Subgroups — #556×D₁₀₉ #28376574

Order 13952.

1112 conjugacy classes of subgroups.

The subgroup lattice has 448 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295750	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295749	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295748	C₂	1	2	yes	maximal, complemented
4	#20295747	C₂	1	2	yes	maximal, complemented
5	#20295746	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295745	C₂	1	2	yes	maximal, complemented
7	#20295744	C₂	1	2	yes	maximal, complemented
8	#20295743	C₂	1	4	yes	maximal, complemented
9	C₄⋊Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#126×D₁₀₉	C₂	1	4	yes	maximal, complemented
11	#124×D₁₀₉	C₂	1	2	yes	maximal
12	C₂²⋊Q₈×D₁₀₉	C₂	1	2	yes	maximal, complemented
13	C₄×Q₈×D₁₀₉	C₂	1	2	yes	maximal, complemented
14	C₄×Q₈×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic
16	#117×D₁₀₉	C₂	1	2	yes	maximal, complemented
17	#556×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
18	C₂×Q₈×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂×Q₈×D₁₀₉	C₂²	1	2	yes	—
20	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
21	C₂²×C₄×D₁₀₉	C₂²	1	2	yes	—
22	#16812699	C₂²	1	1	yes	characteristic, complemented
23	#16812698	C₂²	1	2	yes	complemented
24	#16812698	C₂²	1	2	yes	complemented
25	#16812697	C₂²	1	2	yes	complemented
26	#16812694	C₂²	1	4	yes	complemented
27	#16812694	C₂²	1	4	yes	complemented
28	#16812694	C₂²	1	4	yes	complemented
29	#16812693	C₂²	1	4	yes	complemented
30	#16812692	C₂²	1	4	yes	complemented
31	#16812692	C₂²	1	4	yes	complemented
32	#16812692	C₂²	1	4	yes	complemented
33	#16812688	C₂²	1	2	yes	—
34	#16812687	C₂²	1	2	yes	—
35	#16812686	C₂²	1	2	yes	—
36	#16812685	C₂²	1	4	yes	—
37	#16812685	C₂²	1	4	yes	—
38	#16812679	C₂²	1	2	yes	complemented
39	#16812678	C₂²	1	2	yes	complemented
40	#16812677	C₂²	1	4	yes	complemented
41	#16812676	C₂²	1	4	yes	complemented
42	#16812675	C₂²	1	2	yes	complemented
43	Q₈×Dic₁₀₉	C₂²	1	2	yes	complemented
44	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
45	C₄×Dic₂₁₈	C₂²	1	4	yes	complemented
46	C₄×Dic₂₁₈	C₂²	1	2	yes	complemented
47	C₄×Dic₂₁₈	C₂²	1	2	yes	complemented
48	C₄×Dic₂₁₈	C₂²	1	1	yes	characteristic, complemented
49	#16812664	C₂²	1	2	yes	complemented
50	#16812664	C₂²	1	4	yes	complemented
51	#16812664	C₂²	1	1	yes	characteristic, complemented
52	#16812664	C₂²	1	2	yes	complemented
53	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
54	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
55	#16812661	C₂²	1	1	yes	characteristic
56	C₄×C₂²⋊D₁₀₉	C₂²	1	2	yes	—
57	#16812659	C₂²	1	2	yes	—
58	#16812658	C₂²	1	2	yes	complemented
59	#16812657	C₂²	1	2	yes	complemented
60	#16812657	C₂²	1	2	yes	complemented
61	#16812656	C₂²	1	4	yes	complemented
62	#16812655	C₂²	1	4	yes	complemented
63	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
64	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
65	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
66	C₄⋊C₄×D₁₀₉	C₂²	1	4	yes	—
67	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
68	C₄⋊C₄×D₁₀₉	C₂²	1	2	yes	—
69	C₂²⋊C₄×D₁₀₉	C₂²	1	4	yes	—
70	C₂²⋊C₄×D₁₀₉	C₂²	1	2	yes	—
71	C₂²⋊C₄×D₁₀₉	C₂²	1	4	yes	—
72	C₄²×D₁₀₉	C₂²	1	4	yes	—
73	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
74	C₄²×D₁₀₉	C₂²	1	2	yes	—
75	C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
76	#126×C₁₀₉	C₂²	1	4	yes	complemented
77	#124×C₁₀₉	C₂²	1	2	yes	—
78	C₂²⋊Q₈×C₁₀₉	C₂²	1	2	yes	complemented
79	C₄×Q₈×C₁₀₉	C₂²	1	2	yes	complemented
80	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
81	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
82	#117×C₁₀₉	C₂²	1	2	yes	complemented
83	C₂³×D₁₀₉	C₂³	1	2	yes	—
84	C₂×Dic₂₁₈	C₂³	1	2	yes	—
85	C₂×Dic₂₁₈	C₂³	1	1	yes	characteristic
86	C₂×Dic₂₁₈	C₂³	1	4	yes	—
87	C₂×Dic₂₁₈	C₂³	1	2	yes	—
88	Q₈×D₁₀₉	—	2	4	no	—
89	Q₈×D₁₀₉	—	2	8	no	—
90	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
91	C₂×C₂²⋊D₁₀₉	C₂³	1	2	yes	—
92	D₄×D₁₀₉	—	2	4	no	—
93	C₂²×Dic₁₀₉	C₂³	1	2	yes	—
94	C₂×C₄×D₁₀₉	—	2	8	no	—
95	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
96	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
97	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
98	C₂×C₄×D₁₀₉	C₂³	1	4	yes	—
99	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
100	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
101	C₂×C₄×D₁₀₉	C₂³	1	2	yes	—
102	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
103	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
104	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
105	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
106	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
107	C₄⋊Dic₁₀₉	C₂³	1	4	yes	—
108	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
109	C₄⋊Dic₁₀₉	C₂³	1	2	yes	—
110	#13182008	C₂³	1	2	yes	—
111	#13182008	C₂³	1	4	yes	—
112	#13182008	C₂³	1	2	yes	—
113	#13182008	C₂³	1	4	yes	—
114	#13182008	C₂³	1	4	yes	—
115	#13182008	C₂³	1	2	yes	—
116	#13182008	C₂³	1	2	yes	—
117	#13182008	C₂³	1	4	yes	—
118	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
119	C₂²⋊Dic₁₀₉	C₂³	1	2	yes	—
120	C₂²⋊Dic₁₀₉	C₂³	1	4	yes	—
121	#13182006	C₂³	1	4	yes	—
122	#13182006	C₂³	1	4	yes	—
123	#13182006	C₂³	1	2	yes	—
124	#13182006	C₂³	1	2	yes	—
125	#13182006	C₂³	1	4	yes	—
126	#13182006	C₂³	1	4	yes	—
127	C₄×Dic₁₀₉	C₂³	1	4	yes	—
128	C₄×Dic₁₀₉	C₂³	1	4	yes	—
129	C₄×Dic₁₀₉	C₂³	1	4	yes	—
130	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
131	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
132	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
133	C₄×Dic₁₀₉	C₂³	1	2	yes	—
134	C₄×Dic₁₀₉	C₂³	1	2	yes	—
135	C₄×Dic₁₀₉	C₂³	1	2	yes	—
136	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
137	C₂×Q₈×C₁₀₉	C₂³	1	2	yes	—
138	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
139	C₂²×C₄×C₁₀₉	C₂³	1	2	yes	—
140	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
141	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
142	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
143	C₄⋊C₄×C₁₀₉	C₂³	1	4	yes	—
144	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
145	C₄⋊C₄×C₁₀₉	C₂³	1	2	yes	—
146	C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
147	C₂²⋊C₄×C₁₀₉	C₂³	1	2	yes	—
148	C₂²⋊C₄×C₁₀₉	C₂³	1	4	yes	—
149	C₄²×C₁₀₉	C₂³	1	4	yes	—
150	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
151	C₄²×C₁₀₉	C₂³	1	2	yes	—
152	C₂³×C₁₀₉	C₂⁴	1	2	yes	—
153	C₂²×D₁₀₉	—	2	4	no	—
154	C₂²×D₁₀₉	—	2	4	no	—
155	C₂²×D₁₀₉	—	2	4	no	—
156	C₂²×D₁₀₉	C₂⁴	1	2	yes	—
157	C₂²×D₁₀₉	C₂⁴	1	1	yes	characteristic
158	Q₈×C₁₀₉	—	2	4	no	—
159	Q₈×C₁₀₉	—	2	2	no	—
160	D₄×C₁₀₉	—	2	2	no	—
161	C₂×C₄×C₁₀₉	—	2	4	no	—
162	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
163	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
164	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
165	C₂×C₄×C₁₀₉	C₂⁴	1	4	yes	—
166	C₂×C₄×C₁₀₉	C₂⁴	1	2	yes	—
167	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
168	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
169	C₂²⋊D₁₀₉	—	2	4	no	—
170	C₂×Dic₁₀₉	—	2	4	no	—
171	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
172	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
173	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
174	C₂×Dic₁₀₉	C₂⁴	1	4	yes	—
175	C₂×Dic₁₀₉	C₂⁴	1	2	yes	—
176	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
177	C₂×Dic₁₀₉	C₂⁴	1	1	yes	characteristic
178	D₄₃₆	—	2	2	no	—
179	C₄×D₁₀₉	—	2	4	no	—
180	C₄×D₁₀₉	—	2	4	no	—
181	C₄×D₁₀₉	—	2	8	no	—
182	C₄×D₁₀₉	—	2	4	no	—
183	C₄×D₁₀₉	—	2	2	no	—
184	C₄×D₁₀₉	—	2	4	no	—
185	C₄×D₁₀₉	—	2	4	no	—
186	C₄×D₁₀₉	#41	1	4	yes	—
187	C₄×D₁₀₉	#41	1	4	yes	—
188	Dic₂₁₈	—	2	4	no	—
189	Dic₂₁₈	—	2	2	no	—
190	Dic₂₁₈	—	2	8	no	—
191	Dic₂₁₈	—	2	4	no	—
192	C₂²×C₁₀₉	—	2	2	no	—
193	C₂²×C₁₀₉	—	2	2	no	—
194	C₂²×C₁₀₉	—	2	2	no	—
195	C₂²×C₁₀₉	C₂⁵	1	1	yes	characteristic
196	C₂×D₁₀₉	—	2	2	no	—
197	C₂×D₁₀₉	—	2	2	no	—
198	C₂×D₁₀₉	—	2	2	no	—
199	C₂×D₁₀₉	—	4	8	no	—
200	C₂×D₁₀₉	C₂×#41	1	2	yes	—
201	C₂×D₁₀₉	C₂×#41	1	2	yes	—
202	C₂×D₁₀₉	2₋¹⁺⁴	1	2	yes	—
203	C₄×C₁₀₉	—	2	4	no	—
204	C₄×C₁₀₉	—	2	2	no	—
205	C₄×C₁₀₉	—	2	2	no	—
206	C₄×C₁₀₉	—	2	2	no	—
207	C₄×C₁₀₉	—	2	1	no	—
208	C₄×C₁₀₉	C₂×#41	1	2	yes	—
209	C₄×C₁₀₉	C₂×#41	1	2	yes	—
210	Dic₁₀₉	—	2	4	no	—
211	Dic₁₀₉	—	2	2	no	—
212	Dic₁₀₉	—	2	2	no	—
213	Dic₁₀₉	—	2	2	no	—
214	Dic₁₀₉	—	2	1	no	—
215	Dic₁₀₉	C₂×#41	1	2	yes	—
216	Dic₁₀₉	C₂×#41	1	2	yes	—
217	C₂×C₁₀₉	—	4	2	no	—
218	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
219	C₂×C₁₀₉	C₂²×#41	1	1	yes	characteristic
220	C₂×C₁₀₉	C₂×2₋¹⁺⁴	1	1	yes	characteristic
221	D₁₀₉	—	4	2	no	—
222	D₁₀₉	#556	1	4	yes	direct product factor
223	C₂×#556	—	109	1	no	maximal, Sylow
224	C₁₀₉	C₂×#556	1	1	yes	characteristic, complemented, Sylow
225	#556	—	109	1	no	—
226	#556	—	109	4	no	—
227	#556	—	109	2	no	—
228	#556	—	109	2	no	—
229	#556	—	109	2	no	—
230	#556	—	109	1	no	—
231	#556	—	109	1	no	—
232	#556	—	109	2	no	—
233	#556	D₁₀₉	1	1	yes	characteristic, direct product factor
234	C₂×C₄⋊Q₈	—	109	1	no	—
235	C₂×#126	—	109	4	no	—
236	C₂×#124	—	109	2	no	—
237	C₂×C₂²⋊Q₈	—	109	2	no	—
238	C₂×C₄×Q₈	—	109	2	no	—
239	C₂×C₄×Q₈	—	109	1	no	—
240	C₂×C₄×D₄	—	109	1	no	—
241	C₂×#117	—	109	2	no	—
242	C₂²×Q₈	—	109	1	no	—
243	C₂²×Q₈	—	109	2	no	—
244	C₂²×D₄	—	109	1	no	—
245	C₂³×C₄	—	109	2	no	—
246	C₄⋊Q₈	—	109	2	no	—
247	C₄⋊Q₈	—	109	2	no	—
248	C₄⋊Q₈	—	109	2	no	—
249	C₄⋊Q₈	—	109	1	no	—
250	C₄⋊Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
251	#126	—	109	4	no	—
252	#126	—	109	4	no	—
253	#126	—	109	4	no	—
254	#126	—	109	4	no	—
255	#126	—	109	4	no	—
256	#126	—	109	4	no	—
257	#126	—	109	4	no	—
258	#126	C₂×D₁₀₉	1	4	yes	complemented
259	#124	—	109	2	no	—
260	#124	—	109	2	no	—
261	#124	—	109	4	no	—
262	#124	—	109	4	no	—
263	#124	—	109	2	no	—
264	#124	C₂×D₁₀₉	1	2	yes	—
265	C₂²⋊Q₈	—	109	2	no	—
266	C₂²⋊Q₈	—	109	2	no	—
267	C₂²⋊Q₈	—	109	4	no	—
268	C₂²⋊Q₈	—	109	2	no	—
269	C₂²⋊Q₈	—	109	4	no	—
270	C₂²⋊Q₈	C₂×D₁₀₉	1	2	yes	complemented
271	C₄×Q₈	—	109	2	no	—
272	C₄×Q₈	—	109	1	no	—
273	C₄×Q₈	—	109	4	no	—
274	C₄×Q₈	—	109	2	no	—
275	C₄×Q₈	—	109	2	no	—
276	C₄×Q₈	—	109	1	no	—
277	C₄×Q₈	—	109	2	no	—
278	C₄×Q₈	—	109	4	no	—
279	C₄×Q₈	—	109	2	no	—
280	C₄×Q₈	—	109	1	no	—
281	C₄×Q₈	C₂×D₁₀₉	1	2	yes	complemented
282	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
283	C₄×D₄	—	109	1	no	—
284	C₄×D₄	—	109	2	no	—
285	C₄×D₄	—	109	1	no	—
286	C₄×D₄	—	109	2	no	—
287	C₄×D₄	—	109	1	no	—
288	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
289	#117	—	109	2	no	—
290	#117	—	109	2	no	—
291	#117	—	109	2	no	—
292	#117	—	109	4	no	—
293	#117	—	109	4	no	—
294	#117	C₂×D₁₀₉	1	2	yes	complemented
295	C₂×C₄⋊C₄	—	109	1	no	—
296	C₂×C₄⋊C₄	—	109	2	no	—
297	C₂×C₄⋊C₄	—	109	1	no	—
298	C₂×C₄⋊C₄	—	109	4	no	—
299	C₂×C₄⋊C₄	—	109	2	no	—
300	C₂×C₄⋊C₄	—	109	2	no	—
301	C₂×C₂²⋊C₄	—	109	4	no	—
302	C₂×C₂²⋊C₄	—	109	2	no	—
303	C₂×C₂²⋊C₄	—	109	4	no	—
304	C₂×C₄²	—	109	4	no	—
305	C₂×C₄²	—	109	1	no	—
306	C₂×C₄²	—	109	2	no	—
307	C₂⁴	—	109	2	no	—
308	C₂×Q₈	—	109	2	no	—
309	C₂×Q₈	—	109	1	no	—
310	C₂×Q₈	—	109	4	no	—
311	C₂×Q₈	—	109	2	no	—
312	C₂×Q₈	—	218	4	no	—
313	C₂×Q₈	—	218	8	no	—
314	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
315	C₂×Q₈	C₂²×D₁₀₉	1	2	yes	—
316	C₂×D₄	—	109	2	no	—
317	C₂×D₄	—	109	1	no	—
318	C₂×D₄	—	218	4	no	—
319	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
320	C₂²×C₄	—	109	1	no	—
321	C₂²×C₄	—	109	1	no	—
322	C₂²×C₄	—	109	2	no	—
323	C₂²×C₄	—	109	2	no	—
324	C₂²×C₄	—	109	2	no	—
325	C₂²×C₄	—	109	1	no	—
326	C₂²×C₄	—	109	4	no	—
327	C₂²×C₄	—	109	2	no	—
328	C₂²×C₄	—	109	2	no	—
329	C₂²×C₄	—	109	2	no	—
330	C₂²×C₄	—	218	8	no	—
331	C₂²×C₄	C₂²×D₁₀₉	1	2	yes	—
332	C₄⋊C₄	—	109	2	no	—
333	C₄⋊C₄	—	109	4	no	—
334	C₄⋊C₄	—	109	2	no	—
335	C₄⋊C₄	—	109	4	no	—
336	C₄⋊C₄	—	109	4	no	—
337	C₄⋊C₄	—	109	2	no	—
338	C₄⋊C₄	—	109	2	no	—
339	C₄⋊C₄	—	109	4	no	—
340	C₄⋊C₄	—	109	1	no	—
341	C₄⋊C₄	—	109	2	no	—
342	C₄⋊C₄	—	109	1	no	—
343	C₄⋊C₄	—	109	4	no	—
344	C₄⋊C₄	—	109	2	no	—
345	C₄⋊C₄	—	109	2	no	—
346	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
347	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
348	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
349	C₄⋊C₄	C₂²×D₁₀₉	1	4	yes	—
350	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
351	C₄⋊C₄	C₂²×D₁₀₉	1	2	yes	—
352	C₂²⋊C₄	—	109	4	no	—
353	C₂²⋊C₄	—	109	2	no	—
354	C₂²⋊C₄	—	109	4	no	—
355	C₂²⋊C₄	—	109	4	no	—
356	C₂²⋊C₄	—	109	4	no	—
357	C₂²⋊C₄	—	109	2	no	—
358	C₂²⋊C₄	—	109	2	no	—
359	C₂²⋊C₄	—	109	4	no	—
360	C₂²⋊C₄	—	109	4	no	—
361	C₂²⋊C₄	C₂²×D₁₀₉	1	4	yes	—
362	C₂²⋊C₄	C₂²×D₁₀₉	1	2	yes	—
363	C₂²⋊C₄	C₂²×D₁₀₉	1	4	yes	—
364	C₄²	—	109	4	no	—
365	C₄²	—	109	4	no	—
366	C₄²	—	109	4	no	—
367	C₄²	—	109	1	no	—
368	C₄²	—	109	1	no	—
369	C₄²	—	109	1	no	—
370	C₄²	—	109	2	no	—
371	C₄²	—	109	2	no	—
372	C₄²	—	109	2	no	—
373	C₄²	C₂²×D₁₀₉	1	4	yes	—
374	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
375	C₄²	C₂²×D₁₀₉	1	2	yes	—
376	C₂³	—	109	1	no	—
377	C₂³	—	109	2	no	—
378	C₂³	—	218	4	no	—
379	C₂³	—	218	4	no	—
380	C₂³	—	218	4	no	—
381	C₂³	C₂³×D₁₀₉	1	2	yes	—
382	Q₈	—	2	2	no	—
383	Q₈	—	2	4	no	—
384	Q₈	—	218	4	no	—
385	Q₈	—	218	8	no	—
386	Q₈	—	218	2	no	—
387	Q₈	—	218	4	no	—
388	D₄	—	2	2	no	—
389	D₄	—	218	4	no	—
390	D₄	—	218	2	no	—
391	C₂×C₄	—	2	4	no	—
392	C₂×C₄	—	109	1	no	—
393	C₂×C₄	—	109	1	no	—
394	C₂×C₄	—	109	4	no	—
395	C₂×C₄	—	109	4	no	—
396	C₂×C₄	—	109	2	no	—
397	C₂×C₄	—	109	2	no	—
398	C₂×C₄	—	109	1	no	—
399	C₂×C₄	—	109	4	no	—
400	C₂×C₄	—	109	2	no	—
401	C₂×C₄	—	218	4	no	—
402	C₂×C₄	—	218	4	no	—
403	C₂×C₄	—	218	4	no	—
404	C₂×C₄	—	218	8	no	—
405	C₂×C₄	—	218	4	no	—
406	C₂×C₄	—	218	2	no	—
407	C₂×C₄	—	218	4	no	—
408	C₂×C₄	—	218	4	no	—
409	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
410	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
411	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
412	C₂×C₄	C₂³×D₁₀₉	1	4	yes	—
413	C₂×C₄	C₂³×D₁₀₉	1	2	yes	—
414	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
415	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
416	C₂²	—	2	2	no	—
417	C₂²	—	2	2	no	—
418	C₂²	—	2	2	no	—
419	C₂²	—	109	2	no	—
420	C₂²	—	109	2	no	—
421	C₂²	—	109	2	no	—
422	C₂²	—	436	8	no	—
423	C₂²	—	218	2	no	—
424	C₂²	—	218	2	no	—
425	C₂²	—	218	2	no	—
426	C₂²	C₂⁴×D₁₀₉	1	1	yes	characteristic
427	C₄	—	2	2	no	—
428	C₄	—	2	2	no	—
429	C₄	—	2	4	no	—
430	C₄	—	2	2	no	—
431	C₄	—	2	1	no	—
432	C₄	—	109	2	no	—
433	C₄	—	109	2	no	—
434	C₄	—	218	2	no	—
435	C₄	—	218	2	no	—
436	C₄	—	218	4	no	—
437	C₄	—	218	2	no	—
438	C₄	—	218	1	no	—
439	C₄	#41×D₁₀₉	1	2	yes	—
440	C₄	#41×D₁₀₉	1	2	yes	—
441	C₂	—	4	2	no	—
442	C₂	—	109	4	no	—
443	C₂	—	436	2	no	—
444	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
445	C₂	C₂×#41×D₁₀₉	1	1	yes	characteristic
446	C₂	2₋¹⁺⁴×D₁₀₉	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂²	C₂⁴×D₁₀₉
commutator, socle, cosocle	C₂²×C₁₀₉	C₂⁵
Fitting	#556×C₁₀₉	C₂
prime radical	C₂×D₄×D₁₀₉	C₂²
hypercenter	#556	D₁₀₉
hypocenter	C₁₀₉	C₂×#556
LCS	G ▷ C₂²×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ #556

Complements

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

N	H ≅ G/N	type
1. #20295750	C₂	semidirect
2. #20295749	C₂	semidirect
3. #20295748	C₂	semidirect
4. #20295747	C₂	semidirect
5. #20295746	C₂	semidirect
6. #20295745	C₂	semidirect
7. #20295744	C₂	semidirect
8. #20295743	C₂	semidirect
9. C₄⋊Q₈×D₁₀₉	C₂	semidirect
10. #126×D₁₀₉	C₂	semidirect
12. C₂²⋊Q₈×D₁₀₉	C₂	semidirect
13. C₄×Q₈×D₁₀₉	C₂	semidirect
14. C₄×Q₈×D₁₀₉	C₂	semidirect
16. #117×D₁₀₉	C₂	semidirect
17. #556×C₁₀₉	C₂	semidirect
22. #16812699	C₂²	semidirect
23. #16812698	C₂²	semidirect
24. #16812698	C₂²	semidirect
25. #16812697	C₂²	semidirect
26. #16812694	C₂²	semidirect
27. #16812694	C₂²	semidirect
28. #16812694	C₂²	semidirect
29. #16812693	C₂²	semidirect
30. #16812692	C₂²	semidirect
31. #16812692	C₂²	semidirect
32. #16812692	C₂²	semidirect
38. #16812679	C₂²	semidirect
39. #16812678	C₂²	semidirect
40. #16812677	C₂²	semidirect
41. #16812676	C₂²	semidirect
42. #16812675	C₂²	semidirect
43. Q₈×Dic₁₀₉	C₂²	semidirect
44. Q₈×Dic₁₀₉	C₂²	semidirect
45. C₄×Dic₂₁₈	C₂²	semidirect
46. C₄×Dic₂₁₈	C₂²	semidirect
47. C₄×Dic₂₁₈	C₂²	semidirect
48. C₄×Dic₂₁₈	C₂²	semidirect
49. #16812664	C₂²	semidirect
50. #16812664	C₂²	semidirect
51. #16812664	C₂²	semidirect
52. #16812664	C₂²	semidirect
58. #16812658	C₂²	semidirect
59. #16812657	C₂²	semidirect
60. #16812657	C₂²	semidirect
61. #16812656	C₂²	semidirect
62. #16812655	C₂²	semidirect
75. C₄⋊Q₈×C₁₀₉	C₂²	semidirect
76. #126×C₁₀₉	C₂²	semidirect
78. C₂²⋊Q₈×C₁₀₉	C₂²	semidirect
79. C₄×Q₈×C₁₀₉	C₂²	semidirect
80. C₄×Q₈×C₁₀₉	C₂²	semidirect
82. #117×C₁₀₉	C₂²	semidirect
222. D₁₀₉	#556	direct (N × H)
224. C₁₀₉	C₂×#556	semidirect
233. #556	D₁₀₉	direct (N × H)
250. C₄⋊Q₈	C₂×D₁₀₉	semidirect
258. #126	C₂×D₁₀₉	semidirect
270. C₂²⋊Q₈	C₂×D₁₀₉	semidirect
281. C₄×Q₈	C₂×D₁₀₉	semidirect
282. C₄×Q₈	C₂×D₁₀₉	semidirect
294. #117	C₂×D₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
#20295750	2
#20295749	2
#20295748	2
#20295747	2
#20295746	2
#20295745	2
#20295744	2
#20295743	2
C₄⋊Q₈×D₁₀₉	2
#126×D₁₀₉	2
#124×D₁₀₉	2
C₂²⋊Q₈×D₁₀₉	2
C₄×Q₈×D₁₀₉	2
C₄×D₄×D₁₀₉	2
#117×D₁₀₉	2
#556×C₁₀₉	2
C₂×#556	109

Subgroups — #556×D109 #28376574

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #556×D₁₀₉ #28376574