Subgroups — #28374537

Order 13952.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 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×SD₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	Q₈×D₄₃₆	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295669	C₂	1	1	yes	maximal, characteristic
5	#20295421	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295271	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295266	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295232	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295191	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295180	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295178	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295163	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295124	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295096	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×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
19	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
20	#16812731	—	2	4	no	—
21	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
22	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13182018	C₂²	1	1	yes	characteristic
24	C₂×#13182018	C₂²	1	1	yes	characteristic
25	C₂×#13182017	C₂²	1	1	yes	characteristic
26	C₂×#13182017	C₂²	1	1	yes	characteristic
27	C₂×#13182016	C₂²	1	1	yes	characteristic
28	SD₁₆×D₁₀₉	—	2	4	no	—
29	C₂×#13182012	C₂²	1	1	yes	characteristic, complemented
30	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
31	#16812699	—	2	1	no	—
32	#16812699	C₂²	1	1	yes	characteristic, complemented
33	#16812681	—	2	1	no	—
34	#16812679	—	2	1	no	—
35	#16812679	—	2	1	no	—
36	#16812679	C₂²	1	1	yes	characteristic
37	#16812679	C₂²	1	1	yes	characteristic, complemented
38	#16812675	C₂²	1	1	yes	characteristic
39	#16812672	—	2	1	no	—
40	#16812670	C₂²	1	1	yes	characteristic
41	#16812669	—	2	1	no	—
42	C₄×D₄₃₆	—	2	1	no	—
43	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
44	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
45	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
46	#16812632	C₂²	1	1	yes	characteristic, complemented
47	#16812624	C₂²	1	1	yes	characteristic, complemented
48	#16812624	C₂²	1	1	yes	characteristic, complemented
49	#16812623	C₂²	1	1	yes	characteristic, complemented
50	#16812619	C₂²	1	1	yes	characteristic
51	#16812611	C₂²	1	1	yes	characteristic
52	#16812611	C₂²	1	1	yes	characteristic, complemented
53	#16812610	C₂²	1	1	yes	characteristic, complemented
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	—	4	1	no	—
64	C₂×Dic₂₁₈	—	2	1	no	—
65	C₂×Dic₂₁₈	—	2	1	no	—
66	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
67	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
68	Q₈×D₁₀₉	—	2	2	no	—
69	Q₈×D₁₀₉	—	2	2	no	—
70	Q₈×D₁₀₉	—	4	1	no	—
71	Q₈×D₁₀₉	—	4	1	no	—
72	C₂×D₄₃₆	—	2	1	no	—
73	C₂×D₄₃₆	D₄	1	1	yes	characteristic
74	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
75	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
76	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
77	D₄×D₁₀₉	—	2	2	no	—
78	D₄×D₁₀₉	—	4	1	no	—
79	C₂×C₄×D₁₀₉	—	2	1	no	—
80	C₂×C₄×D₁₀₉	—	2	1	no	—
81	C₂×C₄×D₁₀₉	—	2	1	no	—
82	C₂×C₄×D₁₀₉	—	2	1	no	—
83	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
84	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
85	#13182019	—	2	2	no	—
86	#13182019	—	4	1	no	—
87	#13182018	—	2	2	no	—
88	#13182018	—	2	2	no	—
89	#13182017	—	2	2	no	—
90	#13182017	—	4	1	no	—
91	#13182016	D₄	1	4	yes	complemented
92	#13182012	—	2	2	no	—
93	C₂×#11724784	C₂³	1	1	yes	characteristic
94	C₂×#11724784	C₂³	1	1	yes	characteristic
95	C₈×D₁₀₉	—	2	2	no	—
96	C₄⋊Dic₁₀₉	—	2	1	no	—
97	C₄⋊Dic₁₀₉	—	2	1	no	—
98	C₄⋊Dic₁₀₉	—	2	1	no	—
99	C₄⋊Dic₁₀₉	—	2	1	no	—
100	C₄⋊Dic₁₀₉	D₄	1	1	yes	characteristic
101	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
102	#13182008	—	2	1	no	—
103	C₂²⋊Dic₁₀₉	—	2	1	no	—
104	#13182006	—	2	1	no	—
105	#13182006	—	2	1	no	—
106	#13182006	—	2	1	no	—
107	#13182006	—	2	1	no	—
108	#13182006	D₄	1	1	yes	characteristic
109	#13182006	D₄	1	1	yes	characteristic
110	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
112	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
113	Q₁₆×C₁₀₉	—	2	2	no	—
114	SD₁₆×C₁₀₉	—	2	2	no	—
115	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
117	C₄⋊C₄×C₁₀₉	—	2	1	no	—
118	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
119	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
120	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
121	C₄²×C₁₀₉	—	2	1	no	—
122	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
123	C₂³×C₁₀₉	—	2	1	no	—
124	C₂²×D₁₀₉	—	2	1	no	—
125	C₂²×D₁₀₉	—	4	2	no	—
126	C₂²×D₁₀₉	—	4	2	no	—
127	C₂²×D₁₀₉	—	8	1	no	—
128	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
129	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
130	Q₈×C₁₀₉	—	2	1	no	—
131	Q₈×C₁₀₉	—	2	1	no	—
132	Q₈×C₁₀₉	—	2	1	no	—
133	Q₈×C₁₀₉	C₂×D₄	1	2	yes	—
134	D₄×C₁₀₉	—	2	1	no	—
135	D₄×C₁₀₉	—	2	1	no	—
136	C₂×C₄×C₁₀₉	—	2	1	no	—
137	C₂×C₄×C₁₀₉	—	2	1	no	—
138	C₂×C₄×C₁₀₉	—	2	1	no	—
139	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
140	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
141	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
142	C₂²⋊D₁₀₉	—	4	2	no	—
143	C₂²⋊D₁₀₉	—	8	1	no	—
144	C₂×Dic₁₀₉	—	2	1	no	—
145	C₂×Dic₁₀₉	—	2	1	no	—
146	C₂×Dic₁₀₉	—	2	1	no	—
147	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
149	D₄₃₆	—	2	2	no	—
150	D₄₃₆	—	2	1	no	—
151	D₄₃₆	—	4	2	no	—
152	D₄₃₆	C₂×D₄	1	2	yes	—
153	C₄×D₁₀₉	—	2	1	no	—
154	C₄×D₁₀₉	—	2	1	no	—
155	C₄×D₁₀₉	—	2	1	no	—
156	C₄×D₁₀₉	—	2	1	no	—
157	C₄×D₁₀₉	—	4	2	no	—
158	C₄×D₁₀₉	—	4	2	no	—
159	C₄×D₁₀₉	—	4	2	no	—
160	C₄×D₁₀₉	—	8	1	no	—
161	Dic₂₁₈	—	2	1	no	—
162	Dic₂₁₈	—	2	1	no	—
163	Dic₂₁₈	—	2	1	no	—
164	Dic₂₁₈	—	2	1	no	—
165	Dic₂₁₈	—	4	2	no	—
166	Dic₂₁₈	—	4	2	no	—
167	C₈×C₁₀₉	—	2	1	no	—
168	C₈×C₁₀₉	—	2	1	no	—
169	#11724784	—	2	1	no	—
170	#11724784	C₂×D₄	1	2	yes	—
171	C₂²×C₁₀₉	—	4	1	no	—
172	C₂²×C₁₀₉	—	4	1	no	—
173	C₂²×C₁₀₉	—	4	1	no	—
174	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×D₁₀₉	—	2	1	no	—
176	C₂×D₁₀₉	—	2	1	no	—
177	C₂×D₁₀₉	—	2	1	no	—
178	C₂×D₁₀₉	—	2	2	no	—
179	C₂×D₁₀₉	—	2	1	no	—
180	C₂×D₁₀₉	—	2	1	no	—
181	C₂×D₁₀₉	—	4	1	no	—
182	C₂×D₁₀₉	—	4	1	no	—
183	C₂×D₁₀₉	—	8	4	no	—
184	C₂×D₁₀₉	#137	1	2	yes	complemented
185	C₄×C₁₀₉	—	2	2	no	—
186	C₄×C₁₀₉	—	2	1	no	—
187	C₄×C₁₀₉	—	2	1	no	—
188	C₄×C₁₀₉	—	4	1	no	—
189	C₄×C₁₀₉	—	4	1	no	—
190	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
191	C₄×C₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
192	Dic₁₀₉	—	2	1	no	—
193	Dic₁₀₉	—	2	1	no	—
194	Dic₁₀₉	—	4	1	no	—
195	Dic₁₀₉	—	4	1	no	—
196	Dic₁₀₉	—	4	1	no	—
197	C₂×C₁₀₉	—	8	1	no	—
198	C₂×C₁₀₉	D₄²	1	1	yes	characteristic
199	C₂×C₁₀₉	C₂×#137	1	1	yes	characteristic
200	C₂×C₁₀₉	#577	1	1	yes	characteristic
201	D₁₀₉	—	2	2	no	—
202	D₁₀₉	—	4	1	no	—
203	D₁₀₉	—	4	2	no	—
204	#3266	—	109	1	no	maximal, Sylow
205	C₁₀₉	#3266	1	1	yes	characteristic, complemented, Sylow
206	C₂×#137	—	109	1	no	—
207	C₂²×SD₁₆	—	109	1	no	—
208	D₄×Q₈	—	109	1	no	—
209	#546	—	109	1	no	—
210	#497	—	109	1	no	—
211	#468	—	109	1	no	—
212	#467	—	109	1	no	—
213	#464	D₁₀₉	1	1	yes	characteristic, complemented
214	#461	—	109	1	no	—
215	#452	—	109	1	no	—
216	#451	—	109	1	no	—
217	#450	—	109	1	no	—
218	#448	—	109	1	no	—
219	#440	—	109	1	no	—
220	#435	—	109	1	no	—
221	C₂×#41	—	109	1	no	—
222	C₂²×Q₈	—	109	1	no	—
223	C₂²×Q₈	—	109	1	no	—
224	C₂²×D₄	—	109	1	no	—
225	#137	—	218	4	no	—
226	C₂×Q₁₆	—	109	1	no	—
227	C₂×Q₁₆	—	109	1	no	—
228	C₂×Q₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
229	C₂×SD₁₆	—	109	1	no	—
230	C₂×SD₁₆	—	109	1	no	—
231	C₂×SD₁₆	—	109	1	no	—
232	C₂×SD₁₆	—	109	1	no	—
233	C₂×SD₁₆	—	109	1	no	—
234	C₂×SD₁₆	—	218	4	no	—
235	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
236	C₂×M₁₆	—	109	1	no	—
237	C₂²×C₈	—	109	1	no	—
238	C₄⋊Q₈	—	109	1	no	—
239	C₄⋊Q₈	—	218	1	no	—
240	#124	C₂×D₁₀₉	1	1	yes	characteristic
241	#123	—	218	1	no	—
242	C₂²⋊Q₈	—	109	1	no	—
243	C₂²⋊Q₈	—	109	1	no	—
244	C₂²⋊Q₈	—	109	1	no	—
245	C₂²⋊Q₈	—	218	1	no	—
246	C₂²⋊Q₈	—	218	1	no	—
247	#121	—	109	1	no	—
248	#121	—	218	1	no	—
249	#120	—	218	1	no	—
250	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
251	C₄×D₄	—	109	1	no	—
252	C₄×D₄	—	109	1	no	—
253	C₄×D₄	—	218	1	no	—
254	C₂×C₂²⋊C₄	—	218	1	no	—
255	#107	—	109	1	no	—
256	C₄⋊C₈	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	C₂×D₁₀₉	1	1	yes	characteristic
263	C₂²⋊C₈	—	109	1	no	—
264	C₂²⋊C₈	—	109	1	no	—
265	#97	—	109	1	no	—
266	C₂⁴	—	218	1	no	—
267	#41	—	436	1	no	—
268	#41	—	218	2	no	—
269	C₂×Q₈	—	109	1	no	—
270	C₂×Q₈	—	109	1	no	—
271	C₂×Q₈	—	436	1	no	—
272	C₂×Q₈	—	436	1	no	—
273	C₂×Q₈	—	218	1	no	—
274	C₂×Q₈	—	218	1	no	—
275	C₂×Q₈	—	218	2	no	—
276	C₂×Q₈	—	218	2	no	—
277	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
278	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
279	C₂×D₄	—	109	1	no	—
280	C₂×D₄	—	109	1	no	—
281	C₂×D₄	—	436	1	no	—
282	C₂×D₄	—	218	1	no	—
283	C₂×D₄	—	218	1	no	—
284	C₂×D₄	—	218	2	no	—
285	C₂×D₄	—	218	1	no	—
286	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
287	C₂²×C₄	—	109	1	no	—
288	C₂²×C₄	—	109	1	no	—
289	C₂²×C₄	—	218	1	no	—
290	C₂²×C₄	—	218	1	no	—
291	C₂²×C₄	—	218	1	no	—
292	C₂²×C₄	—	218	1	no	—
293	Q₁₆	—	2	2	no	—
294	Q₁₆	—	436	1	no	—
295	Q₁₆	—	218	2	no	—
296	SD₁₆	—	2	2	no	—
297	SD₁₆	—	109	4	no	—
298	SD₁₆	—	436	1	no	—
299	SD₁₆	—	218	2	no	—
300	SD₁₆	—	218	2	no	—
301	SD₁₆	—	218	2	no	—
302	M₁₆	—	218	2	no	—
303	C₂×C₈	—	109	1	no	—
304	C₂×C₈	—	109	1	no	—
305	C₂×C₈	—	218	2	no	—
306	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
307	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
308	C₄⋊C₄	—	2	1	no	—
309	C₄⋊C₄	—	109	1	no	—
310	C₄⋊C₄	—	109	1	no	—
311	C₄⋊C₄	—	218	1	no	—
312	C₄⋊C₄	—	218	1	no	—
313	C₄⋊C₄	—	218	1	no	—
314	C₄⋊C₄	—	218	1	no	—
315	C₄⋊C₄	—	218	1	no	—
316	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
317	C₂²⋊C₄	—	2	1	no	—
318	C₂²⋊C₄	—	2	1	no	—
319	C₂²⋊C₄	—	109	1	no	—
320	C₂²⋊C₄	—	109	1	no	—
321	C₂²⋊C₄	—	218	1	no	—
322	C₂²⋊C₄	—	218	1	no	—
323	C₂²⋊C₄	—	218	1	no	—
324	C₂²⋊C₄	—	218	1	no	—
325	C₂²⋊C₄	—	218	1	no	—
326	C₄²	—	2	1	no	—
327	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
328	C₂³	—	2	1	no	—
329	C₂³	—	872	1	no	—
330	C₂³	—	109	1	no	—
331	C₂³	—	109	1	no	—
332	C₂³	—	436	2	no	—
333	C₂³	—	436	2	no	—
334	C₂³	—	218	1	no	—
335	Q₈	—	2	1	no	—
336	Q₈	—	2	1	no	—
337	Q₈	—	2	1	no	—
338	Q₈	—	436	2	no	—
339	Q₈	—	436	2	no	—
340	Q₈	—	218	1	no	—
341	Q₈	—	218	1	no	—
342	Q₈	—	218	1	no	—
343	Q₈	—	218	1	no	—
344	Q₈	D₄×D₁₀₉	1	2	yes	—
345	D₄	—	2	1	no	—
346	D₄	—	2	1	no	—
347	D₄	—	872	1	no	—
348	D₄	—	109	2	no	—
349	D₄	—	436	2	no	—
350	D₄	—	436	2	no	—
351	D₄	—	218	2	no	—
352	D₄	—	218	1	no	—
353	C₂×C₄	—	2	1	no	—
354	C₂×C₄	—	2	1	no	—
355	C₂×C₄	—	2	1	no	—
356	C₂×C₄	—	872	1	no	—
357	C₂×C₄	—	109	1	no	—
358	C₂×C₄	—	109	1	no	—
359	C₂×C₄	—	436	2	no	—
360	C₂×C₄	—	436	2	no	—
361	C₂×C₄	—	436	2	no	—
362	C₂×C₄	—	218	1	no	—
363	C₂×C₄	—	218	1	no	—
364	C₂×C₄	—	218	1	no	—
365	C₂×C₄	—	218	1	no	—
366	C₂×C₄	—	218	1	no	—
367	C₂×C₄	—	218	1	no	—
368	C₂×C₄	—	218	1	no	—
369	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
370	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
371	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
372	C₈	—	2	1	no	—
373	C₈	—	2	1	no	—
374	C₈	—	109	2	no	—
375	C₈	—	218	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	4	1	no	—
378	C₂²	—	4	1	no	—
379	C₂²	—	872	4	no	—
380	C₂²	—	109	2	no	—
381	C₂²	—	436	1	no	—
382	C₂²	—	436	1	no	—
383	C₂²	—	218	1	no	—
384	C₂²	—	218	1	no	—
385	C₂²	—	218	1	no	—
386	C₂²	—	218	2	no	—
387	C₂²	—	218	1	no	—
388	C₂²	—	218	1	no	—
389	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	2	no	—
393	C₄	—	4	1	no	—
394	C₄	—	4	1	no	—
395	C₄	—	436	1	no	—
396	C₄	—	436	1	no	—
397	C₄	—	436	1	no	—
398	C₄	—	218	1	no	—
399	C₄	—	218	1	no	—
400	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
401	C₄	#16812745	1	1	yes	characteristic
402	C₂	—	8	1	no	—
403	C₂	—	436	2	no	—
404	C₂	—	436	1	no	—
405	C₂	—	218	2	no	—
406	C₂	#20295660	1	1	yes	characteristic
407	C₂	#137×D₁₀₉	1	1	yes	characteristic
408	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	#464×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	#20295669	C₂
hypercenter	#464	D₁₀₉
hypocenter	C₁₀₉	#3266
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
2. C₂×SD₁₆×D₁₀₉	C₂	semidirect
3. Q₈×D₄₃₆	C₂	semidirect
5. #20295421	C₂	semidirect
6. #20295271	C₂	semidirect
7. #20295266	C₂	semidirect
8. #20295232	C₂	semidirect
9. #20295191	C₂	semidirect
10. #20295180	C₂	semidirect
11. #20295178	C₂	semidirect
12. #20295163	C₂	semidirect
13. #20295124	C₂	semidirect
14. #20295096	C₂	semidirect
15. #464×C₁₀₉	C₂	semidirect
18. C₂×Q₈×D₁₀₉	C₂²	semidirect
21. C₂×#13182019	C₂²	semidirect
22. C₂×#13182019	C₂²	semidirect
29. C₂×#13182012	C₂²	semidirect
32. #16812699	C₂²	semidirect
37. #16812679	C₂²	semidirect
46. #16812632	C₂²	semidirect
47. #16812624	C₂²	semidirect
48. #16812624	C₂²	semidirect
49. #16812623	C₂²	semidirect
52. #16812611	C₂²	semidirect
53. #16812610	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
91. #13182016	D₄	semidirect
184. C₂×D₁₀₉	#137	semidirect
205. C₁₀₉	#3266	semidirect
213. #464	D₁₀₉	semidirect
228. C₂×Q₁₆	C₂×D₁₀₉	semidirect
250. C₄×Q₈	C₂×D₁₀₉	semidirect
256. C₄⋊C₈	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×#16812731	2
C₂×SD₁₆×D₁₀₉	2
Q₈×D₄₃₆	2
#20295669	2
#20295421	2
#20295271	2
#20295266	2
#20295232	2
#20295191	2
#20295180	2
#20295178	2
#20295163	2
#20295124	2
#20295096	2
#464×C₁₀₉	2
#3266	109