Finite Group Databasebeta

← #11788827

Subgroups — #11788827

Order 1152.

675 conjugacy classes of subgroups.

The subgroup lattice has 479 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5526C211yesmaximal, characteristic
2#10594818C211yesmaximal, characteristic, complemented
3#10591111C211yesmaximal, characteristic
4#10591110C211yesmaximal, characteristic
5C2×#63560C211yesmaximal, characteristic, complemented
6#10589397C211yesmaximal, characteristic, complemented
7C3×#4531C211yesmaximal, characteristic, complemented
8#71864—31nomaximal
9#68708—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C3×#926C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#897—22no—
18C3×#886—22no—
19C3×#875C412yescomplemented
20C3×#869C412yescomplemented
21#63955—22no—
22#63843—22no—
23Dic3×Dic6—22no—
24#63569—22no—
25#63568—22no—
26#63560—22no—
27C3×#536—31no—
28#5812—31no—
29#5526D311yescharacteristic
30#5516—31no—
31#5236—31no—
32#5236—31no—
33C2×#836—31no—
34#5139—31no—
35C2×#824—31no—
36#5005—31no—
37C3×H(3,ℤ/4)—31no—
38#4531—31no—
39#4531—31no—
40#4531—61no—
41#4531D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C2×C3×#67—21no—
44C22×C3×Dic3D412yes—
45C3×#235—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C2×C3×D12C2×C411yescharacteristic
50C2×C3×C4×D3—21no—
51C2×C3×Dic6—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6C2×C411yescharacteristic
56C2×C3×Dic6C2×C412yes—
57C2×C3×Dic6D412yes—
58C32×C4⋊C4—21no—
59C32×C22⋊C4—21no—
60C32×C42C2×C412yes—
61#3757—21no—
62C4⋊(C3⋊Dic3)—21no—
63C4×C3⋊Dic3D412yes—
64#3748—21no—
65#3748—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C3×#217—21no—
68C3×(C2×D3)⋊C4—24no—
69C3×C4⋊Dic3—21no—
70C3×C4⋊Dic3—24no—
71C3×C4×Dic3D412yes—
72C3×#208—21no—
73C3×#208—21no—
74C2×C3×C3⋊C8—21no—
75Dic3⋊Dic3—24no—
76Dic32—24no—
77#1912—91noSylow
78C2×C3×#41—31no—
79C22×C3×Q8—31no—
80C2×#235C2×D311yescharacteristic
81C22×Dic6C2×D311yescharacteristic
82C2×C3×M16—31no—
83C3×C4⋊Q8—32no—
84C3×#124—32no—
85C3×#123—62no—
86C3×C22⋊Q8—62no—
87C3×#117—21no—
88C3×#117—31no—
89C3×#117C2×D311yescharacteristic
90C3×#117C2×D311yescharacteristic
91Q8×Dic3—62no—
92Q8×Dic3—62no—
93#926—31no—
94#926—31no—
95#926—61no—
96#926—62no—
97#926C2×D311yescharacteristic
98C2×#208—31no—
99C2×#208—31no—
100C2×#208—61no—
101C2×#208C2×D311yescharacteristic
102#897—22no—
103#887—62no—
104#886—22no—
105#877—62no—
106#875Dic312yescomplemented
107#869Dic312yescomplemented
108C4×Dic6—62no—
109#837—62no—
110#837—62no—
111#836—62no—
112#825—62no—
113#824—62no—
114#805—62no—
115C23×C32C2×D411yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4—22no—
118C2×C32×C4C22×C411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4#4111yescharacteristic
123C2×C32×C4#4111yescharacteristic
124C2×C3⋊Dic3—22no—
125C3×#67—41no—
126C3×#67—41no—
127C2×C3×Dic3—22no—
128C2×C3×Dic3—22no—
129C2×C3×Dic3—21no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3C22⋊C414yes—
132C3×D12—21no—
133C3×D12—21no—
134C3×C4×D3—41no—
135C3×C4×D3—41no—
136C3×Dic6—22no—
137C3×Dic6—22no—
138C3×Dic6—22no—
139C3×Dic6—22no—
140C3×Dic6—21no—
141C3×Dic6—21no—
142C3⋊(C3⋊C8)—41no—
143C3×C3⋊C8—41no—
144#536—31no—
145#519—91no—
146#421—91no—
147#421—91no—
148C2×#101—91no—
149H(3,ℤ/4)—31no—
150H(3,ℤ/4)—91no—
151C3×#41—61no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—61no—
155C2×C3×Q8—32no—
156C2×C3×Q8—32no—
157C2×C3×Q8—31no—
158C2×C3×Q8—61no—
159C2×C3×Q8—61no—
160C2×C3×Q8—61no—
161C2×C3×Q8—61no—
162C2×C3×D4—31no—
163C2×C3×D4—61no—
164C22×C3×C4—21no—
165C22×C3×C4—32no—
166C22×C3×C4—61no—
167C22×C3×C4C22×D311yescharacteristic
168C22×C3×C4C22×D311yescharacteristic
169C2×#67—21no—
170C22×Dic3#6712yes—
171#235—21no—
172#235—21no—
173#235—21no—
174#235—21no—
175C2×D12C2×Dic311yescharacteristic
176C2×C4×D3—21no—
177C2×Dic6—21no—
178C2×Dic6—21no—
179C2×Dic6—21no—
180C2×Dic6—21no—
181C2×Dic6C2×Dic311yescharacteristic
182C2×Dic6C2×Dic312yes—
183C2×Dic6#6712yes—
184C3×M16—61no—
185C3×M16—61no—
186C2×C3×C8—61no—
187C3×C4⋊C4—21no—
188C3×C4⋊C4—21no—
189C3×C4⋊C4—41no—
190C3×C4⋊C4—64no—
191C3×C4⋊C4—61no—
192C3×C22⋊C4—21no—
193C3×C22⋊C4—21no—
194C3×C22⋊C4—41no—
195C3×C22⋊C4—64no—
196C3×C22⋊C4—61no—
197C3×C42—22no—
198C3×C42—32no—
199C3×C42C4×D312yes—
200C3×C42C2×Dic312yes—
201#217—21no—
202#217—61no—
203#217—61no—
204#217—121no—
205(C2×D3)⋊C4—24no—
206C4⋊Dic3—21no—
207C4⋊Dic3—24no—
208C4⋊Dic3—64no—
209C4⋊Dic3—61no—
210C4⋊Dic3—61no—
211C4⋊Dic3—121no—
212Dic3⋊C4—64no—
213C4×Dic3—32no—
214C4×Dic3—32no—
215C4×Dic3—62no—
216C4×Dic3—64no—
217C4×Dic3—64no—
218C4×Dic3D1212yes—
219#208—21no—
220#208—21no—
221#208—61no—
222#208—61no—
223#208—61no—
224#208—61no—
225#208—121no—
226#208—121no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—62no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—61no—
231C22×C32—41no—
232C22×C32C2×C22⋊C411yescharacteristic
233C22×C32#12011yescharacteristic
234C22×C32#12311yescharacteristic
235C2×C3×D3—42no—
236C2×C3×D3—41no—
237C32×C4—42no—
238C32×C4C4×D411yescharacteristic
239C32×C4C4×D411yescharacteristic
240C32×C4#12111yescharacteristic
241C32×C4#12111yescharacteristic
242C3⋊Dic3—42no—
243C3×Dic3—24no—
244C3×Dic3—42no—
245C3×Dic3—41no—
246C2×#41—31no—
247C22×Q8—31no—
248C2×M16—31no—
249C2×M16—91no—
250C4⋊Q8—32no—
251#124—32no—
252#123—62no—
253C22⋊Q8—62no—
254C4×Q8—182no—
255C4×Q8—182no—
256#117—31no—
257#117—91no—
258#117—182no—
259#117D3211yescharacteristic
260#104—182no—
261#104—182no—
262#101—182no—
263C23×C3—21no—
264C23×C3—61no—
265C23×C3D3×D411yescharacteristic
266C23×C3C2×#6711yescharacteristic
267C22×D3—21no—
268C3×Q8—62no—
269C3×Q8—62no—
270C3×Q8—62no—
271C3×Q8—62no—
272C3×Q8—61no—
273C3×Q8—61no—
274C3×D4—61no—
275C3×D4—61no—
276C3×D4—121no—
277C3×D4—121no—
278C2×C3×C4—22no—
279C2×C3×C4—22no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—34no—
287C2×C3×C4—42no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—61no—
291C2×C3×C4—62no—
292C2×C3×C4—121no—
293C2×C3×C4—121no—
294C2×C3×C4C2×C4×D311yescharacteristic
295C2×C3×C4C2×D1211yescharacteristic
296C2×C3×C4#23511yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4D3×D411yescharacteristic
300C2×C3×C4D3×D411yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4#23711yescharacteristic
303C2×C3×C4#23911yescharacteristic
304C2×C3×C4C22×Dic311yescharacteristic
305C2×C3×C4C2×#6711yescharacteristic
306#67—41no—
307#67—41no—
308C2×Dic3—22no—
309C2×Dic3—22no—
310C2×Dic3—22no—
311C2×Dic3—21no—
312C2×Dic3—62no—
313C2×Dic3—62no—
314C2×Dic3—122no—
315C2×Dic3#21714yes—
316D12—21no—
317D12—21no—
318C4×D3—41no—
319C4×D3—41no—
320Dic6—22no—
321Dic6—22no—
322Dic6—22no—
323Dic6—22no—
324Dic6—21no—
325Dic6—21no—
326C3×C8—121no—
327C3⋊C8—41no—
328C3⋊C8—122no—
329C3⋊C8—121no—
330C3⋊C8—121no—
331C2×C32—21no—
332C2×C32—21no—
333C2×C32—21no—
334C2×C32#38611yescharacteristic
335C3×D3—81no—
336#41—61no—
337#41—61no—
338#41—61no—
339#41—61no—
340C2×Q8—32no—
341C2×Q8—32no—
342C2×Q8—31no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×Q8—61no—
347C2×D4—31no—
348C2×D4—61no—
349C22×C4—32no—
350C22×C4—61no—
351C22×C4C2×D3211yescharacteristic
352M16—61no—
353M16—61no—
354M16—181no—
355M16—181no—
356C2×C8—61no—
357C2×C8—181no—
358C4⋊C4—21no—
359C4⋊C4—64no—
360C4⋊C4—61no—
361C4⋊C4—184no—
362C4⋊C4—181no—
363C22⋊C4—21no—
364C22⋊C4—64no—
365C22⋊C4—61no—
366C22⋊C4—181no—
367C42—32no—
368C42—92no—
369C42—184no—
370C42D3×Dic312yes—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—41no—
375C22×C3—41no—
376C22×C3—81no—
377C22×C3—122no—
378C22×C3—121no—
379C22×C3D3×C22⋊C411yescharacteristic
380C22×C3#88211yescharacteristic
381C22×C3#89411yescharacteristic
382C22×C3#93511yescharacteristic
383C22×C3#93711yescharacteristic
384C22×C3C2×#21711yescharacteristic
385C2×D3—42no—
386C2×D3—41no—
387C3×C4—21no—
388C3×C4—21no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—42no—
392C3×C4—42no—
393C3×C4—64no—
394C3×C4—82no—
395C3×C4—122no—
396C3×C4—121no—
397C3×C4C4×D1211yescharacteristic
398C3×C4#88411yescharacteristic
399C3×C4#89311yescharacteristic
400C3×C4#89511yescharacteristic
401C3×C4D4×Dic311yescharacteristic
402C3×C4D4×Dic311yescharacteristic
403C3×C4#93911yescharacteristic
404C3×C4#93911yescharacteristic
405Dic3—24no—
406Dic3—42no—
407Dic3—41no—
408Dic3—122no—
409Dic3—122no—
410Dic3—242no—
411C32#191211yescharacteristic, complemented, Sylow
412C23—61no—
413C23D3×#6711yescharacteristic
414Q8—62no—
415Q8—62no—
416Q8—62no—
417Q8—62no—
418Q8—61no—
419Q8—61no—
420D4—61no—
421D4—61no—
422D4—121no—
423D4—121no—
424C2×C4—22no—
425C2×C4—34no—
426C2×C4—62no—
427C2×C4—62no—
428C2×C4—62no—
429C2×C4—61no—
430C2×C4—121no—
431C2×C4—121no—
432C2×C4—182no—
433C2×C4#379511yescharacteristic
434C2×C4#379611yescharacteristic
435C2×C4D3×D1211yescharacteristic
436C2×C4#380211yescharacteristic
437C2×C4C2×D3×Dic311yescharacteristic
438C2×C4D3×#6711yescharacteristic
439C8—121no—
440C8—361no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—41no—
449C2×C3—41no—
450C2×C3—41no—
451C2×C3—241no—
452C2×C3#466511yescharacteristic
453C2×C3#522011yescharacteristic
454D3—81no—
455C22—41no—
456C22—122no—
457C22—121no—
458C22#6388411yescharacteristic
459C22#6392211yescharacteristic
460C22D3×#21711yescharacteristic
461C4—42no—
462C4—64no—
463C4—122no—
464C4—121no—
465C4—362no—
466C4#6388511yescharacteristic
467C4#6388611yescharacteristic
468C4Dic3×D1211yescharacteristic
469C4#6389811yescharacteristic
470C3—21no—
471C3#6870811yescharacteristic, complemented
472C3#7186411yescharacteristic, complemented
473C2—21no—
474C2—21no—
475C2—21no—
476C2—241no—
477C2#1059137611yescharacteristic
subgroupG/H
centerC2#10591376
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC32×#117C22
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenter#117D32
hypocenterC32#1912
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ #117

Complements

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

NH ≅ G/Ntype
2. #10594818C2semidirect
5. C2×#63560C2semidirect
6. #10589397C2semidirect
7. C3×#4531C2semidirect
19. C3×#875C4semidirect
20. C3×#869C4semidirect
41. #4531D3semidirect
106. #875Dic3semidirect
107. #869Dic3semidirect
411. C32#1912semidirect
471. C3#68708semidirect
472. C3#71864semidirect

Maximal subgroups

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

subgroupindex
C3×#55262
#105948182
#105911112
#105911102
C2×#635602
#105893972
C3×#45312
#718643
#687083