Subgroups — #30874299

Order 17152.

870 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863514	C₂	1	2	yes	maximal
2	C₄×#14524065	C₂	1	1	yes	maximal, characteristic
3	#22568774	C₂	1	2	yes	maximal, complemented
4	#22560957	C₂	1	2	yes	maximal, complemented
5	#22560487	C₂	1	4	yes	maximal, complemented
6	#22560381	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560230	C₂	1	2	yes	maximal, complemented
8	C₈×C₄⋊C₄×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
9	C₂×#14524065	C₂²	1	1	yes	characteristic
10	C₂×#14524049	C₂²	1	4	yes	—
11	C₄×#11761628	C₂²	1	2	yes	—
12	#16863514	—	2	8	no	—
13	C₄×Dic₂₆₈	C₄	1	1	yes	characteristic, complemented
14	C₄×Dic₂₆₈	C₄	1	1	yes	characteristic, complemented
15	C₄×#11761617	C₄	1	2	yes	complemented
16	C₄×#11761617	C₄	1	2	yes	complemented
17	C₄×D₅₃₆	C₄	1	1	yes	characteristic, complemented
18	C₄×D₅₃₆	C₄	1	1	yes	characteristic, complemented
19	C₂×#14523979	C₂²	1	2	yes	—
20	C₂×#14523979	C₂²	1	2	yes	—
21	#16863434	C₂²	1	1	yes	characteristic
22	#16863422	C₂²	1	4	yes	—
23	#16863421	—	2	4	no	—
24	#16863420	C₂²	1	2	yes	—
25	#16863418	—	2	2	no	—
26	C₄⋊C₈×D₆₇	—	2	2	no	—
27	C₂×#14523971	C₂²	1	4	yes	—
28	#16863393	C₂²	1	2	yes	—
29	#16863156	C₂²	1	4	yes	—
30	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
31	C₂×C₄×C₈×C₆₇	C₂²	1	2	yes	—
32	C₂×C₄×C₈×C₆₇	C₂²	1	1	yes	characteristic
33	C₄×C₄⋊C₄×C₆₇	C₂²	1	1	yes	characteristic
34	#336×C₆₇	C₂²	1	2	yes	—
35	C₂×#11761628	C₂³	1	2	yes	—
36	#14524065	D₄	1	4	yes	—
37	#14524065	Q₈	1	4	yes	—
38	C₂×Dic₂₆₈	C₂×C₄	1	1	yes	characteristic
39	C₂×#11761617	C₂×C₄	1	2	yes	—
40	C₂×D₅₃₆	C₂×C₄	1	1	yes	characteristic
41	#14524049	—	2	8	no	—
42	#14524049	—	4	4	no	—
43	C₂×#11761612	C₂³	1	4	yes	—
44	C₂×#11761611	—	2	4	no	—
45	C₂×C₈×D₆₇	—	2	4	no	—
46	C₄×Dic₁₃₄	C₂×C₄	1	2	yes	—
47	C₄×Dic₁₃₄	C₂×C₄	1	2	yes	—
48	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
49	C₄×D₂₆₈	C₂×C₄	1	2	yes	—
50	C₄×C₂²⋊D₆₇	—	2	2	no	—
51	C₄×C₂²⋊D₆₇	—	2	2	no	—
52	#14524002	C₂³	1	2	yes	—
53	#14524000	—	2	2	no	—
54	C₄²×D₆₇	—	2	2	no	—
55	#14523979	—	2	4	no	—
56	#14523979	—	4	2	no	—
57	#14523977	C₂×C₄	1	1	yes	characteristic
58	#14523977	C₂×C₄	1	1	yes	characteristic
59	#14523975	C₂×C₄	1	2	yes	—
60	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
61	C₄⋊(C₆₇⋊C₈)	—	2	2	no	—
62	Dic₆₇⋊C₈	—	2	4	no	—
63	Dic₆₇⋊C₈	—	2	4	no	—
64	#14523971	—	2	8	no	—
65	#14523968	C₂×C₄	1	2	yes	—
66	#14523968	C₂×C₄	1	2	yes	—
67	#14523965	C₂×C₄	1	2	yes	—
68	#14523965	C₂×C₄	1	2	yes	—
69	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
70	C₂²×C₈×C₆₇	C₂³	1	2	yes	—
71	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
72	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
73	C₂×C₄²×C₆₇	C₂³	1	2	yes	—
74	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
75	C₄⋊C₈×C₆₇	D₄	1	1	yes	characteristic
76	C₄⋊C₈×C₆₇	D₄	1	1	yes	characteristic
77	C₄⋊C₈×C₆₇	D₄	1	2	yes	—
78	C₄×C₈×C₆₇	—	2	4	no	—
79	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
80	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
81	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
82	C₄×C₈×C₆₇	C₂×C₄	1	1	yes	characteristic
83	#95×C₆₇	—	2	1	no	—
84	#11761628	—	2	2	no	—
85	#11761628	—	2	2	no	—
86	#11761628	C₂×D₄	1	4	yes	—
87	#11761628	C₂×Q₈	1	4	yes	—
88	C₂×Dic₁₃₄	C₂²×C₄	1	2	yes	—
89	C₂×D₂₆₈	C₂²×C₄	1	2	yes	—
90	C₂×C₂²⋊D₆₇	—	2	2	no	—
91	C₂×C₄×D₆₇	—	2	2	no	—
92	C₂×C₄×D₆₇	—	2	2	no	—
93	C₂×C₄×D₆₇	—	2	2	no	—
94	Dic₂₆₈	C₄⋊C₄	1	4	yes	complemented
95	#11761617	C₄⋊C₄	1	8	yes	complemented
96	D₅₃₆	C₄⋊C₄	1	4	yes	complemented
97	#11761612	—	2	4	no	—
98	#11761612	—	2	4	no	—
99	#11761611	—	4	8	no	—
100	C₂×C₆₇⋊C₈	—	2	4	no	—
101	C₈×D₆₇	—	4	8	no	—
102	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
103	C₄⋊Dic₆₇	C₂²×C₄	1	2	yes	—
104	Dic₆₇⋊C₄	—	2	2	no	—
105	Dic₆₇⋊C₄	—	2	2	no	—
106	C₂²⋊Dic₆₇	—	2	2	no	—
107	(C₂×D₆₇)⋊C₄	—	2	2	no	—
108	(C₂×D₆₇)⋊C₄	—	2	2	no	—
109	C₄×Dic₆₇	—	2	2	no	—
110	C₄×Dic₆₇	—	2	2	no	—
111	C₄×Dic₆₇	—	2	2	no	—
112	C₂²×C₄×C₆₇	—	2	2	no	—
113	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
114	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
116	C₂×C₈×C₆₇	—	2	2	no	—
117	C₂×C₈×C₆₇	—	2	1	no	—
118	C₂×C₈×C₆₇	—	2	2	no	—
119	C₂×C₈×C₆₇	—	2	1	no	—
120	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
121	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
122	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
123	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
124	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
125	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
126	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
127	C₂×C₈×C₆₇	C₂×Q₈	1	2	yes	—
128	C₄⋊C₄×C₆₇	—	2	4	no	—
129	C₄²×C₆₇	—	2	2	no	—
130	C₄²×C₆₇	—	2	2	no	—
131	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
132	C₄²×C₆₇	C₂²×C₄	1	1	yes	characteristic
133	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
135	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
136	C₂²×D₆₇	—	2	2	no	—
137	C₂×C₄×C₆₇	—	2	2	no	—
138	C₂×C₄×C₆₇	—	2	4	no	—
139	C₂×C₄×C₆₇	—	4	1	no	—
140	C₂×C₄×C₆₇	—	4	2	no	—
141	C₂×C₄×C₆₇	—	4	2	no	—
142	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
143	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
144	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
145	C₂×C₄×C₆₇	C₄×D₄	1	1	yes	characteristic
146	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
147	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
148	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
149	C₂×C₄×C₆₇	C₂²×Q₈	1	1	yes	characteristic
150	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
151	C₂×C₄×C₆₇	2₋¹⁺⁴	1	1	yes	characteristic
152	C₂²⋊D₆₇	—	2	4	no	—
153	C₂²⋊D₆₇	—	2	4	no	—
154	C₂×Dic₆₇	—	2	2	no	—
155	C₂×Dic₆₇	—	2	2	no	—
156	C₂×Dic₆₇	—	2	2	no	—
157	D₂₆₈	—	2	2	no	—
158	D₂₆₈	C₂×C₄⋊C₄	1	4	yes	—
159	C₄×D₆₇	—	2	4	no	—
160	C₄×D₆₇	—	2	4	no	—
161	C₄×D₆₇	—	4	4	no	—
162	C₄×D₆₇	—	8	2	no	—
163	Dic₁₃₄	—	2	2	no	—
164	Dic₁₃₄	C₂×C₄⋊C₄	1	4	yes	—
165	C₈×C₆₇	—	2	1	no	—
166	C₈×C₆₇	—	2	1	no	—
167	C₈×C₆₇	—	2	2	no	—
168	C₈×C₆₇	—	2	2	no	—
169	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
170	C₈×C₆₇	C₂×C₄⋊C₄	1	2	yes	—
171	C₆₇⋊C₈	—	4	4	no	—
172	C₂²×C₆₇	—	2	1	no	—
173	C₂²×C₆₇	—	2	1	no	—
174	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
175	C₂²×C₆₇	#547	1	1	yes	characteristic
176	C₂²×C₆₇	#554	1	1	yes	characteristic
177	C₂×D₆₇	—	2	4	no	—
178	C₂×D₆₇	—	4	2	no	—
179	C₂×D₆₇	—	4	2	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	2	1	no	—
182	C₄×C₆₇	—	2	1	no	—
183	C₄×C₆₇	—	4	4	no	—
184	C₄×C₆₇	#443	1	2	yes	complemented
185	C₄×C₆₇	C₂²×C₄⋊C₄	1	1	yes	characteristic
186	C₄×C₆₇	#520	1	1	yes	characteristic
187	C₄×C₆₇	D₄²	1	1	yes	characteristic
188	C₄×C₆₇	D₄×Q₈	1	1	yes	characteristic
189	Dic₆₇	—	2	4	no	—
190	Dic₆₇	—	4	2	no	—
191	Dic₆₇	—	4	2	no	—
192	#22688	—	67	1	no	maximal, Sylow
193	C₂×C₆₇	—	2	1	no	—
194	C₂×C₆₇	—	2	1	no	—
195	C₂×C₆₇	D₄×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₆₇	C₂×#443	1	1	yes	characteristic
197	C₂×C₆₇	#2957	1	1	yes	characteristic
198	D₆₇	—	4	4	no	—
199	C₂×#443	—	67	2	no	—
200	C₄×#135	—	67	1	no	—
201	#2906	—	67	2	no	—
202	#1945	—	67	2	no	—
203	#1866	—	67	4	no	—
204	#1848	—	67	1	no	—
205	#1806	—	67	2	no	—
206	C₈×C₄⋊C₄	D₆₇	1	1	yes	characteristic, complemented
207	C₆₇	#22688	1	1	yes	characteristic, complemented, Sylow
208	C₂×#135	—	67	1	no	—
209	C₂×#131	—	67	4	no	—
210	C₄×#41	—	67	2	no	—
211	#443	—	134	8	no	—
212	C₄×Q₁₆	—	67	1	no	—
213	C₄×Q₁₆	—	67	1	no	—
214	C₄×SD₁₆	—	67	2	no	—
215	C₄×SD₁₆	—	67	2	no	—
216	C₄×D₈	—	67	1	no	—
217	C₄×D₈	—	67	1	no	—
218	C₂×#108	—	67	2	no	—
219	C₂×#108	—	67	2	no	—
220	#427	—	67	1	no	—
221	#424	—	67	4	no	—
222	#424	—	134	4	no	—
223	#423	—	67	2	no	—
224	#423	—	134	2	no	—
225	C₂×C₄⋊C₈	—	134	2	no	—
226	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
227	C₂×#104	—	67	4	no	—
228	#416	—	67	2	no	—
229	C₂×C₄×C₈	C₂×D₆₇	1	2	yes	—
230	C₂×C₄×C₈	C₂×D₆₇	1	1	yes	characteristic
231	C₄×C₄⋊C₄	C₂×D₆₇	1	1	yes	characteristic
232	#339	—	67	4	no	—
233	#336	C₂×D₆₇	1	2	yes	—
234	C₂×#41	—	67	2	no	—
235	#135	—	67	4	no	—
236	#135	—	67	4	no	—
237	C₂×Q₁₆	—	67	1	no	—
238	C₂×SD₁₆	—	67	2	no	—
239	C₂×D₈	—	67	1	no	—
240	#131	—	268	4	no	—
241	#131	—	134	8	no	—
242	C₂×M₁₆	—	67	4	no	—
243	C₂×M₁₆	—	134	4	no	—
244	C₂²×C₈	—	134	4	no	—
245	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
246	C₂²×C₈	C₂²×D₆₇	1	2	yes	—
247	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
248	C₄×Q₈	—	67	2	no	—
249	C₄×Q₈	—	67	2	no	—
250	C₄×D₄	—	67	2	no	—
251	C₄×D₄	—	67	2	no	—
252	C₄×D₄	—	134	2	no	—
253	C₄×D₄	—	134	2	no	—
254	#117	—	67	2	no	—
255	#117	—	134	2	no	—
256	C₂×C₄⋊C₄	—	2	1	no	—
257	C₂×C₄²	—	134	2	no	—
258	C₂×C₄²	C₂²×D₆₇	1	2	yes	—
259	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
260	#108	—	268	2	no	—
261	#108	—	134	4	no	—
262	#107	—	67	1	no	—
263	#107	—	67	1	no	—
264	#106	—	67	2	no	—
265	C₄⋊C₈	—	134	4	no	—
266	C₄⋊C₈	—	134	4	no	—
267	C₄⋊C₈	—	134	2	no	—
268	C₄⋊C₈	—	134	2	no	—
269	C₄⋊C₈	D₂₆₈	1	1	yes	characteristic
270	C₄⋊C₈	D₂₆₈	1	1	yes	characteristic
271	C₄⋊C₈	D₂₆₈	1	2	yes	—
272	#104	—	134	8	no	—
273	#103	—	67	2	no	—
274	#103	—	67	2	no	—
275	#102	—	67	2	no	—
276	#102	—	67	2	no	—
277	C₄×C₈	—	2	4	no	—
278	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
279	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
280	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
281	C₄×C₈	C₄×D₆₇	1	1	yes	characteristic
282	#95	—	2	1	no	—
283	#41	—	67	4	no	—
284	#41	—	67	4	no	—
285	#41	—	134	2	no	—
286	#41	—	134	2	no	—
287	C₂×Q₈	—	67	2	no	—
288	C₂×D₄	—	67	2	no	—
289	C₂×D₄	—	134	2	no	—
290	C₂²×C₄	—	2	2	no	—
291	C₂²×C₄	—	134	2	no	—
292	C₂²×C₄	—	134	2	no	—
293	C₂²×C₄	—	134	2	no	—
294	C₂²×C₄	#11761628	1	1	yes	characteristic
295	C₂²×C₄	#11761628	1	1	yes	characteristic
296	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
297	Q₁₆	—	67	4	no	—
298	SD₁₆	—	67	8	no	—
299	D₈	—	67	4	no	—
300	M₁₆	—	268	8	no	—
301	M₁₆	—	134	4	no	—
302	M₁₆	—	134	4	no	—
303	C₂×C₈	—	2	2	no	—
304	C₂×C₈	—	2	1	no	—
305	C₂×C₈	—	2	2	no	—
306	C₂×C₈	—	2	1	no	—
307	C₂×C₈	—	268	8	no	—
308	C₂×C₈	—	134	4	no	—
309	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
310	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
311	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
312	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
313	C₂×C₈	D₄×D₆₇	1	2	yes	—
314	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
315	C₂×C₈	C₂×D₂₆₈	1	2	yes	—
316	C₂×C₈	Q₈×D₆₇	1	2	yes	—
317	C₄⋊C₄	—	2	4	no	—
318	C₄⋊C₄	—	67	2	no	—
319	C₄⋊C₄	—	67	2	no	—
320	C₄⋊C₄	—	134	2	no	—
321	C₄⋊C₄	—	134	2	no	—
322	C₂²⋊C₄	—	134	2	no	—
323	C₂²⋊C₄	—	134	2	no	—
324	C₂²⋊C₄	—	134	2	no	—
325	C₄²	—	2	2	no	—
326	C₄²	—	2	2	no	—
327	C₄²	—	134	2	no	—
328	C₄²	—	134	2	no	—
329	C₄²	—	134	2	no	—
330	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
331	C₄²	C₂×C₄×D₆₇	1	1	yes	characteristic
332	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
333	C₄²	C₂×D₂₆₈	1	1	yes	characteristic
334	C₂³	—	134	2	no	—
335	C₂³	C₂×#11761628	1	1	yes	characteristic
336	Q₈	—	67	4	no	—
337	Q₈	—	134	2	no	—
338	D₄	—	67	4	no	—
339	D₄	—	134	4	no	—
340	D₄	—	134	4	no	—
341	D₄	—	134	2	no	—
342	C₂×C₄	—	2	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	4	1	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	268	4	no	—
348	C₂×C₄	—	536	2	no	—
349	C₂×C₄	—	134	2	no	—
350	C₂×C₄	—	134	2	no	—
351	C₂×C₄	—	134	2	no	—
352	C₂×C₄	—	134	4	no	—
353	C₂×C₄	—	134	4	no	—
354	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
355	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
356	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
357	C₂×C₄	C₄×D₂₆₈	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
359	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
360	C₂×C₄	C₂²×D₂₆₈	1	1	yes	characteristic
361	C₂×C₄	C₂×Q₈×D₆₇	1	1	yes	characteristic
362	C₂×C₄	#14524089	1	1	yes	characteristic
363	C₂×C₄	#14524090	1	1	yes	characteristic
364	C₈	—	2	2	no	—
365	C₈	—	2	2	no	—
366	C₈	—	2	1	no	—
367	C₈	—	2	1	no	—
368	C₈	—	268	4	no	—
369	C₈	C₄⋊C₄×D₆₇	1	2	yes	—
370	C₈	C₄⋊C₄×D₆₇	1	2	yes	—
371	C₂²	—	2	1	no	—
372	C₂²	—	2	1	no	—
373	C₂²	—	268	2	no	—
374	C₂²	—	268	2	no	—
375	C₂²	—	134	4	no	—
376	C₂²	C₂×C₄×D₂₆₈	1	1	yes	characteristic
377	C₂²	#16864051	1	1	yes	characteristic
378	C₂²	#16864106	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	2	1	no	—
381	C₄	—	2	1	no	—
382	C₄	—	4	4	no	—
383	C₄	—	268	2	no	—
384	C₄	—	268	2	no	—
385	C₄	—	134	4	no	—
386	C₄	#16863514	1	2	yes	complemented
387	C₄	C₂×C₄⋊C₄×D₆₇	1	1	yes	characteristic
388	C₄	#16863876	1	1	yes	characteristic
389	C₄	D₄×D₂₆₈	1	1	yes	characteristic
390	C₄	Q₈×D₂₆₈	1	1	yes	characteristic
391	C₂	—	2	1	no	—
392	C₂	—	2	1	no	—
393	C₂	—	268	4	no	—
394	C₂	C₄⋊C₄×D₂₆₈	1	1	yes	characteristic
395	C₂	C₂×#16863514	1	1	yes	characteristic
396	C₂	#22569127	1	1	yes	characteristic

	subgroup	G/H
center	C₂×C₄	C₂²×D₂₆₈
commutator	C₂×C₄×C₆₇	C₂³×C₄
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₈×C₄⋊C₄×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#14524065	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₈×C₄⋊C₄	D₆₇
hypocenter	C₆₇	#22688
LCS	G ▷ C₂×C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂×C₄⋊C₈ ◁ C₈×C₄⋊C₄

Complements

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

N	H ≅ G/N	type
3. #22568774	C₂	semidirect
4. #22560957	C₂	semidirect
5. #22560487	C₂	semidirect
6. #22560381	C₂	semidirect
7. #22560230	C₂	semidirect
8. C₈×C₄⋊C₄×C₆₇	C₂	semidirect
13. C₄×Dic₂₆₈	C₄	semidirect
14. C₄×Dic₂₆₈	C₄	semidirect
15. C₄×#11761617	C₄	semidirect
16. C₄×#11761617	C₄	semidirect
17. C₄×D₅₃₆	C₄	semidirect
18. C₄×D₅₃₆	C₄	semidirect
94. Dic₂₆₈	C₄⋊C₄	semidirect
95. #11761617	C₄⋊C₄	semidirect
96. D₅₃₆	C₄⋊C₄	semidirect
184. C₄×C₆₇	#443	semidirect
206. C₈×C₄⋊C₄	D₆₇	semidirect
207. C₆₇	#22688	semidirect
386. C₄	#16863514	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863514	2
C₄×#14524065	2
#22568774	2
#22560957	2
#22560487	2
#22560381	2
#22560230	2
C₈×C₄⋊C₄×C₆₇	2
#22688	67