Subgroups — AGL(1,ℤ/8)×#89137 #28379787

Order 13952.

548 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#89137	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×D₄×#89137	C₂	1	1	yes	maximal, characteristic, complemented
3	#20296067	C₂	1	2	yes	maximal, complemented
4	#20296065	C₂	1	2	yes	maximal, complemented
5	SD₁₆×#89137	C₂	1	2	yes	maximal, complemented
6	D₈×#89137	C₂	1	2	yes	maximal, complemented
7	#20296037	C₂	1	1	yes	maximal, characteristic, complemented
8	#20296018	C₂	1	1	yes	maximal, characteristic, complemented
9	#20296017	C₂	1	1	yes	maximal, characteristic, complemented
10	M₁₆×#89137	C₂	1	1	yes	maximal, characteristic, complemented
11	AGL(1,ℤ/8)×D₁₀₉	C₂	1	1	yes	maximal, characteristic
12	C₂³×#89137	—	2	1	no	—
13	D₁₀₉⋊M₁₆	C₂²	1	1	yes	characteristic
14	Q₈×#89137	C₂²	1	1	yes	characteristic, complemented
15	Q₈×#89137	C₂²	1	1	yes	characteristic, complemented
16	D₄×#89137	—	2	1	no	—
17	D₄×#89137	—	2	1	no	—
18	D₄×#89137	—	2	1	no	—
19	D₄×#89137	—	2	1	no	—
20	D₄×#89137	C₂²	1	2	yes	—
21	D₄×#89137	C₂²	1	2	yes	—
22	D₄×#89137	C₂²	1	1	yes	characteristic, complemented
23	D₄×#89137	C₂²	1	1	yes	characteristic, complemented
24	#16812778	—	2	1	no	—
25	#16812778	C₂²	1	1	yes	characteristic
26	C₂×C₄⋊#89137	C₂²	1	1	yes	characteristic
27	C₂×C₂²⋊#89137	—	2	1	no	—
28	C₂×C₄×#89137	—	2	1	no	—
29	C₂×C₄×#89137	C₂²	1	1	yes	characteristic
30	#16812768	C₂²	1	2	yes	complemented
31	#16812767	C₂²	1	2	yes	complemented
32	#16812762	C₂²	1	2	yes	complemented
33	#16812761	C₂²	1	2	yes	—
34	#16812761	C₂²	1	2	yes	—
35	#16812761	C₂²	1	2	yes	complemented
36	#16812753	C₂²	1	2	yes	complemented
37	C₈×#89137	C₂²	1	2	yes	complemented
38	#41×D₁₀₉	C₂²	1	1	yes	characteristic
39	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
40	#16812727	C₄	1	1	yes	characteristic, complemented
41	#16812726	C₄	1	2	yes	complemented
42	#16812725	C₄	1	1	yes	characteristic, complemented
43	#16812724	C₄	1	1	yes	characteristic, complemented
44	#16812723	C₄	1	2	yes	complemented
45	SD₁₆×D₁₀₉	C₂²	1	2	yes	—
46	D₈×D₁₀₉	C₂²	1	2	yes	—
47	M₁₆×D₁₀₉	C₂²	1	1	yes	characteristic
48	AGL(1,ℤ/8)×C₁₀₉	C₄	1	1	yes	characteristic, complemented
49	C₂²×#89137	—	2	1	no	—
50	C₂²×#89137	—	2	1	no	—
51	C₂²×#89137	—	2	1	no	—
52	C₂²×#89137	—	2	2	no	—
53	C₂²×#89137	—	2	2	no	—
54	C₂²×#89137	—	4	4	no	—
55	C₂²×#89137	D₄	1	1	yes	characteristic
56	C₂²×#89137	D₄	1	1	yes	characteristic
57	#13182039	—	2	1	no	—
58	#13182038	—	2	1	no	—
59	D₁₀₉⋊C₈	C₂³	1	2	yes	—
60	C₄⋊#89137	—	2	1	no	—
61	C₄⋊#89137	—	2	1	no	—
62	C₄⋊#89137	—	2	1	no	—
63	C₄⋊#89137	C₂³	1	1	yes	characteristic
64	C₄⋊#89137	C₂³	1	1	yes	characteristic
65	C₄⋊#89137	C₂³	1	2	yes	—
66	C₂²⋊#89137	—	2	1	no	—
67	C₂²⋊#89137	—	2	2	no	—
68	C₂²⋊#89137	—	2	2	no	—
69	C₂²⋊#89137	—	2	1	no	—
70	C₂²⋊#89137	—	2	1	no	—
71	C₄×#89137	—	2	1	no	—
72	C₄×#89137	—	2	1	no	—
73	C₄×#89137	—	2	1	no	—
74	C₄×#89137	D₄	1	1	yes	characteristic
75	C₄×#89137	D₄	1	1	yes	characteristic
76	C₄×#89137	C₂³	1	1	yes	characteristic
77	C₄×#89137	C₂³	1	1	yes	characteristic
78	C₂³×D₁₀₉	—	2	1	no	—
79	#13182030	C₂×C₄	1	1	yes	characteristic, complemented
80	#13182029	—	2	1	no	—
81	#13182029	C₂×C₄	1	1	yes	characteristic, complemented
82	#13182028	—	2	1	no	—
83	#13182028	C₂×C₄	1	1	yes	characteristic, complemented
84	Q₈×D₁₀₉	C₂³	1	1	yes	characteristic
85	C₂×D₄₃₆	C₂×C₄	1	1	yes	characteristic, complemented
86	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
87	D₄×D₁₀₉	—	2	1	no	—
88	D₄×D₁₀₉	—	2	1	no	—
89	D₄×D₁₀₉	—	2	1	no	—
90	D₄×D₁₀₉	C₂×C₄	1	2	yes	complemented
91	D₄×D₁₀₉	C₂³	1	2	yes	—
92	D₄×D₁₀₉	C₂³	1	1	yes	characteristic
93	C₂×C₄×D₁₀₉	—	2	1	no	—
94	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
95	#13182018	C₂×C₄	1	2	yes	complemented
96	#13182017	C₂×C₄	1	2	yes	complemented
97	#13182016	C₂×C₄	1	2	yes	complemented
98	D₈₇₂	C₂×C₄	1	2	yes	complemented
99	#13182014	C₂×C₄	1	2	yes	complemented
100	#13182014	C₂×C₄	1	2	yes	complemented
101	#13182013	C₂×C₄	1	1	yes	characteristic, complemented
102	#13182012	C₂×C₄	1	2	yes	complemented
103	C₈×D₁₀₉	C₂³	1	2	yes	—
104	#41×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
105	C₂×D₄×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
106	SD₁₆×C₁₀₉	C₂×C₄	1	2	yes	complemented
107	D₈×C₁₀₉	C₂×C₄	1	2	yes	complemented
108	M₁₆×C₁₀₉	C₂×C₄	1	1	yes	characteristic, complemented
109	C₂³×C₁₀₉	—	2	1	no	—
110	C₂²×D₁₀₉	—	2	1	no	—
111	C₂²×D₁₀₉	—	2	2	no	—
112	C₂²×D₁₀₉	—	2	1	no	—
113	C₂²×D₁₀₉	—	2	2	no	—
114	C₂²×D₁₀₉	—	4	2	no	—
115	C₂²×D₁₀₉	—	4	2	no	—
116	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
117	C₂×#89137	—	2	2	no	—
118	C₂×#89137	—	2	1	no	—
119	C₂×#89137	—	2	1	no	—
120	C₂×#89137	—	2	2	no	—
121	C₂×#89137	—	4	1	no	—
122	C₂×#89137	—	4	2	no	—
123	C₂×#89137	—	4	4	no	—
124	C₂×#89137	—	4	2	no	—
125	C₂×#89137	—	4	2	no	—
126	C₂×#89137	—	4	4	no	—
127	C₂×#89137	C₂×D₄	1	1	yes	characteristic
128	C₂×#89137	C₂×D₄	1	1	yes	characteristic
129	C₂×#89137	C₂×D₄	1	1	yes	characteristic
130	C₂×#89137	C₂×D₄	1	1	yes	characteristic
131	Q₈×C₁₀₉	C₂²×C₄	1	1	yes	characteristic, complemented
132	D₄×C₁₀₉	—	2	1	no	—
133	D₄×C₁₀₉	—	2	1	no	—
134	D₄×C₁₀₉	C₂²×C₄	1	2	yes	—
135	D₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic, complemented
136	C₂×C₄×C₁₀₉	—	2	1	no	—
137	C₂×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
138	C₂²⋊D₁₀₉	—	2	1	no	—
139	C₂²⋊D₁₀₉	—	2	1	no	—
140	C₂²⋊D₁₀₉	—	2	2	no	—
141	C₂²⋊D₁₀₉	—	2	2	no	—
142	C₂²⋊D₁₀₉	—	2	1	no	—
143	C₂×Dic₁₀₉	—	2	1	no	—
144	C₂×Dic₁₀₉	#41	1	1	yes	characteristic
145	D₄₃₆	—	2	1	no	—
146	D₄₃₆	—	2	1	no	—
147	D₄₃₆	C₂²×C₄	1	2	yes	—
148	D₄₃₆	C₂²×C₄	1	1	yes	characteristic, complemented
149	C₄×D₁₀₉	—	2	1	no	—
150	C₄×D₁₀₉	—	2	1	no	—
151	C₄×D₁₀₉	—	2	1	no	—
152	C₄×D₁₀₉	C₂²×C₄	1	1	yes	characteristic
153	C₄×D₁₀₉	C₂×D₄	1	1	yes	characteristic
154	C₄×D₁₀₉	#41	1	1	yes	characteristic
155	C₄×D₁₀₉	C₂⁴	1	1	yes	characteristic
156	Dic₂₁₈	—	2	1	no	—
157	Dic₂₁₈	C₂²×C₄	1	1	yes	characteristic, complemented
158	#11724786	—	2	2	no	—
159	C₈×C₁₀₉	C₂²×C₄	1	2	yes	complemented
160	#11724784	C₂²×C₄	1	2	yes	complemented
161	C₂²×C₁₀₉	—	2	1	no	—
162	C₂²×C₁₀₉	—	2	2	no	—
163	C₂²×C₁₀₉	—	4	2	no	—
164	C₂²×C₁₀₉	C₄×D₄	1	1	yes	characteristic
165	C₂×D₁₀₉	—	2	1	no	—
166	C₂×D₁₀₉	—	2	1	no	—
167	C₂×D₁₀₉	—	2	1	no	—
168	C₂×D₁₀₉	—	2	2	no	—
169	C₂×D₁₀₉	—	4	4	no	—
170	C₂×D₁₀₉	—	4	2	no	—
171	C₂×D₁₀₉	—	4	2	no	—
172	C₂×D₁₀₉	—	4	1	no	—
173	C₂×D₁₀₉	—	4	1	no	—
174	C₂×D₁₀₉	—	4	2	no	—
175	C₂×D₁₀₉	C₄×D₄	1	1	yes	characteristic
176	C₂×D₁₀₉	C₂²×D₄	1	1	yes	characteristic
177	#89137	—	2	1	no	—
178	#89137	—	2	1	no	—
179	#89137	—	2	1	no	—
180	#89137	—	4	1	no	—
181	#89137	—	4	2	no	—
182	#89137	—	4	1	no	—
183	#89137	AGL(1,ℤ/8)	1	2	yes	direct product factor
184	C₄×C₁₀₉	—	2	1	no	—
185	C₄×C₁₀₉	C₄×D₄	1	1	yes	characteristic
186	C₄×C₁₀₉	C₂³×C₄	1	1	yes	characteristic
187	Dic₁₀₉	—	2	1	no	—
188	Dic₁₀₉	C₄×D₄	1	1	yes	characteristic
189	Dic₁₀₉	C₂×#41	1	1	yes	characteristic
190	C₂×C₁₀₉	—	2	1	no	—
191	C₂×C₁₀₉	—	4	2	no	—
192	C₂×C₁₀₉	—	4	1	no	—
193	C₂×C₁₀₉	C₂×C₄×D₄	1	1	yes	characteristic
194	D₁₀₉	—	2	1	no	—
195	D₁₀₉	—	4	1	no	—
196	D₁₀₉	—	4	2	no	—
197	D₁₀₉	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
198	D₁₀₉	#575	1	1	yes	characteristic
199	C₄×AGL(1,ℤ/8)	—	109	1	no	maximal, Sylow
200	C₁₀₉	C₄×AGL(1,ℤ/8)	1	1	yes	characteristic, complemented, Sylow
201	C₂×AGL(1,ℤ/8)	—	109	1	no	—
202	C₄×#41	—	109	1	no	—
203	C₂×C₄×D₄	—	109	1	no	—
204	#442	—	109	2	no	—
205	#440	—	109	2	no	—
206	C₄×SD₁₆	—	109	2	no	—
207	C₄×D₈	—	109	2	no	—
208	#428	—	109	1	no	—
209	#418	—	109	1	no	—
210	#417	—	109	1	no	—
211	C₄×M₁₆	—	109	1	no	—
212	C₂×#41	—	109	1	no	—
213	C₂²×D₄	—	109	1	no	—
214	C₂³×C₄	—	218	1	no	—
215	AGL(1,ℤ/8)	—	109	1	no	—
216	AGL(1,ℤ/8)	—	109	1	no	—
217	AGL(1,ℤ/8)	—	109	2	no	—
218	AGL(1,ℤ/8)	—	109	2	no	—
219	AGL(1,ℤ/8)	—	109	1	no	—
220	AGL(1,ℤ/8)	#89137	1	1	yes	characteristic, direct product factor
221	C₂×SD₁₆	—	109	2	no	—
222	C₂×D₈	—	109	2	no	—
223	C₂×M₁₆	—	109	1	no	—
224	C₂×M₁₆	—	109	1	no	—
225	C₄×Q₈	—	109	1	no	—
226	C₄×Q₈	—	109	1	no	—
227	C₄×D₄	—	109	2	no	—
228	C₄×D₄	—	109	2	no	—
229	C₄×D₄	—	109	1	no	—
230	C₄×D₄	—	109	1	no	—
231	C₄×D₄	—	218	1	no	—
232	C₄×D₄	—	218	1	no	—
233	C₄×D₄	—	218	1	no	—
234	C₄×D₄	—	218	1	no	—
235	#117	—	109	1	no	—
236	#117	—	218	1	no	—
237	C₂×C₄⋊C₄	—	109	1	no	—
238	C₂×C₂²⋊C₄	—	218	1	no	—
239	C₂×C₄²	—	109	1	no	—
240	C₂×C₄²	—	218	1	no	—
241	#107	—	109	2	no	—
242	#106	—	109	2	no	—
243	#103	—	109	2	no	—
244	#102	—	109	2	no	—
245	#102	—	109	2	no	—
246	#102	—	109	2	no	—
247	#97	—	109	2	no	—
248	C₄×C₈	—	109	2	no	—
249	C₂⁴	—	218	1	no	—
250	#41	—	109	1	no	—
251	#41	—	109	1	no	—
252	#41	—	109	1	no	—
253	#41	—	218	1	no	—
254	#41	—	218	1	no	—
255	#41	C₂×#89137	1	1	yes	characteristic, complemented
256	C₂×Q₈	—	109	1	no	—
257	C₂×D₄	—	109	2	no	—
258	C₂×D₄	—	109	2	no	—
259	C₂×D₄	—	109	1	no	—
260	C₂×D₄	—	109	1	no	—
261	C₂×D₄	—	218	1	no	—
262	C₂×D₄	—	218	1	no	—
263	C₂×D₄	—	218	1	no	—
264	C₂×D₄	—	218	1	no	—
265	C₂×D₄	C₂×#89137	1	1	yes	characteristic, complemented
266	C₂²×C₄	—	109	1	no	—
267	C₂²×C₄	—	109	1	no	—
268	C₂²×C₄	—	109	1	no	—
269	C₂²×C₄	—	436	4	no	—
270	C₂²×C₄	—	218	1	no	—
271	C₂²×C₄	—	218	1	no	—
272	C₂²×C₄	—	218	1	no	—
273	C₂²×C₄	—	218	2	no	—
274	C₂²×C₄	—	218	2	no	—
275	C₂²×C₄	—	218	1	no	—
276	SD₁₆	—	109	2	no	—
277	SD₁₆	—	109	2	no	—
278	SD₁₆	—	109	2	no	—
279	SD₁₆	C₂×#89137	1	2	yes	complemented
280	D₈	—	109	2	no	—
281	D₈	—	109	2	no	—
282	D₈	—	109	2	no	—
283	D₈	C₂×#89137	1	2	yes	complemented
284	M₁₆	—	109	1	no	—
285	M₁₆	—	109	2	no	—
286	M₁₆	—	218	1	no	—
287	M₁₆	—	218	1	no	—
288	M₁₆	C₂×#89137	1	1	yes	characteristic, complemented
289	C₂×C₈	—	109	2	no	—
290	C₂×C₈	—	109	2	no	—
291	C₄⋊C₄	—	109	1	no	—
292	C₄⋊C₄	—	109	1	no	—
293	C₄⋊C₄	—	109	2	no	—
294	C₄⋊C₄	—	218	1	no	—
295	C₄⋊C₄	—	218	1	no	—
296	C₄⋊C₄	—	218	1	no	—
297	C₂²⋊C₄	—	218	2	no	—
298	C₂²⋊C₄	—	218	2	no	—
299	C₂²⋊C₄	—	218	1	no	—
300	C₂²⋊C₄	—	218	1	no	—
301	C₂²⋊C₄	—	218	1	no	—
302	C₄²	—	109	1	no	—
303	C₄²	—	109	1	no	—
304	C₄²	—	109	1	no	—
305	C₄²	—	109	1	no	—
306	C₄²	—	218	1	no	—
307	C₄²	—	218	1	no	—
308	C₄²	—	218	1	no	—
309	C₂³	—	2	1	no	—
310	C₂³	—	109	1	no	—
311	C₂³	—	436	2	no	—
312	C₂³	—	436	2	no	—
313	C₂³	—	218	1	no	—
314	C₂³	—	218	2	no	—
315	C₂³	—	218	2	no	—
316	C₂³	—	218	1	no	—
317	Q₈	—	109	1	no	—
318	Q₈	—	218	1	no	—
319	Q₈	C₂²×#89137	1	1	yes	characteristic, complemented
320	D₄	—	2	1	no	—
321	D₄	—	2	1	no	—
322	D₄	—	109	1	no	—
323	D₄	—	109	2	no	—
324	D₄	—	218	1	no	—
325	D₄	—	218	2	no	—
326	D₄	—	218	2	no	—
327	D₄	—	218	1	no	—
328	D₄	—	218	1	no	—
329	D₄	—	218	1	no	—
330	D₄	—	218	1	no	—
331	D₄	C₂²×#89137	1	2	yes	—
332	D₄	C₂²×#89137	1	1	yes	characteristic, complemented
333	C₂×C₄	—	2	1	no	—
334	C₂×C₄	—	109	1	no	—
335	C₂×C₄	—	109	1	no	—
336	C₂×C₄	—	109	1	no	—
337	C₂×C₄	—	109	1	no	—
338	C₂×C₄	—	109	1	no	—
339	C₂×C₄	—	109	1	no	—
340	C₂×C₄	—	109	1	no	—
341	C₂×C₄	—	109	1	no	—
342	C₂×C₄	—	109	1	no	—
343	C₂×C₄	—	436	4	no	—
344	C₂×C₄	—	436	2	no	—
345	C₂×C₄	—	436	2	no	—
346	C₂×C₄	—	436	4	no	—
347	C₂×C₄	—	436	2	no	—
348	C₂×C₄	—	436	1	no	—
349	C₂×C₄	—	218	1	no	—
350	C₂×C₄	—	218	1	no	—
351	C₂×C₄	—	218	1	no	—
352	C₂×C₄	—	218	2	no	—
353	C₂×C₄	—	218	1	no	—
354	C₂×C₄	—	218	1	no	—
355	C₂×C₄	—	218	2	no	—
356	C₂×C₄	—	218	1	no	—
357	C₂×C₄	C₂²×#89137	1	1	yes	characteristic
358	C₈	—	109	2	no	—
359	C₈	—	218	2	no	—
360	C₈	C₂²×#89137	1	2	yes	complemented
361	C₂²	—	2	1	no	—
362	C₂²	—	2	2	no	—
363	C₂²	—	4	2	no	—
364	C₂²	—	109	1	no	—
365	C₂²	—	109	1	no	—
366	C₂²	—	436	2	no	—
367	C₂²	—	436	2	no	—
368	C₂²	—	436	1	no	—
369	C₂²	—	436	1	no	—
370	C₂²	—	436	2	no	—
371	C₂²	—	436	4	no	—
372	C₂²	—	218	1	no	—
373	C₂²	—	218	1	no	—
374	C₂²	—	218	1	no	—
375	C₂²	—	218	2	no	—
376	C₂²	D₄×#89137	1	1	yes	characteristic
377	C₄	—	2	1	no	—
378	C₄	—	109	2	no	—
379	C₄	—	109	1	no	—
380	C₄	—	109	1	no	—
381	C₄	—	436	2	no	—
382	C₄	—	436	1	no	—
383	C₄	—	436	1	no	—
384	C₄	—	218	1	no	—
385	C₄	—	218	1	no	—
386	C₄	—	218	1	no	—
387	C₄	—	218	1	no	—
388	C₄	D₄×#89137	1	1	yes	characteristic
389	C₄	C₂³×#89137	1	1	yes	characteristic
390	C₂	—	2	1	no	—
391	C₂	—	4	2	no	—
392	C₂	—	4	1	no	—
393	C₂	—	109	1	no	—
394	C₂	—	109	1	no	—
395	C₂	—	436	2	no	—
396	C₂	—	436	1	no	—
397	C₂	—	218	1	no	—
398	C₂	C₂×D₄×#89137	1	1	yes	characteristic

	subgroup	G/H
center	C₂	C₂×D₄×#89137
commutator	C₄×C₁₀₉	C₂³×C₄
Frattini	C₄	C₂³×#89137
Fitting	AGL(1,ℤ/8)×C₁₀₉	C₄
socle	C₂×C₁₀₉	C₂×C₄×D₄
prime radical	AGL(1,ℤ/8)×D₁₀₉	C₂
cosocle	C₄×D₁₀₉	C₂⁴
hypercenter	AGL(1,ℤ/8)	#89137
hypocenter	C₁₀₉	C₄×AGL(1,ℤ/8)
LCS	G ▷ C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂ ◁ C₂×C₄ ◁ AGL(1,ℤ/8)

Complements

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

N	H ≅ G/N	type
1. #41×#89137	C₂	semidirect
2. C₂×D₄×#89137	C₂	semidirect
3. #20296067	C₂	semidirect
4. #20296065	C₂	semidirect
5. SD₁₆×#89137	C₂	semidirect
6. D₈×#89137	C₂	semidirect
7. #20296037	C₂	semidirect
8. #20296018	C₂	semidirect
9. #20296017	C₂	semidirect
10. M₁₆×#89137	C₂	semidirect
14. Q₈×#89137	C₂²	semidirect
15. Q₈×#89137	C₂²	semidirect
22. D₄×#89137	C₂²	semidirect
23. D₄×#89137	C₂²	semidirect
30. #16812768	C₂²	semidirect
31. #16812767	C₂²	semidirect
32. #16812762	C₂²	semidirect
35. #16812761	C₂²	semidirect
36. #16812753	C₂²	semidirect
37. C₈×#89137	C₂²	semidirect
40. #16812727	C₄	semidirect
41. #16812726	C₄	semidirect
42. #16812725	C₄	semidirect
43. #16812724	C₄	semidirect
44. #16812723	C₄	semidirect
48. AGL(1,ℤ/8)×C₁₀₉	C₄	semidirect
79. #13182030	C₂×C₄	semidirect
81. #13182029	C₂×C₄	semidirect
83. #13182028	C₂×C₄	semidirect
85. C₂×D₄₃₆	C₂×C₄	semidirect
90. D₄×D₁₀₉	C₂×C₄	semidirect
95. #13182018	C₂×C₄	semidirect
96. #13182017	C₂×C₄	semidirect
97. #13182016	C₂×C₄	semidirect
98. D₈₇₂	C₂×C₄	semidirect
99. #13182014	C₂×C₄	semidirect
100. #13182014	C₂×C₄	semidirect
101. #13182013	C₂×C₄	semidirect
102. #13182012	C₂×C₄	semidirect
104. #41×C₁₀₉	C₂×C₄	semidirect
105. C₂×D₄×C₁₀₉	C₂×C₄	semidirect
106. SD₁₆×C₁₀₉	C₂×C₄	semidirect
107. D₈×C₁₀₉	C₂×C₄	semidirect
108. M₁₆×C₁₀₉	C₂×C₄	semidirect
131. Q₈×C₁₀₉	C₂²×C₄	semidirect
135. D₄×C₁₀₉	C₂²×C₄	semidirect
148. D₄₃₆	C₂²×C₄	semidirect
157. Dic₂₁₈	C₂²×C₄	semidirect
159. C₈×C₁₀₉	C₂²×C₄	semidirect
160. #11724784	C₂²×C₄	semidirect
183. #89137	AGL(1,ℤ/8)	direct (N × H)
200. C₁₀₉	C₄×AGL(1,ℤ/8)	semidirect
220. AGL(1,ℤ/8)	#89137	direct (N × H)
255. #41	C₂×#89137	semidirect
265. C₂×D₄	C₂×#89137	semidirect
279. SD₁₆	C₂×#89137	semidirect
283. D₈	C₂×#89137	semidirect
288. M₁₆	C₂×#89137	semidirect
319. Q₈	C₂²×#89137	semidirect
332. D₄	C₂²×#89137	semidirect
360. C₈	C₂²×#89137	semidirect

Maximal subgroups

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

subgroup	index
#41×#89137	2
C₂×D₄×#89137	2
#20296067	2
#20296065	2
SD₁₆×#89137	2
D₈×#89137	2
#20296037	2
#20296018	2
#20296017	2
M₁₆×#89137	2
AGL(1,ℤ/8)×D₁₀₉	2
C₄×AGL(1,ℤ/8)	109