Subgroups — #28372523

Order 13952.

500 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×#16812731	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16812726	C₂	1	1	yes	maximal, characteristic
3	#124×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₄×#13182030	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295250	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295248	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295246	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295244	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295242	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295240	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295238	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295048	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	#464×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182030	C₂²	1	1	yes	characteristic
17	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
18	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	#16812731	—	2	4	no	—
20	#16812726	—	2	4	no	—
21	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13182018	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13182016	C₂²	1	1	yes	characteristic
24	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
25	C₂×D₈₇₂	C₂²	1	1	yes	characteristic
26	C₂×#13182014	C₂²	1	1	yes	characteristic
27	C₂×#13182012	C₂²	1	1	yes	characteristic
28	C₂×#13182012	C₂²	1	1	yes	characteristic
29	#16812688	C₂²	1	1	yes	characteristic
30	#16812687	C₂²	1	1	yes	characteristic
31	#16812686	C₂²	1	1	yes	characteristic
32	#16812685	—	2	1	no	—
33	#16812685	—	2	1	no	—
34	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
35	C₄×D₄₃₆	—	2	1	no	—
36	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
37	#16812661	—	2	1	no	—
38	#16812661	C₂²	1	1	yes	characteristic, complemented
39	#16812657	—	2	1	no	—
40	#16812657	C₂²	1	1	yes	characteristic
41	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
42	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
43	C₄²×D₁₀₉	—	2	1	no	—
44	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
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	#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×Q₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
56	#124×C₁₀₉	C₂²	1	1	yes	characteristic
57	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
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
61	C₂³×D₁₀₉	—	2	1	no	—
62	#13182030	—	2	2	no	—
63	#13182030	D₄	1	4	yes	—
64	C₂×Dic₂₁₈	—	2	1	no	—
65	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
66	Q₈×D₁₀₉	—	2	2	no	—
67	Q₈×D₁₀₉	—	2	2	no	—
68	C₂×D₄₃₆	—	2	1	no	—
69	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
70	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
71	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
72	D₄×D₁₀₉	—	2	2	no	—
73	D₄×D₁₀₉	—	2	2	no	—
74	C₂×C₄×D₁₀₉	—	2	1	no	—
75	C₂×C₄×D₁₀₉	—	2	1	no	—
76	C₂×C₄×D₁₀₉	—	2	1	no	—
77	C₂×C₄×D₁₀₉	—	2	1	no	—
78	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
79	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
80	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
81	#13182019	—	2	2	no	—
82	#13182018	—	2	2	no	—
83	#13182016	—	2	2	no	—
84	#13182016	—	2	2	no	—
85	D₈₇₂	—	2	2	no	—
86	#13182014	—	2	2	no	—
87	#13182012	—	2	2	no	—
88	#13182012	—	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	C₂³	1	1	yes	characteristic
93	C₂²⋊Dic₁₀₉	—	2	1	no	—
94	C₂²⋊Dic₁₀₉	—	2	1	no	—
95	#13182006	—	2	1	no	—
96	#13182006	—	2	1	no	—
97	#13182006	—	2	1	no	—
98	#13182006	—	2	1	no	—
99	#13182006	—	2	1	no	—
100	#13182006	—	2	1	no	—
101	#13182006	—	2	1	no	—
102	C₄×Dic₁₀₉	—	2	1	no	—
103	C₄×Dic₁₀₉	—	2	1	no	—
104	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
105	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
106	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
107	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
108	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	Q₁₆×C₁₀₉	—	2	2	no	—
111	SD₁₆×C₁₀₉	—	2	2	no	—
112	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
113	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₄⋊C₄×C₁₀₉	—	2	1	no	—
115	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
117	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
118	C₄²×C₁₀₉	—	2	1	no	—
119	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
120	C₂³×C₁₀₉	—	2	1	no	—
121	C₂²×D₁₀₉	—	2	1	no	—
122	C₂²×D₁₀₉	—	2	1	no	—
123	C₂²×D₁₀₉	—	4	2	no	—
124	C₂²×D₁₀₉	—	4	2	no	—
125	C₂²×D₁₀₉	—	4	2	no	—
126	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
127	Q₈×C₁₀₉	—	2	1	no	—
128	Q₈×C₁₀₉	—	2	1	no	—
129	Q₈×C₁₀₉	—	2	1	no	—
130	Q₈×C₁₀₉	C₂×D₄	1	2	yes	—
131	D₄×C₁₀₉	—	2	1	no	—
132	D₄×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	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	—	4	2	no	—
140	C₂×Dic₁₀₉	—	2	1	no	—
141	C₂×Dic₁₀₉	—	2	1	no	—
142	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
143	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
144	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
145	D₄₃₆	—	2	4	no	—
146	D₄₃₆	—	2	1	no	—
147	D₄₃₆	—	2	1	no	—
148	D₄₃₆	—	2	1	no	—
149	D₄₃₆	C₂×D₄	1	2	yes	—
150	C₄×D₁₀₉	—	2	4	no	—
151	C₄×D₁₀₉	—	4	1	no	—
152	C₄×D₁₀₉	—	4	1	no	—
153	C₄×D₁₀₉	—	4	2	no	—
154	C₄×D₁₀₉	—	4	2	no	—
155	C₄×D₁₀₉	—	4	2	no	—
156	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
157	C₄×D₁₀₉	#41	1	2	yes	—
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	—	4	1	no	—
166	C₂²×C₁₀₉	—	4	1	no	—
167	C₂²×C₁₀₉	—	4	1	no	—
168	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×D₁₀₉	—	2	1	no	—
170	C₂×D₁₀₉	—	2	1	no	—
171	C₂×D₁₀₉	—	2	2	no	—
172	C₂×D₁₀₉	—	4	1	no	—
173	C₂×D₁₀₉	—	4	1	no	—
174	C₂×D₁₀₉	—	4	1	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	2	no	—
180	C₄×C₁₀₉	—	2	1	no	—
181	C₄×C₁₀₉	—	2	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	—	2	1	no	—
188	Dic₁₀₉	—	4	1	no	—
189	Dic₁₀₉	—	4	1	no	—
190	Dic₁₀₉	#121	1	2	yes	—
191	C₂×C₁₀₉	—	8	1	no	—
192	C₂×C₁₀₉	C₂×#121	1	1	yes	characteristic
193	C₂×C₁₀₉	#575	1	1	yes	characteristic
194	C₂×C₁₀₉	#575	1	1	yes	characteristic
195	D₁₀₉	—	2	2	no	—
196	D₁₀₉	—	4	2	no	—
197	D₁₀₉	—	8	1	no	—
198	#3040	—	109	1	no	maximal, Sylow
199	C₁₀₉	#3040	1	1	yes	characteristic, complemented, Sylow
200	C₂×#137	—	109	1	no	—
201	C₂×AGL(1,ℤ/8)	—	109	1	no	—
202	C₂×#124	—	109	1	no	—
203	C₄×#41	—	109	1	no	—
204	#464	—	109	1	no	—
205	#464	—	109	1	no	—
206	#464	—	109	1	no	—
207	#464	D₁₀₉	1	1	yes	characteristic, complemented
208	#463	—	109	1	no	—
209	#463	—	109	1	no	—
210	#463	—	109	1	no	—
211	#463	—	109	1	no	—
212	#423	—	109	1	no	—
213	#419	—	109	1	no	—
214	#418	—	109	1	no	—
215	C₂×#41	—	109	1	no	—
216	C₂²×Q₈	—	109	1	no	—
217	C₂²×D₄	—	109	1	no	—
218	#137	—	218	4	no	—
219	AGL(1,ℤ/8)	—	218	4	no	—
220	C₂×Q₁₆	—	109	1	no	—
221	C₂×Q₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
222	C₂×SD₁₆	—	109	1	no	—
223	C₂×SD₁₆	—	109	1	no	—
224	C₂×SD₁₆	—	109	1	no	—
225	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
226	C₂×D₈	—	109	1	no	—
227	C₂×D₈	—	109	1	no	—
228	C₂×M₁₆	—	109	1	no	—
229	C₂×M₁₆	—	109	1	no	—
230	#124	—	109	1	no	—
231	#124	—	109	1	no	—
232	#124	—	109	1	no	—
233	#124	—	218	1	no	—
234	#124	—	218	1	no	—
235	#124	C₂×D₁₀₉	1	1	yes	characteristic
236	C₄×Q₈	—	109	1	no	—
237	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
238	C₄×D₄	—	109	1	no	—
239	C₄×D₄	—	109	1	no	—
240	C₄×D₄	—	218	1	no	—
241	C₄×D₄	—	218	1	no	—
242	#117	—	109	1	no	—
243	#117	—	218	1	no	—
244	C₂×C₂²⋊C₄	—	218	1	no	—
245	C₂×C₂²⋊C₄	—	218	1	no	—
246	C₂×C₄²	—	109	1	no	—
247	C₂×C₄²	—	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	C₂×D₁₀₉	1	1	yes	characteristic, complemented
256	#102	—	109	1	no	—
257	#102	—	109	1	no	—
258	#102	—	109	1	no	—
259	#102	C₂×D₁₀₉	1	1	yes	characteristic
260	C₂⁴	—	218	1	no	—
261	#41	—	109	4	no	—
262	#41	—	218	2	no	—
263	C₂×Q₈	—	109	1	no	—
264	C₂×Q₈	—	218	1	no	—
265	C₂×Q₈	—	218	2	no	—
266	C₂×Q₈	—	218	2	no	—
267	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
268	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
269	C₂×D₄	—	109	1	no	—
270	C₂×D₄	—	109	1	no	—
271	C₂×D₄	—	218	1	no	—
272	C₂×D₄	—	218	2	no	—
273	C₂×D₄	—	218	2	no	—
274	C₂×D₄	—	218	1	no	—
275	C₂×D₄	C₂²×D₁₀₉	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	—	218	1	no	—
280	C₂²×C₄	—	218	1	no	—
281	C₂²×C₄	—	218	1	no	—
282	C₂²×C₄	—	218	1	no	—
283	Q₁₆	—	2	2	no	—
284	Q₁₆	—	218	2	no	—
285	SD₁₆	—	2	2	no	—
286	SD₁₆	—	218	2	no	—
287	SD₁₆	—	218	2	no	—
288	SD₁₆	—	218	2	no	—
289	D₈	—	218	2	no	—
290	D₈	—	218	2	no	—
291	M₁₆	—	218	2	no	—
292	M₁₆	—	218	2	no	—
293	C₂×C₈	—	109	1	no	—
294	C₂×C₈	—	109	1	no	—
295	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
296	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	109	1	no	—
299	C₄⋊C₄	—	218	1	no	—
300	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
301	C₂²⋊C₄	—	2	1	no	—
302	C₂²⋊C₄	—	2	1	no	—
303	C₂²⋊C₄	—	218	1	no	—
304	C₂²⋊C₄	—	218	1	no	—
305	C₂²⋊C₄	—	218	1	no	—
306	C₂²⋊C₄	—	218	1	no	—
307	C₂²⋊C₄	—	218	1	no	—
308	C₂²⋊C₄	—	218	1	no	—
309	C₂²⋊C₄	—	218	1	no	—
310	C₂²⋊C₄	—	218	1	no	—
311	C₂²⋊C₄	—	218	1	no	—
312	C₄²	—	2	1	no	—
313	C₄²	—	109	1	no	—
314	C₄²	—	109	1	no	—
315	C₄²	—	109	1	no	—
316	C₄²	—	218	1	no	—
317	C₄²	—	218	1	no	—
318	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
319	C₂³	—	2	1	no	—
320	C₂³	—	109	1	no	—
321	C₂³	—	436	2	no	—
322	C₂³	—	436	2	no	—
323	C₂³	—	436	2	no	—
324	C₂³	—	218	1	no	—
325	C₂³	—	218	1	no	—
326	Q₈	—	2	1	no	—
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	D₄×D₁₀₉	1	2	yes	—
333	D₄	—	2	1	no	—
334	D₄	—	2	1	no	—
335	D₄	—	109	2	no	—
336	D₄	—	436	2	no	—
337	D₄	—	218	4	no	—
338	D₄	—	218	1	no	—
339	D₄	—	218	1	no	—
340	D₄	—	218	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	—	109	1	no	—
349	C₂×C₄	—	436	2	no	—
350	C₂×C₄	—	436	1	no	—
351	C₂×C₄	—	436	1	no	—
352	C₂×C₄	—	436	2	no	—
353	C₂×C₄	—	436	2	no	—
354	C₂×C₄	—	218	4	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	—	4	1	no	—
365	C₂²	—	4	1	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	872	4	no	—
368	C₂²	—	109	2	no	—
369	C₂²	—	436	1	no	—
370	C₂²	—	436	1	no	—
371	C₂²	—	436	1	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	2	no	—
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	4	1	no	—
382	C₄	—	4	1	no	—
383	C₄	—	109	2	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	—	8	1	no	—
391	C₂	—	872	1	no	—
392	C₂	—	436	2	no	—
393	C₂	—	218	2	no	—
394	C₂	#121×D₁₀₉	1	1	yes	characteristic
395	C₂	#20295823	1	1	yes	characteristic
396	C₂	#20295825	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#464×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	C₂×#16812726	C₂
hypercenter	#464	D₁₀₉
hypocenter	C₁₀₉	#3040
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #464

Complements

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

N	H ≅ G/N	type
1. C₂×#16812731	C₂	semidirect
3. #124×D₁₀₉	C₂	semidirect
4. C₄×#13182030	C₂	semidirect
5. #20295250	C₂	semidirect
6. #20295248	C₂	semidirect
7. #20295246	C₂	semidirect
8. #20295244	C₂	semidirect
9. #20295242	C₂	semidirect
10. #20295240	C₂	semidirect
11. #20295238	C₂	semidirect
12. #20295048	C₂	semidirect
13. #20295033	C₂	semidirect
14. #20295029	C₂	semidirect
15. #464×C₁₀₉	C₂	semidirect
21. C₂×#13182019	C₂²	semidirect
22. C₂×#13182018	C₂²	semidirect
24. C₂×#13182016	C₂²	semidirect
34. Q₈×Dic₁₀₉	C₂²	semidirect
36. C₄×D₄₃₆	C₂²	semidirect
38. #16812661	C₂²	semidirect
45. C₄⋊#11724784	C₂²	semidirect
46. #16812628	C₂²	semidirect
47. #16812628	C₂²	semidirect
48. #16812624	C₂²	semidirect
49. #16812623	C₂²	semidirect
50. #16812622	C₂²	semidirect
54. C₂×Q₁₆×C₁₀₉	C₂²	semidirect
57. C₄×Q₈×C₁₀₉	C₂²	semidirect
58. C₄⋊C₈×C₁₀₉	C₂²	semidirect
59. #103×C₁₀₉	C₂²	semidirect
199. C₁₀₉	#3040	semidirect
207. #464	D₁₀₉	semidirect
221. C₂×Q₁₆	C₂×D₁₀₉	semidirect
237. C₄×Q₈	C₂×D₁₀₉	semidirect
251. C₄⋊C₈	C₂×D₁₀₉	semidirect
255. #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×#16812731	2
C₂×#16812726	2
#124×D₁₀₉	2
C₄×#13182030	2
#20295250	2
#20295248	2
#20295246	2
#20295244	2
#20295242	2
#20295240	2
#20295238	2
#20295048	2
#20295033	2
#20295029	2
#464×C₁₀₉	2
#3040	109