Group #34207134 — subgroups

Subgroups — #34207134

Order 20224.

650 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 650 conjugacy classes of subgroups — too many to draw. Only its 105 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₂×#19098999	C₂	1	2	yes	maximal, complemented
2	C₂×#19098376	C₂	1	2	yes	maximal, complemented
3	#23764288	C₂	1	1	yes	maximal, characteristic, complemented
4	#23761482	C₂	1	1	yes	maximal, characteristic, complemented
5	C₂×#493×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
6	C₂×#14579183	C₂²	1	1	yes	characteristic
7	#19098999	—	2	4	no	—
8	#19098999	—	2	4	no	—
9	C₂×#14579105	—	2	2	no	—
10	C₂×#14579102	—	2	2	no	—
11	C₂×#14579101	C₂²	1	2	yes	—
12	C₂×#14579097	C₂²	1	1	yes	characteristic
13	C₂×#14579089	—	2	1	no	—
14	#19098529	—	2	1	no	—
15	#19098376	—	2	4	no	—
16	C₂²×D₈×C₇₉	—	2	1	no	—
17	C₂²×D₈×C₇₉	C₂²	1	2	yes	—
18	C₂×#127×C₇₉	—	2	1	no	—
19	#493×C₇₉	—	2	4	no	—
20	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
21	C₂×#11929624	—	2	1	no	—
22	#14579183	—	2	2	no	—
23	#14579183	—	2	2	no	—
24	C₂×Dic₃₁₆	D₄	1	1	yes	characteristic, complemented
25	C₂×#11929613	—	2	1	no	—
26	C₂×D₆₃₂	D₄	1	1	yes	characteristic, complemented
27	C₂×#11929608	—	2	1	no	—
28	#14579105	—	2	8	no	—
29	#14579102	—	2	8	no	—
30	#14579101	—	2	2	no	—
31	#14579101	D₄	1	4	yes	complemented
32	C₂×C₇₉⋊C₁₆	—	2	2	no	—
33	#14579097	—	2	2	no	—
34	#14579089	—	4	2	no	—
35	(C₂×D₇₉)⋊C₈	—	4	2	no	—
36	C₂²×D₄×C₇₉	—	2	2	no	—
37	C₂²×D₄×C₇₉	—	4	2	no	—
38	C₂×D₈×C₇₉	—	2	4	no	—
39	C₂×D₈×C₇₉	—	2	2	no	—
40	C₂×D₈×C₇₉	—	2	2	no	—
41	C₂×D₈×C₇₉	—	2	2	no	—
42	C₂×D₈×C₇₉	—	2	2	no	—
43	C₂×D₈×C₇₉	—	2	2	no	—
44	C₂×D₈×C₇₉	—	4	2	no	—
45	C₂×D₈×C₇₉	—	4	2	no	—
46	C₂×D₈×C₇₉	D₄	1	4	yes	—
47	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
48	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
49	#127×C₇₉	—	2	4	no	—
50	#127×C₇₉	—	4	2	no	—
51	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
52	C₄×C₈×C₇₉	—	2	2	no	—
53	#11929624	—	4	1	no	—
54	#11929624	—	4	1	no	—
55	#11929624	—	4	1	no	—
56	#11929624	—	4	1	no	—
57	C₂×Dic₁₅₈	—	2	1	no	—
58	C₂×D₃₁₆	—	2	1	no	—
59	C₂×C₂²⋊D₇₉	—	4	1	no	—
60	C₂×C₄×D₇₉	—	4	1	no	—
61	Dic₃₁₆	—	2	2	no	—
62	#11929613	—	4	2	no	—
63	D₆₃₂	—	2	2	no	—
64	#11929608	—	4	1	no	—
65	#11929608	—	4	1	no	—
66	C₂×C₇₉⋊C₈	—	4	1	no	—
67	C₇₉⋊C₁₆	—	2	4	no	—
68	C₂⁴×C₇₉	—	4	2	no	—
69	C₂×D₄×C₇₉	—	2	4	no	—
70	C₂×D₄×C₇₉	—	4	8	no	—
71	C₂×D₄×C₇₉	—	4	2	no	—
72	C₂×D₄×C₇₉	—	4	2	no	—
73	C₂×D₄×C₇₉	—	4	2	no	—
74	C₂×D₄×C₇₉	—	4	2	no	—
75	C₂×D₄×C₇₉	—	4	2	no	—
76	C₂×D₄×C₇₉	—	8	8	no	—
77	C₂²×C₄×C₇₉	—	2	1	no	—
78	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
79	D₈×C₇₉	—	2	4	no	—
80	D₈×C₇₉	—	2	4	no	—
81	D₈×C₇₉	—	4	8	no	—
82	D₈×C₇₉	—	4	2	no	—
83	D₈×C₇₉	—	4	2	no	—
84	C₂×C₈×C₇₉	—	2	1	no	—
85	C₂×C₈×C₇₉	—	2	1	no	—
86	C₂×C₈×C₇₉	D₈	1	2	yes	—
87	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
88	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
89	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
90	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
91	C₄²×C₇₉	—	2	1	no	—
92	C₄²×C₇₉	D₈	1	2	yes	—
93	C₂³×C₇₉	—	4	4	no	—
94	C₂³×C₇₉	—	8	8	no	—
95	C₂³×C₇₉	—	8	2	no	—
96	C₂³×C₇₉	—	8	2	no	—
97	C₂³×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
98	C₂²×D₇₉	—	4	1	no	—
99	D₄×C₇₉	—	4	4	no	—
100	D₄×C₇₉	—	4	4	no	—
101	D₄×C₇₉	—	8	16	no	—
102	D₄×C₇₉	—	8	2	no	—
103	D₄×C₇₉	—	8	2	no	—
104	C₂×C₄×C₇₉	—	2	4	no	—
105	C₂×C₄×C₇₉	—	2	2	no	—
106	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
107	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
108	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
109	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
110	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
111	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
112	C₂²⋊D₇₉	—	8	1	no	—
113	C₂²⋊D₇₉	—	8	1	no	—
114	C₂×Dic₇₉	—	4	1	no	—
115	D₃₁₆	—	4	1	no	—
116	D₃₁₆	—	4	1	no	—
117	C₄×D₇₉	—	8	1	no	—
118	C₄×D₇₉	—	8	1	no	—
119	Dic₁₅₈	—	4	1	no	—
120	Dic₁₅₈	—	4	1	no	—
121	C₈×C₇₉	—	2	2	no	—
122	C₈×C₇₉	#120	1	2	yes	—
123	C₈×C₇₉	#121	1	2	yes	—
124	C₇₉⋊C₈	—	8	1	no	—
125	C₂²×C₇₉	—	2	2	no	—
126	C₂²×C₇₉	—	8	8	no	—
127	C₂²×C₇₉	—	8	4	no	—
128	C₂²×C₇₉	—	16	4	no	—
129	C₂²×C₇₉	—	16	4	no	—
130	C₂²×C₇₉	#447	1	1	yes	characteristic
131	C₂²×C₇₉	#459	1	1	yes	characteristic
132	C₂²×C₇₉	#496	1	1	yes	characteristic
133	C₂×D₇₉	—	8	2	no	—
134	C₂×D₇₉	—	8	1	no	—
135	C₄×C₇₉	—	2	4	no	—
136	C₄×C₇₉	#392	1	1	yes	characteristic
137	C₄×C₇₉	#447	1	1	yes	characteristic
138	C₄×C₇₉	#459	1	1	yes	characteristic
139	C₄×C₇₉	#493	1	1	yes	characteristic
140	Dic₇₉	—	8	1	no	—
141	#13331	—	79	1	no	maximal, Sylow
142	C₂×C₇₉	—	2	1	no	—
143	C₂×C₇₉	—	2	1	no	—
144	C₂×C₇₉	—	16	4	no	—
145	C₂×C₇₉	#2011	1	1	yes	characteristic
146	C₂×C₇₉	#2213	1	2	yes	—
147	D₇₉	—	16	1	no	—
148	C₂×#509	—	79	2	no	—
149	C₂×#493	D₇₉	1	1	yes	characteristic, complemented
150	C₂×#361	—	79	2	no	—
151	#1974	—	79	1	no	—
152	#1376	—	79	1	no	—
153	C₇₉	#13331	1	1	yes	characteristic, complemented, Sylow
154	C₂×#135	—	79	1	no	—
155	C₂²×D₈	—	2	1	no	—
156	C₂²×D₈	C₂×D₇₉	1	2	yes	—
157	C₂×#127	—	2	1	no	—
158	#509	—	158	4	no	—
159	#509	—	158	4	no	—
160	C₂×SD₃₂	—	158	2	no	—
161	C₂×D₁₆	—	158	2	no	—
162	C₂×M₃₂	—	79	2	no	—
163	#493	—	2	4	no	—
164	C₂×#108	—	79	1	no	—
165	C₂×#104	—	158	1	no	—
166	#408	—	158	1	no	—
167	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
168	#361	—	158	4	no	—
169	C₂×#41	—	158	1	no	—
170	C₂²×D₄	—	2	2	no	—
171	C₂²×D₄	—	4	2	no	—
172	#135	—	158	2	no	—
173	#135	—	158	2	no	—
174	C₂×Q₁₆	—	79	1	no	—
175	C₂×SD₁₆	—	158	1	no	—
176	C₂×D₈	—	2	4	no	—
177	C₂×D₈	—	2	2	no	—
178	C₂×D₈	—	2	2	no	—
179	C₂×D₈	—	2	2	no	—
180	C₂×D₈	—	2	2	no	—
181	C₂×D₈	—	2	2	no	—
182	C₂×D₈	—	4	2	no	—
183	C₂×D₈	—	4	2	no	—
184	C₂×D₈	—	79	1	no	—
185	C₂×D₈	C₂²⋊D₇₉	1	4	yes	—
186	C₂×M₁₆	—	158	1	no	—
187	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
188	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
189	#127	—	2	4	no	—
190	#127	—	4	2	no	—
191	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
192	SD₃₂	—	158	8	no	—
193	D₁₆	—	158	8	no	—
194	M₃₂	—	79	4	no	—
195	M₃₂	—	158	2	no	—
196	C₂×C₁₆	—	158	2	no	—
197	#108	—	158	2	no	—
198	#104	—	316	2	no	—
199	C₂²⋊C₈	—	316	2	no	—
200	C₄×C₈	—	2	2	no	—
201	C₂⁴	—	4	2	no	—
202	#41	—	316	1	no	—
203	#41	—	316	1	no	—
204	#41	—	316	1	no	—
205	#41	—	316	1	no	—
206	C₂×Q₈	—	158	1	no	—
207	C₂×D₄	—	2	4	no	—
208	C₂×D₄	—	4	8	no	—
209	C₂×D₄	—	4	2	no	—
210	C₂×D₄	—	4	2	no	—
211	C₂×D₄	—	4	2	no	—
212	C₂×D₄	—	4	2	no	—
213	C₂×D₄	—	4	2	no	—
214	C₂×D₄	—	8	8	no	—
215	C₂×D₄	—	316	1	no	—
216	C₂×D₄	—	158	1	no	—
217	C₂²×C₄	—	2	1	no	—
218	C₂²×C₄	—	316	1	no	—
219	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
220	Q₁₆	—	158	2	no	—
221	SD₁₆	—	316	2	no	—
222	D₈	—	2	4	no	—
223	D₈	—	2	4	no	—
224	D₈	—	4	8	no	—
225	D₈	—	4	2	no	—
226	D₈	—	4	2	no	—
227	D₈	—	158	2	no	—
228	M₁₆	—	316	1	no	—
229	M₁₆	—	316	1	no	—
230	C₂×C₈	—	2	1	no	—
231	C₂×C₈	—	2	1	no	—
232	C₂×C₈	—	316	1	no	—
233	C₂×C₈	#11929609	1	2	yes	—
234	C₂×C₈	D₄×D₇₉	1	1	yes	characteristic
235	C₂×C₈	D₄×D₇₉	1	2	yes	—
236	C₂×C₈	C₂×C₂²⋊D₇₉	1	2	yes	—
237	C₂×C₈	#11929623	1	1	yes	characteristic
238	C₄²	—	2	1	no	—
239	C₄²	#11929609	1	2	yes	—
240	C₁₆	—	158	4	no	—
241	C₂³	—	4	4	no	—
242	C₂³	—	8	8	no	—
243	C₂³	—	8	2	no	—
244	C₂³	—	8	2	no	—
245	C₂³	—	316	1	no	—
246	C₂³	#14579187	1	1	yes	characteristic
247	Q₈	—	316	1	no	—
248	Q₈	—	316	1	no	—
249	D₄	—	4	4	no	—
250	D₄	—	4	4	no	—
251	D₄	—	8	16	no	—
252	D₄	—	8	2	no	—
253	D₄	—	8	2	no	—
254	D₄	—	316	1	no	—
255	D₄	—	316	1	no	—
256	D₄	—	632	1	no	—
257	D₄	—	632	1	no	—
258	C₂×C₄	—	2	4	no	—
259	C₂×C₄	—	2	2	no	—
260	C₂×C₄	—	316	1	no	—
261	C₂×C₄	—	632	1	no	—
262	C₂×C₄	—	632	1	no	—
263	C₂×C₄	#14579130	1	1	yes	characteristic
264	C₂×C₄	#14579132	1	1	yes	characteristic
265	C₂×C₄	#14579157	1	1	yes	characteristic
266	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
267	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
268	C₂×C₄	#14579187	1	1	yes	characteristic
269	C₈	—	2	2	no	—
270	C₈	—	632	1	no	—
271	C₈	#14579129	1	2	yes	—
272	C₈	#14579133	1	2	yes	—
273	C₂²	—	2	2	no	—
274	C₂²	—	8	8	no	—
275	C₂²	—	8	4	no	—
276	C₂²	—	16	4	no	—
277	C₂²	—	16	4	no	—
278	C₂²	—	632	2	no	—
279	C₂²	—	632	1	no	—
280	C₂²	#19098697	1	1	yes	characteristic
281	C₂²	#19098755	1	1	yes	characteristic
282	C₂²	#19098950	1	1	yes	characteristic
283	C₄	—	2	4	no	—
284	C₄	—	632	1	no	—
285	C₄	#19098471	1	1	yes	characteristic
286	C₄	#19098697	1	1	yes	characteristic
287	C₄	#19098755	1	1	yes	characteristic
288	C₄	#19098939	1	1	yes	characteristic
289	C₂	—	2	1	no	—
290	C₂	—	2	1	no	—
291	C₂	—	16	4	no	—
292	C₂	—	1264	1	no	—
293	C₂	#23764471	1	1	yes	characteristic
294	C₂	#23765473	1	2	yes	—

subgroup

G/H

class size

multiplicity

normal?

properties

C₂×#19098999

C₂

yes

maximal, complemented

C₂×#19098376

C₂

yes

maximal, complemented

#23764288

C₂

yes

maximal, characteristic, complemented

#23761482

C₂

yes

maximal, characteristic, complemented

C₂×#493×C₇₉

C₂

yes

maximal, characteristic, complemented

C₂×#14579183

C₂²

yes

—

—

—

—

C₂²

yes

—

C₂×#14579097

C₂²

yes

—

—

—

C₂²×D₈×C₇₉

—

C₂²×D₈×C₇₉

C₂²

yes

—

C₂×#127×C₇₉

—

#493×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

—

—

—

C₂×Dic₃₁₆

D₄

yes

characteristic, complemented

C₂×#11929613

—

C₂×D₆₃₂

D₄

yes

characteristic, complemented

—

—

—

—

D₄

yes

complemented

C₂×C₇₉⋊C₁₆

—

#14579097

—

#14579089

—

(C₂×D₇₉)⋊C₈

—

C₂²×D₄×C₇₉

—

C₂²×D₄×C₇₉

—

C₂×D₈×C₇₉

—

C₂×D₈×C₇₉

—

C₂×D₈×C₇₉

—

C₂×D₈×C₇₉

—

C₂×D₈×C₇₉

—

C₂×D₈×C₇₉

—

C₂×D₈×C₇₉

—

C₂×D₈×C₇₉

—

C₂×D₈×C₇₉

D₄

yes

—

C₂²×C₈×C₇₉

D₄

yes

characteristic

C₂²×C₈×C₇₉

C₂³

yes

characteristic

#127×C₇₉

—

#127×C₇₉

—

C₂×C₄²×C₇₉

D₄

yes

characteristic

C₄×C₈×C₇₉

—

—

—

—

—

C₂×Dic₁₅₈

—

C₂×D₃₁₆

—

C₂×C₂²⋊D₇₉

—

C₂×C₄×D₇₉

—

Dic₃₁₆

—

#11929613

—

D₆₃₂

—

#11929608

—

#11929608

—

C₂×C₇₉⋊C₈

—

C₇₉⋊C₁₆

—

C₂⁴×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂×D₄×C₇₉

—

C₂²×C₄×C₇₉

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

D₈×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

D₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

—

C₂×C₈×C₇₉

D₈

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

C₂×D₄

yes

characteristic

C₂×C₈×C₇₉

C₂×D₄

yes

—

C₂×C₈×C₇₉

#41

yes

characteristic

C₄²×C₇₉

—

C₄²×C₇₉

D₈

yes

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

AGL(1,ℤ/8)

yes

characteristic

C₂²×D₇₉

—

D₄×C₇₉

—

100

D₄×C₇₉

—

101

D₄×C₇₉

—

102

D₄×C₇₉

—

103

D₄×C₇₉

—

104

C₂×C₄×C₇₉

—

105

C₂×C₄×C₇₉

—

106

C₂×C₄×C₇₉

#120

yes

characteristic

107

C₂×C₄×C₇₉

#121

yes

characteristic

108

C₂×C₄×C₇₉

#127

yes

characteristic

109

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

110

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

111

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

characteristic

112

C₂²⋊D₇₉

—

113

C₂²⋊D₇₉

—

114

C₂×Dic₇₉

—

115

D₃₁₆

—

116

D₃₁₆

—

117

C₄×D₇₉

—

118

C₄×D₇₉

—

119

Dic₁₅₈

—

120

Dic₁₅₈

—

121

C₈×C₇₉

—

122

C₈×C₇₉

#120

yes

—

123

C₈×C₇₉

#121

yes

—

124

C₇₉⋊C₈

—

125

C₂²×C₇₉

—

126

C₂²×C₇₉

—

127

C₂²×C₇₉

—

128

C₂²×C₇₉

—

129

C₂²×C₇₉

—

130

C₂²×C₇₉

#447

yes

characteristic

131

C₂²×C₇₉

#459

yes

characteristic

132

C₂²×C₇₉

#496

yes

characteristic

133

C₂×D₇₉

—

134

C₂×D₇₉

—

135

C₄×C₇₉

—

136

C₄×C₇₉

#392

yes

characteristic

137

C₄×C₇₉

#447

yes

characteristic

138

C₄×C₇₉

#459

yes

characteristic

139

C₄×C₇₉

#493

yes

characteristic

140

Dic₇₉

—

141

#13331

—

maximal, Sylow

142

C₂×C₇₉

—

143

C₂×C₇₉

—

144

C₂×C₇₉

—

145

C₂×C₇₉

#2011

yes

characteristic

146

C₂×C₇₉

#2213

yes

—

147

D₇₉

—

148

C₂×#509

—

149

C₂×#493

D₇₉

yes

characteristic, complemented

150

C₂×#361

—

151

#1974

—

152

#1376

—

153

C₇₉

#13331

yes

characteristic, complemented, Sylow

154

C₂×#135

—

155

C₂²×D₈

—

156

C₂²×D₈

C₂×D₇₉

yes

—

157

C₂×#127

—

158

#509

—

158

—

159

#509

—

158

—

160

C₂×SD₃₂

—

158

—

161

C₂×D₁₆

—

158

—

162

C₂×M₃₂

—

163

#493

—

164

C₂×#108

—

165

C₂×#104

—

158

—

166

#408

—

158

—

167

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

168

#361

—

158

—

169

C₂×#41

—

158

—

170

C₂²×D₄

—

171

C₂²×D₄

—

172

#135

—

158

—

173

#135

—

158

—

174

C₂×Q₁₆

—

175

C₂×SD₁₆

—

158

—

176

C₂×D₈

—

177

C₂×D₈

—

178

C₂×D₈

—

179

C₂×D₈

—

180

C₂×D₈

—

181

C₂×D₈

—

182

C₂×D₈

—

183

C₂×D₈

—

184

C₂×D₈

—

185

C₂×D₈

C₂²⋊D₇₉

yes

—

186

C₂×M₁₆

—

158

—

187

C₂²×C₈

C₂²⋊D₇₉

yes

characteristic

188

C₂²×C₈

C₂²×D₇₉

yes

characteristic

189

#127

—

190

#127

—

191

C₂×C₄²

C₂²⋊D₇₉

yes

characteristic

192

SD₃₂

—

158

—

193

D₁₆

—

158

—

194

M₃₂

—

195

M₃₂

—

158

—

196

C₂×C₁₆

—

158

—

197

#108

—

158

—

198

#104

—

316

—

199

C₂²⋊C₈

—

316

—

200

C₄×C₈

—

201

C₂⁴

—

202

#41

—

316

—

203

#41

—

316

—

204

#41

—

316

—

205

#41

—

316

—

206

C₂×Q₈

—

158

—

207

C₂×D₄

—

208

C₂×D₄

—

209

C₂×D₄

—

210

C₂×D₄

—

211

C₂×D₄

—

212

C₂×D₄

—

213

C₂×D₄

—

214

C₂×D₄

—

215

C₂×D₄

—

316

—

216

C₂×D₄

—

158

—

217

C₂²×C₄

—

218

C₂²×C₄

—

316

—

219

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

220

Q₁₆

—

158

—

221

SD₁₆

—

316

—

222

D₈

—

223

D₈

—

224

D₈

—

225

D₈

—

226

D₈

—

227

D₈

—

158

—

228

M₁₆

—

316

—

229

M₁₆

—

316

—

230

C₂×C₈

—

231

C₂×C₈

—

232

C₂×C₈

—

316

—

233

C₂×C₈

#11929609

yes

—

234

C₂×C₈

D₄×D₇₉

yes

characteristic

235

C₂×C₈

D₄×D₇₉

yes

—

236

C₂×C₈

C₂×C₂²⋊D₇₉

yes

—

237

C₂×C₈

#11929623

yes

characteristic

238

C₄²

—

239

C₄²

#11929609

yes

—

240

C₁₆

—

158

—

241

C₂³

—

242

C₂³

—

243

C₂³

—

244

C₂³

—

245

C₂³

—

316

—

246

C₂³

#14579187

yes

characteristic

247

Q₈

—

316

—

248

Q₈

—

316

—

249

D₄

—

250

D₄

—

251

D₄

—

252

D₄

—

253

D₄

—

254

D₄

—

316

—

255

D₄

—

316

—

256

D₄

—

632

—

257

D₄

—

632

—

258

C₂×C₄

—

259

C₂×C₄

—

260

C₂×C₄

—

316

—

261

C₂×C₄

—

632

—

262

C₂×C₄

—

632

—

263

C₂×C₄

#14579130

yes

characteristic

264

C₂×C₄

#14579132

yes

characteristic

265

C₂×C₄

#14579157

yes

characteristic

266

C₂×C₄

C₂×#11929609

yes

characteristic

267

C₂×C₄

C₂×#11929609

yes

characteristic

268

C₂×C₄

#14579187

yes

characteristic

269

C₈

—

270

C₈

—

632

—

271

C₈

#14579129

yes

—

272

C₈

#14579133

yes

—

273

C₂²

—

274

C₂²

—

275

C₂²

—

276

C₂²

—

277

C₂²

—

278

C₂²

—

632

—

279

C₂²

—

632

—

280

C₂²

#19098697

yes

characteristic

281

C₂²

#19098755

yes

characteristic

282

C₂²

#19098950

yes

characteristic

283

C₄

—

284

C₄

—

632

—

285

C₄

#19098471

yes

characteristic

286

C₄

#19098697

yes

characteristic

287

C₄

#19098755

yes

characteristic

288

C₄

#19098939

yes

characteristic

289

C₂

—

290

C₂

—

291

C₂

—

292

C₂

—

1264

—

293

C₂

#23764471

yes

characteristic

294

C₂

#23765473

yes

—

	subgroup	G/H
center	C₂²	#19098755
commutator, cosocle	C₂²×C₈×C₇₉	C₂³
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₂×#493×C₇₉	C₂
socle	C₂²×C₇₉	#459
hypercenter	C₂×#493	D₇₉
hypocenter	C₇₉	#13331
LCS	G ▷ C₂²×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#493

subgroup

G/H

center

C₂²

#19098755

commutator, cosocle

C₂²×C₈×C₇₉

C₂³

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₂×#493×C₇₉

C₂

C₂²×C₇₉

D₇₉

C₇₉

G ▷ C₂²×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉

UCS

C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×C₄×C₈ ◁ C₂×#493

N	H ≅ G/N	type
1. C₂×#19098999	C₂	semidirect
2. C₂×#19098376	C₂	semidirect
3. #23764288	C₂	semidirect
4. #23761482	C₂	semidirect
5. C₂×#493×C₇₉	C₂	semidirect
24. C₂×Dic₃₁₆	D₄	semidirect
26. C₂×D₆₃₂	D₄	semidirect
31. #14579101	D₄	semidirect
149. C₂×#493	D₇₉	semidirect
153. C₇₉	#13331	semidirect

H ≅ G/N

type

1. C₂×#19098999

C₂

semidirect

2. C₂×#19098376

C₂

semidirect

3. #23764288

C₂

semidirect

4. #23761482

C₂

semidirect

5. C₂×#493×C₇₉

C₂

semidirect

24. C₂×Dic₃₁₆

D₄

semidirect

26. C₂×D₆₃₂

D₄

semidirect

31. #14579101

D₄

semidirect

149. C₂×#493

D₇₉

semidirect

153. C₇₉

#13331

semidirect

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

subgroup	index
C₂×#19098999	2
C₂×#19098376	2
#23764288	2
#23761482	2
C₂×#493×C₇₉	2
#13331	79

subgroup

index

C₂×#493×C₇₉

Subgroups — #34207134

Conjugacy classes of subgroups

Complements

Maximal subgroups