Finite Group Databasebeta

← #33005578

Subgroups — #33005578

Order 18688.

482 conjugacy classes of subgroups.

The subgroup lattice has 392 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556532C211yesmaximal, characteristic
2C2×C4⋊#11924003C211yesmaximal, characteristic, complemented
3C2×#17988388C211yesmaximal, characteristic, complemented
4C2×#17988387C211yesmaximal, characteristic, complemented
5#22610797C211yesmaximal, characteristic, complemented
6#22608022C211yesmaximal, characteristic, complemented
7C73×#1970C211yesmaximal, characteristic, complemented
8C22×D584C2211yescharacteristic
9C2×#14556532—22no—
10C2×#14556532—22no—
11C2×#14556532—22no—
12C22×#11924003C2211yescharacteristic
13C22×#11924003C2211yescharacteristic
14C2×#14556525C2211yescharacteristic
15C2×#14556513—21no—
16#17988489—21no—
17C4⋊#11924003—22no—
18#17988388—22no—
19#17988387—22no—
20C22×D8×C73C2211yescharacteristic
21C2×#107×C73C2211yescharacteristic
22C2×#102×C73—21no—
23C2×C4×C8×C73C2211yescharacteristic
24#390×C73—21no—
25C22×D292—21no—
26C2×D584—21no—
27C2×D584—21no—
28C2×D584—21no—
29C2×D584—21no—
30C2×D584—21no—
31C2×D584D412yes—
32C2×C4⋊Dic73—21no—
33C2×#11924005—41no—
34C2×#11924005—41no—
35#14556532—28no—
36C2×#11924003—21no—
37C2×#11924003—21no—
38C2×#11924003—21no—
39C2×#11924003—21no—
40C2×#11924003—21no—
41C2×#11924003D412yes—
42#14556525—21no—
43#14556525—21no—
44#14556513—42no—
45C22×D4×C73—21no—
46C2×D8×C73—21no—
47C2×D8×C73—21no—
48C2×D8×C73—21no—
49C2×D8×C73—21no—
50C2×D8×C73—21no—
51C2×D8×C73D412yes—
52C22×C8×C73D411yescharacteristic
53C22×C8×C73C2311yescharacteristic
54C2×C4⋊C4×C73—21no—
55C2×C22⋊C4×C73—41no—
56C2×C22⋊C4×C73—41no—
57C2×C42×C73D411yescharacteristic
58#107×C73—21no—
59#107×C73—21no—
60#102×C73—42no—
61C4×C8×C73—21no—
62C4×C8×C73—21no—
63C23×D73—41no—
64C2×D292—22no—
65C2×D292—41no—
66C2×D292—41no—
67C2×D292—41no—
68C2×D292—41no—
69C2×D292—41no—
70C22×Dic73—41no—
71D584—22no—
72D584—22no—
73D584—41no—
74D584—41no—
75C4⋊Dic73—41no—
76C4⋊Dic73—41no—
77#11924005—82no—
78#11924005—82no—
79#11924003—22no—
80#11924003—41no—
81C24×C73—41no—
82C2×D4×C73—22no—
83C2×D4×C73—41no—
84C2×D4×C73—41no—
85C2×D4×C73—41no—
86C2×D4×C73—41no—
87C2×D4×C73—41no—
88C22×C4×C73—41no—
89C22×C4×C73D811yescharacteristic
90C22×C4×C73D811yescharacteristic
91C22×C4×C73C2×D411yescharacteristic
92D8×C73—22no—
93D8×C73—22no—
94D8×C73—41no—
95D8×C73—41no—
96C2×C8×C73—21no—
97C2×C8×C73—21no—
98C2×C8×C73—21no—
99C2×C8×C73C2×D411yescharacteristic
100C2×C8×C73C2×D411yescharacteristic
101C2×C8×C73C2×D411yescharacteristic
102C2×C8×C73#4111yescharacteristic
103C2×C8×C73#4111yescharacteristic
104C2×C8×C73#4111yescharacteristic
105C4⋊C4×C73—41no—
106C4⋊C4×C73—41no—
107C22⋊C4×C73—82no—
108C22⋊C4×C73—82no—
109C42×C73—21no—
110C42×C73—21no—
111C23×C73—42no—
112C23×C73—81no—
113C23×C73—81no—
114C23×C73—81no—
115C23×C73—81no—
116C23×C73—81no—
117C23×C73—81no—
118C23×C73C2×D811yescharacteristic
119C22×D73—42no—
120C22×D73—81no—
121C22×D73—81no—
122C22×D73—81no—
123C22×D73—81no—
124C22×D73—81no—
125C22×D73—81no—
126D4×C73—42no—
127D4×C73—42no—
128D4×C73—81no—
129D4×C73—81no—
130C2×C4×C73—21no—
131C2×C4×C73—21no—
132C2×C4×C73—21no—
133C2×C4×C73—21no—
134C2×C4×C73—21no—
135C2×C4×C73—81no—
136C2×C4×C73—81no—
137C2×C4×C73—81no—
138C2×C4×C73D1612yescomplemented
139C2×C4×C73#12111yescharacteristic
140C2×C4×C73#12111yescharacteristic
141C2×C4×C73#12111yescharacteristic
142C2×C4×C73#13511yescharacteristic
143C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
144C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
145C2×Dic73—81no—
146C2×Dic73—81no—
147C2×Dic73—81no—
148D292—42no—
149D292—42no—
150D292—81no—
151D292—81no—
152C8×C73—41no—
153C8×C73#12011yescharacteristic
154C8×C73#12311yescharacteristic
155C8×C73#12311yescharacteristic
156C8×C73#12411yescharacteristic
157C22×C73—82no—
158C22×C73—82no—
159C22×C73—82no—
160C22×C73—161no—
161C22×C73—161no—
162C22×C73—161no—
163C22×C73—161no—
164C22×C73#45911yescharacteristic
165C22×C73#45911yescharacteristic
166C22×C73#46611yescharacteristic
167C22×C73C2×D1611yescharacteristic
168C22×C73#50811yescharacteristic
169C22×C73#50911yescharacteristic
170C22×C73#50911yescharacteristic
171C2×D73—82no—
172C2×D73—82no—
173C2×D73—82no—
174C2×D73—161no—
175C2×D73—161no—
176C2×D73—161no—
177C2×D73—161no—
178C4×C73—22no—
179C4×C73—41no—
180C4×C73—161no—
181C4×C73#39411yescharacteristic
182C4×C73#46311yescharacteristic
183C4×C73#46311yescharacteristic
184C4×C73#46911yescharacteristic
185Dic73—161no—
186#13448—731nomaximal, Sylow
187C2×C73—162no—
188C2×C73#205411yescharacteristic
189C2×C73#220611yescharacteristic
190C2×C73#220611yescharacteristic
191C2×C73#221011yescharacteristic
192C2×C73#221011yescharacteristic
193C2×C73#221511yescharacteristic
194C2×C73#221811yescharacteristic
195D73—162no—
196C22×D16—731no—
197C2×C4⋊C16—731no—
198C2×#357—731no—
199C2×#357—731no—
200#1970—731no—
201#1970D7311yescharacteristic, complemented
202#1380—731no—
203C73#1344811yescharacteristic, complemented, Sylow
204C22×D8—731no—
205C22×D8C2×D7311yescharacteristic
206C2×D16—1462no—
207C2×D16—1462no—
208C2×D16—1462no—
209C22×C16—731no—
210C22×C16—731no—
211C2×#107—731no—
212C2×#107C2×D7311yescharacteristic
213C2×#102—21no—
214C2×#102—1461no—
215C2×C4×C8C2×D7311yescharacteristic
216#390—21no—
217#390—1461no—
218C4⋊C16—1462no—
219#357—1462no—
220#357—1462no—
221C22×D4—21no—
222C22×D4—1461no—
223C2×D8—21no—
224C2×D8—21no—
225C2×D8—21no—
226C2×D8—21no—
227C2×D8—21no—
228C2×D8—732no—
229C2×D8—1461no—
230C2×D8—1461no—
231C2×D8—1461no—
232C2×D8—1461no—
233C2×D8—1461no—
234C2×D8D29212yes—
235C22×C8C22⋊D7311yescharacteristic
236C22×C8C22×D7311yescharacteristic
237C2×C4⋊C4—21no—
238C2×C4⋊C4—1461no—
239C2×C22⋊C4—41no—
240C2×C22⋊C4—41no—
241C2×C22⋊C4—2921no—
242C2×C22⋊C4—2921no—
243C2×C42C22⋊D7311yescharacteristic
244D16—1468no—
245C2×C16—732no—
246C2×C16—1461no—
247C2×C16—1461no—
248C2×C16—1461no—
249C2×C16—1461no—
250C2×C16—1461no—
251#107—21no—
252#107—21no—
253#107—1461no—
254#107—1461no—
255#102—42no—
256#102—2922no—
257C4×C8—21no—
258C4×C8—21no—
259C24—41no—
260C24—2921no—
261C2×D4—22no—
262C2×D4—41no—
263C2×D4—41no—
264C2×D4—41no—
265C2×D4—41no—
266C2×D4—41no—
267C2×D4—2921no—
268C2×D4—2921no—
269C2×D4—2921no—
270C2×D4—2921no—
271C2×D4—2921no—
272C2×D4—1462no—
273C22×C4—41no—
274C22×C4—2921no—
275C22×C4#1192401311yescharacteristic
276C22×C4#1192401311yescharacteristic
277C22×C4C2×C22⋊D7311yescharacteristic
278D8—22no—
279D8—22no—
280D8—41no—
281D8—41no—
282D8—2921no—
283D8—2921no—
284D8—1462no—
285D8—1462no—
286C2×C8—21no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8D4×D7311yescharacteristic
290C2×C8D4×D7311yescharacteristic
291C2×C8C2×D29211yescharacteristic
292C2×C8#1192402711yescharacteristic
293C2×C8#1192402711yescharacteristic
294C2×C8#1192402811yescharacteristic
295C4⋊C4—41no—
296C4⋊C4—41no—
297C4⋊C4—2921no—
298C4⋊C4—2921no—
299C22⋊C4—82no—
300C22⋊C4—82no—
301C22⋊C4—5842no—
302C22⋊C4—5842no—
303C42—21no—
304C42—21no—
305C16—2921no—
306C16—1462no—
307C23—42no—
308C23—81no—
309C23—81no—
310C23—81no—
311C23—81no—
312C23—81no—
313C23—81no—
314C23—2922no—
315C23—5841no—
316C23—5841no—
317C23—5841no—
318C23—5841no—
319C23—5841no—
320C23—5841no—
321C23C2×#1192401311yescharacteristic
322D4—42no—
323D4—42no—
324D4—81no—
325D4—81no—
326D4—2922no—
327D4—2922no—
328D4—5841no—
329D4—5841no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—21no—
334C2×C4—21no—
335C2×C4—81no—
336C2×C4—81no—
337C2×C4—81no—
338C2×C4—5841no—
339C2×C4—5841no—
340C2×C4—5841no—
341C2×C4#1455653212yescomplemented
342C2×C4#1455656211yescharacteristic
343C2×C4#1455656311yescharacteristic
344C2×C4#1455656511yescharacteristic
345C2×C4#1455661111yescharacteristic
346C2×C4#1455661611yescharacteristic
347C2×C4#1455661711yescharacteristic
348C8—41no—
349C8#1455656111yescharacteristic
350C8#1455657311yescharacteristic
351C8#1455657511yescharacteristic
352C8#1455657711yescharacteristic
353C22—82no—
354C22—82no—
355C22—82no—
356C22—161no—
357C22—161no—
358C22—161no—
359C22—161no—
360C22—5842no—
361C22—5842no—
362C22—5842no—
363C22—11681no—
364C22—11681no—
365C22—11681no—
366C22—11681no—
367C22#1798877911yescharacteristic
368C22#1798878211yescharacteristic
369C22#1798882111yescharacteristic
370C22C2×#1455653211yescharacteristic
371C22#1798901711yescharacteristic
372C22#1798902211yescharacteristic
373C22#1798902311yescharacteristic
374C4—22no—
375C4—41no—
376C4—161no—
377C4—11681no—
378C4#1798850311yescharacteristic
379C4#1798879911yescharacteristic
380C4#1798880211yescharacteristic
381C4#1798883811yescharacteristic
382C2—162no—
383C2—11682no—
384C2#2261124111yescharacteristic
385C2#2261196311yescharacteristic
386C2#2261196611yescharacteristic
387C2#2261198311yescharacteristic
388C2#2261198611yescharacteristic
389C2#2261201511yescharacteristic
390C2#2261203211yescharacteristic
subgroupG/H
centerC23C2×#11924013
commutator, cosocleC22×C8×C73C23
FrattiniC22×C8C22×D73
FittingC73×#1970C2
socleC23×C73C2×D8
prime radicalC22×#14556532C2
hypercenter#1970D73
hypocenterC73#13448
LCSG ▷ C22×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ #1970

Complements

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

NH ≅ G/Ntype
2. C2×C4⋊#11924003C2semidirect
3. C2×#17988388C2semidirect
4. C2×#17988387C2semidirect
5. #22610797C2semidirect
6. #22608022C2semidirect
7. C73×#1970C2semidirect
138. C2×C4×C73D16semidirect
201. #1970D73semidirect
203. C73#13448semidirect
341. C2×C4#14556532semidirect

Maximal subgroups

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

subgroupindex
C22×#145565322
C2×C4⋊#119240032
C2×#179883882
C2×#179883872
#226107972
#226080222
C73×#19702
#1344873