Subgroups — C₂×#22559623 #30838205

Order 17152.

722 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#16863742	C₂	1	1	yes	maximal, characteristic
2	C₂×#16863691	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×Q₈×C₆₇⋊C₈	C₂	1	1	yes	maximal, characteristic, complemented
4	#22559623	C₂	1	8	yes	maximal, direct product factor
5	C₂×#16863146	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#16863144	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×#16863140	C₂	1	1	yes	maximal, characteristic
8	C₂×#460×C₆₇	C₂	1	1	yes	maximal, characteristic
9	C₂×#14524043	C₂²	1	1	yes	characteristic
10	#16863742	—	2	2	no	—
11	#16863742	C₂²	1	4	yes	—
12	#16863691	—	2	2	no	—
13	#16863691	C₂²	1	4	yes	complemented
14	Q₈×C₆₇⋊C₈	—	2	2	no	—
15	Q₈×C₆₇⋊C₈	C₂²	1	4	yes	complemented
16	C₂×#14523976	—	2	1	no	—
17	C₂×C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
18	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
19	C₂×C₄⋊(C₆₇⋊C₈)	C₂²	1	1	yes	characteristic
20	C₂×#14523967	—	2	1	no	—
21	C₂×#14523964	—	2	1	no	—
22	C₂×#14523964	—	2	1	no	—
23	C₂×C₄×C₆₇⋊C₈	—	2	1	no	—
24	C₂×C₄×C₆₇⋊C₈	C₂²	1	1	yes	characteristic
25	#16863146	C₂²	1	4	yes	complemented
26	#16863144	C₂²	1	4	yes	complemented
27	#16863140	C₂²	1	4	yes	—
28	C₂²×SD₁₆×C₆₇	—	2	1	no	—
29	C₂×#127×C₆₇	C₂²	1	1	yes	characteristic
30	C₂×C₄×Q₈×C₆₇	C₂²	1	1	yes	characteristic
31	#460×C₆₇	—	2	2	no	—
32	#460×C₆₇	C₂²	1	4	yes	—
33	C₂×C₄⋊C₈×C₆₇	C₂²	1	1	yes	characteristic
34	C₂×#102×C₆₇	—	2	1	no	—
35	C₂²×Dic₁₃₄	—	2	1	no	—
36	C₂²×C₆₇⋊C₈	—	2	1	no	—
37	C₂²×C₆₇⋊C₈	—	2	1	no	—
38	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
39	C₂²×C₆₇⋊C₈	D₄	1	1	yes	characteristic
40	#14524043	—	2	1	no	—
41	#14524043	—	2	1	no	—
42	#14524043	—	2	1	no	—
43	#14524043	C₂³	1	2	yes	—
44	C₂×C₄⋊Dic₆₇	—	2	1	no	—
45	C₂×C₄⋊Dic₆₇	—	2	1	no	—
46	#14523976	—	2	4	no	—
47	C₄⋊(C₆₇⋊C₈)	—	2	4	no	—
48	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
49	C₄⋊(C₆₇⋊C₈)	—	2	1	no	—
50	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
51	C₄⋊(C₆₇⋊C₈)	C₂³	1	2	yes	—
52	#14523967	—	2	4	no	—
53	#14523964	—	2	4	no	—
54	#14523964	—	2	4	no	—
55	C₄×C₆₇⋊C₈	—	2	4	no	—
56	C₄×C₆₇⋊C₈	D₄	1	2	yes	—
57	C₄×C₆₇⋊C₈	C₂³	1	2	yes	—
58	C₂²×Q₈×C₆₇	D₄	1	1	yes	characteristic
59	C₂²×D₄×C₆₇	—	2	1	no	—
60	C₂²×D₄×C₆₇	—	2	1	no	—
61	C₂²×D₄×C₆₇	—	2	1	no	—
62	C₂×SD₁₆×C₆₇	—	2	4	no	—
63	C₂×SD₁₆×C₆₇	—	4	4	no	—
64	C₂²×C₈×C₆₇	—	2	1	no	—
65	#127×C₆₇	—	2	1	no	—
66	#127×C₆₇	—	2	1	no	—
67	#127×C₆₇	—	2	1	no	—
68	#127×C₆₇	C₂³	1	2	yes	—
69	C₄×Q₈×C₆₇	—	2	1	no	—
70	C₄×Q₈×C₆₇	—	2	1	no	—
71	C₄×Q₈×C₆₇	D₄	1	2	yes	—
72	C₄×Q₈×C₆₇	C₂³	1	2	yes	—
73	C₂×C₄⋊C₄×C₆₇	—	2	1	no	—
74	C₂×C₄⋊C₄×C₆₇	D₄	1	1	yes	characteristic
75	C₂×C₄²×C₆₇	—	2	1	no	—
76	C₂×C₄²×C₆₇	C₂³	1	1	yes	characteristic
77	C₄⋊C₈×C₆₇	—	2	1	no	—
78	C₄⋊C₈×C₆₇	C₂³	1	2	yes	—
79	#102×C₆₇	—	2	4	no	—
80	C₂×Dic₁₃₄	—	2	2	no	—
81	C₂×Dic₁₃₄	—	4	1	no	—
82	C₂×Dic₁₃₄	—	8	2	no	—
83	C₂²×Dic₆₇	—	4	1	no	—
84	C₂×C₆₇⋊C₈	—	2	2	no	—
85	C₂×C₆₇⋊C₈	—	2	2	no	—
86	C₂×C₆₇⋊C₈	—	2	2	no	—
87	C₂×C₆₇⋊C₈	—	2	2	no	—
88	C₂×C₆₇⋊C₈	—	4	2	no	—
89	C₂×C₆₇⋊C₈	—	4	2	no	—
90	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
91	C₂×C₆₇⋊C₈	C₂×D₄	1	2	yes	—
92	C₄⋊Dic₆₇	—	2	2	no	—
93	C₄⋊Dic₆₇	—	2	2	no	—
94	C₄⋊Dic₆₇	—	4	1	no	—
95	C₄⋊Dic₆₇	—	4	1	no	—
96	C₂⁴×C₆₇	—	4	1	no	—
97	C₂×Q₈×C₆₇	—	2	1	no	—
98	C₂×Q₈×C₆₇	—	2	2	no	—
99	C₂×Q₈×C₆₇	SD₁₆	1	4	yes	—
100	C₂×Q₈×C₆₇	C₂×D₄	1	2	yes	—
101	C₂×D₄×C₆₇	—	2	2	no	—
102	C₂×D₄×C₆₇	—	2	2	no	—
103	C₂×D₄×C₆₇	—	2	2	no	—
104	C₂×D₄×C₆₇	—	4	1	no	—
105	C₂×D₄×C₆₇	—	4	1	no	—
106	C₂×D₄×C₆₇	—	4	1	no	—
107	C₂×D₄×C₆₇	—	4	2	no	—
108	C₂×D₄×C₆₇	—	4	2	no	—
109	C₂×D₄×C₆₇	—	4	2	no	—
110	C₂×D₄×C₆₇	—	4	2	no	—
111	C₂×D₄×C₆₇	—	8	2	no	—
112	C₂²×C₄×C₆₇	—	2	1	no	—
113	C₂²×C₄×C₆₇	—	2	1	no	—
114	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
115	C₂²×C₄×C₆₇	C₂×D₄	1	1	yes	characteristic
116	C₂²×C₄×C₆₇	#41	1	1	yes	characteristic
117	SD₁₆×C₆₇	—	4	8	no	—
118	C₂×C₈×C₆₇	—	2	2	no	—
119	C₂×C₈×C₆₇	—	4	2	no	—
120	C₄⋊C₄×C₆₇	—	2	2	no	—
121	C₄⋊C₄×C₆₇	—	2	1	no	—
122	C₄⋊C₄×C₆₇	—	2	2	no	—
123	C₄⋊C₄×C₆₇	C₂×D₄	1	2	yes	—
124	C₄²×C₆₇	—	2	2	no	—
125	C₄²×C₆₇	—	2	2	no	—
126	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
127	C₄²×C₆₇	C₂×D₄	1	1	yes	characteristic
128	C₄²×C₆₇	#41	1	1	yes	characteristic
129	C₄²×C₆₇	C₂⁴	1	1	yes	characteristic
130	C₂³×C₆₇	—	4	2	no	—
131	C₂³×C₆₇	—	8	2	no	—
132	C₂³×C₆₇	—	8	2	no	—
133	C₂³×C₆₇	—	8	2	no	—
134	C₂³×C₆₇	#121	1	1	yes	characteristic
135	Q₈×C₆₇	—	2	2	no	—
136	Q₈×C₆₇	—	2	4	no	—
137	Q₈×C₆₇	C₂×SD₁₆	1	4	yes	—
138	D₄×C₆₇	—	4	2	no	—
139	D₄×C₆₇	—	4	2	no	—
140	D₄×C₆₇	—	4	2	no	—
141	D₄×C₆₇	—	4	2	no	—
142	D₄×C₆₇	—	8	2	no	—
143	D₄×C₆₇	—	8	2	no	—
144	D₄×C₆₇	—	8	2	no	—
145	D₄×C₆₇	—	8	2	no	—
146	C₂×C₄×C₆₇	—	2	2	no	—
147	C₂×C₄×C₆₇	—	2	4	no	—
148	C₂×C₄×C₆₇	—	2	2	no	—
149	C₂×C₄×C₆₇	—	2	2	no	—
150	C₂×C₄×C₆₇	—	4	2	no	—
151	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
152	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
153	C₂×C₄×C₆₇	#121	1	1	yes	characteristic
154	C₂×C₄×C₆₇	C₂×SD₁₆	1	2	yes	—
155	C₂×C₄×C₆₇	#135	1	2	yes	—
156	C₂×C₄×C₆₇	#135	1	2	yes	—
157	C₂×C₄×C₆₇	#137	1	2	yes	—
158	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
159	C₂×C₄×C₆₇	C₂²×D₄	1	1	yes	characteristic
160	C₂×C₄×C₆₇	C₂×#41	1	1	yes	characteristic
161	C₂×Dic₆₇	—	4	2	no	—
162	C₂×Dic₆₇	—	8	2	no	—
163	Dic₁₃₄	—	8	2	no	—
164	Dic₁₃₄	—	8	2	no	—
165	C₈×C₆₇	—	4	2	no	—
166	C₆₇⋊C₈	—	2	2	no	—
167	C₆₇⋊C₈	—	2	2	no	—
168	C₆₇⋊C₈	—	4	2	no	—
169	C₆₇⋊C₈	—	4	2	no	—
170	C₂²×C₆₇	—	8	2	no	—
171	C₂²×C₆₇	—	8	2	no	—
172	C₂²×C₆₇	—	8	2	no	—
173	C₂²×C₆₇	—	16	4	no	—
174	C₂²×C₆₇	#464	1	2	yes	—
175	C₂²×C₆₇	#465	1	2	yes	—
176	C₂²×C₆₇	#472	1	2	yes	—
177	C₂²×C₆₇	C₂×#121	1	1	yes	characteristic
178	C₄×C₆₇	—	2	4	no	—
179	C₄×C₆₇	—	2	1	no	—
180	C₄×C₆₇	—	2	1	no	—
181	C₄×C₆₇	—	4	2	no	—
182	C₄×C₆₇	#464	1	2	yes	—
183	C₄×C₆₇	#465	1	2	yes	—
184	C₄×C₆₇	C₂²×SD₁₆	1	1	yes	characteristic
185	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
186	C₄×C₆₇	C₂×#135	1	1	yes	characteristic
187	C₄×C₆₇	C₂×#137	1	1	yes	characteristic
188	Dic₆₇	—	8	2	no	—
189	C₂×#1678	—	67	1	no	maximal, Sylow
190	C₂×C₆₇	—	16	2	no	—
191	C₂×C₆₇	#1678	1	4	yes	complemented
192	C₂×C₆₇	C₂×#464	1	1	yes	characteristic
193	C₂×C₆₇	C₂×#465	1	1	yes	characteristic
194	C₂×C₆₇	C₂×#472	1	1	yes	characteristic
195	C₂×#486	—	67	1	no	—
196	C₂×#477	—	67	1	no	—
197	C₂×#460	D₆₇	1	1	yes	characteristic
198	C₂×C₈×Q₈	—	67	1	no	—
199	#1678	—	67	8	no	—
200	C₂×#334	—	67	1	no	—
201	C₂×#333	—	67	1	no	—
202	C₂×#331	—	67	1	no	—
203	C₆₇	C₂×#1678	1	1	yes	characteristic, complemented, Sylow
204	C₂²×SD₁₆	—	2	1	no	—
205	C₂×C₄⋊Q₈	—	67	1	no	—
206	C₂×#127	C₂×D₆₇	1	1	yes	characteristic
207	C₂×C₄×Q₈	C₂×D₆₇	1	1	yes	characteristic
208	#486	—	67	4	no	—
209	#486	—	134	2	no	—
210	#477	—	67	4	no	—
211	#477	—	134	2	no	—
212	#460	—	2	2	no	—
213	#460	C₂×D₆₇	1	4	yes	—
214	C₈×Q₈	—	67	4	no	—
215	C₈×Q₈	—	134	2	no	—
216	C₂×#107	—	134	1	no	—
217	C₂×C₄⋊C₈	—	67	1	no	—
218	C₂×C₄⋊C₈	—	67	1	no	—
219	C₂×C₄⋊C₈	—	134	1	no	—
220	C₂×C₄⋊C₈	C₂×D₆₇	1	1	yes	characteristic
221	C₂×#103	—	134	1	no	—
222	C₂×#102	—	2	1	no	—
223	C₂×#102	—	134	1	no	—
224	C₂×#102	—	134	1	no	—
225	C₂×C₄×C₈	—	67	1	no	—
226	C₂×C₄×C₈	—	134	1	no	—
227	#334	—	67	4	no	—
228	#333	—	67	4	no	—
229	#331	—	67	4	no	—
230	C₂²×Q₈	—	134	1	no	—
231	C₂²×Q₈	C₂²⋊D₆₇	1	1	yes	characteristic
232	C₂²×D₄	—	2	1	no	—
233	C₂²×D₄	—	2	1	no	—
234	C₂²×D₄	—	2	1	no	—
235	C₂×SD₁₆	—	2	4	no	—
236	C₂×SD₁₆	—	4	4	no	—
237	C₂²×C₈	—	2	1	no	—
238	C₂²×C₈	—	67	1	no	—
239	C₂²×C₈	—	67	1	no	—
240	C₂²×C₈	—	134	1	no	—
241	C₂²×C₈	—	134	1	no	—
242	C₄⋊Q₈	—	67	2	no	—
243	C₄⋊Q₈	—	134	1	no	—
244	C₄⋊Q₈	—	134	1	no	—
245	C₄⋊Q₈	—	134	1	no	—
246	#127	—	2	1	no	—
247	#127	—	2	1	no	—
248	#127	—	2	1	no	—
249	#127	C₂²×D₆₇	1	2	yes	—
250	C₄×Q₈	—	2	1	no	—
251	C₄×Q₈	—	2	1	no	—
252	C₄×Q₈	C₂²⋊D₆₇	1	2	yes	—
253	C₄×Q₈	C₂²×D₆₇	1	2	yes	—
254	C₂×C₄⋊C₄	—	2	1	no	—
255	C₂×C₄⋊C₄	—	134	1	no	—
256	C₂×C₄⋊C₄	—	134	1	no	—
257	C₂×C₄⋊C₄	C₂²⋊D₆₇	1	1	yes	characteristic
258	C₂×C₄²	—	2	1	no	—
259	C₂×C₄²	C₂²×D₆₇	1	1	yes	characteristic
260	#107	—	134	4	no	—
261	C₄⋊C₈	—	2	1	no	—
262	C₄⋊C₈	—	67	2	no	—
263	C₄⋊C₈	—	67	2	no	—
264	C₄⋊C₈	—	134	4	no	—
265	C₄⋊C₈	—	134	1	no	—
266	C₄⋊C₈	—	134	1	no	—
267	C₄⋊C₈	C₂²×D₆₇	1	2	yes	—
268	#103	—	134	4	no	—
269	#102	—	2	4	no	—
270	#102	—	134	4	no	—
271	#102	—	134	4	no	—
272	C₄×C₈	—	67	2	no	—
273	C₄×C₈	—	67	2	no	—
274	C₄×C₈	—	134	4	no	—
275	C₂⁴	—	4	1	no	—
276	C₂×Q₈	—	2	1	no	—
277	C₂×Q₈	—	2	2	no	—
278	C₂×Q₈	—	268	1	no	—
279	C₂×Q₈	—	536	2	no	—
280	C₂×Q₈	—	134	2	no	—
281	C₂×Q₈	#11761616	1	4	yes	—
282	C₂×Q₈	C₂×C₂²⋊D₆₇	1	2	yes	—
283	C₂×D₄	—	2	2	no	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	2	2	no	—
286	C₂×D₄	—	4	1	no	—
287	C₂×D₄	—	4	1	no	—
288	C₂×D₄	—	4	1	no	—
289	C₂×D₄	—	4	2	no	—
290	C₂×D₄	—	4	2	no	—
291	C₂×D₄	—	4	2	no	—
292	C₂×D₄	—	4	2	no	—
293	C₂×D₄	—	8	2	no	—
294	C₂²×C₄	—	2	1	no	—
295	C₂²×C₄	—	2	1	no	—
296	C₂²×C₄	—	268	1	no	—
297	C₂²×C₄	D₄×D₆₇	1	1	yes	characteristic
298	C₂²×C₄	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
299	C₂²×C₄	#11761627	1	1	yes	characteristic
300	SD₁₆	—	4	8	no	—
301	C₂×C₈	—	2	2	no	—
302	C₂×C₈	—	4	2	no	—
303	C₂×C₈	—	268	2	no	—
304	C₂×C₈	—	268	2	no	—
305	C₂×C₈	—	67	2	no	—
306	C₂×C₈	—	67	2	no	—
307	C₂×C₈	—	134	2	no	—
308	C₂×C₈	—	134	2	no	—
309	C₂×C₈	—	134	2	no	—
310	C₂×C₈	—	134	2	no	—
311	C₄⋊C₄	—	2	2	no	—
312	C₄⋊C₄	—	2	1	no	—
313	C₄⋊C₄	—	2	2	no	—
314	C₄⋊C₄	—	268	1	no	—
315	C₄⋊C₄	—	268	1	no	—
316	C₄⋊C₄	—	134	2	no	—
317	C₄⋊C₄	—	134	2	no	—
318	C₄⋊C₄	C₂×C₂²⋊D₆₇	1	2	yes	—
319	C₄²	—	2	2	no	—
320	C₄²	—	2	2	no	—
321	C₄²	D₄×D₆₇	1	1	yes	characteristic
322	C₄²	C₂×C₂²⋊D₆₇	1	1	yes	characteristic
323	C₄²	#11761627	1	1	yes	characteristic
324	C₄²	C₂³×D₆₇	1	1	yes	characteristic
325	C₂³	—	4	2	no	—
326	C₂³	—	8	2	no	—
327	C₂³	—	8	2	no	—
328	C₂³	—	8	2	no	—
329	C₂³	#14524015	1	1	yes	characteristic
330	Q₈	—	2	4	no	—
331	Q₈	—	2	2	no	—
332	Q₈	—	536	2	no	—
333	Q₈	—	536	2	no	—
334	Q₈	C₂×#11761616	1	4	yes	—
335	D₄	—	4	2	no	—
336	D₄	—	4	2	no	—
337	D₄	—	4	2	no	—
338	D₄	—	4	2	no	—
339	D₄	—	8	2	no	—
340	D₄	—	8	2	no	—
341	D₄	—	8	2	no	—
342	D₄	—	8	2	no	—
343	C₂×C₄	—	2	4	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	2	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	4	2	no	—
348	C₂×C₄	—	268	2	no	—
349	C₂×C₄	—	536	2	no	—
350	C₂×C₄	#14524015	1	1	yes	characteristic
351	C₂×C₄	#14524015	1	1	yes	characteristic
352	C₂×C₄	#14524015	1	1	yes	characteristic
353	C₂×C₄	C₂×#11761616	1	2	yes	—
354	C₂×C₄	#14524063	1	2	yes	—
355	C₂×C₄	#14524064	1	2	yes	—
356	C₂×C₄	#14524072	1	2	yes	—
357	C₂×C₄	C₂×D₄×D₆₇	1	1	yes	characteristic
358	C₂×C₄	C₂²×C₂²⋊D₆₇	1	1	yes	characteristic
359	C₂×C₄	C₂×#11761627	1	1	yes	characteristic
360	C₈	—	4	2	no	—
361	C₈	—	268	2	no	—
362	C₈	—	268	2	no	—
363	C₈	—	134	2	no	—
364	C₈	—	134	2	no	—
365	C₂²	—	8	2	no	—
366	C₂²	—	8	2	no	—
367	C₂²	—	8	2	no	—
368	C₂²	—	16	4	no	—
369	C₂²	#16863616	1	2	yes	—
370	C₂²	#16863623	1	2	yes	—
371	C₂²	#16863664	1	2	yes	—
372	C₂²	C₂×#14524015	1	1	yes	characteristic
373	C₄	—	2	4	no	—
374	C₄	—	2	1	no	—
375	C₄	—	2	1	no	—
376	C₄	—	4	2	no	—
377	C₄	—	536	2	no	—
378	C₄	#16863616	1	2	yes	—
379	C₄	#16863623	1	2	yes	—
380	C₄	C₂²×#11761616	1	1	yes	characteristic
381	C₄	C₂×#14524063	1	1	yes	characteristic
382	C₄	C₂×#14524064	1	1	yes	characteristic
383	C₄	C₂×#14524072	1	1	yes	characteristic
384	C₂	—	16	2	no	—
385	C₂	#22559623	1	4	yes	direct product factor
386	C₂	C₂×#16863616	1	1	yes	characteristic
387	C₂	C₂×#16863623	1	1	yes	characteristic
388	C₂	C₂×#16863664	1	1	yes	characteristic

	subgroup	G/H
center	C₂³	#14524015
commutator, cosocle	C₄²×C₆₇	C₂⁴
Frattini	C₄²	C₂³×D₆₇
Fitting	C₂×#460×C₆₇	C₂
socle	C₂³×C₆₇	#121
prime radical	C₂×#127×C₆₇	C₂²
hypercenter	C₂×#460	D₆₇
hypocenter	C₆₇	C₂×#1678
LCS	G ▷ C₄²×C₆₇ ▷ C₂²×C₆₇ ▷ C₆₇
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#460

Complements

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

N	H ≅ G/N	type
2. C₂×#16863691	C₂	semidirect
3. C₂×Q₈×C₆₇⋊C₈	C₂	semidirect
4. #22559623	C₂	direct (N × H)
5. C₂×#16863146	C₂	semidirect
6. C₂×#16863144	C₂	semidirect
13. #16863691	C₂²	semidirect
15. Q₈×C₆₇⋊C₈	C₂²	semidirect
25. #16863146	C₂²	semidirect
26. #16863144	C₂²	semidirect
191. C₂×C₆₇	#1678	semidirect
203. C₆₇	C₂×#1678	semidirect
385. C₂	#22559623	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×#16863742	2
C₂×#16863691	2
C₂×Q₈×C₆₇⋊C₈	2
#22559623	2
C₂×#16863146	2
C₂×#16863144	2
C₂×#16863140	2
C₂×#460×C₆₇	2
C₂×#1678	67

Subgroups — C2×#22559623 #30838205

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₂×#22559623 #30838205