Subgroups — C₁₀₉×#29385 #42147379

Order 27904.

662 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	C₁₀₉×#2956	C₂	1	1	yes	maximal, characteristic, complemented
2	C₁₀₉×#2921	C₂	1	1	yes	maximal, characteristic, complemented
3	C₁₀₉×#2102	C₂	1	1	yes	maximal, characteristic, complemented
4	C₁₀₉×#2091	C₂	1	1	yes	maximal, characteristic, complemented
5	C₁₀₉×#2050	C₂	1	1	yes	maximal, characteristic, complemented
6	C₁₀₉×#2010	C₂	1	1	yes	maximal, characteristic
7	C₁₀₉×#1932	C₂	1	2	yes	maximal, complemented
8	C₁₀₉×#1897	C₂	1	2	yes	maximal, complemented
9	C₁₀₉×#1891	C₂	1	2	yes	maximal, complemented
10	C₁₀₉×#1861	C₂	1	2	yes	maximal, complemented
11	C₁₀₉×#1841	C₂	1	1	yes	maximal, characteristic, complemented
12	#575×C₁₀₉	C₂²	1	1	yes	characteristic
13	#568×C₁₀₉	C₂²	1	2	yes	—
14	#525×C₁₀₉	C₂²	1	2	yes	—
15	C₂×#117×C₁₀₉	C₂²	1	1	yes	characteristic
16	#444×C₁₀₉	—	2	2	no	—
17	#443×C₁₀₉	—	2	2	no	—
18	#433×C₁₀₉	—	2	2	no	—
19	#433×C₁₀₉	—	2	2	no	—
20	#430×C₁₀₉	C₂²	1	1	yes	characteristic
21	#430×C₁₀₉	C₂²	1	2	yes	—
22	#423×C₁₀₉	C₂²	1	1	yes	characteristic
23	#423×C₁₀₉	C₂²	1	1	yes	characteristic
24	#421×C₁₀₉	C₂²	1	2	yes	—
25	C₂×#104×C₁₀₉	C₂²	1	2	yes	—
26	C₂×#104×C₁₀₉	C₂²	1	2	yes	—
27	#413×C₁₀₉	C₂²	1	2	yes	—
28	#407×C₁₀₉	C₂²	1	1	yes	characteristic
29	#407×C₁₀₉	C₂²	1	1	yes	characteristic
30	#407×C₁₀₉	C₂²	1	2	yes	—
31	C₄×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
32	C₄×M₁₆×C₁₀₉	C₂²	1	1	yes	characteristic
33	#344×C₁₀₉	C₂²	1	2	yes	—
34	#344×C₁₀₉	C₂²	1	2	yes	—
35	#339×C₁₀₉	C₂²	1	2	yes	—
36	#339×C₁₀₉	C₂²	1	2	yes	—
37	#338×C₁₀₉	C₂²	1	1	yes	characteristic
38	H(3,ℤ/4)×C₁₀₉	C₂²	1	1	yes	characteristic
39	C₂×#41×C₁₀₉	C₂³	1	2	yes	—
40	C₂³×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
41	#137×C₁₀₉	—	2	2	no	—
42	AGL(1,ℤ/8)×C₁₀₉	—	2	2	no	—
43	#135×C₁₀₉	—	2	2	no	—
44	#131×C₁₀₉	—	2	4	no	—
45	#131×C₁₀₉	—	4	2	no	—
46	C₂×M₁₆×C₁₀₉	—	4	2	no	—
47	C₂×M₁₆×C₁₀₉	C₂³	1	2	yes	—
48	C₂×M₁₆×C₁₀₉	C₂³	1	2	yes	—
49	C₂×M₁₆×C₁₀₉	C₂³	1	1	yes	characteristic
50	C₂×M₁₆×C₁₀₉	C₂³	1	1	yes	characteristic
51	C₂×M₁₆×C₁₀₉	C₂³	1	1	yes	characteristic
52	C₂×M₁₆×C₁₀₉	C₂³	1	1	yes	characteristic
53	#123×C₁₀₉	—	2	2	no	—
54	C₂²⋊Q₈×C₁₀₉	—	2	2	no	—
55	#121×C₁₀₉	—	2	2	no	—
56	#120×C₁₀₉	—	2	2	no	—
57	C₄×D₄×C₁₀₉	—	4	2	no	—
58	#117×C₁₀₉	—	2	1	no	—
59	#117×C₁₀₉	—	2	1	no	—
60	#117×C₁₀₉	—	2	2	no	—
61	#117×C₁₀₉	C₂³	1	2	yes	—
62	C₂×C₄⋊C₄×C₁₀₉	—	2	1	no	—
63	C₂×C₂²⋊C₄×C₁₀₉	—	2	1	no	—
64	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
65	C₂×C₄²×C₁₀₉	C₂³	1	1	yes	characteristic
66	#108×C₁₀₉	—	2	2	no	—
67	#108×C₁₀₉	—	4	2	no	—
68	C₄⋊C₈×C₁₀₉	—	2	2	no	—
69	C₄⋊C₈×C₁₀₉	—	2	2	no	—
70	#104×C₁₀₉	—	2	2	no	—
71	#104×C₁₀₉	—	2	2	no	—
72	#104×C₁₀₉	—	2	4	no	—
73	#104×C₁₀₉	—	4	2	no	—
74	#101×C₁₀₉	—	2	2	no	—
75	#100×C₁₀₉	—	2	2	no	—
76	C₂²⋊C₈×C₁₀₉	—	2	2	no	—
77	C₂²⋊C₈×C₁₀₉	—	2	2	no	—
78	C₂²⋊C₈×C₁₀₉	—	4	2	no	—
79	#97×C₁₀₉	—	2	1	no	—
80	#97×C₁₀₉	D₄	1	2	yes	complemented
81	C₄×C₈×C₁₀₉	—	2	1	no	—
82	C₄×C₈×C₁₀₉	D₄	1	2	yes	complemented
83	C₂⁴×C₁₀₉	#41	1	1	yes	characteristic
84	#41×C₁₀₉	—	2	2	no	—
85	#41×C₁₀₉	—	2	2	no	—
86	#41×C₁₀₉	—	2	2	no	—
87	#41×C₁₀₉	—	2	2	no	—
88	C₂×Q₈×C₁₀₉	#41	1	2	yes	—
89	C₂×D₄×C₁₀₉	—	2	2	no	—
90	C₂×D₄×C₁₀₉	—	4	2	no	—
91	C₂×D₄×C₁₀₉	#41	1	2	yes	—
92	C₂²×C₄×C₁₀₉	—	2	1	no	—
93	C₂²×C₄×C₁₀₉	—	2	1	no	—
94	C₂²×C₄×C₁₀₉	—	2	1	no	—
95	C₂²×C₄×C₁₀₉	—	2	1	no	—
96	C₂²×C₄×C₁₀₉	—	2	2	no	—
97	C₂²×C₄×C₁₀₉	—	2	2	no	—
98	C₂²×C₄×C₁₀₉	—	2	2	no	—
99	C₂²×C₄×C₁₀₉	#41	1	1	yes	characteristic
100	C₂²×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
101	Q₁₆×C₁₀₉	—	2	2	no	—
102	SD₁₆×C₁₀₉	—	2	4	no	—
103	D₈×C₁₀₉	—	2	2	no	—
104	M₁₆×C₁₀₉	—	2	2	no	—
105	M₁₆×C₁₀₉	—	2	2	no	—
106	M₁₆×C₁₀₉	—	2	2	no	—
107	M₁₆×C₁₀₉	—	2	2	no	—
108	M₁₆×C₁₀₉	—	2	2	no	—
109	M₁₆×C₁₀₉	—	2	2	no	—
110	M₁₆×C₁₀₉	—	2	2	no	—
111	M₁₆×C₁₀₉	—	2	2	no	—
112	M₁₆×C₁₀₉	—	4	4	no	—
113	C₂×C₈×C₁₀₉	—	2	1	no	—
114	C₂×C₈×C₁₀₉	—	2	1	no	—
115	C₂×C₈×C₁₀₉	—	2	2	no	—
116	C₂×C₈×C₁₀₉	—	2	2	no	—
117	C₂×C₈×C₁₀₉	—	4	4	no	—
118	C₂×C₈×C₁₀₉	C₂×D₄	1	2	yes	—
119	C₂×C₈×C₁₀₉	C₂×D₄	1	2	yes	—
120	C₄⋊C₄×C₁₀₉	—	2	2	no	—
121	C₄⋊C₄×C₁₀₉	—	2	2	no	—
122	C₄⋊C₄×C₁₀₉	—	2	2	no	—
123	C₄⋊C₄×C₁₀₉	—	4	2	no	—
124	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
125	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
126	C₂²⋊C₄×C₁₀₉	—	2	2	no	—
127	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
128	C₂²⋊C₄×C₁₀₉	—	4	2	no	—
129	C₄²×C₁₀₉	—	2	1	no	—
130	C₄²×C₁₀₉	—	2	1	no	—
131	C₄²×C₁₀₉	—	2	2	no	—
132	C₄²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
133	C₄²×C₁₀₉	C₂×D₄	1	1	yes	characteristic
134	C₄²×C₁₀₉	#41	1	2	yes	—
135	C₂³×C₁₀₉	—	2	1	no	—
136	C₂³×C₁₀₉	—	2	2	no	—
137	C₂³×C₁₀₉	—	2	2	no	—
138	C₂³×C₁₀₉	—	8	1	no	—
139	C₂³×C₁₀₉	C₂×#41	1	1	yes	characteristic
140	Q₈×C₁₀₉	—	2	2	no	—
141	Q₈×C₁₀₉	—	2	2	no	—
142	D₄×C₁₀₉	—	2	2	no	—
143	D₄×C₁₀₉	—	2	2	no	—
144	D₄×C₁₀₉	—	4	2	no	—
145	D₄×C₁₀₉	—	4	2	no	—
146	D₄×C₁₀₉	—	8	4	no	—
147	C₂×C₄×C₁₀₉	—	2	1	no	—
148	C₂×C₄×C₁₀₉	—	2	1	no	—
149	C₂×C₄×C₁₀₉	—	2	2	no	—
150	C₂×C₄×C₁₀₉	—	2	1	no	—
151	C₂×C₄×C₁₀₉	—	2	2	no	—
152	C₂×C₄×C₁₀₉	—	2	2	no	—
153	C₂×C₄×C₁₀₉	—	4	1	no	—
154	C₂×C₄×C₁₀₉	—	4	2	no	—
155	C₂×C₄×C₁₀₉	—	4	1	no	—
156	C₂×C₄×C₁₀₉	—	4	2	no	—
157	C₂×C₄×C₁₀₉	—	4	2	no	—
158	C₂×C₄×C₁₀₉	—	4	2	no	—
159	C₂×C₄×C₁₀₉	—	8	1	no	—
160	C₂×C₄×C₁₀₉	—	8	1	no	—
161	C₂×C₄×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
162	C₂×C₄×C₁₀₉	C₂×#41	1	2	yes	—
163	C₂×C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
164	C₂×C₄×C₁₀₉	H(5,𝔽₂)	1	2	yes	—
165	C₈×C₁₀₉	—	2	2	no	—
166	C₈×C₁₀₉	—	2	2	no	—
167	C₈×C₁₀₉	—	4	1	no	—
168	C₈×C₁₀₉	—	4	2	no	—
169	C₈×C₁₀₉	—	4	1	no	—
170	C₈×C₁₀₉	—	4	2	no	—
171	C₂²×C₁₀₉	—	4	1	no	—
172	C₂²×C₁₀₉	—	4	2	no	—
173	C₂²×C₁₀₉	—	4	2	no	—
174	C₂²×C₁₀₉	—	4	2	no	—
175	C₂²×C₁₀₉	—	4	1	no	—
176	C₂²×C₁₀₉	—	4	2	no	—
177	C₂²×C₁₀₉	—	8	2	no	—
178	C₂²×C₁₀₉	#525	1	1	yes	characteristic
179	C₂²×C₁₀₉	#551	1	2	yes	—
180	C₄×C₁₀₉	—	4	1	no	—
181	C₄×C₁₀₉	—	4	1	no	—
182	C₄×C₁₀₉	—	4	2	no	—
183	C₄×C₁₀₉	—	4	1	no	—
184	C₄×C₁₀₉	—	4	2	no	—
185	C₄×C₁₀₉	—	8	2	no	—
186	C₄×C₁₀₉	#525	1	1	yes	characteristic
187	C₄×C₁₀₉	#535	1	1	yes	characteristic
188	C₄×C₁₀₉	#553	1	2	yes	—
189	#29385	C₁₀₉	1	1	yes	maximal, characteristic, direct product factor, Sylow
190	C₂×C₁₀₉	—	2	1	no	—
191	C₂×C₁₀₉	—	2	2	no	—
192	C₂×C₁₀₉	—	8	1	no	—
193	C₂×C₁₀₉	—	8	2	no	—
194	C₂×C₁₀₉	#2598	1	1	yes	characteristic
195	#2956	C₂×C₁₀₉	1	1	yes	characteristic, complemented
196	#2921	C₂×C₁₀₉	1	1	yes	characteristic, complemented
197	#2102	C₂×C₁₀₉	1	1	yes	characteristic, complemented
198	#2091	C₂×C₁₀₉	1	1	yes	characteristic, complemented
199	#2050	C₂×C₁₀₉	1	1	yes	characteristic, complemented
200	#2010	C₂×C₁₀₉	1	1	yes	characteristic
201	#1932	C₂×C₁₀₉	1	2	yes	complemented
202	#1897	C₂×C₁₀₉	1	2	yes	complemented
203	#1891	C₂×C₁₀₉	1	2	yes	complemented
204	#1861	C₂×C₁₀₉	1	2	yes	complemented
205	#1841	C₂×C₁₀₉	1	1	yes	characteristic, complemented
206	C₁₀₉	#29385	1	1	yes	characteristic, direct product factor, Sylow
207	#575	C₂²×C₁₀₉	1	1	yes	characteristic
208	#568	C₂²×C₁₀₉	1	2	yes	—
209	#525	C₂²×C₁₀₉	1	2	yes	—
210	C₂×#117	C₂²×C₁₀₉	1	1	yes	characteristic
211	#444	—	2	2	no	—
212	#443	—	2	2	no	—
213	#433	—	2	2	no	—
214	#433	—	2	2	no	—
215	#430	C₂²×C₁₀₉	1	1	yes	characteristic
216	#430	C₂²×C₁₀₉	1	2	yes	—
217	#423	C₂²×C₁₀₉	1	1	yes	characteristic
218	#423	C₂²×C₁₀₉	1	1	yes	characteristic
219	#421	C₂²×C₁₀₉	1	2	yes	—
220	C₂×#104	C₂²×C₁₀₉	1	2	yes	—
221	C₂×#104	C₂²×C₁₀₉	1	2	yes	—
222	#413	C₂²×C₁₀₉	1	2	yes	—
223	#407	C₂²×C₁₀₉	1	1	yes	characteristic
224	#407	C₂²×C₁₀₉	1	1	yes	characteristic
225	#407	C₂²×C₁₀₉	1	2	yes	—
226	C₄×M₁₆	C₂²×C₁₀₉	1	1	yes	characteristic
227	C₄×M₁₆	C₂²×C₁₀₉	1	1	yes	characteristic
228	#344	C₂²×C₁₀₉	1	2	yes	—
229	#344	C₂²×C₁₀₉	1	2	yes	—
230	#339	C₂²×C₁₀₉	1	2	yes	—
231	#339	C₂²×C₁₀₉	1	2	yes	—
232	#338	C₂²×C₁₀₉	1	1	yes	characteristic
233	H(3,ℤ/4)	C₂²×C₁₀₉	1	1	yes	characteristic
234	C₂×#41	C₂³×C₁₀₉	1	2	yes	—
235	C₂³×C₄	C₂³×C₁₀₉	1	1	yes	characteristic
236	#137	—	2	2	no	—
237	AGL(1,ℤ/8)	—	2	2	no	—
238	#135	—	2	2	no	—
239	#131	—	2	4	no	—
240	#131	—	4	2	no	—
241	C₂×M₁₆	—	4	2	no	—
242	C₂×M₁₆	C₂³×C₁₀₉	1	2	yes	—
243	C₂×M₁₆	C₂³×C₁₀₉	1	2	yes	—
244	C₂×M₁₆	C₂³×C₁₀₉	1	1	yes	characteristic
245	C₂×M₁₆	C₂³×C₁₀₉	1	1	yes	characteristic
246	C₂×M₁₆	C₂³×C₁₀₉	1	1	yes	characteristic
247	C₂×M₁₆	C₂³×C₁₀₉	1	1	yes	characteristic
248	#123	—	2	2	no	—
249	C₂²⋊Q₈	—	2	2	no	—
250	#121	—	2	2	no	—
251	#120	—	2	2	no	—
252	C₄×D₄	—	4	2	no	—
253	#117	—	2	1	no	—
254	#117	—	2	1	no	—
255	#117	—	2	2	no	—
256	#117	C₂³×C₁₀₉	1	2	yes	—
257	C₂×C₄⋊C₄	—	2	1	no	—
258	C₂×C₂²⋊C₄	—	2	1	no	—
259	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
260	C₂×C₄²	C₂³×C₁₀₉	1	1	yes	characteristic
261	#108	—	2	2	no	—
262	#108	—	4	2	no	—
263	C₄⋊C₈	—	2	2	no	—
264	C₄⋊C₈	—	2	2	no	—
265	#104	—	2	2	no	—
266	#104	—	2	2	no	—
267	#104	—	2	4	no	—
268	#104	—	4	2	no	—
269	#101	—	2	2	no	—
270	#100	—	2	2	no	—
271	C₂²⋊C₈	—	2	2	no	—
272	C₂²⋊C₈	—	2	2	no	—
273	C₂²⋊C₈	—	4	2	no	—
274	#97	—	2	1	no	—
275	#97	D₄×C₁₀₉	1	2	yes	complemented
276	C₄×C₈	—	2	1	no	—
277	C₄×C₈	D₄×C₁₀₉	1	2	yes	complemented
278	C₂⁴	#41×C₁₀₉	1	1	yes	characteristic
279	#41	—	2	2	no	—
280	#41	—	2	2	no	—
281	#41	—	2	2	no	—
282	#41	—	2	2	no	—
283	C₂×Q₈	#41×C₁₀₉	1	2	yes	—
284	C₂×D₄	—	2	2	no	—
285	C₂×D₄	—	4	2	no	—
286	C₂×D₄	#41×C₁₀₉	1	2	yes	—
287	C₂²×C₄	—	2	1	no	—
288	C₂²×C₄	—	2	1	no	—
289	C₂²×C₄	—	2	1	no	—
290	C₂²×C₄	—	2	1	no	—
291	C₂²×C₄	—	2	2	no	—
292	C₂²×C₄	—	2	2	no	—
293	C₂²×C₄	—	2	2	no	—
294	C₂²×C₄	#41×C₁₀₉	1	1	yes	characteristic
295	C₂²×C₄	C₂⁴×C₁₀₉	1	1	yes	characteristic
296	Q₁₆	—	2	2	no	—
297	SD₁₆	—	2	4	no	—
298	D₈	—	2	2	no	—
299	M₁₆	—	2	2	no	—
300	M₁₆	—	2	2	no	—
301	M₁₆	—	2	2	no	—
302	M₁₆	—	2	2	no	—
303	M₁₆	—	2	2	no	—
304	M₁₆	—	2	2	no	—
305	M₁₆	—	2	2	no	—
306	M₁₆	—	2	2	no	—
307	M₁₆	—	4	4	no	—
308	C₂×C₈	—	2	1	no	—
309	C₂×C₈	—	2	1	no	—
310	C₂×C₈	—	2	2	no	—
311	C₂×C₈	—	2	2	no	—
312	C₂×C₈	—	4	4	no	—
313	C₂×C₈	C₂×D₄×C₁₀₉	1	2	yes	—
314	C₂×C₈	C₂×D₄×C₁₀₉	1	2	yes	—
315	C₄⋊C₄	—	2	2	no	—
316	C₄⋊C₄	—	2	2	no	—
317	C₄⋊C₄	—	2	2	no	—
318	C₄⋊C₄	—	4	2	no	—
319	C₂²⋊C₄	—	2	2	no	—
320	C₂²⋊C₄	—	2	2	no	—
321	C₂²⋊C₄	—	2	2	no	—
322	C₂²⋊C₄	—	4	2	no	—
323	C₂²⋊C₄	—	4	2	no	—
324	C₄²	—	2	1	no	—
325	C₄²	—	2	1	no	—
326	C₄²	—	2	2	no	—
327	C₄²	C₂×D₄×C₁₀₉	1	1	yes	characteristic
328	C₄²	C₂×D₄×C₁₀₉	1	1	yes	characteristic
329	C₄²	#41×C₁₀₉	1	2	yes	—
330	C₂³	—	2	1	no	—
331	C₂³	—	2	2	no	—
332	C₂³	—	2	2	no	—
333	C₂³	—	8	1	no	—
334	C₂³	C₂×#41×C₁₀₉	1	1	yes	characteristic
335	Q₈	—	2	2	no	—
336	Q₈	—	2	2	no	—
337	D₄	—	2	2	no	—
338	D₄	—	2	2	no	—
339	D₄	—	4	2	no	—
340	D₄	—	4	2	no	—
341	D₄	—	8	4	no	—
342	C₂×C₄	—	2	1	no	—
343	C₂×C₄	—	2	1	no	—
344	C₂×C₄	—	2	2	no	—
345	C₂×C₄	—	2	1	no	—
346	C₂×C₄	—	2	2	no	—
347	C₂×C₄	—	2	2	no	—
348	C₂×C₄	—	4	1	no	—
349	C₂×C₄	—	4	2	no	—
350	C₂×C₄	—	4	1	no	—
351	C₂×C₄	—	4	2	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	4	2	no	—
354	C₂×C₄	—	8	1	no	—
355	C₂×C₄	—	8	1	no	—
356	C₂×C₄	C₂²×D₄×C₁₀₉	1	1	yes	characteristic
357	C₂×C₄	C₂×#41×C₁₀₉	1	2	yes	—
358	C₂×C₄	C₂×#41×C₁₀₉	1	1	yes	characteristic
359	C₂×C₄	H(5,𝔽₂)×C₁₀₉	1	2	yes	—
360	C₈	—	2	2	no	—
361	C₈	—	2	2	no	—
362	C₈	—	4	1	no	—
363	C₈	—	4	2	no	—
364	C₈	—	4	1	no	—
365	C₈	—	4	2	no	—
366	C₂²	—	4	1	no	—
367	C₂²	—	4	2	no	—
368	C₂²	—	4	2	no	—
369	C₂²	—	4	2	no	—
370	C₂²	—	4	1	no	—
371	C₂²	—	4	2	no	—
372	C₂²	—	8	2	no	—
373	C₂²	#525×C₁₀₉	1	1	yes	characteristic
374	C₂²	#551×C₁₀₉	1	2	yes	—
375	C₄	—	4	1	no	—
376	C₄	—	4	1	no	—
377	C₄	—	4	2	no	—
378	C₄	—	4	1	no	—
379	C₄	—	4	2	no	—
380	C₄	—	8	2	no	—
381	C₄	#525×C₁₀₉	1	1	yes	characteristic
382	C₄	#535×C₁₀₉	1	1	yes	characteristic
383	C₄	#553×C₁₀₉	1	2	yes	—
384	C₂	—	2	1	no	—
385	C₂	—	2	2	no	—
386	C₂	—	8	1	no	—
387	C₂	—	8	2	no	—
388	C₂	C₁₀₉×#2598	1	1	yes	characteristic

	subgroup	G/H
center	C₄×C₁₀₉	#535
commutator, Frattini, cosocle	C₂²×C₄	C₂⁴×C₁₀₉
socle	C₂×C₁₀₉	#2598
prime radical	C₁₀₉×#2010	C₂
LCS	G ▷ C₂²×C₄ ▷ C₂ ▷ C₁
UCS	C₁ ◁ C₄×C₁₀₉ ◁ C₂²×C₄×C₁₀₉ ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

N	H ≅ G/N	type
1. C₁₀₉×#2956	C₂	semidirect
2. C₁₀₉×#2921	C₂	semidirect
3. C₁₀₉×#2102	C₂	semidirect
4. C₁₀₉×#2091	C₂	semidirect
5. C₁₀₉×#2050	C₂	semidirect
7. C₁₀₉×#1932	C₂	semidirect
8. C₁₀₉×#1897	C₂	semidirect
9. C₁₀₉×#1891	C₂	semidirect
10. C₁₀₉×#1861	C₂	semidirect
11. C₁₀₉×#1841	C₂	semidirect
80. #97×C₁₀₉	D₄	semidirect
82. C₄×C₈×C₁₀₉	D₄	semidirect
189. #29385	C₁₀₉	direct (N × H)
195. #2956	C₂×C₁₀₉	semidirect
196. #2921	C₂×C₁₀₉	semidirect
197. #2102	C₂×C₁₀₉	semidirect
198. #2091	C₂×C₁₀₉	semidirect
199. #2050	C₂×C₁₀₉	semidirect
201. #1932	C₂×C₁₀₉	semidirect
202. #1897	C₂×C₁₀₉	semidirect
203. #1891	C₂×C₁₀₉	semidirect
204. #1861	C₂×C₁₀₉	semidirect
205. #1841	C₂×C₁₀₉	semidirect
206. C₁₀₉	#29385	direct (N × H)
275. #97	D₄×C₁₀₉	semidirect
277. C₄×C₈	D₄×C₁₀₉	semidirect

Maximal subgroups

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

subgroup	index
C₁₀₉×#2956	2
C₁₀₉×#2921	2
C₁₀₉×#2102	2
C₁₀₉×#2091	2
C₁₀₉×#2050	2
C₁₀₉×#2010	2
C₁₀₉×#1932	2
C₁₀₉×#1897	2
C₁₀₉×#1891	2
C₁₀₉×#1861	2
C₁₀₉×#1841	2
#29385	109

Subgroups — C109×#29385 #42147379

Conjugacy classes of subgroups

Complements

Maximal subgroups

Subgroups — C₁₀₉×#29385 #42147379