Subgroups — #34020271

Order 18688.

1126 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#17989597	C₂	1	1	yes	maximal, characteristic
2	C₂²×#14556660	C₂	1	1	yes	maximal, characteristic
3	#22626368	C₂	1	2	yes	maximal
4	#22625745	C₂	1	4	yes	maximal, complemented
5	C₄×#14556660	C₂	1	4	yes	maximal, complemented
6	#22625619	C₂	1	2	yes	maximal
7	#405×D₇₃	C₂	1	1	yes	maximal, characteristic
8	C₂×#14556670	C₂²	1	2	yes	—
9	C₂²×C₄⋊#64408	C₂²	1	2	yes	—
10	#17989597	C₄	1	8	yes	complemented
11	C₂×#14556660	C₄	1	8	yes	complemented
12	C₂×#14556660	C₂²	1	2	yes	—
13	C₂×#14556660	C₂²	1	2	yes	—
14	C₂×#14556660	C₂²	1	2	yes	—
15	C₂×#14556659	C₂²	1	2	yes	—
16	C₄⋊C₄×#64408	—	2	4	no	—
17	C₄×C₄⋊#64408	C₂²	1	8	yes	—
18	C₂²⋊C₄×#64408	—	2	4	no	—
19	#17989461	C₂²	1	8	yes	—
20	C₂×M₁₆×D₇₃	C₂²	1	1	yes	characteristic
21	C₂²×C₈×D₇₃	C₂²	1	1	yes	characteristic
22	#117×D₇₃	C₂²	1	1	yes	characteristic
23	#17988545	C₄	1	1	yes	characteristic, complemented
24	#17988544	C₄	1	2	yes	complemented
25	#17988543	C₄	1	1	yes	characteristic, complemented
26	#17988542	C₄	1	1	yes	characteristic, complemented
27	#17988541	C₄	1	2	yes	complemented
28	#97×D₇₃	C₂²	1	2	yes	—
29	C₄×C₈×D₇₃	C₂²	1	2	yes	—
30	#405×C₇₃	C₄	1	1	yes	characteristic, complemented
31	C₂³×#64408	—	2	2	no	—
32	#14556670	—	2	4	no	—
33	#14556670	C₂×C₄	1	8	yes	—
34	C₂×C₄⋊#64408	—	2	2	no	—
35	C₂×C₄⋊#64408	—	2	4	no	—
36	C₂×C₄⋊#64408	C₂×C₄	1	8	yes	—
37	C₂×C₄⋊#64408	C₂³	1	4	yes	—
38	C₂×C₄⋊#64408	C₂³	1	4	yes	—
39	C₂×C₂²⋊#64408	—	2	2	no	—
40	C₂×C₄×#64408	—	2	2	no	—
41	C₂×C₄×#64408	—	2	8	no	—
42	#14556660	C₂×C₄	1	8	yes	—
43	#14556660	C₂×C₄	1	8	yes	—
44	#14556660	C₂×C₄	1	8	yes	complemented
45	#14556659	C₂×C₄	1	8	yes	complemented
46	(C₂×#64408)⋊C₄	—	2	8	no	—
47	C₂²×C₄×D₇₃	C₂³	1	1	yes	characteristic
48	C₂×#11924012	C₂×C₄	1	1	yes	characteristic
49	C₂×#11924011	C₂×C₄	1	2	yes	—
50	M₁₆×D₇₃	—	2	2	no	—
51	M₁₆×D₇₃	—	2	2	no	—
52	C₂²×#10596831	C₂×C₄	1	1	yes	characteristic
53	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
54	C₂×C₈×D₇₃	C₂×C₄	1	4	yes	—
55	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
56	C₂×C₈×D₇₃	C₂×C₄	1	1	yes	characteristic
57	C₂×C₈×D₇₃	C₂³	1	2	yes	—
58	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
59	C₂×C₈×D₇₃	C₂³	1	1	yes	characteristic
60	#14556550	C₂×C₄	1	1	yes	characteristic
61	#14556549	Q₈	1	2	yes	—
62	#14556548	C₂×C₄	1	2	yes	—
63	#14556547	Q₈	1	2	yes	—
64	C₄⋊C₄×D₇₃	D₄	1	2	yes	—
65	C₂²⋊C₄×D₇₃	D₄	1	2	yes	—
66	C₄²×D₇₃	C₂³	1	2	yes	—
67	#14556502	C₂×C₄	1	2	yes	complemented
68	#14556501	C₂×C₄	1	2	yes	complemented
69	#14556501	C₂×C₄	1	2	yes	complemented
70	C₄×#10596831	C₂×C₄	1	2	yes	complemented
71	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
72	C₈×Dic₇₃	C₂×C₄	1	2	yes	complemented
73	C₂×M₁₆×C₇₃	C₂×C₄	1	1	yes	characteristic
74	C₂²×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
75	#117×C₇₃	C₂×C₄	1	1	yes	characteristic
76	#97×C₇₃	C₂×C₄	1	2	yes	complemented
77	C₄×C₈×C₇₃	C₂×C₄	1	2	yes	complemented
78	C₂²×#64408	—	2	4	no	—
79	C₂²×#64408	—	2	4	no	—
80	C₂²×#64408	—	2	8	no	—
81	C₂²×#64408	—	8	4	no	—
82	C₄⋊#64408	—	2	8	no	—
83	C₄⋊#64408	—	2	4	no	—
84	C₄⋊#64408	—	2	4	no	—
85	C₄⋊#64408	C₂²×C₄	1	8	yes	—
86	C₄⋊#64408	C₂²×C₄	1	8	yes	—
87	C₂²⋊#64408	—	2	8	no	—
88	C₄×#64408	—	2	8	no	—
89	C₄×#64408	—	8	8	no	—
90	C₂³×D₇₃	C₂×D₄	1	1	yes	characteristic
91	C₂²×Dic₇₃	C₂×Q₈	1	1	yes	characteristic
92	C₂×C₄×D₇₃	C₂²×C₄	1	1	yes	characteristic
93	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
94	C₂×C₄×D₇₃	C₂²×C₄	1	2	yes	—
95	C₂×C₄×D₇₃	C₂×D₄	1	4	yes	—
96	C₂×C₄×D₇₃	C₂×D₄	1	1	yes	characteristic
97	C₂×C₄×D₇₃	C₂×Q₈	1	1	yes	characteristic
98	C₂×C₄×D₇₃	#41	1	2	yes	—
99	C₂×C₄×D₇₃	#41	1	2	yes	—
100	C₂×C₄×D₇₃	C₂⁴	1	1	yes	characteristic
101	#11924012	—	2	2	no	—
102	#11924011	—	2	4	no	—
103	C₂×#10596831	C₄²	1	4	yes	complemented
104	C₂×#10596831	C₂²×C₄	1	2	yes	—
105	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
106	C₂×#10596831	C₂²×C₄	1	1	yes	characteristic
107	C₈×D₇₃	—	2	2	no	—
108	C₈×D₇₃	—	2	2	no	—
109	C₈×D₇₃	C₄²	1	4	yes	complemented
110	C₈×D₇₃	C₄²	1	4	yes	complemented
111	C₈×D₇₃	C₂²×C₄	1	2	yes	—
112	C₈×D₇₃	C₂²×C₄	1	2	yes	—
113	C₈×D₇₃	C₂²×C₄	1	2	yes	—
114	C₈×D₇₃	C₂²×C₄	1	2	yes	—
115	C₄⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
116	#11924007	C₄⋊C₄	1	4	yes	—
117	C₂²⋊Dic₇₃	C₄⋊C₄	1	2	yes	—
118	#11924005	C₄⋊C₄	1	4	yes	—
119	C₄×Dic₇₃	C₂²×C₄	1	2	yes	—
120	C₄×Dic₇₃	C₂×Q₈	1	4	yes	—
121	C₂²×C₄×C₇₃	C₂²×C₄	1	1	yes	characteristic
122	M₁₆×C₇₃	—	2	2	no	—
123	C₂×C₈×C₇₃	C₄²	1	4	yes	complemented
124	C₂×C₈×C₇₃	C₂²×C₄	1	2	yes	—
125	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
126	C₂×C₈×C₇₃	C₂²×C₄	1	1	yes	characteristic
127	C₄⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
128	C₂²⋊C₄×C₇₃	C₄⋊C₄	1	2	yes	—
129	C₄²×C₇₃	C₂²×C₄	1	2	yes	—
130	C₂³×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
131	C₂²×D₇₃	—	2	2	no	—
132	C₂²×D₇₃	—	2	2	no	—
133	C₂²×D₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
134	C₂²×D₇₃	C₄×D₄	1	2	yes	—
135	C₂²×D₇₃	C₄×D₄	1	2	yes	—
136	C₂²×D₇₃	C₂²×D₄	1	1	yes	characteristic
137	C₂×#64408	—	2	8	no	—
138	C₂×#64408	—	2	8	no	—
139	C₂×#64408	—	4	4	no	—
140	C₂×#64408	—	4	8	no	—
141	C₂×#64408	—	4	4	no	—
142	C₂×#64408	—	8	8	no	—
143	C₂×C₄×C₇₃	C₂×C₄²	1	2	yes	—
144	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	4	yes	—
145	C₂×C₄×C₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
146	C₂×C₄×C₇₃	#117	1	2	yes	—
147	C₂×C₄×C₇₃	C₂³×C₄	1	1	yes	characteristic
148	C₂×Dic₇₃	C₂×C₄⋊C₄	1	4	yes	—
149	C₂×Dic₇₃	C₂×C₄⋊C₄	1	1	yes	characteristic
150	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
151	C₂×Dic₇₃	C₄×Q₈	1	2	yes	—
152	C₂×Dic₇₃	C₂²×Q₈	1	1	yes	characteristic
153	C₄×D₇₃	—	2	4	no	—
154	C₄×D₇₃	—	2	4	no	—
155	C₄×D₇₃	C₂×C₄²	1	2	yes	—
156	C₄×D₇₃	#117	1	2	yes	—
157	C₄×D₇₃	C₄×D₄	1	2	yes	—
158	C₄×D₇₃	C₄×D₄	1	2	yes	—
159	C₄×D₇₃	C₄×Q₈	1	2	yes	—
160	C₄×D₇₃	C₄×Q₈	1	2	yes	—
161	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
162	C₄×D₇₃	C₂³×C₄	1	1	yes	characteristic
163	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
164	C₄×D₇₃	C₂×#41	1	1	yes	characteristic
165	C₈×C₇₃	—	2	2	no	—
166	C₈×C₇₃	C₂×C₄²	1	2	yes	—
167	C₈×C₇₃	C₂×C₄²	1	2	yes	—
168	#10596831	—	2	2	no	—
169	#10596831	C₂×C₄²	1	2	yes	—
170	#10596831	C₂×C₄²	1	2	yes	—
171	C₂²×C₇₃	—	2	2	no	—
172	C₂²×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
173	C₂²×C₇₃	C₂²×C₄⋊C₄	1	1	yes	characteristic
174	C₂×D₇₃	—	2	2	no	—
175	C₂×D₇₃	—	2	2	no	—
176	C₂×D₇₃	—	2	2	no	—
177	C₂×D₇₃	—	2	4	no	—
178	C₂×D₇₃	C₄×C₄⋊C₄	1	2	yes	—
179	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
180	C₂×D₇₃	C₂×C₄×D₄	1	1	yes	characteristic
181	C₂×D₇₃	#576	1	2	yes	—
182	C₂×D₇₃	#578	1	2	yes	—
183	#64408	—	4	8	no	—
184	#64408	—	4	8	no	—
185	C₄×C₇₃	—	2	4	no	—
186	C₄×C₇₃	C₄×C₄⋊C₄	1	2	yes	—
187	C₄×C₇₃	C₂²×C₄²	1	1	yes	characteristic
188	C₄×C₇₃	C₂×#117	1	1	yes	characteristic
189	Dic₇₃	—	2	4	no	—
190	Dic₇₃	C₄×C₄⋊C₄	1	2	yes	—
191	Dic₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
192	Dic₇₃	C₂×C₄×Q₈	1	1	yes	characteristic
193	#20455	—	73	1	no	maximal, Sylow
194	C₂×C₇₃	—	2	2	no	—
195	C₂×C₇₃	C₂×C₄×C₄⋊C₄	1	1	yes	characteristic
196	C₂×C₇₃	#2913	1	2	yes	—
197	D₇₃	—	2	2	no	—
198	D₇₃	#2948	1	1	yes	characteristic
199	D₇₃	#2950	1	1	yes	characteristic
200	D₇₃	#2951	1	2	yes	—
201	C₂×#427	—	73	1	no	—
202	C₂²×#107	—	73	1	no	—
203	C₂×#405	—	73	1	no	—
204	#2274	—	73	2	no	—
205	#1776	—	73	4	no	—
206	C₄×#107	—	73	4	no	—
207	#1736	—	73	2	no	—
208	C₇₃	#20455	1	1	yes	characteristic, complemented, Sylow
209	C₂²×M₁₆	—	73	1	no	—
210	C₂³×C₈	—	73	1	no	—
211	C₂×#117	—	73	1	no	—
212	C₂×#117	—	73	2	no	—
213	C₂²×C₄⋊C₄	—	73	2	no	—
214	#427	—	73	8	no	—
215	C₂×#107	—	73	8	no	—
216	C₂×#107	—	73	2	no	—
217	C₂×#107	—	73	2	no	—
218	C₂×#107	—	73	2	no	—
219	C₂×#106	—	73	2	no	—
220	#405	—	73	1	no	—
221	#405	—	73	1	no	—
222	#405	—	73	1	no	—
223	#405	—	73	2	no	—
224	#405	—	73	2	no	—
225	#405	#64408	1	1	yes	characteristic, complemented
226	C₂×#97	—	73	2	no	—
227	C₂×C₄×C₈	—	73	2	no	—
228	C₄×C₄⋊C₄	—	73	8	no	—
229	C₄×C₄⋊C₄	—	146	4	no	—
230	C₄×C₂²⋊C₄	—	146	4	no	—
231	#340	—	73	8	no	—
232	C₂³×C₄	—	73	1	no	—
233	C₂³×C₄	—	146	2	no	—
234	C₂×M₁₆	—	73	1	no	—
235	C₂×M₁₆	—	73	2	no	—
236	C₂×M₁₆	—	146	2	no	—
237	C₂×M₁₆	—	146	2	no	—
238	C₂×M₁₆	C₂×#64408	1	1	yes	characteristic
239	C₂²×C₈	—	73	1	no	—
240	C₂²×C₈	—	73	4	no	—
241	C₂²×C₈	—	73	4	no	—
242	C₂²×C₈	—	73	1	no	—
243	C₂²×C₈	—	73	1	no	—
244	C₂²×C₈	—	73	1	no	—
245	C₂²×C₈	—	73	1	no	—
246	C₂²×C₈	—	73	2	no	—
247	C₂²×C₈	C₂×#64408	1	1	yes	characteristic
248	#117	—	73	1	no	—
249	#117	—	73	2	no	—
250	#117	—	73	2	no	—
251	#117	—	73	2	no	—
252	#117	—	73	8	no	—
253	#117	—	146	4	no	—
254	#117	C₂×#64408	1	1	yes	characteristic
255	C₂×C₄⋊C₄	—	73	2	no	—
256	C₂×C₄⋊C₄	—	73	4	no	—
257	C₂×C₄⋊C₄	—	73	8	no	—
258	C₂×C₄⋊C₄	—	73	4	no	—
259	C₂×C₄⋊C₄	—	146	2	no	—
260	C₂×C₄⋊C₄	—	146	4	no	—
261	C₂×C₂²⋊C₄	—	73	2	no	—
262	C₂×C₂²⋊C₄	—	146	2	no	—
263	C₂×C₄²	—	73	2	no	—
264	C₂×C₄²	—	146	8	no	—
265	C₂×C₄²	—	146	2	no	—
266	#107	—	73	8	no	—
267	#107	—	73	8	no	—
268	#107	—	73	8	no	—
269	#106	—	73	8	no	—
270	#97	—	73	2	no	—
271	#97	—	73	2	no	—
272	#97	—	73	2	no	—
273	#97	C₂×#64408	1	2	yes	complemented
274	C₄×C₈	—	73	2	no	—
275	C₄×C₈	—	73	2	no	—
276	C₄×C₈	—	73	2	no	—
277	C₄×C₈	C₂×#64408	1	2	yes	complemented
278	#95	—	146	8	no	—
279	C₂⁴	—	73	1	no	—
280	C₂²×C₄	—	584	4	no	—
281	C₂²×C₄	—	73	1	no	—
282	C₂²×C₄	—	73	1	no	—
283	C₂²×C₄	—	73	1	no	—
284	C₂²×C₄	—	73	2	no	—
285	C₂²×C₄	—	73	2	no	—
286	C₂²×C₄	—	73	1	no	—
287	C₂²×C₄	—	73	1	no	—
288	C₂²×C₄	—	73	2	no	—
289	C₂²×C₄	—	73	2	no	—
290	C₂²×C₄	—	73	4	no	—
291	C₂²×C₄	—	146	4	no	—
292	C₂²×C₄	—	146	4	no	—
293	C₂²×C₄	—	146	8	no	—
294	C₂²×C₄	C₂²×#64408	1	1	yes	characteristic
295	M₁₆	—	2	2	no	—
296	M₁₆	—	146	4	no	—
297	M₁₆	—	146	2	no	—
298	C₂×C₈	—	73	1	no	—
299	C₂×C₈	—	73	1	no	—
300	C₂×C₈	—	73	4	no	—
301	C₂×C₈	—	73	4	no	—
302	C₂×C₈	—	73	4	no	—
303	C₂×C₈	—	73	2	no	—
304	C₂×C₈	—	73	2	no	—
305	C₂×C₈	—	73	2	no	—
306	C₂×C₈	—	73	2	no	—
307	C₂×C₈	—	73	2	no	—
308	C₂×C₈	—	146	2	no	—
309	C₂×C₈	—	146	2	no	—
310	C₂×C₈	C₄×#64408	1	4	yes	complemented
311	C₂×C₈	C₂²×#64408	1	2	yes	—
312	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
313	C₂×C₈	C₂²×#64408	1	1	yes	characteristic
314	C₄⋊C₄	—	73	4	no	—
315	C₄⋊C₄	—	73	2	no	—
316	C₄⋊C₄	—	73	8	no	—
317	C₄⋊C₄	—	73	8	no	—
318	C₄⋊C₄	—	146	4	no	—
319	C₄⋊C₄	—	146	8	no	—
320	C₄⋊C₄	—	146	4	no	—
321	C₄⋊C₄	C₄⋊#64408	1	2	yes	—
322	C₂²⋊C₄	—	73	2	no	—
323	C₂²⋊C₄	—	73	4	no	—
324	C₂²⋊C₄	—	146	8	no	—
325	C₂²⋊C₄	C₄⋊#64408	1	2	yes	—
326	C₄²	—	584	8	no	—
327	C₄²	—	73	2	no	—
328	C₄²	—	73	4	no	—
329	C₄²	—	146	8	no	—
330	C₄²	C₂²×#64408	1	2	yes	—
331	C₂³	—	73	1	no	—
332	C₂³	—	73	1	no	—
333	C₂³	—	73	2	no	—
334	C₂³	—	73	2	no	—
335	C₂³	—	146	2	no	—
336	C₂³	—	146	2	no	—
337	C₂³	C₂×C₄⋊#64408	1	1	yes	characteristic
338	C₂×C₄	—	292	4	no	—
339	C₂×C₄	—	292	8	no	—
340	C₂×C₄	—	292	4	no	—
341	C₂×C₄	—	584	8	no	—
342	C₂×C₄	—	73	1	no	—
343	C₂×C₄	—	73	1	no	—
344	C₂×C₄	—	73	2	no	—
345	C₂×C₄	—	73	2	no	—
346	C₂×C₄	—	73	1	no	—
347	C₂×C₄	—	73	1	no	—
348	C₂×C₄	—	73	2	no	—
349	C₂×C₄	—	73	1	no	—
350	C₂×C₄	—	73	1	no	—
351	C₂×C₄	—	73	2	no	—
352	C₂×C₄	—	73	2	no	—
353	C₂×C₄	—	73	2	no	—
354	C₂×C₄	—	73	2	no	—
355	C₂×C₄	—	73	2	no	—
356	C₂×C₄	—	73	4	no	—
357	C₂×C₄	—	146	4	no	—
358	C₂×C₄	—	146	4	no	—
359	C₂×C₄	—	146	8	no	—
360	C₂×C₄	—	146	8	no	—
361	C₂×C₄	C₂×C₄×#64408	1	2	yes	—
362	C₂×C₄	C₂×C₄⋊#64408	1	4	yes	—
363	C₂×C₄	C₂×C₄⋊#64408	1	1	yes	characteristic
364	C₂×C₄	#14556670	1	2	yes	—
365	C₂×C₄	C₂³×#64408	1	1	yes	characteristic
366	C₈	—	2	2	no	—
367	C₈	—	73	2	no	—
368	C₈	—	73	2	no	—
369	C₈	—	146	2	no	—
370	C₈	C₂×C₄×#64408	1	2	yes	—
371	C₈	C₂×C₄×#64408	1	2	yes	—
372	C₂²	—	2	2	no	—
373	C₂²	—	73	2	no	—
374	C₂²	—	73	2	no	—
375	C₂²	—	73	1	no	—
376	C₂²	—	73	1	no	—
377	C₂²	—	73	2	no	—
378	C₂²	—	146	2	no	—
379	C₂²	—	146	4	no	—
380	C₂²	—	146	2	no	—
381	C₂²	—	146	2	no	—
382	C₂²	C₄×C₄⋊#64408	1	2	yes	—
383	C₂²	C₂²×C₄⋊#64408	1	1	yes	characteristic
384	C₄	—	2	4	no	—
385	C₄	—	292	8	no	—
386	C₄	—	292	8	no	—
387	C₄	—	73	1	no	—
388	C₄	—	73	1	no	—
389	C₄	—	73	2	no	—
390	C₄	—	146	4	no	—
391	C₄	C₄×C₄⋊#64408	1	2	yes	—
392	C₄	C₂²×C₄×#64408	1	1	yes	characteristic
393	C₄	C₂×#14556670	1	1	yes	characteristic
394	C₂	—	2	2	no	—
395	C₂	—	73	1	no	—
396	C₂	—	73	2	no	—
397	C₂	—	73	1	no	—
398	C₂	—	146	2	no	—
399	C₂	C₂×C₄×C₄⋊#64408	1	1	yes	characteristic
400	C₂	#22626586	1	2	yes	—

	subgroup	G/H
center	C₂²	C₂²×C₄⋊#64408
commutator	C₄×C₇₃	C₂²×C₄²
Frattini	C₂×C₄	C₂³×#64408
Fitting	#405×C₇₃	C₄
socle	C₂²×C₇₃	C₂²×C₄⋊C₄
prime radical	C₂³×D₇₃	C₂×D₄
cosocle	C₂×C₄×D₇₃	C₂⁴
hypercenter	#405	#64408
hypocenter	C₇₃	#20455
LCS	G ▷ C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂² ◁ #117 ◁ #405

Complements

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

N	H ≅ G/N	type
4. #22625745	C₂	semidirect
5. C₄×#14556660	C₂	semidirect
10. #17989597	C₄	semidirect
11. C₂×#14556660	C₄	semidirect
23. #17988545	C₄	semidirect
24. #17988544	C₄	semidirect
25. #17988543	C₄	semidirect
26. #17988542	C₄	semidirect
27. #17988541	C₄	semidirect
30. #405×C₇₃	C₄	semidirect
44. #14556660	C₂×C₄	semidirect
45. #14556659	C₂×C₄	semidirect
67. #14556502	C₂×C₄	semidirect
68. #14556501	C₂×C₄	semidirect
69. #14556501	C₂×C₄	semidirect
70. C₄×#10596831	C₂×C₄	semidirect
71. C₈×Dic₇₃	C₂×C₄	semidirect
72. C₈×Dic₇₃	C₂×C₄	semidirect
76. #97×C₇₃	C₂×C₄	semidirect
77. C₄×C₈×C₇₃	C₂×C₄	semidirect
103. C₂×#10596831	C₄²	semidirect
109. C₈×D₇₃	C₄²	semidirect
110. C₈×D₇₃	C₄²	semidirect
123. C₂×C₈×C₇₃	C₄²	semidirect
208. C₇₃	#20455	semidirect
225. #405	#64408	semidirect
273. #97	C₂×#64408	semidirect
277. C₄×C₈	C₂×#64408	semidirect
310. C₂×C₈	C₄×#64408	semidirect

Maximal subgroups

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

subgroup	index
C₂×#17989597	2
C₂²×#14556660	2
#22626368	2
#22625745	2
C₄×#14556660	2
#22625619	2
#405×D₇₃	2
#20455	73