Finite Group Databasebeta

← #11789679

Subgroups — #11789679

Order 1152.

559 conjugacy classes of subgroups.

The subgroup lattice has 467 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592830C211yesmaximal, characteristic
2#10591130C211yesmaximal, characteristic, complemented
3C2×#63564C211yesmaximal, characteristic
4C2×#63559C211yesmaximal, characteristic
5#10591059C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8#68983—31nomaximal
9#68931—31nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C2×C3×C4⋊Dic3C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17#63648—21no—
18#63648—21no—
19#63575—21no—
20#63573—21no—
21#63564—21no—
22#63564—21no—
23#63559C414yescomplemented
24#63555—21no—
25#63553—21no—
26#5131—31no—
27#5131—31no—
28#5131—61no—
29C2×#823—31no—
30C2×#823—31no—
31#5122—31no—
32#5121—31no—
33C2×#821—31no—
34#5101—31no—
35C2×#809—31no—
36#4964—31no—
37C3×#343—31no—
38C3×#341—31no—
39#4558D311yescharacteristic, complemented
40#4554D311yescharacteristic, complemented
41C23×C3⋊D3—21no—
42C22×C32×C4C2311yescharacteristic
43C2×C4⋊(C3⋊D3)—21no—
44C2×C4⋊(C3⋊D3)—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—21no—
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)C2×C412yes—
49C22×C3×Dic3—21no—
50C32×M16—21no—
51C32×M16—21no—
52C2×C32×C8—21no—
53#3757—21no—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C4⋊(C3⋊Dic3)D411yescharacteristic
56C4×C3⋊Dic3—21no—
57C3×C4⋊Dic3—21no—
58C3×C4⋊Dic3—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208C2×C412yes—
62C3×#208C2×C412yes—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8—21no—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8D411yescharacteristic
68C2×C3×C3⋊C8D411yescharacteristic
69#1931—91noSylow
70C22×D12—31no—
71C22×D12—31no—
72C22×D12—61no—
73C2×C3×M16—21no—
74C2×C3×M16—31no—
75C2×C3×M16—31no—
76C2×C3×M16C2×D311yescharacteristic
77C2×C3×M16C2×D311yescharacteristic
78C22×C3×C8—31no—
79C2×C3×C4⋊C4—31no—
80#926—31no—
81#926—31no—
82#926—61no—
83C2×C4⋊Dic3C2×D311yescharacteristic
84C2×#208C2×D311yescharacteristic
85C2×#208C2×D311yescharacteristic
86C22×C3⋊C8C2×D311yescharacteristic
87#823—34no—
88#823—34no—
89#821—61no—
90#821—61no—
91#821—61no—
92#821—61no—
93#821—61no—
94#821—61no—
95#821—62no—
96#821—62no—
97#818—61no—
98#817—61no—
99#815—61no—
100#815—61no—
101C8×Dic3—61no—
102C8×Dic3—61no—
103#809—61no—
104#809—61no—
105#808—61no—
106#807—61no—
107C23×C32#4111yescharacteristic
108C22×C3⋊D3—22no—
109C22×C3⋊D3—41no—
110C22×C3⋊D3—41no—
111C22×C3⋊D3—81no—
112C22×C3⋊D3—81no—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C2×D411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4#4111yescharacteristic
117C2×C32×C4#4111yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C3⋊Dic3—21no—
120C2×C3⋊Dic3—21no—
121C4⋊(C3⋊D3)—22no—
122C4⋊(C3⋊D3)—22no—
123C4⋊(C3⋊D3)—41no—
124C4⋊(C3⋊D3)—41no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—81no—
127C32×C8—41no—
128C3×C3⋊C8—22no—
129C3×C3⋊C8—22no—
130C3×C3⋊C8—21no—
131C3×C3⋊C8—21no—
132#428—91no—
133#418—91no—
134C2×#102—91no—
135C2×#100—91no—
136#405—91no—
137#343—31no—
138#341—31no—
139C23×D3—61no—
140C23×D3—61no—
141C23×D3—121no—
142C22×C3×C4—21no—
143C22×C3×C4—61no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C22×Dic3—21no—
147C2×D12—32no—
148C2×D12—32no—
149C2×D12—62no—
150C2×D12—62no—
151C2×D12—62no—
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—61no—
162C2×D12—121no—
163C2×D12—121no—
164C2×D12—121no—
165C3×M16—21no—
166C3×M16—21no—
167C3×M16—21no—
168C3×M16—21no—
169C3×M16—32no—
170C3×M16—32no—
171C3×M16—41no—
172C3×M16—41no—
173C3×M16—61no—
174C3×M16—61no—
175C2×C3×C8—22no—
176C2×C3×C8—21no—
177C2×C3×C8—21no—
178C2×C3×C8—31no—
179C2×C3×C8—31no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C2×C3×C8—61no—
183C2×C3×C8—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186#217—61no—
187#217—61no—
188#217—121no—
189C4⋊Dic3—21no—
190C4⋊Dic3—21no—
191C4⋊Dic3—31no—
192C4⋊Dic3—31no—
193C4⋊Dic3—31no—
194C4⋊Dic3—31no—
195C4⋊Dic3—61no—
196C4⋊Dic3—61no—
197C4×Dic3—61no—
198C4×Dic3—61no—
199C4×Dic3—121no—
200#208—21no—
201#208—21no—
202#208C4×D312yes—
203#208C4×D312yes—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8D1211yescharacteristic
209C2×C3⋊C8D1211yescharacteristic
210C22×C32—21no—
211C22×C32—21no—
212C22×C32#11711yescharacteristic
213C22×C32#12111yescharacteristic
214C22×C32#12611yescharacteristic
215C2×C3⋊D3—42no—
216C2×C3⋊D3—82no—
217C2×C3⋊D3—81no—
218C2×C3⋊D3—81no—
219C2×C3⋊D3—82no—
220C32×C4C4×D411yescharacteristic
221C32×C4C4×D411yescharacteristic
222C32×C4#12311yescharacteristic
223C32×C4#12411yescharacteristic
224C3⋊Dic3—41no—
225C3⋊Dic3—41no—
226C3×Dic3—81no—
227C22×D4—91no—
228C2×M16—31no—
229C2×M16—31no—
230C2×M16D3211yescharacteristic
231C22×C8—31no—
232#117—91no—
233C2×C4⋊C4—31no—
234#107—181no—
235#106—181no—
236#102—181no—
237#102—181no—
238#102—181no—
239#102—181no—
240#100—94no—
241#97—181no—
242C4×C8—181no—
243C23×C3—21no—
244C23×C3#23511yescharacteristic
245C23×C3#23911yescharacteristic
246C22×D3—62no—
247C22×D3—62no—
248C22×D3—122no—
249C22×D3—122no—
250C22×D3—122no—
251C22×D3—121no—
252C22×D3—121no—
253C22×D3—121no—
254C22×D3—121no—
255C22×D3—242no—
256C22×D3—242no—
257C22×D3—241no—
258C22×D3—241no—
259C22×D3—241no—
260C22×D3—241no—
261C2×C3×C4—21no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—121no—
268C2×C3×C4—241no—
269C2×C3×C4C2×C4×D311yescharacteristic
270C2×C3×C4C2×C4×D311yescharacteristic
271C2×C3×C4C2×D1211yescharacteristic
272C2×C3×C4#23511yescharacteristic
273C2×C3×C4#23511yescharacteristic
274C2×C3×C4D3×D411yescharacteristic
275C2×C3×C4D3×D411yescharacteristic
276C2×C3×C4D3×D411yescharacteristic
277C2×C3×C4#23711yescharacteristic
278C2×C3×C4#23711yescharacteristic
279C2×C3×C4#23711yescharacteristic
280C2×C3×C4#23911yescharacteristic
281C2×Dic3—41no—
282C2×Dic3—61no—
283C2×Dic3—61no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—81no—
287C2×Dic3—121no—
288C2×Dic3—121no—
289D12—64no—
290D12—62no—
291D12—62no—
292D12—62no—
293D12—62no—
294D12—122no—
295D12—122no—
296D12—122no—
297D12—121no—
298D12—121no—
299D12—121no—
300D12—121no—
301C3×C8—42no—
302C3×C8—41no—
303C3×C8—41no—
304C3×C8—62no—
305C3×C8—62no—
306C3×C8—61no—
307C3×C8—61no—
308C3⋊C8—22no—
309C3⋊C8—22no—
310C3⋊C8—21no—
311C3⋊C8—21no—
312C2×C32—21no—
313C2×C32—21no—
314C2×C32#38811yescharacteristic
315C2×C32#47111yescharacteristic
316C2×C32#47211yescharacteristic
317C3⋊D3—82no—
318C24—181no—
319C2×D4—92no—
320C2×D4—181no—
321C2×D4—181no—
322C2×D4—181no—
323C2×D4—181no—
324C2×D4—181no—
325C22×C4—61no—
326C22×C4C2×D3211yescharacteristic
327M16—21no—
328M16—21no—
329M16—32no—
330M16—32no—
331M16—61no—
332M16—61no—
333C2×C8—21no—
334C2×C8—31no—
335C2×C8—31no—
336C2×C8—61no—
337C2×C8—61no—
338C2×C8—61no—
339C2×C8—61no—
340C4⋊C4—61no—
341C4⋊C4—61no—
342C4⋊C4—91no—
343C4⋊C4—91no—
344C22⋊C4—181no—
345C42—181no—
346C22×C3—21no—
347C22×C3—21no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—41no—
354C22×C3—41no—
355C22×C3#87211yescharacteristic
356C22×C3#88411yescharacteristic
357C22×C3#89211yescharacteristic
358C22×C3#89511yescharacteristic
359C22×C3#89811yescharacteristic
360C22×C3#89811yescharacteristic
361C2×D3—124no—
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—242no—
365C2×D3—242no—
366C2×D3—242no—
367C2×D3—242no—
368C2×D3—244no—
369C2×D3—244no—
370C2×D3—241no—
371C2×D3—241no—
372C2×D3—241no—
373C2×D3—241no—
374C2×D3—242no—
375C2×D3—242no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—21no—
379C3×C4—21no—
380C3×C4—241no—
381C3×C4C4×D1211yescharacteristic
382C3×C4#67⋊C411yescharacteristic
383C3×C4#67⋊C411yescharacteristic
384C3×C4#88511yescharacteristic
385C3×C4#88511yescharacteristic
386C3×C4#88611yescharacteristic
387C3×C4#89311yescharacteristic
388C3×C4#89411yescharacteristic
389Dic3—81no—
390Dic3—121no—
391Dic3—121no—
392Dic3—121no—
393Dic3—121no—
394Dic3—241no—
395Dic3—241no—
396C32#193111yescharacteristic, complemented, Sylow
397C23—182no—
398C23—361no—
399C23—361no—
400C23—721no—
401C23—721no—
402C23#379911yescharacteristic
403D4—182no—
404D4—182no—
405D4—361no—
406D4—361no—
407C2×C4—121no—
408C2×C4—181no—
409C2×C4—181no—
410C2×C4—241no—
411C2×C4#379611yescharacteristic
412C2×C4C4×D3211yescharacteristic
413C2×C4D3×D1211yescharacteristic
414C2×C4#380411yescharacteristic
415C2×C4#380411yescharacteristic
416C2×C4#381111yescharacteristic
417C8—41no—
418C8—62no—
419C8—62no—
420C8—61no—
421C8—61no—
422C2×C3—21no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—41no—
430C2×C3—41no—
431C2×C3#466911yescharacteristic
432C2×C3#467011yescharacteristic
433C2×C3#474911yescharacteristic
434C2×C3#475411yescharacteristic
435C2×C3#489711yescharacteristic
436C2×C3#489811yescharacteristic
437D3—244no—
438D3—242no—
439D3—242no—
440C22—21no—
441C22—21no—
442C22—362no—
443C22—722no—
444C22—722no—
445C22—721no—
446C22—721no—
447C22#6383611yescharacteristic
448C22#6384811yescharacteristic
449C22#6391011yescharacteristic
450C4—241no—
451C4—361no—
452C4—361no—
453C4#6388011yescharacteristic
454C4#6388111yescharacteristic
455C4#6389011yescharacteristic
456C4#6395311yescharacteristic
457C3—21no—
458C3#6893111yescharacteristic, complemented
459C3#6898311yescharacteristic, complemented
460C2—21no—
461C2—21no—
462C2—722no—
463C2#1059098711yescharacteristic
464C2#1059099011yescharacteristic
465C2#1059125911yescharacteristic
subgroupG/H
centerC22#63910
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1931
LCSG ▷ C2×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. #10591130C2semidirect
5. #10591059C2semidirect
6. C3×#4558C2semidirect
7. C3×#4554C2semidirect
23. #63559C4semidirect
39. #4558D3semidirect
40. #4554D3semidirect
396. C32#1931semidirect
458. C3#68931semidirect
459. C3#68983semidirect

Maximal subgroups

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

subgroupindex
#105928302
#105911302
C2×#635642
C2×#635592
#105910592
C3×#45582
C3×#45542
#689833
#689313