Finite Group Databasebeta

← #32990747

Subgroups — #32990747

Order 18688.

350 conjugacy classes of subgroups.

The subgroup lattice has 336 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22610867C211yesmaximal, characteristic
2#22610059C211yesmaximal, characteristic
3#22609937C211yesmaximal, characteristic
4#22609937C211yesmaximal, characteristic
5#22607815C211yesmaximal, characteristic
6#22607815C211yesmaximal, characteristic
7C73×#1277C211yesmaximal, characteristic
8C2×C4×Dic146C2211yescharacteristic
9C2×C4⋊#10596831C2211yescharacteristic
10C2×#14556516—21no—
11C2×#14556516—21no—
12#17988457C2211yescharacteristic
13#17988457C2211yescharacteristic
14#17988350—21no—
15#17988350—21no—
16#17988350—21no—
17#17988350—21no—
18#17988341—21no—
19#17988341—21no—
20C2×C4⋊C8×C73C2211yescharacteristic
21C2×C4⋊C8×C73C2211yescharacteristic
22C2×C4×C8×C73C2211yescharacteristic
23C22×Dic146D411yescharacteristic
24C22×#10596831—21no—
25C4×Dic146—21no—
26C4×Dic146—21no—
27C4×Dic146—21no—
28C4×Dic146—21no—
29C2×C4⋊Dic73—21no—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73D411yescharacteristic
36C2×#11924007—21no—
37C2×C4×Dic73—21no—
38C4⋊#10596831—21no—
39C4⋊#10596831—21no—
40#14556516—42no—
41#14556516—42no—
42C22×C8×C73—21no—
43C22×C8×C73—21no—
44C22×C8×C73D411yescharacteristic
45C22×C8×C73D411yescharacteristic
46C2×C42×C73C2311yescharacteristic
47C4⋊C8×C73—21no—
48C4⋊C8×C73—21no—
49C4⋊C8×C73—21no—
50C4⋊C8×C73—21no—
51C4×C8×C73—21no—
52C4×C8×C73—21no—
53C2×Dic146—21no—
54C2×Dic146—21no—
55C2×Dic146—21no—
56C2×Dic146—21no—
57C2×Dic146—21no—
58C2×Dic146SD1612yes—
59C22×Dic73—21no—
60C22×Dic73—21no—
61C22×Dic73—41no—
62C22×Dic73—41no—
63C2×#10596831—41no—
64C2×#10596831—41no—
65C2×#10596831—41no—
66C4⋊Dic73—21no—
67C4⋊Dic73—21no—
68C4⋊Dic73—41no—
69C4⋊Dic73—41no—
70C4⋊Dic73—41no—
71C4⋊Dic73—41no—
72C4⋊Dic73—41no—
73C4⋊Dic73—41no—
74C4⋊Dic73—41no—
75C4⋊Dic73—41no—
76C4⋊Dic73—81no—
77C4⋊Dic73—81no—
78#11924007—41no—
79#11924007—41no—
80C4×Dic73—41no—
81C4×Dic73—41no—
82C22×C4×C73C2×D411yescharacteristic
83C22×C4×C73C2×D411yescharacteristic
84C22×C4×C73#4111yescharacteristic
85C2×C8×C73—21no—
86C2×C8×C73—21no—
87C2×C8×C73—21no—
88C2×C8×C73—21no—
89C2×C8×C73—21no—
90C2×C8×C73—21no—
91C2×C8×C73—41no—
92C2×C8×C73—41no—
93C2×C8×C73—41no—
94C2×C8×C73—41no—
95C2×C8×C73—41no—
96C2×C8×C73—41no—
97C42×C73#4111yescharacteristic
98C42×C73#4111yescharacteristic
99C42×C73#4111yescharacteristic
100C42×C73#4111yescharacteristic
101C23×C73#12111yescharacteristic
102C2×C4×C73—21no—
103C2×C4×C73—21no—
104C2×C4×C73#12311yescharacteristic
105C2×C4×C73#12311yescharacteristic
106C2×C4×C73#12311yescharacteristic
107C2×C4×C73#12411yescharacteristic
108C2×C4×C73#12611yescharacteristic
109C2×C4×C73#12611yescharacteristic
110C2×C4×C73C2×SD1611yescharacteristic
111C2×C4×C73#13511yescharacteristic
112C2×C4×C73#13511yescharacteristic
113C2×C4×C73#13511yescharacteristic
114C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C73#13711yescharacteristic
116C2×C4×C73#13711yescharacteristic
117C2×C4×C73#13711yescharacteristic
118C2×Dic73—22no—
119C2×Dic73—41no—
120C2×Dic73—41no—
121C2×Dic73—41no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—81no—
125C2×Dic73—81no—
126C2×Dic73—81no—
127C2×Dic73—81no—
128C2×Dic73—81no—
129C2×Dic73—81no—
130Dic146—22no—
131Dic146—22no—
132Dic146—41no—
133Dic146—41no—
134C8×C73—41no—
135C8×C73—41no—
136C8×C73—81no—
137C8×C73—81no—
138#10596831—81no—
139C22×C73#39711yescharacteristic
140C22×C73#46411yescharacteristic
141C22×C73#46411yescharacteristic
142C22×C73#46511yescharacteristic
143C22×C73#46811yescharacteristic
144C22×C73#47211yescharacteristic
145C22×C73#47311yescharacteristic
146C4×C73—21no—
147C4×C73—21no—
148C4×C73#48111yescharacteristic
149C4×C73#48211yescharacteristic
150C4×C73#48311yescharacteristic
151C4×C73#48511yescharacteristic
152C4×C73#48511yescharacteristic
153C4×C73#48511yescharacteristic
154C4×C73#48811yescharacteristic
155C4×C73#49111yescharacteristic
156Dic73—42no—
157Dic73—81no—
158Dic73—161no—
159Dic73—161no—
160#10626—731nomaximal, Sylow
161C2×C73#167811yescharacteristic
162C2×C73#168011yescharacteristic
163C2×C73#169811yescharacteristic
164C2×C73#170011yescharacteristic
165C2×C73#207411yescharacteristic
166C2×C73#207711yescharacteristic
167C2×C73#207811yescharacteristic
168#1984—731no—
169#1834—731no—
170#1803—731no—
171#1803—731no—
172#1296—731no—
173#1296—731no—
174#1277D7311yescharacteristic
175C73#1062611yescharacteristic, complemented, Sylow
176C2×C4×Q8—731no—
177C2×C4⋊C8—731no—
178C2×C4⋊C8C2×D7311yescharacteristic
179C2×C4⋊C8C2×D7311yescharacteristic
180C2×#103—1461no—
181C2×#103—1461no—
182C2×C4×C8C2×D7311yescharacteristic
183#384—731no—
184#384—731no—
185#340—1461no—
186#340—1461no—
187#340—1461no—
188#340—1461no—
189#336—1461no—
190#336—1461no—
191C22×Q8—731no—
192C22×C8—21no—
193C22×C8—21no—
194C22×C8—1461no—
195C22×C8D29211yescharacteristic
196C22×C8D29211yescharacteristic
197C4×Q8—1461no—
198C4×Q8—1461no—
199C4×Q8—1461no—
200C4×Q8—1461no—
201C2×C4⋊C4—731no—
202C2×C4⋊C4—1461no—
203C2×C4⋊C4—1461no—
204C2×C4⋊C4—1461no—
205C2×C4⋊C4—1461no—
206C2×C4⋊C4—1461no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C42—1461no—
210C2×C42C22×D7311yescharacteristic
211C4⋊C8—21no—
212C4⋊C8—21no—
213C4⋊C8—21no—
214C4⋊C8—21no—
215C4⋊C8—1461no—
216C4⋊C8—1461no—
217#103—2922no—
218#103—2922no—
219C4×C8—21no—
220C4×C8—21no—
221C2×Q8—732no—
222C2×Q8—1461no—
223C2×Q8—1461no—
224C2×Q8—1461no—
225C2×Q8—1461no—
226C2×Q8—1461no—
227C22×C4—2921no—
228C22×C4—2921no—
229C22×C4—1461no—
230C22×C4—1461no—
231C22×C4D4×D7311yescharacteristic
232C22×C4C2×D29211yescharacteristic
233C22×C4#1192402911yescharacteristic
234C2×C8—21no—
235C2×C8—21no—
236C2×C8—21no—
237C2×C8—21no—
238C2×C8—21no—
239C2×C8—21no—
240C2×C8—41no—
241C2×C8—41no—
242C2×C8—41no—
243C2×C8—41no—
244C2×C8—41no—
245C2×C8—41no—
246C2×C8—2921no—
247C2×C8—2921no—
248C2×C8—2921no—
249C4⋊C4—2921no—
250C4⋊C4—2921no—
251C4⋊C4—2921no—
252C4⋊C4—2921no—
253C4⋊C4—2921no—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C4⋊C4—2921no—
258C4⋊C4—2921no—
259C4⋊C4—5841no—
260C4⋊C4—5841no—
261C4⋊C4—1461no—
262C4⋊C4—1461no—
263C42—2921no—
264C42—2921no—
265C42#1192402711yescharacteristic
266C42#1192402711yescharacteristic
267C42#1192402811yescharacteristic
268C42#1192402811yescharacteristic
269C23#1455656611yescharacteristic
270Q8—2921no—
271Q8—2921no—
272Q8—1462no—
273Q8—1462no—
274C2×C4—21no—
275C2×C4—21no—
276C2×C4—2921no—
277C2×C4—2921no—
278C2×C4—2921no—
279C2×C4—2921no—
280C2×C4—2921no—
281C2×C4—5841no—
282C2×C4—5841no—
283C2×C4—5841no—
284C2×C4—5841no—
285C2×C4—5841no—
286C2×C4—5841no—
287C2×C4—1462no—
288C2×C4#1455657311yescharacteristic
289C2×C4#1455657311yescharacteristic
290C2×C4#1455657511yescharacteristic
291C2×C4#1455657911yescharacteristic
292C2×C4#1455658611yescharacteristic
293C2×C4#1455658611yescharacteristic
294C2×C4SD16×D7311yescharacteristic
295C2×C4#1455661211yescharacteristic
296C2×C4#1455661311yescharacteristic
297C2×C4#1455661311yescharacteristic
298C2×C4#1455661511yescharacteristic
299C2×C4#1455662311yescharacteristic
300C2×C4#1455662411yescharacteristic
301C2×C4#1455662411yescharacteristic
302C8—41no—
303C8—41no—
304C8—81no—
305C8—81no—
306C8—5841no—
307C22#1798851411yescharacteristic
308C22#1798881011yescharacteristic
309C22#1798881011yescharacteristic
310C22#1798881711yescharacteristic
311C22#1798883411yescharacteristic
312C22#1798885811yescharacteristic
313C22#1798886311yescharacteristic
314C4—21no—
315C4—21no—
316C4—2922no—
317C4—5841no—
318C4—11681no—
319C4—11681no—
320C4#1798890411yescharacteristic
321C4#1798891011yescharacteristic
322C4#1798891611yescharacteristic
323C4#1798892611yescharacteristic
324C4#1798892911yescharacteristic
325C4#1798892911yescharacteristic
326C4#1798894211yescharacteristic
327C4#1798895611yescharacteristic
328C2#2260934811yescharacteristic
329C2#2260936211yescharacteristic
330C2#2260947211yescharacteristic
331C2#2260948611yescharacteristic
332C2#2261135111yescharacteristic
333C2#2261136611yescharacteristic
334C2#2261137311yescharacteristic
subgroupG/H
centerC23#14556566
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1277C2
socle, prime radicalC23×C73#121
hypercenter#1277D73
hypocenterC73#10626
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
175. C73#10626semidirect

Maximal subgroups

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

subgroupindex
#226108672
#226100592
#226099372
#226078152
C73×#12772
#1062673