Finite Group Databasebeta

← C3×#72110 #11792261

Subgroups — C3×#72110 #11792261

Order 1152.

869 conjugacy classes of subgroups.

The subgroup lattice has 655 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×#137C211yesmaximal, characteristic, complemented
2C3×#5833C211yesmaximal, characteristic
3C2×C3×#942C211yesmaximal, characteristic, complemented
4C2×C3×#837C211yesmaximal, characteristic, complemented
5C3×#5229C211yesmaximal, characteristic, complemented
6C2×C3×#825C211yesmaximal, characteristic, complemented
7C3×#4554C211yesmaximal, characteristic, complemented
8C3×#2007—31nomaximal
9#72110C311yesmaximal, characteristic, direct product factor
10C2×C32×#41C2211yescharacteristic
11C22×C32×Q8C2211yescharacteristic
12C2×C3×#235C2211yescharacteristic
13C32×#137—22no—
14C32×#137—22no—
15C2×C32×Q16—21no—
16C2×C32×SD16—21no—
17C2×C32×M16C2211yescharacteristic
18C3×#946—21no—
19C2×C3×#216—21no—
20C3×#942—22no—
21C3×#942—22no—
22C2×C3×#215—21no—
23C3×#939—22no—
24C3×#938—21no—
25C3×#930—21no—
26C2×C3×C4⋊Dic3C2211yescharacteristic
27C3×#924—21no—
28C2×C3×C4×Dic3C2211yescharacteristic
29C2×C3×#208C2211yescharacteristic
30C3×#837—22no—
31C3×C3⋊#95—22no—
32C3×#825—22no—
33C2×C3×#137—21no—
34C2×C3×#137—31no—
35C2×C3×#137D311yescharacteristic, complemented
36C2×C3×#137C2×C311yescharacteristic, complemented
37C3×#537—31no—
38#5833C2×C311yescharacteristic
39C2×#942C2×C311yescharacteristic, complemented
40C2×C3×#104—31no—
41C2×C3×#104—31no—
42C3×#391—31no—
43C2×#837C2×C311yescharacteristic, complemented
44#5229C2×C311yescharacteristic, complemented
45C2×#825C2×C311yescharacteristic, complemented
46C3×#343—31no—
47#4554C2×C311yescharacteristic, complemented
48C32×#41—21no—
49C32×#41—21no—
50C32×#41—21no—
51C32×#41—21no—
52C2×C32×Q8—21no—
53C2×C32×Q8—21no—
54C2×C32×Q8—21no—
55C2×C32×Q8—21no—
56C2×C32×Q8—21no—
57C2×C32×Q8D411yescharacteristic
58C2×C32×Q8D412yescomplemented
59C2×C32×D4—21no—
60C2×C32×D4D411yescharacteristic
61C22×C32×C4—21no—
62C22×C32×C4—21no—
63C22×C32×C4C2311yescharacteristic
64C2×C3×#67—21no—
65C2×C3×#67—22no—
66C22×C3×Dic3—21no—
67C22×C3×Dic3D412yes—
68C3×#235—21no—
69C3×#235—21no—
70C3×#235—21no—
71C3×#235—21no—
72C2×C3×D12D411yescharacteristic
73C2×C3×C4×D3—21no—
74C2×C3×Dic6D411yescharacteristic
75C32×Q16—24no—
76C32×SD16—24no—
77C32×M16—21no—
78C32×M16D412yescomplemented
79C2×C32×C8—21no—
80C3×#217—22no—
81C3×#216—24no—
82C3×#215—24no—
83C3×(C2×D3)⋊C4—22no—
84C3×C4⋊Dic3—21no—
85C3×C4⋊Dic3—21no—
86C3×Dic3⋊C4—22no—
87C3×C4×Dic3—21no—
88C3×C4×Dic3—21no—
89C3×#208—21no—
90C3×#208D412yescomplemented
91C2×C3×C3⋊C8—21no—
92#2007—31noSylow
93C2×C3×#41—21no—
94C2×C3×#41—31no—
95C2×C3×#41C2×D311yescharacteristic
96C2×C3×#41C22×C311yescharacteristic
97C22×C3×Q8—21no—
98C22×C3×Q8C2×D311yescharacteristic
99C22×C3×Q8C22×C311yescharacteristic
100C2×#235C22×C311yescharacteristic
101C3×#137—24no—
102C3×#137—24no—
103C3×#137—22no—
104C3×#137—22no—
105C3×#137—22no—
106C3×#137—22no—
107C3×#137—62no—
108C3×#137—62no—
109C2×C3×Q16—22no—
110C2×C3×Q16—21no—
111C2×C3×Q16—21no—
112C2×C3×Q16—61no—
113C2×C3×SD16—22no—
114C2×C3×SD16—21no—
115C2×C3×SD16—21no—
116C2×C3×SD16—61no—
117C2×C3×M16—21no—
118C2×C3×M16—31no—
119C2×C3×M16C2×D311yescharacteristic
120C2×C3×M16C22×C311yescharacteristic
121C3×C22⋊Q8—61no—
122C3×C22⋊Q8—61no—
123C3×#121—61no—
124C3×#121—62no—
125C3×#121—61no—
126C2×C3×C4⋊C4—31no—
127C2×C3×C42—31no—
128#946—21no—
129C2×#216—21no—
130#942—22no—
131#942—22no—
132C2×#215—21no—
133#939—22no—
134#938—21no—
135#930—21no—
136C2×C4⋊Dic3C22×C311yescharacteristic
137#924—21no—
138C2×C4×Dic3C22×C311yescharacteristic
139C2×#208C22×C311yescharacteristic
140C3×#104—62no—
141C3×#104—62no—
142C3×#95—62no—
143#837—22no—
144C3⋊#95—22no—
145#825—22no—
146C23×C32—21no—
147C23×C32C2×D411yescharacteristic
148C22×C3×D3—21no—
149C32×Q8—22no—
150C32×Q8—21no—
151C32×Q8—22no—
152C32×Q8—21no—
153C32×Q8—41no—
154C32×Q8—41no—
155C32×D4—21no—
156C32×D4—21no—
157C32×D4—41no—
158C32×D4—41no—
159C2×C32×C4—21no—
160C2×C32×C4—22no—
161C2×C32×C4—41no—
162C2×C32×C4—41no—
163C2×C32×C4—41no—
164C2×C32×C4—41no—
165C2×C32×C4C2×D411yescharacteristic
166C2×C32×C4C2×D411yescharacteristic
167C2×C32×C4C2×D411yescharacteristic
168C2×C32×C4C2×D411yescharacteristic
169C2×C32×C4C2×D411yescharacteristic
170C2×C32×C4#4111yescharacteristic
171C3×#67—41no—
172C3×#67—41no—
173C3×#67—82no—
174C2×C3×Dic3—22no—
175C2×C3×Dic3—21no—
176C2×C3×Dic3—22no—
177C2×C3×Dic3—41no—
178C2×C3×Dic3—41no—
179C2×C3×Dic3—42no—
180C3×D12—21no—
181C3×D12—21no—
182C3×C4×D3—41no—
183C3×C4×D3—41no—
184C3×Dic6—21no—
185C3×Dic6—21no—
186C32×C8—22no—
187C3×C3⋊C8—22no—
188C2×#137—31no—
189C2×#137C3×D311yescharacteristic, complemented
190#537—31no—
191C2×#104—31no—
192C2×#104—31no—
193#391—31no—
194#343—31no—
195C3×#41—22no—
196C3×#41—22no—
197C3×#41—21no—
198C3×#41—21no—
199C3×#41—21no—
200C3×#41—21no—
201C3×#41—21no—
202C3×#41—21no—
203C3×#41—21no—
204C3×#41—21no—
205C3×#41—41no—
206C3×#41—41no—
207C3×#41—61no—
208C3×#41—61no—
209C3×#41—61no—
210C3×#41—61no—
211C2×C3×Q8—21no—
212C2×C3×Q8—21no—
213C2×C3×Q8—22no—
214C2×C3×Q8—22no—
215C2×C3×Q8—21no—
216C2×C3×Q8—21no—
217C2×C3×Q8—21no—
218C2×C3×Q8—21no—
219C2×C3×Q8—21no—
220C2×C3×Q8—21no—
221C2×C3×Q8—21no—
222C2×C3×Q8—21no—
223C2×C3×Q8—21no—
224C2×C3×Q8—22no—
225C2×C3×Q8—31no—
226C2×C3×Q8—41no—
227C2×C3×Q8—41no—
228C2×C3×Q8—41no—
229C2×C3×Q8#6711yescharacteristic
230C2×C3×Q8#6712yescomplemented
231C2×C3×Q8C3×D411yescharacteristic
232C2×C3×Q8C3×D412yescomplemented
233C2×C3×D4—21no—
234C2×C3×D4—21no—
235C2×C3×D4—21no—
236C2×C3×D4—31no—
237C2×C3×D4—41no—
238C2×C3×D4—61no—
239C2×C3×D4—62no—
240C2×C3×D4#6711yescharacteristic
241C2×C3×D4C3×D411yescharacteristic
242C22×C3×C4—21no—
243C22×C3×C4—21no—
244C22×C3×C4—21no—
245C22×C3×C4—21no—
246C22×C3×C4—21no—
247C22×C3×C4—32no—
248C22×C3×C4—41no—
249C22×C3×C4—41no—
250C22×C3×C4—61no—
251C22×C3×C4—61no—
252C22×C3×C4C22×D311yescharacteristic
253C22×C3×C4C23×C311yescharacteristic
254C2×#67—21no—
255C2×#67—22no—
256C22×Dic3—21no—
257C22×Dic3C3×D412yes—
258#235—21no—
259#235—21no—
260#235—21no—
261#235—21no—
262C2×D12C3×D411yescharacteristic
263C2×C4×D3—21no—
264C2×Dic6C3×D411yescharacteristic
265C3×Q16—28no—
266C3×Q16—24no—
267C3×Q16—24no—
268C3×Q16—64no—
269C3×SD16—28no—
270C3×SD16—24no—
271C3×SD16—24no—
272C3×SD16—64no—
273C3×M16—22no—
274C3×M16—21no—
275C3×M16—21no—
276C3×M16—22no—
277C3×M16—32no—
278C3×M16—61no—
279C3×M16#6712yescomplemented
280C3×M16C3×D412yescomplemented
281C2×C3×C8—22no—
282C2×C3×C8—21no—
283C2×C3×C8—21no—
284C2×C3×C8—61no—
285C3×C4⋊C4—62no—
286C3×C4⋊C4—61no—
287C3×C4⋊C4—61no—
288C3×C22⋊C4—62no—
289C3×C22⋊C4—62no—
290C3×C42—61no—
291C3×C42—61no—
292#217—22no—
293#216—24no—
294#215—24no—
295(C2×D3)⋊C4—22no—
296C4⋊Dic3—21no—
297C4⋊Dic3—21no—
298Dic3⋊C4—22no—
299C4×Dic3—21no—
300C4×Dic3—21no—
301#208—21no—
302#208C3×D412yescomplemented
303C2×C3⋊C8—21no—
304C22×C32—21no—
305C22×C32—21no—
306C22×C32—41no—
307C22×C32—41no—
308C22×C32—41no—
309C22×C32#12011yescharacteristic
310C22×C32#12111yescharacteristic
311C22×C32#12711yescharacteristic
312C2×C3×D3—41no—
313C2×C3×D3—41no—
314C2×C3×D3—41no—
315C32×C4—41no—
316C32×C4—42no—
317C32×C4#12011yescharacteristic
318C32×C4#12011yescharacteristic
319C32×C4#12111yescharacteristic
320C32×C4#12111yescharacteristic
321C3×Dic3—42no—
322C3×Dic3—41no—
323C3×Dic3—42no—
324C2×#41—31no—
325C2×#41C2×C3×D311yescharacteristic
326C22×Q8C2×C3×D311yescharacteristic
327#137—22no—
328#137—22no—
329#137—62no—
330#137—62no—
331C2×Q16—21no—
332C2×Q16—61no—
333C2×SD16—21no—
334C2×SD16—61no—
335C2×M16—31no—
336C2×M16C2×C3×D311yescharacteristic
337C22⋊Q8—61no—
338C22⋊Q8—61no—
339#121—61no—
340#121—62no—
341#121—61no—
342C2×C4⋊C4—31no—
343C2×C42—31no—
344#104—62no—
345#104—62no—
346#95—62no—
347C23×C3—21no—
348C23×C3—21no—
349C23×C3—21no—
350C23×C3—41no—
351C23×C3—61no—
352C23×C3D3×D411yescharacteristic
353C23×C3C2×C3×D411yescharacteristic
354C22×D3—21no—
355C3×Q8—24no—
356C3×Q8—22no—
357C3×Q8—22no—
358C3×Q8—21no—
359C3×Q8—22no—
360C3×Q8—21no—
361C3×Q8—22no—
362C3×Q8—22no—
363C3×Q8—21no—
364C3×Q8—21no—
365C3×Q8—42no—
366C3×Q8—41no—
367C3×Q8—42no—
368C3×Q8—42no—
369C3×Q8—41no—
370C3×Q8—41no—
371C3×Q8—41no—
372C3×Q8—41no—
373C3×Q8—61no—
374C3×Q8—61no—
375C3×D4—22no—
376C3×D4—21no—
377C3×D4—21no—
378C3×D4—21no—
379C3×D4—21no—
380C3×D4—41no—
381C3×D4—42no—
382C3×D4—42no—
383C3×D4—41no—
384C3×D4—41no—
385C3×D4—41no—
386C3×D4—41no—
387C3×D4—61no—
388C3×D4—61no—
389C3×D4—121no—
390C3×D4—121no—
391C3×D4—242no—
392C2×C3×C4—21no—
393C2×C3×C4—22no—
394C2×C3×C4—21no—
395C2×C3×C4—22no—
396C2×C3×C4—21no—
397C2×C3×C4—21no—
398C2×C3×C4—21no—
399C2×C3×C4—21no—
400C2×C3×C4—21no—
401C2×C3×C4—21no—
402C2×C3×C4—41no—
403C2×C3×C4—42no—
404C2×C3×C4—42no—
405C2×C3×C4—42no—
406C2×C3×C4—42no—
407C2×C3×C4—42no—
408C2×C3×C4—41no—
409C2×C3×C4—41no—
410C2×C3×C4—41no—
411C2×C3×C4—41no—
412C2×C3×C4—41no—
413C2×C3×C4—41no—
414C2×C3×C4—41no—
415C2×C3×C4—41no—
416C2×C3×C4—62no—
417C2×C3×C4—62no—
418C2×C3×C4—61no—
419C2×C3×C4—121no—
420C2×C3×C4—121no—
421C2×C3×C4—121no—
422C2×C3×C4—121no—
423C2×C3×C4—122no—
424C2×C3×C4D3×D411yescharacteristic
425C2×C3×C4D3×D411yescharacteristic
426C2×C3×C4#23711yescharacteristic
427C2×C3×C4C2×#6711yescharacteristic
428C2×C3×C4C2×#6711yescharacteristic
429C2×C3×C4C2×#6711yescharacteristic
430C2×C3×C4C2×C3×D411yescharacteristic
431C2×C3×C4C2×C3×D411yescharacteristic
432C2×C3×C4C2×C3×D411yescharacteristic
433C2×C3×C4C2×C3×D411yescharacteristic
434C2×C3×C4C2×C3×D411yescharacteristic
435C2×C3×C4C3×#4111yescharacteristic
436#67—41no—
437#67—41no—
438#67—82no—
439C2×Dic3—22no—
440C2×Dic3—21no—
441C2×Dic3—22no—
442C2×Dic3—41no—
443C2×Dic3—41no—
444C2×Dic3—42no—
445D12—21no—
446D12—21no—
447C4×D3—41no—
448C4×D3—41no—
449Dic6—21no—
450Dic6—21no—
451C3×C8—24no—
452C3×C8—22no—
453C3×C8—22no—
454C3×C8—62no—
455C3⋊C8—22no—
456C2×C32—21no—
457C2×C32—21no—
458C2×C32—81no—
459C2×C32#39211yescharacteristic
460C2×C32#45511yescharacteristic
461C2×C32#45611yescharacteristic
462C3×D3—81no—
463#41—21no—
464#41—21no—
465#41—21no—
466#41—21no—
467#41—61no—
468#41—61no—
469#41—61no—
470#41—61no—
471C2×Q8—21no—
472C2×Q8—21no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—21no—
476C2×Q8—31no—
477C2×Q8C3×#6711yescharacteristic
478C2×Q8C3×#6712yescomplemented
479C2×D4—21no—
480C2×D4—31no—
481C2×D4—61no—
482C2×D4—62no—
483C2×D4C3×#6711yescharacteristic
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—32no—
487C22×C4—61no—
488C22×C4—61no—
489C22×C4C22×C3×D311yescharacteristic
490Q16—24no—
491Q16—64no—
492SD16—24no—
493SD16—64no—
494M16—21no—
495M16—32no—
496M16—61no—
497M16C3×#6712yescomplemented
498C2×C8—21no—
499C2×C8—61no—
500C4⋊C4—62no—
501C4⋊C4—61no—
502C4⋊C4—61no—
503C22⋊C4—62no—
504C22⋊C4—62no—
505C42—61no—
506C42—61no—
507C22×C3—21no—
508C22×C3—21no—
509C22×C3—21no—
510C22×C3—21no—
511C22×C3—21no—
512C22×C3—21no—
513C22×C3—21no—
514C22×C3—41no—
515C22×C3—41no—
516C22×C3—42no—
517C22×C3—41no—
518C22×C3—41no—
519C22×C3—41no—
520C22×C3—41no—
521C22×C3—41no—
522C22×C3—41no—
523C22×C3—81no—
524C22×C3—81no—
525C22×C3—121no—
526C22×C3—121no—
527C22×C3—121no—
528C22×C3#93711yescharacteristic
529C22×C3#93911yescharacteristic
530C22×C3#94011yescharacteristic
531C22×C3C3×#12011yescharacteristic
532C22×C3C3×#12111yescharacteristic
533C22×C3C3×#12711yescharacteristic
534C2×D3—41no—
535C2×D3—41no—
536C2×D3—41no—
537C3×C4—21no—
538C3×C4—21no—
539C3×C4—21no—
540C3×C4—21no—
541C3×C4—42no—
542C3×C4—44no—
543C3×C4—41no—
544C3×C4—42no—
545C3×C4—41no—
546C3×C4—42no—
547C3×C4—122no—
548C3×C4—122no—
549C3×C4—121no—
550C3×C4#93711yescharacteristic
551C3×C4#93811yescharacteristic
552C3×C4#93911yescharacteristic
553C3×C4#95311yescharacteristic
554C3×C4C3×#12011yescharacteristic
555C3×C4C3×#12011yescharacteristic
556C3×C4C3×#12111yescharacteristic
557C3×C4C3×#12111yescharacteristic
558Dic3—42no—
559Dic3—41no—
560Dic3—42no—
561C32#200711yescharacteristic, complemented, Sylow
562C23—21no—
563C23—61no—
564C23C3×D3×D411yescharacteristic
565Q8—22no—
566Q8—21no—
567Q8—22no—
568Q8—21no—
569Q8—41no—
570Q8—41no—
571Q8—61no—
572Q8—61no—
573D4—21no—
574D4—21no—
575D4—41no—
576D4—41no—
577D4—61no—
578D4—61no—
579D4—121no—
580D4—121no—
581D4—242no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—41no—
588C2×C4—62no—
589C2×C4—62no—
590C2×C4—61no—
591C2×C4—121no—
592C2×C4—121no—
593C2×C4—121no—
594C2×C4—121no—
595C2×C4—122no—
596C2×C4C3×D3×D411yescharacteristic
597C2×C4C3×D3×D411yescharacteristic
598C2×C4C3×#23711yescharacteristic
599C2×C4C2×C3×#6711yescharacteristic
600C2×C4C2×C3×#6711yescharacteristic
601C2×C4C2×C3×#6711yescharacteristic
602C8—22no—
603C8—62no—
604C2×C3—21no—
605C2×C3—21no—
606C2×C3—21no—
607C2×C3—21no—
608C2×C3—21no—
609C2×C3—21no—
610C2×C3—21no—
611C2×C3—41no—
612C2×C3—41no—
613C2×C3—82no—
614C2×C3—81no—
615C2×C3—81no—
616C2×C3—241no—
617C2×C3#520211yescharacteristic
618C2×C3#520511yescharacteristic
619C2×C3#522311yescharacteristic
620C2×C3C3×#39211yescharacteristic
621C2×C3C3×#45511yescharacteristic
622C2×C3C3×#45611yescharacteristic
623D3—81no—
624C22—21no—
625C22—21no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—121no—
630C22—121no—
631C22—121no—
632C22C3×#93711yescharacteristic
633C22C3×#93911yescharacteristic
634C22C3×#94011yescharacteristic
635C4—41no—
636C4—42no—
637C4—122no—
638C4—122no—
639C4—121no—
640C4C3×#93711yescharacteristic
641C4C3×#93811yescharacteristic
642C4C3×#93911yescharacteristic
643C4C3×#95311yescharacteristic
644C3—21no—
645C3#7211011yescharacteristic, direct product factor
646C3C3×#200711yescharacteristic, complemented
647C2—21no—
648C2—21no—
649C2—81no—
650C2—241no—
651C2C3×#520211yescharacteristic
652C2C3×#520511yescharacteristic
653C2C3×#522311yescharacteristic
subgroupG/H
centerC22×C3#937
commutator, cosocleC22×C3×C4C23×C3
FrattiniC22×C4C22×C3×D3
FittingC2×C32×#137C2
socleC22×C32#120
prime radicalC3×#5833C2
hypercenterC2×C3×#137D3
hypocenterC3C3×#2007
LCSG ▷ C22×C3×C4 ▷ C2×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C22×C3×C4 ◁ C2×C3×#137

Complements

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

NH ≅ G/Ntype
1. C2×C32×#137C2semidirect
3. C2×C3×#942C2semidirect
4. C2×C3×#837C2semidirect
5. C3×#5229C2semidirect
6. C2×C3×#825C2semidirect
7. C3×#4554C2semidirect
9. #72110C3direct (N × H)
35. C2×C3×#137D3semidirect
36. C2×C3×#137C2×C3semidirect
39. C2×#942C2×C3semidirect
43. C2×#837C2×C3semidirect
44. #5229C2×C3semidirect
45. C2×#825C2×C3semidirect
47. #4554C2×C3semidirect
58. C2×C32×Q8D4semidirect
78. C32×M16D4semidirect
90. C3×#208D4semidirect
189. C2×#137C3×D3semidirect
230. C2×C3×Q8#67semidirect
232. C2×C3×Q8C3×D4semidirect
279. C3×M16#67semidirect
280. C3×M16C3×D4semidirect
302. #208C3×D4semidirect
478. C2×Q8C3×#67semidirect
497. M16C3×#67semidirect
561. C32#2007semidirect
645. C3#72110direct (N × H)
646. C3C3×#2007semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#1372
C3×#58332
C2×C3×#9422
C2×C3×#8372
C3×#52292
C2×C3×#8252
C3×#45542
C3×#20073
#721103