Group #36449735 — subgroups

Subgroups — #36449735

Order 22784.

570 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 570 conjugacy classes of subgroups — too many to draw. Only its 155 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	#26023342	C₂	1	1	yes	maximal, characteristic
2	#26021201	C₂	1	2	yes	maximal
3	C₂×#19151347	C₂	1	1	yes	maximal, characteristic
4	#26018092	C₂	1	2	yes	maximal
5	C₂×#494×C₈₉	C₂	1	1	yes	maximal, characteristic
6	C₂×C₄⋊#10623494	C₂²	1	2	yes	—
7	#19151505	—	2	2	no	—
8	#19151497	—	2	2	no	—
9	C₄⋊C₄×Dic₈₉	—	2	2	no	—
10	C₄×C₄⋊Dic₈₉	C₂²	1	2	yes	—
11	#19151360	—	2	2	no	—
12	#19151360	—	2	2	no	—
13	#19151347	—	2	2	no	—
14	C₂²×Q₁₆×C₈₉	—	2	2	no	—
15	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
16	C₂×C₄⋊Q₈×C₈₉	C₂²	1	1	yes	characteristic
17	#494×C₈₉	—	2	2	no	—
18	#494×C₈₉	C₄	1	4	yes	complemented
19	C₂×C₄×C₈×C₈₉	C₂²	1	1	yes	characteristic
20	C₂²×#10623494	—	2	2	no	—
21	C₂×C₄⋊Dic₈₉	—	2	2	no	—
22	C₂×C₄⋊Dic₈₉	D₄	1	2	yes	—
23	C₂×C₄⋊Dic₈₉	D₄	1	2	yes	—
24	C₂×C₄×Dic₈₉	—	2	2	no	—
25	C₂×C₄×Dic₈₉	—	2	2	no	—
26	C₄⋊#10623494	—	2	2	no	—
27	C₄⋊#10623494	—	2	2	no	—
28	#15667919	—	2	4	no	—
29	#15667919	—	2	2	no	—
30	C₂²×Q₈×C₈₉	—	2	1	no	—
31	C₂²×Q₈×C₈₉	D₄	1	2	yes	—
32	C₂×Q₁₆×C₈₉	—	2	8	no	—
33	C₂×Q₁₆×C₈₉	—	4	4	no	—
34	C₂×Q₁₆×C₈₉	—	4	4	no	—
35	C₂²×C₈×C₈₉	—	2	1	no	—
36	C₄⋊Q₈×C₈₉	—	2	1	no	—
37	C₄⋊Q₈×C₈₉	—	2	2	no	—
38	C₄⋊Q₈×C₈₉	—	2	2	no	—
39	C₄⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
40	C₄⋊Q₈×C₈₉	C₂×C₄	1	2	yes	—
41	C₄⋊Q₈×C₈₉	D₄	1	2	yes	—
42	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
43	C₂×C₄⋊C₄×C₈₉	—	2	2	no	—
44	C₂×C₄²×C₈₉	C₂³	1	1	yes	characteristic
45	C₄×C₈×C₈₉	—	2	1	no	—
46	C₄×C₈×C₈₉	C₂×C₄	1	2	yes	—
47	C₂²×Dic₈₉	—	2	2	no	—
48	C₂²×Dic₈₉	—	2	2	no	—
49	C₂×#10623494	—	4	2	no	—
50	C₂×#10623494	—	4	2	no	—
51	C₂×#10623494	—	4	2	no	—
52	C₄⋊Dic₈₉	—	2	2	no	—
53	C₄⋊Dic₈₉	—	2	2	no	—
54	C₄⋊Dic₈₉	—	2	2	no	—
55	C₄⋊Dic₈₉	—	8	2	no	—
56	C₄⋊Dic₈₉	Q₁₆	1	4	yes	complemented
57	C₄×Dic₈₉	—	4	2	no	—
58	C₄×Dic₈₉	—	4	2	no	—
59	C₄×Dic₈₉	—	8	2	no	—
60	C₂×Q₈×C₈₉	—	2	2	no	—
61	C₂×Q₈×C₈₉	—	2	2	no	—
62	C₂×Q₈×C₈₉	—	4	2	no	—
63	C₂×Q₈×C₈₉	—	4	2	no	—
64	C₂×Q₈×C₈₉	—	4	2	no	—
65	C₂×Q₈×C₈₉	—	4	2	no	—
66	C₂×Q₈×C₈₉	—	4	1	no	—
67	C₂×Q₈×C₈₉	C₂²⋊C₄	1	4	yes	—
68	C₂²×C₄×C₈₉	—	2	2	no	—
69	C₂²×C₄×C₈₉	—	4	1	no	—
70	C₂²×C₄×C₈₉	C₂×D₄	1	1	yes	characteristic
71	C₂²×C₄×C₈₉	C₂×D₄	1	2	yes	—
72	Q₁₆×C₈₉	—	4	16	no	—
73	C₂×C₈×C₈₉	—	2	2	no	—
74	C₂×C₈×C₈₉	—	2	2	no	—
75	C₂×C₈×C₈₉	—	2	2	no	—
76	C₄⋊C₄×C₈₉	—	2	4	no	—
77	C₄⋊C₄×C₈₉	—	2	4	no	—
78	C₄⋊C₄×C₈₉	—	2	4	no	—
79	C₄⋊C₄×C₈₉	—	4	2	no	—
80	C₄²×C₈₉	C₂²×C₄	1	1	yes	characteristic
81	C₄²×C₈₉	C₂×D₄	1	1	yes	characteristic
82	C₄²×C₈₉	#41	1	2	yes	—
83	C₂³×C₈₉	#120	1	1	yes	characteristic
84	Q₈×C₈₉	—	4	4	no	—
85	Q₈×C₈₉	—	4	4	no	—
86	Q₈×C₈₉	—	8	2	no	—
87	Q₈×C₈₉	—	8	2	no	—
88	C₂×C₄×C₈₉	—	2	1	no	—
89	C₂×C₄×C₈₉	—	2	1	no	—
90	C₂×C₄×C₈₉	—	2	4	no	—
91	C₂×C₄×C₈₉	—	4	2	no	—
92	C₂×C₄×C₈₉	—	4	2	no	—
93	C₂×C₄×C₈₉	—	4	2	no	—
94	C₂×C₄×C₈₉	—	8	1	no	—
95	C₂×C₄×C₈₉	—	8	1	no	—
96	C₂×C₄×C₈₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
97	C₂×C₄×C₈₉	C₄×D₄	1	2	yes	—
98	C₂×C₄×C₈₉	#121	1	2	yes	—
99	C₂×C₄×C₈₉	#123	1	1	yes	characteristic
100	C₂×C₄×C₈₉	C₂×Q₁₆	1	2	yes	—
101	C₂×C₄×C₈₉	#135	1	2	yes	—
102	C₂×C₄×C₈₉	#137	1	2	yes	—
103	C₂×C₄×C₈₉	#137	1	2	yes	—
104	C₂×Dic₈₉	—	2	4	no	—
105	C₂×Dic₈₉	—	4	2	no	—
106	C₂×Dic₈₉	—	4	2	no	—
107	C₂×Dic₈₉	—	4	2	no	—
108	C₂×Dic₈₉	—	4	2	no	—
109	C₂×Dic₈₉	—	4	2	no	—
110	C₈×C₈₉	—	2	4	no	—
111	#10623494	—	8	2	no	—
112	C₂²×C₈₉	#386	1	1	yes	characteristic
113	C₂²×C₈₉	#451	1	2	yes	—
114	C₂²×C₈₉	#452	1	2	yes	—
115	C₂²×C₈₉	#453	1	1	yes	characteristic
116	C₂²×C₈₉	#453	1	1	yes	characteristic
117	C₄×C₈₉	—	2	1	no	—
118	C₄×C₈₉	—	2	1	no	—
119	C₄×C₈₉	—	4	4	no	—
120	C₄×C₈₉	—	8	2	no	—
121	C₄×C₈₉	C₄×Q₁₆	1	2	yes	—
122	C₄×C₈₉	#441	1	2	yes	—
123	C₄×C₈₉	#462	1	2	yes	—
124	C₄×C₈₉	#464	1	2	yes	—
125	Dic₈₉	—	4	4	no	—
126	Dic₈₉	—	8	2	no	—
127	#9066	—	89	1	no	maximal, Sylow
128	C₂×C₈₉	#1632	1	2	yes	—
129	C₂×C₈₉	#1633	1	1	yes	characteristic
130	C₂×C₈₉	#1634	1	1	yes	characteristic
131	C₂×C₈₉	#1878	1	2	yes	—
132	C₂×C₈₉	#1887	1	1	yes	characteristic
133	C₂×#494	D₈₉	1	1	yes	characteristic
134	#2369	—	89	1	no	—
135	#1987	—	89	2	no	—
136	C₂×#333	—	89	1	no	—
137	#1279	—	89	2	no	—
138	C₈₉	#9066	1	1	yes	characteristic, complemented, Sylow
139	C₂²×Q₁₆	—	2	2	no	—
140	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
141	C₂×C₄⋊Q₈	C₂×D₈₉	1	1	yes	characteristic
142	#494	—	2	2	no	—
143	#494	Dic₈₉	1	4	yes	complemented
144	C₂×C₄⋊C₈	—	89	2	no	—
145	C₂×C₄×C₈	C₂×D₈₉	1	1	yes	characteristic
146	#391	—	178	2	no	—
147	#389	—	178	2	no	—
148	C₄×C₄⋊C₄	—	89	2	no	—
149	C₄×C₄⋊C₄	—	178	2	no	—
150	#340	—	178	2	no	—
151	#340	—	178	2	no	—
152	#333	—	178	2	no	—
153	C₂²×Q₈	—	2	1	no	—
154	C₂²×Q₈	C₂²⋊D₈₉	1	2	yes	—
155	C₂×Q₁₆	—	2	8	no	—
156	C₂×Q₁₆	—	4	4	no	—
157	C₂×Q₁₆	—	4	4	no	—
158	C₂²×C₈	—	2	1	no	—
159	C₂²×C₈	—	178	2	no	—
160	C₄⋊Q₈	—	2	1	no	—
161	C₄⋊Q₈	—	2	2	no	—
162	C₄⋊Q₈	—	2	2	no	—
163	C₄⋊Q₈	C₂×Dic₈₉	1	2	yes	—
164	C₄⋊Q₈	C₂×Dic₈₉	1	2	yes	—
165	C₄⋊Q₈	C₂²⋊D₈₉	1	2	yes	—
166	C₂×C₄⋊C₄	—	2	2	no	—
167	C₂×C₄⋊C₄	—	2	2	no	—
168	C₂×C₄⋊C₄	—	89	2	no	—
169	C₂×C₄⋊C₄	—	89	2	no	—
170	C₂×C₄⋊C₄	—	178	2	no	—
171	C₂×C₄²	—	178	2	no	—
172	C₂×C₄²	—	178	2	no	—
173	C₂×C₄²	C₂²×D₈₉	1	1	yes	characteristic
174	C₄⋊C₈	—	178	2	no	—
175	C₄⋊C₈	—	178	2	no	—
176	C₄×C₈	—	2	1	no	—
177	C₄×C₈	C₂×Dic₈₉	1	2	yes	—
178	#95	—	178	4	no	—
179	#95	—	178	2	no	—
180	C₂×Q₈	—	2	2	no	—
181	C₂×Q₈	—	2	2	no	—
182	C₂×Q₈	—	4	2	no	—
183	C₂×Q₈	—	4	2	no	—
184	C₂×Q₈	—	4	2	no	—
185	C₂×Q₈	—	4	2	no	—
186	C₂×Q₈	—	4	1	no	—
187	C₂×Q₈	C₂²⋊Dic₈₉	1	4	yes	—
188	C₂²×C₄	—	2	2	no	—
189	C₂²×C₄	—	4	1	no	—
190	C₂²×C₄	—	178	2	no	—
191	C₂²×C₄	—	178	2	no	—
192	C₂²×C₄	D₄×D₈₉	1	2	yes	—
193	C₂²×C₄	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
194	Q₁₆	—	4	16	no	—
195	C₂×C₈	—	2	2	no	—
196	C₂×C₈	—	2	2	no	—
197	C₂×C₈	—	2	2	no	—
198	C₂×C₈	—	356	2	no	—
199	C₂×C₈	—	356	2	no	—
200	C₂×C₈	—	356	2	no	—
201	C₄⋊C₄	—	2	4	no	—
202	C₄⋊C₄	—	2	4	no	—
203	C₄⋊C₄	—	2	4	no	—
204	C₄⋊C₄	—	4	2	no	—
205	C₄⋊C₄	—	89	4	no	—
206	C₄⋊C₄	—	178	2	no	—
207	C₄⋊C₄	—	178	2	no	—
208	C₄⋊C₄	—	178	2	no	—
209	C₄⋊C₄	—	712	2	no	—
210	C₄²	—	356	2	no	—
211	C₄²	—	356	2	no	—
212	C₄²	—	712	2	no	—
213	C₄²	C₂²×Dic₈₉	1	1	yes	characteristic
214	C₄²	C₂×C₂²⋊D₈₉	1	1	yes	characteristic
215	C₄²	#13083573	1	2	yes	—
216	C₂³	#15667980	1	1	yes	characteristic
217	Q₈	—	4	4	no	—
218	Q₈	—	4	4	no	—
219	Q₈	—	8	2	no	—
220	Q₈	—	8	2	no	—
221	C₂×C₄	—	2	1	no	—
222	C₂×C₄	—	2	1	no	—
223	C₂×C₄	—	2	4	no	—
224	C₂×C₄	—	4	2	no	—
225	C₂×C₄	—	4	2	no	—
226	C₂×C₄	—	4	2	no	—
227	C₂×C₄	—	8	1	no	—
228	C₂×C₄	—	8	1	no	—
229	C₂×C₄	—	356	2	no	—
230	C₂×C₄	—	356	2	no	—
231	C₂×C₄	—	356	2	no	—
232	C₂×C₄	—	356	2	no	—
233	C₂×C₄	—	356	2	no	—
234	C₂×C₄	—	178	4	no	—
235	C₂×C₄	C₂×C₂²⋊Dic₈₉	1	1	yes	characteristic
236	C₂×C₄	D₄×Dic₈₉	1	2	yes	—
237	C₂×C₄	#15667984	1	2	yes	—
238	C₂×C₄	#15667993	1	1	yes	characteristic
239	C₂×C₄	Q₁₆×D₈₉	1	2	yes	—
240	C₂×C₄	#15668035	1	2	yes	—
241	C₂×C₄	#15668044	1	2	yes	—
242	C₂×C₄	#15668044	1	2	yes	—
243	C₈	—	2	4	no	—
244	C₈	—	712	2	no	—
245	C₂²	#19151478	1	1	yes	characteristic
246	C₂²	#19151752	1	2	yes	—
247	C₂²	#19151759	1	2	yes	—
248	C₂²	#19151765	1	1	yes	characteristic
249	C₂²	#19151765	1	1	yes	characteristic
250	C₄	—	2	1	no	—
251	C₄	—	2	1	no	—
252	C₄	—	4	4	no	—
253	C₄	—	8	2	no	—
254	C₄	—	356	4	no	—
255	C₄	—	712	2	no	—
256	C₄	Q₁₆×Dic₈₉	1	2	yes	—
257	C₄	#19151705	1	2	yes	—
258	C₄	#19151806	1	2	yes	—
259	C₄	#19151822	1	2	yes	—
260	C₂	#26019383	1	2	yes	—
261	C₂	#26019390	1	1	yes	characteristic
262	C₂	#26019395	1	1	yes	characteristic
263	C₂	#26020595	1	2	yes	—
264	C₂	#26020651	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#26023342

C₂

yes

maximal, characteristic

#26021201

C₂

yes

maximal

C₂×#19151347

C₂

yes

maximal, characteristic

#26018092

C₂

yes

maximal

C₂×#494×C₈₉

C₂

yes

maximal, characteristic

C₂×C₄⋊#10623494

C₂²

yes

—

#19151505

—

#19151497

—

C₄⋊C₄×Dic₈₉

—

C₄×C₄⋊Dic₈₉

C₂²

yes

—

#19151360

—

#19151360

—

#19151347

—

C₂²×Q₁₆×C₈₉

—

C₂×C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

C₂×C₄⋊Q₈×C₈₉

C₂²

yes

characteristic

#494×C₈₉

—

#494×C₈₉

C₄

yes

complemented

C₂×C₄×C₈×C₈₉

C₂²

yes

characteristic

C₂²×#10623494

—

C₂×C₄⋊Dic₈₉

—

C₂×C₄⋊Dic₈₉

D₄

yes

—

C₂×C₄⋊Dic₈₉

D₄

yes

—

C₂×C₄×Dic₈₉

—

C₂×C₄×Dic₈₉

—

—

—

—

—

C₂²×Q₈×C₈₉

—

C₂²×Q₈×C₈₉

D₄

yes

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂×Q₁₆×C₈₉

—

C₂²×C₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

—

C₄⋊Q₈×C₈₉

C₂×C₄

yes

—

C₄⋊Q₈×C₈₉

C₂×C₄

yes

—

C₄⋊Q₈×C₈₉

D₄

yes

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄⋊C₄×C₈₉

—

C₂×C₄²×C₈₉

C₂³

yes

characteristic

C₄×C₈×C₈₉

—

C₄×C₈×C₈₉

C₂×C₄

yes

—

C₂²×Dic₈₉

—

C₂²×Dic₈₉

—

C₂×#10623494

—

C₂×#10623494

—

C₂×#10623494

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

—

C₄⋊Dic₈₉

Q₁₆

yes

complemented

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₄×Dic₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

—

C₂×Q₈×C₈₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

—

C₂²×C₄×C₈₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₈₉

C₂×D₄

yes

—

Q₁₆×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₂×C₈×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄⋊C₄×C₈₉

—

C₄²×C₈₉

C₂²×C₄

yes

characteristic

C₄²×C₈₉

C₂×D₄

yes

characteristic

C₄²×C₈₉

#41

yes

—

C₂³×C₈₉

#120

yes

characteristic

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

Q₈×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

—

C₂×C₄×C₈₉

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₈₉

C₄×D₄

yes

—

C₂×C₄×C₈₉

#121

yes

—

C₂×C₄×C₈₉

#123

yes

characteristic

100

C₂×C₄×C₈₉

C₂×Q₁₆

yes

—

101

C₂×C₄×C₈₉

#135

yes

—

102

C₂×C₄×C₈₉

#137

yes

—

103

C₂×C₄×C₈₉

#137

yes

—

104

C₂×Dic₈₉

—

105

C₂×Dic₈₉

—

106

C₂×Dic₈₉

—

107

C₂×Dic₈₉

—

108

C₂×Dic₈₉

—

109

C₂×Dic₈₉

—

110

C₈×C₈₉

—

111

#10623494

—

112

C₂²×C₈₉

#386

yes

characteristic

113

C₂²×C₈₉

#451

yes

—

114

C₂²×C₈₉

#452

yes

—

115

C₂²×C₈₉

#453

yes

characteristic

116

C₂²×C₈₉

#453

yes

characteristic

117

C₄×C₈₉

—

118

C₄×C₈₉

—

119

C₄×C₈₉

—

120

C₄×C₈₉

—

121

C₄×C₈₉

C₄×Q₁₆

yes

—

122

C₄×C₈₉

#441

yes

—

123

C₄×C₈₉

#462

yes

—

124

C₄×C₈₉

#464

yes

—

125

Dic₈₉

—

126

Dic₈₉

—

127

#9066

—

maximal, Sylow

128

C₂×C₈₉

#1632

yes

—

129

C₂×C₈₉

#1633

yes

characteristic

130

C₂×C₈₉

#1634

yes

characteristic

131

C₂×C₈₉

#1878

yes

—

132

C₂×C₈₉

#1887

yes

characteristic

133

C₂×#494

D₈₉

yes

characteristic

134

#2369

—

135

#1987

—

136

C₂×#333

—

137

#1279

—

138

C₈₉

#9066

yes

characteristic, complemented, Sylow

139

C₂²×Q₁₆

—

140

C₂×C₄⋊Q₈

C₂×D₈₉

yes

characteristic

141

C₂×C₄⋊Q₈

C₂×D₈₉

yes

characteristic

142

#494

—

143

#494

Dic₈₉

yes

complemented

144

C₂×C₄⋊C₈

—

145

C₂×C₄×C₈

C₂×D₈₉

yes

characteristic

146

#391

—

178

—

147

#389

—

178

—

148

C₄×C₄⋊C₄

—

149

C₄×C₄⋊C₄

—

178

—

150

#340

—

178

—

151

#340

—

178

—

152

#333

—

178

—

153

C₂²×Q₈

—

154

C₂²×Q₈

C₂²⋊D₈₉

yes

—

155

C₂×Q₁₆

—

156

C₂×Q₁₆

—

157

C₂×Q₁₆

—

158

C₂²×C₈

—

159

C₂²×C₈

—

178

—

160

C₄⋊Q₈

—

161

C₄⋊Q₈

—

162

C₄⋊Q₈

—

163

C₄⋊Q₈

C₂×Dic₈₉

yes

—

164

C₄⋊Q₈

C₂×Dic₈₉

yes

—

165

C₄⋊Q₈

C₂²⋊D₈₉

yes

—

166

C₂×C₄⋊C₄

—

167

C₂×C₄⋊C₄

—

168

C₂×C₄⋊C₄

—

169

C₂×C₄⋊C₄

—

170

C₂×C₄⋊C₄

—

178

—

171

C₂×C₄²

—

178

—

172

C₂×C₄²

—

178

—

173

C₂×C₄²

C₂²×D₈₉

yes

characteristic

174

C₄⋊C₈

—

178

—

175

C₄⋊C₈

—

178

—

176

C₄×C₈

—

177

C₄×C₈

C₂×Dic₈₉

yes

—

178

#95

—

178

—

179

#95

—

178

—

180

C₂×Q₈

—

181

C₂×Q₈

—

182

C₂×Q₈

—

183

C₂×Q₈

—

184

C₂×Q₈

—

185

C₂×Q₈

—

186

C₂×Q₈

—

187

C₂×Q₈

C₂²⋊Dic₈₉

yes

—

188

C₂²×C₄

—

189

C₂²×C₄

—

190

C₂²×C₄

—

178

—

191

C₂²×C₄

—

178

—

192

C₂²×C₄

D₄×D₈₉

yes

—

193

C₂²×C₄

C₂×C₂²⋊D₈₉

yes

characteristic

194

Q₁₆

—

195

C₂×C₈

—

196

C₂×C₈

—

197

C₂×C₈

—

198

C₂×C₈

—

356

—

199

C₂×C₈

—

356

—

200

C₂×C₈

—

356

—

201

C₄⋊C₄

—

202

C₄⋊C₄

—

203

C₄⋊C₄

—

204

C₄⋊C₄

—

205

C₄⋊C₄

—

206

C₄⋊C₄

—

178

—

207

C₄⋊C₄

—

178

—

208

C₄⋊C₄

—

178

—

209

C₄⋊C₄

—

712

—

210

C₄²

—

356

—

211

C₄²

—

356

—

212

C₄²

—

712

—

213

C₄²

C₂²×Dic₈₉

yes

characteristic

214

C₄²

C₂×C₂²⋊D₈₉

yes

characteristic

215

C₄²

#13083573

yes

—

216

C₂³

#15667980

yes

characteristic

217

Q₈

—

218

Q₈

—

219

Q₈

—

220

Q₈

—

221

C₂×C₄

—

222

C₂×C₄

—

223

C₂×C₄

—

224

C₂×C₄

—

225

C₂×C₄

—

226

C₂×C₄

—

227

C₂×C₄

—

228

C₂×C₄

—

229

C₂×C₄

—

356

—

230

C₂×C₄

—

356

—

231

C₂×C₄

—

356

—

232

C₂×C₄

—

356

—

233

C₂×C₄

—

356

—

234

C₂×C₄

—

178

—

235

C₂×C₄

C₂×C₂²⋊Dic₈₉

yes

characteristic

236

C₂×C₄

D₄×Dic₈₉

yes

—

237

C₂×C₄

#15667984

yes

—

238

C₂×C₄

#15667993

yes

characteristic

239

C₂×C₄

Q₁₆×D₈₉

yes

—

240

C₂×C₄

#15668035

yes

—

241

C₂×C₄

#15668044

yes

—

242

C₂×C₄

#15668044

yes

—

243

C₈

—

244

C₈

—

712

—

245

C₂²

#19151478

yes

characteristic

246

C₂²

#19151752

yes

—

247

C₂²

#19151759

yes

—

248

C₂²

#19151765

yes

characteristic

249

C₂²

#19151765

yes

characteristic

250

C₄

—

251

C₄

—

252

C₄

—

253

C₄

—

254

C₄

—

356

—

255

C₄

—

712

—

256

C₄

Q₁₆×Dic₈₉

yes

—

257

C₄

#19151705

yes

—

258

C₄

#19151806

yes

—

259

C₄

#19151822

yes

—

260

C₂

#26019383

yes

—

261

C₂

#26019390

yes

characteristic

262

C₂

#26019395

yes

characteristic

263

C₂

#26020595

yes

—

264

C₂

#26020651

yes

characteristic

	subgroup	G/H
center	C₂³	#15667980
commutator	C₄²×C₈₉	C₂²×C₄
Frattini	C₂×C₄²	C₂²×D₈₉
Fitting	C₂×#494×C₈₉	C₂
socle, prime radical	C₂³×C₈₉	#120
cosocle	C₂×C₄²×C₈₉	C₂³
hypercenter	C₂×#494	D₈₉
hypocenter	C₈₉	#9066
LCS	G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉
UCS	C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

subgroup

G/H

center

C₂³

#15667980

commutator

C₄²×C₈₉

C₂²×C₄

Frattini

C₂×C₄²

C₂²×D₈₉

Fitting

C₂×#494×C₈₉

C₂

socle, prime radical

C₂³×C₈₉

#120

cosocle

C₂×C₄²×C₈₉

C₂³

D₈₉

C₈₉

G ▷ C₄²×C₈₉ ▷ C₂²×C₈₉ ▷ C₈₉

UCS

C₁ ◁ C₂³ ◁ C₂×C₄² ◁ C₂×#494

N	H ≅ G/N	type
18. #494×C₈₉	C₄	semidirect
56. C₄⋊Dic₈₉	Q₁₆	semidirect
138. C₈₉	#9066	semidirect
143. #494	Dic₈₉	semidirect

H ≅ G/N

type

18. #494×C₈₉

C₄

semidirect

56. C₄⋊Dic₈₉

Q₁₆

semidirect

138. C₈₉

#9066

semidirect

143. #494

Dic₈₉

semidirect

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

subgroup	index
#26023342	2
#26021201	2
C₂×#19151347	2
#26018092	2
C₂×#494×C₈₉	2
#9066	89

subgroup

index

C₂×#494×C₈₉

Subgroups — #36449735

Conjugacy classes of subgroups

Complements

Maximal subgroups