Subgroups — #28379764

Order 13952.

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×#16812786	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13182038	C₂	1	1	yes	maximal, characteristic, complemented
3	#20296061	C₂	1	1	yes	maximal, characteristic, complemented
4	#20296059	C₂	1	1	yes	maximal, characteristic, complemented
5	#20296058	C₂	1	1	yes	maximal, characteristic, complemented
6	#20296057	C₂	1	1	yes	maximal, characteristic, complemented
7	#20296057	C₂	1	1	yes	maximal, characteristic, complemented
8	#20296055	C₂	1	1	yes	maximal, characteristic, complemented
9	#20296053	C₂	1	1	yes	maximal, characteristic, complemented
10	D₄×#11724786	C₂	1	1	yes	maximal, characteristic, complemented
11	#20296032	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295999	C₂	1	1	yes	maximal, characteristic, complemented
13	C₂×C₂²⋊#11724786	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295990	C₂	1	1	yes	maximal, characteristic, complemented
15	#20295532	C₂	1	1	yes	maximal, characteristic
16	#16812786	—	2	4	no	—
17	C₂×#13182039	C₂²	1	1	yes	characteristic, complemented
18	C₂×#13182038	—	2	4	no	—
19	C₂×#13182038	C₂²	1	1	yes	characteristic
20	C₂×#13182038	C₂²	1	1	yes	characteristic
21	C₂×#13182038	C₂²	1	1	yes	characteristic
22	C₂×#13182038	C₂²	1	1	yes	characteristic
23	C₂×#13182038	C₂²	1	1	yes	characteristic, complemented
24	C₂×D₁₀₉⋊C₈	C₂²	1	1	yes	characteristic, complemented
25	C₂²×#11724786	C₂²	1	1	yes	characteristic
26	C₂²×#11724786	C₂²	1	1	yes	characteristic
27	C₂²×#11724786	C₂²	1	1	yes	characteristic
28	C₂²×#11724786	C₂²	1	1	yes	characteristic
29	C₂²×#11724786	C₂²	1	1	yes	characteristic, complemented
30	#16812766	C₂²	1	1	yes	characteristic, complemented
31	#16812766	C₂²	1	1	yes	characteristic, complemented
32	C₄⋊#11724786	C₂²	1	1	yes	characteristic, complemented
33	C₄⋊#11724786	C₂²	1	1	yes	characteristic, complemented
34	#16812756	C₂²	1	1	yes	characteristic, complemented
35	#16812756	C₂²	1	1	yes	characteristic, complemented
36	C₂²⋊#11724786	C₂²	1	1	yes	characteristic
37	C₂²⋊#11724786	C₂²	1	1	yes	characteristic
38	C₂²⋊#11724786	C₂²	1	1	yes	characteristic
39	C₂²⋊#11724786	C₂²	1	1	yes	characteristic
40	C₂²⋊#11724786	C₂²	1	1	yes	characteristic, complemented
41	C₂²⋊#11724786	C₂²	1	1	yes	characteristic, complemented
42	#16812754	C₂²	1	1	yes	characteristic, complemented
43	#16812754	C₂²	1	1	yes	characteristic, complemented
44	C₄×#11724786	C₂²	1	1	yes	characteristic, complemented
45	C₄×#11724786	C₂²	1	1	yes	characteristic, complemented
46	C₂×#13182028	C₂²	1	1	yes	characteristic
47	C₂³×Dic₁₀₉	C₂²	1	1	yes	characteristic
48	#16812683	C₄	1	1	yes	characteristic
49	#16812680	C₄	1	1	yes	characteristic
50	#16812676	C₄	1	1	yes	characteristic
51	#16812676	C₄	1	1	yes	characteristic
52	#16812671	C₄	1	1	yes	characteristic
53	#16812671	C₄	1	1	yes	characteristic
54	#16812668	C₄	1	1	yes	characteristic
55	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
56	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
57	#16812659	C₂²	1	1	yes	characteristic
58	#16812659	C₂²	1	1	yes	characteristic
59	#16812655	C₂²	1	1	yes	characteristic
60	#120×C₁₀₉	C₄	1	1	yes	characteristic
61	#13182039	—	2	2	no	—
62	#13182038	—	2	2	no	—
63	#13182038	—	2	2	no	—
64	#13182038	—	2	2	no	—
65	#13182038	—	2	2	no	—
66	#13182038	D₄	1	4	yes	complemented
67	D₁₀₉⋊C₈	—	2	2	no	—
68	C₂×#11724786	—	2	2	no	—
69	C₂×#11724786	—	2	2	no	—
70	C₂×#11724786	—	2	2	no	—
71	C₂×#11724786	—	2	2	no	—
72	C₂×#11724786	—	2	2	no	—
73	C₂×#11724786	C₂³	1	1	yes	characteristic
74	C₂×#11724786	C₂³	1	1	yes	characteristic
75	C₂×#11724786	C₂³	1	1	yes	characteristic
76	C₂×#11724786	C₂³	1	1	yes	characteristic
77	C₂×#11724786	C₂³	1	1	yes	characteristic
78	C₂×#11724786	C₂³	1	1	yes	characteristic
79	C₂×#11724786	C₂³	1	1	yes	characteristic
80	C₂×#11724786	C₂³	1	1	yes	characteristic
81	#13182028	—	2	2	no	—
82	#13182028	—	2	2	no	—
83	C₂×Dic₂₁₈	C₂×C₄	1	1	yes	characteristic
84	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	1	yes	characteristic
85	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	1	yes	characteristic
86	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	1	yes	characteristic
87	C₂×C₂²⋊D₁₀₉	C₂×C₄	1	1	yes	characteristic
88	C₂²×Dic₁₀₉	—	2	2	no	—
89	C₂²×Dic₁₀₉	—	2	2	no	—
90	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
91	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
92	C₂²×Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
93	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
94	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
95	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
96	C₂²×Dic₁₀₉	C₂³	1	1	yes	characteristic
97	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
98	C₄⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
99	C₄⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
100	#13182008	C₂×C₄	1	1	yes	characteristic
101	#13182008	C₂×C₄	1	1	yes	characteristic
102	#13182008	C₂×C₄	1	1	yes	characteristic
103	#13182008	C₂×C₄	1	1	yes	characteristic
104	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
105	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
106	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
107	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
108	C₂²⋊Dic₁₀₉	C₂×C₄	1	1	yes	characteristic
109	#13182006	C₂×C₄	1	1	yes	characteristic
110	#13182006	C₂×C₄	1	1	yes	characteristic
111	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
112	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
113	C₂⁴×C₁₀₉	C₂×C₄	1	1	yes	characteristic
114	C₂×D₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
115	C₂×D₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
116	C₂×D₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
117	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic
120	C₂³×C₁₀₉	—	2	2	no	—
121	C₂³×C₁₀₉	—	2	2	no	—
122	C₂³×C₁₀₉	—	4	1	no	—
123	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
124	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
125	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
126	C₂³×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
127	C₂²×D₁₀₉	C₂²×C₄	1	1	yes	characteristic
128	D₄×C₁₀₉	—	2	2	no	—
129	D₄×C₁₀₉	—	2	2	no	—
130	D₄×C₁₀₉	—	4	1	no	—
131	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
132	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
133	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
134	C₂²⋊D₁₀₉	—	2	2	no	—
135	C₂²⋊D₁₀₉	—	2	2	no	—
136	C₂²⋊D₁₀₉	—	2	2	no	—
137	C₂²⋊D₁₀₉	—	4	1	no	—
138	C₂×Dic₁₀₉	—	2	2	no	—
139	C₂×Dic₁₀₉	—	2	2	no	—
140	C₂×Dic₁₀₉	—	2	2	no	—
141	C₂×Dic₁₀₉	—	2	1	no	—
142	C₂×Dic₁₀₉	—	2	1	no	—
143	C₂×Dic₁₀₉	—	2	1	no	—
144	C₂×Dic₁₀₉	—	2	1	no	—
145	C₂×Dic₁₀₉	—	2	1	no	—
146	C₂×Dic₁₀₉	—	2	1	no	—
147	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
148	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
149	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
150	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
151	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
152	C₂×Dic₁₀₉	C₂²×C₄	1	1	yes	characteristic
153	C₂×Dic₁₀₉	C₂×D₄	1	2	yes	—
154	C₂×Dic₁₀₉	#41	1	2	yes	—
155	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
156	C₄×D₁₀₉	—	2	1	no	—
157	C₄×D₁₀₉	—	2	1	no	—
158	Dic₂₁₈	—	2	2	no	—
159	#11724786	—	2	1	no	—
160	#11724786	—	2	1	no	—
161	#11724786	—	2	1	no	—
162	#11724786	—	2	1	no	—
163	#11724786	—	2	1	no	—
164	#11724786	—	2	1	no	—
165	#11724786	C₂×D₄	1	2	yes	—
166	#11724786	C₂×D₄	1	2	yes	—
167	C₂²×C₁₀₉	—	2	1	no	—
168	C₂²×C₁₀₉	—	2	1	no	—
169	C₂²×C₁₀₉	—	2	1	no	—
170	C₂²×C₁₀₉	—	2	1	no	—
171	C₂²×C₁₀₉	—	2	1	no	—
172	C₂²×C₁₀₉	—	2	1	no	—
173	C₂²×C₁₀₉	—	2	1	no	—
174	C₂²×C₁₀₉	—	2	1	no	—
175	C₂²×C₁₀₉	—	2	1	no	—
176	C₂²×C₁₀₉	—	2	1	no	—
177	C₂²×C₁₀₉	—	4	4	no	—
178	C₂²×C₁₀₉	C₄×D₄	1	2	yes	—
179	C₂²×C₁₀₉	#131	1	2	yes	complemented
180	C₂²×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
181	C₂×D₁₀₉	—	2	1	no	—
182	C₂×D₁₀₉	—	2	1	no	—
183	C₂×D₁₀₉	—	2	1	no	—
184	C₄×C₁₀₉	—	2	1	no	—
185	C₄×C₁₀₉	—	2	1	no	—
186	C₄×C₁₀₉	—	2	1	no	—
187	Dic₁₀₉	—	2	1	no	—
188	Dic₁₀₉	—	2	1	no	—
189	Dic₁₀₉	—	2	1	no	—
190	Dic₁₀₉	—	2	1	no	—
191	Dic₁₀₉	—	2	1	no	—
192	Dic₁₀₉	C₄×D₄	1	2	yes	—
193	Dic₁₀₉	C₂²×D₄	1	1	yes	characteristic
194	Dic₁₀₉	C₂×#41	1	1	yes	characteristic
195	C₂×C₁₀₉	—	2	2	no	—
196	C₂×C₁₀₉	—	2	2	no	—
197	C₂×C₁₀₉	—	4	1	no	—
198	C₂×C₁₀₉	—	4	1	no	—
199	C₂×C₁₀₉	C₂×C₄×D₄	1	1	yes	characteristic
200	C₂×C₁₀₉	C₂×#131	1	1	yes	characteristic
201	C₂×C₁₀₉	#568	1	1	yes	characteristic
202	D₁₀₉	—	4	1	no	—
203	#2933	—	109	1	no	maximal, Sylow
204	C₁₀₉	#2933	1	1	yes	characteristic, complemented, Sylow
205	C₂×#131	—	109	1	no	—
206	C₂²×M₁₆	—	109	1	no	—
207	#525	—	109	1	no	—
208	#436	—	109	1	no	—
209	#436	—	109	1	no	—
210	#435	—	109	1	no	—
211	#435	—	109	1	no	—
212	#435	—	109	1	no	—
213	#435	—	109	1	no	—
214	C₈×D₄	—	109	1	no	—
215	C₈×D₄	—	109	1	no	—
216	#424	—	109	1	no	—
217	#408	—	109	1	no	—
218	C₂×C₂²⋊C₈	—	109	1	no	—
219	#405	—	109	1	no	—
220	C₂×#41	—	109	1	no	—
221	C₂³×C₄	—	109	1	no	—
222	#131	—	218	4	no	—
223	C₂×M₁₆	—	109	1	no	—
224	C₂×M₁₆	—	109	1	no	—
225	C₂×M₁₆	—	109	1	no	—
226	C₂×M₁₆	—	109	1	no	—
227	C₂×M₁₆	—	109	1	no	—
228	C₂×M₁₆	—	109	1	no	—
229	C₂×M₁₆	—	218	4	no	—
230	C₂²×C₈	—	109	1	no	—
231	C₂²×C₈	—	109	1	no	—
232	C₂²×C₈	—	109	1	no	—
233	C₂²×C₈	—	109	1	no	—
234	C₂²×C₈	—	109	1	no	—
235	C₂²×C₈	—	109	1	no	—
236	#123	—	109	1	no	—
237	#123	—	109	1	no	—
238	C₂²⋊Q₈	—	109	1	no	—
239	C₂²⋊Q₈	—	109	1	no	—
240	#121	—	109	1	no	—
241	#121	—	109	1	no	—
242	#120	—	109	1	no	—
243	#120	#89137	1	1	yes	characteristic
244	C₄×D₄	—	109	1	no	—
245	C₄×D₄	—	109	1	no	—
246	C₄×D₄	—	109	1	no	—
247	C₄×D₄	—	109	1	no	—
248	#117	—	109	1	no	—
249	C₄⋊C₈	—	109	1	no	—
250	C₄⋊C₈	—	109	1	no	—
251	C₄⋊C₈	—	109	1	no	—
252	C₄⋊C₈	—	109	1	no	—
253	C₂²⋊C₈	—	109	1	no	—
254	C₂²⋊C₈	—	109	1	no	—
255	C₂²⋊C₈	—	109	1	no	—
256	C₂²⋊C₈	—	109	1	no	—
257	C₂²⋊C₈	—	109	1	no	—
258	C₂²⋊C₈	—	109	1	no	—
259	C₂²⋊C₈	—	109	1	no	—
260	C₂²⋊C₈	—	109	1	no	—
261	#97	—	109	1	no	—
262	#97	—	109	1	no	—
263	C₄×C₈	—	109	1	no	—
264	C₄×C₈	—	109	1	no	—
265	C₂⁴	C₂×#89137	1	1	yes	characteristic
266	#41	—	218	2	no	—
267	#41	—	218	2	no	—
268	C₂×Q₈	—	109	1	no	—
269	C₂×D₄	—	109	1	no	—
270	C₂×D₄	—	109	1	no	—
271	C₂×D₄	—	109	1	no	—
272	C₂×D₄	—	109	1	no	—
273	C₂×D₄	C₂×#89137	1	1	yes	characteristic
274	C₂×D₄	C₂×#89137	1	1	yes	characteristic
275	C₂×D₄	C₂×#89137	1	1	yes	characteristic
276	C₂²×C₄	—	109	1	no	—
277	C₂²×C₄	—	109	1	no	—
278	C₂²×C₄	—	109	1	no	—
279	C₂²×C₄	—	109	1	no	—
280	C₂²×C₄	—	109	1	no	—
281	C₂²×C₄	—	109	1	no	—
282	C₂²×C₄	—	109	1	no	—
283	C₂²×C₄	—	109	1	no	—
284	C₂²×C₄	—	218	2	no	—
285	C₂²×C₄	—	218	2	no	—
286	M₁₆	—	109	4	no	—
287	M₁₆	—	218	2	no	—
288	M₁₆	—	218	2	no	—
289	M₁₆	—	218	2	no	—
290	M₁₆	—	218	2	no	—
291	M₁₆	—	218	2	no	—
292	C₂×C₈	—	109	1	no	—
293	C₂×C₈	—	109	1	no	—
294	C₂×C₈	—	109	1	no	—
295	C₂×C₈	—	109	1	no	—
296	C₂×C₈	—	109	1	no	—
297	C₂×C₈	—	109	1	no	—
298	C₂×C₈	—	109	1	no	—
299	C₂×C₈	—	109	1	no	—
300	C₂×C₈	—	218	2	no	—
301	C₂×C₈	—	218	2	no	—
302	C₂×C₈	—	218	2	no	—
303	C₂×C₈	—	218	2	no	—
304	C₂×C₈	—	218	2	no	—
305	C₂×C₈	—	218	2	no	—
306	C₄⋊C₄	—	109	1	no	—
307	C₄⋊C₄	—	109	1	no	—
308	C₄⋊C₄	—	109	1	no	—
309	C₄⋊C₄	—	109	1	no	—
310	C₄⋊C₄	—	109	1	no	—
311	C₄⋊C₄	—	109	1	no	—
312	C₂²⋊C₄	—	109	1	no	—
313	C₂²⋊C₄	—	109	1	no	—
314	C₂²⋊C₄	—	109	1	no	—
315	C₂²⋊C₄	—	109	1	no	—
316	C₂²⋊C₄	—	109	1	no	—
317	C₂²⋊C₄	—	109	1	no	—
318	C₂²⋊C₄	—	109	1	no	—
319	C₂²⋊C₄	C₂×#89137	1	1	yes	characteristic
320	C₂²⋊C₄	C₂×#89137	1	1	yes	characteristic
321	C₂²⋊C₄	C₂×#89137	1	1	yes	characteristic
322	C₄²	—	109	1	no	—
323	C₄²	—	109	1	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	2	2	no	—
326	C₂³	—	4	1	no	—
327	C₂³	—	109	1	no	—
328	C₂³	C₂²×#89137	1	1	yes	characteristic
329	C₂³	C₂²×#89137	1	1	yes	characteristic
330	C₂³	C₂²×#89137	1	1	yes	characteristic
331	C₂³	C₂²×#89137	1	1	yes	characteristic
332	Q₈	—	218	2	no	—
333	D₄	—	2	2	no	—
334	D₄	—	2	2	no	—
335	D₄	—	4	1	no	—
336	D₄	—	436	1	no	—
337	D₄	—	218	2	no	—
338	D₄	—	218	2	no	—
339	D₄	—	218	2	no	—
340	C₂×C₄	—	109	2	no	—
341	C₂×C₄	—	109	2	no	—
342	C₂×C₄	—	109	1	no	—
343	C₂×C₄	—	109	1	no	—
344	C₂×C₄	—	109	1	no	—
345	C₂×C₄	—	109	1	no	—
346	C₂×C₄	—	109	1	no	—
347	C₂×C₄	—	109	1	no	—
348	C₂×C₄	—	109	1	no	—
349	C₂×C₄	—	218	1	no	—
350	C₂×C₄	—	218	1	no	—
351	C₂×C₄	—	218	1	no	—
352	C₂×C₄	—	218	1	no	—
353	C₂×C₄	—	218	1	no	—
354	C₂×C₄	—	218	1	no	—
355	C₂×C₄	—	218	1	no	—
356	C₂×C₄	—	218	2	no	—
357	C₂×C₄	—	218	2	no	—
358	C₂×C₄	—	218	1	no	—
359	C₂×C₄	—	218	2	no	—
360	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
361	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
362	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
363	C₈	—	109	2	no	—
364	C₈	—	109	2	no	—
365	C₈	—	218	1	no	—
366	C₈	—	218	1	no	—
367	C₈	—	218	1	no	—
368	C₈	—	218	1	no	—
369	C₈	—	218	1	no	—
370	C₈	—	218	1	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	—	218	1	no	—
383	C₂²	—	218	1	no	—
384	C₂²	—	218	1	no	—
385	C₂²	D₄×#89137	1	2	yes	—
386	C₂²	#16812786	1	2	yes	complemented
387	C₂²	C₂³×#89137	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	2	1	no	—
390	C₄	—	2	1	no	—
391	C₄	—	109	1	no	—
392	C₄	—	109	1	no	—
393	C₄	—	109	2	no	—
394	C₄	—	218	1	no	—
395	C₄	—	218	1	no	—
396	C₄	—	218	1	no	—
397	C₄	—	218	1	no	—
398	C₄	—	218	1	no	—
399	C₂	—	2	2	no	—
400	C₂	—	2	2	no	—
401	C₂	—	4	1	no	—
402	C₂	—	4	1	no	—
403	C₂	—	436	1	no	—
404	C₂	C₂×D₄×#89137	1	1	yes	characteristic
405	C₂	C₂×#16812786	1	1	yes	characteristic
406	C₂	#20296104	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂³×#89137
commutator, socle	C₂²×C₁₀₉	C₂³×C₄
Fitting	#120×C₁₀₉	C₄
prime radical	#20295532	C₂
cosocle	C₂×Dic₁₀₉	C₂⁴
hypercenter	#120	#89137
hypocenter	C₁₀₉	#2933
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #120

Complements

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

N	H ≅ G/N	type
1. C₂×#16812786	C₂	semidirect
2. C₂²×#13182038	C₂	semidirect
3. #20296061	C₂	semidirect
4. #20296059	C₂	semidirect
5. #20296058	C₂	semidirect
6. #20296057	C₂	semidirect
7. #20296057	C₂	semidirect
8. #20296055	C₂	semidirect
9. #20296053	C₂	semidirect
10. D₄×#11724786	C₂	semidirect
11. #20296032	C₂	semidirect
12. #20295999	C₂	semidirect
13. C₂×C₂²⋊#11724786	C₂	semidirect
14. #20295990	C₂	semidirect
17. C₂×#13182039	C₂²	semidirect
23. C₂×#13182038	C₂²	semidirect
24. C₂×D₁₀₉⋊C₈	C₂²	semidirect
29. C₂²×#11724786	C₂²	semidirect
30. #16812766	C₂²	semidirect
31. #16812766	C₂²	semidirect
32. C₄⋊#11724786	C₂²	semidirect
33. C₄⋊#11724786	C₂²	semidirect
34. #16812756	C₂²	semidirect
35. #16812756	C₂²	semidirect
40. C₂²⋊#11724786	C₂²	semidirect
41. C₂²⋊#11724786	C₂²	semidirect
42. #16812754	C₂²	semidirect
43. #16812754	C₂²	semidirect
44. C₄×#11724786	C₂²	semidirect
45. C₄×#11724786	C₂²	semidirect
66. #13182038	D₄	semidirect
179. C₂²×C₁₀₉	#131	semidirect
204. C₁₀₉	#2933	semidirect
386. C₂²	#16812786	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16812786	2
C₂²×#13182038	2
#20296061	2
#20296059	2
#20296058	2
#20296057	2
#20296055	2
#20296053	2
D₄×#11724786	2
#20296032	2
#20295999	2
C₂×C₂²⋊#11724786	2
#20295990	2
#20295532	2
#2933	109