Group #34207111 — subgroups

Subgroups — #34207111

Order 20224.

594 conjugacy classes of subgroups; only the 127 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 127 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	C₂²×#14579105	C₂	1	2	yes	maximal
2	C₂×#19098943	C₂	1	1	yes	maximal, characteristic, complemented
3	C₂×#19098366	C₂	1	2	yes	maximal, complemented
4	#23761478	C₂	1	1	yes	maximal, characteristic, complemented
5	C₇₉×#1970	C₂	1	1	yes	maximal, characteristic
6	C₂²×Dic₃₁₆	—	2	1	no	—
7	C₂²×Dic₃₁₆	C₂²	1	2	yes	—
8	C₂×#14579161	—	2	1	no	—
9	C₂×#14579105	—	2	4	no	—
10	C₂×#14579105	—	2	4	no	—
11	C₂×#14579105	—	2	4	no	—
12	C₂²×C₇₉⋊C₁₆	C₂²	1	2	yes	—
13	#19098943	—	2	4	no	—
14	#19098366	—	2	4	no	—
15	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
16	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
17	C₂×#102×C₇₉	—	2	1	no	—
18	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
19	#390×C₇₉	—	2	1	no	—
20	C₂²×Dic₁₅₈	—	2	2	no	—
21	C₂×Dic₃₁₆	—	2	2	no	—
22	C₂×Dic₃₁₆	—	2	2	no	—
23	C₂×Dic₃₁₆	—	2	2	no	—
24	C₂×Dic₃₁₆	—	2	2	no	—
25	C₂×Dic₃₁₆	—	2	4	no	—
26	C₂×Dic₃₁₆	—	2	2	no	—
27	C₂×Dic₃₁₆	—	4	2	no	—
28	C₂×Dic₃₁₆	—	4	2	no	—
29	C₂×Dic₃₁₆	D₄	1	4	yes	—
30	#14579161	—	2	4	no	—
31	#14579161	—	4	2	no	—
32	C₂×C₄⋊Dic₇₉	—	4	2	no	—
33	#14579105	—	2	16	no	—
34	C₂×C₇₉⋊C₁₆	—	2	2	no	—
35	C₂×C₇₉⋊C₁₆	—	2	2	no	—
36	C₂×C₇₉⋊C₁₆	D₄	1	4	yes	—
37	C₂²×D₄×C₇₉	—	2	1	no	—
38	C₂×D₈×C₇₉	—	2	2	no	—
39	C₂×D₈×C₇₉	—	2	2	no	—
40	C₂×D₈×C₇₉	—	2	1	no	—
41	C₂×D₈×C₇₉	D₄	1	2	yes	—
42	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
43	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
44	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
45	C₂×C₂²⋊C₄×C₇₉	—	4	2	no	—
46	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
47	#107×C₇₉	—	2	2	no	—
48	#102×C₇₉	—	4	2	no	—
49	C₄×C₈×C₇₉	—	2	2	no	—
50	C₂×Dic₁₅₈	—	2	4	no	—
51	C₂×Dic₁₅₈	—	4	2	no	—
52	C₂×Dic₁₅₈	—	4	2	no	—
53	C₂×Dic₁₅₈	—	4	2	no	—
54	C₂×Dic₁₅₈	—	4	2	no	—
55	C₂×Dic₁₅₈	—	4	2	no	—
56	C₂²×Dic₇₉	—	4	2	no	—
57	Dic₃₁₆	—	2	4	no	—
58	Dic₃₁₆	—	2	4	no	—
59	Dic₃₁₆	—	4	8	no	—
60	Dic₃₁₆	—	4	2	no	—
61	Dic₃₁₆	—	4	2	no	—
62	C₄⋊Dic₇₉	—	4	8	no	—
63	C₇₉⋊C₁₆	—	2	4	no	—
64	C₂⁴×C₇₉	—	4	1	no	—
65	C₂×D₄×C₇₉	—	2	2	no	—
66	C₂×D₄×C₇₉	—	4	1	no	—
67	C₂×D₄×C₇₉	—	4	1	no	—
68	C₂×D₄×C₇₉	—	4	1	no	—
69	C₂×D₄×C₇₉	—	4	1	no	—
70	C₂×D₄×C₇₉	—	4	1	no	—
71	C₂²×C₄×C₇₉	—	4	1	no	—
72	C₂²×C₄×C₇₉	D₈	1	2	yes	—
73	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
74	D₈×C₇₉	—	2	4	no	—
75	D₈×C₇₉	—	4	2	no	—
76	C₂×C₈×C₇₉	—	2	1	no	—
77	C₂×C₈×C₇₉	—	2	1	no	—
78	C₂×C₈×C₇₉	D₈	1	2	yes	—
79	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
80	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
81	C₂×C₈×C₇₉	C₂×D₄	1	2	yes	—
82	C₂×C₈×C₇₉	#41	1	1	yes	characteristic
83	C₄⋊C₄×C₇₉	—	4	1	no	—
84	C₄⋊C₄×C₇₉	—	4	1	no	—
85	C₂²⋊C₄×C₇₉	—	8	4	no	—
86	C₄²×C₇₉	—	2	1	no	—
87	C₄²×C₇₉	—	2	1	no	—
88	C₂³×C₇₉	—	4	2	no	—
89	C₂³×C₇₉	—	8	1	no	—
90	C₂³×C₇₉	—	8	1	no	—
91	C₂³×C₇₉	—	8	2	no	—
92	C₂³×C₇₉	—	8	2	no	—
93	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
94	D₄×C₇₉	—	4	2	no	—
95	D₄×C₇₉	—	4	2	no	—
96	D₄×C₇₉	—	8	1	no	—
97	D₄×C₇₉	—	8	1	no	—
98	C₂×C₄×C₇₉	—	2	2	no	—
99	C₂×C₄×C₇₉	—	2	2	no	—
100	C₂×C₄×C₇₉	—	8	1	no	—
101	C₂×C₄×C₇₉	—	8	2	no	—
102	C₂×C₄×C₇₉	SD₃₂	1	4	yes	complemented
103	C₂×C₄×C₇₉	#120	1	1	yes	characteristic
104	C₂×C₄×C₇₉	#121	1	1	yes	characteristic
105	C₂×C₄×C₇₉	#127	1	1	yes	characteristic
106	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
107	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
108	C₂×C₄×C₇₉	AGL(1,ℤ/8)	1	1	yes	characteristic
109	C₂×Dic₇₉	—	4	4	no	—
110	C₂×Dic₇₉	—	8	2	no	—
111	C₂×Dic₇₉	—	8	2	no	—
112	Dic₁₅₈	—	4	4	no	—
113	Dic₁₅₈	—	4	4	no	—
114	Dic₁₅₈	—	8	2	no	—
115	Dic₁₅₈	—	8	2	no	—
116	C₈×C₇₉	—	2	2	no	—
117	C₈×C₇₉	#120	1	2	yes	—
118	C₈×C₇₉	#121	1	2	yes	—
119	C₂²×C₇₉	—	8	4	no	—
120	C₂²×C₇₉	—	8	2	no	—
121	C₂²×C₇₉	—	16	2	no	—
122	C₂²×C₇₉	—	16	1	no	—
123	C₂²×C₇₉	—	16	1	no	—
124	C₂²×C₇₉	#447	1	1	yes	characteristic
125	C₂²×C₇₉	#459	1	1	yes	characteristic
126	C₂²×C₇₉	#493	1	1	yes	characteristic
127	C₂²×C₇₉	C₂×SD₃₂	1	2	yes	—
128	C₂²×C₇₉	#510	1	2	yes	—
129	C₄×C₇₉	—	2	4	no	—
130	C₄×C₇₉	—	16	1	no	—
131	C₄×C₇₉	#392	1	1	yes	characteristic
132	C₄×C₇₉	#447	1	1	yes	characteristic
133	C₄×C₇₉	#459	1	1	yes	characteristic
134	C₄×C₇₉	#496	1	1	yes	characteristic
135	Dic₇₉	—	8	4	no	—
136	#13327	—	79	1	no	maximal, Sylow
137	C₂×C₇₉	—	16	2	no	—
138	C₂×C₇₉	#2011	1	1	yes	characteristic
139	C₂×C₇₉	#2185	1	2	yes	—
140	C₂×C₇₉	#2208	1	2	yes	—
141	C₂×C₇₉	#2248	1	1	yes	characteristic
142	C₂×C₇₉	#2251	1	1	yes	characteristic
143	C₂²×SD₃₂	—	79	2	no	—
144	C₂×#494	—	79	1	no	—
145	C₂×#358	—	79	2	no	—
146	#1970	D₇₉	1	1	yes	characteristic
147	#1374	—	79	1	no	—
148	C₇₉	#13327	1	1	yes	characteristic, complemented, Sylow
149	C₂²×Q₁₆	—	79	2	no	—
150	C₂²×Q₁₆	—	158	1	no	—
151	C₂²×D₈	C₂×D₇₉	1	1	yes	characteristic
152	C₂×C₄⋊Q₈	—	158	1	no	—
153	C₂×SD₃₂	—	158	4	no	—
154	C₂×SD₃₂	—	158	4	no	—
155	C₂×SD₃₂	—	158	4	no	—
156	C₂²×C₁₆	—	79	2	no	—
157	#494	—	158	4	no	—
158	C₂×#107	C₂×D₇₉	1	1	yes	characteristic
159	C₂×#102	—	2	1	no	—
160	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
161	#390	—	2	1	no	—
162	#358	—	158	4	no	—
163	C₂²×Q₈	—	158	2	no	—
164	C₂²×D₄	—	2	1	no	—
165	C₂×Q₁₆	—	316	2	no	—
166	C₂×Q₁₆	—	316	2	no	—
167	C₂×Q₁₆	—	79	4	no	—
168	C₂×Q₁₆	—	158	4	no	—
169	C₂×Q₁₆	—	158	2	no	—
170	C₂×Q₁₆	—	158	2	no	—
171	C₂×Q₁₆	—	158	2	no	—
172	C₂×Q₁₆	—	158	2	no	—
173	C₂×Q₁₆	—	158	2	no	—
174	C₂×D₈	—	2	2	no	—
175	C₂×D₈	—	2	2	no	—
176	C₂×D₈	—	2	1	no	—
177	C₂×D₈	D₃₁₆	1	2	yes	—
178	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
179	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
180	C₄⋊Q₈	—	316	2	no	—
181	C₄⋊Q₈	—	158	4	no	—
182	C₂×C₄⋊C₄	—	2	1	no	—
183	C₂×C₄⋊C₄	—	316	2	no	—
184	C₂×C₂²⋊C₄	—	4	2	no	—
185	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
186	SD₃₂	—	158	16	no	—
187	C₂×C₁₆	—	79	4	no	—
188	C₂×C₁₆	—	158	2	no	—
189	C₂×C₁₆	—	158	2	no	—
190	#107	—	2	2	no	—
191	#102	—	4	2	no	—
192	C₄×C₈	—	2	2	no	—
193	C₂⁴	—	4	1	no	—
194	C₂×Q₈	—	316	2	no	—
195	C₂×Q₈	—	316	2	no	—
196	C₂×Q₈	—	316	2	no	—
197	C₂×Q₈	—	316	2	no	—
198	C₂×Q₈	—	316	2	no	—
199	C₂×Q₈	—	158	4	no	—
200	C₂×D₄	—	2	2	no	—
201	C₂×D₄	—	4	1	no	—
202	C₂×D₄	—	4	1	no	—
203	C₂×D₄	—	4	1	no	—
204	C₂×D₄	—	4	1	no	—
205	C₂×D₄	—	4	1	no	—
206	C₂²×C₄	—	4	1	no	—
207	C₂²×C₄	—	316	2	no	—
208	C₂²×C₄	#11929609	1	2	yes	—
209	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
210	Q₁₆	—	316	8	no	—
211	Q₁₆	—	316	2	no	—
212	Q₁₆	—	316	2	no	—
213	Q₁₆	—	158	4	no	—
214	Q₁₆	—	158	4	no	—
215	D₈	—	2	4	no	—
216	D₈	—	4	2	no	—
217	C₂×C₈	—	2	1	no	—
218	C₂×C₈	—	2	1	no	—
219	C₂×C₈	#11929609	1	2	yes	—
220	C₂×C₈	D₄×D₇₉	1	2	yes	—
221	C₂×C₈	D₄×D₇₉	1	2	yes	—
222	C₂×C₈	C₂×D₃₁₆	1	1	yes	characteristic
223	C₂×C₈	#11929624	1	1	yes	characteristic
224	C₄⋊C₄	—	4	1	no	—
225	C₄⋊C₄	—	4	1	no	—
226	C₄⋊C₄	—	316	8	no	—
227	C₂²⋊C₄	—	8	4	no	—
228	C₄²	—	2	1	no	—
229	C₄²	—	2	1	no	—
230	C₁₆	—	158	4	no	—
231	C₂³	—	4	2	no	—
232	C₂³	—	8	1	no	—
233	C₂³	—	8	1	no	—
234	C₂³	—	8	2	no	—
235	C₂³	—	8	2	no	—
236	C₂³	C₂×#11929609	1	1	yes	characteristic
237	Q₈	—	316	4	no	—
238	Q₈	—	316	4	no	—
239	Q₈	—	632	2	no	—
240	Q₈	—	632	2	no	—
241	D₄	—	4	2	no	—
242	D₄	—	4	2	no	—
243	D₄	—	8	1	no	—
244	D₄	—	8	1	no	—
245	C₂×C₄	—	2	2	no	—
246	C₂×C₄	—	2	2	no	—
247	C₂×C₄	—	8	1	no	—
248	C₂×C₄	—	8	2	no	—
249	C₂×C₄	—	316	4	no	—
250	C₂×C₄	—	632	2	no	—
251	C₂×C₄	—	632	2	no	—
252	C₂×C₄	#14579105	1	4	yes	complemented
253	C₂×C₄	#14579129	1	1	yes	characteristic
254	C₂×C₄	#14579135	1	1	yes	characteristic
255	C₂×C₄	#14579157	1	1	yes	characteristic
256	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
257	C₂×C₄	#14579186	1	1	yes	characteristic
258	C₂×C₄	#14579186	1	1	yes	characteristic
259	C₈	—	2	2	no	—
260	C₈	#14579131	1	2	yes	—
261	C₈	#14579134	1	2	yes	—
262	C₂²	—	8	4	no	—
263	C₂²	—	8	2	no	—
264	C₂²	—	16	2	no	—
265	C₂²	—	16	1	no	—
266	C₂²	—	16	1	no	—
267	C₂²	#19098696	1	1	yes	characteristic
268	C₂²	#19098758	1	1	yes	characteristic
269	C₂²	#19098939	1	1	yes	characteristic
270	C₂²	C₂×#14579105	1	2	yes	—
271	C₂²	#19099003	1	2	yes	—
272	C₄	—	2	4	no	—
273	C₄	—	16	1	no	—
274	C₄	—	632	4	no	—
275	C₄	#19098472	1	1	yes	characteristic
276	C₄	#19098696	1	1	yes	characteristic
277	C₄	#19098758	1	1	yes	characteristic
278	C₄	#19098953	1	1	yes	characteristic
279	C₂	—	16	2	no	—
280	C₂	#23764470	1	1	yes	characteristic
281	C₂	#23765316	1	2	yes	—
282	C₂	#23765445	1	2	yes	—
283	C₂	#23765655	1	1	yes	characteristic
284	C₂	#23765672	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₂²×#14579105

C₂

yes

maximal

C₂×#19098943

C₂

yes

maximal, characteristic, complemented

C₂×#19098366

C₂

yes

maximal, complemented

#23761478

C₂

yes

maximal, characteristic, complemented

C₇₉×#1970

C₂

yes

maximal, characteristic

C₂²×Dic₃₁₆

—

C₂²×Dic₃₁₆

C₂²

yes

—

—

—

—

—

C₂²×C₇₉⋊C₁₆

C₂²

yes

—

#19098943

—

#19098366

—

C₂²×D₈×C₇₉

C₂²

yes

characteristic

C₂×#107×C₇₉

C₂²

yes

characteristic

C₂×#102×C₇₉

—

C₂×C₄×C₈×C₇₉

C₂²

yes

characteristic

#390×C₇₉

—

C₂²×Dic₁₅₈

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

—

C₂×Dic₃₁₆

D₄

yes

—

#14579161

—

#14579161

—

C₂×C₄⋊Dic₇₉

—

#14579105

—

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

—

C₂×C₇₉⋊C₁₆

D₄

yes

—

C₂²×D₄×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

C₂×C₄⋊C₄×C₇₉

—

C₂×C₂²⋊C₄×C₇₉

—

C₂×C₄²×C₇₉

D₄

yes

characteristic

#107×C₇₉

—

#102×C₇₉

—

C₄×C₈×C₇₉

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂×Dic₁₅₈

—

C₂²×Dic₇₉

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

Dic₃₁₆

—

C₄⋊Dic₇₉

—

C₇₉⋊C₁₆

—

C₂⁴×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

D₈

yes

—

C₂²×C₄×C₇₉

C₂×D₄

yes

characteristic

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

C₄⋊C₄×C₇₉

—

C₄⋊C₄×C₇₉

—

C₂²⋊C₄×C₇₉

—

C₄²×C₇₉

—

C₄²×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

—

C₂³×C₇₉

C₂×D₈

yes

characteristic

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

D₄×C₇₉

—

C₂×C₄×C₇₉

—

C₂×C₄×C₇₉

—

100

C₂×C₄×C₇₉

—

101

C₂×C₄×C₇₉

—

102

C₂×C₄×C₇₉

SD₃₂

yes

complemented

103

C₂×C₄×C₇₉

#120

yes

characteristic

104

C₂×C₄×C₇₉

#121

yes

characteristic

105

C₂×C₄×C₇₉

#127

yes

characteristic

106

C₂×C₄×C₇₉

C₂×D₈

yes

characteristic

107

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

characteristic

108

C₂×C₄×C₇₉

AGL(1,ℤ/8)

yes

characteristic

109

C₂×Dic₇₉

—

110

C₂×Dic₇₉

—

111

C₂×Dic₇₉

—

112

Dic₁₅₈

—

113

Dic₁₅₈

—

114

Dic₁₅₈

—

115

Dic₁₅₈

—

116

C₈×C₇₉

—

117

C₈×C₇₉

#120

yes

—

118

C₈×C₇₉

#121

yes

—

119

C₂²×C₇₉

—

120

C₂²×C₇₉

—

121

C₂²×C₇₉

—

122

C₂²×C₇₉

—

123

C₂²×C₇₉

—

124

C₂²×C₇₉

#447

yes

characteristic

125

C₂²×C₇₉

#459

yes

characteristic

126

C₂²×C₇₉

#493

yes

characteristic

127

C₂²×C₇₉

C₂×SD₃₂

yes

—

128

C₂²×C₇₉

#510

yes

—

129

C₄×C₇₉

—

130

C₄×C₇₉

—

131

C₄×C₇₉

#392

yes

characteristic

132

C₄×C₇₉

#447

yes

characteristic

133

C₄×C₇₉

#459

yes

characteristic

134

C₄×C₇₉

#496

yes

characteristic

135

Dic₇₉

—

136

#13327

—

maximal, Sylow

137

C₂×C₇₉

—

138

C₂×C₇₉

#2011

yes

characteristic

139

C₂×C₇₉

#2185

yes

—

140

C₂×C₇₉

#2208

yes

—

141

C₂×C₇₉

#2248

yes

characteristic

142

C₂×C₇₉

#2251

yes

characteristic

143

C₂²×SD₃₂

—

144

C₂×#494

—

145

C₂×#358

—

146

#1970

D₇₉

yes

characteristic

147

#1374

—

148

C₇₉

#13327

yes

characteristic, complemented, Sylow

149

C₂²×Q₁₆

—

150

C₂²×Q₁₆

—

158

—

151

C₂²×D₈

C₂×D₇₉

yes

characteristic

152

C₂×C₄⋊Q₈

—

158

—

153

C₂×SD₃₂

—

158

—

154

C₂×SD₃₂

—

158

—

155

C₂×SD₃₂

—

158

—

156

C₂²×C₁₆

—

157

#494

—

158

—

158

C₂×#107

C₂×D₇₉

yes

characteristic

159

C₂×#102

—

160

C₂×C₄×C₈

C₂×D₇₉

yes

characteristic

161

#390

—

162

#358

—

158

—

163

C₂²×Q₈

—

158

—

164

C₂²×D₄

—

165

C₂×Q₁₆

—

316

—

166

C₂×Q₁₆

—

316

—

167

C₂×Q₁₆

—

168

C₂×Q₁₆

—

158

—

169

C₂×Q₁₆

—

158

—

170

C₂×Q₁₆

—

158

—

171

C₂×Q₁₆

—

158

—

172

C₂×Q₁₆

—

158

—

173

C₂×Q₁₆

—

158

—

174

C₂×D₈

—

175

C₂×D₈

—

176

C₂×D₈

—

177

C₂×D₈

D₃₁₆

yes

—

178

C₂²×C₈

C₂²⋊D₇₉

yes

characteristic

179

C₂²×C₈

C₂²×D₇₉

yes

characteristic

180

C₄⋊Q₈

—

316

—

181

C₄⋊Q₈

—

158

—

182

C₂×C₄⋊C₄

—

183

C₂×C₄⋊C₄

—

316

—

184

C₂×C₂²⋊C₄

—

185

C₂×C₄²

C₂²⋊D₇₉

yes

characteristic

186

SD₃₂

—

158

—

187

C₂×C₁₆

—

188

C₂×C₁₆

—

158

—

189

C₂×C₁₆

—

158

—

190

#107

—

191

#102

—

192

C₄×C₈

—

193

C₂⁴

—

194

C₂×Q₈

—

316

—

195

C₂×Q₈

—

316

—

196

C₂×Q₈

—

316

—

197

C₂×Q₈

—

316

—

198

C₂×Q₈

—

316

—

199

C₂×Q₈

—

158

—

200

C₂×D₄

—

201

C₂×D₄

—

202

C₂×D₄

—

203

C₂×D₄

—

204

C₂×D₄

—

205

C₂×D₄

—

206

C₂²×C₄

—

207

C₂²×C₄

—

316

—

208

C₂²×C₄

#11929609

yes

—

209

C₂²×C₄

C₂×C₂²⋊D₇₉

yes

characteristic

210

Q₁₆

—

316

—

211

Q₁₆

—

316

—

212

Q₁₆

—

316

—

213

Q₁₆

—

158

—

214

Q₁₆

—

158

—

215

D₈

—

216

D₈

—

217

C₂×C₈

—

218

C₂×C₈

—

219

C₂×C₈

#11929609

yes

—

220

C₂×C₈

D₄×D₇₉

yes

—

221

C₂×C₈

D₄×D₇₉

yes

—

222

C₂×C₈

C₂×D₃₁₆

yes

characteristic

223

C₂×C₈

#11929624

yes

characteristic

224

C₄⋊C₄

—

225

C₄⋊C₄

—

226

C₄⋊C₄

—

316

—

227

C₂²⋊C₄

—

228

C₄²

—

229

C₄²

—

230

C₁₆

—

158

—

231

C₂³

—

232

C₂³

—

233

C₂³

—

234

C₂³

—

235

C₂³

—

236

C₂³

C₂×#11929609

yes

characteristic

237

Q₈

—

316

—

238

Q₈

—

316

—

239

Q₈

—

632

—

240

Q₈

—

632

—

241

D₄

—

242

D₄

—

243

D₄

—

244

D₄

—

245

C₂×C₄

—

246

C₂×C₄

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

316

—

250

C₂×C₄

—

632

—

251

C₂×C₄

—

632

—

252

C₂×C₄

#14579105

yes

complemented

253

C₂×C₄

#14579129

yes

characteristic

254

C₂×C₄

#14579135

yes

characteristic

255

C₂×C₄

#14579157

yes

characteristic

256

C₂×C₄

C₂×#11929609

yes

characteristic

257

C₂×C₄

#14579186

yes

characteristic

258

C₂×C₄

#14579186

yes

characteristic

259

C₈

—

260

C₈

#14579131

yes

—

261

C₈

#14579134

yes

—

262

C₂²

—

263

C₂²

—

264

C₂²

—

265

C₂²

—

266

C₂²

—

267

C₂²

#19098696

yes

characteristic

268

C₂²

#19098758

yes

characteristic

269

C₂²

#19098939

yes

characteristic

270

C₂²

C₂×#14579105

yes

—

271

C₂²

#19099003

yes

—

272

C₄

—

273

C₄

—

274

C₄

—

632

—

275

C₄

#19098472

yes

characteristic

276

C₄

#19098696

yes

characteristic

277

C₄

#19098758

yes

characteristic

278

C₄

#19098953

yes

characteristic

279

C₂

—

280

C₂

#23764470

yes

characteristic

281

C₂

#23765316

yes

—

282

C₂

#23765445

yes

—

283

C₂

#23765655

yes

characteristic

284

C₂

#23765672

yes

characteristic

	subgroup	G/H
center	C₂³	C₂×#11929609
commutator, cosocle	C₂²×C₈×C₇₉	C₂³
Frattini	C₂²×C₈	C₂²×D₇₉
Fitting	C₇₉×#1970	C₂
socle	C₂³×C₇₉	C₂×D₈
prime radical	C₂²×D₈×C₇₉	C₂²
hypercenter	#1970	D₇₉
hypocenter	C₇₉	#13327
LCS	G ▷ C₂²×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1970

subgroup

G/H

center

C₂³

C₂×#11929609

commutator, cosocle

C₂²×C₈×C₇₉

C₂³

Frattini

C₂²×C₈

C₂²×D₇₉

Fitting

C₇₉×#1970

C₂

socle

C₂³×C₇₉

C₂×D₈

prime radical

C₂²×D₈×C₇₉

C₂²

D₇₉

C₇₉

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

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ #1970

N	H ≅ G/N	type
2. C₂×#19098943	C₂	semidirect
3. C₂×#19098366	C₂	semidirect
4. #23761478	C₂	semidirect
102. C₂×C₄×C₇₉	SD₃₂	semidirect
148. C₇₉	#13327	semidirect
252. C₂×C₄	#14579105	semidirect

H ≅ G/N

type

2. C₂×#19098943

C₂

semidirect

3. C₂×#19098366

C₂

semidirect

4. #23761478

C₂

semidirect

102. C₂×C₄×C₇₉

SD₃₂

semidirect

148. C₇₉

#13327

semidirect

252. C₂×C₄

#14579105

semidirect

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

subgroup	index
C₂²×#14579105	2
C₂×#19098943	2
C₂×#19098366	2
#23761478	2
C₇₉×#1970	2
#13327	79

subgroup

index

C₇₉×#1970

Subgroups — #34207111

Conjugacy classes of subgroups

Complements

Maximal subgroups