Subgroups — C₂×#22562088 #31009229

Order 17152.

662 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863826	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863514	C₂	1	1	yes	maximal, characteristic, complemented
3	#22562088	C₂	1	8	yes	maximal, direct product factor
4	C₂×#16863225	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#16863203	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863202	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄×C₆₇⋊C₁₆	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#443×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14524065	C₂²	1	1	yes	characteristic
10	C₂×#14524049	—	2	1	no	—
11	#16863826	C₄	1	4	yes	complemented
12	#16863826	C₂²	1	4	yes	—
13	C₂×#14523989	C₄	1	1	yes	characteristic, complemented
14	C₂×#14523987	C₄	1	1	yes	characteristic, complemented
15	C₂×#14523986	C₄	1	1	yes	characteristic, complemented
16	C₂×#14523984	C₄	1	1	yes	characteristic, complemented
17	C₂²×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
18	C₂²×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
19	#16863514	—	2	2	no	—
20	#16863514	C₂²	1	4	yes	complemented
21	C₂×#14523979	C₂²	1	1	yes	characteristic
22	C₂×#14523971	—	2	1	no	—
23	#16863225	C₂²	1	4	yes	complemented
24	#16863203	C₂²	1	4	yes	complemented
25	#16863202	C₂²	1	4	yes	complemented
26	C₄×C₆₇⋊C₁₆	C₂²	1	4	yes	complemented
27	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
28	C₂×#131×C₆₇	—	2	1	no	—
29	#443×C₆₇	—	2	2	no	—
30	#443×C₆₇	C₂²	1	4	yes	complemented
31	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
32	C₂×#104×C₆₇	—	2	1	no	—
33	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#11761628	—	2	1	no	—
35	#14524065	—	2	1	no	—
36	#14524065	—	2	1	no	—
37	#14524065	C₂×C₄	1	2	yes	—
38	#14524065	C₂³	1	2	yes	—
39	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic
40	C₂×#11761617	—	2	1	no	—
41	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
42	#14524049	—	2	4	no	—
43	#14524049	—	4	2	no	—
44	C₂×#11761612	—	2	1	no	—
45	C₂×#11761611	—	4	1	no	—
46	C₂×C₈×D₆₇	—	4	1	no	—
47	#14523989	C₂×C₄	1	4	yes	complemented
48	#14523987	C₂×C₄	1	4	yes	complemented
49	#14523986	C₂×C₄	1	4	yes	complemented
50	#14523984	C₂×C₄	1	4	yes	complemented
51	C₂×C₆₇⋊C₁₆	—	2	1	no	—
52	C₂×C₆₇⋊C₁₆	—	2	1	no	—
53	C₂×C₆₇⋊C₁₆	C₂×C₄	1	1	yes	characteristic
54	C₂×C₆₇⋊C₁₆	C₂×C₄	1	1	yes	characteristic
55	C₂×C₆₇⋊C₁₆	C₂×C₄	1	2	yes	—
56	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
57	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
58	#14523979	—	2	1	no	—
59	#14523979	C₂³	1	2	yes	—
60	#14523971	—	2	4	no	—
61	C₂×#41×C₆₇	—	2	1	no	—
62	#135×C₆₇	—	2	1	no	—
63	#135×C₆₇	—	2	1	no	—
64	#135×C₆₇	C₂×C₄	1	2	yes	—
65	#135×C₆₇	C₂³	1	2	yes	—
66	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
67	C₂×SD₁₆×C₆₇	—	2	1	no	—
68	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
69	#131×C₆₇	—	2	4	no	—
70	#131×C₆₇	—	4	2	no	—
71	C₂×M₁₆×C₆₇	—	2	1	no	—
72	C₂×M₁₆×C₆₇	—	4	1	no	—
73	C₂²×C₈×C₆₇	—	4	1	no	—
74	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
75	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
76	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
77	#108×C₆₇	—	2	1	no	—
78	#108×C₆₇	C₂³	1	2	yes	—
79	#104×C₆₇	—	2	4	no	—
80	C₄×C₈×C₆₇	D₄	1	2	yes	—
81	C₄×C₈×C₆₇	C₂³	1	2	yes	—
82	#11761628	—	2	2	no	—
83	#11761628	—	2	2	no	—
84	#11761628	—	4	1	no	—
85	#11761628	—	4	1	no	—
86	C₂×Dic₁₃₄	—	2	1	no	—
87	C₂×D₂₆₈	—	2	1	no	—
88	C₂×C₂²⋊D₆₇	—	4	1	no	—
89	C₂×C₄×D₆₇	—	4	1	no	—
90	Dic₂₆₈	—	2	1	no	—
91	Dic₂₆₈	C₂²×C₄	1	2	yes	—
92	#11761617	—	2	2	no	—
93	#11761617	—	2	2	no	—
94	D₅₃₆	—	2	1	no	—
95	D₅₃₆	C₂²×C₄	1	2	yes	—
96	#11761612	—	2	2	no	—
97	#11761612	—	4	1	no	—
98	#11761611	—	4	4	no	—
99	C₂×C₆₇⋊C₈	—	4	1	no	—
100	C₈×D₆₇	—	4	4	no	—
101	C₆₇⋊C₁₆	—	2	2	no	—
102	C₆₇⋊C₁₆	C₂²×C₄	1	2	yes	—
103	C₆₇⋊C₁₆	C₂²×C₄	1	2	yes	—
104	#41×C₆₇	—	2	2	no	—
105	#41×C₆₇	—	2	2	no	—
106	#41×C₆₇	—	4	1	no	—
107	#41×C₆₇	—	4	1	no	—
108	C₂×Q₈×C₆₇	—	2	1	no	—
109	C₂×D₄×C₆₇	—	2	1	no	—
110	C₂×D₄×C₆₇	—	4	1	no	—
111	C₂²×C₄×C₆₇	—	2	1	no	—
112	C₂²×C₄×C₆₇	—	4	1	no	—
113	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
114	Q₁₆×C₆₇	—	2	1	no	—
115	Q₁₆×C₆₇	C₂²×C₄	1	2	yes	—
116	SD₁₆×C₆₇	—	2	2	no	—
117	SD₁₆×C₆₇	—	2	2	no	—
118	D₈×C₆₇	—	2	1	no	—
119	D₈×C₆₇	C₂²×C₄	1	2	yes	—
120	M₁₆×C₆₇	—	2	2	no	—
121	M₁₆×C₆₇	—	4	1	no	—
122	M₁₆×C₆₇	—	4	4	no	—
123	C₂×C₈×C₆₇	—	4	1	no	—
124	C₂×C₈×C₆₇	—	4	4	no	—
125	C₂×C₈×C₆₇	D₈	1	1	yes	characteristic
126	C₂×C₈×C₆₇	D₈	1	2	yes	—
127	C₂×C₈×C₆₇	D₈	1	1	yes	characteristic
128	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
129	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
130	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
131	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
133	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
134	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
135	C₄²×C₆₇	—	2	1	no	—
136	C₄²×C₆₇	C₂×D₄	1	2	yes	—
137	C₂³×C₆₇	—	4	1	no	—
138	C₂³×C₆₇	#135	1	1	yes	characteristic
139	C₂²×D₆₇	—	4	1	no	—
140	Q₈×C₆₇	—	2	2	no	—
141	Q₈×C₆₇	—	4	1	no	—
142	D₄×C₆₇	—	2	2	no	—
143	D₄×C₆₇	—	4	2	no	—
144	D₄×C₆₇	—	4	2	no	—
145	D₄×C₆₇	—	4	1	no	—
146	C₂×C₄×C₆₇	—	2	4	no	—
147	C₂×C₄×C₆₇	—	2	2	no	—
148	C₂×C₄×C₆₇	—	4	1	no	—
149	C₂×C₄×C₆₇	—	4	2	no	—
150	C₂×C₄×C₆₇	—	4	2	no	—
151	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
152	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
153	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
155	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
156	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
157	C₂²⋊D₆₇	—	4	2	no	—
158	C₂²⋊D₆₇	—	4	2	no	—
159	C₂×Dic₆₇	—	4	1	no	—
160	D₂₆₈	—	2	2	no	—
161	D₂₆₈	—	4	1	no	—
162	C₄×D₆₇	—	4	2	no	—
163	C₄×D₆₇	—	4	2	no	—
164	Dic₁₃₄	—	2	2	no	—
165	Dic₁₃₄	—	4	1	no	—
166	C₈×C₆₇	—	4	2	no	—
167	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
168	C₈×C₆₇	C₄×D₄	1	1	yes	characteristic
169	C₈×C₆₇	C₂×D₈	1	2	yes	—
170	C₈×C₆₇	C₂×D₈	1	2	yes	—
171	C₈×C₆₇	C₂³×C₄	1	1	yes	characteristic
172	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
173	C₆₇⋊C₈	—	4	2	no	—
174	C₂²×C₆₇	—	2	2	no	—
175	C₂²×C₆₇	—	4	2	no	—
176	C₂²×C₆₇	—	8	2	no	—
177	C₂²×C₆₇	C₄×D₈	1	1	yes	characteristic
178	C₂²×C₆₇	C₄×D₈	1	1	yes	characteristic
179	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
180	C₂×D₆₇	—	4	2	no	—
181	C₂×D₆₇	—	8	2	no	—
182	C₄×C₆₇	—	2	4	no	—
183	C₄×C₆₇	—	4	2	no	—
184	C₄×C₆₇	C₄×D₈	1	1	yes	characteristic
185	C₄×C₆₇	C₄×D₈	1	1	yes	characteristic
186	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
187	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
188	Dic₆₇	—	4	2	no	—
189	C₂×#2178	—	67	1	no	maximal, Sylow
190	C₂×C₆₇	—	2	1	no	—
191	C₂×C₆₇	—	2	1	no	—
192	C₂×C₆₇	—	8	2	no	—
193	C₂×C₆₇	#2178	1	2	yes	complemented
194	C₂×C₆₇	C₂×C₄×D₈	1	1	yes	characteristic
195	D₆₇	—	8	2	no	—
196	C₂×#508	—	67	1	no	—
197	C₂×#443	—	67	1	no	—
198	C₂×#443	D₆₇	1	1	yes	characteristic, complemented
199	#2178	—	67	8	no	—
200	C₂×#368	—	67	1	no	—
201	C₂×#359	—	67	1	no	—
202	C₂×#359	—	67	1	no	—
203	C₂×C₄×C₁₆	—	67	1	no	—
204	C₆₇	C₂×#2178	1	1	yes	characteristic, complemented, Sylow
205	C₂×#135	—	67	1	no	—
206	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
207	C₂×#131	—	2	1	no	—
208	C₂×#131	—	134	1	no	—
209	#508	—	67	4	no	—
210	#508	—	67	4	no	—
211	C₂×Q₃₂	—	67	1	no	—
212	C₂×SD₃₂	—	67	1	no	—
213	C₂×SD₃₂	—	67	1	no	—
214	C₂×D₁₆	—	67	1	no	—
215	C₂²×C₁₆	—	67	1	no	—
216	C₂²×C₁₆	—	67	1	no	—
217	#443	—	2	2	no	—
218	#443	—	67	4	no	—
219	#443	—	134	2	no	—
220	#443	C₂×D₆₇	1	4	yes	complemented
221	C₂×#108	—	67	1	no	—
222	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
223	C₂×#104	—	2	1	no	—
224	C₂×#104	—	134	1	no	—
225	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
226	#368	—	67	4	no	—
227	#359	—	67	4	no	—
228	#359	—	67	4	no	—
229	C₄×C₁₆	—	67	4	no	—
230	C₂×#41	—	2	1	no	—
231	C₂×#41	—	134	1	no	—
232	#135	—	2	1	no	—
233	#135	—	2	1	no	—
234	#135	—	67	2	no	—
235	#135	—	67	2	no	—
236	#135	—	134	1	no	—
237	#135	—	134	1	no	—
238	#135	C₄×D₆₇	1	2	yes	—
239	#135	C₂²×D₆₇	1	2	yes	—
240	C₂×Q₁₆	—	67	1	no	—
241	C₂×Q₁₆	C₄×D₆₇	1	1	yes	characteristic
242	C₂×SD₁₆	—	2	1	no	—
243	C₂×SD₁₆	—	134	1	no	—
244	C₂×D₈	—	67	1	no	—
245	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic
246	#131	—	2	4	no	—
247	#131	—	4	2	no	—
248	#131	—	268	2	no	—
249	#131	—	134	4	no	—
250	C₂×M₁₆	—	2	1	no	—
251	C₂×M₁₆	—	4	1	no	—
252	C₂×M₁₆	—	268	1	no	—
253	C₂×M₁₆	—	134	1	no	—
254	C₂²×C₈	—	4	1	no	—
255	C₂²×C₈	—	268	1	no	—
256	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
257	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
258	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
259	Q₃₂	—	67	4	no	—
260	SD₃₂	—	67	4	no	—
261	SD₃₂	—	67	4	no	—
262	D₁₆	—	67	4	no	—
263	C₂×C₁₆	—	67	1	no	—
264	C₂×C₁₆	—	67	1	no	—
265	C₂×C₁₆	—	67	2	no	—
266	C₂×C₁₆	—	67	2	no	—
267	C₂×C₁₆	—	67	2	no	—
268	C₂×C₁₆	—	134	1	no	—
269	C₂×C₁₆	—	134	1	no	—
270	#108	—	2	1	no	—
271	#108	—	67	2	no	—
272	#108	—	134	1	no	—
273	#108	C₂²×D₆₇	1	2	yes	—
274	#104	—	2	4	no	—
275	#104	—	134	4	no	—
276	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
277	C₄×C₈	C₂²×D₆₇	1	2	yes	—
278	#41	—	2	2	no	—
279	#41	—	2	2	no	—
280	#41	—	4	1	no	—
281	#41	—	4	1	no	—
282	#41	—	268	1	no	—
283	#41	—	268	1	no	—
284	#41	—	134	2	no	—
285	#41	—	134	2	no	—
286	C₂×Q₈	—	2	1	no	—
287	C₂×Q₈	—	134	1	no	—
288	C₂×D₄	—	2	1	no	—
289	C₂×D₄	—	4	1	no	—
290	C₂×D₄	—	268	1	no	—
291	C₂×D₄	—	134	1	no	—
292	C₂²×C₄	—	2	1	no	—
293	C₂²×C₄	—	4	1	no	—
294	C₂²×C₄	—	268	1	no	—
295	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
296	Q₁₆	—	2	1	no	—
297	Q₁₆	—	67	2	no	—
298	Q₁₆	—	134	1	no	—
299	Q₁₆	C₂×C₄×D₆₇	1	2	yes	—
300	SD₁₆	—	2	2	no	—
301	SD₁₆	—	2	2	no	—
302	SD₁₆	—	134	2	no	—
303	SD₁₆	—	134	2	no	—
304	D₈	—	2	1	no	—
305	D₈	—	67	2	no	—
306	D₈	—	134	1	no	—
307	D₈	C₂×C₄×D₆₇	1	2	yes	—
308	M₁₆	—	2	2	no	—
309	M₁₆	—	4	1	no	—
310	M₁₆	—	4	4	no	—
311	M₁₆	—	268	1	no	—
312	M₁₆	—	268	4	no	—
313	M₁₆	—	134	2	no	—
314	C₂×C₈	—	4	1	no	—
315	C₂×C₈	—	4	4	no	—
316	C₂×C₈	—	268	1	no	—
317	C₂×C₈	—	268	4	no	—
318	C₂×C₈	#11761613	1	1	yes	characteristic
319	C₂×C₈	#11761613	1	2	yes	—
320	C₂×C₈	#11761613	1	1	yes	characteristic
321	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
322	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
323	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
324	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
325	C₂×C₈	#11761628	1	1	yes	characteristic
326	C₂×C₈	#11761628	1	1	yes	characteristic
327	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
328	C₄²	—	2	1	no	—
329	C₄²	C₂×C₂²⋊D₆₇	1	2	yes	—
330	C₁₆	—	67	2	no	—
331	C₁₆	—	67	2	no	—
332	C₁₆	—	134	2	no	—
333	C₂³	—	4	1	no	—
334	C₂³	—	268	1	no	—
335	C₂³	#14524063	1	1	yes	characteristic
336	Q₈	—	2	2	no	—
337	Q₈	—	4	1	no	—
338	Q₈	—	268	1	no	—
339	Q₈	—	134	2	no	—
340	D₄	—	2	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	1	no	—
344	D₄	—	268	2	no	—
345	D₄	—	268	2	no	—
346	D₄	—	268	1	no	—
347	D₄	—	134	2	no	—
348	C₂×C₄	—	2	4	no	—
349	C₂×C₄	—	2	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	268	1	no	—
354	C₂×C₄	—	268	2	no	—
355	C₂×C₄	—	268	2	no	—
356	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
357	C₂×C₄	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
358	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
359	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
360	C₂×C₄	#14524063	1	1	yes	characteristic
361	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
362	C₈	—	4	2	no	—
363	C₈	—	268	2	no	—
364	C₈	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
365	C₈	C₄×C₂²⋊D₆₇	1	1	yes	characteristic
366	C₈	C₂×#11761613	1	2	yes	—
367	C₈	C₂×#11761613	1	2	yes	—
368	C₈	C₂²×C₄×D₆₇	1	1	yes	characteristic
369	C₈	C₂×#11761628	1	1	yes	characteristic
370	C₂²	—	2	2	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	—	268	2	no	—
374	C₂²	—	536	2	no	—
375	C₂²	C₄×#11761613	1	1	yes	characteristic
376	C₂²	C₄×#11761613	1	1	yes	characteristic
377	C₂²	C₂×#14524063	1	1	yes	characteristic
378	C₄	—	2	4	no	—
379	C₄	—	4	2	no	—
380	C₄	—	268	2	no	—
381	C₄	C₄×#11761613	1	1	yes	characteristic
382	C₄	C₄×#11761613	1	1	yes	characteristic
383	C₄	C₂×C₄×C₂²⋊D₆₇	1	1	yes	characteristic
384	C₄	C₂²×#11761613	1	1	yes	characteristic
385	C₂	—	2	1	no	—
386	C₂	—	2	1	no	—
387	C₂	—	8	2	no	—
388	C₂	—	536	2	no	—
389	C₂	#22562088	1	2	yes	direct product factor
390	C₂	C₂×C₄×#11761613	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₈	#11761613
commutator	C₈×C₆₇	C₂³×C₄
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₂×#443×C₆₇	C₂
socle	C₂²×C₆₇	C₄×D₈
prime radical	C₂×#16863826	C₂
cosocle	C₂×C₈×C₆₇	C₂⁴
hypercenter	C₂×#443	D₆₇
hypocenter	C₆₇	C₂×#2178
LCS	G ▷ C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₈ ◁ C₂²×C₈ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
2. C₂×#16863514	C₂	semidirect
3. #22562088	C₂	direct (N × H)
4. C₂×#16863225	C₂	semidirect
5. C₂×#16863203	C₂	semidirect
6. C₂×#16863202	C₂	semidirect
7. C₂×C₄×C₆₇⋊C₁₆	C₂	semidirect
8. C₂×#443×C₆₇	C₂	semidirect
11. #16863826	C₄	semidirect
13. C₂×#14523989	C₄	semidirect
14. C₂×#14523987	C₄	semidirect
15. C₂×#14523986	C₄	semidirect
16. C₂×#14523984	C₄	semidirect
20. #16863514	C₂²	semidirect
23. #16863225	C₂²	semidirect
24. #16863203	C₂²	semidirect
25. #16863202	C₂²	semidirect
26. C₄×C₆₇⋊C₁₆	C₂²	semidirect
30. #443×C₆₇	C₂²	semidirect
47. #14523989	C₂×C₄	semidirect
48. #14523987	C₂×C₄	semidirect
49. #14523986	C₂×C₄	semidirect
50. #14523984	C₂×C₄	semidirect
193. C₂×C₆₇	#2178	semidirect
198. C₂×#443	D₆₇	semidirect
204. C₆₇	C₂×#2178	semidirect
220. #443	C₂×D₆₇	semidirect
389. C₂	#22562088	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×#16863826	2
C₂×#16863514	2
#22562088	2
C₂×#16863225	2
C₂×#16863203	2
C₂×#16863202	2
C₂×C₄×C₆₇⋊C₁₆	2
C₂×#443×C₆₇	2
C₂×#2178	67

Subgroups — C2×#22562088 #31009229

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22562088 #31009229