Finite Group Databasebeta

← #32989801

Subgroups — #32989801

Order 18688.

506 conjugacy classes of subgroups.

The subgroup lattice has 420 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988789C211yesmaximal, characteristic
2#22610725C211yesmaximal, characteristic
3#22609928C211yesmaximal, characteristic
4C2×#17988340C211yesmaximal, characteristic, complemented
5C2×#17988333C211yesmaximal, characteristic, complemented
6#22607814C211yesmaximal, characteristic, complemented
7C73×#1990C211yesmaximal, characteristic, complemented
8C22×#11924015—21no—
9C2×C4×D292C2211yescharacteristic
10#17988789—22no—
11#17988789—22no—
12C2×C4⋊#10596831C2211yescharacteristic
13C2×C4⋊#10596831C2211yescharacteristic
14C2×C4⋊#10596831C2211yescharacteristic
15C2×#14556515—21no—
16C2×#14556511—21no—
17C2×#14556503—21no—
18C2×#14556503—21no—
19#17988349—21no—
20#17988340—22no—
21#17988333—22no—
22C2×C4⋊Q8×C73C2211yescharacteristic
23C2×C4×C8×C73C2211yescharacteristic
24#384×C73C2211yescharacteristic
25#340×C73—21no—
26#340×C73—21no—
27C22×D292D411yescharacteristic
28C22×C4×D73—21no—
29C2×#11924015—24no—
30C2×#11924015—42no—
31C2×#11924015—42no—
32C22×#10596831—21no—
33C22×#10596831—21no—
34C22×#10596831—21no—
35C4×D292—21no—
36C4×D292—21no—
37C4×D292—21no—
38C4×D292—21no—
39C2×C4⋊Dic73D411yescharacteristic
40C2×#11924005—21no—
41C4⋊#10596831—21no—
42C4⋊#10596831—21no—
43C4⋊#10596831—21no—
44C4⋊#10596831—21no—
45C4⋊#10596831—21no—
46C4⋊#10596831D412yes—
47#14556515—24no—
48#14556511—42no—
49#14556503—42no—
50#14556503—42no—
51C22×Q8×C73—21no—
52C22×C8×C73D411yescharacteristic
53C22×C8×C73D411yescharacteristic
54C4⋊Q8×C73—21no—
55C4⋊Q8×C73—21no—
56C4⋊Q8×C73—21no—
57C4⋊Q8×C73D412yes—
58C2×C4⋊C4×C73—21no—
59C2×C4⋊C4×C73—21no—
60C2×C4⋊C4×C73—21no—
61C2×C4⋊C4×C73—21no—
62C2×C4⋊C4×C73—21no—
63C2×C42×C73C2311yescharacteristic
64C4×C8×C73—21no—
65C4×C8×C73—21no—
66C23×D73—21no—
67C2×D292—21no—
68C2×D292—21no—
69C2×D292—21no—
70C2×D292—21no—
71C2×D292—21no—
72C2×D292D812yes—
73C22×Dic73—21no—
74C2×C4×D73—41no—
75C2×C4×D73—41no—
76C2×C4×D73—41no—
77C2×C4×D73—41no—
78C2×C4×D73—41no—
79C2×C4×D73—41no—
80#11924015—48no—
81C2×#10596831—22no—
82C2×#10596831—41no—
83C2×#10596831—41no—
84C2×#10596831—41no—
85C2×#10596831—41no—
86C2×#10596831—41no—
87C2×#10596831—41no—
88C2×#10596831—41no—
89C2×#10596831—41no—
90C4⋊Dic73—21no—
91C4⋊Dic73—21no—
92#11924005—41no—
93#11924005—41no—
94C2×Q8×C73—22no—
95C2×Q8×C73—41no—
96C2×Q8×C73—41no—
97C2×Q8×C73—41no—
98C2×Q8×C73—41no—
99C2×Q8×C73—41no—
100C22×C4×C73—41no—
101C22×C4×C73—41no—
102C22×C4×C73C2×D411yescharacteristic
103C22×C4×C73C2×D411yescharacteristic
104C22×C4×C73#4111yescharacteristic
105C2×C8×C73—21no—
106C2×C8×C73—21no—
107C2×C8×C73—21no—
108C2×C8×C73—21no—
109C2×C8×C73—21no—
110C2×C8×C73SD1612yescomplemented
111C4⋊C4×C73—22no—
112C4⋊C4×C73—22no—
113C4⋊C4×C73—41no—
114C4⋊C4×C73—41no—
115C4⋊C4×C73—41no—
116C4⋊C4×C73—41no—
117C4⋊C4×C73—41no—
118C4⋊C4×C73—41no—
119C4⋊C4×C73—81no—
120C42×C73C2×D411yescharacteristic
121C42×C73C2×D411yescharacteristic
122C42×C73#4111yescharacteristic
123C42×C73#4111yescharacteristic
124C23×C73#12111yescharacteristic
125C22×D73—22no—
126C22×D73—41no—
127C22×D73—41no—
128C22×D73—41no—
129C22×D73—41no—
130C22×D73—41no—
131C22×D73—41no—
132Q8×C73—42no—
133Q8×C73—42no—
134Q8×C73—81no—
135Q8×C73—81no—
136C2×C4×C73—21no—
137C2×C4×C73—21no—
138C2×C4×C73—42no—
139C2×C4×C73—81no—
140C2×C4×C73—81no—
141C2×C4×C73—81no—
142C2×C4×C73—81no—
143C2×C4×C73—81no—
144C2×C4×C73#12011yescharacteristic
145C2×C4×C73#12111yescharacteristic
146C2×C4×C73#12111yescharacteristic
147C2×C4×C73#12311yescharacteristic
148C2×C4×C73#12311yescharacteristic
149C2×C4×C73#12411yescharacteristic
150C2×C4×C73C2×D811yescharacteristic
151C2×C4×C73C2×SD1611yescharacteristic
152C2×C4×C73#13511yescharacteristic
153C2×C4×C73#13511yescharacteristic
154C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C73#13711yescharacteristic
157C2×C4×C73#13711yescharacteristic
158C2×Dic73—41no—
159C2×Dic73—41no—
160C2×Dic73—41no—
161D292—22no—
162D292—22no—
163D292—41no—
164D292—41no—
165C4×D73—81no—
166C4×D73—81no—
167C4×D73—81no—
168C4×D73—81no—
169C8×C73—22no—
170C8×C73—41no—
171#10596831—42no—
172#10596831—81no—
173#10596831—81no—
174C22×C73#39411yescharacteristic
175C22×C73#46111yescharacteristic
176C22×C73#46311yescharacteristic
177C22×C73#46611yescharacteristic
178C22×C73#46811yescharacteristic
179C22×C73#47111yescharacteristic
180C22×C73#47311yescharacteristic
181C2×D73—42no—
182C2×D73—42no—
183C2×D73—42no—
184C2×D73—81no—
185C2×D73—81no—
186C2×D73—81no—
187C2×D73—81no—
188C4×C73—21no—
189C4×C73—21no—
190C4×C73—82no—
191C4×C73—161no—
192C4×C73#44711yescharacteristic
193C4×C73#45211yescharacteristic
194C4×C73#46011yescharacteristic
195C4×C73#46411yescharacteristic
196C4×C73#46511yescharacteristic
197C4×C73#46811yescharacteristic
198C4×C73#48011yescharacteristic
199C4×C73#48211yescharacteristic
200Dic73—81no—
201#10476—731nomaximal, Sylow
202C2×C73#167311yescharacteristic
203C2×C73#168111yescharacteristic
204C2×C73#169111yescharacteristic
205C2×C73#169911yescharacteristic
206C2×C73#203311yescharacteristic
207C2×C73#205211yescharacteristic
208C2×C73#205511yescharacteristic
209D73—82no—
210C2×#461—731no—
211#1990D7311yescharacteristic, complemented
212#1954—731no—
213#1802—731no—
214C2×#335—731no—
215C2×#332—731no—
216#1296—731no—
217C73#1047611yescharacteristic, complemented, Sylow
218C22×SD16—1461no—
219C2×C4⋊Q8C2×D7311yescharacteristic
220C2×C4×D4—731no—
221#461—1462no—
222#461—1462no—
223C2×C4⋊C8—731no—
224C2×C4⋊C8—731no—
225C2×C4⋊C8—731no—
226C2×#103—1461no—
227C2×#102—1461no—
228C2×C22⋊C8—1461no—
229C2×C22⋊C8—1461no—
230C2×C4×C8C2×D7311yescharacteristic
231#384C2×D7311yescharacteristic
232#340—21no—
233#340—21no—
234#340—1461no—
235#335—1462no—
236#332—1462no—
237C22×Q8—21no—
238C22×D4—731no—
239C23×C4—1461no—
240C2×SD16—2922no—
241C2×SD16—2922no—
242C2×SD16—1464no—
243C22×C8—1461no—
244C22×C8—1461no—
245C22×C8—1461no—
246C22×C8C22⋊D7311yescharacteristic
247C22×C8C22⋊D7311yescharacteristic
248C4⋊Q8—21no—
249C4⋊Q8—21no—
250C4⋊Q8—21no—
251C4⋊Q8D29212yes—
252C4×D4—1461no—
253C4×D4—1461no—
254C4×D4—1461no—
255C4×D4—1461no—
256C2×C4⋊C4—21no—
257C2×C4⋊C4—21no—
258C2×C4⋊C4—21no—
259C2×C4⋊C4—21no—
260C2×C4⋊C4—21no—
261C2×C4⋊C4—731no—
262C2×C22⋊C4—1461no—
263C2×C42C22×D7311yescharacteristic
264C4⋊C8—732no—
265C4⋊C8—1461no—
266C4⋊C8—1461no—
267C4⋊C8—1461no—
268C4⋊C8—1461no—
269C4⋊C8—1461no—
270#103—1464no—
271#102—2922no—
272C22⋊C8—2922no—
273C22⋊C8—2922no—
274C4×C8—21no—
275C4×C8—21no—
276C24—1461no—
277C2×Q8—22no—
278C2×Q8—41no—
279C2×Q8—41no—
280C2×Q8—41no—
281C2×Q8—41no—
282C2×Q8—41no—
283C2×D4—732no—
284C2×D4—1461no—
285C2×D4—1461no—
286C2×D4—1461no—
287C2×D4—1461no—
288C2×D4—1461no—
289C22×C4—41no—
290C22×C4—41no—
291C22×C4—2921no—
292C22×C4—2921no—
293C22×C4—2921no—
294C22×C4—2921no—
295C22×C4—2921no—
296C22×C4—2921no—
297C22×C4—1461no—
298C22×C4D4×D7311yescharacteristic
299C22×C4C2×C22⋊D7311yescharacteristic
300C22×C4#1192402711yescharacteristic
301SD16—2928no—
302C2×C8—21no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8—21no—
306C2×C8—21no—
307C2×C8—2921no—
308C2×C8—2921no—
309C2×C8—2921no—
310C2×C8—2921no—
311C2×C8—2921no—
312C2×C8—2921no—
313C2×C8—2921no—
314C2×C8—2921no—
315C2×C8—1462no—
316C2×C8#1192401512yescomplemented
317C4⋊C4—22no—
318C4⋊C4—22no—
319C4⋊C4—41no—
320C4⋊C4—41no—
321C4⋊C4—41no—
322C4⋊C4—41no—
323C4⋊C4—41no—
324C4⋊C4—41no—
325C4⋊C4—81no—
326C4⋊C4—1461no—
327C4⋊C4—1461no—
328C22⋊C4—2921no—
329C22⋊C4—2921no—
330C42D4×D7311yescharacteristic
331C42C2×D29211yescharacteristic
332C42#1192402711yescharacteristic
333C42#1192402811yescharacteristic
334C23—2921no—
335C23—2921no—
336C23—2921no—
337C23—2921no—
338C23—2921no—
339C23—2921no—
340C23—1462no—
341C23#1455656211yescharacteristic
342Q8—42no—
343Q8—42no—
344Q8—81no—
345Q8—81no—
346D4—2921no—
347D4—2921no—
348D4—1462no—
349D4—1462no—
350C2×C4—21no—
351C2×C4—21no—
352C2×C4—42no—
353C2×C4—81no—
354C2×C4—81no—
355C2×C4—81no—
356C2×C4—81no—
357C2×C4—81no—
358C2×C4—2921no—
359C2×C4—2921no—
360C2×C4—2921no—
361C2×C4—5841no—
362C2×C4—5841no—
363C2×C4—5841no—
364C2×C4—5841no—
365C2×C4#1455656111yescharacteristic
366C2×C4#1455656311yescharacteristic
367C2×C4#1455656511yescharacteristic
368C2×C4#1455657311yescharacteristic
369C2×C4#1455657511yescharacteristic
370C2×C4#1455657711yescharacteristic
371C2×C4D8×D7311yescharacteristic
372C2×C4C2×#1192401511yescharacteristic
373C2×C4#1455661011yescharacteristic
374C2×C4#1455661111yescharacteristic
375C2×C4#1455661611yescharacteristic
376C2×C4#1455661811yescharacteristic
377C2×C4#1455662011yescharacteristic
378C2×C4#1455662211yescharacteristic
379C8—22no—
380C8—41no—
381C8—2922no—
382C8—5841no—
383C8—5841no—
384C22—2922no—
385C22—2922no—
386C22—2922no—
387C22—5841no—
388C22—5841no—
389C22—5841no—
390C22—5841no—
391C22#1798850311yescharacteristic
392C22#1798878911yescharacteristic
393C22#1798879911yescharacteristic
394C22#1798882011yescharacteristic
395C22#1798883011yescharacteristic
396C22#1798884711yescharacteristic
397C22#1798885911yescharacteristic
398C4—21no—
399C4—21no—
400C4—82no—
401C4—161no—
402C4—5841no—
403C4#1798872211yescharacteristic
404C4#1798875011yescharacteristic
405C4#1798878711yescharacteristic
406C4#1798880911yescharacteristic
407C4#1798881811yescharacteristic
408C4#1798883511yescharacteristic
409C4#1798889911yescharacteristic
410C4#1798890911yescharacteristic
411C2—5842no—
412C2#2260931711yescharacteristic
413C2#2260936511yescharacteristic
414C2#2260942711yescharacteristic
415C2#2260947511yescharacteristic
416C2#2261111211yescharacteristic
417C2#2261123111yescharacteristic
418C2#2261124611yescharacteristic
subgroupG/H
centerC23#14556562
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1990C2
socleC23×C73#121
prime radicalC22×D292D4
hypercenter#1990D73
hypocenterC73#10476
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1990

Complements

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

NH ≅ G/Ntype
4. C2×#17988340C2semidirect
5. C2×#17988333C2semidirect
6. #22607814C2semidirect
7. C73×#1990C2semidirect
110. C2×C8×C73SD16semidirect
211. #1990D73semidirect
217. C73#10476semidirect
316. C2×C8#11924015semidirect

Maximal subgroups

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

subgroupindex
C2×#179887892
#226107252
#226099282
C2×#179883402
C2×#179883332
#226078142
C73×#19902
#1047673