Finite Group Databasebeta

← #33005589

Subgroups — #33005589

Order 18688.

410 conjugacy classes of subgroups.

The subgroup lattice has 340 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#14556537C211yesmaximal, characteristic
2C2×#17988405C211yesmaximal, characteristic
3C2×#17988392C211yesmaximal, characteristic
4#22610793C211yesmaximal, characteristic
5#22610790C211yesmaximal, characteristic
6#22608022C211yesmaximal, characteristic
7C2×#358×C73C211yesmaximal, characteristic
8C22×Dic292C2211yescharacteristic
9C2×#14556537—22no—
10C2×#14556537—22no—
11C2×#14556537—22no—
12C22×#11924003C2211yescharacteristic
13C2×#14556525C2211yescharacteristic
14C2×#14556515—21no—
15C2×#14556514—21no—
16C2×C8×Dic73C2211yescharacteristic
17#17988494—21no—
18#17988492—21no—
19#17988405—22no—
20#17988392—22no—
21C22×Q16×C73C2211yescharacteristic
22C22×C16×C73C2211yescharacteristic
23C2×#107×C73C2211yescharacteristic
24#358×C73—22no—
25C22×Dic146—21no—
26C2×Dic292—21no—
27C2×Dic292—21no—
28C2×Dic292—21no—
29C2×Dic292—21no—
30C2×Dic292—21no—
31C2×Dic292D412yes—
32C22×#10596831D411yescharacteristic
33C2×C4⋊Dic73—21no—
34C2×C4×Dic73D411yescharacteristic
35#14556537—28no—
36C2×#11924003—21no—
37C2×#11924003—21no—
38C2×#11924003D412yes—
39#14556525—21no—
40#14556525—21no—
41#14556515—42no—
42#14556514—42no—
43C8×Dic73—21no—
44C8×Dic73—21no—
45#14556498—41no—
46#14556498—41no—
47#14556498—41no—
48#14556498—41no—
49C22×Q8×C73—21no—
50C2×Q16×C73—21no—
51C2×Q16×C73—21no—
52C2×Q16×C73—21no—
53C2×Q16×C73—21no—
54C2×Q16×C73—21no—
55C2×Q16×C73D412yes—
56C22×C8×C73C2311yescharacteristic
57C2×C4⋊C4×C73—21no—
58C2×C16×C73—21no—
59C2×C16×C73—21no—
60C2×C16×C73—21no—
61#107×C73—21no—
62#107×C73—21no—
63C2×Dic146—22no—
64C2×Dic146—41no—
65C2×Dic146—41no—
66C2×Dic146—41no—
67C2×Dic146—41no—
68C2×Dic146—41no—
69C22×Dic73—41no—
70C22×Dic73—41no—
71C22×Dic73D811yescharacteristic
72C22×Dic73D811yescharacteristic
73Dic292—22no—
74Dic292—22no—
75Dic292—41no—
76Dic292—41no—
77C2×#10596831—21no—
78C2×#10596831—21no—
79C2×#10596831—21no—
80C4⋊Dic73—41no—
81C4⋊Dic73—41no—
82C4×Dic73—21no—
83C4×Dic73—21no—
84#11924003—22no—
85C2×Q8×C73—22no—
86C2×Q8×C73—41no—
87C2×Q8×C73—41no—
88C2×Q8×C73—41no—
89C2×Q8×C73—41no—
90C2×Q8×C73—41no—
91C22×C4×C73—41no—
92C22×C4×C73—41no—
93C22×C4×C73C2×D411yescharacteristic
94Q16×C73—22no—
95Q16×C73—22no—
96Q16×C73—41no—
97Q16×C73—41no—
98C2×C8×C73C2×D411yescharacteristic
99C2×C8×C73C2×D411yescharacteristic
100C2×C8×C73C2×D411yescharacteristic
101C2×C8×C73#4111yescharacteristic
102C2×C8×C73#4111yescharacteristic
103C2×C8×C73#4111yescharacteristic
104C4⋊C4×C73—41no—
105C4⋊C4×C73—41no—
106C16×C73—41no—
107C23×C73C2×D811yescharacteristic
108Q8×C73—42no—
109Q8×C73—42no—
110Q8×C73—81no—
111Q8×C73—81no—
112C2×C4×C73—42no—
113C2×C4×C73—81no—
114C2×C4×C73—81no—
115C2×C4×C73—81no—
116C2×C4×C73—81no—
117C2×C4×C73—81no—
118C2×C4×C73#12111yescharacteristic
119C2×C4×C73#12111yescharacteristic
120C2×C4×C73#12111yescharacteristic
121C2×C4×C73#13511yescharacteristic
122C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
123C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
124C2×Dic73—21no—
125C2×Dic73—21no—
126C2×Dic73—21no—
127C2×Dic73—21no—
128C2×Dic73—21no—
129C2×Dic73—42no—
130C2×Dic73—81no—
131C2×Dic73—81no—
132C2×Dic73—81no—
133C2×Dic73—81no—
134C2×Dic73—81no—
135C2×Dic73Q3212yescomplemented
136Dic146—42no—
137Dic146—42no—
138Dic146—81no—
139Dic146—81no—
140C8×C73#12011yescharacteristic
141C8×C73#12311yescharacteristic
142C8×C73#12311yescharacteristic
143C8×C73#12411yescharacteristic
144#10596831—41no—
145C22×C73#45911yescharacteristic
146C22×C73#45911yescharacteristic
147C22×C73#46611yescharacteristic
148C22×C73C2×Q3211yescharacteristic
149C22×C73#50811yescharacteristic
150C22×C73#51011yescharacteristic
151C22×C73#51011yescharacteristic
152C4×C73—82no—
153C4×C73—161no—
154C4×C73#39411yescharacteristic
155C4×C73#46311yescharacteristic
156C4×C73#46311yescharacteristic
157C4×C73#46911yescharacteristic
158Dic73—22no—
159Dic73—41no—
160Dic73—82no—
161Dic73—161no—
162#13450—731nomaximal, Sylow
163C2×C73#205411yescharacteristic
164C2×C73#220911yescharacteristic
165C2×C73#220911yescharacteristic
166C2×C73#221111yescharacteristic
167C2×C73#221111yescharacteristic
168C2×C73#221611yescharacteristic
169C2×C73#221911yescharacteristic
170C22×Q32—731no—
171C2×C4⋊C16—731no—
172C2×#358—731no—
173C2×#358D7311yescharacteristic
174#1969—731no—
175#1969—731no—
176#1380—731no—
177C73#1345011yescharacteristic, complemented, Sylow
178C22×Q16—731no—
179C22×Q16C2×D7311yescharacteristic
180C2×Q32—1462no—
181C2×Q32—1462no—
182C2×Q32—1462no—
183C22×C16—731no—
184C22×C16C2×D7311yescharacteristic
185C2×#107—731no—
186C2×#107C2×D7311yescharacteristic
187C2×#103—1461no—
188C2×#103—1461no—
189C2×C4×C8—731no—
190#391—1461no—
191#391—1461no—
192C4⋊C16—1462no—
193#358—22no—
194#358—1462no—
195C22×Q8—21no—
196C22×Q8—1461no—
197C2×Q16—21no—
198C2×Q16—21no—
199C2×Q16—21no—
200C2×Q16—21no—
201C2×Q16—21no—
202C2×Q16—732no—
203C2×Q16—1461no—
204C2×Q16—1461no—
205C2×Q16—1461no—
206C2×Q16—1461no—
207C2×Q16—1461no—
208C2×Q16C22⋊D7312yes—
209C22×C8—731no—
210C22×C8C22×D7311yescharacteristic
211C2×C4⋊C4—21no—
212C2×C4⋊C4—1461no—
213C2×C42—731no—
214Q32—1468no—
215C2×C16—21no—
216C2×C16—21no—
217C2×C16—21no—
218C2×C16—732no—
219C2×C16—1461no—
220C2×C16—1461no—
221#107—21no—
222#107—21no—
223#107—1461no—
224#107—1461no—
225#103—2922no—
226#103—2922no—
227C4×C8—1461no—
228C4×C8—1461no—
229#95—2921no—
230#95—2921no—
231#95—2921no—
232#95—2921no—
233C2×Q8—22no—
234C2×Q8—41no—
235C2×Q8—41no—
236C2×Q8—41no—
237C2×Q8—41no—
238C2×Q8—41no—
239C2×Q8—2921no—
240C2×Q8—2921no—
241C2×Q8—2921no—
242C2×Q8—2921no—
243C2×Q8—2921no—
244C2×Q8—1462no—
245C22×C4—41no—
246C22×C4—41no—
247C22×C4—2921no—
248C22×C4—2921no—
249C22×C4—731no—
250C22×C4—731no—
251C22×C4D4×D7311yescharacteristic
252Q16—22no—
253Q16—22no—
254Q16—41no—
255Q16—41no—
256Q16—2921no—
257Q16—2921no—
258Q16—1462no—
259Q16—1462no—
260C2×C8—1461no—
261C2×C8—1461no—
262C2×C8—1461no—
263C2×C8D4×D7311yescharacteristic
264C2×C8D4×D7311yescharacteristic
265C2×C8C2×C22⋊D7311yescharacteristic
266C2×C8#1192402711yescharacteristic
267C2×C8#1192402811yescharacteristic
268C2×C8#1192402811yescharacteristic
269C4⋊C4—41no—
270C4⋊C4—41no—
271C4⋊C4—2921no—
272C4⋊C4—2921no—
273C42—1461no—
274C42—1461no—
275C16—41no—
276C16—1462no—
277C23D8×D7311yescharacteristic
278Q8—42no—
279Q8—42no—
280Q8—81no—
281Q8—81no—
282Q8—2922no—
283Q8—2922no—
284Q8—5841no—
285Q8—5841no—
286C2×C4—42no—
287C2×C4—81no—
288C2×C4—81no—
289C2×C4—81no—
290C2×C4—81no—
291C2×C4—81no—
292C2×C4—2922no—
293C2×C4—5841no—
294C2×C4—5841no—
295C2×C4—5841no—
296C2×C4—5841no—
297C2×C4—5841no—
298C2×C4—732no—
299C2×C4—1461no—
300C2×C4—1461no—
301C2×C4—1461no—
302C2×C4—1461no—
303C2×C4—1461no—
304C2×C4#1455656311yescharacteristic
305C2×C4#1455656411yescharacteristic
306C2×C4#1455656411yescharacteristic
307C2×C4#1455661211yescharacteristic
308C2×C4#1455661511yescharacteristic
309C2×C4#1455661811yescharacteristic
310C8—2921no—
311C8#1455655911yescharacteristic
312C8#1455657311yescharacteristic
313C8#1455657411yescharacteristic
314C8#1455657711yescharacteristic
315C22#1798878011yescharacteristic
316C22#1798878111yescharacteristic
317C22#1798882211yescharacteristic
318C22Q32×D7311yescharacteristic
319C22#1798901811yescharacteristic
320C22#1798902611yescharacteristic
321C22#1798902911yescharacteristic
322C4—82no—
323C4—161no—
324C4—2921no—
325C4—5842no—
326C4—11681no—
327C4—1462no—
328C4#1798850211yescharacteristic
329C4#1798880111yescharacteristic
330C4#1798880411yescharacteristic
331C4#1798883911yescharacteristic
332C2#2261124011yescharacteristic
333C2#2261197911yescharacteristic
334C2#2261198011yescharacteristic
335C2#2261199111yescharacteristic
336C2#2261199611yescharacteristic
337C2#2261202111yescharacteristic
338C2#2261203811yescharacteristic
subgroupG/H
centerC23D8×D73
commutator, cosocleC22×C8×C73C23
FrattiniC22×C8C22×D73
FittingC2×#358×C73C2
socle, prime radicalC23×C73C2×D8
hypercenterC2×#358D73
hypocenterC73#13450
LCSG ▷ C22×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8 ◁ C2×#358

Complements

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

NH ≅ G/Ntype
135. C2×Dic73Q32semidirect
177. C73#13450semidirect

Maximal subgroups

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

subgroupindex
C22×#145565372
C2×#179884052
C2×#179883922
#226107932
#226107902
#226080222
C2×#358×C732
#1345073