Group #34010422 — subgroups

Subgroups — #34010422

Order 18688.

362 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 362 conjugacy classes of subgroups — too many to draw. Only its 110 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	#22626264	C₂	1	1	yes	maximal, characteristic
2	C₄×#14556666	C₂	1	1	yes	maximal, characteristic
3	#22624898	C₂	1	2	yes	maximal, complemented
4	Q₈⋊#11924031	C₂	1	2	yes	maximal, complemented
5	C₈×Q₈×D₇₃	C₂	1	1	yes	maximal, characteristic
6	C₂×#14556666	—	2	1	no	—
7	C₂×#14556666	—	2	1	no	—
8	#17989508	—	2	1	no	—
9	C₄⋊#11924031	C₂²	1	2	yes	—
10	#17989476	—	2	1	no	—
11	C₄×#11924031	C₂²	1	2	yes	—
12	C₄×Q₈×D₇₃	C₄	1	1	yes	characteristic
13	Q₈×#10596831	C₂²	1	1	yes	characteristic
14	C₈×Dic₁₄₆	—	2	1	no	—
15	C₈×Dic₁₄₆	C₄	1	1	yes	characteristic
16	#17988711	—	2	1	no	—
17	#17988711	C₂²	1	1	yes	characteristic
18	C₄⋊C₈×D₇₃	—	2	1	no	—
19	C₄⋊C₈×D₇₃	C₄	1	1	yes	characteristic
20	C₄×C₈×D₇₃	—	2	1	no	—
21	C₄×C₈×D₇₃	C₂²	1	1	yes	characteristic
22	C₈×Q₈×C₇₃	C₄	1	1	yes	characteristic
23	#14556666	—	2	4	no	—
24	#14556666	—	4	2	no	—
25	C₂×#11924031	—	2	2	no	—
26	C₂×#11924031	—	2	2	no	—
27	C₂×Q₈×D₇₃	C₈	1	1	yes	characteristic
28	C₂×C₈×D₇₃	—	2	1	no	—
29	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
30	C₂×C₈×D₇₃	D₄	1	1	yes	characteristic
31	Q₈×Dic₇₃	C₈	1	1	yes	characteristic
32	C₄×Dic₁₄₆	—	2	1	no	—
33	C₄×Dic₁₄₆	C₂×C₄	1	1	yes	characteristic
34	#14556556	—	2	1	no	—
35	#14556556	C₈	1	1	yes	characteristic
36	C₄⋊C₄×D₇₃	—	2	1	no	—
37	C₄⋊C₄×D₇₃	C₈	1	1	yes	characteristic
38	C₄²×D₇₃	—	2	1	no	—
39	C₄²×D₇₃	C₂×C₄	1	1	yes	characteristic
40	C₄⋊#10596831	—	2	1	no	—
41	C₄⋊#10596831	C₂×C₄	1	1	yes	characteristic
42	#14556520	—	2	1	no	—
43	#14556520	—	2	1	no	—
44	#14556520	—	2	1	no	—
45	C₄×#10596831	—	2	1	no	—
46	C₄×#10596831	C₂³	1	1	yes	characteristic
47	C₈×Dic₇₃	—	2	1	no	—
48	C₈×Dic₇₃	—	2	1	no	—
49	C₈×Dic₇₃	D₄	1	1	yes	characteristic
50	C₈×Dic₇₃	D₄	1	1	yes	characteristic
51	C₄×Q₈×C₇₃	C₂×C₄	1	1	yes	characteristic
52	C₄⋊C₈×C₇₃	—	2	1	no	—
53	C₄⋊C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
54	C₄×C₈×C₇₃	—	2	1	no	—
55	C₄×C₈×C₇₃	C₂×C₄	1	1	yes	characteristic
56	#11924031	—	2	4	no	—
57	#11924031	—	4	2	no	—
58	C₂×Dic₁₄₆	—	2	1	no	—
59	C₂×Dic₁₄₆	C₂×C₈	1	1	yes	characteristic
60	Q₈×D₇₃	—	2	2	no	—
61	Q₈×D₇₃	—	2	2	no	—
62	C₂×C₄×D₇₃	—	2	1	no	—
63	C₂×C₄×D₇₃	—	2	1	no	—
64	C₂×C₄×D₇₃	C₂²⋊C₄	1	1	yes	characteristic
65	C₂×C₄×D₇₃	C₂×C₈	1	1	yes	characteristic
66	C₂×C₄×D₇₃	M₁₆	1	1	yes	characteristic
67	C₂×#10596831	—	2	1	no	—
68	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
69	C₂×#10596831	C₂×D₄	1	1	yes	characteristic
70	C₈×D₇₃	—	2	2	no	—
71	C₈×D₇₃	—	4	2	no	—
72	C₈×D₇₃	SD₁₆	1	2	yes	—
73	C₈×D₇₃	Q₁₆	1	2	yes	—
74	C₄⋊Dic₇₃	—	2	1	no	—
75	C₄⋊Dic₇₃	C₂×C₈	1	1	yes	characteristic
76	#11924007	—	2	1	no	—
77	#11924007	—	2	1	no	—
78	#11924007	—	2	1	no	—
79	C₄×Dic₇₃	—	2	1	no	—
80	C₄×Dic₇₃	—	2	1	no	—
81	C₄×Dic₇₃	—	2	1	no	—
82	C₄×Dic₇₃	C₂²⋊C₄	1	1	yes	characteristic
83	C₄×Dic₇₃	C₂×C₈	1	1	yes	characteristic
84	C₄×Dic₇₃	M₁₆	1	1	yes	characteristic
85	C₂×Q₈×C₇₃	C₂×C₈	1	1	yes	characteristic
86	C₂×C₈×C₇₃	—	2	1	no	—
87	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
88	C₂×C₈×C₇₃	C₂²⋊C₄	1	1	yes	characteristic
89	C₄⋊C₄×C₇₃	—	2	1	no	—
90	C₄⋊C₄×C₇₃	C₂×C₈	1	1	yes	characteristic
91	C₄²×C₇₃	—	2	1	no	—
92	C₄²×C₇₃	C₂²×C₄	1	1	yes	characteristic
93	C₂²×D₇₃	C₂²⋊C₈	1	1	yes	characteristic
94	Q₈×C₇₃	—	2	1	no	—
95	Q₈×C₇₃	M₃₂	1	2	yes	complemented
96	C₂×C₄×C₇₃	—	2	1	no	—
97	C₂×C₄×C₇₃	—	2	1	no	—
98	C₂×C₄×C₇₃	C₂×C₂²⋊C₄	1	1	yes	characteristic
99	C₂×C₄×C₇₃	C₂²×C₈	1	1	yes	characteristic
100	C₂×C₄×C₇₃	C₂×M₁₆	1	1	yes	characteristic
101	C₂×Dic₇₃	—	2	1	no	—
102	C₂×Dic₇₃	—	2	1	no	—
103	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
104	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
105	C₂×Dic₇₃	C₂²⋊C₈	1	1	yes	characteristic
106	C₄×D₇₃	—	2	4	no	—
107	C₄×D₇₃	—	2	1	no	—
108	C₄×D₇₃	—	2	1	no	—
109	C₄×D₇₃	—	4	1	no	—
110	C₄×D₇₃	—	4	2	no	—
111	C₄×D₇₃	#103	1	2	yes	—
112	C₄×D₇₃	#104	1	2	yes	—
113	Dic₁₄₆	—	2	4	no	—
114	Dic₁₄₆	—	2	1	no	—
115	Dic₁₄₆	M₃₂	1	2	yes	complemented
116	C₈×C₇₃	—	2	1	no	—
117	C₈×C₇₃	—	4	1	no	—
118	C₈×C₇₃	#103	1	2	yes	—
119	#10596831	—	2	1	no	—
120	#10596831	—	4	1	no	—
121	#10596831	C₂×SD₁₆	1	1	yes	characteristic
122	#10596831	C₂×Q₁₆	1	1	yes	characteristic
123	C₂²×C₇₃	C₂×C₂²⋊C₈	1	1	yes	characteristic
124	C₂×D₇₃	—	2	1	no	—
125	C₂×D₇₃	—	2	1	no	—
126	C₂×D₇₃	Q₈⋊C₈	1	2	yes	—
127	C₄×C₇₃	—	2	2	no	—
128	C₄×C₇₃	—	2	1	no	—
129	C₄×C₇₃	—	4	1	no	—
130	C₄×C₇₃	C₂×#103	1	1	yes	characteristic
131	C₄×C₇₃	C₂×#104	1	1	yes	characteristic
132	C₄×C₇₃	C₂×M₃₂	1	1	yes	characteristic
133	C₄×C₇₃	C₂×M₃₂	1	1	yes	characteristic
134	Dic₇₃	—	2	1	no	—
135	Dic₇₃	—	2	2	no	—
136	Dic₇₃	—	2	1	no	—
137	Dic₇₃	—	4	1	no	—
138	Dic₇₃	Q₈⋊C₈	1	2	yes	—
139	#11607	—	73	1	no	maximal, Sylow
140	C₂×C₇₃	C₂×Q₈⋊C₈	1	1	yes	characteristic
141	C₂×C₇₃	#2112	1	1	yes	characteristic
142	C₂×C₇₃	#2117	1	1	yes	characteristic
143	D₇₃	—	2	2	no	—
144	C₂×C₈×Q₈	—	73	1	no	—
145	#2150	—	73	1	no	—
146	C₄×M₃₂	—	73	1	no	—
147	Q₈⋊C₁₆	—	73	2	no	—
148	Q₈⋊C₁₆	—	73	2	no	—
149	C₇₃	#11607	1	1	yes	characteristic, complemented, Sylow
150	C₂×C₄×Q₈	—	73	1	no	—
151	C₂×M₃₂	—	146	1	no	—
152	C₂×M₃₂	—	146	1	no	—
153	C₈×Q₈	—	73	1	no	—
154	C₈×Q₈	—	73	1	no	—
155	C₈×Q₈	—	73	1	no	—
156	C₈×Q₈	—	146	1	no	—
157	C₈×Q₈	—	146	1	no	—
158	C₈×Q₈	#64408	1	1	yes	characteristic
159	C₂×C₄⋊C₈	—	73	1	no	—
160	C₂×C₄⋊C₈	—	146	1	no	—
161	C₂×C₄×C₈	—	73	1	no	—
162	C₂×C₄×C₈	—	146	1	no	—
163	C₄⋊C₁₆	—	73	2	no	—
164	C₄⋊C₁₆	—	146	1	no	—
165	#346	—	146	1	no	—
166	C₄×C₁₆	—	73	2	no	—
167	C₂²×Q₈	—	73	1	no	—
168	C₂²×C₈	—	73	1	no	—
169	C₂²×C₈	—	73	1	no	—
170	C₂²×C₈	—	146	1	no	—
171	C₄×Q₈	—	73	1	no	—
172	C₄×Q₈	—	73	1	no	—
173	C₄×Q₈	—	73	1	no	—
174	C₄×Q₈	—	146	1	no	—
175	C₄×Q₈	—	146	1	no	—
176	C₄×Q₈	C₂×#64408	1	1	yes	characteristic
177	C₂×C₄⋊C₄	—	73	1	no	—
178	C₂×C₄⋊C₄	—	146	1	no	—
179	C₂×C₄²	—	73	1	no	—
180	C₂×C₄²	—	146	1	no	—
181	M₃₂	—	292	2	no	—
182	M₃₂	—	146	4	no	—
183	C₂×C₁₆	—	146	2	no	—
184	C₂×C₁₆	—	146	2	no	—
185	C₄⋊C₈	—	2	1	no	—
186	C₄⋊C₈	—	73	1	no	—
187	C₄⋊C₈	—	146	1	no	—
188	C₄⋊C₈	—	146	1	no	—
189	C₄⋊C₈	—	146	1	no	—
190	C₄⋊C₈	—	146	1	no	—
191	C₄⋊C₈	C₂×#64408	1	1	yes	characteristic
192	C₄×C₈	—	2	1	no	—
193	C₄×C₈	—	73	1	no	—
194	C₄×C₈	—	73	1	no	—
195	C₄×C₈	—	73	1	no	—
196	C₄×C₈	—	146	1	no	—
197	C₄×C₈	—	146	1	no	—
198	C₄×C₈	—	146	1	no	—
199	C₄×C₈	C₂×#64408	1	1	yes	characteristic
200	C₂×Q₈	—	73	1	no	—
201	C₂×Q₈	—	146	1	no	—
202	C₂×Q₈	—	146	2	no	—
203	C₂×Q₈	—	146	2	no	—
204	C₂×Q₈	#11924036	1	1	yes	characteristic
205	C₂²×C₄	—	73	1	no	—
206	C₂²×C₄	—	73	1	no	—
207	C₂²×C₄	—	73	1	no	—
208	C₂²×C₄	—	146	1	no	—
209	C₂²×C₄	—	146	1	no	—
210	C₂×C₈	—	2	1	no	—
211	C₂×C₈	—	292	2	no	—
212	C₂×C₈	—	73	1	no	—
213	C₂×C₈	—	73	2	no	—
214	C₂×C₈	—	73	2	no	—
215	C₂×C₈	—	73	1	no	—
216	C₂×C₈	—	146	2	no	—
217	C₂×C₈	—	146	1	no	—
218	C₂×C₈	C₂²⋊#64408	1	1	yes	characteristic
219	C₂×C₈	C₂²⋊#64408	1	1	yes	characteristic
220	C₄⋊C₄	—	2	1	no	—
221	C₄⋊C₄	—	73	1	no	—
222	C₄⋊C₄	—	146	1	no	—
223	C₄⋊C₄	—	146	1	no	—
224	C₄⋊C₄	—	146	1	no	—
225	C₄⋊C₄	—	146	1	no	—
226	C₄⋊C₄	#11924036	1	1	yes	characteristic
227	C₄²	—	2	1	no	—
228	C₄²	—	73	1	no	—
229	C₄²	—	73	1	no	—
230	C₄²	—	73	1	no	—
231	C₄²	—	146	1	no	—
232	C₄²	—	146	1	no	—
233	C₄²	—	146	1	no	—
234	C₄²	C₂²×#64408	1	1	yes	characteristic
235	C₁₆	—	292	2	no	—
236	C₁₆	—	146	4	no	—
237	C₂³	—	73	1	no	—
238	Q₈	—	2	1	no	—
239	Q₈	—	73	2	no	—
240	Q₈	—	146	4	no	—
241	Q₈	—	146	1	no	—
242	Q₈	#14556666	1	2	yes	complemented
243	C₂×C₄	—	2	1	no	—
244	C₂×C₄	—	2	1	no	—
245	C₂×C₄	—	292	1	no	—
246	C₂×C₄	—	292	2	no	—
247	C₂×C₄	—	73	1	no	—
248	C₂×C₄	—	73	2	no	—
249	C₂×C₄	—	73	2	no	—
250	C₂×C₄	—	73	1	no	—
251	C₂×C₄	—	73	1	no	—
252	C₂×C₄	—	146	4	no	—
253	C₂×C₄	—	146	1	no	—
254	C₂×C₄	—	146	1	no	—
255	C₂×C₄	—	146	1	no	—
256	C₂×C₄	—	146	1	no	—
257	C₂×C₄	C₂×C₂²⋊#64408	1	1	yes	characteristic
258	C₂×C₄	C₂×#11924036	1	1	yes	characteristic
259	C₂×C₄	D₇₃⋊M₁₆	1	1	yes	characteristic
260	C₈	—	2	1	no	—
261	C₈	—	4	1	no	—
262	C₈	—	292	1	no	—
263	C₈	—	73	1	no	—
264	C₈	—	73	1	no	—
265	C₈	—	146	1	no	—
266	C₈	#14556654	1	2	yes	—
267	C₂²	—	73	2	no	—
268	C₂²	—	146	1	no	—
269	C₂²	—	146	1	no	—
270	C₂²	#17989555	1	1	yes	characteristic
271	C₄	—	2	2	no	—
272	C₄	—	2	1	no	—
273	C₄	—	4	1	no	—
274	C₄	—	292	1	no	—
275	C₄	—	73	2	no	—
276	C₄	—	146	1	no	—
277	C₄	—	146	2	no	—
278	C₄	—	146	1	no	—
279	C₄	C₂×#14556654	1	1	yes	characteristic
280	C₄	D₇₃⋊#104	1	1	yes	characteristic
281	C₄	#17989643	1	1	yes	characteristic
282	C₄	C₂×#14556666	1	1	yes	characteristic
283	C₂	—	146	2	no	—
284	C₂	#22625220	1	1	yes	characteristic
285	C₂	#22626159	1	1	yes	characteristic
286	C₂	#22626174	1	1	yes	characteristic

subgroup

G/H

class size

multiplicity

normal?

properties

#22626264

C₂

yes

maximal, characteristic

C₄×#14556666

C₂

yes

maximal, characteristic

#22624898

C₂

yes

maximal, complemented

Q₈⋊#11924031

C₂

yes

maximal, complemented

C₈×Q₈×D₇₃

C₂

yes

maximal, characteristic

—

—

—

C₂²

yes

—

#17989476

—

C₄×#11924031

C₂²

yes

—

C₄×Q₈×D₇₃

C₄

yes

characteristic

Q₈×#10596831

C₂²

yes

characteristic

C₈×Dic₁₄₆

—

C₈×Dic₁₄₆

C₄

yes

characteristic

#17988711

—

#17988711

C₂²

yes

characteristic

C₄⋊C₈×D₇₃

—

C₄⋊C₈×D₇₃

C₄

yes

characteristic

C₄×C₈×D₇₃

—

C₄×C₈×D₇₃

C₂²

yes

characteristic

C₈×Q₈×C₇₃

C₄

yes

—

—

—

—

C₂×Q₈×D₇₃

C₈

yes

characteristic

C₂×C₈×D₇₃

—

C₂×C₈×D₇₃

D₄

yes

characteristic

C₂×C₈×D₇₃

D₄

yes

characteristic

Q₈×Dic₇₃

C₈

yes

characteristic

C₄×Dic₁₄₆

—

C₄×Dic₁₄₆

C₂×C₄

yes

characteristic

#14556556

—

#14556556

C₈

yes

characteristic

C₄⋊C₄×D₇₃

—

C₄⋊C₄×D₇₃

C₈

yes

characteristic

C₄²×D₇₃

—

C₄²×D₇₃

C₂×C₄

yes

characteristic

C₄⋊#10596831

—

C₄⋊#10596831

C₂×C₄

yes

—

—

—

—

C₂³

yes

characteristic

C₈×Dic₇₃

—

C₈×Dic₇₃

—

C₈×Dic₇₃

D₄

yes

characteristic

C₈×Dic₇₃

D₄

yes

characteristic

C₄×Q₈×C₇₃

C₂×C₄

yes

characteristic

C₄⋊C₈×C₇₃

—

C₄⋊C₈×C₇₃

C₂×C₄

yes

characteristic

C₄×C₈×C₇₃

—

C₄×C₈×C₇₃

C₂×C₄

yes

characteristic

#11924031

—

#11924031

—

C₂×Dic₁₄₆

—

C₂×Dic₁₄₆

C₂×C₈

yes

characteristic

Q₈×D₇₃

—

Q₈×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

—

C₂×C₄×D₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₄×D₇₃

C₂×C₈

yes

characteristic

C₂×C₄×D₇₃

M₁₆

yes

characteristic

C₂×#10596831

—

C₂×#10596831

C₂×D₄

yes

characteristic

C₂×#10596831

C₂×D₄

yes

characteristic

C₈×D₇₃

—

C₈×D₇₃

—

C₈×D₇₃

SD₁₆

yes

—

C₈×D₇₃

Q₁₆

yes

—

C₄⋊Dic₇₃

—

C₄⋊Dic₇₃

C₂×C₈

yes

—

—

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

—

C₄×Dic₇₃

C₂²⋊C₄

yes

characteristic

C₄×Dic₇₃

C₂×C₈

yes

characteristic

C₄×Dic₇₃

M₁₆

yes

characteristic

C₂×Q₈×C₇₃

C₂×C₈

yes

characteristic

C₂×C₈×C₇₃

—

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₂×C₈×C₇₃

C₂²⋊C₄

yes

characteristic

C₄⋊C₄×C₇₃

—

C₄⋊C₄×C₇₃

C₂×C₈

yes

characteristic

C₄²×C₇₃

—

C₄²×C₇₃

C₂²×C₄

yes

characteristic

C₂²×D₇₃

C₂²⋊C₈

yes

characteristic

Q₈×C₇₃

—

Q₈×C₇₃

M₃₂

yes

complemented

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

—

C₂×C₄×C₇₃

C₂×C₂²⋊C₄

yes

characteristic

C₂×C₄×C₇₃

C₂²×C₈

yes

characteristic

100

C₂×C₄×C₇₃

C₂×M₁₆

yes

characteristic

101

C₂×Dic₇₃

—

102

C₂×Dic₇₃

—

103

C₂×Dic₇₃

C₂²⋊C₈

yes

characteristic

104

C₂×Dic₇₃

C₂²⋊C₈

yes

characteristic

105

C₂×Dic₇₃

C₂²⋊C₈

yes

characteristic

106

C₄×D₇₃

—

107

C₄×D₇₃

—

108

C₄×D₇₃

—

109

C₄×D₇₃

—

110

C₄×D₇₃

—

111

C₄×D₇₃

#103

yes

—

112

C₄×D₇₃

#104

yes

—

113

Dic₁₄₆

—

114

Dic₁₄₆

—

115

Dic₁₄₆

M₃₂

yes

complemented

116

C₈×C₇₃

—

117

C₈×C₇₃

—

118

C₈×C₇₃

#103

yes

—

119

#10596831

—

120

#10596831

—

121

#10596831

C₂×SD₁₆

yes

characteristic

122

#10596831

C₂×Q₁₆

yes

characteristic

123

C₂²×C₇₃

C₂×C₂²⋊C₈

yes

characteristic

124

C₂×D₇₃

—

125

C₂×D₇₃

—

126

C₂×D₇₃

Q₈⋊C₈

yes

—

127

C₄×C₇₃

—

128

C₄×C₇₃

—

129

C₄×C₇₃

—

130

C₄×C₇₃

C₂×#103

yes

characteristic

131

C₄×C₇₃

C₂×#104

yes

characteristic

132

C₄×C₇₃

C₂×M₃₂

yes

characteristic

133

C₄×C₇₃

C₂×M₃₂

yes

characteristic

134

Dic₇₃

—

135

Dic₇₃

—

136

Dic₇₃

—

137

Dic₇₃

—

138

Dic₇₃

Q₈⋊C₈

yes

—

139

#11607

—

maximal, Sylow

140

C₂×C₇₃

C₂×Q₈⋊C₈

yes

characteristic

141

C₂×C₇₃

#2112

yes

characteristic

142

C₂×C₇₃

#2117

yes

characteristic

143

D₇₃

—

144

C₂×C₈×Q₈

—

145

#2150

—

146

C₄×M₃₂

—

147

Q₈⋊C₁₆

—

148

Q₈⋊C₁₆

—

149

C₇₃

#11607

yes

characteristic, complemented, Sylow

150

C₂×C₄×Q₈

—

151

C₂×M₃₂

—

146

—

152

C₂×M₃₂

—

146

—

153

C₈×Q₈

—

154

C₈×Q₈

—

155

C₈×Q₈

—

156

C₈×Q₈

—

146

—

157

C₈×Q₈

—

146

—

158

C₈×Q₈

#64408

yes

characteristic

159

C₂×C₄⋊C₈

—

160

C₂×C₄⋊C₈

—

146

—

161

C₂×C₄×C₈

—

162

C₂×C₄×C₈

—

146

—

163

C₄⋊C₁₆

—

164

C₄⋊C₁₆

—

146

—

165

#346

—

146

—

166

C₄×C₁₆

—

167

C₂²×Q₈

—

168

C₂²×C₈

—

169

C₂²×C₈

—

170

C₂²×C₈

—

146

—

171

C₄×Q₈

—

172

C₄×Q₈

—

173

C₄×Q₈

—

174

C₄×Q₈

—

146

—

175

C₄×Q₈

—

146

—

176

C₄×Q₈

C₂×#64408

yes

characteristic

177

C₂×C₄⋊C₄

—

178

C₂×C₄⋊C₄

—

146

—

179

C₂×C₄²

—

180

C₂×C₄²

—

146

—

181

M₃₂

—

292

—

182

M₃₂

—

146

—

183

C₂×C₁₆

—

146

—

184

C₂×C₁₆

—

146

—

185

C₄⋊C₈

—

186

C₄⋊C₈

—

187

C₄⋊C₈

—

146

—

188

C₄⋊C₈

—

146

—

189

C₄⋊C₈

—

146

—

190

C₄⋊C₈

—

146

—

191

C₄⋊C₈

C₂×#64408

yes

characteristic

192

C₄×C₈

—

193

C₄×C₈

—

194

C₄×C₈

—

195

C₄×C₈

—

196

C₄×C₈

—

146

—

197

C₄×C₈

—

146

—

198

C₄×C₈

—

146

—

199

C₄×C₈

C₂×#64408

yes

characteristic

200

C₂×Q₈

—

201

C₂×Q₈

—

146

—

202

C₂×Q₈

—

146

—

203

C₂×Q₈

—

146

—

204

C₂×Q₈

#11924036

yes

characteristic

205

C₂²×C₄

—

206

C₂²×C₄

—

207

C₂²×C₄

—

208

C₂²×C₄

—

146

—

209

C₂²×C₄

—

146

—

210

C₂×C₈

—

211

C₂×C₈

—

292

—

212

C₂×C₈

—

213

C₂×C₈

—

214

C₂×C₈

—

215

C₂×C₈

—

216

C₂×C₈

—

146

—

217

C₂×C₈

—

146

—

218

C₂×C₈

C₂²⋊#64408

yes

characteristic

219

C₂×C₈

C₂²⋊#64408

yes

characteristic

220

C₄⋊C₄

—

221

C₄⋊C₄

—

222

C₄⋊C₄

—

146

—

223

C₄⋊C₄

—

146

—

224

C₄⋊C₄

—

146

—

225

C₄⋊C₄

—

146

—

226

C₄⋊C₄

#11924036

yes

characteristic

227

C₄²

—

228

C₄²

—

229

C₄²

—

230

C₄²

—

231

C₄²

—

146

—

232

C₄²

—

146

—

233

C₄²

—

146

—

234

C₄²

C₂²×#64408

yes

characteristic

235

C₁₆

—

292

—

236

C₁₆

—

146

—

237

C₂³

—

238

Q₈

—

239

Q₈

—

240

Q₈

—

146

—

241

Q₈

—

146

—

242

Q₈

#14556666

yes

complemented

243

C₂×C₄

—

244

C₂×C₄

—

245

C₂×C₄

—

292

—

246

C₂×C₄

—

292

—

247

C₂×C₄

—

248

C₂×C₄

—

249

C₂×C₄

—

250

C₂×C₄

—

251

C₂×C₄

—

252

C₂×C₄

—

146

—

253

C₂×C₄

—

146

—

254

C₂×C₄

—

146

—

255

C₂×C₄

—

146

—

256

C₂×C₄

—

146

—

257

C₂×C₄

C₂×C₂²⋊#64408

yes

characteristic

258

C₂×C₄

C₂×#11924036

yes

characteristic

259

C₂×C₄

D₇₃⋊M₁₆

yes

characteristic

260

C₈

—

261

C₈

—

262

C₈

—

292

—

263

C₈

—

264

C₈

—

265

C₈

—

146

—

266

C₈

#14556654

yes

—

267

C₂²

—

268

C₂²

—

146

—

269

C₂²

—

146

—

270

C₂²

#17989555

yes

characteristic

271

C₄

—

272

C₄

—

273

C₄

—

274

C₄

—

292

—

275

C₄

—

276

C₄

—

146

—

277

C₄

—

146

—

278

C₄

—

146

—

279

C₄

C₂×#14556654

yes

characteristic

280

C₄

D₇₃⋊#104

yes

characteristic

281

C₄

#17989643

yes

characteristic

282

C₄

C₂×#14556666

yes

characteristic

283

C₂

—

146

—

284

C₂

#22625220

yes

characteristic

285

C₂

#22626159

yes

characteristic

286

C₂

#22626174

yes

characteristic

	subgroup	G/H
center	C₂×C₄	C₂×C₂²⋊#64408
commutator	C₂×C₄×C₇₃	C₂²×C₈
Frattini	C₄²	C₂²×#64408
Fitting	C₈×Q₈×C₇₃	C₄
socle	C₂²×C₇₃	C₂×C₂²⋊C₈
prime radical	C₂²×D₇₃	C₂²⋊C₈
cosocle	C₄×#10596831	C₂³
hypercenter	C₈×Q₈	#64408
hypocenter	C₇₃	#11607
LCS	G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃
UCS	C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₈

subgroup

G/H

center

C₂×C₄

C₂×C₂²⋊#64408

commutator

C₂×C₄×C₇₃

C₂²×C₈

Frattini

C₄²

C₂²×#64408

Fitting

C₈×Q₈×C₇₃

C₄

socle

C₂²×C₇₃

C₂×C₂²⋊C₈

prime radical

C₂²×D₇₃

C₂²⋊C₈

C₂³

C₈×Q₈

C₇₃

G ▷ C₂×C₄×C₇₃ ▷ C₂×C₇₃ ▷ C₇₃

UCS

C₁ ◁ C₂×C₄ ◁ C₄×C₈ ◁ C₈×Q₈

N	H ≅ G/N	type
3. #22624898	C₂	semidirect
4. Q₈⋊#11924031	C₂	semidirect
95. Q₈×C₇₃	M₃₂	semidirect
115. Dic₁₄₆	M₃₂	semidirect
149. C₇₃	#11607	semidirect
242. Q₈	#14556666	semidirect

H ≅ G/N

type

3. #22624898

C₂

semidirect

4. Q₈⋊#11924031

C₂

semidirect

95. Q₈×C₇₃

M₃₂

semidirect

115. Dic₁₄₆

M₃₂

semidirect

149. C₇₃

#11607

semidirect

242. Q₈

#14556666

semidirect

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

subgroup	index
#22626264	2
C₄×#14556666	2
#22624898	2
Q₈⋊#11924031	2
C₈×Q₈×D₇₃	2
#11607	73

subgroup

index

C₈×Q₈×D₇₃

Subgroups — #34010422

Conjugacy classes of subgroups

Complements

Maximal subgroups