Finite Group Databasebeta

← C3×#86714 #11904732

Subgroups — C3×#86714 #11904732

Order 1152.

3189 conjugacy classes of subgroups.

The subgroup lattice has 893 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C2×C3×#1007C211yesmaximal, characteristic, complemented
3C32×#548C211yesmaximal, characteristic, complemented
4C3×#5831C211yesmaximal, characteristic, complemented
5C3×Q8×#67C211yesmaximal, characteristic, complemented
6C3×#5676C213yesmaximal, complemented
7C3×#5675C213yesmaximal, complemented
8C3×#5631C213yesmaximal, complemented
9C3×D3×C22⋊Q8C213yesmaximal, complemented
10C3×#5612C213yesmaximal, complemented
11C3×#5608C213yesmaximal, complemented
12C3×Q8×D12C211yesmaximal, characteristic, complemented
13C3×#5574C211yesmaximal, characteristic, complemented
14C3×#5551C213yesmaximal, complemented
15C3×#5547C213yesmaximal, complemented
16C3×#3489—31nomaximal
17#86714C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic, complemented
20C3×D3×#41—28no—
21C3×#1007—28no—
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2213yescomplemented
24C2×C3×D3×Q8C2211yescharacteristic
25C2×C3×D3×Q8C2211yescharacteristic, complemented
26C2×C3×D3×Q8C2213yescomplemented
27C2×C3×#237C2213yes—
28C2×C3×D3×D4C2213yes—
29C2×C3×#235C2213yes—
30C2×C3×#235C2213yescomplemented
31C2×C3×#235C2213yescomplemented
32C22×C3×C4×D3C2213yes—
33C32×#124C2213yescomplemented
34C32×C22⋊Q8C2213yescomplemented
35C32×#121C2213yescomplemented
36C32×C4×Q8C2211yescharacteristic, complemented
37C32×C4×D4C2213yescomplemented
38C3×#946C2213yes—
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×#944C2213yescomplemented
41C3×#939C2213yescomplemented
42C3×#938C2216yescomplemented
43C3×#938C2213yescomplemented
44C3×#937C2213yes—
45C3×#936C2213yescomplemented
46C3×C4×#67C2213yes—
47C3×C4×#67C2213yescomplemented
48C3×#924C2213yescomplemented
49C3×#924C2213yescomplemented
50C3×#897C2213yes—
51C3×#897C2213yescomplemented
52C3×#896C2213yes—
53C3×#894C2213yescomplemented
54C3×#893C2213yescomplemented
55C3×D3×C4⋊C4C2216yescomplemented
56C3×D3×C4⋊C4C2213yescomplemented
57C3×#884C2211yescharacteristic
58C3×#884C2216yescomplemented
59C3×#883C2213yescomplemented
60C3×#883C2216yescomplemented
61C3×#883C2216yescomplemented
62C3×#882C2213yes—
63C3×D3×C22⋊C4C2216yes—
64C3×#878C2213yescomplemented
65C3×#878C2216yescomplemented
66C3×C4×D12C2213yes—
67C3×C4×D12C2213yescomplemented
68C3×#872C2213yescomplemented
69C3×#869C2213yescomplemented
70C2×C3×2−1+4—31no—
71C22×C3×#41—31no—
72C2×D3×#41C2×C311yescharacteristic, complemented
73C2×#1007C2×C311yescharacteristic, complemented
74C3×D4×Q8—31no—
75C3×D4×Q8—31no—
76C3×#548—21no—
77C3×#548—31no—
78C3×#548D311yescharacteristic, complemented
79C3×#548C2×C311yescharacteristic, complemented
80C3×#547—33no—
81C3×#547—33no—
82C3×#546—33no—
83C3×#546—33no—
84C3×#537—33no—
85C3×#536—33no—
86C3×#525—33no—
87C2×C3×C22⋊Q8—33no—
88C3×#520—31no—
89#5831C2×C311yescharacteristic, complemented
90Q8×#67C2×C311yescharacteristic, complemented
91#5676C2×C313yescomplemented
92#5675C2×C313yescomplemented
93#5631C2×C313yescomplemented
94D3×C22⋊Q8C2×C313yescomplemented
95#5612C2×C313yescomplemented
96#5608C2×C313yescomplemented
97Q8×D12C2×C311yescharacteristic, complemented
98#5574C2×C311yescharacteristic, complemented
99#5551C2×C313yescomplemented
100#5547C2×C313yescomplemented
101C23×C3×D3C2313yes—
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×#67C2316yes—
111C2×C3×#67C2313yes—
112C2×C3×#67C2311yescharacteristic
113C2×C3×#67C2311yescharacteristic
114C2×C3×#67C2313yes—
115C22×C3×Dic3C2313yes—
116C3×#239—212no—
117C3×#239D418yescomplemented
118C3×D3×Q8—24no—
119C3×D3×Q8—24no—
120C3×D3×Q8—212no—
121C3×#237—212no—
122C3×D3×D4—212no—
123C3×#235—212no—
124C3×#235—212no—
125C3×#235—212no—
126C2×C3×D12C2311yescharacteristic
127C2×C3×D12C2313yes—
128C2×C3×D12C2313yes—
129C2×C3×C4×D3—212no—
130C2×C3×C4×D3C2316yes—
131C2×C3×C4×D3C2313yes—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2313yes—
134C2×C3×C4×D3C2313yes—
135C2×C3×C4×D3C2316yes—
136C2×C3×C4×D3C2313yes—
137C2×C3×Dic6C2313yes—
138C2×C3×Dic6C2313yes—
139C2×C3×Dic6C2313yes—
140C32×C4⋊C4C2313yes—
141C32×C4⋊C4C2313yes—
142C32×C22⋊C4C2316yes—
143C32×C22⋊C4C2313yes—
144C32×C22⋊C4C2311yescharacteristic
145C32×C42C2313yes—
146C3×#217C2316yes—
147C3×#217C2313yes—
148C3×#217C2313yes—
149C3×(C2×D3)⋊C4C2313yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2313yes—
153C3×(C2×D3)⋊C4C2311yescharacteristic
154C3×(C2×D3)⋊C4C2313yes—
155C3×C4⋊Dic3C2313yes—
156C3×C4⋊Dic3C2316yes—
157C3×C4⋊Dic3C2313yes—
158C3×Dic3⋊C4C2311yescharacteristic
159C3×Dic3⋊C4C2313yes—
160C3×Dic3⋊C4C2313yes—
161C3×Dic3⋊C4C2316yes—
162C3×Dic3⋊C4C2313yes—
163C3×C4×Dic3C2313yes—
164#3489—31noSylow
165C3×2−1+4—68no—
166C2×C3×#41—21no—
167C2×C3×#41—31no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C2×C3×#41—33no—
171C2×C3×#41—33no—
172C2×C3×#41—33no—
173C2×C3×#41—68no—
174C2×C3×#41C2×D311yescharacteristic
175C2×C3×#41C22×C311yescharacteristic
176C22×C3×Q8—21no—
177C22×C3×Q8—31no—
178C22×C3×Q8—33no—
179C22×C3×Q8—31no—
180C22×C3×Q8C2×D311yescharacteristic, complemented
181C22×C3×Q8C22×C311yescharacteristic, complemented
182C22×C3×D4—33no—
183C23×C3×C4—33no—
184D3×#41—28no—
185#1007—28no—
186C2×#239C22×C311yescharacteristic
187C2×#239C22×C313yescomplemented
188C2×D3×Q8C22×C311yescharacteristic
189C2×D3×Q8C22×C313yescomplemented
190C2×D3×Q8C22×C311yescharacteristic, complemented
191C2×#237C22×C313yes—
192C2×D3×D4C22×C313yes—
193C2×#235C22×C313yes—
194C2×#235C22×C313yescomplemented
195C2×#235C22×C313yescomplemented
196C22×C4×D3C22×C313yes—
197C3×C4⋊Q8—33no—
198C3×C4⋊Q8—33no—
199C3×#124—23no—
200C3×#124—33no—
201C3×#124C2×D313yescomplemented
202C3×#124C22×C313yescomplemented
203C3×#123—33no—
204C3×#123—33no—
205C3×#123—36no—
206C3×#123—36no—
207C3×C22⋊Q8—23no—
208C3×C22⋊Q8—33no—
209C3×C22⋊Q8—33no—
210C3×C22⋊Q8—33no—
211C3×C22⋊Q8—33no—
212C3×C22⋊Q8—33no—
213C3×C22⋊Q8—33no—
214C3×C22⋊Q8—36no—
215C3×C22⋊Q8—33no—
216C3×C22⋊Q8C2×D313yescomplemented
217C3×C22⋊Q8C22×C313yescomplemented
218C3×#121—23no—
219C3×#121—36no—
220C3×#121—33no—
221C3×#121—33no—
222C3×#121—31no—
223C3×#121—36no—
224C3×#121C2×D313yescomplemented
225C3×#121C22×C313yescomplemented
226C3×#120—33no—
227C3×#120—33no—
228C3×C4×Q8—21no—
229C3×C4×Q8—31no—
230C3×C4×Q8C2×D311yescharacteristic, complemented
231C3×C4×Q8C22×C311yescharacteristic, complemented
232C3×C4×D4—23no—
233C3×C4×D4—33no—
234C3×C4×D4—33no—
235C3×C4×D4—33no—
236C3×C4×D4—33no—
237C3×C4×D4—33no—
238C3×C4×D4C2×D313yescomplemented
239C3×C4×D4C22×C313yescomplemented
240C3×#117—33no—
241C2×C3×C4⋊C4—33no—
242C2×C3×C4⋊C4—36no—
243C2×C3×C22⋊C4—36no—
244#946C22×C313yes—
245Q8×Dic3C22×C311yescharacteristic, complemented
246#944C22×C313yescomplemented
247#939C22×C313yescomplemented
248#938C22×C313yescomplemented
249#938C22×C316yescomplemented
250#937C22×C313yes—
251#936C22×C313yescomplemented
252C4×#67C22×C313yes—
253C4×#67C22×C313yescomplemented
254#924C22×C313yescomplemented
255#924C22×C313yescomplemented
256#897C22×C313yes—
257#897C22×C313yescomplemented
258#896C22×C313yes—
259#894C22×C313yescomplemented
260#893C22×C313yescomplemented
261D3×C4⋊C4C22×C316yescomplemented
262D3×C4⋊C4C22×C313yescomplemented
263#884C22×C311yescharacteristic
264#884C22×C316yescomplemented
265#883C22×C316yescomplemented
266#883C22×C316yescomplemented
267#883C22×C313yescomplemented
268#882C22×C313yes—
269D3×C22⋊C4C22×C316yes—
270#878C22×C313yescomplemented
271#878C22×C316yescomplemented
272C4×D12C22×C313yes—
273C4×D12C22×C313yescomplemented
274#872C22×C313yescomplemented
275#869C22×C313yescomplemented
276C23×C32C2413yes—
277C23×C32C2411yescharacteristic
278C22×C3×D3—26no—
279C22×C3×D3—26no—
280C22×C3×D3—43no—
281C22×C3×D3C2411yescharacteristic
282C22×C3×D3C2413yes—
283C22×C3×D3C2411yescharacteristic
284C32×Q8—26no—
285C32×Q8C2×D414yes—
286C32×D4—26no—
287C32×D4—43no—
288C2×C32×C4—26no—
289C2×C32×C4—26no—
290C2×C32×C4C2413yes—
291C2×C32×C4C2411yescharacteristic
292C2×C32×C4C2411yescharacteristic
293C2×C32×C4C2413yes—
294C2×C32×C4C2413yes—
295C3×#67—26no—
296C3×#67—212no—
297C3×#67—22no—
298C3×#67—22no—
299C3×#67—43no—
300C2×C3×Dic3—26no—
301C2×C3×Dic3C2411yescharacteristic
302C2×C3×Dic3C2413yes—
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2413yes—
305C2×C3×Dic3C2411yescharacteristic
306C3×D12—26no—
307C3×D12—22no—
308C3×D12C2×D4112yes—
309C3×C4×D3—26no—
310C3×C4×D3—212no—
311C3×C4×D3—26no—
312C3×C4×D3—26no—
313C3×C4×D3—22no—
314C3×C4×D3—46no—
315C3×C4×D3C2×D4112yes—
316C3×Dic6—26no—
317C3×Dic6—26no—
318C3×Dic6—26no—
319C2×2−1+4—31no—
320C22×#41—31no—
321D4×Q8—31no—
322D4×Q8—31no—
323#548—31no—
324#548C3×D311yescharacteristic, complemented
325#547—33no—
326#547—33no—
327#546—33no—
328#546—33no—
329#537—33no—
330#536—33no—
331#525—33no—
332C2×C22⋊Q8—33no—
333#520—31no—
334C24×C3—33no—
335C23×D3C23×C313yes—
336C3×#41—24no—
337C3×#41—24no—
338C3×#41—38no—
339C3×#41—44no—
340C3×#41—612no—
341C3×#41—612no—
342C3×#41—612no—
343C3×#41—612no—
344C3×#41—612no—
345C2×C3×Q8—24no—
346C2×C3×Q8—24no—
347C2×C3×Q8—21no—
348C2×C3×Q8—23no—
349C2×C3×Q8—33no—
350C2×C3×Q8—33no—
351C2×C3×Q8—33no—
352C2×C3×Q8—44no—
353C2×C3×Q8—612no—
354C2×C3×Q8—64no—
355C2×C3×Q8—64no—
356C2×C3×Q8C22×D313yes—
357C2×C3×Q8C22×D311yescharacteristic
358C2×C3×Q8C23×C313yes—
359C2×C3×Q8C23×C311yescharacteristic
360C2×C3×D4—23no—
361C2×C3×D4—23no—
362C2×C3×D4—31no—
363C2×C3×D4—33no—
364C2×C3×D4—31no—
365C2×C3×D4—36no—
366C2×C3×D4—33no—
367C2×C3×D4—33no—
368C2×C3×D4—31no—
369C2×C3×D4—33no—
370C2×C3×D4—612no—
371C2×C3×D4C22×D313yes—
372C2×C3×D4C22×D313yes—
373C2×C3×D4C23×C313yes—
374C2×C3×D4C23×C313yes—
375C22×C3×C4—23no—
376C22×C3×C4—23no—
377C22×C3×C4—33no—
378C22×C3×C4—33no—
379C22×C3×C4—36no—
380C22×C3×C4—33no—
381C22×C3×C4—33no—
382C22×C3×C4—33no—
383C22×C3×C4—31no—
384C22×C3×C4—36no—
385C22×C3×C4—612no—
386C22×C3×C4C22×D313yes—
387C22×C3×C4C22×D313yes—
388C22×C3×C4C23×C313yes—
389C22×C3×C4C23×C313yes—
390C2×#67C23×C316yes—
391C2×#67C23×C313yes—
392C2×#67C23×C311yescharacteristic
393C2×#67C23×C311yescharacteristic
394C2×#67C23×C313yes—
395C22×Dic3C23×C313yes—
396#239—212no—
397#239C3×D418yescomplemented
398D3×Q8—24no—
399D3×Q8—24no—
400D3×Q8—212no—
401#237—212no—
402D3×D4—212no—
403#235—212no—
404#235—212no—
405#235—212no—
406C2×D12C23×C311yescharacteristic
407C2×D12C23×C313yes—
408C2×D12C23×C313yes—
409C2×C4×D3—212no—
410C2×C4×D3C23×C313yes—
411C2×C4×D3C23×C313yes—
412C2×C4×D3C23×C316yes—
413C2×C4×D3C23×C313yes—
414C2×C4×D3C23×C311yescharacteristic
415C2×C4×D3C23×C316yes—
416C2×C4×D3C23×C313yes—
417C2×Dic6C23×C313yes—
418C2×Dic6C23×C313yes—
419C2×Dic6C23×C313yes—
420C3×C4⋊C4—23no—
421C3×C4⋊C4—23no—
422C3×C4⋊C4—33no—
423C3×C4⋊C4—33no—
424C3×C4⋊C4—36no—
425C3×C4⋊C4—31no—
426C3×C4⋊C4—33no—
427C3×C4⋊C4—33no—
428C3×C4⋊C4—36no—
429C3×C4⋊C4—33no—
430C3×C4⋊C4C22×D313yes—
431C3×C4⋊C4C22×D313yes—
432C3×C4⋊C4C23×C313yes—
433C3×C4⋊C4C23×C313yes—
434C3×C22⋊C4—21no—
435C3×C22⋊C4—23no—
436C3×C22⋊C4—26no—
437C3×C22⋊C4—36no—
438C3×C22⋊C4—33no—
439C3×C22⋊C4—33no—
440C3×C22⋊C4—33no—
441C3×C22⋊C4—33no—
442C3×C22⋊C4—33no—
443C3×C22⋊C4—33no—
444C3×C22⋊C4—31no—
445C3×C22⋊C4—33no—
446C3×C22⋊C4C22×D316yes—
447C3×C22⋊C4C22×D311yescharacteristic
448C3×C22⋊C4C22×D313yes—
449C3×C22⋊C4C23×C316yes—
450C3×C22⋊C4C23×C313yes—
451C3×C22⋊C4C23×C311yescharacteristic
452C3×C42—23no—
453C3×C42—33no—
454C3×C42C22×D313yes—
455C3×C42C23×C313yes—
456#217C23×C316yes—
457#217C23×C313yes—
458#217C23×C313yes—
459(C2×D3)⋊C4C23×C313yes—
460(C2×D3)⋊C4C23×C313yes—
461(C2×D3)⋊C4C23×C313yes—
462(C2×D3)⋊C4C23×C313yes—
463(C2×D3)⋊C4C23×C313yes—
464(C2×D3)⋊C4C23×C311yescharacteristic
465C4⋊Dic3C23×C313yes—
466C4⋊Dic3C23×C316yes—
467C4⋊Dic3C23×C313yes—
468Dic3⋊C4C23×C311yescharacteristic
469Dic3⋊C4C23×C313yes—
470Dic3⋊C4C23×C313yes—
471Dic3⋊C4C23×C316yes—
472Dic3⋊C4C23×C313yes—
473C4×Dic3C23×C313yes—
474C22×C32—21no—
475C22×C32—23no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—23no—
479C22×C32—23no—
480C22×C32C2511yescharacteristic
481C2×C3×D3—21no—
482C2×C3×D3—23no—
483C2×C3×D3—23no—
484C2×C3×D3—21no—
485C2×C3×D3—21no—
486C2×C3×D3—21no—
487C2×C3×D3—21no—
488C2×C3×D3—412no—
489C2×C3×D3C22×D416yes—
490C2×C3×D32−1+412yescomplemented
491C32×C4—23no—
492C32×C4—21no—
493C32×C4—21no—
494C32×C4—23no—
495C32×C4C22×D416yes—
496C3×Dic3—23no—
497C3×Dic3—23no—
498C3×Dic3—21no—
499C3×Dic3—23no—
500C3×Dic3C22×D412yes—
5012−1+4—68no—
502C2×#41—31no—
503C2×#41—33no—
504C2×#41—33no—
505C2×#41—33no—
506C2×#41—33no—
507C2×#41—33no—
508C2×#41—68no—
509C2×#41C2×C3×D311yescharacteristic
510C22×Q8—33no—
511C22×Q8—31no—
512C22×Q8—31no—
513C22×Q8C2×C3×D311yescharacteristic, complemented
514C22×D4—33no—
515C23×C4—33no—
516C4⋊Q8—33no—
517C4⋊Q8—33no—
518#124—33no—
519#124C2×C3×D313yescomplemented
520#123—33no—
521#123—33no—
522#123—36no—
523#123—36no—
524C22⋊Q8—33no—
525C22⋊Q8—33no—
526C22⋊Q8—33no—
527C22⋊Q8—33no—
528C22⋊Q8—33no—
529C22⋊Q8—33no—
530C22⋊Q8—36no—
531C22⋊Q8—33no—
532C22⋊Q8C2×C3×D313yescomplemented
533#121—33no—
534#121—36no—
535#121—33no—
536#121—31no—
537#121—36no—
538#121C2×C3×D313yescomplemented
539#120—33no—
540#120—33no—
541C4×Q8—31no—
542C4×Q8C2×C3×D311yescharacteristic, complemented
543C4×D4—33no—
544C4×D4—33no—
545C4×D4—33no—
546C4×D4—33no—
547C4×D4—33no—
548C4×D4C2×C3×D313yescomplemented
549#117—33no—
550C2×C4⋊C4—33no—
551C2×C4⋊C4—36no—
552C2×C22⋊C4—36no—
553C23×C3—21no—
554C23×C3—23no—
555C23×C3—31no—
556C23×C3—33no—
557C23×C3—31no—
558C23×C3—66no—
559C23×C3—66no—
560C23×C3—123no—
561C23×C3C23×D313yes—
562C23×C3C23×D311yescharacteristic
563C23×C3C24×C313yes—
564C23×C3C24×C311yescharacteristic
565C22×D3—26no—
566C22×D3—26no—
567C22×D3—43no—
568C22×D3C24×C311yescharacteristic
569C22×D3C24×C313yes—
570C22×D3C24×C311yescharacteristic
571C3×Q8—26no—
572C3×Q8—26no—
573C3×Q8—24no—
574C3×Q8—46no—
575C3×Q8—66no—
576C3×Q8—66no—
577C3×Q8—66no—
578C3×Q8D3×D414yes—
579C3×Q8C2×C3×D414yes—
580C3×D4—26no—
581C3×D4—26no—
582C3×D4—312no—
583C3×D4—46no—
584C3×D4—43no—
585C3×D4—43no—
586C3×D4—46no—
587C3×D4—62no—
588C3×D4—66no—
589C3×D4—62no—
590C3×D4—62no—
591C3×D4—612no—
592C3×D4—66no—
593C3×D4—123no—
594C2×C3×C4—26no—
595C2×C3×C4—26no—
596C2×C3×C4—26no—
597C2×C3×C4—26no—
598C2×C3×C4—23no—
599C2×C3×C4—21no—
600C2×C3×C4—23no—
601C2×C3×C4—23no—
602C2×C3×C4—21no—
603C2×C3×C4—31no—
604C2×C3×C4—312no—
605C2×C3×C4—31no—
606C2×C3×C4—33no—
607C2×C3×C4—33no—
608C2×C3×C4—33no—
609C2×C3×C4—46no—
610C2×C3×C4—46no—
611C2×C3×C4—62no—
612C2×C3×C4—66no—
613C2×C3×C4—612no—
614C2×C3×C4—66no—
615C2×C3×C4—66no—
616C2×C3×C4—66no—
617C2×C3×C4—126no—
618C2×C3×C4C23×D311yescharacteristic
619C2×C3×C4C23×D313yes—
620C2×C3×C4C23×D313yes—
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C23×D313yes—
623C2×C3×C4C24×C313yes—
624C2×C3×C4C24×C311yescharacteristic
625C2×C3×C4C24×C311yescharacteristic
626C2×C3×C4C24×C313yes—
627C2×C3×C4C24×C313yes—
628#67—26no—
629#67—212no—
630#67—22no—
631#67—22no—
632#67—43no—
633C2×Dic3—26no—
634C2×Dic3C24×C311yescharacteristic
635C2×Dic3C24×C313yes—
636C2×Dic3C24×C313yes—
637C2×Dic3C24×C313yes—
638C2×Dic3C24×C311yescharacteristic
639D12—26no—
640D12—22no—
641D12C2×C3×D4112yes—
642C4×D3—26no—
643C4×D3—212no—
644C4×D3—26no—
645C4×D3—26no—
646C4×D3—22no—
647C4×D3—46no—
648C4×D3C2×C3×D4112yes—
649Dic6—26no—
650Dic6—26no—
651Dic6—26no—
652C2×C32—41no—
653C2×C32—43no—
654C2×C32C23×D411yescharacteristic
655C2×C32C2×2−1+411yescharacteristic
656C2×C32#58511yescharacteristic
657C3×D3—22no—
658C3×D3—26no—
659C3×D3—41no—
660C24—33no—
661#41—24no—
662#41—38no—
663#41—612no—
664#41—612no—
665#41—612no—
666#41—612no—
667#41—612no—
668C2×Q8—24no—
669C2×Q8—33no—
670C2×Q8—33no—
671C2×Q8—33no—
672C2×Q8—612no—
673C2×Q8—64no—
674C2×Q8—64no—
675C2×Q8C22×C3×D313yes—
676C2×Q8C22×C3×D311yescharacteristic
677C2×D4—31no—
678C2×D4—33no—
679C2×D4—31no—
680C2×D4—36no—
681C2×D4—33no—
682C2×D4—33no—
683C2×D4—31no—
684C2×D4—33no—
685C2×D4—612no—
686C2×D4C22×C3×D313yes—
687C2×D4C22×C3×D313yes—
688C22×C4—33no—
689C22×C4—33no—
690C22×C4—36no—
691C22×C4—33no—
692C22×C4—33no—
693C22×C4—33no—
694C22×C4—31no—
695C22×C4—36no—
696C22×C4—612no—
697C22×C4C22×C3×D313yes—
698C22×C4C22×C3×D313yes—
699C4⋊C4—33no—
700C4⋊C4—33no—
701C4⋊C4—33no—
702C4⋊C4—36no—
703C4⋊C4—36no—
704C4⋊C4—31no—
705C4⋊C4—33no—
706C4⋊C4—33no—
707C4⋊C4C22×C3×D313yes—
708C4⋊C4C22×C3×D313yes—
709C22⋊C4—36no—
710C22⋊C4—33no—
711C22⋊C4—33no—
712C22⋊C4—33no—
713C22⋊C4—33no—
714C22⋊C4—33no—
715C22⋊C4—33no—
716C22⋊C4—31no—
717C22⋊C4—33no—
718C22⋊C4C22×C3×D316yes—
719C22⋊C4C22×C3×D311yescharacteristic
720C22⋊C4C22×C3×D313yes—
721C42—33no—
722C42C22×C3×D313yes—
723C22×C3—22no—
724C22×C3—21no—
725C22×C3—23no—
726C22×C3—21no—
727C22×C3—23no—
728C22×C3—21no—
729C22×C3—23no—
730C22×C3—23no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—23no—
734C22×C3—23no—
735C22×C3—21no—
736C22×C3—21no—
737C22×C3—36no—
738C22×C3—32no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—43no—
742C22×C3—43no—
743C22×C3—43no—
744C22×C3—61no—
745C22×C3—63no—
746C22×C3—61no—
747C22×C3—63no—
748C22×C3—61no—
749C22×C3—61no—
750C22×C3—61no—
751C22×C3—1212no—
752C22×C3C24×D311yescharacteristic
753C22×C3C25×C311yescharacteristic
754C2×D3—21no—
755C2×D3—23no—
756C2×D3—23no—
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—21no—
760C2×D3—21no—
761C2×D3—412no—
762C2×D3C22×C3×D416yes—
763C2×D3C3×2−1+412yescomplemented
764C3×C4—21no—
765C3×C4—23no—
766C3×C4—23no—
767C3×C4—21no—
768C3×C4—23no—
769C3×C4—21no—
770C3×C4—21no—
771C3×C4—23no—
772C3×C4—26no—
773C3×C4—32no—
774C3×C4—41no—
775C3×C4—43no—
776C3×C4—43no—
777C3×C4—41no—
778C3×C4—63no—
779C3×C4—63no—
780C3×C4—63no—
781C3×C4—61no—
782C3×C4C2×D3×D416yes—
783C3×C4C22×C3×D416yes—
784Dic3—23no—
785Dic3—23no—
786Dic3—21no—
787Dic3—23no—
788Dic3C22×C3×D412yes—
789C32#348911yescharacteristic, complemented, Sylow
790C23—31no—
791C23—33no—
792C23—31no—
793C23—66no—
794C23—66no—
795C23—123no—
796C23C23×C3×D313yes—
797C23C23×C3×D311yescharacteristic
798Q8—26no—
799Q8—66no—
800Q8—66no—
801Q8—66no—
802Q8C3×D3×D414yes—
803D4—26no—
804D4—312no—
805D4—43no—
806D4—66no—
807D4—62no—
808D4—62no—
809D4—612no—
810D4—66no—
811D4—62no—
812D4—123no—
813C2×C4—26no—
814C2×C4—26no—
815C2×C4—31no—
816C2×C4—312no—
817C2×C4—31no—
818C2×C4—33no—
819C2×C4—33no—
820C2×C4—33no—
821C2×C4—62no—
822C2×C4—66no—
823C2×C4—612no—
824C2×C4—66no—
825C2×C4—66no—
826C2×C4—66no—
827C2×C4—126no—
828C2×C4C23×C3×D311yescharacteristic
829C2×C4C23×C3×D313yes—
830C2×C4C23×C3×D313yes—
831C2×C4C23×C3×D311yescharacteristic
832C2×C4C23×C3×D313yes—
833C2×C3—21no—
834C2×C3—21no—
835C2×C3—21no—
836C2×C3—42no—
837C2×C3—43no—
838C2×C3—41no—
839C2×C3—43no—
840C2×C3—41no—
841C2×C3—62no—
842C2×C3—66no—
843C2×C3—83no—
844C2×C3—121no—
845C2×C3C22×D3×D411yescharacteristic
846C2×C3#596411yescharacteristic
847C2×C3D3×2−1+411yescharacteristic
848C2×C3C23×C3×D411yescharacteristic
849C2×C3C2×C3×2−1+411yescharacteristic
850C2×C3C3×#58511yescharacteristic
851D3—22no—
852D3—26no—
853D3—41no—
854C22—21no—
855C22—23no—
856C22—21no—
857C22—23no—
858C22—21no—
859C22—23no—
860C22—36no—
861C22—32no—
862C22—61no—
863C22—63no—
864C22—61no—
865C22—63no—
866C22—61no—
867C22—61no—
868C22—61no—
869C22—1212no—
870C22C24×C3×D311yescharacteristic
871C4—21no—
872C4—23no—
873C4—23no—
874C4—21no—
875C4—32no—
876C4—63no—
877C4—63no—
878C4—63no—
879C4—61no—
880C4C2×C3×D3×D416yes—
881C3—21no—
882C3#8671411yescharacteristic, direct product factor
883C3C3×#348911yescharacteristic, complemented
884C2—43no—
885C2—41no—
886C2—62no—
887C2—66no—
888C2—121no—
889C2C22×C3×D3×D411yescharacteristic
890C2C3×#596411yescharacteristic
891C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#548C2
socleC22×C32C25
hypercenterC3×#548D3
hypocenterC3C3×#3489
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×D3×#41C2semidirect
2. C2×C3×#1007C2semidirect
3. C32×#548C2semidirect
4. C3×#5831C2semidirect
5. C3×Q8×#67C2semidirect
6. C3×#5676C2semidirect
7. C3×#5675C2semidirect
8. C3×#5631C2semidirect
9. C3×D3×C22⋊Q8C2semidirect
10. C3×#5612C2semidirect
11. C3×#5608C2semidirect
12. C3×Q8×D12C2semidirect
13. C3×#5574C2semidirect
14. C3×#5551C2semidirect
15. C3×#5547C2semidirect
17. #86714C3direct (N × H)
19. C22×C32×Q8C22semidirect
23. C2×C3×#239C22semidirect
25. C2×C3×D3×Q8C22semidirect
26. C2×C3×D3×Q8C22semidirect
30. C2×C3×#235C22semidirect
31. C2×C3×#235C22semidirect
33. C32×#124C22semidirect
34. C32×C22⋊Q8C22semidirect
35. C32×#121C22semidirect
36. C32×C4×Q8C22semidirect
37. C32×C4×D4C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×#944C22semidirect
41. C3×#939C22semidirect
42. C3×#938C22semidirect
43. C3×#938C22semidirect
45. C3×#936C22semidirect
47. C3×C4×#67C22semidirect
48. C3×#924C22semidirect
49. C3×#924C22semidirect
51. C3×#897C22semidirect
53. C3×#894C22semidirect
54. C3×#893C22semidirect
55. C3×D3×C4⋊C4C22semidirect
56. C3×D3×C4⋊C4C22semidirect
58. C3×#884C22semidirect
59. C3×#883C22semidirect
60. C3×#883C22semidirect
61. C3×#883C22semidirect
64. C3×#878C22semidirect
65. C3×#878C22semidirect
67. C3×C4×D12C22semidirect
68. C3×#872C22semidirect
69. C3×#869C22semidirect
72. C2×D3×#41C2×C3semidirect
73. C2×#1007C2×C3semidirect
78. C3×#548D3semidirect
79. C3×#548C2×C3semidirect
89. #5831C2×C3semidirect
90. Q8×#67C2×C3semidirect
91. #5676C2×C3semidirect
92. #5675C2×C3semidirect
93. #5631C2×C3semidirect
94. D3×C22⋊Q8C2×C3semidirect
95. #5612C2×C3semidirect
96. #5608C2×C3semidirect
97. Q8×D12C2×C3semidirect
98. #5574C2×C3semidirect
99. #5551C2×C3semidirect
100. #5547C2×C3semidirect
117. C3×#239D4semidirect
180. C22×C3×Q8C2×D3semidirect
181. C22×C3×Q8C22×C3semidirect
187. C2×#239C22×C3semidirect
189. C2×D3×Q8C22×C3semidirect
190. C2×D3×Q8C22×C3semidirect
194. C2×#235C22×C3semidirect
195. C2×#235C22×C3semidirect
201. C3×#124C2×D3semidirect
202. C3×#124C22×C3semidirect
216. C3×C22⋊Q8C2×D3semidirect
217. C3×C22⋊Q8C22×C3semidirect
224. C3×#121C2×D3semidirect
225. C3×#121C22×C3semidirect
230. C3×C4×Q8C2×D3semidirect
231. C3×C4×Q8C22×C3semidirect
238. C3×C4×D4C2×D3semidirect
239. C3×C4×D4C22×C3semidirect
245. Q8×Dic3C22×C3semidirect
246. #944C22×C3semidirect
247. #939C22×C3semidirect
248. #938C22×C3semidirect
249. #938C22×C3semidirect
251. #936C22×C3semidirect
253. C4×#67C22×C3semidirect
254. #924C22×C3semidirect
255. #924C22×C3semidirect
257. #897C22×C3semidirect
259. #894C22×C3semidirect
260. #893C22×C3semidirect
261. D3×C4⋊C4C22×C3semidirect
262. D3×C4⋊C4C22×C3semidirect
264. #884C22×C3semidirect
265. #883C22×C3semidirect
266. #883C22×C3semidirect
267. #883C22×C3semidirect
270. #878C22×C3semidirect
271. #878C22×C3semidirect
273. C4×D12C22×C3semidirect
274. #872C22×C3semidirect
275. #869C22×C3semidirect
324. #548C3×D3semidirect
397. #239C3×D4semidirect
490. C2×C3×D32−1+4semidirect
513. C22×Q8C2×C3×D3semidirect
519. #124C2×C3×D3semidirect
532. C22⋊Q8C2×C3×D3semidirect
538. #121C2×C3×D3semidirect
542. C4×Q8C2×C3×D3semidirect
548. C4×D4C2×C3×D3semidirect
763. C2×D3C3×2−1+4semidirect
789. C32#3489semidirect
882. C3#86714direct (N × H)
883. C3C3×#3489semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C2×C3×#10072
C32×#5482
C3×#58312
C3×Q8×#672
C3×#56762
C3×#56752
C3×#56312
C3×D3×C22⋊Q82
C3×#56122
C3×#56082
C3×Q8×D122
C3×#55742
C3×#55512
C3×#55472
C3×#34893
#867143