Subgroups — C₂×#22562337 #31010398

Order 17152.

658 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#14523987	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863813	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#16863671	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562337	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863225	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863211	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863209	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#472×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#14524073	—	2	1	no	—
10	C₂²×Dic₂₆₈	C₂²	1	1	yes	characteristic
11	C₂×#14523987	—	2	1	no	—
12	C₂×#14523987	—	2	1	no	—
13	C₂×#14523987	—	2	2	no	—
14	C₂×#14523987	C₂²	1	4	yes	complemented
15	#16863813	—	2	2	no	—
16	#16863813	C₂²	1	4	yes	complemented
17	C₂×#14523983	—	2	1	no	—
18	C₂×#14523983	C₂²	1	1	yes	characteristic
19	C₂²×C₆₇⋊C₁₆	—	2	1	no	—
20	C₂²×C₆₇⋊C₁₆	C₂²	1	1	yes	characteristic
21	#16863671	—	2	2	no	—
22	#16863671	C₂²	1	4	yes	complemented
23	C₂×#14523979	C₂²	1	1	yes	characteristic
24	C₂×#14523961	—	2	1	no	—
25	#16863225	C₂²	1	4	yes	complemented
26	#16863211	C₂²	1	4	yes	complemented
27	#16863209	C₂²	1	4	yes	complemented
28	C₂×AGL(1,ℤ/8)×C₆₇	—	2	1	no	—
29	C₂²×D₈×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×#131×C₆₇	C₂²	1	1	yes	characteristic
31	#472×C₆₇	—	2	2	no	—
32	#472×C₆₇	C₂²	1	4	yes	—
33	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#100×C₆₇	—	2	1	no	—
35	C₂²×Dic₁₃₄	—	2	1	no	—
36	#14524073	—	2	4	no	—
37	#14524073	—	4	2	no	—
38	C₂×Dic₂₆₈	—	2	1	no	—
39	C₂×Dic₂₆₈	—	2	1	no	—
40	C₂×Dic₂₆₈	—	2	1	no	—
41	C₂×Dic₂₆₈	—	2	1	no	—
42	C₂×Dic₂₆₈	—	2	1	no	—
43	C₂×Dic₂₆₈	C₂³	1	2	yes	—
44	C₂×#11761618	—	4	1	no	—
45	C₂×#11761616	—	4	1	no	—
46	C₂×#11761612	—	2	1	no	—
47	#14523987	—	2	4	no	—
48	#14523987	—	2	4	no	—
49	#14523983	—	2	4	no	—
50	#14523983	—	2	1	no	—
51	#14523983	C₂³	1	2	yes	—
52	C₂×C₆₇⋊C₁₆	—	2	4	no	—
53	C₂×C₆₇⋊C₁₆	—	2	1	no	—
54	C₂×C₆₇⋊C₁₆	D₄	1	1	yes	characteristic
55	C₂×C₆₇⋊C₁₆	D₄	1	1	yes	characteristic
56	C₂×C₆₇⋊C₁₆	D₄	1	2	yes	—
57	C₂×C₆₇⋊C₁₆	C₂³	1	2	yes	—
58	#14523979	—	2	1	no	—
59	#14523979	C₂³	1	2	yes	—
60	#14523961	—	2	4	no	—
61	C₂×#41×C₆₇	D₄	1	1	yes	characteristic
62	C₂²×D₄×C₆₇	—	2	1	no	—
63	AGL(1,ℤ/8)×C₆₇	—	2	4	no	—
64	AGL(1,ℤ/8)×C₆₇	—	4	2	no	—
65	C₂×SD₁₆×C₆₇	—	4	1	no	—
66	C₂×D₈×C₆₇	—	2	1	no	—
67	C₂×D₈×C₆₇	—	2	1	no	—
68	C₂×D₈×C₆₇	—	2	1	no	—
69	C₂×D₈×C₆₇	—	2	1	no	—
70	C₂×D₈×C₆₇	—	2	1	no	—
71	C₂×D₈×C₆₇	—	4	1	no	—
72	C₂×D₈×C₆₇	C₂³	1	2	yes	—
73	#131×C₆₇	—	2	1	no	—
74	#131×C₆₇	—	2	1	no	—
75	#131×C₆₇	D₄	1	2	yes	—
76	#131×C₆₇	C₂³	1	2	yes	—
77	C₂×M₁₆×C₆₇	—	2	1	no	—
78	C₂×M₁₆×C₆₇	—	2	1	no	—
79	C₂×M₁₆×C₆₇	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₆₇	—	2	1	no	—
81	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
82	#108×C₆₇	—	2	1	no	—
83	#108×C₆₇	C₂³	1	2	yes	—
84	#100×C₆₇	—	2	4	no	—
85	C₂×Dic₁₃₄	—	2	2	no	—
86	C₂×Dic₁₃₄	—	4	1	no	—
87	C₂×Dic₁₃₄	—	4	1	no	—
88	C₂×Dic₁₃₄	—	4	1	no	—
89	C₂×Dic₁₃₄	—	4	1	no	—
90	C₂×Dic₁₃₄	—	4	1	no	—
91	C₂²×Dic₆₇	—	4	1	no	—
92	Dic₂₆₈	—	2	2	no	—
93	Dic₂₆₈	—	2	2	no	—
94	Dic₂₆₈	—	4	1	no	—
95	Dic₂₆₈	—	4	1	no	—
96	#11761618	—	4	4	no	—
97	#11761616	—	4	4	no	—
98	#11761612	—	2	2	no	—
99	#11761612	—	4	1	no	—
100	C₂×C₆₇⋊C₈	—	4	1	no	—
101	C₆₇⋊C₁₆	—	2	2	no	—
102	C₆₇⋊C₁₆	C₂×D₄	1	2	yes	—
103	C₆₇⋊C₁₆	C₂×D₄	1	2	yes	—
104	C₂⁴×C₆₇	—	4	1	no	—
105	#41×C₆₇	—	2	1	no	—
106	#41×C₆₇	—	2	1	no	—
107	#41×C₆₇	D₈	1	2	yes	—
108	#41×C₆₇	C₂×D₄	1	2	yes	—
109	C₂×Q₈×C₆₇	D₈	1	1	yes	characteristic
110	C₂×D₄×C₆₇	—	2	1	no	—
111	C₂×D₄×C₆₇	—	2	2	no	—
112	C₂×D₄×C₆₇	—	4	1	no	—
113	C₂×D₄×C₆₇	—	4	1	no	—
114	C₂×D₄×C₆₇	—	4	1	no	—
115	C₂×D₄×C₆₇	—	4	1	no	—
116	C₂×D₄×C₆₇	—	4	1	no	—
117	C₂×D₄×C₆₇	D₈	1	1	yes	characteristic
118	C₂²×C₄×C₆₇	—	2	1	no	—
119	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
120	SD₁₆×C₆₇	—	4	4	no	—
121	D₈×C₆₇	—	2	2	no	—
122	D₈×C₆₇	—	2	2	no	—
123	D₈×C₆₇	—	4	4	no	—
124	D₈×C₆₇	—	4	1	no	—
125	D₈×C₆₇	—	4	1	no	—
126	M₁₆×C₆₇	—	2	1	no	—
127	M₁₆×C₆₇	—	2	2	no	—
128	M₁₆×C₆₇	—	2	2	no	—
129	M₁₆×C₆₇	—	2	2	no	—
130	M₁₆×C₆₇	—	4	1	no	—
131	M₁₆×C₆₇	C₂×D₄	1	2	yes	—
132	C₂×C₈×C₆₇	—	2	1	no	—
133	C₂×C₈×C₆₇	—	2	2	no	—
134	C₂×C₈×C₆₇	—	2	2	no	—
135	C₂×C₈×C₆₇	—	4	1	no	—
136	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
137	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
138	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
140	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
141	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
142	C₂³×C₆₇	—	2	1	no	—
143	C₂³×C₆₇	—	4	2	no	—
144	C₂³×C₆₇	—	8	1	no	—
145	C₂³×C₆₇	—	8	1	no	—
146	C₂³×C₆₇	—	16	2	no	—
147	C₂³×C₆₇	#135	1	1	yes	characteristic
148	Q₈×C₆₇	—	2	1	no	—
149	Q₈×C₆₇	C₂×D₈	1	2	yes	—
150	D₄×C₆₇	—	2	2	no	—
151	D₄×C₆₇	—	2	2	no	—
152	D₄×C₆₇	—	2	1	no	—
153	D₄×C₆₇	—	4	2	no	—
154	D₄×C₆₇	—	4	2	no	—
155	D₄×C₆₇	—	8	1	no	—
156	D₄×C₆₇	—	8	1	no	—
157	D₄×C₆₇	C₂×D₈	1	2	yes	—
158	C₂×C₄×C₆₇	—	2	1	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
162	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
165	C₂×C₄×C₆₇	#135	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
167	C₂×Dic₆₇	—	4	2	no	—
168	C₂×Dic₆₇	—	8	1	no	—
169	C₂×Dic₆₇	—	8	1	no	—
170	Dic₁₃₄	—	4	2	no	—
171	Dic₁₃₄	—	4	2	no	—
172	Dic₁₃₄	—	8	1	no	—
173	Dic₁₃₄	—	8	1	no	—
174	C₈×C₆₇	—	2	2	no	—
175	C₈×C₆₇	—	4	2	no	—
176	C₈×C₆₇	#121	1	1	yes	characteristic
177	C₈×C₆₇	#121	1	1	yes	characteristic
178	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
179	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
180	C₆₇⋊C₈	—	4	2	no	—
181	C₂²×C₆₇	—	2	2	no	—
182	C₂²×C₆₇	—	2	2	no	—
183	C₂²×C₆₇	—	4	2	no	—
184	C₂²×C₆₇	—	8	2	no	—
185	C₂²×C₆₇	—	16	2	no	—
186	C₂²×C₆₇	—	16	2	no	—
187	C₂²×C₆₇	—	16	2	no	—
188	C₂²×C₆₇	#466	1	1	yes	characteristic
189	C₂²×C₆₇	#466	1	1	yes	characteristic
190	C₂²×C₆₇	C₂×#135	1	1	yes	characteristic
191	C₄×C₆₇	—	2	2	no	—
192	C₄×C₆₇	#466	1	1	yes	characteristic
193	C₄×C₆₇	#466	1	1	yes	characteristic
194	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
195	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
196	Dic₆₇	—	8	2	no	—
197	C₂×#2223	—	67	1	no	maximal, Sylow
198	C₂×C₆₇	—	2	1	no	—
199	C₂×C₆₇	—	2	1	no	—
200	C₂×C₆₇	—	4	2	no	—
201	C₂×C₆₇	—	16	2	no	—
202	C₂×C₆₇	#2223	1	2	yes	complemented
203	C₂×C₆₇	C₂×#466	1	1	yes	characteristic
204	C₂²×SD₃₂	—	67	1	no	—
205	C₂×#504	—	67	1	no	—
206	C₂×#473	—	67	1	no	—
207	C₂×#472	D₆₇	1	1	yes	characteristic
208	#2223	—	67	8	no	—
209	C₂×#368	—	67	1	no	—
210	C₂×#362	—	67	1	no	—
211	C₂×#361	—	67	1	no	—
212	C₆₇	C₂×#2223	1	1	yes	characteristic, complemented, Sylow
213	C₂×#137	—	134	1	no	—
214	C₂×AGL(1,ℤ/8)	—	2	1	no	—
215	C₂²×Q₁₆	—	67	1	no	—
216	C₂²×D₈	C₂×D₆₇	1	1	yes	characteristic
217	C₂×#131	C₂×D₆₇	1	1	yes	characteristic
218	C₂×SD₃₂	—	67	4	no	—
219	C₂×SD₃₂	—	134	1	no	—
220	C₂×SD₃₂	—	134	1	no	—
221	C₂×SD₃₂	—	134	2	no	—
222	#504	—	67	4	no	—
223	#504	—	134	2	no	—
224	C₂×M₃₂	—	67	1	no	—
225	C₂×M₃₂	—	134	1	no	—
226	C₂²×C₁₆	—	67	1	no	—
227	C₂²×C₁₆	—	134	1	no	—
228	#473	—	67	4	no	—
229	#473	—	134	2	no	—
230	#472	—	2	2	no	—
231	#472	C₂×D₆₇	1	4	yes	—
232	C₂×#108	—	67	1	no	—
233	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
234	C₂×#101	—	134	1	no	—
235	C₂×#100	—	2	1	no	—
236	#368	—	67	4	no	—
237	#362	—	67	4	no	—
238	#361	—	67	4	no	—
239	C₂×#41	C₂²⋊D₆₇	1	1	yes	characteristic
240	C₂²×Q₈	—	134	1	no	—
241	C₂²×D₄	—	2	1	no	—
242	#137	—	268	2	no	—
243	#137	—	134	4	no	—
244	AGL(1,ℤ/8)	—	2	4	no	—
245	AGL(1,ℤ/8)	—	4	2	no	—
246	C₂×Q₁₆	—	268	1	no	—
247	C₂×Q₁₆	—	67	2	no	—
248	C₂×Q₁₆	—	134	1	no	—
249	C₂×Q₁₆	—	134	1	no	—
250	C₂×Q₁₆	—	134	1	no	—
251	C₂×Q₁₆	—	134	1	no	—
252	C₂×Q₁₆	—	134	1	no	—
253	C₂×SD₁₆	—	4	1	no	—
254	C₂×SD₁₆	—	268	1	no	—
255	C₂×D₈	—	2	1	no	—
256	C₂×D₈	—	2	1	no	—
257	C₂×D₈	—	2	1	no	—
258	C₂×D₈	—	2	1	no	—
259	C₂×D₈	—	2	1	no	—
260	C₂×D₈	—	4	1	no	—
261	C₂×D₈	C₂²×D₆₇	1	2	yes	—
262	#131	—	2	1	no	—
263	#131	—	2	1	no	—
264	#131	C₂²⋊D₆₇	1	2	yes	—
265	#131	C₂²×D₆₇	1	2	yes	—
266	C₂×M₁₆	—	2	1	no	—
267	C₂×M₁₆	—	2	1	no	—
268	C₂×M₁₆	—	134	1	no	—
269	C₂×M₁₆	C₂²⋊D₆₇	1	1	yes	characteristic
270	C₂²×C₈	—	2	1	no	—
271	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
272	SD₃₂	—	134	4	no	—
273	SD₃₂	—	134	4	no	—
274	M₃₂	—	67	2	no	—
275	M₃₂	—	134	4	no	—
276	M₃₂	—	134	1	no	—
277	C₂×C₁₆	—	67	1	no	—
278	C₂×C₁₆	—	67	1	no	—
279	C₂×C₁₆	—	67	2	no	—
280	C₂×C₁₆	—	67	2	no	—
281	C₂×C₁₆	—	134	4	no	—
282	C₂×C₁₆	—	134	1	no	—
283	#108	—	2	1	no	—
284	#108	—	67	2	no	—
285	#108	—	134	1	no	—
286	#108	C₂²×D₆₇	1	2	yes	—
287	#101	—	134	4	no	—
288	#100	—	2	4	no	—
289	C₂⁴	—	4	1	no	—
290	#41	—	2	1	no	—
291	#41	—	2	1	no	—
292	#41	#11761613	1	2	yes	—
293	#41	C₂×C₂²⋊D₆₇	1	2	yes	—
294	C₂×Q₈	—	268	1	no	—
295	C₂×Q₈	—	268	1	no	—
296	C₂×Q₈	—	268	1	no	—
297	C₂×Q₈	—	268	1	no	—
298	C₂×Q₈	—	268	1	no	—
299	C₂×Q₈	—	134	2	no	—
300	C₂×Q₈	#11761613	1	1	yes	characteristic
301	C₂×D₄	—	2	1	no	—
302	C₂×D₄	—	2	2	no	—
303	C₂×D₄	—	4	1	no	—
304	C₂×D₄	—	4	1	no	—
305	C₂×D₄	—	4	1	no	—
306	C₂×D₄	—	4	1	no	—
307	C₂×D₄	—	4	1	no	—
308	C₂×D₄	#11761613	1	1	yes	characteristic
309	C₂²×C₄	—	2	1	no	—
310	C₂²×C₄	—	268	1	no	—
311	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
312	Q₁₆	—	268	4	no	—
313	Q₁₆	—	268	1	no	—
314	Q₁₆	—	268	1	no	—
315	Q₁₆	—	134	2	no	—
316	Q₁₆	—	134	2	no	—
317	SD₁₆	—	4	4	no	—
318	SD₁₆	—	268	4	no	—
319	D₈	—	2	2	no	—
320	D₈	—	2	2	no	—
321	D₈	—	4	4	no	—
322	D₈	—	4	1	no	—
323	D₈	—	4	1	no	—
324	M₁₆	—	2	1	no	—
325	M₁₆	—	2	2	no	—
326	M₁₆	—	2	2	no	—
327	M₁₆	—	2	2	no	—
328	M₁₆	—	4	1	no	—
329	M₁₆	—	268	1	no	—
330	M₁₆	—	134	2	no	—
331	M₁₆	C₂×C₂²⋊D₆₇	1	2	yes	—
332	C₂×C₈	—	2	1	no	—
333	C₂×C₈	—	2	2	no	—
334	C₂×C₈	—	2	2	no	—
335	C₂×C₈	—	4	1	no	—
336	C₂×C₈	—	268	1	no	—
337	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
338	C₂×C₈	D₄×D₆₇	1	1	yes	characteristic
339	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
340	C₂×C₈	#11761627	1	1	yes	characteristic
341	C₂×C₈	#11761627	1	1	yes	characteristic
342	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
343	C₁₆	—	67	2	no	—
344	C₁₆	—	67	2	no	—
345	C₁₆	—	134	2	no	—
346	C₂³	—	2	1	no	—
347	C₂³	—	4	2	no	—
348	C₂³	—	8	1	no	—
349	C₂³	—	8	1	no	—
350	C₂³	—	16	2	no	—
351	C₂³	#14524063	1	1	yes	characteristic
352	Q₈	—	2	1	no	—
353	Q₈	—	268	2	no	—
354	Q₈	—	268	2	no	—
355	Q₈	—	536	1	no	—
356	Q₈	—	536	1	no	—
357	Q₈	C₂×#11761613	1	2	yes	—
358	D₄	—	2	2	no	—
359	D₄	—	2	2	no	—
360	D₄	—	2	1	no	—
361	D₄	—	4	2	no	—
362	D₄	—	4	2	no	—
363	D₄	—	8	1	no	—
364	D₄	—	8	1	no	—
365	D₄	C₂×#11761613	1	2	yes	—
366	C₂×C₄	—	2	1	no	—
367	C₂×C₄	—	2	2	no	—
368	C₂×C₄	—	2	2	no	—
369	C₂×C₄	—	268	2	no	—
370	C₂×C₄	—	536	1	no	—
371	C₂×C₄	—	536	1	no	—
372	C₂×C₄	#14524015	1	1	yes	characteristic
373	C₂×C₄	#14524015	1	1	yes	characteristic
374	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
375	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
376	C₂×C₄	#14524063	1	1	yes	characteristic
377	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
378	C₈	—	2	2	no	—
379	C₈	—	4	2	no	—
380	C₈	—	268	2	no	—
381	C₈	#14524015	1	1	yes	characteristic
382	C₈	#14524015	1	1	yes	characteristic
383	C₈	C₂×D₄×D₆₇	1	1	yes	characteristic
384	C₈	C₂×#11761627	1	1	yes	characteristic
385	C₂²	—	2	2	no	—
386	C₂²	—	2	2	no	—
387	C₂²	—	4	2	no	—
388	C₂²	—	8	2	no	—
389	C₂²	—	16	2	no	—
390	C₂²	—	16	2	no	—
391	C₂²	—	16	2	no	—
392	C₂²	#16863630	1	1	yes	characteristic
393	C₂²	#16863630	1	1	yes	characteristic
394	C₂²	C₂×#14524063	1	1	yes	characteristic
395	C₄	—	2	2	no	—
396	C₄	—	536	2	no	—
397	C₄	#16863630	1	1	yes	characteristic
398	C₄	#16863630	1	1	yes	characteristic
399	C₄	C₂×#14524015	1	1	yes	characteristic
400	C₄	C₂²×#11761613	1	1	yes	characteristic
401	C₂	—	2	1	no	—
402	C₂	—	2	1	no	—
403	C₂	—	4	2	no	—
404	C₂	—	16	2	no	—
405	C₂	#22562337	1	2	yes	direct product factor
406	C₂	C₂×#16863630	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16863630
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting, prime radical	C₂×#472×C₆₇	C₂
socle	C₂²×C₆₇	#466
hypercenter	C₂×#472	D₆₇
hypocenter	C₆₇	C₂×#2223
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#131 ◁ C₂×#472

Complements

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

N	H ≅ G/N	type
1. C₂²×#14523987	C₂	semidirect
2. C₂×#16863813	C₂	semidirect
3. C₂×#16863671	C₂	semidirect
4. #22562337	C₂	direct (N × H)
5. C₂×#16863225	C₂	semidirect
6. C₂×#16863211	C₂	semidirect
7. C₂×#16863209	C₂	semidirect
14. C₂×#14523987	C₂²	semidirect
16. #16863813	C₂²	semidirect
22. #16863671	C₂²	semidirect
25. #16863225	C₂²	semidirect
26. #16863211	C₂²	semidirect
27. #16863209	C₂²	semidirect
202. C₂×C₆₇	#2223	semidirect
212. C₆₇	C₂×#2223	semidirect
405. C₂	#22562337	direct (N × H)

Maximal subgroups

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

subgroup	index
C₂²×#14523987	2
C₂×#16863813	2
C₂×#16863671	2
#22562337	2
C₂×#16863225	2
C₂×#16863211	2
C₂×#16863209	2
C₂×#472×C₆₇	2
C₂×#2223	67

Subgroups — C2×#22562337 #31010398

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22562337 #31010398