Subgroups — #28372542

Order 13952.

494 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812723	C₂	1	1	yes	maximal, characteristic
2	C₂×SD₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295596	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295498	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295240	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295239	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295238	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295232	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295231	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295230	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295229	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295051	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295033	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295019	C₂	1	1	yes	maximal, characteristic, complemented
15	#463×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	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	#16812723	—	2	4	no	—
20	C₂×#13182018	C₂²	1	1	yes	characteristic
21	C₂×#13182018	C₂²	1	1	yes	characteristic
22	C₂×#13182017	C₂²	1	1	yes	characteristic
23	C₂×#13182017	C₂²	1	1	yes	characteristic
24	C₂×#13182016	C₂²	1	1	yes	characteristic
25	SD₁₆×D₁₀₉	—	2	4	no	—
26	C₂×#13182014	C₂²	1	1	yes	characteristic
27	C₂×#13182012	C₂²	1	1	yes	characteristic
28	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
29	#16812699	C₂²	1	1	yes	characteristic, complemented
30	#16812697	C₂²	1	1	yes	characteristic, complemented
31	#16812686	C₂²	1	1	yes	characteristic, complemented
32	#16812681	—	2	1	no	—
33	#16812681	—	2	1	no	—
34	#16812676	—	2	1	no	—
35	#16812676	—	2	1	no	—
36	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
37	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
38	#16812661	C₂²	1	1	yes	characteristic
39	C₄×C₂²⋊D₁₀₉	—	2	1	no	—
40	#16812659	—	2	1	no	—
41	#16812657	C₂²	1	1	yes	characteristic
42	#16812656	C₂²	1	1	yes	characteristic
43	C₂×#13182006	—	2	1	no	—
44	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
45	C₄⋊#11724784	C₂²	1	1	yes	characteristic, complemented
46	#16812628	C₂²	1	1	yes	characteristic, complemented
47	#16812628	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
55	C₂×D₈×C₁₀₉	C₂²	1	1	yes	characteristic
56	#124×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
58	C₄⋊C₈×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	—	2	1	no	—
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×D₄₃₆	C₂³	1	1	yes	characteristic
70	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
72	D₄×D₁₀₉	—	2	2	no	—
73	D₄×D₁₀₉	D₄	1	4	yes	—
74	C₂²×Dic₁₀₉	—	2	1	no	—
75	C₂²×Dic₁₀₉	—	2	1	no	—
76	C₂×C₄×D₁₀₉	—	2	1	no	—
77	C₂×C₄×D₁₀₉	—	2	1	no	—
78	C₂×C₄×D₁₀₉	—	2	1	no	—
79	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
80	#13182018	—	2	2	no	—
81	#13182018	—	2	2	no	—
82	#13182017	—	2	2	no	—
83	#13182017	—	2	2	no	—
84	#13182016	—	2	2	no	—
85	#13182014	—	2	2	no	—
86	#13182012	—	2	2	no	—
87	C₂×#11724784	C₂³	1	1	yes	characteristic
88	C₂×#11724784	C₂³	1	1	yes	characteristic
89	C₈×D₁₀₉	—	2	2	no	—
90	C₄⋊Dic₁₀₉	—	2	1	no	—
91	C₄⋊Dic₁₀₉	—	2	1	no	—
92	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
93	#13182008	—	2	1	no	—
94	#13182008	—	2	1	no	—
95	#13182008	D₄	1	1	yes	characteristic
96	#13182008	D₄	1	1	yes	characteristic
97	C₂²⋊Dic₁₀₉	—	2	1	no	—
98	C₂²⋊Dic₁₀₉	—	2	1	no	—
99	C₂²⋊Dic₁₀₉	—	2	1	no	—
100	#13182006	—	2	1	no	—
101	#13182006	—	2	1	no	—
102	#13182006	—	2	1	no	—
103	#13182006	D₄	1	1	yes	characteristic
104	#13182006	D₄	1	1	yes	characteristic
105	C₄×Dic₁₀₉	—	2	1	no	—
106	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
107	C₂×Q₈×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	C₂²×C₄×C₁₀₉	—	2	1	no	—
111	SD₁₆×C₁₀₉	—	2	2	no	—
112	D₈×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	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
117	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
118	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
119	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
120	C₂³×C₁₀₉	—	2	1	no	—
121	C₂³×C₁₀₉	—	2	1	no	—
122	C₂²×D₁₀₉	—	2	1	no	—
123	C₂²×D₁₀₉	—	2	4	no	—
124	C₂²×D₁₀₉	—	8	1	no	—
125	C₂²×D₁₀₉	—	8	1	no	—
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	—	2	1	no	—
132	D₄×C₁₀₉	C₂×D₄	1	2	yes	—
133	C₂×C₄×C₁₀₉	—	2	1	no	—
134	C₂×C₄×C₁₀₉	—	2	1	no	—
135	C₂×C₄×C₁₀₉	—	8	1	no	—
136	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
137	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
138	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
139	C₂²⋊D₁₀₉	—	2	4	no	—
140	C₂²⋊D₁₀₉	—	4	2	no	—
141	C₂×Dic₁₀₉	—	2	1	no	—
142	C₂×Dic₁₀₉	—	2	1	no	—
143	C₂×Dic₁₀₉	—	2	1	no	—
144	C₂×Dic₁₀₉	—	4	2	no	—
145	C₂×Dic₁₀₉	—	8	1	no	—
146	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
147	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
149	D₄₃₆	—	2	1	no	—
150	D₄₃₆	C₂×D₄	1	2	yes	—
151	C₄×D₁₀₉	—	4	2	no	—
152	C₄×D₁₀₉	—	8	1	no	—
153	C₄×D₁₀₉	—	8	1	no	—
154	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
155	C₄×D₁₀₉	#41	1	2	yes	—
156	Dic₂₁₈	—	2	1	no	—
157	Dic₂₁₈	—	2	1	no	—
158	Dic₂₁₈	—	2	1	no	—
159	Dic₂₁₈	—	2	1	no	—
160	Dic₂₁₈	—	4	2	no	—
161	C₈×C₁₀₉	—	2	1	no	—
162	C₈×C₁₀₉	—	2	1	no	—
163	#11724784	—	2	1	no	—
164	#11724784	—	2	1	no	—
165	C₂²×C₁₀₉	—	2	2	no	—
166	C₂²×C₁₀₉	—	4	1	no	—
167	C₂²×C₁₀₉	—	4	1	no	—
168	C₂²×C₁₀₉	—	4	1	no	—
169	C₂²×C₁₀₉	—	4	1	no	—
170	C₂²×C₁₀₉	—	4	1	no	—
171	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
172	C₂×D₁₀₉	—	2	1	no	—
173	C₂×D₁₀₉	—	2	1	no	—
174	C₂×D₁₀₉	—	2	2	no	—
175	C₂×D₁₀₉	—	4	1	no	—
176	C₂×D₁₀₉	—	4	1	no	—
177	C₂×D₁₀₉	—	8	4	no	—
178	C₂×D₁₀₉	#121	1	2	yes	—
179	C₄×C₁₀₉	—	2	1	no	—
180	C₄×C₁₀₉	—	2	1	no	—
181	C₄×C₁₀₉	—	4	1	no	—
182	C₄×C₁₀₉	—	4	1	no	—
183	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
184	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
185	Dic₁₀₉	—	2	1	no	—
186	Dic₁₀₉	—	2	1	no	—
187	Dic₁₀₉	—	4	1	no	—
188	Dic₁₀₉	—	4	1	no	—
189	Dic₁₀₉	—	4	1	no	—
190	Dic₁₀₉	#121	1	2	yes	—
191	C₂×C₁₀₉	—	4	2	no	—
192	C₂×C₁₀₉	—	8	1	no	—
193	C₂×C₁₀₉	C₂×#121	1	1	yes	characteristic
194	C₂×C₁₀₉	#577	1	1	yes	characteristic
195	C₂×C₁₀₉	#577	1	1	yes	characteristic
196	D₁₀₉	—	2	2	no	—
197	D₁₀₉	—	4	2	no	—
198	#3042	—	109	1	no	maximal, Sylow
199	C₁₀₉	#3042	1	1	yes	characteristic, complemented, Sylow
200	C₂×AGL(1,ℤ/8)	—	109	1	no	—
201	C₂²×SD₁₆	—	109	1	no	—
202	#536	—	109	1	no	—
203	#518	—	109	1	no	—
204	#463	—	109	1	no	—
205	#463	—	109	1	no	—
206	#463	—	109	1	no	—
207	#463	D₁₀₉	1	1	yes	characteristic, complemented
208	#461	—	109	1	no	—
209	#461	—	109	1	no	—
210	#461	—	109	1	no	—
211	#461	—	109	1	no	—
212	#424	—	109	1	no	—
213	#419	—	109	1	no	—
214	#416	—	109	1	no	—
215	C₂×#41	—	109	1	no	—
216	C₂²×Q₈	—	109	1	no	—
217	C₂²×D₄	—	109	1	no	—
218	AGL(1,ℤ/8)	—	218	4	no	—
219	C₂×SD₁₆	—	109	1	no	—
220	C₂×SD₁₆	—	109	1	no	—
221	C₂×SD₁₆	—	109	1	no	—
222	C₂×SD₁₆	—	109	1	no	—
223	C₂×SD₁₆	—	109	1	no	—
224	C₂×SD₁₆	—	218	4	no	—
225	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
226	C₂×D₈	—	109	1	no	—
227	C₂×D₈	C₂×D₁₀₉	1	1	yes	characteristic
228	C₂×M₁₆	—	109	1	no	—
229	C₂²×C₈	—	109	1	no	—
230	C₄⋊Q₈	—	109	1	no	—
231	C₄⋊Q₈	—	109	1	no	—
232	#124	—	109	1	no	—
233	#124	C₂×D₁₀₉	1	1	yes	characteristic, complemented
234	#123	—	218	1	no	—
235	#123	—	218	1	no	—
236	C₂²⋊Q₈	—	218	1	no	—
237	C₂²⋊Q₈	—	218	1	no	—
238	C₄×D₄	—	109	1	no	—
239	C₄×D₄	—	109	1	no	—
240	C₄×D₄	—	109	1	no	—
241	C₄×D₄	—	218	1	no	—
242	C₄×D₄	—	218	1	no	—
243	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
244	#117	—	109	1	no	—
245	#117	—	109	1	no	—
246	C₂×C₂²⋊C₄	—	218	1	no	—
247	C₂×C₂²⋊C₄	—	218	1	no	—
248	C₄⋊C₈	—	109	1	no	—
249	C₄⋊C₈	—	109	1	no	—
250	C₄⋊C₈	—	109	1	no	—
251	C₄⋊C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
252	#103	—	109	1	no	—
253	#103	—	109	1	no	—
254	#103	—	109	1	no	—
255	#103	—	109	1	no	—
256	#103	—	109	1	no	—
257	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
258	#102	—	109	1	no	—
259	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
260	C₂⁴	—	218	1	no	—
261	#41	—	218	2	no	—
262	#41	—	218	2	no	—
263	C₂×Q₈	—	109	1	no	—
264	C₂×Q₈	—	109	1	no	—
265	C₂×Q₈	—	218	1	no	—
266	C₂×Q₈	—	218	2	no	—
267	C₂×Q₈	—	218	2	no	—
268	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
269	C₂×D₄	—	109	4	no	—
270	C₂×D₄	—	109	1	no	—
271	C₂×D₄	—	218	2	no	—
272	C₂×D₄	—	218	1	no	—
273	C₂×D₄	—	218	1	no	—
274	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
275	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	109	1	no	—
278	C₂²×C₄	—	218	1	no	—
279	C₂²×C₄	—	218	1	no	—
280	C₂²×C₄	—	218	1	no	—
281	C₂²×C₄	—	218	1	no	—
282	C₂²×C₄	—	218	1	no	—
283	SD₁₆	—	2	2	no	—
284	SD₁₆	—	218	2	no	—
285	SD₁₆	—	218	2	no	—
286	SD₁₆	—	218	2	no	—
287	SD₁₆	—	218	2	no	—
288	SD₁₆	—	218	2	no	—
289	D₈	—	2	2	no	—
290	D₈	—	218	2	no	—
291	M₁₆	—	218	2	no	—
292	C₂×C₈	—	109	1	no	—
293	C₂×C₈	—	109	1	no	—
294	C₂×C₈	—	218	2	no	—
295	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
296	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
297	C₄⋊C₄	—	109	1	no	—
298	C₄⋊C₄	—	109	1	no	—
299	C₄⋊C₄	—	109	1	no	—
300	C₄⋊C₄	—	218	1	no	—
301	C₄⋊C₄	—	218	1	no	—
302	C₄⋊C₄	—	218	1	no	—
303	C₄⋊C₄	—	218	1	no	—
304	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
305	C₂²⋊C₄	—	2	1	no	—
306	C₂²⋊C₄	—	2	1	no	—
307	C₂²⋊C₄	—	2	1	no	—
308	C₂²⋊C₄	—	109	1	no	—
309	C₂²⋊C₄	—	109	1	no	—
310	C₂²⋊C₄	—	218	1	no	—
311	C₂²⋊C₄	—	218	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	C₄²	—	109	1	no	—
317	C₄²	—	218	1	no	—
318	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
319	C₂³	—	2	1	no	—
320	C₂³	—	2	1	no	—
321	C₂³	—	872	1	no	—
322	C₂³	—	872	1	no	—
323	C₂³	—	109	1	no	—
324	C₂³	—	218	4	no	—
325	C₂³	—	218	1	no	—
326	Q₈	—	2	1	no	—
327	Q₈	—	2	1	no	—
328	Q₈	—	436	2	no	—
329	Q₈	—	218	1	no	—
330	Q₈	—	218	1	no	—
331	Q₈	—	218	1	no	—
332	Q₈	—	218	1	no	—
333	D₄	—	2	1	no	—
334	D₄	—	2	1	no	—
335	D₄	—	2	1	no	—
336	D₄	—	109	2	no	—
337	D₄	—	436	2	no	—
338	D₄	—	218	4	no	—
339	D₄	—	218	1	no	—
340	D₄	D₄×D₁₀₉	1	2	yes	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	8	1	no	—
344	C₂×C₄	—	872	1	no	—
345	C₂×C₄	—	872	1	no	—
346	C₂×C₄	—	872	1	no	—
347	C₂×C₄	—	109	1	no	—
348	C₂×C₄	—	109	2	no	—
349	C₂×C₄	—	109	2	no	—
350	C₂×C₄	—	109	1	no	—
351	C₂×C₄	—	109	1	no	—
352	C₂×C₄	—	436	2	no	—
353	C₂×C₄	—	436	2	no	—
354	C₂×C₄	—	218	1	no	—
355	C₂×C₄	—	218	1	no	—
356	C₂×C₄	—	218	1	no	—
357	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
358	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
359	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
360	C₈	—	2	1	no	—
361	C₈	—	2	1	no	—
362	C₈	—	218	1	no	—
363	C₈	—	218	1	no	—
364	C₂²	—	2	2	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	1	no	—
368	C₂²	—	4	1	no	—
369	C₂²	—	4	1	no	—
370	C₂²	—	872	4	no	—
371	C₂²	—	109	2	no	—
372	C₂²	—	436	1	no	—
373	C₂²	—	436	1	no	—
374	C₂²	—	218	2	no	—
375	C₂²	—	218	1	no	—
376	C₂²	—	218	1	no	—
377	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
378	C₄	—	2	1	no	—
379	C₄	—	2	1	no	—
380	C₄	—	4	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	109	2	no	—
383	C₄	—	436	1	no	—
384	C₄	—	436	1	no	—
385	C₄	—	436	1	no	—
386	C₄	—	218	1	no	—
387	C₄	—	218	1	no	—
388	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
389	C₄	#41×D₁₀₉	1	1	yes	characteristic
390	C₂	—	4	2	no	—
391	C₂	—	8	1	no	—
392	C₂	—	436	2	no	—
393	C₂	—	218	2	no	—
394	C₂	#121×D₁₀₉	1	1	yes	characteristic
395	C₂	#20295833	1	1	yes	characteristic
396	C₂	#20295836	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#463×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	C₂×#16812723	C₂
hypercenter	#463	D₁₀₉
hypocenter	C₁₀₉	#3042
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #463

Complements

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

N	H ≅ G/N	type
2. C₂×SD₁₆×D₁₀₉	C₂	semidirect
3. #20295596	C₂	semidirect
4. #20295498	C₂	semidirect
5. #20295240	C₂	semidirect
6. #20295239	C₂	semidirect
7. #20295238	C₂	semidirect
8. #20295232	C₂	semidirect
9. #20295231	C₂	semidirect
10. #20295230	C₂	semidirect
11. #20295229	C₂	semidirect
12. #20295051	C₂	semidirect
13. #20295033	C₂	semidirect
14. #20295019	C₂	semidirect
15. #463×C₁₀₉	C₂	semidirect
29. #16812699	C₂²	semidirect
30. #16812697	C₂²	semidirect
31. #16812686	C₂²	semidirect
45. C₄⋊#11724784	C₂²	semidirect
46. #16812628	C₂²	semidirect
47. #16812628	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
56. #124×C₁₀₉	C₂²	semidirect
58. C₄⋊C₈×C₁₀₉	C₂²	semidirect
59. #103×C₁₀₉	C₂²	semidirect
60. #102×C₁₀₉	C₂²	semidirect
199. C₁₀₉	#3042	semidirect
207. #463	D₁₀₉	semidirect
233. #124	C₂×D₁₀₉	semidirect
251. C₄⋊C₈	C₂×D₁₀₉	semidirect
257. #103	C₂×D₁₀₉	semidirect
259. #102	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×#16812723	2
C₂×SD₁₆×D₁₀₉	2
#20295596	2
#20295498	2
#20295240	2
#20295239	2
#20295238	2
#20295232	2
#20295231	2
#20295230	2
#20295229	2
#20295051	2
#20295033	2
#20295019	2
#463×C₁₀₉	2
#3042	109