Finite Group Databasebeta

← #33005586

Subgroups — #33005586

Order 18688.

446 conjugacy classes of subgroups.

The subgroup lattice has 366 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556536C211yesmaximal, characteristic
2C2×#17988392C211yesmaximal, characteristic, complemented
3C2×#17988389C211yesmaximal, characteristic
4#22610797C211yesmaximal, characteristic
5#22610792C211yesmaximal, characteristic, complemented
6#22608023C211yesmaximal, characteristic, complemented
7C2×C4⋊C16×C73C211yesmaximal, characteristic, complemented
8C22×Dic292C2211yescharacteristic
9C22×D584C2211yescharacteristic
10C2×#14556536—22no—
11C2×#14556536—22no—
12C2×#14556536—22no—
13C2×#14556525C2211yescharacteristic
14C2×#14556525C2211yescharacteristic
15C2×#14556516—21no—
16C2×#14556513—21no—
17#17988493—21no—
18#17988489—21no—
19#17988392—22no—
20#17988389—22no—
21C22×C16×C73C2211yescharacteristic
22C22×C16×C73C2211yescharacteristic
23C2×C4×C8×C73C2211yescharacteristic
24C4⋊C16×C73—22no—
25C22×Dic146—21no—
26C22×D292—21no—
27C2×Dic292—21no—
28C2×Dic292—21no—
29C2×Dic292—21no—
30C2×Dic292—21no—
31C2×Dic292—21no—
32C2×Dic292D412yes—
33C2×D584—21no—
34C2×D584—21no—
35C2×D584—21no—
36C2×D584—21no—
37C2×D584—21no—
38C2×D584D412yes—
39C2×C4⋊Dic73—21no—
40C2×C4⋊Dic73—21no—
41C2×#11924005—41no—
42C2×#11924005—41no—
43#14556536—28no—
44#14556525—21no—
45#14556525—21no—
46#14556525—21no—
47#14556525—21no—
48#14556516—42no—
49#14556513—42no—
50#14556498—41no—
51#14556498—41no—
52C22×C8×C73D411yescharacteristic
53C22×C8×C73C2311yescharacteristic
54C2×C42×C73D411yescharacteristic
55C2×C16×C73—21no—
56C2×C16×C73—21no—
57C2×C16×C73—21no—
58C2×C16×C73—21no—
59C2×C16×C73—21no—
60C2×C16×C73D412yes—
61C4×C8×C73—21no—
62C4×C8×C73—21no—
63C23×D73—41no—
64C2×Dic146—22no—
65C2×Dic146—41no—
66C2×Dic146—41no—
67C2×Dic146—41no—
68C2×Dic146—41no—
69C2×Dic146—41no—
70C2×D292—22no—
71C2×D292—41no—
72C2×D292—41no—
73C2×D292—41no—
74C2×D292—41no—
75C2×D292—41no—
76C22×Dic73—41no—
77C22×Dic73—41no—
78C22×Dic73—41no—
79Dic292—22no—
80Dic292—22no—
81Dic292—41no—
82Dic292—41no—
83D584—22no—
84D584—22no—
85D584—41no—
86D584—41no—
87C4⋊Dic73—41no—
88C4⋊Dic73—41no—
89C4⋊Dic73—41no—
90C4⋊Dic73—41no—
91#11924005—82no—
92#11924005—82no—
93C22×C4×C73D811yescharacteristic
94C22×C4×C73D811yescharacteristic
95C22×C4×C73C2×D411yescharacteristic
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
105C42×C73—21no—
106C42×C73—21no—
107C16×C73—22no—
108C16×C73—41no—
109C23×C73C2×D811yescharacteristic
110C22×D73—42no—
111C22×D73—81no—
112C22×D73—81no—
113C22×D73—81no—
114C22×D73—81no—
115C22×D73—81no—
116C22×D73—81no—
117C2×C4×C73—21no—
118C2×C4×C73—21no—
119C2×C4×C73—21no—
120C2×C4×C73—21no—
121C2×C4×C73—21no—
122C2×C4×C73SD3212yescomplemented
123C2×C4×C73#12111yescharacteristic
124C2×C4×C73#12111yescharacteristic
125C2×C4×C73#12111yescharacteristic
126C2×C4×C73#13511yescharacteristic
127C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
128C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
129C2×Dic73—42no—
130C2×Dic73—81no—
131C2×Dic73—81no—
132C2×Dic73—81no—
133C2×Dic73—81no—
134C2×Dic73—81no—
135C2×Dic73—81no—
136C2×Dic73—81no—
137C2×Dic73—81no—
138D292—42no—
139D292—42no—
140D292—81no—
141D292—81no—
142Dic146—42no—
143Dic146—42no—
144Dic146—81no—
145Dic146—81no—
146C8×C73—41no—
147C8×C73#12011yescharacteristic
148C8×C73#12311yescharacteristic
149C8×C73#12311yescharacteristic
150C8×C73#12411yescharacteristic
151C22×C73#45911yescharacteristic
152C22×C73#45911yescharacteristic
153C22×C73#46611yescharacteristic
154C22×C73C2×SD3211yescharacteristic
155C22×C73#50811yescharacteristic
156C22×C73#50911yescharacteristic
157C22×C73#51011yescharacteristic
158C2×D73—82no—
159C2×D73—82no—
160C2×D73—82no—
161C2×D73—161no—
162C2×D73—161no—
163C2×D73—161no—
164C2×D73—161no—
165C4×C73—22no—
166C4×C73—41no—
167C4×C73#39411yescharacteristic
168C4×C73#46311yescharacteristic
169C4×C73#46311yescharacteristic
170C4×C73#46911yescharacteristic
171Dic73—82no—
172Dic73—161no—
173Dic73—161no—
174#13449—731nomaximal, Sylow
175C2×C73#205411yescharacteristic
176C2×C73#220711yescharacteristic
177C2×C73#220811yescharacteristic
178C2×C73#221011yescharacteristic
179C2×C73#221111yescharacteristic
180C2×C73#221711yescharacteristic
181C2×C73#222011yescharacteristic
182D73—162no—
183C22×SD32—731no—
184C2×C4⋊C16D7311yescharacteristic, complemented
185C2×#358—731no—
186C2×#357—731no—
187#1970—731no—
188#1969—731no—
189#1380—731no—
190C73#1344911yescharacteristic, complemented, Sylow
191C22×Q16—731no—
192C22×D8—731no—
193C2×SD32—1462no—
194C2×SD32—1462no—
195C2×SD32—1462no—
196C22×C16C2×D7311yescharacteristic
197C22×C16C2×D7311yescharacteristic
198C2×#107—731no—
199C2×#107—731no—
200C2×#103—1461no—
201C2×#102—1461no—
202C2×C4×C8C2×D7311yescharacteristic
203#391—1461no—
204#390—1461no—
205C4⋊C16—22no—
206#358—1462no—
207#357—1462no—
208C22×Q8—1461no—
209C22×D4—1461no—
210C2×Q16—732no—
211C2×Q16—1461no—
212C2×Q16—1461no—
213C2×Q16—1461no—
214C2×Q16—1461no—
215C2×Q16—1461no—
216C2×D8—732no—
217C2×D8—1461no—
218C2×D8—1461no—
219C2×D8—1461no—
220C2×D8—1461no—
221C2×D8—1461no—
222C22×C8D29211yescharacteristic
223C22×C8C22×D7311yescharacteristic
224C2×C4⋊C4—1461no—
225C2×C4⋊C4—1461no—
226C2×C22⋊C4—2921no—
227C2×C22⋊C4—2921no—
228C2×C42D29211yescharacteristic
229SD32—1468no—
230C2×C16—21no—
231C2×C16—21no—
232C2×C16—21no—
233C2×C16—21no—
234C2×C16—21no—
235C2×C16C22⋊D7312yes—
236#107—1461no—
237#107—1461no—
238#107—1461no—
239#107—1461no—
240#103—2922no—
241#102—2922no—
242C4×C8—21no—
243C4×C8—21no—
244#95—2921no—
245#95—2921no—
246C24—2921no—
247C2×Q8—2921no—
248C2×Q8—2921no—
249C2×Q8—2921no—
250C2×Q8—2921no—
251C2×Q8—2921no—
252C2×Q8—1462no—
253C2×D4—2921no—
254C2×D4—2921no—
255C2×D4—2921no—
256C2×D4—2921no—
257C2×D4—2921no—
258C2×D4—1462no—
259C22×C4—2921no—
260C22×C4—2921no—
261C22×C4—2921no—
262C22×C4D58411yescharacteristic
263C22×C4D58411yescharacteristic
264C22×C4C2×D29211yescharacteristic
265Q16—2921no—
266Q16—2921no—
267Q16—1462no—
268Q16—1462no—
269D8—2921no—
270D8—2921no—
271D8—1462no—
272D8—1462no—
273C2×C8—21no—
274C2×C8—21no—
275C2×C8—21no—
276C2×C8D4×D7311yescharacteristic
277C2×C8D4×D7311yescharacteristic
278C2×C8C2×C22⋊D7311yescharacteristic
279C2×C8#1192402811yescharacteristic
280C2×C8#1192402911yescharacteristic
281C2×C8#1192402911yescharacteristic
282C4⋊C4—2921no—
283C4⋊C4—2921no—
284C4⋊C4—2921no—
285C4⋊C4—2921no—
286C22⋊C4—5842no—
287C22⋊C4—5842no—
288C42—21no—
289C42—21no—
290C16—22no—
291C16—41no—
292C23—2922no—
293C23—5841no—
294C23—5841no—
295C23—5841no—
296C23—5841no—
297C23—5841no—
298C23—5841no—
299C23C2×D58411yescharacteristic
300Q8—2922no—
301Q8—2922no—
302Q8—5841no—
303Q8—5841no—
304D4—2922no—
305D4—2922no—
306D4—5841no—
307D4—5841no—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—21no—
313C2×C4—2922no—
314C2×C4—5841no—
315C2×C4—5841no—
316C2×C4—5841no—
317C2×C4—5841no—
318C2×C4—5841no—
319C2×C4—5841no—
320C2×C4—5841no—
321C2×C4—5841no—
322C2×C4#1455653612yescomplemented
323C2×C4#1455656511yescharacteristic
324C2×C4#1455656611yescharacteristic
325C2×C4#1455656611yescharacteristic
326C2×C4#1455661311yescharacteristic
327C2×C4#1455661911yescharacteristic
328C2×C4#1455661911yescharacteristic
329C8—41no—
330C8#1455655911yescharacteristic
331C8#1455657611yescharacteristic
332C8#1455657611yescharacteristic
333C8#1455658011yescharacteristic
334C22—5842no—
335C22—5842no—
336C22—5842no—
337C22—11681no—
338C22—11681no—
339C22—11681no—
340C22—11681no—
341C22#1798878311yescharacteristic
342C22#1798878311yescharacteristic
343C22#1798882311yescharacteristic
344C22C2×#1455653611yescharacteristic
345C22#1798901911yescharacteristic
346C22#1798902511yescharacteristic
347C22#1798903011yescharacteristic
348C4—22no—
349C4—41no—
350C4—5842no—
351C4—11681no—
352C4—11681no—
353C4#1798850411yescharacteristic
354C4#1798880311yescharacteristic
355C4#1798880311yescharacteristic
356C4#1798884011yescharacteristic
357C2—11682no—
358C2#2261124211yescharacteristic
359C2#2261197211yescharacteristic
360C2#2261197711yescharacteristic
361C2#2261198711yescharacteristic
362C2#2261199411yescharacteristic
363C2#2261202711yescharacteristic
364C2#2261204411yescharacteristic
subgroupG/H
centerC23C2×D584
commutator, cosocleC22×C8×C73C23
FrattiniC22×C8C22×D73
FittingC2×C4⋊C16×C73C2
socleC23×C73C2×D8
prime radicalC22×D584C22
hypercenterC2×C4⋊C16D73
hypocenterC73#13449
LCSG ▷ C22×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×C8 ◁ C2×C4⋊C16

Complements

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

NH ≅ G/Ntype
2. C2×#17988392C2semidirect
5. #22610792C2semidirect
6. #22608023C2semidirect
7. C2×C4⋊C16×C73C2semidirect
122. C2×C4×C73SD32semidirect
184. C2×C4⋊C16D73semidirect
190. C73#13449semidirect
322. C2×C4#14556536semidirect

Maximal subgroups

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

subgroupindex
C22×#145565362
C2×#179883922
C2×#179883892
#226107972
#226107922
#226080232
C2×C4⋊C16×C732
#1344973