Finite Group Databasebeta

← #32981412

Subgroups — #32981412

Order 18688.

564 conjugacy classes of subgroups.

The subgroup lattice has 390 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22618954C211yesmaximal, characteristic, complemented
2C2×#17988697C211yesmaximal, characteristic
3#22608322C211yesmaximal, characteristic, complemented
4#22608321C211yesmaximal, characteristic, complemented
5#22607775C211yesmaximal, characteristic, complemented
6#22607761C211yesmaximal, characteristic, complemented
7C73×#1460C211yesmaximal, characteristic, complemented
8C22×#11924013C411yescharacteristic
9C2×C4×D292C2211yescharacteristic
10#17988697—22no—
11#17988697—22no—
12C8×D292—22no—
13#17988652—22no—
14#17988640C2211yescharacteristic
15#17988640C2211yescharacteristic
16C2×#14556522C411yescharacteristic
17C2×#14556512C411yescharacteristic
18C2×#14556511C411yescharacteristic
19C22⋊C8×D73—22no—
20C2×#14556502C2211yescharacteristic
21D4⋊#10596831—22no—
22#17988314—22no—
23C2×C4×D4×C73C2211yescharacteristic
24#431×C73C2211yescharacteristic
25#431×C73C2211yescharacteristic
26#323×C73—22no—
27C22×D292C2×C411yescharacteristic
28C22×C4×D73—21no—
29C2×#11924013—22no—
30C2×#11924013—22no—
31C2×#11924013C814yescomplemented
32C22×#10596831C2×C411yescharacteristic
33C22×#10596831C2×C411yescharacteristic
34C2×C8×D73—24no—
35C4×D292—21no—
36C4×D292—21no—
37C4×D292D412yes—
38C4×D292D412yes—
39C2×C4⋊Dic73C2×C411yescharacteristic
40C2×#11924005—21no—
41#14556522—22no—
42C4⋊#10596831—21no—
43C4⋊#10596831—21no—
44#14556512—22no—
45#14556511—22no—
46C22⋊#10596831—21no—
47C22⋊#10596831—21no—
48#14556503—24no—
49#14556502—21no—
50#14556502—21no—
51C4×#10596831—21no—
52C4×#10596831D412yes—
53C22×D4×C73C2×C411yescharacteristic
54C23×C4×C73—21no—
55C4×D4×C73—21no—
56C4×D4×C73—21no—
57C4×D4×C73—21no—
58C4×D4×C73—21no—
59C2×C4⋊C4×C73C2×C411yescharacteristic
60C2×C22⋊C4×C73—21no—
61C2×C42×C73C2311yescharacteristic
62C4⋊C8×C73—21no—
63C4⋊C8×C73—21no—
64C22⋊C8×C73—21no—
65C22⋊C8×C73D412yes—
66C4×C8×C73—21no—
67C4×C8×C73—21no—
68C23×D73—21no—
69C2×D292—21no—
70C2×D292—21no—
71C2×D292—21no—
72C2×D292C22⋊C412yes—
73C2×D292C2×C812yes—
74C2×D292M1612yes—
75C22×Dic73—21no—
76C2×C4×D73—22no—
77C2×C4×D73—22no—
78C2×C4×D73—82no—
79#11924013—28no—
80C2×#10596831—21no—
81C2×#10596831—21no—
82C2×#10596831—21no—
83C2×#10596831—22no—
84C2×#10596831—21no—
85C2×#10596831—21no—
86C2×#10596831—41no—
87C2×#10596831C2×C812yescomplemented
88C8×D73—84no—
89C4⋊Dic73—21no—
90C4⋊Dic73C22⋊C412yes—
91#11924005—22no—
92#11924005—22no—
93C24×C73—21no—
94C2×D4×C73—21no—
95C2×D4×C73—21no—
96C2×D4×C73—21no—
97C2×D4×C73—21no—
98C2×D4×C73—21no—
99C2×D4×C73C2×C812yescomplemented
100C22×C4×C73—21no—
101C22×C4×C73—41no—
102C22×C4×C73—41no—
103C22×C4×C73—82no—
104C22×C4×C73C22×C411yescharacteristic
105C22×C4×C73C2×D411yescharacteristic
106C22×C4×C73#4111yescharacteristic
107C2×C8×C73—22no—
108C2×C8×C73—41no—
109C4⋊C4×C73—21no—
110C4⋊C4×C73—21no—
111C22⋊C4×C73—41no—
112C22⋊C4×C73—41no—
113C42×C73C2×D411yescharacteristic
114C42×C73C2×D411yescharacteristic
115C42×C73C2×D411yescharacteristic
116C42×C73#4111yescharacteristic
117C23×C73—22no—
118C23×C73—41no—
119C23×C73—41no—
120C23×C73—81no—
121C23×C73—81no—
122C23×C73C4×D411yescharacteristic
123C22×D73—22no—
124C22×D73—22no—
125C22×D73—22no—
126C22×D73—81no—
127C22×D73—81no—
128D4×C73—22no—
129D4×C73—22no—
130D4×C73—41no—
131D4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—41no—
135C2×C4×C73—82no—
136C2×C4×C73—82no—
137C2×C4×C73—81no—
138C2×C4×C73C2×C22⋊C411yescharacteristic
139C2×C4×C73C4×D411yescharacteristic
140C2×C4×C73#12011yescharacteristic
141C2×C4×C73#12111yescharacteristic
142C2×C4×C73#12111yescharacteristic
143C2×C4×C73#12311yescharacteristic
144C2×C4×C73C22×C811yescharacteristic
145C2×C4×C73C2×M1611yescharacteristic
146C2×C4×C73#13111yescharacteristic
147C2×C4×C73#13111yescharacteristic
148C2×Dic73—22no—
149C2×Dic73—81no—
150D292—22no—
151D292—22no—
152D292—22no—
153D292C22⋊C814yes—
154C4×D73—44no—
155C4×D73—82no—
156C8×C73—42no—
157C8×C73—81no—
158#10596831—22no—
159#10596831—42no—
160#10596831—41no—
161#10596831—81no—
162C22×C73—21no—
163C22×C73—21no—
164C22×C73—42no—
165C22×C73—82no—
166C22×C73—82no—
167C22×C73—81no—
168C22×C73—81no—
169C22×C73#38611yescharacteristic
170C22×C73C8×D411yescharacteristic
171C22×C73#43511yescharacteristic
172C2×D73—24no—
173C2×D73—42no—
174C2×D73—42no—
175C2×D73—82no—
176C2×D73—82no—
177C4×C73—21no—
178C4×C73—21no—
179C4×C73—21no—
180C4×C73—21no—
181C4×C73—81no—
182C4×C73C2×C22⋊C811yescharacteristic
183C4×C73#40811yescharacteristic
184C4×C73C8×D411yescharacteristic
185C4×C73#43511yescharacteristic
186Dic73—42no—
187#9089—731nomaximal, Sylow
188C2×C73—21no—
189C2×C73—21no—
190C2×C73—82no—
191C2×C73#186911yescharacteristic
192C2×C73#190311yescharacteristic
193C2×C73#190411yescharacteristic
194D73—44no—
195#2972—731no—
196C2×#442—731no—
197#1478—731no—
198#1478—731no—
199#1460D7311yescharacteristic, complemented
200#1281—731no—
201#1275—731no—
202C73#908911yescharacteristic, complemented, Sylow
203C22×D8—731no—
204C2×C4×D4—731no—
205C2×C4×D4C2×D7311yescharacteristic
206#442—1462no—
207#442—1462no—
208C8×D4—1462no—
209C8×D4—1462no—
210#431—731no—
211#431—731no—
212#431C2×D7311yescharacteristic
213#431C2×D7311yescharacteristic
214C2×#106—731no—
215C2×#102—731no—
216C2×#102—731no—
217C2×C22⋊C8—1462no—
218C2×#97—731no—
219D4⋊C8—1462no—
220D4⋊C8—1462no—
221#323—22no—
222C22×D4—731no—
223C22×D4C4×D7311yescharacteristic
224C23×C4—21no—
225C23×C4—1461no—
226C2×D8—734no—
227C2×D8—1462no—
228C2×D8—1462no—
229C22×C8—731no—
230C22×C8—731no—
231C22×C8—1464no—
232C4×D4—21no—
233C4×D4—21no—
234C4×D4—21no—
235C4×D4—21no—
236C4×D4—732no—
237C4×D4—732no—
238C4×D4—1461no—
239C4×D4—1461no—
240C2×C4⋊C4—731no—
241C2×C4⋊C4C4×D7311yescharacteristic
242C2×C22⋊C4—21no—
243C2×C22⋊C4—1461no—
244C2×C42C22×D7311yescharacteristic
245#106—1462no—
246C4⋊C8—21no—
247C4⋊C8—21no—
248C4⋊C8—1461no—
249C4⋊C8—1461no—
250#102—1462no—
251#102—1462no—
252C22⋊C8—21no—
253C22⋊C8—1464no—
254C22⋊C8—1461no—
255C22⋊C8—1461no—
256C22⋊C8C22⋊D7312yes—
257#97—1461no—
258#97—1461no—
259C4×C8—21no—
260C4×C8—21no—
261C4×C8—732no—
262C4×C8—1461no—
263C24—21no—
264C24—1461no—
265C2×D4—21no—
266C2×D4—21no—
267C2×D4—21no—
268C2×D4—21no—
269C2×D4—21no—
270C2×D4—732no—
271C2×D4—732no—
272C2×D4—732no—
273C2×D4—1461no—
274C2×D4—1461no—
275C2×D4—1461no—
276C2×D4C8×D7312yescomplemented
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—82no—
281C22×C4—5842no—
282C22×C4—1462no—
283C22×C4—1461no—
284C22×C4—1462no—
285C22×C4C2×C4×D7311yescharacteristic
286C22×C4C2×C22⋊D7311yescharacteristic
287C22×C4#1192402811yescharacteristic
288D8—1468no—
289C2×C8—22no—
290C2×C8—41no—
291C2×C8—2921no—
292C2×C8—5844no—
293C2×C8—732no—
294C2×C8—1461no—
295C2×C8—1462no—
296C2×C8—1461no—
297C2×C8—1461no—
298C2×C8—1461no—
299C2×C8—1461no—
300C4⋊C4—21no—
301C4⋊C4—21no—
302C4⋊C4—732no—
303C4⋊C4—1461no—
304C22⋊C4—41no—
305C22⋊C4—41no—
306C22⋊C4—1462no—
307C22⋊C4—1462no—
308C42D4×D7311yescharacteristic
309C42D4×D7311yescharacteristic
310C42D4×D7311yescharacteristic
311C42#1192402711yescharacteristic
312C23—22no—
313C23—41no—
314C23—41no—
315C23—81no—
316C23—81no—
317C23—5841no—
318C23—5841no—
319C23—1462no—
320C23—1462no—
321C23—1462no—
322C23C4×C22⋊D7311yescharacteristic
323D4—22no—
324D4—22no—
325D4—41no—
326D4—41no—
327D4—734no—
328D4—1462no—
329D4—1462no—
330D4—1462no—
331C2×C4—41no—
332C2×C4—41no—
333C2×C4—41no—
334C2×C4—82no—
335C2×C4—82no—
336C2×C4—81no—
337C2×C4—2924no—
338C2×C4—5842no—
339C2×C4—5841no—
340C2×C4—1462no—
341C2×C4C22⋊C4×D7311yescharacteristic
342C2×C4#1455655111yescharacteristic
343C2×C4#1455655911yescharacteristic
344C2×C4#1455656211yescharacteristic
345C2×C4#1455656411yescharacteristic
346C2×C4#1455657311yescharacteristic
347C2×C4C2×C8×D7311yescharacteristic
348C2×C4M16×D7311yescharacteristic
349C2×C4#1455659711yescharacteristic
350C2×C4#1455659911yescharacteristic
351C8—42no—
352C8—81no—
353C8—2922no—
354C8—2921no—
355C8—5841no—
356C8—1462no—
357C22—21no—
358C22—21no—
359C22—42no—
360C22—82no—
361C22—82no—
362C22—81no—
363C22—81no—
364C22—2922no—
365C22—2922no—
366C22—5842no—
367C22—5842no—
368C22—1464no—
369C22#1798846311yescharacteristic
370C22C8×C22⋊D7311yescharacteristic
371C22#1798865611yescharacteristic
372C4—21no—
373C4—21no—
374C4—21no—
375C4—21no—
376C4—81no—
377C4—2922no—
378C4C22⋊C8×D7311yescharacteristic
379C4#1798855211yescharacteristic
380C4#1798865011yescharacteristic
381C4#1798866111yescharacteristic
382C2—21no—
383C2—21no—
384C2—82no—
385C2—2924no—
386C2#2261022011yescharacteristic
387C2#2261041411yescharacteristic
388C2#2261042111yescharacteristic
subgroupG/H
centerC22#17988463
commutatorC2×C4×C73C22×C8
FrattiniC2×C42C22×D73
FittingC73×#1460C2
socleC22×C73#386
prime radicalC22×#11924013C4
cosocleC2×C42×C73C23
hypercenter#1460D73
hypocenterC73#9089
LCSG ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1460

Complements

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

NH ≅ G/Ntype
1. #22618954C2semidirect
3. #22608322C2semidirect
4. #22608321C2semidirect
5. #22607775C2semidirect
6. #22607761C2semidirect
7. C73×#1460C2semidirect
31. C2×#11924013C8semidirect
87. C2×#10596831C2×C8semidirect
99. C2×D4×C73C2×C8semidirect
199. #1460D73semidirect
202. C73#9089semidirect
276. C2×D4C8×D73semidirect

Maximal subgroups

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

subgroupindex
#226189542
C2×#179886972
#226083222
#226083212
#226077752
#226077612
C73×#14602
#908973