Subgroups — C₆₇×#20053 #30699304

Order 17152.

800 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	C₆₇×#3325	C₂	1	2	yes	maximal, complemented
2	D₄×D₈×C₆₇	C₂	1	2	yes	maximal, complemented
3	C₆₇×#1721	C₂	1	1	yes	maximal, characteristic, complemented
4	C₆₇×#1687	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1677	C₂	1	2	yes	maximal, complemented
6	C₆₇×#1629	C₂	1	1	yes	maximal, characteristic, complemented
7	C₆₇×#1624	C₂	1	1	yes	maximal, characteristic, complemented
8	C₆₇×#1619	C₂	1	2	yes	maximal, complemented
9	C₆₇×#1586	C₂	1	2	yes	maximal, complemented
10	C₂²×D₈×C₆₇	—	2	2	no	—
11	#555×C₆₇	C₂²	1	1	yes	characteristic, complemented
12	D₄²×C₆₇	C₂²	1	1	yes	characteristic
13	D₄²×C₆₇	C₂²	1	2	yes	complemented
14	#493×C₆₇	C₂²	1	2	yes	complemented
15	#493×C₆₇	C₂²	1	1	yes	characteristic, complemented
16	#492×C₆₇	C₂²	1	1	yes	characteristic, complemented
17	#486×C₆₇	C₂²	1	2	yes	complemented
18	#482×C₆₇	—	2	2	no	—
19	#476×C₆₇	C₂²	1	2	yes	complemented
20	#469×C₆₇	—	2	2	no	—
21	#466×C₆₇	—	2	2	no	—
22	#459×C₆₇	C₂²	1	2	yes	—
23	#459×C₆₇	C₂²	1	2	yes	complemented
24	#459×C₆₇	C₂²	1	2	yes	complemented
25	#447×C₆₇	—	2	2	no	—
26	#447×C₆₇	—	2	2	no	—
27	#447×C₆₇	—	2	2	no	—
28	C₄×D₈×C₆₇	C₂²	1	2	yes	—
29	#436×C₆₇	C₂²	1	2	yes	complemented
30	C₈×D₄×C₆₇	C₂²	1	2	yes	complemented
31	#418×C₆₇	—	2	2	no	—
32	#334×C₆₇	C₂²	1	2	yes	complemented
33	#333×C₆₇	C₂²	1	1	yes	characteristic, complemented
34	#331×C₆₇	C₂²	1	2	yes	complemented
35	#331×C₆₇	C₂²	1	1	yes	characteristic, complemented
36	D₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
37	D₄⋊C₈×C₆₇	C₂²	1	2	yes	complemented
38	#322×C₆₇	C₂²	1	1	yes	characteristic, complemented
39	C₂²×D₄×C₆₇	—	2	2	no	—
40	C₂²×D₄×C₆₇	—	2	2	no	—
41	C₂²×D₄×C₆₇	—	2	2	no	—
42	C₂×SD₁₆×C₆₇	—	4	1	no	—
43	C₂×D₈×C₆₇	—	2	2	no	—
44	C₂×D₈×C₆₇	—	2	2	no	—
45	C₂×D₈×C₆₇	—	2	2	no	—
46	C₂×D₈×C₆₇	—	2	2	no	—
47	C₂×D₈×C₆₇	—	2	2	no	—
48	C₂×D₈×C₆₇	—	4	1	no	—
49	C₂×D₈×C₆₇	—	4	8	no	—
50	C₂×D₈×C₆₇	D₄	1	2	yes	—
51	C₂×M₁₆×C₆₇	—	2	2	no	—
52	C₂²×C₈×C₆₇	—	2	2	no	—
53	C₄⋊Q₈×C₆₇	C₂³	1	1	yes	characteristic
54	#127×C₆₇	C₂³	1	2	yes	—
55	#127×C₆₇	C₂³	1	1	yes	characteristic
56	#124×C₆₇	—	4	1	no	—
57	#121×C₆₇	—	2	2	no	—
58	#121×C₆₇	—	2	2	no	—
59	#121×C₆₇	—	2	2	no	—
60	#121×C₆₇	—	2	2	no	—
61	#120×C₆₇	—	4	1	no	—
62	#120×C₆₇	—	4	2	no	—
63	C₄×D₄×C₆₇	C₂³	1	2	yes	—
64	C₄×D₄×C₆₇	C₂³	1	2	yes	—
65	#117×C₆₇	—	2	2	no	—
66	#107×C₆₇	D₄	1	2	yes	—
67	#106×C₆₇	—	2	2	no	—
68	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
69	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
70	#102×C₆₇	—	2	2	no	—
71	#102×C₆₇	—	2	2	no	—
72	#102×C₆₇	—	2	2	no	—
73	#102×C₆₇	—	2	2	no	—
74	#102×C₆₇	—	2	2	no	—
75	#102×C₆₇	—	2	2	no	—
76	#102×C₆₇	D₄	1	2	yes	—
77	#102×C₆₇	D₄	1	2	yes	—
78	C₂²⋊C₈×C₆₇	—	2	2	no	—
79	C₂²⋊C₈×C₆₇	—	2	2	no	—
80	C₄×C₈×C₆₇	C₂³	1	1	yes	characteristic
81	C₄×C₈×C₆₇	C₂³	1	2	yes	—
82	C₂⁴×C₆₇	—	4	1	no	—
83	C₂⁴×C₆₇	—	4	2	no	—
84	C₂×Q₈×C₆₇	—	2	1	no	—
85	C₂×D₄×C₆₇	—	2	2	no	—
86	C₂×D₄×C₆₇	—	2	2	no	—
87	C₂×D₄×C₆₇	—	2	2	no	—
88	C₂×D₄×C₆₇	—	2	2	no	—
89	C₂×D₄×C₆₇	—	2	1	no	—
90	C₂×D₄×C₆₇	—	4	2	no	—
91	C₂×D₄×C₆₇	—	4	2	no	—
92	C₂×D₄×C₆₇	—	4	2	no	—
93	C₂×D₄×C₆₇	—	4	4	no	—
94	C₂×D₄×C₆₇	—	4	4	no	—
95	C₂×D₄×C₆₇	—	4	4	no	—
96	C₂×D₄×C₆₇	—	4	1	no	—
97	C₂×D₄×C₆₇	—	8	2	no	—
98	C₂×D₄×C₆₇	—	8	2	no	—
99	C₂×D₄×C₆₇	—	8	2	no	—
100	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₆₇	C₂×D₄	1	2	yes	—
102	C₂²×C₄×C₆₇	—	2	2	no	—
103	C₂²×C₄×C₆₇	—	2	2	no	—
104	SD₁₆×C₆₇	—	8	2	no	—
105	D₈×C₆₇	—	2	4	no	—
106	D₈×C₆₇	—	4	4	no	—
107	D₈×C₆₇	—	4	4	no	—
108	D₈×C₆₇	—	4	4	no	—
109	D₈×C₆₇	—	8	2	no	—
110	D₈×C₆₇	—	8	2	no	—
111	D₈×C₆₇	—	8	2	no	—
112	M₁₆×C₆₇	—	8	2	no	—
113	C₂×C₈×C₆₇	—	2	1	no	—
114	C₂×C₈×C₆₇	—	2	2	no	—
115	C₂×C₈×C₆₇	—	2	2	no	—
116	C₂×C₈×C₆₇	—	4	4	no	—
117	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
118	C₂×C₈×C₆₇	C₂×D₄	1	2	yes	—
119	C₄⋊C₄×C₆₇	—	2	2	no	—
120	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
121	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
122	C₂²⋊C₄×C₆₇	—	2	2	no	—
123	C₂²⋊C₄×C₆₇	—	2	2	no	—
124	C₂²⋊C₄×C₆₇	—	4	2	no	—
125	C₂²⋊C₄×C₆₇	—	4	1	no	—
126	C₂²⋊C₄×C₆₇	—	4	2	no	—
127	C₄²×C₆₇	—	4	1	no	—
128	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
129	C₂³×C₆₇	—	2	2	no	—
130	C₂³×C₆₇	—	2	2	no	—
131	C₂³×C₆₇	—	4	2	no	—
132	C₂³×C₆₇	—	4	1	no	—
133	C₂³×C₆₇	—	8	4	no	—
134	C₂³×C₆₇	—	8	4	no	—
135	C₂³×C₆₇	—	8	4	no	—
136	C₂³×C₆₇	—	16	1	no	—
137	C₂³×C₆₇	—	16	2	no	—
138	Q₈×C₆₇	—	8	1	no	—
139	D₄×C₆₇	—	2	2	no	—
140	D₄×C₆₇	—	2	2	no	—
141	D₄×C₆₇	—	2	2	no	—
142	D₄×C₆₇	—	4	2	no	—
143	D₄×C₆₇	—	4	2	no	—
144	D₄×C₆₇	—	4	2	no	—
145	D₄×C₆₇	—	4	2	no	—
146	D₄×C₆₇	—	4	2	no	—
147	D₄×C₆₇	—	4	2	no	—
148	D₄×C₆₇	—	8	2	no	—
149	D₄×C₆₇	—	8	1	no	—
150	D₄×C₆₇	—	8	4	no	—
151	D₄×C₆₇	—	8	4	no	—
152	D₄×C₆₇	—	8	4	no	—
153	D₄×C₆₇	—	16	1	no	—
154	D₄×C₆₇	AGL(1,ℤ/8)	1	4	yes	—
155	C₂×C₄×C₆₇	—	2	2	no	—
156	C₂×C₄×C₆₇	—	2	2	no	—
157	C₂×C₄×C₆₇	—	4	2	no	—
158	C₂×C₄×C₆₇	—	4	2	no	—
159	C₂×C₄×C₆₇	—	4	2	no	—
160	C₂×C₄×C₆₇	—	4	2	no	—
161	C₂×C₄×C₆₇	—	4	1	no	—
162	C₂×C₄×C₆₇	C₂²×D₄	1	2	yes	—
163	C₂×C₄×C₆₇	H(5,𝔽₂)	1	1	yes	characteristic
164	C₈×C₆₇	—	2	2	no	—
165	C₈×C₆₇	—	2	2	no	—
166	C₈×C₆₇	—	2	2	no	—
167	C₈×C₆₇	—	4	2	no	—
168	C₈×C₆₇	—	4	2	no	—
169	C₂²×C₆₇	—	2	4	no	—
170	C₂²×C₆₇	—	4	2	no	—
171	C₂²×C₆₇	—	4	2	no	—
172	C₂²×C₆₇	—	4	2	no	—
173	C₂²×C₆₇	—	4	2	no	—
174	C₂²×C₆₇	—	4	2	no	—
175	C₂²×C₆₇	—	8	2	no	—
176	C₂²×C₆₇	—	8	2	no	—
177	C₂²×C₆₇	—	8	2	no	—
178	C₂²×C₆₇	—	8	2	no	—
179	C₂²×C₆₇	—	8	1	no	—
180	C₂²×C₆₇	—	16	4	no	—
181	C₂²×C₆₇	—	16	8	no	—
182	C₂²×C₆₇	D₄²	1	1	yes	characteristic
183	C₄×C₆₇	—	2	1	no	—
184	C₄×C₆₇	—	4	2	no	—
185	C₄×C₆₇	—	4	2	no	—
186	C₄×C₆₇	—	8	1	no	—
187	C₄×C₆₇	C₂×AGL(1,ℤ/8)	1	2	yes	—
188	C₄×C₆₇	#576	1	2	yes	—
189	#20053	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₆₇	—	4	4	no	—
191	C₂×C₆₇	—	8	2	no	—
192	C₂×C₆₇	—	16	1	no	—
193	C₂×C₆₇	—	16	2	no	—
194	C₂×C₆₇	#3264	1	2	yes	—
195	C₂×C₆₇	#3292	1	1	yes	characteristic
196	#3325	C₂×C₆₇	1	2	yes	complemented
197	D₄×D₈	C₂×C₆₇	1	2	yes	complemented
198	#1721	C₂×C₆₇	1	1	yes	characteristic, complemented
199	#1687	C₂×C₆₇	1	2	yes	complemented
200	#1677	C₂×C₆₇	1	2	yes	complemented
201	#1629	C₂×C₆₇	1	1	yes	characteristic, complemented
202	#1624	C₂×C₆₇	1	1	yes	characteristic, complemented
203	#1619	C₂×C₆₇	1	2	yes	complemented
204	#1586	C₂×C₆₇	1	2	yes	complemented
205	C₆₇	#20053	1	1	yes	characteristic, direct product factor, Sylow
206	C₂²×D₈	—	2	2	no	—
207	#555	C₂²×C₆₇	1	1	yes	characteristic, complemented
208	D₄²	C₂²×C₆₇	1	1	yes	characteristic
209	D₄²	C₂²×C₆₇	1	2	yes	complemented
210	#493	C₂²×C₆₇	1	2	yes	complemented
211	#493	C₂²×C₆₇	1	1	yes	characteristic, complemented
212	#492	C₂²×C₆₇	1	1	yes	characteristic, complemented
213	#486	C₂²×C₆₇	1	2	yes	complemented
214	#482	—	2	2	no	—
215	#476	C₂²×C₆₇	1	2	yes	complemented
216	#469	—	2	2	no	—
217	#466	—	2	2	no	—
218	#459	C₂²×C₆₇	1	2	yes	—
219	#459	C₂²×C₆₇	1	2	yes	complemented
220	#459	C₂²×C₆₇	1	2	yes	complemented
221	#447	—	2	2	no	—
222	#447	—	2	2	no	—
223	#447	—	2	2	no	—
224	C₄×D₈	C₂²×C₆₇	1	2	yes	—
225	#436	C₂²×C₆₇	1	2	yes	complemented
226	C₈×D₄	C₂²×C₆₇	1	2	yes	complemented
227	#418	—	2	2	no	—
228	#334	C₂²×C₆₇	1	2	yes	complemented
229	#333	C₂²×C₆₇	1	1	yes	characteristic, complemented
230	#331	C₂²×C₆₇	1	2	yes	complemented
231	#331	C₂²×C₆₇	1	1	yes	characteristic, complemented
232	D₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
233	D₄⋊C₈	C₂²×C₆₇	1	2	yes	complemented
234	#322	C₂²×C₆₇	1	1	yes	characteristic, complemented
235	C₂²×D₄	—	2	2	no	—
236	C₂²×D₄	—	2	2	no	—
237	C₂²×D₄	—	2	2	no	—
238	C₂×SD₁₆	—	4	1	no	—
239	C₂×D₈	—	2	2	no	—
240	C₂×D₈	—	2	2	no	—
241	C₂×D₈	—	2	2	no	—
242	C₂×D₈	—	2	2	no	—
243	C₂×D₈	—	2	2	no	—
244	C₂×D₈	—	4	1	no	—
245	C₂×D₈	—	4	8	no	—
246	C₂×D₈	D₄×C₆₇	1	2	yes	—
247	C₂×M₁₆	—	2	2	no	—
248	C₂²×C₈	—	2	2	no	—
249	C₄⋊Q₈	C₂³×C₆₇	1	1	yes	characteristic
250	#127	C₂³×C₆₇	1	1	yes	characteristic
251	#127	C₂³×C₆₇	1	2	yes	—
252	#124	—	4	1	no	—
253	#121	—	2	2	no	—
254	#121	—	2	2	no	—
255	#121	—	2	2	no	—
256	#121	—	2	2	no	—
257	#120	—	4	1	no	—
258	#120	—	4	2	no	—
259	C₄×D₄	C₂³×C₆₇	1	2	yes	—
260	C₄×D₄	C₂³×C₆₇	1	2	yes	—
261	#117	—	2	2	no	—
262	#107	D₄×C₆₇	1	2	yes	—
263	#106	—	2	2	no	—
264	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
265	C₄⋊C₈	C₂³×C₆₇	1	2	yes	—
266	#102	—	2	2	no	—
267	#102	—	2	2	no	—
268	#102	—	2	2	no	—
269	#102	—	2	2	no	—
270	#102	—	2	2	no	—
271	#102	—	2	2	no	—
272	#102	D₄×C₆₇	1	2	yes	—
273	#102	D₄×C₆₇	1	2	yes	—
274	C₂²⋊C₈	—	2	2	no	—
275	C₂²⋊C₈	—	2	2	no	—
276	C₄×C₈	C₂³×C₆₇	1	1	yes	characteristic
277	C₄×C₈	C₂³×C₆₇	1	2	yes	—
278	C₂⁴	—	4	1	no	—
279	C₂⁴	—	4	2	no	—
280	C₂×Q₈	—	2	1	no	—
281	C₂×D₄	—	2	2	no	—
282	C₂×D₄	—	2	2	no	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	1	no	—
286	C₂×D₄	—	4	2	no	—
287	C₂×D₄	—	4	2	no	—
288	C₂×D₄	—	4	2	no	—
289	C₂×D₄	—	4	4	no	—
290	C₂×D₄	—	4	4	no	—
291	C₂×D₄	—	4	4	no	—
292	C₂×D₄	—	4	1	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂×D₄	—	8	2	no	—
295	C₂×D₄	—	8	2	no	—
296	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
297	C₂×D₄	C₂×D₄×C₆₇	1	2	yes	—
298	C₂²×C₄	—	2	2	no	—
299	C₂²×C₄	—	2	2	no	—
300	SD₁₆	—	8	2	no	—
301	D₈	—	2	4	no	—
302	D₈	—	4	4	no	—
303	D₈	—	4	4	no	—
304	D₈	—	4	4	no	—
305	D₈	—	8	2	no	—
306	D₈	—	8	2	no	—
307	D₈	—	8	2	no	—
308	M₁₆	—	8	2	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
314	C₂×C₈	C₂×D₄×C₆₇	1	2	yes	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
317	C₄⋊C₄	C₂×D₄×C₆₇	1	2	yes	—
318	C₂²⋊C₄	—	2	2	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	4	2	no	—
321	C₂²⋊C₄	—	4	1	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₄²	—	4	1	no	—
324	C₄²	C₂⁴×C₆₇	1	1	yes	characteristic
325	C₂³	—	2	2	no	—
326	C₂³	—	2	2	no	—
327	C₂³	—	4	2	no	—
328	C₂³	—	4	1	no	—
329	C₂³	—	8	4	no	—
330	C₂³	—	8	4	no	—
331	C₂³	—	8	4	no	—
332	C₂³	—	16	1	no	—
333	C₂³	—	16	2	no	—
334	Q₈	—	8	1	no	—
335	D₄	—	2	2	no	—
336	D₄	—	2	2	no	—
337	D₄	—	2	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	4	2	no	—
342	D₄	—	4	2	no	—
343	D₄	—	4	2	no	—
344	D₄	—	8	2	no	—
345	D₄	—	8	1	no	—
346	D₄	—	8	4	no	—
347	D₄	—	8	4	no	—
348	D₄	—	8	4	no	—
349	D₄	—	16	1	no	—
350	D₄	AGL(1,ℤ/8)×C₆₇	1	4	yes	—
351	C₂×C₄	—	2	2	no	—
352	C₂×C₄	—	2	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	4	2	no	—
355	C₂×C₄	—	4	2	no	—
356	C₂×C₄	—	4	2	no	—
357	C₂×C₄	—	4	1	no	—
358	C₂×C₄	C₂²×D₄×C₆₇	1	2	yes	—
359	C₂×C₄	H(5,𝔽₂)×C₆₇	1	1	yes	characteristic
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	2	2	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	2	no	—
365	C₂²	—	2	4	no	—
366	C₂²	—	4	2	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	2	no	—
371	C₂²	—	8	2	no	—
372	C₂²	—	8	1	no	—
373	C₂²	—	8	2	no	—
374	C₂²	—	8	2	no	—
375	C₂²	—	8	2	no	—
376	C₂²	—	16	4	no	—
377	C₂²	—	16	8	no	—
378	C₂²	D₄²×C₆₇	1	1	yes	characteristic
379	C₄	—	2	1	no	—
380	C₄	—	4	2	no	—
381	C₄	—	4	2	no	—
382	C₄	—	8	1	no	—
383	C₄	C₂×AGL(1,ℤ/8)×C₆₇	1	2	yes	—
384	C₄	#576×C₆₇	1	2	yes	—
385	C₂	—	4	4	no	—
386	C₂	—	8	2	no	—
387	C₂	—	16	1	no	—
388	C₂	—	16	2	no	—
389	C₂	C₆₇×#3264	1	2	yes	—
390	C₂	C₆₇×#3292	1	1	yes	characteristic

	subgroup	G/H
center, socle	C₂²×C₆₇	D₄²
commutator, Frattini, cosocle	C₄²	C₂⁴×C₆₇
LCS	G ▷ C₄² ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₆₇ ◁ C₄²×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₆₇×#3325	C₂	semidirect
2. D₄×D₈×C₆₇	C₂	semidirect
3. C₆₇×#1721	C₂	semidirect
4. C₆₇×#1687	C₂	semidirect
5. C₆₇×#1677	C₂	semidirect
6. C₆₇×#1629	C₂	semidirect
7. C₆₇×#1624	C₂	semidirect
8. C₆₇×#1619	C₂	semidirect
9. C₆₇×#1586	C₂	semidirect
11. #555×C₆₇	C₂²	semidirect
13. D₄²×C₆₇	C₂²	semidirect
14. #493×C₆₇	C₂²	semidirect
15. #493×C₆₇	C₂²	semidirect
16. #492×C₆₇	C₂²	semidirect
17. #486×C₆₇	C₂²	semidirect
19. #476×C₆₇	C₂²	semidirect
23. #459×C₆₇	C₂²	semidirect
24. #459×C₆₇	C₂²	semidirect
29. #436×C₆₇	C₂²	semidirect
30. C₈×D₄×C₆₇	C₂²	semidirect
32. #334×C₆₇	C₂²	semidirect
33. #333×C₆₇	C₂²	semidirect
34. #331×C₆₇	C₂²	semidirect
35. #331×C₆₇	C₂²	semidirect
36. D₄⋊C₈×C₆₇	C₂²	semidirect
37. D₄⋊C₈×C₆₇	C₂²	semidirect
38. #322×C₆₇	C₂²	semidirect
189. #20053	C₆₇	direct (N × H)
196. #3325	C₂×C₆₇	semidirect
197. D₄×D₈	C₂×C₆₇	semidirect
198. #1721	C₂×C₆₇	semidirect
199. #1687	C₂×C₆₇	semidirect
200. #1677	C₂×C₆₇	semidirect
201. #1629	C₂×C₆₇	semidirect
202. #1624	C₂×C₆₇	semidirect
203. #1619	C₂×C₆₇	semidirect
204. #1586	C₂×C₆₇	semidirect
205. C₆₇	#20053	direct (N × H)
207. #555	C₂²×C₆₇	semidirect
209. D₄²	C₂²×C₆₇	semidirect
210. #493	C₂²×C₆₇	semidirect
211. #493	C₂²×C₆₇	semidirect
212. #492	C₂²×C₆₇	semidirect
213. #486	C₂²×C₆₇	semidirect
215. #476	C₂²×C₆₇	semidirect
219. #459	C₂²×C₆₇	semidirect
220. #459	C₂²×C₆₇	semidirect
225. #436	C₂²×C₆₇	semidirect
226. C₈×D₄	C₂²×C₆₇	semidirect
228. #334	C₂²×C₆₇	semidirect
229. #333	C₂²×C₆₇	semidirect
230. #331	C₂²×C₆₇	semidirect
231. #331	C₂²×C₆₇	semidirect
232. D₄⋊C₈	C₂²×C₆₇	semidirect
233. D₄⋊C₈	C₂²×C₆₇	semidirect
234. #322	C₂²×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₆₇×#3325	2
D₄×D₈×C₆₇	2
C₆₇×#1721	2
C₆₇×#1687	2
C₆₇×#1677	2
C₆₇×#1629	2
C₆₇×#1624	2
C₆₇×#1619	2
C₆₇×#1586	2
#20053	67

Subgroups — C67×#20053 #30699304

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#20053 #30699304