₄	—	73	1	no	—
269	C₂²×C₄	—	73	1	no	—
270	C₂²×C₄	—	73	1	no	—
271	C₂²×C₄	—	73	1	no	—
272	C₂²×C₄	—	73	1	no	—
273	C₂²×C₄	—	73	1	no	—
274	C₂²×C₄	—	73	1	no	—
275	C₂²×C₄	—	73	1	no	—
276	C₂²×C₄	—	73	2	no	—
277	C₂²×C₄	—	73	2	no	—
278	C₂²×C₄	—	146	2	no	—
279	C₂²×C₄	—	146	2	no	—
280	C₂²×C₄	—	146	2	no	—
281	C₂²×C₄	—	146	2	no	—
282	C₂²×C₄	—	146	2	no	—
283	C₂²×C₄	—	146	1	no	—
284	C₂²×C₄	C₂×#10596842	1	1	yes	characteristic
285	C₂×C₈	—	292	8	no	—
286	C₂×C₈	—	146	8	no	—
287	C₄²	—	2	1	no	—
288	C₄²	—	73	2	no	—
289	C₄²	—	73	2	no	—
290	C₄²	—	73	2	no	—
291	C₄²	—	73	2	no	—
292	C₄²	—	73	2	no	—
293	C₄²	—	73	1	no	—
294	C₄²	—	73	1	no	—
295	C₄²	—	73	2	no	—
296	C₄²	—	73	1	no	—
297	C₄²	—	73	1	no	—
298	C₄²	—	73	4	no	—
299	C₄²	—	73	2	no	—
300	C₄²	—	146	2	no	—
301	C₄²	—	146	2	no	—
302	C₄²	—	146	2	no	—
303	C₄²	—	146	2	no	—
304	C₄²	—	146	2	no	—
305	C₄²	—	146	1	no	—
306	C₄²	C₂×#10596842	1	2	yes	complemented
307	C₂³	—	73	1	no	—
308	C₂³	—	73	1	no	—
309	C₂³	—	73	1	no	—
310	C₂³	—	73	1	no	—
311	C₂³	—	73	1	no	—
312	C₂³	—	73	1	no	—
313	C₂³	—	146	4	no	—
314	C₂³	C₂²⋊#10596842	1	1	yes	characteristic
315	C₂×C₄	—	2	2	no	—
316	C₂×C₄	—	4	2	no	—
317	C₂×C₄	—	292	4	no	—
318	C₂×C₄	—	292	4	no	—
319	C₂×C₄	—	292	2	no	—
320	C₂×C₄	—	292	4	no	—
321	C₂×C₄	—	292	4	no	—
322	C₂×C₄	—	292	4	no	—
323	C₂×C₄	—	292	2	no	—
324	C₂×C₄	—	292	2	no	—
325	C₂×C₄	—	292	2	no	—
326	C₂×C₄	—	292	2	no	—
327	C₂×C₄	—	73	1	no	—
328	C₂×C₄	—	73	1	no	—
329	C₂×C₄	—	73	1	no	—
330	C₂×C₄	—	73	1	no	—
331	C₂×C₄	—	73	1	no	—
332	C₂×C₄	—	73	1	no	—
333	C₂×C₄	—	73	1	no	—
334	C₂×C₄	—	73	1	no	—
335	C₂×C₄	—	73	1	no	—
336	C₂×C₄	—	73	1	no	—
337	C₂×C₄	—	73	1	no	—
338	C₂×C₄	—	73	1	no	—
339	C₂×C₄	—	73	1	no	—
340	C₂×C₄	—	73	1	no	—
341	C₂×C₄	—	73	1	no	—
342	C₂×C₄	—	73	1	no	—
343	C₂×C₄	—	73	1	no	—
344	C₂×C₄	—	73	1	no	—
345	C₂×C₄	—	73	1	no	—
346	C₂×C₄	—	73	1	no	—
347	C₂×C₄	—	73	1	no	—
348	C₂×C₄	—	73	1	no	—
349	C₂×C₄	—	73	2	no	—
350	C₂×C₄	—	73	2	no	—
351	C₂×C₄	—	73	2	no	—
352	C₂×C₄	—	73	2	no	—
353	C₂×C₄	—	146	4	no	—
354	C₂×C₄	—	146	2	no	—
355	C₂×C₄	—	146	4	no	—
356	C₂×C₄	—	146	4	no	—
357	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
358	C₂×C₄	C₄×#10596842	1	1	yes	characteristic
359	C₂×C₄	C₂²⋊#10596842	1	1	yes	characteristic
360	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
361	C₂×C₄	C₄⋊#10596842	1	1	yes	characteristic
362	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
363	C₈	—	292	8	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	73	4	no	—
366	C₂²	—	73	1	no	—
367	C₂²	—	73	1	no	—
368	C₂²	—	73	1	no	—
369	C₂²	—	73	1	no	—
370	C₂²	—	146	2	no	—
371	C₂²	—	146	2	no	—
372	C₂²	—	146	2	no	—
373	C₂²	—	146	2	no	—
374	C₂²	—	146	2	no	—
375	C₂²	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
376	C₂²	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
377	C₂²	C₂×C₂²⋊#10596842	1	1	yes	characteristic
378	C₄	—	4	2	no	—
379	C₄	—	292	2	no	—
380	C₄	—	292	4	no	—
381	C₄	—	73	1	no	—
382	C₄	—	73	1	no	—
383	C₄	—	73	1	no	—
384	C₄	—	73	1	no	—
385	C₄	—	146	2	no	—
386	C₄	—	146	2	no	—
387	C₄	—	146	2	no	—
388	C₄	—	146	2	no	—
389	C₄	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
390	C₄	(C₂×#10596842)⋊C₄	1	1	yes	characteristic
391	C₄	C₂×C₄×#10596842	1	1	yes	characteristic
392	C₄	C₂×C₄⋊#10596842	1	1	yes	characteristic
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	73	2	no	—
396	C₂	—	73	2	no	—
397	C₂	—	146	1	no	—
398	C₂	—	146	1	no	—
399	C₂	#22626934	1	2	yes	direct product factor
400	C₂	C₂×(C₂×#10596842)⋊C₄	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₄×#10596842
commutator	C₄×C₇₃	C₂×C₄×C₈
Frattini	C₂×C₄	C₂²×#10596842
Fitting	C₂×C₄²×C₇₃	C₈
socle	C₂²×C₇₃	#336
prime radical	C₂³×D₇₃	C₂²⋊C₄
cosocle	C₂×C₄×#64408	C₂³
hypercenter	C₂×C₄²	#10596842
hypocenter	C₇₃	C₂×#1274
LCS	G ▷ C₄×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄²

Complements

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

N	H ≅ G/N	type
2. #22626934	C₂	direct (N × H)
6. #17989700	C₄	semidirect
10. C₂×C₄×#10596842	C₄	semidirect
24. C₄×#10596842	C₂×C₄	semidirect
30. C₂×C₄×#64408	C₈	semidirect
31. C₂×C₄×#64408	C₈	semidirect
47. C₂×C₄×Dic₇₃	C₈	semidirect
50. C₄²×D₇₃	C₈	semidirect
52. C₂×C₄²×C₇₃	C₈	semidirect
76. C₄×#64408	C₂×C₈	semidirect
101. C₄×Dic₇₃	C₂×C₈	semidirect
105. C₄²×C₇₃	C₂×C₈	semidirect
195. C₂×C₇₃	#1274	semidirect
199. D₇₃	#1274	semidirect
204. C₇₃	C₂×#1274	semidirect
245. C₂×C₄²	#10596842	semidirect
306. C₄²	C₂×#10596842	semidirect
399. C₂	#22626934	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#17989700	2
#22626934	2
C₂×#17989523	2
C₂×#1274	73

Subgroups — C2×#22626934 #34033224

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22626934 #34033224