Finite Group Databasebeta

← #32979067

Subgroups — #32979067

Order 18688.

510 conjugacy classes of subgroups.

The subgroup lattice has 394 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988664C211yesmaximal, characteristic
2#22610087C211yesmaximal, characteristic, complemented
3#22609932C211yesmaximal, characteristic
4#22609928C211yesmaximal, characteristic
5C2×#17988339C211yesmaximal, characteristic, complemented
6#22607815C211yesmaximal, characteristic, complemented
7C73×#1296C211yesmaximal, characteristic, complemented
8C22×#11924011—21no—
9C2×C4×D292C2211yescharacteristic
10#17988664—22no—
11#17988664C414yescomplemented
12C2×#14556522—21no—
13C2×#14556522—21no—
14C2×C4⋊#10596831C2211yescharacteristic
15C2×#14556513—21no—
16C2×#14556511—21no—
17C2×#14556503—21no—
18C2×C4×#10596831C2211yescharacteristic
19#17988457C2211yescharacteristic
20#17988350—21no—
21#17988349—21no—
22#17988339—22no—
23C2×C4⋊C8×C73C2211yescharacteristic
24C2×C4⋊C8×C73C2211yescharacteristic
25#384×C73C2211yescharacteristic
26C22×D292D411yescharacteristic
27C22×C4×D73—21no—
28C2×#11924011—24no—
29C2×#11924011—42no—
30C2×#11924011—42no—
31C22×#10596831—21no—
32C22×#10596831D411yescharacteristic
33C22×#10596831D411yescharacteristic
34C4×D292—21no—
35C4×D292—21no—
36C4×D292C2×C412yes—
37C4×D292Q812yes—
38C2×C4⋊Dic73—21no—
39C2×C4⋊Dic73—21no—
40C2×C4⋊Dic73—21no—
41C2×C4⋊Dic73D411yescharacteristic
42C2×#11924005—21no—
43#14556522—42no—
44#14556522—42no—
45C4⋊#10596831—21no—
46C4⋊#10596831—21no—
47#14556513—42no—
48#14556511—42no—
49#14556503—24no—
50C4×#10596831C2×C412yes—
51C4×#10596831D412yes—
52C22×C8×C73—21no—
53C22×C8×C73—21no—
54C2×C4⋊C4×C73—21no—
55C2×C4⋊C4×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C42×C73C2311yescharacteristic
58C4⋊C8×C73—21no—
59C4⋊C8×C73—21no—
60C4⋊C8×C73—21no—
61C4⋊C8×C73C2×C412yes—
62C23×D73—21no—
63C2×D292—21no—
64C2×D292—21no—
65C2×D292—21no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292C4⋊C412yes—
69C22×Dic73—21no—
70C22×Dic73—41no—
71C2×C4×D73—22no—
72C2×C4×D73—22no—
73C2×C4×D73—41no—
74C2×C4×D73—41no—
75C2×C4×D73—41no—
76C2×C4×D73—41no—
77#11924011—48no—
78C2×#10596831—21no—
79C2×#10596831—21no—
80C2×#10596831—41no—
81C2×#10596831—41no—
82C2×#10596831—41no—
83C2×#10596831C22⋊C412yes—
84C2×#10596831C22⋊C412yes—
85C2×#10596831D812yes—
86C2×#10596831SD1612yes—
87C4⋊Dic73—21no—
88C4⋊Dic73—41no—
89C4⋊Dic73—41no—
90C4⋊Dic73—41no—
91C4⋊Dic73—41no—
92C4⋊Dic73—81no—
93C4⋊Dic73C4⋊C412yes—
94#11924005—22no—
95#11924005—22no—
96C22×C4×C73—41no—
97C22×C4×C73C2×D411yescharacteristic
98C22×C4×C73C2×D411yescharacteristic
99C22×C4×C73#4111yescharacteristic
100C2×C8×C73—22no—
101C2×C8×C73—41no—
102C2×C8×C73—41no—
103C2×C8×C73—41no—
104C2×C8×C73—41no—
105C2×C8×C73—41no—
106C4⋊C4×C73—41no—
107C4⋊C4×C73—41no—
108C4⋊C4×C73—41no—
109C4⋊C4×C73—41no—
110C4⋊C4×C73—81no—
111C42×C73C22×C411yescharacteristic
112C42×C73C2×D411yescharacteristic
113C42×C73C2×Q811yescharacteristic
114C42×C73#4111yescharacteristic
115C23×C73#12111yescharacteristic
116C22×D73—22no—
117C22×D73—41no—
118C22×D73—41no—
119C22×D73—41no—
120C22×D73—41no—
121C22×D73—41no—
122C22×D73—41no—
123C2×C4×C73—21no—
124C2×C4×C73—21no—
125C2×C4×C73—81no—
126C2×C4×C73—81no—
127C2×C4×C73—81no—
128C2×C4×C73C2×C22⋊C411yescharacteristic
129C2×C4×C73C2×C4⋊C411yescharacteristic
130C2×C4×C73#11711yescharacteristic
131C2×C4×C73#12111yescharacteristic
132C2×C4×C73C22⋊Q811yescharacteristic
133C2×C4×C73C22⋊Q811yescharacteristic
134C2×C4×C73C2×D811yescharacteristic
135C2×C4×C73C2×SD1611yescharacteristic
136C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
137C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
138C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
139C2×C4×C73#13711yescharacteristic
140C2×C4×C73#13711yescharacteristic
141C2×C4×C73#13711yescharacteristic
142C2×Dic73—22no—
143C2×Dic73—41no—
144C2×Dic73—41no—
145C2×Dic73—81no—
146C2×Dic73—81no—
147C2×Dic73—81no—
148D292—22no—
149D292—22no—
150D292—41no—
151D292—41no—
152C4×D73—42no—
153C4×D73—42no—
154C4×D73—42no—
155C4×D73—42no—
156C8×C73—42no—
157C8×C73—81no—
158#10596831—22no—
159#10596831—81no—
160#10596831#10214yescomplemented
161C22×C73#38011yescharacteristic
162C22×C73#45911yescharacteristic
163C22×C73#46111yescharacteristic
164C22×C73#46811yescharacteristic
165C22×C73#46811yescharacteristic
166C22×C73#47111yescharacteristic
167C22×C73#47111yescharacteristic
168C2×D73—42no—
169C2×D73—42no—
170C2×D73—42no—
171C2×D73—81no—
172C2×D73—81no—
173C2×D73—81no—
174C2×D73—81no—
175C4×C73—21no—
176C4×C73—21no—
177C4×C73—161no—
178C4×C73C2×#10211yescharacteristic
179C4×C73#41711yescharacteristic
180C4×C73#42811yescharacteristic
181C4×C73#42811yescharacteristic
182C4×C73#46911yescharacteristic
183C4×C73#47011yescharacteristic
184C4×C73#47411yescharacteristic
185C4×C73#47611yescharacteristic
186Dic73—42no—
187Dic73—161no—
188#8650—731nomaximal, Sylow
189C2×C73#168511yescharacteristic
190C2×C73#168511yescharacteristic
191C2×C73#169111yescharacteristic
192C2×C73#169111yescharacteristic
193C2×C73#180211yescharacteristic
194C2×C73#180911yescharacteristic
195C2×C73#181511yescharacteristic
196D73—82no—
197C2×#436—731no—
198#1844—731no—
199#1802—731no—
200#1802—731no—
201C2×#335—731no—
202#1296—731no—
203#1296D7311yescharacteristic, complemented
204C73#865011yescharacteristic, complemented, Sylow
205C22×M16—1461no—
206C2×C4×D4—731no—
207#436—734no—
208#436—1462no—
209C2×#106—1461no—
210C2×#106—1461no—
211C2×C4⋊C8—731no—
212C2×C4⋊C8C2×D7311yescharacteristic
213C2×C4⋊C8C2×D7311yescharacteristic
214C2×#102—1461no—
215C2×#102—1461no—
216C2×C22⋊C8—1461no—
217C2×C4×C8—731no—
218#384—731no—
219#384C2×D7311yescharacteristic
220#340—1461no—
221#340—1461no—
222#335—1462no—
223C22×D4—731no—
224C23×C4—1461no—
225C2×M16—2922no—
226C2×M16—2922no—
227C2×M16—1464no—
228C22×C8—21no—
229C22×C8—21no—
230C22×C8—731no—
231C22×C8—731no—
232C22×C8—1461no—
233C4×D4—732no—
234C4×D4—732no—
235C4×D4—1461no—
236C4×D4—1461no—
237C2×C4⋊C4—21no—
238C2×C4⋊C4—21no—
239C2×C4⋊C4—21no—
240C2×C4⋊C4—731no—
241C2×C4⋊C4—1461no—
242C2×C4⋊C4—1461no—
243C2×C4⋊C4—1461no—
244C2×C22⋊C4—1461no—
245C2×C42C22×D7311yescharacteristic
246#106—2922no—
247#106—2922no—
248C4⋊C8—21no—
249C4⋊C8—21no—
250C4⋊C8—21no—
251C4⋊C8—1461no—
252C4⋊C8—1461no—
253C4⋊C8C4×D7312yes—
254#102—2922no—
255#102—2922no—
256C22⋊C8—1464no—
257C4×C8—732no—
258C4×C8—732no—
259C24—1461no—
260C2×D4—732no—
261C2×D4—1461no—
262C2×D4—1461no—
263C2×D4—1461no—
264C2×D4—1461no—
265C2×D4—1461no—
266C22×C4—41no—
267C22×C4—2921no—
268C22×C4—2921no—
269C22×C4—2921no—
270C22×C4—2921no—
271C22×C4—2921no—
272C22×C4—1461no—
273C22×C4—1462no—
274C22×C4—1462no—
275C22×C4D4×D7311yescharacteristic
276C22×C4D4×D7311yescharacteristic
277C22×C4#1192402811yescharacteristic
278M16—2928no—
279C2×C8—22no—
280C2×C8—41no—
281C2×C8—41no—
282C2×C8—41no—
283C2×C8—41no—
284C2×C8—41no—
285C2×C8—2921no—
286C2×C8—2921no—
287C2×C8—2921no—
288C2×C8—732no—
289C2×C8—732no—
290C2×C8—732no—
291C2×C8—732no—
292C2×C8—1461no—
293C2×C8—1461no—
294C4⋊C4—41no—
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—41no—
298C4⋊C4—81no—
299C4⋊C4—2921no—
300C4⋊C4—2921no—
301C4⋊C4—2921no—
302C4⋊C4—2921no—
303C4⋊C4—5841no—
304C4⋊C4—732no—
305C4⋊C4—1461no—
306C22⋊C4—1462no—
307C22⋊C4—1462no—
308C42C2×C4×D7311yescharacteristic
309C42D4×D7311yescharacteristic
310C42Q8×D7311yescharacteristic
311C42#1192402811yescharacteristic
312C23—2921no—
313C23—2921no—
314C23—2921no—
315C23—2921no—
316C23—2921no—
317C23—2921no—
318C23—1462no—
319C23#1455656411yescharacteristic
320D4—2921no—
321D4—2921no—
322D4—1462no—
323D4—1462no—
324C2×C4—21no—
325C2×C4—21no—
326C2×C4—81no—
327C2×C4—81no—
328C2×C4—81no—
329C2×C4—2921no—
330C2×C4—2921no—
331C2×C4—2922no—
332C2×C4—2922no—
333C2×C4—2922no—
334C2×C4—2922no—
335C2×C4—5841no—
336C2×C4—5841no—
337C2×C4—5841no—
338C2×C4—1462no—
339C2×C4C22⋊C4×D7311yescharacteristic
340C2×C4C4⋊C4×D7311yescharacteristic
341C2×C4#1455654811yescharacteristic
342C2×C4#1455656411yescharacteristic
343C2×C4#1455656911yescharacteristic
344C2×C4#1455656911yescharacteristic
345C2×C4D8×D7311yescharacteristic
346C2×C4SD16×D7311yescharacteristic
347C2×C4#1455661511yescharacteristic
348C2×C4#1455661811yescharacteristic
349C2×C4#1455661811yescharacteristic
350C2×C4#1455662011yescharacteristic
351C2×C4#1455662311yescharacteristic
352C2×C4#1455662311yescharacteristic
353C8—42no—
354C8—81no—
355C8—5841no—
356C8—734no—
357C8—1462no—
358C22—2922no—
359C22—2922no—
360C22—2922no—
361C22—5841no—
362C22—5841no—
363C22—5841no—
364C22—5841no—
365C22#1798844611yescharacteristic
366C22#1798878111yescharacteristic
367C22#1798879111yescharacteristic
368C22#1798883211yescharacteristic
369C22#1798883611yescharacteristic
370C22#1798884911yescharacteristic
371C22#1798885311yescharacteristic
372C4—21no—
373C4—21no—
374C4—161no—
375C4—2922no—
376C4—11681no—
377C4#102×D7311yescharacteristic
378C4#1798858711yescharacteristic
379C4#1798862611yescharacteristic
380C4#1798862811yescharacteristic
381C4#1798883911yescharacteristic
382C4#1798884411yescharacteristic
383C4#1798886611yescharacteristic
384C4#1798887611yescharacteristic
385C2—5842no—
386C2#2260939511yescharacteristic
387C2#2260939911yescharacteristic
388C2#2260942911yescharacteristic
389C2#2260943311yescharacteristic
390C2#2260993011yescharacteristic
391C2#2260996311yescharacteristic
392C2#2260998911yescharacteristic
subgroupG/H
centerC23#14556564
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1296C2
socleC23×C73#121
prime radicalC22×D292D4
cosocleC2×C42×C73C23
hypercenter#1296D73
hypocenterC73#8650
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1296

Complements

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

NH ≅ G/Ntype
2. #22610087C2semidirect
5. C2×#17988339C2semidirect
6. #22607815C2semidirect
7. C73×#1296C2semidirect
11. #17988664C4semidirect
160. #10596831#102semidirect
203. #1296D73semidirect
204. C73#8650semidirect

Maximal subgroups

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

subgroupindex
C2×#179886642
#226100872
#226099322
#226099282
C2×#179883392
#226078152
C73×#12962
#865073