Subgroups — #36366892

Order 22144.

1556 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14583826	C₂	1	1	yes	maximal, characteristic, complemented
2	#26012069	C₂	1	4	yes	maximal, complemented
3	#26012065	C₂	1	2	yes	maximal, complemented
4	#26012062	C₂	1	2	yes	maximal, complemented
5	#26012058	C₂	1	2	yes	maximal, complemented
6	#26012055	C₂	1	2	yes	maximal, complemented
7	#26012050	C₂	1	4	yes	maximal, complemented
8	#26012037	C₂	1	4	yes	maximal, complemented
9	#26012002	C₂	1	4	yes	maximal, complemented
10	#26011998	C₂	1	4	yes	maximal, complemented
11	C₂×#19149638	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂²×#41×C₁₇₃	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×#14583826	—	2	8	no	—
14	C₂×#14583826	C₂²	1	2	yes	—
15	C₂×#14583826	C₂²	1	2	yes	—
16	C₂×#14583826	C₂²	1	2	yes	complemented
17	C₂×#14583826	C₂²	1	2	yes	complemented
18	C₂²×Dic₃₄₆	C₂²	1	1	yes	characteristic, complemented
19	C₂²×D₆₉₂	C₂²	1	1	yes	characteristic, complemented
20	C₂²×C₂²⋊D₁₇₃	C₂²	1	2	yes	—
21	C₂²×C₄×D₁₇₃	C₂²	1	2	yes	complemented
22	#19149677	C₂²	1	4	yes	complemented
23	#19149675	C₂²	1	4	yes	complemented
24	#19149668	C₂²	1	4	yes	complemented
25	#19149666	C₂²	1	4	yes	complemented
26	#19149662	C₂²	1	8	yes	complemented
27	#19149660	C₂²	1	8	yes	complemented
28	#19149658	C₂²	1	8	yes	complemented
29	#19149655	C₂²	1	8	yes	complemented
30	#19149653	C₂²	1	8	yes	complemented
31	#19149651	C₂²	1	16	yes	complemented
32	#19149650	C₂²	1	8	yes	complemented
33	#19149648	C₂²	1	8	yes	complemented
34	#19149647	C₂²	1	8	yes	complemented
35	C₄×C₂²⋊D₁₇₃	C₂²	1	16	yes	complemented
36	#19149638	C₂²	1	2	yes	complemented
37	#19149638	C₂²	1	2	yes	complemented
38	#19149638	C₂²	1	2	yes	complemented
39	#19149638	C₂²	1	2	yes	complemented
40	C₂×C₄⋊Dic₁₇₃	C₂²	1	2	yes	complemented
41	C₂×C₂²⋊Dic₁₇₃	C₂²	1	2	yes	—
42	C₂×C₄×Dic₁₇₃	C₂²	1	2	yes	complemented
43	C₂×#41×C₁₇₃	—	2	8	no	—
44	C₂×#41×C₁₇₃	C₂²	1	2	yes	—
45	C₂×#41×C₁₇₃	C₂²	1	2	yes	—
46	C₂×#41×C₁₇₃	C₂²	1	2	yes	complemented
47	C₂×#41×C₁₇₃	C₂²	1	2	yes	complemented
48	C₂²×Q₈×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
49	C₂²×D₄×C₁₇₃	C₂²	1	2	yes	—
50	C₂²×D₄×C₁₇₃	C₂²	1	1	yes	characteristic, complemented
51	C₂³×C₄×C₁₇₃	C₂²	1	1	yes	characteristic
52	C₂³×C₄×C₁₇₃	C₂²	1	2	yes	complemented
53	C₂³×D₁₇₃	C₂³	1	2	yes	—
54	#14583826	—	2	8	no	—
55	#14583826	—	2	8	no	—
56	#14583826	—	2	8	no	—
57	#14583826	—	2	8	no	—
58	C₂×Dic₃₄₆	—	2	4	no	—
59	C₂×Dic₃₄₆	C₂³	1	2	yes	—
60	C₂×Dic₃₄₆	C₂³	1	2	yes	—
61	C₂×D₆₉₂	—	2	4	no	—
62	C₂×D₆₉₂	C₂³	1	2	yes	—
63	C₂×D₆₉₂	C₂³	1	2	yes	—
64	C₂×C₂²⋊D₁₇₃	—	2	8	no	—
65	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
66	C₂×C₂²⋊D₁₇₃	C₂³	1	4	yes	—
67	C₂×C₂²⋊D₁₇₃	C₂³	1	16	yes	—
68	C₂²×Dic₁₇₃	C₂³	1	2	yes	—
69	C₂²×Dic₁₇₃	C₂³	1	4	yes	—
70	C₂×C₄×D₁₇₃	—	2	8	no	—
71	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
72	C₂×C₄×D₁₇₃	C₂³	1	4	yes	—
73	C₄⋊Dic₁₇₃	C₂³	1	4	yes	—
74	C₄⋊Dic₁₇₃	C₂³	1	4	yes	—
75	#14583805	C₂³	1	16	yes	—
76	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
77	C₂²⋊Dic₁₇₃	C₂³	1	4	yes	—
78	C₂²⋊Dic₁₇₃	C₂³	1	16	yes	—
79	#14583803	C₂³	1	16	yes	—
80	C₄×Dic₁₇₃	C₂³	1	4	yes	—
81	C₄×Dic₁₇₃	C₂³	1	4	yes	—
82	C₂⁴×C₁₇₃	C₂³	1	2	yes	—
83	C₂⁴×C₁₇₃	C₂³	1	1	yes	characteristic
84	#41×C₁₇₃	—	2	8	no	—
85	#41×C₁₇₃	—	2	8	no	—
86	#41×C₁₇₃	—	2	8	no	—
87	#41×C₁₇₃	—	2	8	no	—
88	C₂×Q₈×C₁₇₃	—	2	4	no	—
89	C₂×Q₈×C₁₇₃	C₂³	1	2	yes	—
90	C₂×Q₈×C₁₇₃	C₂³	1	2	yes	—
91	C₂×D₄×C₁₇₃	—	2	8	no	—
92	C₂×D₄×C₁₇₃	—	2	4	no	—
93	C₂×D₄×C₁₇₃	C₂³	1	4	yes	—
94	C₂×D₄×C₁₇₃	C₂³	1	4	yes	—
95	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
96	C₂×D₄×C₁₇₃	C₂³	1	2	yes	—
97	C₂²×C₄×C₁₇₃	—	2	8	no	—
98	C₂²×C₄×C₁₇₃	D₄	1	8	yes	complemented
99	C₂²×C₄×C₁₇₃	C₂³	1	2	yes	—
100	C₂²×C₄×C₁₇₃	C₂³	1	4	yes	—
101	C₂²×C₄×C₁₇₃	C₂³	1	4	yes	—
102	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
106	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
107	C₂²×C₄×C₁₇₃	C₂³	1	1	yes	characteristic
108	C₂²×D₁₇₃	—	2	4	no	—
109	C₂²×D₁₇₃	—	4	4	no	—
110	C₂²×D₁₇₃	C₂⁴	1	4	yes	—
111	Dic₃₄₆	—	2	4	no	—
112	Dic₃₄₆	—	2	4	no	—
113	D₆₉₂	—	2	4	no	—
114	D₆₉₂	—	2	4	no	—
115	C₂²⋊D₁₇₃	—	2	8	no	—
116	C₂²⋊D₁₇₃	—	2	8	no	—
117	C₂²⋊D₁₇₃	—	4	16	no	—
118	C₂×Dic₁₇₃	—	2	4	no	—
119	C₂×Dic₁₇₃	—	4	4	no	—
120	C₂×Dic₁₇₃	C₂⁴	1	4	yes	—
121	C₂×Dic₁₇₃	C₂⁴	1	8	yes	—
122	C₄×D₁₇₃	—	2	8	no	—
123	C₄×D₁₇₃	—	2	8	no	—
124	C₂³×C₁₇₃	—	2	4	no	—
125	C₂³×C₁₇₃	—	4	2	no	—
126	C₂³×C₁₇₃	—	4	4	no	—
127	C₂³×C₁₇₃	C₂×D₄	1	4	yes	—
128	C₂³×C₁₇₃	C₂⁴	1	4	yes	—
129	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
130	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
131	C₂³×C₁₇₃	C₂⁴	1	1	yes	characteristic
132	Q₈×C₁₇₃	—	2	4	no	—
133	Q₈×C₁₇₃	—	2	4	no	—
134	D₄×C₁₇₃	—	2	8	no	—
135	D₄×C₁₇₃	—	2	8	no	—
136	D₄×C₁₇₃	—	2	4	no	—
137	D₄×C₁₇₃	—	2	4	no	—
138	C₂×C₄×C₁₇₃	—	2	4	no	—
139	C₂×C₄×C₁₇₃	—	2	8	no	—
140	C₂×C₄×C₁₇₃	—	2	8	no	—
141	C₂×C₄×C₁₇₃	C₂×D₄	1	4	yes	—
142	C₂×C₄×C₁₇₃	C₂×D₄	1	4	yes	—
143	C₂×C₄×C₁₇₃	C₂×D₄	1	4	yes	—
144	C₂×C₄×C₁₇₃	C₂×D₄	1	4	yes	—
145	C₂×C₄×C₁₇₃	C₂×D₄	1	4	yes	—
146	C₂×C₄×C₁₇₃	C₂×D₄	1	4	yes	—
147	C₂×C₄×C₁₇₃	C₂⁴	1	4	yes	—
148	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
149	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
150	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
151	C₂×C₄×C₁₇₃	C₂⁴	1	1	yes	characteristic
152	C₂²×C₁₇₃	—	2	2	no	—
153	C₂²×C₁₇₃	—	2	2	no	—
154	C₂²×C₁₇₃	—	2	2	no	—
155	C₂²×C₁₇₃	—	2	4	no	—
156	C₂²×C₁₇₃	—	2	8	no	—
157	C₂²×C₁₇₃	—	4	4	no	—
158	C₂²×C₁₇₃	—	4	8	no	—
159	C₂²×C₁₇₃	C₂²×D₄	1	2	yes	—
160	C₂²×C₁₇₃	C₂²×D₄	1	2	yes	—
161	C₂²×C₁₇₃	C₂²×D₄	1	2	yes	—
162	C₂²×C₁₇₃	C₂⁵	1	1	yes	characteristic
163	C₂×D₁₇₃	—	2	4	no	—
164	C₂×D₁₇₃	—	2	8	no	—
165	C₂×D₁₇₃	—	4	8	no	—
166	C₄×C₁₇₃	—	2	4	no	—
167	C₄×C₁₇₃	C₂²×D₄	1	2	yes	—
168	C₄×C₁₇₃	C₂²×D₄	1	2	yes	—
169	C₄×C₁₇₃	C₂²×D₄	1	2	yes	—
170	C₄×C₁₇₃	C₂²×D₄	1	2	yes	—
171	Dic₁₇₃	—	2	4	no	—
172	Dic₁₇₃	—	2	8	no	—
173	C₂×C₁₇₃	—	2	2	no	—
174	C₂×C₁₇₃	—	2	2	no	—
175	C₂×C₁₇₃	—	2	2	no	—
176	C₂×C₁₇₃	—	4	4	no	—
177	C₂×C₁₇₃	C₂³×D₄	1	1	yes	characteristic
178	C₂×C₁₇₃	#585	1	2	yes	—
179	D₁₇₃	—	4	4	no	—
180	C₁₇₃	#3449	1	1	yes	characteristic, complemented, Sylow
181	#3449	—	173	1	no	maximal, Sylow
182	C₂²×#41	—	173	1	no	—
183	C₂²×#41	D₁₇₃	1	1	yes	characteristic, complemented
184	#537	—	173	4	no	—
185	#536	—	173	2	no	—
186	#536	—	173	2	no	—
187	#535	—	173	2	no	—
188	#535	—	173	2	no	—
189	#534	—	173	4	no	—
190	#532	—	173	4	no	—
191	#525	—	173	4	no	—
192	#525	—	173	4	no	—
193	C₂×#117	—	173	1	no	—
194	C₂×#41	—	2	8	no	—
195	C₂×#41	—	346	8	no	—
196	C₂×#41	—	173	2	no	—
197	C₂×#41	—	173	2	no	—
198	C₂×#41	—	173	2	no	—
199	C₂×#41	—	173	2	no	—
200	C₂×#41	C₂×D₁₇₃	1	2	yes	—
201	C₂×#41	C₂×D₁₇₃	1	2	yes	—
202	C₂×#41	C₂×D₁₇₃	1	2	yes	complemented
203	C₂×#41	C₂×D₁₇₃	1	2	yes	complemented
204	C₂²×Q₈	—	173	1	no	—
205	C₂²×Q₈	C₂×D₁₇₃	1	1	yes	characteristic, complemented
206	C₂²×D₄	—	173	2	no	—
207	C₂²×D₄	—	173	1	no	—
208	C₂²×D₄	C₂×D₁₇₃	1	2	yes	—
209	C₂²×D₄	C₂×D₁₇₃	1	1	yes	characteristic, complemented
210	C₂³×C₄	—	173	2	no	—
211	C₂³×C₄	C₂×D₁₇₃	1	1	yes	characteristic
212	C₂³×C₄	C₂×D₁₇₃	1	2	yes	complemented
213	C₄⋊Q₈	—	173	4	no	—
214	#127	—	173	4	no	—
215	#124	—	173	4	no	—
216	#124	—	173	4	no	—
217	#123	—	173	8	no	—
218	#123	—	173	8	no	—
219	C₂²⋊Q₈	—	173	8	no	—
220	C₂²⋊Q₈	—	173	8	no	—
221	#121	—	173	8	no	—
222	#121	—	173	16	no	—
223	#121	—	173	8	no	—
224	#120	—	173	8	no	—
225	#120	—	173	8	no	—
226	C₄×D₄	—	173	16	no	—
227	#117	—	173	2	no	—
228	#117	—	173	2	no	—
229	#117	—	173	2	no	—
230	#117	—	173	2	no	—
231	C₂×C₄⋊C₄	—	173	2	no	—
232	C₂×C₂²⋊C₄	—	173	2	no	—
233	C₂×C₄²	—	173	2	no	—
234	C₂⁴	—	173	2	no	—
235	C₂⁴	C₂²×D₁₇₃	1	2	yes	—
236	C₂⁴	C₂²×D₁₇₃	1	1	yes	characteristic
237	#41	—	2	8	no	—
238	#41	—	2	8	no	—
239	#41	—	2	8	no	—
240	#41	—	2	8	no	—
241	#41	—	346	8	no	—
242	#41	—	346	8	no	—
243	#41	—	346	8	no	—
244	#41	—	346	8	no	—
245	C₂×Q₈	—	2	4	no	—
246	C₂×Q₈	—	346	4	no	—
247	C₂×Q₈	—	173	2	no	—
248	C₂×Q₈	—	173	2	no	—
249	C₂×Q₈	C₂²×D₁₇₃	1	2	yes	—
250	C₂×Q₈	C₂²×D₁₇₃	1	2	yes	—
251	C₂×D₄	—	2	8	no	—
252	C₂×D₄	—	2	4	no	—
253	C₂×D₄	—	346	8	no	—
254	C₂×D₄	—	346	4	no	—
255	C₂×D₄	—	173	4	no	—
256	C₂×D₄	—	173	4	no	—
257	C₂×D₄	—	173	16	no	—
258	C₂×D₄	—	173	2	no	—
259	C₂×D₄	—	173	2	no	—
260	C₂×D₄	C₂²×D₁₇₃	1	4	yes	—
261	C₂×D₄	C₂²×D₁₇₃	1	4	yes	—
262	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
263	C₂×D₄	C₂²×D₁₇₃	1	2	yes	—
264	C₂²×C₄	—	2	8	no	—
265	C₂²×C₄	—	346	8	no	—
266	C₂²×C₄	—	173	2	no	—
267	C₂²×C₄	—	173	4	no	—
268	C₂²×C₄	—	173	4	no	—
269	C₂²×C₄	—	173	4	no	—
270	C₂²×C₄	C₂²⋊D₁₇₃	1	8	yes	complemented
271	C₂²×C₄	C₂²×D₁₇₃	1	4	yes	—
272	C₂²×C₄	C₂²×D₁₇₃	1	2	yes	—
273	C₂²×C₄	C₂²×D₁₇₃	1	4	yes	—
274	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
275	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
276	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
277	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
278	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
279	C₂²×C₄	C₂²×D₁₇₃	1	1	yes	characteristic
280	C₄⋊C₄	—	173	4	no	—
281	C₄⋊C₄	—	173	4	no	—
282	C₄⋊C₄	—	173	16	no	—
283	C₂²⋊C₄	—	173	4	no	—
284	C₂²⋊C₄	—	173	4	no	—
285	C₂²⋊C₄	—	173	16	no	—
286	C₂²⋊C₄	—	173	16	no	—
287	C₄²	—	173	4	no	—
288	C₄²	—	173	4	no	—
289	C₂³	—	2	4	no	—
290	C₂³	—	4	2	no	—
291	C₂³	—	4	4	no	—
292	C₂³	—	346	4	no	—
293	C₂³	—	173	4	no	—
294	C₂³	—	692	4	no	—
295	C₂³	C₂×C₂²⋊D₁₇₃	1	4	yes	—
296	C₂³	C₂³×D₁₇₃	1	4	yes	—
297	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
298	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
299	C₂³	C₂³×D₁₇₃	1	1	yes	characteristic
300	Q₈	—	2	4	no	—
301	Q₈	—	2	4	no	—
302	Q₈	—	346	4	no	—
303	Q₈	—	346	4	no	—
304	D₄	—	2	8	no	—
305	D₄	—	2	8	no	—
306	D₄	—	2	4	no	—
307	D₄	—	2	4	no	—
308	D₄	—	346	8	no	—
309	D₄	—	346	8	no	—
310	D₄	—	346	4	no	—
311	D₄	—	346	4	no	—
312	D₄	—	692	16	no	—
313	C₂×C₄	—	2	4	no	—
314	C₂×C₄	—	2	8	no	—
315	C₂×C₄	—	2	8	no	—
316	C₂×C₄	—	346	4	no	—
317	C₂×C₄	—	346	8	no	—
318	C₂×C₄	—	346	8	no	—
319	C₂×C₄	—	173	8	no	—
320	C₂×C₄	—	173	4	no	—
321	C₂×C₄	—	692	4	no	—
322	C₂×C₄	C₂×C₂²⋊D₁₇₃	1	4	yes	—
323	C₂×C₄	C₂×C₂²⋊D₁₇₃	1	4	yes	—
324	C₂×C₄	C₂×C₂²⋊D₁₇₃	1	4	yes	—
325	C₂×C₄	C₂×C₂²⋊D₁₇₃	1	4	yes	—
326	C₂×C₄	C₂×C₂²⋊D₁₇₃	1	4	yes	—
327	C₂×C₄	C₂×C₂²⋊D₁₇₃	1	4	yes	—
328	C₂×C₄	C₂³×D₁₇₃	1	4	yes	—
329	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
330	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
331	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
332	C₂×C₄	C₂³×D₁₇₃	1	1	yes	characteristic
333	C₂²	—	2	2	no	—
334	C₂²	—	2	2	no	—
335	C₂²	—	2	2	no	—
336	C₂²	—	2	4	no	—
337	C₂²	—	2	8	no	—
338	C₂²	—	4	4	no	—
339	C₂²	—	4	8	no	—
340	C₂²	—	346	4	no	—
341	C₂²	—	346	8	no	—
342	C₂²	—	692	8	no	—
343	C₂²	C₂²×C₂²⋊D₁₇₃	1	2	yes	—
344	C₂²	C₂²×C₂²⋊D₁₇₃	1	2	yes	—
345	C₂²	C₂²×C₂²⋊D₁₇₃	1	2	yes	—
346	C₂²	C₂⁴×D₁₇₃	1	1	yes	characteristic
347	C₄	—	2	4	no	—
348	C₄	—	346	4	no	—
349	C₄	—	346	8	no	—
350	C₄	C₂²×C₂²⋊D₁₇₃	1	2	yes	—
351	C₄	C₂²×C₂²⋊D₁₇₃	1	2	yes	—
352	C₄	C₂²×C₂²⋊D₁₇₃	1	2	yes	—
353	C₄	C₂²×C₂²⋊D₁₇₃	1	2	yes	—
354	C₂	—	2	2	no	—
355	C₂	—	2	2	no	—
356	C₂	—	2	2	no	—
357	C₂	—	4	4	no	—
358	C₂	—	692	4	no	—
359	C₂	C₂³×C₂²⋊D₁₇₃	1	1	yes	characteristic
360	C₂	#26012327	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂³×D₁₇₃
commutator, socle, cosocle	C₂²×C₁₇₃	C₂⁵
Frattini	C₂²	C₂⁴×D₁₇₃
Fitting	C₂²×#41×C₁₇₃	C₂
hypercenter	C₂²×#41	D₁₇₃
hypocenter	C₁₇₃	#3449
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×#41

Complements

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

N	H ≅ G/N	type
1. C₂²×#14583826	C₂	semidirect
2. #26012069	C₂	semidirect
3. #26012065	C₂	semidirect
4. #26012062	C₂	semidirect
5. #26012058	C₂	semidirect
6. #26012055	C₂	semidirect
7. #26012050	C₂	semidirect
8. #26012037	C₂	semidirect
9. #26012002	C₂	semidirect
10. #26011998	C₂	semidirect
11. C₂×#19149638	C₂	semidirect
12. C₂²×#41×C₁₇₃	C₂	semidirect
16. C₂×#14583826	C₂²	semidirect
17. C₂×#14583826	C₂²	semidirect
18. C₂²×Dic₃₄₆	C₂²	semidirect
19. C₂²×D₆₉₂	C₂²	semidirect
21. C₂²×C₄×D₁₇₃	C₂²	semidirect
22. #19149677	C₂²	semidirect
23. #19149675	C₂²	semidirect
24. #19149668	C₂²	semidirect
25. #19149666	C₂²	semidirect
26. #19149662	C₂²	semidirect
27. #19149660	C₂²	semidirect
28. #19149658	C₂²	semidirect
29. #19149655	C₂²	semidirect
30. #19149653	C₂²	semidirect
31. #19149651	C₂²	semidirect
32. #19149650	C₂²	semidirect
33. #19149648	C₂²	semidirect
34. #19149647	C₂²	semidirect
35. C₄×C₂²⋊D₁₇₃	C₂²	semidirect
36. #19149638	C₂²	semidirect
37. #19149638	C₂²	semidirect
38. #19149638	C₂²	semidirect
39. #19149638	C₂²	semidirect
40. C₂×C₄⋊Dic₁₇₃	C₂²	semidirect
42. C₂×C₄×Dic₁₇₃	C₂²	semidirect
46. C₂×#41×C₁₇₃	C₂²	semidirect
47. C₂×#41×C₁₇₃	C₂²	semidirect
48. C₂²×Q₈×C₁₇₃	C₂²	semidirect
50. C₂²×D₄×C₁₇₃	C₂²	semidirect
52. C₂³×C₄×C₁₇₃	C₂²	semidirect
98. C₂²×C₄×C₁₇₃	D₄	semidirect
180. C₁₇₃	#3449	semidirect
183. C₂²×#41	D₁₇₃	semidirect
202. C₂×#41	C₂×D₁₇₃	semidirect
203. C₂×#41	C₂×D₁₇₃	semidirect
205. C₂²×Q₈	C₂×D₁₇₃	semidirect
209. C₂²×D₄	C₂×D₁₇₃	semidirect
212. C₂³×C₄	C₂×D₁₇₃	semidirect
270. C₂²×C₄	C₂²⋊D₁₇₃	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#14583826	2
#26012069	2
#26012065	2
#26012062	2
#26012058	2
#26012055	2
#26012050	2
#26012037	2
#26012002	2
#26011998	2
C₂×#19149638	2
C₂²×#41×C₁₇₃	2
#3449	173