Finite Group Databasebeta

← #11785519

Subgroups — #11785519

Order 1152.

579 conjugacy classes of subgroups.

The subgroup lattice has 441 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63817C211yesmaximal, characteristic
2#10592831C211yesmaximal, characteristic
3C2×C3×#822C211yesmaximal, characteristic, complemented
4C2×#63577C211yesmaximal, characteristic, complemented
5#10591078C211yesmaximal, characteristic
6C3×C3⋊#338C211yesmaximal, characteristic, complemented
7#10589159C211yesmaximal, characteristic, complemented
8#70718—31nomaximal
9#68724—31nomaximal
10C2×#3828C2211yescharacteristic
11C2×C32×M16C2211yescharacteristic
12C2×#3748C2211yescharacteristic
13C2×C3×#208C2211yescharacteristic
14C2×C3×#208C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C22×C3×C3⋊C8C2211yescharacteristic
17C2×#3712C412yes—
18#63817—22no—
19#63817—22no—
20C2×#3710C412yes—
21#63651—21no—
22#63650—21no—
23C3×#822—22no—
24#63577—22no—
25#63561—21no—
26#63559—21no—
27C2×#907—31no—
28C2×#901—31no—
29C2×C3×#108—31no—
30#5132—31no—
31#5132—31no—
32#5132—31no—
33#5132—31no—
34#5132—61no—
35C2×#822—31no—
36C2×#822D311yescharacteristic, complemented
37C2×#819—31no—
38C3×#338—31no—
39C3⋊#338—31no—
40C3⋊#338—31no—
41C3⋊#338D311yescharacteristic, complemented
42C22×C32×C4C2311yescharacteristic
43C2×#638Q812yes—
44#3828—21no—
45#3828—21no—
46#3828—21no—
47#3828—21no—
48C2×C4⋊(C3⋊D3)D411yescharacteristic
49C2×C4×C3⋊D3C2×C412yes—
50C2×#634D411yescharacteristic
51C32×M16—21no—
52C32×M16—21no—
53C2×C32×C8—21no—
54#3748—21no—
55#3748—21no—
56C2×C3⋊(C3⋊C8)—21no—
57C3×#208—21no—
58C3×#208—21no—
59C3×#208—21no—
60C3×#208—21no—
61C3×#208—21no—
62C3×#208—21no—
63C2×C3×C3⋊C8—21no—
64C2×C3×C3⋊C8—21no—
65C2×C3×C3⋊C8C2×C412yes—
66C2×C3×C3⋊C8C2×C411yescharacteristic
67C2×C3×C3⋊C8C2×C411yescharacteristic
68C2×C3×C3⋊C8D412yes—
69C2×C3×C3⋊C8D412yes—
70#3712—24no—
71#3710—24no—
72#1813—91noSylow
73C2×#235—31no—
74C2×#235—31no—
75C2×#235—61no—
76C2×C3×M16—21no—
77C2×C3×M16—31no—
78C2×C3×M16—31no—
79C2×C3×M16—31no—
80C2×C3×M16C2×D311yescharacteristic
81C2×C3×M16C2×D311yescharacteristic
82C22×C3×C8—31no—
83C2×#208—31no—
84C2×#208—31no—
85C2×#208—61no—
86C2×#208C2×D311yescharacteristic
87C2×#208C2×D311yescharacteristic
88C2×#208C2×D311yescharacteristic
89C22×C3⋊C8C2×D311yescharacteristic
90#907—62no—
91#907—62no—
92#901—62no—
93#901—62no—
94C2×ΓL(1,𝔽25)—32no—
95C2×ΓL(1,𝔽25)—32no—
96C2×D3×C8—32no—
97C2×D3×C8—32no—
98C3×#108—62no—
99#824—61no—
100#824—61no—
101#824—61no—
102#824—61no—
103#824—62no—
104#823—61no—
105#823—61no—
106#823—61no—
107#823—61no—
108#823—62no—
109#822—22no—
110#822—62no—
111#819—62no—
112C23×C32C2×Q811yescharacteristic
113C22×C3⋊D3C4⋊C412yes—
114C2×C32×C4C22×C411yescharacteristic
115C2×C32×C4C2×D411yescharacteristic
116C2×C32×C4C2×D411yescharacteristic
117C2×C32×C4C2×D411yescharacteristic
118C2×C32×C4#4111yescharacteristic
119C2×C32×C4#4111yescharacteristic
120#638—22no—
121#638—22no—
122C2×C3⋊Dic3C4⋊C412yes—
123C4⋊(C3⋊D3)—21no—
124C4⋊(C3⋊D3)—21no—
125C4×C3⋊D3—22no—
126C4×C3⋊D3—22no—
127#634—21no—
128#634—21no—
129C32×C8—41no—
130C3⋊(C3⋊C8)—41no—
131C3×C3⋊C8—22no—
132C3×C3⋊C8—41no—
133C3×C3⋊C8—41no—
134C3×C3⋊C8C22⋊C412yes—
135C3×C3⋊C8C22⋊C412yes—
136C2×#131—91no—
137C2×#108—31no—
138C2×#108—91no—
139#413—91no—
140#413—91no—
141#338—31no—
142#338—91no—
143C22×C3×C4—21no—
144C22×C3×C4C22×D311yescharacteristic
145C22×C3×C4C22×D311yescharacteristic
146C2×#67—32no—
147C2×#67—32no—
148C2×#67—62no—
149#235—61no—
150#235—61no—
151#235—61no—
152#235—61no—
153#235—61no—
154#235—61no—
155#235—61no—
156#235—61no—
157#235—121no—
158#235—121no—
159#235—121no—
160#235—121no—
161C2×D12—31no—
162C2×D12—31no—
163C2×D12—61no—
164C2×C4×D3—32no—
165C2×C4×D3—32no—
166C2×C4×D3—62no—
167C2×Dic6—31no—
168C2×Dic6—31no—
169C2×Dic6—61no—
170C3×M16—22no—
171C3×M16—21no—
172C3×M16—21no—
173C3×M16—21no—
174C3×M16—21no—
175C3×M16—41no—
176C3×M16—61no—
177C3×M16—61no—
178C3×M16—61no—
179C3×M16—61no—
180C3×M16—61no—
181C3×M16—61no—
182C2×C3×C8—21no—
183C2×C3×C8—21no—
184C2×C3×C8—31no—
185C2×C3×C8—31no—
186C2×C3×C8—32no—
187C2×C3×C8—32no—
188C2×C3×C8—32no—
189C2×C3×C8—41no—
190C2×C3×C8—61no—
191C2×C3×C8—61no—
192#208—21no—
193#208—21no—
194#208—21no—
195#208—21no—
196#208—21no—
197#208—21no—
198#208—62no—
199#208—61no—
200#208—61no—
201#208—61no—
202#208—61no—
203#208—121no—
204C2×C3⋊C8—21no—
205C2×C3⋊C8—21no—
206C2×C3⋊C8—61no—
207C2×C3⋊C8—61no—
208C2×C3⋊C8—121no—
209C2×C3⋊C8C4×D312yes—
210C2×C3⋊C8C4×D311yescharacteristic
211C2×C3⋊C8C4×D311yescharacteristic
212C2×C3⋊C8D1212yes—
213C2×C3⋊C8#6712yes—
214ΓL(1,𝔽25)—64no—
215ΓL(1,𝔽25)—64no—
216D3×C8—64no—
217D3×C8—64no—
218C22×C32—41no—
219C22×C32C2×C4⋊C411yescharacteristic
220C22×C32C22⋊Q811yescharacteristic
221C22×C32C22⋊Q811yescharacteristic
222C2×C3⋊D3—22no—
223C2×C3⋊D3—42no—
224C32×C4C2×C22⋊C411yescharacteristic
225C32×C4#11711yescharacteristic
226C32×C4#12111yescharacteristic
227C32×C4#12111yescharacteristic
228C3⋊Dic3—22no—
229C2×#41—91no—
230#131—182no—
231#131—182no—
232C2×M16—31no—
233C2×M16—31no—
234C2×M16—31no—
235C2×M16—92no—
236C2×M16—91no—
237C2×M16D3211yescharacteristic
238C22×C8—31no—
239C22×C8—92no—
240#108—62no—
241#108—182no—
242#101—181no—
243#101—181no—
244#100—181no—
245#100—181no—
246C23×C3—21no—
247C23×C3D3×Q811yescharacteristic
248C23×C3D3×Q811yescharacteristic
249C22×D3—32no—
250C22×D3—32no—
251C22×D3—62no—
252C2×C3×C4—21no—
253C2×C3×C4—21no—
254C2×C3×C4—21no—
255C2×C3×C4—21no—
256C2×C3×C4—21no—
257C2×C3×C4—21no—
258C2×C3×C4C2×C4×D311yescharacteristic
259C2×C3×C4C2×C4×D311yescharacteristic
260C2×C3×C4C2×D1211yescharacteristic
261C2×C3×C4#23511yescharacteristic
262C2×C3×C4#23511yescharacteristic
263C2×C3×C4D3×D411yescharacteristic
264C2×C3×C4D3×D411yescharacteristic
265C2×C3×C4D3×D411yescharacteristic
266C2×C3×C4D3×D411yescharacteristic
267C2×C3×C4#23711yescharacteristic
268C2×C3×C4#23911yescharacteristic
269C2×C3×C4C2×#6711yescharacteristic
270#67—62no—
271#67—62no—
272#67—62no—
273#67—62no—
274#67—122no—
275#67—122no—
276C2×Dic3—32no—
277C2×Dic3—32no—
278C2×Dic3—62no—
279D12—61no—
280D12—61no—
281D12—61no—
282D12—61no—
283D12—121no—
284D12—121no—
285C4×D3—62no—
286C4×D3—62no—
287C4×D3—62no—
288C4×D3—62no—
289C4×D3—122no—
290C4×D3—122no—
291Dic6—61no—
292Dic6—61no—
293Dic6—61no—
294Dic6—61no—
295Dic6—121no—
296Dic6—121no—
297C3×C8—32no—
298C3×C8—32no—
299C3×C8—42no—
300C3×C8—41no—
301C3×C8—41no—
302C3×C8—62no—
303C3×C8—121no—
304C3×C8—121no—
305C3⋊C8—22no—
306C3⋊C8—41no—
307C3⋊C8—41no—
308C3⋊C8—122no—
309C3⋊C8—121no—
310C3⋊C8—121no—
311C3⋊C8(C2×D3)⋊C412yes—
312C3⋊C8(C2×D3)⋊C412yes—
313C2×C32—21no—
314C2×C32—21no—
315C2×C32—21no—
316C2×C32#38011yescharacteristic
317C3⋊D3—42no—
318#41—181no—
319#41—181no—
320#41—181no—
321#41—181no—
322C2×Q8—91no—
323C2×D4—92no—
324C2×D4—91no—
325C22×C4—92no—
326C22×C4C2×D3211yescharacteristic
327M16—21no—
328M16—21no—
329M16—61no—
330M16—61no—
331M16—61no—
332M16—61no—
333M16—61no—
334M16—61no—
335M16—184no—
336M16—181no—
337M16—181no—
338C2×C8—21no—
339C2×C8—31no—
340C2×C8—31no—
341C2×C8—32no—
342C2×C8—32no—
343C2×C8—32no—
344C2×C8—61no—
345C2×C8—61no—
346C2×C8—184no—
347C2×C8—181no—
348C22×C3—21no—
349C22×C3—21no—
350C22×C3—21no—
351C22×C3—41no—
352C22×C3—41no—
353C22×C3—81no—
354C22×C3D3×C4⋊C411yescharacteristic
355C22×C3D3×C4⋊C411yescharacteristic
356C22×C3#89611yescharacteristic
357C22×C3#89611yescharacteristic
358C22×C3#89711yescharacteristic
359C22×C3#94611yescharacteristic
360C2×D3—62no—
361C2×D3—62no—
362C2×D3—122no—
363C2×D3—122no—
364C2×D3—122no—
365C2×D3—242no—
366C3×C4—21no—
367C3×C4—21no—
368C3×C4—21no—
369C3×C4—21no—
370C3×C4#87211yescharacteristic
371C3×C4D3×C22⋊C411yescharacteristic
372C3×C4#88411yescharacteristic
373C3×C4#88411yescharacteristic
374C3×C4#89211yescharacteristic
375C3×C4#89511yescharacteristic
376C3×C4C2×(C2×D3)⋊C411yescharacteristic
377C3×C4#93811yescharacteristic
378Dic3—62no—
379Dic3—62no—
380Dic3—122no—
381C32#181311yescharacteristic, complemented, Sylow
382C23—92no—
383C23#379711yescharacteristic
384Q8—181no—
385Q8—181no—
386D4—182no—
387D4—182no—
388D4—181no—
389D4—181no—
390C2×C4—92no—
391C2×C4—182no—
392C2×C4—182no—
393C2×C4#379911yescharacteristic
394C2×C4C4×D3211yescharacteristic
395C2×C4D3×D1211yescharacteristic
396C2×C4#380411yescharacteristic
397C2×C4D3×#6711yescharacteristic
398C2×C4#381111yescharacteristic
399C8—32no—
400C8—32no—
401C8—41no—
402C8—62no—
403C8—121no—
404C8—121no—
405C8—361no—
406C2×C3—21no—
407C2×C3—21no—
408C2×C3—21no—
409C2×C3—21no—
410C2×C3—21no—
411C2×C3—21no—
412C2×C3—21no—
413C2×C3—41no—
414C2×C3—41no—
415C2×C3—41no—
416C2×C3#466711yescharacteristic
417C2×C3#498711yescharacteristic
418D3—122no—
419D3—122no—
420D3—242no—
421C22—41no—
422C22—182no—
423C22—362no—
424C22#6388311yescharacteristic
425C22#6388811yescharacteristic
426C22#6389511yescharacteristic
427C4—182no—
428C4#6383611yescharacteristic
429C4#6391011yescharacteristic
430C4D3×(C2×D3)⋊C411yescharacteristic
431C4#6395811yescharacteristic
432C3—21no—
433C3#6872411yescharacteristic, complemented
434C3#7071811yescharacteristic, complemented
435C2—21no—
436C2—21no—
437C2—21no—
438C2—362no—
439C2#1059136711yescharacteristic
subgroupG/H
centerC4#63836
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#380
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1813
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. C2×#63577C2semidirect
6. C3×C3⋊#338C2semidirect
7. #10589159C2semidirect
36. C2×#822D3semidirect
41. C3⋊#338D3semidirect
381. C32#1813semidirect
433. C3#68724semidirect
434. C3#70718semidirect

Maximal subgroups

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

subgroupindex
C2×#638172
#105928312
C2×C3×#8222
C2×#635772
#105910782
C3×C3⋊#3382
#105891592
#707183
#687243