Subgroups — C₄×#19149724 #36366768

Order 22144.

1660 conjugacy classes of subgroups.

The subgroup lattice has 316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19149724	C₂	1	1	yes	maximal, characteristic
2	#26011972	C₂	1	2	yes	maximal, complemented
3	#26011970	C₂	1	4	yes	maximal, complemented
4	#26011966	C₂	1	1	yes	maximal, characteristic, complemented
5	#26011964	C₂	1	4	yes	maximal, complemented
6	#26011963	C₂	1	4	yes	maximal, complemented
7	C₄×#14583826	C₂	1	2	yes	maximal, complemented
8	C₄×#14583825	C₂	1	4	yes	maximal, complemented
9	C₂×C₄×C₂²⋊D₁₇₃	C₂	1	4	yes	maximal, complemented
10	C₄×D₄×D₁₇₃	C₂	1	4	yes	maximal, complemented
11	C₂×C₄×D₄×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
12	#19149724	C₄	1	16	yes	direct product factor
13	C₂×#14583826	C₂²	1	2	yes	—
14	C₂×#14583825	C₂²	1	4	yes	—
15	C₂²×C₂²⋊D₁₇₃	C₂²	1	4	yes	—
16	C₂×D₄×D₁₇₃	C₂²	1	4	yes	—
17	C₂²×C₄×D₁₇₃	C₂²	1	4	yes	complemented
18	C₄×Dic₃₄₆	C₂²	1	2	yes	complemented
19	C₄×Dic₃₄₆	C₂²	1	2	yes	complemented
20	#19149644	C₂²	1	4	yes	complemented
21	C₄×D₆₉₂	C₂²	1	2	yes	complemented
22	C₄×D₆₉₂	C₂²	1	2	yes	complemented
23	D₄×Dic₁₇₃	C₂²	1	4	yes	complemented
24	D₄×Dic₁₇₃	C₂²	1	4	yes	complemented
25	#19149641	C₂²	1	4	yes	complemented
26	C₄×C₂²⋊D₁₇₃	C₂²	1	8	yes	complemented
27	C₄×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
28	C₄×C₂²⋊D₁₇₃	C₂²	1	8	yes	complemented
29	C₄×C₂²⋊D₁₇₃	C₂²	1	8	yes	complemented
30	C₄×C₂²⋊D₁₇₃	C₂²	1	4	yes	complemented
31	#19149639	C₂²	1	8	yes	complemented
32	#19149639	C₂²	1	8	yes	complemented
33	#19149638	C₂²	1	2	yes	complemented
34	#19149637	C₂²	1	4	yes	complemented
35	#19149636	C₂²	1	4	yes	complemented
36	#19149635	C₂²	1	8	yes	complemented
37	C₂×#14583805	C₂²	1	4	yes	complemented
38	C₄⋊C₄×D₁₇₃	C₂²	1	4	yes	complemented
39	C₂×C₂²⋊Dic₁₇₃	C₂²	1	4	yes	complemented
40	C₂×#14583803	C₂²	1	4	yes	complemented
41	C₂²⋊C₄×D₁₇₃	C₂²	1	8	yes	complemented
42	C₂×C₄×Dic₁₇₃	C₂²	1	4	yes	complemented
43	C₄²×D₁₇₃	C₂²	1	4	yes	complemented
44	C₂²×D₄×C₁₇₃	C₂²	1	1	yes	characteristic
45	C₂³×C₄×C₁₇₃	C₂²	1	2	yes	complemented
46	C₄×D₄×C₁₇₃	C₂²	1	4	yes	complemented
47	C₄×D₄×C₁₇₃	C₂²	1	4	yes	complemented
48	C₂×C₄⋊C₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
49	C₂×C₂²⋊C₄×C₁₇₃	C₂²	1	2	yes	complemented
50	C₂×C₄²×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
51	C₂³×D₁₇₃	C₂³	1	4	yes	—
52	#14583826	C₂×C₄	1	16	yes	complemented
53	#14583825	C₂×C₄	1	32	yes	complemented
54	C₂×Dic₃₄₆	C₂³	1	2	yes	—
55	C₂×D₆₉₂	C₂³	1	2	yes	—
56	C₂×C₂²⋊D₁₇₃	C₂×C₄	1	32	yes	complemented
57	C₂×C₂²⋊D₁₇₃	C₂³	1	8	yes	—
58	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
59	D₄×D₁₇₃	C₂×C₄	1	32	yes	complemented
60	C₂²×Dic₁₇₃	C₂³	1	4	yes	—
61	C₂²×Dic₁₇₃	C₂³	1	4	yes	—
62	C₂²×Dic₁₇₃	C₂³	1	4	yes	—
63	C₂×C₄×D₁₇₃	—	4	8	no	—
64	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
65	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
66	C₂×C₄×D₁₇₃	C₂³	1	8	yes	—
67	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
68	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
69	C₄⋊Dic₁₇₃	C₂³	1	2	yes	—
70	#14583805	C₂³	1	8	yes	—
71	#14583805	C₂³	1	4	yes	—
72	#14583805	C₂³	1	4	yes	—
73	C₂²⋊Dic₁₇₃	C₂³	1	8	yes	—
74	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
75	#14583803	C₂³	1	4	yes	—
76	#14583803	C₂³	1	8	yes	—
77	#14583803	C₂³	1	4	yes	—
78	C₄×Dic₁₇₃	C₂³	1	4	yes	—
79	C₄×Dic₁₇₃	C₂³	1	4	yes	—
80	C₄×Dic₁₇₃	C₂³	1	4	yes	—
81	C₄×Dic₁₇₃	C₂³	1	8	yes	—
82	C₂⁴×C₁₇₃	C₂³	1	2	yes	—
83	C₂×D₄×C₁₇₃	C₂×C₄	1	8	yes	complemented
84	C₂×D₄×C₁₇₃	C₂³	1	4	yes	—
85	C₂²×C₄×C₁₇₃	—	4	4	no	—
86	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
87	C₂²×C₄×C₁₇₃	C₂³	1	4	yes	—
88	C₂²×C₄×C₁₇₃	C₂³	1	4	yes	—
89	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
90	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
91	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
92	C₄⋊C₄×C₁₇₃	C₂³	1	4	yes	—
93	C₂²⋊C₄×C₁₇₃	C₂³	1	8	yes	—
94	C₄²×C₁₇₃	C₂³	1	2	yes	—
95	C₄²×C₁₇₃	C₂³	1	2	yes	—
96	C₂²×D₁₇₃	—	4	4	no	—
97	C₂²×D₁₇₃	—	4	4	no	—
98	C₂²×D₁₇₃	C₂²×C₄	1	16	yes	complemented
99	C₂²×D₁₇₃	C₂⁴	1	4	yes	—
100	Dic₃₄₆	C₂²×C₄	1	8	yes	complemented
101	D₆₉₂	C₂²×C₄	1	8	yes	complemented
102	C₂²⋊D₁₇₃	C₂²×C₄	1	32	yes	complemented
103	C₂²⋊D₁₇₃	C₂²×C₄	1	16	yes	complemented
104	C₂×Dic₁₇₃	—	4	4	no	—
105	C₂×Dic₁₇₃	—	4	4	no	—
106	C₂×Dic₁₇₃	C₂²×C₄	1	16	yes	complemented
107	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
108	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
109	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
110	C₄×D₁₇₃	—	2	8	no	—
111	C₄×D₁₇₃	—	4	8	no	—
112	C₄×D₁₇₃	—	4	4	no	—
113	C₄×D₁₇₃	C₂²×C₄	1	16	yes	complemented
114	C₂³×C₁₇₃	—	4	2	no	—
115	C₂³×C₁₇₃	—	4	2	no	—
116	C₂³×C₁₇₃	C₂²×C₄	1	8	yes	complemented
117	C₂³×C₁₇₃	C₂⁴	1	4	yes	—
118	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
119	D₄×C₁₇₃	C₂²×C₄	1	16	yes	complemented
120	C₂×C₄×C₁₇₃	—	2	8	no	—
121	C₂×C₄×C₁₇₃	—	2	2	no	—
122	C₂×C₄×C₁₇₃	—	4	4	no	—
123	C₂×C₄×C₁₇₃	—	4	2	no	—
124	C₂×C₄×C₁₇₃	—	4	1	no	—
125	C₂×C₄×C₁₇₃	C₂²×C₄	1	4	yes	complemented
126	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
127	C₂×C₄×C₁₇₃	C₂⁴	1	4	yes	—
128	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
129	C₂×C₄×C₁₇₃	C₂⁴	1	2	yes	—
130	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
131	C₂²×C₁₇₃	—	2	1	no	—
132	C₂²×C₁₇₃	—	2	4	no	—
133	C₂²×C₁₇₃	—	2	1	no	—
134	C₂²×C₁₇₃	—	2	4	no	—
135	C₂²×C₁₇₃	—	4	8	no	—
136	C₂²×C₁₇₃	C₂³×C₄	1	2	yes	—
137	C₂²×C₁₇₃	C₂³×C₄	1	8	yes	—
138	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
139	C₂×D₁₇₃	—	2	4	no	—
140	C₂×D₁₇₃	—	2	4	no	—
141	C₂×D₁₇₃	—	4	16	no	—
142	C₂×D₁₇₃	C₂³×C₄	1	8	yes	—
143	C₄×C₁₇₃	—	2	1	no	—
144	C₄×C₁₇₃	—	2	4	no	—
145	C₄×C₁₇₃	—	2	2	no	—
146	C₄×C₁₇₃	C₂³×C₄	1	4	yes	—
147	C₄×C₁₇₃	H(5,𝔽₂)	1	2	yes	complemented
148	Dic₁₇₃	—	2	4	no	—
149	Dic₁₇₃	—	2	4	no	—
150	Dic₁₇₃	C₂³×C₄	1	8	yes	—
151	C₂×C₁₇₃	—	2	8	no	—
152	C₂×C₁₇₃	—	2	2	no	—
153	C₂×C₁₇₃	C₂⁴×C₄	1	1	yes	characteristic
154	C₂×C₁₇₃	C₂×H(5,𝔽₂)	1	1	yes	characteristic
155	C₂×C₁₇₃	#585	1	1	yes	characteristic
156	D₁₇₃	—	2	8	no	—
157	C₁₇₃	C₄×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
158	C₄×H(5,𝔽₂)	—	173	1	no	maximal, Sylow
159	C₂×H(5,𝔽₂)	—	173	1	no	—
160	#520	—	173	4	no	—
161	#520	—	173	2	no	—
162	#518	—	173	1	no	—
163	#518	—	173	4	no	—
164	#518	—	173	4	no	—
165	C₄×#41	—	173	4	no	—
166	C₄×#41	—	173	2	no	—
167	C₂×C₄×D₄	—	173	4	no	—
168	C₂×C₄×D₄	—	173	4	no	—
169	C₂×C₄×D₄	D₁₇₃	1	1	yes	characteristic, complemented
170	H(5,𝔽₂)	—	173	16	no	—
171	C₂×#41	—	173	4	no	—
172	C₂×#41	—	173	2	no	—
173	C₂²×D₄	—	173	4	no	—
174	C₂²×D₄	—	173	4	no	—
175	C₂²×D₄	C₂×D₁₇₃	1	1	yes	characteristic
176	C₂³×C₄	—	173	4	no	—
177	C₂³×C₄	C₂×D₁₇₃	1	2	yes	complemented
178	C₄×Q₈	—	173	4	no	—
179	C₄×Q₈	—	173	2	no	—
180	C₄×Q₈	—	173	2	no	—
181	C₄×D₄	—	173	4	no	—
182	C₄×D₄	—	173	4	no	—
183	C₄×D₄	—	173	8	no	—
184	C₄×D₄	—	173	4	no	—
185	C₄×D₄	—	173	8	no	—
186	C₄×D₄	—	173	8	no	—
187	C₄×D₄	—	173	4	no	—
188	C₄×D₄	—	173	4	no	—
189	C₄×D₄	—	173	8	no	—
190	C₄×D₄	—	173	8	no	—
191	C₄×D₄	—	173	2	no	—
192	C₄×D₄	—	173	2	no	—
193	C₄×D₄	C₂×D₁₇₃	1	4	yes	complemented
194	C₄×D₄	C₂×D₁₇₃	1	4	yes	complemented
195	#117	—	173	2	no	—
196	#117	—	173	4	no	—
197	#117	—	173	8	no	—
198	#117	—	173	4	no	—
199	C₂×C₄⋊C₄	—	173	4	no	—
200	C₂×C₄⋊C₄	—	173	4	no	—
201	C₂×C₄⋊C₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
202	C₂×C₂²⋊C₄	—	173	4	no	—
203	C₂×C₂²⋊C₄	—	173	4	no	—
204	C₂×C₂²⋊C₄	—	173	8	no	—
205	C₂×C₂²⋊C₄	C₂×D₁₇₃	1	2	yes	complemented
206	C₂×C₄²	—	173	4	no	—
207	C₂×C₄²	—	173	4	no	—
208	C₂×C₄²	C₂×D₁₇₃	1	1	yes	characteristic, complemented
209	C₂⁴	—	173	4	no	—
210	C₂⁴	C₂²×D₁₇₃	1	2	yes	—
211	#41	—	173	32	no	—
212	#41	—	173	16	no	—
213	C₂×Q₈	—	173	2	no	—
214	C₂×D₄	—	173	32	no	—
215	C₂×D₄	—	173	4	no	—
216	C₂×D₄	—	173	8	no	—
217	C₂×D₄	—	173	32	no	—
218	C₂×D₄	—	173	2	no	—
219	C₂×D₄	C₄×D₁₇₃	1	8	yes	complemented
220	C₂×D₄	C₂²×D₁₇₃	1	4	yes	—
221	C₂²×C₄	—	4	4	no	—
222	C₂²×C₄	—	173	4	no	—
223	C₂²×C₄	—	173	4	no	—
224	C₂²×C₄	—	173	4	no	—
225	C₂²×C₄	—	173	4	no	—
226	C₂²×C₄	—	173	4	no	—
227	C₂²×C₄	—	173	4	no	—
228	C₂²×C₄	—	173	8	no	—
229	C₂²×C₄	—	692	8	no	—
230	C₂²×C₄	C₂²×D₁₇₃	1	4	yes	—
231	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
232	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
233	C₂²×C₄	C₂²×D₁₇₃	1	4	yes	—
234	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
235	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
236	C₄⋊C₄	—	173	8	no	—
237	C₄⋊C₄	—	173	4	no	—
238	C₄⋊C₄	—	173	2	no	—
239	C₄⋊C₄	—	173	4	no	—
240	C₄⋊C₄	—	173	2	no	—
241	C₄⋊C₄	C₂²×D₁₇₃	1	4	yes	—
242	C₂²⋊C₄	—	173	4	no	—
243	C₂²⋊C₄	—	173	8	no	—
244	C₂²⋊C₄	—	173	8	no	—
245	C₂²⋊C₄	—	173	4	no	—
246	C₂²⋊C₄	—	173	4	no	—
247	C₂²⋊C₄	C₂²×D₁₇₃	1	8	yes	—
248	C₄²	—	173	4	no	—
249	C₄²	—	173	8	no	—
250	C₄²	—	173	4	no	—
251	C₄²	—	173	4	no	—
252	C₄²	C₂²×D₁₇₃	1	2	yes	—
253	C₄²	C₂²×D₁₇₃	1	2	yes	—
254	C₂³	—	4	2	no	—
255	C₂³	—	4	2	no	—
256	C₂³	—	173	4	no	—
257	C₂³	—	173	16	no	—
258	C₂³	—	692	4	no	—
259	C₂³	—	692	4	no	—
260	C₂³	C₂×C₄×D₁₇₃	1	8	yes	complemented
261	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
262	C₂³	C₂³×D₁₇₃	1	4	yes	—
263	Q₈	—	173	8	no	—
264	D₄	—	173	32	no	—
265	D₄	—	173	16	no	—
266	D₄	—	173	8	no	—
267	D₄	C₂×C₄×D₁₇₃	1	16	yes	complemented
268	C₂×C₄	—	2	2	no	—
269	C₂×C₄	—	2	8	no	—
270	C₂×C₄	—	4	4	no	—
271	C₂×C₄	—	4	2	no	—
272	C₂×C₄	—	4	1	no	—
273	C₂×C₄	—	346	8	no	—
274	C₂×C₄	—	173	4	no	—
275	C₂×C₄	—	173	4	no	—
276	C₂×C₄	—	173	16	no	—
277	C₂×C₄	—	173	4	no	—
278	C₂×C₄	—	173	16	no	—
279	C₂×C₄	—	692	4	no	—
280	C₂×C₄	—	692	8	no	—
281	C₂×C₄	—	692	4	no	—
282	C₂×C₄	—	692	4	no	—
283	C₂×C₄	C₂×C₄×D₁₇₃	1	4	yes	complemented
284	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
285	C₂×C₄	C₂³×D₁₇₃	1	4	yes	—
286	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
287	C₂×C₄	C₂³×D₁₇₃	1	2	yes	—
288	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
289	C₂²	—	2	1	no	—
290	C₂²	—	2	4	no	—
291	C₂²	—	2	1	no	—
292	C₂²	—	2	4	no	—
293	C₂²	—	4	8	no	—
294	C₂²	—	346	4	no	—
295	C₂²	—	346	4	no	—
296	C₂²	—	173	8	no	—
297	C₂²	—	692	16	no	—
298	C₂²	C₂²×C₄×D₁₇₃	1	8	yes	—
299	C₂²	C₂²×C₄×D₁₇₃	1	2	yes	—
300	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
301	C₄	—	2	1	no	—
302	C₄	—	2	4	no	—
303	C₄	—	2	2	no	—
304	C₄	—	346	4	no	—
305	C₄	—	346	4	no	—
306	C₄	—	173	8	no	—
307	C₄	C₂²×C₄×D₁₇₃	1	4	yes	—
308	C₄	#19149724	1	2	yes	direct product factor
309	C₂	—	2	2	no	—
310	C₂	—	2	8	no	—
311	C₂	—	346	8	no	—
312	C₂	C₂³×C₄×D₁₇₃	1	1	yes	characteristic
313	C₂	C₂×#19149724	1	1	yes	characteristic
314	C₂	#26012327	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₇₃
commutator	C₂×C₁₇₃	C₂⁴×C₄
Frattini	C₂²	C₂⁴×D₁₇₃
Fitting	C₂×C₄×D₄×C₁₇₃	C₂
socle, cosocle	C₂²×C₁₇₃	C₂⁵
prime radical	C₂×#19149724	C₂
hypercenter	C₂×C₄×D₄	D₁₇₃
hypocenter	C₁₇₃	C₄×H(5,𝔽₂)
LCS	G ▷ C₂×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄×D₄

Complements

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

N	H ≅ G/N	type
2. #26011972	C₂	semidirect
3. #26011970	C₂	semidirect
4. #26011966	C₂	semidirect
5. #26011964	C₂	semidirect
6. #26011963	C₂	semidirect
7. C₄×#14583826	C₂	semidirect
8. C₄×#14583825	C₂	semidirect
9. C₂×C₄×C₂²⋊D₁₇₃	C₂	semidirect
10. C₄×D₄×D₁₇₃	C₂	semidirect
11. C₂×C₄×D₄×C₁₇₃	C₂	semidirect
12. #19149724	C₄	direct (N × H)
17. C₂²×C₄×D₁₇₃	C₂²	semidirect
18. C₄×Dic₃₄₆	C₂²	semidirect
19. C₄×Dic₃₄₆	C₂²	semidirect
20. #19149644	C₂²	semidirect
21. C₄×D₆₉₂	C₂²	semidirect
22. C₄×D₆₉₂	C₂²	semidirect
23. D₄×Dic₁₇₃	C₂²	semidirect
24. D₄×Dic₁₇₃	C₂²	semidirect
25. #19149641	C₂²	semidirect
26. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
27. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
28. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
29. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
30. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
31. #19149639	C₂²	semidirect
32. #19149639	C₂²	semidirect
33. #19149638	C₂²	semidirect
34. #19149637	C₂²	semidirect
35. #19149636	C₂²	semidirect
36. #19149635	C₂²	semidirect
37. C₂×#14583805	C₂²	semidirect
38. C₄⋊C₄×D₁₇₃	C₂²	semidirect
39. C₂×C₂²⋊Dic₁₇₃	C₂²	semidirect
40. C₂×#14583803	C₂²	semidirect
41. C₂²⋊C₄×D₁₇₃	C₂²	semidirect
42. C₂×C₄×Dic₁₇₃	C₂²	semidirect
43. C₄²×D₁₇₃	C₂²	semidirect
45. C₂³×C₄×C₁₇₃	C₂²	semidirect
46. C₄×D₄×C₁₇₃	C₂²	semidirect
47. C₄×D₄×C₁₇₃	C₂²	semidirect
48. C₂×C₄⋊C₄×C₁₇₃	C₂²	semidirect
49. C₂×C₂²⋊C₄×C₁₇₃	C₂²	semidirect
50. C₂×C₄²×C₁₇₃	C₂²	semidirect
52. #14583826	C₂×C₄	semidirect
53. #14583825	C₂×C₄	semidirect
56. C₂×C₂²⋊D₁₇₃	C₂×C₄	semidirect
59. D₄×D₁₇₃	C₂×C₄	semidirect
83. C₂×D₄×C₁₇₃	C₂×C₄	semidirect
98. C₂²×D₁₇₃	C₂²×C₄	semidirect
100. Dic₃₄₆	C₂²×C₄	semidirect
101. D₆₉₂	C₂²×C₄	semidirect
102. C₂²⋊D₁₇₃	C₂²×C₄	semidirect
103. C₂²⋊D₁₇₃	C₂²×C₄	semidirect
106. C₂×Dic₁₇₃	C₂²×C₄	semidirect
113. C₄×D₁₇₃	C₂²×C₄	semidirect
116. C₂³×C₁₇₃	C₂²×C₄	semidirect
119. D₄×C₁₇₃	C₂²×C₄	semidirect
125. C₂×C₄×C₁₇₃	C₂²×C₄	semidirect
147. C₄×C₁₇₃	H(5,𝔽₂)	semidirect
157. C₁₇₃	C₄×H(5,𝔽₂)	semidirect
169. C₂×C₄×D₄	D₁₇₃	semidirect
177. C₂³×C₄	C₂×D₁₇₃	semidirect
193. C₄×D₄	C₂×D₁₇₃	semidirect
194. C₄×D₄	C₂×D₁₇₃	semidirect
201. C₂×C₄⋊C₄	C₂×D₁₇₃	semidirect
205. C₂×C₂²⋊C₄	C₂×D₁₇₃	semidirect
208. C₂×C₄²	C₂×D₁₇₃	semidirect
219. C₂×D₄	C₄×D₁₇₃	semidirect
260. C₂³	C₂×C₄×D₁₇₃	semidirect
267. D₄	C₂×C₄×D₁₇₃	semidirect
283. C₂×C₄	C₂×C₄×D₁₇₃	semidirect
308. C₄	#19149724	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×#19149724	2
#26011972	2
#26011970	2
#26011966	2
#26011964	2
#26011963	2
C₄×#14583826	2
C₄×#14583825	2
C₂×C₄×C₂²⋊D₁₇₃	2
C₄×D₄×D₁₇₃	2
C₂×C₄×D₄×C₁₇₃	2
C₄×H(5,𝔽₂)	173

Subgroups — C4×#19149724 #36366768

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#19149724 #36366768