Subgroups — #34443331

Order 20224.

612 conjugacy classes of subgroups.

The subgroup lattice has 408 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#23773970	C₂	1	1	yes	maximal, characteristic, complemented
2	#23765597	C₂	1	1	yes	maximal, characteristic, complemented
3	#23765580	C₂	1	1	yes	maximal, characteristic, complemented
4	#23765557	C₂	1	2	yes	maximal, complemented
5	#23765455	C₂	1	2	yes	maximal, complemented
6	#23765329	C₂	1	1	yes	maximal, characteristic, complemented
7	#23765312	C₂	1	1	yes	maximal, characteristic
8	#23765274	C₂	1	2	yes	maximal, complemented
9	#23765264	C₂	1	2	yes	maximal, complemented
10	#23765203	C₂	1	1	yes	maximal, characteristic, complemented
11	C₂×C₄×D₈×C₇₉	C₂	1	1	yes	maximal, characteristic, complemented
12	#19099097	—	2	1	no	—
13	C₂×#14579105	C₂²	1	2	yes	—
14	C₂×#14579102	C₂²	1	2	yes	—
15	#19098965	C₂²	1	1	yes	characteristic, complemented
16	#19098947	C₂²	1	1	yes	characteristic, complemented
17	#19098918	—	2	1	no	—
18	#19098804	C₂²	1	1	yes	characteristic
19	#19098799	C₂²	1	1	yes	characteristic
20	#19098792	—	2	1	no	—
21	C₄×Dic₃₁₆	C₂²	1	1	yes	characteristic, complemented
22	C₄×#11929613	—	2	1	no	—
23	C₄×D₆₃₂	C₂²	1	1	yes	characteristic, complemented
24	#19098390	C₂²	1	2	yes	complemented
25	#19098388	C₂²	1	2	yes	complemented
26	C₄⋊(C₇₉⋊C₁₆)	C₂²	1	2	yes	complemented
27	#19098366	C₂²	1	2	yes	complemented
28	#19098364	C₂²	1	2	yes	—
29	#19098364	C₂²	1	2	yes	—
30	#19098363	C₂²	1	2	yes	complemented
31	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
32	C₂²⋊(C₇₉⋊C₁₆)	C₂²	1	1	yes	characteristic
33	#19098339	C₂²	1	2	yes	complemented
34	C₂²×D₈×C₇₉	C₂²	1	1	yes	characteristic
35	C₂×C₄×D₄×C₇₉	—	2	1	no	—
36	C₄×D₈×C₇₉	—	2	1	no	—
37	C₄×D₈×C₇₉	—	2	1	no	—
38	C₄×D₈×C₇₉	C₂²	1	2	yes	—
39	C₄×D₈×C₇₉	C₂²	1	2	yes	—
40	C₂×#107×C₇₉	C₂²	1	1	yes	characteristic
41	C₂×#102×C₇₉	—	2	1	no	—
42	C₂×C₄×C₈×C₇₉	C₂²	1	1	yes	characteristic
43	C₂×Dic₃₁₆	C₂³	1	1	yes	characteristic
44	C₂×#11929613	—	2	1	no	—
45	C₂×D₆₃₂	C₂³	1	1	yes	characteristic
46	#14579155	—	4	1	no	—
47	#14579153	—	2	1	no	—
48	#14579149	—	2	1	no	—
49	#14579144	—	4	1	no	—
50	#14579140	—	2	1	no	—
51	#14579135	—	2	1	no	—
52	C₄×Dic₁₅₈	—	2	1	no	—
53	C₄×D₃₁₆	—	2	1	no	—
54	C₄×C₂²⋊D₇₉	—	4	1	no	—
55	#14579118	—	4	1	no	—
56	#14579105	—	2	4	no	—
57	#14579102	—	2	4	no	—
58	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
59	C₂×C₇₉⋊C₁₆	C₂³	1	2	yes	—
60	#14579095	C₂³	1	1	yes	characteristic
61	#14579095	C₂³	1	1	yes	characteristic
62	#14579093	—	2	1	no	—
63	#14579086	—	2	1	no	—
64	#14579086	—	2	1	no	—
65	#14579083	—	2	1	no	—
66	#14579083	—	2	1	no	—
67	C₂²×D₄×C₇₉	—	2	1	no	—
68	C₂³×C₄×C₇₉	—	4	1	no	—
69	C₂×D₈×C₇₉	—	2	4	no	—
70	C₂×D₈×C₇₉	—	2	1	no	—
71	C₂×D₈×C₇₉	C₂³	1	2	yes	—
72	C₂²×C₈×C₇₉	D₄	1	1	yes	characteristic
73	C₂²×C₈×C₇₉	C₂³	1	1	yes	characteristic
74	C₄×D₄×C₇₉	—	2	2	no	—
75	C₄×D₄×C₇₉	—	2	2	no	—
76	C₄×D₄×C₇₉	—	4	1	no	—
77	C₄×D₄×C₇₉	—	4	1	no	—
78	C₂×C₄⋊C₄×C₇₉	—	2	1	no	—
79	C₂×C₂²⋊C₄×C₇₉	—	4	1	no	—
80	C₂×C₄²×C₇₉	D₄	1	1	yes	characteristic
81	#107×C₇₉	—	2	1	no	—
82	#107×C₇₉	C₂³	1	2	yes	—
83	#102×C₇₉	—	2	2	no	—
84	#102×C₇₉	—	2	2	no	—
85	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
86	C₄×C₈×C₇₉	D₄	1	1	yes	characteristic
87	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
88	C₄×C₈×C₇₉	C₂³	1	1	yes	characteristic
89	C₂×Dic₁₅₈	—	2	1	no	—
90	C₂×D₃₁₆	—	2	1	no	—
91	C₂×C₂²⋊D₇₉	—	4	1	no	—
92	C₂×C₄×D₇₉	—	4	1	no	—
93	Dic₃₁₆	—	2	2	no	—
94	#11929613	—	4	2	no	—
95	D₆₃₂	—	2	2	no	—
96	C₄⋊Dic₇₉	—	2	1	no	—
97	C₄⋊Dic₇₉	—	2	1	no	—
98	Dic₇₉⋊C₄	—	4	1	no	—
99	Dic₇₉⋊C₄	—	4	1	no	—
100	Dic₇₉⋊C₄	—	4	1	no	—
101	Dic₇₉⋊C₄	—	4	1	no	—
102	C₂²⋊Dic₇₉	—	4	1	no	—
103	(C₂×D₇₉)⋊C₄	—	4	1	no	—
104	(C₂×D₇₉)⋊C₄	—	4	1	no	—
105	(C₂×D₇₉)⋊C₄	—	4	1	no	—
106	(C₂×D₇₉)⋊C₄	—	4	1	no	—
107	C₄×Dic₇₉	—	4	1	no	—
108	C₇₉⋊C₁₆	—	2	2	no	—
109	C₇₉⋊C₁₆	—	2	2	no	—
110	C₂⁴×C₇₉	—	4	1	no	—
111	C₂×D₄×C₇₉	—	2	4	no	—
112	C₂×D₄×C₇₉	—	2	2	no	—
113	C₂×D₄×C₇₉	—	4	2	no	—
114	C₂×D₄×C₇₉	—	4	1	no	—
115	C₂²×C₄×C₇₉	—	4	1	no	—
116	C₂²×C₄×C₇₉	—	4	2	no	—
117	C₂²×C₄×C₇₉	—	4	2	no	—
118	C₂²×C₄×C₇₉	—	8	4	no	—
119	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
120	C₂²×C₄×C₇₉	D₈	1	1	yes	characteristic
121	C₂²×C₄×C₇₉	C₂×D₄	1	1	yes	characteristic
122	D₈×C₇₉	—	2	4	no	—
123	D₈×C₇₉	—	2	2	no	—
124	D₈×C₇₉	#41	1	4	yes	—
125	C₂×C₈×C₇₉	—	2	2	no	—
126	C₂×C₈×C₇₉	—	4	1	no	—
127	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
128	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
129	C₂×C₈×C₇₉	C₂×D₄	1	1	yes	characteristic
130	C₂×C₈×C₇₉	C₂⁴	1	1	yes	characteristic
131	C₄⋊C₄×C₇₉	—	2	2	no	—
132	C₄⋊C₄×C₇₉	—	4	1	no	—
133	C₂²⋊C₄×C₇₉	—	4	2	no	—
134	C₂²⋊C₄×C₇₉	—	4	2	no	—
135	C₄²×C₇₉	D₈	1	1	yes	characteristic
136	C₄²×C₇₉	D₈	1	1	yes	characteristic
137	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
138	C₄²×C₇₉	C₂×D₄	1	1	yes	characteristic
139	C₂³×C₇₉	—	4	4	no	—
140	C₂³×C₇₉	—	4	2	no	—
141	C₂³×C₇₉	—	8	2	no	—
142	C₂³×C₇₉	—	8	2	no	—
143	C₂³×C₇₉	C₂×D₈	1	1	yes	characteristic
144	C₂²×D₇₉	—	4	1	no	—
145	D₄×C₇₉	—	2	4	no	—
146	D₄×C₇₉	—	4	4	no	—
147	D₄×C₇₉	—	4	2	no	—
148	C₂×C₄×C₇₉	—	2	2	no	—
149	C₂×C₄×C₇₉	—	2	1	no	—
150	C₂×C₄×C₇₉	—	2	1	no	—
151	C₂×C₄×C₇₉	—	4	1	no	—
152	C₂×C₄×C₇₉	—	4	2	no	—
153	C₂×C₄×C₇₉	—	8	4	no	—
154	C₂×C₄×C₇₉	—	8	4	no	—
155	C₂×C₄×C₇₉	—	8	2	no	—
156	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
157	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
158	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
159	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
160	C₂×C₄×C₇₉	C₂×D₈	1	1	yes	characteristic
161	C₂×C₄×C₇₉	C₂²×D₄	1	1	yes	characteristic
162	C₂²⋊D₇₉	—	8	2	no	—
163	C₂×Dic₇₉	—	4	1	no	—
164	C₂×Dic₇₉	—	4	1	no	—
165	C₂×Dic₇₉	—	4	1	no	—
166	D₃₁₆	—	4	1	no	—
167	D₃₁₆	—	4	1	no	—
168	C₄×D₇₉	—	8	2	no	—
169	Dic₁₅₈	—	4	1	no	—
170	Dic₁₅₈	—	4	1	no	—
171	C₈×C₇₉	—	2	1	no	—
172	C₈×C₇₉	—	2	1	no	—
173	C₈×C₇₉	—	2	1	no	—
174	C₈×C₇₉	C₂×#41	1	2	yes	—
175	C₂²×C₇₉	—	2	1	no	—
176	C₂²×C₇₉	—	2	1	no	—
177	C₂²×C₇₉	—	4	4	no	—
178	C₂²×C₇₉	—	8	8	no	—
179	C₂²×C₇₉	—	8	2	no	—
180	C₂²×C₇₉	—	8	2	no	—
181	C₂²×C₇₉	#509	1	2	yes	—
182	C₂²×C₇₉	C₂²×D₈	1	1	yes	characteristic
183	C₂×D₇₉	—	8	1	no	—
184	C₂×D₇₉	—	8	1	no	—
185	C₂×D₇₉	—	8	1	no	—
186	C₄×C₇₉	—	2	1	no	—
187	C₄×C₇₉	—	2	1	no	—
188	C₄×C₇₉	—	2	1	no	—
189	C₄×C₇₉	—	2	1	no	—
190	C₄×C₇₉	—	2	1	no	—
191	C₄×C₇₉	—	8	2	no	—
192	C₄×C₇₉	#525	1	1	yes	characteristic
193	C₄×C₇₉	#575	1	1	yes	characteristic
194	Dic₇₉	—	8	1	no	—
195	Dic₇₉	—	8	1	no	—
196	Dic₇₉	—	8	1	no	—
197	#33674	—	79	1	no	maximal, Sylow
198	C₂×C₇₉	—	2	2	no	—
199	C₂×C₇₉	—	8	4	no	—
200	C₂×C₇₉	#3100	1	1	yes	characteristic
201	C₂×C₇₉	C₂×#509	1	1	yes	characteristic
202	C₂×C₇₉	#3414	1	1	yes	characteristic
203	D₇₉	—	16	1	no	—
204	#3168	—	79	1	no	—
205	C₂×C₄×D₈	D₇₉	1	1	yes	characteristic, complemented
206	#2235	—	79	1	no	—
207	#2232	—	79	1	no	—
208	#2228	—	79	2	no	—
209	#2210	—	79	2	no	—
210	#2187	—	79	1	no	—
211	#2184	—	79	1	no	—
212	#2177	—	79	2	no	—
213	#2175	—	79	2	no	—
214	#2163	—	79	1	no	—
215	C₇₉	#33674	1	1	yes	characteristic, complemented, Sylow
216	C₂²×D₈	C₂×D₇₉	1	1	yes	characteristic
217	#529	—	158	1	no	—
218	C₂×C₄×D₄	—	2	1	no	—
219	C₂×SD₃₂	—	79	2	no	—
220	C₂×D₁₆	—	79	2	no	—
221	#499	—	79	1	no	—
222	#495	—	79	1	no	—
223	#488	—	158	1	no	—
224	#467	—	79	1	no	—
225	#466	—	79	1	no	—
226	#465	—	158	1	no	—
227	C₄×Q₁₆	—	79	1	no	—
228	C₄×SD₁₆	—	158	1	no	—
229	C₄×D₈	—	2	1	no	—
230	C₄×D₈	—	2	1	no	—
231	C₄×D₈	—	79	1	no	—
232	C₄×D₈	C₂×D₇₉	1	2	yes	—
233	C₄×D₈	C₂×D₇₉	1	2	yes	—
234	C₂×#107	C₂×D₇₉	1	1	yes	characteristic
235	C₂×#102	—	2	1	no	—
236	C₂×C₄×C₈	C₂×D₇₉	1	1	yes	characteristic
237	#367	—	79	2	no	—
238	#366	—	79	2	no	—
239	C₄⋊C₁₆	—	79	2	no	—
240	#358	—	79	2	no	—
241	#357	—	79	2	no	—
242	#357	—	79	2	no	—
243	#357	—	79	2	no	—
244	C₂²⋊C₁₆	—	79	1	no	—
245	C₂²⋊C₁₆	—	79	1	no	—
246	#346	—	79	2	no	—
247	C₂²×D₄	—	2	1	no	—
248	C₂³×C₄	—	4	1	no	—
249	C₂×Q₁₆	—	79	1	no	—
250	C₂×SD₁₆	—	158	1	no	—
251	C₂×D₈	—	2	4	no	—
252	C₂×D₈	—	2	1	no	—
253	C₂×D₈	—	79	1	no	—
254	C₂×D₈	C₂²×D₇₉	1	2	yes	—
255	C₂²×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
256	C₂²×C₈	C₂²×D₇₉	1	1	yes	characteristic
257	#126	—	316	1	no	—
258	#125	—	158	1	no	—
259	#124	—	158	1	no	—
260	#123	—	316	1	no	—
261	C₂²⋊Q₈	—	158	1	no	—
262	#121	—	158	1	no	—
263	C₄×Q₈	—	158	1	no	—
264	C₄×D₄	—	2	2	no	—
265	C₄×D₄	—	2	2	no	—
266	C₄×D₄	—	4	1	no	—
267	C₄×D₄	—	4	1	no	—
268	C₄×D₄	—	316	1	no	—
269	C₄×D₄	—	158	1	no	—
270	#117	—	316	1	no	—
271	C₂×C₄⋊C₄	—	2	1	no	—
272	C₂×C₂²⋊C₄	—	4	1	no	—
273	C₂×C₄²	C₂²⋊D₇₉	1	1	yes	characteristic
274	SD₃₂	—	158	4	no	—
275	D₁₆	—	158	4	no	—
276	C₂×C₁₆	—	79	2	no	—
277	C₂×C₁₆	—	79	2	no	—
278	#107	—	2	1	no	—
279	#107	—	79	1	no	—
280	#107	—	79	1	no	—
281	#107	C₂²×D₇₉	1	2	yes	—
282	#106	—	158	1	no	—
283	#103	—	158	1	no	—
284	#103	—	158	1	no	—
285	#102	—	2	2	no	—
286	#102	—	2	2	no	—
287	#102	—	158	1	no	—
288	#102	—	158	1	no	—
289	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
290	C₄×C₈	C₂²⋊D₇₉	1	1	yes	characteristic
291	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
292	C₄×C₈	C₂²×D₇₉	1	1	yes	characteristic
293	C₂⁴	—	4	1	no	—
294	C₂×Q₈	—	158	1	no	—
295	C₂×D₄	—	2	4	no	—
296	C₂×D₄	—	2	2	no	—
297	C₂×D₄	—	4	2	no	—
298	C₂×D₄	—	4	1	no	—
299	C₂×D₄	—	316	1	no	—
300	C₂×D₄	—	158	1	no	—
301	C₂²×C₄	—	4	1	no	—
302	C₂²×C₄	—	4	2	no	—
303	C₂²×C₄	—	4	2	no	—
304	C₂²×C₄	—	8	4	no	—
305	C₂²×C₄	—	316	1	no	—
306	C₂²×C₄	#11929609	1	1	yes	characteristic
307	C₂²×C₄	#11929609	1	1	yes	characteristic
308	C₂²×C₄	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
309	Q₁₆	—	158	2	no	—
310	SD₁₆	—	316	2	no	—
311	D₈	—	2	4	no	—
312	D₈	—	2	2	no	—
313	D₈	—	158	2	no	—
314	D₈	#11929624	1	4	yes	—
315	C₂×C₈	—	2	2	no	—
316	C₂×C₈	—	4	1	no	—
317	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
318	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
319	C₂×C₈	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
320	C₂×C₈	C₂³×D₇₉	1	1	yes	characteristic
321	C₄⋊C₄	—	2	2	no	—
322	C₄⋊C₄	—	4	1	no	—
323	C₄⋊C₄	—	316	1	no	—
324	C₄⋊C₄	—	316	1	no	—
325	C₄⋊C₄	—	316	1	no	—
326	C₄⋊C₄	—	316	1	no	—
327	C₄⋊C₄	—	158	1	no	—
328	C₄⋊C₄	—	158	1	no	—
329	C₂²⋊C₄	—	4	2	no	—
330	C₂²⋊C₄	—	4	2	no	—
331	C₂²⋊C₄	—	316	1	no	—
332	C₂²⋊C₄	—	316	1	no	—
333	C₂²⋊C₄	—	316	1	no	—
334	C₂²⋊C₄	—	316	1	no	—
335	C₂²⋊C₄	—	316	1	no	—
336	C₄²	—	316	1	no	—
337	C₄²	#11929609	1	1	yes	characteristic
338	C₄²	#11929609	1	1	yes	characteristic
339	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
340	C₄²	C₂×C₂²⋊D₇₉	1	1	yes	characteristic
341	C₁₆	—	158	2	no	—
342	C₁₆	—	158	2	no	—
343	C₂³	—	4	4	no	—
344	C₂³	—	4	2	no	—
345	C₂³	—	8	2	no	—
346	C₂³	—	8	2	no	—
347	C₂³	—	316	1	no	—
348	C₂³	C₂×#11929609	1	1	yes	characteristic
349	Q₈	—	316	1	no	—
350	Q₈	—	316	1	no	—
351	D₄	—	2	4	no	—
352	D₄	—	4	4	no	—
353	D₄	—	4	2	no	—
354	D₄	—	316	1	no	—
355	D₄	—	316	1	no	—
356	D₄	—	632	2	no	—
357	C₂×C₄	—	2	2	no	—
358	C₂×C₄	—	2	1	no	—
359	C₂×C₄	—	2	1	no	—
360	C₂×C₄	—	4	1	no	—
361	C₂×C₄	—	4	2	no	—
362	C₂×C₄	—	8	4	no	—
363	C₂×C₄	—	8	4	no	—
364	C₂×C₄	—	8	2	no	—
365	C₂×C₄	—	316	1	no	—
366	C₂×C₄	—	316	1	no	—
367	C₂×C₄	—	316	1	no	—
368	C₂×C₄	—	632	2	no	—
369	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
370	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
371	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
372	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
373	C₂×C₄	C₂×#11929609	1	1	yes	characteristic
374	C₂×C₄	C₂²×C₂²⋊D₇₉	1	1	yes	characteristic
375	C₈	—	2	1	no	—
376	C₈	—	2	1	no	—
377	C₈	—	2	1	no	—
378	C₈	C₂×#11929624	1	2	yes	—
379	C₂²	—	2	1	no	—
380	C₂²	—	2	1	no	—
381	C₂²	—	4	4	no	—
382	C₂²	—	8	8	no	—
383	C₂²	—	8	2	no	—
384	C₂²	—	8	2	no	—
385	C₂²	—	632	1	no	—
386	C₂²	—	632	1	no	—
387	C₂²	—	632	1	no	—
388	C₂²	#19098999	1	2	yes	—
389	C₂²	C₂²×#11929609	1	1	yes	characteristic
390	C₄	—	2	1	no	—
391	C₄	—	2	1	no	—
392	C₄	—	2	1	no	—
393	C₄	—	2	1	no	—
394	C₄	—	2	1	no	—
395	C₄	—	8	2	no	—
396	C₄	—	632	1	no	—
397	C₄	—	632	1	no	—
398	C₄	—	632	1	no	—
399	C₄	#19099074	1	1	yes	characteristic
400	C₄	#19099361	1	1	yes	characteristic
401	C₂	—	2	2	no	—
402	C₂	—	8	4	no	—
403	C₂	—	1264	1	no	—
404	C₂	#23773400	1	1	yes	characteristic
405	C₂	C₂×#19098999	1	1	yes	characteristic
406	C₂	#23776534	1	1	yes	characteristic

	subgroup	G/H
center	C₂²	C₂²×#11929609
commutator, cosocle	C₂×C₈×C₇₉	C₂⁴
Frattini	C₂×C₈	C₂³×D₇₉
Fitting	C₂×C₄×D₈×C₇₉	C₂
socle	C₂²×C₇₉	C₂²×D₈
prime radical	#23765312	C₂
hypercenter	C₂×C₄×D₈	D₇₉
hypocenter	C₇₉	#33674
LCS	G ▷ C₂×C₈×C₇₉ ▷ C₄×C₇₉ ▷ C₂×C₇₉ ▷ C₇₉
UCS	C₁ ◁ C₂² ◁ C₂×C₄² ◁ C₂×C₄×C₈ ◁ C₂×C₄×D₈

Complements

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

N	H ≅ G/N	type
1. #23773970	C₂	semidirect
2. #23765597	C₂	semidirect
3. #23765580	C₂	semidirect
4. #23765557	C₂	semidirect
5. #23765455	C₂	semidirect
6. #23765329	C₂	semidirect
8. #23765274	C₂	semidirect
9. #23765264	C₂	semidirect
10. #23765203	C₂	semidirect
11. C₂×C₄×D₈×C₇₉	C₂	semidirect
15. #19098965	C₂²	semidirect
16. #19098947	C₂²	semidirect
21. C₄×Dic₃₁₆	C₂²	semidirect
23. C₄×D₆₃₂	C₂²	semidirect
24. #19098390	C₂²	semidirect
25. #19098388	C₂²	semidirect
26. C₄⋊(C₇₉⋊C₁₆)	C₂²	semidirect
27. #19098366	C₂²	semidirect
30. #19098363	C₂²	semidirect
33. #19098339	C₂²	semidirect
205. C₂×C₄×D₈	D₇₉	semidirect
215. C₇₉	#33674	semidirect

Maximal subgroups

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

subgroup	index
#23773970	2
#23765597	2
#23765580	2
#23765557	2
#23765455	2
#23765329	2
#23765312	2
#23765274	2
#23765264	2
#23765203	2
C₂×C₄×D₈×C₇₉	2
#33674	79