Subgroups — #3542

Order 128.

580 conjugacy classes of subgroups.

The subgroup lattice has 361 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#	subgroup	G/H	class size	multiplicity	normal?	properties
1	#562	C₂	1	2	yes	maximal, complemented
2	#560	C₂	1	2	yes	maximal, complemented
3	#555	C₂	1	1	yes	maximal, characteristic, complemented
4	#553	C₂	1	1	yes	maximal, characteristic, complemented
5	#552	C₂	1	1	yes	maximal, characteristic, complemented
6	#551	C₂	1	2	yes	maximal, complemented
7	#550	C₂	1	1	yes	maximal, characteristic, complemented
8	#547	C₂	1	1	yes	maximal, characteristic, complemented
9	#546	C₂	1	2	yes	maximal, complemented
10	#546	C₂	1	1	yes	maximal, characteristic, complemented
11	#546	C₂	1	1	yes	maximal, characteristic, complemented
12	D₄²	C₂	1	1	yes	maximal, characteristic, complemented
13	#542	C₂	1	1	yes	maximal, characteristic, complemented
14	#540	C₂	1	1	yes	maximal, characteristic, complemented
15	#540	C₂	1	2	yes	maximal, complemented
16	#538	C₂	1	2	yes	maximal, complemented
17	#537	C₂	1	1	yes	maximal, characteristic, complemented
18	#535	C₂	1	2	yes	maximal, complemented
19	#535	C₂	1	1	yes	maximal, characteristic, complemented
20	#534	C₂	1	2	yes	maximal, complemented
21	#525	C₂	1	1	yes	maximal, characteristic, complemented
22	#525	C₂	1	1	yes	maximal, characteristic, complemented
23	C₂×#121	C₂	1	1	yes	maximal, characteristic, complemented
24	C₂×#41	C₂²	1	1	yes	characteristic, complemented
25	C₂×#41	C₂²	1	1	yes	characteristic, complemented
26	C₂×#41	C₂²	1	2	yes	complemented
27	C₂×#41	C₂²	1	1	yes	characteristic, complemented
28	C₂²×D₄	C₂²	1	1	yes	characteristic
29	C₂²×D₄	C₂²	1	2	yes	—
30	C₂²×D₄	C₂²	1	2	yes	complemented
31	C₂²×D₄	C₂²	1	1	yes	characteristic, complemented
32	C₂³×C₄	C₂²	1	1	yes	characteristic, complemented
33	C₄⋊Q₈	C₂²	1	1	yes	characteristic, complemented
34	#127	C₂²	1	2	yes	complemented
35	#127	C₂²	1	2	yes	complemented
36	#127	C₂²	1	1	yes	characteristic, complemented
37	#126	C₂²	1	2	yes	complemented
38	#126	C₂²	1	2	yes	complemented
39	#126	C₂²	1	2	yes	complemented
40	#125	C₂²	1	1	yes	characteristic, complemented
41	#125	C₂²	1	2	yes	complemented
42	#124	C₂²	1	2	yes	complemented
43	#124	C₂²	1	2	yes	complemented
44	#124	C₂²	1	2	yes	complemented
45	#124	C₂²	1	2	yes	complemented
46	#124	C₂²	1	1	yes	characteristic, complemented
47	#123	C₂²	1	2	yes	—
48	#123	C₂²	1	1	yes	characteristic, complemented
49	#123	C₂²	1	1	yes	characteristic, complemented
50	#123	C₂²	1	2	yes	complemented
51	#123	C₂²	1	2	yes	complemented
52	#123	C₂²	1	2	yes	complemented
53	#123	C₂²	1	2	yes	complemented
54	#123	C₂²	1	2	yes	complemented
55	#123	C₂²	1	2	yes	complemented
56	#123	C₂²	1	2	yes	complemented
57	#123	C₂²	1	2	yes	complemented
58	#123	C₂²	1	2	yes	complemented
59	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
60	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
61	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
62	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
63	C₂²⋊Q₈	C₂²	1	1	yes	characteristic, complemented
64	C₂²⋊Q₈	C₂²	1	2	yes	complemented
65	C₂²⋊Q₈	C₂²	1	2	yes	complemented
66	C₂²⋊Q₈	C₂²	1	2	yes	complemented
67	#121	C₂²	1	1	yes	characteristic
68	#121	C₂²	1	1	yes	characteristic
69	#121	C₂²	1	1	yes	characteristic
70	#121	C₂²	1	1	yes	characteristic
71	#121	C₂²	1	1	yes	characteristic, complemented
72	#121	C₂²	1	2	yes	complemented
73	#121	C₂²	1	1	yes	characteristic, complemented
74	#121	C₂²	1	2	yes	complemented
75	#121	C₂²	1	1	yes	characteristic, complemented
76	#121	C₂²	1	1	yes	characteristic, complemented
77	#121	C₂²	1	2	yes	complemented
78	#121	C₂²	1	2	yes	complemented
79	#121	C₂²	1	2	yes	complemented
80	#121	C₂²	1	2	yes	complemented
81	#121	C₂²	1	2	yes	complemented
82	#121	C₂²	1	2	yes	complemented
83	#121	C₂²	1	1	yes	characteristic, complemented
84	#121	C₂²	1	2	yes	complemented
85	#121	C₂²	1	1	yes	characteristic, complemented
86	#121	C₂²	1	2	yes	complemented
87	#121	C₂²	1	1	yes	characteristic, complemented
88	#121	C₂²	1	2	yes	complemented
89	#121	C₂²	1	2	yes	complemented
90	#121	C₂²	1	2	yes	complemented
91	#121	C₂²	1	2	yes	complemented
92	#120	C₂²	1	1	yes	characteristic
93	#120	C₂²	1	2	yes	—
94	#120	C₂²	1	2	yes	complemented
95	#120	C₂²	1	1	yes	characteristic, complemented
96	#120	C₂²	1	2	yes	complemented
97	#120	C₂²	1	2	yes	complemented
98	#120	C₂²	1	2	yes	complemented
99	#120	C₂²	1	2	yes	complemented
100	#120	C₂²	1	2	yes	complemented
101	C₄×Q₈	C₂²	1	1	yes	characteristic, complemented
102	C₄×D₄	C₂²	1	1	yes	characteristic
103	C₄×D₄	C₂²	1	2	yes	complemented
104	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
105	C₄×D₄	C₂²	1	2	yes	complemented
106	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
107	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
108	C₄×D₄	C₂²	1	2	yes	complemented
109	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
110	C₄×D₄	C₂²	1	2	yes	complemented
111	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
112	C₄×D₄	C₂²	1	1	yes	characteristic, complemented
113	#117	C₂²	1	1	yes	characteristic, complemented
114	#117	C₂²	1	1	yes	characteristic, complemented
115	#117	C₂²	1	2	yes	complemented
116	#117	C₂²	1	1	yes	characteristic, complemented
117	#117	C₂²	1	2	yes	complemented
118	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
119	C₂×C₄⋊C₄	C₂²	1	1	yes	characteristic, complemented
120	C₂×C₂²⋊C₄	C₂²	1	2	yes	complemented
121	C₂×C₂²⋊C₄	C₂²	1	2	yes	complemented
122	C₂×C₂²⋊C₄	C₂²	1	2	yes	complemented
123	C₂⁴	C₂³	1	2	yes	—
124	C₂⁴	C₂³	1	1	yes	characteristic
125	C₂⁴	C₂³	1	2	yes	—
126	#41	—	4	2	no	—
127	#41	—	4	4	no	—
128	#41	—	4	2	no	—
129	#41	—	4	2	no	—
130	C₂×Q₈	C₂³	1	1	yes	characteristic
131	C₂×Q₈	C₂³	1	1	yes	characteristic
132	C₂×Q₈	C₂³	1	2	yes	—
133	C₂×D₄	—	4	2	no	—
134	C₂×D₄	—	4	2	no	—
135	C₂×D₄	—	4	4	no	—
136	C₂×D₄	—	4	4	no	—
137	C₂×D₄	C₂³	1	1	yes	characteristic
138	C₂×D₄	C₂³	1	2	yes	—
139	C₂×D₄	C₂³	1	1	yes	characteristic
140	C₂×D₄	C₂³	1	1	yes	characteristic
141	C₂×D₄	C₂³	1	1	yes	characteristic
142	C₂×D₄	C₂³	1	1	yes	characteristic
143	C₂×D₄	C₂³	1	1	yes	characteristic
144	C₂×D₄	C₂³	1	2	yes	—
145	C₂×D₄	C₂³	1	2	yes	—
146	C₂×D₄	C₂³	1	2	yes	—
147	C₂×D₄	C₂³	1	1	yes	characteristic
148	C₂×D₄	C₂³	1	1	yes	characteristic
149	C₂×D₄	C₂³	1	2	yes	—
150	C₂×D₄	C₂³	1	1	yes	characteristic
151	C₂×D₄	C₂³	1	2	yes	—
152	C₂×D₄	C₂³	1	2	yes	—
153	C₂×D₄	C₂³	1	2	yes	—
154	C₂×D₄	C₂³	1	2	yes	—
155	C₂×D₄	C₂³	1	2	yes	—
156	C₂×D₄	C₂³	1	2	yes	—
157	C₂×D₄	C₂³	1	1	yes	characteristic
158	C₂×D₄	C₂³	1	2	yes	—
159	C₂×D₄	C₂³	1	2	yes	—
160	C₂×D₄	C₂³	1	2	yes	—
161	C₂×D₄	C₂³	1	2	yes	—
162	C₂²×C₄	—	4	2	no	—
163	C₂²×C₄	C₂³	1	2	yes	—
164	C₂²×C₄	C₂³	1	1	yes	characteristic
165	C₂²×C₄	C₂³	1	1	yes	characteristic
166	C₂²×C₄	C₂³	1	1	yes	characteristic
167	C₂²×C₄	C₂³	1	1	yes	characteristic
168	C₂²×C₄	C₂³	1	1	yes	characteristic
169	C₂²×C₄	C₂³	1	1	yes	characteristic
170	C₂²×C₄	C₂³	1	2	yes	—
171	C₂²×C₄	C₂³	1	2	yes	—
172	C₂²×C₄	C₂³	1	2	yes	—
173	C₂²×C₄	C₂³	1	2	yes	—
174	C₂²×C₄	C₂³	1	2	yes	—
175	C₂²×C₄	C₂³	1	1	yes	characteristic
176	C₂²×C₄	C₂³	1	2	yes	—
177	C₂²×C₄	C₂³	1	1	yes	characteristic
178	C₄⋊C₄	C₂³	1	1	yes	characteristic
179	C₄⋊C₄	C₂³	1	1	yes	characteristic
180	C₄⋊C₄	C₂³	1	1	yes	characteristic
181	C₄⋊C₄	C₂³	1	2	yes	—
182	C₄⋊C₄	C₂³	1	2	yes	—
183	C₄⋊C₄	C₂³	1	1	yes	characteristic
184	C₄⋊C₄	C₂³	1	1	yes	characteristic
185	C₄⋊C₄	C₂³	1	1	yes	characteristic
186	C₄⋊C₄	C₂³	1	2	yes	—
187	C₄⋊C₄	C₂³	1	2	yes	—
188	C₄⋊C₄	C₂³	1	1	yes	characteristic
189	C₄⋊C₄	C₂³	1	2	yes	—
190	C₄⋊C₄	C₂³	1	1	yes	characteristic
191	C₄⋊C₄	C₂³	1	1	yes	characteristic
192	C₄⋊C₄	C₂³	1	2	yes	—
193	C₄⋊C₄	C₂³	1	2	yes	—
194	C₄⋊C₄	C₂³	1	2	yes	—
195	C₄⋊C₄	C₂³	1	1	yes	characteristic
196	C₄⋊C₄	C₂³	1	2	yes	—
197	C₂²⋊C₄	C₂³	1	1	yes	characteristic
198	C₂²⋊C₄	C₂³	1	2	yes	—
199	C₂²⋊C₄	C₂³	1	1	yes	characteristic
200	C₂²⋊C₄	C₂³	1	2	yes	—
201	C₂²⋊C₄	C₂³	1	2	yes	—
202	C₂²⋊C₄	C₂³	1	2	yes	—
203	C₂²⋊C₄	C₂³	1	2	yes	—
204	C₂²⋊C₄	C₂³	1	2	yes	—
205	C₂²⋊C₄	C₂³	1	2	yes	—
206	C₂²⋊C₄	C₂³	1	2	yes	—
207	C₂²⋊C₄	C₂³	1	2	yes	—
208	C₂²⋊C₄	C₂³	1	1	yes	characteristic
209	C₂²⋊C₄	C₂³	1	2	yes	—
210	C₂²⋊C₄	C₂³	1	1	yes	characteristic
211	C₂²⋊C₄	C₂³	1	2	yes	—
212	C₂²⋊C₄	C₂³	1	2	yes	—
213	C₂²⋊C₄	C₂³	1	1	yes	characteristic
214	C₂²⋊C₄	C₂³	1	1	yes	characteristic
215	C₂²⋊C₄	C₂³	1	1	yes	characteristic
216	C₂²⋊C₄	C₂³	1	2	yes	—
217	C₂²⋊C₄	C₂³	1	1	yes	characteristic
218	C₂²⋊C₄	C₂³	1	2	yes	—
219	C₂²⋊C₄	C₂³	1	2	yes	—
220	C₂²⋊C₄	C₂³	1	2	yes	—
221	C₂²⋊C₄	C₂³	1	1	yes	characteristic
222	C₂²⋊C₄	C₂³	1	2	yes	—
223	C₂²⋊C₄	C₂³	1	2	yes	—
224	C₂²⋊C₄	C₂³	1	2	yes	—
225	C₂²⋊C₄	C₂³	1	1	yes	characteristic
226	C₄²	C₂³	1	2	yes	—
227	C₄²	C₂³	1	2	yes	—
228	C₄²	C₂³	1	1	yes	characteristic
229	C₄²	C₂³	1	1	yes	characteristic
230	C₄²	C₂³	1	2	yes	—
231	C₂³	—	2	2	no	—
232	C₂³	—	2	4	no	—
233	C₂³	—	4	1	no	—
234	C₂³	—	4	1	no	—
235	C₂³	—	4	2	no	—
236	C₂³	—	4	2	no	—
237	C₂³	—	4	2	no	—
238	C₂³	—	4	2	no	—
239	C₂³	—	4	2	no	—
240	C₂³	C₂⁴	1	1	yes	characteristic
241	C₂³	C₂⁴	1	2	yes	—
242	C₂³	C₂⁴	1	1	yes	characteristic
243	C₂³	C₂⁴	1	1	yes	characteristic
244	C₂³	C₂⁴	1	2	yes	—
245	C₂³	C₂⁴	1	2	yes	—
246	C₂³	C₂⁴	1	1	yes	characteristic
247	C₂³	C₂⁴	1	1	yes	characteristic
248	Q₈	—	2	2	no	—
249	Q₈	—	4	1	no	—
250	Q₈	—	4	2	no	—
251	D₄	—	2	2	no	—
252	D₄	—	2	4	no	—
253	D₄	—	2	2	no	—
254	D₄	—	2	2	no	—
255	D₄	—	2	2	no	—
256	D₄	—	2	2	no	—
257	D₄	—	4	2	no	—
258	D₄	—	4	2	no	—
259	D₄	—	4	2	no	—
260	D₄	—	4	2	no	—
261	D₄	—	4	2	no	—
262	D₄	—	4	2	no	—
263	D₄	—	4	2	no	—
264	D₄	—	4	2	no	—
265	D₄	—	4	1	no	—
266	D₄	—	4	2	no	—
267	D₄	—	4	2	no	—
268	D₄	—	4	2	no	—
269	D₄	—	4	1	no	—
270	D₄	—	4	1	no	—
271	D₄	—	4	1	no	—
272	D₄	—	4	1	no	—
273	D₄	—	4	2	no	—
274	D₄	—	4	2	no	—
275	D₄	—	4	2	no	—
276	C₂×C₄	—	2	4	no	—
277	C₂×C₄	—	2	2	no	—
278	C₂×C₄	—	2	2	no	—
279	C₂×C₄	—	2	2	no	—
280	C₂×C₄	—	2	2	no	—
281	C₂×C₄	—	2	2	no	—
282	C₂×C₄	—	4	1	no	—
283	C₂×C₄	—	4	1	no	—
284	C₂×C₄	—	4	1	no	—
285	C₂×C₄	—	4	2	no	—
286	C₂×C₄	—	4	2	no	—
287	C₂×C₄	—	4	2	no	—
288	C₂×C₄	—	4	2	no	—
289	C₂×C₄	—	4	2	no	—
290	C₂×C₄	—	4	2	no	—
291	C₂×C₄	C₂⁴	1	1	yes	characteristic
292	C₂×C₄	C₂⁴	1	2	yes	—
293	C₂×C₄	C₂⁴	1	1	yes	characteristic
294	C₂×C₄	C₂⁴	1	1	yes	characteristic
295	C₂×C₄	C₂⁴	1	2	yes	—
296	C₂×C₄	C₂⁴	1	1	yes	characteristic
297	C₂×C₄	C₂⁴	1	1	yes	characteristic
298	C₂×C₄	C₂⁴	1	2	yes	—
299	C₂×C₄	C₂⁴	1	2	yes	—
300	C₂×C₄	C₂⁴	1	1	yes	characteristic
301	C₂×C₄	C₂⁴	1	1	yes	characteristic
302	C₂×C₄	C₂⁴	1	1	yes	characteristic
303	C₂×C₄	C₂⁴	1	2	yes	—
304	C₂×C₄	C₂⁴	1	1	yes	characteristic
305	C₂×C₄	C₂⁴	1	1	yes	characteristic
306	C₂²	—	2	1	no	—
307	C₂²	—	2	1	no	—
308	C₂²	—	2	1	no	—
309	C₂²	—	2	1	no	—
310	C₂²	—	2	1	no	—
311	C₂²	—	2	1	no	—
312	C₂²	—	2	1	no	—
313	C₂²	—	2	2	no	—
314	C₂²	—	2	2	no	—
315	C₂²	—	2	2	no	—
316	C₂²	—	2	2	no	—
317	C₂²	—	2	1	no	—
318	C₂²	—	2	2	no	—
319	C₂²	—	2	1	no	—
320	C₂²	—	2	1	no	—
321	C₂²	—	2	2	no	—
322	C₂²	—	2	2	no	—
323	C₂²	—	2	1	no	—
324	C₂²	—	2	1	no	—
325	C₂²	—	2	1	no	—
326	C₂²	—	2	2	no	—
327	C₂²	—	2	1	no	—
328	C₂²	—	2	2	no	—
329	C₂²	—	4	4	no	—
330	C₂²	—	8	4	no	—
331	C₂²	—	8	4	no	—
332	C₂²	H(5,𝔽₂)	1	2	yes	—
333	C₂²	C₂⁵	1	1	yes	characteristic
334	C₄	—	2	1	no	—
335	C₄	—	2	2	no	—
336	C₄	—	2	1	no	—
337	C₄	—	2	1	no	—
338	C₄	—	2	1	no	—
339	C₄	—	2	2	no	—
340	C₄	—	2	1	no	—
341	C₄	—	2	1	no	—
342	C₄	—	2	2	no	—
343	C₄	—	2	1	no	—
344	C₄	—	2	2	no	—
345	C₄	—	2	1	no	—
346	C₄	—	2	2	no	—
347	C₄	—	2	1	no	—
348	C₄	H(5,𝔽₂)	1	2	yes	—
349	C₂	—	2	2	no	—
350	C₂	—	4	1	no	—
351	C₂	—	4	1	no	—
352	C₂	—	4	1	no	—
353	C₂	—	4	2	no	—
354	C₂	—	4	2	no	—
355	C₂	—	4	1	no	—
356	C₂	—	4	2	no	—
357	C₂	C₂×H(5,𝔽₂)	1	1	yes	characteristic
358	C₂	C₂×H(5,𝔽₂)	1	1	yes	characteristic
359	C₂	#585	1	1	yes	characteristic

	subgroup	G/H
center, commutator, Frattini, socle, cosocle	C₂²	C₂⁵
LCS	G ▷ C₂² ▷ C₁
UCS	C₁ ◁ C₂² ◁ G
LECS	G ▷ C₂² ▷ C₁

Complements

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

N	H ≅ G/N	type
1. #562	C₂	semidirect
2. #560	C₂	semidirect
3. #555	C₂	semidirect
4. #553	C₂	semidirect
5. #552	C₂	semidirect
6. #551	C₂	semidirect
7. #550	C₂	semidirect
8. #547	C₂	semidirect
9. #546	C₂	semidirect
10. #546	C₂	semidirect
11. #546	C₂	semidirect
12. D₄²	C₂	semidirect
13. #542	C₂	semidirect
14. #540	C₂	semidirect
15. #540	C₂	semidirect
16. #538	C₂	semidirect
17. #537	C₂	semidirect
18. #535	C₂	semidirect
19. #535	C₂	semidirect
20. #534	C₂	semidirect
21. #525	C₂	semidirect
22. #525	C₂	semidirect
23. C₂×#121	C₂	semidirect
24. C₂×#41	C₂²	semidirect
25. C₂×#41	C₂²	semidirect
26. C₂×#41	C₂²	semidirect
27. C₂×#41	C₂²	semidirect
30. C₂²×D₄	C₂²	semidirect
31. C₂²×D₄	C₂²	semidirect
32. C₂³×C₄	C₂²	semidirect
33. C₄⋊Q₈	C₂²	semidirect
34. #127	C₂²	semidirect
35. #127	C₂²	semidirect
36. #127	C₂²	semidirect
37. #126	C₂²	semidirect
38. #126	C₂²	semidirect
39. #126	C₂²	semidirect
40. #125	C₂²	semidirect
41. #125	C₂²	semidirect
42. #124	C₂²	semidirect
43. #124	C₂²	semidirect
44. #124	C₂²	semidirect
45. #124	C₂²	semidirect
46. #124	C₂²	semidirect
48. #123	C₂²	semidirect
49. #123	C₂²	semidirect
50. #123	C₂²	semidirect
51. #123	C₂²	semidirect
52. #123	C₂²	semidirect
53. #123	C₂²	semidirect
54. #123	C₂²	semidirect
55. #123	C₂²	semidirect
56. #123	C₂²	semidirect
57. #123	C₂²	semidirect
58. #123	C₂²	semidirect
59. C₂²⋊Q₈	C₂²	semidirect
60. C₂²⋊Q₈	C₂²	semidirect
61. C₂²⋊Q₈	C₂²	semidirect
62. C₂²⋊Q₈	C₂²	semidirect
63. C₂²⋊Q₈	C₂²	semidirect
64. C₂²⋊Q₈	C₂²	semidirect
65. C₂²⋊Q₈	C₂²	semidirect
66. C₂²⋊Q₈	C₂²	semidirect
71. #121	C₂²	semidirect
72. #121	C₂²	semidirect
73. #121	C₂²	semidirect
74. #121	C₂²	semidirect
75. #121	C₂²	semidirect
76. #121	C₂²	semidirect
77. #121	C₂²	semidirect
78. #121	C₂²	semidirect
79. #121	C₂²	semidirect
80. #121	C₂²	semidirect
81. #121	C₂²	semidirect
82. #121	C₂²	semidirect
83. #121	C₂²	semidirect
84. #121	C₂²	semidirect
85. #121	C₂²	semidirect
86. #121	C₂²	semidirect
87. #121	C₂²	semidirect
88. #121	C₂²	semidirect
89. #121	C₂²	semidirect
90. #121	C₂²	semidirect
91. #121	C₂²	semidirect
94. #120	C₂²	semidirect
95. #120	C₂²	semidirect
96. #120	C₂²	semidirect
97. #120	C₂²	semidirect
98. #120	C₂²	semidirect
99. #120	C₂²	semidirect
100. #120	C₂²	semidirect
101. C₄×Q₈	C₂²	semidirect
103. C₄×D₄	C₂²	semidirect
104. C₄×D₄	C₂²	semidirect
105. C₄×D₄	C₂²	semidirect
106. C₄×D₄	C₂²	semidirect
107. C₄×D₄	C₂²	semidirect
108. C₄×D₄	C₂²	semidirect
109. C₄×D₄	C₂²	semidirect
110. C₄×D₄	C₂²	semidirect
111. C₄×D₄	C₂²	semidirect
112. C₄×D₄	C₂²	semidirect
113. #117	C₂²	semidirect
114. #117	C₂²	semidirect
115. #117	C₂²	semidirect
116. #117	C₂²	semidirect
117. #117	C₂²	semidirect
118. C₂×C₄⋊C₄	C₂²	semidirect
119. C₂×C₄⋊C₄	C₂²	semidirect
120. C₂×C₂²⋊C₄	C₂²	semidirect
121. C₂×C₂²⋊C₄	C₂²	semidirect
122. C₂×C₂²⋊C₄	C₂²	semidirect

Maximal subgroups

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

subgroup	index
#562	2
#560	2
#555	2
#553	2
#552	2
#551	2
#550	2
#547	2
#546	2
D₄²	2
#542	2
#540	2
#538	2
#537	2
#535	2
#534	2
#525	2
C₂×#121	2