Finite Group Databasebeta

← #33241551

Subgroups — #33241551

Order 18688.

554 conjugacy classes of subgroups.

The subgroup lattice has 398 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#22620501C211yesmaximal, characteristic, complemented
2#22612214C211yesmaximal, characteristic, complemented
3#22612195C211yesmaximal, characteristic, complemented
4#22612172C211yesmaximal, characteristic, complemented
5#22612170C211yesmaximal, characteristic, complemented
6#22612042C212yesmaximal, complemented
7#22612032C212yesmaximal, complemented
8C4×#14556535C212yesmaximal, complemented
9C4×#14556532C212yesmaximal, complemented
10C4×#14556531C211yesmaximal, characteristic, complemented
11C73×#3169C211yesmaximal, characteristic, complemented
12#17989121—21no—
13C2×#14556535C2212yes—
14C2×#14556532C2212yes—
15C2×#14556531C2212yes—
16#17988989C2211yescharacteristic
17#17988971C2211yescharacteristic
18#17988942—21no—
19#17988828C2211yescharacteristic
20#17988823C2211yescharacteristic
21#17988816—21no—
22C4×Dic292C2211yescharacteristic
23C4×#11924017—21no—
24C4×D584C2211yescharacteristic
25#17988414C2212yes—
26#17988412C2212yes—
27#17988390C2212yes—
28#17988388C2212yes—
29#17988388C2212yes—
30#17988387C2212yes—
31#17988363C2211yescharacteristic
32#17988363C2211yescharacteristic
33C4×#11924003C2212yes—
34#532×C73—21no—
35#500×C73C2211yescharacteristic
36#493×C73C2211yescharacteristic
37#486×C73—21no—
38#466×C73—21no—
39#466×C73C2212yes—
40C4×D8×C73—21no—
41C4×D8×C73C2212yes—
42C2×C4×C8×C73C2211yescharacteristic
43C2×Dic292C2311yescharacteristic
44C2×#11924017—21no—
45C2×D584C2311yescharacteristic
46#14556585—41no—
47#14556583—21no—
48#14556579—21no—
49#14556574—41no—
50#14556570—21no—
51#14556565—21no—
52C4×Dic146—21no—
53C4×D292—21no—
54C4×C22⋊D73—41no—
55#14556548—41no—
56#14556535—24no—
57#14556532—24no—
58#14556531—24no—
59C2×#11924003C2312yes—
60C2×#11924003C2312yes—
61#14556525C2311yescharacteristic
62#14556525C2311yescharacteristic
63#14556523—21no—
64#14556516—21no—
65#14556516—21no—
66#14556513—21no—
67#14556513—21no—
68C2×#41×C73—41no—
69C2×D8×C73—21no—
70C2×D8×C73C2312yes—
71C22×C8×C73D411yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C4⋊Q8×C73—21no—
74#127×C73—21no—
75#124×C73—41no—
76#121×C73—22no—
77#121×C73—41no—
78C4×D4×C73—22no—
79C4×D4×C73—41no—
80C2×C42×C73D411yescharacteristic
81#107×C73—21no—
82#107×C73C2312yes—
83#102×C73—22no—
84#102×C73—22no—
85C4×C8×C73D411yescharacteristic
86C4×C8×C73D411yescharacteristic
87C4×C8×C73C2311yescharacteristic
88C4×C8×C73C2311yescharacteristic
89C2×Dic146—21no—
90C2×D292—21no—
91C2×C22⋊D73—41no—
92C2×C4×D73—41no—
93Dic292—22no—
94#11924017—42no—
95D584—22no—
96C4⋊Dic73—21no—
97C4⋊Dic73—21no—
98#11924007—41no—
99#11924007—41no—
100#11924007—41no—
101#11924007—41no—
102C22⋊Dic73—41no—
103#11924005—41no—
104#11924005—41no—
105#11924005—41no—
106#11924005—41no—
107C4×Dic73—41no—
108#11924003—22no—
109#11924003#4114yescomplemented
110#41×C73—84no—
111C2×Q8×C73—41no—
112C2×D4×C73—22no—
113C2×D4×C73—42no—
114C2×D4×C73—41no—
115C2×D4×C73—41no—
116C22×C4×C73—42no—
117C22×C4×C73D811yescharacteristic
118C22×C4×C73D811yescharacteristic
119C22×C4×C73C2×D411yescharacteristic
120D8×C73—22no—
121D8×C73—22no—
122D8×C73—42no—
123C2×C8×C73—22no—
124C2×C8×C73—22no—
125C2×C8×C73C2×D411yescharacteristic
126C2×C8×C73C2×D411yescharacteristic
127C2×C8×C73C2×D411yescharacteristic
128C2×C8×C73C2411yescharacteristic
129C4⋊C4×C73—22no—
130C4⋊C4×C73—41no—
131C22⋊C4×C73—42no—
132C22⋊C4×C73—42no—
133C42×C73D811yescharacteristic
134C42×C73D811yescharacteristic
135C42×C73C2×D411yescharacteristic
136C42×C73C2×D411yescharacteristic
137C23×C73—42no—
138C23×C73C2×D811yescharacteristic
139C22×D73—41no—
140Q8×C73—82no—
141D4×C73—42no—
142D4×C73—42no—
143D4×C73—82no—
144D4×C73—82no—
145D4×C73—84no—
146C2×C4×C73—21no—
147C2×C4×C73—21no—
148C2×C4×C73—22no—
149C2×C4×C73—41no—
150C2×C4×C73—42no—
151C2×C4×C73—84no—
152C2×C4×C73C2×D811yescharacteristic
153C2×C4×C73C2×D811yescharacteristic
154C2×C4×C73C2×D811yescharacteristic
155C2×C4×C73C2×D811yescharacteristic
156C2×C4×C73C2×D811yescharacteristic
157C2×C4×C73C22×D411yescharacteristic
158C22⋊D73—82no—
159C2×Dic73—41no—
160C2×Dic73—41no—
161C2×Dic73—41no—
162D292—41no—
163D292—41no—
164C4×D73—82no—
165Dic146—41no—
166Dic146—41no—
167C8×C73—21no—
168C8×C73—21no—
169C8×C73#13512yes—
170C8×C73C2×#4112yes—
171C22×C73—21no—
172C22×C73—21no—
173C22×C73—21no—
174C22×C73—82no—
175C22×C73—82no—
176C22×C73—82no—
177C22×C73C22×D811yescharacteristic
178C2×D73—81no—
179C2×D73—81no—
180C2×D73—81no—
181C4×C73—21no—
182C4×C73—21no—
183C4×C73—21no—
184C4×C73—21no—
185C4×C73—82no—
186C4×C73#50912yes—
187C4×C73#53211yescharacteristic
188C4×C73C2×#13511yescharacteristic
189Dic73—81no—
190Dic73—81no—
191Dic73—81no—
192#33737—731nomaximal, Sylow
193C2×C73—41no—
194C2×C73—162no—
195C2×C73#316911yescharacteristic
196C2×C73C2×#50911yescharacteristic
197C2×C73#341411yescharacteristic
198D73—161no—
199#3169D7311yescharacteristic, complemented
200#3168—731no—
201#2255—731no—
202#2250—731no—
203#2244—731no—
204#2243—731no—
205#2220—732no—
206#2218—732no—
207C4×SD32—732no—
208C4×D16—732no—
209C4×M32—731no—
210C73#3373711yescharacteristic, complemented, Sylow
211#532—21no—
212#529—1461no—
213C2×SD32—732no—
214C2×D16—732no—
215C2×M32—732no—
216#500C2×D7311yescharacteristic
217#499—731no—
218#495—731no—
219#493C2×D7311yescharacteristic
220#488—1461no—
221#486—21no—
222#467—731no—
223#466—21no—
224#466—731no—
225#466C2×D7312yes—
226#465—1461no—
227C4×Q16—731no—
228C4×SD16—1461no—
229C4×D8—21no—
230C4×D8—731no—
231C4×D8C2×D7312yes—
232C2×C4×C8C2×D7311yescharacteristic
233#367—732no—
234#366—732no—
235#358—732no—
236#357—732no—
237#357—732no—
238#357—732no—
239#346—731no—
240#346—731no—
241C4×C16—732no—
242C2×#41—41no—
243C2×Q16—731no—
244C2×SD16—1461no—
245C2×D8—21no—
246C2×D8—731no—
247C2×D8C22×D7312yes—
248C22×C8C22⋊D7311yescharacteristic
249C22×C8C22×D7311yescharacteristic
250C4⋊Q8—21no—
251#127—21no—
252#126—2921no—
253#125—1461no—
254#124—41no—
255#124—1461no—
256#123—2921no—
257C22⋊Q8—1461no—
258#121—22no—
259#121—41no—
260#121—1461no—
261C4×Q8—1461no—
262C4×D4—22no—
263C4×D4—41no—
264C4×D4—2921no—
265C4×D4—1461no—
266#117—2921no—
267C2×C42C22⋊D7311yescharacteristic
268SD32—1464no—
269D16—1464no—
270M32—1464no—
271C2×C16—732no—
272C2×C16—732no—
273#107—21no—
274#107—731no—
275#107—731no—
276#107C22×D7312yes—
277#106—1461no—
278#103—1461no—
279#103—1461no—
280#102—22no—
281#102—22no—
282#102—1461no—
283#102—1461no—
284C4×C8C22⋊D7311yescharacteristic
285C4×C8C22⋊D7311yescharacteristic
286C4×C8C22×D7311yescharacteristic
287C4×C8C22×D7311yescharacteristic
288#41—84no—
289C2×Q8—41no—
290C2×Q8—1461no—
291C2×D4—22no—
292C2×D4—42no—
293C2×D4—41no—
294C2×D4—41no—
295C2×D4—2921no—
296C2×D4—1461no—
297C22×C4—42no—
298C22×C4—2921no—
299C22×C4#1192401311yescharacteristic
300C22×C4#1192401311yescharacteristic
301C22×C4C2×C22⋊D7311yescharacteristic
302Q16—1462no—
303SD16—2922no—
304D8—22no—
305D8—22no—
306D8—42no—
307D8—1462no—
308C2×C8—22no—
309C2×C8—22no—
310C2×C8C2×C22⋊D7311yescharacteristic
311C2×C8C2×C22⋊D7311yescharacteristic
312C2×C8C2×C22⋊D7311yescharacteristic
313C2×C8C23×D7311yescharacteristic
314C4⋊C4—22no—
315C4⋊C4—41no—
316C4⋊C4—2921no—
317C4⋊C4—2921no—
318C4⋊C4—2921no—
319C4⋊C4—2921no—
320C4⋊C4—1461no—
321C4⋊C4—1461no—
322C22⋊C4—42no—
323C22⋊C4—42no—
324C22⋊C4—2921no—
325C22⋊C4—2921no—
326C22⋊C4—2921no—
327C22⋊C4—2921no—
328C22⋊C4—2921no—
329C42—2921no—
330C42#1192401311yescharacteristic
331C42#1192401311yescharacteristic
332C42C2×C22⋊D7311yescharacteristic
333C42C2×C22⋊D7311yescharacteristic
334C16—734no—
335C16—1462no—
336C23—42no—
337C23—2921no—
338C23C2×#1192401311yescharacteristic
339Q8—82no—
340Q8—2921no—
341Q8—2921no—
342D4—42no—
343D4—42no—
344D4—82no—
345D4—82no—
346D4—84no—
347D4—2921no—
348D4—2921no—
349D4—5842no—
350C2×C4—21no—
351C2×C4—22no—
352C2×C4—21no—
353C2×C4—41no—
354C2×C4—42no—
355C2×C4—84no—
356C2×C4—2921no—
357C2×C4—2921no—
358C2×C4—2921no—
359C2×C4—5842no—
360C2×C4C2×#1192401311yescharacteristic
361C2×C4C2×#1192401311yescharacteristic
362C2×C4C2×#1192401311yescharacteristic
363C2×C4C2×#1192401311yescharacteristic
364C2×C4C2×#1192401311yescharacteristic
365C2×C4C22×C22⋊D7311yescharacteristic
366C8—21no—
367C8—21no—
368C8#1455661112yes—
369C8#41×D7312yes—
370C22—21no—
371C22—21no—
372C22—21no—
373C22—82no—
374C22—82no—
375C22—82no—
376C22—5841no—
377C22—5841no—
378C22—5841no—
379C22C22×#1192401311yescharacteristic
380C4—21no—
381C4—21no—
382C4—21no—
383C4—21no—
384C4—82no—
385C4—5841no—
386C4—5841no—
387C4—5841no—
388C4#1798902312yes—
389C4#1798913311yescharacteristic
390C4C2×#1455661111yescharacteristic
391C2—41no—
392C2—162no—
393C2—11681no—
394C2#2262050611yescharacteristic
395C2C2×#1798902311yescharacteristic
396C2#2262306511yescharacteristic
subgroupG/H
centerC2×C4C2×#11924013
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#3169C2
socleC22×C73C22×D8
hypercenter#3169D73
hypocenterC73#33737
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3169

Complements

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

NH ≅ G/Ntype
1. #22620501C2semidirect
2. #22612214C2semidirect
3. #22612195C2semidirect
4. #22612172C2semidirect
5. #22612170C2semidirect
6. #22612042C2semidirect
7. #22612032C2semidirect
8. C4×#14556535C2semidirect
9. C4×#14556532C2semidirect
10. C4×#14556531C2semidirect
11. C73×#3169C2semidirect
109. #11924003#41semidirect
199. #3169D73semidirect
210. C73#33737semidirect

Maximal subgroups

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

subgroupindex
#226205012
#226122142
#226121952
#226121722
#226121702
#226120422
#226120322
C4×#145565352
C4×#145565322
C4×#145565312
C73×#31692
#3373773