Subgroups — #28374841

Order 13952.

494 conjugacy classes of subgroups.

The subgroup lattice has 410 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#20295677	C₂	1	1	yes	maximal, characteristic, complemented
2	D₄×C₂²⋊D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
3	#20295371	C₂	1	1	yes	maximal, characteristic, complemented
4	#20295339	C₂	1	1	yes	maximal, characteristic, complemented
5	#20295338	C₂	1	1	yes	maximal, characteristic, complemented
6	#20295304	C₂	1	1	yes	maximal, characteristic, complemented
7	#20295262	C₂	1	1	yes	maximal, characteristic, complemented
8	#20295261	C₂	1	1	yes	maximal, characteristic, complemented
9	#20295220	C₂	1	1	yes	maximal, characteristic, complemented
10	#20295161	C₂	1	1	yes	maximal, characteristic, complemented
11	#20295160	C₂	1	1	yes	maximal, characteristic, complemented
12	#20295106	C₂	1	1	yes	maximal, characteristic, complemented
13	C₈×C₂²⋊D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
14	#102×D₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
15	C₂×#102×C₁₀₉	C₂	1	1	yes	maximal, characteristic, complemented
16	C₂×#13182029	—	2	1	no	—
17	C₂²×C₂²⋊D₁₀₉	—	2	1	no	—
18	C₂×D₄×D₁₀₉	C₂²	1	1	yes	characteristic
19	C₂×D₈₇₂	C₂²	1	1	yes	characteristic, complemented
20	C₂×#13182014	C₂²	1	1	yes	characteristic
21	C₂×#13182014	C₂²	1	1	yes	characteristic, complemented
22	C₂×C₈×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
23	#16812698	C₂²	1	1	yes	characteristic, complemented
24	#16812695	C₂²	1	1	yes	characteristic
25	#16812684	—	2	1	no	—
26	#16812682	—	2	1	no	—
27	#16812677	—	2	1	no	—
28	#16812674	C₂²	1	1	yes	characteristic, complemented
29	#16812673	C₂²	1	1	yes	characteristic
30	#16812673	C₂²	1	1	yes	characteristic, complemented
31	#16812671	—	2	1	no	—
32	#16812670	C₂²	1	1	yes	characteristic
33	#16812668	—	2	1	no	—
34	#16812667	—	2	1	no	—
35	D₄×Dic₁₀₉	C₂²	1	1	yes	characteristic
36	#16812661	C₂²	1	1	yes	characteristic, complemented
37	C₄×C₂²⋊D₁₀₉	C₂²	1	1	yes	characteristic
38	C₄⋊C₄×D₁₀₉	C₂²	1	1	yes	characteristic, complemented
39	#16812633	C₂²	1	1	yes	characteristic, complemented
40	#16812632	C₂²	1	1	yes	characteristic, complemented
41	#16812632	C₂²	1	1	yes	characteristic, complemented
42	#16812628	C₂²	1	1	yes	characteristic, complemented
43	#16812621	C₂²	1	1	yes	characteristic, complemented
44	#16812621	C₂²	1	1	yes	characteristic, complemented
45	#16812620	C₂²	1	1	yes	characteristic
46	#16812620	C₂²	1	1	yes	characteristic, complemented
47	#16812619	C₂²	1	1	yes	characteristic, complemented
48	#16812619	C₂²	1	1	yes	characteristic, complemented
49	C₂²⋊#11724784	C₂²	1	1	yes	characteristic, complemented
50	#16812611	C₂²	1	1	yes	characteristic, complemented
51	C₈×Dic₁₀₉	C₂²	1	1	yes	characteristic, complemented
52	C₂²×D₄×C₁₀₉	C₂²	1	1	yes	characteristic
53	C₂²×C₈×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
54	C₂×C₄⋊C₄×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
55	#102×C₁₀₉	C₂²	1	1	yes	characteristic
56	#102×C₁₀₉	C₂²	1	1	yes	characteristic
57	#102×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
58	#102×C₁₀₉	C₂²	1	1	yes	characteristic, complemented
59	C₂³×D₁₀₉	—	2	1	no	—
60	#13182029	—	4	4	no	—
61	C₂×Dic₂₁₈	—	2	1	no	—
62	C₂×D₄₃₆	—	2	1	no	—
63	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
64	C₂×D₄₃₆	C₂³	1	1	yes	characteristic
65	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
66	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
67	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
68	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
69	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
70	C₂×C₂²⋊D₁₀₉	—	2	1	no	—
71	C₂×C₂²⋊D₁₀₉	—	4	4	no	—
72	C₂×C₂²⋊D₁₀₉	D₄	1	1	yes	characteristic
73	D₄×D₁₀₉	—	2	2	no	—
74	D₄×D₁₀₉	—	4	1	no	—
75	C₂²×Dic₁₀₉	—	2	1	no	—
76	C₂×C₄×D₁₀₉	—	2	1	no	—
77	C₂×C₄×D₁₀₉	—	2	1	no	—
78	C₂×C₄×D₁₀₉	C₂³	1	1	yes	characteristic
79	D₈₇₂	—	4	1	no	—
80	#13182014	—	2	2	no	—
81	#13182014	—	4	1	no	—
82	C₂×#11724784	C₂³	1	1	yes	characteristic
83	C₂×#11724784	C₂³	1	1	yes	characteristic
84	C₈×D₁₀₉	—	4	1	no	—
85	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
86	C₄⋊Dic₁₀₉	C₂³	1	1	yes	characteristic
87	#13182008	—	2	1	no	—
88	#13182008	—	2	1	no	—
89	#13182008	D₄	1	1	yes	characteristic
90	C₂²⋊Dic₁₀₉	—	2	1	no	—
91	C₂²⋊Dic₁₀₉	—	2	1	no	—
92	C₂²⋊Dic₁₀₉	D₄	1	1	yes	characteristic
93	#13182006	—	2	1	no	—
94	#13182006	—	2	1	no	—
95	#13182006	—	2	1	no	—
96	#13182006	—	2	1	no	—
97	#13182006	D₄	1	1	yes	characteristic
98	C₄×Dic₁₀₉	C₂³	1	1	yes	characteristic
99	C₂⁴×C₁₀₉	—	2	1	no	—
100	C₂×D₄×C₁₀₉	—	2	2	no	—
101	C₂×D₄×C₁₀₉	—	2	1	no	—
102	C₂×D₄×C₁₀₉	—	4	1	no	—
103	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
104	C₂×D₄×C₁₀₉	C₂³	1	1	yes	characteristic
105	C₂²×C₄×C₁₀₉	—	2	1	no	—
106	C₂²×C₄×C₁₀₉	C₂³	1	1	yes	characteristic
107	C₂×C₈×C₁₀₉	—	4	1	no	—
108	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
109	C₂×C₈×C₁₀₉	C₂³	1	1	yes	characteristic
110	C₄⋊C₄×C₁₀₉	—	2	1	no	—
111	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
112	C₄⋊C₄×C₁₀₉	C₂³	1	1	yes	characteristic
113	C₂³×C₁₀₉	—	2	1	no	—
114	C₂³×C₁₀₉	—	2	1	no	—
115	C₂³×C₁₀₉	—	4	2	no	—
116	C₂³×C₁₀₉	—	4	2	no	—
117	C₂³×C₁₀₉	—	8	1	no	—
118	C₂³×C₁₀₉	C₂×D₄	1	1	yes	characteristic
119	C₂²×D₁₀₉	—	2	1	no	—
120	C₂²×D₁₀₉	—	2	1	no	—
121	C₂²×D₁₀₉	—	4	2	no	—
122	C₂²×D₁₀₉	—	4	2	no	—
123	C₂²×D₁₀₉	—	8	1	no	—
124	C₂²×D₁₀₉	C₂×D₄	1	1	yes	characteristic
125	D₄×C₁₀₉	—	2	1	no	—
126	D₄×C₁₀₉	—	2	1	no	—
127	D₄×C₁₀₉	—	2	1	no	—
128	D₄×C₁₀₉	—	4	2	no	—
129	D₄×C₁₀₉	#41	1	2	yes	complemented
130	C₂×C₄×C₁₀₉	—	2	1	no	—
131	C₂×C₄×C₁₀₉	—	2	1	no	—
132	C₂×C₄×C₁₀₉	—	2	1	no	—
133	C₂×C₄×C₁₀₉	—	2	1	no	—
134	C₂×C₄×C₁₀₉	—	4	2	no	—
135	C₂×C₄×C₁₀₉	C₂×D₄	1	1	yes	characteristic
136	C₂×C₄×C₁₀₉	C₂⁴	1	1	yes	characteristic
137	C₂²⋊D₁₀₉	—	4	2	no	—
138	C₂²⋊D₁₀₉	—	4	2	no	—
139	C₂²⋊D₁₀₉	—	4	2	no	—
140	C₂²⋊D₁₀₉	—	4	2	no	—
141	C₂²⋊D₁₀₉	—	4	2	no	—
142	C₂²⋊D₁₀₉	—	8	1	no	—
143	C₂²⋊D₁₀₉	D₈	1	4	yes	complemented
144	C₂×Dic₁₀₉	—	2	1	no	—
145	C₂×Dic₁₀₉	—	2	1	no	—
146	C₂×Dic₁₀₉	—	4	2	no	—
147	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
148	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
149	C₂×Dic₁₀₉	C₂×D₄	1	1	yes	characteristic
150	D₄₃₆	—	2	1	no	—
151	D₄₃₆	—	2	1	no	—
152	D₄₃₆	—	2	1	no	—
153	D₄₃₆	—	2	1	no	—
154	D₄₃₆	—	4	2	no	—
155	C₄×D₁₀₉	—	2	1	no	—
156	C₄×D₁₀₉	—	2	1	no	—
157	C₄×D₁₀₉	—	4	2	no	—
158	C₄×D₁₀₉	—	4	2	no	—
159	Dic₂₁₈	—	4	2	no	—
160	C₈×C₁₀₉	—	2	1	no	—
161	C₈×C₁₀₉	—	2	1	no	—
162	#11724784	—	2	1	no	—
163	#11724784	—	2	1	no	—
164	C₂²×C₁₀₉	—	2	1	no	—
165	C₂²×C₁₀₉	—	2	1	no	—
166	C₂²×C₁₀₉	—	2	2	no	—
167	C₂²×C₁₀₉	—	4	1	no	—
168	C₂²×C₁₀₉	—	4	1	no	—
169	C₂²×C₁₀₉	—	4	1	no	—
170	C₂²×C₁₀₉	—	4	1	no	—
171	C₂²×C₁₀₉	—	4	1	no	—
172	C₂²×C₁₀₉	—	8	4	no	—
173	C₂²×C₁₀₉	C₂×D₈	1	2	yes	—
174	C₂²×C₁₀₉	C₂²×D₄	1	1	yes	characteristic
175	C₂×D₁₀₉	—	2	1	no	—
176	C₂×D₁₀₉	—	2	1	no	—
177	C₂×D₁₀₉	—	4	1	no	—
178	C₂×D₁₀₉	—	4	1	no	—
179	C₂×D₁₀₉	—	4	1	no	—
180	C₂×D₁₀₉	—	4	1	no	—
181	C₂×D₁₀₉	—	4	1	no	—
182	C₂×D₁₀₉	—	4	1	no	—
183	C₂×D₁₀₉	—	8	4	no	—
184	C₂×D₁₀₉	C₂×D₈	1	2	yes	—
185	C₄×C₁₀₉	—	2	1	no	—
186	C₄×C₁₀₉	—	4	1	no	—
187	C₄×C₁₀₉	—	4	1	no	—
188	C₄×C₁₀₉	C₂×#41	1	1	yes	characteristic
189	C₄×C₁₀₉	H(5,𝔽₂)	1	1	yes	characteristic
190	Dic₁₀₉	—	2	1	no	—
191	Dic₁₀₉	—	2	1	no	—
192	Dic₁₀₉	—	4	1	no	—
193	Dic₁₀₉	—	4	1	no	—
194	Dic₁₀₉	C₂×D₈	1	2	yes	—
195	C₂×C₁₀₉	—	2	2	no	—
196	C₂×C₁₀₉	—	4	2	no	—
197	C₂×C₁₀₉	—	8	1	no	—
198	C₂×C₁₀₉	#546	1	1	yes	characteristic
199	C₂×C₁₀₉	C₂²×D₈	1	1	yes	characteristic
200	C₂×C₁₀₉	#577	1	1	yes	characteristic
201	D₁₀₉	—	2	2	no	—
202	D₁₀₉	—	8	1	no	—
203	D₁₀₉	—	8	1	no	—
204	#3294	—	109	1	no	maximal, Sylow
205	C₁₀₉	#3294	1	1	yes	characteristic, complemented, Sylow
206	#547	—	109	1	no	—
207	D₄²	—	109	1	no	—
208	#486	—	109	1	no	—
209	#480	—	109	1	no	—
210	#480	—	109	1	no	—
211	#474	—	109	1	no	—
212	#466	—	109	1	no	—
213	#466	—	109	1	no	—
214	#459	—	109	1	no	—
215	#447	—	109	1	no	—
216	#447	—	109	1	no	—
217	C₄×D₈	—	109	1	no	—
218	C₈×D₄	—	109	1	no	—
219	C₂×#102	—	109	1	no	—
220	C₂×#102	D₁₀₉	1	1	yes	characteristic, complemented
221	C₂×#41	—	218	1	no	—
222	C₂²×D₄	—	109	1	no	—
223	C₂²×D₄	—	218	1	no	—
224	C₂²×D₄	C₂×D₁₀₉	1	1	yes	characteristic
225	C₂×D₈	—	109	1	no	—
226	C₂×D₈	—	109	1	no	—
227	C₂×D₈	—	109	1	no	—
228	C₂²×C₈	—	109	1	no	—
229	C₂²×C₈	C₂×D₁₀₉	1	1	yes	characteristic, complemented
230	C₄⋊Q₈	—	109	1	no	—
231	#127	—	109	1	no	—
232	#123	—	218	1	no	—
233	#123	—	218	1	no	—
234	C₂²⋊Q₈	—	218	1	no	—
235	#121	—	109	1	no	—
236	#121	—	109	1	no	—
237	#121	—	109	1	no	—
238	#121	—	109	1	no	—
239	#121	—	218	1	no	—
240	#120	—	218	1	no	—
241	#120	—	218	1	no	—
242	C₄×D₄	—	109	1	no	—
243	C₄×D₄	—	109	1	no	—
244	C₄×D₄	—	109	1	no	—
245	C₂×C₄⋊C₄	—	109	1	no	—
246	C₂×C₄⋊C₄	C₂×D₁₀₉	1	1	yes	characteristic, complemented
247	#107	—	109	1	no	—
248	#107	—	109	1	no	—
249	#107	—	109	1	no	—
250	C₄⋊C₈	—	109	1	no	—
251	#102	—	109	1	no	—
252	#102	—	109	1	no	—
253	#102	—	109	1	no	—
254	#102	—	109	1	no	—
255	#102	—	109	1	no	—
256	#102	—	109	1	no	—
257	#102	C₂×D₁₀₉	1	1	yes	characteristic
258	#102	C₂×D₁₀₉	1	1	yes	characteristic
259	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
260	#102	C₂×D₁₀₉	1	1	yes	characteristic, complemented
261	C₂²⋊C₈	—	109	1	no	—
262	C₂²⋊C₈	—	109	1	no	—
263	C₄×C₈	—	109	1	no	—
264	C₂⁴	—	2	1	no	—
265	C₂⁴	—	218	1	no	—
266	#41	—	436	4	no	—
267	C₂×Q₈	—	218	1	no	—
268	C₂×D₄	—	2	2	no	—
269	C₂×D₄	—	2	1	no	—
270	C₂×D₄	—	4	1	no	—
271	C₂×D₄	—	109	1	no	—
272	C₂×D₄	—	109	1	no	—
273	C₂×D₄	—	109	1	no	—
274	C₂×D₄	—	436	4	no	—
275	C₂×D₄	—	436	1	no	—
276	C₂×D₄	—	218	1	no	—
277	C₂×D₄	—	218	1	no	—
278	C₂×D₄	—	218	1	no	—
279	C₂×D₄	—	218	1	no	—
280	C₂×D₄	—	218	1	no	—
281	C₂×D₄	—	218	1	no	—
282	C₂×D₄	—	218	1	no	—
283	C₂×D₄	—	218	2	no	—
284	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
285	C₂×D₄	C₂²×D₁₀₉	1	1	yes	characteristic
286	C₂²×C₄	—	2	1	no	—
287	C₂²×C₄	—	109	1	no	—
288	C₂²×C₄	—	218	1	no	—
289	C₂²×C₄	—	218	1	no	—
290	C₂²×C₄	—	218	1	no	—
291	C₂²×C₄	C₂²×D₁₀₉	1	1	yes	characteristic
292	D₈	—	436	1	no	—
293	D₈	—	436	1	no	—
294	D₈	—	218	2	no	—
295	C₂×C₈	—	4	1	no	—
296	C₂×C₈	—	109	1	no	—
297	C₂×C₈	—	109	1	no	—
298	C₂×C₈	—	436	1	no	—
299	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
300	C₂×C₈	C₂²×D₁₀₉	1	1	yes	characteristic
301	C₄⋊C₄	—	2	1	no	—
302	C₄⋊C₄	—	109	1	no	—
303	C₄⋊C₄	—	109	1	no	—
304	C₄⋊C₄	—	109	1	no	—
305	C₄⋊C₄	—	218	1	no	—
306	C₄⋊C₄	—	218	1	no	—
307	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
308	C₄⋊C₄	C₂²×D₁₀₉	1	1	yes	characteristic
309	C₂²⋊C₄	—	109	1	no	—
310	C₂²⋊C₄	—	109	1	no	—
311	C₂²⋊C₄	—	218	1	no	—
312	C₂²⋊C₄	—	218	1	no	—
313	C₂²⋊C₄	—	218	1	no	—
314	C₂²⋊C₄	—	218	1	no	—
315	C₂²⋊C₄	—	218	1	no	—
316	C₂²⋊C₄	—	218	1	no	—
317	C₄²	—	109	1	no	—
318	C₂³	—	2	1	no	—
319	C₂³	—	2	1	no	—
320	C₂³	—	4	2	no	—
321	C₂³	—	4	2	no	—
322	C₂³	—	8	1	no	—
323	C₂³	—	872	1	no	—
324	C₂³	—	109	1	no	—
325	C₂³	—	436	2	no	—
326	C₂³	—	436	2	no	—
327	C₂³	—	218	1	no	—
328	C₂³	—	218	1	no	—
329	C₂³	D₄×D₁₀₉	1	1	yes	characteristic
330	Q₈	—	436	2	no	—
331	D₄	—	2	1	no	—
332	D₄	—	2	1	no	—
333	D₄	—	2	1	no	—
334	D₄	—	4	2	no	—
335	D₄	—	872	1	no	—
336	D₄	—	109	4	no	—
337	D₄	—	436	2	no	—
338	D₄	—	436	2	no	—
339	D₄	—	436	2	no	—
340	D₄	—	436	2	no	—
341	D₄	—	436	2	no	—
342	D₄	—	436	2	no	—
343	D₄	—	218	1	no	—
344	D₄	—	218	1	no	—
345	D₄	—	218	1	no	—
346	D₄	—	218	1	no	—
347	D₄	#13182029	1	2	yes	complemented
348	C₂×C₄	—	2	1	no	—
349	C₂×C₄	—	2	1	no	—
350	C₂×C₄	—	2	1	no	—
351	C₂×C₄	—	2	1	no	—
352	C₂×C₄	—	4	2	no	—
353	C₂×C₄	—	109	1	no	—
354	C₂×C₄	—	109	1	no	—
355	C₂×C₄	—	109	1	no	—
356	C₂×C₄	—	436	2	no	—
357	C₂×C₄	—	436	2	no	—
358	C₂×C₄	—	436	2	no	—
359	C₂×C₄	—	218	1	no	—
360	C₂×C₄	—	218	1	no	—
361	C₂×C₄	—	218	1	no	—
362	C₂×C₄	—	218	1	no	—
363	C₂×C₄	D₄×D₁₀₉	1	1	yes	characteristic
364	C₂×C₄	C₂³×D₁₀₉	1	1	yes	characteristic
365	C₈	—	2	1	no	—
366	C₈	—	2	1	no	—
367	C₈	—	218	1	no	—
368	C₈	—	218	1	no	—
369	C₂²	—	2	1	no	—
370	C₂²	—	2	1	no	—
371	C₂²	—	2	2	no	—
372	C₂²	—	4	1	no	—
373	C₂²	—	4	1	no	—
374	C₂²	—	4	1	no	—
375	C₂²	—	4	1	no	—
376	C₂²	—	4	1	no	—
377	C₂²	—	8	4	no	—
378	C₂²	—	872	4	no	—
379	C₂²	—	109	2	no	—
380	C₂²	—	436	1	no	—
381	C₂²	—	436	1	no	—
382	C₂²	—	436	1	no	—
383	C₂²	—	436	1	no	—
384	C₂²	—	436	1	no	—
385	C₂²	—	436	1	no	—
386	C₂²	—	218	1	no	—
387	C₂²	—	218	1	no	—
388	C₂²	D₈×D₁₀₉	1	2	yes	—
389	C₂²	C₂×D₄×D₁₀₉	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	4	1	no	—
392	C₄	—	4	1	no	—
393	C₄	—	109	2	no	—
394	C₄	—	436	1	no	—
395	C₄	—	436	1	no	—
396	C₄	—	218	1	no	—
397	C₄	—	218	1	no	—
398	C₄	C₂×#13182029	1	1	yes	characteristic
399	C₄	#16812744	1	1	yes	characteristic
400	C₂	—	2	2	no	—
401	C₂	—	4	2	no	—
402	C₂	—	8	1	no	—
403	C₂	—	872	1	no	—
404	C₂	—	872	1	no	—
405	C₂	—	218	2	no	—
406	C₂	#20295666	1	1	yes	characteristic
407	C₂	C₂×D₈×D₁₀₉	1	1	yes	characteristic
408	C₂	#20295832	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂×D₄×D₁₀₉
commutator, cosocle	C₂×C₄×C₁₀₉	C₂⁴
Frattini	C₂×C₄	C₂³×D₁₀₉
Fitting	C₂×#102×C₁₀₉	C₂
socle	C₂²×C₁₀₉	C₂²×D₄
hypercenter	C₂×#102	D₁₀₉
hypocenter	C₁₀₉	#3294
LCS	G ▷ C₂×C₄×C₁₀₉ ▷ C₂×C₁₀₉ ▷ C₁₀₉
UCS	C₁ ◁ C₂² ◁ C₂²×C₄ ◁ C₂×#102

Complements

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

N	H ≅ G/N	type
1. #20295677	C₂	semidirect
2. D₄×C₂²⋊D₁₀₉	C₂	semidirect
3. #20295371	C₂	semidirect
4. #20295339	C₂	semidirect
5. #20295338	C₂	semidirect
6. #20295304	C₂	semidirect
7. #20295262	C₂	semidirect
8. #20295261	C₂	semidirect
9. #20295220	C₂	semidirect
10. #20295161	C₂	semidirect
11. #20295160	C₂	semidirect
12. #20295106	C₂	semidirect
13. C₈×C₂²⋊D₁₀₉	C₂	semidirect
14. #102×D₁₀₉	C₂	semidirect
15. C₂×#102×C₁₀₉	C₂	semidirect
19. C₂×D₈₇₂	C₂²	semidirect
21. C₂×#13182014	C₂²	semidirect
22. C₂×C₈×D₁₀₉	C₂²	semidirect
23. #16812698	C₂²	semidirect
28. #16812674	C₂²	semidirect
30. #16812673	C₂²	semidirect
36. #16812661	C₂²	semidirect
38. C₄⋊C₄×D₁₀₉	C₂²	semidirect
39. #16812633	C₂²	semidirect
40. #16812632	C₂²	semidirect
41. #16812632	C₂²	semidirect
42. #16812628	C₂²	semidirect
43. #16812621	C₂²	semidirect
44. #16812621	C₂²	semidirect
46. #16812620	C₂²	semidirect
47. #16812619	C₂²	semidirect
48. #16812619	C₂²	semidirect
49. C₂²⋊#11724784	C₂²	semidirect
50. #16812611	C₂²	semidirect
51. C₈×Dic₁₀₉	C₂²	semidirect
53. C₂²×C₈×C₁₀₉	C₂²	semidirect
54. C₂×C₄⋊C₄×C₁₀₉	C₂²	semidirect
57. #102×C₁₀₉	C₂²	semidirect
58. #102×C₁₀₉	C₂²	semidirect
129. D₄×C₁₀₉	#41	semidirect
143. C₂²⋊D₁₀₉	D₈	semidirect
205. C₁₀₉	#3294	semidirect
220. C₂×#102	D₁₀₉	semidirect
229. C₂²×C₈	C₂×D₁₀₉	semidirect
246. C₂×C₄⋊C₄	C₂×D₁₀₉	semidirect
259. #102	C₂×D₁₀₉	semidirect
260. #102	C₂×D₁₀₉	semidirect
347. D₄	#13182029	semidirect

Maximal subgroups

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

subgroup	index
#20295677	2
D₄×C₂²⋊D₁₀₉	2
#20295371	2
#20295339	2
#20295338	2
#20295304	2
#20295262	2
#20295261	2
#20295220	2
#20295161	2
#20295160	2
#20295106	2
C₈×C₂²⋊D₁₀₉	2
#102×D₁₀₉	2
C₂×#102×C₁₀₉	2
#3294	109