Group #42127396 — subgroups

Subgroups — C₁₀₉×#9402 #42127396

Order 27904.

486 conjugacy classes of subgroups; only the 138 normal subgroups are shown.

normal subgroups only

This group has 486 conjugacy classes of subgroups — too many to draw. Only its 138 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	C₁₀₉×#2983	C₂	1	1	yes	maximal, characteristic
2	C₁₀₉×#2546	C₂	1	1	yes	maximal, characteristic
3	C₁₀₉×#1801	C₂	1	1	yes	maximal, characteristic
4	C₁₀₉×#1546	C₂	1	2	yes	maximal
5	C₁₀₉×#1303	C₂	1	2	yes	maximal
6	C₂×C₄⋊Q₈×C₁₀₉	—	2	1	no	—
7	C₂×C₄⋊Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
8	C₂×C₄×Q₈×C₁₀₉	C₂²	1	1	yes	characteristic
9	#446×C₁₀₉	—	2	4	no	—
10	#432×C₁₀₉	—	2	2	no	—
11	#431×C₁₀₉	C₂²	1	2	yes	—
12	#423×C₁₀₉	C₂²	1	2	yes	—
13	C₂×#101×C₁₀₉	—	2	1	no	—
14	#398×C₁₀₉	C₄	1	4	yes	—
15	#391×C₁₀₉	—	2	1	no	—
16	#389×C₁₀₉	—	2	2	no	—
17	C₄×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic
18	#343×C₁₀₉	—	2	1	no	—
19	#332×C₁₀₉	—	2	4	no	—
20	C₂²×Q₈×C₁₀₉	—	2	1	no	—
21	C₂²×Q₈×C₁₀₉	D₄	1	1	yes	characteristic
22	C₂×M₁₆×C₁₀₉	—	2	2	no	—
23	C₄⋊Q₈×C₁₀₉	—	2	2	no	—
24	C₄⋊Q₈×C₁₀₉	—	2	2	no	—
25	C₄⋊Q₈×C₁₀₉	—	4	4	no	—
26	C₄×Q₈×C₁₀₉	—	2	2	no	—
27	C₄×Q₈×C₁₀₉	—	2	2	no	—
28	C₂×C₄⋊C₄×C₁₀₉	—	2	1	no	—
29	C₂×C₄⋊C₄×C₁₀₉	—	2	4	no	—
30	C₂×C₄⋊C₄×C₁₀₉	—	2	1	no	—
31	C₂×C₄⋊C₄×C₁₀₉	C₂×C₄	1	2	yes	—
32	C₂×C₄⋊C₄×C₁₀₉	C₂×C₄	1	2	yes	—
33	C₂×C₄⋊C₄×C₁₀₉	D₄	1	1	yes	characteristic
34	C₂×C₄²×C₁₀₉	—	2	1	no	—
35	C₂×C₄²×C₁₀₉	D₄	1	2	yes	—
36	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
37	C₄⋊C₈×C₁₀₉	—	2	4	no	—
38	C₄⋊C₈×C₁₀₉	—	2	2	no	—
39	C₄⋊C₈×C₁₀₉	—	2	2	no	—
40	C₄⋊C₈×C₁₀₉	D₄	1	4	yes	—
41	#101×C₁₀₉	—	4	2	no	—
42	C₂²⋊C₈×C₁₀₉	—	2	2	no	—
43	#97×C₁₀₉	—	2	4	no	—
44	C₄×C₈×C₁₀₉	—	2	2	no	—
45	#95×C₁₀₉	—	2	4	no	—
46	#95×C₁₀₉	C₂×C₄	1	2	yes	—
47	C₂×Q₈×C₁₀₉	—	2	2	no	—
48	C₂×Q₈×C₁₀₉	—	2	1	no	—
49	C₂×Q₈×C₁₀₉	—	2	2	no	—
50	C₂×Q₈×C₁₀₉	—	2	1	no	—
51	C₂×Q₈×C₁₀₉	—	4	2	no	—
52	C₂×Q₈×C₁₀₉	—	4	2	no	—
53	C₂×Q₈×C₁₀₉	—	4	1	no	—
54	C₂×Q₈×C₁₀₉	—	4	1	no	—
55	C₂²×C₄×C₁₀₉	—	2	2	no	—
56	C₂²×C₄×C₁₀₉	—	2	2	no	—
57	C₂²×C₄×C₁₀₉	C₂²⋊C₄	1	2	yes	—
58	C₂²×C₄×C₁₀₉	C₂²⋊C₄	1	2	yes	—
59	C₂²×C₄×C₁₀₉	C₂²×C₄	1	1	yes	characteristic
60	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
61	C₂²×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
62	M₁₆×C₁₀₉	—	4	2	no	—
63	M₁₆×C₁₀₉	—	4	2	no	—
64	C₂×C₈×C₁₀₉	—	2	4	no	—
65	C₂×C₈×C₁₀₉	—	4	2	no	—
66	C₄⋊C₄×C₁₀₉	—	2	4	no	—
67	C₄⋊C₄×C₁₀₉	—	2	4	no	—
68	C₄⋊C₄×C₁₀₉	—	2	2	no	—
69	C₄⋊C₄×C₁₀₉	—	2	4	no	—
70	C₄⋊C₄×C₁₀₉	—	4	8	no	—
71	C₄⋊C₄×C₁₀₉	—	4	1	no	—
72	C₄⋊C₄×C₁₀₉	—	4	1	no	—
73	C₄²×C₁₀₉	—	2	2	no	—
74	C₄²×C₁₀₉	—	2	2	no	—
75	C₄²×C₁₀₉	—	4	2	no	—
76	C₄²×C₁₀₉	C₂×D₄	1	2	yes	—
77	C₄²×C₁₀₉	#41	1	2	yes	—
78	C₂³×C₁₀₉	C₂×C₂²⋊C₄	1	1	yes	characteristic
79	Q₈×C₁₀₉	—	4	2	no	—
80	Q₈×C₁₀₉	—	4	2	no	—
81	Q₈×C₁₀₉	—	8	2	no	—
82	Q₈×C₁₀₉	—	8	2	no	—
83	C₂×C₄×C₁₀₉	—	2	2	no	—
84	C₂×C₄×C₁₀₉	—	2	4	no	—
85	C₂×C₄×C₁₀₉	—	2	2	no	—
86	C₂×C₄×C₁₀₉	—	2	2	no	—
87	C₂×C₄×C₁₀₉	—	2	2	no	—
88	C₂×C₄×C₁₀₉	—	2	2	no	—
89	C₂×C₄×C₁₀₉	—	4	1	no	—
90	C₂×C₄×C₁₀₉	—	4	2	no	—
91	C₂×C₄×C₁₀₉	—	4	2	no	—
92	C₂×C₄×C₁₀₉	—	4	2	no	—
93	C₂×C₄×C₁₀₉	—	4	2	no	—
94	C₂×C₄×C₁₀₉	—	4	2	no	—
95	C₂×C₄×C₁₀₉	—	4	2	no	—
96	C₂×C₄×C₁₀₉	C₄×D₄	1	2	yes	—
97	C₂×C₄×C₁₀₉	#120	1	1	yes	characteristic
98	C₂×C₄×C₁₀₉	#121	1	2	yes	—
99	C₂×C₄×C₁₀₉	#123	1	1	yes	characteristic
100	C₂×C₄×C₁₀₉	AGL(1,ℤ/8)	1	2	yes	—
101	C₂×C₄×C₁₀₉	AGL(1,ℤ/8)	1	1	yes	characteristic
102	C₂×C₄×C₁₀₉	#137	1	1	yes	characteristic
103	C₈×C₁₀₉	—	4	4	no	—
104	C₈×C₁₀₉	—	8	2	no	—
105	C₂²×C₁₀₉	—	2	1	no	—
106	C₂²×C₁₀₉	—	2	1	no	—
107	C₂²×C₁₀₉	#386	1	1	yes	characteristic
108	C₂²×C₁₀₉	#417	1	1	yes	characteristic
109	C₂²×C₁₀₉	#418	1	1	yes	characteristic
110	C₄×C₁₀₉	—	2	1	no	—
111	C₄×C₁₀₉	—	2	2	no	—
112	C₄×C₁₀₉	—	4	4	no	—
113	C₄×C₁₀₉	—	4	2	no	—
114	C₄×C₁₀₉	—	4	2	no	—
115	C₄×C₁₀₉	—	8	2	no	—
116	C₄×C₁₀₉	#456	1	2	yes	—
117	C₄×C₁₀₉	#468	1	2	yes	—
118	C₄×C₁₀₉	#469	1	2	yes	—
119	#9402	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
120	C₂×C₁₀₉	—	2	1	no	—
121	C₂×C₁₀₉	—	2	1	no	—
122	C₂×C₁₀₉	#1886	1	1	yes	characteristic
123	C₂×C₁₀₉	#1895	1	1	yes	characteristic
124	C₂×C₁₀₉	#1915	1	1	yes	characteristic
125	#2983	C₂×C₁₀₉	1	1	yes	characteristic
126	#2546	C₂×C₁₀₉	1	1	yes	characteristic
127	#1801	C₂×C₁₀₉	1	1	yes	characteristic
128	#1546	C₂×C₁₀₉	1	2	yes	—
129	#1303	C₂×C₁₀₉	1	2	yes	—
130	C₁₀₉	#9402	1	1	yes	characteristic, direct product factor, Sylow
131	C₂×C₄⋊Q₈	—	2	1	no	—
132	C₂×C₄⋊Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
133	C₂×C₄×Q₈	C₂²×C₁₀₉	1	1	yes	characteristic
134	#446	—	2	4	no	—
135	#432	—	2	2	no	—
136	#431	C₂²×C₁₀₉	1	2	yes	—
137	#423	C₂²×C₁₀₉	1	2	yes	—
138	C₂×#101	—	2	1	no	—
139	#398	C₄×C₁₀₉	1	4	yes	—
140	#391	—	2	1	no	—
141	#389	—	2	2	no	—
142	C₄×C₄⋊C₄	C₂²×C₁₀₉	1	1	yes	characteristic
143	#343	—	2	1	no	—
144	#332	—	2	4	no	—
145	C₂²×Q₈	—	2	1	no	—
146	C₂²×Q₈	D₄×C₁₀₉	1	1	yes	characteristic
147	C₂×M₁₆	—	2	2	no	—
148	C₄⋊Q₈	—	2	2	no	—
149	C₄⋊Q₈	—	2	2	no	—
150	C₄⋊Q₈	—	4	4	no	—
151	C₄×Q₈	—	2	2	no	—
152	C₄×Q₈	—	2	2	no	—
153	C₂×C₄⋊C₄	—	2	1	no	—
154	C₂×C₄⋊C₄	—	2	4	no	—
155	C₂×C₄⋊C₄	—	2	1	no	—
156	C₂×C₄⋊C₄	C₂×C₄×C₁₀₉	1	2	yes	—
157	C₂×C₄⋊C₄	C₂×C₄×C₁₀₉	1	2	yes	—
158	C₂×C₄⋊C₄	D₄×C₁₀₉	1	1	yes	characteristic
159	C₂×C₄²	—	2	1	no	—
160	C₂×C₄²	D₄×C₁₀₉	1	2	yes	—
161	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
162	C₄⋊C₈	—	2	4	no	—
163	C₄⋊C₈	—	2	2	no	—
164	C₄⋊C₈	—	2	2	no	—
165	C₄⋊C₈	D₄×C₁₀₉	1	4	yes	—
166	#101	—	4	2	no	—
167	C₂²⋊C₈	—	2	2	no	—
168	#97	—	2	4	no	—
169	C₄×C₈	—	2	2	no	—
170	#95	—	2	4	no	—
171	#95	C₂×C₄×C₁₀₉	1	2	yes	—
172	C₂×Q₈	—	2	2	no	—
173	C₂×Q₈	—	2	1	no	—
174	C₂×Q₈	—	2	2	no	—
175	C₂×Q₈	—	2	1	no	—
176	C₂×Q₈	—	4	2	no	—
177	C₂×Q₈	—	4	2	no	—
178	C₂×Q₈	—	4	1	no	—
179	C₂×Q₈	—	4	1	no	—
180	C₂²×C₄	—	2	2	no	—
181	C₂²×C₄	—	2	2	no	—
182	C₂²×C₄	C₂²⋊C₄×C₁₀₉	1	2	yes	—
183	C₂²×C₄	C₂²⋊C₄×C₁₀₉	1	2	yes	—
184	C₂²×C₄	C₂²×C₄×C₁₀₉	1	1	yes	characteristic
185	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
186	C₂²×C₄	C₂×D₄×C₁₀₉	1	1	yes	characteristic
187	M₁₆	—	4	2	no	—
188	M₁₆	—	4	2	no	—
189	C₂×C₈	—	2	4	no	—
190	C₂×C₈	—	4	2	no	—
191	C₄⋊C₄	—	2	4	no	—
192	C₄⋊C₄	—	2	4	no	—
193	C₄⋊C₄	—	2	2	no	—
194	C₄⋊C₄	—	2	4	no	—
195	C₄⋊C₄	—	4	8	no	—
196	C₄⋊C₄	—	4	1	no	—
197	C₄⋊C₄	—	4	1	no	—
198	C₄²	—	2	2	no	—
199	C₄²	—	2	2	no	—
200	C₄²	—	4	2	no	—
201	C₄²	C₂×D₄×C₁₀₉	1	2	yes	—
202	C₄²	#41×C₁₀₉	1	2	yes	—
203	C₂³	C₂×C₂²⋊C₄×C₁₀₉	1	1	yes	characteristic
204	Q₈	—	4	2	no	—
205	Q₈	—	4	2	no	—
206	Q₈	—	8	2	no	—
207	Q₈	—	8	2	no	—
208	C₂×C₄	—	2	2	no	—
209	C₂×C₄	—	2	4	no	—
210	C₂×C₄	—	2	2	no	—
211	C₂×C₄	—	2	2	no	—
212	C₂×C₄	—	2	2	no	—
213	C₂×C₄	—	2	2	no	—
214	C₂×C₄	—	4	1	no	—
215	C₂×C₄	—	4	2	no	—
216	C₂×C₄	—	4	2	no	—
217	C₂×C₄	—	4	2	no	—
218	C₂×C₄	—	4	2	no	—
219	C₂×C₄	—	4	2	no	—
220	C₂×C₄	—	4	2	no	—
221	C₂×C₄	C₄×D₄×C₁₀₉	1	2	yes	—
222	C₂×C₄	#120×C₁₀₉	1	1	yes	characteristic
223	C₂×C₄	#121×C₁₀₉	1	2	yes	—
224	C₂×C₄	#123×C₁₀₉	1	1	yes	characteristic
225	C₂×C₄	AGL(1,ℤ/8)×C₁₀₉	1	2	yes	—
226	C₂×C₄	AGL(1,ℤ/8)×C₁₀₉	1	1	yes	characteristic
227	C₂×C₄	#137×C₁₀₉	1	1	yes	characteristic
228	C₈	—	4	4	no	—
229	C₈	—	8	2	no	—
230	C₂²	—	2	1	no	—
231	C₂²	—	2	1	no	—
232	C₂²	#386×C₁₀₉	1	1	yes	characteristic
233	C₂²	#417×C₁₀₉	1	1	yes	characteristic
234	C₂²	#418×C₁₀₉	1	1	yes	characteristic
235	C₄	—	2	2	no	—
236	C₄	—	2	1	no	—
237	C₄	—	4	4	no	—
238	C₄	—	4	2	no	—
239	C₄	—	4	2	no	—
240	C₄	—	8	2	no	—
241	C₄	#456×C₁₀₉	1	2	yes	—
242	C₄	#468×C₁₀₉	1	2	yes	—
243	C₄	#469×C₁₀₉	1	2	yes	—
244	C₂	—	2	1	no	—
245	C₂	—	2	1	no	—
246	C₂	C₁₀₉×#1886	1	1	yes	characteristic
247	C₂	C₁₀₉×#1895	1	1	yes	characteristic
248	C₂	C₁₀₉×#1915	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

C₁₀₉×#2983

C₂

yes

maximal, characteristic

C₁₀₉×#2546

C₂

yes

maximal, characteristic

C₁₀₉×#1801

C₂

yes

maximal, characteristic

C₁₀₉×#1546

C₂

yes

maximal

C₁₀₉×#1303

C₂

yes

maximal

C₂×C₄⋊Q₈×C₁₀₉

—

C₂×C₄⋊Q₈×C₁₀₉

C₂²

yes

characteristic

C₂×C₄×Q₈×C₁₀₉

C₂²

yes

characteristic

#446×C₁₀₉

—

#432×C₁₀₉

—

#431×C₁₀₉

C₂²

yes

—

#423×C₁₀₉

C₂²

yes

—

C₂×#101×C₁₀₉

—

#398×C₁₀₉

C₄

yes

—

#391×C₁₀₉

—

#389×C₁₀₉

—

C₄×C₄⋊C₄×C₁₀₉

C₂²

yes

characteristic

#343×C₁₀₉

—

#332×C₁₀₉

—

C₂²×Q₈×C₁₀₉

—

C₂²×Q₈×C₁₀₉

D₄

yes

characteristic

C₂×M₁₆×C₁₀₉

—

C₄⋊Q₈×C₁₀₉

—

C₄⋊Q₈×C₁₀₉

—

C₄⋊Q₈×C₁₀₉

—

C₄×Q₈×C₁₀₉

—

C₄×Q₈×C₁₀₉

—

C₂×C₄⋊C₄×C₁₀₉

—

C₂×C₄⋊C₄×C₁₀₉

—

C₂×C₄⋊C₄×C₁₀₉

—

C₂×C₄⋊C₄×C₁₀₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₀₉

C₂×C₄

yes

—

C₂×C₄⋊C₄×C₁₀₉

D₄

yes

characteristic

C₂×C₄²×C₁₀₉

—

C₂×C₄²×C₁₀₉

D₄

yes

—

C₂×C₄²×C₁₀₉

C₂³

yes

characteristic

C₄⋊C₈×C₁₀₉

—

C₄⋊C₈×C₁₀₉

—

C₄⋊C₈×C₁₀₉

—

C₄⋊C₈×C₁₀₉

D₄

yes

—

#101×C₁₀₉

—

C₂²⋊C₈×C₁₀₉

—

#97×C₁₀₉

—

C₄×C₈×C₁₀₉

—

#95×C₁₀₉

—

#95×C₁₀₉

C₂×C₄

yes

—

C₂×Q₈×C₁₀₉

—

C₂×Q₈×C₁₀₉

—

C₂×Q₈×C₁₀₉

—

C₂×Q₈×C₁₀₉

—

C₂×Q₈×C₁₀₉

—

C₂×Q₈×C₁₀₉

—

C₂×Q₈×C₁₀₉

—

C₂×Q₈×C₁₀₉

—

C₂²×C₄×C₁₀₉

—

C₂²×C₄×C₁₀₉

—

C₂²×C₄×C₁₀₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₀₉

C₂²⋊C₄

yes

—

C₂²×C₄×C₁₀₉

C₂²×C₄

yes

characteristic

C₂²×C₄×C₁₀₉

C₂×D₄

yes

characteristic

C₂²×C₄×C₁₀₉

C₂×D₄

yes

characteristic

M₁₆×C₁₀₉

—

M₁₆×C₁₀₉

—

C₂×C₈×C₁₀₉

—

C₂×C₈×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄⋊C₄×C₁₀₉

—

C₄²×C₁₀₉

—

C₄²×C₁₀₉

—

C₄²×C₁₀₉

—

C₄²×C₁₀₉

C₂×D₄

yes

—

C₄²×C₁₀₉

#41

yes

—

C₂³×C₁₀₉

C₂×C₂²⋊C₄

yes

characteristic

Q₈×C₁₀₉

—

Q₈×C₁₀₉

—

Q₈×C₁₀₉

—

Q₈×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

—

C₂×C₄×C₁₀₉

C₄×D₄

yes

—

C₂×C₄×C₁₀₉

#120

yes

characteristic

C₂×C₄×C₁₀₉

#121

yes

—

C₂×C₄×C₁₀₉

#123

yes

characteristic

100

C₂×C₄×C₁₀₉

AGL(1,ℤ/8)

yes

—

101

C₂×C₄×C₁₀₉

AGL(1,ℤ/8)

yes

characteristic

102

C₂×C₄×C₁₀₉

#137

yes

characteristic

103

C₈×C₁₀₉

—

104

C₈×C₁₀₉

—

105

C₂²×C₁₀₉

—

106

C₂²×C₁₀₉

—

107

C₂²×C₁₀₉

#386

yes

characteristic

108

C₂²×C₁₀₉

#417

yes

characteristic

109

C₂²×C₁₀₉

#418

yes

characteristic

110

C₄×C₁₀₉

—

111

C₄×C₁₀₉

—

112

C₄×C₁₀₉

—

113

C₄×C₁₀₉

—

114

C₄×C₁₀₉

—

115

C₄×C₁₀₉

—

116

C₄×C₁₀₉

#456

yes

—

117

C₄×C₁₀₉

#468

yes

—

118

C₄×C₁₀₉

#469

yes

—

119

#9402

C₁₀₉

yes

maximal, characteristic, direct product factor, Sylow

120

C₂×C₁₀₉

—

121

C₂×C₁₀₉

—

122

C₂×C₁₀₉

#1886

yes

characteristic

123

C₂×C₁₀₉

#1895

yes

characteristic

124

C₂×C₁₀₉

#1915

yes

characteristic

125

#2983

C₂×C₁₀₉

yes

characteristic

126

#2546

C₂×C₁₀₉

yes

characteristic

127

#1801

C₂×C₁₀₉

yes

characteristic

128

#1546

C₂×C₁₀₉

yes

—

129

#1303

C₂×C₁₀₉

yes

—

130

C₁₀₉

#9402

yes

characteristic, direct product factor, Sylow

131

C₂×C₄⋊Q₈

—

132

C₂×C₄⋊Q₈

C₂²×C₁₀₉

yes

characteristic

133

C₂×C₄×Q₈

C₂²×C₁₀₉

yes

characteristic

134

#446

—

135

#432

—

136

#431

C₂²×C₁₀₉

yes

—

137

#423

C₂²×C₁₀₉

yes

—

138

C₂×#101

—

139

#398

C₄×C₁₀₉

yes

—

140

#391

—

141

#389

—

142

C₄×C₄⋊C₄

C₂²×C₁₀₉

yes

characteristic

143

#343

—

144

#332

—

145

C₂²×Q₈

—

146

C₂²×Q₈

D₄×C₁₀₉

yes

characteristic

147

C₂×M₁₆

—

148

C₄⋊Q₈

—

149

C₄⋊Q₈

—

150

C₄⋊Q₈

—

151

C₄×Q₈

—

152

C₄×Q₈

—

153

C₂×C₄⋊C₄

—

154

C₂×C₄⋊C₄

—

155

C₂×C₄⋊C₄

—

156

C₂×C₄⋊C₄

C₂×C₄×C₁₀₉

yes

—

157

C₂×C₄⋊C₄

C₂×C₄×C₁₀₉

yes

—

158

C₂×C₄⋊C₄

D₄×C₁₀₉

yes

characteristic

159

C₂×C₄²

—

160

C₂×C₄²

D₄×C₁₀₉

yes

—

161

C₂×C₄²

C₂³×C₁₀₉

yes

characteristic

162

C₄⋊C₈

—

163

C₄⋊C₈

—

164

C₄⋊C₈

—

165

C₄⋊C₈

D₄×C₁₀₉

yes

—

166

#101

—

167

C₂²⋊C₈

—

168

#97

—

169

C₄×C₈

—

170

#95

—

171

#95

C₂×C₄×C₁₀₉

yes

—

172

C₂×Q₈

—

173

C₂×Q₈

—

174

C₂×Q₈

—

175

C₂×Q₈

—

176

C₂×Q₈

—

177

C₂×Q₈

—

178

C₂×Q₈

—

179

C₂×Q₈

—

180

C₂²×C₄

—

181

C₂²×C₄

—

182

C₂²×C₄

C₂²⋊C₄×C₁₀₉

yes

—

183

C₂²×C₄

C₂²⋊C₄×C₁₀₉

yes

—

184

C₂²×C₄

C₂²×C₄×C₁₀₉

yes

characteristic

185

C₂²×C₄

C₂×D₄×C₁₀₉

yes

characteristic

186

C₂²×C₄

C₂×D₄×C₁₀₉

yes

characteristic

187

M₁₆

—

188

M₁₆

—

189

C₂×C₈

—

190

C₂×C₈

—

191

C₄⋊C₄

—

192

C₄⋊C₄

—

193

C₄⋊C₄

—

194

C₄⋊C₄

—

195

C₄⋊C₄

—

196

C₄⋊C₄

—

197

C₄⋊C₄

—

198

C₄²

—

199

C₄²

—

200

C₄²

—

201

C₄²

C₂×D₄×C₁₀₉

yes

—

202

C₄²

#41×C₁₀₉

yes

—

203

C₂³

C₂×C₂²⋊C₄×C₁₀₉

yes

characteristic

204

Q₈

—

205

Q₈

—

206

Q₈

—

207

Q₈

—

208

C₂×C₄

—

209

C₂×C₄

—

210

C₂×C₄

—

211

C₂×C₄

—

212

C₂×C₄

—

213

C₂×C₄

—

214

C₂×C₄

—

215

C₂×C₄

—

216

C₂×C₄

—

217

C₂×C₄

—

218

C₂×C₄

—

219

C₂×C₄

—

220

C₂×C₄

—

221

C₂×C₄

C₄×D₄×C₁₀₉

yes

—

222

C₂×C₄

#120×C₁₀₉

yes

characteristic

223

C₂×C₄

#121×C₁₀₉

yes

—

224

C₂×C₄

#123×C₁₀₉

yes

characteristic

225

C₂×C₄

AGL(1,ℤ/8)×C₁₀₉

yes

—

226

C₂×C₄

AGL(1,ℤ/8)×C₁₀₉

yes

characteristic

227

C₂×C₄

#137×C₁₀₉

yes

characteristic

228

C₈

—

229

C₈

—

230

C₂²

—

231

C₂²

—

232

C₂²

#386×C₁₀₉

yes

characteristic

233

C₂²

#417×C₁₀₉

yes

characteristic

234

C₂²

#418×C₁₀₉

yes

characteristic

235

C₄

—

236

C₄

—

237

C₄

—

238

C₄

—

239

C₄

—

240

C₄

—

241

C₄

#456×C₁₀₉

yes

—

242

C₄

#468×C₁₀₉

yes

—

243

C₄

#469×C₁₀₉

yes

—

244

C₂

—

245

C₂

—

246

C₂

C₁₀₉×#1886

yes

characteristic

247

C₂

C₁₀₉×#1895

yes

characteristic

248

C₂

C₁₀₉×#1915

yes

characteristic

	subgroup	G/H
center, socle	C₂²×C₁₀₉	#386
commutator	C₂²×C₄	C₂²×C₄×C₁₀₉
Frattini, cosocle	C₂×C₄²	C₂³×C₁₀₉
prime radical	C₂³×C₁₀₉	C₂×C₂²⋊C₄
LCS	G ▷ C₂²×C₄ ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂²×C₁₀₉ ◁ C₂×C₄²×C₁₀₉ ◁ G

subgroup

G/H

center, socle

C₂²×C₁₀₉

#386

commutator

C₂²×C₄

C₂²×C₄×C₁₀₉

Frattini, cosocle

C₂×C₄²

C₂³×C₁₀₉

prime radical

C₂³×C₁₀₉

C₂×C₂²⋊C₄

LCS

G ▷ C₂²×C₄ ▷ C₂² ▷ C₁

UCS

C₁ ◁ C₂²×C₁₀₉ ◁ C₂×C₄²×C₁₀₉ ◁ G

N	H ≅ G/N	type
119. #9402	C₁₀₉	direct (N × H)
130. C₁₀₉	#9402	direct (N × H)

H ≅ G/N

type

119. #9402

C₁₀₉

direct (N × H)

130. C₁₀₉

#9402

direct (N × H)

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

subgroup	index
C₁₀₉×#2983	2
C₁₀₉×#2546	2
C₁₀₉×#1801	2
C₁₀₉×#1546	2
C₁₀₉×#1303	2
#9402	109

subgroup

index

C₁₀₉×#2983

C₁₀₉×#2546

C₁₀₉×#1801

C₁₀₉×#1546

C₁₀₉×#1303

#9402

109

Subgroups — C₁₀₉×#9402 #42127396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C109×#9402 #42127396

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#9402 #42127396