Finite Group Databasebeta

← #11775611

Subgroups — #11775611

Order 1152.

737 conjugacy classes of subgroups.

The subgroup lattice has 475 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64133C211yesmaximal, characteristic
2C3×#5212C211yesmaximal, characteristic
3C2×C3×#830C211yesmaximal, characteristic
4#10589154C214yesmaximal, complemented
5#69946—31nomaximal
6#69510—31nomaximal
7C23×C32×C4C2211yescharacteristic
8C22×#634C411yescharacteristic, complemented
9C2×#3757—21no—
10C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
11#64133—21no—
12#64133—21no—
13#64133C412yescomplemented
14#64133C2212yes—
15C2×#3750—21no—
16C2×C3×#217—21no—
17C2×C3×C4⋊Dic3—21no—
18C22×C3×C3⋊C8—21no—
19C3×C3⋊#95C2212yes—
20C3×#830—21no—
21C3×#830C2212yes—
22C2×#924—31no—
23C2×#924—31no—
24C2×#924—61no—
25C2×C3×C22⋊C8—31no—
26C3×#380—31no—
27#5212D311yescharacteristic
28C2×#830D311yescharacteristic
29#4467—34no—
30#4452—34no—
31C24×C32D411yescharacteristic
32C22×C32×C4—42no—
33C22×C32×C4C2×C411yescharacteristic
34C22×C32×C4C2×C411yescharacteristic
35C22×C32×C4D411yescharacteristic
36C22×C32×C4D411yescharacteristic
37C22×C32×C4D411yescharacteristic
38C22×C32×C4C2311yescharacteristic
39C22×C3⋊Dic3—21no—
40C22×C3⋊Dic3—21no—
41C2×#634—21no—
42C2×#634—42no—
43C2×#634C2×C412yes—
44C22×C3×Dic3—22no—
45#3757—22no—
46#3757—22no—
47C4⋊(C3⋊Dic3)—21no—
48C4⋊(C3⋊Dic3)C2×C412yes—
49#3750—22no—
50#3750—22no—
51C3×#217—42no—
52C3×C4⋊Dic3—42no—
53C2×C3×C3⋊C8—22no—
54C2×C3×C3⋊C8—42no—
55#1520—91noSylow
56C23×C3×C4—21no—
57C23×C3×C4C2×D311yescharacteristic
58C23×C3×C4C2×D311yescharacteristic
59C22×Dic6—31no—
60C22×Dic6—31no—
61C22×Dic6—61no—
62C22×C3×C8—61no—
63C2×C3×C4⋊C4—61no—
64C2×C3×C22⋊C4—61no—
65C2×#217—21no—
66C2×#217—62no—
67C2×#217—61no—
68C2×#217—61no—
69C2×C4⋊Dic3—21no—
70C2×C4⋊Dic3—31no—
71C2×C4⋊Dic3—31no—
72C2×C4⋊Dic3—61no—
73#924—32no—
74#924—32no—
75#924—32no—
76#924—32no—
77#924—62no—
78#924—62no—
79#924—62no—
80#924—62no—
81#924—61no—
82#924—61no—
83#924—61no—
84#924—61no—
85C2×Dic3⋊C4—62no—
86C2×Dic3⋊C4—61no—
87C2×Dic3⋊C4—61no—
88C22×C3⋊C8—21no—
89C3×C22⋊C8—32no—
90C3×C22⋊C8—61no—
91C3×#95—32no—
92C3⋊#95C2×D312yes—
93#830—21no—
94#830C2×D312yes—
95C23×C32—41no—
96C23×C32—41no—
97C23×C32C22⋊C411yescharacteristic
98C23×C32C22⋊C411yescharacteristic
99C23×C32SD1612yes—
100C23×C32Q1612yes—
101C23×C32C2×D411yescharacteristic
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—22no—
105C2×C32×C4—41no—
106C2×C32×C4—41no—
107C2×C32×C4—41no—
108C2×C32×C4C22⋊C411yescharacteristic
109C2×C32×C4C22⋊C411yescharacteristic
110C2×C32×C4C22×C411yescharacteristic
111C2×C32×C4C2×D411yescharacteristic
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—22no—
114C2×C3⋊Dic3—42no—
115C2×C3⋊Dic3—42no—
116#634—42no—
117#634—42no—
118C2×C3×Dic3—42no—
119C2×C3×Dic3—42no—
120C2×C3×Dic3—42no—
121C3×C3⋊C8—42no—
122C2×C22⋊Q8—91no—
123C2×C22⋊C8—31no—
124#380—31no—
125#328—94no—
126C24×C3—21no—
127C24×C3D1211yescharacteristic
128C24×C3#6711yescharacteristic
129C22×C3×C4—21no—
130C22×C3×C4—21no—
131C22×C3×C4—21no—
132C22×C3×C4—21no—
133C22×C3×C4—21no—
134C22×C3×C4—21no—
135C22×C3×C4—42no—
136C22×C3×C4—42no—
137C22×C3×C4—44no—
138C22×C3×C4—62no—
139C22×C3×C4C4×D311yescharacteristic
140C22×C3×C4C4×D311yescharacteristic
141C22×C3×C4C4×D311yescharacteristic
142C22×C3×C4C4×D311yescharacteristic
143C22×C3×C4D1211yescharacteristic
144C22×C3×C4D1211yescharacteristic
145C22×C3×C4D1211yescharacteristic
146C22×C3×C4#6711yescharacteristic
147C22×C3×C4#6711yescharacteristic
148C22×C3×C4#6711yescharacteristic
149C22×C3×C4C22×D311yescharacteristic
150C22×C3×C4C22×D311yescharacteristic
151C22×Dic3—22no—
152C22×Dic3—62no—
153C22×Dic3—62no—
154C22×Dic3—61no—
155C22×Dic3—61no—
156C22×Dic3—61no—
157C22×Dic3—61no—
158C2×Dic6—32no—
159C2×Dic6—32no—
160C2×Dic6—62no—
161C2×Dic6—62no—
162C2×Dic6—61no—
163C2×Dic6—61no—
164C2×Dic6—124no—
165C2×Dic6—122no—
166C2×Dic6—122no—
167C2×C3×C8—62no—
168C2×C3×C8—122no—
169C3×C4⋊C4—122no—
170C3×C22⋊C4—122no—
171#217—42no—
172#217—64no—
173#217—64no—
174#217—62no—
175#217—62no—
176#217—62no—
177#217—62no—
178C4⋊Dic3—32no—
179C4⋊Dic3—32no—
180C4⋊Dic3—42no—
181C4⋊Dic3—62no—
182C4⋊Dic3—62no—
183C4⋊Dic3—61no—
184C4⋊Dic3—61no—
185Dic3⋊C4—64no—
186Dic3⋊C4—64no—
187Dic3⋊C4—62no—
188Dic3⋊C4—62no—
189Dic3⋊C4—62no—
190Dic3⋊C4—62no—
191C2×C3⋊C8—22no—
192C2×C3⋊C8—42no—
193C22×C32—21no—
194C22×C32—21no—
195C22×C32—21no—
196C22×C32—21no—
197C22×C32—21no—
198C22×C32—21no—
199C22×C32—42no—
200C22×C32—42no—
201C22×C32#10312yes—
202C22×C32#10312yes—
203C22×C32C2×C22⋊C411yescharacteristic
204C22×C32C2×SD1611yescharacteristic
205C22×C32C2×Q1611yescharacteristic
206C32×C4—21no—
207C32×C4—21no—
208C32×C4—21no—
209C32×C4#9912yes—
210C3⋊Dic3—42no—
211C3⋊Dic3—42no—
212C3×Dic3—82no—
213C22×Q8—91no—
214C23×C4D3211yescharacteristic
215C22×C8—61no—
216C22⋊Q8—92no—
217C22⋊Q8—92no—
218C22⋊Q8—181no—
219C22⋊Q8—181no—
220C2×C4⋊C4—61no—
221C2×C4⋊C4—91no—
222C2×C4⋊C4—181no—
223C2×C22⋊C4—61no—
224C2×C22⋊C4—181no—
225C22⋊C8—32no—
226C22⋊C8—61no—
227#95—32no—
228C23×C3—22no—
229C23×C3—22no—
230C23×C3—21no—
231C23×C3—21no—
232C23×C3—21no—
233C23×C3—41no—
234C23×C3—41no—
235C23×C3—41no—
236C23×C3—41no—
237C23×C3—42no—
238C23×C3—42no—
239C23×C3#20412yes—
240C23×C3Dic1212yes—
241C23×C3(C2×D3)⋊C411yescharacteristic
242C23×C3(C2×D3)⋊C411yescharacteristic
243C23×C3(C2×D3)⋊C411yescharacteristic
244C23×C3(C2×D3)⋊C411yescharacteristic
245C23×C3#21412yes—
246C23×C3#21612yes—
247C23×C3C2×D1211yescharacteristic
248C23×C3C2×#6711yescharacteristic
249C2×C3×C4—24no—
250C2×C3×C4—22no—
251C2×C3×C4—22no—
252C2×C3×C4—22no—
253C2×C3×C4—22no—
254C2×C3×C4—22no—
255C2×C3×C4—22no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—42no—
261C2×C3×C4—42no—
262C2×C3×C4—41no—
263C2×C3×C4—41no—
264C2×C3×C4—41no—
265C2×C3×C4—41no—
266C2×C3×C4—41no—
267C2×C3×C4—41no—
268C2×C3×C4—42no—
269C2×C3×C4—42no—
270C2×C3×C4—42no—
271C2×C3×C4—122no—
272C2×C3×C4—122no—
273C2×C3×C4—122no—
274C2×C3×C4(C2×D3)⋊C411yescharacteristic
275C2×C3×C4(C2×D3)⋊C411yescharacteristic
276C2×C3×C4(C2×D3)⋊C411yescharacteristic
277C2×C3×C4(C2×D3)⋊C411yescharacteristic
278C2×C3×C4C2×C4×D311yescharacteristic
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×D1211yescharacteristic
281C2×C3×C4C2×#6711yescharacteristic
282C2×Dic3—42no—
283C2×Dic3—42no—
284C2×Dic3—42no—
285C2×Dic3—64no—
286C2×Dic3—64no—
287C2×Dic3—62no—
288C2×Dic3—62no—
289C2×Dic3—62no—
290C2×Dic3—62no—
291C2×Dic3—124no—
292C2×Dic3—122no—
293C2×Dic3—122no—
294C2×Dic3—124no—
295C2×Dic3—122no—
296C2×Dic3—122no—
297Dic6—124no—
298Dic6—124no—
299Dic6—122no—
300Dic6—122no—
301Dic6—122no—
302Dic6—122no—
303C3×C8—122no—
304C3⋊C8—42no—
305C2×C32—22no—
306C2×C32—21no—
307C2×C32—22no—
308C2×C32—21no—
309C2×C32C2×#9911yescharacteristic
310C2×C32C2×#10311yescharacteristic
311C2×C32#42111yescharacteristic
312C24#62611yescharacteristic
313C2×Q8—92no—
314C2×Q8—181no—
315C2×Q8—362no—
316C22×C4—42no—
317C22×C4—62no—
318C22×C4—181no—
319C22×C4—181no—
320C22×C4#62411yescharacteristic
321C22×C4#62411yescharacteristic
322C22×C4#62611yescharacteristic
323C22×C4#62611yescharacteristic
324C22×C4#62611yescharacteristic
325C22×C4C2×D3211yescharacteristic
326C2×C8—62no—
327C2×C8—122no—
328C4⋊C4—92no—
329C4⋊C4—122no—
330C4⋊C4—181no—
331C4⋊C4—182no—
332C4⋊C4—182no—
333C22⋊C4—122no—
334C22⋊C4—182no—
335C22⋊C4—182no—
336C22×C3—22no—
337C22×C3—22no—
338C22×C3—21no—
339C22×C3—21no—
340C22×C3—21no—
341C22×C3—21no—
342C22×C3—21no—
343C22×C3—21no—
344C22×C3—21no—
345C22×C3—21no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—22no—
351C22×C3—22no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—41no—
356C22×C3—41no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—42no—
360C22×C3—42no—
361C22×C3—42no—
362C22×C3—42no—
363C22×C3—44no—
364C22×C3—44no—
365C22×C3#81012yes—
366C22×C3#81012yes—
367C22×C3#81612yes—
368C22×C3#81612yes—
369C22×C3C2×#20411yescharacteristic
370C22×C3C2×Dic1211yescharacteristic
371C22×C3C2×(C2×D3)⋊C411yescharacteristic
372C22×C3C2×(C2×D3)⋊C411yescharacteristic
373C22×C3C2×#21411yescharacteristic
374C22×C3C2×#21611yescharacteristic
375C3×C4—22no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—21no—
381C3×C4—21no—
382C3×C4—22no—
383C3×C4—41no—
384C3×C4—41no—
385C3×C4—242no—
386C3×C4#80612yes—
387C3×C4#80612yes—
388Dic3—82no—
389Dic3—124no—
390Dic3—124no—
391Dic3—122no—
392Dic3—122no—
393Dic3—122no—
394Dic3—122no—
395C32#152011yescharacteristic, complemented, Sylow
396C23—41no—
397C23—41no—
398C23#371612yes—
399C23#371912yes—
400C23#372211yescharacteristic
401C23#372211yescharacteristic
402C23C2×#62611yescharacteristic
403Q8—362no—
404Q8—362no—
405C2×C4—22no—
406C2×C4—22no—
407C2×C4—22no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—122no—
412C2×C4—122no—
413C2×C4—122no—
414C2×C4—182no—
415C2×C4—182no—
416C2×C4—362no—
417C2×C4—362no—
418C2×C4#372211yescharacteristic
419C2×C4#372211yescharacteristic
420C2×C4C2×#62411yescharacteristic
421C2×C4C2×#62611yescharacteristic
422C8—122no—
423C2×C3—24no—
424C2×C3—21no—
425C2×C3—22no—
426C2×C3—22no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—22no—
430C2×C3—22no—
431C2×C3—21no—
432C2×C3—21no—
433C2×C3—21no—
434C2×C3—21no—
435C2×C3—41no—
436C2×C3—42no—
437C2×C3—41no—
438C2×C3C2×#80611yescharacteristic
439C2×C3C2×#80611yescharacteristic
440C2×C3C2×#81011yescharacteristic
441C2×C3#500511yescharacteristic
442C2×C3C2×#81611yescharacteristic
443C2×C3#513911yescharacteristic
444C22—21no—
445C22—21no—
446C22—21no—
447C22—21no—
448C22—21no—
449C22—21no—
450C22—42no—
451C22—42no—
452C22#6356712yes—
453C22#6356712yes—
454C22C2×#371611yescharacteristic
455C22C2×#371911yescharacteristic
456C22C2×#372211yescharacteristic
457C4—21no—
458C4—21no—
459C4—21no—
460C4—242no—
461C4—362no—
462C4—362no—
463C4#6358112yes—
464C3—21no—
465C3#6951011yescharacteristic, complemented
466C3#6994611yescharacteristic, complemented
467C2—21no—
468C2—22no—
469C2—22no—
470C2—21no—
471C2C2×#6356711yescharacteristic
472C2#1059111311yescharacteristic
473C2C2×#6358111yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radicalC24×C32D4
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1520
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
4. #10589154C2semidirect
8. C22×#634C4semidirect
10. C2×C4⋊(C3⋊Dic3)C4semidirect
13. #64133C4semidirect
395. C32#1520semidirect
465. C3#69510semidirect
466. C3#69946semidirect

Maximal subgroups

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

subgroupindex
C2×#641332
C3×#52122
C2×C3×#8302
#105891542
#699463
#695103