Finite Group Databasebeta

← #32980171

Subgroups — #32980171

Order 18688.

618 conjugacy classes of subgroups.

The subgroup lattice has 426 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4⋊C4×D292C211yesmaximal, characteristic
2#22610087C211yesmaximal, characteristic, complemented
3#22609928C211yesmaximal, characteristic
4C2×#17988314C211yesmaximal, characteristic
5#22607815C211yesmaximal, characteristic, complemented
6#22607772C211yesmaximal, characteristic, complemented
7C73×#1948C211yesmaximal, characteristic, complemented
8C2×C4×D292—21no—
9C2×C4×D292C2211yescharacteristic
10C2×C4⋊C4×D73—21no—
11C2×#14556522—22no—
12C2×C4⋊#10596831C2211yescharacteristic
13C2×#14556511—21no—
14C2×C4×#10596831C2211yescharacteristic
15#17988485—21no—
16#17988461—22no—
17#17988457C2211yescharacteristic
18#17988444—21no—
19#17988349—21no—
20#17988314C414yescomplemented
21C2×#106×C73—21no—
22C2×C4⋊C8×C73C2211yescharacteristic
23#384×C73C2211yescharacteristic
24C4×C4⋊C4×C73C2211yescharacteristic
25#340×C73—21no—
26C22×D292D411yescharacteristic
27C22×C4×D73—22no—
28C22×C4×D73—21no—
29C22×#10596831—21no—
30C22×#10596831—21no—
31C4×D292—21no—
32C4×D292—21no—
33C4×D292—42no—
34C4×D292—42no—
35C4×D292C2×C412yes—
36C4×D292Q812yes—
37C2×C4⋊Dic73—21no—
38C2×C4⋊Dic73—21no—
39C2×C4⋊Dic73D411yescharacteristic
40C2×C4⋊Dic73D412yes—
41C2×#11924007—22no—
42C4⋊C4×D73—42no—
43C4⋊C4×D73—42no—
44C2×#11924005—22no—
45C2×#11924005—21no—
46#14556522—44no—
47C4⋊#10596831—21no—
48C4⋊#10596831—21no—
49#14556511—42no—
50C4×#10596831—21no—
51C4×#10596831C2×C412yescomplemented
52#14556498—22no—
53C22×C8×C73—21no—
54C2×C4⋊C4×C73—21no—
55C2×C4⋊C4×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C4⋊C4×C73D411yescharacteristic
58C2×C4⋊C4×C73D411yescharacteristic
59C2×C42×C73—21no—
60C2×C42×C73C2311yescharacteristic
61#106×C73—42no—
62C4⋊C8×C73—21no—
63C4⋊C8×C73C2×C412yescomplemented
64#95×C73—21no—
65C23×D73—21no—
66C2×D292—21no—
67C2×D292—21no—
68C2×D292—21no—
69C2×D292C4⋊C412yes—
70C2×D292SD1612yes—
71C2×D292SD1612yes—
72C22×Dic73—21no—
73C22×Dic73—22no—
74C2×C4×D73—22no—
75C2×C4×D73—22no—
76C2×C4×D73—41no—
77C2×C4×D73—41no—
78C2×C4×D73—41no—
79C2×C4×D73—41no—
80C2×C4×D73—44no—
81C2×C4×D73—44no—
82C2×C4×D73—82no—
83C2×#10596831—22no—
84C2×#10596831—22no—
85C2×#10596831—22no—
86C2×#10596831—41no—
87C2×#10596831—41no—
88C2×#10596831—41no—
89C4⋊Dic73—21no—
90C4⋊Dic73—41no—
91C4⋊Dic73—41no—
92C4⋊Dic73—41no—
93C4⋊Dic73—41no—
94C4⋊Dic73—42no—
95C4⋊Dic73C4⋊C412yes—
96#11924007—44no—
97#11924005—22no—
98#11924005—22no—
99#11924005—44no—
100C22×C4×C73—21no—
101C22×C4×C73—21no—
102C22×C4×C73—41no—
103C22×C4×C73C2×D411yescharacteristic
104C22×C4×C73C2×D411yescharacteristic
105C22×C4×C73C2×D411yescharacteristic
106C2×C8×C73—22no—
107C2×C8×C73—41no—
108C2×C8×C73—41no—
109C4⋊C4×C73—21no—
110C4⋊C4×C73—21no—
111C4⋊C4×C73—21no—
112C4⋊C4×C73—42no—
113C4⋊C4×C73—41no—
114C4⋊C4×C73—41no—
115C4⋊C4×C73—41no—
116C4⋊C4×C73—41no—
117C4⋊C4×C73SD1612yes—
118C42×C73—41no—
119C42×C73—41no—
120C42×C73C22×C411yescharacteristic
121C42×C73C2×Q811yescharacteristic
122C42×C73#4111yescharacteristic
123C42×C73#4111yescharacteristic
124C23×C73#12011yescharacteristic
125C22×D73—22no—
126C22×D73—22no—
127C22×D73—22no—
128C22×D73—41no—
129C22×D73—41no—
130C22×D73—41no—
131C22×D73—41no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—22no—
135C2×C4×C73—41no—
136C2×C4×C73—41no—
137C2×C4×C73—41no—
138C2×C4×C73—41no—
139C2×C4×C73—41no—
140C2×C4×C73—81no—
141C2×C4×C73—81no—
142C2×C4×C73—81no—
143C2×C4×C73C2×C4⋊C411yescharacteristic
144C2×C4×C73C4×D411yescharacteristic
145C2×C4×C73C4×D411yescharacteristic
146C2×C4×C73C22⋊Q811yescharacteristic
147C2×C4×C73C22⋊Q811yescharacteristic
148C2×C4×C73#12311yescharacteristic
149C2×C4×C73C2×SD1611yescharacteristic
150C2×C4×C73C2×SD1611yescharacteristic
151C2×C4×C73C2×SD1611yescharacteristic
152C2×C4×C73#13511yescharacteristic
153C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
154C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
155C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
156C2×C4×C73#13711yescharacteristic
157C2×Dic73—22no—
158C2×Dic73—41no—
159C2×Dic73—41no—
160C2×Dic73—42no—
161C2×Dic73—42no—
162C2×Dic73—42no—
163D292—22no—
164D292—22no—
165D292—22no—
166D292#10614yescomplemented
167C4×D73—42no—
168C4×D73—42no—
169C4×D73—42no—
170C4×D73—42no—
171C4×D73—88no—
172C8×C73—42no—
173#10596831—24no—
174#10596831—81no—
175C22×C73#38511yescharacteristic
176C22×C73#44811yescharacteristic
177C22×C73#44911yescharacteristic
178C22×C73#45011yescharacteristic
179C22×C73#45011yescharacteristic
180C22×C73#45311yescharacteristic
181C22×C73#45611yescharacteristic
182C2×D73—24no—
183C2×D73—42no—
184C2×D73—42no—
185C2×D73—42no—
186C2×D73—42no—
187C2×D73—42no—
188C2×D73—42no—
189C4×C73—21no—
190C4×C73—21no—
191C4×C73—42no—
192C4×C73—81no—
193C4×C73—161no—
194C4×C73C2×#10611yescharacteristic
195C4×C73#42811yescharacteristic
196C4×C73C4×SD1611yescharacteristic
197C4×C73#44211yescharacteristic
198C4×C73#47611yescharacteristic
199C4×C73#47811yescharacteristic
200C4×C73#48111yescharacteristic
201C4×C73#48311yescharacteristic
202Dic73—42no—
203Dic73—82no—
204#8886—731nomaximal, Sylow
205C2×C73#162211yescharacteristic
206C2×C73#162911yescharacteristic
207C2×C73#165111yescharacteristic
208C2×C73#165411yescharacteristic
209C2×C73#185311yescharacteristic
210C2×C73#185911yescharacteristic
211C2×C73#186411yescharacteristic
212D73—44no—
213D4×C4⋊C4—731no—
214#1948D7311yescharacteristic, complemented
215#1844—731no—
216#1802—731no—
217C2×D4⋊C8—731no—
218#1296—731no—
219#1279—731no—
220C73#888611yescharacteristic, complemented, Sylow
221C2×C4×D4—731no—
222C2×C4×D4—1461no—
223C22×C4⋊C4—1461no—
224C2×#106—21no—
225C2×#106—1462no—
226C2×C4⋊C8—731no—
227C2×C4⋊C8C2×D7311yescharacteristic
228C2×#102—1461no—
229C2×C4×C8—731no—
230#389—1461no—
231#385—1462no—
232#384—731no—
233#384C2×D7311yescharacteristic
234#380—1461no—
235C4×C4⋊C4C2×D7311yescharacteristic
236#340—21no—
237#340—1461no—
238D4⋊C8—734no—
239C22×D4—731no—
240C23×C4—1462no—
241C23×C4—1461no—
242C22×C8—21no—
243C22×C8—1461no—
244C22×C8—1461no—
245C4×D4—2922no—
246C4×D4—2922no—
247C4×D4—732no—
248C4×D4—732no—
249C4×D4—1461no—
250C4×D4—1461no—
251C2×C4⋊C4—21no—
252C2×C4⋊C4—21no—
253C2×C4⋊C4—21no—
254C2×C4⋊C4—2922no—
255C2×C4⋊C4—2922no—
256C2×C4⋊C4—732no—
257C2×C4⋊C4—731no—
258C2×C4⋊C4—1462no—
259C2×C4⋊C4—1461no—
260C2×C4⋊C4—1461no—
261C2×C4⋊C4C22⋊D7311yescharacteristic
262C2×C4⋊C4C22⋊D7311yescharacteristic
263C2×C22⋊C4—1462no—
264C2×C22⋊C4—1461no—
265C2×C42—21no—
266C2×C42C22×D7311yescharacteristic
267#106—42no—
268#106—2924no—
269C4⋊C8—21no—
270C4⋊C8—1461no—
271C4⋊C8—1461no—
272C4⋊C8C4×D7312yescomplemented
273#102—2922no—
274C4×C8—732no—
275C4×C8—1461no—
276#95—21no—
277#95—1462no—
278C24—1461no—
279C2×D4—732no—
280C2×D4—732no—
281C2×D4—732no—
282C2×D4—1461no—
283C2×D4—1461no—
284C2×D4—1461no—
285C22×C4—21no—
286C22×C4—21no—
287C22×C4—41no—
288C22×C4—2924no—
289C22×C4—2924no—
290C22×C4—2921no—
291C22×C4—2921no—
292C22×C4—2921no—
293C22×C4—2921no—
294C22×C4—5842no—
295C22×C4—1462no—
296C22×C4—1461no—
297C22×C4—1462no—
298C22×C4—1462no—
299C22×C4D4×D7311yescharacteristic
300C22×C4D4×D7311yescharacteristic
301C22×C4C2×C22⋊D7311yescharacteristic
302C2×C8—22no—
303C2×C8—41no—
304C2×C8—41no—
305C2×C8—2921no—
306C2×C8—2921no—
307C2×C8—2921no—
308C2×C8—1462no—
309C2×C8—1462no—
310C2×C8—1462no—
311C4⋊C4—21no—
312C4⋊C4—21no—
313C4⋊C4—21no—
314C4⋊C4—42no—
315C4⋊C4—41no—
316C4⋊C4—41no—
317C4⋊C4—41no—
318C4⋊C4—41no—
319C4⋊C4—2922no—
320C4⋊C4—2924no—
321C4⋊C4—2921no—
322C4⋊C4—2921no—
323C4⋊C4—2921no—
324C4⋊C4—2921no—
325C4⋊C4—732no—
326C4⋊C4—1461no—
327C4⋊C4#1192401512yes—
328C22⋊C4—2924no—
329C22⋊C4—1462no—
330C22⋊C4—1462no—
331C42—41no—
332C42—41no—
333C42C2×C4×D7311yescharacteristic
334C42Q8×D7311yescharacteristic
335C42#1192402811yescharacteristic
336C42#1192402911yescharacteristic
337C23—2921no—
338C23—2921no—
339C23—2921no—
340C23—2921no—
341C23—1462no—
342C23—1462no—
343C23—1462no—
344C23#1455655911yescharacteristic
345D4—734no—
346D4—1462no—
347D4—1462no—
348D4—1462no—
349C2×C4—21no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—41no—
353C2×C4—41no—
354C2×C4—41no—
355C2×C4—41no—
356C2×C4—41no—
357C2×C4—81no—
358C2×C4—81no—
359C2×C4—81no—
360C2×C4—2921no—
361C2×C4—2921no—
362C2×C4—2922no—
363C2×C4—2922no—
364C2×C4—2922no—
365C2×C4—2922no—
366C2×C4—2922no—
367C2×C4—2922no—
368C2×C4—2922no—
369C2×C4—5848no—
370C2×C4—1462no—
371C2×C4C4⋊C4×D7311yescharacteristic
372C2×C4C4×C22⋊D7311yescharacteristic
373C2×C4#1455655311yescharacteristic
374C2×C4#1455656711yescharacteristic
375C2×C4#1455656911yescharacteristic
376C2×C4#1455657611yescharacteristic
377C2×C4SD16×D7311yescharacteristic
378C2×C4SD16×D7311yescharacteristic
379C2×C4C2×#1192401511yescharacteristic
380C2×C4#1455661111yescharacteristic
381C2×C4#1455661611yescharacteristic
382C2×C4#1455661711yescharacteristic
383C2×C4#1455661811yescharacteristic
384C2×C4#1455662011yescharacteristic
385C8—42no—
386C8—5841no—
387C8—1464no—
388C22—2922no—
389C22—2922no—
390C22—2922no—
391C22—2922no—
392C22—2922no—
393C22—2922no—
394C22—1464no—
395C22#1798845811yescharacteristic
396C22#1798872411yescharacteristic
397C22#1798873011yescharacteristic
398C22#1798873611yescharacteristic
399C22#1798873711yescharacteristic
400C22#1798875311yescharacteristic
401C22#1798876811yescharacteristic
402C4—21no—
403C4—21no—
404C4—42no—
405C4—81no—
406C4—161no—
407C4—2922no—
408C4—5842no—
409C4#106×D7311yescharacteristic
410C4#1798862611yescharacteristic
411C4C4×#1192401511yescharacteristic
412C4#1798869711yescharacteristic
413C4#1798887411yescharacteristic
414C4#1798888411yescharacteristic
415C4#1798890711yescharacteristic
416C4#1798891911yescharacteristic
417C2—2924no—
418C2#2260900211yescharacteristic
419C2#2260904611yescharacteristic
420C2#2260919311yescharacteristic
421C2#2260921311yescharacteristic
422C2#2261012211yescharacteristic
423C2#2261015411yescharacteristic
424C2#2261019111yescharacteristic
subgroupG/H
centerC23#14556559
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1948C2
socleC23×C73#120
prime radicalC22×D292D4
cosocleC2×C42×C73C23
hypercenter#1948D73
hypocenterC73#8886
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1948

Complements

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

NH ≅ G/Ntype
2. #22610087C2semidirect
5. #22607815C2semidirect
6. #22607772C2semidirect
7. C73×#1948C2semidirect
20. #17988314C4semidirect
51. C4×#10596831C2×C4semidirect
63. C4⋊C8×C73C2×C4semidirect
166. D292#106semidirect
214. #1948D73semidirect
220. C73#8886semidirect
272. C4⋊C8C4×D73semidirect

Maximal subgroups

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

subgroupindex
C4⋊C4×D2922
#226100872
#226099282
C2×#179883142
#226078152
#226077722
C73×#19482
#888673