Subgroups — #72246014

Order 4704.

691 conjugacy classes of subgroups.

The subgroup lattice has 344 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#72246012	C₂	1	2	yes	maximal, complemented
2	#72246012	C₂	1	2	yes	maximal, complemented
3	#72246009	C₂	1	2	yes	maximal, complemented
4	#72246009	C₂	1	2	yes	maximal, complemented
5	#72245079	C₂	1	1	yes	maximal, characteristic, complemented
6	#72245079	C₂	1	1	yes	maximal, characteristic, complemented
7	C₂×C₄⋊#64425	C₂	1	1	yes	maximal, characteristic, complemented
8	#72222022	C₂	1	4	yes	maximal, complemented
9	#13096690	C₃	1	1	yes	maximal, characteristic, complemented, Hall
10	C₂²×#64425	C₂²	1	2	yes	complemented
11	C₂×#64422⋊C₂	C₂²	1	4	yes	complemented
12	C₂×C₄×#3862	C₂²	1	1	yes	characteristic, complemented
13	C₄⋊#64425	C₂²	1	2	yes	complemented
14	C₄⋊#64425	C₂²	1	2	yes	complemented
15	#11924212	C₂²	1	2	yes	complemented
16	#11924212	C₂²	1	2	yes	complemented
17	C₄⋊#64422	C₂²	1	1	yes	characteristic, complemented
18	C₄⋊#64422	C₂²	1	1	yes	characteristic, complemented
19	C₄×#64422	C₂²	1	2	yes	complemented
20	C₄×#64422	C₂²	1	2	yes	complemented
21	#11924208	C₂²	1	1	yes	characteristic, complemented
22	#11924208	C₂²	1	1	yes	characteristic, complemented
23	#11924181	C₂²	1	4	yes	complemented
24	#11924181	C₂²	1	4	yes	complemented
25	#11924179	C₂²	1	4	yes	complemented
26	C₂×C₄⋊(C₇⋊D₇)	C₂×C₃	1	1	yes	characteristic, complemented
27	C₇×#1157	C₂×C₃	1	1	yes	characteristic, complemented
28	C₇×#1157	C₂×C₃	1	1	yes	characteristic, complemented
29	#11716115	C₂×C₃	1	4	yes	complemented
30	D₇×D₂₈	C₂×C₃	1	2	yes	complemented
31	D₇×D₂₈	C₂×C₃	1	2	yes	complemented
32	#11716103	C₂×C₃	1	2	yes	complemented
33	#11716103	C₂×C₃	1	2	yes	complemented
34	#10621518	—	7	1	no	maximal
35	#10621518	—	7	1	no	maximal
36	C₂²×#3862	C₂³	1	1	yes	characteristic
37	C₂×#64425	—	4	2	no	—
38	C₂×#64425	C₂³	1	4	yes	—
39	C₂×#64422	C₂³	1	2	yes	—
40	C₂×#64422	C₂³	1	2	yes	—
41	#64422⋊C₂	—	4	4	no	—
42	C₄×#3862	C₂³	1	1	yes	characteristic
43	C₄×#3862	C₂³	1	1	yes	characteristic
44	#10596872	C₂³	1	2	yes	—
45	#10596872	C₂³	1	2	yes	—
46	C₂²×C₇⋊D₇	C₂²×C₃	1	2	yes	complemented
47	C₂×D₇²	C₂²×C₃	1	4	yes	complemented
48	C₂×C₄×C₇²	C₂²×C₃	1	1	yes	characteristic, complemented
49	C₄⋊(C₇⋊D₇)	C₂²×C₃	1	2	yes	complemented
50	C₄⋊(C₇⋊D₇)	C₂²×C₃	1	2	yes	complemented
51	C₇×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
52	C₇×C₂²⋊D₇	C₂²×C₃	1	2	yes	complemented
53	C₇×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
54	C₇×D₂₈	C₂²×C₃	1	1	yes	characteristic, complemented
55	C₄×C₇×D₇	C₂²×C₃	1	2	yes	complemented
56	C₄×C₇×D₇	C₂²×C₃	1	2	yes	complemented
57	C₇×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
58	C₇×Dic₁₄	C₂²×C₃	1	1	yes	characteristic, complemented
59	#87641	C₂²×C₃	1	4	yes	complemented
60	#87641	C₂²×C₃	1	4	yes	complemented
61	#87639	C₂²×C₃	1	4	yes	complemented
62	#41×ΓL(1,𝔽₈)	—	7	1	no	—
63	#41×ΓL(1,𝔽₈)	—	7	1	no	—
64	#66659	—	7	2	no	—
65	#66659	—	7	2	no	—
66	D₄×AGL(1,𝔽₇)	—	7	4	no	—
67	D₄×AGL(1,𝔽₇)	—	7	4	no	—
68	D₄×AGL(1,𝔽₇)	—	7	2	no	—
69	D₄×AGL(1,𝔽₇)	—	7	2	no	—
70	#1157⋊C₃	—	7	2	no	—
71	#1157⋊C₃	—	7	2	no	—
72	#1157⋊C₃	—	14	1	no	—
73	#1157⋊C₃	—	14	1	no	—
74	C₂×C₄⋊AGL(1,𝔽₇)	—	7	1	no	—
75	C₂×C₄⋊AGL(1,𝔽₇)	—	7	1	no	—
76	C₂×C₄⋊AGL(1,𝔽₇)	—	7	2	no	—
77	C₂×C₄⋊AGL(1,𝔽₇)	—	7	2	no	—
78	C₂×#3862	—	2	1	no	—
79	C₂×#3862	C₂⁴	1	1	yes	characteristic
80	#64425	—	2	4	no	—
81	#64422	—	2	2	no	—
82	#64422	—	2	2	no	—
83	#6553	—	7	1	no	—
84	#6553	—	7	1	no	—
85	C₂²×C₇²	C₂³×C₃	1	1	yes	characteristic
86	C₂×C₇⋊D₇	—	4	2	no	—
87	C₂×C₇⋊D₇	C₂³×C₃	1	4	yes	—
88	C₂×C₇×D₇	C₂³×C₃	1	2	yes	—
89	C₂×C₇×D₇	C₂³×C₃	1	2	yes	—
90	D₇²	—	4	4	no	—
91	C₄×C₇²	C₂³×C₃	1	1	yes	characteristic
92	C₄×C₇²	C₂³×C₃	1	1	yes	characteristic
93	C₇×Dic₇	C₂³×C₃	1	2	yes	—
94	C₇×Dic₇	C₂³×C₃	1	2	yes	—
95	C₂²×AGL(1,𝔽₇)	—	7	2	no	—
96	C₂²×AGL(1,𝔽₇)	—	7	2	no	—
97	C₂²×AGL(1,𝔽₇)	—	7	4	no	—
98	C₂²×AGL(1,𝔽₇)	—	7	4	no	—
99	Q₈×ΓL(1,𝔽₈)	—	7	1	no	—
100	Q₈×ΓL(1,𝔽₈)	—	7	1	no	—
101	D₄×ΓL(1,𝔽₈)	—	7	2	no	—
102	D₄×ΓL(1,𝔽₈)	—	7	1	no	—
103	D₄×ΓL(1,𝔽₈)	—	7	2	no	—
104	D₄×ΓL(1,𝔽₈)	—	7	1	no	—
105	C₂×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
106	C₂×C₄×ΓL(1,𝔽₈)	—	7	2	no	—
107	C₂×C₄×ΓL(1,𝔽₈)	—	14	1	no	—
108	C₂×C₄×ΓL(1,𝔽₈)	—	14	1	no	—
109	(C₂²⋊D₇)⋊C₃	—	7	4	no	—
110	(C₂²⋊D₇)⋊C₃	—	7	4	no	—
111	(C₂²⋊D₇)⋊C₃	—	14	2	no	—
112	(C₂²⋊D₇)⋊C₃	—	14	2	no	—
113	C₄⋊AGL(1,𝔽₇)	—	7	4	no	—
114	C₄⋊AGL(1,𝔽₇)	—	7	4	no	—
115	C₄⋊AGL(1,𝔽₇)	—	7	2	no	—
116	C₄⋊AGL(1,𝔽₇)	—	7	2	no	—
117	C₄⋊AGL(1,𝔽₇)	—	7	2	no	—
118	C₄⋊AGL(1,𝔽₇)	—	7	2	no	—
119	C₄⋊AGL(1,𝔽₇)	—	14	1	no	—
120	C₄⋊AGL(1,𝔽₇)	—	14	1	no	—
121	C₄×AGL(1,𝔽₇)	—	7	4	no	—
122	C₄×AGL(1,𝔽₇)	—	7	4	no	—
123	C₄×AGL(1,𝔽₇)	—	14	2	no	—
124	C₄×AGL(1,𝔽₇)	—	14	2	no	—
125	ΓL(1,𝔽₈)⋊Q₈	—	14	1	no	—
126	ΓL(1,𝔽₈)⋊Q₈	—	14	1	no	—
127	#3862	H(5,𝔽₂)	1	1	yes	characteristic, complemented, Hall
128	C₇×#41	—	7	1	no	—
129	C₇×#41	—	7	1	no	—
130	#1161	—	7	2	no	—
131	#1161	—	7	2	no	—
132	D₄×D₇	—	7	4	no	—
133	D₄×D₇	—	7	4	no	—
134	D₄×D₇	—	7	2	no	—
135	D₄×D₇	—	7	2	no	—
136	#1157	—	7	2	no	—
137	#1157	—	7	2	no	—
138	#1157	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
139	#1157	AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
140	C₂×D₂₈	—	7	1	no	—
141	C₂×D₂₈	—	7	1	no	—
142	C₂×D₂₈	—	7	2	no	—
143	C₂×D₂₈	—	7	2	no	—
144	C₂×D₂₈	—	42	1	no	—
145	C₂×C₇²	—	2	1	no	—
146	C₂×C₇²	C₂⁴×C₃	1	1	yes	characteristic
147	C₇⋊D₇	—	2	4	no	—
148	C₇×D₇	—	2	2	no	—
149	C₇×D₇	—	2	2	no	—
150	C₃×H(5,𝔽₂)	—	49	1	no	Hall
151	C₂²×ΓL(1,𝔽₈)	—	7	2	no	—
152	C₂²×ΓL(1,𝔽₈)	—	7	2	no	—
153	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
154	C₂²×ΓL(1,𝔽₈)	—	14	1	no	—
155	C₂×AGL(1,𝔽₇)	—	7	4	no	—
156	C₂×AGL(1,𝔽₇)	—	7	4	no	—
157	C₂×AGL(1,𝔽₇)	—	14	2	no	—
158	C₂×AGL(1,𝔽₇)	—	14	2	no	—
159	C₂×AGL(1,𝔽₇)	—	28	2	no	—
160	C₂×AGL(1,𝔽₇)	—	28	2	no	—
161	C₂×AGL(1,𝔽₇)	—	28	4	no	—
162	C₂×AGL(1,𝔽₇)	—	28	4	no	—
163	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
164	C₄×ΓL(1,𝔽₈)	—	7	2	no	—
165	C₄×ΓL(1,𝔽₈)	—	14	1	no	—
166	C₄×ΓL(1,𝔽₈)	—	14	1	no	—
167	C₄×ΓL(1,𝔽₈)	—	14	1	no	—
168	C₄×ΓL(1,𝔽₈)	—	14	1	no	—
169	ΓL(1,𝔽₈)⋊C₄	—	14	2	no	—
170	ΓL(1,𝔽₈)⋊C₄	—	14	2	no	—
171	C₂²×D₇	—	7	2	no	—
172	C₂²×D₇	—	7	2	no	—
173	C₂²×D₇	—	7	4	no	—
174	C₂²×D₇	—	7	4	no	—
175	C₂²×D₇	—	42	2	no	—
176	C₇×Q₈	—	7	1	no	—
177	C₇×Q₈	—	7	1	no	—
178	C₇×D₄	—	7	2	no	—
179	C₇×D₄	—	7	2	no	—
180	C₇×D₄	—	7	1	no	—
181	C₇×D₄	—	7	1	no	—
182	C₂×C₄×C₇	—	6	1	no	—
183	C₂×C₄×C₇	—	7	2	no	—
184	C₂×C₄×C₇	—	7	2	no	—
185	C₂×C₄×C₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
186	C₂×C₄×C₇	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
187	C₂²⋊D₇	—	7	4	no	—
188	C₂²⋊D₇	—	7	4	no	—
189	C₂²⋊D₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
190	C₂²⋊D₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
191	D₂₈	—	7	4	no	—
192	D₂₈	—	7	4	no	—
193	D₂₈	—	7	2	no	—
194	D₂₈	—	7	2	no	—
195	D₂₈	—	7	2	no	—
196	D₂₈	—	7	2	no	—
197	D₂₈	—	42	2	no	—
198	D₂₈	—	42	2	no	—
199	D₂₈	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
200	D₂₈	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
201	C₄×D₇	—	7	4	no	—
202	C₄×D₇	—	7	4	no	—
203	C₄×D₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
204	C₄×D₇	C₂×AGL(1,𝔽₇)	1	2	yes	complemented
205	Dic₁₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
206	Dic₁₄	C₂×AGL(1,𝔽₇)	1	1	yes	characteristic, complemented
207	C₇²	C₃×H(5,𝔽₂)	1	1	yes	characteristic, complemented, Sylow
208	C₃×#41	—	49	1	no	—
209	C₃×#41	—	49	2	no	—
210	C₃×#41	—	49	2	no	—
211	C₃×#41	—	98	1	no	—
212	C₂×C₃×D₄	—	49	2	no	—
213	C₂×C₃×D₄	—	49	4	no	—
214	C₂×C₃×D₄	—	49	1	no	—
215	C₂×C₃×D₄	—	49	2	no	—
216	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
217	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
218	C₂×ΓL(1,𝔽₈)	—	14	1	no	—
219	C₂×ΓL(1,𝔽₈)	—	14	2	no	—
220	C₂×ΓL(1,𝔽₈)	—	28	1	no	—
221	C₂×ΓL(1,𝔽₈)	—	28	1	no	—
222	AGL(1,𝔽₇)	—	14	4	no	—
223	AGL(1,𝔽₇)	—	14	4	no	—
224	AGL(1,𝔽₇)	—	28	2	no	—
225	AGL(1,𝔽₇)	—	28	2	no	—
226	H(5,𝔽₂)	—	49	1	no	Sylow
227	C₂²×C₇	—	6	1	no	—
228	C₂²×C₇	—	7	2	no	—
229	C₂²×C₇	—	7	2	no	—
230	C₂²×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
231	C₂²×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
232	C₂×D₇	—	7	4	no	—
233	C₂×D₇	—	7	4	no	—
234	C₂×D₇	—	28	4	no	—
235	C₂×D₇	—	28	4	no	—
236	C₂×D₇	—	28	2	no	—
237	C₂×D₇	—	28	2	no	—
238	C₂×D₇	—	42	4	no	—
239	C₂×D₇	—	84	2	no	—
240	C₂×D₇	—	84	2	no	—
241	C₂×D₇	C₂²×AGL(1,𝔽₇)	1	2	yes	—
242	C₂×D₇	C₂²×AGL(1,𝔽₇)	1	2	yes	—
243	C₄×C₇	—	6	1	no	—
244	C₄×C₇	—	6	1	no	—
245	C₄×C₇	—	7	2	no	—
246	C₄×C₇	—	7	2	no	—
247	C₄×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
248	C₄×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
249	C₄×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
250	C₄×C₇	C₂²×AGL(1,𝔽₇)	1	1	yes	characteristic
251	Dic₇	C₂²×AGL(1,𝔽₇)	1	2	yes	—
252	Dic₇	C₂²×AGL(1,𝔽₇)	1	2	yes	—
253	C₂³×C₃	—	49	4	no	—
254	C₂³×C₃	—	49	2	no	—
255	C₃×Q₈	—	49	1	no	—
256	C₃×Q₈	—	98	1	no	—
257	C₃×D₄	—	49	2	no	—
258	C₃×D₄	—	49	1	no	—
259	C₃×D₄	—	49	4	no	—
260	C₃×D₄	—	49	2	no	—
261	C₃×D₄	—	49	2	no	—
262	C₃×D₄	—	49	4	no	—
263	C₃×D₄	—	98	1	no	—
264	C₃×D₄	—	98	2	no	—
265	C₂×C₃×C₄	—	49	2	no	—
266	C₂×C₃×C₄	—	49	4	no	—
267	C₂×C₃×C₄	—	98	2	no	—
268	C₂×C₃×C₄	—	98	1	no	—
269	ΓL(1,𝔽₈)	—	14	1	no	—
270	ΓL(1,𝔽₈)	—	14	1	no	—
271	#41	—	7	1	no	—
272	#41	—	7	1	no	—
273	#41	—	49	2	no	—
274	#41	—	49	2	no	—
275	C₂×D₄	—	49	2	no	—
276	C₂×D₄	—	49	2	no	—
277	C₂×D₄	—	49	4	no	—
278	C₂×D₄	—	49	1	no	—
279	C₂×C₇	—	2	1	no	—
280	C₂×C₇	—	2	1	no	—
281	C₂×C₇	—	6	1	no	—
282	C₂×C₇	—	6	1	no	—
283	C₂×C₇	—	6	1	no	—
284	C₂×C₇	—	14	2	no	—
285	C₂×C₇	—	14	2	no	—
286	C₂×C₇	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
287	C₂×C₇	C₂³×AGL(1,𝔽₇)	1	1	yes	characteristic
288	D₇	—	2	2	no	—
289	D₇	—	2	2	no	—
290	D₇	—	14	4	no	—
291	D₇	—	14	4	no	—
292	D₇	—	84	4	no	—
293	C₂²×C₃	—	49	2	no	—
294	C₂²×C₃	—	49	4	no	—
295	C₂²×C₃	—	98	2	no	—
296	C₂²×C₃	—	98	1	no	—
297	C₂²×C₃	—	196	2	no	—
298	C₂²×C₃	—	196	4	no	—
299	C₃×C₄	—	49	2	no	—
300	C₃×C₄	—	98	2	no	—
301	C₃×C₄	—	98	1	no	—
302	C₃×C₄	—	98	1	no	—
303	C₂³	—	49	4	no	—
304	C₂³	—	49	2	no	—
305	Q₈	—	7	1	no	—
306	Q₈	—	7	1	no	—
307	D₄	—	7	2	no	—
308	D₄	—	7	2	no	—
309	D₄	—	7	1	no	—
310	D₄	—	7	1	no	—
311	D₄	—	49	4	no	—
312	D₄	—	49	4	no	—
313	D₄	—	49	2	no	—
314	D₄	—	49	2	no	—
315	C₂×C₄	—	7	2	no	—
316	C₂×C₄	—	7	2	no	—
317	C₂×C₄	—	49	4	no	—
318	C₂×C₄	#64422⋊C₂	1	1	yes	characteristic, complemented
319	C₇	—	6	1	no	—
320	C₇	#10621518	1	1	yes	characteristic, complemented
321	C₇	#10621518	1	1	yes	characteristic, complemented
322	C₂×C₃	—	98	2	no	—
323	C₂×C₃	—	98	4	no	—
324	C₂×C₃	—	98	1	no	—
325	C₂×C₃	—	196	1	no	—
326	C₂×C₃	—	196	2	no	—
327	C₂²	—	7	2	no	—
328	C₂²	—	7	2	no	—
329	C₂²	—	49	4	no	—
330	C₂²	—	196	2	no	—
331	C₂²	—	196	4	no	—
332	C₂²	C₂×#64422⋊C₂	1	1	yes	characteristic
333	C₄	—	7	2	no	—
334	C₄	—	7	2	no	—
335	C₄	C₂×#64422⋊C₂	1	1	yes	characteristic
336	C₄	C₂×#64422⋊C₂	1	1	yes	characteristic
337	C₃	—	98	1	no	Sylow
338	C₂	—	2	1	no	—
339	C₂	—	14	2	no	—
340	C₂	—	14	2	no	—
341	C₂	—	98	4	no	—
342	C₂	C₂²×#64422⋊C₂	1	1	yes	characteristic

	subgroup	G/H
center, Frattini	C₂	C₂²×#64422⋊C₂
commutator, socle, cosocle	C₂×C₇²	C₂⁴×C₃
Fitting	C₂×C₄×C₇²	C₂²×C₃
hypercenter	C₂×C₄	#64422⋊C₂
hypocenter	C₇²	C₃×H(5,𝔽₂)
LCS	G ▷ C₂×C₇² ▷ C₇²
UCS	C₁ ◁ C₂ ◁ C₂×C₄

Complements

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

N	H ≅ G/N	type
1. #72246012	C₂	semidirect
2. #72246012	C₂	semidirect
3. #72246009	C₂	semidirect
4. #72246009	C₂	semidirect
5. #72245079	C₂	semidirect
6. #72245079	C₂	semidirect
7. C₂×C₄⋊#64425	C₂	semidirect
8. #72222022	C₂	semidirect
9. #13096690	C₃	semidirect
10. C₂²×#64425	C₂²	semidirect
11. C₂×#64422⋊C₂	C₂²	semidirect
12. C₂×C₄×#3862	C₂²	semidirect
13. C₄⋊#64425	C₂²	semidirect
14. C₄⋊#64425	C₂²	semidirect
15. #11924212	C₂²	semidirect
16. #11924212	C₂²	semidirect
17. C₄⋊#64422	C₂²	semidirect
18. C₄⋊#64422	C₂²	semidirect
19. C₄×#64422	C₂²	semidirect
20. C₄×#64422	C₂²	semidirect
21. #11924208	C₂²	semidirect
22. #11924208	C₂²	semidirect
23. #11924181	C₂²	semidirect
24. #11924181	C₂²	semidirect
25. #11924179	C₂²	semidirect
26. C₂×C₄⋊(C₇⋊D₇)	C₂×C₃	semidirect
27. C₇×#1157	C₂×C₃	semidirect
28. C₇×#1157	C₂×C₃	semidirect
29. #11716115	C₂×C₃	semidirect
30. D₇×D₂₈	C₂×C₃	semidirect
31. D₇×D₂₈	C₂×C₃	semidirect
32. #11716103	C₂×C₃	semidirect
33. #11716103	C₂×C₃	semidirect
46. C₂²×C₇⋊D₇	C₂²×C₃	semidirect
47. C₂×D₇²	C₂²×C₃	semidirect
48. C₂×C₄×C₇²	C₂²×C₃	semidirect
49. C₄⋊(C₇⋊D₇)	C₂²×C₃	semidirect
50. C₄⋊(C₇⋊D₇)	C₂²×C₃	semidirect
51. C₇×C₂²⋊D₇	C₂²×C₃	semidirect
52. C₇×C₂²⋊D₇	C₂²×C₃	semidirect
53. C₇×D₂₈	C₂²×C₃	semidirect
54. C₇×D₂₈	C₂²×C₃	semidirect
55. C₄×C₇×D₇	C₂²×C₃	semidirect
56. C₄×C₇×D₇	C₂²×C₃	semidirect
57. C₇×Dic₁₄	C₂²×C₃	semidirect
58. C₇×Dic₁₄	C₂²×C₃	semidirect
59. #87641	C₂²×C₃	semidirect
60. #87641	C₂²×C₃	semidirect
61. #87639	C₂²×C₃	semidirect
127. #3862	H(5,𝔽₂)	semidirect
138. #1157	AGL(1,𝔽₇)	semidirect
139. #1157	AGL(1,𝔽₇)	semidirect
185. C₂×C₄×C₇	C₂×AGL(1,𝔽₇)	semidirect
186. C₂×C₄×C₇	C₂×AGL(1,𝔽₇)	semidirect
189. C₂²⋊D₇	C₂×AGL(1,𝔽₇)	semidirect
190. C₂²⋊D₇	C₂×AGL(1,𝔽₇)	semidirect
199. D₂₈	C₂×AGL(1,𝔽₇)	semidirect
200. D₂₈	C₂×AGL(1,𝔽₇)	semidirect
203. C₄×D₇	C₂×AGL(1,𝔽₇)	semidirect
204. C₄×D₇	C₂×AGL(1,𝔽₇)	semidirect
205. Dic₁₄	C₂×AGL(1,𝔽₇)	semidirect
206. Dic₁₄	C₂×AGL(1,𝔽₇)	semidirect
207. C₇²	C₃×H(5,𝔽₂)	semidirect
318. C₂×C₄	#64422⋊C₂	semidirect
320. C₇	#10621518	semidirect
321. C₇	#10621518	semidirect

Maximal subgroups

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

subgroup	index
#72246012	2
#72246009	2
#72245079	2
C₂×C₄⋊#64425	2
#72222022	2
#13096690	3
#10621518	7