Subgroups — C₂×#22621724 #33962202

Order 18688.

2682 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989393	C₂	1	4	yes	maximal, complemented
2	#22621724	C₂	1	16	yes	maximal, direct product factor
3	C₂×#17988847	C₂	1	4	yes	maximal, complemented
4	C₂×#17988769	C₂	1	2	yes	maximal, complemented
5	C₂×#17988754	C₂	1	2	yes	maximal, complemented
6	C₂×#17988705	C₂	1	2	yes	maximal, complemented
7	C₂×#492×C₇₃	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#14556639	C₂²	1	2	yes	—
9	C₂×#14556636	C₂²	1	2	yes	complemented
10	#17989393	—	2	16	no	—
11	#17989393	C₂²	1	32	yes	complemented
12	C₂×#14556622	C₂²	1	4	yes	complemented
13	C₂×#14556620	—	2	4	no	—
14	C₂×#14556618	—	2	4	no	—
15	C₂×#14556617	C₂²	1	4	yes	—
16	C₂×#14556613	C₂²	1	2	yes	—
17	C₂×#14556612	—	2	4	no	—
18	C₂×SD₁₆×D₇₃	—	2	4	no	—
19	C₂×#14556597	C₂²	1	4	yes	complemented
20	#17988847	C₂²	1	32	yes	complemented
21	#17988769	C₂²	1	16	yes	complemented
22	#17988754	C₂²	1	16	yes	complemented
23	#17988705	C₂²	1	16	yes	complemented
24	C₂×#14556527	C₂²	1	2	yes	complemented
25	C₂×#14556519	C₂²	1	4	yes	complemented
26	C₂×#14556510	C₂²	1	2	yes	complemented
27	C₂×#14556508	C₂²	1	2	yes	complemented
28	C₂²×SD₁₆×C₇₃	C₂²	1	4	yes	complemented
29	C₂×C₄⋊Q₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
30	C₂×#127×C₇₃	C₂²	1	1	yes	characteristic
31	#492×C₇₃	C₂²	1	8	yes	complemented
32	C₂×C₄×C₈×C₇₃	C₂²	1	1	yes	characteristic, complemented
33	#14556639	—	2	8	no	—
34	#14556639	—	4	2	no	—
35	#14556639	C₂³	1	8	yes	—
36	#14556636	—	2	8	no	—
37	#14556636	—	4	2	no	—
38	#14556636	C₂³	1	8	yes	complemented
39	C₂×#11924029	—	2	4	no	—
40	C₂×#11924028	—	4	2	no	—
41	C₂×#11924028	C₂³	1	4	yes	—
42	C₂×#11924027	—	2	4	no	—
43	C₂×Q₈×D₇₃	—	2	4	no	—
44	C₂²×C₂²⋊D₇₃	—	4	2	no	—
45	C₂×D₄×D₇₃	—	2	4	no	—
46	#14556622	—	2	8	no	—
47	#14556622	C₂³	1	16	yes	complemented
48	#14556620	—	2	32	no	—
49	#14556618	—	2	32	no	—
50	#14556617	—	2	8	no	—
51	#14556617	C₂³	1	16	yes	—
52	#14556613	D₄	1	8	yes	complemented
53	#14556613	C₂³	1	8	yes	—
54	#14556612	—	2	32	no	—
55	C₂×Dic₂₉₂	D₄	1	2	yes	complemented
56	C₂×#11924018	—	2	4	no	—
57	C₂×#11924017	D₄	1	4	yes	complemented
58	C₂×#11924016	—	2	4	no	—
59	C₂×#11924015	—	2	4	no	—
60	SD₁₆×D₇₃	—	2	32	no	—
61	C₂×D₅₈₄	D₄	1	2	yes	complemented
62	C₂×#11924013	—	2	4	no	—
63	#14556597	—	2	8	no	—
64	#14556597	C₂³	1	16	yes	complemented
65	C₂×#11924012	C₂³	1	4	yes	—
66	C₂×#11924011	—	2	4	no	—
67	C₂×C₈×D₇₃	—	2	4	no	—
68	#14556527	C₂³	1	8	yes	complemented
69	#14556519	C₂³	1	16	yes	complemented
70	#14556510	C₂³	1	8	yes	complemented
71	#14556508	C₂³	1	8	yes	complemented
72	C₂²×Q₈×C₇₃	C₂³	1	2	yes	—
73	C₂²×D₄×C₇₃	—	4	1	no	—
74	C₂²×D₄×C₇₃	C₂³	1	2	yes	—
75	C₂×SD₁₆×C₇₃	—	2	4	no	—
76	C₂×SD₁₆×C₇₃	—	2	8	no	—
77	C₂×SD₁₆×C₇₃	—	2	4	no	—
78	C₂×SD₁₆×C₇₃	C₂³	1	16	yes	complemented
79	C₂²×C₈×C₇₃	C₂³	1	2	yes	—
80	C₄⋊Q₈×C₇₃	—	4	1	no	—
81	C₄⋊Q₈×C₇₃	C₂³	1	4	yes	complemented
82	#127×C₇₃	—	4	1	no	—
83	#127×C₇₃	C₂³	1	4	yes	—
84	C₂×C₄⋊C₄×C₇₃	—	4	1	no	—
85	C₂×C₄²×C₇₃	C₂³	1	1	yes	characteristic
86	C₄×C₈×C₇₃	C₂³	1	4	yes	complemented
87	C₂³×D₇₃	—	4	2	no	—
88	#11924029	—	2	16	no	—
89	#11924029	—	4	8	no	—
90	#11924028	—	2	4	no	—
91	#11924028	—	2	4	no	—
92	#11924028	—	4	8	no	—
93	#11924028	—	4	8	no	—
94	#11924028	C₂×D₄	1	8	yes	—
95	#11924028	C₂⁴	1	8	yes	—
96	#11924027	—	2	16	no	—
97	#11924027	—	4	8	no	—
98	C₂×Dic₁₄₆	—	4	2	no	—
99	C₂×Dic₁₄₆	C₂×D₄	1	4	yes	—
100	Q₈×D₇₃	—	2	16	no	—
101	Q₈×D₇₃	—	4	8	no	—
102	C₂×D₂₉₂	—	4	2	no	—
103	C₂×D₂₉₂	C₂×D₄	1	4	yes	—
104	C₂×C₂²⋊D₇₃	—	2	4	no	—
105	C₂×C₂²⋊D₇₃	—	4	4	no	—
106	C₂×C₂²⋊D₇₃	—	4	8	no	—
107	C₂×C₂²⋊D₇₃	—	4	8	no	—
108	D₄×D₇₃	—	2	16	no	—
109	D₄×D₇₃	—	4	8	no	—
110	C₂²×Dic₇₃	—	4	2	no	—
111	C₂×C₄×D₇₃	—	2	4	no	—
112	C₂×C₄×D₇₃	—	4	4	no	—
113	Dic₂₉₂	C₂×D₄	1	8	yes	complemented
114	#11924018	—	2	16	no	—
115	#11924017	C₂×D₄	1	16	yes	complemented
116	#11924016	—	2	16	no	—
117	#11924015	—	2	16	no	—
118	D₅₈₄	C₂×D₄	1	8	yes	complemented
119	#11924013	—	2	16	no	—
120	#11924012	—	2	4	no	—
121	#11924012	C₂⁴	1	8	yes	—
122	#11924011	—	2	16	no	—
123	C₂×#10596831	—	2	4	no	—
124	C₈×D₇₃	—	2	16	no	—
125	C₂⁴×C₇₃	—	2	2	no	—
126	C₂×Q₈×C₇₃	—	2	2	no	—
127	C₂×Q₈×C₇₃	—	2	4	no	—
128	C₂×Q₈×C₇₃	—	2	4	no	—
129	C₂×Q₈×C₇₃	C₂⁴	1	4	yes	—
130	C₂×D₄×C₇₃	—	2	4	no	—
131	C₂×D₄×C₇₃	—	2	4	no	—
132	C₂×D₄×C₇₃	—	2	2	no	—
133	C₂×D₄×C₇₃	—	4	4	no	—
134	C₂×D₄×C₇₃	—	8	4	no	—
135	C₂×D₄×C₇₃	C₂⁴	1	4	yes	—
136	C₂²×C₄×C₇₃	—	2	1	no	—
137	C₂²×C₄×C₇₃	—	2	2	no	—
138	C₂²×C₄×C₇₃	C₂⁴	1	1	yes	characteristic
139	SD₁₆×C₇₃	—	2	16	no	—
140	SD₁₆×C₇₃	—	2	16	no	—
141	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
142	C₂×C₈×C₇₃	C₂×D₄	1	2	yes	—
143	C₂×C₈×C₇₃	C₂×D₄	1	4	yes	—
144	C₂×C₈×C₇₃	C₂⁴	1	4	yes	—
145	C₄⋊C₄×C₇₃	—	4	4	no	—
146	C₄²×C₇₃	—	2	1	no	—
147	C₄²×C₇₃	C₂⁴	1	2	yes	—
148	C₂³×C₇₃	—	2	4	no	—
149	C₂³×C₇₃	—	4	2	no	—
150	C₂³×C₇₃	—	4	2	no	—
151	C₂³×C₇₃	—	8	4	no	—
152	C₂³×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
153	C₂²×D₇₃	—	2	4	no	—
154	C₂²×D₇₃	—	4	8	no	—
155	C₂²×D₇₃	—	16	4	no	—
156	Q₈×C₇₃	—	2	8	no	—
157	Q₈×C₇₃	—	4	4	no	—
158	D₄×C₇₃	—	2	8	no	—
159	D₄×C₇₃	—	4	4	no	—
160	D₄×C₇₃	—	8	8	no	—
161	C₂×C₄×C₇₃	—	2	4	no	—
162	C₂×C₄×C₇₃	—	2	2	no	—
163	C₂×C₄×C₇₃	—	2	4	no	—
164	C₂×C₄×C₇₃	—	4	2	no	—
165	C₂×C₄×C₇₃	—	4	2	no	—
166	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
167	C₂×C₄×C₇₃	C₂²×D₄	1	2	yes	—
168	C₂×C₄×C₇₃	H(5,𝔽₂)	1	1	yes	characteristic
169	C₂×C₄×C₇₃	C₂⁵	1	1	yes	characteristic
170	C₂²⋊D₇₃	—	2	8	no	—
171	C₂²⋊D₇₃	—	2	8	no	—
172	C₂²⋊D₇₃	—	4	16	no	—
173	C₂×Dic₇₃	—	2	4	no	—
174	C₂×Dic₇₃	—	4	8	no	—
175	D₂₉₂	—	2	4	no	—
176	D₂₉₂	—	4	8	no	—
177	D₂₉₂	C₂²×D₄	1	8	yes	—
178	C₄×D₇₃	—	2	8	no	—
179	C₄×D₇₃	—	2	8	no	—
180	C₄×D₇₃	—	4	16	no	—
181	Dic₁₄₆	—	2	4	no	—
182	Dic₁₄₆	—	4	8	no	—
183	Dic₁₄₆	C₂²×D₄	1	8	yes	—
184	C₈×C₇₃	C₂²×D₄	1	4	yes	—
185	C₈×C₇₃	C₂²×D₄	1	4	yes	—
186	#10596831	—	2	8	no	—
187	C₂²×C₇₃	—	2	2	no	—
188	C₂²×C₇₃	—	4	4	no	—
189	C₂²×C₇₃	—	8	4	no	—
190	C₂²×C₇₃	—	8	4	no	—
191	C₂²×C₇₃	—	16	2	no	—
192	C₂²×C₇₃	D₄²	1	1	yes	characteristic
193	C₂²×C₇₃	D₄²	1	1	yes	characteristic
194	C₂²×C₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
195	C₂×D₇₃	—	2	8	no	—
196	C₂×D₇₃	—	4	8	no	—
197	C₂×D₇₃	—	16	8	no	—
198	C₄×C₇₃	—	2	4	no	—
199	C₄×C₇₃	—	4	4	no	—
200	C₄×C₇₃	D₄²	1	2	yes	—
201	C₄×C₇₃	C₂³×D₄	1	2	yes	—
202	Dic₇₃	—	2	8	no	—
203	C₂×#3291	—	73	1	no	maximal, Sylow
204	C₂×C₇₃	—	2	1	no	—
205	C₂×C₇₃	—	2	1	no	—
206	C₂×C₇₃	—	8	4	no	—
207	C₂×C₇₃	#3291	1	2	yes	complemented
208	C₂×C₇₃	C₂×D₄²	1	1	yes	characteristic
209	D₇₃	—	4	8	no	—
210	C₂×#577	—	73	4	no	—
211	#3291	—	73	16	no	—
212	C₂×#492	D₇₃	1	1	yes	characteristic, complemented
213	C₂×#471	—	73	4	no	—
214	C₂×#456	—	73	2	no	—
215	C₂×#453	—	73	2	no	—
216	C₂×#443	—	73	2	no	—
217	C₇₃	C₂×#3291	1	1	yes	characteristic, complemented, Sylow
218	C₂×2₋¹⁺⁴	—	73	2	no	—
219	C₂×H(5,𝔽₂)	—	73	2	no	—
220	#577	—	73	32	no	—
221	#577	—	146	16	no	—
222	C₂×#137	—	73	4	no	—
223	C₂×#137	—	146	4	no	—
224	C₂×AGL(1,ℤ/8)	—	73	4	no	—
225	C₂×AGL(1,ℤ/8)	—	146	4	no	—
226	C₂×#135	—	73	2	no	—
227	C₂×#135	—	146	4	no	—
228	C₂²×SD₁₆	—	146	4	no	—
229	C₂²×SD₁₆	C₂×D₇₃	1	4	yes	complemented
230	C₂×#131	—	73	4	no	—
231	C₂×C₄⋊Q₈	C₂×D₇₃	1	1	yes	characteristic, complemented
232	C₂×#127	C₂×D₇₃	1	1	yes	characteristic
233	#492	C₂×D₇₃	1	8	yes	complemented
234	#471	—	73	32	no	—
235	#456	—	73	16	no	—
236	#453	—	73	16	no	—
237	#443	—	73	16	no	—
238	C₂×#108	—	73	2	no	—
239	C₂×#104	—	73	4	no	—
240	C₂×#101	—	73	2	no	—
241	C₂×#100	—	73	2	no	—
242	C₂×C₄×C₈	C₂×D₇₃	1	1	yes	characteristic, complemented
243	2₋¹⁺⁴	—	292	2	no	—
244	2₋¹⁺⁴	—	73	8	no	—
245	2₋¹⁺⁴	—	146	8	no	—
246	H(5,𝔽₂)	—	292	2	no	—
247	H(5,𝔽₂)	—	73	8	no	—
248	H(5,𝔽₂)	—	146	8	no	—
249	C₂×#41	—	292	2	no	—
250	C₂×#41	—	73	4	no	—
251	C₂×#41	—	146	4	no	—
252	C₂×#41	—	146	4	no	—
253	C₂²×Q₈	—	146	4	no	—
254	C₂²×Q₈	C₂²×D₇₃	1	2	yes	—
255	C₂²×D₄	—	4	1	no	—
256	C₂²×D₄	—	292	2	no	—
257	C₂²×D₄	—	146	4	no	—
258	C₂²×D₄	C₂²×D₇₃	1	2	yes	—
259	#137	—	73	16	no	—
260	#137	—	146	32	no	—
261	#137	—	146	8	no	—
262	AGL(1,ℤ/8)	—	73	16	no	—
263	AGL(1,ℤ/8)	—	146	32	no	—
264	AGL(1,ℤ/8)	—	146	8	no	—
265	#135	—	73	8	no	—
266	#135	—	73	8	no	—
267	#135	—	146	32	no	—
268	C₂×Q₁₆	—	73	2	no	—
269	C₂×Q₁₆	—	146	4	no	—
270	C₂×SD₁₆	—	2	4	no	—
271	C₂×SD₁₆	—	2	4	no	—
272	C₂×SD₁₆	—	2	8	no	—
273	C₂×SD₁₆	—	73	4	no	—
274	C₂×SD₁₆	—	146	32	no	—
275	C₂×SD₁₆	—	146	4	no	—
276	C₂×SD₁₆	—	146	4	no	—
277	C₂×SD₁₆	C₂²×D₇₃	1	16	yes	complemented
278	C₂×D₈	—	73	2	no	—
279	C₂×D₈	—	146	4	no	—
280	#131	—	73	16	no	—
281	#131	—	146	8	no	—
282	C₂×M₁₆	—	73	4	no	—
283	C₂×M₁₆	—	146	4	no	—
284	C₂²×C₈	—	146	4	no	—
285	C₂²×C₈	C₂²×D₇₃	1	2	yes	—
286	C₄⋊Q₈	—	4	1	no	—
287	C₄⋊Q₈	C₂²×D₇₃	1	4	yes	complemented
288	#127	—	4	1	no	—
289	#127	C₂²×D₇₃	1	4	yes	—
290	C₂×C₄⋊C₄	—	4	1	no	—
291	C₂×C₄²	C₂²×D₇₃	1	1	yes	characteristic
292	#108	—	73	8	no	—
293	#104	—	73	16	no	—
294	#101	—	73	8	no	—
295	#100	—	73	8	no	—
296	C₄×C₈	C₂²×D₇₃	1	4	yes	complemented
297	C₂⁴	—	2	2	no	—
298	C₂⁴	—	292	2	no	—
299	#41	—	292	8	no	—
300	#41	—	292	8	no	—
301	#41	—	292	8	no	—
302	#41	—	292	8	no	—
303	#41	—	73	8	no	—
304	#41	—	73	8	no	—
305	#41	—	146	16	no	—
306	#41	—	146	16	no	—
307	#41	—	146	4	no	—
308	#41	—	146	4	no	—
309	C₂×Q₈	—	2	2	no	—
310	C₂×Q₈	—	2	4	no	—
311	C₂×Q₈	—	2	4	no	—
312	C₂×Q₈	—	292	2	no	—
313	C₂×Q₈	—	292	8	no	—
314	C₂×Q₈	—	73	4	no	—
315	C₂×Q₈	—	146	16	no	—
316	C₂×Q₈	C₂³×D₇₃	1	4	yes	—
317	C₂×D₄	—	2	4	no	—
318	C₂×D₄	—	2	4	no	—
319	C₂×D₄	—	2	2	no	—
320	C₂×D₄	—	4	4	no	—
321	C₂×D₄	—	8	4	no	—
322	C₂×D₄	—	292	2	no	—
323	C₂×D₄	—	292	8	no	—
324	C₂×D₄	—	292	8	no	—
325	C₂×D₄	—	292	8	no	—
326	C₂×D₄	—	292	4	no	—
327	C₂×D₄	—	73	4	no	—
328	C₂×D₄	—	146	16	no	—
329	C₂×D₄	—	146	4	no	—
330	C₂×D₄	C₂³×D₇₃	1	4	yes	—
331	C₂²×C₄	—	2	1	no	—
332	C₂²×C₄	—	2	2	no	—
333	C₂²×C₄	—	292	4	no	—
334	C₂²×C₄	—	292	2	no	—
335	C₂²×C₄	—	146	4	no	—
336	C₂²×C₄	C₂³×D₇₃	1	1	yes	characteristic
337	Q₁₆	—	73	8	no	—
338	Q₁₆	—	146	16	no	—
339	SD₁₆	—	2	16	no	—
340	SD₁₆	—	2	16	no	—
341	SD₁₆	—	73	16	no	—
342	SD₁₆	—	146	16	no	—
343	SD₁₆	—	146	16	no	—
344	D₈	—	73	8	no	—
345	D₈	—	146	16	no	—
346	M₁₆	—	73	8	no	—
347	M₁₆	—	146	4	no	—
348	M₁₆	—	146	16	no	—
349	C₂×C₈	—	146	4	no	—
350	C₂×C₈	—	146	16	no	—
351	C₂×C₈	D₄×D₇₃	1	2	yes	—
352	C₂×C₈	D₄×D₇₃	1	2	yes	—
353	C₂×C₈	D₄×D₇₃	1	4	yes	—
354	C₂×C₈	C₂³×D₇₃	1	4	yes	—
355	C₄⋊C₄	—	4	4	no	—
356	C₄²	—	2	1	no	—
357	C₄²	C₂³×D₇₃	1	2	yes	—
358	C₂³	—	2	4	no	—
359	C₂³	—	4	2	no	—
360	C₂³	—	4	2	no	—
361	C₂³	—	8	4	no	—
362	C₂³	—	292	8	no	—
363	C₂³	—	1168	4	no	—
364	C₂³	—	146	4	no	—
365	C₂³	#14556636	1	1	yes	characteristic
366	Q₈	—	2	8	no	—
367	Q₈	—	4	4	no	—
368	Q₈	—	292	8	no	—
369	Q₈	—	73	8	no	—
370	Q₈	—	146	4	no	—
371	D₄	—	2	8	no	—
372	D₄	—	4	4	no	—
373	D₄	—	8	8	no	—
374	D₄	—	292	8	no	—
375	D₄	—	292	16	no	—
376	D₄	—	73	8	no	—
377	D₄	—	146	8	no	—
378	D₄	—	146	8	no	—
379	D₄	—	146	4	no	—
380	C₂×C₄	—	2	4	no	—
381	C₂×C₄	—	2	2	no	—
382	C₂×C₄	—	2	4	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	4	2	no	—
385	C₂×C₄	—	292	16	no	—
386	C₂×C₄	—	292	8	no	—
387	C₂×C₄	—	146	4	no	—
388	C₂×C₄	—	146	8	no	—
389	C₂×C₄	—	146	8	no	—
390	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
391	C₂×C₄	C₂×D₄×D₇₃	1	2	yes	—
392	C₂×C₄	#14556636	1	1	yes	characteristic
393	C₂×C₄	C₂⁴×D₇₃	1	1	yes	characteristic
394	C₈	—	146	8	no	—
395	C₈	C₂×D₄×D₇₃	1	4	yes	—
396	C₈	C₂×D₄×D₇₃	1	4	yes	—
397	C₂²	—	2	2	no	—
398	C₂²	—	4	4	no	—
399	C₂²	—	8	4	no	—
400	C₂²	—	8	4	no	—
401	C₂²	—	16	2	no	—
402	C₂²	—	292	8	no	—
403	C₂²	—	1168	8	no	—
404	C₂²	—	146	8	no	—
405	C₂²	#17989222	1	1	yes	characteristic
406	C₂²	#17989222	1	1	yes	characteristic
407	C₂²	C₂×#14556636	1	1	yes	characteristic
408	C₄	—	2	4	no	—
409	C₄	—	4	4	no	—
410	C₄	—	146	8	no	—
411	C₄	#17989222	1	2	yes	—
412	C₄	C₂²×D₄×D₇₃	1	2	yes	—
413	C₂	—	2	1	no	—
414	C₂	—	2	1	no	—
415	C₂	—	8	4	no	—
416	C₂	—	292	8	no	—
417	C₂	#22621724	1	2	yes	direct product factor
418	C₂	C₂×#17989222	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#17989222
commutator, cosocle	C₂×C₄×C₇₃	C₂⁵
Frattini	C₂×C₄	C₂⁴×D₇₃
Fitting	C₂×#492×C₇₃	C₂
socle	C₂²×C₇₃	D₄²
hypercenter	C₂×#492	D₇₃
hypocenter	C₇₃	C₂×#3291
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#492

Complements

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

N	H ≅ G/N	type
1. C₂×#17989393	C₂	semidirect
2. #22621724	C₂	direct (N × H)
3. C₂×#17988847	C₂	semidirect
4. C₂×#17988769	C₂	semidirect
5. C₂×#17988754	C₂	semidirect
6. C₂×#17988705	C₂	semidirect
7. C₂×#492×C₇₃	C₂	semidirect
9. C₂×#14556636	C₂²	semidirect
11. #17989393	C₂²	semidirect
12. C₂×#14556622	C₂²	semidirect
19. C₂×#14556597	C₂²	semidirect
20. #17988847	C₂²	semidirect
21. #17988769	C₂²	semidirect
22. #17988754	C₂²	semidirect
23. #17988705	C₂²	semidirect
24. C₂×#14556527	C₂²	semidirect
25. C₂×#14556519	C₂²	semidirect
26. C₂×#14556510	C₂²	semidirect
27. C₂×#14556508	C₂²	semidirect
28. C₂²×SD₁₆×C₇₃	C₂²	semidirect
29. C₂×C₄⋊Q₈×C₇₃	C₂²	semidirect
31. #492×C₇₃	C₂²	semidirect
32. C₂×C₄×C₈×C₇₃	C₂²	semidirect
38. #14556636	C₂³	semidirect
47. #14556622	C₂³	semidirect
52. #14556613	D₄	semidirect
55. C₂×Dic₂₉₂	D₄	semidirect
57. C₂×#11924017	D₄	semidirect
61. C₂×D₅₈₄	D₄	semidirect
64. #14556597	C₂³	semidirect
68. #14556527	C₂³	semidirect
69. #14556519	C₂³	semidirect
70. #14556510	C₂³	semidirect
71. #14556508	C₂³	semidirect
78. C₂×SD₁₆×C₇₃	C₂³	semidirect
81. C₄⋊Q₈×C₇₃	C₂³	semidirect
86. C₄×C₈×C₇₃	C₂³	semidirect
113. Dic₂₉₂	C₂×D₄	semidirect
115. #11924017	C₂×D₄	semidirect
118. D₅₈₄	C₂×D₄	semidirect
207. C₂×C₇₃	#3291	semidirect
212. C₂×#492	D₇₃	semidirect
217. C₇₃	C₂×#3291	semidirect
229. C₂²×SD₁₆	C₂×D₇₃	semidirect
231. C₂×C₄⋊Q₈	C₂×D₇₃	semidirect
233. #492	C₂×D₇₃	semidirect
242. C₂×C₄×C₈	C₂×D₇₃	semidirect
277. C₂×SD₁₆	C₂²×D₇₃	semidirect
287. C₄⋊Q₈	C₂²×D₇₃	semidirect
296. C₄×C₈	C₂²×D₇₃	semidirect
417. C₂	#22621724	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×#17989393	2
#22621724	2
C₂×#17988847	2
C₂×#17988769	2
C₂×#17988754	2
C₂×#17988705	2
C₂×#492×C₇₃	2
C₂×#3291	73

Subgroups — C2×#22621724 #33962202

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22621724 #33962202