Finite Group Databasebeta

← #11795435

Subgroups — #11795435

Order 1152.

681 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
1C2×#63648C211yesmaximal, characteristic
2C2×C3×#818C211yesmaximal, characteristic, complemented
3#10591349C211yesmaximal, characteristic, complemented
4#10591320C211yesmaximal, characteristic
5C2×#63575C211yesmaximal, characteristic, complemented
6C2×#63564C211yesmaximal, characteristic
7C3×#4550C211yesmaximal, characteristic, complemented
8#70641—31nomaximal
9#68681—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C32×C8C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4×Dic3C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×Dic3⋊Dic3—22no—
18C2×#3722—22no—
19#63648—22no—
20C3×#818—22no—
21#63575—22no—
22#63564—22no—
23C2×C3×#107—31no—
24C2×#821—31no—
25C2×#821—31no—
26C2×#821—31no—
27C2×#821—61no—
28C2×#818—31no—
29C2×#818D311yescharacteristic, complemented
30#4988—31no—
31#4975—31no—
32C2×#809—31no—
33C2×#807—31no—
34#4939—31no—
35#4935—31no—
36C3×#336—31no—
37#4550D311yescharacteristic, complemented
38C23×C3⋊D3—21no—
39C22×C32×C4C2311yescharacteristic
40C22×C3⋊Dic3—21no—
41C2×C4⋊(C3⋊D3)—21no—
42C2×C4⋊(C3⋊D3)—21no—
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)Q812yes—
47C22×C3×Dic3—21no—
48C22×C3×Dic3—21no—
49C22×C3×Dic3D412yes—
50C2×C32×C8—21no—
51C2×C32×C8—21no—
52C2×C32×C8D412yes—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)—21no—
55C3×C4⋊Dic3—21no—
56C3×C4⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×C4×Dic3—21no—
60C3×C4×Dic3—21no—
61C2×C3×C3⋊C8—21no—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8D412yes—
64Dic3⋊Dic3—44no—
65#3722—44no—
66#2093—91noSylow
67C22×D12—31no—
68C22×D12—31no—
69C22×D12—61no—
70C22×C3×C8—21no—
71C22×C3×C8—31no—
72C22×C3×C8C2×D311yescharacteristic
73C22×C3×C8C2×D311yescharacteristic
74C2×C3×C4⋊C4—31no—
75C2×C3×C4⋊C4—31no—
76C2×C3×C42—31no—
77C2×(C2×D3)⋊C4—62no—
78C2×(C2×D3)⋊C4—62no—
79C2×C4⋊Dic3—31no—
80C2×C4⋊Dic3—31no—
81C2×C4⋊Dic3—61no—
82C2×C4⋊Dic3—62no—
83C2×C4⋊Dic3C2×D311yescharacteristic
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×Dic3⋊C4—62no—
86C2×C4×Dic3C2×D311yescharacteristic
87C22×C3⋊C8C2×D311yescharacteristic
88C3×#107—62no—
89#821—62no—
90#821—64no—
91#821—62no—
92#821—62no—
93#818—22no—
94#818—62no—
95#809—62no—
96#807—62no—
97C23×C32C2×D411yescharacteristic
98C22×C3⋊D3—22no—
99C22×C3⋊D3—41no—
100C22×C3⋊D3—41no—
101C22×C3⋊D3—42no—
102C22×C3⋊D3—42no—
103C2×C32×C4C2×D411yescharacteristic
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×Q811yescharacteristic
106C2×C32×C4#4111yescharacteristic
107C2×C32×C4#4111yescharacteristic
108C2×C32×C4#4111yescharacteristic
109C2×C3⋊Dic3—41no—
110C2×C3⋊Dic3—42no—
111C4⋊(C3⋊D3)—22no—
112C4⋊(C3⋊D3)—22no—
113C4⋊(C3⋊D3)—41no—
114C4⋊(C3⋊D3)—41no—
115C2×C3×Dic3—22no—
116C2×C3×Dic3—22no—
117C2×C3×Dic3—41no—
118C2×C3×Dic3—41no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C2×C3×Dic3D814yes—
122C32×C8—22no—
123C3×C3⋊C8—22no—
124C2×#107—31no—
125C2×#107—91no—
126C2×#102—91no—
127C2×#102—91no—
128#390—91no—
129#384—91no—
130#336—31no—
131C23×D3—61no—
132C23×D3—61no—
133C23×D3—121no—
134C22×C3×C4—21no—
135C22×C3×C4—32no—
136C22×C3×C4—61no—
137C22×C3×C4—61no—
138C22×C3×C4C22×D311yescharacteristic
139C22×C3×C4C22×D311yescharacteristic
140C22×Dic3—21no—
141C22×Dic3—21no—
142C22×Dic3—61no—
143C22×Dic3—61no—
144C22×Dic3—121no—
145C22×Dic3D1212yes—
146C2×D12—32no—
147C2×D12—32no—
148C2×D12—62no—
149C2×D12—62no—
150C2×D12—62no—
151C2×D12—61no—
152C2×D12—61no—
153C2×D12—61no—
154C2×D12—61no—
155C2×D12—61no—
156C2×D12—61no—
157C2×D12—61no—
158C2×D12—61no—
159C2×D12—61no—
160C2×D12—61no—
161C2×D12—121no—
162C2×D12—121no—
163C2×D12—121no—
164C2×C3×C8—21no—
165C2×C3×C8—21no—
166C2×C3×C8—21no—
167C2×C3×C8—21no—
168C2×C3×C8—22no—
169C2×C3×C8—32no—
170C2×C3×C8—41no—
171C2×C3×C8—41no—
172C2×C3×C8—61no—
173C2×C3×C8—61no—
174C2×C3×C8D1212yes—
175C2×C3×C8#6712yes—
176C3×C4⋊C4—61no—
177C3×C4⋊C4—61no—
178C3×C4⋊C4—61no—
179C3×C4⋊C4—61no—
180C3×C42—61no—
181C3×C42—61no—
182(C2×D3)⋊C4—124no—
183(C2×D3)⋊C4—124no—
184C4⋊Dic3—21no—
185C4⋊Dic3—21no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—62no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3—121no—
194C4⋊Dic3—124no—
195Dic3⋊C4—124no—
196C4×Dic3—21no—
197C4×Dic3—21no—
198C2×C3⋊C8—21no—
199C2×C3⋊C8—21no—
200C2×C3⋊C8D1212yes—
201C22×C32C22⋊Q811yescharacteristic
202C22×C32#12311yescharacteristic
203C22×C32#12711yescharacteristic
204C22×C32C2×D812yes—
205C22×C32#13712yes—
206C2×C3⋊D3—42no—
207C2×C3⋊D3—44no—
208C2×C3⋊D3—82no—
209C2×C3⋊D3—81no—
210C2×C3⋊D3—81no—
211C32×C4C22⋊Q811yescharacteristic
212C32×C4C22⋊Q811yescharacteristic
213C32×C4#12311yescharacteristic
214C32×C4#12311yescharacteristic
215C3⋊Dic3—81no—
216C3×Dic3—24no—
217C3×Dic3—81no—
218C3×Dic3—81no—
219C22×D4—91no—
220C22×C8—31no—
221C22×C8D3211yescharacteristic
222C2×C4⋊C4—31no—
223C2×C4⋊C4—31no—
224C2×C4⋊C4—91no—
225C2×C4⋊C4—182no—
226C2×C22⋊C4—182no—
227C2×C42—31no—
228#107—62no—
229#107—182no—
230#102—182no—
231#102—182no—
232C23×C3—21no—
233C23×C3C2×D1211yescharacteristic
234C23×C3D3×D411yescharacteristic
235C22×D3—62no—
236C22×D3—62no—
237C22×D3—122no—
238C22×D3—122no—
239C22×D3—122no—
240C22×D3—121no—
241C22×D3—121no—
242C22×D3—121no—
243C22×D3—122no—
244C22×D3—122no—
245C22×D3—122no—
246C22×D3—122no—
247C22×D3—121no—
248C22×D3—242no—
249C22×D3—242no—
250C2×C3×C4—21no—
251C2×C3×C4—21no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—34no—
257C2×C3×C4—62no—
258C2×C3×C4—62no—
259C2×C3×C4—121no—
260C2×C3×C4—121no—
261C2×C3×C4—122no—
262C2×C3×C4—122no—
263C2×C3×C4C2×D1211yescharacteristic
264C2×C3×C4C2×D1211yescharacteristic
265C2×C3×C4#23511yescharacteristic
266C2×C3×C4#23511yescharacteristic
267C2×C3×C4D3×D411yescharacteristic
268C2×C3×C4#23711yescharacteristic
269C2×C3×C4#23711yescharacteristic
270C2×C3×C4#23711yescharacteristic
271C2×C3×C4D3×Q811yescharacteristic
272C2×C3×C4D3×Q811yescharacteristic
273C2×C3×C4#23911yescharacteristic
274C2×C3×C4C2×#6711yescharacteristic
275C2×Dic3—22no—
276C2×Dic3—22no—
277C2×Dic3—42no—
278C2×Dic3—42no—
279C2×Dic3—41no—
280C2×Dic3—41no—
281C2×Dic3—122no—
282C2×Dic3—121no—
283C2×Dic3—122no—
284C2×Dic3—122no—
285C2×Dic3—121no—
286C2×Dic3—242no—
287C2×Dic3D2414yes—
288D12—64no—
289D12—62no—
290D12—62no—
291D12—62no—
292D12—62no—
293D12—122no—
294D12—122no—
295D12—122no—
296D12—121no—
297D12—121no—
298D12—121no—
299D12—121no—
300C3×C8—22no—
301C3×C8—22no—
302C3×C8—42no—
303C3×C8—62no—
304C3⋊C8—22no—
305C2×C32#39911yescharacteristic
306C2×C32#47412yes—
307C2×C32#48012yes—
308C2×C32#49311yescharacteristic
309C2×C32#49711yescharacteristic
310C3⋊D3—82no—
311C24—181no—
312C2×D4—92no—
313C2×D4—181no—
314C2×D4—181no—
315C2×D4—181no—
316C2×D4—181no—
317C2×D4—181no—
318C22×C4—32no—
319C22×C4—61no—
320C22×C4—61no—
321C22×C4—181no—
322C22×C4C2×D3211yescharacteristic
323C2×C8—21no—
324C2×C8—21no—
325C2×C8—32no—
326C2×C8—61no—
327C2×C8—61no—
328C2×C8#62612yes—
329C4⋊C4—61no—
330C4⋊C4—61no—
331C4⋊C4—61no—
332C4⋊C4—61no—
333C4⋊C4—181no—
334C4⋊C4—181no—
335C4⋊C4—364no—
336C22⋊C4—364no—
337C42—61no—
338C42—61no—
339C22×C3—22no—
340C22×C3—22no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3#87411yescharacteristic
345C22×C3#88611yescharacteristic
346C22×C3#89411yescharacteristic
347C22×C3#89611yescharacteristic
348C22×C3#89711yescharacteristic
349C22×C3C2×D2412yes—
350C22×C3#90912yes—
351C22×C3D3×D812yes—
352C22×C3#91812yes—
353C22×C3#94011yescharacteristic
354C2×D3—124no—
355C2×D3—124no—
356C2×D3—122no—
357C2×D3—122no—
358C2×D3—124no—
359C2×D3—244no—
360C2×D3—242no—
361C2×D3—242no—
362C2×D3—244no—
363C2×D3—242no—
364C2×D3—241no—
365C2×D3—241no—
366C2×D3—241no—
367C2×D3—241no—
368C2×D3—242no—
369C3×C4—21no—
370C3×C4—21no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—64no—
374C3×C4—241no—
375C3×C4—241no—
376C3×C4#88611yescharacteristic
377C3×C4#88611yescharacteristic
378C3×C4#89411yescharacteristic
379C3×C4#89611yescharacteristic
380C3×C4#89711yescharacteristic
381C3×C4#89711yescharacteristic
382C3×C4#92911yescharacteristic
383C3×C4#94611yescharacteristic
384Dic3—24no—
385Dic3—81no—
386Dic3—81no—
387Dic3—242no—
388Dic3—241no—
389Dic3—241no—
390C32#209311yescharacteristic, complemented, Sylow
391C23—182no—
392C23—362no—
393C23—362no—
394C23—361no—
395C23—361no—
396C23D3×D1211yescharacteristic
397D4—182no—
398D4—182no—
399D4—361no—
400D4—361no—
401C2×C4—34no—
402C2×C4—62no—
403C2×C4—62no—
404C2×C4—122no—
405C2×C4—122no—
406C2×C4—121no—
407C2×C4—121no—
408C2×C4—362no—
409C2×C4—361no—
410C2×C4#379611yescharacteristic
411C2×C4#379711yescharacteristic
412C2×C4D3×D1211yescharacteristic
413C2×C4#380411yescharacteristic
414C2×C4#380411yescharacteristic
415C2×C4C2×#62611yescharacteristic
416C8—22no—
417C8—62no—
418C2×C3—22no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—22no—
423C2×C3#467711yescharacteristic
424C2×C3#469511yescharacteristic
425C2×C3#471511yescharacteristic
426C2×C3#473612yes—
427C2×C3#484612yes—
428C2×C3#488212yes—
429C2×C3#489012yes—
430C2×C3#499311yescharacteristic
431C2×C3#515111yescharacteristic
432C2×C3#519011yescharacteristic
433D3—244no—
434D3—242no—
435D3—242no—
436C22—364no—
437C22—362no—
438C22—721no—
439C22—721no—
440C22—722no—
441C22D3×D2412yes—
442C22#6380112yes—
443C22#6389011yescharacteristic
444C22#6389511yescharacteristic
445C22#6391111yescharacteristic
446C4—64no—
447C4—241no—
448C4—241no—
449C4—721no—
450C4#6387111yescharacteristic
451C4#6389011yescharacteristic
452C4#6389511yescharacteristic
453C4#6396611yescharacteristic
454C3—21no—
455C3#6868111yescharacteristic, complemented
456C3#7064111yescharacteristic, complemented
457C2—722no—
458C2#1059067912yes—
459C2#1059076412yes—
460C2#1059088011yescharacteristic
461C2#1059089911yescharacteristic
462C2#1059135011yescharacteristic
subgroupG/H
centerC23D3×D12
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC22×C8D32
hypocenterC32#2093
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
2. C2×C3×#818C2semidirect
3. #10591349C2semidirect
5. C2×#63575C2semidirect
7. C3×#4550C2semidirect
29. C2×#818D3semidirect
37. #4550D3semidirect
390. C32#2093semidirect
455. C3#68681semidirect
456. C3#70641semidirect

Maximal subgroups

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

subgroupindex
C2×#636482
C2×C3×#8182
#105913492
#105913202
C2×#635752
C2×#635642
C3×#45502
#706413
#686813