Finite Group Databasebeta

← #33005139

Subgroups — #33005139

Order 18688.

498 conjugacy classes of subgroups.

The subgroup lattice has 396 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988823C211yesmaximal, characteristic
2C2×#17988412C211yesmaximal, characteristic, complemented
3C2×#17988387C211yesmaximal, characteristic, complemented
4C2×#17988387C211yesmaximal, characteristic, complemented
5C2×C22⋊#11924003C211yesmaximal, characteristic, complemented
6#22608022C211yesmaximal, characteristic, complemented
7C73×#1808C211yesmaximal, characteristic, complemented
8C22×D584C2211yescharacteristic
9C2×#14556565—21no—
10C22×#11924003C2211yescharacteristic
11C22×#11924003C2211yescharacteristic
12#17988823—22no—
13#17988823—22no—
14C2×#14556525C2211yescharacteristic
15C2×#14556513—21no—
16#17988412—22no—
17#17988387—22no—
18#17988387—22no—
19C22⋊#11924003—22no—
20C23×C8×C73C2211yescharacteristic
21C2×#107×C73C2211yescharacteristic
22C2×#107×C73C2211yescharacteristic
23#380×C73—21no—
24#340×C73—21no—
25C22×D292—21no—
26C22×C22⋊D73—41no—
27C2×D584—21no—
28C2×D584—21no—
29C2×D584—21no—
30C2×D584—21no—
31C2×D584—21no—
32C2×D584D412yes—
33#14556565—24no—
34#14556565—42no—
35C2×C4⋊Dic73—21no—
36C2×#11924005—41no—
37C2×#11924003—21no—
38C2×#11924003—21no—
39C2×#11924003—21no—
40C2×#11924003—21no—
41C2×#11924003—21no—
42C2×#11924003D412yescomplemented
43#14556525—21no—
44#14556525D412yes—
45#14556513—24no—
46C23×C4×C73D411yescharacteristic
47C22×C8×C73—21no—
48C22×C8×C73—21no—
49C22×C8×C73—21no—
50C22×C8×C73—21no—
51C22×C8×C73—21no—
52C22×C8×C73—21no—
53C22×C8×C73D411yescharacteristic
54C22×C8×C73C2311yescharacteristic
55C2×C4⋊C4×C73—21no—
56C2×C4⋊C4×C73—21no—
57C2×C22⋊C4×C73—41no—
58#107×C73—21no—
59#107×C73—21no—
60#107×C73—21no—
61#107×C73—21no—
62#95×C73—41no—
63C23×D73—41no—
64C2×D292—22no—
65C2×D292—41no—
66C2×D292—41no—
67C2×D292—41no—
68C2×D292—41no—
69C2×D292—41no—
70C2×C22⋊D73—44no—
71C2×C22⋊D73—82no—
72C2×C22⋊D73—82no—
73C22×Dic73—41no—
74D584—22no—
75D584—22no—
76D584—41no—
77D584—41no—
78C4⋊Dic73—22no—
79C4⋊Dic73—41no—
80#11924005—44no—
81#11924003—22no—
82#11924003—41no—
83C24×C73D811yescharacteristic
84C22×C4×C73—21no—
85C22×C4×C73—21no—
86C22×C4×C73—21no—
87C22×C4×C73—21no—
88C22×C4×C73—21no—
89C22×C4×C73—21no—
90C22×C4×C73—41no—
91C22×C4×C73—41no—
92C22×C4×C73D811yescharacteristic
93C22×C4×C73C2×D411yescharacteristic
94C2×C8×C73—21no—
95C2×C8×C73—21no—
96C2×C8×C73—21no—
97C2×C8×C73—41no—
98C2×C8×C73—41no—
99C2×C8×C73—41no—
100C2×C8×C73—41no—
101C2×C8×C73C2×D411yescharacteristic
102C2×C8×C73C2×D411yescharacteristic
103C2×C8×C73C2×D411yescharacteristic
104C2×C8×C73#4111yescharacteristic
105C2×C8×C73#4111yescharacteristic
106C2×C8×C73#4111yescharacteristic
107C4⋊C4×C73—41no—
108C4⋊C4×C73—41no—
109C4⋊C4×C73—41no—
110C4⋊C4×C73—41no—
111C22⋊C4×C73—82no—
112C23×C73—21no—
113C23×C73—21no—
114C23×C73—21no—
115C23×C73—21no—
116C23×C73—21no—
117C23×C73—21no—
118C23×C73D1612yes—
119C23×C73C2×D811yescharacteristic
120C22×D73—42no—
121C22×D73—81no—
122C22×D73—81no—
123C22×D73—81no—
124C22×D73—81no—
125C22×D73—81no—
126C22×D73—81no—
127C2×C4×C73—21no—
128C2×C4×C73—21no—
129C2×C4×C73—21no—
130C2×C4×C73—41no—
131C2×C4×C73—41no—
132C2×C4×C73—41no—
133C2×C4×C73—41no—
134C2×C4×C73—81no—
135C2×C4×C73—81no—
136C2×C4×C73—81no—
137C2×C4×C73—81no—
138C2×C4×C73—81no—
139C2×C4×C73—81no—
140C2×C4×C73#12011yescharacteristic
141C2×C4×C73#12111yescharacteristic
142C2×C4×C73#12311yescharacteristic
143C2×C4×C73#13511yescharacteristic
144C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
145C2×C4×C73#13711yescharacteristic
146C22⋊D73—88no—
147C2×Dic73—42no—
148C2×Dic73—81no—
149C2×Dic73—81no—
150D292—42no—
151D292—42no—
152D292—81no—
153D292—81no—
154C8×C73—41no—
155C8×C73#12111yescharacteristic
156C8×C73#12111yescharacteristic
157C8×C73#12311yescharacteristic
158C8×C73#12411yescharacteristic
159C22×C73—22no—
160C22×C73—22no—
161C22×C73—22no—
162C22×C73—41no—
163C22×C73—41no—
164C22×C73—41no—
165C22×C73—41no—
166C22×C73#44711yescharacteristic
167C22×C73#46611yescharacteristic
168C22×C73#48011yescharacteristic
169C22×C73C2×D1611yescharacteristic
170C22×C73#50811yescharacteristic
171C22×C73#50911yescharacteristic
172C22×C73#51011yescharacteristic
173C2×D73—82no—
174C2×D73—82no—
175C2×D73—82no—
176C2×D73—161no—
177C2×D73—161no—
178C2×D73—161no—
179C2×D73—161no—
180C4×C73—41no—
181C4×C73—161no—
182C4×C73—161no—
183C4×C73#39411yescharacteristic
184C4×C73#45211yescharacteristic
185C4×C73#46811yescharacteristic
186C4×C73#48211yescharacteristic
187Dic73—82no—
188#13380—731nomaximal, Sylow
189C2×C73—42no—
190C2×C73#203311yescharacteristic
191C2×C73#218411yescharacteristic
192C2×C73#218911yescharacteristic
193C2×C73#221511yescharacteristic
194C2×C73#222011yescharacteristic
195C2×C73#223211yescharacteristic
196C2×C73#223411yescharacteristic
197D73—162no—
198C2×#466—731no—
199C2×#366—731no—
200C2×#357—731no—
201C2×#357—731no—
202C2×C22⋊C16—731no—
203#1808D7311yescharacteristic, complemented
204#1380—731no—
205C73#1338011yescharacteristic, complemented, Sylow
206C22×D8—731no—
207C23×C8C2×D7311yescharacteristic
208C2×#121—1461no—
209C22×C16—731no—
210C22×C16—731no—
211#466—1462no—
212#466—1462no—
213C2×#107—731no—
214C2×#107C2×D7311yescharacteristic
215C2×#107C2×D7311yescharacteristic
216C2×#102—1461no—
217#380—21no—
218#366—1462no—
219#357—1462no—
220#357—1462no—
221C22⋊C16—1462no—
222#340—21no—
223C22×D4—2921no—
224C22×D4—1461no—
225C23×C4C22⋊D7311yescharacteristic
226C2×D8—732no—
227C2×D8—1461no—
228C2×D8—1461no—
229C2×D8—1461no—
230C2×D8—1461no—
231C2×D8—1461no—
232C22×C8—21no—
233C22×C8—21no—
234C22×C8—21no—
235C22×C8—21no—
236C22×C8—21no—
237C22×C8—21no—
238C22×C8C22⋊D7311yescharacteristic
239C22×C8C22×D7311yescharacteristic
240#121—2922no—
241#121—1464no—
242C2×C4⋊C4—21no—
243C2×C4⋊C4—21no—
244C2×C4⋊C4—1461no—
245C2×C22⋊C4—41no—
246C2×C22⋊C4—2921no—
247C2×C16—732no—
248C2×C16—1461no—
249C2×C16—1461no—
250C2×C16—1461no—
251C2×C16—1461no—
252C2×C16—1461no—
253#107—21no—
254#107—21no—
255#107—21no—
256#107—21no—
257#107—732no—
258#107—1461no—
259#102—1464no—
260#95—41no—
261C24—2921no—
262C24#1192401311yescharacteristic
263C2×D4—2924no—
264C2×D4—2921no—
265C2×D4—2921no—
266C2×D4—2921no—
267C2×D4—2921no—
268C2×D4—2921no—
269C2×D4—5842no—
270C2×D4—5842no—
271C2×D4—1462no—
272C22×C4—21no—
273C22×C4—21no—
274C22×C4—21no—
275C22×C4—21no—
276C22×C4—21no—
277C22×C4—21no—
278C22×C4—41no—
279C22×C4—41no—
280C22×C4—2921no—
281C22×C4#1192401311yescharacteristic
282C22×C4C2×C22⋊D7311yescharacteristic
283D8—2921no—
284D8—2921no—
285D8—1462no—
286D8—1462no—
287C2×C8—21no—
288C2×C8—21no—
289C2×C8—21no—
290C2×C8—41no—
291C2×C8—41no—
292C2×C8—41no—
293C2×C8—41no—
294C2×C8D4×D7311yescharacteristic
295C2×C8D4×D7311yescharacteristic
296C2×C8D4×D7311yescharacteristic
297C2×C8#1192402711yescharacteristic
298C2×C8#1192402811yescharacteristic
299C2×C8#1192402811yescharacteristic
300C4⋊C4—41no—
301C4⋊C4—41no—
302C4⋊C4—41no—
303C4⋊C4—41no—
304C4⋊C4—2921no—
305C4⋊C4—1462no—
306C22⋊C4—82no—
307C22⋊C4—2924no—
308C16—2921no—
309C16—1462no—
310C23—21no—
311C23—21no—
312C23—21no—
313C23—21no—
314C23—21no—
315C23—21no—
316C23—2922no—
317C23—5841no—
318C23—5841no—
319C23—5841no—
320C23—5841no—
321C23—5841no—
322C23—5841no—
323C23#1455653212yes—
324C23C2×#1192401311yescharacteristic
325D4—2922no—
326D4—2922no—
327D4—5848no—
328D4—5841no—
329D4—5841no—
330C2×C4—21no—
331C2×C4—21no—
332C2×C4—21no—
333C2×C4—41no—
334C2×C4—41no—
335C2×C4—41no—
336C2×C4—41no—
337C2×C4—81no—
338C2×C4—81no—
339C2×C4—81no—
340C2×C4—81no—
341C2×C4—81no—
342C2×C4—81no—
343C2×C4—2922no—
344C2×C4—5841no—
345C2×C4—5841no—
346C2×C4#1455655911yescharacteristic
347C2×C4#1455656311yescharacteristic
348C2×C4#1455657411yescharacteristic
349C2×C4#1455661111yescharacteristic
350C2×C4#1455661611yescharacteristic
351C2×C4#1455662211yescharacteristic
352C8—41no—
353C8#1455656411yescharacteristic
354C8#1455656411yescharacteristic
355C8#1455657311yescharacteristic
356C8#1455657711yescharacteristic
357C22—22no—
358C22—22no—
359C22—22no—
360C22—41no—
361C22—41no—
362C22—41no—
363C22—41no—
364C22—5842no—
365C22—5842no—
366C22—5842no—
367C22—11681no—
368C22—11681no—
369C22—11681no—
370C22—11681no—
371C22#1798872011yescharacteristic
372C22#1798882111yescharacteristic
373C22#1798890011yescharacteristic
374C22C2×#1455653211yescharacteristic
375C22#1798901711yescharacteristic
376C22#1798902211yescharacteristic
377C22#1798902811yescharacteristic
378C4—41no—
379C4—161no—
380C4—161no—
381C4—5842no—
382C4#1798850211yescharacteristic
383C4#1798874711yescharacteristic
384C4#1798883511yescharacteristic
385C4#1798891111yescharacteristic
386C2—42no—
387C2—11682no—
388C2#2261111311yescharacteristic
389C2#2261184211yescharacteristic
390C2#2261186911yescharacteristic
391C2#2261201511yescharacteristic
392C2#2261204611yescharacteristic
393C2#2261211111yescharacteristic
394C2#2261212211yescharacteristic
subgroupG/H
centerC23C2×#11924013
commutator, cosocleC22×C8×C73C23
FrattiniC22×C8C22×D73
FittingC73×#1808C2
socleC23×C73C2×D8
prime radicalC2×#17988823C2
hypercenter#1808D73
hypocenterC73#13380
LCSG ▷ C22×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C23×C4 ◁ C23×C8 ◁ #1808

Complements

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

NH ≅ G/Ntype
2. C2×#17988412C2semidirect
3. C2×#17988387C2semidirect
4. C2×#17988387C2semidirect
5. C2×C22⋊#11924003C2semidirect
6. #22608022C2semidirect
7. C73×#1808C2semidirect
42. C2×#11924003D4semidirect
203. #1808D73semidirect
205. C73#13380semidirect

Maximal subgroups

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

subgroupindex
C2×#179888232
C2×#179884122
C2×#179883872
C2×C22⋊#119240032
#226080222
C73×#18082
#1338073