Finite Group Databasebeta

← #32980473

Subgroups — #32980473

Order 18688.

426 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618674C211yesmaximal, characteristic
2#22610704C211yesmaximal, characteristic, complemented
3#22608578C211yesmaximal, characteristic
4#22608381C211yesmaximal, characteristic
5#22607767C211yesmaximal, characteristic, complemented
6#22607765C211yesmaximal, characteristic, complemented
7C73×#1570C211yesmaximal, characteristic, complemented
8C2×#14556597—21no—
9#17989137C2211yescharacteristic
10#17988664—21no—
11#17988657—22no—
12#17988652—21no—
13C2×#14556526—21no—
14C2×C4⋊#10596831C2211yescharacteristic
15#17988553—21no—
16C4×#11924012C2211yescharacteristic
17C2×C4×#10596831C2211yescharacteristic
18#17988351—21no—
19#17988332C411yescharacteristic
20#17988332C411yescharacteristic
21#17988330C411yescharacteristic
22#17988330C411yescharacteristic
23#17988314—22no—
24#431×C73C2211yescharacteristic
25#423×C73C2211yescharacteristic
26C2×C4⋊C8×C73C2211yescharacteristic
27#334×C73—21no—
28#334×C73—21no—
29C2×#11924028—21no—
30#14556597—42no—
31#14556597—42no—
32C2×#11924012D411yescharacteristic
33C2×#11924012D411yescharacteristic
34C2×#11924011—22no—
35C22×#10596831—21no—
36C22×#10596831—21no—
37C2×C8×D73—22no—
38#14556591C2×C411yescharacteristic
39#14556588C2×C411yescharacteristic
40#14556579—21no—
41#14556565—21no—
42#14556565Q812yes—
43C4×D292—21no—
44C4×D292D412yes—
45#14556526—42no—
46C4⋊#10596831—21no—
47C4⋊#10596831C2×C411yescharacteristic
48C4⋊#10596831C2×C411yescharacteristic
49#14556503—22no—
50#14556503—22no—
51#14556502—21no—
52C4×#10596831—21no—
53C4×#10596831—21no—
54C4×#10596831—21no—
55C2×M16×C73—21no—
56C22×C8×C73—21no—
57C2×C42×C73C2311yescharacteristic
58C4⋊C8×C73—21no—
59C4⋊C8×C73—21no—
60C4⋊C8×C73—21no—
61C4⋊C8×C73C2×C411yescharacteristic
62C4⋊C8×C73C2×C411yescharacteristic
63C4⋊C8×C73D411yescharacteristic
64C4⋊C8×C73D411yescharacteristic
65C22⋊C8×C73—21no—
66C4×C8×C73—21no—
67#11924028—41no—
68#11924028—41no—
69#11924028—41no—
70#11924028—41no—
71C2×Dic146—21no—
72C2×D292—21no—
73C2×D292—21no—
74C2×D292C4⋊C412yes—
75C2×C22⋊D73—22no—
76C2×C4×D73—22no—
77#11924012—21no—
78#11924012—21no—
79#11924012—21no—
80#11924012SD1612yes—
81#11924011—44no—
82C2×#10596831—21no—
83C2×#10596831—22no—
84C2×#10596831—21no—
85C2×#10596831—21no—
86C2×#10596831—21no—
87C2×#10596831—41no—
88C2×#10596831—41no—
89C2×#10596831—41no—
90C2×#10596831—41no—
91C8×D73—44no—
92C4⋊Dic73—21no—
93C4⋊Dic73C4⋊C412yes—
94#11924005—22no—
95#11924005—22no—
96C22×C4×C73C2×D411yescharacteristic
97C22×C4×C73C2×Q811yescharacteristic
98C22×C4×C73#4111yescharacteristic
99M16×C73—41no—
100M16×C73—41no—
101C2×C8×C73—21no—
102C2×C8×C73—21no—
103C2×C8×C73—21no—
104C2×C8×C73—21no—
105C2×C8×C73—41no—
106C2×C8×C73—41no—
107C2×C8×C73—41no—
108C42×C73C22×C411yescharacteristic
109C42×C73C2×D411yescharacteristic
110C42×C73C2×D411yescharacteristic
111C42×C73#4111yescharacteristic
112C23×C73C22⋊Q811yescharacteristic
113C22×D73—22no—
114C2×C4×C73—21no—
115C2×C4×C73—21no—
116C2×C4×C73—41no—
117C2×C4×C73C2×C4⋊C411yescharacteristic
118C2×C4×C73C4×D411yescharacteristic
119C2×C4×C73C4×D411yescharacteristic
120C2×C4×C73#12011yescharacteristic
121C2×C4×C73C22⋊Q811yescharacteristic
122C2×C4×C73#12311yescharacteristic
123C2×C4×C73C2×SD1611yescharacteristic
124C2×C4×C73#13511yescharacteristic
125C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
126C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
127C22⋊D73—42no—
128C22⋊D73—42no—
129C2×Dic73—22no—
130D292—42no—
131D292—41no—
132D292—41no—
133D292—41no—
134D292—41no—
135C4×D73—42no—
136C4×D73—42no—
137Dic146—41no—
138Dic146—41no—
139C8×C73—41no—
140C8×C73—41no—
141C8×C73—41no—
142C8×C73—41no—
143C8×C73—81no—
144#10596831—22no—
145#10596831—42no—
146#10596831—41no—
147#10596831—41no—
148#10596831—41no—
149C22×C73—21no—
150C22×C73—21no—
151C22×C73#38511yescharacteristic
152C22×C73#47611yescharacteristic
153C22×C73#47811yescharacteristic
154C2×D73—42no—
155C2×D73—42no—
156C2×D73—42no—
157C4×C73—21no—
158C4×C73—21no—
159C4×C73—21no—
160C4×C73C4×SD1611yescharacteristic
161C4×C73#44211yescharacteristic
162C4×C73#44311yescharacteristic
163C4×C73#44411yescharacteristic
164C4×C73#44911yescharacteristic
165C4×C73#45011yescharacteristic
166Dic73—42no—
167#8932—731nomaximal, Sylow
168C2×C73—21no—
169C2×C73—21no—
170C2×C73#185811yescharacteristic
171C2×C73#186411yescharacteristic
172C2×C73#186611yescharacteristic
173D73—82no—
174#2935—731no—
175#1950—731no—
176#1570D7311yescharacteristic, complemented
177#1540—731no—
178#1492—731no—
179#1278—731no—
180#1277—731no—
181C73#893211yescharacteristic, complemented, Sylow
182C2×#131—1461no—
183#532—731no—
184#436—1461no—
185#435—1462no—
186C8×D4—1461no—
187#431C2×D7311yescharacteristic
188C2×#108—1461no—
189#423C2×D7311yescharacteristic
190C2×C4⋊C8—731no—
191C2×C4⋊C8C2×D7311yescharacteristic
192#408—1461no—
193C4×M16—731no—
194C2×C4×C8—731no—
195#341—1461no—
196#334—21no—
197#334—21no—
198#332—731no—
199#332—731no—
200#331—731no—
201#331—731no—
202D4⋊C8—1462no—
203C2×#41—1461no—
204#131—2922no—
205#131—2922no—
206C2×M16—21no—
207C2×M16—731no—
208C2×M16—731no—
209C2×M16—1462no—
210C22×C8—21no—
211C22×C8—1462no—
212C22×C8—1461no—
213C22×C8—1461no—
214C4⋊Q8—731no—
215#127—731no—
216#124—1461no—
217#121—732no—
218#121—1461no—
219C4×D4—732no—
220C4×D4—1461no—
221C2×C42C22×D7311yescharacteristic
222#108—2922no—
223C4⋊C8—21no—
224C4⋊C8—21no—
225C4⋊C8—21no—
226C4⋊C8—731no—
227C4⋊C8—731no—
228C4⋊C8—1461no—
229C4⋊C8C4×D7311yescharacteristic
230C4⋊C8C4×D7311yescharacteristic
231C4⋊C8C22⋊D7311yescharacteristic
232C4⋊C8C22⋊D7311yescharacteristic
233C22⋊C8—21no—
234C22⋊C8—1462no—
235C22⋊C8—1462no—
236#97—1461no—
237C4×C8—21no—
238C4×C8—1461no—
239C4×C8—1461no—
240C4×C8—1461no—
241#41—2921no—
242#41—2921no—
243#41—2921no—
244#41—2921no—
245C2×Q8—1461no—
246C2×D4—732no—
247C2×D4—1462no—
248C2×D4—1461no—
249C2×D4—1461no—
250C22×C4—1462no—
251C22×C4D4×D7311yescharacteristic
252C22×C4Q8×D7311yescharacteristic
253C22×C4#1192402811yescharacteristic
254M16—41no—
255M16—41no—
256M16—2924no—
257M16—732no—
258M16—1461no—
259M16—1461no—
260M16—1461no—
261C2×C8—21no—
262C2×C8—21no—
263C2×C8—21no—
264C2×C8—21no—
265C2×C8—41no—
266C2×C8—41no—
267C2×C8—41no—
268C2×C8—2924no—
269C2×C8—2921no—
270C2×C8—2921no—
271C2×C8—2921no—
272C2×C8—2921no—
273C2×C8—1462no—
274C2×C8—1461no—
275C2×C8—1461no—
276C2×C8—1461no—
277C2×C8—1461no—
278C4⋊C4—732no—
279C4⋊C4—1461no—
280C22⋊C4—1462no—
281C22⋊C4—1462no—
282C42C2×C4×D7311yescharacteristic
283C42D4×D7311yescharacteristic
284C42C2×C22⋊D7311yescharacteristic
285C42#1192402911yescharacteristic
286C23—1462no—
287C23#1455656911yescharacteristic
288Q8—2921no—
289Q8—2921no—
290D4—2922no—
291D4—2922no—
292D4—2922no—
293D4—2921no—
294D4—2921no—
295D4—2921no—
296D4—2921no—
297C2×C4—21no—
298C2×C4—21no—
299C2×C4—41no—
300C2×C4—2922no—
301C2×C4—2922no—
302C2×C4—1462no—
303C2×C4C4⋊C4×D7311yescharacteristic
304C2×C4C4×C22⋊D7311yescharacteristic
305C2×C4#1455655311yescharacteristic
306C2×C4#1455655911yescharacteristic
307C2×C4#1455656711yescharacteristic
308C2×C4#1455657611yescharacteristic
309C2×C4SD16×D7311yescharacteristic
310C2×C4#1455661211yescharacteristic
311C2×C4#1455661811yescharacteristic
312C2×C4#1455661811yescharacteristic
313C8—41no—
314C8—41no—
315C8—41no—
316C8—41no—
317C8—81no—
318C8—2922no—
319C8—2921no—
320C8—2921no—
321C8—2921no—
322C8—1462no—
323C22—21no—
324C22—21no—
325C22—2922no—
326C22—2922no—
327C22—2922no—
328C22#1798845811yescharacteristic
329C22#1798887611yescharacteristic
330C22#1798888611yescharacteristic
331C4—21no—
332C4—21no—
333C4—21no—
334C4—2922no—
335C4#1798867411yescharacteristic
336C4#1798869811yescharacteristic
337C4#1798870211yescharacteristic
338C4#1798870711yescharacteristic
339C4#1798873111yescharacteristic
340C4#1798873611yescharacteristic
341C2—21no—
342C2—21no—
343C2—5842no—
344C2#2261014911yescharacteristic
345C2#2261018911yescharacteristic
346C2#2261020511yescharacteristic
subgroupG/H
centerC2×C4#14556559
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1570C2
socleC22×C73#385
prime radical#17989137C22
cosocleC2×C42×C73C23
hypercenter#1570D73
hypocenterC73#8932
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
2. #22610704C2semidirect
5. #22607767C2semidirect
6. #22607765C2semidirect
7. C73×#1570C2semidirect
176. #1570D73semidirect
181. C73#8932semidirect

Maximal subgroups

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

subgroupindex
#226186742
#226107042
#226085782
#226083812
#226077672
#226077652
C73×#15702
#893273