Finite Group Databasebeta

← #32982140

Subgroups — #32982140

Order 18688.

610 conjugacy classes of subgroups.

The subgroup lattice has 428 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988789C211yesmaximal, characteristic
2C2×C8×D292C211yesmaximal, characteristic
3#22609928C211yesmaximal, characteristic
4C2×#17988333C211yesmaximal, characteristic, complemented
5#22607814C211yesmaximal, characteristic, complemented
6#22607766C211yesmaximal, characteristic, complemented
7C73×#1990C211yesmaximal, characteristic, complemented
8C22×#11924015—21no—
9C22×C8×D73—21no—
10C2×C4×D292C2211yescharacteristic
11#17988789—22no—
12#17988789C414yescomplemented
13C8×D292—22no—
14C8×D292—22no—
15C2×C4⋊#10596831C2211yescharacteristic
16C2×C4⋊#10596831C2211yescharacteristic
17C2×C4⋊#10596831C2211yescharacteristic
18C2×#14556515—21no—
19C2×#14556511—21no—
20C2×#14556503—21no—
21#17988349—21no—
22#17988333—22no—
23C2×C4⋊Q8×C73C2211yescharacteristic
24C2×C4×C8×C73C2211yescharacteristic
25#384×C73C2211yescharacteristic
26#340×C73—21no—
27#340×C73—21no—
28C22×D292D411yescharacteristic
29C22×C4×D73—21no—
30C2×#11924015—24no—
31C2×#11924015—42no—
32C2×#11924015—42no—
33C22×#10596831—21no—
34C22×#10596831—21no—
35C22×#10596831—21no—
36C2×C8×D73—24no—
37C2×C8×D73—42no—
38C2×C8×D73—42no—
39C4×D292—21no—
40C4×D292—21no—
41C4×D292C2×C412yes—
42C4×D292D412yes—
43C2×C4⋊Dic73D411yescharacteristic
44C2×#11924005—21no—
45C4⋊#10596831—21no—
46C4⋊#10596831—21no—
47C4⋊#10596831—21no—
48C4⋊#10596831—21no—
49C4⋊#10596831C2×C412yes—
50C4⋊#10596831D412yes—
51#14556515—24no—
52#14556511—42no—
53#14556503—24no—
54C22×Q8×C73—21no—
55C22×C8×C73D411yescharacteristic
56C22×C8×C73D411yescharacteristic
57C4⋊Q8×C73—21no—
58C4⋊Q8×C73—21no—
59C4⋊Q8×C73—21no—
60C4⋊Q8×C73C2×C412yes—
61C2×C4⋊C4×C73—21no—
62C2×C4⋊C4×C73—21no—
63C2×C4⋊C4×C73—21no—
64C2×C4⋊C4×C73—21no—
65C2×C4⋊C4×C73—21no—
66C2×C42×C73C2311yescharacteristic
67C4×C8×C73—21no—
68C4×C8×C73—21no—
69C23×D73—21no—
70C2×D292—21no—
71C2×D292—21no—
72C2×D292—21no—
73C2×D292C22⋊C412yes—
74C2×D292D812yes—
75C2×D292SD1612yes—
76C22×Dic73—21no—
77C2×C4×D73—22no—
78C2×C4×D73—22no—
79C2×C4×D73—41no—
80C2×C4×D73—41no—
81C2×C4×D73—41no—
82C2×C4×D73—41no—
83#11924015—48no—
84C2×#10596831—22no—
85C2×#10596831—22no—
86C2×#10596831—41no—
87C2×#10596831—41no—
88C2×#10596831—41no—
89C2×#10596831—41no—
90C2×#10596831—41no—
91C2×#10596831—41no—
92C2×#10596831—41no—
93C8×D73—48no—
94C4⋊Dic73—21no—
95C4⋊Dic73C22⋊C412yes—
96#11924005—22no—
97#11924005—22no—
98C2×Q8×C73—22no—
99C2×Q8×C73—41no—
100C2×Q8×C73—41no—
101C2×Q8×C73—41no—
102C2×Q8×C73—41no—
103C2×Q8×C73—41no—
104C22×C4×C73—41no—
105C22×C4×C73—41no—
106C22×C4×C73C2×D411yescharacteristic
107C22×C4×C73C2×D411yescharacteristic
108C22×C4×C73#4111yescharacteristic
109C2×C8×C73—21no—
110C2×C8×C73—21no—
111C2×C8×C73—21no—
112C2×C8×C73—21no—
113C2×C8×C73—21no—
114C2×C8×C73SD1612yescomplemented
115C4⋊C4×C73—22no—
116C4⋊C4×C73—22no—
117C4⋊C4×C73—41no—
118C4⋊C4×C73—41no—
119C4⋊C4×C73—41no—
120C4⋊C4×C73—41no—
121C4⋊C4×C73—41no—
122C4⋊C4×C73—41no—
123C4⋊C4×C73—81no—
124C42×C73C22×C411yescharacteristic
125C42×C73C2×D411yescharacteristic
126C42×C73C2×D411yescharacteristic
127C42×C73#4111yescharacteristic
128C23×C73#12111yescharacteristic
129C22×D73—22no—
130C22×D73—22no—
131C22×D73—22no—
132C22×D73—41no—
133C22×D73—41no—
134C22×D73—41no—
135C22×D73—41no—
136Q8×C73—42no—
137Q8×C73—42no—
138Q8×C73—81no—
139Q8×C73—81no—
140C2×C4×C73—21no—
141C2×C4×C73—21no—
142C2×C4×C73—42no—
143C2×C4×C73—81no—
144C2×C4×C73—81no—
145C2×C4×C73—81no—
146C2×C4×C73—81no—
147C2×C4×C73—81no—
148C2×C4×C73C2×C22⋊C411yescharacteristic
149C2×C4×C73C4×D411yescharacteristic
150C2×C4×C73C4×D411yescharacteristic
151C2×C4×C73#12011yescharacteristic
152C2×C4×C73#12111yescharacteristic
153C2×C4×C73#12311yescharacteristic
154C2×C4×C73C2×D811yescharacteristic
155C2×C4×C73C2×SD1611yescharacteristic
156C2×C4×C73C2×SD1611yescharacteristic
157C2×C4×C73#13511yescharacteristic
158C2×C4×C73#13511yescharacteristic
159C2×C4×C73#13511yescharacteristic
160C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C73#13711yescharacteristic
162C2×Dic73—22no—
163C2×Dic73—41no—
164C2×Dic73—41no—
165D292—22no—
166D292—22no—
167D292—22no—
168D292#10214yes—
169C4×D73—42no—
170C4×D73—42no—
171C4×D73—42no—
172C4×D73—42no—
173C8×C73—22no—
174C8×C73—41no—
175#10596831—42no—
176#10596831—42no—
177#10596831—81no—
178C22×C73#38611yescharacteristic
179C22×C73#46111yescharacteristic
180C22×C73#46311yescharacteristic
181C22×C73#46511yescharacteristic
182C22×C73#46611yescharacteristic
183C22×C73#47111yescharacteristic
184C22×C73#47311yescharacteristic
185C2×D73—24no—
186C2×D73—42no—
187C2×D73—42no—
188C2×D73—42no—
189C2×D73—42no—
190C2×D73—42no—
191C2×D73—42no—
192C4×C73—21no—
193C4×C73—21no—
194C4×C73—82no—
195C4×C73—161no—
196C4×C73C2×#10211yescharacteristic
197C4×C73#41611yescharacteristic
198C4×C73C4×SD1611yescharacteristic
199C4×C73#44011yescharacteristic
200C4×C73#45011yescharacteristic
201C4×C73#45211yescharacteristic
202C4×C73#46511yescharacteristic
203C4×C73#46611yescharacteristic
204Dic73—42no—
205#9217—731nomaximal, Sylow
206C2×C73#167111yescharacteristic
207C2×C73#167311yescharacteristic
208C2×C73#167911yescharacteristic
209C2×C73#168111yescharacteristic
210C2×C73#187711yescharacteristic
211C2×C73#189311yescharacteristic
212C2×C73#190811yescharacteristic
213D73—44no—
214C2×#461—731no—
215C2×C8×D4—731no—
216#1990D7311yescharacteristic, complemented
217#1802—731no—
218C2×#332—731no—
219#1296—731no—
220#1277—731no—
221C73#921711yescharacteristic, complemented, Sylow
222C22×SD16—1461no—
223C23×C8—1461no—
224C2×C4⋊Q8C2×D7311yescharacteristic
225C2×C4×D4—731no—
226#461—734no—
227#461—1462no—
228C8×D4—1462no—
229C8×D4—1462no—
230C2×C4⋊C8—731no—
231C2×C4⋊C8—731no—
232C2×C4⋊C8—731no—
233C2×#103—1461no—
234C2×#102—1461no—
235C2×C22⋊C8—1461no—
236C2×C4×C8C2×D7311yescharacteristic
237#384C2×D7311yescharacteristic
238#340—21no—
239#340—21no—
240#340—1461no—
241#332—1462no—
242C22×Q8—21no—
243C22×D4—731no—
244C23×C4—1461no—
245C2×SD16—2922no—
246C2×SD16—2922no—
247C2×SD16—1464no—
248C22×C8—2922no—
249C22×C8—2922no—
250C22×C8—1464no—
251C22×C8—1461no—
252C22×C8—1461no—
253C22×C8—1461no—
254C22×C8C22⋊D7311yescharacteristic
255C22×C8C22⋊D7311yescharacteristic
256C4⋊Q8—21no—
257C4⋊Q8—21no—
258C4⋊Q8—21no—
259C4⋊Q8C4×D7312yes—
260C4×D4—732no—
261C4×D4—732no—
262C4×D4—1461no—
263C4×D4—1461no—
264C2×C4⋊C4—21no—
265C2×C4⋊C4—21no—
266C2×C4⋊C4—21no—
267C2×C4⋊C4—21no—
268C2×C4⋊C4—21no—
269C2×C4⋊C4—731no—
270C2×C22⋊C4—1461no—
271C2×C42C22×D7311yescharacteristic
272C4⋊C8—732no—
273C4⋊C8—732no—
274C4⋊C8—1461no—
275C4⋊C8—1461no—
276C4⋊C8—1461no—
277C4⋊C8—1461no—
278#103—1464no—
279#102—2922no—
280C22⋊C8—1464no—
281C4×C8—21no—
282C4×C8—21no—
283C24—1461no—
284C2×Q8—22no—
285C2×Q8—41no—
286C2×Q8—41no—
287C2×Q8—41no—
288C2×Q8—41no—
289C2×Q8—41no—
290C2×D4—732no—
291C2×D4—732no—
292C2×D4—732no—
293C2×D4—1461no—
294C2×D4—1461no—
295C2×D4—1461no—
296C22×C4—41no—
297C22×C4—41no—
298C22×C4—2921no—
299C22×C4—2921no—
300C22×C4—2921no—
301C22×C4—2921no—
302C22×C4—1461no—
303C22×C4—1462no—
304C22×C4—1462no—
305C22×C4D4×D7311yescharacteristic
306C22×C4C2×C22⋊D7311yescharacteristic
307C22×C4#1192402711yescharacteristic
308SD16—2928no—
309C2×C8—21no—
310C2×C8—21no—
311C2×C8—21no—
312C2×C8—21no—
313C2×C8—21no—
314C2×C8—2928no—
315C2×C8—2921no—
316C2×C8—2921no—
317C2×C8—2921no—
318C2×C8—2921no—
319C2×C8—2921no—
320C2×C8—2921no—
321C2×C8—2921no—
322C2×C8—1462no—
323C2×C8—1462no—
324C2×C8#1192401512yescomplemented
325C4⋊C4—22no—
326C4⋊C4—22no—
327C4⋊C4—41no—
328C4⋊C4—41no—
329C4⋊C4—41no—
330C4⋊C4—41no—
331C4⋊C4—41no—
332C4⋊C4—41no—
333C4⋊C4—81no—
334C4⋊C4—732no—
335C4⋊C4—1461no—
336C22⋊C4—1462no—
337C22⋊C4—1462no—
338C42C2×C4×D7311yescharacteristic
339C42D4×D7311yescharacteristic
340C42D4×D7311yescharacteristic
341C42#1192402811yescharacteristic
342C23—2921no—
343C23—2921no—
344C23—2921no—
345C23—2921no—
346C23—1462no—
347C23—1462no—
348C23—1462no—
349C23#1455656211yescharacteristic
350Q8—42no—
351Q8—42no—
352Q8—81no—
353Q8—81no—
354D4—734no—
355D4—1462no—
356D4—1462no—
357D4—1462no—
358C2×C4—21no—
359C2×C4—21no—
360C2×C4—42no—
361C2×C4—81no—
362C2×C4—81no—
363C2×C4—81no—
364C2×C4—81no—
365C2×C4—81no—
366C2×C4—2921no—
367C2×C4—2921no—
368C2×C4—2922no—
369C2×C4—2922no—
370C2×C4—2922no—
371C2×C4—2922no—
372C2×C4—1462no—
373C2×C4C22⋊C4×D7311yescharacteristic
374C2×C4#1455655111yescharacteristic
375C2×C4C4×C22⋊D7311yescharacteristic
376C2×C4#1455655911yescharacteristic
377C2×C4#1455656411yescharacteristic
378C2×C4#1455657311yescharacteristic
379C2×C4D8×D7311yescharacteristic
380C2×C4SD16×D7311yescharacteristic
381C2×C4C2×#1192401511yescharacteristic
382C2×C4#1455661011yescharacteristic
383C2×C4#1455661111yescharacteristic
384C2×C4#1455661211yescharacteristic
385C2×C4#1455661611yescharacteristic
386C2×C4#1455662211yescharacteristic
387C8—22no—
388C8—41no—
389C8—2922no—
390C8—2922no—
391C8—5841no—
392C22—2922no—
393C22—2922no—
394C22—2922no—
395C22—2922no—
396C22—2922no—
397C22—2922no—
398C22—1464no—
399C22#1798846311yescharacteristic
400C22#1798878911yescharacteristic
401C22#1798879911yescharacteristic
402C22#1798881311yescharacteristic
403C22#1798882011yescharacteristic
404C22#1798884711yescharacteristic
405C22#1798885911yescharacteristic
406C4—21no—
407C4—21no—
408C4—82no—
409C4—161no—
410C4—2922no—
411C4#102×D7311yescharacteristic
412C4#1798858011yescharacteristic
413C4C4×#1192401511yescharacteristic
414C4#1798868511yescharacteristic
415C4#1798873711yescharacteristic
416C4#1798874711yescharacteristic
417C4#1798881511yescharacteristic
418C4#1798882211yescharacteristic
419C2—2924no—
420C2#2260930311yescharacteristic
421C2#2260931711yescharacteristic
422C2#2260935111yescharacteristic
423C2#2260936511yescharacteristic
424C2#2261026811yescharacteristic
425C2#2261035611yescharacteristic
426C2#2261044911yescharacteristic
subgroupG/H
centerC23#14556562
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1990C2
socleC23×C73#121
prime radicalC22×D292D4
cosocleC2×C42×C73C23
hypercenter#1990D73
hypocenterC73#9217
LCSG ▷ 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×#17988333C2semidirect
5. #22607814C2semidirect
6. #22607766C2semidirect
7. C73×#1990C2semidirect
12. #17988789C4semidirect
114. C2×C8×C73SD16semidirect
216. #1990D73semidirect
221. C73#9217semidirect
324. 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
C2×C8×D2922
#226099282
C2×#179883332
#226078142
#226077662
C73×#19902
#921773