Subgroups — C₆₇×#11108 #30690359

Order 17152.

866 conjugacy classes of subgroups.

The subgroup lattice has 400 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂²×#108×C₆₇	C₂	1	1	yes	maximal, characteristic, complemented
2	C₂×#421×C₆₇	C₂	1	2	yes	maximal
3	C₂×#408×C₆₇	C₂	1	1	yes	maximal, characteristic
4	C₂×#344×C₆₇	C₂	1	2	yes	maximal, complemented
5	C₆₇×#1735	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂²×#41×C₆₇	C₂²	1	1	yes	characteristic
7	C₂²×M₁₆×C₆₇	C₂²	1	1	yes	characteristic
8	C₂²×M₁₆×C₆₇	C₂²	1	2	yes	—
9	C₂³×C₈×C₆₇	C₂²	1	1	yes	characteristic
10	C₂×#117×C₆₇	C₂²	1	2	yes	—
11	C₂×#108×C₆₇	—	2	4	no	—
12	C₂×#108×C₆₇	—	2	2	no	—
13	#421×C₆₇	—	2	4	no	—
14	#421×C₆₇	—	2	4	no	—
15	C₂×#104×C₆₇	—	2	4	no	—
16	#408×C₆₇	—	2	2	no	—
17	#408×C₆₇	C₄	1	4	yes	complemented
18	C₂×C₂²⋊C₈×C₆₇	—	2	2	no	—
19	#344×C₆₇	—	2	4	no	—
20	#340×C₆₇	—	2	2	no	—
21	C₂×#41×C₆₇	—	2	1	no	—
22	C₂×#41×C₆₇	—	2	1	no	—
23	C₂×#41×C₆₇	—	2	2	no	—
24	C₂×#41×C₆₇	—	2	2	no	—
25	C₂×#41×C₆₇	—	2	2	no	—
26	C₂×#41×C₆₇	—	2	2	no	—
27	C₂×#41×C₆₇	C₂×C₄	1	2	yes	—
28	C₂×#41×C₆₇	D₄	1	2	yes	—
29	C₂²×Q₈×C₆₇	Q₈	1	1	yes	characteristic
30	C₂²×D₄×C₆₇	—	2	1	no	—
31	C₂²×D₄×C₆₇	Q₈	1	1	yes	characteristic
32	C₂³×C₄×C₆₇	—	2	1	no	—
33	C₂³×C₄×C₆₇	C₂³	1	1	yes	characteristic
34	C₂×M₁₆×C₆₇	—	2	2	no	—
35	C₂×M₁₆×C₆₇	—	2	1	no	—
36	C₂×M₁₆×C₆₇	—	2	2	no	—
37	C₂×M₁₆×C₆₇	—	2	2	no	—
38	C₂×M₁₆×C₆₇	—	2	2	no	—
39	C₂×M₁₆×C₆₇	—	2	2	no	—
40	C₂×M₁₆×C₆₇	—	2	2	no	—
41	C₂×M₁₆×C₆₇	—	2	2	no	—
42	C₂×M₁₆×C₆₇	C₂×C₄	1	2	yes	—
43	C₂×M₁₆×C₆₇	D₄	1	4	yes	—
44	C₂²×C₈×C₆₇	—	2	2	no	—
45	C₂²×C₈×C₆₇	—	2	2	no	—
46	C₂²×C₈×C₆₇	—	2	1	no	—
47	C₂²×C₈×C₆₇	—	2	2	no	—
48	C₂²×C₈×C₆₇	C₂×C₄	1	2	yes	—
49	C₂²×C₈×C₆₇	D₄	1	2	yes	—
50	C₂²×C₈×C₆₇	D₄	1	2	yes	—
51	#117×C₆₇	—	2	2	no	—
52	#117×C₆₇	—	2	2	no	—
53	#117×C₆₇	—	2	2	no	—
54	#117×C₆₇	D₄	1	4	yes	—
55	C₂×C₄⋊C₄×C₆₇	—	2	2	no	—
56	C₂×C₂²⋊C₄×C₆₇	—	2	2	no	—
57	C₂×C₄²×C₆₇	—	2	2	no	—
58	#108×C₆₇	—	2	8	no	—
59	#104×C₆₇	—	2	16	no	—
60	C₂²⋊C₈×C₆₇	—	2	8	no	—
61	C₂⁴×C₆₇	—	2	1	no	—
62	C₂⁴×C₆₇	#41	1	1	yes	characteristic
63	#41×C₆₇	—	2	4	no	—
64	#41×C₆₇	—	2	4	no	—
65	#41×C₆₇	—	2	4	no	—
66	#41×C₆₇	—	2	4	no	—
67	#41×C₆₇	—	4	2	no	—
68	#41×C₆₇	—	4	2	no	—
69	#41×C₆₇	—	4	2	no	—
70	#41×C₆₇	—	4	2	no	—
71	C₂×Q₈×C₆₇	—	2	1	no	—
72	C₂×Q₈×C₆₇	—	2	2	no	—
73	C₂×Q₈×C₆₇	—	2	2	no	—
74	C₂×Q₈×C₆₇	C₄⋊C₄	1	2	yes	—
75	C₂×D₄×C₆₇	—	2	2	no	—
76	C₂×D₄×C₆₇	—	2	2	no	—
77	C₂×D₄×C₆₇	—	2	2	no	—
78	C₂×D₄×C₆₇	—	2	2	no	—
79	C₂×D₄×C₆₇	—	2	1	no	—
80	C₂×D₄×C₆₇	—	4	2	no	—
81	C₂×D₄×C₆₇	—	4	2	no	—
82	C₂×D₄×C₆₇	C₄⋊C₄	1	2	yes	—
83	C₂²×C₄×C₆₇	—	2	1	no	—
84	C₂²×C₄×C₆₇	—	2	2	no	—
85	C₂²×C₄×C₆₇	—	2	2	no	—
86	C₂²×C₄×C₆₇	—	4	1	no	—
87	C₂²×C₄×C₆₇	—	4	1	no	—
88	C₂²×C₄×C₆₇	—	4	1	no	—
89	C₂²×C₄×C₆₇	—	4	1	no	—
90	C₂²×C₄×C₆₇	—	4	2	no	—
91	C₂²×C₄×C₆₇	C₂²×C₄	1	1	yes	characteristic
92	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
93	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
94	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
95	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
96	C₂²×C₄×C₆₇	C₂×D₄	1	2	yes	—
97	C₂²×C₄×C₆₇	C₂×Q₈	1	1	yes	characteristic
98	C₂²×C₄×C₆₇	#41	1	2	yes	—
99	C₂²×C₄×C₆₇	#41	1	2	yes	—
100	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
101	M₁₆×C₆₇	—	2	4	no	—
102	M₁₆×C₆₇	—	2	4	no	—
103	M₁₆×C₆₇	—	2	4	no	—
104	M₁₆×C₆₇	—	4	2	no	—
105	M₁₆×C₆₇	—	4	2	no	—
106	M₁₆×C₆₇	—	4	2	no	—
107	C₂×C₈×C₆₇	—	2	4	no	—
108	C₂×C₈×C₆₇	—	2	2	no	—
109	C₂×C₈×C₆₇	—	2	4	no	—
110	C₂×C₈×C₆₇	—	2	2	no	—
111	C₂×C₈×C₆₇	—	2	2	no	—
112	C₂×C₈×C₆₇	—	2	4	no	—
113	C₂×C₈×C₆₇	—	4	2	no	—
114	C₂×C₈×C₆₇	—	4	2	no	—
115	C₂×C₈×C₆₇	—	4	1	no	—
116	C₂×C₈×C₆₇	—	4	1	no	—
117	C₂×C₈×C₆₇	C₂²⋊C₄	1	4	yes	—
118	C₄⋊C₄×C₆₇	—	2	4	no	—
119	C₄⋊C₄×C₆₇	—	4	2	no	—
120	C₂²⋊C₄×C₆₇	—	2	4	no	—
121	C₂²⋊C₄×C₆₇	—	4	2	no	—
122	C₄²×C₆₇	—	2	4	no	—
123	C₄²×C₆₇	—	4	2	no	—
124	C₂³×C₆₇	—	2	2	no	—
125	C₂³×C₆₇	—	4	2	no	—
126	C₂³×C₆₇	—	4	4	no	—
127	C₂³×C₆₇	—	4	1	no	—
128	C₂³×C₆₇	—	4	1	no	—
129	C₂³×C₆₇	#117	1	1	yes	characteristic
130	C₂³×C₆₇	#121	1	1	yes	characteristic
131	C₂³×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
132	C₂³×C₆₇	#123	1	2	yes	—
133	C₂³×C₆₇	#124	1	2	yes	—
134	Q₈×C₆₇	—	2	4	no	—
135	Q₈×C₆₇	—	4	2	no	—
136	D₄×C₆₇	—	2	4	no	—
137	D₄×C₆₇	—	4	4	no	—
138	D₄×C₆₇	—	4	4	no	—
139	D₄×C₆₇	—	4	2	no	—
140	C₂×C₄×C₆₇	—	2	2	no	—
141	C₂×C₄×C₆₇	—	4	1	no	—
142	C₂×C₄×C₆₇	—	4	1	no	—
143	C₂×C₄×C₆₇	—	4	2	no	—
144	C₂×C₄×C₆₇	—	4	2	no	—
145	C₂×C₄×C₆₇	—	4	2	no	—
146	C₂×C₄×C₆₇	—	4	2	no	—
147	C₂×C₄×C₆₇	—	4	4	no	—
148	C₂×C₄×C₆₇	—	8	4	no	—
149	C₂×C₄×C₆₇	C₂×C₂²⋊C₄	1	1	yes	characteristic
150	C₂×C₄×C₆₇	C₂×C₄⋊C₄	1	1	yes	characteristic
151	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
152	C₂×C₄×C₆₇	C₄×D₄	1	2	yes	—
153	C₂×C₄×C₆₇	#120	1	2	yes	—
154	C₂×C₄×C₆₇	#120	1	1	yes	characteristic
155	C₂×C₄×C₆₇	#121	1	2	yes	—
156	C₂×C₄×C₆₇	#121	1	2	yes	—
157	C₂×C₄×C₆₇	#121	1	2	yes	—
158	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
160	C₂×C₄×C₆₇	C₂²⋊Q₈	1	2	yes	—
161	C₂×C₄×C₆₇	C₂²⋊Q₈	1	1	yes	characteristic
162	C₂×C₄×C₆₇	#123	1	2	yes	—
163	C₂×C₄×C₆₇	#123	1	1	yes	characteristic
164	C₂×C₄×C₆₇	#124	1	1	yes	characteristic
165	C₂×C₄×C₆₇	#126	1	2	yes	—
166	C₂×C₄×C₆₇	#127	1	1	yes	characteristic
167	C₈×C₆₇	—	2	4	no	—
168	C₈×C₆₇	—	4	2	no	—
169	C₈×C₆₇	—	4	4	no	—
170	C₂²×C₆₇	—	2	2	no	—
171	C₂²×C₆₇	—	2	2	no	—
172	C₂²×C₆₇	—	2	2	no	—
173	C₂²×C₆₇	—	4	2	no	—
174	C₂²×C₆₇	—	4	2	no	—
175	C₂²×C₆₇	—	4	4	no	—
176	C₂²×C₆₇	—	4	2	no	—
177	C₂²×C₆₇	—	8	2	no	—
178	C₂²×C₆₇	—	8	2	no	—
179	C₂²×C₆₇	#380	1	1	yes	characteristic
180	C₂²×C₆₇	#388	1	2	yes	—
181	C₂²×C₆₇	#393	1	1	yes	characteristic
182	C₂²×C₆₇	#394	1	2	yes	—
183	C₂²×C₆₇	#399	1	1	yes	characteristic
184	C₄×C₆₇	—	4	2	no	—
185	C₄×C₆₇	—	8	4	no	—
186	C₄×C₆₇	#385	1	2	yes	—
187	C₄×C₆₇	#386	1	1	yes	characteristic
188	C₄×C₆₇	#390	1	1	yes	characteristic
189	C₄×C₆₇	#392	1	1	yes	characteristic
190	C₄×C₆₇	#396	1	2	yes	—
191	C₄×C₆₇	#397	1	1	yes	characteristic
192	#11108	C₆₇	1	1	yes	maximal, characteristic, direct product factor, Sylow
193	C₂×C₆₇	—	2	2	no	—
194	C₂×C₆₇	—	2	1	no	—
195	C₂×C₆₇	—	2	1	no	—
196	C₂×C₆₇	—	2	2	no	—
197	C₂×C₆₇	—	8	2	no	—
198	C₂×C₆₇	#1439	1	1	yes	characteristic
199	C₂×C₆₇	#1814	1	2	yes	—
200	C₂²×#108	C₂×C₆₇	1	1	yes	characteristic, complemented
201	C₂×#421	C₂×C₆₇	1	2	yes	—
202	C₂×#408	C₂×C₆₇	1	1	yes	characteristic
203	C₂×#344	C₂×C₆₇	1	2	yes	complemented
204	#1735	C₂×C₆₇	1	1	yes	characteristic, complemented
205	C₆₇	#11108	1	1	yes	characteristic, direct product factor, Sylow
206	C₂²×#41	C₂²×C₆₇	1	1	yes	characteristic
207	C₂²×M₁₆	C₂²×C₆₇	1	1	yes	characteristic
208	C₂²×M₁₆	C₂²×C₆₇	1	2	yes	—
209	C₂³×C₈	C₂²×C₆₇	1	1	yes	characteristic
210	C₂×#117	C₂²×C₆₇	1	2	yes	—
211	C₂×#108	—	2	4	no	—
212	C₂×#108	—	2	2	no	—
213	#421	—	2	4	no	—
214	#421	—	2	4	no	—
215	C₂×#104	—	2	4	no	—
216	#408	—	2	2	no	—
217	#408	C₄×C₆₇	1	4	yes	complemented
218	C₂×C₂²⋊C₈	—	2	2	no	—
219	#344	—	2	4	no	—
220	#340	—	2	2	no	—
221	C₂×#41	—	2	1	no	—
222	C₂×#41	—	2	1	no	—
223	C₂×#41	—	2	2	no	—
224	C₂×#41	—	2	2	no	—
225	C₂×#41	—	2	2	no	—
226	C₂×#41	—	2	2	no	—
227	C₂×#41	C₂×C₄×C₆₇	1	2	yes	—
228	C₂×#41	D₄×C₆₇	1	2	yes	—
229	C₂²×Q₈	Q₈×C₆₇	1	1	yes	characteristic
230	C₂²×D₄	—	2	1	no	—
231	C₂²×D₄	Q₈×C₆₇	1	1	yes	characteristic
232	C₂³×C₄	—	2	1	no	—
233	C₂³×C₄	C₂³×C₆₇	1	1	yes	characteristic
234	C₂×M₁₆	—	2	2	no	—
235	C₂×M₁₆	—	2	1	no	—
236	C₂×M₁₆	—	2	2	no	—
237	C₂×M₁₆	—	2	2	no	—
238	C₂×M₁₆	—	2	2	no	—
239	C₂×M₁₆	—	2	2	no	—
240	C₂×M₁₆	—	2	2	no	—
241	C₂×M₁₆	—	2	2	no	—
242	C₂×M₁₆	C₂×C₄×C₆₇	1	2	yes	—
243	C₂×M₁₆	D₄×C₆₇	1	4	yes	—
244	C₂²×C₈	—	2	2	no	—
245	C₂²×C₈	—	2	2	no	—
246	C₂²×C₈	—	2	1	no	—
247	C₂²×C₈	—	2	2	no	—
248	C₂²×C₈	C₂×C₄×C₆₇	1	2	yes	—
249	C₂²×C₈	D₄×C₆₇	1	2	yes	—
250	C₂²×C₈	D₄×C₆₇	1	2	yes	—
251	#117	—	2	2	no	—
252	#117	—	2	2	no	—
253	#117	—	2	2	no	—
254	#117	D₄×C₆₇	1	4	yes	—
255	C₂×C₄⋊C₄	—	2	2	no	—
256	C₂×C₂²⋊C₄	—	2	2	no	—
257	C₂×C₄²	—	2	2	no	—
258	#108	—	2	8	no	—
259	#104	—	2	16	no	—
260	C₂²⋊C₈	—	2	8	no	—
261	C₂⁴	—	2	1	no	—
262	C₂⁴	#41×C₆₇	1	1	yes	characteristic
263	#41	—	2	4	no	—
264	#41	—	2	4	no	—
265	#41	—	2	4	no	—
266	#41	—	2	4	no	—
267	#41	—	4	2	no	—
268	#41	—	4	2	no	—
269	#41	—	4	2	no	—
270	#41	—	4	2	no	—
271	C₂×Q₈	—	2	1	no	—
272	C₂×Q₈	—	2	2	no	—
273	C₂×Q₈	—	2	2	no	—
274	C₂×Q₈	C₄⋊C₄×C₆₇	1	2	yes	—
275	C₂×D₄	—	2	2	no	—
276	C₂×D₄	—	2	2	no	—
277	C₂×D₄	—	2	2	no	—
278	C₂×D₄	—	2	2	no	—
279	C₂×D₄	—	2	1	no	—
280	C₂×D₄	—	4	2	no	—
281	C₂×D₄	—	4	2	no	—
282	C₂×D₄	C₄⋊C₄×C₆₇	1	2	yes	—
283	C₂²×C₄	—	2	1	no	—
284	C₂²×C₄	—	2	2	no	—
285	C₂²×C₄	—	2	2	no	—
286	C₂²×C₄	—	4	1	no	—
287	C₂²×C₄	—	4	1	no	—
288	C₂²×C₄	—	4	1	no	—
289	C₂²×C₄	—	4	1	no	—
290	C₂²×C₄	—	4	2	no	—
291	C₂²×C₄	C₂²×C₄×C₆₇	1	1	yes	characteristic
292	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
293	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
294	C₂²×C₄	C₂×D₄×C₆₇	1	1	yes	characteristic
295	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
296	C₂²×C₄	C₂×D₄×C₆₇	1	2	yes	—
297	C₂²×C₄	C₂×Q₈×C₆₇	1	1	yes	characteristic
298	C₂²×C₄	#41×C₆₇	1	2	yes	—
299	C₂²×C₄	#41×C₆₇	1	2	yes	—
300	C₂²×C₄	#41×C₆₇	1	1	yes	characteristic
301	M₁₆	—	2	4	no	—
302	M₁₆	—	2	4	no	—
303	M₁₆	—	2	4	no	—
304	M₁₆	—	4	2	no	—
305	M₁₆	—	4	2	no	—
306	M₁₆	—	4	2	no	—
307	C₂×C₈	—	2	4	no	—
308	C₂×C₈	—	2	2	no	—
309	C₂×C₈	—	2	4	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	2	4	no	—
313	C₂×C₈	—	4	2	no	—
314	C₂×C₈	—	4	2	no	—
315	C₂×C₈	—	4	1	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	C₂²⋊C₄×C₆₇	1	4	yes	—
318	C₄⋊C₄	—	2	4	no	—
319	C₄⋊C₄	—	4	2	no	—
320	C₂²⋊C₄	—	2	4	no	—
321	C₂²⋊C₄	—	4	2	no	—
322	C₄²	—	2	4	no	—
323	C₄²	—	4	2	no	—
324	C₂³	—	2	2	no	—
325	C₂³	—	4	2	no	—
326	C₂³	—	4	4	no	—
327	C₂³	—	4	1	no	—
328	C₂³	—	4	1	no	—
329	C₂³	#117×C₆₇	1	1	yes	characteristic
330	C₂³	#121×C₆₇	1	1	yes	characteristic
331	C₂³	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
332	C₂³	#123×C₆₇	1	2	yes	—
333	C₂³	#124×C₆₇	1	2	yes	—
334	Q₈	—	2	4	no	—
335	Q₈	—	4	2	no	—
336	D₄	—	2	4	no	—
337	D₄	—	4	4	no	—
338	D₄	—	4	4	no	—
339	D₄	—	4	2	no	—
340	C₂×C₄	—	2	2	no	—
341	C₂×C₄	—	4	1	no	—
342	C₂×C₄	—	4	1	no	—
343	C₂×C₄	—	4	2	no	—
344	C₂×C₄	—	4	2	no	—
345	C₂×C₄	—	4	2	no	—
346	C₂×C₄	—	4	2	no	—
347	C₂×C₄	—	4	4	no	—
348	C₂×C₄	—	8	4	no	—
349	C₂×C₄	C₂×C₂²⋊C₄×C₆₇	1	1	yes	characteristic
350	C₂×C₄	C₂×C₄⋊C₄×C₆₇	1	1	yes	characteristic
351	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
352	C₂×C₄	C₄×D₄×C₆₇	1	2	yes	—
353	C₂×C₄	#120×C₆₇	1	2	yes	—
354	C₂×C₄	#120×C₆₇	1	1	yes	characteristic
355	C₂×C₄	#121×C₆₇	1	2	yes	—
356	C₂×C₄	#121×C₆₇	1	2	yes	—
357	C₂×C₄	#121×C₆₇	1	2	yes	—
358	C₂×C₄	#121×C₆₇	1	1	yes	characteristic
359	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
360	C₂×C₄	C₂²⋊Q₈×C₆₇	1	2	yes	—
361	C₂×C₄	C₂²⋊Q₈×C₆₇	1	1	yes	characteristic
362	C₂×C₄	#123×C₆₇	1	2	yes	—
363	C₂×C₄	#123×C₆₇	1	1	yes	characteristic
364	C₂×C₄	#124×C₆₇	1	1	yes	characteristic
365	C₂×C₄	#126×C₆₇	1	2	yes	—
366	C₂×C₄	#127×C₆₇	1	1	yes	characteristic
367	C₈	—	2	4	no	—
368	C₈	—	4	2	no	—
369	C₈	—	4	4	no	—
370	C₂²	—	2	2	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	2	2	no	—
373	C₂²	—	4	2	no	—
374	C₂²	—	4	2	no	—
375	C₂²	—	4	4	no	—
376	C₂²	—	4	2	no	—
377	C₂²	—	8	2	no	—
378	C₂²	—	8	2	no	—
379	C₂²	#380×C₆₇	1	1	yes	characteristic
380	C₂²	#388×C₆₇	1	2	yes	—
381	C₂²	#393×C₆₇	1	1	yes	characteristic
382	C₂²	#394×C₆₇	1	2	yes	—
383	C₂²	#399×C₆₇	1	1	yes	characteristic
384	C₄	—	4	2	no	—
385	C₄	—	8	4	no	—
386	C₄	#385×C₆₇	1	2	yes	—
387	C₄	#386×C₆₇	1	1	yes	characteristic
388	C₄	#390×C₆₇	1	1	yes	characteristic
389	C₄	#392×C₆₇	1	1	yes	characteristic
390	C₄	#396×C₆₇	1	2	yes	—
391	C₄	#397×C₆₇	1	1	yes	characteristic
392	C₂	—	2	2	no	—
393	C₂	—	2	1	no	—
394	C₂	—	2	1	no	—
395	C₂	—	2	2	no	—
396	C₂	—	8	2	no	—
397	C₂	C₆₇×#1439	1	1	yes	characteristic
398	C₂	C₆₇×#1814	1	2	yes	—

	subgroup	G/H
center	C₂×C₄×C₆₇	#121
commutator	C₂²×C₄	C₂²×C₄×C₆₇
Frattini, cosocle	C₂³×C₄	C₂³×C₆₇
socle	C₂²×C₆₇	#380
prime radical	C₂²×#41×C₆₇	C₂²
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₂×C₄×C₆₇ ◁ C₂³×C₄×C₆₇ ◁ G

Complements

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

N	H ≅ G/N	type
1. C₂²×#108×C₆₇	C₂	semidirect
4. C₂×#344×C₆₇	C₂	semidirect
5. C₆₇×#1735	C₂	semidirect
17. #408×C₆₇	C₄	semidirect
192. #11108	C₆₇	direct (N × H)
200. C₂²×#108	C₂×C₆₇	semidirect
203. C₂×#344	C₂×C₆₇	semidirect
204. #1735	C₂×C₆₇	semidirect
205. C₆₇	#11108	direct (N × H)
217. #408	C₄×C₆₇	semidirect

Maximal subgroups

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

subgroup	index
C₂²×#108×C₆₇	2
C₂×#421×C₆₇	2
C₂×#408×C₆₇	2
C₂×#344×C₆₇	2
C₆₇×#1735	2
#11108	67

Subgroups — C67×#11108 #30690359

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₆₇×#11108 #30690359