Finite Group Databasebeta

← #11775125

Subgroups — #11775125

Order 1152.

833 conjugacy classes of subgroups.

The subgroup lattice has 577 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10596262C211yesmaximal, characteristic
2C2×C3×C3⋊#95C211yesmaximal, characteristic, complemented
3C3×#5207C211yesmaximal, characteristic, complemented
4#10589154C212yesmaximal, complemented
5#10589151C212yesmaximal, complemented
6#69976—31nomaximal
7#69398—31nomaximal
8C23×C32×C4C2211yescharacteristic
9C2×#3828C411yescharacteristic, complemented
10C23×C3×Dic3—21no—
11#64162—21no—
12#64139C411yescharacteristic, complemented
13#64139C2211yescharacteristic
14#64138—21no—
15C4×#638—21no—
16C4×#638—21no—
17#64135C411yescharacteristic, complemented
18#64133C411yescharacteristic, complemented
19#64133C2211yescharacteristic
20C2×C3×#208—21no—
21C3×C3⋊#95—21no—
22C3×C3⋊#95C2212yes—
23C3×#830—21no—
24C3×#830C2212yes—
25#5791—31no—
26#5791—31no—
27#5791—61no—
28C3×#407—31no—
29C2×C3×#95—31no—
30C2×C3⋊#95D311yescharacteristic, complemented
31#5207D311yescharacteristic, complemented
32#4470—32no—
33#4467—32no—
34#4452—32no—
35#4451—32no—
36C24×C32D411yescharacteristic
37C22×C32×C4—42no—
38C22×C32×C4C2×C411yescharacteristic
39C22×C32×C4C2×C411yescharacteristic
40C22×C32×C4D411yescharacteristic
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C2×#638—21no—
45C2×#638—21no—
46C2×#638—21no—
47#3828—42no—
48C2×C4⋊(C3⋊D3)C2×C411yescharacteristic, complemented
49C2×C4×C3⋊D3—21no—
50C2×#634C2×C411yescharacteristic, complemented
51C22×C3×Dic3—24no—
52C22×C3×Dic3—22no—
53C22×C3×Dic3—42no—
54C22×C3×Dic3—42no—
55#3757—21no—
56#3757—21no—
57#3757—21no—
58#3752—21no—
59#3752—21no—
60C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
61C4⋊(C3⋊Dic3)C2×C411yescharacteristic, complemented
62#3750—21no—
63#3750—21no—
64C4×C3⋊Dic3—21no—
65C3×#208—42no—
66C2×C3×C3⋊C8—22no—
67#1504—91noSylow
68C23×C3×C4—21no—
69C23×C3×C4—61no—
70C23×C3×C4C2×D311yescharacteristic
71C23×C3×C4C2×D311yescharacteristic
72C23×Dic3—21no—
73C2×#235—31no—
74C2×#235—31no—
75C2×#235—61no—
76C2×C3×M16—61no—
77#953—62no—
78#953—61no—
79#953—61no—
80#930—31no—
81#930—31no—
82#930—31no—
83#930—31no—
84#930—61no—
85#930—61no—
86#929—62no—
87#929—61no—
88#929—61no—
89C4×#67—62no—
90C4×#67—62no—
91C4×#67—61no—
92C4×#67—61no—
93C4×#67—61no—
94C4×#67—61no—
95#926—31no—
96#926—31no—
97#926—61no—
98#924—31no—
99#924—31no—
100#924—31no—
101#924—31no—
102#924—61no—
103#924—61no—
104C2×#208—21no—
105C3×C22⋊C8—32no—
106C3×C22⋊C8—61no—
107C3×#95—32no—
108C3×#95—61no—
109C3⋊#95—21no—
110C3⋊#95C2×D312yes—
111#830—21no—
112#830C2×D312yes—
113C23×C32—22no—
114C23×C32—22no—
115C23×C32—21no—
116C23×C32—21no—
117C23×C32C22⋊C411yescharacteristic
118C23×C32C22⋊C411yescharacteristic
119C23×C32C2×D411yescharacteristic
120C22×C3⋊D3—21no—
121C2×C32×C4—22no—
122C2×C32×C4—22no—
123C2×C32×C4—41no—
124C2×C32×C4—41no—
125C2×C32×C4—41no—
126C2×C32×C4—41no—
127C2×C32×C4C22⋊C411yescharacteristic
128C2×C32×C4C22⋊C411yescharacteristic
129C2×C32×C4C22×C411yescharacteristic
130C2×C32×C4C2×D411yescharacteristic
131#638—42no—
132#638—42no—
133#638—41no—
134#638—41no—
135C2×C3⋊Dic3—21no—
136C2×C3⋊Dic3—21no—
137C2×C3⋊Dic3—21no—
138C4⋊(C3⋊D3)—41no—
139C4×C3⋊D3—42no—
140#634—41no—
141C2×C3×Dic3—24no—
142C2×C3×Dic3—48no—
143C2×C3×Dic3—42no—
144C2×C3×Dic3—42no—
145C3×C3⋊C8—42no—
146#525—91no—
147#407—31no—
148C2×#95—31no—
149#328—92no—
150#327—92no—
151C24×C3—21no—
152C24×C3D1211yescharacteristic
153C24×C3#6711yescharacteristic
154C22×C3×C4—21no—
155C22×C3×C4—21no—
156C22×C3×C4—21no—
157C22×C3×C4—21no—
158C22×C3×C4—21no—
159C22×C3×C4—21no—
160C22×C3×C4—42no—
161C22×C3×C4—42no—
162C22×C3×C4—44no—
163C22×C3×C4—64no—
164C22×C3×C4—62no—
165C22×C3×C4—122no—
166C22×C3×C4—122no—
167C22×C3×C4C4×D311yescharacteristic
168C22×C3×C4C4×D311yescharacteristic
169C22×C3×C4C4×D311yescharacteristic
170C22×C3×C4C4×D311yescharacteristic
171C22×C3×C4D1211yescharacteristic
172C22×C3×C4D1211yescharacteristic
173C22×C3×C4D1211yescharacteristic
174C22×C3×C4#6711yescharacteristic
175C22×C3×C4#6711yescharacteristic
176C22×C3×C4#6711yescharacteristic
177C22×C3×C4C22×D311yescharacteristic
178C22×C3×C4C22×D311yescharacteristic
179C2×#67—62no—
180C2×#67—62no—
181C2×#67—62no—
182C2×#67—61no—
183C2×#67—61no—
184C2×#67—61no—
185C2×#67—61no—
186C2×#67—61no—
187C2×#67—61no—
188C22×Dic3—24no—
189C22×Dic3—22no—
190C22×Dic3—42no—
191C22×Dic3—42no—
192#235—124no—
193#235—122no—
194#235—122no—
195C2×D12—31no—
196C2×D12—31no—
197C2×D12—61no—
198C2×C4×D3—62no—
199C2×C4×D3—61no—
200C2×C4×D3—61no—
201C2×Dic6—31no—
202C2×Dic6—31no—
203C2×Dic6—61no—
204C3×M16—122no—
205C2×C3×C8—62no—
206#217—62no—
207#217—62no—
208#217—62no—
209#217—61no—
210#217—61no—
211#217—61no—
212#217—61no—
213#217—61no—
214#217—61no—
215(C2×D3)⋊C4—62no—
216(C2×D3)⋊C4—62no—
217(C2×D3)⋊C4—61no—
218(C2×D3)⋊C4—61no—
219(C2×D3)⋊C4—61no—
220(C2×D3)⋊C4—61no—
221C4⋊Dic3—31no—
222C4⋊Dic3—31no—
223C4⋊Dic3—31no—
224C4⋊Dic3—31no—
225C4⋊Dic3—61no—
226C4⋊Dic3—61no—
227Dic3⋊C4—62no—
228Dic3⋊C4—62no—
229Dic3⋊C4—61no—
230Dic3⋊C4—61no—
231Dic3⋊C4—61no—
232Dic3⋊C4—61no—
233C4×Dic3—62no—
234C4×Dic3—61no—
235C4×Dic3—61no—
236#208—42no—
237C2×C3⋊C8—22no—
238C22×C32—24no—
239C22×C32—24no—
240C22×C32—21no—
241C22×C32—21no—
242C22×C32—21no—
243C22×C32—21no—
244C22×C32—21no—
245C22×C32—21no—
246C22×C32#9912yes—
247C22×C32#10412yes—
248C22×C32C2×C22⋊C411yescharacteristic
249C22×C32AGL(1,ℤ/8)11yescharacteristic
250C22×C32#13711yescharacteristic
251C2×C3⋊D3—41no—
252C2×C3⋊D3—41no—
253C2×C3⋊D3—41no—
254C32×C4—21no—
255C32×C4—21no—
256C32×C4—21no—
257C32×C4—21no—
258C3⋊Dic3—41no—
259C3⋊Dic3—41no—
260C3⋊Dic3—41no—
261C3×Dic3—44no—
262C2×#41—91no—
263C23×C4—61no—
264C23×C4D3211yescharacteristic
265C2×M16—61no—
266#123—181no—
267C22⋊Q8—91no—
268C22⋊Q8—91no—
269#121—91no—
270#121—91no—
271#120—181no—
272C4×D4—181no—
273C4×D4—181no—
274#117—91no—
275C22⋊C8—32no—
276C22⋊C8—61no—
277#95—32no—
278#95—61no—
279C23×C3—22no—
280C23×C3—22no—
281C23×C3—22no—
282C23×C3—22no—
283C23×C3—21no—
284C23×C3—21no—
285C23×C3—21no—
286C23×C3—21no—
287C23×C3—21no—
288C23×C3—21no—
289C23×C3—21no—
290C23×C3—42no—
291C23×C3—42no—
292C23×C3—41no—
293C23×C3—41no—
294C23×C3(C2×D3)⋊C411yescharacteristic
295C23×C3(C2×D3)⋊C411yescharacteristic
296C23×C3(C2×D3)⋊C411yescharacteristic
297C23×C3(C2×D3)⋊C411yescharacteristic
298C23×C3C2×D1211yescharacteristic
299C23×C3C2×#6711yescharacteristic
300C22×D3—62no—
301C22×D3—61no—
302C22×D3—61no—
303C2×C3×C4—24no—
304C2×C3×C4—22no—
305C2×C3×C4—22no—
306C2×C3×C4—22no—
307C2×C3×C4—22no—
308C2×C3×C4—21no—
309C2×C3×C4—21no—
310C2×C3×C4—21no—
311C2×C3×C4—21no—
312C2×C3×C4—42no—
313C2×C3×C4—41no—
314C2×C3×C4—41no—
315C2×C3×C4—41no—
316C2×C3×C4—41no—
317C2×C3×C4—41no—
318C2×C3×C4—41no—
319C2×C3×C4—41no—
320C2×C3×C4—41no—
321C2×C3×C4—42no—
322C2×C3×C4—42no—
323C2×C3×C4—42no—
324C2×C3×C4—42no—
325C2×C3×C4—64no—
326C2×C3×C4—128no—
327C2×C3×C4—122no—
328C2×C3×C4—122no—
329C2×C3×C4(C2×D3)⋊C411yescharacteristic
330C2×C3×C4(C2×D3)⋊C411yescharacteristic
331C2×C3×C4(C2×D3)⋊C411yescharacteristic
332C2×C3×C4(C2×D3)⋊C411yescharacteristic
333C2×C3×C4C2×C4×D311yescharacteristic
334C2×C3×C4C2×C4×D311yescharacteristic
335C2×C3×C4C2×D1211yescharacteristic
336C2×C3×C4C2×#6711yescharacteristic
337#67—124no—
338#67—124no—
339#67—122no—
340#67—122no—
341#67—122no—
342#67—122no—
343#67—122no—
344#67—122no—
345#67—121no—
346#67—121no—
347#67—121no—
348#67—121no—
349C2×Dic3—24no—
350C2×Dic3—48no—
351C2×Dic3—42no—
352C2×Dic3—42no—
353C2×Dic3—62no—
354C2×Dic3—62no—
355C2×Dic3—62no—
356C2×Dic3—61no—
357C2×Dic3—61no—
358C2×Dic3—61no—
359C2×Dic3—61no—
360C2×Dic3—61no—
361C2×Dic3—61no—
362D12—121no—
363D12—121no—
364D12—122no—
365C4×D3—124no—
366C4×D3—122no—
367C4×D3—122no—
368Dic6—122no—
369Dic6—121no—
370Dic6—121no—
371C3×C8—122no—
372C3⋊C8—42no—
373C2×C32—21no—
374C2×C32—22no—
375C2×C32—22no—
376C2×C32—21no—
377C2×C32C2×#9911yescharacteristic
378C2×C32#41711yescharacteristic
379C2×C32C2×#10411yescharacteristic
380C3⋊D3—81no—
381C24#62611yescharacteristic
382#41—362no—
383C2×Q8—91no—
384C2×D4—91no—
385C2×D4—181no—
386C2×D4—181no—
387C2×D4—181no—
388C22×C4—42no—
389C22×C4—64no—
390C22×C4—62no—
391C22×C4—122no—
392C22×C4—122no—
393C22×C4—181no—
394C22×C4#62411yescharacteristic
395C22×C4#62411yescharacteristic
396C22×C4#62611yescharacteristic
397C22×C4#62611yescharacteristic
398C22×C4#62611yescharacteristic
399C22×C4C2×D3211yescharacteristic
400M16—122no—
401C2×C8—62no—
402C4⋊C4—91no—
403C4⋊C4—91no—
404C4⋊C4—181no—
405C4⋊C4—181no—
406C22⋊C4—181no—
407C22⋊C4—181no—
408C22⋊C4—181no—
409C22⋊C4—181no—
410C22⋊C4—181no—
411C42—181no—
412C22×C3—24no—
413C22×C3—24no—
414C22×C3—24no—
415C22×C3—24no—
416C22×C3—21no—
417C22×C3—21no—
418C22×C3—21no—
419C22×C3—21no—
420C22×C3—21no—
421C22×C3—21no—
422C22×C3—21no—
423C22×C3—21no—
424C22×C3—21no—
425C22×C3—21no—
426C22×C3—21no—
427C22×C3—21no—
428C22×C3—22no—
429C22×C3—21no—
430C22×C3—21no—
431C22×C3—22no—
432C22×C3—21no—
433C22×C3—41no—
434C22×C3—41no—
435C22×C3—41no—
436C22×C3—41no—
437C22×C3—41no—
438C22×C3—41no—
439C22×C3—44no—
440C22×C3—44no—
441C22×C3#80512yes—
442C22×C3#80612yes—
443C22×C3#80612yes—
444C22×C3#82512yes—
445C22×C3#90811yescharacteristic
446C22×C3#90911yescharacteristic
447C22×C3C2×(C2×D3)⋊C411yescharacteristic
448C22×C3C2×(C2×D3)⋊C411yescharacteristic
449C22×C3#93211yescharacteristic
450C22×C3#94211yescharacteristic
451C2×D3—122no—
452C2×D3—122no—
453C2×D3—122no—
454C2×D3—121no—
455C2×D3—121no—
456C2×D3—121no—
457C2×D3—121no—
458C2×D3—121no—
459C2×D3—121no—
460C3×C4—22no—
461C3×C4—22no—
462C3×C4—21no—
463C3×C4—21no—
464C3×C4—21no—
465C3×C4—21no—
466C3×C4—21no—
467C3×C4—21no—
468C3×C4—21no—
469C3×C4—21no—
470C3×C4—41no—
471C3×C4—41no—
472C3×C4—124no—
473Dic3—44no—
474Dic3—122no—
475Dic3—122no—
476Dic3—122no—
477Dic3—121no—
478Dic3—121no—
479Dic3—121no—
480Dic3—121no—
481Dic3—121no—
482Dic3—121no—
483C32#150411yescharacteristic, complemented, Sylow
484C23—22no—
485C23—21no—
486C23—21no—
487C23—22no—
488C23—181no—
489C23#372211yescharacteristic
490C23#372211yescharacteristic
491C23C2×#62611yescharacteristic
492Q8—361no—
493D4—361no—
494D4—362no—
495D4—361no—
496D4—361no—
497D4—362no—
498C2×C4—22no—
499C2×C4—22no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—64no—
505C2×C4—128no—
506C2×C4—122no—
507C2×C4—122no—
508C2×C4—181no—
509C2×C4—181no—
510C2×C4—181no—
511C2×C4—362no—
512C2×C4#372211yescharacteristic
513C2×C4#372211yescharacteristic
514C2×C4C2×#62411yescharacteristic
515C2×C4C2×#62611yescharacteristic
516C8—122no—
517C2×C3—21no—
518C2×C3—22no—
519C2×C3—22no—
520C2×C3—21no—
521C2×C3—21no—
522C2×C3—22no—
523C2×C3—22no—
524C2×C3—21no—
525C2×C3—21no—
526C2×C3—21no—
527C2×C3—21no—
528C2×C3—41no—
529C2×C3—42no—
530C2×C3—41no—
531C2×C3—42no—
532C2×C3C2×#80511yescharacteristic
533C2×C3C2×#80611yescharacteristic
534C2×C3C2×#80611yescharacteristic
535C2×C3#496611yescharacteristic
536C2×C3#513311yescharacteristic
537C2×C3C2×#82511yescharacteristic
538D3—242no—
539D3—241no—
540D3—241no—
541C22—24no—
542C22—24no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—21no—
547C22—21no—
548C22—21no—
549C22—361no—
550C22—361no—
551C22—361no—
552C22#6357012yes—
553C22#6358112yes—
554C22#6383011yescharacteristic
555C22#6383311yescharacteristic
556C22C2×#372211yescharacteristic
557C4—21no—
558C4—21no—
559C4—21no—
560C4—21no—
561C4—124no—
562C4—361no—
563C4—361no—
564C4—361no—
565C3—21no—
566C3#6939811yescharacteristic, complemented
567C3#6997611yescharacteristic, complemented
568C2—21no—
569C2—22no—
570C2—21no—
571C2—22no—
572C2—721no—
573C2#1059110611yescharacteristic
574C2C2×#6357011yescharacteristic
575C2C2×#6358111yescharacteristic
subgroupG/H
centerC22C2×#3722
commutatorC2×C32×C4C22×C4
FrattiniC22×C4C2×D32
FittingC23×C32×C4C22
socleC22×C32C2×C22⋊C4
prime radical#10596262C2
cosocleC22×C32×C4C23
hypercenterC23×C4D32
hypocenterC32#1504
LCSG ▷ C2×C32×C4 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
2. C2×C3×C3⋊#95C2semidirect
3. C3×#5207C2semidirect
4. #10589154C2semidirect
5. #10589151C2semidirect
9. C2×#3828C4semidirect
12. #64139C4semidirect
17. #64135C4semidirect
18. #64133C4semidirect
30. C2×C3⋊#95D3semidirect
31. #5207D3semidirect
48. C2×C4⋊(C3⋊D3)C2×C4semidirect
50. C2×#634C2×C4semidirect
60. C4⋊(C3⋊Dic3)C2×C4semidirect
61. C4⋊(C3⋊Dic3)C2×C4semidirect
483. C32#1504semidirect
566. C3#69398semidirect
567. C3#69976semidirect

Maximal subgroups

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

subgroupindex
#105962622
C2×C3×C3⋊#952
C3×#52072
#105891542
#105891512
#699763
#693983