Finite Group Databasebeta

← #11793954

Subgroups — #11793954

Order 1152.

577 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#909C211yesmaximal, characteristic
2C2×#63649C211yesmaximal, characteristic, complemented
3C2×#63565C211yesmaximal, characteristic, complemented
4#10591087C211yesmaximal, characteristic
5C2×#63560C211yesmaximal, characteristic, complemented
6#10591071C211yesmaximal, characteristic
7C3×#4554C211yesmaximal, characteristic, complemented
8#72105—31nomaximal
9#68987—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13C2×#3748C2211yescharacteristic
14C22×C3⋊(C3⋊C8)C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C3×#909—22no—
18C3×#909—22no—
19C2×C3×Dic12—21no—
20C2×C3×#204—21no—
21#63649—22no—
22#63565—21no—
23#63565—22no—
24#63562—21no—
25#63560—22no—
26(C2×D3)⋊(C3⋊C8)—22no—
27C2×C3×#137—31no—
28C2×#909D311yescharacteristic
29#5234—31no—
30#5232—31no—
31C2×#836—31no—
32C2×#835—31no—
33C2×#824—31no—
34#5129—31no—
35C2×#822—31no—
36C2×#822—31no—
37C2×#822—61no—
38C2×#810—31no—
39#4966—31no—
40C3×#343—31no—
41#4554D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C2×C3×#67—21no—
44C22×C3×Dic3—21no—
45C22×C3×Dic3—21no—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3—21no—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6D411yescharacteristic
58C2×C3×Dic6D412yes—
59C32×M16—21no—
60C32×M16D412yes—
61C2×C32×C8—21no—
62#3748—21no—
63#3748—21no—
64C2×C3⋊(C3⋊C8)—21no—
65C2×C3⋊(C3⋊C8)—21no—
66C2×C3⋊(C3⋊C8)—21no—
67C2×C3⋊(C3⋊C8)D412yes—
68C3×C4⋊Dic3—21no—
69C3×C4⋊Dic3—21no—
70C3×#208—21no—
71C3×#208—21no—
72C2×C3×C3⋊C8—21no—
73C3×Dic12—24no—
74C3×#204—24no—
75#2052—91noSylow
76C2×C3×#41—31no—
77C22×C3×Q8—31no—
78C2×#235C2×D311yescharacteristic
79C22×Dic6C2×D311yescharacteristic
80C3×#137—62no—
81C3×#137—62no—
82C2×C3×Q16—61no—
83C2×C3×SD16—61no—
84C2×C3×M16—21no—
85C2×C3×M16—31no—
86C2×C3×M16C2×D311yescharacteristic
87C2×C3×M16C2×D311yescharacteristic
88C2×C3×C4⋊C4—31no—
89C2×C4⋊Dic3C2×D311yescharacteristic
90C2×#208—31no—
91C2×#208—31no—
92C2×#208—61no—
93C2×#208C2×D311yescharacteristic
94C22×C3⋊C8—31no—
95C22×C3⋊C8—31no—
96C22×C3⋊C8—61no—
97#909—22no—
98#909—22no—
99C2×Dic12—21no—
100C2×#204—21no—
101#836—62no—
102#835—62no—
103#835—61no—
104#832—61no—
105#830—62no—
106#824—62no—
107#822—64no—
108#822—62no—
109#822—62no—
110(C2×D3)⋊C8—62no—
111#810—62no—
112#810—61no—
113#809—61no—
114C23×C32#4111yescharacteristic
115C22×C3×D3—21no—
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4#4111yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C3×#67—41no—
123C3×#67—41no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—22no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—41no—
128C2×C3×Dic3—41no—
129C2×C3×Dic3—81no—
130C3×D12—21no—
131C3×D12—21no—
132C3×C4×D3—41no—
133C3×C4×D3—41no—
134C3×Dic6—22no—
135C3×Dic6—21no—
136C3×Dic6—22no—
137C3×Dic6—21no—
138C3×Dic6—41no—
139C3×Dic6—41no—
140C32×C8—22no—
141C3⋊(C3⋊C8)—22no—
142C3⋊(C3⋊C8)—41no—
143C3×C3⋊C8—41no—
144C2×#137—31no—
145C2×#108—91no—
146#417—91no—
147C2×#103—91no—
148C2×#101—91no—
149#408—91no—
150#343—31no—
151C3×#41—61no—
152C3×#41—61no—
153C3×#41—61no—
154C3×#41—61no—
155C2×C3×Q8—31no—
156C2×C3×Q8—32no—
157C2×C3×Q8—61no—
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—61no—
166C22×C3×C4—61no—
167C22×C3×C4—61no—
168C22×C3×C4C22×D311yescharacteristic
169C22×C3×C4C22×D311yescharacteristic
170C2×#67—21no—
171C22×Dic3—21no—
172C22×Dic3—21no—
173#235—21no—
174#235—21no—
175#235—21no—
176#235—21no—
177C2×D12#6711yescharacteristic
178C2×C4×D3—21no—
179C2×Dic6—21no—
180C2×Dic6—21no—
181C2×Dic6—21no—
182C2×Dic6—21no—
183C2×Dic6—21no—
184C2×Dic6#6711yescharacteristic
185C2×Dic6#6712yes—
186C3×Q16—64no—
187C3×SD16—64no—
188C3×M16—21no—
189C3×M16—21no—
190C3×M16—22no—
191C3×M16—41no—
192C3×M16—61no—
193C3×M16—61no—
194C3×M16D1212yes—
195C3×M16#6712yes—
196C2×C3×C8—21no—
197C2×C3×C8—21no—
198C2×C3×C8—41no—
199C2×C3×C8—61no—
200C3×C4⋊C4—61no—
201C3×C4⋊C4—61no—
202C4⋊Dic3—21no—
203C4⋊Dic3—21no—
204#208—21no—
205#208—21no—
206#208—62no—
207#208—61no—
208#208—61no—
209#208—61no—
210#208—61no—
211#208—121no—
212C2×C3⋊C8—21no—
213C2×C3⋊C8—32no—
214C2×C3⋊C8—32no—
215C2×C3⋊C8—62no—
216C2×C3⋊C8—62no—
217C2×C3⋊C8—62no—
218C2×C3⋊C8—61no—
219C2×C3⋊C8—61no—
220C2×C3⋊C8—61no—
221C2×C3⋊C8—61no—
222C2×C3⋊C8—61no—
223C2×C3⋊C8—61no—
224C2×C3⋊C8—121no—
225Dic12—24no—
226#204—24no—
227C22×C32—21no—
228C22×C32—21no—
229C22×C32#12111yescharacteristic
230C22×C32#12311yescharacteristic
231C22×C32#12411yescharacteristic
232C2×C3×D3—41no—
233C2×C3×D3—41no—
234C2×C3×D3—41no—
235C32×C4#12011yescharacteristic
236C32×C4#12111yescharacteristic
237C32×C4#12111yescharacteristic
238C32×C4#12311yescharacteristic
239C3×Dic3—42no—
240C3×Dic3—41no—
241C3×Dic3—81no—
242C2×#41—31no—
243C22×Q8—31no—
244#137—62no—
245#137—62no—
246C2×Q16—61no—
247C2×SD16—61no—
248C2×M16—31no—
249C2×M16—91no—
250C2×M16D3211yescharacteristic
251C22×C8—91no—
252C2×C4⋊C4—31no—
253#108—182no—
254#103—182no—
255#103—181no—
256#102—181no—
257#101—182no—
258C22⋊C8—182no—
259C23×C3—21no—
260C23×C3—61no—
261C23×C3#23511yescharacteristic
262C23×C3#23711yescharacteristic
263C22×D3—21no—
264C3×Q8—62no—
265C3×Q8—61no—
266C3×Q8—62no—
267C3×Q8—61no—
268C3×Q8—121no—
269C3×Q8—121no—
270C3×D4—61no—
271C3×D4—61no—
272C3×D4—121no—
273C3×D4—121no—
274C2×C3×C4—21no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—61no—
281C2×C3×C4—62no—
282C2×C3×C4—121no—
283C2×C3×C4—121no—
284C2×C3×C4—121no—
285C2×C3×C4—121no—
286C2×C3×C4—121no—
287C2×C3×C4—241no—
288C2×C3×C4C2×D1211yescharacteristic
289C2×C3×C4#23511yescharacteristic
290C2×C3×C4D3×D411yescharacteristic
291C2×C3×C4D3×D411yescharacteristic
292C2×C3×C4D3×D411yescharacteristic
293C2×C3×C4D3×D411yescharacteristic
294C2×C3×C4#23711yescharacteristic
295C2×C3×C4#23711yescharacteristic
296C2×C3×C4#23911yescharacteristic
297C2×C3×C4C2×#6711yescharacteristic
298C2×C3×C4C2×#6711yescharacteristic
299C2×C3×C4C2×#6711yescharacteristic
300#67—41no—
301#67—41no—
302C2×Dic3—22no—
303C2×Dic3—21no—
304C2×Dic3—41no—
305C2×Dic3—41no—
306C2×Dic3—41no—
307C2×Dic3—81no—
308D12—21no—
309D12—21no—
310C4×D3—41no—
311C4×D3—41no—
312Dic6—21no—
313Dic6—22no—
314Dic6—22no—
315Dic6—21no—
316Dic6—41no—
317Dic6—41no—
318C3×C8—22no—
319C3×C8—22no—
320C3×C8—42no—
321C3×C8—121no—
322C3⋊C8—41no—
323C3⋊C8—64no—
324C3⋊C8—62no—
325C3⋊C8—62no—
326C3⋊C8—122no—
327C3⋊C8—121no—
328C3⋊C8—121no—
329C2×C32—21no—
330C2×C32—21no—
331C2×C32#39411yescharacteristic
332C2×C32#47111yescharacteristic
333C2×C32#47311yescharacteristic
334C3×D3—81no—
335#41—61no—
336#41—61no—
337#41—61no—
338#41—61no—
339C2×Q8—32no—
340C2×Q8—31no—
341C2×Q8—61no—
342C2×Q8—61no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×D4—31no—
347C2×D4—61no—
348C22×C4—61no—
349C22×C4—61no—
350C22×C4—61no—
351C22×C4C2×D3211yescharacteristic
352Q16—64no—
353SD16—64no—
354M16—21no—
355M16—61no—
356M16—61no—
357M16—181no—
358M16—181no—
359M16#62612yes—
360C2×C8—21no—
361C2×C8—61no—
362C2×C8—92no—
363C2×C8—181no—
364C2×C8—181no—
365C2×C8—181no—
366C4⋊C4—61no—
367C4⋊C4—61no—
368C22×C3—21no—
369C22×C3—21no—
370C22×C3—21no—
371C22×C3—21no—
372C22×C3—21no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—41no—
376C22×C3—41no—
377C22×C3—121no—
378C22×C3—121no—
379C22×C3—121no—
380C22×C3#87511yescharacteristic
381C22×C3#88411yescharacteristic
382C22×C3#89411yescharacteristic
383C22×C3#93511yescharacteristic
384C22×C3#93611yescharacteristic
385C22×C3#93911yescharacteristic
386C2×D3—41no—
387C2×D3—41no—
388C2×D3—41no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—121no—
394C3×C4—122no—
395C3×C4—241no—
396C3×C4#88211yescharacteristic
397C3×C4#88411yescharacteristic
398C3×C4#89411yescharacteristic
399C3×C4#89511yescharacteristic
400C3×C4#93511yescharacteristic
401C3×C4#93811yescharacteristic
402C3×C4#93911yescharacteristic
403C3×C4#95311yescharacteristic
404Dic3—42no—
405Dic3—41no—
406Dic3—81no—
407C32#205211yescharacteristic, complemented, Sylow
408C23—61no—
409C23#379511yescharacteristic
410Q8—61no—
411Q8—62no—
412Q8—62no—
413Q8—61no—
414Q8—121no—
415Q8—121no—
416D4—61no—
417D4—61no—
418D4—121no—
419D4—121no—
420C2×C4—62no—
421C2×C4—61no—
422C2×C4—121no—
423C2×C4—121no—
424C2×C4—121no—
425C2×C4—121no—
426C2×C4—121no—
427C2×C4—241no—
428C2×C4#379511yescharacteristic
429C2×C4#379611yescharacteristic
430C2×C4#380211yescharacteristic
431C2×C4C2×#62611yescharacteristic
432C2×C4D3×#6711yescharacteristic
433C2×C4D3×#6711yescharacteristic
434C8—22no—
435C8—121no—
436C8—182no—
437C8—361no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—41no—
446C2×C3—41no—
447C2×C3—241no—
448C2×C3#467211yescharacteristic
449C2×C3#474811yescharacteristic
450C2×C3#475511yescharacteristic
451C2×C3#520311yescharacteristic
452C2×C3#520411yescharacteristic
453C2×C3#522211yescharacteristic
454D3—81no—
455C22—21no—
456C22—21no—
457C22—121no—
458C22—121no—
459C22—121no—
460C22#6386011yescharacteristic
461C22#6388411yescharacteristic
462C22#6388511yescharacteristic
463C4—121no—
464C4—122no—
465C4—241no—
466C4#6388411yescharacteristic
467C4#6388511yescharacteristic
468C4#6391611yescharacteristic
469C4#6397711yescharacteristic
470C3—21no—
471C3#6898711yescharacteristic, complemented
472C3#7210511yescharacteristic, complemented
473C2—21no—
474C2—21no—
475C2—241no—
476C2#1059097911yescharacteristic
477C2#1059098111yescharacteristic
478C2#1059130211yescharacteristic
subgroupG/H
centerC22#63885
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×C3×#235C22
hypercenterC2×M16D32
hypocenterC32#2052
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
2. C2×#63649C2semidirect
3. C2×#63565C2semidirect
5. C2×#63560C2semidirect
7. C3×#4554C2semidirect
41. #4554D3semidirect
407. C32#2052semidirect
471. C3#68987semidirect
472. C3#72105semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#9092
C2×#636492
C2×#635652
#105910872
C2×#635602
#105910712
C3×#45542
#721053
#689873