Finite Group Databasebeta

← #11803451

Subgroups — #11803451

Order 1152.

1668 conjugacy classes of subgroups.

The subgroup lattice has 561 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64105C211yesmaximal, characteristic
2C2×#64101C211yesmaximal, characteristic
3C2×C4×#634C211yesmaximal, characteristic, complemented
4C32×#387C211yesmaximal, characteristic, complemented
5#10592683C211yesmaximal, characteristic, complemented
6#10592677C211yesmaximal, characteristic, complemented
7#10592639C211yesmaximal, characteristic
8#10592369C211yesmaximal, characteristic
9#10592369C211yesmaximal, characteristic
10#10592368C211yesmaximal, characteristic
11#10592366C211yesmaximal, characteristic
12#10592348C211yesmaximal, characteristic, complemented
13#10592346C211yesmaximal, characteristic, complemented
14#10592346C211yesmaximal, characteristic, complemented
15#10592345C211yesmaximal, characteristic, complemented
16#74947—34nomaximal
17C22×C4×C3⋊D3C2211yescharacteristic
18C22×#634C2211yescharacteristic
19C2×C32×C4⋊C4C2211yescharacteristic
20C2×C32×C4⋊C4C2211yescharacteristic
21C2×C32×C42C2211yescharacteristic
22C2×#3752C2211yescharacteristic
23C2×#3752C2211yescharacteristic
24C2×#3752C2211yescharacteristic
25C2×#3752C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
30C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
31C2×#3750C2211yescharacteristic
32C2×#3750C2211yescharacteristic
33C2×#3750C2211yescharacteristic
34C2×#3750C2211yescharacteristic
35C2×#3750C2211yescharacteristic
36C2×#3750C2211yescharacteristic
37C2×C4×C3⋊Dic3C2211yescharacteristic
38C2×C4×C3⋊Dic3C2211yescharacteristic
39C2×C4×C3⋊Dic3C2211yescharacteristic
40C2×C4×C3⋊Dic3C2211yescharacteristic
41C2×C4×C3⋊Dic3C2211yescharacteristic
42#64105C418yescomplemented
43#64101—24no—
44C4×#634—24no—
45C32×#95C2211yescharacteristic
46C32×#95C2211yescharacteristic
47C32×#95C2211yescharacteristic
48C32×#95C2211yescharacteristic
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63658C2211yescharacteristic
54#63658C2211yescharacteristic
55C2×#896—34no—
56C2×#892—34no—
57C2×C4×Dic6—34no—
58C3×#387D314yescomplemented
59#4984—34no—
60#4978—34no—
61#4940—34no—
62#4670—34no—
63#4670—34no—
64#4669—34no—
65#4667—34no—
66#4649—34no—
67#4647—34no—
68#4647—34no—
69#4646—34no—
70C23×C3⋊D3C2311yescharacteristic
71C22×C32×C4C2311yescharacteristic
72C22×C32×C4C2311yescharacteristic
73C22×C32×C4C2311yescharacteristic
74C22×C32×C4C2311yescharacteristic
75C22×C32×C4C2311yescharacteristic
76C22×C32×C4C2311yescharacteristic
77C22×C32×C4C2311yescharacteristic
78C22×C3⋊Dic3C2311yescharacteristic
79C22×C3⋊Dic3C2311yescharacteristic
80C22×C3⋊Dic3C2311yescharacteristic
81C22×C3⋊Dic3C2311yescharacteristic
82C22×C3⋊Dic3C2311yescharacteristic
83C22×C3⋊Dic3C2311yescharacteristic
84C22×C3⋊Dic3C2311yescharacteristic
85C2×C4×C3⋊D3—22no—
86C2×C4×C3⋊D3—22no—
87C2×C4×C3⋊D3C2×C414yes—
88C2×#634—22no—
89C2×#634—22no—
90C2×#634C2×C414yes—
91C32×C4⋊C4—22no—
92C32×C4⋊C4C2×C414yes—
93C32×C42—22no—
94#3752—22no—
95#3752—22no—
96#3752—41no—
97#3752—41no—
98#3752C2×C414yes—
99#3752C2×C414yes—
100C4⋊(C3⋊Dic3)—22no—
101C4⋊(C3⋊Dic3)—22no—
102C4⋊(C3⋊Dic3)—41no—
103#3750—22no—
104#3750—22no—
105#3750—22no—
106#3750—41no—
107#3750C2×C414yes—
108#3750C2×C414yes—
109C4×C3⋊Dic3—22no—
110C4×C3⋊Dic3—22no—
111C4×C3⋊Dic3—41no—
112C4×C3⋊Dic3—41no—
113C4×C3⋊Dic3D414yes—
114#2323—91noSylow
115C22×C4×D3—34no—
116C22×Dic6—34no—
117C2×C3×C4⋊C4C2×D314yes—
118C2×C3×C4⋊C4C2×D314yes—
119C2×C3×C42C2×D314yes—
120C2×(C2×D3)⋊C4—34no—
121C2×(C2×D3)⋊C4—34no—
122C2×(C2×D3)⋊C4—34no—
123C2×(C2×D3)⋊C4—34no—
124C2×(C2×D3)⋊C4—34no—
125C2×(C2×D3)⋊C4—34no—
126C2×C4⋊Dic3—34no—
127C2×C4⋊Dic3—34no—
128C2×C4⋊Dic3—34no—
129C2×Dic3⋊C4—34no—
130C2×Dic3⋊C4—34no—
131C2×Dic3⋊C4—34no—
132C2×Dic3⋊C4—34no—
133C2×Dic3⋊C4—34no—
134C2×Dic3⋊C4—34no—
135C2×C4×Dic3—34no—
136C2×C4×Dic3—34no—
137C2×C4×Dic3—34no—
138C2×C4×Dic3—34no—
139C2×C4×Dic3—34no—
140#896—332no—
141#892—616no—
142C4×Dic6—616no—
143C3×#95C2×D314yes—
144C3×#95C2×D314yes—
145C3×#95C2×D314yes—
146C3×#95C2×D314yes—
147C3⋊#95—34no—
148C3⋊#95—34no—
149C3⋊#95—34no—
150C3⋊#95—34no—
151C3⋊#95—34no—
152C3⋊#95—34no—
153C23×C32C2411yescharacteristic
154C22×C3⋊D3—21no—
155C22×C3⋊D3—21no—
156C22×C3⋊D3—21no—
157C22×C3⋊D3—21no—
158C22×C3⋊D3—21no—
159C22×C3⋊D3—21no—
160C22×C3⋊D3C22×C412yes—
161C2×C32×C4—21no—
162C2×C32×C4—21no—
163C2×C32×C4—21no—
164C2×C32×C4—21no—
165C2×C32×C4—21no—
166C2×C32×C4—21no—
167C2×C32×C4—21no—
168C2×C32×C4—21no—
169C2×C32×C4—21no—
170C2×C32×C4—21no—
171C2×C32×C4—21no—
172C2×C32×C4—21no—
173C2×C32×C4—21no—
174C2×C32×C4—21no—
175C2×C32×C4—21no—
176C2×C32×C4—21no—
177C2×C32×C4—21no—
178C2×C32×C4C22×C412yes—
179C2×C32×C4C22×C412yes—
180C2×C32×C4C22×C412yes—
181C2×C32×C4C2×D412yes—
182C2×C3⋊Dic3—21no—
183C2×C3⋊Dic3—21no—
184C2×C3⋊Dic3—21no—
185C2×C3⋊Dic3—21no—
186C2×C3⋊Dic3—21no—
187C2×C3⋊Dic3—21no—
188C2×C3⋊Dic3—21no—
189C2×C3⋊Dic3—21no—
190C2×C3⋊Dic3—21no—
191C2×C3⋊Dic3—21no—
192C2×C3⋊Dic3—21no—
193C2×C3⋊Dic3—21no—
194C2×C3⋊Dic3—21no—
195C2×C3⋊Dic3—21no—
196C2×C3⋊Dic3—21no—
197C2×C3⋊Dic3C22×C412yes—
198C2×C3⋊Dic3C22×C412yes—
199C2×C3⋊Dic3C22×C412yes—
200C2×C3⋊Dic3C2×D412yes—
201C2×C3⋊Dic3C2×D412yes—
202C2×C3⋊Dic3#4112yes—
203C4×C3⋊D3—28no—
204#634—28no—
205C2×C22⋊Q8—91no—
206C2×C4×Q8—91no—
207C2×#117—91no—
208#391—91no—
209#389—91no—
210#389—91no—
211#389—91no—
212#388—91no—
213#388—91no—
214#388—91no—
215#388—91no—
216#387—91no—
217#387C3⋊D311yescharacteristic, complemented
218#380—91no—
219C4×C4⋊C4—91no—
220C23×D3—34no—
221C22×C3×C4C22×D314yes—
222C22×C3×C4C22×D314yes—
223C22×C3×C4C22×D314yes—
224C22×C3×C4C22×D314yes—
225C22×C3×C4C22×D314yes—
226C22×C3×C4C22×D314yes—
227C22×C3×C4C22×D314yes—
228C22×Dic3—34no—
229C22×Dic3—34no—
230C22×Dic3—34no—
231C22×Dic3—34no—
232C22×Dic3—34no—
233C22×Dic3—34no—
234C22×Dic3—34no—
235C2×C4×D3—316no—
236C2×C4×D3—68no—
237C2×C4×D3—68no—
238C2×Dic6—316no—
239C2×Dic6—68no—
240C2×Dic6—68no—
241C3×C4⋊C4—28no—
242C3×C4⋊C4C4×D3116yes—
243C3×C42—28no—
244(C2×D3)⋊C4—316no—
245(C2×D3)⋊C4—316no—
246(C2×D3)⋊C4—68no—
247(C2×D3)⋊C4—68no—
248(C2×D3)⋊C4—124no—
249(C2×D3)⋊C4—124no—
250C4⋊Dic3—68no—
251C4⋊Dic3—68no—
252C4⋊Dic3—124no—
253Dic3⋊C4—316no—
254Dic3⋊C4—316no—
255Dic3⋊C4—68no—
256Dic3⋊C4—68no—
257Dic3⋊C4—68no—
258Dic3⋊C4—124no—
259C4×Dic3—316no—
260C4×Dic3—68no—
261C4×Dic3—68no—
262C4×Dic3—124no—
263C4×Dic3—124no—
264C22×C32C23×C411yescharacteristic
265C22×C32C22×D411yescharacteristic
266C22×C32C2×#4111yescharacteristic
267C22×C32H(5,𝔽2)11yescharacteristic
268C22×C322−1+411yescharacteristic
269C22×C322−1+411yescharacteristic
270C22×C322−1+411yescharacteristic
271C2×C3⋊D3—22no—
272C2×C3⋊D3—22no—
273C2×C3⋊D3—22no—
274C2×C3⋊D3—41no—
275C2×C3⋊D3—41no—
276C2×C3⋊D3—41no—
277C2×C3⋊D3—41no—
278C32×C4—22no—
279C32×C4—22no—
280C32×C4—22no—
281C32×C4—22no—
282C32×C4—41no—
283C32×C4—41no—
284C32×C4—41no—
285C3⋊Dic3—22no—
286C3⋊Dic3—22no—
287C3⋊Dic3—22no—
288C3⋊Dic3—41no—
289C3⋊Dic3—41no—
290C3⋊Dic3—41no—
291C3⋊Dic3C4×D414yes—
292C22×Q8—91no—
293C23×C4—91no—
294C22⋊Q8—98no—
295C4×Q8—184no—
296#117—184no—
297C2×C4⋊C4—91no—
298C2×C4⋊C4—91no—
299C2×C4⋊C4—91no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—91no—
302C2×C4⋊C4—91no—
303C2×C4⋊C4—91no—
304C2×C4⋊C4—91no—
305C2×C4⋊C4—91no—
306C2×C4⋊C4C2×C3⋊D311yescharacteristic
307C2×C4⋊C4C2×C3⋊D311yescharacteristic
308C2×C22⋊C4—91no—
309C2×C22⋊C4—91no—
310C2×C22⋊C4—91no—
311C2×C22⋊C4—91no—
312C2×C22⋊C4—91no—
313C2×C22⋊C4—91no—
314C2×C42—91no—
315C2×C42—91no—
316C2×C42—91no—
317C2×C42—91no—
318C2×C42—91no—
319C2×C42C2×C3⋊D311yescharacteristic
320#95—91no—
321#95—91no—
322#95—91no—
323#95—91no—
324#95—91no—
325#95—91no—
326#95C2×C3⋊D311yescharacteristic
327#95C2×C3⋊D311yescharacteristic
328#95C2×C3⋊D311yescharacteristic
329#95C2×C3⋊D311yescharacteristic
330C23×C3C23×D314yes—
331C22×D3—38no—
332C22×D3—64no—
333C22×D3—64no—
334C22×D3—64no—
335C22×D3—64no—
336C22×D3—64no—
337C22×D3—64no—
338C2×C3×C4—24no—
339C2×C3×C4—24no—
340C2×C3×C4—24no—
341C2×C3×C4—24no—
342C2×C3×C4—24no—
343C2×C3×C4—24no—
344C2×C3×C4—24no—
345C2×C3×C4—24no—
346C2×C3×C4—24no—
347C2×C3×C4—24no—
348C2×C3×C4—24no—
349C2×C3×C4—24no—
350C2×C3×C4—24no—
351C2×C3×C4—24no—
352C2×C3×C4—24no—
353C2×C3×C4—24no—
354C2×C3×C4—24no—
355C2×C3×C4C2×C4×D318yes—
356C2×C3×C4C2×C4×D318yes—
357C2×C3×C4C2×C4×D318yes—
358C2×C3×C4D3×D418yes—
359C2×Dic3—38no—
360C2×Dic3—38no—
361C2×Dic3—38no—
362C2×Dic3—38no—
363C2×Dic3—38no—
364C2×Dic3—38no—
365C2×Dic3—64no—
366C2×Dic3—64no—
367C2×Dic3—64no—
368C2×Dic3—64no—
369C2×Dic3—64no—
370C2×Dic3—64no—
371C2×Dic3—64no—
372C2×Dic3—64no—
373C2×Dic3—64no—
374C2×Dic3—64no—
375C2×Dic3—64no—
376C2×Dic3—64no—
377C2×Dic3—64no—
378C2×Dic3—64no—
379C2×Dic3—64no—
380C4×D3—632no—
381Dic6—632no—
382C2×C32C2×C4×D411yescharacteristic
383C2×C32#51911yescharacteristic
384C2×C32#52011yescharacteristic
385C2×C32#53611yescharacteristic
386C2×C32#53711yescharacteristic
387C2×C32#54111yescharacteristic
388C2×C32#54211yescharacteristic
389C3⋊D3—42no—
390C24—91no—
391C2×Q8—94no—
392C2×Q8—182no—
393C2×Q8—182no—
394C22×C4—91no—
395C22×C4—91no—
396C22×C4—91no—
397C22×C4—91no—
398C22×C4—94no—
399C22×C4—91no—
400C22×C4—91no—
401C22×C4—91no—
402C22×C4—182no—
403C22×C4—182no—
404C22×C4C22×C3⋊D311yescharacteristic
405C22×C4C22×C3⋊D311yescharacteristic
406C22×C4C22×C3⋊D311yescharacteristic
407C22×C4C22×C3⋊D311yescharacteristic
408C22×C4C22×C3⋊D311yescharacteristic
409C22×C4C22×C3⋊D311yescharacteristic
410C22×C4C22×C3⋊D311yescharacteristic
411C4⋊C4—22no—
412C4⋊C4—94no—
413C4⋊C4—94no—
414C4⋊C4—182no—
415C4⋊C4—182no—
416C4⋊C4—182no—
417C4⋊C4—182no—
418C4⋊C4—182no—
419C4⋊C4—361no—
420C4⋊C4—361no—
421C4⋊C4C4×C3⋊D314yes—
422C22⋊C4—94no—
423C22⋊C4—94no—
424C22⋊C4—182no—
425C22⋊C4—182no—
426C22⋊C4—361no—
427C22⋊C4—361no—
428C42—22no—
429C42—94no—
430C42—182no—
431C42—182no—
432C42—361no—
433C42—361no—
434C22×C3C22×C4×D314yes—
435C22×C3C2×D3×D414yes—
436C22×C3#100714yes—
437C22×C3D3×#4114yes—
438C22×C3#100914yes—
439C22×C3#101014yes—
440C22×C3#101014yes—
441C2×D3—68no—
442C2×D3—68no—
443C2×D3—68no—
444C2×D3—124no—
445C2×D3—124no—
446C2×D3—124no—
447C2×D3—124no—
448C3×C4—28no—
449C3×C4—28no—
450C3×C4—28no—
451C3×C4—28no—
452C3×C4—44no—
453C3×C4—44no—
454C3×C4—44no—
455Dic3—316no—
456Dic3—68no—
457Dic3—68no—
458Dic3—68no—
459Dic3—124no—
460Dic3—124no—
461Dic3—124no—
462C32#232311yescharacteristic, complemented, Sylow
463C23—92no—
464C23—181no—
465C23—181no—
466C23—181no—
467C23—181no—
468C23—181no—
469C23—181no—
470C23C23×C3⋊D311yescharacteristic
471Q8—188no—
472C2×C4—21no—
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—21no—
488C2×C4—21no—
489C2×C4—92no—
490C2×C4—92no—
491C2×C4—92no—
492C2×C4—92no—
493C2×C4—92no—
494C2×C4—92no—
495C2×C4—188no—
496C2×C4—181no—
497C2×C4—181no—
498C2×C4—181no—
499C2×C4—181no—
500C2×C4—181no—
501C2×C4—181no—
502C2×C4—181no—
503C2×C4—181no—
504C2×C4—181no—
505C2×C4—181no—
506C2×C4—181no—
507C2×C4—181no—
508C2×C4—181no—
509C2×C4—181no—
510C2×C4—181no—
511C2×C4C2×C4×C3⋊D312yes—
512C2×C4C2×C4×C3⋊D312yes—
513C2×C4C2×C4×C3⋊D312yes—
514C2×C4D4×C3⋊D312yes—
515C2×C3#552314yes—
516C2×C3C4×D3×D414yes—
517C2×C3#557214yes—
518C2×C3#562914yes—
519C2×C3#564814yes—
520C2×C3#569614yes—
521C2×C3#571014yes—
522D3—128no—
523C22—182no—
524C22—182no—
525C22—182no—
526C22—361no—
527C22—361no—
528C22—361no—
529C22—361no—
530C22C22×C4×C3⋊D311yescharacteristic
531C22C2×D4×C3⋊D311yescharacteristic
532C22#6436411yescharacteristic
533C22#41×C3⋊D311yescharacteristic
534C22#6436611yescharacteristic
535C22#6436711yescharacteristic
536C22#6436711yescharacteristic
537C4—22no—
538C4—22no—
539C4—22no—
540C4—22no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—94no—
545C4—182no—
546C4—182no—
547C4—182no—
548C4—361no—
549C4—361no—
550C4—361no—
551C3#7494714yescomplemented
552C2—362no—
553C2#1059599411yescharacteristic
554C2C4×D4×C3⋊D311yescharacteristic
555C2#1059604311yescharacteristic
556C2#1059610011yescharacteristic
557C2#1059611911yescharacteristic
558C2#1059616711yescharacteristic
559C2#1059618111yescharacteristic
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#387C2
socle, cosocleC23×C32C24
prime radicalC23×C3⋊D3C23
hypercenter#387C3⋊D3
hypocenterC32#2323
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #387

Complements

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

NH ≅ G/Ntype
3. C2×C4×#634C2semidirect
4. C32×#387C2semidirect
5. #10592683C2semidirect
6. #10592677C2semidirect
12. #10592348C2semidirect
13. #10592346C2semidirect
14. #10592346C2semidirect
15. #10592345C2semidirect
42. #64105C4semidirect
58. C3×#387D3semidirect
217. #387C3⋊D3semidirect
462. C32#2323semidirect
551. C3#74947semidirect

Maximal subgroups

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

subgroupindex
C2×#641052
C2×#641012
C2×C4×#6342
C32×#3872
#105926832
#105926772
#105926392
#105923692
#105923682
#105923662
#105923482
#105923462
#105923452
#749473