Finite Group Databasebeta

← #32989650

Subgroups — #32989650

Order 18688.

376 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 376 conjugacy classes of subgroups — too many to draw. Only its 97 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988883C211yesmaximal, characteristic
2#22609924C211yesmaximal, characteristic
3#22608617C211yesmaximal, characteristic
4#22608611C211yesmaximal, characteristic
5#22608325C211yesmaximal, characteristic
6#22607828C211yesmaximal, characteristic
7C73×#1570C211yesmaximal, characteristic
8C2×#14556591C2211yescharacteristic
9C2×C4×Dic146C2211yescharacteristic
10#17988883—22no—
11#17988883—22no—
12#17988640C2211yescharacteristic
13C2×#14556525—21no—
14#17988611C2211yescharacteristic
15C2×#14556516—21no—
16C2×#14556509—21no—
17#17988355—21no—
18#17988335—22no—
19#17988332—22no—
20#17988317—22no—
21#431×C73C2211yescharacteristic
22#423×C73C2211yescharacteristic
23C2×C4⋊C8×C73C2211yescharacteristic
24#334×C73—22no—
25C22×Dic146—21no—
26C22×Dic146D411yescharacteristic
27C2×#11924012—21no—
28#14556591—21no—
29#14556591—21no—
30#14556591—21no—
31#14556591D412yes—
32C4×Dic146—21no—
33C4×Dic146—21no—
34C4×Dic146—21no—
35C4×Dic146—21no—
36C2×C4⋊Dic73—21no—
37C2×C4⋊Dic73—21no—
38C2×C4⋊Dic73D411yescharacteristic
39C2×#11924007—21no—
40C2×C4×Dic73—21no—
41#14556525—24no—
42C4⋊#10596831—21no—
43C4⋊#10596831—21no—
44C4⋊#10596831—21no—
45#14556516—24no—
46#14556509—42no—
47C22⋊#10596831—21no—
48C4×#10596831—21no—
49C2×M16×C73—21no—
50C22×C8×C73—21no—
51C2×C42×C73C2311yescharacteristic
52C4⋊C8×C73—21no—
53C4⋊C8×C73—21no—
54C4⋊C8×C73—21no—
55C4⋊C8×C73D412yes—
56C4⋊C8×C73D412yes—
57C22⋊C8×C73—21no—
58C4×C8×C73—21no—
59C2×Dic146—21no—
60C2×Dic146—21no—
61C2×Dic146—21no—
62C2×Dic146—21no—
63C2×Dic146—21no—
64C2×Dic146—22no—
65C2×Dic146—41no—
66C2×Dic146—82no—
67C2×Dic146SD1612yes—
68C22×Dic73—21no—
69C22×Dic73—21no—
70C22×Dic73—41no—
71#11924012—41no—
72#11924012—41no—
73C2×#10596831—41no—
74C2×#10596831—41no—
75C4⋊Dic73—22no—
76C4⋊Dic73—21no—
77C4⋊Dic73—21no—
78C4⋊Dic73—22no—
79C4⋊Dic73—41no—
80C4⋊Dic73—41no—
81#11924007—41no—
82#11924007—41no—
83C4×Dic73—41no—
84C4×Dic73—41no—
85C22×C4×C73C2×D411yescharacteristic
86C22×C4×C73#4111yescharacteristic
87C22×C4×C73#4111yescharacteristic
88M16×C73—41no—
89M16×C73—41no—
90C2×C8×C73—22no—
91C2×C8×C73—22no—
92C2×C8×C73—41no—
93C2×C8×C73—41no—
94C2×C8×C73—41no—
95C42×C73C2×D411yescharacteristic
96C42×C73C2×D411yescharacteristic
97C42×C73C2×D411yescharacteristic
98C42×C73#4111yescharacteristic
99C23×C73#12311yescharacteristic
100C2×C4×C73—22no—
101C2×C4×C73—41no—
102C2×C4×C73#12011yescharacteristic
103C2×C4×C73#12111yescharacteristic
104C2×C4×C73#12111yescharacteristic
105C2×C4×C73#12111yescharacteristic
106C2×C4×C73#12311yescharacteristic
107C2×C4×C73#12411yescharacteristic
108C2×C4×C73C2×SD1611yescharacteristic
109C2×C4×C73#13511yescharacteristic
110C2×C4×C73#13711yescharacteristic
111C2×C4×C73#13711yescharacteristic
112C2×Dic73—22no—
113C2×Dic73—41no—
114C2×Dic73—41no—
115C2×Dic73—41no—
116C2×Dic73—42no—
117C2×Dic73—82no—
118C2×Dic73—81no—
119Dic146—22no—
120Dic146—22no—
121Dic146—41no—
122Dic146—41no—
123Dic146—82no—
124Dic146—82no—
125C8×C73—42no—
126C8×C73—42no—
127C8×C73—81no—
128#10596831—81no—
129#10596831—81no—
130C22×C73—21no—
131C22×C73—21no—
132C22×C73#39411yescharacteristic
133C22×C73#48311yescharacteristic
134C22×C73#48511yescharacteristic
135C4×C73—21no—
136C4×C73—21no—
137C4×C73—21no—
138C4×C73#44811yescharacteristic
139C4×C73#45211yescharacteristic
140C4×C73#46511yescharacteristic
141C4×C73#47011yescharacteristic
142C4×C73#47312yes—
143Dic73—42no—
144Dic73—82no—
145Dic73—81no—
146#10454—731nomaximal, Sylow
147C2×C73—21no—
148C2×C73—21no—
149C2×C73#203511yescharacteristic
150C2×C73#204711yescharacteristic
151C2×C73#204811yescharacteristic
152C2×#477—731no—
153#1801—731no—
154#1570D7311yescharacteristic
155#1549—731no—
156#1548—731no—
157#1479—731no—
158#1301—731no—
159C73#1045411yescharacteristic, complemented, Sylow
160C2×C4⋊Q8—731no—
161C2×C4×Q8—731no—
162#477—1462no—
163#477—1462no—
164#431—731no—
165#431C2×D7311yescharacteristic
166C2×#107—1461no—
167#423—731no—
168#423C2×D7311yescharacteristic
169C2×C4⋊C8C2×D7311yescharacteristic
170C2×#103—1461no—
171C2×#101—1461no—
172#343—1461no—
173#334—22no—
174#333—1462no—
175#332—1462no—
176Q8⋊C8—1462no—
177C22×Q8—731no—
178C22×Q8—1461no—
179C2×M16—21no—
180C2×M16—1461no—
181C22×C8—21no—
182C4⋊Q8—732no—
183C4⋊Q8—1461no—
184C4⋊Q8—1461no—
185C4⋊Q8—1461no—
186C4×Q8—1461no—
187C4×Q8—1461no—
188C4×Q8—1461no—
189C4×Q8—1461no—
190C2×C4⋊C4—731no—
191C2×C4⋊C4—1461no—
192C2×C4⋊C4—1461no—
193C2×C4⋊C4—1461no—
194C2×C42—1461no—
195C2×C42C22×D7311yescharacteristic
196#107—1464no—
197C4⋊C8—21no—
198C4⋊C8—21no—
199C4⋊C8—21no—
200C4⋊C8—1461no—
201C4⋊C8—1461no—
202C4⋊C8—1461no—
203C4⋊C8D29212yes—
204C4⋊C8C22⋊D7312yes—
205#103—1464no—
206#101—2922no—
207C22⋊C8—21no—
208C22⋊C8—1461no—
209C4×C8—21no—
210C4×C8—1461no—
211C2×Q8—2921no—
212C2×Q8—5842no—
213C2×Q8—732no—
214C2×Q8—1461no—
215C2×Q8—1461no—
216C2×Q8—1462no—
217C2×Q8—1461no—
218C2×Q8—1461no—
219C2×Q8—1461no—
220C22×C4—2921no—
221C22×C4—1461no—
222C22×C4—1461no—
223C22×C4D4×D7311yescharacteristic
224C22×C4#1192402811yescharacteristic
225C22×C4#1192402911yescharacteristic
226M16—41no—
227M16—41no—
228M16—2921no—
229M16—2921no—
230C2×C8—22no—
231C2×C8—22no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—2921no—
236C2×C8—2921no—
237C4⋊C4—2921no—
238C4⋊C4—2921no—
239C4⋊C4—2921no—
240C4⋊C4—2921no—
241C4⋊C4—1462no—
242C4⋊C4—1461no—
243C4⋊C4—1461no—
244C4⋊C4—1462no—
245C42—2921no—
246C42—2921no—
247C42D4×D7311yescharacteristic
248C42C2×C22⋊D7311yescharacteristic
249C42C2×D29211yescharacteristic
250C42#1192402911yescharacteristic
251C23#1455657611yescharacteristic
252Q8—2921no—
253Q8—2921no—
254Q8—5842no—
255Q8—5842no—
256Q8—1462no—
257Q8—1462no—
258C2×C4—22no—
259C2×C4—41no—
260C2×C4—2921no—
261C2×C4—2921no—
262C2×C4—2921no—
263C2×C4—2922no—
264C2×C4—5842no—
265C2×C4—5841no—
266C2×C4—1462no—
267C2×C4#1455655911yescharacteristic
268C2×C4#1455656511yescharacteristic
269C2×C4#1455656611yescharacteristic
270C2×C4#1455656611yescharacteristic
271C2×C4#1455657611yescharacteristic
272C2×C4#1455658011yescharacteristic
273C2×C4SD16×D7311yescharacteristic
274C2×C4#1455661211yescharacteristic
275C2×C4#1455662011yescharacteristic
276C2×C4#1455662011yescharacteristic
277C8—42no—
278C8—42no—
279C8—81no—
280C8—5841no—
281C8—5841no—
282C22—21no—
283C22—21no—
284C22#1798850411yescharacteristic
285C22#1798891911yescharacteristic
286C22#1798893111yescharacteristic
287C4—21no—
288C4—21no—
289C4—21no—
290C4—2922no—
291C4—5842no—
292C4—5841no—
293C4#1798872411yescharacteristic
294C4#1798874611yescharacteristic
295C4#1798881711yescharacteristic
296C4#1798884611yescharacteristic
297C4#1798886212yes—
298C2—21no—
299C2—21no—
300C2#2261112911yescharacteristic
301C2#2261119911yescharacteristic
302C2#2261120611yescharacteristic
subgroupG/H
centerC22#17988504
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1570C2
socleC22×C73#394
prime radicalC23×C73#123
hypercenter#1570D73
hypocenterC73#10454
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
159. C73#10454semidirect

Maximal subgroups

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

subgroupindex
C2×#179888832
#226099242
#226086172
#226086112
#226083252
#226078282
C73×#15702
#1045473