Finite Group Databasebeta

← #29574360

Subgroups — #29574360

Order 15616.

376 conjugacy classes of subgroups.

The subgroup lattice has 338 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1Q8×#11758194C211yesmaximal, characteristic
2#21446592C211yesmaximal, characteristic
3#21444574C211yesmaximal, characteristic
4C2×Q8⋊#92418C211yesmaximal, characteristic
5#21443715C211yesmaximal, characteristic
6#21443655C211yesmaximal, characteristic
7C61×#1487C211yesmaximal, characteristic
8#16839893—22no—
9#16839893—21no—
10Q8×#92418—21no—
11C2×#14519712—21no—
12#16839786—21no—
13#16839786C2211yescharacteristic
14C2×C4⋊#92418C2211yescharacteristic
15C4×#11758194—21no—
16C4×#11758194C2211yescharacteristic
17C2×C4×#92418C2211yescharacteristic
18#16839526—21no—
19#16839512—22no—
20Q8⋊#92418C411yescharacteristic
21Q8⋊#92418C411yescharacteristic
22Q8⋊#92418C411yescharacteristic
23Q8⋊#92418C411yescharacteristic
24C2×C4×Q8×C61C2211yescharacteristic
25C61×#431C2211yescharacteristic
26C61×#423C2211yescharacteristic
27C61×Q8⋊C8—21no—
28C61×Q8⋊C8—21no—
29C2×#11758194—21no—
30C2×#11758194D411yescharacteristic
31C2×#11758194D411yescharacteristic
32C22×#92418—21no—
33C22×#92418—21no—
34#14519712—42no—
35C4⋊#92418—22no—
36C4⋊#92418—22no—
37C4⋊#92418—21no—
38C4⋊#92418—21no—
39C4⋊#92418C2×C411yescharacteristic
40C4⋊#92418C2×C411yescharacteristic
41C4⋊#92418D412yes—
42#14519688—22no—
43#14519688—21no—
44C4×#92418—22no—
45C4×#92418—21no—
46C4×#92418—21no—
47C4×#92418C2×C411yescharacteristic
48C4×#92418C2×C411yescharacteristic
49C22×Q8×C61Q811yescharacteristic
50C2×M16×C61—21no—
51C4×Q8×C61—21no—
52C4×Q8×C61—21no—
53C4×Q8×C61C2×C411yescharacteristic
54C4×Q8×C61C2×C411yescharacteristic
55C4×Q8×C61D411yescharacteristic
56C4×Q8×C61D411yescharacteristic
57C2×C4⋊C4×C61—21no—
58C2×C4⋊C4×C61Q811yescharacteristic
59C2×C42×C61—21no—
60C2×C42×C61C2311yescharacteristic
61C4⋊C8×C61—21no—
62C4⋊C8×C61—21no—
63C4⋊C8×C61—21no—
64C22⋊C8×C61—21no—
65C4×C8×C61—21no—
66C2×Q8×C61—21no—
67C2×Q8×C61—22no—
68C2×Q8×C61—41no—
69C2×Q8×C61C4⋊C411yescharacteristic
70C2×Q8×C61C4⋊C411yescharacteristic
71C22×C4×C61—21no—
72C22×C4×C61—21no—
73C22×C4×C61C2×D411yescharacteristic
74C22×C4×C61C2×Q811yescharacteristic
75C22×C4×C61#4111yescharacteristic
76M16×C61—41no—
77M16×C61—41no—
78C2×C8×C61—41no—
79C2×C8×C61—41no—
80C4⋊C4×C61—21no—
81C4⋊C4×C61—21no—
82C4⋊C4×C61—21no—
83C4⋊C4×C61—21no—
84C4⋊C4×C61—21no—
85C4⋊C4×C61C4⋊C411yescharacteristic
86C4⋊C4×C61C4⋊C411yescharacteristic
87C42×C61—21no—
88C42×C61—21no—
89C42×C61—21no—
90C42×C61—21no—
91C42×C61C22×C411yescharacteristic
92C42×C61C2×D411yescharacteristic
93C42×C61C2×D411yescharacteristic
94C42×C61#4111yescharacteristic
95#11758194—21no—
96#11758194—21no—
97#11758194—21no—
98#11758194—41no—
99#11758194—41no—
100#11758194SD1612yes—
101C2×#92418—21no—
102C2×#92418—21no—
103C2×#92418—21no—
104C2×#92418—21no—
105C2×#92418—21no—
106C2×#92418—21no—
107C2×#92418—22no—
108C2×#92418—42no—
109C2×#92418—41no—
110C2×#92418—41no—
111C23×C61C22⋊Q811yescharacteristic
112Q8×C61—21no—
113Q8×C61—21no—
114Q8×C61—21no—
115Q8×C61—42no—
116Q8×C61#10812yescomplemented
117C2×C4×C61—21no—
118C2×C4×C61—21no—
119C2×C4×C61—21no—
120C2×C4×C61—21no—
121C2×C4×C61—21no—
122C2×C4×C61—21no—
123C2×C4×C61—41no—
124C2×C4×C61—42no—
125C2×C4×C61—81no—
126C2×C4×C61C2×C4⋊C411yescharacteristic
127C2×C4×C61C4×D411yescharacteristic
128C2×C4×C61C4×D411yescharacteristic
129C2×C4×C61#12011yescharacteristic
130C2×C4×C61C22⋊Q811yescharacteristic
131C2×C4×C61#12311yescharacteristic
132C2×C4×C61C2×SD1611yescharacteristic
133C2×C4×C61#13511yescharacteristic
134C2×C4×C61#13711yescharacteristic
135C2×C4×C61#13711yescharacteristic
136C8×C61—81no—
137C8×C61—81no—
138#92418—22no—
139#92418—22no—
140#92418—41no—
141#92418—41no—
142#92418—41no—
143#92418—41no—
144#92418—42no—
145#8909—611nomaximal, Sylow
146C22×C61—21no—
147C22×C61—21no—
148C22×C61#38511yescharacteristic
149C22×C61#47511yescharacteristic
150C22×C61#47911yescharacteristic
151C4×C61—21no—
152C4×C61—22no—
153C4×C61—21no—
154C4×C61—21no—
155C4×C61—41no—
156C4×C61—41no—
157C4×C61—41no—
158C4×C61C2×#10811yescharacteristic
159C4×C61#43011yescharacteristic
160C4×C61C4×SD1611yescharacteristic
161C4×C61#44111yescharacteristic
162C4×C61#44811yescharacteristic
163C4×C61#45211yescharacteristic
164Q8×M16—611no—
165#1950—611no—
166#1566—611no—
167#1487D6111yescharacteristic
168C2×Q8⋊C8—611no—
169#1301—611no—
170#1278—611no—
171C2×C61—21no—
172C2×C61—21no—
173C2×C61#185511yescharacteristic
174C2×C61#186111yescharacteristic
175C2×C61#186511yescharacteristic
176C2×C4×Q8C2×D6111yescharacteristic
177#446—1222no—
178#446—1221no—
179C8×Q8—1221no—
180#431C2×D6111yescharacteristic
181C2×#108—1221no—
182#423—611no—
183#423—1221no—
184#423C2×D6111yescharacteristic
185C2×C4⋊C8—611no—
186C4×M16—611no—
187C4×M16—1221no—
188C2×C4×C8—611no—
189#341—1221no—
190#334—1222no—
191Q8⋊C8—21no—
192Q8⋊C8—21no—
193Q8⋊C8—611no—
194Q8⋊C8—611no—
195Q8⋊C8—611no—
196Q8⋊C8—611no—
197C61#890911yescharacteristic, complemented, Sylow
198C22×Q8Dic12211yescharacteristic
199C2×M16—21no—
200C2×M16—611no—
201C2×M16—611no—
202C2×M16—1221no—
203C22×C8—1221no—
204C22×C8—1221no—
205C4×Q8—21no—
206C4×Q8—21no—
207C4×Q8C4×D6111yescharacteristic
208C4×Q8C4×D6111yescharacteristic
209C4×Q8C22⋊D6111yescharacteristic
210C4×Q8C22⋊D6111yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4Dic12211yescharacteristic
213C2×C42—21no—
214C2×C42C22×D6111yescharacteristic
215#108—2442no—
216C4⋊C8—21no—
217C4⋊C8—21no—
218C4⋊C8—21no—
219C4⋊C8—611no—
220C4⋊C8—611no—
221C4⋊C8—612no—
222C4⋊C8—1222no—
223C4⋊C8—1222no—
224C4⋊C8—1221no—
225C4⋊C8—1221no—
226C22⋊C8—21no—
227#97—1222no—
228#97—1221no—
229C4×C8—21no—
230C4×C8—611no—
231C4×C8—611no—
232C4×C8—1222no—
233C4×C8—1221no—
234C4×C8—1221no—
235C2×Q8—21no—
236C2×Q8—22no—
237C2×Q8—41no—
238C2×Q8#1175819611yescharacteristic
239C2×Q8#1175819611yescharacteristic
240C22×C4—21no—
241C22×C4—21no—
242C22×C4C2×Dic12211yescharacteristic
243C22×C4D4×D6111yescharacteristic
244C22×C4#1175822411yescharacteristic
245M16—41no—
246M16—41no—
247M16—612no—
248M16—1221no—
249M16—1221no—
250M16—1221no—
251M16—2441no—
252M16—2441no—
253C2×C8—41no—
254C2×C8—41no—
255C2×C8—1221no—
256C2×C8—1221no—
257C2×C8—1221no—
258C2×C8—1221no—
259C2×C8—1221no—
260C2×C8—1222no—
261C2×C8—1221no—
262C2×C8—2442no—
263C2×C8—2441no—
264C2×C8—2441no—
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—21no—
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4#1175819611yescharacteristic
271C4⋊C4#1175819611yescharacteristic
272C42—21no—
273C42—21no—
274C42—21no—
275C42—21no—
276C42C2×C4×D6111yescharacteristic
277C42D4×D6111yescharacteristic
278C42#1175822411yescharacteristic
279C42C2×C22⋊D6111yescharacteristic
280C23#1451975411yescharacteristic
281Q8—21no—
282Q8—21no—
283Q8—21no—
284Q8—42no—
285Q8#1451971212yescomplemented
286C2×C4—21no—
287C2×C4—21no—
288C2×C4—21no—
289C2×C4—21no—
290C2×C4—21no—
291C2×C4—21no—
292C2×C4—41no—
293C2×C4—42no—
294C2×C4—81no—
295C2×C4C2×#1175819611yescharacteristic
296C2×C4#1451973711yescharacteristic
297C2×C4#1451973711yescharacteristic
298C2×C4#1451974511yescharacteristic
299C2×C4#1451975411yescharacteristic
300C2×C4#1451975811yescharacteristic
301C2×C4SD16×D6111yescharacteristic
302C2×C4#1451980011yescharacteristic
303C2×C4#1451980611yescharacteristic
304C2×C4#1451980911yescharacteristic
305C8—81no—
306C8—81no—
307C8—1222no—
308C8—1222no—
309C8—2441no—
310C8—2441no—
311C8—2441no—
312C8—2441no—
313C8—2442no—
314C22—21no—
315C22—21no—
316C22#1683963411yescharacteristic
317C22#1684004511yescharacteristic
318C22#1684007111yescharacteristic
319C4—21no—
320C4—22no—
321C4—21no—
322C4—21no—
323C4—41no—
324C4—41no—
325C4—41no—
326C4C2×#1451971211yescharacteristic
327C4#1683981011yescharacteristic
328C4#1683984711yescharacteristic
329C4#1683986611yescharacteristic
330C4#1683989911yescharacteristic
331C4#1683992311yescharacteristic
332C2—21no—
333C2—21no—
334C2#2144602311yescharacteristic
335C2#2144605711yescharacteristic
336C2#2144608511yescharacteristic
subgroupG/H
centerC2×C4#14519745
commutatorC42×C61C22×C4
FrattiniC2×C42C22×D61
FittingC61×#1487C2
socleC22×C61#385
prime radicalC23×C61C22⋊Q8
cosocleC2×C42×C61C23
hypercenter#1487D61
hypocenterC61#8909
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1487

Complements

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

NH ≅ G/Ntype
116. Q8×C61#108semidirect
197. C61#8909semidirect
285. Q8#14519712semidirect

Maximal subgroups

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

subgroupindex
Q8×#117581942
#214465922
#214445742
C2×Q8⋊#924182
#214437152
#214436552
C61×#14872
#890961