Finite Group Databasebeta

← #1386×D73 #33000897

Subgroups — #1386×D73 #33000897

Order 18688.

630 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×M32×D73C211yesmaximal, characteristic
2#427×D73C211yesmaximal, characteristic
3C2×#106×D73C211yesmaximal, characteristic
4#22608038C211yesmaximal, characteristic, complemented
5#22608037C211yesmaximal, characteristic, complemented
6#22608036C211yesmaximal, characteristic, complemented
7C73×#1386C211yesmaximal, characteristic, complemented
8C22×C8×D73C2211yescharacteristic
9#117×D73—21no—
10C2×C4⋊C4×D73—21no—
11C2×#14556531C2211yescharacteristic
12C2×#14556530—21no—
13M32×D73—22no—
14M32×D73C414yescomplemented
15C2×C16×D73—21no—
16#17988625C2211yescharacteristic
17#17988624C412yescomplemented
18#17988623—21no—
19#17988622—21no—
20#107×D73C412yescomplemented
21C2×#14556523C2211yescharacteristic
22C2×#14556522—21no—
23#106×D73—22no—
24#106×D73—21no—
25#106×D73C414yescomplemented
26C2×M32×C73C2211yescharacteristic
27#427×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C22×C4×D73—41no—
30C22×C4×D73D411yescharacteristic
31C22×#10596831D411yescharacteristic
32C2×C8×D73C2×C412yes—
33C2×C8×D73C2×C412yes—
34C2×C8×D73C2×C411yescharacteristic
35C2×C8×D73C2×C411yescharacteristic
36C2×C8×D73D411yescharacteristic
37C2×C8×D73D412yes—
38C2×C8×D73D411yescharacteristic
39C2×C8×D73Q812yes—
40#14556550—21no—
41#14556549—22no—
42#14556548—41no—
43#14556547—41no—
44C2×C4⋊Dic73—21no—
45C2×#11924007—41no—
46C4⋊C4×D73—24no—
47C4⋊C4×D73—22no—
48C4⋊C4×D73—42no—
49C22⋊C4×D73—41no—
50C42×D73—41no—
51#14556531—21no—
52#14556531C2×C412yescomplemented
53#14556530—24no—
54C2×#11924003—21no—
55C16×D73—24no—
56#14556525C2×C412yescomplemented
57#14556524—22no—
58#14556523—21no—
59#14556523—21no—
60#14556523C2×C412yescomplemented
61#14556522—24no—
62#14556522—22no—
63C22×C8×C73C2311yescharacteristic
64#117×C73—21no—
65C2×C4⋊C4×C73—21no—
66M32×C73—21no—
67M32×C73C2×C412yescomplemented
68C2×C16×C73—21no—
69#107×C73C2×C412yescomplemented
70#106×C73—21no—
71#106×C73—21no—
72#106×C73C2×C412yescomplemented
73C23×D73D811yescharacteristic
74C22×Dic73—41no—
75C22×Dic73D811yescharacteristic
76C2×C4×D73—42no—
77C2×C4×D73—44no—
78C2×C4×D73—84no—
79C2×C4×D73C22⋊C412yes—
80C2×C4×D73C22⋊C411yescharacteristic
81C2×C4×D73C22⋊C411yescharacteristic
82C2×C4×D73C4⋊C412yes—
83C2×C4×D73SD1611yescharacteristic
84C2×C4×D73SD1612yes—
85C2×C4×D73SD1611yescharacteristic
86C2×C4×D73Q1612yes—
87C2×#10596831C22⋊C412yes—
88C2×#10596831C22⋊C411yescharacteristic
89C2×#10596831C22⋊C411yescharacteristic
90C2×#10596831C4⋊C412yes—
91C8×D73C4212yes—
92C8×D73C4212yes—
93C8×D73C22⋊C412yes—
94C8×D73C22⋊C412yes—
95C8×D73C4⋊C412yes—
96C8×D73C4⋊C412yes—
97C8×D73C4⋊C412yes—
98C8×D73C4⋊C412yes—
99C4⋊Dic73—22no—
100C4⋊Dic73—22no—
101C4⋊Dic73—41no—
102#11924007—44no—
103#11924007—42no—
104C22⋊Dic73—41no—
105#11924005—42no—
106C4×Dic73—41no—
107C4×Dic73—42no—
108#11924003—22no—
109C22×C4×C73—41no—
110C22×C4×C73C2×D411yescharacteristic
111C2×C8×C73C22×C411yescharacteristic
112C2×C8×C73C22×C411yescharacteristic
113C2×C8×C73C22×C411yescharacteristic
114C2×C8×C73C2×D411yescharacteristic
115C2×C8×C73C2×D411yescharacteristic
116C2×C8×C73C2×Q811yescharacteristic
117C4⋊C4×C73—22no—
118C4⋊C4×C73—22no—
119C4⋊C4×C73—41no—
120C22⋊C4×C73—41no—
121C42×C73—41no—
122C16×C73—22no—
123C23×C73C2×D811yescharacteristic
124C22×D73—24no—
125C22×D73#10211yescharacteristic
126C22×D73#10212yes—
127C22×D73#10211yescharacteristic
128C22×D73#10712yes—
129C2×C4×C73—42no—
130C2×C4×C73—42no—
131C2×C4×C73—82no—
132C2×C4×C73C2×C22⋊C411yescharacteristic
133C2×C4×C73C2×C22⋊C411yescharacteristic
134C2×C4×C73C2×C4⋊C411yescharacteristic
135C2×C4×C73C2×SD1611yescharacteristic
136C2×C4×C73C2×SD1611yescharacteristic
137C2×C4×C73C2×Q1611yescharacteristic
138C2×Dic73—42no—
139C2×Dic73—42no—
140C2×Dic73—82no—
141C2×Dic73#10211yescharacteristic
142C2×Dic73#10212yes—
143C2×Dic73#10211yescharacteristic
144C2×Dic73#10712yes—
145C4×D73—88no—
146C4×D73—84no—
147C4×D73#9512yes—
148C4×D73#9512yes—
149C4×D73#10312yes—
150C4×D73#10312yes—
151C4×D73#10312yes—
152C4×D73#10312yes—
153C4×D73#10612yes—
154C4×D73#10612yes—
155C8×C73C2×C4211yescharacteristic
156C8×C73C2×C22⋊C411yescharacteristic
157C8×C73C2×C4⋊C411yescharacteristic
158C8×C73C2×C4⋊C411yescharacteristic
159#10596831#9512yes—
160#10596831#9512yes—
161C22×C73—22no—
162C22×C73C2×#10211yescharacteristic
163C22×C73C2×#10211yescharacteristic
164C22×C73C2×#10711yescharacteristic
165C2×D73—22no—
166C2×D73—24no—
167C2×D73—24no—
168C2×D73#34012yes—
169C2×D73#34012yes—
170C2×D73#36014yes—
171C4×C73—82no—
172C4×C73—82no—
173C4×C73C2×#9511yescharacteristic
174C4×C73C2×#10311yescharacteristic
175C4×C73C2×#10311yescharacteristic
176C4×C73C2×#10611yescharacteristic
177Dic73—82no—
178Dic73—82no—
179Dic73#34012yes—
180Dic73#34012yes—
181C2×#1386—731nomaximal, Sylow
182C2×C73—21no—
183C2×C73—21no—
184C2×C73C2×#34011yescharacteristic
185C2×C73C2×#36012yes—
186D73—22no—
187D73#138614yesdirect product factor
188C22×M32—731no—
189C2×#427—731no—
190C22×#106—731no—
191#1386—731no—
192#1386—731no—
193#1386—731no—
194#1386D7311yescharacteristic, direct product factor
195C73C2×#138611yescharacteristic, complemented, Sylow
196C23×C8—731no—
197C2×#117—1461no—
198C22×C4⋊C4—1461no—
199C2×M32—731no—
200C2×M32—734no—
201C2×M32—1461no—
202C2×M32—1462no—
203C2×M32C2×D7311yescharacteristic
204C22×C16—1461no—
205#427—731no—
206#427—732no—
207#427—1461no—
208#427—1461no—
209#427C2×D7311yescharacteristic
210C2×#107—732no—
211C2×#106—731no—
212C2×#106—734no—
213C2×#106—1462no—
214C2×#106—1461no—
215C2×#106—1461no—
216C2×#106C2×D7311yescharacteristic
217C23×C4—2921no—
218C23×C4—731no—
219C22×C8—731no—
220C22×C8—732no—
221C22×C8—731no—
222C22×C8—731no—
223C22×C8—732no—
224C22×C8—731no—
225C22×C8—732no—
226C22×C8—731no—
227C22×C8—732no—
228C22×C8C22×D7311yescharacteristic
229#117—21no—
230#117—2921no—
231#117—2921no—
232#117—1462no—
233#117—1461no—
234C2×C4⋊C4—21no—
235C2×C4⋊C4—2922no—
236C2×C4⋊C4—2921no—
237C2×C4⋊C4—1464no—
238C2×C4⋊C4—1462no—
239C2×C4⋊C4—1461no—
240C2×C22⋊C4—2921no—
241C2×C42—2921no—
242M32—21no—
243M32—732no—
244M32—1464no—
245M32—1461no—
246M32C4×D7312yescomplemented
247C2×C16—21no—
248C2×C16—1464no—
249C2×C16—1461no—
250#107—732no—
251#107—1462no—
252#107C4×D7312yescomplemented
253#106—21no—
254#106—21no—
255#106—732no—
256#106—1464no—
257#106—1462no—
258#106—1461no—
259#106—1461no—
260#106C4×D7312yescomplemented
261C24—731no—
262C22×C4—41no—
263C22×C4—2922no—
264C22×C4—2924no—
265C22×C4—2921no—
266C22×C4—5844no—
267C22×C4—731no—
268C22×C4—732no—
269C22×C4—731no—
270C22×C4—731no—
271C22×C4—732no—
272C22×C4—731no—
273C22×C4—732no—
274C22×C4—731no—
275C22×C4—732no—
276C22×C4D4×D7311yescharacteristic
277C2×C8—732no—
278C2×C8—731no—
279C2×C8—731no—
280C2×C8—732no—
281C2×C8—732no—
282C2×C8—732no—
283C2×C8—732no—
284C2×C8—732no—
285C2×C8—732no—
286C2×C8—732no—
287C2×C8—732no—
288C2×C8—732no—
289C2×C8C2×C4×D7311yescharacteristic
290C2×C8C2×C4×D7311yescharacteristic
291C2×C8C2×C4×D7311yescharacteristic
292C2×C8D4×D7311yescharacteristic
293C2×C8D4×D7311yescharacteristic
294C2×C8Q8×D7311yescharacteristic
295C4⋊C4—22no—
296C4⋊C4—22no—
297C4⋊C4—41no—
298C4⋊C4—2924no—
299C4⋊C4—2922no—
300C4⋊C4—2921no—
301C4⋊C4—1462no—
302C4⋊C4—1462no—
303C22⋊C4—41no—
304C22⋊C4—2922no—
305C22⋊C4—2921no—
306C42—41no—
307C42—2922no—
308C42—2921no—
309C16—22no—
310C16—1462no—
311C23—731no—
312C23—732no—
313C23—732no—
314C23—731no—
315C23—1464no—
316C23D8×D7311yescharacteristic
317C2×C4—42no—
318C2×C4—42no—
319C2×C4—82no—
320C2×C4—2922no—
321C2×C4—2922no—
322C2×C4—5844no—
323C2×C4—5848no—
324C2×C4—5842no—
325C2×C4—732no—
326C2×C4—732no—
327C2×C4—731no—
328C2×C4—731no—
329C2×C4—732no—
330C2×C4—732no—
331C2×C4—732no—
332C2×C4—732no—
333C2×C4—732no—
334C2×C4—732no—
335C2×C4—732no—
336C2×C4—732no—
337C2×C4C22⋊C4×D7311yescharacteristic
338C2×C4C22⋊C4×D7311yescharacteristic
339C2×C4C4⋊C4×D7311yescharacteristic
340C2×C4SD16×D7311yescharacteristic
341C2×C4SD16×D7311yescharacteristic
342C2×C4Q16×D7311yescharacteristic
343C8—732no—
344C8—732no—
345C8C42×D7311yescharacteristic
346C8C22⋊C4×D7311yescharacteristic
347C8C4⋊C4×D7311yescharacteristic
348C8C4⋊C4×D7311yescharacteristic
349C22—22no—
350C22—734no—
351C22—732no—
352C22—732no—
353C22—1464no—
354C22—1464no—
355C22—1462no—
356C22#102×D7311yescharacteristic
357C22#102×D7311yescharacteristic
358C22#107×D7311yescharacteristic
359C4—82no—
360C4—82no—
361C4—5842no—
362C4—5842no—
363C4—732no—
364C4—732no—
365C4#95×D7311yescharacteristic
366C4#103×D7311yescharacteristic
367C4#103×D7311yescharacteristic
368C4#106×D7311yescharacteristic
369C2—21no—
370C2—21no—
371C2—734no—
372C2—1462no—
373C2#340×D7311yescharacteristic
374C2#360×D7312yes—
subgroupG/H
centerC22#102×D73
commutatorC8×C73C2×C42
FrattiniC22×C8C22×D73
FittingC73×#1386C2
socleC22×C73C2×#102
prime radicalC23×D73D8
cosocleC22×C8×C73C23
hypercenter#1386D73
hypocenterC73C2×#1386
LCSG ▷ C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×C8 ◁ #1386

Complements

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

NH ≅ G/Ntype
4. #22608038C2semidirect
5. #22608037C2semidirect
6. #22608036C2semidirect
7. C73×#1386C2semidirect
14. M32×D73C4semidirect
17. #17988624C4semidirect
20. #107×D73C4semidirect
25. #106×D73C4semidirect
52. #14556531C2×C4semidirect
56. #14556525C2×C4semidirect
60. #14556523C2×C4semidirect
67. M32×C73C2×C4semidirect
69. #107×C73C2×C4semidirect
72. #106×C73C2×C4semidirect
187. D73#1386direct (N × H)
194. #1386D73direct (N × H)
195. C73C2×#1386semidirect
246. M32C4×D73semidirect
252. #107C4×D73semidirect
260. #106C4×D73semidirect

Maximal subgroups

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

subgroupindex
C2×M32×D732
#427×D732
C2×#106×D732
#226080382
#226080372
#226080362
C73×#13862
C2×#138673