Finite Group Databasebeta

← #32984389

Subgroups — #32984389

Order 18688.

386 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
1#22610892C211yesmaximal, characteristic
2#22610853C211yesmaximal, characteristic
3#22610690C211yesmaximal, characteristic
4#22609798C211yesmaximal, characteristic
5C2×#17988334C211yesmaximal, characteristic
6#22607815C211yesmaximal, characteristic
7C73×#1277C211yesmaximal, characteristic
8C2×#14556591C2211yescharacteristic
9C2×#14556525—21no—
10C2×C4⋊#10596831C2211yescharacteristic
11C2×#14556516—21no—
12C2×#14556516—21no—
13C2×#14556501—21no—
14#17988457C2211yescharacteristic
15C4×C4⋊Dic73C2211yescharacteristic
16#17988350—21no—
17#17988350—21no—
18#17988350—21no—
19#17988341—21no—
20#17988334C414yescomplemented
21C2×C4⋊C8×C73C2211yescharacteristic
22C2×C4⋊C8×C73C2211yescharacteristic
23C2×C4×C8×C73C2211yescharacteristic
24C22×Dic146—21no—
25C22×#10596831—21no—
26#14556591—21no—
27#14556591—21no—
28#14556591—21no—
29#14556591C2×C412yes—
30C2×C4⋊Dic73—21no—
31C2×C4⋊Dic73—21no—
32C2×C4⋊Dic73—21no—
33C2×C4⋊Dic73—21no—
34C2×C4⋊Dic73—21no—
35C2×C4⋊Dic73D411yescharacteristic
36C2×C4⋊Dic73D411yescharacteristic
37C2×C4×Dic73—21no—
38#14556525—42no—
39C4⋊#10596831—21no—
40C4⋊#10596831C2×C412yes—
41#14556516—42no—
42#14556516—42no—
43#14556501—42no—
44#14556498—21no—
45C22×C8×C73—21no—
46C22×C8×C73—21no—
47C22×C8×C73D411yescharacteristic
48C22×C8×C73D411yescharacteristic
49C2×C42×C73C2311yescharacteristic
50C4⋊C8×C73—21no—
51C4⋊C8×C73—21no—
52C4⋊C8×C73—21no—
53C4⋊C8×C73C2×C412yes—
54C4×C8×C73—21no—
55C4×C8×C73—21no—
56C2×Dic146—22no—
57C2×Dic146—41no—
58C2×Dic146—41no—
59C2×Dic146—41no—
60C2×Dic146—41no—
61C2×Dic146—41no—
62C22×Dic73—21no—
63C22×Dic73—21no—
64C22×Dic73—41no—
65C22×Dic73—41no—
66C2×#10596831—22no—
67C2×#10596831—41no—
68C2×#10596831—41no—
69C4⋊Dic73—22no—
70C4⋊Dic73—22no—
71C4⋊Dic73—21no—
72C4⋊Dic73—21no—
73C4⋊Dic73—21no—
74C4⋊Dic73—21no—
75C4⋊Dic73—41no—
76C4⋊Dic73—41no—
77C4⋊Dic73—41no—
78C4⋊Dic73—41no—
79C4⋊Dic73—41no—
80C4⋊Dic73—41no—
81C4⋊Dic73—81no—
82C4×Dic73—41no—
83C4×Dic73—41no—
84C22×C4×C73C2×D411yescharacteristic
85C22×C4×C73C2×D411yescharacteristic
86C22×C4×C73#4111yescharacteristic
87C2×C8×C73—21no—
88C2×C8×C73—21no—
89C2×C8×C73—22no—
90C2×C8×C73—21no—
91C2×C8×C73—21no—
92C2×C8×C73—21no—
93C2×C8×C73—41no—
94C2×C8×C73—41no—
95C2×C8×C73—41no—
96C2×C8×C73—41no—
97C2×C8×C73—41no—
98C2×C8×C73Q1612yes—
99C42×C73C22×C411yescharacteristic
100C42×C73#4111yescharacteristic
101C42×C73#4111yescharacteristic
102C42×C73#4111yescharacteristic
103C23×C73#12111yescharacteristic
104C2×C4×C73—21no—
105C2×C4×C73—21no—
106C2×C4×C73#11711yescharacteristic
107C2×C4×C73C4×D411yescharacteristic
108C2×C4×C73C4×D411yescharacteristic
109C2×C4×C73#12311yescharacteristic
110C2×C4×C73#12411yescharacteristic
111C2×C4×C73#12611yescharacteristic
112C2×C4×C73C2×Q1611yescharacteristic
113C2×C4×C73#13511yescharacteristic
114C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
115C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
116C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
117C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
118C2×C4×C73#13711yescharacteristic
119C2×C4×C73#13711yescharacteristic
120C2×Dic73—42no—
121C2×Dic73—41no—
122C2×Dic73—41no—
123C2×Dic73—41no—
124C2×Dic73—41no—
125C2×Dic73—41no—
126C2×Dic73—41no—
127C2×Dic73—81no—
128C2×Dic73—81no—
129C2×Dic73—81no—
130C2×Dic73—81no—
131C2×Dic73—81no—
132Dic146—42no—
133Dic146—42no—
134Dic146—81no—
135Dic146—81no—
136C8×C73—22no—
137C8×C73—42no—
138C8×C73—41no—
139C8×C73—81no—
140#10596831—42no—
141C22×C73#38811yescharacteristic
142C22×C73#46211yescharacteristic
143C22×C73#46311yescharacteristic
144C22×C73#46811yescharacteristic
145C22×C73#46911yescharacteristic
146C22×C73#47111yescharacteristic
147C22×C73#47311yescharacteristic
148C4×C73—21no—
149C4×C73—21no—
150C4×C73C4×Q1611yescharacteristic
151C4×C73#44011yescharacteristic
152C4×C73#44011yescharacteristic
153C4×C73#44211yescharacteristic
154C4×C73#48411yescharacteristic
155C4×C73#48511yescharacteristic
156C4×C73#48911yescharacteristic
157C4×C73#49011yescharacteristic
158Dic73—82no—
159Dic73—81no—
160Dic73—81no—
161Dic73—161no—
162#9574—731nomaximal, Sylow
163C2×C73#169211yescharacteristic
164C2×C73#169411yescharacteristic
165C2×C73#169911yescharacteristic
166C2×C73#170111yescharacteristic
167C2×C73#192811yescharacteristic
168C2×C73#193011yescharacteristic
169C2×C73#193611yescharacteristic
170#1990—731no—
171#1981—731no—
172#1947—731no—
173#1770—731no—
174C2×#332—731no—
175#1296—731no—
176#1277D7311yescharacteristic
177C73#957411yescharacteristic, complemented, Sylow
178C2×C4⋊Q8—731no—
179C2×#107—1461no—
180C2×C4⋊C8—731no—
181C2×C4⋊C8C2×D7311yescharacteristic
182C2×C4⋊C8C2×D7311yescharacteristic
183C2×#103—1461no—
184C2×#103—1461no—
185C2×#97—1461no—
186C2×C4×C8C2×D7311yescharacteristic
187#384—731no—
188C4×C4⋊C4—731no—
189#340—1461no—
190#340—1461no—
191#340—1461no—
192#336—1461no—
193#332—734no—
194C22×Q8—1461no—
195C22×C8—21no—
196C22×C8—21no—
197C22×C8—1461no—
198C22×C8D29211yescharacteristic
199C22×C8D29211yescharacteristic
200C4⋊Q8—732no—
201C4⋊Q8—1461no—
202C4⋊Q8—1461no—
203C4⋊Q8—1461no—
204C2×C4⋊C4—731no—
205C2×C4⋊C4—731no—
206C2×C4⋊C4—1461no—
207C2×C4⋊C4—1461no—
208C2×C4⋊C4—1461no—
209C2×C4⋊C4—1461no—
210C2×C4⋊C4—1461no—
211C2×C42—1461no—
212C2×C42C22×D7311yescharacteristic
213#107—2922no—
214C4⋊C8—21no—
215C4⋊C8—21no—
216C4⋊C8—21no—
217C4⋊C8—732no—
218C4⋊C8—1461no—
219C4⋊C8C4×D7312yes—
220#103—2922no—
221#103—2922no—
222#97—2922no—
223C4×C8—21no—
224C4×C8—21no—
225#95—1461no—
226C2×Q8—2921no—
227C2×Q8—2921no—
228C2×Q8—2921no—
229C2×Q8—2921no—
230C2×Q8—2921no—
231C2×Q8—1462no—
232C22×C4—2921no—
233C22×C4—2921no—
234C22×C4—1461no—
235C22×C4—1461no—
236C22×C4D4×D7311yescharacteristic
237C22×C4C2×D29211yescharacteristic
238C22×C4#1192402911yescharacteristic
239C2×C8—21no—
240C2×C8—21no—
241C2×C8—22no—
242C2×C8—21no—
243C2×C8—21no—
244C2×C8—21no—
245C2×C8—41no—
246C2×C8—41no—
247C2×C8—41no—
248C2×C8—41no—
249C2×C8—41no—
250C2×C8—2921no—
251C2×C8—2921no—
252C2×C8—1462no—
253C2×C8Dic29212yes—
254C4⋊C4—2921no—
255C4⋊C4—2921no—
256C4⋊C4—2921no—
257C4⋊C4—2921no—
258C4⋊C4—2921no—
259C4⋊C4—2921no—
260C4⋊C4—5841no—
261C4⋊C4—1462no—
262C4⋊C4—1462no—
263C4⋊C4—1461no—
264C4⋊C4—1461no—
265C4⋊C4—1461no—
266C4⋊C4—1461no—
267C42—2921no—
268C42—2921no—
269C42C2×C4×D7311yescharacteristic
270C42#1192402711yescharacteristic
271C42#1192402711yescharacteristic
272C42#1192402811yescharacteristic
273C23#1455656611yescharacteristic
274Q8—2922no—
275Q8—2922no—
276Q8—5841no—
277Q8—5841no—
278C2×C4—21no—
279C2×C4—21no—
280C2×C4—2922no—
281C2×C4—2921no—
282C2×C4—2921no—
283C2×C4—2921no—
284C2×C4—2921no—
285C2×C4—2921no—
286C2×C4—2921no—
287C2×C4—5841no—
288C2×C4—5841no—
289C2×C4—5841no—
290C2×C4—5841no—
291C2×C4—5841no—
292C2×C4#1455654911yescharacteristic
293C2×C4#1455655111yescharacteristic
294C2×C4C4×D29211yescharacteristic
295C2×C4#1455657511yescharacteristic
296C2×C4#1455657711yescharacteristic
297C2×C4#1455658611yescharacteristic
298C2×C4C2×Dic29211yescharacteristic
299C2×C4#1455661311yescharacteristic
300C2×C4#1455661511yescharacteristic
301C2×C4#1455661811yescharacteristic
302C2×C4#1455661811yescharacteristic
303C2×C4#1455661911yescharacteristic
304C2×C4#1455662311yescharacteristic
305C2×C4#1455662411yescharacteristic
306C8—22no—
307C8—41no—
308C8—42no—
309C8—81no—
310C8—2922no—
311C22#1798847911yescharacteristic
312C22#1798879811yescharacteristic
313C22#1798880311yescharacteristic
314C22#1798883411yescharacteristic
315C22#1798884111yescharacteristic
316C22#1798885111yescharacteristic
317C22#1798886311yescharacteristic
318C4—21no—
319C4—21no—
320C4—5841no—
321C4—5841no—
322C4—5842no—
323C4—11681no—
324C4C4×Dic29211yescharacteristic
325C4#1798868911yescharacteristic
326C4#1798869011yescharacteristic
327C4#1798869611yescharacteristic
328C4#1798892311yescharacteristic
329C4#1798892911yescharacteristic
330C4#1798894811yescharacteristic
331C4#1798895011yescharacteristic
332C2#2260943811yescharacteristic
333C2#2260945011yescharacteristic
334C2#2260947911yescharacteristic
335C2#2260949311yescharacteristic
336C2#2261057311yescharacteristic
337C2#2261058711yescharacteristic
338C2#2261062911yescharacteristic
subgroupG/H
centerC23#14556566
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#1277C2
socle, prime radicalC23×C73#121
cosocleC2×C42×C73C23
hypercenter#1277D73
hypocenterC73#9574
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
20. #17988334C4semidirect
177. C73#9574semidirect

Maximal subgroups

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

subgroupindex
#226108922
#226108532
#226106902
#226097982
C2×#179883342
#226078152
C73×#12772
#957473