Finite Group Databasebeta

← #11788917

Subgroups — #11788917

Order 1152.

661 conjugacy classes of subgroups.

The subgroup lattice has 474 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10594855C211yesmaximal, characteristic
2#10594776C211yesmaximal, characteristic
3C2×C3×#824C211yesmaximal, characteristic, complemented
4C3×#5132C211yesmaximal, characteristic
5C2×#63560C211yesmaximal, characteristic, complemented
6#10589422C211yesmaximal, characteristic, complemented
7#10589171C211yesmaximal, characteristic, complemented
8#70138—31nomaximal
9#70124—31nomaximal
10C2×C3×#235C2211yescharacteristic
11C22×C3×Dic6C2211yescharacteristic
12C2×C32×M16C2211yescharacteristic
13#64135C2211yescharacteristic
14C2×#3748C2211yescharacteristic
15C2×C3×#208C2211yescharacteristic
16C2×C3×#208C2211yescharacteristic
17#63961C414yes—
18#63873—21no—
19#63863—21no—
20#63856—22no—
21#63815—22no—
22#63814—22no—
23D3×#208—22no—
24C3×#824—21no—
25C3×#824—22no—
26C3×#823—21no—
27#63560—22no—
28#5825—31no—
29#5819—31no—
30#5816—31no—
31#5745—31no—
32C3×#413—31no—
33C2×C3×#101—31no—
34C2×#836—31no—
35C2×#824—31no—
36C2×#824D311yescharacteristic, complemented
37#5132D311yescharacteristic
38#4559—31no—
39#4556—31no—
40#4556—31no—
41#4556—31no—
42#4556—61no—
43C22×C32×C4C2311yescharacteristic
44C2×C3×#67C2×C412yes—
45C22×C3×Dic3C2×C412yes—
46C3×#235—21no—
47C3×#235—21no—
48C3×#235—21no—
49C3×#235—21no—
50C2×C3×D12D411yescharacteristic
51C2×C3×C4×D3D412yes—
52C2×C3×Dic6—21no—
53C2×C3×Dic6—21no—
54C2×C3×Dic6—21no—
55C2×C3×Dic6—21no—
56C2×C3×Dic6—21no—
57C2×C3×Dic6—21no—
58C2×C3×Dic6D411yescharacteristic
59C32×M16—21no—
60C32×M16—21no—
61C2×C32×C8—21no—
62#3757C2×C412yes—
63C4⋊(C3⋊Dic3)—21no—
64C4×C3⋊Dic3—21no—
65#3748—21no—
66#3748D412yes—
67C2×C3⋊(C3⋊C8)—21no—
68C3×#208—21no—
69C3×#208—21no—
70C3×#208—21no—
71C3×#208D412yes—
72C2×C3×C3⋊C8—21no—
73C2×C3×C3⋊C8—21no—
74#3724—24no—
75(C2×D3)⋊Dic3—24no—
76#3711—24no—
77D3×C3⋊C8—24no—
78#1915—91noSylow
79C2×C3×#41—31no—
80C22×C3×Q8—31no—
81C2×#235C2×D311yescharacteristic
82C22×Dic6C2×D311yescharacteristic
83C2×C3×M16—21no—
84C2×C3×M16—31no—
85C2×C3×M16—31no—
86C2×C3×M16C2×D311yescharacteristic
87C2×C3×M16C2×D311yescharacteristic
88#948—62no—
89#948—62no—
90#947—61no—
91#946—62no—
92#944—61no—
93#944—61no—
94#936—61no—
95#935—34no—
96#929—34no—
97#926—31no—
98#926—31no—
99#926—61no—
100#924—62no—
101C2×#208—31no—
102C2×#208—31no—
103C2×#208—61no—
104C2×#208—62no—
105C2×#208C2×D311yescharacteristic
106C2×#208C2×D311yescharacteristic
107#907—62no—
108D3×M16—62no—
109#901—62no—
110C3×#101—62no—
111C3×#101—61no—
112C3×#100—61no—
113#836—62no—
114#824—21no—
115#824—22no—
116#824—62no—
117#823—21no—
118C23×C32C22×C411yescharacteristic
119C22×C3×D3C22⋊C412yes—
120C2×C32×C4C2×D411yescharacteristic
121C2×C32×C4C2×D411yescharacteristic
122C2×C32×C4C2×D411yescharacteristic
123C2×C32×C4C2×D411yescharacteristic
124C2×C32×C4#4111yescharacteristic
125C2×C32×C4#4111yescharacteristic
126C2×C3⋊Dic3—22no—
127C3×#67—22no—
128C3×#67—22no—
129C2×C3×Dic3—22no—
130C2×C3×Dic3—22no—
131C2×C3×Dic3—22no—
132C2×C3×Dic3C22⋊C412yes—
133C3×D12—21no—
134C3×D12—21no—
135C3×C4×D3—22no—
136C3×C4×D3—22no—
137C3×Dic6—21no—
138C3×Dic6—21no—
139C3×Dic6—41no—
140C3×Dic6—41no—
141C3×Dic6—41no—
142C3×Dic6—41no—
143C32×C8—41no—
144C3⋊(C3⋊C8)—22no—
145C3×C3⋊C8—22no—
146C3×C3⋊C8—41no—
147#568—91no—
148#536—91no—
149#413—31no—
150C2×#101—31no—
151C2×#101—91no—
152#344—91no—
153#344—91no—
154C3×#41—61no—
155C3×#41—61no—
156C3×#41—61no—
157C3×#41—61no—
158C2×C3×Q8—31no—
159C2×C3×Q8—61no—
160C2×C3×Q8—61no—
161C2×C3×Q8—61no—
162C2×C3×Q8—61no—
163C2×C3×Q8—61no—
164C2×C3×Q8—61no—
165C2×C3×D4—32no—
166C2×C3×D4—31no—
167C22×C3×C4—21no—
168C22×C3×C4—32no—
169C22×C3×C4—32no—
170C22×C3×C4C22×D311yescharacteristic
171C22×C3×C4C22×D311yescharacteristic
172C2×#67C4×D312yes—
173C22×Dic3C4×D312yes—
174#235—21no—
175#235—21no—
176#235—21no—
177#235—21no—
178C2×D12#6711yescharacteristic
179C2×C4×D3D1212yes—
180C2×Dic6—21no—
181C2×Dic6—21no—
182C2×Dic6—21no—
183C2×Dic6—21no—
184C2×Dic6—21no—
185C2×Dic6—21no—
186C2×Dic6#6711yescharacteristic
187C3×M16—21no—
188C3×M16—21no—
189C3×M16—21no—
190C3×M16—21no—
191C3×M16—32no—
192C3×M16—41no—
193C3×M16—41no—
194C3×M16—61no—
195C3×M16—61no—
196C3×M16—61no—
197C2×C3×C8—22no—
198C2×C3×C8—21no—
199C2×C3×C8—21no—
200C2×C3×C8—61no—
201C2×C3×C8—61no—
202#217—32no—
203#217—32no—
204#217—62no—
205#217—64no—
206(C2×D3)⋊C4—64no—
207C4⋊Dic3—61no—
208C4⋊Dic3—61no—
209C4⋊Dic3—121no—
210Dic3⋊C4—64no—
211Dic3⋊C4—64no—
212C4×Dic3—61no—
213C4×Dic3—61no—
214C4×Dic3—121no—
215#208—21no—
216#208—21no—
217#208—21no—
218#208—32no—
219#208—32no—
220#208—62no—
221#208—64no—
222#208—61no—
223#208—61no—
224#208—121no—
225#208#6712yes—
226C2×C3⋊C8—21no—
227C2×C3⋊C8—21no—
228C2×C3⋊C8—64no—
229C2×C3⋊C8—61no—
230C2×C3⋊C8—61no—
231C2×C3⋊C8—121no—
232ΓL(1,𝔽25)—64no—
233D3×C8—64no—
234C22×C32—41no—
235C22×C32C2×C22⋊C411yescharacteristic
236C22×C32C4×D411yescharacteristic
237C22×C32C4×D411yescharacteristic
238C2×C3×D3—22no—
239C2×C3×D3—42no—
240C32×C4#12011yescharacteristic
241C32×C4#12111yescharacteristic
242C32×C4#12111yescharacteristic
243C32×C4#12311yescharacteristic
244C3⋊Dic3—42no—
245C3×Dic3—22no—
246C3×Dic3—42no—
247C2×#41—31no—
248C22×Q8—31no—
249#131—182no—
250#131—182no—
251C2×M16—31no—
252C2×M16—31no—
253C2×M16—91no—
254C2×M16—182no—
255C2×M16D3211yescharacteristic
256C4⋊Q8—181no—
257#124—181no—
258#123—94no—
259C22⋊Q8—182no—
260#117—91no—
261#101—62no—
262#101—61no—
263#101—182no—
264#100—61no—
265C23×C3—21no—
266C23×C3—32no—
267C23×C3C2×C4×D311yescharacteristic
268C23×C3C2×C4×D311yescharacteristic
269C22×D3(C2×D3)⋊C412yes—
270C3×Q8—61no—
271C3×Q8—61no—
272C3×Q8—121no—
273C3×Q8—121no—
274C3×Q8—121no—
275C3×Q8—121no—
276C3×D4—62no—
277C3×D4—62no—
278C3×D4—61no—
279C3×D4—61no—
280C2×C3×C4—21no—
281C2×C3×C4—21no—
282C2×C3×C4—21no—
283C2×C3×C4—21no—
284C2×C3×C4—21no—
285C2×C3×C4—21no—
286C2×C3×C4—32no—
287C2×C3×C4—62no—
288C2×C3×C4—62no—
289C2×C3×C4—62no—
290C2×C3×C4—62no—
291C2×C3×C4—62no—
292C2×C3×C4C2×D1211yescharacteristic
293C2×C3×C4#23511yescharacteristic
294C2×C3×C4D3×D411yescharacteristic
295C2×C3×C4D3×D411yescharacteristic
296C2×C3×C4D3×D411yescharacteristic
297C2×C3×C4D3×D411yescharacteristic
298C2×C3×C4D3×D411yescharacteristic
299C2×C3×C4#23711yescharacteristic
300C2×C3×C4#23711yescharacteristic
301C2×C3×C4#23711yescharacteristic
302C2×C3×C4C2×#6711yescharacteristic
303C2×C3×C4C2×#6711yescharacteristic
304#67—22no—
305#67—22no—
306C2×Dic3—22no—
307C2×Dic3—22no—
308C2×Dic3—22no—
309C2×Dic3—62no—
310C2×Dic3—62no—
311C2×Dic3—122no—
312C2×Dic3(C2×D3)⋊C412yes—
313D12—21no—
314D12—21no—
315C4×D3—22no—
316C4×D3—22no—
317Dic6—21no—
318Dic6—21no—
319Dic6—41no—
320Dic6—41no—
321Dic6—41no—
322Dic6—41no—
323C3×C8—42no—
324C3×C8—41no—
325C3×C8—41no—
326C3×C8—62no—
327C3×C8—121no—
328C3⋊C8—22no—
329C3⋊C8—41no—
330C3⋊C8—62no—
331C3⋊C8—62no—
332C3⋊C8—122no—
333C2×C32—21no—
334C2×C32—21no—
335C2×C32—21no—
336C2×C32#38611yescharacteristic
337C3×D3—42no—
338#41—61no—
339#41—61no—
340#41—61no—
341#41—61no—
342C2×Q8—31no—
343C2×Q8—61no—
344C2×Q8—61no—
345C2×Q8—61no—
346C2×Q8—61no—
347C2×Q8—61no—
348C2×Q8—61no—
349C2×D4—32no—
350C2×D4—31no—
351C22×C4—32no—
352C22×C4—32no—
353C22×C4C2×D3211yescharacteristic
354M16—21no—
355M16—21no—
356M16—32no—
357M16—61no—
358M16—61no—
359M16—61no—
360M16—92no—
361M16—184no—
362M16—181no—
363C2×C8—21no—
364C2×C8—61no—
365C2×C8—61no—
366C2×C8—184no—
367C2×C8—181no—
368C4⋊C4—184no—
369C4⋊C4—181no—
370C22⋊C4—92no—
371C22⋊C4—184no—
372C42—181no—
373C22×C3—21no—
374C22×C3—21no—
375C22×C3—21no—
376C22×C3—41no—
377C22×C3—41no—
378C22×C3—62no—
379C22×C3—81no—
380C22×C3—122no—
381C22×C3D3×C22⋊C411yescharacteristic
382C22×C3#67⋊C411yescharacteristic
383C22×C3#67⋊C411yescharacteristic
384C22×C3#67⋊C411yescharacteristic
385C22×C3C2×(C2×D3)⋊C411yescharacteristic
386C22×C3C4×#6711yescharacteristic
387C2×D3—22no—
388C2×D3—42no—
389C3×C4—21no—
390C3×C4—21no—
391C3×C4—21no—
392C3×C4—21no—
393C3×C4—62no—
394C3×C4—122no—
395C3×C4#88211yescharacteristic
396C3×C4#88311yescharacteristic
397C3×C4#88411yescharacteristic
398C3×C4#88611yescharacteristic
399C3×C4#93711yescharacteristic
400C3×C4#93811yescharacteristic
401C3×C4#93911yescharacteristic
402C3×C4#93911yescharacteristic
403Dic3—22no—
404Dic3—42no—
405Dic3—122no—
406Dic3—122no—
407Dic3—242no—
408C32#191511yescharacteristic, complemented, Sylow
409C23—32no—
410C23C4×D3211yescharacteristic
411Q8—61no—
412Q8—61no—
413Q8—121no—
414Q8—121no—
415Q8—121no—
416Q8—121no—
417D4—62no—
418D4—62no—
419D4—61no—
420D4—61no—
421C2×C4—32no—
422C2×C4—62no—
423C2×C4—62no—
424C2×C4—62no—
425C2×C4—62no—
426C2×C4—62no—
427C2×C4—182no—
428C2×C4#379511yescharacteristic
429C2×C4D3×D1211yescharacteristic
430C2×C4#380211yescharacteristic
431C2×C4#380511yescharacteristic
432C2×C4D3×#6711yescharacteristic
433C2×C4D3×#6711yescharacteristic
434C8—41no—
435C8—62no—
436C8—121no—
437C8—182no—
438C2×C3—21no—
439C2×C3—21no—
440C2×C3—21no—
441C2×C3—21no—
442C2×C3—21no—
443C2×C3—21no—
444C2×C3—21no—
445C2×C3—41no—
446C2×C3—41no—
447C2×C3—41no—
448C2×C3—122no—
449C2×C3#495611yescharacteristic
450C2×C3#495811yescharacteristic
451D3—42no—
452C22—41no—
453C22—62no—
454C22—122no—
455C22#6387911yescharacteristic
456C22#6390211yescharacteristic
457C22D3×(C2×D3)⋊C411yescharacteristic
458C4—62no—
459C4—122no—
460C4—362no—
461C4#6388511yescharacteristic
462C4#6389111yescharacteristic
463C4#6392211yescharacteristic
464C4#6397011yescharacteristic
465C3—21no—
466C3#7012411yescharacteristic, complemented
467C3#7013811yescharacteristic, complemented
468C2—21no—
469C2—21no—
470C2—21no—
471C2—122no—
472C2#1059136311yescharacteristic
subgroupG/H
centerC2#10591363
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC2×C32×M16C22
socleC2×C32#386
prime radicalC2×C3×#235C22
cosocleC22×C32×C4C23
hypercenterC2×M16D32
hypocenterC32#1915
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×M16

Complements

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

NH ≅ G/Ntype
3. C2×C3×#824C2semidirect
5. C2×#63560C2semidirect
6. #10589422C2semidirect
7. #10589171C2semidirect
36. C2×#824D3semidirect
408. C32#1915semidirect
466. C3#70124semidirect
467. C3#70138semidirect

Maximal subgroups

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

subgroupindex
#105948552
#105947762
C2×C3×#8242
C3×#51322
C2×#635602
#105894222
#105891712
#701383
#701243