Finite Group Databasebeta

← #11802739

Subgroups — #11802739

Order 1152.

1889 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3799C211yesmaximal, characteristic
2C2×C3×#872C211yesmaximal, characteristic, complemented
3C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
4#10592638C211yesmaximal, characteristic, complemented
5C3×#4929C211yesmaximal, characteristic, complemented
6#10591367C214yesmaximal, complemented
7#10591364C214yesmaximal, complemented
8#10591320C211yesmaximal, characteristic, complemented
9#10591220C211yesmaximal, characteristic, complemented
10#82270—31nomaximal
11#76482—31nomaximal
12C22×C4⋊(C3⋊D3)C2211yescharacteristic
13C22×C3×C4×D3C2211yescharacteristic
14C22×C3×Dic6C2211yescharacteristic
15C22×#626C2212yes—
16C22×#624C2212yes—
17C22×D3×Dic3C2212yes—
18C2×#3799—24no—
19C2×#3799—24no—
20C2×#3799C418yescomplemented
21C2×C32×C42C2211yescharacteristic
22C2×#3752C2214yes—
23C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
24C2×C3×(C2×D3)⋊C4C2212yes—
25C2×C3×C4⋊Dic3C2211yescharacteristic
26C2×C3×Dic3⋊C4C2212yes—
27C2×C3×C4×Dic3C2211yescharacteristic
28C3×#872—24no—
29C2×Dic3⋊Dic3C2212yes—
30C2×#3722C2214yes—
31D3×C4⋊Dic3—24no—
32C3×C3⋊#95C2214yes—
33#63579C2214yes—
34C22×#239—31no—
35C22×#235—31no—
36C2×C3×#117—31no—
37C22×C4⋊Dic3—31no—
38C2×D3×C4⋊C4—31no—
39C2×#872D311yescharacteristic, complemented
40C3×#391—31no—
41#5229—31no—
42#4988—31no—
43#4987—34no—
44#4958—34no—
45#4939—31no—
46#4939—31no—
47#4939—31no—
48#4939—61no—
49#4929—31no—
50#4929D311yescharacteristic, complemented
51#4667—34no—
52#4665—34no—
53C23×C3⋊D3C2312yes—
54C23×C3×D3C2311yescharacteristic
55C22×C32×C4C2312yes—
56C22×C32×C4C2311yescharacteristic
57C22×C3⋊Dic3C2312yes—
58C2×C4⋊(C3⋊D3)—22no—
59C2×C4⋊(C3⋊D3)—22no—
60C2×C4⋊(C3⋊D3)C2×C414yescomplemented
61C22×C3×Dic3C2312yes—
62C22×C3×Dic3C2312yes—
63C22×C3×Dic3C2312yes—
64C22×C3×Dic3C2311yescharacteristic
65C2×C3×C4×D3C2×C414yes—
66C2×C3×C4×D3D414yes—
67C2×C3×C4×D3D414yes—
68C2×C3×Dic6—22no—
69C2×C3×Dic6—22no—
70C2×C3×Dic6C2×C414yescomplemented
71C2×#626—24no—
72C2×#626—24no—
73C2×#626C2×C418yes—
74C2×#624—24no—
75C2×#624—24no—
76C2×#624C2×C418yescomplemented
77C2×D3×Dic3—24no—
78C2×D3×Dic3—44no—
79#3799—232no—
80C32×C42—22no—
81#3752—44no—
82C4⋊(C3⋊Dic3)—22no—
83C3×(C2×D3)⋊C4—24no—
84C3×C4⋊Dic3—22no—
85C3×Dic3⋊C4—24no—
86C3×C4×Dic3—22no—
87Dic3⋊Dic3—24no—
88#3722—44no—
89#2311—91noSylow
90C22×C3×Q8—31no—
91C23×C3×C4—31no—
92C22×#67—32no—
93C23×Dic3—32no—
94C2×#239—38no—
95C2×#239—64no—
96C2×#239—64no—
97C2×#235—38no—
98C2×#235—64no—
99C2×#235—64no—
100C22×D12—32no—
101C22×D12—31no—
102C22×D12—31no—
103C22×D12—61no—
104C22×C4×D3—32no—
105C22×C4×D3—32no—
106C22×C4×D3—32no—
107C22×C4×D3C2×D311yescharacteristic
108C22×Dic6C2×D311yescharacteristic
109C3×#117—64no—
110C2×C3×C4⋊C4—32no—
111C2×C3×C4⋊C4—31no—
112C2×C3×C22⋊C4—32no—
113C2×C3×C42—21no—
114C2×C3×C42—31no—
115C2×C3×C42C2×D311yescharacteristic
116C2×C3×C42C2×D311yescharacteristic
117C2×(C2×D3)⋊C4—34no—
118C2×(C2×D3)⋊C4—34no—
119C2×(C2×D3)⋊C4—34no—
120C2×(C2×D3)⋊C4—34no—
121C2×(C2×D3)⋊C4—64no—
122C2×(C2×D3)⋊C4C2×D312yes—
123C2×C4⋊Dic3—31no—
124C2×C4⋊Dic3—31no—
125C2×C4⋊Dic3—32no—
126C2×C4⋊Dic3—61no—
127C2×C4⋊Dic3—64no—
128C2×C4⋊Dic3C2×D311yescharacteristic
129C2×Dic3⋊C4—32no—
130C2×Dic3⋊C4C2×D312yes—
131C2×C4×Dic3C2×D311yescharacteristic
132D3×C4⋊C4—64no—
133#872—24no—
134C3×#95—34no—
135C3⋊#95—34no—
136C3⋊#95—34no—
137C3⋊#95C2×D314yes—
138C23×C32C2411yescharacteristic
139C22×C3⋊D3—22no—
140C22×C3⋊D3—22no—
141C22×C3⋊D3—24no—
142C22×C3⋊D3—24no—
143C22×C3⋊D3C22×C414yes—
144C22×C3×D3—22no—
145C22×C3×D3—22no—
146C22×C3×D3C22×C412yes—
147C22×C3×D3C2×D412yes—
148C22×C3×D3C2×D412yes—
149C2×C32×C4—22no—
150C2×C32×C4—22no—
151C2×C32×C4—22no—
152C2×C32×C4C22×C412yes—
153C2×C32×C4C2×D412yes—
154C2×C32×C4C2×D412yes—
155C2×C3⋊Dic3—22no—
156C2×C3⋊Dic3—24no—
157C4⋊(C3⋊D3)—28no—
158C2×C3×Dic3—22no—
159C2×C3×Dic3—22no—
160C2×C3×Dic3—22no—
161C2×C3×Dic3—22no—
162C2×C3×Dic3—22no—
163C2×C3×Dic3—24no—
164C2×C3×Dic3—22no—
165C2×C3×Dic3C22×C414yes—
166C2×C3×Dic3C22×C412yes—
167C2×C3×Dic3C2×D412yes—
168C2×C3×Dic3C2×D412yes—
169C3×C4×D3C22⋊C4116yescomplemented
170C3×Dic6—28no—
171#626—216no—
172#624—216no—
173D3×Dic3—48no—
174C22×#41—91no—
175C2×#117—31no—
176C22×C4⋊C4—91no—
177#391—31no—
178#391—91no—
179#390—91no—
180#390—91no—
181#386—94no—
182#380—94no—
183C24×C3—31no—
184C23×D3—32no—
185C23×D3—32no—
186C23×D3—62no—
187C23×D3C22×D311yescharacteristic
188C2×C3×Q8—34no—
189C2×C3×Q8—62no—
190C2×C3×Q8—62no—
191C22×C3×C4—21no—
192C22×C3×C4—22no—
193C22×C3×C4—31no—
194C22×C3×C4—34no—
195C22×C3×C4—34no—
196C22×C3×C4—34no—
197C22×C3×C4—32no—
198C22×C3×C4—32no—
199C22×C3×C4—32no—
200C22×C3×C4C22×D312yes—
201C22×C3×C4C22×D312yes—
202C22×C3×C4C22×D311yescharacteristic
203C22×C3×C4C22×D311yescharacteristic
204C2×#67—38no—
205C2×#67—64no—
206C2×#67—64no—
207C22×Dic3—32no—
208C22×Dic3—32no—
209C22×Dic3—62no—
210C22×Dic3—64no—
211C22×Dic3—124no—
212C22×Dic3C22×D312yes—
213C22×Dic3C22×D312yes—
214C22×Dic3C22×D312yes—
215C22×Dic3C22×D311yescharacteristic
216#239—632no—
217#235—632no—
218C2×D12—38no—
219C2×D12—34no—
220C2×D12—34no—
221C2×D12—64no—
222C2×D12—64no—
223C2×D12—64no—
224C2×D12—62no—
225C2×D12—62no—
226C2×D12—62no—
227C2×D12—62no—
228C2×D12—122no—
229C2×D12—122no—
230C2×C4×D3—38no—
231C2×C4×D3—38no—
232C2×C4×D3—64no—
233C2×C4×D3—64no—
234C2×C4×D3—64no—
235C2×C4×D3—64no—
236C2×C4×D3—64no—
237C2×C4×D3—124no—
238C2×C4×D3C4×D314yes—
239C2×C4×D3D1214yes—
240C2×C4×D3#6714yes—
241C2×Dic6—22no—
242C2×Dic6—22no—
243C2×Dic6C4×D314yescomplemented
244C3×C4⋊C4—64no—
245C3×C4⋊C4—62no—
246C3×C22⋊C4—64no—
247C3×C42—22no—
248C3×C42—22no—
249C3×C42—42no—
250C3×C42—62no—
251(C2×D3)⋊C4—24no—
252(C2×D3)⋊C4—124no—
253(C2×D3)⋊C4—124no—
254(C2×D3)⋊C4—124no—
255(C2×D3)⋊C4—124no—
256(C2×D3)⋊C4—128no—
257C4⋊Dic3—22no—
258C4⋊Dic3—64no—
259C4⋊Dic3—62no—
260C4⋊Dic3—62no—
261C4⋊Dic3—122no—
262Dic3⋊C4—24no—
263Dic3⋊C4—64no—
264C4×Dic3—22no—
265C22×C32C23×C411yescharacteristic
266C22×C32C22×D411yescharacteristic
267C22×C32C22×D411yescharacteristic
268C22×C32H(5,𝔽2)12yes—
269C22×C322−1+412yes—
270C2×C3⋊D3—24no—
271C2×C3⋊D3—28no—
272C2×C3⋊D3—42no—
273C2×C3⋊D3—42no—
274C2×C3⋊D3—44no—
275C2×C3×D3—24no—
276C2×C3×D3—22no—
277C2×C3×D3—22no—
278C2×C3×D3—24no—
279C2×C3×D3C2×C22⋊C414yes—
280C32×C4—42no—
281C32×C4C2×C22⋊C414yes—
282C3⋊Dic3—42no—
283C3×Dic3—24no—
284C3×Dic3—42no—
285C3×Dic3—42no—
286C3×Dic3C2×C22⋊C414yes—
287C2×#41—98no—
288C2×#41—184no—
289C2×#41—184no—
290C22×Q8—31no—
291C22×D4—92no—
292C22×D4—91no—
293C23×C4—31no—
294C23×C4—92no—
295C23×C4—92no—
296#117—64no—
297C2×C4⋊C4—31no—
298C2×C4⋊C4—32no—
299C2×C4⋊C4—92no—
300C2×C4⋊C4—91no—
301C2×C4⋊C4—184no—
302C2×C22⋊C4—32no—
303C2×C22⋊C4—94no—
304C2×C22⋊C4—94no—
305C2×C42—31no—
306C2×C42D3211yescharacteristic
307#95—34no—
308#95—94no—
309C23×C3—21no—
310C23×C3—32no—
311C23×C3—32no—
312C23×C3—32no—
313C23×C3—62no—
314C23×C3—62no—
315C23×C3C23×D311yescharacteristic
316C23×C3C23×D311yescharacteristic
317C22×D3—22no—
318C22×D3—22no—
319C22×D3—34no—
320C22×D3—34no—
321C22×D3—64no—
322C22×D3—62no—
323C22×D3—62no—
324C22×D3—62no—
325C22×D3—64no—
326C22×D3—64no—
327C22×D3—64no—
328C22×D3—64no—
329C22×D3—62no—
330C22×D3—124no—
331C22×D3—122no—
332C22×D3—122no—
333C22×D3—124no—
334C22×D3C2×C4×D312yes—
335C22×D3C2×D1212yes—
336C22×D3C2×#6712yes—
337C3×Q8—68no—
338C2×C3×C4—24no—
339C2×C3×C4—22no—
340C2×C3×C4—22no—
341C2×C3×C4—22no—
342C2×C3×C4—22no—
343C2×C3×C4—22no—
344C2×C3×C4—22no—
345C2×C3×C4—22no—
346C2×C3×C4—22no—
347C2×C3×C4—22no—
348C2×C3×C4—32no—
349C2×C3×C4—32no—
350C2×C3×C4—32no—
351C2×C3×C4—316no—
352C2×C3×C4—34no—
353C2×C3×C4—42no—
354C2×C3×C4—42no—
355C2×C3×C4—62no—
356C2×C3×C4—62no—
357C2×C3×C4—62no—
358C2×C3×C4—62no—
359C2×C3×C4—62no—
360C2×C3×C4—62no—
361C2×C3×C4—64no—
362C2×C3×C4C2×C4×D312yes—
363C2×C3×C4C2×C4×D312yes—
364C2×C3×C4C2×D1212yes—
365C2×C3×C4D3×D412yes—
366C2×C3×C4D3×D412yes—
367C2×C3×C4C2×#6712yes—
368#67—616no—
369C2×Dic3—22no—
370C2×Dic3—22no—
371C2×Dic3—22no—
372C2×Dic3—22no—
373C2×Dic3—24no—
374C2×Dic3—22no—
375C2×Dic3—22no—
376C2×Dic3—62no—
377C2×Dic3—62no—
378C2×Dic3—64no—
379C2×Dic3—64no—
380C2×Dic3—122no—
381C2×Dic3—124no—
382C2×Dic3—128no—
383C2×Dic3C2×C4×D314yes—
384C2×Dic3C2×C4×D312yes—
385C2×Dic3C2×D1212yes—
386C2×Dic3C2×#6712yes—
387D12—616no—
388D12—68no—
389D12—68no—
390D12—128no—
391C4×D3—616no—
392C4×D3—616no—
393C4×D3—128no—
394C4×D3(C2×D3)⋊C4116yescomplemented
395Dic6—28no—
396C2×C32C22×C22⋊C411yescharacteristic
397C2×C32#52012yes—
398C2×C32#53511yescharacteristic
399C2×C32#53611yescharacteristic
400C2×C32#53712yes—
401C3⋊D3—44no—
402C3×D3—24no—
403C24—31no—
404C24—92no—
405#41—1832no—
406C2×Q8—34no—
407C2×Q8—62no—
408C2×Q8—62no—
409C2×D4—98no—
410C2×D4—94no—
411C2×D4—184no—
412C2×D4—184no—
413C2×D4—182no—
414C2×D4—182no—
415C22×C4—31no—
416C22×C4—34no—
417C22×C4—34no—
418C22×C4—34no—
419C22×C4—32no—
420C22×C4—32no—
421C22×C4—32no—
422C22×C4—98no—
423C22×C4—92no—
424C22×C4—184no—
425C22×C4—184no—
426C22×C4—184no—
427C22×C4—364no—
428C22×C4C2×D3212yes—
429C22×C4C2×D3211yescharacteristic
430C4⋊C4—64no—
431C4⋊C4—62no—
432C4⋊C4—184no—
433C4⋊C4—182no—
434C22⋊C4—64no—
435C22⋊C4—364no—
436C22⋊C4—364no—
437C42—22no—
438C42—62no—
439C22×C3—22no—
440C22×C3—21no—
441C22×C3—21no—
442C22×C3—22no—
443C22×C3—21no—
444C22×C3—34no—
445C22×C3—62no—
446C22×C3—62no—
447C22×C3—64no—
448C22×C3—64no—
449C22×C3C22×C4×D311yescharacteristic
450C22×C3C22×C4×D311yescharacteristic
451C22×C3C22×D1211yescharacteristic
452C22×C3C2×D3×D411yescharacteristic
453C22×C3C2×D3×D411yescharacteristic
454C22×C3#100712yes—
455C22×C3#100912yes—
456C22×C3#100912yes—
457C22×C3#101012yes—
458C22×C3C22×#6711yescharacteristic
459C2×D3—24no—
460C2×D3—22no—
461C2×D3—22no—
462C2×D3—24no—
463C2×D3—64no—
464C2×D3—68no—
465C2×D3—64no—
466C2×D3—68no—
467C2×D3—124no—
468C2×D3—128no—
469C2×D3—122no—
470C2×D3—122no—
471C2×D3—122no—
472C2×D3—122no—
473C2×D3—124no—
474C2×D3—124no—
475C2×D3—244no—
476C2×D3—242no—
477C2×D3—242no—
478C2×D3C2×(C2×D3)⋊C414yes—
479C3×C4—24no—
480C3×C4—34no—
481C3×C4—44no—
482C3×C4—42no—
483C3×C4—42no—
484C3×C4—64no—
485C3×C4—122no—
486C3×C4—122no—
487C3×C4D3×C22⋊C414yes—
488C3×C4C2×(C2×D3)⋊C414yes—
489Dic3—24no—
490Dic3—42no—
491Dic3—42no—
492Dic3—122no—
493Dic3—122no—
494Dic3—242no—
495Dic3C2×(C2×D3)⋊C414yes—
496C32#231111yescharacteristic, complemented, Sylow
497C23—32no—
498C23—32no—
499C23—32no—
500C23—62no—
501C23—62no—
502C23—94no—
503C23—184no—
504C23—182no—
505C23—184no—
506C23—182no—
507C23C22×D3211yescharacteristic
508Q8—68no—
509D4—1816no—
510D4—188no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—32no—
515C2×C4—32no—
516C2×C4—32no—
517C2×C4—316no—
518C2×C4—34no—
519C2×C4—62no—
520C2×C4—62no—
521C2×C4—62no—
522C2×C4—62no—
523C2×C4—62no—
524C2×C4—64no—
525C2×C4—62no—
526C2×C4—1816no—
527C2×C4—182no—
528C2×C4—184no—
529C2×C4—368no—
530C2×C4C4×D3212yes—
531C2×C4D3×D1212yes—
532C2×C4D3×#6712yes—
533C2×C3—22no—
534C2×C3—22no—
535C2×C3—21no—
536C2×C3—21no—
537C2×C3—21no—
538C2×C3—64no—
539C2×C3C2×D3×C22⋊C411yescharacteristic
540C2×C3#552312yes—
541C2×C3#552511yescharacteristic
542C2×C3#552611yescharacteristic
543C2×C3#557412yes—
544C2×C3#562912yes—
545C2×C3#567411yescharacteristic
546C2×C3#572411yescharacteristic
547C2×C3C22×(C2×D3)⋊C411yescharacteristic
548C2×C3#583312yes—
549D3—24no—
550D3—124no—
551D3—124no—
552D3—244no—
553C22—34no—
554C22—64no—
555C22—64no—
556C22—62no—
557C22—62no—
558C22—188no—
559C22—184no—
560C22—364no—
561C22—362no—
562C22—362no—
563C22#6429712yes—
564C22C2×C4×D3211yescharacteristic
565C22C2×D3×D1211yescharacteristic
566C22#6430812yes—
567C22C2×D3×#6711yescharacteristic
568C4—34no—
569C4—42no—
570C4—64no—
571C4—122no—
572C4—122no—
573C4—362no—
574C4D3×(C2×D3)⋊C414yes—
575C3—21no—
576C3#7648211yescharacteristic, complemented
577C3#8227011yescharacteristic, complemented
578C2—64no—
579C2—364no—
580C2#1059389012yes—
581C2#1059389311yescharacteristic
582C2#1059400111yescharacteristic
583C2#1059489412yes—
584C2C2×D3×(C2×D3)⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC22×#3799C2
hypercenterC2×C42D32
hypocenterC32#2311
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×C3×#872C2semidirect
3. C2×D3×C4⋊Dic3C2semidirect
4. #10592638C2semidirect
5. C3×#4929C2semidirect
6. #10591367C2semidirect
7. #10591364C2semidirect
8. #10591320C2semidirect
9. #10591220C2semidirect
20. C2×#3799C4semidirect
39. C2×#872D3semidirect
50. #4929D3semidirect
60. C2×C4⋊(C3⋊D3)C2×C4semidirect
70. C2×C3×Dic6C2×C4semidirect
76. C2×#624C2×C4semidirect
169. C3×C4×D3C22⋊C4semidirect
243. C2×Dic6C4×D3semidirect
394. C4×D3(C2×D3)⋊C4semidirect
496. C32#2311semidirect
576. C3#76482semidirect
577. C3#82270semidirect

Maximal subgroups

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

subgroupindex
C22×#37992
C2×C3×#8722
C2×D3×C4⋊Dic32
#105926382
C3×#49292
#105913672
#105913642
#105913202
#105912202
#822703
#764823