Subgroups — C₂×#22562278 #31010203

Order 17152.

706 conjugacy classes of subgroups.

The subgroup lattice has 424 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863836	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#16863831	C₂	1	1	yes	maximal, characteristic
3	C₂×#16863780	C₂	1	1	yes	maximal, characteristic, complemented
4	#22562278	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863217	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863211	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863208	C₂	1	1	yes	maximal, characteristic, complemented
8	C₂×#443×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂²×Dic₂₆₈	C₂²	1	1	yes	characteristic
10	C₂²×#11761617	—	2	1	no	—
11	C₂²×D₅₃₆	C₂²	1	1	yes	characteristic
12	C₂×#14524031	—	2	1	no	—
13	#16863836	—	2	2	no	—
14	#16863836	C₂²	1	4	yes	complemented
15	#16863831	—	2	2	no	—
16	#16863831	C₂²	1	4	yes	—
17	C₂×#14523989	—	2	1	no	—
18	C₂×#14523987	—	2	1	no	—
19	C₂×#14523986	—	2	1	no	—
20	C₂×#14523984	—	2	1	no	—
21	C₂×#14523983	C₂²	1	1	yes	characteristic
22	C₂×#14523983	C₂²	1	1	yes	characteristic
23	#16863780	—	2	2	no	—
24	#16863780	C₂²	1	4	yes	complemented
25	#16863217	C₂²	1	4	yes	complemented
26	#16863211	C₂²	1	4	yes	complemented
27	#16863208	C₂²	1	4	yes	complemented
28	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
29	C₂×#131×C₆₇	—	2	1	no	—
30	#443×C₆₇	—	2	2	no	—
31	#443×C₆₇	C₂²	1	4	yes	complemented
32	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
33	C₂×#104×C₆₇	—	2	1	no	—
34	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
35	C₂²×Dic₁₃₄	—	2	1	no	—
36	C₂²×D₂₆₈	—	2	1	no	—
37	C₂×Dic₂₆₈	—	2	1	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	C₂³	1	2	yes	—
43	C₂×#11761617	—	2	4	no	—
44	C₂×#11761617	—	4	1	no	—
45	C₂×#11761617	—	4	1	no	—
46	C₂×#11761617	—	4	2	no	—
47	C₂×D₅₃₆	—	2	1	no	—
48	C₂×D₅₃₆	—	2	1	no	—
49	C₂×D₅₃₆	—	2	1	no	—
50	C₂×D₅₃₆	—	2	1	no	—
51	C₂×D₅₃₆	—	2	1	no	—
52	C₂×D₅₃₆	C₂³	1	2	yes	—
53	#14524031	—	2	4	no	—
54	#14524031	—	4	2	no	—
55	C₂×(C₂×D₆₇)⋊C₄	—	4	2	no	—
56	#14523989	—	2	4	no	—
57	#14523987	—	2	4	no	—
58	#14523986	—	2	4	no	—
59	#14523984	—	2	4	no	—
60	#14523983	—	2	1	no	—
61	#14523983	—	2	1	no	—
62	#14523983	C₂³	1	2	yes	—
63	#14523983	C₂³	1	2	yes	—
64	C₂×C₆₇⋊C₁₆	—	2	1	no	—
65	C₂×C₆₇⋊C₁₆	—	2	1	no	—
66	C₂×#41×C₆₇	—	2	1	no	—
67	#135×C₆₇	—	2	1	no	—
68	#135×C₆₇	—	2	1	no	—
69	#135×C₆₇	D₄	1	2	yes	—
70	#135×C₆₇	C₂³	1	2	yes	—
71	C₂×Q₁₆×C₆₇	D₄	1	1	yes	characteristic
72	C₂×SD₁₆×C₆₇	—	2	1	no	—
73	C₂×D₈×C₆₇	D₄	1	1	yes	characteristic
74	#131×C₆₇	—	2	4	no	—
75	#131×C₆₇	—	4	2	no	—
76	C₂×M₁₆×C₆₇	—	2	1	no	—
77	C₂×M₁₆×C₆₇	—	4	1	no	—
78	C₂²×C₈×C₆₇	—	4	1	no	—
79	C₂²×C₈×C₆₇	D₄	1	1	yes	characteristic
80	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₂×C₄²×C₆₇	D₄	1	1	yes	characteristic
82	#108×C₆₇	—	2	1	no	—
83	#108×C₆₇	C₂³	1	2	yes	—
84	#104×C₆₇	—	2	4	no	—
85	C₄×C₈×C₆₇	D₄	1	2	yes	—
86	C₄×C₈×C₆₇	C₂³	1	2	yes	—
87	C₂³×D₆₇	—	4	1	no	—
88	C₂×Dic₁₃₄	—	2	2	no	—
89	C₂×Dic₁₃₄	—	4	1	no	—
90	C₂×Dic₁₃₄	—	4	1	no	—
91	C₂×Dic₁₃₄	—	4	1	no	—
92	C₂×Dic₁₃₄	—	4	1	no	—
93	C₂×Dic₁₃₄	—	4	1	no	—
94	C₂×D₂₆₈	—	2	2	no	—
95	C₂×D₂₆₈	—	4	1	no	—
96	C₂×D₂₆₈	—	4	1	no	—
97	C₂×D₂₆₈	—	4	1	no	—
98	C₂×D₂₆₈	—	4	1	no	—
99	C₂×D₂₆₈	—	4	1	no	—
100	C₂²×Dic₆₇	—	4	1	no	—
101	Dic₂₆₈	—	2	2	no	—
102	Dic₂₆₈	—	2	2	no	—
103	Dic₂₆₈	—	4	1	no	—
104	Dic₂₆₈	—	4	1	no	—
105	#11761617	—	4	4	no	—
106	#11761617	—	4	4	no	—
107	D₅₃₆	—	2	2	no	—
108	D₅₃₆	—	2	2	no	—
109	D₅₃₆	—	4	1	no	—
110	D₅₃₆	—	4	1	no	—
111	(C₂×D₆₇)⋊C₄	—	4	8	no	—
112	C₆₇⋊C₁₆	—	2	2	no	—
113	C₆₇⋊C₁₆	—	2	2	no	—
114	#41×C₆₇	—	2	2	no	—
115	#41×C₆₇	—	2	2	no	—
116	#41×C₆₇	—	4	1	no	—
117	#41×C₆₇	—	4	1	no	—
118	C₂×Q₈×C₆₇	—	2	1	no	—
119	C₂×D₄×C₆₇	—	2	1	no	—
120	C₂×D₄×C₆₇	—	4	1	no	—
121	C₂²×C₄×C₆₇	—	2	1	no	—
122	C₂²×C₄×C₆₇	—	4	1	no	—
123	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
124	Q₁₆×C₆₇	—	2	1	no	—
125	Q₁₆×C₆₇	C₂×D₄	1	2	yes	—
126	SD₁₆×C₆₇	—	2	2	no	—
127	SD₁₆×C₆₇	—	2	2	no	—
128	D₈×C₆₇	—	2	1	no	—
129	D₈×C₆₇	C₂×D₄	1	2	yes	—
130	M₁₆×C₆₇	—	2	2	no	—
131	M₁₆×C₆₇	—	4	1	no	—
132	M₁₆×C₆₇	—	4	4	no	—
133	C₂×C₈×C₆₇	—	4	1	no	—
134	C₂×C₈×C₆₇	—	4	4	no	—
135	C₂×C₈×C₆₇	D₈	1	1	yes	characteristic
136	C₂×C₈×C₆₇	D₈	1	1	yes	characteristic
137	C₂×C₈×C₆₇	D₈	1	2	yes	—
138	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
139	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
140	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
141	C₂×C₈×C₆₇	C₂×D₄	1	1	yes	characteristic
142	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
143	C₂×C₈×C₆₇	#41	1	1	yes	characteristic
144	C₂×C₈×C₆₇	C₂⁴	1	1	yes	characteristic
145	C₄²×C₆₇	—	2	1	no	—
146	C₄²×C₆₇	C₂×D₄	1	2	yes	—
147	C₂³×C₆₇	—	4	1	no	—
148	C₂³×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
149	C₂²×D₆₇	—	4	2	no	—
150	C₂²×D₆₇	—	8	4	no	—
151	C₂²×D₆₇	—	8	1	no	—
152	C₂²×D₆₇	—	8	1	no	—
153	Q₈×C₆₇	—	2	2	no	—
154	Q₈×C₆₇	—	4	1	no	—
155	D₄×C₆₇	—	2	2	no	—
156	D₄×C₆₇	—	4	2	no	—
157	D₄×C₆₇	—	4	2	no	—
158	D₄×C₆₇	—	4	1	no	—
159	C₂×C₄×C₆₇	—	2	2	no	—
160	C₂×C₄×C₆₇	—	4	2	no	—
161	C₂×C₄×C₆₇	—	4	1	no	—
162	C₂×C₄×C₆₇	—	4	2	no	—
163	C₂×C₄×C₆₇	—	4	2	no	—
164	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
165	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂×D₈	1	1	yes	characteristic
168	C₂×C₄×C₆₇	AGL(1,ℤ/8)	1	1	yes	characteristic
169	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
170	C₂×Dic₆₇	—	4	2	no	—
171	C₂×Dic₆₇	—	8	1	no	—
172	C₂×Dic₆₇	—	8	1	no	—
173	D₂₆₈	—	4	2	no	—
174	D₂₆₈	—	4	2	no	—
175	D₂₆₈	—	8	1	no	—
176	D₂₆₈	—	8	1	no	—
177	Dic₁₃₄	—	4	2	no	—
178	Dic₁₃₄	—	4	2	no	—
179	Dic₁₃₄	—	8	1	no	—
180	Dic₁₃₄	—	8	1	no	—
181	C₈×C₆₇	—	4	2	no	—
182	C₈×C₆₇	#121	1	1	yes	characteristic
183	C₈×C₆₇	#121	1	1	yes	characteristic
184	C₈×C₆₇	C₂×D₈	1	2	yes	—
185	C₈×C₆₇	C₂×D₈	1	2	yes	—
186	C₈×C₆₇	C₂²×D₄	1	1	yes	characteristic
187	C₈×C₆₇	C₂×#41	1	1	yes	characteristic
188	C₂²×C₆₇	—	2	2	no	—
189	C₂²×C₆₇	—	4	2	no	—
190	C₂²×C₆₇	—	8	2	no	—
191	C₂²×C₆₇	#459	1	1	yes	characteristic
192	C₂²×C₆₇	#459	1	1	yes	characteristic
193	C₂²×C₆₇	C₂×AGL(1,ℤ/8)	1	1	yes	characteristic
194	C₂×D₆₇	—	8	4	no	—
195	C₂×D₆₇	—	8	2	no	—
196	C₂×D₆₇	—	16	2	no	—
197	C₂×D₆₇	—	16	2	no	—
198	C₄×C₆₇	—	4	2	no	—
199	C₄×C₆₇	—	4	2	no	—
200	C₄×C₆₇	#459	1	1	yes	characteristic
201	C₄×C₆₇	#459	1	1	yes	characteristic
202	C₄×C₆₇	C₂×#121	1	1	yes	characteristic
203	C₄×C₆₇	C₂²×D₈	1	1	yes	characteristic
204	Dic₆₇	—	8	2	no	—
205	C₂×#2212	—	67	1	no	maximal, Sylow
206	C₂×C₆₇	—	2	1	no	—
207	C₂×C₆₇	—	2	1	no	—
208	C₂×C₆₇	—	8	2	no	—
209	C₂×C₆₇	#2212	1	2	yes	complemented
210	C₂×C₆₇	C₂×#459	1	1	yes	characteristic
211	D₆₇	—	16	2	no	—
212	C₂×#510	—	67	1	no	—
213	C₂×#509	—	67	1	no	—
214	C₂×#495	—	67	1	no	—
215	C₂×#443	D₆₇	1	1	yes	characteristic, complemented
216	#2212	—	67	8	no	—
217	C₂×#364	—	67	1	no	—
218	C₂×#362	—	67	1	no	—
219	C₂×#361	—	67	1	no	—
220	C₆₇	C₂×#2212	1	1	yes	characteristic, complemented, Sylow
221	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
222	C₂²×Q₁₆	—	67	1	no	—
223	C₂²×SD₁₆	—	134	1	no	—
224	C₂²×D₈	—	67	1	no	—
225	C₂×#131	—	2	1	no	—
226	C₂×#124	—	134	1	no	—
227	#510	—	67	4	no	—
228	#510	—	134	2	no	—
229	#509	—	67	4	no	—
230	#509	—	134	2	no	—
231	C₂×Q₃₂	—	134	1	no	—
232	C₂×SD₃₂	—	134	1	no	—
233	C₂×SD₃₂	—	134	1	no	—
234	C₂×D₁₆	—	134	1	no	—
235	C₂×M₃₂	—	67	1	no	—
236	C₂×M₃₂	—	67	1	no	—
237	#495	—	67	4	no	—
238	#495	—	134	2	no	—
239	#443	—	2	2	no	—
240	#443	C₂×D₆₇	1	4	yes	complemented
241	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
242	C₂×#104	—	2	1	no	—
243	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
244	#364	—	67	4	no	—
245	#362	—	67	4	no	—
246	#361	—	67	4	no	—
247	C₂×#41	—	2	1	no	—
248	C₂²×Q₈	—	134	1	no	—
249	C₂²×D₄	—	134	1	no	—
250	#135	—	2	1	no	—
251	#135	—	2	1	no	—
252	#135	D₂₆₈	1	2	yes	—
253	#135	C₂²×D₆₇	1	2	yes	—
254	C₂×Q₁₆	—	67	2	no	—
255	C₂×Q₁₆	—	134	1	no	—
256	C₂×Q₁₆	—	134	1	no	—
257	C₂×Q₁₆	—	134	1	no	—
258	C₂×Q₁₆	—	134	1	no	—
259	C₂×Q₁₆	—	134	1	no	—
260	C₂×Q₁₆	D₂₆₈	1	1	yes	characteristic
261	C₂×SD₁₆	—	2	1	no	—
262	C₂×SD₁₆	—	268	1	no	—
263	C₂×SD₁₆	—	268	1	no	—
264	C₂×SD₁₆	—	268	2	no	—
265	C₂×SD₁₆	—	134	4	no	—
266	C₂×D₈	—	67	2	no	—
267	C₂×D₈	—	134	1	no	—
268	C₂×D₈	—	134	1	no	—
269	C₂×D₈	—	134	1	no	—
270	C₂×D₈	—	134	1	no	—
271	C₂×D₈	—	134	1	no	—
272	C₂×D₈	D₂₆₈	1	1	yes	characteristic
273	#131	—	2	4	no	—
274	#131	—	4	2	no	—
275	C₂×M₁₆	—	2	1	no	—
276	C₂×M₁₆	—	4	1	no	—
277	C₂²×C₈	—	4	1	no	—
278	C₂²×C₈	C₂²⋊D₆₇	1	1	yes	characteristic
279	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
280	#124	—	268	2	no	—
281	#124	—	134	4	no	—
282	C₂×C₂²⋊C₄	—	268	2	no	—
283	C₂×C₄²	C₂²⋊D₆₇	1	1	yes	characteristic
284	Q₃₂	—	134	4	no	—
285	SD₃₂	—	134	4	no	—
286	SD₃₂	—	134	4	no	—
287	D₁₆	—	134	4	no	—
288	M₃₂	—	67	2	no	—
289	M₃₂	—	67	2	no	—
290	M₃₂	—	134	1	no	—
291	M₃₂	—	134	1	no	—
292	C₂×C₁₆	—	134	1	no	—
293	C₂×C₁₆	—	134	1	no	—
294	#108	—	2	1	no	—
295	#108	C₂²×D₆₇	1	2	yes	—
296	#104	—	2	4	no	—
297	C₄×C₈	C₂²⋊D₆₇	1	2	yes	—
298	C₄×C₈	C₂²×D₆₇	1	2	yes	—
299	C₂⁴	—	268	1	no	—
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	#41	—	4	1	no	—
303	#41	—	4	1	no	—
304	C₂×Q₈	—	2	1	no	—
305	C₂×Q₈	—	268	1	no	—
306	C₂×Q₈	—	268	1	no	—
307	C₂×Q₈	—	268	1	no	—
308	C₂×Q₈	—	268	1	no	—
309	C₂×Q₈	—	268	1	no	—
310	C₂×Q₈	—	134	2	no	—
311	C₂×D₄	—	2	1	no	—
312	C₂×D₄	—	4	1	no	—
313	C₂×D₄	—	268	1	no	—
314	C₂×D₄	—	268	1	no	—
315	C₂×D₄	—	268	1	no	—
316	C₂×D₄	—	268	1	no	—
317	C₂×D₄	—	268	1	no	—
318	C₂×D₄	—	134	2	no	—
319	C₂²×C₄	—	2	1	no	—
320	C₂²×C₄	—	4	1	no	—
321	C₂²×C₄	—	268	1	no	—
322	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
323	Q₁₆	—	2	1	no	—
324	Q₁₆	—	268	1	no	—
325	Q₁₆	—	268	1	no	—
326	Q₁₆	—	134	2	no	—
327	Q₁₆	—	134	2	no	—
328	Q₁₆	C₂×D₂₆₈	1	2	yes	—
329	SD₁₆	—	2	2	no	—
330	SD₁₆	—	2	2	no	—
331	SD₁₆	—	268	4	no	—
332	SD₁₆	—	268	4	no	—
333	D₈	—	2	1	no	—
334	D₈	—	268	1	no	—
335	D₈	—	268	1	no	—
336	D₈	—	134	2	no	—
337	D₈	—	134	2	no	—
338	D₈	C₂×D₂₆₈	1	2	yes	—
339	M₁₆	—	2	2	no	—
340	M₁₆	—	4	1	no	—
341	M₁₆	—	4	4	no	—
342	C₂×C₈	—	4	1	no	—
343	C₂×C₈	—	4	4	no	—
344	C₂×C₈	#11761613	1	1	yes	characteristic
345	C₂×C₈	#11761613	1	1	yes	characteristic
346	C₂×C₈	#11761613	1	2	yes	—
347	C₂×C₈	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
348	C₂×C₈	C₂×C₂²⋊D₆₇	1	2	yes	—
349	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
350	C₂×C₈	C₂×D₂₆₈	1	1	yes	characteristic
351	C₂×C₈	#11761628	1	1	yes	characteristic
352	C₂×C₈	#11761628	1	1	yes	characteristic
353	C₂×C₈	C₂³×D₆₇	1	1	yes	characteristic
354	C₂²⋊C₄	—	268	8	no	—
355	C₄²	—	2	1	no	—
356	C₄²	C₂×C₂²⋊D₆₇	1	2	yes	—
357	C₁₆	—	134	2	no	—
358	C₁₆	—	134	2	no	—
359	C₂³	—	4	1	no	—
360	C₂³	—	268	2	no	—
361	C₂³	—	536	4	no	—
362	C₂³	—	536	1	no	—
363	C₂³	—	536	1	no	—
364	C₂³	#14524068	1	1	yes	characteristic
365	Q₈	—	2	2	no	—
366	Q₈	—	4	1	no	—
367	Q₈	—	268	2	no	—
368	Q₈	—	268	2	no	—
369	Q₈	—	536	1	no	—
370	Q₈	—	536	1	no	—
371	D₄	—	2	2	no	—
372	D₄	—	4	2	no	—
373	D₄	—	4	2	no	—
374	D₄	—	4	1	no	—
375	D₄	—	268	2	no	—
376	D₄	—	268	2	no	—
377	D₄	—	536	1	no	—
378	D₄	—	536	1	no	—
379	C₂×C₄	—	2	2	no	—
380	C₂×C₄	—	4	2	no	—
381	C₂×C₄	—	4	1	no	—
382	C₂×C₄	—	4	2	no	—
383	C₂×C₄	—	4	2	no	—
384	C₂×C₄	—	268	2	no	—
385	C₂×C₄	—	536	1	no	—
386	C₂×C₄	—	536	1	no	—
387	C₂×C₄	#14524017	1	1	yes	characteristic
388	C₂×C₄	#14524017	1	1	yes	characteristic
389	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
390	C₂×C₄	C₂×#11761613	1	1	yes	characteristic
391	C₂×C₄	#14524068	1	1	yes	characteristic
392	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
393	C₈	—	4	2	no	—
394	C₈	#14524017	1	1	yes	characteristic
395	C₈	#14524017	1	1	yes	characteristic
396	C₈	C₂×#11761613	1	2	yes	—
397	C₈	C₂×#11761613	1	2	yes	—
398	C₈	C₂²×D₂₆₈	1	1	yes	characteristic
399	C₈	C₂×#11761628	1	1	yes	characteristic
400	C₂²	—	2	2	no	—
401	C₂²	—	4	2	no	—
402	C₂²	—	8	2	no	—
403	C₂²	—	536	4	no	—
404	C₂²	—	536	2	no	—
405	C₂²	—	1072	2	no	—
406	C₂²	—	1072	2	no	—
407	C₂²	#16863591	1	1	yes	characteristic
408	C₂²	#16863591	1	1	yes	characteristic
409	C₂²	C₂×#14524068	1	1	yes	characteristic
410	C₄	—	4	2	no	—
411	C₄	—	4	2	no	—
412	C₄	—	536	2	no	—
413	C₄	#16863591	1	1	yes	characteristic
414	C₄	#16863591	1	1	yes	characteristic
415	C₄	C₂×#14524017	1	1	yes	characteristic
416	C₄	C₂²×#11761613	1	1	yes	characteristic
417	C₂	—	2	1	no	—
418	C₂	—	2	1	no	—
419	C₂	—	8	2	no	—
420	C₂	—	1072	2	no	—
421	C₂	#22562278	1	2	yes	direct product factor
422	C₂	C₂×#16863591	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	#16863591
commutator, cosocle	C₂×C₈×C₆₇	C₂⁴
Frattini	C₂×C₈	C₂³×D₆₇
Fitting	C₂×#443×C₆₇	C₂
socle	C₂²×C₆₇	#459
prime radical	C₂×#16863831	C₂
hypercenter	C₂×#443	D₆₇
hypocenter	C₆₇	C₂×#2212
LCS	G ▷ C₂×C₈×C₆₇ ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#443

Complements

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

N	H ≅ G/N	type
1. C₂×#16863836	C₂	semidirect
3. C₂×#16863780	C₂	semidirect
4. #22562278	C₂	direct (N × H)
5. C₂×#16863217	C₂	semidirect
6. C₂×#16863211	C₂	semidirect
7. C₂×#16863208	C₂	semidirect
8. C₂×#443×C₆₇	C₂	semidirect
14. #16863836	C₂²	semidirect
24. #16863780	C₂²	semidirect
25. #16863217	C₂²	semidirect
26. #16863211	C₂²	semidirect
27. #16863208	C₂²	semidirect
31. #443×C₆₇	C₂²	semidirect
209. C₂×C₆₇	#2212	semidirect
215. C₂×#443	D₆₇	semidirect
220. C₆₇	C₂×#2212	semidirect
240. #443	C₂×D₆₇	semidirect
421. C₂	#22562278	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×#16863836	2
C₂×#16863831	2
C₂×#16863780	2
#22562278	2
C₂×#16863217	2
C₂×#16863211	2
C₂×#16863208	2
C₂×#443×C₆₇	2
C₂×#2212	67

Subgroups — C2×#22562278 #31010203

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22562278 #31010203