Subgroups — #444×Dic₆₇ #30854405

Order 17152.

1022 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	C₂×#16863518	C₂	1	1	yes	maximal, characteristic
2	#135×Dic₆₇	C₂	1	1	yes	maximal, characteristic
3	#131×Dic₆₇	C₂	1	2	yes	maximal, complemented
4	#108×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
5	#22560096	C₂	1	1	yes	maximal, characteristic, complemented
6	#22560093	C₂	1	1	yes	maximal, characteristic, complemented
7	#22560054	C₂	1	2	yes	maximal, complemented
8	#22560051	C₂	1	2	yes	maximal, complemented
9	#104×Dic₆₇	C₂	1	2	yes	maximal, complemented
10	#97×Dic₆₇	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×#444×C₆₇	C₂	1	1	yes	maximal, characteristic
12	C₂×#14524050	C₂²	1	2	yes	—
13	#41×Dic₆₇	C₂²	1	2	yes	—
14	#16863518	C₄	1	8	yes	complemented
15	Q₁₆×Dic₆₇	C₄	1	2	yes	complemented
16	SD₁₆×Dic₆₇	C₄	1	4	yes	complemented
17	D₈×Dic₆₇	C₄	1	2	yes	complemented
18	C₂×#14523979	C₂²	1	1	yes	characteristic
19	#16863434	C₂²	1	1	yes	characteristic
20	C₂×#14523970	C₂²	1	2	yes	—
21	#16863392	C₂²	1	2	yes	—
22	#16863354	—	2	2	no	—
23	#16863354	C₂²	1	2	yes	—
24	#16863351	—	2	2	no	—
25	#16863351	C₂²	1	2	yes	—
26	M₁₆×Dic₆₇	—	2	2	no	—
27	M₁₆×Dic₆₇	C₂²	1	2	yes	—
28	C₂×#14523954	C₂²	1	1	yes	characteristic
29	C₂×#14523953	C₂²	1	1	yes	characteristic
30	C₂×#14523953	C₂²	1	1	yes	characteristic
31	C₂×C₈×Dic₆₇	—	2	2	no	—
32	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
33	C₂×C₈×Dic₆₇	C₂²	1	1	yes	characteristic
34	C₄²×Dic₆₇	C₂²	1	1	yes	characteristic
35	#16863160	C₂²	1	2	yes	—
36	#16863157	C₂²	1	2	yes	—
37	#16863156	C₂²	1	2	yes	—
38	C₂×#135×C₆₇	C₂²	1	1	yes	characteristic
39	C₂×#131×C₆₇	C₂²	1	2	yes	—
40	#444×C₆₇	C₄	1	8	yes	complemented
41	C₂×#108×C₆₇	C₂²	1	1	yes	characteristic
42	C₂×#104×C₆₇	C₂²	1	2	yes	—
43	C₂×#97×C₆₇	C₂²	1	1	yes	characteristic
44	#14524050	—	2	4	no	—
45	#14524050	C₂×C₄	1	8	yes	complemented
46	C₂×#11761612	—	2	2	no	—
47	C₂×#11761612	C₂³	1	2	yes	—
48	C₂²×C₆₇⋊C₈	—	2	2	no	—
49	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
50	C₂²×C₆₇⋊C₈	C₂³	1	1	yes	characteristic
51	Q₈×Dic₆₇	C₂×C₄	1	4	yes	—
52	D₄×Dic₆₇	—	2	4	no	—
53	D₄×Dic₆₇	C₂×C₄	1	4	yes	—
54	#14524002	—	2	2	no	—
55	#14524002	C₂³	1	2	yes	—
56	C₂×C₄×Dic₆₇	—	2	2	no	—
57	C₂×C₄×Dic₆₇	—	2	2	no	—
58	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
59	C₂×C₄×Dic₆₇	C₂³	1	1	yes	characteristic
60	#14523979	C₂×C₄	1	4	yes	complemented
61	#14523977	C₂×C₄	1	2	yes	—
62	#14523975	C₂×C₄	1	2	yes	—
63	#14523970	C₂×C₄	1	8	yes	complemented
64	#14523967	C₂×C₄	1	4	yes	—
65	#14523964	C₂×C₄	1	4	yes	—
66	#14523954	—	2	2	no	—
67	#14523953	—	2	2	no	—
68	#14523953	—	2	2	no	—
69	#14523953	—	2	2	no	—
70	#14523953	—	2	2	no	—
71	#14523953	C₂×C₄	1	4	yes	complemented
72	C₈×Dic₆₇	—	2	2	no	—
73	C₈×Dic₆₇	—	2	2	no	—
74	C₈×Dic₆₇	—	2	2	no	—
75	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
76	C₈×Dic₆₇	C₂×C₄	1	2	yes	—
77	C₈×Dic₆₇	D₄	1	2	yes	—
78	C₈×Dic₆₇	D₄	1	2	yes	—
79	C₂×#41×C₆₇	C₂³	1	2	yes	—
80	#135×C₆₇	C₂×C₄	1	4	yes	—
81	#135×C₆₇	C₂×C₄	1	4	yes	—
82	C₂×Q₁₆×C₆₇	C₂×C₄	1	1	yes	characteristic
83	C₂×SD₁₆×C₆₇	C₂×C₄	1	2	yes	—
84	C₂×D₈×C₆₇	C₂×C₄	1	1	yes	characteristic
85	#131×C₆₇	—	2	4	no	—
86	#131×C₆₇	C₂×C₄	1	8	yes	complemented
87	C₂×M₁₆×C₆₇	—	2	2	no	—
88	C₂×M₁₆×C₆₇	C₂³	1	2	yes	—
89	C₂²×C₈×C₆₇	—	2	2	no	—
90	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
91	C₂²×C₈×C₆₇	C₂³	1	1	yes	characteristic
92	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
93	#108×C₆₇	C₂×C₄	1	4	yes	complemented
94	#104×C₆₇	C₂×C₄	1	8	yes	complemented
95	#97×C₆₇	C₂×C₄	1	4	yes	complemented
96	C₂²×Dic₆₇	—	2	1	no	—
97	C₂²×Dic₆₇	—	2	4	no	—
98	C₂²×Dic₆₇	#41	1	2	yes	—
99	#11761612	—	2	2	no	—
100	#11761612	—	2	8	no	—
101	#11761612	C₂²×C₄	1	4	yes	—
102	C₂×C₆₇⋊C₈	—	2	2	no	—
103	C₂×C₆₇⋊C₈	—	2	1	no	—
104	C₂×C₆₇⋊C₈	—	2	1	no	—
105	C₂×C₆₇⋊C₈	—	2	8	no	—
106	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
107	C₂×C₆₇⋊C₈	C₂²×C₄	1	2	yes	—
108	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
109	C₂×C₆₇⋊C₈	#41	1	2	yes	—
110	C₄⋊Dic₆₇	—	2	4	no	—
111	C₄⋊Dic₆₇	C₂²×C₄	1	4	yes	—
112	C₂²⋊Dic₆₇	—	2	2	no	—
113	C₂²⋊Dic₆₇	—	2	4	no	—
114	C₄×Dic₆₇	—	2	2	no	—
115	C₄×Dic₆₇	—	2	1	no	—
116	C₄×Dic₆₇	—	2	4	no	—
117	C₄×Dic₆₇	—	4	4	no	—
118	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
119	C₄×Dic₆₇	C₂²×C₄	1	2	yes	—
120	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
121	C₄×Dic₆₇	C₂×D₄	1	1	yes	characteristic
122	#41×C₆₇	—	2	2	no	—
123	#41×C₆₇	—	2	2	no	—
124	#41×C₆₇	C₂²×C₄	1	4	yes	—
125	#41×C₆₇	C₂²×C₄	1	4	yes	—
126	C₂×Q₈×C₆₇	C₂²×C₄	1	2	yes	—
127	C₂×D₄×C₆₇	—	2	2	no	—
128	C₂×D₄×C₆₇	C₂²×C₄	1	2	yes	—
129	C₂²×C₄×C₆₇	—	2	2	no	—
130	C₂²×C₄×C₆₇	—	2	1	no	—
131	C₂²×C₄×C₆₇	C₂⁴	1	1	yes	characteristic
132	Q₁₆×C₆₇	C₄²	1	4	yes	complemented
133	SD₁₆×C₆₇	C₄²	1	8	yes	complemented
134	D₈×C₆₇	C₄²	1	4	yes	complemented
135	M₁₆×C₆₇	—	2	2	no	—
136	M₁₆×C₆₇	—	2	8	no	—
137	M₁₆×C₆₇	C₂²×C₄	1	4	yes	—
138	C₂×C₈×C₆₇	—	2	2	no	—
139	C₂×C₈×C₆₇	—	2	8	no	—
140	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
141	C₂×C₈×C₆₇	C₂²×C₄	1	1	yes	characteristic
142	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
143	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
144	C₂×C₈×C₆₇	C₂²×C₄	1	2	yes	—
145	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
146	C₂×C₈×C₆₇	#41	1	2	yes	—
147	C₄²×C₆₇	—	2	1	no	—
148	C₄²×C₆₇	C₂²×C₄	1	2	yes	—
149	C₂³×C₆₇	—	2	2	no	—
150	C₂³×C₆₇	C₂×#41	1	1	yes	characteristic
151	Q₈×C₆₇	—	2	2	no	—
152	Q₈×C₆₇	C₂×C₄²	1	4	yes	—
153	D₄×C₆₇	—	2	4	no	—
154	D₄×C₆₇	—	2	4	no	—
155	D₄×C₆₇	—	2	2	no	—
156	D₄×C₆₇	C₂×C₄²	1	4	yes	—
157	C₂×C₄×C₆₇	—	2	2	no	—
158	C₂×C₄×C₆₇	—	2	4	no	—
159	C₂×C₄×C₆₇	—	2	4	no	—
160	C₂×C₄×C₆₇	—	2	2	no	—
161	C₂×C₄×C₆₇	—	4	2	no	—
162	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
163	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
164	C₂×C₄×C₆₇	C₂³×C₄	1	1	yes	characteristic
165	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
166	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
167	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
168	C₂×Dic₆₇	—	2	4	no	—
169	C₂×Dic₆₇	—	2	4	no	—
170	C₂×Dic₆₇	—	2	2	no	—
171	C₂×Dic₆₇	—	4	2	no	—
172	C₂×Dic₆₇	—	4	8	no	—
173	C₂×Dic₆₇	C₄×D₄	1	2	yes	—
174	C₂×Dic₆₇	C₄×D₄	1	2	yes	—
175	C₈×C₆₇	—	2	4	no	—
176	C₈×C₆₇	C₂×C₄²	1	2	yes	—
177	C₈×C₆₇	C₂×C₄²	1	2	yes	—
178	C₈×C₆₇	C₄×D₄	1	4	yes	—
179	C₆₇⋊C₈	—	2	4	no	—
180	C₆₇⋊C₈	—	2	2	no	—
181	C₆₇⋊C₈	C₄×D₄	1	4	yes	—
182	C₂²×C₆₇	—	2	2	no	—
183	C₂²×C₆₇	—	2	4	no	—
184	C₂²×C₆₇	—	4	4	no	—
185	C₂²×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
186	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
187	C₂²×C₆₇	C₄×#41	1	1	yes	characteristic
188	C₄×C₆₇	—	2	4	no	—
189	C₄×C₆₇	—	4	2	no	—
190	C₄×C₆₇	C₂²×C₄²	1	1	yes	characteristic
191	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
192	C₄×C₆₇	C₂×C₄×D₄	1	1	yes	characteristic
193	C₄×C₆₇	C₄×#41	1	1	yes	characteristic
194	Dic₆₇	—	2	2	no	—
195	Dic₆₇	—	4	2	no	—
196	Dic₆₇	—	4	4	no	—
197	Dic₆₇	#444	1	4	yes	direct product factor
198	C₄×#444	—	67	1	no	maximal, Sylow
199	C₂×C₆₇	—	2	1	no	—
200	C₂×C₆₇	—	2	1	no	—
201	C₂×C₆₇	—	4	4	no	—
202	C₂×C₆₇	C₄²×D₄	1	1	yes	characteristic
203	C₂×C₆₇	C₂×#444	1	2	yes	—
204	C₂×#444	—	67	1	no	—
205	C₂×#444	D₆₇	1	1	yes	characteristic
206	C₄×#135	—	67	1	no	—
207	C₄×#131	—	67	2	no	—
208	C₄×#108	—	67	1	no	—
209	#1773	—	67	1	no	—
210	#1773	—	67	1	no	—
211	#1765	—	67	2	no	—
212	#1765	—	67	2	no	—
213	C₄×#104	—	67	2	no	—
214	C₄×#97	—	67	1	no	—
215	C₆₇	C₄×#444	1	1	yes	characteristic, complemented, Sylow
216	C₂×#135	C₂×D₆₇	1	1	yes	characteristic
217	C₂×#131	—	67	2	no	—
218	C₂×#131	C₂×D₆₇	1	2	yes	—
219	C₄×#41	—	67	2	no	—
220	#444	—	67	8	no	—
221	#444	Dic₆₇	1	8	yes	direct product factor
222	C₄×Q₁₆	—	67	2	no	—
223	C₄×SD₁₆	—	67	4	no	—
224	C₄×D₈	—	67	2	no	—
225	C₂×#108	—	67	1	no	—
226	C₂×#108	C₂×D₆₇	1	1	yes	characteristic
227	#427	—	67	1	no	—
228	C₂×#104	—	67	2	no	—
229	C₂×#104	C₂×D₆₇	1	2	yes	—
230	#416	—	67	2	no	—
231	#405	—	67	2	no	—
232	#405	—	67	2	no	—
233	#405	—	134	2	no	—
234	#405	—	134	2	no	—
235	C₄×M₁₆	—	67	2	no	—
236	C₄×M₁₆	—	134	2	no	—
237	C₂×#97	—	67	1	no	—
238	C₂×#97	—	67	1	no	—
239	C₂×#97	—	67	1	no	—
240	C₂×#97	C₂×D₆₇	1	1	yes	characteristic
241	C₂×C₄×C₈	—	67	1	no	—
242	C₂×C₄×C₈	—	67	1	no	—
243	C₂×C₄×C₈	—	134	2	no	—
244	C₄³	—	67	1	no	—
245	#341	—	67	2	no	—
246	#339	—	67	2	no	—
247	#339	—	67	2	no	—
248	C₂×#41	C₂²×D₆₇	1	2	yes	—
249	#135	C₄×D₆₇	1	4	yes	—
250	#135	C₂×Dic₆₇	1	4	yes	—
251	C₂×Q₁₆	C₄×D₆₇	1	1	yes	characteristic
252	C₂×SD₁₆	C₄×D₆₇	1	2	yes	—
253	C₂×D₈	C₄×D₆₇	1	1	yes	characteristic
254	#131	—	2	4	no	—
255	#131	—	67	8	no	—
256	#131	—	134	4	no	—
257	#131	C₂×Dic₆₇	1	8	yes	complemented
258	C₂×M₁₆	—	2	2	no	—
259	C₂×M₁₆	—	67	2	no	—
260	C₂×M₁₆	—	134	2	no	—
261	C₂×M₁₆	C₂²×D₆₇	1	2	yes	—
262	C₂²×C₈	—	2	2	no	—
263	C₂²×C₈	—	67	1	no	—
264	C₂²×C₈	—	67	1	no	—
265	C₂²×C₈	—	134	2	no	—
266	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
267	C₂²×C₈	C₂²×D₆₇	1	1	yes	characteristic
268	C₄×Q₈	—	67	4	no	—
269	C₄×D₄	—	67	4	no	—
270	C₄×D₄	—	134	4	no	—
271	#117	—	67	2	no	—
272	#117	—	134	2	no	—
273	C₂×C₄²	—	67	1	no	—
274	C₂×C₄²	—	67	1	no	—
275	C₂×C₄²	—	134	2	no	—
276	C₂×C₄²	—	134	2	no	—
277	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
278	#108	—	67	4	no	—
279	#108	C₂×Dic₆₇	1	4	yes	complemented
280	#107	—	67	2	no	—
281	#106	—	67	2	no	—
282	#104	—	67	8	no	—
283	#104	C₂×Dic₆₇	1	8	yes	complemented
284	#103	—	67	4	no	—
285	#102	—	67	4	no	—
286	#97	—	67	4	no	—
287	#97	—	134	2	no	—
288	#97	—	134	2	no	—
289	#97	—	134	2	no	—
290	#97	—	134	2	no	—
291	#97	—	134	2	no	—
292	#97	C₂×Dic₆₇	1	4	yes	complemented
293	C₄×C₈	—	67	2	no	—
294	C₄×C₈	—	67	2	no	—
295	C₄×C₈	—	67	2	no	—
296	C₄×C₈	—	67	2	no	—
297	C₄×C₈	—	134	2	no	—
298	C₄×C₈	—	134	2	no	—
299	C₄×C₈	—	134	2	no	—
300	#41	—	2	2	no	—
301	#41	—	2	2	no	—
302	#41	C₂×C₄×D₆₇	1	4	yes	—
303	#41	C₂²×Dic₆₇	1	4	yes	—
304	C₂×Q₈	C₂×C₄×D₆₇	1	2	yes	—
305	C₂×D₄	—	2	2	no	—
306	C₂×D₄	C₂×C₄×D₆₇	1	2	yes	—
307	C₂²×C₄	—	2	2	no	—
308	C₂²×C₄	—	2	1	no	—
309	C₂²×C₄	—	67	2	no	—
310	C₂²×C₄	—	134	4	no	—
311	C₂²×C₄	—	134	1	no	—
312	C₂²×C₄	C₂³×D₆₇	1	1	yes	characteristic
313	Q₁₆	C₄×Dic₆₇	1	4	yes	complemented
314	SD₁₆	C₄×Dic₆₇	1	8	yes	complemented
315	D₈	C₄×Dic₆₇	1	4	yes	complemented
316	M₁₆	—	2	2	no	—
317	M₁₆	—	2	8	no	—
318	M₁₆	—	67	4	no	—
319	M₁₆	—	134	8	no	—
320	M₁₆	—	134	2	no	—
321	M₁₆	C₂²×Dic₆₇	1	4	yes	—
322	C₂×C₈	—	2	2	no	—
323	C₂×C₈	—	2	8	no	—
324	C₂×C₈	—	67	2	no	—
325	C₂×C₈	—	67	2	no	—
326	C₂×C₈	—	67	2	no	—
327	C₂×C₈	—	67	2	no	—
328	C₂×C₈	—	134	8	no	—
329	C₂×C₈	—	134	2	no	—
330	C₂×C₈	—	134	1	no	—
331	C₂×C₈	—	134	1	no	—
332	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
333	C₂×C₈	C₂×C₄×D₆₇	1	1	yes	characteristic
334	C₂×C₈	C₂×C₄×D₆₇	1	2	yes	—
335	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
336	C₂×C₈	C₂²×Dic₆₇	1	2	yes	—
337	C₂×C₈	D₄×D₆₇	1	2	yes	—
338	C₂×C₈	#11761627	1	2	yes	—
339	C₄⋊C₄	—	67	4	no	—
340	C₄⋊C₄	—	134	4	no	—
341	C₂²⋊C₄	—	134	4	no	—
342	C₂²⋊C₄	—	134	2	no	—
343	C₄²	—	2	1	no	—
344	C₄²	—	268	4	no	—
345	C₄²	—	67	2	no	—
346	C₄²	—	67	1	no	—
347	C₄²	—	67	1	no	—
348	C₄²	—	67	2	no	—
349	C₄²	—	134	4	no	—
350	C₄²	—	134	2	no	—
351	C₄²	—	134	1	no	—
352	C₄²	C₂²×Dic₆₇	1	2	yes	—
353	C₂³	—	2	2	no	—
354	C₂³	#41×D₆₇	1	1	yes	characteristic
355	Q₈	—	2	2	no	—
356	Q₈	C₂×C₄×Dic₆₇	1	4	yes	—
357	D₄	—	2	4	no	—
358	D₄	—	2	4	no	—
359	D₄	—	2	2	no	—
360	D₄	C₂×C₄×Dic₆₇	1	4	yes	—
361	C₂×C₄	—	2	2	no	—
362	C₂×C₄	—	2	4	no	—
363	C₂×C₄	—	2	4	no	—
364	C₂×C₄	—	2	2	no	—
365	C₂×C₄	—	4	2	no	—
366	C₂×C₄	—	268	2	no	—
367	C₂×C₄	—	268	8	no	—
368	C₂×C₄	—	67	2	no	—
369	C₂×C₄	—	67	2	no	—
370	C₂×C₄	—	134	4	no	—
371	C₂×C₄	—	134	2	no	—
372	C₂×C₄	—	134	4	no	—
373	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₄×D₆₇	1	1	yes	characteristic
375	C₂×C₄	C₂³×Dic₆₇	1	1	yes	characteristic
376	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
377	C₂×C₄	#41×D₆₇	1	1	yes	characteristic
378	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
379	C₈	—	2	4	no	—
380	C₈	—	67	4	no	—
381	C₈	—	134	4	no	—
382	C₈	—	134	2	no	—
383	C₈	C₂×C₄×Dic₆₇	1	2	yes	—
384	C₈	C₂×C₄×Dic₆₇	1	2	yes	—
385	C₈	D₄×Dic₆₇	1	4	yes	—
386	C₂²	—	2	2	no	—
387	C₂²	—	2	4	no	—
388	C₂²	—	4	4	no	—
389	C₂²	C₄×D₄×D₆₇	1	1	yes	characteristic
390	C₂²	C₄×#11761627	1	1	yes	characteristic
391	C₂²	#41×Dic₆₇	1	1	yes	characteristic
392	C₄	—	2	4	no	—
393	C₄	—	4	2	no	—
394	C₄	—	268	2	no	—
395	C₄	—	268	4	no	—
396	C₄	—	67	4	no	—
397	C₄	—	134	2	no	—
398	C₄	C₂²×C₄×Dic₆₇	1	1	yes	characteristic
399	C₄	C₄×D₄×D₆₇	1	1	yes	characteristic
400	C₄	C₂×D₄×Dic₆₇	1	1	yes	characteristic
401	C₄	C₄×#11761627	1	1	yes	characteristic
402	C₂	—	2	1	no	—
403	C₂	—	2	1	no	—
404	C₂	—	4	4	no	—
405	C₂	C₄×D₄×Dic₆₇	1	1	yes	characteristic
406	C₂	#444×D₆₇	1	2	yes	—

	subgroup	G/H
center	C₂×C₄	C₂×D₄×D₆₇
commutator	C₄×C₆₇	C₂²×C₄²
Frattini	C₂²×C₄	C₂³×D₆₇
Fitting	C₂×#444×C₆₇	C₂
socle	C₂²×C₆₇	C₂×C₄×D₄
prime radical	C₂×#135×C₆₇	C₂²
cosocle	C₂²×C₄×C₆₇	C₂⁴
hypercenter	C₂×#444	D₆₇
hypocenter	C₆₇	C₄×#444
LCS	G ▷ C₄×C₆₇ ▷ C₂×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂×C₄ ◁ C₂²×C₈ ◁ C₂×#444

Complements

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

N	H ≅ G/N	type
3. #131×Dic₆₇	C₂	semidirect
4. #108×Dic₆₇	C₂	semidirect
5. #22560096	C₂	semidirect
6. #22560093	C₂	semidirect
7. #22560054	C₂	semidirect
8. #22560051	C₂	semidirect
9. #104×Dic₆₇	C₂	semidirect
10. #97×Dic₆₇	C₂	semidirect
14. #16863518	C₄	semidirect
15. Q₁₆×Dic₆₇	C₄	semidirect
16. SD₁₆×Dic₆₇	C₄	semidirect
17. D₈×Dic₆₇	C₄	semidirect
40. #444×C₆₇	C₄	semidirect
45. #14524050	C₂×C₄	semidirect
60. #14523979	C₂×C₄	semidirect
63. #14523970	C₂×C₄	semidirect
71. #14523953	C₂×C₄	semidirect
86. #131×C₆₇	C₂×C₄	semidirect
93. #108×C₆₇	C₂×C₄	semidirect
94. #104×C₆₇	C₂×C₄	semidirect
95. #97×C₆₇	C₂×C₄	semidirect
132. Q₁₆×C₆₇	C₄²	semidirect
133. SD₁₆×C₆₇	C₄²	semidirect
134. D₈×C₆₇	C₄²	semidirect
197. Dic₆₇	#444	direct (N × H)
215. C₆₇	C₄×#444	semidirect
221. #444	Dic₆₇	direct (N × H)
257. #131	C₂×Dic₆₇	semidirect
279. #108	C₂×Dic₆₇	semidirect
283. #104	C₂×Dic₆₇	semidirect
292. #97	C₂×Dic₆₇	semidirect
313. Q₁₆	C₄×Dic₆₇	semidirect
314. SD₁₆	C₄×Dic₆₇	semidirect
315. D₈	C₄×Dic₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂×#16863518	2
#135×Dic₆₇	2
#131×Dic₆₇	2
#108×Dic₆₇	2
#22560096	2
#22560093	2
#22560054	2
#22560051	2
#104×Dic₆₇	2
#97×Dic₆₇	2
C₂×#444×C₆₇	2
C₄×#444	67

Subgroups — #444×Dic67 #30854405

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — #444×Dic₆₇ #30854405