Finite Group Databasebeta

← #11784905

Subgroups — #11784905

Order 1152.

1501 conjugacy classes of subgroups.

The subgroup lattice has 482 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64364C211yesmaximal, characteristic
2C3×#5229C211yesmaximal, characteristic, complemented
3C2×C3×#836C211yesmaximal, characteristic, complemented
4C2×#63570C212yesmaximal, complemented
5#10591106C212yesmaximal, complemented
6#70121—31nomaximal
7#69692—31nomaximal
8C22×C32×Q8C2211yescharacteristic
9#64364—22no—
10#64364—24no—
11#64364C414yescomplemented
12C2×#3832—22no—
13C2×Q8×C3⋊D3—22no—
14C2×#3828—22no—
15C2×#3828C2212yes—
16C2×C3×C4⋊Dic3C2211yescharacteristic
17C2×C3×C4×Dic3C2211yescharacteristic
18C2×C3×#208C2212yes—
19C3×#836—22no—
20C3×C3⋊#95—22no—
21#63570—24no—
22#63567—22no—
23#63564—22no—
24C2×#1007—31no—
25C2×#1007—31no—
26C2×#1007—61no—
27C2×C3×#101—31no—
28C3×#391—31no—
29#5229D311yescharacteristic, complemented
30C2×#836D311yescharacteristic, complemented
31C2×#825—32no—
32#5133—32no—
33#4966—32no—
34C2×#805—32no—
35C2×C32×Q8—22no—
36C2×C32×Q8—22no—
37C2×C32×Q8C2×C412yes—
38C2×C32×Q8D412yes—
39C22×C32×C4D412yes—
40C22×C32×C4C2311yescharacteristic
41C2×#638—22no—
42#3832—28no—
43#3832—28no—
44Q8×C3⋊D3—28no—
45Q8×C3⋊D3—28no—
46#3828—28no—
47#3828—28no—
48#3828—22no—
49#3828—22no—
50#3828C2×C414yes—
51#3828D414yes—
52C2×C4⋊(C3⋊D3)—22no—
53C2×C4⋊(C3⋊D3)D412yes—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3—22no—
56C2×#634—22no—
57C2×#634D412yes—
58C22×C3×Dic3—21no—
59C22×C3×Dic3—21no—
60C3×C4⋊Dic3—22no—
61C3×C4×Dic3—22no—
62C3×#208—22no—
63C3×#208—22no—
64C2×C3×C3⋊C8—22no—
65#1793—91noSylow
66C22×C3×Q8—21no—
67C22×C3×Q8C2×D311yescharacteristic
68C22×C3×Q8C2×D311yescharacteristic
69#1007—34no—
70#1007—34no—
71#1007—64no—
72#1007—64no—
73#1007—64no—
74#1007—68no—
75#1007—64no—
76#1007—62no—
77#1007—62no—
78C2×#239—62no—
79C2×#239—62no—
80C2×#239—64no—
81C2×D3×Q8—62no—
82C2×D3×Q8—62no—
83C2×D3×Q8—64no—
84C2×#235—32no—
85C2×#235—32no—
86C2×#235—62no—
87C2×#235—64no—
88C2×#235—62no—
89C2×#235—62no—
90C2×C3×M16—32no—
91C2×C3×C4⋊C4—31no—
92C2×C3×C42—31no—
93C2×C4⋊Dic3C2×D311yescharacteristic
94C2×C4×Dic3C2×D311yescharacteristic
95C2×#208C2×D312yes—
96C3×#101—62no—
97C3×#95—62no—
98#836—22no—
99C3⋊#95—22no—
100#825—64no—
101#821—62no—
102#816—62no—
103#810—62no—
104#809—62no—
105#805—64no—
106C23×C32C2×D411yescharacteristic
107C22×C3⋊D3—22no—
108C32×Q8—24no—
109C32×Q8—24no—
110C2×C32×C4—22no—
111C2×C32×C4—22no—
112C2×C32×C4C22⋊C414yes—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D412yes—
116C2×C32×C4C2×D412yes—
117#638—24no—
118#638—24no—
119C2×C3⋊Dic3—22no—
120C4⋊(C3⋊D3)—28no—
121C4⋊(C3⋊D3)—22no—
122C4⋊(C3⋊D3)C22⋊C414yes—
123C4×C3⋊D3—216no—
124C4×C3⋊D3—24no—
125C4×C3⋊D3—24no—
126#634—28no—
127#634—22no—
128#634C22⋊C414yes—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—41no—
131C2×C3×Dic3—41no—
132C2×C3×Dic3—42no—
133C2×C3×Dic3—41no—
134C3×C3⋊C8—42no—
135C2×2−1+4—91no—
136C2×#104—92no—
137#417—92no—
138C2×#101—31no—
139#391—31no—
140C2×C3×Q8—24no—
141C2×C3×Q8—24no—
142C2×C3×Q8—22no—
143C2×C3×Q8—22no—
144C2×C3×Q8—22no—
145C2×C3×Q8—22no—
146C2×C3×Q8—22no—
147C2×C3×Q8—22no—
148C2×C3×Q8C4×D312yes—
149C2×C3×Q8C4×D312yes—
150C2×C3×Q8D1212yes—
151C2×C3×Q8#6712yes—
152C22×C3×C4—22no—
153C22×C3×C4—21no—
154C22×C3×C4—61no—
155C22×C3×C4—61no—
156C22×C3×C4D1212yes—
157C22×C3×C4#6712yes—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—64no—
161C2×#67—62no—
162C2×#67—62no—
163C22×Dic3—21no—
164C22×Dic3—21no—
165#239—68no—
166#239—68no—
167#239—616no—
168#239—616no—
169#239—68no—
170#239—68no—
171D3×Q8—68no—
172D3×Q8—68no—
173D3×Q8—616no—
174D3×Q8—616no—
175D3×Q8—68no—
176D3×Q8—68no—
177#235—34no—
178#235—34no—
179#235—34no—
180#235—34no—
181#235—64no—
182#235—64no—
183#235—616no—
184#235—68no—
185#235—68no—
186#235—616no—
187#235—64no—
188#235—64no—
189#235—68no—
190#235—68no—
191#235—62no—
192#235—62no—
193#235—62no—
194#235—62no—
195C2×D12—32no—
196C2×D12—32no—
197C2×D12—62no—
198C2×D12—64no—
199C2×D12—62no—
200C2×D12—62no—
201C2×C4×D3—68no—
202C2×C4×D3—64no—
203C2×C4×D3—64no—
204C2×C4×D3—64no—
205C2×C4×D3—62no—
206C2×C4×D3—62no—
207C2×Dic6—32no—
208C2×Dic6—32no—
209C2×Dic6—62no—
210C2×Dic6—64no—
211C2×Dic6—62no—
212C2×Dic6—62no—
213C3×M16—62no—
214C3×M16—62no—
215C2×C3×C8—62no—
216C3×C4⋊C4—62no—
217C3×C42—62no—
218C4⋊Dic3—22no—
219C4×Dic3—22no—
220#208—22no—
221#208—22no—
222C2×C3⋊C8—22no—
223C22×C32—21no—
224C22×C32—21no—
225C22×C32C2×C22⋊C411yescharacteristic
226C22×C32#12011yescharacteristic
227C22×C32#12011yescharacteristic
228C2×C3⋊D3—24no—
229C2×C3⋊D3—42no—
230C2×C3⋊D3—42no—
231C32×C4—24no—
232C32×C4C2×C22⋊C412yes—
233C32×C4#12012yes—
234C3⋊Dic3—24no—
235C3×Dic3—42no—
236C3×Dic3—81no—
2372−1+4—94no—
2382−1+4—184no—
2392−1+4—182no—
240C2×#41—92no—
241C2×#41—182no—
242C2×#41—182no—
243C22×Q8—182no—
244C22×Q8D3211yescharacteristic
245C2×M16—32no—
246C2×C4⋊C4—31no—
247C2×C42—31no—
248#104—184no—
249#103—182no—
250#102—182no—
251#101—62no—
252#95—62no—
253C23×C3—21no—
254C23×C3C2×D1211yescharacteristic
255C23×C3C2×#6711yescharacteristic
256C22×D3—64no—
257C22×D3—62no—
258C22×D3—62no—
259C3×Q8—28no—
260C3×Q8—28no—
261C3×Q8—24no—
262C3×Q8—24no—
263C3×Q8—24no—
264C3×Q8—24no—
265C2×C3×C4—24no—
266C2×C3×C4—24no—
267C2×C3×C4—22no—
268C2×C3×C4—22no—
269C2×C3×C4—22no—
270C2×C3×C4—22no—
271C2×C3×C4—24no—
272C2×C3×C4—21no—
273C2×C3×C4—21no—
274C2×C3×C4—22no—
275C2×C3×C4—22no—
276C2×C3×C4—62no—
277C2×C3×C4—121no—
278C2×C3×C4—121no—
279C2×C3×C4—122no—
280C2×C3×C4—121no—
281C2×C3×C4(C2×D3)⋊C414yes—
282C2×C3×C4(C2×D3)⋊C414yes—
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×C4×D311yescharacteristic
285C2×C3×C4C2×D1211yescharacteristic
286C2×C3×C4D3×D412yes—
287C2×C3×C4D3×D412yes—
288C2×C3×C4D3×D412yes—
289C2×C3×C4D3×D412yes—
290C2×C3×C4C2×#6711yescharacteristic
291#67—68no—
292#67—68no—
293#67—64no—
294#67—64no—
295#67—64no—
296#67—64no—
297C2×Dic3—22no—
298C2×Dic3—41no—
299C2×Dic3—41no—
300C2×Dic3—42no—
301C2×Dic3—41no—
302C2×Dic3—64no—
303C2×Dic3—62no—
304C2×Dic3—62no—
305D12—34no—
306D12—34no—
307D12—64no—
308D12—616no—
309D12—68no—
310D12—68no—
311D12—64no—
312D12—62no—
313D12—62no—
314C4×D3—632no—
315C4×D3—616no—
316C4×D3—616no—
317C4×D3—68no—
318C4×D3—68no—
319C4×D3—64no—
320C4×D3—64no—
321C4×D3—64no—
322C4×D3—64no—
323Dic6—34no—
324Dic6—34no—
325Dic6—64no—
326Dic6—616no—
327Dic6—68no—
328Dic6—68no—
329Dic6—64no—
330Dic6—62no—
331Dic6—62no—
332C3×C8—122no—
333C3⋊C8—42no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#37911yescharacteristic
337C2×C32#45411yescharacteristic
338C2×C32#45611yescharacteristic
339C3⋊D3—44no—
340#41—94no—
341#41—94no—
342#41—188no—
343#41—188no—
344#41—188no—
345#41—188no—
346#41—182no—
347#41—182no—
348C2×Q8—22no—
349C2×Q8—22no—
350C2×Q8—92no—
351C2×Q8—182no—
352C2×Q8—188no—
353C2×Q8—188no—
354C2×Q8#62412yes—
355C2×Q8#62612yes—
356C2×D4—92no—
357C2×D4—182no—
358C2×D4—182no—
359C22×C4—61no—
360C22×C4—61no—
361C22×C4—184no—
362C22×C4—182no—
363C22×C4#62612yes—
364C22×C4C2×D3211yescharacteristic
365M16—62no—
366M16—62no—
367C2×C8—62no—
368C4⋊C4—62no—
369C42—62no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—21no—
377C22×C3—41no—
378C22×C3—41no—
379C22×C3#88211yescharacteristic
380C22×C3#88211yescharacteristic
381C22×C3C2×(C2×D3)⋊C411yescharacteristic
382C22×C3C2×(C2×D3)⋊C411yescharacteristic
383C22×C3#93711yescharacteristic
384C22×C3#93711yescharacteristic
385C2×D3—68no—
386C2×D3—64no—
387C2×D3—64no—
388C2×D3—124no—
389C2×D3—124no—
390C2×D3—122no—
391C2×D3—122no—
392C2×D3—122no—
393C2×D3—122no—
394C3×C4—28no—
395C3×C4—24no—
396C3×C4—24no—
397C3×C4—22no—
398C3×C4—22no—
399C3×C4—122no—
400C3×C4—241no—
401C3×C4D3×C22⋊C412yes—
402C3×C4D3×C22⋊C412yes—
403C3×C4#88212yes—
404C3×C4#93712yes—
405Dic3—42no—
406Dic3—68no—
407Dic3—64no—
408Dic3—64no—
409Dic3—81no—
410C32#179311yescharacteristic, complemented, Sylow
411C23—182no—
412C23C2×#62611yescharacteristic
413Q8—24no—
414Q8—24no—
415Q8—94no—
416Q8—188no—
417Q8—182no—
418D4—94no—
419D4—188no—
420D4—184no—
421D4—184no—
422D4—182no—
423C2×C4—22no—
424C2×C4—22no—
425C2×C4—62no—
426C2×C4—121no—
427C2×C4—121no—
428C2×C4—122no—
429C2×C4—121no—
430C2×C4—1816no—
431C2×C4—182no—
432C2×C4—184no—
433C2×C4—184no—
434C2×C4#372214yes—
435C2×C4C2×#62411yescharacteristic
436C2×C4C2×#62611yescharacteristic
437C2×C4#381112yes—
438C2×C4#381112yes—
439C8—122no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—41no—
448C2×C3—41no—
449C2×C3#475211yescharacteristic
450C2×C3#475311yescharacteristic
451C2×C3#495511yescharacteristic
452C2×C3#495511yescharacteristic
453C2×C3#506211yescharacteristic
454C2×C3#509511yescharacteristic
455D3—128no—
456D3—124no—
457D3—124no—
458C22—21no—
459C22—21no—
460C22—184no—
461C22—362no—
462C22—362no—
463C22C2×#372211yescharacteristic
464C22#6398111yescharacteristic
465C22#6398111yescharacteristic
466C4—24no—
467C4—122no—
468C4—184no—
469C4—241no—
470C4#6397412yes—
471C4#6398112yes—
472C3—21no—
473C3#6969211yescharacteristic, complemented
474C3#7012111yescharacteristic, complemented
475C2—21no—
476C2—21no—
477C2—364no—
478C2#1059164711yescharacteristic
479C2#1059165011yescharacteristic
480C2#1059171411yescharacteristic
subgroupG/H
centerC22#63981
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC22×C32#120
prime radicalC2×#64364C2
cosocleC22×C32×C4C23
hypercenterC22×Q8D32
hypocenterC32#1793
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
2. C3×#5229C2semidirect
3. C2×C3×#836C2semidirect
4. C2×#63570C2semidirect
5. #10591106C2semidirect
11. #64364C4semidirect
29. #5229D3semidirect
30. C2×#836D3semidirect
410. C32#1793semidirect
473. C3#69692semidirect
474. C3#70121semidirect

Maximal subgroups

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

subgroupindex
C2×#643642
C3×#52292
C2×C3×#8362
C2×#635702
#105911062
#701213
#696923