Finite Group Databasebeta

← C3×#86735 #11904461

Subgroups — C3×#86735 #11904461

Order 1152.

3129 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×#1010C211yesmaximal, characteristic, complemented
2C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
3C32×#548C211yesmaximal, characteristic, complemented
4C3×#5831C211yesmaximal, characteristic, complemented
5C3×Q8×#67C211yesmaximal, characteristic, complemented
6C3×#5677C213yesmaximal, complemented
7C3×#5675C213yesmaximal, complemented
8C3×#5632C213yesmaximal, complemented
9C3×#5628C213yesmaximal, complemented
10C3×#5606C213yesmaximal, complemented
11C3×#5598C213yesmaximal, complemented
12C3×Q8×D12C211yesmaximal, characteristic, complemented
13C3×#5572C211yesmaximal, characteristic, complemented
14C3×#5547C213yesmaximal, complemented
15C3×D4×Dic6C213yesmaximal, complemented
16C3×#3486—31nomaximal
17#86735C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic, complemented
19C22×C32×Q8C2211yescharacteristic
20C3×#1010—28no—
21C2×C3×D3×Q8—28no—
22C2×C3×D3×Q8C2211yescharacteristic
23C2×C3×D3×Q8C2213yes—
24C2×C3×D3×Q8C2213yes—
25C2×C3×D3×Q8C2211yescharacteristic
26C2×C3×D3×Q8C2211yescharacteristic, complemented
27C2×C3×#237C2213yes—
28C2×C3×#237C2213yescomplemented
29C2×C3×#235C2213yes—
30C22×C3×C4×D3C2213yes—
31C22×C3×Dic6C2213yes—
32C22×C3×Dic6C2213yescomplemented
33C32×#124C2213yescomplemented
34C32×C22⋊Q8C2213yescomplemented
35C32×#121C2213yes—
36C32×C4×Q8C2211yescharacteristic, complemented
37C32×C4×D4C2213yes—
38C3×#946C2213yescomplemented
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×#944C2213yescomplemented
41C3×#939C2213yes—
42C3×#938C2213yes—
43C3×#937C2213yes—
44C3×#936C2213yescomplemented
45C3×D4×Dic3C2216yes—
46C3×C4×#67C2213yes—
47C3×C4×#67C2213yes—
48C3×#924C2213yes—
49C3×#924C2213yescomplemented
50C3×#897C2213yes—
51C3×#897C2213yescomplemented
52C3×#896C2213yes—
53C3×#894C2213yes—
54C3×#892C2213yes—
55C3×#888C2216yescomplemented
56C3×#887C2213yescomplemented
57C3×#885C2216yescomplemented
58C3×#884C2213yes—
59C3×#883C2213yes—
60C3×#883C2216yes—
61C3×#882C2211yescharacteristic
62C3×#67⋊C4C2216yes—
63C3×#878C2213yes—
64C3×#878C2216yescomplemented
65C3×#878C2216yescomplemented
66C3×C4×D12C2213yes—
67C3×#872C2213yes—
68C3×#869C2213yescomplemented
69C3×C4×Dic6C2213yescomplemented
70C2×C3×2−1+4—31no—
71C23×C3×Q8—31no—
72C2×#1010C2×C311yescharacteristic, complemented
73C22×D3×Q8C2×C311yescharacteristic, complemented
74C3×D4×Q8—31no—
75C3×D4×Q8—33no—
76C3×D4×Q8—31no—
77C3×D4×Q8—33no—
78C3×#548—21no—
79C3×#548—31no—
80C3×#548—33no—
81C3×#548—33no—
82C3×#548D311yescharacteristic, complemented
83C3×#548C2×C311yescharacteristic, complemented
84C3×#536—33no—
85C3×#536—33no—
86C3×#525—33no—
87C3×#525—33no—
88C3×#519—31no—
89#5831C2×C311yescharacteristic, complemented
90Q8×#67C2×C311yescharacteristic, complemented
91#5677C2×C313yescomplemented
92#5675C2×C313yescomplemented
93#5632C2×C313yescomplemented
94#5628C2×C313yescomplemented
95#5606C2×C313yescomplemented
96#5598C2×C313yescomplemented
97Q8×D12C2×C311yescharacteristic, complemented
98#5572C2×C311yescharacteristic, complemented
99#5547C2×C313yescomplemented
100D4×Dic6C2×C313yescomplemented
101C23×C3×D3C2311yescharacteristic
102C32×#41—24no—
103C2×C32×Q8—24no—
104C2×C32×Q8C2313yes—
105C2×C32×Q8C2311yescharacteristic
106C2×C32×D4C2313yes—
107C2×C32×D4C2313yes—
108C22×C32×C4C2313yes—
109C22×C32×C4C2313yes—
110C2×C3×#67C2313yes—
111C2×C3×#67C2311yescharacteristic
112C2×C3×#67C2313yes—
113C2×C3×#67C2313yes—
114C22×C3×Dic3C2313yes—
115C22×C3×Dic3C2316yes—
116C3×D3×Q8—24no—
117C3×D3×Q8—24no—
118C3×D3×Q8—212no—
119C3×D3×Q8—212no—
120C3×D3×Q8D418yescomplemented
121C3×#237—212no—
122C3×#237—212no—
123C3×#235—212no—
124C2×C3×D12C2311yescharacteristic
125C2×C3×D12C2311yescharacteristic
126C2×C3×C4×D3—212no—
127C2×C3×C4×D3C2313yes—
128C2×C3×C4×D3C2313yes—
129C2×C3×C4×D3C2313yes—
130C2×C3×C4×D3C2313yes—
131C2×C3×C4×D3C2313yes—
132C2×C3×Dic6—212no—
133C2×C3×Dic6—212no—
134C2×C3×Dic6C2313yes—
135C2×C3×Dic6C2316yes—
136C2×C3×Dic6C2313yes—
137C2×C3×Dic6C2313yes—
138C2×C3×Dic6C2313yes—
139C32×C4⋊C4C2313yes—
140C32×C4⋊C4C2313yes—
141C32×C22⋊C4C2311yescharacteristic
142C32×C22⋊C4C2313yes—
143C32×C22⋊C4C2316yes—
144C32×C42C2313yes—
145C3×#217C2313yes—
146C3×#217C2313yes—
147C3×#217C2316yes—
148C3×(C2×D3)⋊C4C2313yes—
149C3×(C2×D3)⋊C4C2311yescharacteristic
150C3×(C2×D3)⋊C4C2311yescharacteristic
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2313yes—
153C3×(C2×D3)⋊C4C2313yes—
154C3×C4⋊Dic3C2313yes—
155C3×C4⋊Dic3C2316yes—
156C3×C4⋊Dic3C2313yes—
157C3×Dic3⋊C4C2313yes—
158C3×Dic3⋊C4C2313yes—
159C3×Dic3⋊C4C2313yes—
160C3×Dic3⋊C4C2313yes—
161C3×Dic3⋊C4C2316yes—
162C3×C4×Dic3C2316yes—
163C3×C4×Dic3C2313yes—
164#3486—31noSylow
165C3×2−1+4—68no—
166C2×C3×#41—21no—
167C2×C3×#41—33no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C2×C3×#41C2×D311yescharacteristic, complemented
171C2×C3×#41C22×C311yescharacteristic, complemented
172C22×C3×Q8—21no—
173C22×C3×Q8—31no—
174C22×C3×Q8—33no—
175C22×C3×Q8—33no—
176C22×C3×Q8—31no—
177C22×C3×Q8—31no—
178C22×C3×Q8—33no—
179C22×C3×Q8—33no—
180C22×C3×Q8—68no—
181C22×C3×Q8C2×D311yescharacteristic
182C22×C3×Q8C22×C311yescharacteristic
183C23×C3×C4—33no—
184#1010—28no—
185C2×D3×Q8—28no—
186C2×D3×Q8C22×C313yes—
187C2×D3×Q8C22×C313yes—
188C2×D3×Q8C22×C311yescharacteristic
189C2×D3×Q8C22×C311yescharacteristic
190C2×D3×Q8C22×C311yescharacteristic, complemented
191C2×#237C22×C313yes—
192C2×#237C22×C313yescomplemented
193C2×#235C22×C313yes—
194C22×C4×D3C22×C313yes—
195C22×Dic6C22×C313yes—
196C22×Dic6C22×C313yescomplemented
197C3×C4⋊Q8—33no—
198C3×C4⋊Q8—36no—
199C3×C4⋊Q8—33no—
200C3×#124—23no—
201C3×#124—33no—
202C3×#124—36no—
203C3×#124C2×D313yescomplemented
204C3×#124C22×C313yescomplemented
205C3×#123—33no—
206C3×#123—36no—
207C3×#123—33no—
208C3×C22⋊Q8—23no—
209C3×C22⋊Q8—33no—
210C3×C22⋊Q8—33no—
211C3×C22⋊Q8—33no—
212C3×C22⋊Q8—33no—
213C3×C22⋊Q8—33no—
214C3×C22⋊Q8—33no—
215C3×C22⋊Q8—33no—
216C3×C22⋊Q8—36no—
217C3×C22⋊Q8—36no—
218C3×C22⋊Q8C2×D313yescomplemented
219C3×C22⋊Q8C22×C313yescomplemented
220C3×#121—23no—
221C3×#121—33no—
222C3×#121—33no—
223C3×#121—33no—
224C3×#121C2×D313yes—
225C3×#121C22×C313yes—
226C3×#120—33no—
227C3×#120—31no—
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—36no—
236C3×C4×D4—33no—
237C3×C4×D4—33no—
238C3×C4×D4—36no—
239C3×C4×D4—33no—
240C3×C4×D4C2×D313yes—
241C3×C4×D4C22×C313yes—
242C3×#117—33no—
243C3×#117—33no—
244#946C22×C313yescomplemented
245Q8×Dic3C22×C311yescharacteristic, complemented
246#944C22×C313yescomplemented
247#939C22×C313yes—
248#938C22×C313yes—
249#937C22×C313yes—
250#936C22×C313yescomplemented
251D4×Dic3C22×C316yes—
252C4×#67C22×C313yes—
253C4×#67C22×C313yes—
254#924C22×C313yes—
255#924C22×C313yescomplemented
256#897C22×C313yes—
257#897C22×C313yescomplemented
258#896C22×C313yes—
259#894C22×C313yes—
260#892C22×C313yes—
261#888C22×C316yescomplemented
262#887C22×C313yescomplemented
263#885C22×C316yescomplemented
264#884C22×C313yes—
265#883C22×C313yes—
266#883C22×C316yes—
267#882C22×C311yescharacteristic
268#67⋊C4C22×C316yes—
269#878C22×C313yes—
270#878C22×C316yescomplemented
271#878C22×C316yescomplemented
272C4×D12C22×C313yes—
273#872C22×C313yes—
274#869C22×C313yescomplemented
275C4×Dic6C22×C313yescomplemented
276C23×C32C2413yes—
277C23×C32C2411yescharacteristic
278C22×C3×D3—22no—
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3C2411yescharacteristic
282C22×C3×D3C2411yescharacteristic
283C22×C3×D3C2411yescharacteristic
284C32×Q8—26no—
285C32×Q8C2×D414yes—
286C32×D4—26no—
287C32×D4—26no—
288C2×C32×C4—26no—
289C2×C32×C4—26no—
290C2×C32×C4C2413yes—
291C2×C32×C4C2411yescharacteristic
292C2×C32×C4C2413yes—
293C2×C32×C4C2411yescharacteristic
294C2×C32×C4C2413yes—
295C3×#67—22no—
296C3×#67—26no—
297C3×#67—26no—
298C3×#67—26no—
299C2×C3×Dic3—26no—
300C2×C3×Dic3—212no—
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2413yes—
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2413yes—
305C2×C3×Dic3C2413yes—
306C3×D12—22no—
307C3×D12—22no—
308C3×C4×D3—26no—
309C3×C4×D3—26no—
310C3×C4×D3—26no—
311C3×C4×D3—26no—
312C3×C4×D3C2×D4112yes—
313C3×Dic6—26no—
314C3×Dic6—26no—
315C3×Dic6—26no—
316C3×Dic6—212no—
317C3×Dic6C2×D4112yes—
318C2×2−1+4—31no—
319C23×Q8—31no—
320D4×Q8—31no—
321D4×Q8—33no—
322D4×Q8—31no—
323D4×Q8—33no—
324#548—31no—
325#548—33no—
326#548—33no—
327#548C3×D311yescharacteristic, complemented
328#536—33no—
329#536—33no—
330#525—33no—
331#525—33no—
332#519—31no—
333C24×C3—31no—
334C23×D3C23×C311yescharacteristic
335C3×#41—24no—
336C3×#41—24no—
337C3×#41—44no—
338C3×#41—612no—
339C3×#41—612no—
340C3×#41—612no—
341C2×C3×Q8—24no—
342C2×C3×Q8—24no—
343C2×C3×Q8—21no—
344C2×C3×Q8—23no—
345C2×C3×Q8—38no—
346C2×C3×Q8—33no—
347C2×C3×Q8—36no—
348C2×C3×Q8—33no—
349C2×C3×Q8—33no—
350C2×C3×Q8—33no—
351C2×C3×Q8—44no—
352C2×C3×Q8—612no—
353C2×C3×Q8—612no—
354C2×C3×Q8—612no—
355C2×C3×Q8—612no—
356C2×C3×Q8—64no—
357C2×C3×Q8—64no—
358C2×C3×Q8C22×D313yes—
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×Q8C23×C313yes—
361C2×C3×Q8C23×C311yescharacteristic
362C2×C3×D4—23no—
363C2×C3×D4—23no—
364C2×C3×D4—33no—
365C2×C3×D4—31no—
366C2×C3×D4—33no—
367C2×C3×D4—33no—
368C2×C3×D4—31no—
369C2×C3×D4—31no—
370C2×C3×D4C22×D313yes—
371C2×C3×D4C22×D313yes—
372C2×C3×D4C23×C313yes—
373C2×C3×D4C23×C313yes—
374C22×C3×C4—23no—
375C22×C3×C4—23no—
376C22×C3×C4—33no—
377C22×C3×C4—33no—
378C22×C3×C4—36no—
379C22×C3×C4—33no—
380C22×C3×C4—33no—
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×C313yes—
391C2×#67C23×C313yes—
392C22×Dic3C23×C313yes—
393C22×Dic3C23×C316yes—
394D3×Q8—24no—
395D3×Q8—24no—
396D3×Q8—212no—
397D3×Q8—212no—
398D3×Q8C3×D418yescomplemented
399#237—212no—
400#237—212no—
401#235—212no—
402C2×D12C23×C311yescharacteristic
403C2×D12C23×C311yescharacteristic
404C2×C4×D3—212no—
405C2×C4×D3C23×C313yes—
406C2×C4×D3C23×C313yes—
407C2×C4×D3C23×C313yes—
408C2×C4×D3C23×C313yes—
409C2×C4×D3C23×C313yes—
410C2×Dic6—212no—
411C2×Dic6—212no—
412C2×Dic6C23×C313yes—
413C2×Dic6C23×C313yes—
414C2×Dic6C23×C313yes—
415C2×Dic6C23×C316yes—
416C2×Dic6C23×C313yes—
417C3×C4⋊C4—23no—
418C3×C4⋊C4—23no—
419C3×C4⋊C4—33no—
420C3×C4⋊C4—33no—
421C3×C4⋊C4—33no—
422C3×C4⋊C4—33no—
423C3×C4⋊C4—36no—
424C3×C4⋊C4—33no—
425C3×C4⋊C4—36no—
426C3×C4⋊C4—33no—
427C3×C4⋊C4C22×D313yes—
428C3×C4⋊C4C22×D313yes—
429C3×C4⋊C4C23×C313yes—
430C3×C4⋊C4C23×C313yes—
431C3×C22⋊C4—21no—
432C3×C22⋊C4—23no—
433C3×C22⋊C4—26no—
434C3×C22⋊C4—33no—
435C3×C22⋊C4—33no—
436C3×C22⋊C4—36no—
437C3×C22⋊C4—33no—
438C3×C22⋊C4—31no—
439C3×C22⋊C4—31no—
440C3×C22⋊C4—33no—
441C3×C22⋊C4—33no—
442C3×C22⋊C4—33no—
443C3×C22⋊C4C22×D316yes—
444C3×C22⋊C4C22×D311yescharacteristic
445C3×C22⋊C4C22×D313yes—
446C3×C22⋊C4C23×C311yescharacteristic
447C3×C22⋊C4C23×C313yes—
448C3×C22⋊C4C23×C316yes—
449C3×C42—23no—
450C3×C42—36no—
451C3×C42—33no—
452C3×C42C22×D313yes—
453C3×C42C23×C313yes—
454#217C23×C313yes—
455#217C23×C313yes—
456#217C23×C316yes—
457(C2×D3)⋊C4C23×C311yescharacteristic
458(C2×D3)⋊C4C23×C313yes—
459(C2×D3)⋊C4C23×C313yes—
460(C2×D3)⋊C4C23×C313yes—
461(C2×D3)⋊C4C23×C311yescharacteristic
462(C2×D3)⋊C4C23×C313yes—
463C4⋊Dic3C23×C313yes—
464C4⋊Dic3C23×C313yes—
465C4⋊Dic3C23×C316yes—
466Dic3⋊C4C23×C313yes—
467Dic3⋊C4C23×C313yes—
468Dic3⋊C4C23×C313yes—
469Dic3⋊C4C23×C313yes—
470Dic3⋊C4C23×C316yes—
471C4×Dic3C23×C316yes—
472C4×Dic3C23×C313yes—
473C22×C32—21no—
474C22×C32—21no—
475C22×C32—23no—
476C22×C32—23no—
477C22×C32—23no—
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—21no—
486C2×C3×D3—21no—
487C2×C3×D3—21no—
488C2×C3×D3C22×D412yes—
489C2×C3×D32−1+412yescomplemented
490C32×C4—21no—
491C32×C4—23no—
492C32×C4—21no—
493C32×C4—23no—
494C32×C4C22×D416yes—
495C3×Dic3—23no—
496C3×Dic3—23no—
497C3×Dic3—21no—
498C3×Dic3—23no—
499C3×Dic3C22×D416yes—
5002−1+4—68no—
501C2×#41—33no—
502C2×#41—33no—
503C2×#41—33no—
504C2×#41C2×C3×D311yescharacteristic, complemented
505C22×Q8—31no—
506C22×Q8—33no—
507C22×Q8—33no—
508C22×Q8—31no—
509C22×Q8—31no—
510C22×Q8—33no—
511C22×Q8—33no—
512C22×Q8—68no—
513C22×Q8C2×C3×D311yescharacteristic
514C23×C4—33no—
515C4⋊Q8—33no—
516C4⋊Q8—36no—
517C4⋊Q8—33no—
518#124—33no—
519#124—36no—
520#124C2×C3×D313yescomplemented
521#123—33no—
522#123—36no—
523#123—33no—
524C22⋊Q8—33no—
525C22⋊Q8—33no—
526C22⋊Q8—33no—
527C22⋊Q8—33no—
528C22⋊Q8—33no—
529C22⋊Q8—33no—
530C22⋊Q8—33no—
531C22⋊Q8—36no—
532C22⋊Q8—36no—
533C22⋊Q8C2×C3×D313yescomplemented
534#121—33no—
535#121—33no—
536#121—33no—
537#121C2×C3×D313yes—
538#120—33no—
539#120—31no—
540C4×Q8—31no—
541C4×Q8—33no—
542C4×Q8—33no—
543C4×Q8C2×C3×D311yescharacteristic, complemented
544C4×D4—36no—
545C4×D4—33no—
546C4×D4—33no—
547C4×D4—36no—
548C4×D4—33no—
549C4×D4C2×C3×D313yes—
550#117—33no—
551#117—33no—
552C23×C3—21no—
553C23×C3—23no—
554C23×C3—31no—
555C23×C3—31no—
556C23×C3—31no—
557C23×C3—62no—
558C23×C3—62no—
559C23×C3—62no—
560C23×C3C23×D313yes—
561C23×C3C23×D311yescharacteristic
562C23×C3C24×C313yes—
563C23×C3C24×C311yescharacteristic
564C22×D3—22no—
565C22×D3—22no—
566C22×D3—22no—
567C22×D3C24×C311yescharacteristic
568C22×D3C24×C311yescharacteristic
569C22×D3C24×C311yescharacteristic
570C3×Q8—26no—
571C3×Q8—26no—
572C3×Q8—24no—
573C3×Q8—312no—
574C3×Q8—46no—
575C3×Q8—612no—
576C3×Q8—66no—
577C3×Q8—66no—
578C3×Q8—66no—
579C3×Q8D3×D414yes—
580C3×Q8C2×C3×D414yes—
581C3×D4—26no—
582C3×D4—26no—
583C3×D4—26no—
584C3×D4—26no—
585C3×D4—46no—
586C3×D4—46no—
587C3×D4—62no—
588C3×D4—62no—
589C3×D4—66no—
590C3×D4—66no—
591C3×D4—66no—
592C3×D4—62no—
593C2×C3×C4—26no—
594C2×C3×C4—26no—
595C2×C3×C4—26no—
596C2×C3×C4—26no—
597C2×C3×C4—23no—
598C2×C3×C4—21no—
599C2×C3×C4—23no—
600C2×C3×C4—23no—
601C2×C3×C4—21no—
602C2×C3×C4—33no—
603C2×C3×C4—312no—
604C2×C3×C4—31no—
605C2×C3×C4—33no—
606C2×C3×C4—33no—
607C2×C3×C4—33no—
608C2×C3×C4—46no—
609C2×C3×C4—46no—
610C2×C3×C4—66no—
611C2×C3×C4—66no—
612C2×C3×C4—66no—
613C2×C3×C4—612no—
614C2×C3×C4—66no—
615C2×C3×C4—66no—
616C2×C3×C4C23×D313yes—
617C2×C3×C4C23×D311yescharacteristic
618C2×C3×C4C23×D313yes—
619C2×C3×C4C23×D311yescharacteristic
620C2×C3×C4C23×D313yes—
621C2×C3×C4C24×C313yes—
622C2×C3×C4C24×C311yescharacteristic
623C2×C3×C4C24×C313yes—
624C2×C3×C4C24×C311yescharacteristic
625C2×C3×C4C24×C313yes—
626#67—22no—
627#67—26no—
628#67—26no—
629#67—26no—
630C2×Dic3—26no—
631C2×Dic3—212no—
632C2×Dic3C24×C311yescharacteristic
633C2×Dic3C24×C313yes—
634C2×Dic3C24×C313yes—
635C2×Dic3C24×C313yes—
636C2×Dic3C24×C313yes—
637D12—22no—
638D12—22no—
639C4×D3—26no—
640C4×D3—26no—
641C4×D3—26no—
642C4×D3—26no—
643C4×D3C2×C3×D4112yes—
644Dic6—26no—
645Dic6—26no—
646Dic6—26no—
647Dic6—212no—
648Dic6C2×C3×D4112yes—
649C2×C32—22no—
650C2×C32—43no—
651C2×C32C23×D411yescharacteristic
652C2×C32C2×2−1+411yescharacteristic
653C2×C32C2×2−1+411yescharacteristic
654C3×D3—22no—
655C3×D3—22no—
656C3×D3—41no—
657C24—31no—
658#41—24no—
659#41—612no—
660#41—612no—
661#41—612no—
662C2×Q8—24no—
663C2×Q8—38no—
664C2×Q8—33no—
665C2×Q8—36no—
666C2×Q8—33no—
667C2×Q8—33no—
668C2×Q8—33no—
669C2×Q8—612no—
670C2×Q8—612no—
671C2×Q8—612no—
672C2×Q8—612no—
673C2×Q8—64no—
674C2×Q8—64no—
675C2×Q8C22×C3×D313yes—
676C2×Q8C22×C3×D311yescharacteristic
677C2×D4—33no—
678C2×D4—31no—
679C2×D4—33no—
680C2×D4—33no—
681C2×D4—31no—
682C2×D4—31no—
683C2×D4C22×C3×D313yes—
684C2×D4C22×C3×D313yes—
685C22×C4—33no—
686C22×C4—33no—
687C22×C4—36no—
688C22×C4—33no—
689C22×C4—33no—
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—33no—
700C4⋊C4—36no—
701C4⋊C4—36no—
702C4⋊C4—33no—
703C4⋊C4C22×C3×D313yes—
704C4⋊C4C22×C3×D313yes—
705C22⋊C4—33no—
706C22⋊C4—36no—
707C22⋊C4—33no—
708C22⋊C4—33no—
709C22⋊C4—31no—
710C22⋊C4—31no—
711C22⋊C4—33no—
712C22⋊C4—33no—
713C22⋊C4—33no—
714C22⋊C4C22×C3×D316yes—
715C22⋊C4C22×C3×D311yescharacteristic
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—23no—
725C22×C3—23no—
726C22×C3—23no—
727C22×C3—23no—
728C22×C3—23no—
729C22×C3—23no—
730C22×C3—22no—
731C22×C3—21no—
732C22×C3—32no—
733C22×C3—32no—
734C22×C3—41no—
735C22×C3—41no—
736C22×C3—43no—
737C22×C3—43no—
738C22×C3—43no—
739C22×C3—68no—
740C22×C3—61no—
741C22×C3—61no—
742C22×C3—61no—
743C22×C3—61no—
744C22×C3—61no—
745C22×C3—61no—
746C22×C3—61no—
747C22×C3#101012yescomplemented
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—21no—
757C2×D3—21no—
758C2×D3—21no—
759C2×D3C22×C3×D412yes—
760C2×D3C3×2−1+412yescomplemented
761C3×C4—21no—
762C3×C4—23no—
763C3×C4—23no—
764C3×C4—21no—
765C3×C4—21no—
766C3×C4—23no—
767C3×C4—21no—
768C3×C4—23no—
769C3×C4—26no—
770C3×C4—36no—
771C3×C4—41no—
772C3×C4—43no—
773C3×C4—43no—
774C3×C4—41no—
775C3×C4—63no—
776C3×C4—63no—
777C3×C4—61no—
778C3×C4—63no—
779C3×C4C2×D3×D416yes—
780C3×C4C22×C3×D416yes—
781Dic3—23no—
782Dic3—23no—
783Dic3—21no—
784Dic3—23no—
785Dic3C22×C3×D416yes—
786C32#348611yescharacteristic, complemented, Sylow
787C23—31no—
788C23—31no—
789C23—31no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23C23×C3×D313yes—
794C23C23×C3×D311yescharacteristic
795Q8—26no—
796Q8—312no—
797Q8—612no—
798Q8—66no—
799Q8—66no—
800Q8—66no—
801Q8C3×D3×D414yes—
802D4—26no—
803D4—26no—
804D4—62no—
805D4—62no—
806D4—66no—
807D4—66no—
808D4—66no—
809D4—62no—
810C2×C4—26no—
811C2×C4—26no—
812C2×C4—33no—
813C2×C4—312no—
814C2×C4—31no—
815C2×C4—33no—
816C2×C4—33no—
817C2×C4—33no—
818C2×C4—66no—
819C2×C4—66no—
820C2×C4—66no—
821C2×C4—612no—
822C2×C4—66no—
823C2×C4—66no—
824C2×C4C23×C3×D313yes—
825C2×C4C23×C3×D311yescharacteristic
826C2×C4C23×C3×D313yes—
827C2×C4C23×C3×D311yescharacteristic
828C2×C4C23×C3×D313yes—
829C2×C3—22no—
830C2×C3—22no—
831C2×C3—21no—
832C2×C3—21no—
833C2×C3—21no—
834C2×C3—42no—
835C2×C3—43no—
836C2×C3—43no—
837C2×C3—62no—
838C2×C3—62no—
839C2×C3—83no—
840C2×C3—121no—
841C2×C3C22×D3×D411yescharacteristic
842C2×C3C2×#101011yescharacteristic
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—41no—
850C22—21no—
851C22—21no—
852C22—23no—
853C22—23no—
854C22—23no—
855C22—32no—
856C22—32no—
857C22—68no—
858C22—61no—
859C22—61no—
860C22—61no—
861C22—61no—
862C22—61no—
863C22—61no—
864C22—61no—
865C22C3×#101012yescomplemented
866C22C24×C3×D311yescharacteristic
867C4—21no—
868C4—23no—
869C4—23no—
870C4—21no—
871C4—36no—
872C4—63no—
873C4—63no—
874C4—61no—
875C4—63no—
876C4C2×C3×D3×D416yes—
877C3—21no—
878C3#8673511yescharacteristic, direct product factor
879C3C3×#348611yescharacteristic, complemented
880C2—22no—
881C2—43no—
882C2—62no—
883C2—62no—
884C2—121no—
885C2C22×C3×D3×D411yescharacteristic
886C2C2×C3×#101011yescharacteristic
887C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#548C2
socleC22×C32C25
hypercenterC3×#548D3
hypocenterC3C3×#3486
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C22×C3 ◁ C3×#548

Complements

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

NH ≅ G/Ntype
1. C2×C3×#1010C2semidirect
2. C22×C3×D3×Q8C2semidirect
3. C32×#548C2semidirect
4. C3×#5831C2semidirect
5. C3×Q8×#67C2semidirect
6. C3×#5677C2semidirect
7. C3×#5675C2semidirect
8. C3×#5632C2semidirect
9. C3×#5628C2semidirect
10. C3×#5606C2semidirect
11. C3×#5598C2semidirect
12. C3×Q8×D12C2semidirect
13. C3×#5572C2semidirect
14. C3×#5547C2semidirect
15. C3×D4×Dic6C2semidirect
17. #86735C3direct (N × H)
18. C2×C32×#41C22semidirect
26. C2×C3×D3×Q8C22semidirect
28. C2×C3×#237C22semidirect
32. C22×C3×Dic6C22semidirect
33. C32×#124C22semidirect
34. C32×C22⋊Q8C22semidirect
36. C32×C4×Q8C22semidirect
38. C3×#946C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×#944C22semidirect
44. C3×#936C22semidirect
49. C3×#924C22semidirect
51. C3×#897C22semidirect
55. C3×#888C22semidirect
56. C3×#887C22semidirect
57. C3×#885C22semidirect
64. C3×#878C22semidirect
65. C3×#878C22semidirect
68. C3×#869C22semidirect
69. C3×C4×Dic6C22semidirect
72. C2×#1010C2×C3semidirect
73. C22×D3×Q8C2×C3semidirect
82. C3×#548D3semidirect
83. C3×#548C2×C3semidirect
89. #5831C2×C3semidirect
90. Q8×#67C2×C3semidirect
91. #5677C2×C3semidirect
92. #5675C2×C3semidirect
93. #5632C2×C3semidirect
94. #5628C2×C3semidirect
95. #5606C2×C3semidirect
96. #5598C2×C3semidirect
97. Q8×D12C2×C3semidirect
98. #5572C2×C3semidirect
99. #5547C2×C3semidirect
100. D4×Dic6C2×C3semidirect
120. C3×D3×Q8D4semidirect
170. C2×C3×#41C2×D3semidirect
171. C2×C3×#41C22×C3semidirect
190. C2×D3×Q8C22×C3semidirect
192. C2×#237C22×C3semidirect
196. C22×Dic6C22×C3semidirect
203. C3×#124C2×D3semidirect
204. C3×#124C22×C3semidirect
218. C3×C22⋊Q8C2×D3semidirect
219. C3×C22⋊Q8C22×C3semidirect
232. C3×C4×Q8C2×D3semidirect
233. C3×C4×Q8C22×C3semidirect
244. #946C22×C3semidirect
245. Q8×Dic3C22×C3semidirect
246. #944C22×C3semidirect
250. #936C22×C3semidirect
255. #924C22×C3semidirect
257. #897C22×C3semidirect
261. #888C22×C3semidirect
262. #887C22×C3semidirect
263. #885C22×C3semidirect
270. #878C22×C3semidirect
271. #878C22×C3semidirect
274. #869C22×C3semidirect
275. C4×Dic6C22×C3semidirect
327. #548C3×D3semidirect
398. D3×Q8C3×D4semidirect
478. C22×C322−1+4semidirect
489. C2×C3×D32−1+4semidirect
504. C2×#41C2×C3×D3semidirect
520. #124C2×C3×D3semidirect
533. C22⋊Q8C2×C3×D3semidirect
543. C4×Q8C2×C3×D3semidirect
747. C22×C3#1010semidirect
748. C22×C3C3×2−1+4semidirect
760. C2×D3C3×2−1+4semidirect
786. C32#3486semidirect
865. C22C3×#1010semidirect
878. C3#86735direct (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×#10102
C22×C3×D3×Q82
C32×#5482
C3×#58312
C3×Q8×#672
C3×#56772
C3×#56752
C3×#56322
C3×#56282
C3×#56062
C3×#55982
C3×Q8×D122
C3×#55722
C3×#55472
C3×D4×Dic62
C3×#34863
#867353