Finite Group Databasebeta

← #33004248

Subgroups — #33004248

Order 18688.

490 conjugacy classes of subgroups.

The subgroup lattice has 350 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17988970C211yesmaximal, characteristic
2C2×#17988404C211yesmaximal, characteristic, complemented
3C2×#17988402C211yesmaximal, characteristic, complemented
4C2×#17988400C211yesmaximal, characteristic
5M32×Dic73C211yesmaximal, characteristic, complemented
6#22610101C211yesmaximal, characteristic, complemented
7C2×#361×C73C211yesmaximal, characteristic
8C22×Dic292C2211yescharacteristic
9C22×#11924016—21no—
10C2×#14556578—21no—
11C2×#14556531C2211yescharacteristic
12#17988970—21no—
13#17988970—21no—
14#17988970C412yes—
15#17988970C412yes—
16C2×#14556527C2211yescharacteristic
17C2×#14556526—21no—
18#17988610—21no—
19C2×C8×Dic73C2211yescharacteristic
20#17988404—22no—
21#17988402—22no—
22#17988400—22no—
23#17988362—21no—
24C16×Dic73—21no—
25C22×D8×C73C2211yescharacteristic
26C2×M32×C73C2211yescharacteristic
27C2×#108×C73C2211yescharacteristic
28#361×C73—22no—
29C22×Dic146—21no—
30C2×Dic292—21no—
31C2×Dic292—21no—
32C2×Dic292—21no—
33C2×Dic292—21no—
34C2×Dic292—21no—
35C2×Dic292C2×C412yes—
36C2×#11924016—22no—
37C2×#11924016—22no—
38C2×#11924016—42no—
39C2×#11924016—42no—
40C2×#11924012—21no—
41C22×#10596831D411yescharacteristic
42#14556578—22no—
43#14556578—22no—
44#14556578—42no—
45C2×C22⋊Dic73—42no—
46C2×C4×Dic73D411yescharacteristic
47#14556531—21no—
48#14556531D412yes—
49C2×#11924003—21no—
50#14556527—21no—
51#14556527—21no—
52#14556526—42no—
53#14556520—42no—
54C8×Dic73C2×C411yescharacteristic
55C8×Dic73C2×C411yescharacteristic
56C8×Dic73D411yescharacteristic
57C8×Dic73D411yescharacteristic
58C22×D4×C73—21no—
59C2×D8×C73—21no—
60C2×D8×C73—21no—
61C2×D8×C73—21no—
62C2×D8×C73—21no—
63C2×D8×C73—21no—
64C2×D8×C73C2×C412yes—
65C2×M16×C73—21no—
66C22×C8×C73C2311yescharacteristic
67M32×C73—21no—
68M32×C73D412yes—
69C2×C16×C73—21no—
70#108×C73—21no—
71#108×C73—21no—
72C2×Dic146—22no—
73C2×Dic146—41no—
74C2×Dic146—41no—
75C2×Dic146—41no—
76C2×Dic146—41no—
77C2×Dic146—41no—
78C22×Dic73—41no—
79C22×Dic73SD1612yes—
80Dic292—22no—
81Dic292—22no—
82Dic292—41no—
83Dic292—41no—
84#11924016—44no—
85#11924016—44no—
86#11924012—41no—
87#11924012—41no—
88C2×#10596831—41no—
89C2×#10596831C22⋊C411yescharacteristic
90C2×#10596831C22⋊C411yescharacteristic
91C2×#10596831D812yes—
92C2×#10596831SD1612yes—
93C22⋊Dic73—44no—
94C22⋊Dic73—44no—
95C4×Dic73C22⋊C411yescharacteristic
96C4×Dic73C22⋊C411yescharacteristic
97C4×Dic73D812yes—
98#11924003—22no—
99C24×C73—41no—
100C2×D4×C73—22no—
101C2×D4×C73—41no—
102C2×D4×C73—41no—
103C2×D4×C73—41no—
104C2×D4×C73—41no—
105C2×D4×C73—41no—
106C22×C4×C73C2×D411yescharacteristic
107D8×C73—22no—
108D8×C73—22no—
109D8×C73—41no—
110D8×C73—41no—
111M16×C73—41no—
112M16×C73—41no—
113C2×C8×C73—41no—
114C2×C8×C73C22×C411yescharacteristic
115C2×C8×C73C2×D411yescharacteristic
116C2×C8×C73C2×D411yescharacteristic
117C2×C8×C73C2×D411yescharacteristic
118C2×C8×C73#4111yescharacteristic
119C2×C8×C73#4111yescharacteristic
120C16×C73—22no—
121C23×C73—42no—
122C23×C73—84no—
123C23×C73—81no—
124C23×C73—81no—
125C23×C73C2×SD1611yescharacteristic
126D4×C73—42no—
127D4×C73—42no—
128D4×C73—81no—
129D4×C73—81no—
130C2×C4×C73C2×C22⋊C411yescharacteristic
131C2×C4×C73#12411yescharacteristic
132C2×C4×C73#12711yescharacteristic
133C2×C4×C73C2×D811yescharacteristic
134C2×C4×C73C2×D811yescharacteristic
135C2×C4×C73C2×SD1611yescharacteristic
136C2×Dic73—42no—
137C2×Dic73—42no—
138C2×Dic73—81no—
139C2×Dic73—81no—
140C2×Dic73#10212yes—
141C2×Dic73#10212yes—
142Dic146—42no—
143Dic146—42no—
144Dic146—81no—
145Dic146—81no—
146C8×C73—81no—
147C8×C73C4×D411yescharacteristic
148C8×C73C4×D411yescharacteristic
149C8×C73#12111yescharacteristic
150C8×C73#12111yescharacteristic
151#10596831—81no—
152#10596831#10212yes—
153#10596831#10212yes—
154C22×C73—22no—
155C22×C73—84no—
156C22×C73—82no—
157C22×C73—162no—
158C22×C73—162no—
159C22×C73C2×#10211yescharacteristic
160C22×C73#48611yescharacteristic
161C22×C73#49211yescharacteristic
162C4×C73#39011yescharacteristic
163C4×C73C2×#10211yescharacteristic
164C4×C73#48611yescharacteristic
165C4×C73#49311yescharacteristic
166Dic73—22no—
167Dic73—22no—
168Dic73—82no—
169#13214—731nomaximal, Sylow
170C2×C73—21no—
171C2×C73—21no—
172C2×C73—162no—
173C2×C73#195711yescharacteristic
174C2×C73#214812yes—
175C2×#495—731no—
176C2×#362—731no—
177C2×#362—731no—
178C2×#361—731no—
179C2×#361D7311yescharacteristic
180C4×M32—731no—
181#1848—731no—
182C73#1321411yescharacteristic, complemented, Sylow
183C22×Q16—731no—
184C22×SD16—1461no—
185C22×D8C2×D7311yescharacteristic
186C2×#124—1461no—
187C2×M32—731no—
188C2×M32C2×D7311yescharacteristic
189#495—732no—
190#495—732no—
191#495—1461no—
192#495—1461no—
193C2×#108—731no—
194C2×#108—1461no—
195C2×#108C2×D7311yescharacteristic
196#423—1461no—
197C2×C4×C8—731no—
198#362—1462no—
199#362—1462no—
200#361—22no—
201#361—1462no—
202#346—1461no—
203C4×C16—1461no—
204C22×Q8—1461no—
205C22×D4—21no—
206C2×Q16—732no—
207C2×Q16—1461no—
208C2×Q16—1461no—
209C2×Q16—1461no—
210C2×Q16—1461no—
211C2×Q16—1461no—
212C2×SD16—2922no—
213C2×SD16—2922no—
214C2×SD16—1462no—
215C2×SD16—1462no—
216C2×D8—21no—
217C2×D8—21no—
218C2×D8—21no—
219C2×D8—21no—
220C2×D8—21no—
221C2×D8C4×D7312yes—
222C2×M16—21no—
223C2×M16—1461no—
224C22×C8—731no—
225C22×C8C22×D7311yescharacteristic
226#124—2922no—
227#124—1462no—
228#124—1462no—
229C2×C22⋊C4—2922no—
230C2×C42—731no—
231M32—21no—
232M32—732no—
233M32—1461no—
234M32C22⋊D7312yes—
235C2×C16—21no—
236C2×C16—1461no—
237#108—21no—
238#108—21no—
239#108—2922no—
240#108—1461no—
241#108—1461no—
242C4⋊C8—2922no—
243C4×C8—731no—
244C4×C8—731no—
245C4×C8—731no—
246C4×C8—731no—
247C24—41no—
248C2×Q8—2921no—
249C2×Q8—2921no—
250C2×Q8—2921no—
251C2×Q8—2921no—
252C2×Q8—2921no—
253C2×Q8—1462no—
254C2×D4—22no—
255C2×D4—41no—
256C2×D4—41no—
257C2×D4—41no—
258C2×D4—41no—
259C2×D4—41no—
260C22×C4—2921no—
261C22×C4—732no—
262C22×C4D4×D7311yescharacteristic
263Q16—2921no—
264Q16—2921no—
265Q16—1462no—
266Q16—1462no—
267SD16—2924no—
268SD16—2924no—
269D8—22no—
270D8—22no—
271D8—41no—
272D8—41no—
273M16—41no—
274M16—41no—
275M16—2921no—
276M16—2921no—
277C2×C8—41no—
278C2×C8—2921no—
279C2×C8—731no—
280C2×C8—731no—
281C2×C8—732no—
282C2×C8—732no—
283C2×C8C2×C4×D7311yescharacteristic
284C2×C8D4×D7311yescharacteristic
285C2×C8D4×D7311yescharacteristic
286C2×C8C2×C22⋊D7311yescharacteristic
287C2×C8#1192402711yescharacteristic
288C2×C8#1192402811yescharacteristic
289C22⋊C4—2924no—
290C22⋊C4—2924no—
291C42—731no—
292C42—731no—
293C42—732no—
294C16—22no—
295C16—1462no—
296C23—42no—
297C23—84no—
298C23—81no—
299C23—81no—
300C23SD16×D7311yescharacteristic
301Q8—2922no—
302Q8—2922no—
303Q8—5841no—
304Q8—5841no—
305D4—42no—
306D4—42no—
307D4—81no—
308D4—81no—
309C2×C4—2922no—
310C2×C4—2922no—
311C2×C4—5841no—
312C2×C4—5841no—
313C2×C4—732no—
314C2×C4—732no—
315C2×C4C22⋊C4×D7311yescharacteristic
316C2×C4#1455657711yescharacteristic
317C2×C4#1455658711yescharacteristic
318C2×C4D8×D7311yescharacteristic
319C2×C4D8×D7311yescharacteristic
320C2×C4SD16×D7311yescharacteristic
321C8—81no—
322C8—5841no—
323C8—732no—
324C8—732no—
325C8#1455655111yescharacteristic
326C8C4×C22⋊D7311yescharacteristic
327C8#1455656311yescharacteristic
328C8#1455656411yescharacteristic
329C22—22no—
330C22—82no—
331C22—84no—
332C22—162no—
333C22—162no—
334C22#102×D7311yescharacteristic
335C22#1798893211yescharacteristic
336C22#1798895811yescharacteristic
337C4—5842no—
338C4—1462no—
339C4—1462no—
340C4#1798848711yescharacteristic
341C4#102×D7311yescharacteristic
342C4#1798893211yescharacteristic
343C4#1798896211yescharacteristic
344C2—21no—
345C2—21no—
346C2—162no—
347C2#2261073511yescharacteristic
348C2#2261167712yes—
subgroupG/H
centerC22#102×D73
commutatorC2×C8×C73C22×C4
FrattiniC22×C8C22×D73
FittingC2×#361×C73C2
socleC22×C73C2×#102
prime radicalC22×D8×C73C22
cosocleC22×C8×C73C23
hypercenterC2×#361D73
hypocenterC73#13214
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ C2×#361

Complements

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

NH ≅ G/Ntype
2. C2×#17988404C2semidirect
3. C2×#17988402C2semidirect
5. M32×Dic73C2semidirect
6. #22610101C2semidirect
182. C73#13214semidirect

Maximal subgroups

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

subgroupindex
C2×#179889702
C2×#179884042
C2×#179884022
C2×#179884002
M32×Dic732
#226101012
C2×#361×C732
#1321473