Subgroups — #28373516

Order 13952.

596 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812726	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16812723	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16812720	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×D₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295594	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295589	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295415	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295414	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295412	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295408	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295407	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295402	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295401	C₂	1	1	yes	maximal, characteristic, complemented
14	#20294983	C₂	1	1	yes	maximal, characteristic, complemented
15	#496×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182030	C₂²	1	1	yes	characteristic
17	C₂×#13182028	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
20	#16812726	—	2	4	no	—
21	#16812723	—	2	4	no	—
22	#16812720	—	2	4	no	—
23	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13182018	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13182018	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13182017	C₂²	1	1	yes	characteristic, complemented
27	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
28	C₂×D₈₇₂	C₂²	1	1	yes	characteristic
29	C₂×D₈₇₂	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13182014	C₂²	1	1	yes	characteristic
31	C₂×#13182014	C₂²	1	1	yes	characteristic
32	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
33	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
34	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
35	D₈×D₁₀₉	—	2	4	no	—
36	C₂×#13182012	C₂²	1	1	yes	characteristic
37	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
38	#16812696	C₂²	1	1	yes	characteristic, complemented
39	#16812695	C₂²	1	1	yes	characteristic, complemented
40	#16812695	C₂²	1	1	yes	characteristic, complemented
41	#16812688	C₂²	1	1	yes	characteristic, complemented
42	#16812687	C₂²	1	1	yes	characteristic, complemented
43	#16812686	C₂²	1	1	yes	characteristic, complemented
44	#16812672	—	2	2	no	—
45	#16812671	—	2	2	no	—
46	#16812669	—	2	2	no	—
47	#16812667	—	2	2	no	—
48	#16812656	C₂²	1	1	yes	characteristic
49	#16812609	C₂²	1	1	yes	characteristic, complemented
50	C₄×#11724784	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×D₈×C₁₀₉	C₂²	1	1	yes	characteristic
55	C₂×D₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
56	#127×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	#124×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	#97×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₀₉	—	2	1	no	—
60	C₂³×D₁₀₉	—	2	1	no	—
61	#13182030	—	2	2	no	—
62	#13182030	—	2	2	no	—
63	#13182028	—	2	2	no	—
64	#13182028	—	2	2	no	—
65	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
66	C₂×D₄₃₆	—	2	1	no	—
67	C₂×D₄₃₆	—	2	2	no	—
68	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
69	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
70	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
74	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
75	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
76	D₄×D₁₀₉	—	2	2	no	—
77	D₄×D₁₀₉	—	2	2	no	—
78	D₄×D₁₀₉	—	2	2	no	—
79	D₄×D₁₀₉	—	2	2	no	—
80	C₂²×Dic₁₀₉	—	2	1	no	—
81	C₂×C₄×D₁₀₉	—	2	1	no	—
82	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
83	#13182019	—	2	2	no	—
84	#13182018	—	2	2	no	—
85	#13182018	—	2	2	no	—
86	#13182017	—	2	2	no	—
87	#13182016	—	2	2	no	—
88	D₈₇₂	—	2	2	no	—
89	D₈₇₂	—	2	2	no	—
90	#13182014	—	2	2	no	—
91	#13182014	—	2	2	no	—
92	#13182014	—	2	2	no	—
93	#13182014	—	2	2	no	—
94	#13182014	—	2	2	no	—
95	#13182012	D₄	1	4	yes	complemented
96	C₂×#11724784	C₂³	1	1	yes	characteristic
97	C₂×#11724784	C₂³	1	1	yes	characteristic
98	C₈×D₁₀₉	D₄	1	4	yes	complemented
99	#13182008	D₄	1	2	yes	—
100	C₂²⋊Dic₁₀₉	—	2	2	no	—
101	#13182006	—	2	2	no	—
102	#13182006	—	2	2	no	—
103	#13182006	D₄	1	2	yes	—
104	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
105	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
106	C₂×D₄×C₁₀₉	—	2	2	no	—
107	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
108	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	SD₁₆×C₁₀₉	—	2	2	no	—
111	SD₁₆×C₁₀₉	—	2	2	no	—
112	D₈×C₁₀₉	—	2	2	no	—
113	D₈×C₁₀₉	—	2	2	no	—
114	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
117	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
118	C₂³×C₁₀₉	—	2	1	no	—
119	C₂³×C₁₀₉	—	2	1	no	—
120	C₂³×C₁₀₉	—	2	1	no	—
121	C₂²×D₁₀₉	—	2	1	no	—
122	C₂²×D₁₀₉	—	2	1	no	—
123	C₂²×D₁₀₉	—	2	1	no	—
124	C₂²×D₁₀₉	—	4	2	no	—
125	C₂²×D₁₀₉	—	4	2	no	—
126	C₂²×D₁₀₉	—	8	2	no	—
127	C₂²×D₁₀₉	—	8	2	no	—
128	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
129	Q₈×C₁₀₉	—	2	1	no	—
130	Q₈×C₁₀₉	—	2	1	no	—
131	D₄×C₁₀₉	—	2	1	no	—
132	D₄×C₁₀₉	—	2	1	no	—
133	D₄×C₁₀₉	—	2	1	no	—
134	D₄×C₁₀₉	—	2	1	no	—
135	D₄×C₁₀₉	—	2	1	no	—
136	D₄×C₁₀₉	—	2	1	no	—
137	D₄×C₁₀₉	—	8	2	no	—
138	C₂×C₄×C₁₀₉	—	2	1	no	—
139	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
140	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
141	C₂²⋊D₁₀₉	—	4	2	no	—
142	C₂²⋊D₁₀₉	—	4	2	no	—
143	C₂²⋊D₁₀₉	—	4	2	no	—
144	C₂²⋊D₁₀₉	—	8	2	no	—
145	C₂²⋊D₁₀₉	—	8	2	no	—
146	C₂×Dic₁₀₉	—	2	1	no	—
147	C₂×Dic₁₀₉	—	4	2	no	—
148	C₂×Dic₁₀₉	C₂×D₄	1	2	yes	—
149	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
150	D₄₃₆	—	2	1	no	—
151	D₄₃₆	—	2	1	no	—
152	D₄₃₆	—	2	1	no	—
153	D₄₃₆	—	2	1	no	—
154	D₄₃₆	—	2	1	no	—
155	D₄₃₆	—	2	1	no	—
156	D₄₃₆	—	4	2	no	—
157	D₄₃₆	—	8	2	no	—
158	C₄×D₁₀₉	—	4	2	no	—
159	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
160	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
161	Dic₂₁₈	—	2	1	no	—
162	Dic₂₁₈	—	2	1	no	—
163	C₈×C₁₀₉	C₂×D₄	1	2	yes	—
164	C₈×C₁₀₉	C₂×D₄	1	2	yes	—
165	#11724784	C₂×D₄	1	2	yes	—
166	#11724784	C₂×D₄	1	2	yes	—
167	C₂²×C₁₀₉	—	4	1	no	—
168	C₂²×C₁₀₉	—	4	1	no	—
169	C₂²×C₁₀₉	—	4	1	no	—
170	C₂²×C₁₀₉	—	4	2	no	—
171	C₂²×C₁₀₉	—	4	2	no	—
172	C₂²×C₁₀₉	—	4	2	no	—
173	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
174	C₂×D₁₀₉	—	2	2	no	—
175	C₂×D₁₀₉	—	4	1	no	—
176	C₂×D₁₀₉	—	4	1	no	—
177	C₂×D₁₀₉	—	4	1	no	—
178	C₂×D₁₀₉	—	4	2	no	—
179	C₂×D₁₀₉	—	4	2	no	—
180	C₂×D₁₀₉	—	4	2	no	—
181	C₂×D₁₀₉	—	8	4	no	—
182	C₂×D₁₀₉	—	8	4	no	—
183	C₂×D₁₀₉	#127	1	2	yes	—
184	C₄×C₁₀₉	—	2	2	no	—
185	C₄×C₁₀₉	—	4	1	no	—
186	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
187	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
188	Dic₁₀₉	—	2	2	no	—
189	Dic₁₀₉	—	4	1	no	—
190	Dic₁₀₉	#127	1	2	yes	—
191	C₂×C₁₀₉	—	8	1	no	—
192	C₂×C₁₀₉	—	8	1	no	—
193	C₂×C₁₀₉	—	8	1	no	—
194	C₂×C₁₀₉	C₂×#127	1	1	yes	characteristic
195	C₂×C₁₀₉	#576	1	2	yes	—
196	D₁₀₉	—	2	2	no	—
197	D₁₀₉	—	8	1	no	—
198	D₁₀₉	—	8	1	no	—
199	D₁₀₉	—	8	1	no	—
200	#3155	—	109	1	no	maximal, Sylow
201	C₁₀₉	#3155	1	1	yes	characteristic, complemented, Sylow
202	C₂×AGL(1,ℤ/8)	—	109	1	no	—
203	C₂×AGL(1,ℤ/8)	—	109	1	no	—
204	C₂×#135	—	109	1	no	—
205	C₂²×D₈	—	109	1	no	—
206	#535	—	109	1	no	—
207	#535	—	109	1	no	—
208	#496	—	109	1	no	—
209	#496	—	109	1	no	—
210	#496	—	109	1	no	—
211	#496	D₁₀₉	1	1	yes	characteristic, complemented
212	#495	—	109	1	no	—
213	#495	—	109	1	no	—
214	#493	—	109	1	no	—
215	#493	—	109	1	no	—
216	#405	—	109	1	no	—
217	C₂×#41	—	109	1	no	—
218	C₂×#41	—	109	1	no	—
219	C₂²×D₄	—	109	1	no	—
220	C₂²×D₄	—	109	1	no	—
221	AGL(1,ℤ/8)	—	218	4	no	—
222	AGL(1,ℤ/8)	—	218	4	no	—
223	#135	—	218	4	no	—
224	C₂×Q₁₆	—	109	1	no	—
225	C₂×SD₁₆	—	109	1	no	—
226	C₂×SD₁₆	—	109	1	no	—
227	C₂×SD₁₆	—	109	1	no	—
228	C₂×SD₁₆	—	109	1	no	—
229	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
230	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
231	C₂×D₈	—	109	1	no	—
232	C₂×D₈	—	109	1	no	—
233	C₂×D₈	—	109	1	no	—
234	C₂×D₈	—	109	1	no	—
235	C₂×D₈	—	109	1	no	—
236	C₂×D₈	—	109	1	no	—
237	C₂×D₈	—	109	1	no	—
238	C₂×D₈	—	218	4	no	—
239	C₂×D₈	C₂×D₁₀₉	1	1	yes	characteristic
240	C₂×D₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
241	C₂×M₁₆	—	109	1	no	—
242	C₂²×C₈	—	109	1	no	—
243	#127	—	109	1	no	—
244	#127	—	109	1	no	—
245	#127	—	109	1	no	—
246	#127	C₂×D₁₀₉	1	1	yes	characteristic, complemented
247	#124	—	109	1	no	—
248	#124	—	109	1	no	—
249	#124	—	109	1	no	—
250	#124	C₂×D₁₀₉	1	1	yes	characteristic, complemented
251	#121	—	218	2	no	—
252	#121	—	218	2	no	—
253	#120	—	218	2	no	—
254	#120	—	218	2	no	—
255	#117	—	109	1	no	—
256	#97	—	109	1	no	—
257	#97	C₂×D₁₀₉	1	1	yes	characteristic, complemented
258	C₄×C₈	—	109	1	no	—
259	C₄×C₈	—	109	1	no	—
260	C₂⁴	—	218	1	no	—
261	C₂⁴	—	218	1	no	—
262	#41	—	218	2	no	—
263	#41	—	218	2	no	—
264	#41	—	218	2	no	—
265	#41	—	218	2	no	—
266	C₂×Q₈	—	109	1	no	—
267	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	109	1	no	—
270	C₂×D₄	—	109	1	no	—
271	C₂×D₄	—	109	1	no	—
272	C₂×D₄	—	218	1	no	—
273	C₂×D₄	—	218	2	no	—
274	C₂×D₄	—	218	2	no	—
275	C₂×D₄	—	218	2	no	—
276	C₂×D₄	—	218	2	no	—
277	C₂×D₄	—	218	2	no	—
278	C₂×D₄	—	218	2	no	—
279	C₂×D₄	—	218	1	no	—
280	C₂×D₄	—	218	1	no	—
281	C₂×D₄	—	218	1	no	—
282	C₂×D₄	—	218	2	no	—
283	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
284	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
285	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
286	C₂²×C₄	—	109	1	no	—
287	C₂²×C₄	—	218	1	no	—
288	C₂²×C₄	—	218	1	no	—
289	Q₁₆	—	218	2	no	—
290	SD₁₆	—	2	2	no	—
291	SD₁₆	—	2	2	no	—
292	SD₁₆	—	218	2	no	—
293	SD₁₆	—	218	2	no	—
294	SD₁₆	—	218	2	no	—
295	SD₁₆	—	218	2	no	—
296	D₈	—	2	2	no	—
297	D₈	—	2	2	no	—
298	D₈	—	218	2	no	—
299	D₈	—	218	2	no	—
300	D₈	—	218	2	no	—
301	D₈	—	218	2	no	—
302	D₈	—	218	2	no	—
303	D₈	—	218	2	no	—
304	D₈	—	218	2	no	—
305	M₁₆	—	109	4	no	—
306	C₂×C₈	—	109	1	no	—
307	C₂×C₈	—	109	1	no	—
308	C₂×C₈	—	109	4	no	—
309	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
310	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
311	C₄⋊C₄	—	109	2	no	—
312	C₂²⋊C₄	—	2	2	no	—
313	C₂²⋊C₄	—	109	2	no	—
314	C₂²⋊C₄	—	218	2	no	—
315	C₂²⋊C₄	—	218	2	no	—
316	C₂²⋊C₄	—	218	2	no	—
317	C₄²	—	109	1	no	—
318	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	2	1	no	—
322	C₂³	—	872	2	no	—
323	C₂³	—	872	2	no	—
324	C₂³	—	109	1	no	—
325	C₂³	—	436	2	no	—
326	C₂³	—	436	2	no	—
327	C₂³	—	218	1	no	—
328	C₂³	—	218	1	no	—
329	C₂³	—	218	1	no	—
330	Q₈	—	2	1	no	—
331	Q₈	—	2	1	no	—
332	Q₈	—	218	1	no	—
333	Q₈	—	218	1	no	—
334	D₄	—	2	1	no	—
335	D₄	—	2	1	no	—
336	D₄	—	2	1	no	—
337	D₄	—	2	1	no	—
338	D₄	—	2	1	no	—
339	D₄	—	2	1	no	—
340	D₄	—	8	2	no	—
341	D₄	—	872	2	no	—
342	D₄	—	872	2	no	—
343	D₄	—	872	2	no	—
344	D₄	—	436	2	no	—
345	D₄	—	436	2	no	—
346	D₄	—	436	2	no	—
347	D₄	—	436	2	no	—
348	D₄	—	218	1	no	—
349	D₄	—	218	1	no	—
350	D₄	—	218	1	no	—
351	D₄	—	218	1	no	—
352	D₄	—	218	1	no	—
353	D₄	—	218	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	2	no	—
359	C₂×C₄	—	436	2	no	—
360	C₂×C₄	—	436	2	no	—
361	C₂×C₄	—	218	1	no	—
362	C₂×C₄	D₄×D₁₀₉	1	2	yes	—
363	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
364	C₈	—	109	2	no	—
365	C₈	—	109	2	no	—
366	C₈	D₄×D₁₀₉	1	2	yes	—
367	C₈	D₄×D₁₀₉	1	2	yes	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	4	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	872	4	no	—
375	C₂²	—	872	4	no	—
376	C₂²	—	109	2	no	—
377	C₂²	—	436	1	no	—
378	C₂²	—	436	1	no	—
379	C₂²	—	436	1	no	—
380	C₂²	—	436	2	no	—
381	C₂²	—	436	2	no	—
382	C₂²	—	436	2	no	—
383	C₂²	—	218	2	no	—
384	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
385	C₄	—	2	2	no	—
386	C₄	—	4	1	no	—
387	C₄	—	109	2	no	—
388	C₄	—	436	1	no	—
389	C₄	—	218	2	no	—
390	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
391	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
392	C₂	—	8	1	no	—
393	C₂	—	8	1	no	—
394	C₂	—	8	1	no	—
395	C₂	—	872	1	no	—
396	C₂	—	872	1	no	—
397	C₂	—	872	1	no	—
398	C₂	—	218	2	no	—
399	C₂	#127×D₁₀₉	1	1	yes	characteristic
400	C₂	#20295830	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#496×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
hypercenter	#496	D₁₀₉
hypocenter	C₁₀₉	#3155
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #496

Complements

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

N	H ≅ G/N	type
1. C₂×#16812726	C₂	semidirect
2. C₂×#16812723	C₂	semidirect
3. C₂×#16812720	C₂	semidirect
4. C₂×D₈×D₁₀₉	C₂	semidirect
5. #20295594	C₂	semidirect
6. #20295589	C₂	semidirect
7. #20295415	C₂	semidirect
8. #20295414	C₂	semidirect
9. #20295412	C₂	semidirect
10. #20295408	C₂	semidirect
11. #20295407	C₂	semidirect
12. #20295402	C₂	semidirect
13. #20295401	C₂	semidirect
14. #20294983	C₂	semidirect
15. #496×C₁₀₉	C₂	semidirect
23. C₂×#13182019	C₂²	semidirect
24. C₂×#13182018	C₂²	semidirect
25. C₂×#13182018	C₂²	semidirect
26. C₂×#13182017	C₂²	semidirect
27. C₂×#13182016	C₂²	semidirect
29. C₂×D₈₇₂	C₂²	semidirect
32. C₂×#13182014	C₂²	semidirect
33. C₂×#13182014	C₂²	semidirect
34. C₂×#13182014	C₂²	semidirect
38. #16812696	C₂²	semidirect
39. #16812695	C₂²	semidirect
40. #16812695	C₂²	semidirect
41. #16812688	C₂²	semidirect
42. #16812687	C₂²	semidirect
43. #16812686	C₂²	semidirect
49. #16812609	C₂²	semidirect
50. C₄×#11724784	C₂²	semidirect
51. C₈×Dic₁₀₉	C₂²	semidirect
52. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
53. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
55. C₂×D₈×C₁₀₉	C₂²	semidirect
56. #127×C₁₀₉	C₂²	semidirect
57. #124×C₁₀₉	C₂²	semidirect
58. #97×C₁₀₉	C₂²	semidirect
95. #13182012	D₄	semidirect
98. C₈×D₁₀₉	D₄	semidirect
201. C₁₀₉	#3155	semidirect
211. #496	D₁₀₉	semidirect
229. C₂×SD₁₆	C₂×D₁₀₉	semidirect
230. C₂×SD₁₆	C₂×D₁₀₉	semidirect
240. C₂×D₈	C₂×D₁₀₉	semidirect
246. #127	C₂×D₁₀₉	semidirect
250. #124	C₂×D₁₀₉	semidirect
257. #97	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×#16812726	2
C₂×#16812723	2
C₂×#16812720	2
C₂×D₈×D₁₀₉	2
#20295594	2
#20295589	2
#20295415	2
#20295414	2
#20295412	2
#20295408	2
#20295407	2
#20295402	2
#20295401	2
#20294983	2
#496×C₁₀₉	2
#3155	109