Subgroups — #28372655

Order 13952.

496 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812728	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂²×#13182012	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295536	C₂	1	1	yes	maximal, characteristic
4	C₂²⋊Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295285	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295283	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295271	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295269	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295267	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295265	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295253	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295065	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295033	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295024	C₂	1	1	yes	maximal, characteristic, complemented
15	#465×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182028	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	#16812728	—	2	4	no	—
20	C₂×Dic₄₃₆	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13182017	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13182012	—	2	4	no	—
24	C₂×#13182012	C₂²	1	1	yes	characteristic
25	C₂×#13182012	C₂²	1	1	yes	characteristic
26	C₂×#13182012	C₂²	1	1	yes	characteristic
27	C₂×#13182012	C₂²	1	1	yes	characteristic
28	C₂²×#11724784	C₂²	1	1	yes	characteristic
29	#16812681	—	2	1	no	—
30	#16812679	C₂²	1	1	yes	characteristic
31	#16812679	C₂²	1	1	yes	characteristic
32	#16812678	C₂²	1	1	yes	characteristic
33	#16812678	C₂²	1	1	yes	characteristic
34	#16812677	—	2	1	no	—
35	#16812676	—	2	1	no	—
36	#16812675	C₂²	1	1	yes	characteristic
37	#16812670	C₂²	1	1	yes	characteristic
38	#16812667	—	2	1	no	—
39	D₄×Dic₁₀₉	—	2	1	no	—
40	#16812659	—	2	1	no	—
41	#16812657	C₂²	1	1	yes	characteristic
42	C₄⋊C₄×D₁₀₉	—	2	1	no	—
43	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
44	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
45	#16812633	C₂²	1	1	yes	characteristic, complemented
46	#16812632	C₂²	1	1	yes	characteristic, complemented
47	#16812630	C₂²	1	1	yes	characteristic, complemented
48	#16812624	C₂²	1	1	yes	characteristic, complemented
49	#16812624	C₂²	1	1	yes	characteristic, complemented
50	#16812623	C₂²	1	1	yes	characteristic, complemented
51	#16812622	C₂²	1	1	yes	characteristic, complemented
52	#16812622	C₂²	1	1	yes	characteristic, complemented
53	#16812620	C₂²	1	1	yes	characteristic, complemented
54	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	C₂²×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
56	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
57	#121×C₁₀₉	C₂²	1	1	yes	characteristic
58	#106×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	#103×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	#102×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₀₉	D₄	1	1	yes	characteristic
62	#13182028	—	2	2	no	—
63	#13182028	—	2	2	no	—
64	C₂×Dic₂₁₈	—	2	1	no	—
65	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
66	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
67	Q₈×D₁₀₉	—	2	2	no	—
68	Q₈×D₁₀₉	—	2	2	no	—
69	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
71	C₂²×Dic₁₀₉	—	2	1	no	—
72	C₂²×Dic₁₀₉	D₄	1	1	yes	characteristic
73	C₂×C₄×D₁₀₉	—	2	2	no	—
74	C₂×C₄×D₁₀₉	—	2	2	no	—
75	C₂×C₄×D₁₀₉	—	2	1	no	—
76	C₂×C₄×D₁₀₉	—	2	1	no	—
77	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
79	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
80	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
81	Dic₄₃₆	—	2	2	no	—
82	#13182019	—	2	2	no	—
83	#13182017	—	2	2	no	—
84	#13182012	—	2	2	no	—
85	#13182012	—	2	2	no	—
86	#13182012	—	2	2	no	—
87	#13182012	D₄	1	4	yes	complemented
88	C₂×#11724784	—	2	2	no	—
89	C₂×#11724784	C₂³	1	1	yes	characteristic
90	C₂×#11724784	C₂³	1	1	yes	characteristic
91	C₄⋊Dic₁₀₉	—	2	1	no	—
92	C₄⋊Dic₁₀₉	—	2	1	no	—
93	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
94	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
95	#13182008	—	2	1	no	—
96	#13182008	—	2	1	no	—
97	#13182008	—	2	1	no	—
98	#13182008	—	2	1	no	—
99	C₂²⋊Dic₁₀₉	—	2	1	no	—
100	C₂²⋊Dic₁₀₉	—	2	1	no	—
101	C₂²⋊Dic₁₀₉	—	2	1	no	—
102	#13182006	—	2	1	no	—
103	#13182006	—	2	1	no	—
104	#13182006	—	2	1	no	—
105	#13182006	—	2	1	no	—
106	C₄×Dic₁₀₉	—	2	1	no	—
107	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₁₀₉	—	2	1	no	—
109	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	SD₁₆×C₁₀₉	—	2	2	no	—
112	C₂×C₈×C₁₀₉	—	2	2	no	—
113	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
115	C₄⋊C₄×C₁₀₉	—	2	1	no	—
116	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
118	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
119	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
120	C₂³×C₁₀₉	—	2	1	no	—
121	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
122	C₂²×D₁₀₉	—	2	2	no	—
123	C₂²×D₁₀₉	—	2	2	no	—
124	C₂²×D₁₀₉	—	4	1	no	—
125	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
126	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
127	Q₈×C₁₀₉	—	2	1	no	—
128	Q₈×C₁₀₉	—	2	1	no	—
129	D₄×C₁₀₉	—	2	1	no	—
130	D₄×C₁₀₉	—	2	1	no	—
131	D₄×C₁₀₉	—	4	2	no	—
132	C₂×C₄×C₁₀₉	—	2	1	no	—
133	C₂×C₄×C₁₀₉	—	2	1	no	—
134	C₂×C₄×C₁₀₉	—	2	1	no	—
135	C₂×C₄×C₁₀₉	—	2	1	no	—
136	C₂×C₄×C₁₀₉	—	2	1	no	—
137	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
139	C₂²⋊D₁₀₉	—	4	2	no	—
140	C₂²⋊D₁₀₉	—	4	2	no	—
141	C₂×Dic₁₀₉	—	2	2	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	—	4	2	no	—
147	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
149	C₄×D₁₀₉	—	2	2	no	—
150	C₄×D₁₀₉	—	2	1	no	—
151	C₄×D₁₀₉	—	2	1	no	—
152	C₄×D₁₀₉	—	2	2	no	—
153	C₄×D₁₀₉	—	4	2	no	—
154	C₄×D₁₀₉	—	4	2	no	—
155	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
156	C₄×D₁₀₉	#41	1	2	yes	—
157	Dic₂₁₈	—	2	1	no	—
158	Dic₂₁₈	—	2	1	no	—
159	Dic₂₁₈	—	2	1	no	—
160	Dic₂₁₈	—	2	1	no	—
161	Dic₂₁₈	—	4	2	no	—
162	C₈×C₁₀₉	—	2	1	no	—
163	C₈×C₁₀₉	C₂×D₄	1	2	yes	—
164	#11724784	—	2	1	no	—
165	#11724784	C₂×D₄	1	2	yes	—
166	C₂²×C₁₀₉	—	2	1	no	—
167	C₂²×C₁₀₉	—	2	1	no	—
168	C₂²×C₁₀₉	—	4	1	no	—
169	C₂²×C₁₀₉	—	4	1	no	—
170	C₂²×C₁₀₉	—	4	1	no	—
171	C₂²×C₁₀₉	#137	1	2	yes	complemented
172	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
173	C₂×D₁₀₉	—	2	1	no	—
174	C₂×D₁₀₉	—	2	1	no	—
175	C₂×D₁₀₉	—	2	1	no	—
176	C₂×D₁₀₉	—	2	1	no	—
177	C₂×D₁₀₉	—	2	1	no	—
178	C₂×D₁₀₉	—	4	4	no	—
179	C₂×D₁₀₉	#121	1	2	yes	—
180	C₄×C₁₀₉	—	2	1	no	—
181	C₄×C₁₀₉	—	4	1	no	—
182	C₄×C₁₀₉	—	4	1	no	—
183	C₄×C₁₀₉	—	4	1	no	—
184	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
185	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
186	Dic₁₀₉	—	2	1	no	—
187	Dic₁₀₉	—	4	1	no	—
188	Dic₁₀₉	—	4	1	no	—
189	Dic₁₀₉	—	4	1	no	—
190	Dic₁₀₉	—	4	1	no	—
191	Dic₁₀₉	#121	1	2	yes	—
192	C₂×C₁₀₉	—	2	2	no	—
193	C₂×C₁₀₉	—	8	1	no	—
194	C₂×C₁₀₉	C₂×#121	1	1	yes	characteristic
195	C₂×C₁₀₉	C₂×#137	1	1	yes	characteristic
196	C₂×C₁₀₉	#575	1	1	yes	characteristic
197	D₁₀₉	—	2	2	no	—
198	D₁₀₉	—	4	1	no	—
199	#3056	—	109	1	no	maximal, Sylow
200	C₁₀₉	#3056	1	1	yes	characteristic, complemented, Sylow
201	C₂×#137	—	109	1	no	—
202	C₂²×M₁₆	—	109	1	no	—
203	#525	—	109	1	no	—
204	C₂×C₂²⋊Q₈	—	109	1	no	—
205	#470	—	109	1	no	—
206	#470	—	109	1	no	—
207	#468	—	109	1	no	—
208	#468	—	109	1	no	—
209	#467	—	109	1	no	—
210	#467	—	109	1	no	—
211	#465	—	109	1	no	—
212	#465	D₁₀₉	1	1	yes	characteristic, complemented
213	#428	—	109	1	no	—
214	#419	—	109	1	no	—
215	#417	—	109	1	no	—
216	C₂×#41	—	109	1	no	—
217	C₂²×Q₈	—	109	1	no	—
218	C₂³×C₄	—	109	1	no	—
219	#137	—	218	4	no	—
220	C₂×Q₁₆	—	109	1	no	—
221	C₂×Q₁₆	—	109	1	no	—
222	C₂×SD₁₆	—	109	1	no	—
223	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
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	—	218	4	no	—
229	C₂²×C₈	—	109	1	no	—
230	C₂²×C₈	C₂×D₁₀₉	1	1	yes	characteristic
231	#123	—	218	1	no	—
232	C₂²⋊Q₈	—	109	1	no	—
233	C₂²⋊Q₈	—	109	1	no	—
234	C₂²⋊Q₈	—	109	1	no	—
235	C₂²⋊Q₈	—	109	1	no	—
236	C₂²⋊Q₈	—	109	1	no	—
237	C₂²⋊Q₈	—	218	1	no	—
238	C₂²⋊Q₈	—	218	1	no	—
239	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic
240	#121	—	109	1	no	—
241	#121	C₂×D₁₀₉	1	1	yes	characteristic
242	#120	—	218	1	no	—
243	C₄×D₄	—	218	1	no	—
244	C₄×D₄	—	218	1	no	—
245	#117	—	109	1	no	—
246	C₂×C₄⋊C₄	—	109	1	no	—
247	C₂×C₄⋊C₄	—	218	1	no	—
248	C₂×C₂²⋊C₄	—	218	1	no	—
249	#107	—	109	1	no	—
250	#107	—	109	1	no	—
251	#106	—	109	1	no	—
252	#106	C₂×D₁₀₉	1	1	yes	characteristic, complemented
253	#103	—	109	1	no	—
254	#103	—	109	1	no	—
255	#103	—	109	1	no	—
256	#103	—	109	1	no	—
257	#103	—	109	1	no	—
258	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
259	#102	—	109	1	no	—
260	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
261	C₂⁴	—	109	1	no	—
262	#41	—	218	2	no	—
263	#41	—	218	2	no	—
264	C₂×Q₈	—	109	1	no	—
265	C₂×Q₈	—	109	1	no	—
266	C₂×Q₈	—	218	1	no	—
267	C₂×Q₈	—	218	2	no	—
268	C₂×Q₈	—	218	2	no	—
269	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
270	C₂×D₄	—	2	1	no	—
271	C₂×D₄	—	218	1	no	—
272	C₂×D₄	—	218	1	no	—
273	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
274	C₂²×C₄	—	109	1	no	—
275	C₂²×C₄	—	109	1	no	—
276	C₂²×C₄	—	109	1	no	—
277	C₂²×C₄	—	109	1	no	—
278	C₂²×C₄	—	109	1	no	—
279	C₂²×C₄	—	218	2	no	—
280	C₂²×C₄	—	218	2	no	—
281	C₂²×C₄	—	218	1	no	—
282	C₂²×C₄	—	218	1	no	—
283	C₂²×C₄	—	218	1	no	—
284	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
285	Q₁₆	—	218	2	no	—
286	Q₁₆	—	218	2	no	—
287	SD₁₆	—	2	2	no	—
288	SD₁₆	—	218	2	no	—
289	M₁₆	—	109	4	no	—
290	M₁₆	—	218	2	no	—
291	M₁₆	—	218	2	no	—
292	M₁₆	—	218	2	no	—
293	C₂×C₈	—	2	2	no	—
294	C₂×C₈	—	109	1	no	—
295	C₂×C₈	—	109	1	no	—
296	C₂×C₈	—	218	2	no	—
297	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
298	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
299	C₄⋊C₄	—	2	1	no	—
300	C₄⋊C₄	—	109	1	no	—
301	C₄⋊C₄	—	109	1	no	—
302	C₄⋊C₄	—	218	1	no	—
303	C₄⋊C₄	—	218	1	no	—
304	C₄⋊C₄	—	218	1	no	—
305	C₄⋊C₄	—	218	1	no	—
306	C₄⋊C₄	—	218	1	no	—
307	C₄⋊C₄	—	218	1	no	—
308	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
309	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
310	C₂²⋊C₄	—	2	1	no	—
311	C₂²⋊C₄	—	2	1	no	—
312	C₂²⋊C₄	—	218	1	no	—
313	C₂²⋊C₄	—	218	1	no	—
314	C₂²⋊C₄	—	218	1	no	—
315	C₂²⋊C₄	—	218	1	no	—
316	C₂²⋊C₄	—	218	1	no	—
317	C₂²⋊C₄	—	218	1	no	—
318	C₂²⋊C₄	—	218	1	no	—
319	C₄²	—	218	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	109	1	no	—
322	C₂³	—	109	1	no	—
323	C₂³	—	436	1	no	—
324	C₂³	—	218	2	no	—
325	C₂³	—	218	2	no	—
326	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
327	Q₈	—	2	1	no	—
328	Q₈	—	2	1	no	—
329	Q₈	—	436	2	no	—
330	Q₈	—	218	1	no	—
331	Q₈	—	218	1	no	—
332	Q₈	—	218	1	no	—
333	Q₈	—	218	1	no	—
334	D₄	—	2	1	no	—
335	D₄	—	2	1	no	—
336	D₄	—	4	2	no	—
337	D₄	—	436	2	no	—
338	D₄	—	436	2	no	—
339	C₂×C₄	—	2	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	109	1	no	—
345	C₂×C₄	—	109	2	no	—
346	C₂×C₄	—	109	2	no	—
347	C₂×C₄	—	109	1	no	—
348	C₂×C₄	—	436	2	no	—
349	C₂×C₄	—	436	2	no	—
350	C₂×C₄	—	436	2	no	—
351	C₂×C₄	—	218	2	no	—
352	C₂×C₄	—	218	2	no	—
353	C₂×C₄	—	218	2	no	—
354	C₂×C₄	—	218	1	no	—
355	C₂×C₄	—	218	1	no	—
356	C₂×C₄	—	218	1	no	—
357	C₂×C₄	—	218	1	no	—
358	C₂×C₄	—	218	1	no	—
359	C₂×C₄	—	218	1	no	—
360	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
361	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
362	C₈	—	2	1	no	—
363	C₈	—	109	2	no	—
364	C₈	—	218	1	no	—
365	C₈	D₄×D₁₀₉	1	2	yes	—
366	C₂²	—	2	1	no	—
367	C₂²	—	2	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	109	2	no	—
372	C₂²	—	436	4	no	—
373	C₂²	—	218	1	no	—
374	C₂²	—	218	1	no	—
375	C₂²	—	218	1	no	—
376	C₂²	—	218	1	no	—
377	C₂²	—	218	1	no	—
378	C₂²	#16812728	1	2	yes	complemented
379	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
380	C₄	—	2	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	4	1	no	—
384	C₄	—	109	2	no	—
385	C₄	—	436	1	no	—
386	C₄	—	436	1	no	—
387	C₄	—	436	1	no	—
388	C₄	—	436	1	no	—
389	C₄	—	218	1	no	—
390	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
391	C₄	#41×D₁₀₉	1	1	yes	characteristic
392	C₂	—	2	2	no	—
393	C₂	—	8	1	no	—
394	C₂	—	436	1	no	—
395	C₂	—	218	2	no	—
396	C₂	#121×D₁₀₉	1	1	yes	characteristic
397	C₂	C₂×#16812728	1	1	yes	characteristic
398	C₂	#20295823	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#465×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	#20295536	C₂
hypercenter	#465	D₁₀₉
hypocenter	C₁₀₉	#3056
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ #465

Complements

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

N	H ≅ G/N	type
1. C₂×#16812728	C₂	semidirect
2. C₂²×#13182012	C₂	semidirect
4. C₂²⋊Q₈×D₁₀₉	C₂	semidirect
5. #20295285	C₂	semidirect
6. #20295283	C₂	semidirect
7. #20295271	C₂	semidirect
8. #20295269	C₂	semidirect
9. #20295267	C₂	semidirect
10. #20295265	C₂	semidirect
11. #20295253	C₂	semidirect
12. #20295065	C₂	semidirect
13. #20295033	C₂	semidirect
14. #20295024	C₂	semidirect
15. #465×C₁₀₉	C₂	semidirect
20. C₂×Dic₄₃₆	C₂²	semidirect
21. C₂×#13182019	C₂²	semidirect
22. C₂×#13182017	C₂²	semidirect
45. #16812633	C₂²	semidirect
46. #16812632	C₂²	semidirect
47. #16812630	C₂²	semidirect
48. #16812624	C₂²	semidirect
49. #16812624	C₂²	semidirect
50. #16812623	C₂²	semidirect
51. #16812622	C₂²	semidirect
52. #16812622	C₂²	semidirect
53. #16812620	C₂²	semidirect
54. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
58. #106×C₁₀₉	C₂²	semidirect
59. #103×C₁₀₉	C₂²	semidirect
60. #102×C₁₀₉	C₂²	semidirect
87. #13182012	D₄	semidirect
171. C₂²×C₁₀₉	#137	semidirect
200. C₁₀₉	#3056	semidirect
212. #465	D₁₀₉	semidirect
223. C₂×SD₁₆	C₂×D₁₀₉	semidirect
252. #106	C₂×D₁₀₉	semidirect
258. #103	C₂×D₁₀₉	semidirect
260. #102	C₂×D₁₀₉	semidirect
378. C₂²	#16812728	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16812728	2
C₂²×#13182012	2
#20295536	2
C₂²⋊Q₈×D₁₀₉	2
#20295285	2
#20295283	2
#20295271	2
#20295269	2
#20295267	2
#20295265	2
#20295253	2
#20295065	2
#20295033	2
#20295024	2
#465×C₁₀₉	2
#3056	109