Finite Group Databasebeta

← #11784101

Subgroups — #11784101

Order 1152.

685 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63817C211yesmaximal, characteristic
2C2×#63652C211yesmaximal, characteristic
3C3×#5122C211yesmaximal, characteristic, complemented
4#10591105C211yesmaximal, characteristic
5C2×#63553C211yesmaximal, characteristic, complemented
6C3×#4558C211yesmaximal, characteristic, complemented
7#10589160C211yesmaximal, characteristic, complemented
8#69887—31nomaximal
9#68926—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×C4×C3⋊Dic3C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C22×C3×C3⋊C8C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3712—21no—
18#63817—22no—
19#63817C414yescomplemented
20C2×#3710—21no—
21#63652C414yescomplemented
22C3×#815—21no—
23C3×C8×Dic3—21no—
24#63567C412yescomplemented
25#63564C412yescomplemented
26#63553—22no—
27C2×#907—31no—
28C2×#901—31no—
29C3×#405—31no—
30C2×#825—31no—
31C2×#825—31no—
32C2×#825—61no—
33#5122D311yescharacteristic, complemented
34#5113—31no—
35C2×C8×Dic3—31no—
36C2×C8×Dic3—31no—
37#5002—31no—
38C3×#341—31no—
39#4558D311yescharacteristic, complemented
40#4555—31no—
41#4532—31no—
42C22×C32×C4C2311yescharacteristic
43C2×#638—21no—
44C22×C3⋊Dic3—21no—
45#3828—21no—
46#3828—21no—
47#3828C2×C412yes—
48#3828C2×C412yes—
49C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
50C2×C4×C3⋊D3—21no—
51C2×#634C2×C411yescharacteristic
52C32×M16—21no—
53C32×M16C2×C412yes—
54C2×C32×C8—21no—
55C4×C3⋊Dic3—21no—
56C4×C3⋊Dic3C2×C412yes—
57C3×#217—21no—
58C3×C4⋊Dic3C2×C412yes—
59C3×C4×Dic3—21no—
60C3×#208—21no—
61C3×#208C2×C412yes—
62C2×C3×C3⋊C8—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8C2×C412yes—
66C2×C3×C3⋊C8C2×C412yes—
67C2×C3×C3⋊C8D412yes—
68C2×C3×C3⋊C8D411yescharacteristic
69C2×C3×C3⋊C8D411yescharacteristic
70#3712—24no—
71#3710—24no—
72#1764—91noSylow
73C2×#235—31no—
74C2×#235—31no—
75C2×#235—61no—
76C2×C3×M16—21no—
77C2×C3×M16—31no—
78C2×C3×M16C2×D311yescharacteristic
79C2×C3×M16C2×D311yescharacteristic
80C22×C3×C8—31no—
81C22×C3×C8—31no—
82C3×#117—31no—
83#926C2×D311yescharacteristic
84C2×C4×Dic3—31no—
85C2×C4×Dic3—31no—
86C2×C4×Dic3—61no—
87C2×#208C2×D311yescharacteristic
88C22×C3⋊C8C2×D311yescharacteristic
89C22×C3⋊C8C2×D311yescharacteristic
90#907—34no—
91#907—62no—
92#901—34no—
93#901—62no—
94C2×ΓL(1,𝔽25)—61no—
95C2×ΓL(1,𝔽25)—61no—
96C2×D3×C8—61no—
97C2×D3×C8—61no—
98C3×#97—61no—
99C3×C4×C8—61no—
100#825—34no—
101#825—34no—
102#825—64no—
103#821—32no—
104#816—32no—
105#815—21no—
106C8×Dic3—21no—
107C8×Dic3—62no—
108C8×Dic3—62no—
109#810—32no—
110#809—32no—
111C23×C32#4111yescharacteristic
112C22×C3⋊D3—21no—
113C2×C32×C4C22×C411yescharacteristic
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C22×C411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119#638—22no—
120#638—22no—
121C2×C3⋊Dic3—24no—
122C2×C3⋊Dic3—22no—
123C2×C3⋊Dic3—21no—
124C4⋊(C3⋊D3)—21no—
125C4⋊(C3⋊D3)C4212yes—
126C4×C3⋊D3—22no—
127C4×C3⋊D3—22no—
128#634—21no—
129#634C4212yes—
130C2×C3×Dic3—22no—
131C32×C8—22no—
132C3×C3⋊C8—22no—
133C3×C3⋊C8—22no—
134C3×C3⋊C8C22⋊C412yes—
135C3×C3⋊C8C22⋊C412yes—
136C2×#131—91no—
137C2×#104—91no—
138#416—91no—
139#405—31no—
140C2×C4×C8—91no—
141#341—31no—
142#339—91no—
143C22×C3×C4—21no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C2×#67—61no—
147C2×#67—61no—
148C2×#67—121no—
149C22×Dic3—61no—
150C22×Dic3—61no—
151C22×Dic3—121no—
152#235—32no—
153#235—32no—
154#235—32no—
155#235—32no—
156#235—62no—
157#235—62no—
158#235—61no—
159#235—61no—
160#235—61no—
161#235—61no—
162#235—121no—
163#235—121no—
164C2×D12—31no—
165C2×D12—31no—
166C2×D12—61no—
167C2×C4×D3—61no—
168C2×C4×D3—61no—
169C2×C4×D3—121no—
170C2×Dic6—31no—
171C2×Dic6—31no—
172C2×Dic6—61no—
173C3×M16—21no—
174C3×M16—21no—
175C3×M16—22no—
176C3×M16—32no—
177C3×M16—41no—
178C3×M16—61no—
179C3×M16C4×D312yes—
180C3×M16C4×D312yes—
181C2×C3×C8—21no—
182C2×C3×C8—21no—
183C2×C3×C8—32no—
184C2×C3×C8—32no—
185C2×C3×C8—31no—
186C2×C3×C8—31no—
187C2×C3×C8—32no—
188C2×C3×C8—41no—
189C2×C3×C8—61no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192C3×C4⋊C4—32no—
193C3×C22⋊C4—61no—
194C3×C42—61no—
195#217—21no—
196C4⋊Dic3C4×D312yes—
197C4×Dic3—21no—
198C4×Dic3—32no—
199C4×Dic3—32no—
200C4×Dic3—62no—
201C4×Dic3—61no—
202C4×Dic3—61no—
203C4×Dic3—121no—
204#208—21no—
205#208C4×D312yes—
206C2×C3⋊C8—21no—
207C2×C3⋊C8—21no—
208C2×C3⋊C8—21no—
209C2×C3⋊C8C4×D312yes—
210C2×C3⋊C8C4×D312yes—
211C2×C3⋊C8D1212yes—
212C2×C3⋊C8#6711yescharacteristic
213C2×C3⋊C8#6711yescharacteristic
214ΓL(1,𝔽25)—64no—
215ΓL(1,𝔽25)—64no—
216D3×C8—64no—
217D3×C8—64no—
218C22×C32—22no—
219C22×C32#11711yescharacteristic
220C22×C32C4×D411yescharacteristic
221C22×C32C4×D411yescharacteristic
222C2×C3⋊D3—22no—
223C2×C3⋊D3—42no—
224C32×C4C2×C4211yescharacteristic
225C32×C4C2×C22⋊C411yescharacteristic
226C32×C4C4×D411yescharacteristic
227C32×C4C4×D411yescharacteristic
228C3⋊Dic3—24no—
229C3⋊Dic3—22no—
230C3×Dic3—42no—
231C2×#41—91no—
232#131—94no—
233#131—182no—
234C2×M16—31no—
235C2×M16—181no—
236C2×M16D3211yescharacteristic
237C22×C8—31no—
238C22×C8—31no—
239C22×C8—181no—
240#117—31no—
241C2×C42—91no—
242#104—94no—
243#103—92no—
244#102—92no—
245#97—61no—
246C4×C8—61no—
247C4×C8—182no—
248C23×C3—21no—
249C23×C3#23511yescharacteristic
250C23×C3#23911yescharacteristic
251C22×D3—61no—
252C22×D3—61no—
253C22×D3—121no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4—21no—
259C2×C3×C4—21no—
260C2×C3×C4—62no—
261C2×C3×C4C2×C4×D311yescharacteristic
262C2×C3×C4C2×C4×D311yescharacteristic
263C2×C3×C4C2×C4×D311yescharacteristic
264C2×C3×C4C2×C4×D311yescharacteristic
265C2×C3×C4C2×C4×D311yescharacteristic
266C2×C3×C4C2×C4×D311yescharacteristic
267C2×C3×C4C2×D1211yescharacteristic
268C2×C3×C4#23511yescharacteristic
269C2×C3×C4D3×D411yescharacteristic
270C2×C3×C4D3×D411yescharacteristic
271C2×C3×C4#23711yescharacteristic
272C2×C3×C4C2×#6711yescharacteristic
273#67—62no—
274#67—62no—
275#67—62no—
276#67—62no—
277#67—122no—
278#67—122no—
279C2×Dic3—22no—
280C2×Dic3—64no—
281C2×Dic3—64no—
282C2×Dic3—62no—
283C2×Dic3—62no—
284C2×Dic3—61no—
285C2×Dic3—61no—
286C2×Dic3—122no—
287C2×Dic3—121no—
288C2×Dic3—124no—
289D12—32no—
290D12—32no—
291D12—62no—
292D12—61no—
293D12—61no—
294D12—121no—
295C4×D3—62no—
296C4×D3—62no—
297C4×D3—62no—
298C4×D3—62no—
299C4×D3—122no—
300C4×D3—122no—
301Dic6—32no—
302Dic6—32no—
303Dic6—62no—
304Dic6—61no—
305Dic6—61no—
306Dic6—121no—
307C3×C8—22no—
308C3×C8—22no—
309C3×C8—32no—
310C3×C8—32no—
311C3×C8—42no—
312C3×C8—62no—
313C3×C8—62no—
314C3⋊C8—22no—
315C3⋊C8—22no—
316C3⋊C8(C2×D3)⋊C412yes—
317C3⋊C8(C2×D3)⋊C412yes—
318C2×C32—21no—
319C2×C32—21no—
320C2×C32C4×C22⋊C411yescharacteristic
321C2×C32#44312yes—
322C3⋊D3—42no—
323#41—92no—
324#41—92no—
325#41—181no—
326#41—181no—
327C2×Q8—91no—
328C2×D4—91no—
329C2×D4—181no—
330C22×C4—181no—
331C22×C4—181no—
332C22×C4C2×D3211yescharacteristic
333M16—21no—
334M16—32no—
335M16—61no—
336M16—184no—
337M16#62412yes—
338C2×C8—21no—
339C2×C8—32no—
340C2×C8—32no—
341C2×C8—31no—
342C2×C8—31no—
343C2×C8—32no—
344C2×C8—61no—
345C2×C8—61no—
346C2×C8—61no—
347C2×C8—184no—
348C4⋊C4—32no—
349C22⋊C4—61no—
350C42—61no—
351C42—92no—
352C42—181no—
353C22×C3—22no—
354C22×C3—22no—
355C22×C3—21no—
356C22×C3—21no—
357C22×C3—21no—
358C22×C3—42no—
359C22×C3#87211yescharacteristic
360C22×C3C4×D1211yescharacteristic
361C22×C3#89211yescharacteristic
362C22×C3#89311yescharacteristic
363C22×C3#89311yescharacteristic
364C22×C3C4×#6711yescharacteristic
365C2×D3—62no—
366C2×D3—62no—
367C2×D3—122no—
368C2×D3—122no—
369C2×D3—122no—
370C2×D3—242no—
371C3×C4—21no—
372C3×C4—21no—
373C3×C4—21no—
374C3×C4—21no—
375C3×C4—122no—
376C3×C4C42×D311yescharacteristic
377C3×C4C42×D311yescharacteristic
378C3×C4C4×D1211yescharacteristic
379C3×C4D3×C22⋊C411yescharacteristic
380C3×C4#67⋊C411yescharacteristic
381C3×C4#67⋊C411yescharacteristic
382C3×C4C2×(C2×D3)⋊C411yescharacteristic
383C3×C4C4×#6711yescharacteristic
384Dic3—42no—
385Dic3—64no—
386Dic3—64no—
387Dic3—62no—
388Dic3—62no—
389Dic3—122no—
390Dic3—124no—
391C32#176411yescharacteristic, complemented, Sylow
392C23—181no—
393C23#379911yescharacteristic
394Q8—92no—
395Q8—181no—
396D4—92no—
397D4—182no—
398D4—182no—
399D4—181no—
400C2×C4—62no—
401C2×C4—184no—
402C2×C4—182no—
403C2×C4—181no—
404C2×C4—182no—
405C2×C4—182no—
406C2×C4C4×D3211yescharacteristic
407C2×C4C4×D3211yescharacteristic
408C2×C4D3×D1211yescharacteristic
409C2×C4#380411yescharacteristic
410C2×C4C2×#62411yescharacteristic
411C2×C4D3×#6711yescharacteristic
412C8—22no—
413C8—32no—
414C8—32no—
415C8—62no—
416C8—62no—
417C2×C3—21no—
418C2×C3—21no—
419C2×C3—21no—
420C2×C3—21no—
421C2×C3—21no—
422C2×C3—22no—
423C2×C3—41no—
424C2×C3—41no—
425C2×C3#466611yescharacteristic
426C2×C3#489512yes—
427C2×C3C4×(C2×D3)⋊C411yescharacteristic
428C2×C3#514412yes—
429D3—122no—
430D3—122no—
431D3—242no—
432C22—22no—
433C22—182no—
434C22—362no—
435C22#6383611yescharacteristic
436C22#6389411yescharacteristic
437C22#6390411yescharacteristic
438C4—122no—
439C4—184no—
440C4—182no—
441C4#6388011yescharacteristic
442C4C4×#62411yescharacteristic
443C4D3×(C2×D3)⋊C411yescharacteristic
444C4#6395211yescharacteristic
445C3—21no—
446C3#6892611yescharacteristic, complemented
447C3#6988711yescharacteristic, complemented
448C2—21no—
449C2—21no—
450C2—362no—
451C2#1059099512yes—
452C2#1059123311yescharacteristic
subgroupG/H
centerC2×C4D3×#67
commutatorC32×C4C2×C42
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC22×C32C4×D4
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1764
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C3×#5122C2semidirect
5. C2×#63553C2semidirect
6. C3×#4558C2semidirect
7. #10589160C2semidirect
19. #63817C4semidirect
21. #63652C4semidirect
24. #63567C4semidirect
25. #63564C4semidirect
33. #5122D3semidirect
39. #4558D3semidirect
391. C32#1764semidirect
446. C3#68926semidirect
447. C3#69887semidirect

Maximal subgroups

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

subgroupindex
C2×#638172
C2×#636522
C3×#51222
#105911052
C2×#635532
C3×#45582
#105891602
#698873
#689263