Subgroups — #28374527

Order 13952.

546 conjugacy classes of subgroups.

The subgroup lattice has 438 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16812726	C₂	1	1	yes	maximal, characteristic, complemented
2	#20295687	C₂	1	1	yes	maximal, characteristic, complemented
3	D₄×C₂²⋊D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295412	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295269	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295262	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295243	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295224	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295175	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295170	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295165	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295160	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295127	C₂	1	1	yes	maximal, characteristic, complemented
14	#20295097	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂²×SD₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182030	C₂²	1	1	yes	characteristic, complemented
17	C₂²×C₂²⋊D₁₀₉	—	2	1	no	—
18	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	#16812726	—	2	4	no	—
20	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
21	C₂×#13182016	C₂²	1	1	yes	characteristic, complemented
22	C₂×D₈₇₂	C₂²	1	1	yes	characteristic, complemented
23	C₂×#13182014	C₂²	1	1	yes	characteristic
24	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
25	C₂×#13182012	C₂²	1	1	yes	characteristic, complemented
26	#16812695	C₂²	1	1	yes	characteristic
27	#16812688	—	2	1	no	—
28	#16812688	C₂²	1	1	yes	characteristic, complemented
29	#16812675	—	2	1	no	—
30	#16812675	C₂²	1	1	yes	characteristic, complemented
31	#16812673	—	2	1	no	—
32	#16812673	C₂²	1	1	yes	characteristic
33	#16812673	C₂²	1	1	yes	characteristic, complemented
34	#16812671	—	2	1	no	—
35	#16812670	C₂²	1	1	yes	characteristic
36	#16812668	—	2	1	no	—
37	#16812667	—	2	1	no	—
38	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
39	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
40	C₄×C₂²⋊D₁₀₉	—	2	1	no	—
41	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
42	#16812633	C₂²	1	1	yes	characteristic, complemented
43	#16812628	C₂²	1	1	yes	characteristic, complemented
44	#16812623	C₂²	1	1	yes	characteristic, complemented
45	#16812623	C₂²	1	1	yes	characteristic, complemented
46	#16812621	C₂²	1	1	yes	characteristic, complemented
47	#16812621	C₂²	1	1	yes	characteristic, complemented
48	#16812620	C₂²	1	1	yes	characteristic
49	#16812620	C₂²	1	1	yes	characteristic, complemented
50	C₂²⋊#11724784	C₂²	1	1	yes	characteristic, complemented
51	#16812611	C₂²	1	1	yes	characteristic, complemented
52	#16812609	C₂²	1	1	yes	characteristic, complemented
53	C₂²×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
54	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
55	C₂×SD₁₆×C₁₀₉	—	2	4	no	—
56	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
57	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
58	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	C₂²×C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
61	C₂³×D₁₀₉	—	2	1	no	—
62	#13182030	—	2	2	no	—
63	#13182030	—	4	1	no	—
64	C₂×D₄₃₆	—	2	1	no	—
65	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
66	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
67	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
68	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
69	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
72	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
73	C₂×C₂²⋊D₁₀₉	—	4	4	no	—
74	C₂×C₂²⋊D₁₀₉	D₄	1	1	yes	characteristic
75	D₄×D₁₀₉	—	2	2	no	—
76	D₄×D₁₀₉	—	4	1	no	—
77	C₂²×Dic₁₀₉	—	2	1	no	—
78	C₂×C₄×D₁₀₉	—	2	1	no	—
79	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
80	#13182016	—	2	2	no	—
81	#13182016	—	4	1	no	—
82	D₈₇₂	—	2	2	no	—
83	#13182014	—	2	2	no	—
84	#13182014	—	4	1	no	—
85	#13182012	—	2	2	no	—
86	C₂×#11724784	C₂³	1	1	yes	characteristic
87	C₂×#11724784	C₂³	1	1	yes	characteristic
88	C₄⋊Dic₁₀₉	—	2	1	no	—
89	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
90	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
91	#13182008	—	2	1	no	—
92	#13182008	D₄	1	1	yes	characteristic
93	C₂²⋊Dic₁₀₉	—	2	1	no	—
94	C₂²⋊Dic₁₀₉	—	2	1	no	—
95	C₂²⋊Dic₁₀₉	D₄	1	1	yes	characteristic
96	#13182006	—	2	1	no	—
97	#13182006	—	2	1	no	—
98	#13182006	—	2	1	no	—
99	#13182006	—	2	1	no	—
100	#13182006	—	2	1	no	—
101	#13182006	D₄	1	1	yes	characteristic
102	C₄×Dic₁₀₉	—	2	1	no	—
103	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
104	C₂⁴×C₁₀₉	—	2	1	no	—
105	C₂×Q₈×C₁₀₉	—	2	1	no	—
106	C₂×Q₈×C₁₀₉	—	2	2	no	—
107	C₂×Q₈×C₁₀₉	—	4	1	no	—
108	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₂×D₄×C₁₀₉	—	2	2	no	—
111	C₂×D₄×C₁₀₉	—	2	1	no	—
112	C₂×D₄×C₁₀₉	—	4	1	no	—
113	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
115	C₂²×C₄×C₁₀₉	—	2	1	no	—
116	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
117	SD₁₆×C₁₀₉	—	2	2	no	—
118	SD₁₆×C₁₀₉	—	2	2	no	—
119	SD₁₆×C₁₀₉	—	2	2	no	—
120	SD₁₆×C₁₀₉	D₄	1	4	yes	complemented
121	C₂×C₈×C₁₀₉	—	2	2	no	—
122	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
123	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
124	C₂³×C₁₀₉	—	2	1	no	—
125	C₂³×C₁₀₉	—	2	1	no	—
126	C₂³×C₁₀₉	—	4	2	no	—
127	C₂³×C₁₀₉	—	4	2	no	—
128	C₂³×C₁₀₉	—	8	1	no	—
129	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
130	C₂²×D₁₀₉	—	2	1	no	—
131	C₂²×D₁₀₉	—	2	1	no	—
132	C₂²×D₁₀₉	—	4	2	no	—
133	C₂²×D₁₀₉	—	4	2	no	—
134	C₂²×D₁₀₉	—	8	1	no	—
135	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
136	Q₈×C₁₀₉	—	2	1	no	—
137	Q₈×C₁₀₉	—	2	1	no	—
138	Q₈×C₁₀₉	—	2	1	no	—
139	Q₈×C₁₀₉	—	4	2	no	—
140	Q₈×C₁₀₉	C₂×D₄	1	2	yes	complemented
141	D₄×C₁₀₉	—	2	1	no	—
142	D₄×C₁₀₉	—	2	1	no	—
143	D₄×C₁₀₉	—	2	1	no	—
144	D₄×C₁₀₉	—	4	2	no	—
145	D₄×C₁₀₉	C₂×D₄	1	2	yes	—
146	C₂×C₄×C₁₀₉	—	2	1	no	—
147	C₂×C₄×C₁₀₉	—	2	1	no	—
148	C₂×C₄×C₁₀₉	—	2	1	no	—
149	C₂×C₄×C₁₀₉	—	2	1	no	—
150	C₂×C₄×C₁₀₉	—	4	2	no	—
151	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
152	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
153	C₂²⋊D₁₀₉	—	2	2	no	—
154	C₂²⋊D₁₀₉	—	4	2	no	—
155	C₂²⋊D₁₀₉	—	4	2	no	—
156	C₂²⋊D₁₀₉	—	4	2	no	—
157	C₂²⋊D₁₀₉	—	4	2	no	—
158	C₂²⋊D₁₀₉	—	4	2	no	—
159	C₂²⋊D₁₀₉	—	8	1	no	—
160	C₂×Dic₁₀₉	—	2	1	no	—
161	C₂×Dic₁₀₉	—	2	1	no	—
162	C₂×Dic₁₀₉	—	4	2	no	—
163	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
164	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
165	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
166	D₄₃₆	—	2	1	no	—
167	D₄₃₆	—	2	1	no	—
168	D₄₃₆	—	2	1	no	—
169	D₄₃₆	—	2	1	no	—
170	D₄₃₆	—	4	2	no	—
171	C₄×D₁₀₉	—	2	1	no	—
172	C₄×D₁₀₉	—	2	1	no	—
173	C₄×D₁₀₉	—	4	2	no	—
174	C₈×C₁₀₉	—	2	1	no	—
175	C₈×C₁₀₉	C₂×D₄	1	2	yes	complemented
176	#11724784	—	2	1	no	—
177	#11724784	—	2	1	no	—
178	C₂²×C₁₀₉	—	2	1	no	—
179	C₂²×C₁₀₉	—	2	1	no	—
180	C₂²×C₁₀₉	—	2	2	no	—
181	C₂²×C₁₀₉	—	4	1	no	—
182	C₂²×C₁₀₉	—	4	1	no	—
183	C₂²×C₁₀₉	—	4	1	no	—
184	C₂²×C₁₀₉	—	4	1	no	—
185	C₂²×C₁₀₉	—	4	1	no	—
186	C₂²×C₁₀₉	—	8	4	no	—
187	C₂²×C₁₀₉	AGL(1,ℤ/8)	1	2	yes	complemented
188	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
189	C₂×D₁₀₉	—	2	1	no	—
190	C₂×D₁₀₉	—	2	1	no	—
191	C₂×D₁₀₉	—	2	1	no	—
192	C₂×D₁₀₉	—	4	1	no	—
193	C₂×D₁₀₉	—	4	1	no	—
194	C₂×D₁₀₉	—	4	1	no	—
195	C₂×D₁₀₉	—	4	1	no	—
196	C₂×D₁₀₉	—	4	1	no	—
197	C₂×D₁₀₉	—	4	1	no	—
198	C₂×D₁₀₉	—	8	4	no	—
199	C₄×C₁₀₉	—	2	2	no	—
200	C₄×C₁₀₉	—	2	1	no	—
201	C₄×C₁₀₉	—	4	1	no	—
202	C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
203	C₄×C₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
204	Dic₁₀₉	—	2	1	no	—
205	Dic₁₀₉	—	2	1	no	—
206	Dic₁₀₉	—	2	1	no	—
207	Dic₁₀₉	—	4	1	no	—
208	Dic₁₀₉	—	4	1	no	—
209	C₂×C₁₀₉	—	2	2	no	—
210	C₂×C₁₀₉	—	4	2	no	—
211	C₂×C₁₀₉	—	8	1	no	—
212	C₂×C₁₀₉	D₄²	1	1	yes	characteristic
213	C₂×C₁₀₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
214	C₂×C₁₀₉	#577	1	1	yes	characteristic
215	D₁₀₉	—	4	1	no	—
216	D₁₀₉	—	8	1	no	—
217	D₁₀₉	—	8	1	no	—
218	#3265	—	109	1	no	maximal, Sylow
219	C₁₀₉	#3265	1	1	yes	characteristic, complemented, Sylow
220	C₂×AGL(1,ℤ/8)	—	109	1	no	—
221	C₂²×SD₁₆	D₁₀₉	1	1	yes	characteristic, complemented
222	#548	—	109	1	no	—
223	D₄²	—	109	1	no	—
224	#496	—	109	1	no	—
225	#468	—	109	1	no	—
226	#466	—	109	1	no	—
227	#463	—	109	1	no	—
228	#460	—	109	1	no	—
229	#450	—	109	1	no	—
230	#449	—	109	1	no	—
231	#448	—	109	1	no	—
232	#447	—	109	1	no	—
233	#440	—	109	1	no	—
234	#435	—	109	1	no	—
235	C₂×#41	—	109	1	no	—
236	C₂²×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
237	C₂²×D₄	—	109	1	no	—
238	C₂²×D₄	—	218	1	no	—
239	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic
240	AGL(1,ℤ/8)	—	218	4	no	—
241	C₂×SD₁₆	—	2	4	no	—
242	C₂×SD₁₆	—	109	1	no	—
243	C₂×SD₁₆	—	109	1	no	—
244	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
245	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
246	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
247	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic, complemented
248	C₂×D₈	—	109	1	no	—
249	C₂×D₈	—	109	1	no	—
250	C₂×D₈	—	109	1	no	—
251	C₂×M₁₆	—	109	1	no	—
252	C₂²×C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
253	#127	—	109	1	no	—
254	#124	—	109	1	no	—
255	#124	—	218	1	no	—
256	C₂²⋊Q₈	—	109	1	no	—
257	C₂²⋊Q₈	—	218	1	no	—
258	#121	—	109	1	no	—
259	#121	—	109	1	no	—
260	#121	—	109	1	no	—
261	#121	—	218	1	no	—
262	#121	—	218	1	no	—
263	#120	—	218	1	no	—
264	#120	—	218	1	no	—
265	C₄×Q₈	—	109	1	no	—
266	C₄×D₄	—	109	1	no	—
267	C₄×D₄	—	109	1	no	—
268	C₄×D₄	—	218	1	no	—
269	#107	—	109	1	no	—
270	C₄⋊C₈	—	109	1	no	—
271	#103	—	109	1	no	—
272	#103	—	109	1	no	—
273	#102	—	109	1	no	—
274	#102	—	109	1	no	—
275	#102	—	109	1	no	—
276	#102	—	109	1	no	—
277	C₂²⋊C₈	—	109	1	no	—
278	C₂²⋊C₈	—	109	1	no	—
279	#97	—	109	1	no	—
280	C₂⁴	—	2	1	no	—
281	C₂⁴	—	218	1	no	—
282	#41	—	436	1	no	—
283	#41	—	218	2	no	—
284	C₂×Q₈	—	2	1	no	—
285	C₂×Q₈	—	2	2	no	—
286	C₂×Q₈	—	4	1	no	—
287	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
288	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
289	C₂×D₄	—	2	2	no	—
290	C₂×D₄	—	2	1	no	—
291	C₂×D₄	—	4	1	no	—
292	C₂×D₄	—	109	1	no	—
293	C₂×D₄	—	109	1	no	—
294	C₂×D₄	—	109	1	no	—
295	C₂×D₄	—	436	4	no	—
296	C₂×D₄	—	436	1	no	—
297	C₂×D₄	—	218	1	no	—
298	C₂×D₄	—	218	1	no	—
299	C₂×D₄	—	218	1	no	—
300	C₂×D₄	—	218	1	no	—
301	C₂×D₄	—	218	1	no	—
302	C₂×D₄	—	218	1	no	—
303	C₂×D₄	—	218	1	no	—
304	C₂×D₄	—	218	2	no	—
305	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
306	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
307	C₂²×C₄	—	2	1	no	—
308	C₂²×C₄	—	109	1	no	—
309	C₂²×C₄	—	218	1	no	—
310	C₂²×C₄	—	218	1	no	—
311	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
312	SD₁₆	—	2	2	no	—
313	SD₁₆	—	2	2	no	—
314	SD₁₆	—	2	2	no	—
315	SD₁₆	—	436	1	no	—
316	SD₁₆	—	218	2	no	—
317	SD₁₆	C₂²⋊D₁₀₉	1	4	yes	complemented
318	D₈	—	436	1	no	—
319	D₈	—	218	2	no	—
320	D₈	—	218	2	no	—
321	M₁₆	—	218	2	no	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	109	1	no	—
324	C₂×C₈	—	109	1	no	—
325	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
326	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
327	C₄⋊C₄	—	109	1	no	—
328	C₄⋊C₄	—	109	1	no	—
329	C₄⋊C₄	—	109	1	no	—
330	C₄⋊C₄	—	218	1	no	—
331	C₄⋊C₄	—	218	1	no	—
332	C₂²⋊C₄	—	109	1	no	—
333	C₂²⋊C₄	—	109	1	no	—
334	C₂²⋊C₄	—	218	1	no	—
335	C₂²⋊C₄	—	218	1	no	—
336	C₂²⋊C₄	—	218	1	no	—
337	C₂²⋊C₄	—	218	1	no	—
338	C₂²⋊C₄	—	218	1	no	—
339	C₂²⋊C₄	—	218	1	no	—
340	C₂²⋊C₄	—	218	1	no	—
341	C₄²	—	109	1	no	—
342	C₄²	—	218	1	no	—
343	C₂³	—	2	1	no	—
344	C₂³	—	2	1	no	—
345	C₂³	—	4	2	no	—
346	C₂³	—	4	2	no	—
347	C₂³	—	8	1	no	—
348	C₂³	—	872	1	no	—
349	C₂³	—	109	1	no	—
350	C₂³	—	436	2	no	—
351	C₂³	—	436	2	no	—
352	C₂³	—	218	1	no	—
353	C₂³	—	218	1	no	—
354	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
355	Q₈	—	2	1	no	—
356	Q₈	—	2	1	no	—
357	Q₈	—	2	1	no	—
358	Q₈	—	4	2	no	—
359	Q₈	C₂×C₂²⋊D₁₀₉	1	2	yes	complemented
360	D₄	—	2	1	no	—
361	D₄	—	2	1	no	—
362	D₄	—	2	1	no	—
363	D₄	—	4	2	no	—
364	D₄	—	872	1	no	—
365	D₄	—	436	2	no	—
366	D₄	—	436	2	no	—
367	D₄	—	436	2	no	—
368	D₄	—	436	2	no	—
369	D₄	—	436	2	no	—
370	D₄	—	436	2	no	—
371	D₄	—	218	2	no	—
372	D₄	—	218	1	no	—
373	D₄	—	218	1	no	—
374	D₄	—	218	1	no	—
375	D₄	—	218	1	no	—
376	D₄	C₂×C₂²⋊D₁₀₉	1	2	yes	—
377	C₂×C₄	—	2	1	no	—
378	C₂×C₄	—	2	1	no	—
379	C₂×C₄	—	2	1	no	—
380	C₂×C₄	—	2	1	no	—
381	C₂×C₄	—	4	2	no	—
382	C₂×C₄	—	109	1	no	—
383	C₂×C₄	—	109	1	no	—
384	C₂×C₄	—	109	1	no	—
385	C₂×C₄	—	436	2	no	—
386	C₂×C₄	—	436	2	no	—
387	C₂×C₄	—	218	1	no	—
388	C₂×C₄	—	218	1	no	—
389	C₂×C₄	—	218	1	no	—
390	C₂×C₄	—	218	1	no	—
391	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
392	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
393	C₈	—	2	1	no	—
394	C₈	—	218	1	no	—
395	C₈	—	218	1	no	—
396	C₈	C₂×C₂²⋊D₁₀₉	1	2	yes	complemented
397	C₂²	—	2	1	no	—
398	C₂²	—	2	1	no	—
399	C₂²	—	2	2	no	—
400	C₂²	—	4	1	no	—
401	C₂²	—	4	1	no	—
402	C₂²	—	4	1	no	—
403	C₂²	—	4	1	no	—
404	C₂²	—	4	1	no	—
405	C₂²	—	8	4	no	—
406	C₂²	—	872	4	no	—
407	C₂²	—	436	1	no	—
408	C₂²	—	436	1	no	—
409	C₂²	—	436	1	no	—
410	C₂²	—	436	1	no	—
411	C₂²	—	436	1	no	—
412	C₂²	—	436	1	no	—
413	C₂²	—	218	1	no	—
414	C₂²	—	218	1	no	—
415	C₂²	—	218	1	no	—
416	C₂²	#16812726	1	2	yes	complemented
417	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
418	C₄	—	2	1	no	—
419	C₄	—	2	2	no	—
420	C₄	—	4	1	no	—
421	C₄	—	436	1	no	—
422	C₄	—	436	1	no	—
423	C₄	—	218	1	no	—
424	C₄	—	218	1	no	—
425	C₄	—	218	1	no	—
426	C₄	C₂²×C₂²⋊D₁₀₉	1	1	yes	characteristic
427	C₄	#16812744	1	1	yes	characteristic
428	C₂	—	2	2	no	—
429	C₂	—	4	2	no	—
430	C₂	—	8	1	no	—
431	C₂	—	872	1	no	—
432	C₂	—	872	1	no	—
433	C₂	—	436	1	no	—
434	C₂	D₄×C₂²⋊D₁₀₉	1	1	yes	characteristic
435	C₂	C₂×#16812726	1	1	yes	characteristic
436	C₂	#20295832	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	C₂²×SD₁₆×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
hypercenter	C₂²×SD₁₆	D₁₀₉
hypocenter	C₁₀₉	#3265
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂²×SD₁₆

Complements

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

N	H ≅ G/N	type
1. C₂×#16812726	C₂	semidirect
2. #20295687	C₂	semidirect
3. D₄×C₂²⋊D₁₀₉	C₂	semidirect
4. #20295412	C₂	semidirect
5. #20295269	C₂	semidirect
6. #20295262	C₂	semidirect
7. #20295243	C₂	semidirect
8. #20295224	C₂	semidirect
9. #20295175	C₂	semidirect
10. #20295170	C₂	semidirect
11. #20295165	C₂	semidirect
12. #20295160	C₂	semidirect
13. #20295127	C₂	semidirect
14. #20295097	C₂	semidirect
15. C₂²×SD₁₆×C₁₀₉	C₂	semidirect
16. C₂×#13182030	C₂²	semidirect
20. C₂×#13182016	C₂²	semidirect
21. C₂×#13182016	C₂²	semidirect
22. C₂×D₈₇₂	C₂²	semidirect
24. C₂×#13182014	C₂²	semidirect
25. C₂×#13182012	C₂²	semidirect
28. #16812688	C₂²	semidirect
30. #16812675	C₂²	semidirect
33. #16812673	C₂²	semidirect
38. Q₈×Dic₁₀₉	C₂²	semidirect
42. #16812633	C₂²	semidirect
43. #16812628	C₂²	semidirect
44. #16812623	C₂²	semidirect
45. #16812623	C₂²	semidirect
46. #16812621	C₂²	semidirect
47. #16812621	C₂²	semidirect
49. #16812620	C₂²	semidirect
50. C₂²⋊#11724784	C₂²	semidirect
51. #16812611	C₂²	semidirect
52. #16812609	C₂²	semidirect
53. C₂²×Q₈×C₁₀₉	C₂²	semidirect
58. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
59. C₂×SD₁₆×C₁₀₉	C₂²	semidirect
60. C₂²×C₈×C₁₀₉	C₂²	semidirect
120. SD₁₆×C₁₀₉	D₄	semidirect
140. Q₈×C₁₀₉	C₂×D₄	semidirect
175. C₈×C₁₀₉	C₂×D₄	semidirect
187. C₂²×C₁₀₉	AGL(1,ℤ/8)	semidirect
219. C₁₀₉	#3265	semidirect
221. C₂²×SD₁₆	D₁₀₉	semidirect
236. C₂²×Q₈	C₂×D₁₀₉	semidirect
246. C₂×SD₁₆	C₂×D₁₀₉	semidirect
247. C₂×SD₁₆	C₂×D₁₀₉	semidirect
252. C₂²×C₈	C₂×D₁₀₉	semidirect
317. SD₁₆	C₂²⋊D₁₀₉	semidirect
359. Q₈	C₂×C₂²⋊D₁₀₉	semidirect
396. C₈	C₂×C₂²⋊D₁₀₉	semidirect
416. C₂²	#16812726	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16812726	2
#20295687	2
D₄×C₂²⋊D₁₀₉	2
#20295412	2
#20295269	2
#20295262	2
#20295243	2
#20295224	2
#20295175	2
#20295170	2
#20295165	2
#20295160	2
#20295127	2
#20295097	2
C₂²×SD₁₆×C₁₀₉	2
#3265	109