Finite Group Databasebeta

← #11785558

Subgroups — #11785558

Order 1152.

589 conjugacy classes of subgroups.

The subgroup lattice has 481 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63817C211yesmaximal, characteristic
2#10592838C211yesmaximal, characteristic
3C2×C3×#822C211yesmaximal, characteristic, complemented
4#10591122C211yesmaximal, characteristic, complemented
5#10591113C211yesmaximal, characteristic
6C3×#4556C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#70719—31nomaximal
9#69032—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12#64135C2211yescharacteristic
13C3×#926C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3712—21no—
18#63817—21no—
19#63817—21no—
20#63817C412yescomplemented
21#63817C412yescomplemented
22C2×#3710—21no—
23#63652—22no—
24C3×#822—21no—
25C3×#822—21no—
26#63575—21no—
27#63573—21no—
28#63570—22no—
29C2×#907—31no—
30C2×#901—31no—
31C2×C3×#108—31no—
32#5139—31no—
33#5139—31no—
34#5139—31no—
35#5139—61no—
36C2×#822D311yescharacteristic, complemented
37#5106—31no—
38#5005—31no—
39#4998—31no—
40C3×#344—31no—
41#4559—31no—
42#4556—31no—
43#4556D311yescharacteristic, complemented
44C22×C32×C4C2311yescharacteristic
45C2×#638—21no—
46#3828—21no—
47#3828—21no—
48#3828C2×C412yes—
49#3828D412yes—
50C2×C4⋊(C3⋊D3)Q811yescharacteristic
51C2×C4×C3⋊D3—21no—
52C2×#634Q811yescharacteristic
53C32×M16—21no—
54C32×M16—21no—
55C2×C32×C8—21no—
56#3757—21no—
57C4⋊(C3⋊Dic3)—21no—
58C4×C3⋊Dic3—21no—
59C3×#217—21no—
60C3×C4⋊Dic3—21no—
61C3×C4×Dic3—21no—
62C3×#208—21no—
63C3×#208—21no—
64C3×#208—21no—
65C3×#208C2×C412yes—
66C2×C3×C3⋊C8—21no—
67C2×C3×C3⋊C8—21no—
68C2×C3×C3⋊C8C2×C411yescharacteristic
69C2×C3×C3⋊C8C2×C411yescharacteristic
70C2×C3×C3⋊C8D411yescharacteristic
71C2×C3×C3⋊C8D411yescharacteristic
72C2×C3×C3⋊C8D411yescharacteristic
73C2×C3×C3⋊C8D411yescharacteristic
74#3712—22no—
75#3712—22no—
76#3710—22no—
77#3710—22no—
78#1814—91noSylow
79C2×#235—31no—
80C2×#235—31no—
81C2×#235—61no—
82C2×C3×M16—21no—
83C2×C3×M16—31no—
84C2×C3×M16—31no—
85C2×C3×M16C2×D311yescharacteristic
86C2×C3×M16C2×D311yescharacteristic
87C22×C3×C8—31no—
88C3×#117—31no—
89#926—31no—
90#926—31no—
91#926—61no—
92#926C2×D311yescharacteristic
93C2×#208C2×D311yescharacteristic
94C2×#208C2×D311yescharacteristic
95C22×C3⋊C8C2×D311yescharacteristic
96#907—32no—
97#907—32no—
98#907—61no—
99#907—61no—
100#901—32no—
101#901—32no—
102#901—61no—
103#901—61no—
104C2×ΓL(1,𝔽25)—61no—
105C2×ΓL(1,𝔽25)—61no—
106C2×D3×C8—61no—
107C2×D3×C8—61no—
108C3×#108—61no—
109C3×#108—61no—
110#825—62no—
111#825—62no—
112#825—62no—
113#825—64no—
114#822—21no—
115#822—21no—
116#818—61no—
117#817—61no—
118#808—61no—
119#807—61no—
120#805—62no—
121C23×C32#4111yescharacteristic
122C22×C3⋊D3—21no—
123C2×C32×C4C22×C411yescharacteristic
124C2×C32×C4C2×D411yescharacteristic
125C2×C32×C4C2×D411yescharacteristic
126C2×C32×C4C2×D411yescharacteristic
127C2×C32×C4C2×Q811yescharacteristic
128C2×C32×C4#4111yescharacteristic
129#638—22no—
130#638—22no—
131C2×C3⋊Dic3—21no—
132C2×C3⋊Dic3—41no—
133C4⋊(C3⋊D3)—21no—
134C4⋊(C3⋊D3)C4⋊C412yes—
135C4×C3⋊D3—22no—
136C4×C3⋊D3—22no—
137#634—21no—
138#634C4⋊C412yes—
139C2×C3×Dic3—41no—
140C32×C8—41no—
141C3×C3⋊C8—22no—
142C3×C3⋊C8—41no—
143C3×C3⋊C8C22⋊C411yescharacteristic
144C3×C3⋊C8C22⋊C411yescharacteristic
145C3×C3⋊C8C22⋊C411yescharacteristic
146C3×C3⋊C8C22⋊C411yescharacteristic
147C2×#131—91no—
148C2×#108—31no—
149#427—91no—
150#421—91no—
151#421—91no—
152#344—31no—
153#344—91no—
154C22×C3×C4—21no—
155C22×C3×C4C22×D311yescharacteristic
156C22×C3×C4C22×D311yescharacteristic
157C2×#67—61no—
158C2×#67—61no—
159C2×#67—121no—
160#235—32no—
161#235—32no—
162#235—32no—
163#235—32no—
164#235—62no—
165#235—62no—
166#235—61no—
167#235—61no—
168#235—61no—
169#235—61no—
170#235—121no—
171#235—121no—
172C2×D12—31no—
173C2×D12—31no—
174C2×D12—61no—
175C2×C4×D3—61no—
176C2×C4×D3—61no—
177C2×C4×D3—121no—
178C2×Dic6—31no—
179C2×Dic6—31no—
180C2×Dic6—61no—
181C3×M16—22no—
182C3×M16—21no—
183C3×M16—21no—
184C3×M16—21no—
185C3×M16—21no—
186C3×M16—32no—
187C3×M16—41no—
188C3×M16—61no—
189C3×M16—61no—
190C3×M16—61no—
191C2×C3×C8—21no—
192C2×C3×C8—21no—
193C2×C3×C8—31no—
194C2×C3×C8—31no—
195C2×C3×C8—31no—
196C2×C3×C8—31no—
197C2×C3×C8—31no—
198C2×C3×C8—31no—
199C2×C3×C8—41no—
200C2×C3×C8—61no—
201C2×C3×C8—61no—
202C3×C4⋊C4—61no—
203C3×C22⋊C4—61no—
204C3×C42—61no—
205#217—21no—
206#217—61no—
207#217—61no—
208#217—121no—
209C4⋊Dic3—21no—
210C4⋊Dic3—61no—
211C4⋊Dic3—61no—
212C4⋊Dic3—121no—
213C4×Dic3—21no—
214C4×Dic3—62no—
215C4×Dic3—61no—
216C4×Dic3—61no—
217#208—21no—
218#208—21no—
219#208—21no—
220#208C4×D312yes—
221C2×C3⋊C8—21no—
222C2×C3⋊C8—21no—
223C2×C3⋊C8C4×D311yescharacteristic
224C2×C3⋊C8C4×D311yescharacteristic
225C2×C3⋊C8D1211yescharacteristic
226C2×C3⋊C8D1211yescharacteristic
227C2×C3⋊C8#6711yescharacteristic
228C2×C3⋊C8#6711yescharacteristic
229ΓL(1,𝔽25)—62no—
230ΓL(1,𝔽25)—62no—
231ΓL(1,𝔽25)—62no—
232ΓL(1,𝔽25)—62no—
233D3×C8—62no—
234D3×C8—62no—
235D3×C8—62no—
236D3×C8—62no—
237C22×C32—41no—
238C22×C32#11711yescharacteristic
239C22×C32#12111yescharacteristic
240C22×C32C22⋊Q811yescharacteristic
241C2×C3⋊D3—22no—
242C2×C3⋊D3—42no—
243C32×C4C2×C22⋊C411yescharacteristic
244C32×C4C2×C4⋊C411yescharacteristic
245C32×C4#12111yescharacteristic
246C32×C4C22⋊Q811yescharacteristic
247C3⋊Dic3—22no—
248C3⋊Dic3—81no—
249C3×Dic3—81no—
250C2×#41—91no—
251#131—92no—
252#131—92no—
253#131—181no—
254#131—181no—
255C2×M16—31no—
256C2×M16—31no—
257C2×M16—181no—
258C2×M16D3211yescharacteristic
259C22×C8—31no—
260C22×C8—181no—
261#117—31no—
262#117—91no—
263#108—61no—
264#108—61no—
265#107—181no—
266#106—181no—
267#104—182no—
268#104—182no—
269C23×C3—21no—
270C23×C3#23511yescharacteristic
271C23×C3#23911yescharacteristic
272C22×D3—61no—
273C22×D3—61no—
274C22×D3—121no—
275C2×C3×C4—21no—
276C2×C3×C4—21no—
277C2×C3×C4—21no—
278C2×C3×C4—21no—
279C2×C3×C4—21no—
280C2×C3×C4—21no—
281C2×C3×C4—121no—
282C2×C3×C4C2×C4×D311yescharacteristic
283C2×C3×C4C2×C4×D311yescharacteristic
284C2×C3×C4C2×D1211yescharacteristic
285C2×C3×C4#23511yescharacteristic
286C2×C3×C4D3×D411yescharacteristic
287C2×C3×C4D3×D411yescharacteristic
288C2×C3×C4D3×D411yescharacteristic
289C2×C3×C4D3×D411yescharacteristic
290C2×C3×C4#23711yescharacteristic
291C2×C3×C4D3×Q811yescharacteristic
292C2×C3×C4D3×Q811yescharacteristic
293C2×C3×C4C2×#6711yescharacteristic
294#67—62no—
295#67—62no—
296#67—62no—
297#67—62no—
298#67—122no—
299#67—122no—
300C2×Dic3—41no—
301C2×Dic3—61no—
302C2×Dic3—61no—
303C2×Dic3—121no—
304C2×Dic3—122no—
305C2×Dic3—121no—
306C2×Dic3—121no—
307D12—32no—
308D12—32no—
309D12—62no—
310D12—61no—
311D12—61no—
312D12—121no—
313C4×D3—62no—
314C4×D3—62no—
315C4×D3—62no—
316C4×D3—62no—
317C4×D3—122no—
318C4×D3—122no—
319Dic6—32no—
320Dic6—32no—
321Dic6—62no—
322Dic6—61no—
323Dic6—61no—
324Dic6—121no—
325C3×C8—31no—
326C3×C8—31no—
327C3×C8—31no—
328C3×C8—31no—
329C3×C8—42no—
330C3×C8—41no—
331C3×C8—41no—
332C3×C8—62no—
333C3×C8—121no—
334C3⋊C8—22no—
335C3⋊C8—41no—
336C3⋊C8(C2×D3)⋊C411yescharacteristic
337C3⋊C8(C2×D3)⋊C411yescharacteristic
338C3⋊C8(C2×D3)⋊C411yescharacteristic
339C3⋊C8(C2×D3)⋊C411yescharacteristic
340C2×C32—21no—
341C2×C32—21no—
342C2×C32—21no—
343C2×C32#38011yescharacteristic
344C3⋊D3—42no—
345#41—92no—
346#41—92no—
347#41—181no—
348#41—181no—
349C2×Q8—91no—
350C2×D4—91no—
351C2×D4—181no—
352C22×C4—181no—
353C22×C4C2×D3211yescharacteristic
354M16—21no—
355M16—21no—
356M16—32no—
357M16—61no—
358M16—61no—
359M16—61no—
360M16—182no—
361M16—182no—
362C2×C8—21no—
363C2×C8—31no—
364C2×C8—31no—
365C2×C8—31no—
366C2×C8—31no—
367C2×C8—31no—
368C2×C8—31no—
369C2×C8—61no—
370C2×C8—61no—
371C2×C8—182no—
372C2×C8—182no—
373C4⋊C4—61no—
374C4⋊C4—181no—
375C22⋊C4—61no—
376C22⋊C4—181no—
377C42—61no—
378C42—181no—
379C22×C3—21no—
380C22×C3—21no—
381C22×C3—21no—
382C22×C3—41no—
383C22×C3—41no—
384C22×C3—81no—
385C22×C3#87211yescharacteristic
386C22×C3#88411yescharacteristic
387C22×C3#89211yescharacteristic
388C22×C3#89511yescharacteristic
389C22×C3#89611yescharacteristic
390C22×C3#94611yescharacteristic
391C2×D3—62no—
392C2×D3—62no—
393C2×D3—122no—
394C2×D3—122no—
395C2×D3—122no—
396C2×D3—242no—
397C3×C4—21no—
398C3×C4—21no—
399C3×C4—21no—
400C3×C4—21no—
401C3×C4—241no—
402C3×C4D3×C22⋊C411yescharacteristic
403C3×C4#88411yescharacteristic
404C3×C4D3×C4⋊C411yescharacteristic
405C3×C4D3×C4⋊C411yescharacteristic
406C3×C4#89611yescharacteristic
407C3×C4#89711yescharacteristic
408C3×C4C2×(C2×D3)⋊C411yescharacteristic
409C3×C4#93811yescharacteristic
410Dic3—62no—
411Dic3—62no—
412Dic3—81no—
413Dic3—122no—
414Dic3—241no—
415Dic3—241no—
416Dic3—242no—
417C32#181411yescharacteristic, complemented, Sylow
418C23—181no—
419C23#379911yescharacteristic
420Q8—92no—
421Q8—181no—
422D4—92no—
423D4—182no—
424D4—182no—
425D4—181no—
426C2×C4—121no—
427C2×C4—181no—
428C2×C4—182no—
429C2×C4—182no—
430C2×C4—361no—
431C2×C4#379711yescharacteristic
432C2×C4C4×D3211yescharacteristic
433C2×C4D3×D1211yescharacteristic
434C2×C4#380411yescharacteristic
435C2×C4D3×#6711yescharacteristic
436C2×C4#381111yescharacteristic
437C8—31no—
438C8—31no—
439C8—31no—
440C8—31no—
441C8—41no—
442C8—62no—
443C8—121no—
444C2×C3—21no—
445C2×C3—21no—
446C2×C3—21no—
447C2×C3—21no—
448C2×C3—21no—
449C2×C3—21no—
450C2×C3—21no—
451C2×C3—41no—
452C2×C3—41no—
453C2×C3—41no—
454C2×C3#466711yescharacteristic
455C2×C3#498711yescharacteristic
456D3—122no—
457D3—122no—
458D3—242no—
459C22—41no—
460C22—182no—
461C22—362no—
462C22#6383611yescharacteristic
463C22#6388811yescharacteristic
464C22#6391011yescharacteristic
465C4—182no—
466C4—241no—
467C4—721no—
468C4#6388311yescharacteristic
469C4#6389511yescharacteristic
470C4D3×(C2×D3)⋊C411yescharacteristic
471C4#6395811yescharacteristic
472C3—21no—
473C3#6903211yescharacteristic, complemented
474C3#7071911yescharacteristic, complemented
475C2—21no—
476C2—21no—
477C2—21no—
478C2—362no—
479C2#1059136711yescharacteristic
subgroupG/H
centerC4#63958
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#380
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1814
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×C3×#822C2semidirect
4. #10591122C2semidirect
6. C3×#4556C2semidirect
7. #10589171C2semidirect
20. #63817C4semidirect
21. #63817C4semidirect
36. C2×#822D3semidirect
43. #4556D3semidirect
417. C32#1814semidirect
473. C3#69032semidirect
474. C3#70719semidirect

Maximal subgroups

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

subgroupindex
C2×#638172
#105928382
C2×C3×#8222
#105911222
#105911132
C3×#45562
#105891712
#707193
#690323