Subgroups — #28371857

Order 13952.

506 conjugacy classes of subgroups.

The subgroup lattice has 378 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	#20295505	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295498	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295138	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295136	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295126	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295125	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295117	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×#13182018	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295106	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295067	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295019	C₂	1	1	yes	maximal, characteristic, complemented
13	#102×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#20294980	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182028	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
18	#16812723	C₄	1	8	yes	complemented
19	C₂×#13182018	C₂²	1	1	yes	characteristic
20	C₂×#13182017	C₂²	1	1	yes	characteristic
21	C₂×#13182014	C₂²	1	1	yes	characteristic
22	C₂×#13182012	C₂²	1	1	yes	characteristic
23	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
24	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
25	#16812664	C₂²	1	1	yes	characteristic, complemented
26	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
27	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
28	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
29	#16812661	C₂²	1	1	yes	characteristic
30	C₄×C₂²⋊D₁₀₉	—	2	1	no	—
31	C₄×C₂²⋊D₁₀₉	—	2	1	no	—
32	#16812659	—	2	1	no	—
33	#16812659	—	2	1	no	—
34	#16812657	C₂²	1	1	yes	characteristic
35	#16812656	C₂²	1	1	yes	characteristic
36	#16812655	—	2	1	no	—
37	C₂×#13182008	—	2	1	no	—
38	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
39	C₂×#13182006	—	2	1	no	—
40	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
41	#16812632	C₂²	1	1	yes	characteristic, complemented
42	#16812631	C₂²	1	1	yes	characteristic, complemented
43	#16812630	C₂²	1	1	yes	characteristic, complemented
44	#16812624	C₂²	1	1	yes	characteristic, complemented
45	#16812622	C₂²	1	1	yes	characteristic, complemented
46	#16812621	C₂²	1	1	yes	characteristic
47	#16812620	C₂²	1	1	yes	characteristic
48	#16812620	C₂²	1	1	yes	characteristic, complemented
49	#16812619	C₂²	1	1	yes	characteristic
50	#16812610	C₂²	1	1	yes	characteristic, complemented
51	#16812609	C₂²	1	1	yes	characteristic, complemented
52	C₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
53	C₂×D₈×C₁₀₉	C₂²	1	1	yes	characteristic
54	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
55	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
56	#107×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	#102×C₁₀₉	C₂²	1	1	yes	characteristic
58	#102×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₁₀₉	—	2	1	no	—
61	#13182028	—	2	2	no	—
62	#13182028	C₂×C₄	1	4	yes	complemented
63	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
64	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
66	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
67	D₄×D₁₀₉	—	2	2	no	—
68	D₄×D₁₀₉	C₂×C₄	1	4	yes	complemented
69	C₂²×Dic₁₀₉	—	2	1	no	—
70	C₂²×Dic₁₀₉	—	2	1	no	—
71	C₂²×Dic₁₀₉	—	2	1	no	—
72	C₂×C₄×D₁₀₉	—	2	1	no	—
73	C₂×C₄×D₁₀₉	—	2	1	no	—
74	C₂×C₄×D₁₀₉	—	2	1	no	—
75	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
76	#13182018	C₂×C₄	1	4	yes	complemented
77	#13182017	C₂×C₄	1	4	yes	complemented
78	#13182014	C₂×C₄	1	4	yes	complemented
79	#13182012	C₂×C₄	1	4	yes	complemented
80	C₂×#11724784	C₂³	1	1	yes	characteristic
81	C₂×#11724784	C₂³	1	1	yes	characteristic
82	C₈×D₁₀₉	—	2	2	no	—
83	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
84	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
85	#13182008	—	2	1	no	—
86	#13182008	—	2	1	no	—
87	#13182008	—	2	1	no	—
88	#13182008	D₄	1	1	yes	characteristic
89	#13182008	D₄	1	1	yes	characteristic
90	C₂²⋊Dic₁₀₉	—	2	1	no	—
91	C₂²⋊Dic₁₀₉	—	2	1	no	—
92	#13182006	—	2	1	no	—
93	#13182006	—	2	1	no	—
94	#13182006	—	2	1	no	—
95	#13182006	D₄	1	1	yes	characteristic
96	#13182006	D₄	1	1	yes	characteristic
97	C₄×Dic₁₀₉	—	2	1	no	—
98	C₄×Dic₁₀₉	—	2	1	no	—
99	C₄×Dic₁₀₉	—	2	1	no	—
100	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
101	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
102	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
103	C₂²×C₄×C₁₀₉	—	2	1	no	—
104	C₂²×C₄×C₁₀₉	—	2	1	no	—
105	D₈×C₁₀₉	C₂×C₄	1	4	yes	complemented
106	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
108	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
111	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
112	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
113	C₂³×C₁₀₉	—	2	1	no	—
114	C₂³×C₁₀₉	—	2	1	no	—
115	C₂²×D₁₀₉	—	2	1	no	—
116	C₂²×D₁₀₉	—	2	4	no	—
117	C₂²×D₁₀₉	—	8	1	no	—
118	C₂²×D₁₀₉	—	8	1	no	—
119	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
120	D₄×C₁₀₉	—	2	1	no	—
121	D₄×C₁₀₉	—	2	1	no	—
122	D₄×C₁₀₉	C₂²×C₄	1	2	yes	—
123	D₄×C₁₀₉	C₂²×C₄	1	2	yes	—
124	C₂×C₄×C₁₀₉	—	2	1	no	—
125	C₂×C₄×C₁₀₉	—	2	1	no	—
126	C₂×C₄×C₁₀₉	—	8	1	no	—
127	C₂×C₄×C₁₀₉	—	8	1	no	—
128	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
131	C₂²⋊D₁₀₉	—	2	4	no	—
132	C₂²⋊D₁₀₉	—	2	4	no	—
133	C₂×Dic₁₀₉	—	2	1	no	—
134	C₂×Dic₁₀₉	—	2	4	no	—
135	C₂×Dic₁₀₉	—	2	1	no	—
136	C₂×Dic₁₀₉	—	2	1	no	—
137	C₂×Dic₁₀₉	—	8	1	no	—
138	C₂×Dic₁₀₉	—	8	1	no	—
139	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
140	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
141	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
142	D₄₃₆	—	2	1	no	—
143	D₄₃₆	C₂²×C₄	1	2	yes	—
144	C₄×D₁₀₉	—	8	1	no	—
145	C₄×D₁₀₉	—	8	1	no	—
146	C₄×D₁₀₉	—	8	1	no	—
147	C₄×D₁₀₉	C₂²×C₄	1	2	yes	—
148	C₄×D₁₀₉	#41	1	2	yes	—
149	Dic₂₁₈	—	2	1	no	—
150	Dic₂₁₈	C₂²×C₄	1	2	yes	—
151	C₈×C₁₀₉	—	2	1	no	—
152	C₈×C₁₀₉	C₂²×C₄	1	2	yes	—
153	#11724784	—	2	1	no	—
154	#11724784	C₂²×C₄	1	2	yes	—
155	C₂²×C₁₀₉	—	2	2	no	—
156	C₂²×C₁₀₉	—	2	2	no	—
157	C₂²×C₁₀₉	—	4	1	no	—
158	C₂²×C₁₀₉	—	4	1	no	—
159	C₂²×C₁₀₉	—	4	1	no	—
160	C₂²×C₁₀₉	—	4	1	no	—
161	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×D₁₀₉	—	2	1	no	—
163	C₂×D₁₀₉	—	2	1	no	—
164	C₂×D₁₀₉	—	2	2	no	—
165	C₂×D₁₀₉	—	4	1	no	—
166	C₂×D₁₀₉	—	4	1	no	—
167	C₂×D₁₀₉	—	8	4	no	—
168	C₂×D₁₀₉	C₄×D₄	1	2	yes	—
169	C₄×C₁₀₉	—	2	1	no	—
170	C₄×C₁₀₉	—	2	1	no	—
171	C₄×C₁₀₉	—	4	1	no	—
172	C₄×C₁₀₉	—	4	1	no	—
173	C₄×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
174	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
175	Dic₁₀₉	—	2	2	no	—
176	Dic₁₀₉	—	2	1	no	—
177	Dic₁₀₉	—	2	1	no	—
178	Dic₁₀₉	—	4	1	no	—
179	Dic₁₀₉	—	4	1	no	—
180	Dic₁₀₉	C₄×D₄	1	2	yes	—
181	C₂×C₁₀₉	—	4	2	no	—
182	C₂×C₁₀₉	—	4	2	no	—
183	C₂×C₁₀₉	C₂×C₄×D₄	1	1	yes	characteristic
184	C₂×C₁₀₉	#576	1	1	yes	characteristic
185	C₂×C₁₀₉	#577	1	1	yes	characteristic
186	D₁₀₉	—	2	2	no	—
187	D₁₀₉	—	4	2	no	—
188	#2946	—	109	1	no	maximal, Sylow
189	C₁₀₉	#2946	1	1	yes	characteristic, complemented, Sylow
190	C₂×AGL(1,ℤ/8)	—	109	1	no	—
191	#520	—	109	1	no	—
192	#518	—	109	1	no	—
193	#442	—	109	1	no	—
194	#442	—	109	1	no	—
195	#440	—	109	1	no	—
196	#440	—	109	1	no	—
197	C₄×SD₁₆	—	109	1	no	—
198	C₄×SD₁₆	—	109	1	no	—
199	C₄×D₈	—	109	1	no	—
200	C₄×D₈	D₁₀₉	1	1	yes	characteristic, complemented
201	#428	—	109	1	no	—
202	#416	—	109	1	no	—
203	C₂×#102	—	109	1	no	—
204	#405	—	109	1	no	—
205	C₂×#41	—	109	1	no	—
206	C₂²×D₄	—	109	1	no	—
207	AGL(1,ℤ/8)	—	109	8	no	—
208	C₂×SD₁₆	—	109	1	no	—
209	C₂×SD₁₆	—	109	1	no	—
210	C₂×D₈	—	109	1	no	—
211	C₂×D₈	C₂×D₁₀₉	1	1	yes	characteristic
212	C₂×M₁₆	—	109	1	no	—
213	C₂²×C₈	—	109	1	no	—
214	C₄×Q₈	—	109	1	no	—
215	C₄×Q₈	—	109	1	no	—
216	C₄×D₄	—	109	1	no	—
217	C₄×D₄	—	109	1	no	—
218	C₄×D₄	—	109	1	no	—
219	C₄×D₄	—	109	1	no	—
220	C₄×D₄	—	218	1	no	—
221	C₄×D₄	—	218	1	no	—
222	C₄×D₄	—	218	1	no	—
223	C₄×D₄	—	218	1	no	—
224	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
225	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
226	#117	—	109	1	no	—
227	#117	—	109	1	no	—
228	#117	—	218	1	no	—
229	C₂×C₄⋊C₄	—	109	1	no	—
230	C₂×C₄⋊C₄	—	218	1	no	—
231	C₂×C₂²⋊C₄	—	218	1	no	—
232	C₂×C₂²⋊C₄	—	218	1	no	—
233	#107	—	109	1	no	—
234	#107	C₂×D₁₀₉	1	1	yes	characteristic, complemented
235	#106	—	109	1	no	—
236	#106	—	109	1	no	—
237	#103	—	109	1	no	—
238	#103	—	109	1	no	—
239	#102	—	109	1	no	—
240	#102	—	109	1	no	—
241	#102	—	109	1	no	—
242	#102	—	109	1	no	—
243	#102	C₂×D₁₀₉	1	1	yes	characteristic
244	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
245	#97	—	109	1	no	—
246	#97	—	109	1	no	—
247	C₄×C₈	—	109	1	no	—
248	C₄×C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
249	C₂⁴	—	218	1	no	—
250	#41	—	109	4	no	—
251	#41	—	218	2	no	—
252	C₂×Q₈	—	109	1	no	—
253	C₂×D₄	—	109	4	no	—
254	C₂×D₄	—	109	1	no	—
255	C₂×D₄	—	218	2	no	—
256	C₂×D₄	—	218	1	no	—
257	C₂×D₄	—	218	1	no	—
258	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
259	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
260	C₂²×C₄	—	2	1	no	—
261	C₂²×C₄	—	2	1	no	—
262	C₂²×C₄	—	109	1	no	—
263	C₂²×C₄	—	218	1	no	—
264	C₂²×C₄	—	218	1	no	—
265	C₂²×C₄	—	218	1	no	—
266	C₂²×C₄	—	218	1	no	—
267	C₂²×C₄	—	218	1	no	—
268	C₂²×C₄	—	218	1	no	—
269	SD₁₆	—	109	4	no	—
270	SD₁₆	—	109	4	no	—
271	D₈	—	109	4	no	—
272	D₈	C₄×D₁₀₉	1	4	yes	complemented
273	M₁₆	—	109	4	no	—
274	C₂×C₈	—	109	1	no	—
275	C₂×C₈	—	109	1	no	—
276	C₂×C₈	—	218	2	no	—
277	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
278	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
279	C₄⋊C₄	—	109	1	no	—
280	C₄⋊C₄	—	109	1	no	—
281	C₄⋊C₄	—	109	1	no	—
282	C₄⋊C₄	—	109	1	no	—
283	C₄⋊C₄	—	218	1	no	—
284	C₄⋊C₄	—	218	1	no	—
285	C₄⋊C₄	—	218	1	no	—
286	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
287	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
288	C₂²⋊C₄	—	2	1	no	—
289	C₂²⋊C₄	—	2	1	no	—
290	C₂²⋊C₄	—	109	1	no	—
291	C₂²⋊C₄	—	109	1	no	—
292	C₂²⋊C₄	—	218	1	no	—
293	C₂²⋊C₄	—	218	1	no	—
294	C₂²⋊C₄	—	218	1	no	—
295	C₂²⋊C₄	—	218	1	no	—
296	C₂²⋊C₄	—	218	1	no	—
297	C₄²	—	109	1	no	—
298	C₄²	—	218	1	no	—
299	C₄²	—	218	1	no	—
300	C₄²	—	218	1	no	—
301	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
302	C₂³	—	2	1	no	—
303	C₂³	—	2	1	no	—
304	C₂³	—	872	1	no	—
305	C₂³	—	872	1	no	—
306	C₂³	—	109	1	no	—
307	C₂³	—	218	4	no	—
308	C₂³	—	218	1	no	—
309	Q₈	—	109	2	no	—
310	Q₈	—	218	1	no	—
311	D₄	—	2	1	no	—
312	D₄	—	2	1	no	—
313	D₄	—	109	2	no	—
314	D₄	—	218	4	no	—
315	D₄	—	218	4	no	—
316	D₄	—	218	1	no	—
317	D₄	C₂×C₄×D₁₀₉	1	2	yes	—
318	D₄	C₂×C₄×D₁₀₉	1	2	yes	—
319	C₂×C₄	—	2	1	no	—
320	C₂×C₄	—	2	1	no	—
321	C₂×C₄	—	8	1	no	—
322	C₂×C₄	—	8	1	no	—
323	C₂×C₄	—	872	1	no	—
324	C₂×C₄	—	872	1	no	—
325	C₂×C₄	—	872	1	no	—
326	C₂×C₄	—	872	1	no	—
327	C₂×C₄	—	872	1	no	—
328	C₂×C₄	—	109	1	no	—
329	C₂×C₄	—	109	2	no	—
330	C₂×C₄	—	109	2	no	—
331	C₂×C₄	—	109	1	no	—
332	C₂×C₄	—	109	1	no	—
333	C₂×C₄	—	218	4	no	—
334	C₂×C₄	—	218	1	no	—
335	C₂×C₄	—	218	1	no	—
336	C₂×C₄	—	218	1	no	—
337	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
338	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
339	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
340	C₈	—	2	1	no	—
341	C₈	—	109	2	no	—
342	C₈	—	218	1	no	—
343	C₈	C₂×C₄×D₁₀₉	1	2	yes	—
344	C₂²	—	2	2	no	—
345	C₂²	—	2	2	no	—
346	C₂²	—	4	1	no	—
347	C₂²	—	4	1	no	—
348	C₂²	—	4	1	no	—
349	C₂²	—	4	1	no	—
350	C₂²	—	872	4	no	—
351	C₂²	—	109	2	no	—
352	C₂²	—	436	1	no	—
353	C₂²	—	436	1	no	—
354	C₂²	—	218	2	no	—
355	C₂²	—	218	1	no	—
356	C₂²	—	218	1	no	—
357	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
358	C₄	—	2	1	no	—
359	C₄	—	2	1	no	—
360	C₄	—	4	1	no	—
361	C₄	—	4	1	no	—
362	C₄	—	109	2	no	—
363	C₄	—	436	1	no	—
364	C₄	—	436	1	no	—
365	C₄	—	218	2	no	—
366	C₄	—	218	1	no	—
367	C₄	—	218	1	no	—
368	C₄	C₂²×C₄×D₁₀₉	1	1	yes	characteristic
369	C₄	#41×D₁₀₉	1	1	yes	characteristic
370	C₂	—	4	2	no	—
371	C₂	—	4	2	no	—
372	C₂	—	436	2	no	—
373	C₂	—	218	2	no	—
374	C₂	C₄×D₄×D₁₀₉	1	1	yes	characteristic
375	C₂	#20295827	1	1	yes	characteristic
376	C₂	#20295833	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator	C₄×C₁₀₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	C₄×D₈×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	C₂×#16812723	C₂
cosocle	C₂×C₄×C₁₀₉	C₂⁴
hypercenter	C₄×D₈	D₁₀₉
hypocenter	C₁₀₉	#2946
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ C₄×D₈

Complements

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

N	H ≅ G/N	type
2. #20295505	C₂	semidirect
3. #20295498	C₂	semidirect
4. #20295138	C₂	semidirect
5. #20295136	C₂	semidirect
6. #20295126	C₂	semidirect
7. #20295125	C₂	semidirect
8. #20295117	C₂	semidirect
9. C₄×#13182018	C₂	semidirect
10. #20295106	C₂	semidirect
11. #20295067	C₂	semidirect
12. #20295019	C₂	semidirect
13. #102×D₁₀₉	C₂	semidirect
14. #20294980	C₂	semidirect
15. C₄×D₈×C₁₀₉	C₂	semidirect
18. #16812723	C₄	semidirect
24. C₄×Dic₂₁₈	C₂²	semidirect
25. #16812664	C₂²	semidirect
28. D₄×Dic₁₀₉	C₂²	semidirect
41. #16812632	C₂²	semidirect
42. #16812631	C₂²	semidirect
43. #16812630	C₂²	semidirect
44. #16812624	C₂²	semidirect
45. #16812622	C₂²	semidirect
48. #16812620	C₂²	semidirect
50. #16812610	C₂²	semidirect
51. #16812609	C₂²	semidirect
52. C₈×Dic₁₀₉	C₂²	semidirect
55. C₄×D₄×C₁₀₉	C₂²	semidirect
56. #107×C₁₀₉	C₂²	semidirect
58. #102×C₁₀₉	C₂²	semidirect
59. C₄×C₈×C₁₀₉	C₂²	semidirect
62. #13182028	C₂×C₄	semidirect
68. D₄×D₁₀₉	C₂×C₄	semidirect
76. #13182018	C₂×C₄	semidirect
77. #13182017	C₂×C₄	semidirect
78. #13182014	C₂×C₄	semidirect
79. #13182012	C₂×C₄	semidirect
105. D₈×C₁₀₉	C₂×C₄	semidirect
189. C₁₀₉	#2946	semidirect
200. C₄×D₈	D₁₀₉	semidirect
225. C₄×D₄	C₂×D₁₀₉	semidirect
234. #107	C₂×D₁₀₉	semidirect
244. #102	C₂×D₁₀₉	semidirect
248. C₄×C₈	C₂×D₁₀₉	semidirect
272. D₈	C₄×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
#20295505	2
#20295498	2
#20295138	2
#20295136	2
#20295126	2
#20295125	2
#20295117	2
C₄×#13182018	2
#20295106	2
#20295067	2
#20295019	2
#102×D₁₀₉	2
#20294980	2
C₄×D₈×C₁₀₉	2
#2946	109