Finite Group Databasebeta

← #11804835

Subgroups — #11804835

Order 1152.

1965 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3798C211yesmaximal, characteristic
2C2×#63880C212yesmaximal, complemented
3#10592363C211yesmaximal, characteristic, complemented
4C3×#4666C211yesmaximal, characteristic, complemented
5C3×#4664C211yesmaximal, characteristic, complemented
6#10591370C211yesmaximal, characteristic, complemented
7#10591363C212yesmaximal, complemented
8D3×C3⋊#95C211yesmaximal, characteristic, complemented
9#10591295C211yesmaximal, characteristic, complemented
10#10591275C212yesmaximal, complemented
11#10591191C212yesmaximal, complemented
12#74121—31nomaximal
13#73573—31nomaximal
14C22×C4×C3⋊D3C2211yescharacteristic
15C22×C3×C4×D3C2211yescharacteristic
16C22×C3×C4×D3C2211yescharacteristic
17C22×#627C2211yescharacteristic
18C22×#626C2211yescharacteristic
19C22×#626C2211yescharacteristic
20C22×#625C2211yescharacteristic
21C22×#624C2212yes—
22C22×D3×Dic3C2212yes—
23C2×#3798—28no—
24C2×#3798C418yescomplemented
25C2×#3752C2212yes—
26C2×C3×(C2×D3)⋊C4C2212yes—
27C2×C3×(C2×D3)⋊C4C2212yes—
28C2×C3×C4×Dic3C2212yes—
29C2×Dic3⋊Dic3C2212yes—
30C2×(C2×D3)⋊Dic3C2212yes—
31#63880—28no—
32C32×#95C2211yescharacteristic
33#63658C2211yescharacteristic
34#63658C2212yes—
35C3×C3⋊#95C2212yes—
36C3×C3⋊#95C2211yescharacteristic
37C3×C3⋊#95C2211yescharacteristic
38#63579C2212yes—
39#63579C2212yes—
40C22×#235—31no—
41C22×#235—31no—
42C2×#67⋊C4—32no—
43C2×C4×D12—32no—
44C3×#381—31no—
45C3×C4×C22⋊C4—31no—
46#5212—31no—
47C2×C3⋊#95—31no—
48#4958—32no—
49#4956—32no—
50#4956—32no—
51#4929—32no—
52#4667—31no—
53#4666D311yescharacteristic, complemented
54#4665—32no—
55#4664—31no—
56#4664—31no—
57#4664—61no—
58#4664D311yescharacteristic, complemented
59D3×#95—31no—
60D3×#95—31no—
61D3×#95—31no—
62#4646—32no—
63C23×C3⋊D3C2311yescharacteristic
64C23×C3×D3C2311yescharacteristic
65C23×C3×D3C2311yescharacteristic
66C22×C32×C4C2312yes—
67C22×C32×C4C2311yescharacteristic
68C22×C3⋊Dic3C2312yes—
69C22×C3⋊Dic3C2311yescharacteristic
70C2×C4×C3⋊D3—24no—
71C2×C4×C3⋊D3C2×C414yescomplemented
72C22×C3×Dic3C2312yes—
73C22×C3×Dic3C2311yescharacteristic
74C22×C3×Dic3C2312yes—
75C22×C3×Dic3C2311yescharacteristic
76C2×C3×C4×D3—24no—
77C2×C3×C4×D3—24no—
78C2×C3×C4×D3C2×C414yescomplemented
79C2×C3×C4×D3C2×C414yescomplemented
80C2×#627—24no—
81C2×#627C2×C414yescomplemented
82C2×#626—24no—
83C2×#626C2×C414yes—
84C2×#626C2×C414yescomplemented
85C2×#626D418yes—
86C2×#625—24no—
87C2×#625C2×C414yescomplemented
88C2×#624—24no—
89C2×#624—24no—
90C2×#624—42no—
91C2×D3×Dic3—24no—
92C2×D3×Dic3—24no—
93C2×D3×Dic3—42no—
94#3798—232no—
95#3752—24no—
96C3×(C2×D3)⋊C4—24no—
97C3×(C2×D3)⋊C4—24no—
98C3×C4×Dic3—24no—
99Dic3⋊Dic3—24no—
100(C2×D3)⋊Dic3—42no—
101#2339—91noSylow
102C23×C3×C4—31no—
103C23×C3×C4—31no—
104C22×#67—31no—
105C22×#67—31no—
106C22×#67—31no—
107C22×#67—31no—
108C23×Dic3—32no—
109C2×#235—38no—
110C2×#235—38no—
111C2×#235—68no—
112C2×#235—68no—
113C22×D12—31no—
114C22×D12—31no—
115C22×C4×D3—31no—
116C22×C4×D3—31no—
117C22×C4×D3—32no—
118C22×C4×D3—32no—
119C22×C4×D3—32no—
120C22×C4×D3—61no—
121C22×C4×D3C2×D311yescharacteristic
122C22×C4×D3C2×D311yescharacteristic
123C22×Dic6—31no—
124C22×Dic6—31no—
125C2×C3×C22⋊C4—32no—
126C2×C3×C22⋊C4—32no—
127C2×C3×C42—32no—
128C2×#217—32no—
129C2×(C2×D3)⋊C4—32no—
130C2×(C2×D3)⋊C4—32no—
131C2×(C2×D3)⋊C4—32no—
132C2×(C2×D3)⋊C4—62no—
133C2×(C2×D3)⋊C4C2×D312yes—
134C2×(C2×D3)⋊C4C2×D312yes—
135C2×C4⋊Dic3—32no—
136C2×Dic3⋊C4—32no—
137C2×C4×Dic3C2×D312yes—
138#67⋊C4—68no—
139C4×D12—68no—
140C3×#95—21no—
141C3×#95—32no—
142C3×#95—31no—
143C3×#95—31no—
144C3×#95C2×D311yescharacteristic
145C3×#95C2×D311yescharacteristic
146C3⋊#95—32no—
147C3⋊#95—31no—
148C3⋊#95—31no—
149C3⋊#95—32no—
150C3⋊#95—32no—
151C3⋊#95—32no—
152C3⋊#95—32no—
153C3⋊#95—32no—
154C3⋊#95—61no—
155C3⋊#95—62no—
156C3⋊#95C2×D311yescharacteristic
157C3⋊#95C2×D311yescharacteristic
158C3⋊#95C2×D312yes—
159C23×C32C2411yescharacteristic
160C22×C3⋊D3—22no—
161C22×C3⋊D3—21no—
162C22×C3⋊D3—21no—
163C22×C3⋊D3C22×C412yes—
164C22×C3⋊D3C2×D414yes—
165C22×C3×D3—22no—
166C22×C3×D3—21no—
167C22×C3×D3—21no—
168C22×C3×D3—22no—
169C22×C3×D3—22no—
170C22×C3×D3—21no—
171C22×C3×D3—21no—
172C22×C3×D3C22×C412yes—
173C22×C3×D3C22×C412yes—
174C22×C3×D3C2×D414yes—
175C2×C32×C4—22no—
176C2×C32×C4—22no—
177C2×C32×C4—22no—
178C2×C32×C4—22no—
179C2×C32×C4C22×C412yes—
180C2×C3⋊Dic3—22no—
181C2×C3⋊Dic3—22no—
182C2×C3⋊Dic3—22no—
183C2×C3⋊Dic3—22no—
184C2×C3⋊Dic3C22×C412yes—
185C4×C3⋊D3—28no—
186C2×C3×Dic3—22no—
187C2×C3×Dic3—22no—
188C2×C3×Dic3—22no—
189C2×C3×Dic3—22no—
190C2×C3×Dic3—22no—
191C2×C3×Dic3—22no—
192C2×C3×Dic3C22×C412yes—
193C2×C3×Dic3C22×C412yes—
194C2×C3×Dic3C2×D414yes—
195C2×C3×Dic3#4114yescomplemented
196C3×C4×D3—28no—
197C3×C4×D3—28no—
198#627—28no—
199#626—28no—
200#626C22⋊C4116yescomplemented
201#625—28no—
202#624—48no—
203D3×Dic3—48no—
204C22×#41—91no—
205C2×C4×D4—92no—
206#391—92no—
207#386—92no—
208#386—92no—
209#381—31no—
210#381—91no—
211#380—91no—
212C4×C22⋊C4—31no—
213C2×#95—91no—
214C2×#95—91no—
215C24×C3—31no—
216C24×C3—31no—
217C23×D3—31no—
218C23×D3—31no—
219C23×D3—61no—
220C23×D3C22×D311yescharacteristic
221C23×D3C22×D311yescharacteristic
222C22×C3×C4—21no—
223C22×C3×C4—22no—
224C22×C3×C4—31no—
225C22×C3×C4—31no—
226C22×C3×C4—32no—
227C22×C3×C4—34no—
228C22×C3×C4—34no—
229C22×C3×C4—32no—
230C22×C3×C4—64no—
231C22×C3×C4—64no—
232C22×C3×C4C22×D312yes—
233C22×C3×C4C22×D312yes—
234C22×C3×C4C22×D311yescharacteristic
235C22×C3×C4C22×D311yescharacteristic
236C2×#67—34no—
237C2×#67—34no—
238C2×#67—34no—
239C2×#67—34no—
240C2×#67—38no—
241C2×#67—64no—
242C2×#67—64no—
243C2×#67—64no—
244C22×Dic3—31no—
245C22×Dic3—31no—
246C22×Dic3—32no—
247C22×Dic3—32no—
248C22×Dic3—61no—
249C22×Dic3—62no—
250C22×Dic3—64no—
251C22×Dic3—64no—
252C22×Dic3—122no—
253C22×Dic3C22×D312yes—
254C22×Dic3C22×D311yescharacteristic
255C22×Dic3C22×D312yes—
256C22×Dic3C22×D311yescharacteristic
257#235—632no—
258#235—632no—
259C2×D12—34no—
260C2×D12—38no—
261C2×D12—34no—
262C2×D12—64no—
263C2×C4×D3—24no—
264C2×C4×D3—24no—
265C2×C4×D3—34no—
266C2×C4×D3—34no—
267C2×C4×D3—64no—
268C2×C4×D3—64no—
269C2×C4×D3—64no—
270C2×C4×D3—64no—
271C2×C4×D3—64no—
272C2×C4×D3—64no—
273C2×C4×D3—64no—
274C2×C4×D3—64no—
275C2×C4×D3—64no—
276C2×C4×D3—124no—
277C2×C4×D3—122no—
278C2×C4×D3—122no—
279C2×C4×D3—122no—
280C2×C4×D3C4×D314yescomplemented
281C2×C4×D3C4×D314yescomplemented
282C2×Dic6—34no—
283C2×Dic6—34no—
284C2×Dic6—64no—
285C2×Dic6—64no—
286C3×C22⋊C4—64no—
287C3×C22⋊C4—64no—
288C3×C42—64no—
289#217—122no—
290(C2×D3)⋊C4—24no—
291(C2×D3)⋊C4—24no—
292(C2×D3)⋊C4—64no—
293(C2×D3)⋊C4—64no—
294(C2×D3)⋊C4—124no—
295(C2×D3)⋊C4—122no—
296C4⋊Dic3—64no—
297Dic3⋊C4—64no—
298C4×Dic3—24no—
299C22×C32C23×C411yescharacteristic
300C22×C32C22×D412yes—
301C22×C32C2×#4112yes—
302C22×C32H(5,𝔽2)11yescharacteristic
303C22×C322−1+411yescharacteristic
304C2×C3⋊D3—22no—
305C2×C3⋊D3—22no—
306C2×C3⋊D3—24no—
307C2×C3⋊D3—24no—
308C2×C3⋊D3C2×C22⋊C414yes—
309C2×C3×D3—22no—
310C2×C3×D3—22no—
311C2×C3×D3—24no—
312C2×C3×D3—24no—
313C2×C3×D3—22no—
314C2×C3×D3—22no—
315C2×C3×D3—22no—
316C2×C3×D3—42no—
317C2×C3×D3—42no—
318C2×C3×D3C2×C22⋊C414yes—
319C32×C4—22no—
320C32×C4—42no—
321C3⋊Dic3—22no—
322C3⋊Dic3—42no—
323C3×Dic3—22no—
324C3×Dic3—24no—
325C3×Dic3—42no—
326C3×Dic3C2×C22⋊C414yes—
327C2×#41—98no—
328C2×#41—188no—
329C22×Q8—91no—
330C22×D4—91no—
331C22×D4—91no—
332C22×D4—91no—
333C23×C4—31no—
334C23×C4—31no—
335C23×C4—92no—
336C23×C4—92no—
337C23×C4—91no—
338C4×D4—188no—
339C2×C4⋊C4—92no—
340C2×C22⋊C4—32no—
341C2×C22⋊C4—32no—
342C2×C22⋊C4—92no—
343C2×C22⋊C4—92no—
344C2×C42—32no—
345#95—31no—
346#95—31no—
347#95—32no—
348#95—92no—
349#95—92no—
350#95—91no—
351#95—92no—
352#95D3211yescharacteristic
353C23×C3—21no—
354C23×C3—32no—
355C23×C3—34no—
356C23×C3—32no—
357C23×C3—62no—
358C23×C3—61no—
359C23×C3—61no—
360C23×C3—62no—
361C23×C3—62no—
362C23×C3—61no—
363C23×C3—61no—
364C23×C3C23×D311yescharacteristic
365C23×C3C23×D311yescharacteristic
366C22×D3—22no—
367C22×D3—21no—
368C22×D3—21no—
369C22×D3—22no—
370C22×D3—22no—
371C22×D3—21no—
372C22×D3—21no—
373C22×D3—32no—
374C22×D3—32no—
375C22×D3—34no—
376C22×D3—34no—
377C22×D3—62no—
378C22×D3—64no—
379C22×D3—62no—
380C22×D3—62no—
381C22×D3—61no—
382C22×D3—61no—
383C22×D3—61no—
384C22×D3—61no—
385C22×D3—122no—
386C22×D3—121no—
387C22×D3—121no—
388C22×D3C2×C4×D312yes—
389C22×D3C2×C4×D312yes—
390C22×D3D3×D414yes—
391C2×C3×C4—22no—
392C2×C3×C4—22no—
393C2×C3×C4—22no—
394C2×C3×C4—22no—
395C2×C3×C4—22no—
396C2×C3×C4—22no—
397C2×C3×C4—22no—
398C2×C3×C4—22no—
399C2×C3×C4—22no—
400C2×C3×C4—32no—
401C2×C3×C4—34no—
402C2×C3×C4—32no—
403C2×C3×C4—34no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—68no—
409C2×C3×C4—68no—
410C2×C3×C4—62no—
411C2×C3×C4—62no—
412C2×C3×C4—62no—
413C2×C3×C4—62no—
414C2×C3×C4—62no—
415C2×C3×C4—62no—
416C2×C3×C4C2×C4×D312yes—
417C2×C3×C4C2×C4×D312yes—
418#67—316no—
419#67—68no—
420#67—68no—
421#67—68no—
422C2×Dic3—22no—
423C2×Dic3—22no—
424C2×Dic3—22no—
425C2×Dic3—22no—
426C2×Dic3—22no—
427C2×Dic3—22no—
428C2×Dic3—32no—
429C2×Dic3—32no—
430C2×Dic3—62no—
431C2×Dic3—62no—
432C2×Dic3—62no—
433C2×Dic3—62no—
434C2×Dic3—62no—
435C2×Dic3—62no—
436C2×Dic3—62no—
437C2×Dic3—62no—
438C2×Dic3—62no—
439C2×Dic3—122no—
440C2×Dic3—122no—
441C2×Dic3—122no—
442C2×Dic3—122no—
443C2×Dic3—128no—
444C2×Dic3C2×C4×D312yes—
445C2×Dic3C2×C4×D312yes—
446C2×Dic3#23514yescomplemented
447C2×Dic3D3×D414yes—
448D12—316no—
449D12—68no—
450C4×D3—28no—
451C4×D3—28no—
452C4×D3—68no—
453C4×D3—68no—
454C4×D3—128no—
455C4×D3—128no—
456C4×D3—128no—
457C4×D3—128no—
458Dic6—68no—
459Dic6—68no—
460C2×C32C22×C22⋊C411yescharacteristic
461C2×C32C4×#4111yescharacteristic
462C2×C32#52011yescharacteristic
463C2×C32#54612yes—
464C2×C32#54712yes—
465C3⋊D3—24no—
466C3×D3—24no—
467C3×D3—42no—
468C24—31no—
469C24—31no—
470C24—91no—
471#41—1832no—
472C2×Q8—94no—
473C2×Q8—184no—
474C2×D4—98no—
475C2×D4—94no—
476C2×D4—94no—
477C2×D4—94no—
478C2×D4—184no—
479C2×D4—184no—
480C22×C4—31no—
481C22×C4—31no—
482C22×C4—32no—
483C22×C4—34no—
484C22×C4—34no—
485C22×C4—32no—
486C22×C4—64no—
487C22×C4—64no—
488C22×C4—91no—
489C22×C4—94no—
490C22×C4—92no—
491C22×C4—184no—
492C22×C4—184no—
493C22×C4—184no—
494C22×C4—184no—
495C22×C4—184no—
496C22×C4—362no—
497C22×C4—362no—
498C22×C4C2×D3212yes—
499C22×C4C2×D3211yescharacteristic
500C4⋊C4—184no—
501C22⋊C4—64no—
502C22⋊C4—64no—
503C22⋊C4—184no—
504C22⋊C4—362no—
505C42—64no—
506C22×C3—21no—
507C22×C3—22no—
508C22×C3—21no—
509C22×C3—22no—
510C22×C3—21no—
511C22×C3—34no—
512C22×C3—62no—
513C22×C3—62no—
514C22×C3—64no—
515C22×C3—64no—
516C22×C3—62no—
517C22×C3—62no—
518C22×C3—62no—
519C22×C3—122no—
520C22×C3—122no—
521C22×C3C22×C4×D311yescharacteristic
522C22×C3C22×C4×D311yescharacteristic
523C22×C3C2×#23512yes—
524C22×C3C2×D3×D412yes—
525C22×C3C2×D3×D412yes—
526C22×C3D3×#4112yes—
527C22×C3#100911yescharacteristic
528C22×C3#100911yescharacteristic
529C22×C3#101011yescharacteristic
530C22×C3#101011yescharacteristic
531C2×D3—24no—
532C2×D3—24no—
533C2×D3—22no—
534C2×D3—22no—
535C2×D3—22no—
536C2×D3—22no—
537C2×D3—22no—
538C2×D3—34no—
539C2×D3—34no—
540C2×D3—42no—
541C2×D3—42no—
542C2×D3—64no—
543C2×D3—64no—
544C2×D3—64no—
545C2×D3—62no—
546C2×D3—62no—
547C2×D3—62no—
548C2×D3—62no—
549C2×D3—64no—
550C2×D3—64no—
551C2×D3—124no—
552C2×D3—124no—
553C2×D3—122no—
554C2×D3—122no—
555C2×D3D3×C22⋊C414yes—
556C3×C4—22no—
557C3×C4—22no—
558C3×C4—34no—
559C3×C4—42no—
560C3×C4—42no—
561C3×C4—42no—
562C3×C4—64no—
563C3×C4—62no—
564C3×C4—82no—
565C3×C4—122no—
566Dic3—22no—
567Dic3—24no—
568Dic3—42no—
569Dic3—62no—
570Dic3—62no—
571Dic3—122no—
572Dic3—122no—
573Dic3—122no—
574Dic3—242no—
575Dic3D3×C22⋊C414yes—
576C32#233911yescharacteristic, complemented, Sylow
577C23—32no—
578C23—34no—
579C23—32no—
580C23—62no—
581C23—61no—
582C23—61no—
583C23—62no—
584C23—61no—
585C23—62no—
586C23—61no—
587C23—92no—
588C23—94no—
589C23—182no—
590C23—181no—
591C23—181no—
592C23C22×D3211yescharacteristic
593Q8—188no—
594D4—916no—
595D4—188no—
596D4—188no—
597C2×C4—22no—
598C2×C4—22no—
599C2×C4—22no—
600C2×C4—22no—
601C2×C4—32no—
602C2×C4—34no—
603C2×C4—32no—
604C2×C4—34no—
605C2×C4—68no—
606C2×C4—68no—
607C2×C4—62no—
608C2×C4—62no—
609C2×C4—62no—
610C2×C4—62no—
611C2×C4—62no—
612C2×C4—62no—
613C2×C4—92no—
614C2×C4—188no—
615C2×C4—182no—
616C2×C4—182no—
617C2×C4—182no—
618C2×C4—182no—
619C2×C4—368no—
620C2×C4—368no—
621C2×C4C4×D3212yes—
622C2×C3—22no—
623C2×C3—22no—
624C2×C3—21no—
625C2×C3—21no—
626C2×C3—21no—
627C2×C3—64no—
628C2×C3—122no—
629C2×C3C4×#23511yescharacteristic
630C2×C3C2×D3×C22⋊C411yescharacteristic
631C2×C3C2×D3×C22⋊C411yescharacteristic
632C2×C3#552211yescharacteristic
633C2×C3#552311yescharacteristic
634C2×C3#552311yescharacteristic
635C2×C3#555012yes—
636C2×C3#555112yes—
637C2×C3#565412yes—
638C2×C3#565512yes—
639D3—24no—
640D3—42no—
641D3—64no—
642D3—64no—
643D3—124no—
644C22—34no—
645C22—64no—
646C22—64no—
647C22—62no—
648C22—62no—
649C22—62no—
650C22—62no—
651C22—62no—
652C22—94no—
653C22—122no—
654C22—122no—
655C22—184no—
656C22—184no—
657C22—182no—
658C22—182no—
659C22C2×C4×D3211yescharacteristic
660C22D3×#23512yes—
661C22#6430911yescharacteristic
662C22D32×D412yes—
663C22#6432011yescharacteristic
664C4—22no—
665C4—34no—
666C4—42no—
667C4—64no—
668C4—62no—
669C4—122no—
670C4—182no—
671C4—362no—
672C3—21no—
673C3#7357311yescharacteristic, complemented
674C3#7412111yescharacteristic, complemented
675C2—64no—
676C2—122no—
677C2—184no—
678C2#1059396511yescharacteristic
679C2#1059418812yes—
680C2D32×C22⋊C411yescharacteristic
681C2#1059451111yescharacteristic
682C2#1059461912yes—
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC22×#3798C2
hypercenter#95D32
hypocenterC32#2339
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
2. C2×#63880C2semidirect
3. #10592363C2semidirect
4. C3×#4666C2semidirect
5. C3×#4664C2semidirect
6. #10591370C2semidirect
7. #10591363C2semidirect
8. D3×C3⋊#95C2semidirect
9. #10591295C2semidirect
10. #10591275C2semidirect
11. #10591191C2semidirect
24. C2×#3798C4semidirect
53. #4666D3semidirect
58. #4664D3semidirect
71. C2×C4×C3⋊D3C2×C4semidirect
78. C2×C3×C4×D3C2×C4semidirect
79. C2×C3×C4×D3C2×C4semidirect
81. C2×#627C2×C4semidirect
84. C2×#626C2×C4semidirect
87. C2×#625C2×C4semidirect
195. C2×C3×Dic3#41semidirect
200. #626C22⋊C4semidirect
280. C2×C4×D3C4×D3semidirect
281. C2×C4×D3C4×D3semidirect
446. C2×Dic3#235semidirect
576. C32#2339semidirect
673. C3#73573semidirect
674. C3#74121semidirect

Maximal subgroups

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

subgroupindex
C22×#37982
C2×#638802
#105923632
C3×#46662
C3×#46642
#105913702
#105913632
D3×C3⋊#952
#105912952
#105912752
#105911912
#741213
#735733