Subgroups — C₁₀₉×#19261 #42137255

Order 27904.

710 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×#3169	C₂	1	1	yes	maximal, characteristic
2	C₁₀₉×#3037	C₂	1	2	yes	maximal, complemented
3	C₂×C₈×Q₈×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₉×#1682	C₂	1	4	yes	maximal, complemented
5	C₁₀₉×#1674	C₂	1	2	yes	maximal, complemented
6	C₁₀₉×#1668	C₂	1	2	yes	maximal, complemented
7	C₁₀₉×#1567	C₂	1	1	yes	maximal, characteristic, complemented
8	C₁₀₉×#1547	C₂	1	2	yes	maximal, complemented
9	C₂×#137×C₁₀₉	—	2	2	no	—
10	#532×C₁₀₉	C₂²	1	2	yes	—
11	C₂×C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
12	#500×C₁₀₉	C₂²	1	1	yes	characteristic
13	#493×C₁₀₉	C₂²	1	1	yes	characteristic
14	#486×C₁₀₉	C₂²	1	2	yes	—
15	#466×C₁₀₉	—	2	1	no	—
16	#466×C₁₀₉	—	2	1	no	—
17	#464×C₁₀₉	—	2	4	no	—
18	#462×C₁₀₉	C₂²	1	4	yes	—
19	#460×C₁₀₉	C₂²	1	4	yes	—
20	C₈×Q₈×C₁₀₉	—	2	1	no	—
21	C₈×Q₈×C₁₀₉	—	2	1	no	—
22	C₈×Q₈×C₁₀₉	C₂²	1	2	yes	—
23	C₈×Q₈×C₁₀₉	C₂²	1	2	yes	—
24	C₄×D₈×C₁₀₉	—	2	1	no	—
25	C₄×D₈×C₁₀₉	—	2	1	no	—
26	#423×C₁₀₉	C₂²	1	2	yes	—
27	C₂×C₄⋊C₈×C₁₀₉	—	2	1	no	—
28	C₂×C₄⋊C₈×C₁₀₉	C₂²	1	1	yes	characteristic
29	#417×C₁₀₉	—	2	2	no	—
30	C₂×C₄×C₈×C₁₀₉	—	2	1	no	—
31	C₂×C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic
32	#335×C₁₀₉	C₂²	1	2	yes	—
33	#335×C₁₀₉	C₂²	1	2	yes	—
34	#332×C₁₀₉	C₂²	1	4	yes	—
35	#331×C₁₀₉	C₂²	1	4	yes	—
36	C₂×#41×C₁₀₉	—	2	2	no	—
37	C₂²×Q₈×C₁₀₉	D₄	1	1	yes	characteristic
38	#137×C₁₀₉	—	4	8	no	—
39	C₂×Q₁₆×C₁₀₉	—	2	4	no	—
40	C₂×SD₁₆×C₁₀₉	—	2	4	no	—
41	C₂×D₈×C₁₀₉	—	2	1	no	—
42	C₂×D₈×C₁₀₉	—	2	1	no	—
43	C₂×M₁₆×C₁₀₉	—	2	2	no	—
44	C₂²×C₈×C₁₀₉	—	2	1	no	—
45	C₂²×C₈×C₁₀₉	D₄	1	1	yes	characteristic
46	C₂²×C₈×C₁₀₉	D₄	1	1	yes	characteristic
47	C₄⋊Q₈×C₁₀₉	C₂³	1	2	yes	—
48	#127×C₁₀₉	C₂³	1	2	yes	—
49	#124×C₁₀₉	—	2	2	no	—
50	#121×C₁₀₉	—	2	2	no	—
51	#121×C₁₀₉	—	2	2	no	—
52	C₄×Q₈×C₁₀₉	—	2	1	no	—
53	C₄×Q₈×C₁₀₉	—	2	1	no	—
54	C₄×Q₈×C₁₀₉	D₄	1	2	yes	—
55	C₄×Q₈×C₁₀₉	C₂³	1	2	yes	—
56	C₄×D₄×C₁₀₉	—	2	2	no	—
57	C₄×D₄×C₁₀₉	—	2	2	no	—
58	C₂×C₄⋊C₄×C₁₀₉	—	2	1	no	—
59	C₂×C₄⋊C₄×C₁₀₉	D₄	1	1	yes	characteristic
60	C₂×C₄²×C₁₀₉	—	2	1	no	—
61	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
62	#107×C₁₀₉	—	2	1	no	—
63	#107×C₁₀₉	—	2	1	no	—
64	C₄⋊C₈×C₁₀₉	—	2	2	no	—
65	C₄⋊C₈×C₁₀₉	—	2	2	no	—
66	C₄⋊C₈×C₁₀₉	—	2	1	no	—
67	C₄⋊C₈×C₁₀₉	—	2	2	no	—
68	C₄⋊C₈×C₁₀₉	C₂³	1	2	yes	—
69	C₄⋊C₈×C₁₀₉	C₂³	1	4	yes	—
70	#103×C₁₀₉	—	2	4	no	—
71	#102×C₁₀₉	—	2	2	no	—
72	#102×C₁₀₉	—	2	2	no	—
73	#102×C₁₀₉	—	2	4	no	—
74	C₄×C₈×C₁₀₉	—	2	2	no	—
75	C₄×C₈×C₁₀₉	—	2	2	no	—
76	C₄×C₈×C₁₀₉	D₄	1	1	yes	characteristic
77	C₄×C₈×C₁₀₉	D₄	1	1	yes	characteristic
78	C₄×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
79	C₄×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
80	#41×C₁₀₉	—	4	4	no	—
81	#41×C₁₀₉	—	4	4	no	—
82	C₂×Q₈×C₁₀₉	—	2	1	no	—
83	C₂×Q₈×C₁₀₉	—	2	2	no	—
84	C₂×Q₈×C₁₀₉	—	2	2	no	—
85	C₂×Q₈×C₁₀₉	D₈	1	4	yes	complemented
86	C₂×Q₈×C₁₀₉	C₂×D₄	1	2	yes	—
87	C₂×D₄×C₁₀₉	—	2	2	no	—
88	C₂×D₄×C₁₀₉	—	2	2	no	—
89	C₂×D₄×C₁₀₉	—	2	2	no	—
90	C₂×D₄×C₁₀₉	—	4	2	no	—
91	C₂²×C₄×C₁₀₉	—	2	1	no	—
92	C₂²×C₄×C₁₀₉	—	2	1	no	—
93	C₂²×C₄×C₁₀₉	—	4	2	no	—
94	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
96	C₂²×C₄×C₁₀₉	#41	1	1	yes	characteristic
97	Q₁₆×C₁₀₉	—	4	8	no	—
98	SD₁₆×C₁₀₉	—	4	8	no	—
99	D₈×C₁₀₉	—	4	2	no	—
100	D₈×C₁₀₉	—	4	2	no	—
101	M₁₆×C₁₀₉	—	4	4	no	—
102	C₂×C₈×C₁₀₉	—	2	2	no	—
103	C₂×C₈×C₁₀₉	—	2	2	no	—
104	C₂×C₈×C₁₀₉	—	2	4	no	—
105	C₂×C₈×C₁₀₉	—	4	1	no	—
106	C₂×C₈×C₁₀₉	—	4	2	no	—
107	C₂×C₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
109	C₂×C₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
110	C₂×C₈×C₁₀₉	C₂×D₄	1	1	yes	characteristic
111	C₄⋊C₄×C₁₀₉	—	2	2	no	—
112	C₄⋊C₄×C₁₀₉	—	2	1	no	—
113	C₄⋊C₄×C₁₀₉	—	2	2	no	—
114	C₄⋊C₄×C₁₀₉	—	2	2	no	—
115	C₄⋊C₄×C₁₀₉	—	2	2	no	—
116	C₄⋊C₄×C₁₀₉	C₂×D₄	1	2	yes	—
117	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
118	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
119	C₄²×C₁₀₉	—	2	2	no	—
120	C₄²×C₁₀₉	—	2	2	no	—
121	C₄²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
122	C₄²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
123	C₄²×C₁₀₉	#41	1	1	yes	characteristic
124	C₄²×C₁₀₉	C₂⁴	1	1	yes	characteristic
125	C₂³×C₁₀₉	—	4	2	no	—
126	C₂³×C₁₀₉	#121	1	1	yes	characteristic
127	Q₈×C₁₀₉	—	2	2	no	—
128	Q₈×C₁₀₉	—	2	4	no	—
129	Q₈×C₁₀₉	—	4	2	no	—
130	Q₈×C₁₀₉	—	4	2	no	—
131	Q₈×C₁₀₉	C₂×D₈	1	4	yes	—
132	D₄×C₁₀₉	—	4	2	no	—
133	D₄×C₁₀₉	—	4	2	no	—
134	D₄×C₁₀₉	—	4	2	no	—
135	D₄×C₁₀₉	—	4	2	no	—
136	D₄×C₁₀₉	—	8	2	no	—
137	D₄×C₁₀₉	—	8	4	no	—
138	C₂×C₄×C₁₀₉	—	2	2	no	—
139	C₂×C₄×C₁₀₉	—	2	4	no	—
140	C₂×C₄×C₁₀₉	—	2	1	no	—
141	C₂×C₄×C₁₀₉	—	2	1	no	—
142	C₂×C₄×C₁₀₉	—	2	2	no	—
143	C₂×C₄×C₁₀₉	—	4	1	no	—
144	C₂×C₄×C₁₀₉	—	4	2	no	—
145	C₂×C₄×C₁₀₉	—	4	2	no	—
146	C₂×C₄×C₁₀₉	—	8	4	no	—
147	C₂×C₄×C₁₀₉	#121	1	1	yes	characteristic
148	C₂×C₄×C₁₀₉	#121	1	1	yes	characteristic
149	C₂×C₄×C₁₀₉	#121	1	1	yes	characteristic
150	C₂×C₄×C₁₀₉	C₂×D₈	1	2	yes	—
151	C₂×C₄×C₁₀₉	#135	1	2	yes	—
152	C₂×C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
153	C₂×C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
154	C₂×C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
155	C₈×C₁₀₉	—	2	1	no	—
156	C₈×C₁₀₉	—	2	1	no	—
157	C₈×C₁₀₉	—	2	1	no	—
158	C₈×C₁₀₉	—	4	4	no	—
159	C₈×C₁₀₉	—	4	2	no	—
160	C₈×C₁₀₉	#137	1	2	yes	complemented
161	C₂²×C₁₀₉	—	2	1	no	—
162	C₂²×C₁₀₉	—	2	1	no	—
163	C₂²×C₁₀₉	—	8	2	no	—
164	C₂²×C₁₀₉	—	8	2	no	—
165	C₂²×C₁₀₉	—	8	2	no	—
166	C₂²×C₁₀₉	#466	1	2	yes	—
167	C₂²×C₁₀₉	C₂×#121	1	1	yes	characteristic
168	C₄×C₁₀₉	—	2	1	no	—
169	C₄×C₁₀₉	—	2	4	no	—
170	C₄×C₁₀₉	—	2	1	no	—
171	C₄×C₁₀₉	—	2	1	no	—
172	C₄×C₁₀₉	—	4	2	no	—
173	C₄×C₁₀₉	—	8	2	no	—
174	C₄×C₁₀₉	#466	1	2	yes	—
175	C₄×C₁₀₉	C₂²×D₈	1	1	yes	characteristic
176	C₄×C₁₀₉	C₂×#135	1	1	yes	characteristic
177	C₄×C₁₀₉	C₂×#137	1	1	yes	characteristic
178	C₄×C₁₀₉	#575	1	1	yes	characteristic
179	#19261	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
180	C₂×C₁₀₉	—	2	2	no	—
181	C₂×C₁₀₉	—	16	2	no	—
182	C₂×C₁₀₉	#3037	1	1	yes	characteristic
183	C₂×C₁₀₉	C₂×#466	1	1	yes	characteristic
184	C₂×C₁₀₉	#3067	1	1	yes	characteristic
185	#3169	C₂×C₁₀₉	1	1	yes	characteristic
186	#3037	C₂×C₁₀₉	1	2	yes	complemented
187	C₂×C₈×Q₈	C₂×C₁₀₉	1	1	yes	characteristic, complemented
188	#1682	C₂×C₁₀₉	1	4	yes	complemented
189	#1674	C₂×C₁₀₉	1	2	yes	complemented
190	#1668	C₂×C₁₀₉	1	2	yes	complemented
191	#1567	C₂×C₁₀₉	1	1	yes	characteristic, complemented
192	#1547	C₂×C₁₀₉	1	2	yes	complemented
193	C₁₀₉	#19261	1	1	yes	characteristic, direct product factor, Sylow
194	C₂×#137	—	2	2	no	—
195	#532	C₂²×C₁₀₉	1	2	yes	—
196	C₂×C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
197	#500	C₂²×C₁₀₉	1	1	yes	characteristic
198	#493	C₂²×C₁₀₉	1	1	yes	characteristic
199	#486	C₂²×C₁₀₉	1	2	yes	—
200	#466	—	2	1	no	—
201	#466	—	2	1	no	—
202	#464	—	2	4	no	—
203	#462	C₂²×C₁₀₉	1	4	yes	—
204	#460	C₂²×C₁₀₉	1	4	yes	—
205	C₈×Q₈	—	2	1	no	—
206	C₈×Q₈	—	2	1	no	—
207	C₈×Q₈	C₂²×C₁₀₉	1	2	yes	—
208	C₈×Q₈	C₂²×C₁₀₉	1	2	yes	—
209	C₄×D₈	—	2	1	no	—
210	C₄×D₈	—	2	1	no	—
211	#423	C₂²×C₁₀₉	1	2	yes	—
212	C₂×C₄⋊C₈	—	2	1	no	—
213	C₂×C₄⋊C₈	C₂²×C₁₀₉	1	1	yes	characteristic
214	#417	—	2	2	no	—
215	C₂×C₄×C₈	—	2	1	no	—
216	C₂×C₄×C₈	C₂²×C₁₀₉	1	1	yes	characteristic
217	#335	C₂²×C₁₀₉	1	2	yes	—
218	#335	C₂²×C₁₀₉	1	2	yes	—
219	#332	C₂²×C₁₀₉	1	4	yes	—
220	#331	C₂²×C₁₀₉	1	4	yes	—
221	C₂×#41	—	2	2	no	—
222	C₂²×Q₈	D₄×C₁₀₉	1	1	yes	characteristic
223	#137	—	4	8	no	—
224	C₂×Q₁₆	—	2	4	no	—
225	C₂×SD₁₆	—	2	4	no	—
226	C₂×D₈	—	2	1	no	—
227	C₂×D₈	—	2	1	no	—
228	C₂×M₁₆	—	2	2	no	—
229	C₂²×C₈	—	2	1	no	—
230	C₂²×C₈	D₄×C₁₀₉	1	1	yes	characteristic
231	C₂²×C₈	D₄×C₁₀₉	1	1	yes	characteristic
232	C₄⋊Q₈	C₂³×C₁₀₉	1	2	yes	—
233	#127	C₂³×C₁₀₉	1	2	yes	—
234	#124	—	2	2	no	—
235	#121	—	2	2	no	—
236	#121	—	2	2	no	—
237	C₄×Q₈	—	2	1	no	—
238	C₄×Q₈	—	2	1	no	—
239	C₄×Q₈	D₄×C₁₀₉	1	2	yes	—
240	C₄×Q₈	C₂³×C₁₀₉	1	2	yes	—
241	C₄×D₄	—	2	2	no	—
242	C₄×D₄	—	2	2	no	—
243	C₂×C₄⋊C₄	—	2	1	no	—
244	C₂×C₄⋊C₄	D₄×C₁₀₉	1	1	yes	characteristic
245	C₂×C₄²	—	2	1	no	—
246	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
247	#107	—	2	1	no	—
248	#107	—	2	1	no	—
249	C₄⋊C₈	—	2	2	no	—
250	C₄⋊C₈	—	2	2	no	—
251	C₄⋊C₈	—	2	1	no	—
252	C₄⋊C₈	—	2	2	no	—
253	C₄⋊C₈	C₂³×C₁₀₉	1	2	yes	—
254	C₄⋊C₈	C₂³×C₁₀₉	1	4	yes	—
255	#103	—	2	4	no	—
256	#102	—	2	2	no	—
257	#102	—	2	2	no	—
258	#102	—	2	4	no	—
259	C₄×C₈	—	2	2	no	—
260	C₄×C₈	—	2	2	no	—
261	C₄×C₈	D₄×C₁₀₉	1	1	yes	characteristic
262	C₄×C₈	D₄×C₁₀₉	1	1	yes	characteristic
263	C₄×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
264	C₄×C₈	C₂³×C₁₀₉	1	1	yes	characteristic
265	#41	—	4	4	no	—
266	#41	—	4	4	no	—
267	C₂×Q₈	—	2	1	no	—
268	C₂×Q₈	—	2	2	no	—
269	C₂×Q₈	—	2	2	no	—
270	C₂×Q₈	D₈×C₁₀₉	1	4	yes	complemented
271	C₂×Q₈	C₂×D₄×C₁₀₉	1	2	yes	—
272	C₂×D₄	—	2	2	no	—
273	C₂×D₄	—	2	2	no	—
274	C₂×D₄	—	2	2	no	—
275	C₂×D₄	—	4	2	no	—
276	C₂²×C₄	—	2	1	no	—
277	C₂²×C₄	—	2	1	no	—
278	C₂²×C₄	—	4	2	no	—
279	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
280	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
281	C₂²×C₄	#41×C₁₀₉	1	1	yes	characteristic
282	Q₁₆	—	4	8	no	—
283	SD₁₆	—	4	8	no	—
284	D₈	—	4	2	no	—
285	D₈	—	4	2	no	—
286	M₁₆	—	4	4	no	—
287	C₂×C₈	—	2	2	no	—
288	C₂×C₈	—	2	2	no	—
289	C₂×C₈	—	2	4	no	—
290	C₂×C₈	—	4	1	no	—
291	C₂×C₈	—	4	2	no	—
292	C₂×C₈	C₂×D₄×C₁₀₉	1	1	yes	characteristic
293	C₂×C₈	C₂×D₄×C₁₀₉	1	1	yes	characteristic
294	C₂×C₈	C₂×D₄×C₁₀₉	1	1	yes	characteristic
295	C₂×C₈	C₂×D₄×C₁₀₉	1	1	yes	characteristic
296	C₄⋊C₄	—	2	2	no	—
297	C₄⋊C₄	—	2	1	no	—
298	C₄⋊C₄	—	2	2	no	—
299	C₄⋊C₄	—	2	2	no	—
300	C₄⋊C₄	—	2	2	no	—
301	C₄⋊C₄	C₂×D₄×C₁₀₉	1	2	yes	—
302	C₂²⋊C₄	—	4	2	no	—
303	C₂²⋊C₄	—	4	2	no	—
304	C₄²	—	2	2	no	—
305	C₄²	—	2	2	no	—
306	C₄²	C₂×D₄×C₁₀₉	1	1	yes	characteristic
307	C₄²	C₂×D₄×C₁₀₉	1	1	yes	characteristic
308	C₄²	#41×C₁₀₉	1	1	yes	characteristic
309	C₄²	C₂⁴×C₁₀₉	1	1	yes	characteristic
310	C₂³	—	4	2	no	—
311	C₂³	#121×C₁₀₉	1	1	yes	characteristic
312	Q₈	—	2	2	no	—
313	Q₈	—	2	4	no	—
314	Q₈	—	4	2	no	—
315	Q₈	—	4	2	no	—
316	Q₈	C₂×D₈×C₁₀₉	1	4	yes	—
317	D₄	—	4	2	no	—
318	D₄	—	4	2	no	—
319	D₄	—	4	2	no	—
320	D₄	—	4	2	no	—
321	D₄	—	8	2	no	—
322	D₄	—	8	4	no	—
323	C₂×C₄	—	2	2	no	—
324	C₂×C₄	—	2	4	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	2	1	no	—
327	C₂×C₄	—	2	2	no	—
328	C₂×C₄	—	4	1	no	—
329	C₂×C₄	—	4	2	no	—
330	C₂×C₄	—	4	2	no	—
331	C₂×C₄	—	8	4	no	—
332	C₂×C₄	#121×C₁₀₉	1	1	yes	characteristic
333	C₂×C₄	#121×C₁₀₉	1	1	yes	characteristic
334	C₂×C₄	#121×C₁₀₉	1	1	yes	characteristic
335	C₂×C₄	C₂×D₈×C₁₀₉	1	2	yes	—
336	C₂×C₄	#135×C₁₀₉	1	2	yes	—
337	C₂×C₄	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
338	C₂×C₄	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
339	C₂×C₄	C₂×#41×C₁₀₉	1	1	yes	characteristic
340	C₈	—	2	1	no	—
341	C₈	—	2	1	no	—
342	C₈	—	2	1	no	—
343	C₈	—	4	4	no	—
344	C₈	—	4	2	no	—
345	C₈	#137×C₁₀₉	1	2	yes	complemented
346	C₂²	—	2	1	no	—
347	C₂²	—	2	1	no	—
348	C₂²	—	8	2	no	—
349	C₂²	—	8	2	no	—
350	C₂²	—	8	2	no	—
351	C₂²	#466×C₁₀₉	1	2	yes	—
352	C₂²	C₂×#121×C₁₀₉	1	1	yes	characteristic
353	C₄	—	2	1	no	—
354	C₄	—	2	4	no	—
355	C₄	—	2	1	no	—
356	C₄	—	2	1	no	—
357	C₄	—	4	2	no	—
358	C₄	—	8	2	no	—
359	C₄	#466×C₁₀₉	1	2	yes	—
360	C₄	C₂²×D₈×C₁₀₉	1	1	yes	characteristic
361	C₄	C₂×#135×C₁₀₉	1	1	yes	characteristic
362	C₄	C₂×#137×C₁₀₉	1	1	yes	characteristic
363	C₄	#575×C₁₀₉	1	1	yes	characteristic
364	C₂	—	2	2	no	—
365	C₂	—	16	2	no	—
366	C₂	C₁₀₉×#3037	1	1	yes	characteristic
367	C₂	C₂×#466×C₁₀₉	1	1	yes	characteristic
368	C₂	C₁₀₉×#3067	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₉	C₂×#121
commutator, Frattini, cosocle	C₄²	C₂⁴×C₁₀₉
prime radical	C₁₀₉×#3169	C₂
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ C₂×C₄²×C₁₀₉ ◁ G

Complements

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

N	H ≅ G/N	type
2. C₁₀₉×#3037	C₂	semidirect
3. C₂×C₈×Q₈×C₁₀₉	C₂	semidirect
4. C₁₀₉×#1682	C₂	semidirect
5. C₁₀₉×#1674	C₂	semidirect
6. C₁₀₉×#1668	C₂	semidirect
7. C₁₀₉×#1567	C₂	semidirect
8. C₁₀₉×#1547	C₂	semidirect
85. C₂×Q₈×C₁₀₉	D₈	semidirect
160. C₈×C₁₀₉	#137	semidirect
179. #19261	C₁₀₉	direct (N × H)
186. #3037	C₂×C₁₀₉	semidirect
187. C₂×C₈×Q₈	C₂×C₁₀₉	semidirect
188. #1682	C₂×C₁₀₉	semidirect
189. #1674	C₂×C₁₀₉	semidirect
190. #1668	C₂×C₁₀₉	semidirect
191. #1567	C₂×C₁₀₉	semidirect
192. #1547	C₂×C₁₀₉	semidirect
193. C₁₀₉	#19261	direct (N × H)
270. C₂×Q₈	D₈×C₁₀₉	semidirect
345. C₈	#137×C₁₀₉	semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroup	index
C₁₀₉×#3169	2
C₁₀₉×#3037	2
C₂×C₈×Q₈×C₁₀₉	2
C₁₀₉×#1682	2
C₁₀₉×#1674	2
C₁₀₉×#1668	2
C₁₀₉×#1567	2
C₁₀₉×#1547	2
#19261	109

Subgroups — C109×#19261 #42137255

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#19261 #42137255