Finite Group Databasebeta

← #14472144

Subgroups — #14472144

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#11756343C211yesmaximal, characteristic
2C3×#65901C211yesmaximal, characteristic, complemented
3C5×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#11747095C211yesmaximal, characteristic, complemented
5C4×#6662C212yesmaximal, complemented
6#11747065C212yesmaximal
7C4×#6658C211yesmaximal, characteristic
8#11746971C211yesmaximal, characteristic
9#11746934C212yesmaximal, complemented
10#11746933C212yesmaximal
11#11746921C211yesmaximal, characteristic, complemented
12#10611665—31nomaximal, Hall
13C3×C4×C5×Q8C2211yescharacteristic
14#91835—21no—
15#91787—22no—
16#91781—21no—
17#91764C2212yes—
18C4×D60C2211yescharacteristic
19#91758C2211yescharacteristic
20C4×Dic30C2212yes—
21C3×#4090—21no—
22C3×#4035—22no—
23C3×#4033—21no—
24C3×#4016C2212yes—
25C3×#4015C2211yescharacteristic
26C3×C4×Dic10C2212yes—
27C3×C4×Dic10C2211yescharacteristic
28C2×#6662C2212yes—
29C2×#6658C2211yescharacteristic
30C5×C4⋊(C3⋊C8)C2211yescharacteristic
31C5×C4⋊(C3⋊C8)C2212yes—
32C4×C5×C3⋊C8C2212yes—
33C4×C5×C3⋊C8C2211yescharacteristic
34#90990C2212yes—
35#90987C2211yescharacteristic
36#90974C2212yes—
37#90974C2212yes—
38#90974C2212yes—
39#90971C2211yescharacteristic
40#90968C2211yescharacteristic
41#90968C2212yes—
42#83689—51nomaximal, Hall
43#65918—31no—
44#65901D311yescharacteristic, complemented
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×D60C2311yescharacteristic
56C2×C4×D15—21no—
57C2×Dic30C2312yes—
58C2×C3×Dic10—21no—
59C2×C3×Dic10C2311yescharacteristic
60C3×C5×C4⋊C4D411yescharacteristic
61C3×C5×C4⋊C4D412yes—
62C3×C42×C5C2312yes—
63C3×C42×C5C2311yescharacteristic
64#6714—21no—
65#6714—22no—
66#6714—22no—
67C4⋊Dic15—21no—
68C4⋊Dic15—21no—
69C4⋊Dic15C2311yescharacteristic
70#6712—22no—
71C4×Dic15—22no—
72C2×C5×C3⋊C8C2311yescharacteristic
73C2×C5×C3⋊C8C2312yes—
74C2×C5×C3⋊C8C2311yescharacteristic
75C3×C4⋊Dic5—21no—
76C3×C4⋊Dic5C2311yescharacteristic
77C3×C4⋊Dic5C2312yes—
78C3×#683—22no—
79C3×#683—22no—
80C3×#683—21no—
81C3×#683—22no—
82C3×C4×Dic5—21no—
83C3×C4×Dic5—22no—
84#6662—24no—
85#6658—22no—
86C3×#557—51no—
87#5584—51no—
88#5093—51no—
89#5087—51no—
90#5068—52no—
91#5063—52no—
92#5031—51no—
93C4×#216—52no—
94#5028—52no—
95C4×#215—51no—
96Q8×C3⋊C8D511yescharacteristic, complemented
97C4×C5×Q8C2×D311yescharacteristic
98#4092—61no—
99#4090—21no—
100C2×Dic20—32no—
101C2×#677—31no—
102#4044—62no—
103#4038—61no—
104#4035—22no—
105#4033—21no—
106#4021—32no—
107C4×D20—31no—
108#4016C2×D312yes—
109#4015—31no—
110#4015C2×D311yescharacteristic
111C4×Dic10—32no—
112C4×Dic10C2×D312yes—
113C4×Dic10C2×D311yescharacteristic
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—31no—
123#3948—32no—
124#3948—32no—
125#3948—32no—
126#3364—151noSylow
127C22×D15—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—22no—
136D60—21no—
137D60—21no—
138C4×D15—42no—
139Dic30—22no—
140Dic30—22no—
141C2×C3×Dic5—21no—
142C2×C3×Dic5—21no—
143C2×C3×Dic5—22no—
144C3×Dic10—21no—
145C3×Dic10—42no—
146C3×Dic10#4112yes—
147C5×C3⋊C8—21no—
148C5×C3⋊C8—22no—
149C5×C3⋊C8—21no—
150C3×C4⋊Q8—51no—
151C3×C4⋊Q8—101no—
152C3×#125—52no—
153C3×#125—102no—
154C3×C4×Q8—51no—
155C3×C4×Q8—52no—
156C3×C4×Q8—101no—
157C3×C4×Q8C2×D511yescharacteristic
158#946—101no—
159C2×#216—52no—
160C2×#215—51no—
161#898—102no—
162#892—101no—
163#875—52no—
164C4×D12—51no—
165#869—51no—
166C4×Dic6—52no—
167#835—51no—
168#810—52no—
169#810—52no—
170#810—52no—
171#809—51no—
172#809—52no—
173#808—51no—
174#807—52no—
175C4⋊(C3⋊C8)C2×D512yes—
176C4⋊(C3⋊C8)C2×D511yescharacteristic
177C4×C3⋊C8C2×D511yescharacteristic
178C4×C3⋊C8C2×D512yes—
179C2×C5×Q8#6711yescharacteristic
180C2×D20—31no—
181C2×C4×D5—61no—
182C2×Dic10—21no—
183C2×Dic10—32no—
184C2×Dic10C22×D311yescharacteristic
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—61no—
193#685—62no—
194#685—62no—
195C4⋊Dic5—21no—
196C4⋊Dic5—31no—
197C4⋊Dic5—61no—
198C4⋊Dic5—61no—
199C4⋊Dic5C22×D311yescharacteristic
200C4⋊Dic5C22×D312yes—
201#683—21no—
202#683—22no—
203#683—22no—
204#683—22no—
205#683—62no—
206C4×Dic5—22no—
207C4×Dic5—21no—
208C4×Dic5—62no—
209Dic20—64no—
210#677—62no—
211#557—51no—
212#556—151no—
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×D15—41no—
224C2×D15—41no—
225C2×D15—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—42no—
233Dic15—41no—
234C3×Dic5—22no—
235C3×Dic5—42no—
236C3×Dic5—41no—
237C2×C3×Q8—51no—
238C2×C3×Q8—101no—
239C2×C3×Q8D2011yescharacteristic
240C2×D12—51no—
241C2×C4×D3—101no—
242C2×Dic6—52no—
243C3×C4⋊C4—52no—
244C3×C4⋊C4—51no—
245C3×C4⋊C4—101no—
246C3×C4⋊C4—102no—
247C3×C4⋊C4—102no—
248C3×C4⋊C4—102no—
249C3×C4⋊C4—101no—
250C3×C4⋊C4D2011yescharacteristic
251C3×C4⋊C4D2012yes—
252C3×C42—102no—
253C3×C42—101no—
254C3×C42C22×D512yes—
255C3×C42C22×D511yescharacteristic
256#216—104no—
257#215—102no—
258(C2×D3)⋊C4—101no—
259(C2×D3)⋊C4—102no—
260(C2×D3)⋊C4—102no—
261C4⋊Dic3—51no—
262C4⋊Dic3—101no—
263C4⋊Dic3—101no—
264Dic3⋊C4—102no—
265C4×Dic3—102no—
266C2×C3⋊C8C22×D511yescharacteristic
267C2×C3⋊C8C22×D512yes—
268C2×C3⋊C8C22×D511yescharacteristic
269C22×D5—61no—
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—21no—
278C2×Dic5—22no—
279C2×Dic5—61no—
280C2×Dic5—62no—
281D20—61no—
282D20—61no—
283C4×D5—122no—
284Dic10—21no—
285Dic10—42no—
286Dic10—62no—
287Dic10—62no—
288Dic10#23912yes—
289C5×C8—61no—
290C5×C8—62no—
291C5×C8—61no—
292C2×Q16—152no—
293C2×SD16—151no—
294C4⋊Q8—51no—
295C4⋊Q8—101no—
296C4⋊Q8—151no—
297#126—302no—
298#125—52no—
299#125—102no—
300#124—152no—
301C22⋊Q8—301no—
302C4×Q8—51no—
303C4×Q8—52no—
304C4×Q8—101no—
305C4×Q8—152no—
306C4×Q8D3×D511yescharacteristic
307C4×D4—151no—
308#117—301no—
309#107—152no—
310#106—151no—
311C4⋊C8—31no—
312C4⋊C8—32no—
313#103—152no—
314#103—152no—
315#103—152no—
316#103—151no—
317#102—151no—
318#102—152no—
319C4×C8—31no—
320C4×C8—32no—
321C2×C3×C5#54811yescharacteristic
322C2×C3×C5C2×#13511yescharacteristic
323C2×C3×C5#57811yescharacteristic
324D15—81no—
325C22×D3—101no—
326C3×Q8—22no—
327C3×Q8—52no—
328C3×Q8—101no—
329C3×Q8—202no—
330C2×C3×C4—101no—
331C2×C3×C4—101no—
332C2×C3×C4—102no—
333C2×C3×C4C2×D2012yes—
334C2×C3×C4C2×D2012yes—
335C2×C3×C4C2×D2011yescharacteristic
336C2×C3×C4C2×D2011yescharacteristic
337C2×C3×C4C23×D511yescharacteristic
338C2×Dic3—101no—
339C2×Dic3—102no—
340D12—101no—
341D12—101no—
342C4×D3—202no—
343Dic6—102no—
344Dic6—102no—
345C3⋊C8—21no—
346C3⋊C8—21no—
347C3⋊C8—22no—
348C22×C5C22×#6711yescharacteristic
349C2×D5—121no—
350C2×D5—121no—
351C2×D5—121no—
352C4×C5—22no—
353C4×C5—22no—
354C4×C5—21no—
355C4×C5#95012yes—
356C4×C5C2×#23911yescharacteristic
357C4×C5#100711yescharacteristic
358Dic5—22no—
359Dic5—42no—
360Dic5—41no—
361Dic5—122no—
362Dic5—121no—
363C2×Q8—51no—
364C2×Q8—101no—
365C2×Q8—152no—
366C2×Q8#120211yescharacteristic
367C2×D4—151no—
368C22×C4—301no—
369Q16—304no—
370SD16—302no—
371C2×C8—31no—
372C2×C8—32no—
373C2×C8—31no—
374C4⋊C4—51no—
375C4⋊C4—52no—
376C4⋊C4—101no—
377C4⋊C4—102no—
378C4⋊C4—102no—
379C4⋊C4—102no—
380C4⋊C4—101no—
381C4⋊C4—151no—
382C4⋊C4—301no—
383C4⋊C4—302no—
384C4⋊C4—301no—
385C4⋊C4#120211yescharacteristic
386C4⋊C4#120212yes—
387C22⋊C4—302no—
388C22⋊C4—301no—
389C22⋊C4—302no—
390C42—102no—
391C42—101no—
392C42—302no—
393C42C2×D3×D511yescharacteristic
394C42C2×D3×D512yes—
395C3×C5#336411yescharacteristic, complemented, Hall
396C22×C3C22×D2011yescharacteristic
397C2×D3—201no—
398C2×D3—201no—
399C2×D3—201no—
400C3×C4—22no—
401C3×C4—22no—
402C3×C4—21no—
403C3×C4—102no—
404C3×C4—202no—
405C3×C4—201no—
406C3×C4#405012yes—
407C3×C4#414711yescharacteristic
408C3×C4D5×#4111yescharacteristic
409Dic3—201no—
410Dic3—202no—
411C2×C5#581711yescharacteristic
412C2×C5C2×#95011yescharacteristic
413C2×C5#583811yescharacteristic
414D5—241no—
415C23—301no—
416Q8—22no—
417Q8—52no—
418Q8—101no—
419Q8—202no—
420Q8—302no—
421Q8—302no—
422D4—301no—
423D4—301no—
424C2×C4—101no—
425C2×C4—101no—
426C2×C4—102no—
427C2×C4—301no—
428C2×C4—302no—
429C2×C4—602no—
430C2×C4C2×#120212yes—
431C2×C4C2×#120211yescharacteristic
432C2×C4C2×#120212yes—
433C2×C4C2×#120211yescharacteristic
434C2×C4C22×D3×D511yescharacteristic
435C8—61no—
436C8—61no—
437C8—62no—
438C2×C3#6591011yescharacteristic
439C2×C3C2×#405011yescharacteristic
440C2×C3#6608711yescharacteristic
441D3—401no—
442C5#8368911yescharacteristic, complemented, Sylow
443C22—601no—
444C22—601no—
445C22—601no—
446C22C22×#120211yescharacteristic
447C4—22no—
448C4—21no—
449C4—22no—
450C4—102no—
451C4—201no—
452C4—202no—
453C4—602no—
454C4—601no—
455C4#9131112yes—
456C4#9202911yescharacteristic
457C4D5×#23911yescharacteristic
458C3#1061166511yescharacteristic, complemented, Sylow
459C2—1201no—
460C2C2×#9131111yescharacteristic
461C2#1175512811yescharacteristic
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×D60C23
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
2. C3×#65901C2semidirect
3. C5×Q8×C3⋊C8C2semidirect
4. #11747095C2semidirect
5. C4×#6662C2semidirect
9. #11746934C2semidirect
11. #11746921C2semidirect
44. #65901D3semidirect
96. Q8×C3⋊C8D5semidirect
395. C3×C5#3364semidirect
442. C5#83689semidirect
458. C3#10611665semidirect

Maximal subgroups

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

subgroupindex
#117563432
C3×#659012
C5×Q8×C3⋊C82
#117470952
C4×#66622
#117470652
C4×#66582
#117469712
#117469342
#117469332
#117469212
#106116653
#836895