Finite Group Databasebeta

← #11861729

Subgroups — #11861729

Order 1152.

807 conjugacy classes of subgroups.

The subgroup lattice has 526 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C3×#5580C211yesmaximal, characteristic
2#10592723C211yesmaximal, characteristic, complemented
3C3×Q8×C3⋊C8C211yesmaximal, characteristic, complemented
4#10590339C211yesmaximal, characteristic, complemented
5#10590330C212yesmaximal, complemented
6C3⋊C8×D12C211yesmaximal, characteristic, complemented
7C3⋊C8×D12C212yesmaximal, complemented
8#10590318C212yesmaximal, complemented
9C4×D3×C3⋊C8C211yesmaximal, characteristic, complemented
10#10590263C211yesmaximal, characteristic, complemented
11#10590253C212yesmaximal, complemented
12#83126—31nomaximal
13#79903—31nomaximal
14C32×C4×Q8C2211yescharacteristic
15C3×#947C411yescharacteristic
16C3×#946C411yescharacteristic
17C3×#898C412yes—
18C3×#895C411yescharacteristic
19C3×#894C412yes—
20C3×#890C411yescharacteristic
21C3×C4×D12C2212yes—
22C3×C4×D12C2211yescharacteristic
23C3×#872C2212yes—
24C3×C42×D3C2211yescharacteristic
25C2×#3711C2212yes—
26C2×D3×C3⋊C8C2211yescharacteristic
27C2×D3×C3⋊C8C2211yescharacteristic
28C2×D3×C3⋊C8C2212yes—
29C4⋊(C3⋊(C3⋊C8))C2212yes—
30C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
31#63630C2212yes—
32C4×C3⋊(C3⋊C8)C2211yescharacteristic
33C3×C4⋊(C3⋊C8)C2212yes—
34C3×C4⋊(C3⋊C8)C2211yescharacteristic
35C3×C4×C3⋊C8C2211yescharacteristic
36C3×C4×C3⋊C8C2212yes—
37(C2×D3)⋊(C3⋊C8)C2212yes—
38(C2×D3)⋊(C3⋊C8)C2212yes—
39(C2×D3)⋊(C3⋊C8)C2212yes—
40#63554C2212yes—
41Dic3×C3⋊C8C2211yescharacteristic
42Dic3×C3⋊C8C2211yescharacteristic
43C3×#529—31no—
44#5580D311yescharacteristic
45C3×C8×Q8—31no—
46#5024—31no—
47#5024—31no—
48#5024—61no—
49Q8×C3⋊C8D311yescharacteristic, complemented
50#5012—31no—
51#5011—32no—
52D4×C3⋊C8—31no—
53D4×C3⋊C8—32no—
54#5000—32no—
55#4997—32no—
56#4926—31no—
57C2×C4×C3⋊C8—31no—
58#4840—32no—
59#4838—31no—
60#4836—32no—
61#4835—31no—
62#4689—32no—
63C8×D12—31no—
64C8×D12—32no—
65C4×D3×C8—31no—
66C2×C32×Q8C2×C411yescharacteristic
67C2×C3×D12C2×C412yes—
68C2×C3×D12C2×C411yescharacteristic
69C2×C3×C4×D3C2×C411yescharacteristic
70C2×C3×C4×D3C2×C411yescharacteristic
71C2×C3×C4×D3C2311yescharacteristic
72C2×C3×C4×D3C2312yes—
73C32×C4⋊C4C2×C411yescharacteristic
74C32×C4⋊C4C2×C412yes—
75C32×C42C2311yescharacteristic
76C32×C42C2312yes—
77C2×C3⋊(C3⋊C8)C2311yescharacteristic
78C2×C3⋊(C3⋊C8)C2312yes—
79C2×C3⋊(C3⋊C8)C2311yescharacteristic
80C3×(C2×D3)⋊C4C2×C412yes—
81C3×(C2×D3)⋊C4C2×C412yes—
82C3×(C2×D3)⋊C4C2×C412yes—
83C3×(C2×D3)⋊C4C2×C412yes—
84C3×(C2×D3)⋊C4C2×C412yes—
85C3×C4⋊Dic3C2×C412yes—
86C3×C4⋊Dic3C2×C411yescharacteristic
87C3×Dic3⋊C4C2×C412yes—
88C3×Dic3⋊C4C2×C412yes—
89C3×C4×Dic3C2×C411yescharacteristic
90C3×C4×Dic3C2×C411yescharacteristic
91C3×C4×Dic3C2311yescharacteristic
92C2×C3×C3⋊C8C2311yescharacteristic
93C2×C3×C3⋊C8C2312yes—
94C2×C3×C3⋊C8C2311yescharacteristic
95#3711—24no—
96D3×C3⋊C8—22no—
97D3×C3⋊C8—22no—
98D3×C3⋊C8—24no—
99#2966—91noSylow
100C3×#126—32no—
101C3×#125—31no—
102C3×#124—31no—
103C3×#123—32no—
104C3×C22⋊Q8—31no—
105C3×#121—31no—
106C3×C4×Q8—21no—
107C3×C4×Q8C2×D311yescharacteristic
108C3×C4×Q8C2×D311yescharacteristic
109C3×C4×D4—32no—
110C3×C4×D4—31no—
111C3×#117—32no—
112C2×C3×C42—31no—
113#947Dic311yescharacteristic
114#946Dic311yescharacteristic
115C2×#208—32no—
116C22×C3⋊C8—31no—
117C22×C3⋊C8—31no—
118C22×C3⋊C8—32no—
119C2×ΓL(1,𝔽25)—32no—
120C2×D3×C8—31no—
121C2×D3×C8—31no—
122C2×D3×C8—32no—
123#898Dic312yes—
124#895Dic311yescharacteristic
125#894Dic312yes—
126#890Dic311yescharacteristic
127C4×D12C2×D312yes—
128C4×D12C2×D311yescharacteristic
129#872C2×D312yes—
130C42×D3C2×D311yescharacteristic
131C3×C4⋊C8—31no—
132C3×C4⋊C8—32no—
133C3×C4×C8—31no—
134C3×C4×C8—32no—
135#830—32no—
136#830—32no—
137#830—32no—
138(C2×D3)⋊C8—32no—
139(C2×D3)⋊C8—32no—
140(C2×D3)⋊C8—32no—
141#815—32no—
142C8×Dic3—31no—
143C8×Dic3—31no—
144C4⋊(C3⋊C8)—31no—
145C4⋊(C3⋊C8)—31no—
146C4⋊(C3⋊C8)—32no—
147C4⋊(C3⋊C8)—32no—
148C4⋊(C3⋊C8)—61no—
149C4⋊(C3⋊C8)—62no—
150C4⋊(C3⋊C8)C2×D311yescharacteristic
151C4⋊(C3⋊C8)C2×D312yes—
152#803—32no—
153#803—32no—
154#803—32no—
155#803—62no—
156C4×C3⋊C8—31no—
157C4×C3⋊C8—31no—
158C4×C3⋊C8—31no—
159C4×C3⋊C8—31no—
160C4×C3⋊C8—61no—
161C4×C3⋊C8C2×D311yescharacteristic
162C4×C3⋊C8C2×D312yes—
163C22×C3×D3C22×C412yes—
164C22×C3×D3C22×C411yescharacteristic
165C32×Q8—22no—
166C2×C32×C4C22×C411yescharacteristic
167C2×C32×C4C22×C412yes—
168C2×C32×C4C22×C412yes—
169C2×C32×C4C22×C411yescharacteristic
170C2×C32×C4C2411yescharacteristic
171C2×C3×Dic3C22×C411yescharacteristic
172C2×C3×Dic3C22×C411yescharacteristic
173C2×C3×Dic3C22×C411yescharacteristic
174C2×C3×Dic3C22×C412yes—
175C3×D12—24no—
176C3×D12—22no—
177C3×C4×D3—22no—
178C3×C4×D3—22no—
179C3×C4×D3—21no—
180C3×C4×D3—22no—
181C3×C4×D3—21no—
182C3×C4×D3—22no—
183C3⋊(C3⋊C8)—21no—
184C3⋊(C3⋊C8)—22no—
185C3⋊(C3⋊C8)#4112yes—
186C3×C3⋊C8—21no—
187C3×C3⋊C8—22no—
188C3×C3⋊C8#4112yes—
189#529—31no—
190#446—91no—
191C8×Q8—31no—
192#436—91no—
193#435—92no—
194C8×D4—91no—
195C8×D4—92no—
196#433—92no—
197#432—91no—
198#405—92no—
199C2×C4×C8—91no—
200C2×C3×Q8—21no—
201C2×C3×Q8C4×D311yescharacteristic
202C2×C3×Q8C2×Dic311yescharacteristic
203C2×C3×D4—32no—
204C2×C3×D4—31no—
205C22×C3×C4—31no—
206C22×C3×C4—31no—
207C22×C3×C4—31no—
208C22×C3×C4—32no—
209C2×D12C2×Dic312yes—
210C2×D12C2×Dic311yescharacteristic
211C2×C4×D3C2×Dic311yescharacteristic
212C2×C4×D3C2×Dic311yescharacteristic
213C2×C4×D3C22×D311yescharacteristic
214C2×C4×D3C22×D312yes—
215C2×C3×C8—31no—
216C2×C3×C8—31no—
217C2×C3×C8—32no—
218C3×C4⋊C4—21no—
219C3×C4⋊C4—22no—
220C3×C4⋊C4—32no—
221C3×C4⋊C4—32no—
222C3×C4⋊C4—31no—
223C3×C4⋊C4—32no—
224C3×C4⋊C4C4×D311yescharacteristic
225C3×C4⋊C4C4×D312yes—
226C3×C4⋊C4C2×Dic311yescharacteristic
227C3×C4⋊C4C2×Dic312yes—
228C3×C22⋊C4—32no—
229C3×C22⋊C4—32no—
230C3×C22⋊C4—32no—
231C3×C22⋊C4—32no—
232C3×C22⋊C4—32no—
233C3×C42—21no—
234C3×C42—22no—
235C3×C42—31no—
236C3×C42—31no—
237C3×C42—31no—
238C3×C42C22×D311yescharacteristic
239C3×C42C22×D312yes—
240C3×C42C22×D311yescharacteristic
241C3×C42C22×D312yes—
242(C2×D3)⋊C4C2×Dic312yes—
243(C2×D3)⋊C4C2×Dic312yes—
244(C2×D3)⋊C4C2×Dic312yes—
245(C2×D3)⋊C4C2×Dic312yes—
246(C2×D3)⋊C4C2×Dic312yes—
247C4⋊Dic3C2×Dic312yes—
248C4⋊Dic3C2×Dic311yescharacteristic
249Dic3⋊C4C2×Dic312yes—
250Dic3⋊C4C2×Dic312yes—
251C4×Dic3C2×Dic311yescharacteristic
252C4×Dic3C2×Dic311yescharacteristic
253C4×Dic3C22×D311yescharacteristic
254#208—64no—
255C2×C3⋊C8—31no—
256C2×C3⋊C8—31no—
257C2×C3⋊C8—31no—
258C2×C3⋊C8—31no—
259C2×C3⋊C8—32no—
260C2×C3⋊C8—32no—
261C2×C3⋊C8—61no—
262C2×C3⋊C8—61no—
263C2×C3⋊C8—62no—
264C2×C3⋊C8—62no—
265C2×C3⋊C8—62no—
266C2×C3⋊C8—64no—
267C2×C3⋊C8C22×D311yescharacteristic
268C2×C3⋊C8C22×D312yes—
269C2×C3⋊C8C22×D311yescharacteristic
270ΓL(1,𝔽25)—64no—
271D3×C8—62no—
272D3×C8—62no—
273D3×C8—64no—
274C22×C32C23×C411yescharacteristic
275C2×C3×D3—21no—
276C2×C3×D3—21no—
277C2×C3×D3—22no—
278C2×C3×D3—22no—
279C2×C3×D3—22no—
280C2×C3×D3#13112yes—
281C32×C4—21no—
282C32×C4—22no—
283C32×C4—22no—
284C32×C4#13112yes—
285C32×C4C2×#4111yescharacteristic
286C32×C4C2×#4111yescharacteristic
287C3×Dic3—21no—
288C3×Dic3—22no—
289C3×Dic3—21no—
290C3×Dic3—21no—
291C2×M16—92no—
292C22×C8—91no—
293C22×C8—91no—
294C22×C8—92no—
295#126—32no—
296#125—31no—
297#124—31no—
298#123—32no—
299C22⋊Q8—31no—
300#121—31no—
301C4×Q8D3211yescharacteristic
302C4×D4—32no—
303C4×D4—31no—
304#117—32no—
305C2×C42—31no—
306C4⋊C8—31no—
307C4⋊C8—32no—
308C4⋊C8—91no—
309C4⋊C8—92no—
310C22⋊C8—92no—
311C22⋊C8—92no—
312C22⋊C8—92no—
313#97—92no—
314#97—92no—
315C4×C8—31no—
316C4×C8—32no—
317C4×C8—91no—
318C4×C8—91no—
319C4×C8—91no—
320C23×C3—31no—
321C23×C3—32no—
322C22×D3C22×Dic312yes—
323C22×D3C22×Dic311yescharacteristic
324C3×Q8—22no—
325C3×Q8—22no—
326C3×Q8—42no—
327C3×D4—64no—
328C3×D4—62no—
329C2×C3×C4—21no—
330C2×C3×C4—21no—
331C2×C3×C4—21no—
332C2×C3×C4—22no—
333C2×C3×C4—22no—
334C2×C3×C4—31no—
335C2×C3×C4—31no—
336C2×C3×C4—31no—
337C2×C3×C4—32no—
338C2×C3×C4—62no—
339C2×C3×C4—62no—
340C2×C3×C4—61no—
341C2×C3×C4—62no—
342C2×C3×C4—61no—
343C2×C3×C4—62no—
344C2×C3×C4C2×C4×D311yescharacteristic
345C2×C3×C4C2×C4×D312yes—
346C2×C3×C4C2×C4×D312yes—
347C2×C3×C4C2×C4×D311yescharacteristic
348C2×C3×C4C22×Dic311yescharacteristic
349C2×C3×C4C22×Dic312yes—
350C2×C3×C4C22×Dic312yes—
351C2×C3×C4C22×Dic311yescharacteristic
352C2×C3×C4C23×D311yescharacteristic
353C2×C3×C4C23×D311yescharacteristic
354C2×Dic3C22×Dic311yescharacteristic
355C2×Dic3C22×Dic311yescharacteristic
356C2×Dic3C22×Dic311yescharacteristic
357C2×Dic3C22×Dic312yes—
358D12—24no—
359D12—22no—
360C4×D3—22no—
361C4×D3—22no—
362C4×D3—21no—
363C4×D3—22no—
364C4×D3—21no—
365C4×D3—22no—
366C3×C8—32no—
367C3×C8—61no—
368C3×C8—62no—
369C3⋊C8—21no—
370C3⋊C8—22no—
371C3⋊C8—32no—
372C3⋊C8—32no—
373C3⋊C8—62no—
374C3⋊C8—61no—
375C3⋊C8—62no—
376C3⋊C8—61no—
377C3⋊C8—62no—
378C3⋊C8—121no—
379C3⋊C8—122no—
380C3⋊C8#23912yes—
381C2×C32C4×#4111yescharacteristic
382C2×C32C2×#13111yescharacteristic
383C2×C32C2×#13111yescharacteristic
384C3×D3—22no—
385C3×D3—42no—
386C2×Q8D3×Dic311yescharacteristic
387C2×D4—32no—
388C2×D4—31no—
389C22×C4—31no—
390C22×C4—32no—
391C22×C4—31no—
392C22×C4—31no—
393M16—184no—
394C2×C8—31no—
395C2×C8—31no—
396C2×C8—32no—
397C2×C8—91no—
398C2×C8—91no—
399C2×C8—92no—
400C2×C8—182no—
401C2×C8—184no—
402C2×C8—182no—
403C4⋊C4—32no—
404C4⋊C4—32no—
405C4⋊C4—31no—
406C4⋊C4—32no—
407C4⋊C4D3×Dic311yescharacteristic
408C4⋊C4D3×Dic312yes—
409C22⋊C4—32no—
410C22⋊C4—32no—
411C22⋊C4—32no—
412C22⋊C4—32no—
413C22⋊C4—32no—
414C42—31no—
415C42—31no—
416C42—31no—
417C42C2×D3211yescharacteristic
418C42C2×D3212yes—
419C22×C3—21no—
420C22×C3—32no—
421C22×C3—61no—
422C22×C3—61no—
423C22×C3—62no—
424C22×C3—62no—
425C22×C3—62no—
426C22×C3C22×C4×D311yescharacteristic
427C22×C3C23×Dic311yescharacteristic
428C2×D3—21no—
429C2×D3—21no—
430C2×D3—22no—
431C2×D3—22no—
432C2×D3—22no—
433C2×D3#94812yes—
434C3×C4—22no—
435C3×C4—21no—
436C3×C4—22no—
437C3×C4—21no—
438C3×C4—22no—
439C3×C4—22no—
440C3×C4—21no—
441C3×C4—21no—
442C3×C4—22no—
443C3×C4—42no—
444C3×C4—41no—
445C3×C4—42no—
446C3×C4—61no—
447C3×C4—61no—
448C3×C4—61no—
449C3×C4—62no—
450C3×C4#90112yes—
451C3×C4#94812yes—
452C3×C4C2×#23911yescharacteristic
453C3×C4D3×#4111yescharacteristic
454C3×C4D3×#4111yescharacteristic
455C3×C4D3×#4111yescharacteristic
456Dic3—21no—
457Dic3—21no—
458Dic3—21no—
459Dic3—22no—
460C32#296611yescharacteristic, complemented, Sylow
461C23—31no—
462C23—32no—
463Q8—22no—
464D4—64no—
465D4—62no—
466C2×C4—31no—
467C2×C4—31no—
468C2×C4—31no—
469C2×C4—32no—
470C2×C4—62no—
471C2×C4—61no—
472C2×C4—62no—
473C2×C4—61no—
474C2×C4—62no—
475C2×C4—62no—
476C2×C4C2×D3×Dic311yescharacteristic
477C2×C4C2×D3×Dic312yes—
478C2×C4C2×D3×Dic312yes—
479C2×C4C2×D3×Dic311yescharacteristic
480C2×C4C22×D3211yescharacteristic
481C8—32no—
482C8—61no—
483C8—62no—
484C8—92no—
485C8—181no—
486C8—182no—
487C2×C3—21no—
488C2×C3—21no—
489C2×C3—21no—
490C2×C3—62no—
491C2×C3—122no—
492C2×C3C4×#23911yescharacteristic
493C2×C3C2×#90111yescharacteristic
494C2×C3D3×#13111yescharacteristic
495C2×C3C2×#94811yescharacteristic
496C2×C3C2×#94811yescharacteristic
497C2×C3Dic3×#4111yescharacteristic
498D3—22no—
499D3—42no—
500C22—32no—
501C22—61no—
502C22—61no—
503C22—62no—
504C22—62no—
505C22—62no—
506C22C22×D3×Dic311yescharacteristic
507C4—21no—
508C4—22no—
509C4—22no—
510C4—61no—
511C4—62no—
512C4—61no—
513C4—61no—
514C4#6381412yes—
515C4D3×#23911yescharacteristic
516C4#6431911yescharacteristic
517C3—21no—
518C3#7990311yescharacteristic, complemented
519C3#8312611yescharacteristic, complemented
520C2—62no—
521C2—122no—
522C2C2×#6381411yescharacteristic
523C2Dic3×#23911yescharacteristic
524C2D3×#94811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC32×C4×Q8C22
prime radicalC3×#895C4
cosocleC2×C32×C4C24
hypercenterC4×Q8D32
hypocenterC32#2966
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
2. #10592723C2semidirect
3. C3×Q8×C3⋊C8C2semidirect
4. #10590339C2semidirect
5. #10590330C2semidirect
6. C3⋊C8×D12C2semidirect
7. C3⋊C8×D12C2semidirect
8. #10590318C2semidirect
9. C4×D3×C3⋊C8C2semidirect
10. #10590263C2semidirect
11. #10590253C2semidirect
49. Q8×C3⋊C8D3semidirect
460. C32#2966semidirect
518. C3#79903semidirect
519. C3#83126semidirect

Maximal subgroups

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

subgroupindex
C3×#55802
#105927232
C3×Q8×C3⋊C82
#105903392
#105903302
C3⋊C8×D122
#105903182
C4×D3×C3⋊C82
#105902632
#105902532
#831263
#799033