Subgroups — #36370295

Order 22144.

502 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19149766	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#14583835	C₂	1	1	yes	maximal, characteristic, complemented
3	#26012526	C₂	1	1	yes	maximal, characteristic, complemented
4	#26012524	C₂	1	1	yes	maximal, characteristic, complemented
5	#26012523	C₂	1	1	yes	maximal, characteristic, complemented
6	#26012522	C₂	1	1	yes	maximal, characteristic, complemented
7	#26012522	C₂	1	1	yes	maximal, characteristic, complemented
8	#26012520	C₂	1	1	yes	maximal, characteristic, complemented
9	#26012518	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#13063443	C₂	1	1	yes	maximal, characteristic, complemented
11	#26012497	C₂	1	1	yes	maximal, characteristic, complemented
12	#26012464	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂²⋊#13063443	C₂	1	1	yes	maximal, characteristic, complemented
14	#26012455	C₂	1	1	yes	maximal, characteristic, complemented
15	#26011997	C₂	1	1	yes	maximal, characteristic
16	#19149766	—	2	4	no	—
17	C₂×#14583836	C₂²	1	1	yes	characteristic, complemented
18	C₂×#14583835	—	2	4	no	—
19	C₂×#14583835	C₂²	1	1	yes	characteristic
20	C₂×#14583835	C₂²	1	1	yes	characteristic
21	C₂×#14583835	C₂²	1	1	yes	characteristic
22	C₂×#14583835	C₂²	1	1	yes	characteristic
23	C₂×#14583835	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₁₇₃⋊C₈	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#13063443	C₂²	1	1	yes	characteristic
26	C₂²×#13063443	C₂²	1	1	yes	characteristic
27	C₂²×#13063443	C₂²	1	1	yes	characteristic
28	C₂²×#13063443	C₂²	1	1	yes	characteristic
29	C₂²×#13063443	C₂²	1	1	yes	characteristic, complemented
30	#19149746	C₂²	1	1	yes	characteristic, complemented
31	#19149746	C₂²	1	1	yes	characteristic, complemented
32	C₄⋊#13063443	C₂²	1	1	yes	characteristic, complemented
33	C₄⋊#13063443	C₂²	1	1	yes	characteristic, complemented
34	#19149736	C₂²	1	1	yes	characteristic, complemented
35	#19149736	C₂²	1	1	yes	characteristic, complemented
36	C₂²⋊#13063443	C₂²	1	1	yes	characteristic
37	C₂²⋊#13063443	C₂²	1	1	yes	characteristic
38	C₂²⋊#13063443	C₂²	1	1	yes	characteristic
39	C₂²⋊#13063443	C₂²	1	1	yes	characteristic
40	C₂²⋊#13063443	C₂²	1	1	yes	characteristic, complemented
41	C₂²⋊#13063443	C₂²	1	1	yes	characteristic, complemented
42	#19149734	C₂²	1	1	yes	characteristic, complemented
43	#19149734	C₂²	1	1	yes	characteristic, complemented
44	C₄×#13063443	C₂²	1	1	yes	characteristic, complemented
45	C₄×#13063443	C₂²	1	1	yes	characteristic, complemented
46	C₂×#14583825	C₂²	1	1	yes	characteristic
47	C₂³×Dic₁₇₃	C₂²	1	1	yes	characteristic
48	#19149663	C₄	1	1	yes	characteristic
49	#19149660	C₄	1	1	yes	characteristic
50	#19149656	C₄	1	1	yes	characteristic
51	#19149656	C₄	1	1	yes	characteristic
52	#19149651	C₄	1	1	yes	characteristic
53	#19149651	C₄	1	1	yes	characteristic
54	#19149648	C₄	1	1	yes	characteristic
55	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
56	D₄×Dic₁₇₃	C₂²	1	1	yes	characteristic
57	#19149639	C₂²	1	1	yes	characteristic
58	#19149639	C₂²	1	1	yes	characteristic
59	#19149635	C₂²	1	1	yes	characteristic
60	#120×C₁₇₃	C₄	1	1	yes	characteristic
61	#14583836	—	2	2	no	—
62	#14583835	—	2	2	no	—
63	#14583835	—	2	2	no	—
64	#14583835	—	2	2	no	—
65	#14583835	—	2	2	no	—
66	#14583835	D₄	1	4	yes	complemented
67	D₁₇₃⋊C₈	—	2	2	no	—
68	C₂×#13063443	—	2	2	no	—
69	C₂×#13063443	—	2	2	no	—
70	C₂×#13063443	—	2	2	no	—
71	C₂×#13063443	—	2	2	no	—
72	C₂×#13063443	—	2	2	no	—
73	C₂×#13063443	C₂³	1	1	yes	characteristic
74	C₂×#13063443	C₂³	1	1	yes	characteristic
75	C₂×#13063443	C₂³	1	1	yes	characteristic
76	C₂×#13063443	C₂³	1	1	yes	characteristic
77	C₂×#13063443	C₂³	1	1	yes	characteristic
78	C₂×#13063443	C₂³	1	1	yes	characteristic
79	C₂×#13063443	C₂³	1	1	yes	characteristic
80	C₂×#13063443	C₂³	1	1	yes	characteristic
81	#14583825	—	2	2	no	—
82	#14583825	—	2	2	no	—
83	C₂×Dic₃₄₆	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊D₁₇₃	C₂×C₄	1	1	yes	characteristic
85	C₂×C₂²⋊D₁₇₃	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊D₁₇₃	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊D₁₇₃	C₂×C₄	1	1	yes	characteristic
88	C₂²×Dic₁₇₃	—	2	2	no	—
89	C₂²×Dic₁₇₃	—	2	2	no	—
90	C₂²×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
91	C₂²×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
92	C₂²×Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
93	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
94	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
95	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
96	C₂²×Dic₁₇₃	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₁₇₃	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
99	C₄⋊Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
100	#14583805	C₂×C₄	1	1	yes	characteristic
101	#14583805	C₂×C₄	1	1	yes	characteristic
102	#14583805	C₂×C₄	1	1	yes	characteristic
103	#14583805	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
108	C₂²⋊Dic₁₇₃	C₂×C₄	1	1	yes	characteristic
109	#14583803	C₂×C₄	1	1	yes	characteristic
110	#14583803	C₂×C₄	1	1	yes	characteristic
111	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
112	C₄×Dic₁₇₃	C₂³	1	1	yes	characteristic
113	C₂⁴×C₁₇₃	C₂×C₄	1	1	yes	characteristic
114	C₂×D₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
115	C₂×D₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
116	C₂×D₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₇₃	C₂×C₄	1	1	yes	characteristic
120	#13063443	—	2	1	no	—
121	#13063443	—	2	1	no	—
122	#13063443	—	2	1	no	—
123	#13063443	—	2	1	no	—
124	#13063443	—	2	1	no	—
125	#13063443	—	2	1	no	—
126	#13063443	C₂×D₄	1	2	yes	—
127	#13063443	C₂×D₄	1	2	yes	—
128	C₂²×D₁₇₃	C₂²×C₄	1	1	yes	characteristic
129	Dic₃₄₆	—	2	2	no	—
130	C₂²⋊D₁₇₃	—	2	2	no	—
131	C₂²⋊D₁₇₃	—	2	2	no	—
132	C₂²⋊D₁₇₃	—	2	2	no	—
133	C₂²⋊D₁₇₃	—	4	1	no	—
134	C₂×Dic₁₇₃	—	2	2	no	—
135	C₂×Dic₁₇₃	—	2	2	no	—
136	C₂×Dic₁₇₃	—	2	2	no	—
137	C₂×Dic₁₇₃	—	2	1	no	—
138	C₂×Dic₁₇₃	—	2	1	no	—
139	C₂×Dic₁₇₃	—	2	1	no	—
140	C₂×Dic₁₇₃	—	2	1	no	—
141	C₂×Dic₁₇₃	—	2	1	no	—
142	C₂×Dic₁₇₃	—	2	1	no	—
143	C₂×Dic₁₇₃	C₂²×C₄	1	1	yes	characteristic
144	C₂×Dic₁₇₃	C₂²×C₄	1	1	yes	characteristic
145	C₂×Dic₁₇₃	C₂²×C₄	1	1	yes	characteristic
146	C₂×Dic₁₇₃	C₂²×C₄	1	1	yes	characteristic
147	C₂×Dic₁₇₃	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₇₃	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₇₃	C₂×D₄	1	2	yes	—
150	C₂×Dic₁₇₃	#41	1	2	yes	—
151	C₂×Dic₁₇₃	C₂⁴	1	1	yes	characteristic
152	C₄×D₁₇₃	—	2	1	no	—
153	C₄×D₁₇₃	—	2	1	no	—
154	C₂³×C₁₇₃	—	2	2	no	—
155	C₂³×C₁₇₃	—	2	2	no	—
156	C₂³×C₁₇₃	—	4	1	no	—
157	C₂³×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
158	C₂³×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
159	C₂³×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
160	C₂³×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
161	D₄×C₁₇₃	—	2	2	no	—
162	D₄×C₁₇₃	—	2	2	no	—
163	D₄×C₁₇₃	—	4	1	no	—
164	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
165	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
166	C₂×C₄×C₁₇₃	C₂²×C₄	1	1	yes	characteristic
167	C₂²×C₁₇₃	—	2	1	no	—
168	C₂²×C₁₇₃	—	2	1	no	—
169	C₂²×C₁₇₃	—	2	1	no	—
170	C₂²×C₁₇₃	—	2	1	no	—
171	C₂²×C₁₇₃	—	2	1	no	—
172	C₂²×C₁₇₃	—	2	1	no	—
173	C₂²×C₁₇₃	—	2	1	no	—
174	C₂²×C₁₇₃	—	2	1	no	—
175	C₂²×C₁₇₃	—	2	1	no	—
176	C₂²×C₁₇₃	—	2	1	no	—
177	C₂²×C₁₇₃	—	4	4	no	—
178	C₂²×C₁₇₃	C₄×D₄	1	2	yes	—
179	C₂²×C₁₇₃	#131	1	2	yes	complemented
180	C₂²×C₁₇₃	C₂³×C₄	1	1	yes	characteristic
181	C₂×D₁₇₃	—	2	1	no	—
182	C₂×D₁₇₃	—	2	1	no	—
183	C₂×D₁₇₃	—	2	1	no	—
184	C₄×C₁₇₃	—	2	1	no	—
185	C₄×C₁₇₃	—	2	1	no	—
186	C₄×C₁₇₃	—	2	1	no	—
187	Dic₁₇₃	—	2	1	no	—
188	Dic₁₇₃	—	2	1	no	—
189	Dic₁₇₃	—	2	1	no	—
190	Dic₁₇₃	—	2	1	no	—
191	Dic₁₇₃	—	2	1	no	—
192	Dic₁₇₃	C₄×D₄	1	2	yes	—
193	Dic₁₇₃	C₂²×D₄	1	1	yes	characteristic
194	Dic₁₇₃	C₂×#41	1	1	yes	characteristic
195	C₂×C₁₇₃	—	2	2	no	—
196	C₂×C₁₇₃	—	2	2	no	—
197	C₂×C₁₇₃	—	4	1	no	—
198	C₂×C₁₇₃	—	4	1	no	—
199	C₂×C₁₇₃	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂×C₁₇₃	C₂×#131	1	1	yes	characteristic
201	C₂×C₁₇₃	#568	1	1	yes	characteristic
202	D₁₇₃	—	4	1	no	—
203	C₁₇₃	#2933	1	1	yes	characteristic, complemented, Sylow
204	#2933	—	173	1	no	maximal, Sylow
205	C₂×#131	—	173	1	no	—
206	C₂²×M₁₆	—	173	1	no	—
207	#525	—	173	1	no	—
208	#436	—	173	1	no	—
209	#436	—	173	1	no	—
210	#435	—	173	1	no	—
211	#435	—	173	1	no	—
212	#435	—	173	1	no	—
213	#435	—	173	1	no	—
214	C₈×D₄	—	173	1	no	—
215	C₈×D₄	—	173	1	no	—
216	#424	—	173	1	no	—
217	#408	—	173	1	no	—
218	C₂×C₂²⋊C₈	—	173	1	no	—
219	#405	—	173	1	no	—
220	C₂×#41	—	173	1	no	—
221	C₂³×C₄	—	173	1	no	—
222	#131	—	346	4	no	—
223	C₂×M₁₆	—	346	4	no	—
224	C₂×M₁₆	—	173	1	no	—
225	C₂×M₁₆	—	173	1	no	—
226	C₂×M₁₆	—	173	1	no	—
227	C₂×M₁₆	—	173	1	no	—
228	C₂×M₁₆	—	173	1	no	—
229	C₂×M₁₆	—	173	1	no	—
230	C₂²×C₈	—	173	1	no	—
231	C₂²×C₈	—	173	1	no	—
232	C₂²×C₈	—	173	1	no	—
233	C₂²×C₈	—	173	1	no	—
234	C₂²×C₈	—	173	1	no	—
235	C₂²×C₈	—	173	1	no	—
236	#123	—	173	1	no	—
237	#123	—	173	1	no	—
238	C₂²⋊Q₈	—	173	1	no	—
239	C₂²⋊Q₈	—	173	1	no	—
240	#121	—	173	1	no	—
241	#121	—	173	1	no	—
242	#120	—	173	1	no	—
243	#120	#10621924	1	1	yes	characteristic
244	C₄×D₄	—	173	1	no	—
245	C₄×D₄	—	173	1	no	—
246	C₄×D₄	—	173	1	no	—
247	C₄×D₄	—	173	1	no	—
248	#117	—	173	1	no	—
249	C₄⋊C₈	—	173	1	no	—
250	C₄⋊C₈	—	173	1	no	—
251	C₄⋊C₈	—	173	1	no	—
252	C₄⋊C₈	—	173	1	no	—
253	C₂²⋊C₈	—	173	1	no	—
254	C₂²⋊C₈	—	173	1	no	—
255	C₂²⋊C₈	—	173	1	no	—
256	C₂²⋊C₈	—	173	1	no	—
257	C₂²⋊C₈	—	173	1	no	—
258	C₂²⋊C₈	—	173	1	no	—
259	C₂²⋊C₈	—	173	1	no	—
260	C₂²⋊C₈	—	173	1	no	—
261	#97	—	173	1	no	—
262	#97	—	173	1	no	—
263	C₄×C₈	—	173	1	no	—
264	C₄×C₈	—	173	1	no	—
265	C₂⁴	C₂×#10621924	1	1	yes	characteristic
266	#41	—	346	2	no	—
267	#41	—	346	2	no	—
268	C₂×Q₈	—	173	1	no	—
269	C₂×D₄	—	173	1	no	—
270	C₂×D₄	—	173	1	no	—
271	C₂×D₄	—	173	1	no	—
272	C₂×D₄	—	173	1	no	—
273	C₂×D₄	C₂×#10621924	1	1	yes	characteristic
274	C₂×D₄	C₂×#10621924	1	1	yes	characteristic
275	C₂×D₄	C₂×#10621924	1	1	yes	characteristic
276	C₂²×C₄	—	346	2	no	—
277	C₂²×C₄	—	346	2	no	—
278	C₂²×C₄	—	173	1	no	—
279	C₂²×C₄	—	173	1	no	—
280	C₂²×C₄	—	173	1	no	—
281	C₂²×C₄	—	173	1	no	—
282	C₂²×C₄	—	173	1	no	—
283	C₂²×C₄	—	173	1	no	—
284	C₂²×C₄	—	173	1	no	—
285	C₂²×C₄	—	173	1	no	—
286	M₁₆	—	346	2	no	—
287	M₁₆	—	346	2	no	—
288	M₁₆	—	346	2	no	—
289	M₁₆	—	346	2	no	—
290	M₁₆	—	346	2	no	—
291	M₁₆	—	173	4	no	—
292	C₂×C₈	—	346	2	no	—
293	C₂×C₈	—	346	2	no	—
294	C₂×C₈	—	346	2	no	—
295	C₂×C₈	—	346	2	no	—
296	C₂×C₈	—	346	2	no	—
297	C₂×C₈	—	346	2	no	—
298	C₂×C₈	—	173	1	no	—
299	C₂×C₈	—	173	1	no	—
300	C₂×C₈	—	173	1	no	—
301	C₂×C₈	—	173	1	no	—
302	C₂×C₈	—	173	1	no	—
303	C₂×C₈	—	173	1	no	—
304	C₂×C₈	—	173	1	no	—
305	C₂×C₈	—	173	1	no	—
306	C₄⋊C₄	—	173	1	no	—
307	C₄⋊C₄	—	173	1	no	—
308	C₄⋊C₄	—	173	1	no	—
309	C₄⋊C₄	—	173	1	no	—
310	C₄⋊C₄	—	173	1	no	—
311	C₄⋊C₄	—	173	1	no	—
312	C₂²⋊C₄	—	173	1	no	—
313	C₂²⋊C₄	—	173	1	no	—
314	C₂²⋊C₄	—	173	1	no	—
315	C₂²⋊C₄	—	173	1	no	—
316	C₂²⋊C₄	—	173	1	no	—
317	C₂²⋊C₄	—	173	1	no	—
318	C₂²⋊C₄	—	173	1	no	—
319	C₂²⋊C₄	C₂×#10621924	1	1	yes	characteristic
320	C₂²⋊C₄	C₂×#10621924	1	1	yes	characteristic
321	C₂²⋊C₄	C₂×#10621924	1	1	yes	characteristic
322	C₄²	—	173	1	no	—
323	C₄²	—	173	1	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	173	1	no	—
328	C₂³	C₂²×#10621924	1	1	yes	characteristic
329	C₂³	C₂²×#10621924	1	1	yes	characteristic
330	C₂³	C₂²×#10621924	1	1	yes	characteristic
331	C₂³	C₂²×#10621924	1	1	yes	characteristic
332	Q₈	—	346	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	2	2	no	—
335	D₄	—	4	1	no	—
336	D₄	—	346	2	no	—
337	D₄	—	346	2	no	—
338	D₄	—	346	2	no	—
339	D₄	—	692	1	no	—
340	C₂×C₄	—	346	1	no	—
341	C₂×C₄	—	346	1	no	—
342	C₂×C₄	—	346	2	no	—
343	C₂×C₄	—	346	1	no	—
344	C₂×C₄	—	346	1	no	—
345	C₂×C₄	—	346	1	no	—
346	C₂×C₄	—	346	1	no	—
347	C₂×C₄	—	346	1	no	—
348	C₂×C₄	—	346	2	no	—
349	C₂×C₄	—	346	2	no	—
350	C₂×C₄	—	346	1	no	—
351	C₂×C₄	—	173	1	no	—
352	C₂×C₄	—	173	1	no	—
353	C₂×C₄	—	173	1	no	—
354	C₂×C₄	—	173	1	no	—
355	C₂×C₄	—	173	1	no	—
356	C₂×C₄	—	173	2	no	—
357	C₂×C₄	—	173	2	no	—
358	C₂×C₄	—	173	1	no	—
359	C₂×C₄	—	173	1	no	—
360	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
361	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
362	C₂×C₄	C₂²×#10621924	1	1	yes	characteristic
363	C₈	—	346	1	no	—
364	C₈	—	346	1	no	—
365	C₈	—	346	1	no	—
366	C₈	—	346	1	no	—
367	C₈	—	346	1	no	—
368	C₈	—	346	1	no	—
369	C₈	—	173	2	no	—
370	C₈	—	173	2	no	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	2	1	no	—
375	C₂²	—	2	1	no	—
376	C₂²	—	2	1	no	—
377	C₂²	—	2	1	no	—
378	C₂²	—	2	1	no	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	346	1	no	—
383	C₂²	—	346	1	no	—
384	C₂²	—	346	1	no	—
385	C₂²	D₄×#10621924	1	2	yes	—
386	C₂²	#19149766	1	2	yes	complemented
387	C₂²	C₂³×#10621924	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	346	1	no	—
392	C₄	—	346	1	no	—
393	C₄	—	346	1	no	—
394	C₄	—	346	1	no	—
395	C₄	—	346	1	no	—
396	C₄	—	173	1	no	—
397	C₄	—	173	1	no	—
398	C₄	—	173	2	no	—
399	C₂	—	2	2	no	—
400	C₂	—	2	2	no	—
401	C₂	—	4	1	no	—
402	C₂	—	4	1	no	—
403	C₂	—	692	1	no	—
404	C₂	C₂×D₄×#10621924	1	1	yes	characteristic
405	C₂	C₂×#19149766	1	1	yes	characteristic
406	C₂	#26012569	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#10621924
commutator, socle	C₂²×C₁₇₃	C₂³×C₄
Fitting	#120×C₁₇₃	C₄
prime radical	#26011997	C₂
cosocle	C₂×Dic₁₇₃	C₂⁴
hypercenter	#120	#10621924
hypocenter	C₁₇₃	#2933
LCS	G ▷ C₂²×C₁₇₃ ▷ C₁₇₃
UCS	C₁ ◁ C₂² ◁ #120

Complements

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

N	H ≅ G/N	type
1. C₂×#19149766	C₂	semidirect
2. C₂²×#14583835	C₂	semidirect
3. #26012526	C₂	semidirect
4. #26012524	C₂	semidirect
5. #26012523	C₂	semidirect
6. #26012522	C₂	semidirect
7. #26012522	C₂	semidirect
8. #26012520	C₂	semidirect
9. #26012518	C₂	semidirect
10. D₄×#13063443	C₂	semidirect
11. #26012497	C₂	semidirect
12. #26012464	C₂	semidirect
13. C₂×C₂²⋊#13063443	C₂	semidirect
14. #26012455	C₂	semidirect
17. C₂×#14583836	C₂²	semidirect
23. C₂×#14583835	C₂²	semidirect
24. C₂×D₁₇₃⋊C₈	C₂²	semidirect
29. C₂²×#13063443	C₂²	semidirect
30. #19149746	C₂²	semidirect
31. #19149746	C₂²	semidirect
32. C₄⋊#13063443	C₂²	semidirect
33. C₄⋊#13063443	C₂²	semidirect
34. #19149736	C₂²	semidirect
35. #19149736	C₂²	semidirect
40. C₂²⋊#13063443	C₂²	semidirect
41. C₂²⋊#13063443	C₂²	semidirect
42. #19149734	C₂²	semidirect
43. #19149734	C₂²	semidirect
44. C₄×#13063443	C₂²	semidirect
45. C₄×#13063443	C₂²	semidirect
66. #14583835	D₄	semidirect
179. C₂²×C₁₇₃	#131	semidirect
203. C₁₇₃	#2933	semidirect
386. C₂²	#19149766	semidirect

Maximal subgroups

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

subgroup	index
C₂×#19149766	2
C₂²×#14583835	2
#26012526	2
#26012524	2
#26012523	2
#26012522	2
#26012520	2
#26012518	2
D₄×#13063443	2
#26012497	2
#26012464	2
C₂×C₂²⋊#13063443	2
#26012455	2
#26011997	2
#2933	173