Finite Group Databasebeta

← C3×#86759 #11904473

Subgroups — C3×#86759 #11904473

Order 1152.

3124 conjugacy classes of subgroups.

The subgroup lattice has 889 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#1007C211yesmaximal, characteristic, complemented
2C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
3C32×D4×Q8C211yesmaximal, characteristic, complemented
4C3×#5817C211yesmaximal, characteristic, complemented
5C3×Q8×#67C211yesmaximal, characteristic, complemented
6C3×#5727C213yesmaximal, complemented
7C3×#5724C213yesmaximal, complemented
8C3×#5633C213yesmaximal, complemented
9C3×#5632C213yesmaximal, complemented
10C3×#5628C213yesmaximal, complemented
11C3×#5627C213yesmaximal, complemented
12C3×#5576C211yesmaximal, characteristic, complemented
13C3×#5572C211yesmaximal, characteristic, complemented
14C3×#5552C213yesmaximal, complemented
15C3×#5547C213yesmaximal, complemented
16C3×#3486—31nomaximal
17#86759C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic, complemented
20C3×#1007—28no—
21C2×C3×#239C2213yes—
22C2×C3×#239C2211yescharacteristic, complemented
23C2×C3×D3×Q8—28no—
24C2×C3×D3×Q8C2211yescharacteristic
25C2×C3×D3×Q8C2213yes—
26C2×C3×D3×Q8C2213yes—
27C2×C3×D3×Q8C2211yescharacteristic
28C2×C3×D3×Q8C2213yescomplemented
29C2×C3×#235C2213yes—
30C2×C3×#235C2213yescomplemented
31C22×C3×C4×D3C2213yes—
32C22×C3×Dic6C2213yes—
33C32×C4⋊Q8C2213yescomplemented
34C32×C22⋊Q8C2213yes—
35C32×C22⋊Q8C2213yescomplemented
36C32×C4×Q8C2211yescharacteristic, complemented
37C32×C4×D4C2213yes—
38C3×#947C2213yescomplemented
39C3×#946C2213yes—
40C3×#946C2213yescomplemented
41C3×Q8×Dic3C2211yescharacteristic, complemented
42C3×#944C2213yescomplemented
43C3×#939C2213yes—
44C3×#937C2211yescharacteristic
45C3×#930C2213yes—
46C3×C4×#67C2213yes—
47C3×C4×#67C2213yes—
48C3×#924C2213yescomplemented
49C3×#897C2213yescomplemented
50C3×#896C2213yes—
51C3×#896C2216yescomplemented
52C3×#896C2216yescomplemented
53C3×#895C2213yes—
54C3×#894C2213yes—
55C3×#894C2216yes—
56C3×#893C2216yes—
57C3×#892C2213yes—
58C3×#888C2216yescomplemented
59C3×#887C2213yescomplemented
60C3×#885C2216yescomplemented
61C3×#884C2213yes—
62C3×#883C2213yes—
63C3×#882C2213yes—
64C3×#67⋊C4C2216yes—
65C3×#878C2213yes—
66C3×#875C2213yescomplemented
67C3×C4×D12C2213yes—
68C3×#872C2213yes—
69C3×C4×Dic6C2213yescomplemented
70C2×C3×2−1+4—31no—
71C23×C3×Q8—31no—
72C2×#1007C2×C311yescharacteristic, complemented
73C22×D3×Q8C2×C311yescharacteristic, complemented
74C3×D4×Q8—21no—
75C3×D4×Q8—31no—
76C3×D4×Q8—33no—
77C3×D4×Q8—33no—
78C3×D4×Q8D311yescharacteristic, complemented
79C3×D4×Q8C2×C311yescharacteristic, complemented
80C3×#548—31no—
81C3×#548—33no—
82C3×#548—31no—
83C3×#548—33no—
84C3×#536—33no—
85C3×#536—33no—
86C3×#525—33no—
87C3×#525—33no—
88C3×#519—31no—
89#5817C2×C311yescharacteristic, complemented
90Q8×#67C2×C311yescharacteristic, complemented
91#5727C2×C313yescomplemented
92#5724C2×C313yescomplemented
93#5633C2×C313yescomplemented
94#5632C2×C313yescomplemented
95#5628C2×C313yescomplemented
96#5627C2×C313yescomplemented
97#5576C2×C311yescharacteristic, complemented
98#5572C2×C311yescharacteristic, complemented
99#5552C2×C313yescomplemented
100#5547C2×C313yescomplemented
101C23×C3×D3C2311yescharacteristic
102C2×C32×Q8—24no—
103C2×C32×Q8—24no—
104C2×C32×Q8C2313yes—
105C2×C32×Q8C2313yes—
106C2×C32×Q8C2311yescharacteristic
107C2×C32×D4C2311yescharacteristic
108C22×C32×C4C2313yes—
109C22×C32×C4C2313yes—
110C2×C3×#67C2313yes—
111C2×C3×#67C2311yescharacteristic
112C2×C3×#67C2311yescharacteristic
113C2×C3×#67C2313yes—
114C22×C3×Dic3C2313yes—
115C3×#239—24no—
116C3×#239—212no—
117C3×D3×Q8—24no—
118C3×D3×Q8—212no—
119C3×D3×Q8—212no—
120C3×D3×Q8—212no—
121C3×D3×Q8D418yescomplemented
122C3×#235—212no—
123C3×#235—212no—
124C2×C3×D12C2313yes—
125C2×C3×D12C2313yes—
126C2×C3×D12C2313yes—
127C2×C3×C4×D3—212no—
128C2×C3×C4×D3C2316yes—
129C2×C3×C4×D3C2313yes—
130C2×C3×C4×D3C2313yes—
131C2×C3×C4×D3C2313yes—
132C2×C3×C4×D3C2313yes—
133C2×C3×C4×D3C2313yes—
134C2×C3×Dic6—212no—
135C2×C3×Dic6C2313yes—
136C2×C3×Dic6C2316yes—
137C2×C3×Dic6C2313yes—
138C2×C3×Dic6C2313yes—
139C32×C4⋊C4C2313yes—
140C32×C4⋊C4C2316yes—
141C32×C4⋊C4C2313yes—
142C32×C22⋊C4C2313yes—
143C32×C22⋊C4C2313yes—
144C32×C42C2313yes—
145C3×#217C2311yescharacteristic
146C3×#217C2313yes—
147C3×(C2×D3)⋊C4C2316yes—
148C3×(C2×D3)⋊C4C2313yes—
149C3×(C2×D3)⋊C4C2313yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×(C2×D3)⋊C4C2316yes—
152C3×(C2×D3)⋊C4C2311yescharacteristic
153C3×(C2×D3)⋊C4C2313yes—
154C3×(C2×D3)⋊C4C2311yescharacteristic
155C3×C4⋊Dic3C2313yes—
156C3×C4⋊Dic3C2313yes—
157C3×Dic3⋊C4C2313yes—
158C3×Dic3⋊C4C2313yes—
159C3×Dic3⋊C4C2316yes—
160C3×Dic3⋊C4C2313yes—
161C3×Dic3⋊C4C2313yes—
162C3×C4×Dic3C2316yes—
163C3×C4×Dic3C2313yes—
164#3486—31noSylow
165C3×2−1+4—68no—
166C2×C3×#41—33no—
167C2×C3×#41—31no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C22×C3×Q8—21no—
171C22×C3×Q8—21no—
172C22×C3×Q8—31no—
173C22×C3×Q8—33no—
174C22×C3×Q8—33no—
175C22×C3×Q8—31no—
176C22×C3×Q8—33no—
177C22×C3×Q8—33no—
178C22×C3×Q8—68no—
179C22×C3×Q8C2×D311yescharacteristic
180C22×C3×Q8C2×D311yescharacteristic, complemented
181C22×C3×Q8C22×C311yescharacteristic
182C22×C3×Q8C22×C311yescharacteristic, complemented
183C23×C3×C4—33no—
184#1007—28no—
185C2×#239C22×C313yes—
186C2×#239C22×C311yescharacteristic, complemented
187C2×D3×Q8—28no—
188C2×D3×Q8C22×C313yes—
189C2×D3×Q8C22×C313yes—
190C2×D3×Q8C22×C311yescharacteristic
191C2×D3×Q8C22×C311yescharacteristic
192C2×D3×Q8C22×C313yescomplemented
193C2×#235C22×C313yes—
194C2×#235C22×C313yescomplemented
195C22×C4×D3C22×C313yes—
196C22×Dic6C22×C313yes—
197C3×C4⋊Q8—23no—
198C3×C4⋊Q8—33no—
199C3×C4⋊Q8—36no—
200C3×C4⋊Q8C2×D313yescomplemented
201C3×C4⋊Q8C22×C313yescomplemented
202C3×#124—33no—
203C3×#124—36no—
204C3×#124—33no—
205C3×#123—36no—
206C3×#123—33no—
207C3×#123—33no—
208C3×C22⋊Q8—23no—
209C3×C22⋊Q8—23no—
210C3×C22⋊Q8—33no—
211C3×C22⋊Q8—33no—
212C3×C22⋊Q8—33no—
213C3×C22⋊Q8—33no—
214C3×C22⋊Q8—36no—
215C3×C22⋊Q8—36no—
216C3×C22⋊Q8—33no—
217C3×C22⋊Q8—33no—
218C3×C22⋊Q8C2×D313yes—
219C3×C22⋊Q8C2×D313yescomplemented
220C3×C22⋊Q8C22×C313yes—
221C3×C22⋊Q8C22×C313yescomplemented
222C3×#121—33no—
223C3×#121—33no—
224C3×#121—33no—
225C3×#121—33no—
226C3×#120—31no—
227C3×#120—33no—
228C3×C4×Q8—21no—
229C3×C4×Q8—31no—
230C3×C4×Q8—33no—
231C3×C4×Q8—33no—
232C3×C4×Q8C2×D311yescharacteristic, complemented
233C3×C4×Q8C22×C311yescharacteristic, complemented
234C3×C4×D4—23no—
235C3×C4×D4—33no—
236C3×C4×D4—33no—
237C3×C4×D4—36no—
238C3×C4×D4—36no—
239C3×C4×D4—33no—
240C3×C4×D4C2×D313yes—
241C3×C4×D4C22×C313yes—
242C3×#117—33no—
243C3×#117—33no—
244#947C22×C313yescomplemented
245#946C22×C313yes—
246#946C22×C313yescomplemented
247Q8×Dic3C22×C311yescharacteristic, complemented
248#944C22×C313yescomplemented
249#939C22×C313yes—
250#937C22×C311yescharacteristic
251#930C22×C313yes—
252C4×#67C22×C313yes—
253C4×#67C22×C313yes—
254#924C22×C313yescomplemented
255#897C22×C313yescomplemented
256#896C22×C313yes—
257#896C22×C316yescomplemented
258#896C22×C316yescomplemented
259#895C22×C313yes—
260#894C22×C313yes—
261#894C22×C316yes—
262#893C22×C316yes—
263#892C22×C313yes—
264#888C22×C316yescomplemented
265#887C22×C313yescomplemented
266#885C22×C316yescomplemented
267#884C22×C313yes—
268#883C22×C313yes—
269#882C22×C313yes—
270#67⋊C4C22×C316yes—
271#878C22×C313yes—
272#875C22×C313yescomplemented
273C4×D12C22×C313yes—
274#872C22×C313yes—
275C4×Dic6C22×C313yescomplemented
276C23×C32C2411yescharacteristic
277C23×C32C2411yescharacteristic
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3C2413yes—
282C22×C3×D3C2411yescharacteristic
283C22×C3×D3C2411yescharacteristic
284C32×Q8—26no—
285C32×Q8—26no—
286C32×Q8C2×D414yes—
287C32×D4—22no—
288C2×C32×C4—26no—
289C2×C32×C4—26no—
290C2×C32×C4C2413yes—
291C2×C32×C4C2411yescharacteristic
292C2×C32×C4C2413yes—
293C2×C32×C4C2413yes—
294C2×C32×C4C2413yes—
295C3×#67—26no—
296C3×#67—22no—
297C3×#67—22no—
298C3×#67—26no—
299C2×C3×Dic3—26no—
300C2×C3×Dic3C2411yescharacteristic
301C2×C3×Dic3C2413yes—
302C2×C3×Dic3C2411yescharacteristic
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2413yes—
305C3×D12—26no—
306C3×D12—26no—
307C3×D12—26no—
308C3×C4×D3—26no—
309C3×C4×D3—26no—
310C3×C4×D3—26no—
311C3×C4×D3—26no—
312C3×C4×D3—212no—
313C3×C4×D3C2×D4112yes—
314C3×Dic6—26no—
315C3×Dic6—212no—
316C3×Dic6—26no—
317C3×Dic6C2×D4112yes—
318C2×2−1+4—31no—
319C23×Q8—31no—
320D4×Q8—31no—
321D4×Q8—33no—
322D4×Q8—33no—
323D4×Q8C3×D311yescharacteristic, complemented
324#548—31no—
325#548—33no—
326#548—31no—
327#548—33no—
328#536—33no—
329#536—33no—
330#525—33no—
331#525—33no—
332#519—31no—
333C24×C3—31no—
334C23×D3C23×C311yescharacteristic
335C3×#41—612no—
336C3×#41—612no—
337C3×#41—612no—
338C3×#41—64no—
339C2×C3×Q8—24no—
340C2×C3×Q8—24no—
341C2×C3×Q8—24no—
342C2×C3×Q8—24no—
343C2×C3×Q8—21no—
344C2×C3×Q8—23no—
345C2×C3×Q8—23no—
346C2×C3×Q8—38no—
347C2×C3×Q8—33no—
348C2×C3×Q8—36no—
349C2×C3×Q8—33no—
350C2×C3×Q8—33no—
351C2×C3×Q8—44no—
352C2×C3×Q8—44no—
353C2×C3×Q8—612no—
354C2×C3×Q8—612no—
355C2×C3×Q8—612no—
356C2×C3×Q8—612no—
357C2×C3×Q8—64no—
358C2×C3×Q8C22×D313yes—
359C2×C3×Q8C22×D313yes—
360C2×C3×Q8C22×D311yescharacteristic
361C2×C3×Q8C23×C313yes—
362C2×C3×Q8C23×C313yes—
363C2×C3×Q8C23×C311yescharacteristic
364C2×C3×D4—21no—
365C2×C3×D4—31no—
366C2×C3×D4—33no—
367C2×C3×D4—31no—
368C2×C3×D4—33no—
369C2×C3×D4—33no—
370C2×C3×D4—33no—
371C2×C3×D4—33no—
372C2×C3×D4C22×D311yescharacteristic
373C2×C3×D4C23×C311yescharacteristic
374C22×C3×C4—23no—
375C22×C3×C4—23no—
376C22×C3×C4—33no—
377C22×C3×C4—33no—
378C22×C3×C4—33no—
379C22×C3×C4—33no—
380C22×C3×C4—36no—
381C22×C3×C4—33no—
382C22×C3×C4—33no—
383C22×C3×C4—612no—
384C22×C3×C4C22×D313yes—
385C22×C3×C4C22×D313yes—
386C22×C3×C4C23×C313yes—
387C22×C3×C4C23×C313yes—
388C2×#67C23×C313yes—
389C2×#67C23×C311yescharacteristic
390C2×#67C23×C311yescharacteristic
391C2×#67C23×C313yes—
392C22×Dic3C23×C313yes—
393#239—24no—
394#239—212no—
395D3×Q8—24no—
396D3×Q8—212no—
397D3×Q8—212no—
398D3×Q8—212no—
399D3×Q8C3×D418yescomplemented
400#235—212no—
401#235—212no—
402C2×D12C23×C313yes—
403C2×D12C23×C313yes—
404C2×D12C23×C313yes—
405C2×C4×D3—212no—
406C2×C4×D3C23×C313yes—
407C2×C4×D3C23×C313yes—
408C2×C4×D3C23×C316yes—
409C2×C4×D3C23×C313yes—
410C2×C4×D3C23×C313yes—
411C2×C4×D3C23×C313yes—
412C2×Dic6—212no—
413C2×Dic6C23×C313yes—
414C2×Dic6C23×C313yes—
415C2×Dic6C23×C316yes—
416C2×Dic6C23×C313yes—
417C3×C4⋊C4—23no—
418C3×C4⋊C4—23no—
419C3×C4⋊C4—26no—
420C3×C4⋊C4—33no—
421C3×C4⋊C4—33no—
422C3×C4⋊C4—33no—
423C3×C4⋊C4—36no—
424C3×C4⋊C4—33no—
425C3×C4⋊C4—33no—
426C3×C4⋊C4—33no—
427C3×C4⋊C4C22×D313yes—
428C3×C4⋊C4C22×D316yes—
429C3×C4⋊C4C22×D313yes—
430C3×C4⋊C4C23×C313yes—
431C3×C4⋊C4C23×C316yes—
432C3×C4⋊C4C23×C313yes—
433C3×C22⋊C4—23no—
434C3×C22⋊C4—23no—
435C3×C22⋊C4—31no—
436C3×C22⋊C4—33no—
437C3×C22⋊C4—33no—
438C3×C22⋊C4—31no—
439C3×C22⋊C4—33no—
440C3×C22⋊C4—31no—
441C3×C22⋊C4—33no—
442C3×C22⋊C4—36no—
443C3×C22⋊C4—36no—
444C3×C22⋊C4—33no—
445C3×C22⋊C4C22×D313yes—
446C3×C22⋊C4C22×D313yes—
447C3×C22⋊C4C23×C313yes—
448C3×C22⋊C4C23×C313yes—
449C3×C42—23no—
450C3×C42—36no—
451C3×C42—33no—
452C3×C42C22×D313yes—
453C3×C42C23×C313yes—
454#217C23×C311yescharacteristic
455#217C23×C313yes—
456(C2×D3)⋊C4C23×C311yescharacteristic
457(C2×D3)⋊C4C23×C313yes—
458(C2×D3)⋊C4C23×C311yescharacteristic
459(C2×D3)⋊C4C23×C313yes—
460(C2×D3)⋊C4C23×C316yes—
461(C2×D3)⋊C4C23×C313yes—
462(C2×D3)⋊C4C23×C313yes—
463(C2×D3)⋊C4C23×C316yes—
464C4⋊Dic3C23×C313yes—
465C4⋊Dic3C23×C313yes—
466Dic3⋊C4C23×C313yes—
467Dic3⋊C4C23×C313yes—
468Dic3⋊C4C23×C313yes—
469Dic3⋊C4C23×C316yes—
470Dic3⋊C4C23×C313yes—
471C4×Dic3C23×C316yes—
472C4×Dic3C23×C313yes—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C322−1+412yescomplemented
479C22×C32C2511yescharacteristic
480C2×C3×D3—28no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—23no—
486C2×C3×D3—23no—
487C2×C3×D3—23no—
488C2×C3×D3C22×D412yes—
489C2×C3×D32−1+412yescomplemented
490C32×C4—21no—
491C32×C4—23no—
492C32×C4—23no—
493C32×C4—23no—
494C32×C4C22×D416yes—
495C3×Dic3—23no—
496C3×Dic3—21no—
497C3×Dic3—23no—
498C3×Dic3—21no—
499C3×Dic3C22×D416yes—
5002−1+4—68no—
501C2×#41—33no—
502C2×#41—31no—
503C2×#41—33no—
504C2×#41—33no—
505C22×Q8—31no—
506C22×Q8—33no—
507C22×Q8—33no—
508C22×Q8—31no—
509C22×Q8—33no—
510C22×Q8—33no—
511C22×Q8—68no—
512C22×Q8C2×C3×D311yescharacteristic
513C22×Q8C2×C3×D311yescharacteristic, complemented
514C23×C4—33no—
515C4⋊Q8—33no—
516C4⋊Q8—36no—
517C4⋊Q8C2×C3×D313yescomplemented
518#124—33no—
519#124—36no—
520#124—33no—
521#123—36no—
522#123—33no—
523#123—33no—
524C22⋊Q8—33no—
525C22⋊Q8—33no—
526C22⋊Q8—33no—
527C22⋊Q8—33no—
528C22⋊Q8—36no—
529C22⋊Q8—36no—
530C22⋊Q8—33no—
531C22⋊Q8—33no—
532C22⋊Q8C2×C3×D313yes—
533C22⋊Q8C2×C3×D313yescomplemented
534#121—33no—
535#121—33no—
536#121—33no—
537#121—33no—
538#120—31no—
539#120—33no—
540C4×Q8—31no—
541C4×Q8—33no—
542C4×Q8—33no—
543C4×Q8C2×C3×D311yescharacteristic, complemented
544C4×D4—33no—
545C4×D4—33no—
546C4×D4—36no—
547C4×D4—36no—
548C4×D4—33no—
549C4×D4C2×C3×D313yes—
550#117—33no—
551#117—33no—
552C23×C3—21no—
553C23×C3—21no—
554C23×C3—31no—
555C23×C3—31no—
556C23×C3—33no—
557C23×C3—62no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3C23×D311yescharacteristic
561C23×C3C23×D311yescharacteristic
562C23×C3C24×C311yescharacteristic
563C23×C3C24×C311yescharacteristic
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3C24×C313yes—
568C22×D3C24×C311yescharacteristic
569C22×D3C24×C311yescharacteristic
570C3×Q8—26no—
571C3×Q8—26no—
572C3×Q8—26no—
573C3×Q8—26no—
574C3×Q8—24no—
575C3×Q8—312no—
576C3×Q8—46no—
577C3×Q8—46no—
578C3×Q8—612no—
579C3×Q8—66no—
580C3×Q8—66no—
581C3×Q8D3×D414yes—
582C3×Q8C2×C3×D414yes—
583C3×D4—24no—
584C3×D4—22no—
585C3×D4—22no—
586C3×D4—66no—
587C3×D4—66no—
588C3×D4—66no—
589C3×D4—62no—
590C3×D4—62no—
591C3×D4—66no—
592C3×D4—66no—
593C2×C3×C4—26no—
594C2×C3×C4—26no—
595C2×C3×C4—26no—
596C2×C3×C4—26no—
597C2×C3×C4—21no—
598C2×C3×C4—23no—
599C2×C3×C4—23no—
600C2×C3×C4—23no—
601C2×C3×C4—23no—
602C2×C3×C4—33no—
603C2×C3×C4—312no—
604C2×C3×C4—33no—
605C2×C3×C4—31no—
606C2×C3×C4—33no—
607C2×C3×C4—31no—
608C2×C3×C4—46no—
609C2×C3×C4—46no—
610C2×C3×C4—66no—
611C2×C3×C4—612no—
612C2×C3×C4—66no—
613C2×C3×C4—66no—
614C2×C3×C4—66no—
615C2×C3×C4—66no—
616C2×C3×C4C23×D313yes—
617C2×C3×C4C23×D311yescharacteristic
618C2×C3×C4C23×D313yes—
619C2×C3×C4C23×D313yes—
620C2×C3×C4C23×D313yes—
621C2×C3×C4C24×C313yes—
622C2×C3×C4C24×C311yescharacteristic
623C2×C3×C4C24×C313yes—
624C2×C3×C4C24×C313yes—
625C2×C3×C4C24×C313yes—
626#67—26no—
627#67—22no—
628#67—22no—
629#67—26no—
630C2×Dic3—26no—
631C2×Dic3C24×C311yescharacteristic
632C2×Dic3C24×C313yes—
633C2×Dic3C24×C311yescharacteristic
634C2×Dic3C24×C313yes—
635C2×Dic3C24×C313yes—
636D12—26no—
637D12—26no—
638D12—26no—
639C4×D3—26no—
640C4×D3—26no—
641C4×D3—26no—
642C4×D3—26no—
643C4×D3—212no—
644C4×D3C2×C3×D4112yes—
645Dic6—26no—
646Dic6—212no—
647Dic6—26no—
648Dic6C2×C3×D4112yes—
649C2×C32—22no—
650C2×C32—41no—
651C2×C32C23×D411yescharacteristic
652C2×C32C2×2−1+411yescharacteristic
653C2×C32C2×2−1+411yescharacteristic
654C3×D3—22no—
655C3×D3—22no—
656C3×D3—43no—
657C24—31no—
658#41—612no—
659#41—612no—
660#41—612no—
661#41—64no—
662C2×Q8—24no—
663C2×Q8—24no—
664C2×Q8—38no—
665C2×Q8—33no—
666C2×Q8—36no—
667C2×Q8—33no—
668C2×Q8—33no—
669C2×Q8—612no—
670C2×Q8—612no—
671C2×Q8—612no—
672C2×Q8—612no—
673C2×Q8—64no—
674C2×Q8C22×C3×D313yes—
675C2×Q8C22×C3×D313yes—
676C2×Q8C22×C3×D311yescharacteristic
677C2×D4—31no—
678C2×D4—33no—
679C2×D4—31no—
680C2×D4—33no—
681C2×D4—33no—
682C2×D4—33no—
683C2×D4—33no—
684C2×D4C22×C3×D311yescharacteristic
685C22×C4—33no—
686C22×C4—33no—
687C22×C4—33no—
688C22×C4—33no—
689C22×C4—36no—
690C22×C4—33no—
691C22×C4—33no—
692C22×C4—612no—
693C22×C4C22×C3×D313yes—
694C22×C4C22×C3×D313yes—
695C4⋊C4—33no—
696C4⋊C4—33no—
697C4⋊C4—33no—
698C4⋊C4—33no—
699C4⋊C4—36no—
700C4⋊C4—33no—
701C4⋊C4—33no—
702C4⋊C4C22×C3×D313yes—
703C4⋊C4C22×C3×D316yes—
704C4⋊C4C22×C3×D313yes—
705C22⋊C4—31no—
706C22⋊C4—33no—
707C22⋊C4—33no—
708C22⋊C4—31no—
709C22⋊C4—33no—
710C22⋊C4—31no—
711C22⋊C4—33no—
712C22⋊C4—36no—
713C22⋊C4—36no—
714C22⋊C4—33no—
715C22⋊C4C22×C3×D313yes—
716C22⋊C4C22×C3×D313yes—
717C42—36no—
718C42—33no—
719C42C22×C3×D313yes—
720C22×C3—21no—
721C22×C3—21no—
722C22×C3—21no—
723C22×C3—21no—
724C22×C3—22no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—21no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—22no—
732C22×C3—21no—
733C22×C3—32no—
734C22×C3—32no—
735C22×C3—41no—
736C22×C3—41no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—68no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—63no—
745C22×C3—63no—
746C22×C3—63no—
747C22×C3#100712yescomplemented
748C22×C3C3×2−1+412yescomplemented
749C22×C3C24×D311yescharacteristic
750C22×C3C25×C311yescharacteristic
751C2×D3—28no—
752C2×D3—21no—
753C2×D3—21no—
754C2×D3—21no—
755C2×D3—21no—
756C2×D3—23no—
757C2×D3—23no—
758C2×D3—23no—
759C2×D3C22×C3×D412yes—
760C2×D3C3×2−1+412yescomplemented
761C3×C4—22no—
762C3×C4—23no—
763C3×C4—23no—
764C3×C4—21no—
765C3×C4—23no—
766C3×C4—23no—
767C3×C4—23no—
768C3×C4—23no—
769C3×C4—21no—
770C3×C4—26no—
771C3×C4—36no—
772C3×C4—43no—
773C3×C4—43no—
774C3×C4—43no—
775C3×C4—61no—
776C3×C4—63no—
777C3×C4—63no—
778C3×C4—61no—
779C3×C4C2×D3×D416yes—
780C3×C4C22×C3×D416yes—
781Dic3—23no—
782Dic3—21no—
783Dic3—23no—
784Dic3—21no—
785Dic3C22×C3×D416yes—
786C32#348611yescharacteristic, complemented, Sylow
787C23—31no—
788C23—31no—
789C23—33no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23C23×C3×D311yescharacteristic
794C23C23×C3×D311yescharacteristic
795Q8—26no—
796Q8—26no—
797Q8—312no—
798Q8—612no—
799Q8—66no—
800Q8—66no—
801Q8C3×D3×D414yes—
802D4—22no—
803D4—66no—
804D4—66no—
805D4—66no—
806D4—62no—
807D4—62no—
808D4—66no—
809D4—66no—
810C2×C4—26no—
811C2×C4—26no—
812C2×C4—33no—
813C2×C4—312no—
814C2×C4—33no—
815C2×C4—31no—
816C2×C4—33no—
817C2×C4—31no—
818C2×C4—66no—
819C2×C4—612no—
820C2×C4—66no—
821C2×C4—66no—
822C2×C4—66no—
823C2×C4—66no—
824C2×C4C23×C3×D313yes—
825C2×C4C23×C3×D311yescharacteristic
826C2×C4C23×C3×D313yes—
827C2×C4C23×C3×D313yes—
828C2×C4C23×C3×D313yes—
829C2×C3—22no—
830C2×C3—22no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—42no—
836C2×C3—41no—
837C2×C3—41no—
838C2×C3—62no—
839C2×C3—62no—
840C2×C3—123no—
841C2×C3C22×D3×D411yescharacteristic
842C2×C3C2×#100711yescharacteristic
843C2×C3D3×2−1+411yescharacteristic
844C2×C3C23×C3×D411yescharacteristic
845C2×C3C2×C3×2−1+411yescharacteristic
846C2×C3C2×C3×2−1+411yescharacteristic
847D3—22no—
848D3—22no—
849D3—43no—
850C22—21no—
851C22—21no—
852C22—21no—
853C22—21no—
854C22—21no—
855C22—32no—
856C22—32no—
857C22—68no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—63no—
863C22—63no—
864C22—63no—
865C22C3×#100712yescomplemented
866C22C24×C3×D311yescharacteristic
867C4—23no—
868C4—23no—
869C4—21no—
870C4—23no—
871C4—36no—
872C4—61no—
873C4—63no—
874C4—63no—
875C4—61no—
876C4C2×C3×D3×D416yes—
877C3—21no—
878C3#8675911yescharacteristic, direct product factor
879C3C3×#348611yescharacteristic, complemented
880C2—22no—
881C2—41no—
882C2—62no—
883C2—62no—
884C2—123no—
885C2C22×C3×D3×D411yescharacteristic
886C2C2×C3×#100711yescharacteristic
887C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×D4×Q8C2
socleC22×C32C25
hypercenterC3×D4×Q8D3
hypocenterC3C3×#3486
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×D4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1007C2semidirect
2. C22×C3×D3×Q8C2semidirect
3. C32×D4×Q8C2semidirect
4. C3×#5817C2semidirect
5. C3×Q8×#67C2semidirect
6. C3×#5727C2semidirect
7. C3×#5724C2semidirect
8. C3×#5633C2semidirect
9. C3×#5632C2semidirect
10. C3×#5628C2semidirect
11. C3×#5627C2semidirect
12. C3×#5576C2semidirect
13. C3×#5572C2semidirect
14. C3×#5552C2semidirect
15. C3×#5547C2semidirect
17. #86759C3direct (N × H)
19. C22×C32×Q8C22semidirect
22. C2×C3×#239C22semidirect
28. C2×C3×D3×Q8C22semidirect
30. C2×C3×#235C22semidirect
33. C32×C4⋊Q8C22semidirect
35. C32×C22⋊Q8C22semidirect
36. C32×C4×Q8C22semidirect
38. C3×#947C22semidirect
40. C3×#946C22semidirect
41. C3×Q8×Dic3C22semidirect
42. C3×#944C22semidirect
48. C3×#924C22semidirect
49. C3×#897C22semidirect
51. C3×#896C22semidirect
52. C3×#896C22semidirect
58. C3×#888C22semidirect
59. C3×#887C22semidirect
60. C3×#885C22semidirect
66. C3×#875C22semidirect
69. C3×C4×Dic6C22semidirect
72. C2×#1007C2×C3semidirect
73. C22×D3×Q8C2×C3semidirect
78. C3×D4×Q8D3semidirect
79. C3×D4×Q8C2×C3semidirect
89. #5817C2×C3semidirect
90. Q8×#67C2×C3semidirect
91. #5727C2×C3semidirect
92. #5724C2×C3semidirect
93. #5633C2×C3semidirect
94. #5632C2×C3semidirect
95. #5628C2×C3semidirect
96. #5627C2×C3semidirect
97. #5576C2×C3semidirect
98. #5572C2×C3semidirect
99. #5552C2×C3semidirect
100. #5547C2×C3semidirect
121. C3×D3×Q8D4semidirect
180. C22×C3×Q8C2×D3semidirect
182. C22×C3×Q8C22×C3semidirect
186. C2×#239C22×C3semidirect
192. C2×D3×Q8C22×C3semidirect
194. C2×#235C22×C3semidirect
200. C3×C4⋊Q8C2×D3semidirect
201. C3×C4⋊Q8C22×C3semidirect
219. C3×C22⋊Q8C2×D3semidirect
221. C3×C22⋊Q8C22×C3semidirect
232. C3×C4×Q8C2×D3semidirect
233. C3×C4×Q8C22×C3semidirect
244. #947C22×C3semidirect
246. #946C22×C3semidirect
247. Q8×Dic3C22×C3semidirect
248. #944C22×C3semidirect
254. #924C22×C3semidirect
255. #897C22×C3semidirect
257. #896C22×C3semidirect
258. #896C22×C3semidirect
264. #888C22×C3semidirect
265. #887C22×C3semidirect
266. #885C22×C3semidirect
272. #875C22×C3semidirect
275. C4×Dic6C22×C3semidirect
323. D4×Q8C3×D3semidirect
399. D3×Q8C3×D4semidirect
478. C22×C322−1+4semidirect
489. C2×C3×D32−1+4semidirect
513. C22×Q8C2×C3×D3semidirect
517. C4⋊Q8C2×C3×D3semidirect
533. C22⋊Q8C2×C3×D3semidirect
543. C4×Q8C2×C3×D3semidirect
747. C22×C3#1007semidirect
748. C22×C3C3×2−1+4semidirect
760. C2×D3C3×2−1+4semidirect
786. C32#3486semidirect
865. C22C3×#1007semidirect
878. C3#86759direct (N × H)
879. C3C3×#3486semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#10072
C22×C3×D3×Q82
C32×D4×Q82
C3×#58172
C3×Q8×#672
C3×#57272
C3×#57242
C3×#56332
C3×#56322
C3×#56282
C3×#56272
C3×#55762
C3×#55722
C3×#55522
C3×#55472
C3×#34863
#867593