Finite Group Databasebeta

← #11792012

Subgroups — #11792012

Order 1152.

913 conjugacy classes of subgroups.

The subgroup lattice has 645 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3756C211yesmaximal, characteristic, complemented
2C2×C3×#946C211yesmaximal, characteristic
3C2×#63857C211yesmaximal, characteristic
4C2×C3×#835C211yesmaximal, characteristic, complemented
5C2×#63567C211yesmaximal, characteristic, complemented
6C2×(C2×D3)⋊(C3⋊C8)C211yesmaximal, characteristic
7#10589163C211yesmaximal, characteristic, complemented
8#71700—31nomaximal
9#70273—31nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×#634C2211yescharacteristic
12C22×C3×C4×D3C2211yescharacteristic
13C2×#3756—22no—
14C2×#3756—22no—
15C2×#3756—22no—
16C22×C3⋊(C3⋊C8)C2211yescharacteristic
17C3×#946—22no—
18C3×#946—22no—
19C2×C3×(C2×D3)⋊C4—21no—
20C2×C3×C4⋊Dic3C2211yescharacteristic
21C2×C3×C4⋊Dic3C2211yescharacteristic
22C2×C3×Dic3⋊C4—21no—
23C22×C3×C3⋊C8C2211yescharacteristic
24C2×Dic3⋊Dic3—21no—
25C2×(C2×D3)⋊Dic3—21no—
26#63857—22no—
27#63857—22no—
28C3×#835—22no—
29#63567—22no—
30(C2×D3)⋊(C3⋊C8)—22no—
31C2×C3×C22⋊Q8—31no—
32C2×#946D311yescharacteristic
33C22×#216—31no—
34C22×#216—31no—
35C22×#216—61no—
36C2×#924—31no—
37C2×#897—31no—
38C2×C3×#103—31no—
39C2×#835D311yescharacteristic, complemented
40C2×#830—31no—
41C2×(C2×D3)⋊C8—31no—
42C2×#816—31no—
43C2×#810—31no—
44#4529—31no—
45#4529—31no—
46C23×C3×D3D411yescharacteristic
47C2×C32×Q8—21no—
48C2×C32×Q8—21no—
49C2×C32×Q8—21no—
50C2×C32×Q8—21no—
51C2×C32×Q8—21no—
52C2×C32×Q8D412yes—
53C22×C32×C4—21no—
54C22×C32×C4C2311yescharacteristic
55C22×C3⋊Dic3—21no—
56C2×#634—21no—
57C2×#634—21no—
58C2×#634—21no—
59C2×#634—21no—
60C2×#634—21no—
61C2×#634D412yes—
62C22×C3×Dic3—21no—
63C22×C3×Dic3—21no—
64C22×C3×Dic3D411yescharacteristic
65C2×C3×C4×D3—21no—
66C2×C3×C4×D3—21no—
67C2×C3×C4×D3—21no—
68C2×C3×C4×D3—21no—
69C2×C3×C4×D3—21no—
70C2×C3×C4×D3—21no—
71#3756—28no—
72C2×C3⋊(C3⋊C8)—21no—
73C2×C3⋊(C3⋊C8)—21no—
74C2×C3⋊(C3⋊C8)D412yes—
75C3×(C2×D3)⋊C4—24no—
76C3×C4⋊Dic3—21no—
77C3×C4⋊Dic3—21no—
78C3×C4⋊Dic3D412yes—
79C3×C4⋊Dic3D412yes—
80C3×Dic3⋊C4—24no—
81C2×C3×C3⋊C8—21no—
82C2×C3×C3⋊C8—21no—
83C2×C3×C3⋊C8—21no—
84Dic3⋊Dic3—24no—
85(C2×D3)⋊Dic3—24no—
86#2001—91noSylow
87C22×C3×Q8—21no—
88C22×C3×Q8C2×D311yescharacteristic
89C22×C3×Q8C2×D311yescharacteristic
90C23×C3×C4—31no—
91C22×C4×D3C2×D311yescharacteristic
92C22×Dic6—31no—
93C22×Dic6—31no—
94C22×Dic6—61no—
95C22×C3×C8—31no—
96C3×C22⋊Q8—62no—
97C3×C22⋊Q8—62no—
98C2×C3×C4⋊C4—31no—
99C2×C3×C4⋊C4—31no—
100C2×C3×C4⋊C4—61no—
101C2×C3×C22⋊C4—61no—
102C2×#217—61no—
103#946—22no—
104#946—22no—
105C2×#216—62no—
106C2×#216—62no—
107C2×#216—62no—
108C2×#216—62no—
109C2×#216—64no—
110C2×#216—64no—
111C2×#216—64no—
112C2×#216—62no—
113C2×#216—62no—
114C2×(C2×D3)⋊C4—21no—
115C2×(C2×D3)⋊C4—61no—
116C2×C4⋊Dic3—61no—
117C2×C4⋊Dic3C2×D311yescharacteristic
118C2×C4⋊Dic3C2×D311yescharacteristic
119#924—62no—
120#924—62no—
121C2×Dic3⋊C4—21no—
122C2×Dic3⋊C4—61no—
123C22×C3⋊C8—31no—
124C22×C3⋊C8—31no—
125C22×C3⋊C8—61no—
126C22×C3⋊C8C2×D311yescharacteristic
127#897—62no—
128#897—62no—
129C3×#103—62no—
130#835—22no—
131#830—62no—
132(C2×D3)⋊C8—62no—
133#816—62no—
134#810—62no—
135C23×C32C2×D411yescharacteristic
136C22×C3×D3—21no—
137C22×C3×D3—21no—
138C22×C3×D3—21no—
139C22×C3×D3—21no—
140C22×C3×D3—21no—
141C22×C3×D3—21no—
142C22×C3×D3Q1612yescomplemented
143C32×Q8—22no—
144C32×Q8—22no—
145C32×Q8—41no—
146C32×Q8—41no—
147C2×C32×C4—22no—
148C2×C32×C4—41no—
149C2×C32×C4—41no—
150C2×C32×C4C2×D411yescharacteristic
151C2×C32×C4C2×D411yescharacteristic
152C2×C32×C4C2×D411yescharacteristic
153C2×C32×C4C2×D411yescharacteristic
154C2×C32×C4C2×D411yescharacteristic
155C2×C32×C4#4111yescharacteristic
156C2×C3⋊Dic3—22no—
157C2×C3⋊Dic3—41no—
158C2×C3⋊Dic3—41no—
159#634—22no—
160#634—22no—
161#634—41no—
162#634—41no—
163C2×C3×Dic3—22no—
164C2×C3×Dic3—21no—
165C2×C3×Dic3—21no—
166C2×C3×Dic3—22no—
167C2×C3×Dic3—21no—
168C2×C3×Dic3—41no—
169C2×C3×Dic3—41no—
170C2×C3×Dic3—41no—
171C2×C3×Dic3—41no—
172C3×C4×D3—41no—
173C3×C4×D3—41no—
174C3×C4×D3—41no—
175C3×C4×D3—41no—
176C3⋊(C3⋊C8)—22no—
177C3×C3⋊C8—41no—
178C22×Q16—91no—
179C2×C22⋊Q8—31no—
180C2×C22⋊Q8—91no—
181C2×#103—31no—
182C2×#103—91no—
183C2×C22⋊C8—91no—
184#340—91no—
185C24×C3—31no—
186C23×D3#6711yescharacteristic
187C2×C3×Q8—21no—
188C2×C3×Q8—21no—
189C2×C3×Q8—22no—
190C2×C3×Q8—22no—
191C2×C3×Q8—21no—
192C2×C3×Q8—21no—
193C2×C3×Q8—21no—
194C2×C3×Q8—21no—
195C2×C3×Q8—21no—
196C2×C3×Q8—21no—
197C2×C3×Q8—21no—
198C2×C3×Q8—21no—
199C2×C3×Q8—22no—
200C2×C3×Q8—41no—
201C2×C3×Q8—41no—
202C2×C3×Q8—41no—
203C2×C3×Q8D1212yes—
204C2×C3×Q8#6712yes—
205C22×C3×C4—21no—
206C22×C3×C4—21no—
207C22×C3×C4—21no—
208C22×C3×C4—31no—
209C22×C3×C4—41no—
210C22×C3×C4—61no—
211C22×C3×C4—61no—
212C22×C3×C4—61no—
213C22×C3×C4—61no—
214C22×C3×C4—61no—
215C22×C3×C4—61no—
216C22×C3×C4—61no—
217C22×C3×C4—61no—
218C22×C3×C4C22×D311yescharacteristic
219C22×C3×C4C22×D311yescharacteristic
220C22×Dic3—21no—
221C22×Dic3—21no—
222C22×Dic3—61no—
223C22×Dic3—61no—
224C22×Dic3—121no—
225C22×Dic3#6711yescharacteristic
226C2×C4×D3—21no—
227C2×C4×D3—21no—
228C2×C4×D3—21no—
229C2×C4×D3—21no—
230C2×C4×D3—21no—
231C2×C4×D3—21no—
232C2×Dic6—32no—
233C2×Dic6—32no—
234C2×Dic6—62no—
235C2×Dic6—62no—
236C2×Dic6—62no—
237C2×Dic6—61no—
238C2×Dic6—61no—
239C2×Dic6—61no—
240C2×Dic6—61no—
241C2×Dic6—61no—
242C2×Dic6—61no—
243C2×Dic6—61no—
244C2×Dic6—61no—
245C2×Dic6—61no—
246C2×Dic6—61no—
247C2×Dic6—121no—
248C2×Dic6—121no—
249C2×Dic6—121no—
250C2×C3×C8—61no—
251C2×C3×C8—61no—
252C2×C3×C8—61no—
253C3×C4⋊C4—32no—
254C3×C4⋊C4—32no—
255C3×C4⋊C4—64no—
256C3×C4⋊C4—61no—
257C3×C4⋊C4—61no—
258C3×C22⋊C4—64no—
259#217—64no—
260#216—616no—
261#216—68no—
262#216—68no—
263(C2×D3)⋊C4—24no—
264(C2×D3)⋊C4—64no—
265C4⋊Dic3—21no—
266C4⋊Dic3—21no—
267C4⋊Dic3—64no—
268C4⋊Dic3#6712yes—
269C4⋊Dic3#6712yes—
270Dic3⋊C4—24no—
271Dic3⋊C4—64no—
272C2×C3⋊C8—21no—
273C2×C3⋊C8—21no—
274C2×C3⋊C8—21no—
275C2×C3⋊C8—32no—
276C2×C3⋊C8—32no—
277C2×C3⋊C8—62no—
278C2×C3⋊C8—62no—
279C2×C3⋊C8—62no—
280C2×C3⋊C8—61no—
281C2×C3⋊C8—61no—
282C2×C3⋊C8—61no—
283C2×C3⋊C8—61no—
284C22×C32#12011yescharacteristic
285C22×C32#12011yescharacteristic
286C22×C32#12111yescharacteristic
287C22×C32C2×Q1611yescharacteristic
288C22×C32#13511yescharacteristic
289C22×C32#13711yescharacteristic
290C22×C32#13711yescharacteristic
291C2×C3×D3—22no—
292C2×C3×D3—22no—
293C2×C3×D3—22no—
294C2×C3×D3—41no—
295C2×C3×D3—41no—
296C2×C3×D3—41no—
297C2×C3×D3—41no—
298C32×C4—42no—
299C32×C4#12011yescharacteristic
300C32×C4#12111yescharacteristic
301C32×C4#12111yescharacteristic
302C32×C4#12711yescharacteristic
303C3⋊Dic3—42no—
304C3×Dic3—41no—
305C3×Dic3—42no—
306C3×Dic3—42no—
307C22×Q8—91no—
308C22×Q8D3211yescharacteristic
309C23×C4—31no—
310C2×Q16—182no—
311C2×Q16—182no—
312C2×Q16—182no—
313C22×C8—31no—
314C22×C8—91no—
315C22⋊Q8—62no—
316C22⋊Q8—62no—
317C22⋊Q8—182no—
318C22⋊Q8—182no—
319C2×C4⋊C4—31no—
320C2×C4⋊C4—31no—
321C2×C4⋊C4—61no—
322C2×C4⋊C4—181no—
323C2×C22⋊C4—61no—
324C2×C22⋊C4—181no—
325#103—62no—
326#103—182no—
327C22⋊C8—182no—
328C23×C3—21no—
329C23×C3—32no—
330C23×C3—61no—
331C23×C3—61no—
332C23×C3—61no—
333C23×C3—61no—
334C23×C3—61no—
335C23×C3—61no—
336C23×C3D3×D411yescharacteristic
337C23×C3C2×#6711yescharacteristic
338C22×D3—21no—
339C22×D3—21no—
340C22×D3—21no—
341C22×D3—21no—
342C22×D3—21no—
343C22×D3—21no—
344C22×D3#21612yescomplemented
345C3×Q8—24no—
346C3×Q8—22no—
347C3×Q8—22no—
348C3×Q8—22no—
349C3×Q8—22no—
350C3×Q8—42no—
351C3×Q8—42no—
352C3×Q8—42no—
353C3×Q8—41no—
354C3×Q8—41no—
355C3×Q8—41no—
356C3×Q8—41no—
357C2×C3×C4—22no—
358C2×C3×C4—22no—
359C2×C3×C4—21no—
360C2×C3×C4—21no—
361C2×C3×C4—21no—
362C2×C3×C4—21no—
363C2×C3×C4—21no—
364C2×C3×C4—21no—
365C2×C3×C4—42no—
366C2×C3×C4—42no—
367C2×C3×C4—42no—
368C2×C3×C4—41no—
369C2×C3×C4—41no—
370C2×C3×C4—41no—
371C2×C3×C4—41no—
372C2×C3×C4—62no—
373C2×C3×C4—61no—
374C2×C3×C4—61no—
375C2×C3×C4—61no—
376C2×C3×C4—62no—
377C2×C3×C4—121no—
378C2×C3×C4—121no—
379C2×C3×C4—121no—
380C2×C3×C4—121no—
381C2×C3×C4—121no—
382C2×C3×C4—121no—
383C2×C3×C4—121no—
384C2×C3×C4—121no—
385C2×C3×C4C2×D1211yescharacteristic
386C2×C3×C4#23511yescharacteristic
387C2×C3×C4D3×D411yescharacteristic
388C2×C3×C4D3×D411yescharacteristic
389C2×C3×C4D3×D411yescharacteristic
390C2×C3×C4D3×D411yescharacteristic
391C2×C3×C4D3×D411yescharacteristic
392C2×C3×C4D3×D411yescharacteristic
393C2×C3×C4#23711yescharacteristic
394C2×C3×C4C2×#6711yescharacteristic
395C2×C3×C4C2×#6711yescharacteristic
396C2×C3×C4C2×#6711yescharacteristic
397C2×Dic3—22no—
398C2×Dic3—21no—
399C2×Dic3—21no—
400C2×Dic3—21no—
401C2×Dic3—22no—
402C2×Dic3—41no—
403C2×Dic3—41no—
404C2×Dic3—41no—
405C2×Dic3—41no—
406C2×Dic3—62no—
407C2×Dic3—62no—
408C2×Dic3—122no—
409C2×Dic3—122no—
410C2×Dic3—122no—
411C2×Dic3—121no—
412C2×Dic3—121no—
413C2×Dic3—121no—
414C2×Dic3—121no—
415C4×D3—41no—
416C4×D3—41no—
417C4×D3—41no—
418C4×D3—41no—
419Dic6—64no—
420Dic6—62no—
421Dic6—62no—
422Dic6—62no—
423Dic6—62no—
424Dic6—122no—
425Dic6—122no—
426Dic6—122no—
427Dic6—121no—
428Dic6—121no—
429Dic6—121no—
430Dic6—121no—
431C3×C8—121no—
432C3⋊C8—41no—
433C3⋊C8—64no—
434C3⋊C8—62no—
435C3⋊C8—62no—
436C2×C32#39211yescharacteristic
437C2×C32#45111yescharacteristic
438C2×C32#45111yescharacteristic
439C2×C32#45211yescharacteristic
440C2×C32#45211yescharacteristic
441C2×C32#46711yescharacteristic
442C2×C32#47011yescharacteristic
443C3×D3—42no—
444C24—31no—
445C2×Q8—21no—
446C2×Q8—21no—
447C2×Q8—21no—
448C2×Q8—21no—
449C2×Q8—21no—
450C2×Q8—92no—
451C2×Q8—181no—
452C2×Q8—181no—
453C2×Q8—181no—
454C2×Q8—181no—
455C2×Q8—181no—
456C2×Q8#62612yes—
457C22×C4—21no—
458C22×C4—31no—
459C22×C4—61no—
460C22×C4—61no—
461C22×C4—61no—
462C22×C4—61no—
463C22×C4—61no—
464C22×C4—61no—
465C22×C4—61no—
466C22×C4—61no—
467C22×C4—181no—
468C22×C4C2×D3211yescharacteristic
469Q16—188no—
470C2×C8—61no—
471C2×C8—61no—
472C2×C8—61no—
473C2×C8—92no—
474C2×C8—181no—
475C2×C8—181no—
476C4⋊C4—32no—
477C4⋊C4—32no—
478C4⋊C4—64no—
479C4⋊C4—61no—
480C4⋊C4—61no—
481C4⋊C4—184no—
482C22⋊C4—64no—
483C22⋊C4—184no—
484C22×C3—21no—
485C22×C3—21no—
486C22×C3—21no—
487C22×C3—21no—
488C22×C3—21no—
489C22×C3—21no—
490C22×C3—21no—
491C22×C3—62no—
492C22×C3—62no—
493C22×C3—62no—
494C22×C3—121no—
495C22×C3—121no—
496C22×C3—121no—
497C22×C3—121no—
498C22×C3#88211yescharacteristic
499C22×C3#88411yescharacteristic
500C22×C3#91511yescharacteristic
501C22×C3#91611yescharacteristic
502C22×C3D3×Q1611yescharacteristic
503C22×C3#91811yescharacteristic
504C22×C3#93711yescharacteristic
505C22×C3#93711yescharacteristic
506C22×C3#93911yescharacteristic
507C22×C3#94211yescharacteristic
508C22×C3C2×#21611yescharacteristic
509C22×C3#95011yescharacteristic
510C22×C3#95111yescharacteristic
511C22×C3#95311yescharacteristic
512C2×D3—22no—
513C2×D3—22no—
514C2×D3—22no—
515C2×D3—41no—
516C2×D3—41no—
517C2×D3—41no—
518C2×D3—41no—
519C3×C4—21no—
520C3×C4—21no—
521C3×C4—21no—
522C3×C4—21no—
523C3×C4—44no—
524C3×C4—42no—
525C3×C4—42no—
526C3×C4—121no—
527C3×C4—122no—
528C3×C4—122no—
529C3×C4#88211yescharacteristic
530C3×C4#88411yescharacteristic
531C3×C4#93011yescharacteristic
532C3×C4#93711yescharacteristic
533C3×C4#93811yescharacteristic
534C3×C4#93911yescharacteristic
535C3×C4#94011yescharacteristic
536C3×C4#94011yescharacteristic
537Dic3—42no—
538Dic3—41no—
539Dic3—42no—
540Dic3—124no—
541Dic3—122no—
542Dic3—122no—
543C32#200111yescharacteristic, complemented, Sylow
544C23—32no—
545C23—61no—
546C23—61no—
547C23—61no—
548C23—61no—
549C23—61no—
550C23—61no—
551C23D3×#6711yescharacteristic
552Q8—22no—
553Q8—22no—
554Q8—41no—
555Q8—41no—
556Q8—182no—
557Q8—182no—
558Q8—361no—
559Q8—361no—
560C2×C4—22no—
561C2×C4—41no—
562C2×C4—41no—
563C2×C4—61no—
564C2×C4—62no—
565C2×C4—61no—
566C2×C4—62no—
567C2×C4—61no—
568C2×C4—121no—
569C2×C4—121no—
570C2×C4—121no—
571C2×C4—121no—
572C2×C4—121no—
573C2×C4—121no—
574C2×C4—121no—
575C2×C4—121no—
576C2×C4—182no—
577C2×C4—361no—
578C2×C4—361no—
579C2×C4#380411yescharacteristic
580C2×C4C2×#62611yescharacteristic
581C2×C4D3×#6711yescharacteristic
582C2×C4D3×#6711yescharacteristic
583C2×C4#381111yescharacteristic
584C2×C4#381111yescharacteristic
585C8—121no—
586C8—182no—
587C2×C3—21no—
588C2×C3—21no—
589C2×C3—21no—
590C2×C3—21no—
591C2×C3—21no—
592C2×C3—21no—
593C2×C3—21no—
594C2×C3—122no—
595C2×C3#480811yescharacteristic
596C2×C3#480911yescharacteristic
597C2×C3#481311yescharacteristic
598C2×C3#481611yescharacteristic
599C2×C3#496011yescharacteristic
600C2×C3#504711yescharacteristic
601C2×C3#505011yescharacteristic
602C2×C3#505111yescharacteristic
603C2×C3#505211yescharacteristic
604C2×C3#517311yescharacteristic
605C2×C3#518611yescharacteristic
606C2×C3#522311yescharacteristic
607C2×C3#522811yescharacteristic
608C2×C3#523911yescharacteristic
609D3—42no—
610C22—62no—
611C22—62no—
612C22—62no—
613C22—121no—
614C22—121no—
615C22—121no—
616C22—121no—
617C22D3×#21611yescharacteristic
618C22#6394311yescharacteristic
619C22#6394611yescharacteristic
620C22#6394711yescharacteristic
621C22#6397111yescharacteristic
622C22#6397711yescharacteristic
623C22#6398311yescharacteristic
624C4—42no—
625C4—122no—
626C4—122no—
627C4—121no—
628C4—362no—
629C4#6395811yescharacteristic
630C4#6397811yescharacteristic
631C4#6397911yescharacteristic
632C4#6398111yescharacteristic
633C3—21no—
634C3#7027311yescharacteristic, complemented
635C3#7170011yescharacteristic, complemented
636C2—122no—
637C2#1059159511yescharacteristic
638C2#1059159611yescharacteristic
639C2#1059159811yescharacteristic
640C2#1059159911yescharacteristic
641C2#1059165311yescharacteristic
642C2#1059165511yescharacteristic
643C2#1059172411yescharacteristic
subgroupG/H
centerC23D3×#67
commutator, cosocleC22×C32×C4C23
FrattiniC22×C4C2×D32
FittingC22×C32×Q8C22
socleC23×C32C2×D4
prime radicalC23×C3×D3D4
hypercenterC22×Q8D32
hypocenterC32#2001
LCSG ▷ C22×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×C4 ◁ C22×Q8

Complements

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

NH ≅ G/Ntype
1. C22×#3756C2semidirect
4. C2×C3×#835C2semidirect
5. C2×#63567C2semidirect
7. #10589163C2semidirect
39. C2×#835D3semidirect
142. C22×C3×D3Q16semidirect
344. C22×D3#216semidirect
543. C32#2001semidirect
634. C3#70273semidirect
635. C3#71700semidirect

Maximal subgroups

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

subgroupindex
C22×#37562
C2×C3×#9462
C2×#638572
C2×C3×#8352
C2×#635672
C2×(C2×D3)⋊(C3⋊C8)2
#105891632
#717003
#702733