Subgroups — #135×#10596842 #34034522

Order 18688.

750 conjugacy classes of subgroups.

The subgroup lattice has 418 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#41×#10596842	C₂	1	2	yes	maximal, complemented
2	Q₁₆×#10596842	C₂	1	2	yes	maximal, complemented
3	SD₁₆×#10596842	C₂	1	4	yes	maximal, complemented
4	D₈×#10596842	C₂	1	2	yes	maximal, complemented
5	#22627055	C₂	1	1	yes	maximal, characteristic, complemented
6	#22627049	C₂	1	2	yes	maximal, complemented
7	C₂×C₈×#10596842	C₂	1	1	yes	maximal, characteristic, complemented
8	#135×#64408	C₂	1	1	yes	maximal, characteristic
9	Q₈×#10596842	C₂²	1	4	yes	—
10	D₄×#10596842	—	2	4	no	—
11	D₄×#10596842	C₂²	1	4	yes	—
12	#17989700	—	2	2	no	—
13	#17989700	C₂²	1	2	yes	—
14	C₂×C₄×#10596842	—	2	2	no	—
15	C₂×C₄×#10596842	C₂²	1	1	yes	characteristic
16	C₂×C₄×#10596842	C₂²	1	1	yes	characteristic
17	#17989677	C₂²	1	2	yes	—
18	#17989676	C₂²	1	2	yes	—
19	Q₈⋊#10596842	C₂²	1	4	yes	—
20	D₄⋊#10596842	C₂²	1	4	yes	—
21	C₈×#10596842	C₂²	1	2	yes	—
22	C₈×#10596842	C₂²	1	2	yes	—
23	#41×#64408	C₂²	1	2	yes	—
24	Q₁₆×#64408	C₄	1	1	yes	characteristic
25	Q₁₆×#64408	C₂²	1	1	yes	characteristic
26	SD₁₆×#64408	C₄	1	2	yes	—
27	SD₁₆×#64408	C₂²	1	2	yes	—
28	D₈×#64408	C₄	1	1	yes	characteristic
29	D₈×#64408	C₂²	1	1	yes	characteristic
30	#17989597	C₄	1	1	yes	characteristic
31	#17989577	C₄	1	2	yes	—
32	C₂×C₈×#64408	C₂²	1	1	yes	characteristic
33	#135×D₇₃	C₄	1	1	yes	characteristic
34	C₂²×#10596842	—	2	4	no	—
35	C₂²×#10596842	—	2	1	no	—
36	C₂²×#10596842	D₄	1	2	yes	—
37	C₄⋊#10596842	—	2	4	no	—
38	C₄⋊#10596842	C₂³	1	4	yes	—
39	C₂²⋊#10596842	—	2	4	no	—
40	C₂²⋊#10596842	—	2	2	no	—
41	C₄×#10596842	—	2	4	no	—
42	C₄×#10596842	—	2	2	no	—
43	C₄×#10596842	—	2	1	no	—
44	C₄×#10596842	D₄	1	1	yes	characteristic
45	C₄×#10596842	D₄	1	1	yes	characteristic
46	C₄×#10596842	C₂³	1	2	yes	—
47	C₄×#10596842	C₂³	1	2	yes	—
48	C₂×#11924036	C₂×C₄	1	1	yes	characteristic
49	Q₈×#64408	C₂×C₄	1	2	yes	—
50	Q₈×#64408	C₂³	1	2	yes	—
51	D₄×#64408	—	2	2	no	—
52	D₄×#64408	—	2	2	no	—
53	D₄×#64408	C₂×C₄	1	2	yes	—
54	D₄×#64408	C₂³	1	2	yes	—
55	#14556670	—	2	2	no	—
56	#14556670	C₂×C₄	1	2	yes	—
57	C₂×C₄×#64408	—	2	2	no	—
58	C₂×C₄×#64408	C₂³	1	1	yes	characteristic
59	#14556660	C₂×C₄	1	1	yes	characteristic
60	#14556660	C₂×C₄	1	1	yes	characteristic
61	#14556659	C₂×C₄	1	2	yes	—
62	#14556654	C₂×C₄	1	2	yes	—
63	#14556654	C₂×C₄	1	2	yes	—
64	#14556653	C₂×C₄	1	2	yes	—
65	#14556653	C₂×C₄	1	2	yes	—
66	C₈×#64408	C₂×C₄	1	1	yes	characteristic
67	C₈×#64408	C₂×C₄	1	1	yes	characteristic
68	C₈×#64408	C₂³	1	1	yes	characteristic
69	C₈×#64408	C₂³	1	1	yes	characteristic
70	#41×D₇₃	C₂×C₄	1	2	yes	—
71	#14556614	C₈	1	1	yes	characteristic, complemented
72	#14556613	C₈	1	1	yes	characteristic, complemented
73	#14556612	C₈	1	2	yes	complemented
74	#14556611	C₈	1	2	yes	complemented
75	#14556610	C₈	1	1	yes	characteristic, complemented
76	Q₁₆×D₇₃	C₂×C₄	1	1	yes	characteristic
77	SD₁₆×D₇₃	C₂×C₄	1	2	yes	—
78	D₈×D₇₃	C₂×C₄	1	1	yes	characteristic
79	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
80	#135×C₇₃	C₈	1	1	yes	characteristic, complemented
81	C₂×#10596842	—	2	4	no	—
82	C₂×#10596842	—	2	2	no	—
83	C₂×#10596842	—	2	4	no	—
84	C₂×#10596842	—	2	4	no	—
85	C₂×#10596842	—	4	8	no	—
86	C₂×#10596842	C₂×D₄	1	2	yes	—
87	C₂×#10596842	C₂×D₄	1	2	yes	—
88	C₂²×#64408	—	2	2	no	—
89	C₂²×#64408	—	2	2	no	—
90	C₂²×#64408	C₂×D₄	1	1	yes	characteristic
91	C₂²×#64408	#41	1	1	yes	characteristic
92	#11924036	—	2	1	no	—
93	#11924036	C₂²×C₄	1	1	yes	characteristic
94	#11924036	C₂²×C₄	1	1	yes	characteristic
95	C₂×#10596833	—	2	1	no	—
96	C₄⋊#64408	—	2	2	no	—
97	C₄⋊#64408	—	2	2	no	—
98	C₄⋊#64408	C₂²×C₄	1	2	yes	—
99	C₄⋊#64408	C₂²×C₄	1	2	yes	—
100	C₂²⋊#64408	—	2	2	no	—
101	C₂²⋊#64408	—	2	2	no	—
102	C₂²⋊#64408	—	2	2	no	—
103	C₄×#64408	—	2	2	no	—
104	C₄×#64408	—	2	2	no	—
105	C₄×#64408	—	2	2	no	—
106	C₄×#64408	C₂²×C₄	1	1	yes	characteristic
107	C₄×#64408	C₂×D₄	1	1	yes	characteristic
108	C₄×#64408	#41	1	1	yes	characteristic
109	C₄×#64408	C₂⁴	1	1	yes	characteristic
110	#11924029	C₂×C₈	1	2	yes	complemented
111	#11924028	—	2	2	no	—
112	#11924028	C₂×C₈	1	2	yes	complemented
113	#11924027	—	2	2	no	—
114	#11924027	C₂×C₈	1	2	yes	complemented
115	Q₈×D₇₃	C₂²×C₄	1	2	yes	—
116	D₄×D₇₃	—	2	2	no	—
117	D₄×D₇₃	C₂²×C₄	1	2	yes	—
118	C₂×C₄×D₇₃	—	2	2	no	—
119	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
120	Dic₂₉₂	C₂×C₈	1	1	yes	characteristic, complemented
121	#11924018	C₂×C₈	1	2	yes	complemented
122	#11924017	C₂×C₈	1	2	yes	complemented
123	#11924016	C₂×C₈	1	2	yes	complemented
124	#11924015	C₂×C₈	1	2	yes	complemented
125	D₅₈₄	C₂×C₈	1	1	yes	characteristic, complemented
126	#11924013	C₂×C₈	1	2	yes	complemented
127	C₂×#10596831	C₂×C₈	1	1	yes	characteristic, complemented
128	C₈×D₇₃	C₂×C₈	1	1	yes	characteristic, complemented
129	C₈×D₇₃	C₂×C₈	1	1	yes	characteristic, complemented
130	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
131	C₈×D₇₃	C₂²×C₄	1	1	yes	characteristic
132	#41×C₇₃	C₂×C₈	1	2	yes	complemented
133	Q₁₆×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
134	SD₁₆×C₇₃	C₂×C₈	1	2	yes	complemented
135	D₈×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
136	C₂×C₈×C₇₃	C₂×C₈	1	1	yes	characteristic, complemented
137	C₂²×D₇₃	—	2	2	no	—
138	C₂²×D₇₃	C₄×D₄	1	1	yes	characteristic
139	C₂×#64408	—	2	2	no	—
140	C₂×#64408	—	2	2	no	—
141	C₂×#64408	—	2	2	no	—
142	C₂×#64408	—	2	2	no	—
143	C₂×#64408	—	4	4	no	—
144	C₂×#64408	—	4	4	no	—
145	C₂×#64408	C₄×D₄	1	1	yes	characteristic
146	C₂×#64408	C₄×D₄	1	1	yes	characteristic
147	C₂×#64408	C₂²×D₄	1	1	yes	characteristic
148	C₂×#64408	C₂×#41	1	1	yes	characteristic
149	#10596842	—	2	4	no	—
150	#10596842	—	2	2	no	—
151	#10596842	—	4	4	no	—
152	#10596842	#135	1	4	yes	direct product factor
153	Q₈×C₇₃	C₂²×C₈	1	2	yes	—
154	D₄×C₇₃	—	2	2	no	—
155	D₄×C₇₃	C₂²×C₈	1	2	yes	—
156	C₂×C₄×C₇₃	—	2	2	no	—
157	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
158	C₂²⋊D₇₃	—	2	2	no	—
159	C₂²⋊D₇₃	—	2	2	no	—
160	C₂²⋊D₇₃	—	2	2	no	—
161	C₂×Dic₇₃	—	2	2	no	—
162	C₂×Dic₇₃	#131	1	1	yes	characteristic
163	D₂₉₂	—	2	2	no	—
164	D₂₉₂	C₂²×C₈	1	2	yes	—
165	C₄×D₇₃	—	2	2	no	—
166	C₄×D₇₃	—	2	2	no	—
167	C₄×D₇₃	—	2	2	no	—
168	C₄×D₇₃	C₄×D₄	1	1	yes	characteristic
169	C₄×D₇₃	C₂²×C₈	1	1	yes	characteristic
170	C₄×D₇₃	#131	1	1	yes	characteristic
171	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
172	Dic₁₄₆	—	2	2	no	—
173	Dic₁₄₆	C₂²×C₈	1	2	yes	—
174	#10596833	—	2	1	no	—
175	#10596833	—	2	1	no	—
176	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
177	C₈×C₇₃	C₂²×C₈	1	1	yes	characteristic
178	#10596831	C₂²×C₈	1	1	yes	characteristic
179	#10596831	C₂²×C₈	1	1	yes	characteristic
180	C₂²×C₇₃	—	2	2	no	—
181	C₂²×C₇₃	C₈×D₄	1	1	yes	characteristic
182	C₂×D₇₃	—	2	1	no	—
183	C₂×D₇₃	—	2	1	no	—
184	C₂×D₇₃	—	2	2	no	—
185	C₂×D₇₃	—	4	2	no	—
186	C₂×D₇₃	—	4	2	no	—
187	C₂×D₇₃	C₈×D₄	1	1	yes	characteristic
188	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
189	#64408	—	2	1	no	—
190	#64408	—	2	1	no	—
191	#64408	—	4	2	no	—
192	#64408	—	4	2	no	—
193	#64408	#443	1	2	yes	—
194	#64408	C₂×#135	1	2	yes	—
195	C₄×C₇₃	—	2	2	no	—
196	C₄×C₇₃	C₈×D₄	1	1	yes	characteristic
197	C₄×C₇₃	C₂³×C₈	1	1	yes	characteristic
198	Dic₇₃	—	2	2	no	—
199	Dic₇₃	C₈×D₄	1	1	yes	characteristic
200	Dic₇₃	C₂×#131	1	1	yes	characteristic
201	C₈×#135	—	73	1	no	maximal, Sylow
202	C₂×C₇₃	—	2	1	no	—
203	C₂×C₇₃	—	4	2	no	—
204	C₂×C₇₃	C₂×C₈×D₄	1	1	yes	characteristic
205	D₇₃	—	2	1	no	—
206	D₇₃	—	4	2	no	—
207	D₇₃	C₄×#135	1	1	yes	characteristic
208	D₇₃	C₂×#443	1	1	yes	characteristic
209	C₈×#41	—	73	2	no	—
210	C₄×#135	—	73	1	no	—
211	C₈×Q₁₆	—	73	2	no	—
212	C₈×SD₁₆	—	73	4	no	—
213	C₈×D₈	—	73	2	no	—
214	#1564	—	73	1	no	—
215	#1476	—	73	2	no	—
216	C₂×C₈²	—	73	1	no	—
217	C₇₃	C₈×#135	1	1	yes	characteristic, complemented, Sylow
218	C₂×#135	—	73	1	no	—
219	C₄×#41	—	73	2	no	—
220	C₈×Q₈	—	73	4	no	—
221	C₄×Q₁₆	—	73	1	no	—
222	C₄×Q₁₆	—	73	1	no	—
223	C₄×SD₁₆	—	73	2	no	—
224	C₄×SD₁₆	—	73	2	no	—
225	C₄×D₈	—	73	1	no	—
226	C₄×D₈	—	73	1	no	—
227	C₈×D₄	—	73	4	no	—
228	C₈×D₄	—	146	4	no	—
229	#431	—	73	2	no	—
230	#431	—	146	2	no	—
231	#427	—	73	1	no	—
232	#416	—	73	2	no	—
233	C₂×C₄×C₈	—	73	1	no	—
234	C₂×C₄×C₈	—	73	1	no	—
235	C₂×C₄×C₈	—	73	1	no	—
236	C₂×C₄×C₈	—	146	2	no	—
237	#335	—	73	2	no	—
238	#334	—	73	2	no	—
239	Q₈⋊C₈	—	73	4	no	—
240	D₄⋊C₈	—	73	4	no	—
241	C₈²	—	73	2	no	—
242	C₈²	—	73	2	no	—
243	C₂×#41	—	73	2	no	—
244	#135	—	73	2	no	—
245	#135	—	73	1	no	—
246	#135	—	73	2	no	—
247	#135	—	73	1	no	—
248	#135	—	73	1	no	—
249	#135	#10596842	1	1	yes	characteristic, direct product factor
250	C₂×Q₁₆	—	73	1	no	—
251	C₂×SD₁₆	—	73	2	no	—
252	C₂×D₈	—	73	1	no	—
253	C₂²×C₈	—	73	1	no	—
254	C₂²×C₈	—	73	1	no	—
255	C₂²×C₈	—	73	2	no	—
256	C₂²×C₈	—	146	4	no	—
257	C₂²×C₈	—	146	1	no	—
258	C₄×Q₈	—	73	2	no	—
259	C₄×Q₈	—	73	2	no	—
260	C₄×D₄	—	73	2	no	—
261	C₄×D₄	—	73	2	no	—
262	C₄×D₄	—	146	2	no	—
263	C₄×D₄	—	146	2	no	—
264	#117	—	73	2	no	—
265	#117	—	146	2	no	—
266	C₂×C₄²	—	73	1	no	—
267	C₂×C₄²	—	146	2	no	—
268	#107	—	73	1	no	—
269	#107	—	73	1	no	—
270	#106	—	73	2	no	—
271	C₄⋊C₈	—	73	4	no	—
272	C₄⋊C₈	—	146	4	no	—
273	#103	—	73	2	no	—
274	#103	—	73	2	no	—
275	#102	—	73	2	no	—
276	#102	—	73	2	no	—
277	C₂²⋊C₈	—	146	4	no	—
278	C₂²⋊C₈	—	146	2	no	—
279	C₄×C₈	—	73	1	no	—
280	C₄×C₈	—	73	1	no	—
281	C₄×C₈	—	73	2	no	—
282	C₄×C₈	—	73	1	no	—
283	C₄×C₈	—	73	1	no	—
284	C₄×C₈	—	73	1	no	—
285	C₄×C₈	—	73	1	no	—
286	C₄×C₈	—	73	2	no	—
287	C₄×C₈	—	146	1	no	—
288	C₄×C₈	—	146	2	no	—
289	C₄×C₈	—	146	4	no	—
290	#41	—	73	2	no	—
291	#41	—	73	2	no	—
292	#41	—	73	2	no	—
293	#41	—	146	2	no	—
294	#41	—	146	2	no	—
295	#41	C₂×#10596842	1	2	yes	complemented
296	C₂×Q₈	—	73	2	no	—
297	C₂×D₄	—	73	2	no	—
298	C₂×D₄	—	146	2	no	—
299	C₂²×C₄	—	73	1	no	—
300	C₂²×C₄	—	73	1	no	—
301	C₂²×C₄	—	73	1	no	—
302	C₂²×C₄	—	146	2	no	—
303	C₂²×C₄	—	146	2	no	—
304	C₂²×C₄	—	146	2	no	—
305	Q₁₆	—	73	2	no	—
306	Q₁₆	—	73	1	no	—
307	Q₁₆	C₂×#10596842	1	1	yes	characteristic, complemented
308	SD₁₆	—	73	2	no	—
309	SD₁₆	—	73	2	no	—
310	SD₁₆	—	73	2	no	—
311	SD₁₆	C₂×#10596842	1	2	yes	complemented
312	D₈	—	73	2	no	—
313	D₈	—	73	1	no	—
314	D₈	C₂×#10596842	1	1	yes	characteristic, complemented
315	C₂×C₈	—	292	8	no	—
316	C₂×C₈	—	73	2	no	—
317	C₂×C₈	—	73	1	no	—
318	C₂×C₈	—	73	1	no	—
319	C₂×C₈	—	73	1	no	—
320	C₂×C₈	—	73	1	no	—
321	C₂×C₈	—	73	1	no	—
322	C₂×C₈	—	73	1	no	—
323	C₂×C₈	—	73	1	no	—
324	C₂×C₈	—	73	2	no	—
325	C₂×C₈	—	146	4	no	—
326	C₂×C₈	—	146	4	no	—
327	C₂×C₈	—	146	1	no	—
328	C₂×C₈	—	146	1	no	—
329	C₂×C₈	—	146	2	no	—
330	C₂×C₈	—	146	4	no	—
331	C₂×C₈	C₂×#10596842	1	1	yes	characteristic, complemented
332	C₄⋊C₄	—	73	2	no	—
333	C₄⋊C₄	—	73	2	no	—
334	C₄⋊C₄	—	146	2	no	—
335	C₄⋊C₄	—	146	2	no	—
336	C₂²⋊C₄	—	146	2	no	—
337	C₂²⋊C₄	—	146	2	no	—
338	C₂²⋊C₄	—	146	2	no	—
339	C₄²	—	73	1	no	—
340	C₄²	—	73	1	no	—
341	C₄²	—	73	1	no	—
342	C₄²	—	73	1	no	—
343	C₄²	—	146	2	no	—
344	C₄²	—	146	2	no	—
345	C₄²	—	146	2	no	—
346	C₂³	—	73	1	no	—
347	C₂³	—	146	2	no	—
348	Q₈	—	73	2	no	—
349	Q₈	—	146	2	no	—
350	Q₈	C₂²×#10596842	1	2	yes	—
351	D₄	—	2	2	no	—
352	D₄	—	73	2	no	—
353	D₄	—	146	2	no	—
354	D₄	—	146	2	no	—
355	D₄	—	146	2	no	—
356	D₄	—	146	2	no	—
357	D₄	C₂²×#10596842	1	2	yes	—
358	C₂×C₄	—	2	2	no	—
359	C₂×C₄	—	292	4	no	—
360	C₂×C₄	—	292	4	no	—
361	C₂×C₄	—	73	1	no	—
362	C₂×C₄	—	73	1	no	—
363	C₂×C₄	—	73	1	no	—
364	C₂×C₄	—	73	1	no	—
365	C₂×C₄	—	73	1	no	—
366	C₂×C₄	—	73	1	no	—
367	C₂×C₄	—	73	1	no	—
368	C₂×C₄	—	73	1	no	—
369	C₂×C₄	—	73	1	no	—
370	C₂×C₄	—	146	2	no	—
371	C₂×C₄	—	146	2	no	—
372	C₂×C₄	—	146	2	no	—
373	C₂×C₄	—	146	2	no	—
374	C₂×C₄	—	146	2	no	—
375	C₂×C₄	—	146	2	no	—
376	C₂×C₄	—	146	2	no	—
377	C₂×C₄	—	146	2	no	—
378	C₂×C₄	C₂²×#10596842	1	1	yes	characteristic
379	C₈	—	292	4	no	—
380	C₈	—	73	4	no	—
381	C₈	—	73	1	no	—
382	C₈	—	73	1	no	—
383	C₈	—	146	1	no	—
384	C₈	—	146	1	no	—
385	C₈	—	146	2	no	—
386	C₈	—	146	4	no	—
387	C₈	C₂²×#10596842	1	1	yes	characteristic
388	C₈	C₂²×#10596842	1	1	yes	characteristic
389	C₂²	—	2	2	no	—
390	C₂²	—	292	2	no	—
391	C₂²	—	292	2	no	—
392	C₂²	—	73	1	no	—
393	C₂²	—	73	1	no	—
394	C₂²	—	146	1	no	—
395	C₂²	—	146	1	no	—
396	C₂²	—	146	2	no	—
397	C₂²	D₄×#10596842	1	1	yes	characteristic
398	C₄	—	2	2	no	—
399	C₄	—	292	2	no	—
400	C₄	—	292	2	no	—
401	C₄	—	73	2	no	—
402	C₄	—	73	2	no	—
403	C₄	—	73	1	no	—
404	C₄	—	73	1	no	—
405	C₄	—	146	1	no	—
406	C₄	—	146	1	no	—
407	C₄	—	146	2	no	—
408	C₄	D₄×#10596842	1	1	yes	characteristic
409	C₄	C₂³×#10596842	1	1	yes	characteristic
410	C₂	—	2	1	no	—
411	C₂	—	4	2	no	—
412	C₂	—	292	2	no	—
413	C₂	—	73	1	no	—
414	C₂	—	73	1	no	—
415	C₂	—	146	1	no	—
416	C₂	C₂×D₄×#10596842	1	1	yes	characteristic

	subgroup	G/H
center	C₄	D₄×#10596842
commutator	C₄×C₇₃	C₂³×C₈
Frattini	C₄	C₂³×#10596842
Fitting	#135×C₇₃	C₈
socle	C₂×C₇₃	C₂×C₈×D₄
prime radical	#135×D₇₃	C₄
cosocle	C₄×#64408	C₂⁴
hypercenter	#135	#10596842
hypocenter	C₇₃	C₈×#135
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₄ ◁ C₂×C₄ ◁ #135

Complements

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

N	H ≅ G/N	type
1. #41×#10596842	C₂	semidirect
2. Q₁₆×#10596842	C₂	semidirect
3. SD₁₆×#10596842	C₂	semidirect
4. D₈×#10596842	C₂	semidirect
5. #22627055	C₂	semidirect
6. #22627049	C₂	semidirect
7. C₂×C₈×#10596842	C₂	semidirect
71. #14556614	C₈	semidirect
72. #14556613	C₈	semidirect
73. #14556612	C₈	semidirect
74. #14556611	C₈	semidirect
75. #14556610	C₈	semidirect
80. #135×C₇₃	C₈	semidirect
110. #11924029	C₂×C₈	semidirect
112. #11924028	C₂×C₈	semidirect
114. #11924027	C₂×C₈	semidirect
120. Dic₂₉₂	C₂×C₈	semidirect
121. #11924018	C₂×C₈	semidirect
122. #11924017	C₂×C₈	semidirect
123. #11924016	C₂×C₈	semidirect
124. #11924015	C₂×C₈	semidirect
125. D₅₈₄	C₂×C₈	semidirect
126. #11924013	C₂×C₈	semidirect
127. C₂×#10596831	C₂×C₈	semidirect
128. C₈×D₇₃	C₂×C₈	semidirect
129. C₈×D₇₃	C₂×C₈	semidirect
132. #41×C₇₃	C₂×C₈	semidirect
133. Q₁₆×C₇₃	C₂×C₈	semidirect
134. SD₁₆×C₇₃	C₂×C₈	semidirect
135. D₈×C₇₃	C₂×C₈	semidirect
136. C₂×C₈×C₇₃	C₂×C₈	semidirect
152. #10596842	#135	direct (N × H)
217. C₇₃	C₈×#135	semidirect
249. #135	#10596842	direct (N × H)
295. #41	C₂×#10596842	semidirect
307. Q₁₆	C₂×#10596842	semidirect
311. SD₁₆	C₂×#10596842	semidirect
314. D₈	C₂×#10596842	semidirect
331. C₂×C₈	C₂×#10596842	semidirect

Maximal subgroups

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

subgroup	index
#41×#10596842	2
Q₁₆×#10596842	2
SD₁₆×#10596842	2
D₈×#10596842	2
#22627055	2
#22627049	2
C₂×C₈×#10596842	2
#135×#64408	2
C₈×#135	73