Subgroups — C₄×#16812726 #28371841

Order 13952.

548 conjugacy classes of subgroups.

The subgroup lattice has 384 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
2	C₄×#13182030	C₂	1	1	yes	maximal, characteristic, complemented
3	C₄×D₄×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295137	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295135	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295129	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295127	C₂	1	1	yes	maximal, characteristic, complemented
8	C₄×#13182016	C₂	1	1	yes	maximal, characteristic, complemented
9	C₄×D₈₇₂	C₂	1	1	yes	maximal, characteristic, complemented
10	C₄×#13182014	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295065	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295029	C₂	1	1	yes	maximal, characteristic, complemented
13	#20295026	C₂	1	1	yes	maximal, characteristic, complemented
14	C₄×#13182012	C₂	1	1	yes	maximal, characteristic, complemented
15	C₄×SD₁₆×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182030	C₂²	1	1	yes	characteristic
17	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
18	C₂²×C₄×D₁₀₉	—	2	1	no	—
19	#16812726	C₄	1	8	yes	direct product factor
20	C₂×#13182016	C₂²	1	1	yes	characteristic
21	C₂×D₈₇₂	C₂²	1	1	yes	characteristic
22	C₂×#13182014	C₂²	1	1	yes	characteristic
23	C₂×#13182012	C₂²	1	1	yes	characteristic
24	C₂×#13182012	C₂²	1	1	yes	characteristic
25	Q₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
26	C₄×D₄₃₆	—	2	1	no	—
27	C₄×D₄₃₆	C₂²	1	1	yes	characteristic
28	C₄×D₄₃₆	C₂²	1	1	yes	characteristic, complemented
29	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
30	#16812661	—	2	1	no	—
31	#16812661	C₂²	1	1	yes	characteristic
32	#16812661	C₂²	1	1	yes	characteristic, complemented
33	C₄×C₂²⋊D₁₀₉	—	2	1	no	—
34	#16812659	—	2	1	no	—
35	#16812657	—	2	1	no	—
36	#16812657	C₂²	1	1	yes	characteristic
37	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic
38	C₂²⋊C₄×D₁₀₉	—	2	1	no	—
39	C₄²×D₁₀₉	—	2	1	no	—
40	C₄²×D₁₀₉	C₂²	1	1	yes	characteristic
41	#16812633	C₂²	1	1	yes	characteristic, complemented
42	#16812632	C₂²	1	1	yes	characteristic, complemented
43	#16812630	C₂²	1	1	yes	characteristic, complemented
44	#16812623	C₂²	1	1	yes	characteristic, complemented
45	#16812621	C₂²	1	1	yes	characteristic
46	#16812621	C₂²	1	1	yes	characteristic, complemented
47	#16812620	C₂²	1	1	yes	characteristic
48	#16812619	C₂²	1	1	yes	characteristic
49	#16812619	C₂²	1	1	yes	characteristic, complemented
50	#16812609	C₂²	1	1	yes	characteristic, complemented
51	#16812609	C₂²	1	1	yes	characteristic, complemented
52	C₄×#11724784	C₂²	1	1	yes	characteristic, complemented
53	C₂×SD₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
54	C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	C₄×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
56	#106×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
57	#103×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	#102×C₁₀₉	C₂²	1	1	yes	characteristic
59	C₄×C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
60	C₂³×D₁₀₉	—	2	1	no	—
61	#13182030	—	2	2	no	—
62	#13182030	C₂×C₄	1	4	yes	complemented
63	C₂×D₄₃₆	—	2	1	no	—
64	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
65	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
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	C₂×C₄×D₁₀₉	—	2	1	no	—
71	C₂×C₄×D₁₀₉	—	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	—	2	1	no	—
76	C₂×C₄×D₁₀₉	—	4	4	no	—
77	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
78	C₂×C₄×D₁₀₉	D₄	1	1	yes	characteristic
79	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
80	#13182016	C₂×C₄	1	4	yes	complemented
81	D₈₇₂	C₂×C₄	1	4	yes	complemented
82	#13182014	C₂×C₄	1	4	yes	complemented
83	#13182012	—	2	2	no	—
84	#13182012	C₂×C₄	1	4	yes	complemented
85	C₂×#11724784	C₂³	1	1	yes	characteristic
86	C₂×#11724784	C₂³	1	1	yes	characteristic
87	C₄⋊Dic₁₀₉	—	2	1	no	—
88	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
89	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
90	#13182008	—	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	—	2	1	no	—
96	#13182006	—	2	1	no	—
97	C₄×Dic₁₀₉	—	2	1	no	—
98	C₄×Dic₁₀₉	—	2	1	no	—
99	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
100	C₄×Dic₁₀₉	D₄	1	1	yes	characteristic
101	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
102	C₂×Q₈×C₁₀₉	C₂³	1	1	yes	characteristic
103	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
104	C₂²×C₄×C₁₀₉	—	2	1	no	—
105	SD₁₆×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	—	2	1	no	—
109	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
111	C₂²⋊C₄×C₁₀₉	—	2	1	no	—
112	C₄²×C₁₀₉	—	2	1	no	—
113	C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
114	C₂³×C₁₀₉	—	2	1	no	—
115	C₂²×D₁₀₉	—	2	1	no	—
116	C₂²×D₁₀₉	—	2	1	no	—
117	C₂²×D₁₀₉	—	2	4	no	—
118	C₂²×D₁₀₉	—	4	2	no	—
119	C₂²×D₁₀₉	—	4	2	no	—
120	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
121	Q₈×C₁₀₉	—	2	1	no	—
122	Q₈×C₁₀₉	C₂²×C₄	1	2	yes	complemented
123	D₄×C₁₀₉	—	2	1	no	—
124	D₄×C₁₀₉	C₂²×C₄	1	2	yes	—
125	C₂×C₄×C₁₀₉	—	2	1	no	—
126	C₂×C₄×C₁₀₉	—	2	1	no	—
127	C₂×C₄×C₁₀₉	—	2	1	no	—
128	C₂×C₄×C₁₀₉	—	4	2	no	—
129	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
131	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
132	C₂²⋊D₁₀₉	—	2	4	no	—
133	C₂×Dic₁₀₉	—	2	1	no	—
134	C₂×Dic₁₀₉	—	2	1	no	—
135	C₂×Dic₁₀₉	—	4	2	no	—
136	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
137	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
138	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
139	D₄₃₆	—	2	4	no	—
140	D₄₃₆	—	2	1	no	—
141	D₄₃₆	—	2	1	no	—
142	D₄₃₆	C₂²×C₄	1	2	yes	—
143	D₄₃₆	C₂²×C₄	1	2	yes	complemented
144	C₄×D₁₀₉	—	2	2	no	—
145	C₄×D₁₀₉	—	2	4	no	—
146	C₄×D₁₀₉	—	4	1	no	—
147	C₄×D₁₀₉	—	4	2	no	—
148	C₄×D₁₀₉	—	4	2	no	—
149	C₄×D₁₀₉	—	4	2	no	—
150	C₄×D₁₀₉	—	4	2	no	—
151	C₄×D₁₀₉	—	4	2	no	—
152	C₄×D₁₀₉	C₂²×C₄	1	2	yes	—
153	C₄×D₁₀₉	#41	1	2	yes	—
154	C₈×C₁₀₉	—	2	1	no	—
155	C₈×C₁₀₉	C₂²×C₄	1	2	yes	complemented
156	#11724784	—	2	1	no	—
157	#11724784	C₂²×C₄	1	2	yes	complemented
158	C₂²×C₁₀₉	—	2	2	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	—	2	2	no	—
166	C₂×D₁₀₉	—	4	8	no	—
167	C₂×D₁₀₉	—	4	1	no	—
168	C₂×D₁₀₉	—	4	1	no	—
169	C₂×D₁₀₉	—	4	1	no	—
170	C₂×D₁₀₉	—	4	1	no	—
171	C₂×D₁₀₉	C₄×D₄	1	2	yes	—
172	C₄×C₁₀₉	—	2	2	no	—
173	C₄×C₁₀₉	—	2	1	no	—
174	C₄×C₁₀₉	—	4	1	no	—
175	C₄×C₁₀₉	—	4	1	no	—
176	C₄×C₁₀₉	AGL(1,ℤ/8)	1	2	yes	complemented
177	C₄×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
178	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
179	Dic₁₀₉	—	2	1	no	—
180	Dic₁₀₉	—	2	1	no	—
181	Dic₁₀₉	—	4	1	no	—
182	Dic₁₀₉	—	4	1	no	—
183	Dic₁₀₉	C₄×D₄	1	2	yes	—
184	C₂×C₁₀₉	—	4	2	no	—
185	C₂×C₁₀₉	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂×C₁₀₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
187	C₂×C₁₀₉	#575	1	1	yes	characteristic
188	D₁₀₉	—	2	2	no	—
189	D₁₀₉	—	4	2	no	—
190	D₁₀₉	—	4	2	no	—
191	C₄×AGL(1,ℤ/8)	—	109	1	no	maximal, Sylow
192	C₁₀₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
193	C₂×AGL(1,ℤ/8)	—	109	1	no	—
194	C₄×#41	—	109	1	no	—
195	C₂×C₄×D₄	—	109	1	no	—
196	#442	—	109	1	no	—
197	#442	—	109	1	no	—
198	#440	—	109	1	no	—
199	#440	—	109	1	no	—
200	C₄×SD₁₆	—	109	1	no	—
201	C₄×SD₁₆	D₁₀₉	1	1	yes	characteristic, complemented
202	C₄×D₈	—	109	1	no	—
203	C₄×D₈	—	109	1	no	—
204	#428	—	109	1	no	—
205	#418	—	109	1	no	—
206	#417	—	109	1	no	—
207	C₄×M₁₆	—	109	1	no	—
208	C₂×#41	—	109	1	no	—
209	C₂²×D₄	—	109	1	no	—
210	C₂³×C₄	—	218	1	no	—
211	AGL(1,ℤ/8)	—	109	8	no	—
212	C₂×SD₁₆	—	109	1	no	—
213	C₂×SD₁₆	C₂×D₁₀₉	1	1	yes	characteristic
214	C₂×D₈	—	109	1	no	—
215	C₂×D₈	—	109	1	no	—
216	C₂×M₁₆	—	109	1	no	—
217	C₂×M₁₆	—	109	1	no	—
218	C₄×Q₈	—	109	1	no	—
219	C₄×Q₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
220	C₄×D₄	—	109	1	no	—
221	C₄×D₄	—	109	1	no	—
222	C₄×D₄	—	109	1	no	—
223	C₄×D₄	—	109	1	no	—
224	C₄×D₄	—	109	1	no	—
225	C₄×D₄	—	218	1	no	—
226	C₄×D₄	—	218	1	no	—
227	C₄×D₄	—	218	1	no	—
228	C₄×D₄	—	218	1	no	—
229	C₄×D₄	C₂×D₁₀₉	1	1	yes	characteristic
230	#117	—	109	1	no	—
231	#117	—	218	1	no	—
232	C₂×C₄⋊C₄	—	109	1	no	—
233	C₂×C₂²⋊C₄	—	218	1	no	—
234	C₂×C₄²	—	109	1	no	—
235	C₂×C₄²	—	218	1	no	—
236	#107	—	109	1	no	—
237	#107	—	109	1	no	—
238	#106	—	109	1	no	—
239	#106	C₂×D₁₀₉	1	1	yes	characteristic, complemented
240	#103	—	109	1	no	—
241	#103	C₂×D₁₀₉	1	1	yes	characteristic, complemented
242	#102	—	109	1	no	—
243	#102	—	109	1	no	—
244	#102	—	109	1	no	—
245	#102	—	109	1	no	—
246	#102	—	109	1	no	—
247	#102	C₂×D₁₀₉	1	1	yes	characteristic
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	—	109	4	no	—
254	#41	—	218	2	no	—
255	C₂×Q₈	C₂²×D₁₀₉	1	1	yes	characteristic
256	C₂×D₄	—	109	4	no	—
257	C₂×D₄	—	109	1	no	—
258	C₂×D₄	—	109	1	no	—
259	C₂×D₄	—	218	1	no	—
260	C₂×D₄	—	218	2	no	—
261	C₂×D₄	—	218	1	no	—
262	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
263	C₂²×C₄	—	2	1	no	—
264	C₂²×C₄	—	109	1	no	—
265	C₂²×C₄	—	109	1	no	—
266	C₂²×C₄	—	109	1	no	—
267	C₂²×C₄	—	436	4	no	—
268	C₂²×C₄	—	218	1	no	—
269	C₂²×C₄	—	218	1	no	—
270	C₂²×C₄	—	218	1	no	—
271	C₂²×C₄	—	218	1	no	—
272	C₂²×C₄	—	218	1	no	—
273	C₂²×C₄	—	218	1	no	—
274	C₂²×C₄	—	218	1	no	—
275	SD₁₆	—	109	4	no	—
276	SD₁₆	C₄×D₁₀₉	1	4	yes	complemented
277	D₈	—	109	4	no	—
278	D₈	—	109	4	no	—
279	M₁₆	—	109	4	no	—
280	M₁₆	—	218	2	no	—
281	C₂×C₈	—	109	1	no	—
282	C₂×C₈	—	109	1	no	—
283	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
284	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
285	C₄⋊C₄	—	2	1	no	—
286	C₄⋊C₄	—	109	1	no	—
287	C₄⋊C₄	—	109	1	no	—
288	C₄⋊C₄	—	218	1	no	—
289	C₄⋊C₄	—	218	1	no	—
290	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
291	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
292	C₂²⋊C₄	—	2	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	C₂²⋊C₄	—	218	1	no	—
298	C₂²⋊C₄	—	218	1	no	—
299	C₄²	—	2	1	no	—
300	C₄²	—	109	1	no	—
301	C₄²	—	109	1	no	—
302	C₄²	—	109	1	no	—
303	C₄²	—	218	1	no	—
304	C₄²	—	218	1	no	—
305	C₄²	C₂²×D₁₀₉	1	1	yes	characteristic
306	C₂³	—	2	1	no	—
307	C₂³	—	109	1	no	—
308	C₂³	—	436	2	no	—
309	C₂³	—	436	2	no	—
310	C₂³	—	218	4	no	—
311	C₂³	—	218	1	no	—
312	C₂³	—	218	1	no	—
313	Q₈	—	2	1	no	—
314	Q₈	C₂×C₄×D₁₀₉	1	2	yes	complemented
315	D₄	—	2	1	no	—
316	D₄	—	109	2	no	—
317	D₄	—	109	2	no	—
318	D₄	—	218	4	no	—
319	D₄	—	218	4	no	—
320	D₄	—	218	1	no	—
321	D₄	—	218	1	no	—
322	D₄	C₂×C₄×D₁₀₉	1	2	yes	—
323	C₂×C₄	—	2	1	no	—
324	C₂×C₄	—	2	1	no	—
325	C₂×C₄	—	2	1	no	—
326	C₂×C₄	—	4	2	no	—
327	C₂×C₄	—	109	1	no	—
328	C₂×C₄	—	109	2	no	—
329	C₂×C₄	—	109	2	no	—
330	C₂×C₄	—	109	1	no	—
331	C₂×C₄	—	109	1	no	—
332	C₂×C₄	—	436	1	no	—
333	C₂×C₄	—	436	2	no	—
334	C₂×C₄	—	436	2	no	—
335	C₂×C₄	—	436	2	no	—
336	C₂×C₄	—	436	2	no	—
337	C₂×C₄	—	436	2	no	—
338	C₂×C₄	—	436	2	no	—
339	C₂×C₄	—	218	4	no	—
340	C₂×C₄	—	218	1	no	—
341	C₂×C₄	—	218	1	no	—
342	C₂×C₄	—	218	2	no	—
343	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
344	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
345	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
346	C₈	—	2	1	no	—
347	C₈	—	109	2	no	—
348	C₈	—	218	1	no	—
349	C₈	C₂×C₄×D₁₀₉	1	2	yes	complemented
350	C₂²	—	2	2	no	—
351	C₂²	—	4	1	no	—
352	C₂²	—	4	1	no	—
353	C₂²	—	109	2	no	—
354	C₂²	—	436	8	no	—
355	C₂²	—	436	1	no	—
356	C₂²	—	436	1	no	—
357	C₂²	—	436	1	no	—
358	C₂²	—	436	1	no	—
359	C₂²	—	218	2	no	—
360	C₂²	—	218	2	no	—
361	C₂²	—	218	1	no	—
362	C₂²	—	218	1	no	—
363	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
364	C₄	—	2	2	no	—
365	C₄	—	2	1	no	—
366	C₄	—	4	1	no	—
367	C₄	—	4	1	no	—
368	C₄	—	109	2	no	—
369	C₄	—	436	1	no	—
370	C₄	—	436	1	no	—
371	C₄	—	218	1	no	—
372	C₄	—	218	1	no	—
373	C₄	#16812726	1	2	yes	direct product factor
374	C₄	C₂²×C₄×D₁₀₉	1	1	yes	characteristic
375	C₄	#41×D₁₀₉	1	1	yes	characteristic
376	C₂	—	4	2	no	—
377	C₂	—	436	2	no	—
378	C₂	—	436	2	no	—
379	C₂	—	218	2	no	—
380	C₂	C₄×D₄×D₁₀₉	1	1	yes	characteristic
381	C₂	C₂×#16812726	1	1	yes	characteristic
382	C₂	#20295823	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	D₄×D₁₀₉
commutator	C₄×C₁₀₉	C₂³×C₄
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	C₄×SD₁₆×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
prime radical	C₂×#16812726	C₂
cosocle	C₂×C₄×C₁₀₉	C₂⁴
hypercenter	C₄×SD₁₆	D₁₀₉
hypocenter	C₁₀₉	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂×C₄ ◁ C₄² ◁ C₄×SD₁₆

Complements

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

N	H ≅ G/N	type
2. C₄×#13182030	C₂	semidirect
3. C₄×D₄×D₁₀₉	C₂	semidirect
4. #20295137	C₂	semidirect
5. #20295135	C₂	semidirect
6. #20295129	C₂	semidirect
7. #20295127	C₂	semidirect
8. C₄×#13182016	C₂	semidirect
9. C₄×D₈₇₂	C₂	semidirect
10. C₄×#13182014	C₂	semidirect
11. #20295065	C₂	semidirect
12. #20295029	C₂	semidirect
13. #20295026	C₂	semidirect
14. C₄×#13182012	C₂	semidirect
15. C₄×SD₁₆×C₁₀₉	C₂	semidirect
19. #16812726	C₄	direct (N × H)
25. Q₈×Dic₁₀₉	C₂²	semidirect
28. C₄×D₄₃₆	C₂²	semidirect
32. #16812661	C₂²	semidirect
41. #16812633	C₂²	semidirect
42. #16812632	C₂²	semidirect
43. #16812630	C₂²	semidirect
44. #16812623	C₂²	semidirect
46. #16812621	C₂²	semidirect
49. #16812619	C₂²	semidirect
50. #16812609	C₂²	semidirect
51. #16812609	C₂²	semidirect
52. C₄×#11724784	C₂²	semidirect
54. C₄×Q₈×C₁₀₉	C₂²	semidirect
56. #106×C₁₀₉	C₂²	semidirect
57. #103×C₁₀₉	C₂²	semidirect
59. C₄×C₈×C₁₀₉	C₂²	semidirect
62. #13182030	C₂×C₄	semidirect
68. D₄×D₁₀₉	C₂×C₄	semidirect
80. #13182016	C₂×C₄	semidirect
81. D₈₇₂	C₂×C₄	semidirect
82. #13182014	C₂×C₄	semidirect
84. #13182012	C₂×C₄	semidirect
105. SD₁₆×C₁₀₉	C₂×C₄	semidirect
122. Q₈×C₁₀₉	C₂²×C₄	semidirect
143. D₄₃₆	C₂²×C₄	semidirect
155. C₈×C₁₀₉	C₂²×C₄	semidirect
157. #11724784	C₂²×C₄	semidirect
176. C₄×C₁₀₉	AGL(1,ℤ/8)	semidirect
192. C₁₀₉	C₄×AGL(1,ℤ/8)	semidirect
201. C₄×SD₁₆	D₁₀₉	semidirect
219. C₄×Q₈	C₂×D₁₀₉	semidirect
239. #106	C₂×D₁₀₉	semidirect
241. #103	C₂×D₁₀₉	semidirect
251. C₄×C₈	C₂×D₁₀₉	semidirect
276. SD₁₆	C₄×D₁₀₉	semidirect
314. Q₈	C₂×C₄×D₁₀₉	semidirect
349. C₈	C₂×C₄×D₁₀₉	semidirect
373. C₄	#16812726	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂×#16812726	2
C₄×#13182030	2
C₄×D₄×D₁₀₉	2
#20295137	2
#20295135	2
#20295129	2
#20295127	2
C₄×#13182016	2
C₄×D₈₇₂	2
C₄×#13182014	2
#20295065	2
#20295029	2
#20295026	2
C₄×#13182012	2
C₄×SD₁₆×C₁₀₉	2
C₄×AGL(1,ℤ/8)	109

Subgroups — C4×#16812726 #28371841

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₄×#16812726 #28371841