Finite Group Databasebeta

← #14472143

Subgroups — #14472143

Order 1920.

672 conjugacy classes of subgroups.

The subgroup lattice has 464 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11756326C211yesmaximal, characteristic, complemented
2C3×#65918C211yesmaximal, characteristic
3C5×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#11747104C211yesmaximal, characteristic, complemented
5C4×#6662C212yesmaximal, complemented
6#11747084C212yesmaximal
7C4×#6657C211yesmaximal, characteristic
8#11746944C212yesmaximal, complemented
9#11746920C211yesmaximal, characteristic, complemented
10#11746891C212yesmaximal
11#11746889C211yesmaximal, characteristic
12#10611665—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14#91833—21no—
15#91778—22no—
16#91776—21no—
17#91759C2212yes—
18#91758C2211yescharacteristic
19C4×Dic30C2212yes—
20C4×Dic30C2211yescharacteristic
21C3×#4092—21no—
22C3×#4044—22no—
23C3×#4038—21no—
24C3×#4021C2212yes—
25C3×C4×D20C2211yescharacteristic
26C3×#4015C2211yescharacteristic
27C3×C4×Dic10C2212yes—
28C2×#6662C2212yes—
29C2×#6657C2211yescharacteristic
30C5×C4⋊(C3⋊C8)C2212yes—
31C5×C4⋊(C3⋊C8)C2211yescharacteristic
32C4×C5×C3⋊C8C2212yes—
33C4×C5×C3⋊C8C2211yescharacteristic
34#90990C2212yes—
35#90987C2211yescharacteristic
36#90974C2211yescharacteristic
37#90971C2212yes—
38#90971C2212yes—
39#90971C2212yes—
40#90965C2212yes—
41#90965C2211yescharacteristic
42#83676—51nomaximal, Hall
43#65918D311yescharacteristic
44#65901—31no—
45C5×C8×Q8—31no—
46#65138—31no—
47#65135—31no—
48#65134—32no—
49#65118—32no—
50C4×Dic20—32no—
51#64986—32no—
52C4×#677—31no—
53#64970—31no—
54C2×C3×C5×Q8D411yescharacteristic
55C2×Dic30—21no—
56C2×Dic30C2311yescharacteristic
57C2×C3×D20C2311yescharacteristic
58C2×C3×C4×D5—21no—
59C2×C3×Dic10C2312yes—
60C3×C5×C4⋊C4D411yescharacteristic
61C3×C5×C4⋊C4D412yes—
62C3×C42×C5C2311yescharacteristic
63C3×C42×C5C2312yes—
64C4⋊Dic15—21no—
65C4⋊Dic15C2311yescharacteristic
66C4⋊Dic15C2312yes—
67#6712—21no—
68#6712—22no—
69#6712—22no—
70#6712—22no—
71C4×Dic15—22no—
72C4×Dic15—21no—
73C2×C5×C3⋊C8C2311yescharacteristic
74C2×C5×C3⋊C8C2312yes—
75C2×C5×C3⋊C8C2311yescharacteristic
76C3×#685—22no—
77C3×#685—21no—
78C3×#685—22no—
79C3×C4⋊Dic5—21no—
80C3×C4⋊Dic5—21no—
81C3×C4⋊Dic5C2311yescharacteristic
82C3×#683—22no—
83C3×C4×Dic5—22no—
84#6662—24no—
85#6657—22no—
86C3×#556—51no—
87#5567—51no—
88#5090—51no—
89#5079—51no—
90#5056—52no—
91#5054—52no—
92C4×#216—52no—
93Q8×C3⋊C8D511yescharacteristic, complemented
94#5022—52no—
95C4×#214—51no—
96#5007—51no—
97C4×C5×Q8C2×D311yescharacteristic
98#4092—21no—
99#4090—61no—
100C2×Dic20—32no—
101C2×#677—31no—
102#4044—22no—
103#4038—21no—
104#4035—62no—
105#4033—61no—
106#4021C2×D312yes—
107C4×D20C2×D311yescharacteristic
108#4016—32no—
109#4015—31no—
110#4015C2×D311yescharacteristic
111C4×Dic10—32no—
112C4×Dic10—31no—
113C4×Dic10C2×D312yes—
114C5×C4⋊C8—32no—
115C5×C4⋊C8—31no—
116C4×C5×C8—31no—
117C4×C5×C8—32no—
118#3953—32no—
119#3953—31no—
120#3950—32no—
121#3949—31no—
122#3948—32no—
123#3948—32no—
124#3948—32no—
125#3948—31no—
126#3364—151noSylow
127C22×C3×D5—21no—
128C3×C5×Q8—22no—
129C2×C3×C4×C5C2×D412yes—
130C2×C3×C4×C5C2×D412yes—
131C2×C3×C4×C5C2×D411yescharacteristic
132C2×C3×C4×C5C2×D411yescharacteristic
133C2×C3×C4×C5C2411yescharacteristic
134C2×Dic15—21no—
135C2×Dic15—21no—
136C2×Dic15—22no—
137Dic30—21no—
138Dic30—42no—
139Dic30#4112yes—
140C2×C3×Dic5—21no—
141C2×C3×Dic5—22no—
142C3×D20—21no—
143C3×D20—21no—
144C3×C4×D5—42no—
145C3×Dic10—22no—
146C3×Dic10—22no—
147C5×C3⋊C8—21no—
148C5×C3⋊C8—22no—
149C5×C3⋊C8—21no—
150C3×C4⋊Q8—51no—
151C3×#126—102no—
152C3×#124—52no—
153C3×C22⋊Q8—101no—
154C3×C4×Q8—52no—
155C3×C4×Q8C2×D511yescharacteristic
156C3×C4×D4—51no—
157C3×#117—101no—
158#944—101no—
159C2×#216—52no—
160C2×#214—51no—
161#889—102no—
162#887—101no—
163#870—52no—
164#869—51no—
165C4×Dic6—51no—
166C4×Dic6—52no—
167#835—52no—
168#835—52no—
169#835—52no—
170#832—52no—
171#832—51no—
172#810—51no—
173#808—51no—
174#807—52no—
175C4⋊(C3⋊C8)C2×D511yescharacteristic
176C4⋊(C3⋊C8)C2×D512yes—
177C4×C3⋊C8C2×D511yescharacteristic
178C4×C3⋊C8C2×D512yes—
179C2×C5×Q8#6711yescharacteristic
180C2×D20C22×D311yescharacteristic
181C2×C4×D5—21no—
182C2×Dic10—31no—
183C2×Dic10—61no—
184C2×Dic10C22×D312yes—
185C2×C5×C8—31no—
186C2×C5×C8—31no—
187C2×C5×C8—32no—
188C5×C4⋊C4#6711yescharacteristic
189C5×C4⋊C4#6712yes—
190C42×C5C22×D312yes—
191C42×C5C22×D311yescharacteristic
192#685—21no—
193#685—22no—
194#685—22no—
195C4⋊Dic5—21no—
196C4⋊Dic5—21no—
197C4⋊Dic5—31no—
198C4⋊Dic5—32no—
199C4⋊Dic5—61no—
200C4⋊Dic5C22×D311yescharacteristic
201#683—22no—
202#683—61no—
203#683—62no—
204#683—62no—
205#683—62no—
206C4×Dic5—22no—
207C4×Dic5—62no—
208C4×Dic5—61no—
209Dic20—64no—
210#677—62no—
211#557—151no—
212#556—51no—
213#488—152no—
214#487—151no—
215#479—152no—
216#474—151no—
217#464—152no—
218#462—151no—
219C8×Q8—31no—
220C4×Q16—152no—
221C4×SD16—151no—
222C22×C3×C5C22×D411yescharacteristic
223C2×C3×D5—41no—
224C2×C3×D5—41no—
225C2×C3×D5—41no—
226C3×C4×C5—22no—
227C3×C4×C5—22no—
228C3×C4×C5—21no—
229C3×C4×C5#13512yes—
230C3×C4×C5C2×#4111yescharacteristic
231C3×C4×C52−1+411yescharacteristic
232Dic15—22no—
233Dic15—42no—
234Dic15—41no—
235C3×Dic5—42no—
236C3×Dic5—41no—
237C2×C3×Q8—52no—
238C2×C3×Q8D2011yescharacteristic
239C2×C3×D4—51no—
240C22×C3×C4—101no—
241C2×Dic6—51no—
242C2×Dic6—101no—
243C3×C4⋊C4—51no—
244C3×C4⋊C4—102no—
245C3×C4⋊C4—101no—
246C3×C4⋊C4—101no—
247C3×C4⋊C4D2011yescharacteristic
248C3×C4⋊C4D2012yes—
249C3×C22⋊C4—102no—
250C3×C22⋊C4—101no—
251C3×C22⋊C4—102no—
252C3×C42—102no—
253C3×C42C22×D511yescharacteristic
254C3×C42C22×D512yes—
255#216—104no—
256#214—102no—
257C4⋊Dic3—52no—
258C4⋊Dic3—51no—
259C4⋊Dic3—101no—
260Dic3⋊C4—101no—
261Dic3⋊C4—102no—
262Dic3⋊C4—102no—
263Dic3⋊C4—102no—
264C4×Dic3—102no—
265C4×Dic3—101no—
266C2×C3⋊C8C22×D511yescharacteristic
267C2×C3⋊C8C22×D512yes—
268C2×C3⋊C8C22×D511yescharacteristic
269C22×D5—21no—
270C5×Q8—22no—
271C2×C4×C5C2×#6712yes—
272C2×C4×C5C2×#6712yes—
273C2×C4×C5C2×#6711yescharacteristic
274C2×C4×C5C2×#6711yescharacteristic
275C2×C4×C5C23×D311yescharacteristic
276C2×Dic5—21no—
277C2×Dic5—22no—
278C2×Dic5—61no—
279C2×Dic5—61no—
280C2×Dic5—62no—
281D20—21no—
282D20—21no—
283C4×D5—42no—
284Dic10—22no—
285Dic10—22no—
286Dic10—32no—
287Dic10—61no—
288Dic10—122no—
289C5×C8—61no—
290C5×C8—62no—
291C5×C8—61no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—51no—
295C4⋊Q8—151no—
296C4⋊Q8—301no—
297#126—102no—
298#125—152no—
299#125—302no—
300#124—52no—
301C22⋊Q8—101no—
302C4×Q8—52no—
303C4×Q8—151no—
304C4×Q8—152no—
305C4×Q8—301no—
306C4×Q8D3×D511yescharacteristic
307C4×D4—51no—
308#117—101no—
309#107—152no—
310#106—151no—
311C4⋊C8—31no—
312C4⋊C8—32no—
313#103—151no—
314#103—152no—
315#103—152no—
316#103—152no—
317#102—151no—
318#102—152no—
319C4×C8—31no—
320C4×C8—32no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324C3×D5—81no—
325C23×C3—101no—
326C3×Q8—22no—
327C3×Q8—102no—
328C3×Q8—102no—
329C3×D4—101no—
330C3×D4—101no—
331C2×C3×C4—101no—
332C2×C3×C4—102no—
333C2×C3×C4—202no—
334C2×C3×C4C2×D2012yes—
335C2×C3×C4C2×D2012yes—
336C2×C3×C4C2×D2011yescharacteristic
337C2×C3×C4C2×D2011yescharacteristic
338C2×C3×C4C23×D511yescharacteristic
339C2×Dic3—101no—
340C2×Dic3—101no—
341C2×Dic3—102no—
342Dic6—52no—
343Dic6—101no—
344Dic6—202no—
345C3⋊C8—21no—
346C3⋊C8—21no—
347C3⋊C8—22no—
348C22×C5C22×#6711yescharacteristic
349C2×D5—41no—
350C2×D5—41no—
351C2×D5—41no—
352C4×C5—22no—
353C4×C5—22no—
354C4×C5—21no—
355C4×C5#95012yes—
356C4×C5D3×#4111yescharacteristic
357C4×C5#101011yescharacteristic
358Dic5—41no—
359Dic5—42no—
360Dic5—62no—
361Dic5—122no—
362Dic5—121no—
363C2×Q8—52no—
364C2×Q8—151no—
365C2×Q8—301no—
366C2×Q8#120211yescharacteristic
367C2×D4—51no—
368C22×C4—101no—
369Q16—304no—
370SD16—302no—
371C2×C8—31no—
372C2×C8—32no—
373C2×C8—31no—
374C4⋊C4—51no—
375C4⋊C4—101no—
376C4⋊C4—102no—
377C4⋊C4—101no—
378C4⋊C4—151no—
379C4⋊C4—152no—
380C4⋊C4—301no—
381C4⋊C4—302no—
382C4⋊C4—302no—
383C4⋊C4—302no—
384C4⋊C4—301no—
385C4⋊C4#120211yescharacteristic
386C4⋊C4#120212yes—
387C22⋊C4—102no—
388C22⋊C4—101no—
389C22⋊C4—102no—
390C42—102no—
391C42—302no—
392C42—301no—
393C42C2×D3×D511yescharacteristic
394C42C2×D3×D512yes—
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3—201no—
397C22×C3—201no—
398C22×C3—201no—
399C22×C3C22×D2011yescharacteristic
400C3×C4—22no—
401C3×C4—22no—
402C3×C4—21no—
403C3×C4—201no—
404C3×C4—202no—
405C3×C4#405012yes—
406C3×C4#414711yescharacteristic
407C3×C4D5×#4111yescharacteristic
408Dic3—102no—
409Dic3—202no—
410Dic3—201no—
411C2×C5C2×#95011yescharacteristic
412C2×C5#583111yescharacteristic
413C2×C5#583811yescharacteristic
414D5—81no—
415C23—101no—
416Q8—22no—
417Q8—102no—
418Q8—102no—
419Q8—152no—
420Q8—301no—
421Q8—602no—
422D4—101no—
423D4—101no—
424C2×C4—101no—
425C2×C4—102no—
426C2×C4—202no—
427C2×C4—301no—
428C2×C4—301no—
429C2×C4—302no—
430C2×C4C2×#120212yes—
431C2×C4C2×#120211yescharacteristic
432C2×C4C2×#120212yes—
433C2×C4C2×#120211yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—61no—
436C8—61no—
437C8—62no—
438C2×C3—401no—
439C2×C3#6591011yescharacteristic
440C2×C3C2×#405011yescharacteristic
441C2×C3#6608711yescharacteristic
442C5#8367611yescharacteristic, complemented, Sylow
443C22—201no—
444C22—201no—
445C22—201no—
446C22C22×#120211yescharacteristic
447C4—22no—
448C4—21no—
449C4—22no—
450C4—201no—
451C4—202no—
452C4—302no—
453C4—601no—
454C4—602no—
455C4#9131112yes—
456C4#9202811yescharacteristic
457C4#9203411yescharacteristic
458C3#1061166511yescharacteristic, complemented, Sylow
459C2—401no—
460C2C2×#9131111yescharacteristic
461C2#1175525711yescharacteristic
462C2#1175531211yescharacteristic
subgroupG/H
centerC22C22×#1202
commutator, cosocleC2×C3×C4×C5C24
FrattiniC2×C4C22×D3×D5
FittingC3×C4×C5×Q8C22
socleC22×C3×C5C22×D4
prime radicalC2×C3×D20C23
hypercenterC4×Q8D3×D5
hypocenterC3×C5#3364
LCSG ▷ C2×C3×C4×C5 ▷ C2×C3×C5 ▷ C3×C5
UCSC1 ◁ C22 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
1. #11756326C2semidirect
3. C5×Q8×C3⋊C8C2semidirect
4. #11747104C2semidirect
5. C4×#6662C2semidirect
8. #11746944C2semidirect
9. #11746920C2semidirect
93. Q8×C3⋊C8D5semidirect
395. C3×C5#3364semidirect
442. C5#83676semidirect
458. C3#10611665semidirect

Maximal subgroups

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

subgroupindex
#117563262
C3×#659182
C5×Q8×C3⋊C82
#117471042
C4×#66622
#117470842
C4×#66572
#117469442
#117469202
#117468912
#117468892
#106116653
#836765