Finite Group Databasebeta

← #33240245

Subgroups — #33240245

Order 18688.

718 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#17989017C212yesmaximal, complemented
2C4×#14556613C211yesmaximal, characteristic, complemented
3#22611990C212yesmaximal, complemented
4#22611983C212yesmaximal, complemented
5#22611978C211yesmaximal, characteristic, complemented
6#22611973C211yesmaximal, characteristic, complemented
7#22611968C211yesmaximal, characteristic, complemented
8#22611963C211yesmaximal, characteristic, complemented
9C2×C4⋊#11924003C211yesmaximal, characteristic, complemented
10#22611638C212yesmaximal, complemented
11C73×#3147C211yesmaximal, characteristic, complemented
12C2×#14556613C2211yescharacteristic
13C4×#11924028—21no—
14#17989017—28no—
15C2×#14556537C2212yes—
16C2×#14556535C2212yes—
17C2×#14556534C2212yes—
18C2×#14556532C2212yes—
19C22×#11924003C2212yes—
20C4×Dic292C2211yescharacteristic
21C4×Dic292C2211yescharacteristic
22C4×#11924017—21no—
23C4×#11924017—21no—
24C4×D584C2211yescharacteristic
25C4×D584C2211yescharacteristic
26#17988625C2211yescharacteristic
27#17988584—21no—
28C4⋊#11924003C2211yescharacteristic
29C4⋊#11924003C2211yescharacteristic
30C4⋊#11924003C2212yes—
31#17988391C2212yes—
32#17988391C2212yes—
33#17988388C2212yes—
34#17988388C2212yes—
35C2×#135×C73—21no—
36C2×#135×C73C2212yes—
37#532×C73—21no—
38#495×C73—21no—
39#495×C73C2212yes—
40#494×C73C2211yescharacteristic
41#493×C73C2211yescharacteristic
42#492×C73—21no—
43C2×C4×C8×C73C2211yescharacteristic
44C2×#11924028—21no—
45#14556613—22no—
46#14556613D414yescomplemented
47C2×Dic292C2311yescharacteristic
48C2×#11924017—21no—
49C2×D584C2311yescharacteristic
50C4×Dic146—21no—
51C4×Dic146—21no—
52C4×D292—21no—
53C4×D292—21no—
54C4×C22⋊D73—41no—
55C4×C22⋊D73—41no—
56#14556550—21no—
57#14556548—41no—
58C42×D73—41no—
59#14556537—24no—
60#14556535—24no—
61#14556534—24no—
62#14556532—24no—
63C2×#11924003—24no—
64C2×#11924003C2312yes—
65C2×#11924003C2312yes—
66#14556525C2311yescharacteristic
67#14556525C2311yescharacteristic
68#14556523—21no—
69#14556516—21no—
70#14556516—21no—
71#14556513—21no—
72#14556513—21no—
73C2×#41×C73—22no—
74#135×C73—24no—
75#135×C73—24no—
76#135×C73—44no—
77C2×Q16×C73—21no—
78C2×Q16×C73C2312yes—
79C2×SD16×C73—22no—
80C2×SD16×C73—22no—
81C2×D8×C73—21no—
82C2×D8×C73C2312yes—
83C22×C8×C73D411yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C4⋊Q8×C73—21no—
86#127×C73—21no—
87#124×C73—22no—
88#121×C73—41no—
89#121×C73—41no—
90C4×D4×C73—41no—
91C4×D4×C73—41no—
92C2×C42×C73D411yescharacteristic
93C4×C8×C73D411yescharacteristic
94C4×C8×C73D411yescharacteristic
95C4×C8×C73C2311yescharacteristic
96C4×C8×C73C2311yescharacteristic
97#11924028—24no—
98#11924028—42no—
99C2×Dic146—21no—
100C2×D292—21no—
101C2×C22⋊D73—41no—
102C2×C4×D73—41no—
103C2×C4×D73—41no—
104C2×C4×D73—41no—
105Dic292—21no—
106Dic292C2×D412yes—
107#11924017—24no—
108D584—21no—
109D584C2×D412yes—
110C4⋊Dic73—21no—
111C4⋊Dic73—21no—
112#11924007—41no—
113#11924007—41no—
114C22⋊Dic73—41no—
115#11924005—41no—
116#11924005—41no—
117C4×Dic73—41no—
118C4×Dic73—41no—
119C4×Dic73—41no—
120#11924003—22no—
121#11924003—22no—
122#41×C73—44no—
123#41×C73—44no—
124C2×Q8×C73—22no—
125C2×D4×C73—22no—
126C2×D4×C73—42no—
127C2×D4×C73—41no—
128C2×D4×C73—41no—
129C22×C4×C73—42no—
130C22×C4×C73D811yescharacteristic
131C22×C4×C73D811yescharacteristic
132C22×C4×C73C2×D411yescharacteristic
133Q16×C73—22no—
134Q16×C73—22no—
135Q16×C73—42no—
136SD16×C73—44no—
137SD16×C73—44no—
138D8×C73—22no—
139D8×C73—22no—
140D8×C73—42no—
141C2×C8×C73—22no—
142C2×C8×C73C2×D412yes—
143C2×C8×C73C2×D411yescharacteristic
144C2×C8×C73C2×D411yescharacteristic
145C2×C8×C73C2×D411yescharacteristic
146C2×C8×C73#4112yes—
147C2×C8×C73C2411yescharacteristic
148C4⋊C4×C73—41no—
149C4⋊C4×C73—41no—
150C22⋊C4×C73—42no—
151C22⋊C4×C73—42no—
152C42×C73D811yescharacteristic
153C42×C73D811yescharacteristic
154C42×C73C2×D411yescharacteristic
155C42×C73C2×D411yescharacteristic
156C23×C73—42no—
157C23×C73C2×D811yescharacteristic
158C22×D73—41no—
159Q8×C73—42no—
160Q8×C73—42no—
161D4×C73—42no—
162D4×C73—42no—
163D4×C73—82no—
164D4×C73—84no—
165D4×C73—82no—
166C2×C4×C73—22no—
167C2×C4×C73—41no—
168C2×C4×C73—42no—
169C2×C4×C73—84no—
170C2×C4×C73#12112yes—
171C2×C4×C73C2×D811yescharacteristic
172C2×C4×C73C2×D811yescharacteristic
173C2×C4×C73C2×D811yescharacteristic
174C2×C4×C73C2×D811yescharacteristic
175C2×C4×C73C2×D811yescharacteristic
176C2×C4×C73AGL(1,ℤ/8)12yes—
177C2×C4×C73C22×D411yescharacteristic
178C22⋊D73—44no—
179C2×Dic73—41no—
180C2×Dic73—41no—
181C2×Dic73—41no—
182D292—22no—
183D292—41no—
184C4×D73—44no—
185C4×D73—82no—
186C4×D73—82no—
187Dic146—22no—
188Dic146—41no—
189C8×C73—21no—
190C8×C73—21no—
191C8×C73#12112yes—
192C8×C73C22×D411yescharacteristic
193C8×C73C2×#4111yescharacteristic
194C22×C73—21no—
195C22×C73—21no—
196C22×C73—82no—
197C22×C73—82no—
198C22×C73—82no—
199C22×C73#45912yes—
200C22×C73C22×D811yescharacteristic
201C2×D73—42no—
202C2×D73—81no—
203C2×D73—81no—
204C4×C73—21no—
205C4×C73—21no—
206C4×C73—21no—
207C4×C73—82no—
208C4×C73#45912yes—
209C4×C73#50812yescomplemented
210C4×C73C2×#12111yescharacteristic
211C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
212Dic73—42no—
213Dic73—81no—
214Dic73—81no—
215#33579—731nomaximal, Sylow
216C2×C73—22no—
217C2×C73—162no—
218C2×C73C2×#45911yescharacteristic
219C2×C73C2×#50811yescharacteristic
220C2×C73#341411yescharacteristic
221D73—82no—
222C2×#508—732no—
223#3147D7311yescharacteristic, complemented
224C4×#135—731no—
225#2211—732no—
226#2210—732no—
227#2209—731no—
228#2208—731no—
229#2207—731no—
230#2206—731no—
231C2×C4⋊C16—731no—
232#2138—732no—
233C73#3357911yescharacteristic, complemented, Sylow
234C2×#135—21no—
235C2×#135—731no—
236C2×#135C2×D7312yes—
237#532—21no—
238C4×#41—1461no—
239#508—1468no—
240C2×Q32—732no—
241C2×SD32—732no—
242C2×SD32—732no—
243C2×D16—732no—
244C22×C16—732no—
245#495—21no—
246#495C2×D7312yes—
247#494C2×D7311yescharacteristic
248#493C2×D7311yescharacteristic
249#492—21no—
250C4×Q16—731no—
251C4×Q16—731no—
252C4×SD16—1461no—
253C4×SD16—1461no—
254C4×D8—731no—
255C4×D8—731no—
256#427—731no—
257#416—1461no—
258C2×C4×C8C2×D7311yescharacteristic
259C4⋊C16—731no—
260C4⋊C16—731no—
261C4⋊C16—732no—
262#358—732no—
263#358—732no—
264#357—732no—
265#357—732no—
266C2×#41—22no—
267C2×#41—1461no—
268#135—24no—
269#135—24no—
270#135—44no—
271#135—734no—
272#135—1462no—
273C2×Q16—21no—
274C2×Q16—731no—
275C2×Q16C22×D7312yes—
276C2×SD16—22no—
277C2×SD16—22no—
278C2×SD16—1461no—
279C2×D8—21no—
280C2×D8—731no—
281C2×D8C22×D7312yes—
282C22×C8C22⋊D7311yescharacteristic
283C22×C8C22×D7311yescharacteristic
284C4⋊Q8—21no—
285#127—21no—
286#124—22no—
287#121—41no—
288#121—41no—
289C4×Q8—1461no—
290C4×Q8—1461no—
291C4×D4—41no—
292C4×D4—41no—
293C4×D4—2921no—
294C4×D4—2921no—
295C4×D4—1461no—
296C4×D4—1461no—
297#117—2921no—
298#117—1461no—
299C2×C42—2921no—
300C2×C42C22⋊D7311yescharacteristic
301Q32—1464no—
302SD32—1464no—
303SD32—1464no—
304D16—1464no—
305C2×C16—732no—
306C2×C16—732no—
307C2×C16—1464no—
308#107—731no—
309#107—731no—
310#106—1461no—
311#103—1461no—
312#103—1461no—
313#102—1461no—
314#102—1461no—
315C4×C8C22⋊D7311yescharacteristic
316C4×C8C22⋊D7311yescharacteristic
317C4×C8C22×D7311yescharacteristic
318C4×C8C22×D7311yescharacteristic
319#41—44no—
320#41—44no—
321#41—2922no—
322#41—1464no—
323C2×Q8—22no—
324C2×Q8—1461no—
325C2×D4—22no—
326C2×D4—42no—
327C2×D4—41no—
328C2×D4—41no—
329C2×D4—2921no—
330C2×D4—1461no—
331C22×C4—42no—
332C22×C4—2921no—
333C22×C4—2921no—
334C22×C4—2921no—
335C22×C4#1192401311yescharacteristic
336C22×C4#1192401311yescharacteristic
337C22×C4C2×C22⋊D7311yescharacteristic
338Q16—22no—
339Q16—22no—
340Q16—42no—
341Q16—732no—
342Q16—1461no—
343SD16—44no—
344SD16—44no—
345SD16—1464no—
346D8—22no—
347D8—22no—
348D8—42no—
349D8—732no—
350D8—1461no—
351C2×C8—22no—
352C2×C8D4×D7312yes—
353C2×C8C2×C22⋊D7311yescharacteristic
354C2×C8C2×C22⋊D7311yescharacteristic
355C2×C8C2×C22⋊D7311yescharacteristic
356C2×C8#1192402712yes—
357C2×C8C23×D7311yescharacteristic
358C4⋊C4—41no—
359C4⋊C4—41no—
360C4⋊C4—2921no—
361C4⋊C4—2921no—
362C4⋊C4—1461no—
363C4⋊C4—1461no—
364C22⋊C4—42no—
365C22⋊C4—42no—
366C22⋊C4—2921no—
367C22⋊C4—2921no—
368C22⋊C4—2921no—
369C42—2921no—
370C42—2921no—
371C42—2921no—
372C42#1192401311yescharacteristic
373C42#1192401311yescharacteristic
374C42C2×C22⋊D7311yescharacteristic
375C42C2×C22⋊D7311yescharacteristic
376C16—1462no—
377C16—1462no—
378C23—42no—
379C23—2921no—
380C23C2×#1192401311yescharacteristic
381Q8—42no—
382Q8—42no—
383Q8—2921no—
384Q8—1462no—
385D4—42no—
386D4—42no—
387D4—82no—
388D4—84no—
389D4—82no—
390D4—2924no—
391D4—2921no—
392D4—1462no—
393C2×C4—22no—
394C2×C4—41no—
395C2×C4—42no—
396C2×C4—84no—
397C2×C4—2921no—
398C2×C4—2924no—
399C2×C4—2921no—
400C2×C4—2921no—
401C2×C4—5842no—
402C2×C4—5842no—
403C2×C4#1455656212yes—
404C2×C4C2×#1192401311yescharacteristic
405C2×C4C2×#1192401311yescharacteristic
406C2×C4C2×#1192401311yescharacteristic
407C2×C4C2×#1192401311yescharacteristic
408C2×C4C2×#1192401311yescharacteristic
409C2×C4#1455661712yes—
410C2×C4C22×C22⋊D7311yescharacteristic
411C8—21no—
412C8—21no—
413C8#1455656212yes—
414C8C2×D4×D7311yescharacteristic
415C8C2×#1192402711yescharacteristic
416C22—21no—
417C22—21no—
418C22—82no—
419C22—82no—
420C22—82no—
421C22—2922no—
422C22—5841no—
423C22—5841no—
424C22#1798877912yes—
425C22C22×#1192401311yescharacteristic
426C4—21no—
427C4—21no—
428C4—21no—
429C4—82no—
430C4—2922no—
431C4—5841no—
432C4—5841no—
433C4#1798877912yes—
434C4#1798901712yescomplemented
435C4C2×#1455656211yescharacteristic
436C4C2×#1455661711yescharacteristic
437C2—22no—
438C2—162no—
439C2—5842no—
440C2C2×#1798877911yescharacteristic
441C2C2×#1798901711yescharacteristic
442C2#2262306511yescharacteristic
subgroupG/H
centerC2×C4C2×#11924013
commutator, cosocleC2×C8×C73C24
FrattiniC2×C8C23×D73
FittingC73×#3147C2
socleC22×C73C22×D8
hypercenter#3147D73
hypocenterC73#33579
LCSG ▷ C2×C8×C73 ▷ C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×C4×C8 ◁ #3147

Complements

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

NH ≅ G/Ntype
1. C2×#17989017C2semidirect
2. C4×#14556613C2semidirect
3. #22611990C2semidirect
4. #22611983C2semidirect
5. #22611978C2semidirect
6. #22611973C2semidirect
7. #22611968C2semidirect
8. #22611963C2semidirect
9. C2×C4⋊#11924003C2semidirect
10. #22611638C2semidirect
11. C73×#3147C2semidirect
46. #14556613D4semidirect
209. C4×C73#508semidirect
223. #3147D73semidirect
233. C73#33579semidirect
434. C4#17989017semidirect

Maximal subgroups

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

subgroupindex
C2×#179890172
C4×#145566132
#226119902
#226119832
#226119782
#226119732
#226119682
#226119632
C2×C4⋊#119240032
#226116382
C73×#31472
#3357973