Group #31816185 — subgroups

Subgroups — #31816185

Order 17792.

388 conjugacy classes of subgroups; only the 131 normal subgroups are shown.

normal subgroups only

This group has 388 conjugacy classes of subgroups — too many to draw. Only its 131 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	#22581508	C₂	1	1	yes	maximal, characteristic, complemented
2	C₄×#14555784	C₂	1	1	yes	maximal, characteristic
3	#22581259	C₂	1	2	yes	maximal, complemented
4	#22581251	C₂	1	2	yes	maximal, complemented
5	#22581249	C₂	1	1	yes	maximal, characteristic, complemented
6	#22581243	C₂	1	1	yes	maximal, characteristic, complemented
7	#22581235	C₂	1	1	yes	maximal, characteristic, complemented
8	#22580990	C₂	1	2	yes	maximal, complemented
9	C₄⋊C₈×D₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
10	#22580946	C₂	1	2	yes	maximal
11	#474×C₁₃₉	C₂	1	1	yes	maximal, characteristic, complemented
12	C₂×#14555784	C₂²	1	1	yes	characteristic
13	C₂×C₈×D₁₃₉	C₂²	1	2	yes	—
14	#17984842	C₂²	1	1	yes	characteristic
15	#17984833	C₂²	1	2	yes	—
16	#17984822	—	2	1	no	—
17	#17984818	—	2	1	no	—
18	Q₈×Dic₁₃₉	—	2	1	no	—
19	C₄×Dic₂₇₈	C₂²	1	1	yes	characteristic
20	#17984807	—	2	1	no	—
21	#17984807	C₂²	1	1	yes	characteristic
22	D₄×Dic₁₃₉	C₂²	1	1	yes	characteristic
23	C₄×C₂²⋊D₁₃₉	—	2	1	no	—
24	(C₂²⋊D₁₃₉)⋊C₄	—	2	1	no	—
25	#17984800	C₂²	1	2	yes	—
26	#17984800	C₂²	1	1	yes	characteristic
27	#17984798	—	2	1	no	—
28	C₂×C₄×Dic₁₃₉	—	2	1	no	—
29	C₄²×D₁₃₉	C₂²	1	1	yes	characteristic
30	#17984776	C₂²	1	2	yes	—
31	#17984773	C₂²	1	2	yes	—
32	#17984773	C₂²	1	2	yes	—
33	C₄⋊(C₁₃₉⋊C₈)	C₂²	1	1	yes	characteristic
34	Dic₁₃₉⋊C₈	C₂²	1	2	yes	—
35	#17984767	C₂²	1	2	yes	—
36	#17984765	C₂²	1	2	yes	—
37	#17984763	C₂²	1	2	yes	—
38	C₄⋊Q₈×C₁₃₉	C₂²	1	1	yes	characteristic
39	C₄×D₄×C₁₃₉	C₂²	1	1	yes	characteristic
40	#107×C₁₃₉	C₂²	1	2	yes	—
41	C₄⋊C₈×C₁₃₉	C₂²	1	1	yes	characteristic
42	#102×C₁₃₉	C₂²	1	2	yes	—
43	#14555784	—	2	2	no	—
44	#14555784	Q₈	1	4	yes	complemented
45	C₂×Dic₂₇₈	—	2	1	no	—
46	C₂×Dic₂₇₈	C₂³	1	1	yes	characteristic
47	C₂×C₂²⋊D₁₃₉	—	2	1	no	—
48	C₂²×Dic₁₃₉	—	2	1	no	—
49	C₂²×Dic₁₃₉	—	2	1	no	—
50	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
51	C₂×C₄×D₁₃₉	D₄	1	1	yes	characteristic
52	C₂×C₄×D₁₃₉	C₂³	1	1	yes	characteristic
53	C₂×C₁₃₉⋊C₈	C₂³	1	2	yes	—
54	C₈×D₁₃₉	—	2	4	no	—
55	C₄⋊Dic₁₃₉	—	2	2	no	—
56	C₄⋊Dic₁₃₉	—	2	1	no	—
57	C₄⋊Dic₁₃₉	C₂³	1	1	yes	characteristic
58	C₄⋊Dic₁₃₉	C₂³	1	2	yes	—
59	Dic₁₃₉⋊C₄	—	2	1	no	—
60	Dic₁₃₉⋊C₄	—	2	2	no	—
61	Dic₁₃₉⋊C₄	—	2	1	no	—
62	C₂²⋊Dic₁₃₉	—	2	1	no	—
63	(C₂×D₁₃₉)⋊C₄	—	2	1	no	—
64	(C₂×D₁₃₉)⋊C₄	—	2	2	no	—
65	C₄×Dic₁₃₉	—	2	1	no	—
66	C₄×Dic₁₃₉	—	2	1	no	—
67	C₄×Dic₁₃₉	—	2	2	no	—
68	C₄×Dic₁₃₉	—	2	1	no	—
69	C₄×Dic₁₃₉	D₄	1	1	yes	characteristic
70	C₄×Dic₁₃₉	D₄	1	1	yes	characteristic
71	C₄×Dic₁₃₉	C₂³	1	1	yes	characteristic
72	C₂×Q₈×C₁₃₉	—	2	1	no	—
73	C₂×D₄×C₁₃₉	C₂³	1	1	yes	characteristic
74	C₂²×C₄×C₁₃₉	—	2	1	no	—
75	C₂×C₈×C₁₃₉	C₂³	1	2	yes	—
76	C₄⋊C₄×C₁₃₉	—	2	1	no	—
77	C₄⋊C₄×C₁₃₉	C₂³	1	1	yes	characteristic
78	C₄⋊C₄×C₁₃₉	C₂³	1	2	yes	—
79	C₂²⋊C₄×C₁₃₉	—	2	1	no	—
80	C₄²×C₁₃₉	C₂³	1	1	yes	characteristic
81	C₂²×D₁₃₉	C₂×D₄	1	1	yes	characteristic
82	Dic₂₇₈	—	2	1	no	—
83	Dic₂₇₈	—	4	2	no	—
84	Dic₂₇₈	C₂×Q₈	1	2	yes	—
85	C₂²⋊D₁₃₉	—	2	4	no	—
86	C₂×Dic₁₃₉	—	2	1	no	—
87	C₂×Dic₁₃₉	—	2	4	no	—
88	C₂×Dic₁₃₉	—	2	1	no	—
89	C₂×Dic₁₃₉	—	2	2	no	—
90	C₂×Dic₁₃₉	—	4	2	no	—
91	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
92	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
93	C₂×Dic₁₃₉	C₂×D₄	1	1	yes	characteristic
94	C₄×D₁₃₉	—	2	2	no	—
95	C₄×D₁₃₉	—	4	1	no	—
96	C₄×D₁₃₉	C₂×Q₈	1	2	yes	—
97	C₄×D₁₃₉	#41	1	2	yes	—
98	C₁₃₉⋊C₈	—	2	2	no	—
99	C₂³×C₁₃₉	—	2	1	no	—
100	Q₈×C₁₃₉	—	4	2	no	—
101	D₄×C₁₃₉	—	2	1	no	—
102	D₄×C₁₃₉	C₂×Q₈	1	2	yes	—
103	C₂×C₄×C₁₃₉	—	2	1	no	—
104	C₂×C₄×C₁₃₉	—	2	2	no	—
105	C₂×C₄×C₁₃₉	—	4	2	no	—
106	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
107	C₂×C₄×C₁₃₉	C₂×D₄	1	1	yes	characteristic
108	C₂×C₄×C₁₃₉	C₂⁴	1	1	yes	characteristic
109	C₈×C₁₃₉	—	2	2	no	—
110	C₂²×C₁₃₉	—	2	2	no	—
111	C₂²×C₁₃₉	—	4	1	no	—
112	C₂²×C₁₃₉	—	4	1	no	—
113	C₂²×C₁₃₉	C₂²×D₄	1	1	yes	characteristic
114	C₂×D₁₃₉	—	2	1	no	—
115	C₂×D₁₃₉	—	2	1	no	—
116	C₂×D₁₃₉	C₂²⋊Q₈	1	2	yes	—
117	C₄×C₁₃₉	—	2	1	no	—
118	C₄×C₁₃₉	—	4	1	no	—
119	C₄×C₁₃₉	—	4	2	no	—
120	C₄×C₁₃₉	#135	1	2	yes	—
121	C₄×C₁₃₉	C₂²×Q₈	1	1	yes	characteristic
122	C₄×C₁₃₉	C₂×#41	1	1	yes	characteristic
123	Dic₁₃₉	—	2	2	no	—
124	Dic₁₃₉	—	2	1	no	—
125	Dic₁₃₉	—	2	1	no	—
126	Dic₁₃₉	—	4	1	no	—
127	Dic₁₃₉	—	4	2	no	—
128	Dic₁₃₉	C₂²⋊Q₈	1	2	yes	—
129	C₂×C₁₃₉	—	4	2	no	—
130	C₂×C₁₃₉	C₂×C₂²⋊Q₈	1	1	yes	characteristic
131	C₂×C₁₃₉	C₂×#135	1	1	yes	characteristic
132	C₂×C₁₃₉	#575	1	1	yes	characteristic
133	D₁₃₉	—	2	2	no	—
134	C₁₃₉	#3076	1	1	yes	characteristic, complemented, Sylow
135	#3076	—	139	1	no	maximal, Sylow
136	#533	—	139	1	no	—
137	C₄×#41	—	139	1	no	—
138	#479	—	139	2	no	—
139	#478	—	139	2	no	—
140	#477	—	139	1	no	—
141	#476	—	139	1	no	—
142	#475	—	139	1	no	—
143	#474	D₁₃₉	1	1	yes	characteristic, complemented
144	#427	—	139	2	no	—
145	C₂×C₄⋊C₈	—	139	1	no	—
146	#416	—	139	2	no	—
147	C₂×#41	—	139	1	no	—
148	C₂²×C₈	—	139	2	no	—
149	C₄⋊Q₈	—	139	1	no	—
150	C₄⋊Q₈	C₂×D₁₃₉	1	1	yes	characteristic
151	#125	—	139	2	no	—
152	C₂²⋊Q₈	—	278	1	no	—
153	C₂²⋊Q₈	—	278	1	no	—
154	C₄×Q₈	—	278	1	no	—
155	C₄×Q₈	—	278	1	no	—
156	C₄×Q₈	—	139	1	no	—
157	C₄×Q₈	—	139	1	no	—
158	C₄×D₄	—	278	1	no	—
159	C₄×D₄	—	278	1	no	—
160	C₄×D₄	—	139	1	no	—
161	C₄×D₄	C₂×D₁₃₉	1	1	yes	characteristic
162	#117	—	278	1	no	—
163	#117	—	139	1	no	—
164	#117	—	139	2	no	—
165	C₂×C₄²	—	278	1	no	—
166	C₂×C₄²	—	139	1	no	—
167	#107	—	139	2	no	—
168	#107	C₂×D₁₃₉	1	2	yes	—
169	#106	—	139	2	no	—
170	#106	—	139	2	no	—
171	C₄⋊C₈	—	139	2	no	—
172	C₄⋊C₈	—	139	1	no	—
173	C₄⋊C₈	C₂×D₁₃₉	1	1	yes	characteristic
174	#103	—	139	2	no	—
175	#103	—	139	2	no	—
176	#102	—	139	2	no	—
177	#102	C₂×D₁₃₉	1	2	yes	—
178	#41	—	278	2	no	—
179	#41	—	139	4	no	—
180	C₂×Q₈	—	2	1	no	—
181	C₂×Q₈	—	278	1	no	—
182	C₂×Q₈	—	139	1	no	—
183	C₂×D₄	—	278	1	no	—
184	C₂×D₄	C₂²×D₁₃₉	1	1	yes	characteristic
185	C₂²×C₄	—	2	1	no	—
186	C₂²×C₄	—	278	1	no	—
187	C₂²×C₄	—	278	1	no	—
188	C₂²×C₄	—	139	1	no	—
189	C₂²×C₄	—	139	1	no	—
190	C₂²×C₄	—	139	1	no	—
191	C₂×C₈	—	278	4	no	—
192	C₂×C₈	—	139	2	no	—
193	C₂×C₈	C₂²×D₁₃₉	1	2	yes	—
194	C₄⋊C₄	—	2	1	no	—
195	C₄⋊C₄	—	278	1	no	—
196	C₄⋊C₄	—	278	2	no	—
197	C₄⋊C₄	—	278	2	no	—
198	C₄⋊C₄	—	278	1	no	—
199	C₄⋊C₄	—	278	1	no	—
200	C₄⋊C₄	—	139	2	no	—
201	C₄⋊C₄	—	139	1	no	—
202	C₄⋊C₄	C₂²×D₁₃₉	1	2	yes	—
203	C₄⋊C₄	C₂²×D₁₃₉	1	1	yes	characteristic
204	C₂²⋊C₄	—	2	1	no	—
205	C₂²⋊C₄	—	278	1	no	—
206	C₂²⋊C₄	—	278	2	no	—
207	C₂²⋊C₄	—	278	1	no	—
208	C₄²	—	278	1	no	—
209	C₄²	—	278	1	no	—
210	C₄²	—	278	2	no	—
211	C₄²	—	278	1	no	—
212	C₄²	—	139	1	no	—
213	C₄²	—	139	1	no	—
214	C₄²	—	139	1	no	—
215	C₄²	C₂²×D₁₃₉	1	1	yes	characteristic
216	C₂³	—	2	1	no	—
217	C₂³	—	139	1	no	—
218	Q₈	—	4	2	no	—
219	Q₈	—	278	1	no	—
220	Q₈	—	556	2	no	—
221	Q₈	—	139	2	no	—
222	D₄	—	2	1	no	—
223	D₄	—	278	4	no	—
224	D₄	Q₈×D₁₃₉	1	2	yes	—
225	C₂×C₄	—	2	1	no	—
226	C₂×C₄	—	2	2	no	—
227	C₂×C₄	—	4	2	no	—
228	C₂×C₄	—	278	1	no	—
229	C₂×C₄	—	278	4	no	—
230	C₂×C₄	—	278	2	no	—
231	C₂×C₄	—	278	1	no	—
232	C₂×C₄	—	278	2	no	—
233	C₂×C₄	—	556	1	no	—
234	C₂×C₄	—	556	2	no	—
235	C₂×C₄	—	139	1	no	—
236	C₂×C₄	—	139	1	no	—
237	C₂×C₄	—	139	1	no	—
238	C₂×C₄	—	139	2	no	—
239	C₂×C₄	—	139	2	no	—
240	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
241	C₂×C₄	D₄×D₁₃₉	1	1	yes	characteristic
242	C₂×C₄	C₂³×D₁₃₉	1	1	yes	characteristic
243	C₈	—	2	2	no	—
244	C₈	—	278	2	no	—
245	C₂²	—	2	2	no	—
246	C₂²	—	4	1	no	—
247	C₂²	—	4	1	no	—
248	C₂²	—	278	1	no	—
249	C₂²	—	278	1	no	—
250	C₂²	—	139	2	no	—
251	C₂²	C₂×D₄×D₁₃₉	1	1	yes	characteristic
252	C₄	—	2	1	no	—
253	C₄	—	4	1	no	—
254	C₄	—	4	2	no	—
255	C₄	—	278	2	no	—
256	C₄	—	278	1	no	—
257	C₄	—	278	1	no	—
258	C₄	—	556	1	no	—
259	C₄	—	556	2	no	—
260	C₄	—	139	2	no	—
261	C₄	#17984861	1	2	yes	—
262	C₄	C₂×Q₈×D₁₃₉	1	1	yes	characteristic
263	C₄	#41×D₁₃₉	1	1	yes	characteristic
264	C₂	—	4	2	no	—
265	C₂	—	278	2	no	—
266	C₂	C₂²⋊Q₈×D₁₃₉	1	1	yes	characteristic
267	C₂	C₂×#17984861	1	1	yes	characteristic
268	C₂	#22581752	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22581508

C₂

yes

maximal, characteristic, complemented

C₄×#14555784

C₂

yes

maximal, characteristic

#22581259

C₂

yes

maximal, complemented

#22581251

C₂

yes

maximal, complemented

#22581249

C₂

yes

maximal, characteristic, complemented

#22581243

C₂

yes

maximal, characteristic, complemented

#22581235

C₂

yes

maximal, characteristic, complemented

#22580990

C₂

yes

maximal, complemented

C₄⋊C₈×D₁₃₉

C₂

yes

maximal, characteristic, complemented

#22580946

C₂

yes

maximal

#474×C₁₃₉

C₂

yes

maximal, characteristic, complemented

C₂×#14555784

C₂²

yes

characteristic

C₂×C₈×D₁₃₉

C₂²

yes

—

#17984842

C₂²

yes

characteristic

#17984833

C₂²

yes

—

#17984822

—

#17984818

—

Q₈×Dic₁₃₉

—

C₄×Dic₂₇₈

C₂²

yes

characteristic

#17984807

—

#17984807

C₂²

yes

characteristic

D₄×Dic₁₃₉

C₂²

yes

characteristic

C₄×C₂²⋊D₁₃₉

—

(C₂²⋊D₁₃₉)⋊C₄

—

#17984800

C₂²

yes

—

#17984800

C₂²

yes

characteristic

#17984798

—

C₂×C₄×Dic₁₃₉

—

C₄²×D₁₃₉

C₂²

yes

characteristic

#17984776

C₂²

yes

—

#17984773

C₂²

yes

—

#17984773

C₂²

yes

—

C₄⋊(C₁₃₉⋊C₈)

C₂²

yes

characteristic

Dic₁₃₉⋊C₈

C₂²

yes

—

#17984767

C₂²

yes

—

#17984765

C₂²

yes

—

#17984763

C₂²

yes

—

C₄⋊Q₈×C₁₃₉

C₂²

yes

characteristic

C₄×D₄×C₁₃₉

C₂²

yes

characteristic

#107×C₁₃₉

C₂²

yes

—

C₄⋊C₈×C₁₃₉

C₂²

yes

characteristic

#102×C₁₃₉

C₂²

yes

—

#14555784

—

#14555784

Q₈

yes

complemented

C₂×Dic₂₇₈

—

C₂×Dic₂₇₈

C₂³

yes

characteristic

C₂×C₂²⋊D₁₃₉

—

C₂²×Dic₁₃₉

—

C₂²×Dic₁₃₉

—

C₂×C₄×D₁₃₉

D₄

yes

characteristic

C₂×C₄×D₁₃₉

D₄

yes

characteristic

C₂×C₄×D₁₃₉

C₂³

yes

characteristic

C₂×C₁₃₉⋊C₈

C₂³

yes

—

C₈×D₁₃₉

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

—

C₄⋊Dic₁₃₉

C₂³

yes

characteristic

C₄⋊Dic₁₃₉

C₂³

yes

—

Dic₁₃₉⋊C₄

—

Dic₁₃₉⋊C₄

—

Dic₁₃₉⋊C₄

—

C₂²⋊Dic₁₃₉

—

(C₂×D₁₃₉)⋊C₄

—

(C₂×D₁₃₉)⋊C₄

—

C₄×Dic₁₃₉

—

C₄×Dic₁₃₉

—

C₄×Dic₁₃₉

—

C₄×Dic₁₃₉

—

C₄×Dic₁₃₉

D₄

yes

characteristic

C₄×Dic₁₃₉

D₄

yes

characteristic

C₄×Dic₁₃₉

C₂³

yes

characteristic

C₂×Q₈×C₁₃₉

—

C₂×D₄×C₁₃₉

C₂³

yes

characteristic

C₂²×C₄×C₁₃₉

—

C₂×C₈×C₁₃₉

C₂³

yes

—

C₄⋊C₄×C₁₃₉

—

C₄⋊C₄×C₁₃₉

C₂³

yes

characteristic

C₄⋊C₄×C₁₃₉

C₂³

yes

—

C₂²⋊C₄×C₁₃₉

—

C₄²×C₁₃₉

C₂³

yes

characteristic

C₂²×D₁₃₉

C₂×D₄

yes

characteristic

Dic₂₇₈

—

Dic₂₇₈

—

Dic₂₇₈

C₂×Q₈

yes

—

C₂²⋊D₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

—

C₂×Dic₁₃₉

C₂×D₄

yes

characteristic

C₂×Dic₁₃₉

C₂×D₄

yes

characteristic

C₂×Dic₁₃₉

C₂×D₄

yes

characteristic

C₄×D₁₃₉

—

C₄×D₁₃₉

—

C₄×D₁₃₉

C₂×Q₈

yes

—

C₄×D₁₃₉

#41

yes

—

C₁₃₉⋊C₈

—

C₂³×C₁₃₉

—

100

Q₈×C₁₃₉

—

101

D₄×C₁₃₉

—

102

D₄×C₁₃₉

C₂×Q₈

yes

—

103

C₂×C₄×C₁₃₉

—

104

C₂×C₄×C₁₃₉

—

105

C₂×C₄×C₁₃₉

—

106

C₂×C₄×C₁₃₉

C₂×D₄

yes

characteristic

107

C₂×C₄×C₁₃₉

C₂×D₄

yes

characteristic

108

C₂×C₄×C₁₃₉

C₂⁴

yes

characteristic

109

C₈×C₁₃₉

—

110

C₂²×C₁₃₉

—

111

C₂²×C₁₃₉

—

112

C₂²×C₁₃₉

—

113

C₂²×C₁₃₉

C₂²×D₄

yes

characteristic

114

C₂×D₁₃₉

—

115

C₂×D₁₃₉

—

116

C₂×D₁₃₉

C₂²⋊Q₈

yes

—

117

C₄×C₁₃₉

—

118

C₄×C₁₃₉

—

119

C₄×C₁₃₉

—

120

C₄×C₁₃₉

#135

yes

—

121

C₄×C₁₃₉

C₂²×Q₈

yes

characteristic

122

C₄×C₁₃₉

C₂×#41

yes

characteristic

123

Dic₁₃₉

—

124

Dic₁₃₉

—

125

Dic₁₃₉

—

126

Dic₁₃₉

—

127

Dic₁₃₉

—

128

Dic₁₃₉

C₂²⋊Q₈

yes

—

129

C₂×C₁₃₉

—

130

C₂×C₁₃₉

C₂×C₂²⋊Q₈

yes

characteristic

131

C₂×C₁₃₉

C₂×#135

yes

characteristic

132

C₂×C₁₃₉

#575

yes

characteristic

133

D₁₃₉

—

134

C₁₃₉

#3076

yes

characteristic, complemented, Sylow

135

#3076

—

139

maximal, Sylow

136

#533

—

139

—

137

C₄×#41

—

139

—

138

#479

—

139

—

139

#478

—

139

—

140

#477

—

139

—

141

#476

—

139

—

142

#475

—

139

—

143

#474

D₁₃₉

yes

characteristic, complemented

144

#427

—

139

—

145

C₂×C₄⋊C₈

—

139

—

146

#416

—

139

—

147

C₂×#41

—

139

—

148

C₂²×C₈

—

139

—

149

C₄⋊Q₈

—

139

—

150

C₄⋊Q₈

C₂×D₁₃₉

yes

characteristic

151

#125

—

139

—

152

C₂²⋊Q₈

—

278

—

153

C₂²⋊Q₈

—

278

—

154

C₄×Q₈

—

278

—

155

C₄×Q₈

—

278

—

156

C₄×Q₈

—

139

—

157

C₄×Q₈

—

139

—

158

C₄×D₄

—

278

—

159

C₄×D₄

—

278

—

160

C₄×D₄

—

139

—

161

C₄×D₄

C₂×D₁₃₉

yes

characteristic

162

#117

—

278

—

163

#117

—

139

—

164

#117

—

139

—

165

C₂×C₄²

—

278

—

166

C₂×C₄²

—

139

—

167

#107

—

139

—

168

#107

C₂×D₁₃₉

yes

—

169

#106

—

139

—

170

#106

—

139

—

171

C₄⋊C₈

—

139

—

172

C₄⋊C₈

—

139

—

173

C₄⋊C₈

C₂×D₁₃₉

yes

characteristic

174

#103

—

139

—

175

#103

—

139

—

176

#102

—

139

—

177

#102

C₂×D₁₃₉

yes

—

178

#41

—

278

—

179

#41

—

139

—

180

C₂×Q₈

—

181

C₂×Q₈

—

278

—

182

C₂×Q₈

—

139

—

183

C₂×D₄

—

278

—

184

C₂×D₄

C₂²×D₁₃₉

yes

characteristic

185

C₂²×C₄

—

186

C₂²×C₄

—

278

—

187

C₂²×C₄

—

278

—

188

C₂²×C₄

—

139

—

189

C₂²×C₄

—

139

—

190

C₂²×C₄

—

139

—

191

C₂×C₈

—

278

—

192

C₂×C₈

—

139

—

193

C₂×C₈

C₂²×D₁₃₉

yes

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

278

—

196

C₄⋊C₄

—

278

—

197

C₄⋊C₄

—

278

—

198

C₄⋊C₄

—

278

—

199

C₄⋊C₄

—

278

—

200

C₄⋊C₄

—

139

—

201

C₄⋊C₄

—

139

—

202

C₄⋊C₄

C₂²×D₁₃₉

yes

—

203

C₄⋊C₄

C₂²×D₁₃₉

yes

characteristic

204

C₂²⋊C₄

—

205

C₂²⋊C₄

—

278

—

206

C₂²⋊C₄

—

278

—

207

C₂²⋊C₄

—

278

—

208

C₄²

—

278

—

209

C₄²

—

278

—

210

C₄²

—

278

—

211

C₄²

—

278

—

212

C₄²

—

139

—

213

C₄²

—

139

—

214

C₄²

—

139

—

215

C₄²

C₂²×D₁₃₉

yes

characteristic

216

C₂³

—

217

C₂³

—

139

—

218

Q₈

—

219

Q₈

—

278

—

220

Q₈

—

556

—

221

Q₈

—

139

—

222

D₄

—

223

D₄

—

278

—

224

D₄

Q₈×D₁₃₉

yes

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

278

—

229

C₂×C₄

—

278

—

230

C₂×C₄

—

278

—

231

C₂×C₄

—

278

—

232

C₂×C₄

—

278

—

233

C₂×C₄

—

556

—

234

C₂×C₄

—

556

—

235

C₂×C₄

—

139

—

236

C₂×C₄

—

139

—

237

C₂×C₄

—

139

—

238

C₂×C₄

—

139

—

239

C₂×C₄

—

139

—

240

C₂×C₄

D₄×D₁₃₉

yes

characteristic

241

C₂×C₄

D₄×D₁₃₉

yes

characteristic

242

C₂×C₄

C₂³×D₁₃₉

yes

characteristic

243

C₈

—

244

C₈

—

278

—

245

C₂²

—

246

C₂²

—

247

C₂²

—

248

C₂²

—

278

—

249

C₂²

—

278

—

250

C₂²

—

139

—

251

C₂²

C₂×D₄×D₁₃₉

yes

characteristic

252

C₄

—

253

C₄

—

254

C₄

—

255

C₄

—

278

—

256

C₄

—

278

—

257

C₄

—

278

—

258

C₄

—

556

—

259

C₄

—

556

—

260

C₄

—

139

—

261

C₄

#17984861

yes

—

262

C₄

C₂×Q₈×D₁₃₉

yes

characteristic

263

C₄

#41×D₁₃₉

yes

characteristic

264

C₂

—

265

C₂

—

278

—

266

C₂

C₂²⋊Q₈×D₁₃₉

yes

characteristic

267

C₂

C₂×#17984861

yes

characteristic

268

C₂

#22581752

yes

characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₃₉
commutator, cosocle	C₂×C₄×C₁₃₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₃₉
Fitting	#474×C₁₃₉	C₂
socle	C₂²×C₁₃₉	C₂²×D₄
prime radical	C₂×#14555784	C₂²
hypercenter	#474	D₁₃₉
hypocenter	C₁₃₉	#3076
LCS	G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉
UCS	C₁ ◁ C₂² ◁ C₄² ◁ #474

subgroup

G/H

center

C₂²

C₂×D₄×D₁₃₉

commutator, cosocle

C₂×C₄×C₁₃₉

C₂⁴

Frattini

C₂×C₄

C₂³×D₁₃₉

Fitting

#474×C₁₃₉

C₂

socle

C₂²×C₁₃₉

C₂²×D₄

C₂²

D₁₃₉

C₁₃₉

G ▷ C₂×C₄×C₁₃₉ ▷ C₂×C₁₃₉ ▷ C₁₃₉

UCS

C₁ ◁ C₂² ◁ C₄² ◁ #474

N	H ≅ G/N	type
1. #22581508	C₂	semidirect
3. #22581259	C₂	semidirect
4. #22581251	C₂	semidirect
5. #22581249	C₂	semidirect
6. #22581243	C₂	semidirect
7. #22581235	C₂	semidirect
8. #22580990	C₂	semidirect
9. C₄⋊C₈×D₁₃₉	C₂	semidirect
11. #474×C₁₃₉	C₂	semidirect
44. #14555784	Q₈	semidirect
134. C₁₃₉	#3076	semidirect
143. #474	D₁₃₉	semidirect

H ≅ G/N

type

1. #22581508

C₂

semidirect

3. #22581259

C₂

semidirect

4. #22581251

C₂

semidirect

5. #22581249

C₂

semidirect

6. #22581243

C₂

semidirect

7. #22581235

C₂

semidirect

8. #22580990

C₂

semidirect

9. C₄⋊C₈×D₁₃₉

C₂

semidirect

11. #474×C₁₃₉

C₂

semidirect

44. #14555784

Q₈

semidirect

134. C₁₃₉

#3076

semidirect

143. #474

D₁₃₉

semidirect

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

subgroup	index
#22581508	2
C₄×#14555784	2
#22581259	2
#22581251	2
#22581249	2
#22581243	2
#22581235	2
#22580990	2
C₄⋊C₈×D₁₃₉	2
#22580946	2
#474×C₁₃₉	2
#3076	139

subgroup

index

C₄⋊C₈×D₁₃₉

#474×C₁₃₉

139

Subgroups — #31816185

Conjugacy classes of subgroups

Complements

Maximal subgroups