Subgroups — #28372666

Order 13952.

492 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×SD₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16812705	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295599	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295592	C₂	1	1	yes	maximal, characteristic
5	#20295275	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295274	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295271	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295270	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295256	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295255	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295252	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295061	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295033	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295029	C₂	1	1	yes	maximal, characteristic, complemented
15	#465×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182029	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂×#13182018	C₂²	1	1	yes	characteristic
20	C₂×#13182017	C₂²	1	1	yes	characteristic
21	C₂×#13182016	C₂²	1	1	yes	characteristic
22	SD₁₆×D₁₀₉	—	2	4	no	—
23	#16812705	—	2	4	no	—
24	C₂×#13182013	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13182012	C₂²	1	1	yes	characteristic
26	C₂×#13182012	C₂²	1	1	yes	characteristic, complemented
27	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
29	#16812698	—	2	1	no	—
30	#16812695	—	2	1	no	—
31	#16812685	—	2	1	no	—
32	#16812685	—	2	1	no	—
33	#16812684	—	2	1	no	—
34	#16812681	—	2	1	no	—
35	#16812679	C₂²	1	1	yes	characteristic, complemented
36	#16812678	C₂²	1	1	yes	characteristic, complemented
37	#16812675	C₂²	1	1	yes	characteristic, complemented
38	#16812674	C₂²	1	1	yes	characteristic
39	#16812673	C₂²	1	1	yes	characteristic
40	#16812670	C₂²	1	1	yes	characteristic
41	#16812669	—	2	1	no	—
42	#16812667	—	2	1	no	—
43	#16812657	C₂²	1	1	yes	characteristic
44	#16812657	C₂²	1	1	yes	characteristic
45	#16812632	C₂²	1	1	yes	characteristic, complemented
46	#16812632	C₂²	1	1	yes	characteristic, complemented
47	#16812631	C₂²	1	1	yes	characteristic, complemented
48	#16812624	C₂²	1	1	yes	characteristic, complemented
49	#16812623	C₂²	1	1	yes	characteristic, complemented
50	#16812622	C₂²	1	1	yes	characteristic, complemented
51	#16812621	C₂²	1	1	yes	characteristic
52	#16812620	C₂²	1	1	yes	characteristic
53	#16812619	C₂²	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
55	C₂²×C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
56	C₂²⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
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
61	C₂³×D₁₀₉	—	2	1	no	—
62	#13182029	—	2	2	no	—
63	#13182029	—	2	2	no	—
64	C₂×Dic₂₁₈	—	2	1	no	—
65	C₂×Dic₂₁₈	D₄	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×D₄₃₆	—	2	1	no	—
70	C₂×D₄₃₆	D₄	1	1	yes	characteristic
71	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
74	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
75	C₂×C₂²⋊D₁₀₉	D₄	1	1	yes	characteristic
76	C₂×C₂²⋊D₁₀₉	D₄	1	1	yes	characteristic
77	D₄×D₁₀₉	—	2	2	no	—
78	D₄×D₁₀₉	—	2	2	no	—
79	C₂×C₄×D₁₀₉	—	2	1	no	—
80	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
81	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
82	#13182018	—	2	2	no	—
83	#13182017	—	2	2	no	—
84	#13182016	—	2	2	no	—
85	#13182013	—	2	2	no	—
86	#13182012	—	2	2	no	—
87	#13182012	—	2	2	no	—
88	C₂×#11724784	C₂³	1	1	yes	characteristic
89	C₂×#11724784	C₂³	1	1	yes	characteristic
90	C₈×D₁₀₉	—	2	2	no	—
91	C₈×D₁₀₉	D₄	1	4	yes	complemented
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	C₂²⋊Dic₁₀₉	—	2	1	no	—
98	C₂²⋊Dic₁₀₉	—	2	1	no	—
99	#13182006	—	2	1	no	—
100	#13182006	—	2	1	no	—
101	#13182006	—	2	1	no	—
102	#13182006	—	2	1	no	—
103	#13182006	—	2	1	no	—
104	#13182006	—	2	1	no	—
105	C₄×Dic₁₀₉	—	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	1	no	—
123	C₂²×D₁₀₉	—	4	2	no	—
124	C₂²×D₁₀₉	—	8	1	no	—
125	C₂²×D₁₀₉	—	8	1	no	—
126	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
127	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
128	Q₈×C₁₀₉	—	2	1	no	—
129	Q₈×C₁₀₉	—	2	1	no	—
130	D₄×C₁₀₉	—	2	1	no	—
131	D₄×C₁₀₉	—	2	1	no	—
132	D₄×C₁₀₉	—	8	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	—	2	1	no	—
138	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
139	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
140	C₂²⋊D₁₀₉	—	2	2	no	—
141	C₂²⋊D₁₀₉	—	2	2	no	—
142	C₂²⋊D₁₀₉	—	4	2	no	—
143	C₂²⋊D₁₀₉	—	8	1	no	—
144	C₂²⋊D₁₀₉	—	8	1	no	—
145	C₂×Dic₁₀₉	—	2	1	no	—
146	C₂×Dic₁₀₉	—	2	1	no	—
147	C₂×Dic₁₀₉	—	2	1	no	—
148	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
149	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
150	D₄₃₆	—	2	2	no	—
151	D₄₃₆	—	2	1	no	—
152	D₄₃₆	—	2	1	no	—
153	D₄₃₆	—	8	1	no	—
154	C₄×D₁₀₉	—	2	1	no	—
155	C₄×D₁₀₉	—	2	1	no	—
156	C₄×D₁₀₉	—	4	2	no	—
157	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
158	C₄×D₁₀₉	#41	1	2	yes	—
159	Dic₂₁₈	—	2	2	no	—
160	Dic₂₁₈	—	2	1	no	—
161	Dic₂₁₈	—	2	1	no	—
162	Dic₂₁₈	—	4	2	no	—
163	C₈×C₁₀₉	—	2	1	no	—
164	C₈×C₁₀₉	C₂×D₄	1	2	yes	—
165	#11724784	—	2	1	no	—
166	#11724784	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	—	4	1	no	—
171	C₂²×C₁₀₉	—	4	1	no	—
172	C₂²×C₁₀₉	—	4	1	no	—
173	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
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	—	2	1	no	—
179	C₂×D₁₀₉	—	4	1	no	—
180	C₂×D₁₀₉	—	4	1	no	—
181	C₂×D₁₀₉	—	4	1	no	—
182	C₂×D₁₀₉	—	8	4	no	—
183	C₂×D₁₀₉	#121	1	2	yes	—
184	C₄×C₁₀₉	—	2	1	no	—
185	C₄×C₁₀₉	—	4	1	no	—
186	C₄×C₁₀₉	—	4	1	no	—
187	C₄×C₁₀₉	—	4	1	no	—
188	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
189	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
190	Dic₁₀₉	—	2	1	no	—
191	Dic₁₀₉	—	4	1	no	—
192	Dic₁₀₉	—	4	1	no	—
193	Dic₁₀₉	—	4	1	no	—
194	Dic₁₀₉	#121	1	2	yes	—
195	C₂×C₁₀₉	—	4	1	no	—
196	C₂×C₁₀₉	—	8	1	no	—
197	C₂×C₁₀₉	C₂×#121	1	1	yes	characteristic
198	C₂×C₁₀₉	#577	1	1	yes	characteristic
199	C₂×C₁₀₉	#577	1	1	yes	characteristic
200	D₁₀₉	—	2	2	no	—
201	D₁₀₉	—	4	1	no	—
202	D₁₀₉	—	8	1	no	—
203	#3057	—	109	1	no	maximal, Sylow
204	C₁₀₉	#3057	1	1	yes	characteristic, complemented, Sylow
205	C₂²×SD₁₆	—	109	1	no	—
206	C₂×#131	—	109	1	no	—
207	#536	—	109	1	no	—
208	#535	—	109	1	no	—
209	#468	—	109	1	no	—
210	#468	—	109	1	no	—
211	#468	—	109	1	no	—
212	#468	—	109	1	no	—
213	#465	—	109	1	no	—
214	#465	—	109	1	no	—
215	#465	—	109	1	no	—
216	#465	D₁₀₉	1	1	yes	characteristic, complemented
217	#427	—	109	1	no	—
218	#419	—	109	1	no	—
219	#418	—	109	1	no	—
220	C₂×#41	—	109	1	no	—
221	C₂²×Q₈	—	109	1	no	—
222	C₂²×D₄	—	109	1	no	—
223	C₂×SD₁₆	—	109	1	no	—
224	C₂×SD₁₆	—	109	1	no	—
225	C₂×SD₁₆	—	109	1	no	—
226	C₂×SD₁₆	—	218	4	no	—
227	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
228	#131	—	218	4	no	—
229	C₂×M₁₆	—	109	1	no	—
230	C₂×M₁₆	—	109	1	no	—
231	C₂×M₁₆	—	109	1	no	—
232	C₂²×C₈	—	109	1	no	—
233	C₂²×C₈	—	109	1	no	—
234	C₂²×C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
235	C₄⋊Q₈	—	218	1	no	—
236	#127	—	218	1	no	—
237	#124	—	218	1	no	—
238	#124	—	218	1	no	—
239	#123	—	218	1	no	—
240	#123	—	218	1	no	—
241	C₂²⋊Q₈	—	109	1	no	—
242	C₂²⋊Q₈	—	109	1	no	—
243	C₂²⋊Q₈	—	109	1	no	—
244	C₂²⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
245	#121	—	109	1	no	—
246	#121	—	109	1	no	—
247	#121	—	109	1	no	—
248	#121	C₂×D₁₀₉	1	1	yes	characteristic
249	#120	—	218	1	no	—
250	#120	—	218	1	no	—
251	#117	—	109	1	no	—
252	#117	—	109	1	no	—
253	#107	—	109	1	no	—
254	#107	—	109	1	no	—
255	#106	—	109	1	no	—
256	#106	C₂×D₁₀₉	1	1	yes	characteristic, complemented
257	#103	—	109	1	no	—
258	#103	—	109	1	no	—
259	#103	—	109	1	no	—
260	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
261	#102	—	109	1	no	—
262	#102	—	109	1	no	—
263	#102	—	109	1	no	—
264	#102	C₂×D₁₀₉	1	1	yes	characteristic
265	C₂⁴	—	218	1	no	—
266	#41	—	218	2	no	—
267	#41	—	218	2	no	—
268	C₂×Q₈	—	109	1	no	—
269	C₂×Q₈	—	109	1	no	—
270	C₂×Q₈	—	218	1	no	—
271	C₂×Q₈	—	218	2	no	—
272	C₂×Q₈	—	218	2	no	—
273	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
274	C₂×D₄	—	2	1	no	—
275	C₂×D₄	—	109	1	no	—
276	C₂×D₄	—	109	1	no	—
277	C₂×D₄	—	109	1	no	—
278	C₂×D₄	—	109	1	no	—
279	C₂×D₄	—	218	1	no	—
280	C₂×D₄	—	218	2	no	—
281	C₂×D₄	—	218	2	no	—
282	C₂×D₄	—	218	1	no	—
283	C₂×D₄	—	218	1	no	—
284	C₂×D₄	—	218	1	no	—
285	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
286	C₂²×C₄	—	109	1	no	—
287	C₂²×C₄	—	109	1	no	—
288	C₂²×C₄	—	218	1	no	—
289	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
290	SD₁₆	—	2	2	no	—
291	SD₁₆	—	218	2	no	—
292	SD₁₆	—	218	2	no	—
293	SD₁₆	—	218	2	no	—
294	M₁₆	—	218	2	no	—
295	M₁₆	—	218	2	no	—
296	M₁₆	—	218	2	no	—
297	C₂×C₈	—	2	2	no	—
298	C₂×C₈	—	109	1	no	—
299	C₂×C₈	—	109	4	no	—
300	C₂×C₈	—	109	1	no	—
301	C₂×C₈	—	218	2	no	—
302	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
303	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
304	C₄⋊C₄	—	2	1	no	—
305	C₄⋊C₄	—	109	1	no	—
306	C₄⋊C₄	—	109	1	no	—
307	C₄⋊C₄	—	218	1	no	—
308	C₄⋊C₄	—	218	1	no	—
309	C₄⋊C₄	—	218	1	no	—
310	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
311	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
312	C₂²⋊C₄	—	2	1	no	—
313	C₂²⋊C₄	—	2	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	C₂²⋊C₄	—	218	1	no	—
320	C₂²⋊C₄	—	218	1	no	—
321	C₂²⋊C₄	—	218	1	no	—
322	C₄²	—	218	1	no	—
323	C₄²	—	218	1	no	—
324	C₂³	—	2	1	no	—
325	C₂³	—	872	1	no	—
326	C₂³	—	872	1	no	—
327	C₂³	—	109	1	no	—
328	C₂³	—	109	1	no	—
329	C₂³	—	436	2	no	—
330	C₂³	—	218	1	no	—
331	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
332	Q₈	—	2	1	no	—
333	Q₈	—	2	1	no	—
334	Q₈	—	436	2	no	—
335	Q₈	—	218	2	no	—
336	Q₈	—	218	1	no	—
337	Q₈	—	218	1	no	—
338	D₄	—	2	1	no	—
339	D₄	—	2	1	no	—
340	D₄	—	8	1	no	—
341	D₄	—	872	1	no	—
342	D₄	—	872	1	no	—
343	D₄	—	872	1	no	—
344	D₄	—	436	2	no	—
345	D₄	—	218	2	no	—
346	D₄	—	218	2	no	—
347	D₄	—	218	2	no	—
348	D₄	—	218	1	no	—
349	D₄	—	218	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	2	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	109	1	no	—
356	C₂×C₄	—	109	2	no	—
357	C₂×C₄	—	109	2	no	—
358	C₂×C₄	—	109	1	no	—
359	C₂×C₄	—	436	2	no	—
360	C₂×C₄	—	218	1	no	—
361	C₂×C₄	—	218	1	no	—
362	C₂×C₄	—	218	1	no	—
363	C₂×C₄	—	218	1	no	—
364	C₂×C₄	—	218	1	no	—
365	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
366	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
367	C₈	—	2	1	no	—
368	C₈	—	109	2	no	—
369	C₈	—	218	1	no	—
370	C₈	D₄×D₁₀₉	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	2	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	872	4	no	—
378	C₂²	—	109	2	no	—
379	C₂²	—	436	1	no	—
380	C₂²	—	436	1	no	—
381	C₂²	—	436	1	no	—
382	C₂²	—	218	1	no	—
383	C₂²	—	218	1	no	—
384	C₂²	—	218	1	no	—
385	C₂²	—	218	1	no	—
386	C₂²	—	218	1	no	—
387	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
388	C₄	—	2	1	no	—
389	C₄	—	4	1	no	—
390	C₄	—	4	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	109	2	no	—
393	C₄	—	436	1	no	—
394	C₄	—	436	1	no	—
395	C₄	—	436	1	no	—
396	C₄	—	218	1	no	—
397	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
398	C₄	#41×D₁₀₉	1	1	yes	characteristic
399	C₂	—	4	1	no	—
400	C₂	—	8	1	no	—
401	C₂	—	872	1	no	—
402	C₂	—	436	1	no	—
403	C₂	—	218	2	no	—
404	C₂	#121×D₁₀₉	1	1	yes	characteristic
405	C₂	#20295832	1	1	yes	characteristic
406	C₂	#20295833	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	#20295592	C₂
hypercenter	#465	D₁₀₉
hypocenter	C₁₀₉	#3057
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×SD₁₆×D₁₀₉	C₂	semidirect
2. C₂×#16812705	C₂	semidirect
3. #20295599	C₂	semidirect
5. #20295275	C₂	semidirect
6. #20295274	C₂	semidirect
7. #20295271	C₂	semidirect
8. #20295270	C₂	semidirect
9. #20295256	C₂	semidirect
10. #20295255	C₂	semidirect
11. #20295252	C₂	semidirect
12. #20295061	C₂	semidirect
13. #20295033	C₂	semidirect
14. #20295029	C₂	semidirect
15. #465×C₁₀₉	C₂	semidirect
24. C₂×#13182013	C₂²	semidirect
26. C₂×#13182012	C₂²	semidirect
28. C₂×C₈×D₁₀₉	C₂²	semidirect
35. #16812679	C₂²	semidirect
36. #16812678	C₂²	semidirect
37. #16812675	C₂²	semidirect
45. #16812632	C₂²	semidirect
46. #16812632	C₂²	semidirect
47. #16812631	C₂²	semidirect
48. #16812624	C₂²	semidirect
49. #16812623	C₂²	semidirect
50. #16812622	C₂²	semidirect
55. C₂²×C₈×C₁₀₉	C₂²	semidirect
56. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
58. #106×C₁₀₉	C₂²	semidirect
59. #103×C₁₀₉	C₂²	semidirect
91. C₈×D₁₀₉	D₄	semidirect
204. C₁₀₉	#3057	semidirect
216. #465	D₁₀₉	semidirect
234. C₂²×C₈	C₂×D₁₀₉	semidirect
244. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
256. #106	C₂×D₁₀₉	semidirect
260. #103	C₂×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₂×SD₁₆×D₁₀₉	2
C₂×#16812705	2
#20295599	2
#20295592	2
#20295275	2
#20295274	2
#20295271	2
#20295270	2
#20295256	2
#20295255	2
#20295252	2
#20295061	2
#20295033	2
#20295029	2
#465×C₁₀₉	2
#3057	109