Finite Group Databasebeta

← #11785620

Subgroups — #11785620

Order 1152.

581 conjugacy classes of subgroups.

The subgroup lattice has 458 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63815C211yesmaximal, characteristic
2C2×#63649C211yesmaximal, characteristic, complemented
3C3×#5133C211yesmaximal, characteristic
4C2×#63576C211yesmaximal, characteristic, complemented
5#10591087C211yesmaximal, characteristic
6C3×#4554C211yesmaximal, characteristic, complemented
7#10589167C211yesmaximal, characteristic, complemented
8#70300—31nomaximal
9#69001—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×C4⋊Dic3C2211yescharacteristic
15C2×C3×C4⋊Dic3C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3711—21no—
18#63815—22no—
19#63815C414yescomplemented
20C2×D3×C3⋊C8—21no—
21#63649—22no—
22C3×#821—21no—
23C3×#816—21no—
24#63576—21no—
25#63576—21no—
26#63565—21no—
27#63562—21no—
28C2×#948—31no—
29C2×#907—31no—
30C3×#417—31no—
31#5232—31no—
32#5133D311yescharacteristic
33C2×#822—31no—
34C2×#822—31no—
35C2×#822—61no—
36#4966—31no—
37C2×#807—31no—
38C2×#807—31no—
39C3×#343—31no—
40#4554—31no—
41#4554D311yescharacteristic, complemented
42#4530—31no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67—21no—
45C22×C3×Dic3—21no—
46C22×C3×Dic3—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235C2×C412yes—
50C3×#235Q812yes—
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×M16—21no—
55C32×M16—21no—
56C2×C32×C8—21no—
57#3748—21no—
58#3748—21no—
59C2×C3⋊(C3⋊C8)—21no—
60C2×C3⋊(C3⋊C8)C2×C412yes—
61C2×C3⋊(C3⋊C8)D411yescharacteristic
62C2×C3⋊(C3⋊C8)D412yes—
63C2×C3⋊(C3⋊C8)D411yescharacteristic
64C3×C4⋊Dic3—21no—
65C3×C4⋊Dic3—21no—
66C3×C4⋊Dic3—21no—
67C3×C4⋊Dic3—21no—
68C3×#208—21no—
69C3×#208C2×C412yes—
70C2×C3×C3⋊C8—21no—
71#3711—24no—
72D3×C3⋊C8—24no—
73#1816—91noSylow
74C2×C3×#41—31no—
75C2×#235C2×D311yescharacteristic
76C2×C3×M16—21no—
77C2×C3×M16—31no—
78C2×C3×M16C2×D311yescharacteristic
79C2×C3×M16C2×D311yescharacteristic
80C2×C3×C4⋊C4—31no—
81C2×C3×C4⋊C4—31no—
82#948—34no—
83#948—62no—
84C2×C4⋊Dic3C2×D311yescharacteristic
85C2×C4⋊Dic3C2×D311yescharacteristic
86C2×#208—31no—
87C2×#208—31no—
88C2×#208—61no—
89C2×#208—61no—
90C2×#208C2×D311yescharacteristic
91C22×C3⋊C8—31no—
92C22×C3⋊C8—31no—
93C22×C3⋊C8—61no—
94C22×C3⋊C8—61no—
95#907—34no—
96#907—62no—
97C2×ΓL(1,𝔽25)—61no—
98C2×D3×C8—61no—
99C3×#103—61no—
100C3×#102—61no—
101#835—61no—
102#832—61no—
103#822—62no—
104#822—62no—
105#822—64no—
106#821—21no—
107#816—21no—
108#810—61no—
109#809—61no—
110#807—61no—
111#807—61no—
112#807—61no—
113#807—61no—
114C23×C32#4111yescharacteristic
115C22×C3×D3—21no—
116C2×C32×C4C22×C411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4C2×D411yescharacteristic
119C2×C32×C4C2×D411yescharacteristic
120C2×C32×C4C2×Q811yescharacteristic
121C2×C32×C4#4111yescharacteristic
122C3×#67—22no—
123C3×#67—22no—
124C2×C3×Dic3—21no—
125C2×C3×Dic3—41no—
126C2×C3×Dic3—41no—
127C2×C3×Dic3—81no—
128C2×C3×Dic3—81no—
129C3×D12—21no—
130C3×D12C4⋊C412yes—
131C3×C4×D3—22no—
132C3×C4×D3—22no—
133C3×Dic6—21no—
134C3×Dic6C4⋊C412yes—
135C32×C8—41no—
136C3⋊(C3⋊C8)—41no—
137C3⋊(C3⋊C8)C22⋊C412yes—
138C3⋊(C3⋊C8)C22⋊C412yes—
139C3×C3⋊C8—22no—
140C2×#131—91no—
141C2×#108—91no—
142C2×#107—91no—
143#417—31no—
144#417—91no—
145#343—31no—
146#343—91no—
147C3×#41—32no—
148C3×#41—32no—
149C3×#41—61no—
150C3×#41—61no—
151C2×C3×Q8—31no—
152C2×C3×D4—31no—
153C2×C3×D4—61no—
154C22×C3×C4—21no—
155C22×C3×C4—61no—
156C22×C3×C4—61no—
157C22×C3×C4—61no—
158C22×C3×C4C22×D311yescharacteristic
159C22×C3×C4C22×D311yescharacteristic
160C2×#67—21no—
161C22×Dic3—21no—
162C22×Dic3—21no—
163#235—21no—
164#235—21no—
165#235Dic612yes—
166#235C4×D312yes—
167C2×D12#6711yescharacteristic
168C2×C4×D3—21no—
169C2×Dic6#6711yescharacteristic
170C3×M16—22no—
171C3×M16—21no—
172C3×M16—21no—
173C3×M16—21no—
174C3×M16—21no—
175C3×M16—32no—
176C3×M16—41no—
177C3×M16—61no—
178C2×C3×C8—21no—
179C2×C3×C8—21no—
180C2×C3×C8—41no—
181C2×C3×C8—61no—
182C3×C4⋊C4—61no—
183C3×C4⋊C4—61no—
184C3×C4⋊C4—61no—
185C3×C4⋊C4—61no—
186C4⋊Dic3—21no—
187C4⋊Dic3—21no—
188C4⋊Dic3—21no—
189C4⋊Dic3—21no—
190#208—21no—
191#208—64no—
192#208—62no—
193#208—61no—
194#208—61no—
195#208—61no—
196#208—61no—
197#208—121no—
198#208C4×D312yes—
199C2×C3⋊C8—21no—
200C2×C3⋊C8—32no—
201C2×C3⋊C8—32no—
202C2×C3⋊C8—31no—
203C2×C3⋊C8—31no—
204C2×C3⋊C8—31no—
205C2×C3⋊C8—31no—
206C2×C3⋊C8—32no—
207C2×C3⋊C8—32no—
208C2×C3⋊C8—62no—
209C2×C3⋊C8—62no—
210C2×C3⋊C8—61no—
211C2×C3⋊C8—61no—
212C2×C3⋊C8—64no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—61no—
215C2×C3⋊C8—121no—
216ΓL(1,𝔽25)—64no—
217D3×C8—64no—
218C22×C32—21no—
219C22×C32—21no—
220C22×C32#11711yescharacteristic
221C22×C32#12111yescharacteristic
222C22×C32C22⋊Q811yescharacteristic
223C2×C3×D3—22no—
224C2×C3×D3—41no—
225C2×C3×D3—41no—
226C32×C4C2×C22⋊C411yescharacteristic
227C32×C4C2×C4⋊C411yescharacteristic
228C32×C4#12111yescharacteristic
229C32×C4C22⋊Q811yescharacteristic
230C3×Dic3—22no—
231C3×Dic3—81no—
232C3×Dic3—81no—
233C2×#41—31no—
234#131—94no—
235#131—182no—
236C2×M16—31no—
237C2×M16—91no—
238C2×M16—181no—
239C2×M16D3211yescharacteristic
240C22×C8—91no—
241C22×C8—181no—
242C2×C4⋊C4—31no—
243C2×C4⋊C4—31no—
244#108—182no—
245#107—181no—
246#107—181no—
247#103—61no—
248#103—181no—
249#102—61no—
250#102—181no—
251C23×C3—21no—
252C23×C3—61no—
253C23×C3#23511yescharacteristic
254C23×C3#23711yescharacteristic
255C22×D3—21no—
256C3×Q8—32no—
257C3×Q8—61no—
258C3×D4—32no—
259C3×D4—62no—
260C3×D4—62no—
261C3×D4—61no—
262C2×C3×C4—21no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—61no—
269C2×C3×C4—62no—
270C2×C3×C4—62no—
271C2×C3×C4—121no—
272C2×C3×C4—121no—
273C2×C3×C4—241no—
274C2×C3×C4—241no—
275C2×C3×C4C2×Dic611yescharacteristic
276C2×C3×C4C2×C4×D311yescharacteristic
277C2×C3×C4C2×C4×D311yescharacteristic
278C2×C3×C4#23511yescharacteristic
279C2×C3×C4D3×D411yescharacteristic
280C2×C3×C4D3×D411yescharacteristic
281C2×C3×C4D3×D411yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4#23711yescharacteristic
285C2×C3×C4D3×Q811yescharacteristic
286C2×C3×C4C2×#6711yescharacteristic
287#67—22no—
288#67—22no—
289C2×Dic3—21no—
290C2×Dic3—41no—
291C2×Dic3—41no—
292C2×Dic3—81no—
293C2×Dic3—81no—
294D12—21no—
295D12Dic3⋊C412yes—
296C4×D3—22no—
297C4×D3—22no—
298Dic6—21no—
299Dic6Dic3⋊C412yes—
300C3×C8—42no—
301C3×C8—41no—
302C3×C8—41no—
303C3×C8—62no—
304C3⋊C8—22no—
305C3⋊C8—32no—
306C3⋊C8—32no—
307C3⋊C8—32no—
308C3⋊C8—32no—
309C3⋊C8—62no—
310C3⋊C8—62no—
311C3⋊C8—122no—
312C3⋊C8—121no—
313C3⋊C8—121no—
314C2×C32—21no—
315C2×C32—21no—
316C2×C32#38011yescharacteristic
317C2×C32#47211yescharacteristic
318C2×C32#47311yescharacteristic
319C3×D3—42no—
320#41—32no—
321#41—32no—
322#41—61no—
323#41—61no—
324C2×Q8—31no—
325C2×D4—31no—
326C2×D4—61no—
327C22×C4—61no—
328C22×C4—61no—
329C22×C4—61no—
330C22×C4C2×D3211yescharacteristic
331M16—21no—
332M16—21no—
333M16—32no—
334M16—61no—
335M16—184no—
336M16—181no—
337M16—181no—
338C2×C8—21no—
339C2×C8—61no—
340C2×C8—92no—
341C2×C8—91no—
342C2×C8—91no—
343C2×C8—92no—
344C2×C8—184no—
345C2×C8—181no—
346C4⋊C4—61no—
347C4⋊C4—61no—
348C4⋊C4—61no—
349C4⋊C4—61no—
350C22×C3—21no—
351C22×C3—21no—
352C22×C3—21no—
353C22×C3—21no—
354C22×C3—21no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—41no—
358C22×C3—41no—
359C22×C3—62no—
360C22×C3—121no—
361C22×C3—121no—
362C22×C3#87211yescharacteristic
363C22×C3#87711yescharacteristic
364C22×C3#87811yescharacteristic
365C22×C3#88411yescharacteristic
366C22×C3#89611yescharacteristic
367C22×C3#93911yescharacteristic
368C2×D3—22no—
369C2×D3—41no—
370C2×D3—41no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—62no—
376C3×C4—241no—
377C3×C4—241no—
378C3×C4#87811yescharacteristic
379C3×C4D3×C22⋊C411yescharacteristic
380C3×C4D3×C22⋊C411yescharacteristic
381C3×C4#88411yescharacteristic
382C3×C4D3×C4⋊C411yescharacteristic
383C3×C4#89611yescharacteristic
384C3×C4C2×Dic3⋊C411yescharacteristic
385C3×C4#93911yescharacteristic
386Dic3—22no—
387Dic3—81no—
388Dic3—81no—
389C32#181611yescharacteristic, complemented, Sylow
390C23—61no—
391C23#379511yescharacteristic
392Q8—32no—
393Q8—61no—
394D4—32no—
395D4—62no—
396D4—62no—
397D4—61no—
398C2×C4—61no—
399C2×C4—62no—
400C2×C4—62no—
401C2×C4—121no—
402C2×C4—121no—
403C2×C4—241no—
404C2×C4—241no—
405C2×C4D3×Dic611yescharacteristic
406C2×C4C4×D3211yescharacteristic
407C2×C4#380211yescharacteristic
408C2×C4#380411yescharacteristic
409C2×C4D3×#6711yescharacteristic
410C2×C4#381111yescharacteristic
411C8—41no—
412C8—62no—
413C8—92no—
414C8—92no—
415C8—361no—
416C2×C3—21no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—21no—
423C2×C3—41no—
424C2×C3—41no—
425C2×C3—122no—
426C2×C3#466711yescharacteristic
427C2×C3#474911yescharacteristic
428C2×C3#475511yescharacteristic
429C2×C3#494211yescharacteristic
430C2×C3#519911yescharacteristic
431C2×C3#520411yescharacteristic
432D3—42no—
433C22—21no—
434C22—21no—
435C22—62no—
436C22—121no—
437C22—121no—
438C22#6387711yescharacteristic
439C22#6388511yescharacteristic
440C22#6389611yescharacteristic
441C4—62no—
442C4—241no—
443C4—241no—
444C4D3×Dic3⋊C411yescharacteristic
445C4#6389911yescharacteristic
446C4#6392111yescharacteristic
447C4#6397111yescharacteristic
448C3—21no—
449C3#6900111yescharacteristic, complemented
450C3#7030011yescharacteristic, complemented
451C2—21no—
452C2—21no—
453C2—122no—
454C2#1059098111yescharacteristic
455C2#1059098211yescharacteristic
456C2#1059136911yescharacteristic
subgroupG/H
centerC22#63885
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32#121
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1816
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. C2×#63649C2semidirect
4. C2×#63576C2semidirect
6. C3×#4554C2semidirect
7. #10589167C2semidirect
19. #63815C4semidirect
41. #4554D3semidirect
389. C32#1816semidirect
449. C3#69001semidirect
450. C3#70300semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
C2×#636492
C3×#51332
C2×#635762
#105910872
C3×#45542
#105891672
#703003
#690013