Finite Group Databasebeta

← #11785593

Subgroups — #11785593

Order 1152.

593 conjugacy classes of subgroups.

The subgroup lattice has 463 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63815C211yesmaximal, characteristic
2C2×#63635C211yesmaximal, characteristic, complemented
3C3×#4966C211yesmaximal, characteristic
4C2×#63578C211yesmaximal, characteristic, complemented
5#10591088C211yesmaximal, characteristic
6C3×#4530C211yesmaximal, characteristic, complemented
7#10589168C211yesmaximal, characteristic, complemented
8#70299—31nomaximal
9#69000—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C2×C32×C4⋊C4C2211yescharacteristic
12C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
13C22×C3⋊(C3⋊C8)C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17C2×#3711—21no—
18#63815—22no—
19#63815C414yescomplemented
20C2×D3×C3⋊C8—21no—
21#63635—21no—
22#63635—21no—
23C3×#810—21no—
24C3×#809—21no—
25#63578—22no—
26#63566—21no—
27#63563—21no—
28C2×#948—31no—
29C2×#907—31no—
30C3×#417—31no—
31#5232—31no—
32#5133—31no—
33C2×#822—31no—
34C2×#822—31no—
35#4966D311yescharacteristic
36C2×#808—31no—
37C2×#808—31no—
38C2×#808—61no—
39C3×#343—31no—
40#4554—31no—
41#4554—31no—
42#4530D311yescharacteristic, complemented
43C22×C32×C4—21no—
44C22×C32×C4C2311yescharacteristic
45C22×C3⋊Dic3—21no—
46C2×C3×#67—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235C2×C412yes—
50C3×#235Q812yes—
51C2×C3×D12D411yescharacteristic
52C2×C3×C4×D3—21no—
53C2×C3×Dic6D411yescharacteristic
54C32×C4⋊C4—21no—
55C32×C4⋊C4—21no—
56C4⋊(C3⋊Dic3)—21no—
57C4⋊(C3⋊Dic3)—21no—
58C2×C3⋊(C3⋊C8)C2×C412yes—
59C2×C3⋊(C3⋊C8)D411yescharacteristic
60C2×C3⋊(C3⋊C8)D412yes—
61C2×C3⋊(C3⋊C8)D411yescharacteristic
62C3×#208—21no—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208—21no—
66C3×#208—21no—
67C3×#208C2×C412yes—
68C2×C3×C3⋊C8—21no—
69C2×C3×C3⋊C8—21no—
70C2×C3×C3⋊C8—21no—
71#3711—24no—
72D3×C3⋊C8—24no—
73#1815—91noSylow
74C2×C3×#41—31no—
75C2×#235C2×D311yescharacteristic
76C2×C3×M16—31no—
77C2×C3×M16—31no—
78C2×C3×M16—31no—
79C2×C3×C4⋊C4—21no—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C2×D311yescharacteristic
82#948—34no—
83#948—62no—
84C2×C4⋊Dic3—31no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—61no—
87C2×#208—61no—
88C2×#208C2×D311yescharacteristic
89C2×#208C2×D311yescharacteristic
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#821—61no—
106#816—61no—
107#810—21no—
108#809—21no—
109#808—61no—
110#808—61no—
111#808—61no—
112#808—61no—
113#808—62no—
114#808—62no—
115C23×C32#4111yescharacteristic
116C22×C3×D3—21no—
117C2×C32×C4—41no—
118C2×C32×C4—81no—
119C2×C32×C4C22×C411yescharacteristic
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×Q811yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C3⋊Dic3—41no—
126C2×C3⋊Dic3—81no—
127C3×#67—22no—
128C3×#67—22no—
129C2×C3×Dic3—21no—
130C3×D12—21no—
131C3×D12C4⋊C412yes—
132C3×C4×D3—22no—
133C3×C4×D3—22no—
134C3×Dic6—21no—
135C3×Dic6C4⋊C412yes—
136C3⋊(C3⋊C8)C22⋊C412yes—
137C3⋊(C3⋊C8)C22⋊C412yes—
138C3×C3⋊C8—22no—
139C3×C3⋊C8—41no—
140C3×C3⋊C8—41no—
141C2×#131—91no—
142C2×#108—91no—
143C2×#106—91no—
144#417—31no—
145#417—91no—
146#343—31no—
147#343—91no—
148C3×#41—32no—
149C3×#41—32no—
150C3×#41—61no—
151C3×#41—61no—
152C2×C3×Q8—31no—
153C2×C3×D4—31no—
154C2×C3×D4—61no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—41no—
159C22×C3×C4—61no—
160C22×C3×C4C22×D311yescharacteristic
161C22×C3×C4C22×D311yescharacteristic
162C2×#67—21no—
163C22×Dic3—61no—
164C22×Dic3—61no—
165C22×Dic3—121no—
166#235—21no—
167#235—21no—
168#235Dic612yes—
169#235C4×D312yes—
170C2×D12#6711yescharacteristic
171C2×C4×D3—21no—
172C2×Dic6#6711yescharacteristic
173C3×M16—32no—
174C3×M16—61no—
175C3×M16—61no—
176C3×M16—61no—
177C3×M16—61no—
178C3×M16—61no—
179C2×C3×C8—61no—
180C2×C3×C8—61no—
181C2×C3×C8—61no—
182C3×C4⋊C4—22no—
183C3×C4⋊C4—21no—
184C3×C4⋊C4—21no—
185C3×C4⋊C4—21no—
186C3×C4⋊C4—21no—
187C3×C4⋊C4—41no—
188C4⋊Dic3—62no—
189C4⋊Dic3—61no—
190C4⋊Dic3—61no—
191C4⋊Dic3—61no—
192C4⋊Dic3—61no—
193C4⋊Dic3—121no—
194#208—21no—
195#208—21no—
196#208—21no—
197#208—21no—
198#208—21no—
199#208—64no—
200#208C4×D312yes—
201C2×C3⋊C8—21no—
202C2×C3⋊C8—21no—
203C2×C3⋊C8—21no—
204C2×C3⋊C8—32no—
205C2×C3⋊C8—32no—
206C2×C3⋊C8—31no—
207C2×C3⋊C8—31no—
208C2×C3⋊C8—31no—
209C2×C3⋊C8—31no—
210C2×C3⋊C8—32no—
211C2×C3⋊C8—32no—
212C2×C3⋊C8—61no—
213C2×C3⋊C8—61no—
214C2×C3⋊C8—62no—
215C2×C3⋊C8—62no—
216C2×C3⋊C8—64no—
217ΓL(1,𝔽25)—64no—
218D3×C8—64no—
219C22×C32—21no—
220C22×C32—21no—
221C22×C32#11711yescharacteristic
222C22×C32#12111yescharacteristic
223C22×C32C22⋊Q811yescharacteristic
224C2×C3×D3—22no—
225C2×C3×D3—41no—
226C2×C3×D3—41no—
227C32×C4—81no—
228C32×C4C2×C22⋊C411yescharacteristic
229C32×C4C2×C4⋊C411yescharacteristic
230C32×C4#12111yescharacteristic
231C32×C4C22⋊Q811yescharacteristic
232C3⋊Dic3—81no—
233C3×Dic3—22no—
234C2×#41—31no—
235#131—94no—
236#131—182no—
237C2×M16—31no—
238C2×M16—31no—
239C2×M16—31no—
240C2×M16—181no—
241C22×C8—91no—
242C22×C8—181no—
243C2×C4⋊C4—91no—
244C2×C4⋊C4D3211yescharacteristic
245#108—182no—
246#106—181no—
247#106—181no—
248#103—61no—
249#103—181no—
250#102—61no—
251#102—181no—
252C23×C3—21no—
253C23×C3—61no—
254C23×C3#23511yescharacteristic
255C23×C3#23711yescharacteristic
256C22×D3—21no—
257C3×Q8—32no—
258C3×Q8—61no—
259C3×D4—32no—
260C3×D4—62no—
261C3×D4—62no—
262C3×D4—61no—
263C2×C3×C4—21no—
264C2×C3×C4—21no—
265C2×C3×C4—21no—
266C2×C3×C4—21no—
267C2×C3×C4—21no—
268C2×C3×C4—21no—
269C2×C3×C4—42no—
270C2×C3×C4—41no—
271C2×C3×C4—41no—
272C2×C3×C4—61no—
273C2×C3×C4—62no—
274C2×C3×C4—62no—
275C2×C3×C4—82no—
276C2×C3×C4—81no—
277C2×C3×C4—81no—
278C2×C3×C4C2×Dic611yescharacteristic
279C2×C3×C4C2×C4×D311yescharacteristic
280C2×C3×C4C2×C4×D311yescharacteristic
281C2×C3×C4#23511yescharacteristic
282C2×C3×C4D3×D411yescharacteristic
283C2×C3×C4D3×D411yescharacteristic
284C2×C3×C4D3×D411yescharacteristic
285C2×C3×C4D3×D411yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4#23711yescharacteristic
288C2×C3×C4D3×Q811yescharacteristic
289C2×C3×C4C2×#6711yescharacteristic
290#67—22no—
291#67—22no—
292C2×Dic3—21no—
293C2×Dic3—122no—
294C2×Dic3—121no—
295C2×Dic3—121no—
296C2×Dic3—242no—
297C2×Dic3—241no—
298C2×Dic3—241no—
299D12—21no—
300D12Dic3⋊C412yes—
301C4×D3—22no—
302C4×D3—22no—
303Dic6—21no—
304Dic6Dic3⋊C412yes—
305C3×C8—62no—
306C3×C8—121no—
307C3×C8—121no—
308C3⋊C8—22no—
309C3⋊C8—32no—
310C3⋊C8—32no—
311C3⋊C8—32no—
312C3⋊C8—32no—
313C3⋊C8—41no—
314C3⋊C8—41no—
315C3⋊C8—62no—
316C3⋊C8—62no—
317C2×C32—21no—
318C2×C32—21no—
319C2×C32#38011yescharacteristic
320C2×C32#47111yescharacteristic
321C2×C32#47111yescharacteristic
322C3×D3—42no—
323#41—32no—
324#41—32no—
325#41—61no—
326#41—61no—
327C2×Q8—31no—
328C2×D4—31no—
329C2×D4—61no—
330C22×C4—21no—
331C22×C4—61no—
332C22×C4—181no—
333C22×C4C2×D3211yescharacteristic
334M16—32no—
335M16—61no—
336M16—61no—
337M16—61no—
338M16—61no—
339M16—61no—
340M16—184no—
341C2×C8—61no—
342C2×C8—61no—
343C2×C8—61no—
344C2×C8—92no—
345C2×C8—92no—
346C2×C8—91no—
347C2×C8—91no—
348C2×C8—184no—
349C4⋊C4—21no—
350C4⋊C4—21no—
351C4⋊C4—181no—
352C4⋊C4—181no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—21no—
359C22×C3—21no—
360C22×C3—21no—
361C22×C3—21no—
362C22×C3—62no—
363C22×C3—121no—
364C22×C3—121no—
365C22×C3#87211yescharacteristic
366C22×C3#87711yescharacteristic
367C22×C3#87811yescharacteristic
368C22×C3#88411yescharacteristic
369C22×C3#89611yescharacteristic
370C22×C3#93911yescharacteristic
371C2×D3—22no—
372C2×D3—41no—
373C2×D3—41no—
374C3×C4—21no—
375C3×C4—21no—
376C3×C4—21no—
377C3×C4—21no—
378C3×C4—62no—
379C3×C4—82no—
380C3×C4—81no—
381C3×C4—81no—
382C3×C4#87811yescharacteristic
383C3×C4D3×C22⋊C411yescharacteristic
384C3×C4D3×C22⋊C411yescharacteristic
385C3×C4#88411yescharacteristic
386C3×C4D3×C4⋊C411yescharacteristic
387C3×C4#89611yescharacteristic
388C3×C4C2×Dic3⋊C411yescharacteristic
389C3×C4#93911yescharacteristic
390Dic3—22no—
391Dic3—242no—
392Dic3—241no—
393Dic3—241no—
394C32#181511yescharacteristic, complemented, Sylow
395C23—61no—
396C23#380411yescharacteristic
397Q8—32no—
398Q8—61no—
399D4—32no—
400D4—62no—
401D4—62no—
402D4—61no—
403C2×C4—41no—
404C2×C4—61no—
405C2×C4—62no—
406C2×C4—62no—
407C2×C4—81no—
408C2×C4—361no—
409C2×C4—721no—
410C2×C4D3×Dic611yescharacteristic
411C2×C4#379511yescharacteristic
412C2×C4C4×D3211yescharacteristic
413C2×C4#380211yescharacteristic
414C2×C4D3×#6711yescharacteristic
415C2×C4#381111yescharacteristic
416C8—62no—
417C8—92no—
418C8—92no—
419C8—121no—
420C8—121no—
421C2×C3—22no—
422C2×C3—22no—
423C2×C3—21no—
424C2×C3—21no—
425C2×C3—21no—
426C2×C3—21no—
427C2×C3—21no—
428C2×C3—21no—
429C2×C3—21no—
430C2×C3—122no—
431C2×C3#466711yescharacteristic
432C2×C3#474811yescharacteristic
433C2×C3#475411yescharacteristic
434C2×C3#494211yescharacteristic
435C2×C3#520011yescharacteristic
436C2×C3#520311yescharacteristic
437D3—42no—
438C22—21no—
439C22—21no—
440C22—62no—
441C22—121no—
442C22—121no—
443C22#6387711yescharacteristic
444C22#6389911yescharacteristic
445C22#6397111yescharacteristic
446C4—62no—
447C4—81no—
448C4—721no—
449C4D3×Dic3⋊C411yescharacteristic
450C4#6388511yescharacteristic
451C4#6389611yescharacteristic
452C4#6392111yescharacteristic
453C3—21no—
454C3#6900011yescharacteristic, complemented
455C3#7029911yescharacteristic, complemented
456C2—21no—
457C2—21no—
458C2—122no—
459C2#1059136911yescharacteristic
460C2#1059150711yescharacteristic
461C2#1059164311yescharacteristic
subgroupG/H
centerC22#63971
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×C4⋊C4C22
socleC22×C32#121
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×C4⋊C4D32
hypocenterC32#1815
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63635C2semidirect
4. C2×#63578C2semidirect
6. C3×#4530C2semidirect
7. #10589168C2semidirect
19. #63815C4semidirect
42. #4530D3semidirect
394. C32#1815semidirect
454. C3#69000semidirect
455. C3#70299semidirect

Maximal subgroups

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

subgroupindex
C2×#638152
C2×#636352
C3×#49662
C2×#635782
#105910882
C3×#45302
#105891682
#702993
#690003