Subgroups — #28373501

Order 13952.

564 conjugacy classes of subgroups.

The subgroup lattice has 386 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812728	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16812726	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16812720	C₂	1	1	yes	maximal, characteristic, complemented
4	C₂×SD₁₆×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295601	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295589	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295418	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295417	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295413	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295412	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295410	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295407	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295397	C₂	1	1	yes	maximal, characteristic, complemented
14	#20294980	C₂	1	1	yes	maximal, characteristic, complemented
15	#492×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×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
20	#16812728	—	2	4	no	—
21	#16812726	—	2	4	no	—
22	#16812720	—	2	4	no	—
23	C₂×Dic₄₃₆	C₂²	1	1	yes	characteristic, complemented
24	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13182019	C₂²	1	1	yes	characteristic, complemented
26	C₂×#13182018	C₂²	1	1	yes	characteristic
27	C₂×#13182018	C₂²	1	1	yes	characteristic, complemented
28	C₂×#13182017	C₂²	1	1	yes	characteristic
29	C₂×#13182017	C₂²	1	1	yes	characteristic, complemented
30	C₂×#13182016	C₂²	1	1	yes	characteristic
31	C₂×#13182016	C₂²	1	1	yes	characteristic
32	SD₁₆×D₁₀₉	—	2	4	no	—
33	C₂×D₈₇₂	C₂²	1	1	yes	characteristic
34	C₂×#13182014	C₂²	1	1	yes	characteristic
35	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
36	C₂×#13182012	C₂²	1	1	yes	characteristic
37	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic
38	#16812697	C₂²	1	1	yes	characteristic, complemented
39	#16812695	C₂²	1	1	yes	characteristic
40	#16812688	C₂²	1	1	yes	characteristic, complemented
41	#16812687	C₂²	1	1	yes	characteristic
42	#16812687	C₂²	1	1	yes	characteristic, complemented
43	#16812686	C₂²	1	1	yes	characteristic
44	#16812684	—	2	2	no	—
45	#16812677	—	2	2	no	—
46	#16812671	—	2	2	no	—
47	#16812667	—	2	2	no	—
48	#16812656	C₂²	1	1	yes	characteristic
49	#16812610	C₂²	1	1	yes	characteristic, complemented
50	#16812609	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
52	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
53	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
54	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
56	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	#127×C₁₀₉	C₂²	1	1	yes	characteristic
58	C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₀₉	—	2	1	no	—
60	#13182030	—	2	2	no	—
61	#13182030	—	2	2	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	—	2	1	no	—
70	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
71	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
72	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
74	C₂×C₂²⋊D₁₀₉	—	2	2	no	—
75	D₄×D₁₀₉	—	2	2	no	—
76	D₄×D₁₀₉	—	2	2	no	—
77	C₂²×Dic₁₀₉	—	2	1	no	—
78	C₂×C₄×D₁₀₉	—	2	1	no	—
79	C₂×C₄×D₁₀₉	—	2	1	no	—
80	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
81	Dic₄₃₆	—	2	2	no	—
82	#13182019	—	2	2	no	—
83	#13182019	—	2	2	no	—
84	#13182018	—	2	2	no	—
85	#13182018	—	2	2	no	—
86	#13182017	—	2	2	no	—
87	#13182017	—	2	2	no	—
88	#13182016	—	2	2	no	—
89	#13182016	—	2	2	no	—
90	D₈₇₂	—	2	2	no	—
91	#13182014	—	2	2	no	—
92	#13182014	—	2	2	no	—
93	#13182012	D₄	1	4	yes	complemented
94	C₂×#11724784	C₂³	1	1	yes	characteristic
95	C₂×#11724784	C₂³	1	1	yes	characteristic
96	C₈×D₁₀₉	D₄	1	4	yes	complemented
97	#13182008	—	2	2	no	—
98	#13182008	D₄	1	2	yes	—
99	C₂²⋊Dic₁₀₉	—	2	2	no	—
100	#13182006	—	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×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
107	C₂×D₄×C₁₀₉	—	2	2	no	—
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	SD₁₆×C₁₀₉	—	2	2	no	—
113	SD₁₆×C₁₀₉	—	2	2	no	—
114	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
115	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
116	C₄⋊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	C₂²×D₁₀₉	—	2	1	no	—
121	C₂²×D₁₀₉	—	2	1	no	—
122	C₂²×D₁₀₉	—	4	2	no	—
123	C₂²×D₁₀₉	—	8	2	no	—
124	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
125	Q₈×C₁₀₉	—	2	1	no	—
126	Q₈×C₁₀₉	—	2	1	no	—
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	—	2	1	no	—
133	D₄×C₁₀₉	—	8	2	no	—
134	C₂×C₄×C₁₀₉	—	2	1	no	—
135	C₂×C₄×C₁₀₉	—	2	1	no	—
136	C₂×C₄×C₁₀₉	C₂×D₄	1	2	yes	—
137	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
138	C₂²⋊D₁₀₉	—	4	2	no	—
139	C₂²⋊D₁₀₉	—	4	2	no	—
140	C₂²⋊D₁₀₉	—	8	2	no	—
141	C₂×Dic₁₀₉	—	2	1	no	—
142	C₂×Dic₁₀₉	—	2	1	no	—
143	C₂×Dic₁₀₉	—	4	2	no	—
144	C₂×Dic₁₀₉	C₂×D₄	1	2	yes	—
145	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
146	D₄₃₆	—	2	1	no	—
147	D₄₃₆	—	2	1	no	—
148	D₄₃₆	—	2	1	no	—
149	D₄₃₆	—	2	1	no	—
150	D₄₃₆	—	4	2	no	—
151	C₄×D₁₀₉	—	4	2	no	—
152	C₄×D₁₀₉	—	4	2	no	—
153	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
154	C₄×D₁₀₉	C₂×D₄	1	2	yes	—
155	Dic₂₁₈	—	2	1	no	—
156	Dic₂₁₈	—	2	1	no	—
157	Dic₂₁₈	—	2	1	no	—
158	Dic₂₁₈	—	2	1	no	—
159	Dic₂₁₈	—	4	2	no	—
160	C₈×C₁₀₉	C₂×D₄	1	2	yes	—
161	C₈×C₁₀₉	C₂×D₄	1	2	yes	—
162	#11724784	C₂×D₄	1	2	yes	—
163	#11724784	C₂×D₄	1	2	yes	—
164	C₂²×C₁₀₉	—	4	1	no	—
165	C₂²×C₁₀₉	—	4	1	no	—
166	C₂²×C₁₀₉	—	4	2	no	—
167	C₂²×C₁₀₉	—	4	2	no	—
168	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
169	C₂×D₁₀₉	—	2	2	no	—
170	C₂×D₁₀₉	—	4	1	no	—
171	C₂×D₁₀₉	—	4	1	no	—
172	C₂×D₁₀₉	—	4	2	no	—
173	C₂×D₁₀₉	—	4	2	no	—
174	C₂×D₁₀₉	—	8	4	no	—
175	C₂×D₁₀₉	#127	1	2	yes	—
176	C₄×C₁₀₉	—	2	2	no	—
177	C₄×C₁₀₉	—	4	1	no	—
178	C₄×C₁₀₉	—	4	1	no	—
179	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
180	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
181	Dic₁₀₉	—	2	2	no	—
182	Dic₁₀₉	—	4	1	no	—
183	Dic₁₀₉	—	4	1	no	—
184	Dic₁₀₉	#127	1	2	yes	—
185	C₂×C₁₀₉	—	8	1	no	—
186	C₂×C₁₀₉	—	8	1	no	—
187	C₂×C₁₀₉	C₂×#127	1	1	yes	characteristic
188	C₂×C₁₀₉	#577	1	2	yes	—
189	D₁₀₉	—	2	2	no	—
190	D₁₀₉	—	8	1	no	—
191	D₁₀₉	—	8	1	no	—
192	#3154	—	109	1	no	maximal, Sylow
193	C₁₀₉	#3154	1	1	yes	characteristic, complemented, Sylow
194	C₂×#137	—	109	1	no	—
195	C₂×AGL(1,ℤ/8)	—	109	1	no	—
196	C₂×#135	—	109	1	no	—
197	C₂²×SD₁₆	—	109	1	no	—
198	#536	—	109	1	no	—
199	#535	—	109	1	no	—
200	#497	—	109	1	no	—
201	#497	—	109	1	no	—
202	#496	—	109	1	no	—
203	#496	—	109	1	no	—
204	#495	—	109	1	no	—
205	#495	—	109	1	no	—
206	#492	—	109	1	no	—
207	#492	D₁₀₉	1	1	yes	characteristic, complemented
208	#405	—	109	1	no	—
209	C₂×#41	—	109	1	no	—
210	C₂×#41	—	109	1	no	—
211	C₂²×Q₈	—	109	1	no	—
212	C₂²×D₄	—	109	1	no	—
213	#137	—	218	4	no	—
214	AGL(1,ℤ/8)	—	218	4	no	—
215	#135	—	218	4	no	—
216	C₂×Q₁₆	—	109	1	no	—
217	C₂×Q₁₆	—	109	1	no	—
218	C₂×Q₁₆	—	109	1	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	—	109	1	no	—
225	C₂×SD₁₆	—	218	4	no	—
226	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
227	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
228	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
229	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
230	C₂×D₈	—	109	1	no	—
231	C₂×D₈	—	109	1	no	—
232	C₂×D₈	—	109	1	no	—
233	C₂×M₁₆	—	109	1	no	—
234	C₂²×C₈	—	109	1	no	—
235	C₄⋊Q₈	—	109	1	no	—
236	C₄⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
237	#127	—	109	1	no	—
238	#127	C₂×D₁₀₉	1	1	yes	characteristic
239	#124	—	109	1	no	—
240	#124	—	109	1	no	—
241	#124	—	109	1	no	—
242	#124	—	109	1	no	—
243	#123	—	218	2	no	—
244	C₂²⋊Q₈	—	218	2	no	—
245	#121	—	218	2	no	—
246	#120	—	218	2	no	—
247	#117	—	109	1	no	—
248	#97	—	109	1	no	—
249	#97	—	109	1	no	—
250	C₄×C₈	—	109	1	no	—
251	C₄×C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
252	C₂⁴	—	218	1	no	—
253	#41	—	218	2	no	—
254	#41	—	218	2	no	—
255	#41	—	218	2	no	—
256	#41	—	218	2	no	—
257	C₂×Q₈	—	109	1	no	—
258	C₂×Q₈	—	109	1	no	—
259	C₂×Q₈	—	218	1	no	—
260	C₂×Q₈	—	218	2	no	—
261	C₂×Q₈	—	218	2	no	—
262	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
263	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
264	C₂×D₄	—	2	2	no	—
265	C₂×D₄	—	109	1	no	—
266	C₂×D₄	—	109	1	no	—
267	C₂×D₄	—	218	1	no	—
268	C₂×D₄	—	218	2	no	—
269	C₂×D₄	—	218	2	no	—
270	C₂×D₄	—	218	2	no	—
271	C₂×D₄	—	218	1	no	—
272	C₂×D₄	—	218	1	no	—
273	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
274	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
275	C₂²×C₄	—	109	1	no	—
276	C₂²×C₄	—	218	1	no	—
277	C₂²×C₄	—	218	1	no	—
278	C₂²×C₄	—	218	1	no	—
279	Q₁₆	—	218	2	no	—
280	Q₁₆	—	218	2	no	—
281	Q₁₆	—	218	2	no	—
282	SD₁₆	—	2	2	no	—
283	SD₁₆	—	2	2	no	—
284	SD₁₆	—	2	2	no	—
285	SD₁₆	—	2	2	no	—
286	SD₁₆	—	218	2	no	—
287	SD₁₆	—	218	2	no	—
288	SD₁₆	—	218	2	no	—
289	SD₁₆	—	218	2	no	—
290	SD₁₆	—	218	2	no	—
291	SD₁₆	—	218	2	no	—
292	D₈	—	218	2	no	—
293	D₈	—	218	2	no	—
294	D₈	—	218	2	no	—
295	M₁₆	—	109	4	no	—
296	C₂×C₈	—	109	1	no	—
297	C₂×C₈	—	109	1	no	—
298	C₂×C₈	—	109	4	no	—
299	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
301	C₄⋊C₄	—	2	2	no	—
302	C₄⋊C₄	—	109	2	no	—
303	C₄⋊C₄	—	218	2	no	—
304	C₂²⋊C₄	—	109	2	no	—
305	C₂²⋊C₄	—	218	2	no	—
306	C₂²⋊C₄	—	218	2	no	—
307	C₂²⋊C₄	—	218	2	no	—
308	C₂²⋊C₄	—	218	2	no	—
309	C₄²	—	109	1	no	—
310	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
311	C₂³	—	2	1	no	—
312	C₂³	—	2	1	no	—
313	C₂³	—	872	2	no	—
314	C₂³	—	109	1	no	—
315	C₂³	—	436	2	no	—
316	C₂³	—	218	1	no	—
317	C₂³	—	218	1	no	—
318	Q₈	—	2	1	no	—
319	Q₈	—	2	1	no	—
320	Q₈	—	2	1	no	—
321	Q₈	—	2	1	no	—
322	Q₈	—	436	2	no	—
323	Q₈	—	218	1	no	—
324	Q₈	—	218	1	no	—
325	Q₈	—	218	1	no	—
326	Q₈	—	218	1	no	—
327	D₄	—	2	1	no	—
328	D₄	—	2	1	no	—
329	D₄	—	2	1	no	—
330	D₄	—	2	1	no	—
331	D₄	—	8	2	no	—
332	D₄	—	872	2	no	—
333	D₄	—	436	2	no	—
334	D₄	—	436	2	no	—
335	D₄	—	436	2	no	—
336	D₄	—	218	1	no	—
337	D₄	—	218	1	no	—
338	D₄	—	218	1	no	—
339	D₄	—	218	1	no	—
340	C₂×C₄	—	2	1	no	—
341	C₂×C₄	—	2	1	no	—
342	C₂×C₄	—	109	1	no	—
343	C₂×C₄	—	109	2	no	—
344	C₂×C₄	—	109	2	no	—
345	C₂×C₄	—	109	2	no	—
346	C₂×C₄	—	436	2	no	—
347	C₂×C₄	—	436	2	no	—
348	C₂×C₄	—	436	2	no	—
349	C₂×C₄	—	218	1	no	—
350	C₂×C₄	—	218	1	no	—
351	C₂×C₄	D₄×D₁₀₉	1	2	yes	—
352	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
353	C₈	—	109	2	no	—
354	C₈	—	109	2	no	—
355	C₈	D₄×D₁₀₉	1	2	yes	—
356	C₈	D₄×D₁₀₉	1	2	yes	—
357	C₂²	—	4	1	no	—
358	C₂²	—	4	1	no	—
359	C₂²	—	4	2	no	—
360	C₂²	—	4	2	no	—
361	C₂²	—	872	4	no	—
362	C₂²	—	109	2	no	—
363	C₂²	—	436	1	no	—
364	C₂²	—	436	1	no	—
365	C₂²	—	436	2	no	—
366	C₂²	—	436	2	no	—
367	C₂²	—	218	2	no	—
368	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
369	C₄	—	2	2	no	—
370	C₄	—	4	1	no	—
371	C₄	—	4	1	no	—
372	C₄	—	109	2	no	—
373	C₄	—	436	1	no	—
374	C₄	—	436	1	no	—
375	C₄	—	218	2	no	—
376	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
377	C₄	C₂×D₄×D₁₀₉	1	1	yes	characteristic
378	C₂	—	8	1	no	—
379	C₂	—	8	1	no	—
380	C₂	—	872	1	no	—
381	C₂	—	872	1	no	—
382	C₂	—	218	2	no	—
383	C₂	#127×D₁₀₉	1	1	yes	characteristic
384	C₂	#20295832	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	#492×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
hypercenter	#492	D₁₀₉
hypocenter	C₁₀₉	#3154
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #492

Complements

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

N	H ≅ G/N	type
1. C₂×#16812728	C₂	semidirect
2. C₂×#16812726	C₂	semidirect
3. C₂×#16812720	C₂	semidirect
4. C₂×SD₁₆×D₁₀₉	C₂	semidirect
5. #20295601	C₂	semidirect
6. #20295589	C₂	semidirect
7. #20295418	C₂	semidirect
8. #20295417	C₂	semidirect
9. #20295413	C₂	semidirect
10. #20295412	C₂	semidirect
11. #20295410	C₂	semidirect
12. #20295407	C₂	semidirect
13. #20295397	C₂	semidirect
14. #20294980	C₂	semidirect
15. #492×C₁₀₉	C₂	semidirect
23. C₂×Dic₄₃₆	C₂²	semidirect
24. C₂×#13182019	C₂²	semidirect
25. C₂×#13182019	C₂²	semidirect
27. C₂×#13182018	C₂²	semidirect
29. C₂×#13182017	C₂²	semidirect
35. C₂×#13182014	C₂²	semidirect
38. #16812697	C₂²	semidirect
40. #16812688	C₂²	semidirect
42. #16812687	C₂²	semidirect
49. #16812610	C₂²	semidirect
50. #16812609	C₂²	semidirect
51. C₈×Dic₁₀₉	C₂²	semidirect
54. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
55. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
56. C₄⋊Q₈×C₁₀₉	C₂²	semidirect
58. C₄×C₈×C₁₀₉	C₂²	semidirect
93. #13182012	D₄	semidirect
96. C₈×D₁₀₉	D₄	semidirect
193. C₁₀₉	#3154	semidirect
207. #492	D₁₀₉	semidirect
228. C₂×SD₁₆	C₂×D₁₀₉	semidirect
229. C₂×SD₁₆	C₂×D₁₀₉	semidirect
236. C₄⋊Q₈	C₂×D₁₀₉	semidirect
251. C₄×C₈	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×#16812728	2
C₂×#16812726	2
C₂×#16812720	2
C₂×SD₁₆×D₁₀₉	2
#20295601	2
#20295589	2
#20295418	2
#20295417	2
#20295413	2
#20295412	2
#20295410	2
#20295407	2
#20295397	2
#20294980	2
#492×C₁₀₉	2
#3154	109