Finite Group Databasebeta

← C3×#86745 #11904726

Subgroups — C3×#86745 #11904726

Order 1152.

3184 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×#1007C211yesmaximal, characteristic, complemented
2C22×C3×#239C211yesmaximal, characteristic, complemented
3C32×D4×Q8C211yesmaximal, characteristic, complemented
4C3×#5817C211yesmaximal, characteristic, complemented
5C3×Q8×#67C211yesmaximal, characteristic, complemented
6C3×#5726C213yesmaximal, complemented
7C3×#5724C213yesmaximal, complemented
8C3×#5631C213yesmaximal, complemented
9C3×#5630C213yesmaximal, complemented
10C3×#5629C213yesmaximal, complemented
11C3×D3×C22⋊Q8C213yesmaximal, complemented
12C3×#5576C211yesmaximal, characteristic, complemented
13C3×#5574C211yesmaximal, characteristic, complemented
14C3×#5550C213yesmaximal, complemented
15C3×#5547C213yesmaximal, complemented
16C3×#3489—31nomaximal
17#86745C311yesmaximal, characteristic, direct product factor
18C22×C32×Q8C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic, complemented
20C3×#1007—28no—
21C2×C3×#239—28no—
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2213yes—
24C2×C3×#239C2213yes—
25C2×C3×#239C2211yescharacteristic
26C2×C3×#239C2213yescomplemented
27C2×C3×D3×Q8C2211yescharacteristic, complemented
28C2×C3×D3×Q8C2213yescomplemented
29C2×C3×#235C2213yescomplemented
30C2×C3×#235C2213yescomplemented
31C22×C3×D12C2213yes—
32C22×C3×C4×D3C2213yes—
33C32×C4⋊Q8C2213yescomplemented
34C32×C22⋊Q8C2213yes—
35C32×C22⋊Q8C2213yescomplemented
36C32×C4×Q8C2211yescharacteristic, complemented
37C32×C4×D4C2213yes—
38C3×#947C2213yescomplemented
39C3×#946C2213yescomplemented
40C3×#946C2213yescomplemented
41C3×Q8×Dic3C2211yescharacteristic, complemented
42C3×#944C2213yescomplemented
43C3×#939C2211yescharacteristic
44C3×#937C2213yes—
45C3×#930C2213yescomplemented
46C3×C4×#67C2213yes—
47C3×C4×#67C2213yescomplemented
48C3×#924C2213yes—
49C3×#897C2213yescomplemented
50C3×#896C2213yescomplemented
51C3×#896C2216yescomplemented
52C3×#895C2213yescomplemented
53C3×#895C2216yescomplemented
54C3×#894C2213yescomplemented
55C3×#894C2216yescomplemented
56C3×#894C2216yescomplemented
57C3×#893C2213yescomplemented
58C3×D3×C4⋊C4C2213yescomplemented
59C3×D3×C4⋊C4C2216yescomplemented
60C3×#884C2213yescomplemented
61C3×#884C2216yescomplemented
62C3×#883C2213yescomplemented
63C3×#882C2213yes—
64C3×D3×C22⋊C4C2216yes—
65C3×#878C2213yes—
66C3×#875C2213yescomplemented
67C3×C4×D12C2213yescomplemented
68C3×C4×D12C2213yescomplemented
69C3×#872C2213yescomplemented
70C2×C3×2−1+4—31no—
71C22×C3×#41—31no—
72C2×#1007C2×C311yescharacteristic, complemented
73C22×#239C2×C311yescharacteristic, complemented
74C3×D4×Q8—21no—
75C3×D4×Q8—31no—
76C3×D4×Q8D311yescharacteristic, complemented
77C3×D4×Q8C2×C311yescharacteristic, complemented
78C3×#548—31no—
79C3×#548—31no—
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#5817C2×C311yescharacteristic, complemented
90Q8×#67C2×C311yescharacteristic, complemented
91#5726C2×C313yescomplemented
92#5724C2×C313yescomplemented
93#5631C2×C313yescomplemented
94#5630C2×C313yescomplemented
95#5629C2×C313yescomplemented
96D3×C22⋊Q8C2×C313yescomplemented
97#5576C2×C311yescharacteristic, complemented
98#5574C2×C311yescharacteristic, complemented
99#5550C2×C313yescomplemented
100#5547C2×C313yescomplemented
101C23×C3×D3C2313yes—
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×#67C2311yescharacteristic
111C2×C3×#67C2313yes—
112C2×C3×#67C2311yescharacteristic
113C2×C3×#67C2313yes—
114C22×C3×Dic3C2311yescharacteristic
115C3×#239—24no—
116C3×#239—212no—
117C3×#239—212no—
118C3×#239—212no—
119C3×#239D418yescomplemented
120C3×D3×Q8—24no—
121C3×D3×Q8—212no—
122C3×#235—212no—
123C3×#235—212no—
124C2×C3×D12—212no—
125C2×C3×D12C2313yes—
126C2×C3×D12C2316yes—
127C2×C3×D12C2313yes—
128C2×C3×D12C2313yes—
129C2×C3×D12C2313yes—
130C2×C3×C4×D3—212no—
131C2×C3×C4×D3C2316yes—
132C2×C3×C4×D3C2313yes—
133C2×C3×C4×D3C2313yes—
134C2×C3×C4×D3C2313yes—
135C2×C3×C4×D3C2313yes—
136C2×C3×C4×D3C2316yes—
137C2×C3×C4×D3C2313yes—
138C2×C3×Dic6C2313yes—
139C2×C3×Dic6C2313yes—
140C32×C4⋊C4C2313yes—
141C32×C4⋊C4C2316yes—
142C32×C4⋊C4C2313yes—
143C32×C22⋊C4C2313yes—
144C32×C22⋊C4C2313yes—
145C32×C42C2313yes—
146C3×#217C2313yes—
147C3×#217C2311yescharacteristic
148C3×(C2×D3)⋊C4C2316yes—
149C3×(C2×D3)⋊C4C2316yes—
150C3×(C2×D3)⋊C4C2313yes—
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2313yes—
153C3×(C2×D3)⋊C4C2313yes—
154C3×(C2×D3)⋊C4C2311yescharacteristic
155C3×(C2×D3)⋊C4C2313yes—
156C3×C4⋊Dic3C2313yes—
157C3×C4⋊Dic3C2313yes—
158C3×Dic3⋊C4C2313yes—
159C3×Dic3⋊C4C2313yes—
160C3×Dic3⋊C4C2313yes—
161C3×Dic3⋊C4C2316yes—
162C3×Dic3⋊C4C2311yescharacteristic
163C3×C4×Dic3C2313yes—
164#3489—31noSylow
165C3×2−1+4—68no—
166C2×C3×#41—31no—
167C2×C3×#41—33no—
168C2×C3×#41—33no—
169C2×C3×#41—31no—
170C2×C3×#41—33no—
171C2×C3×#41—33no—
172C2×C3×#41—33no—
173C2×C3×#41—68no—
174C22×C3×Q8—21no—
175C22×C3×Q8—21no—
176C22×C3×Q8—33no—
177C22×C3×Q8—31no—
178C22×C3×Q8C2×D311yescharacteristic
179C22×C3×Q8C2×D311yescharacteristic, complemented
180C22×C3×Q8C22×C311yescharacteristic
181C22×C3×Q8C22×C311yescharacteristic, complemented
182C22×C3×D4—33no—
183C23×C3×C4—33no—
184#1007—28no—
185C2×#239—28no—
186C2×#239C22×C313yes—
187C2×#239C22×C313yes—
188C2×#239C22×C311yescharacteristic
189C2×#239C22×C311yescharacteristic
190C2×#239C22×C313yescomplemented
191C2×D3×Q8C22×C313yescomplemented
192C2×D3×Q8C22×C311yescharacteristic, complemented
193C2×#235C22×C313yescomplemented
194C2×#235C22×C313yescomplemented
195C22×D12C22×C313yes—
196C22×C4×D3C22×C313yes—
197C3×C4⋊Q8—23no—
198C3×C4⋊Q8—33no—
199C3×C4⋊Q8C2×D313yescomplemented
200C3×C4⋊Q8C22×C313yescomplemented
201C3×#124—33no—
202C3×#124—33no—
203C3×#123—33no—
204C3×#123—36no—
205C3×#123—36no—
206C3×#123—33no—
207C3×C22⋊Q8—23no—
208C3×C22⋊Q8—23no—
209C3×C22⋊Q8—33no—
210C3×C22⋊Q8—33no—
211C3×C22⋊Q8—33no—
212C3×C22⋊Q8—36no—
213C3×C22⋊Q8—33no—
214C3×C22⋊Q8—33no—
215C3×C22⋊Q8—33no—
216C3×C22⋊Q8C2×D313yes—
217C3×C22⋊Q8C2×D313yescomplemented
218C3×C22⋊Q8C22×C313yes—
219C3×C22⋊Q8C22×C313yescomplemented
220C3×#121—31no—
221C3×#121—33no—
222C3×#121—36no—
223C3×#121—33no—
224C3×#121—33no—
225C3×#121—36no—
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×D313yes—
239C3×C4×D4C22×C313yes—
240C3×#117—33no—
241C2×C3×C4⋊C4—33no—
242C2×C3×C4⋊C4—36no—
243C2×C3×C22⋊C4—36no—
244#947C22×C313yescomplemented
245#946C22×C313yescomplemented
246#946C22×C313yescomplemented
247Q8×Dic3C22×C311yescharacteristic, complemented
248#944C22×C313yescomplemented
249#939C22×C311yescharacteristic
250#937C22×C313yes—
251#930C22×C313yescomplemented
252C4×#67C22×C313yes—
253C4×#67C22×C313yescomplemented
254#924C22×C313yes—
255#897C22×C313yescomplemented
256#896C22×C313yescomplemented
257#896C22×C316yescomplemented
258#895C22×C316yescomplemented
259#895C22×C313yescomplemented
260#894C22×C316yescomplemented
261#894C22×C316yescomplemented
262#894C22×C313yescomplemented
263#893C22×C313yescomplemented
264D3×C4⋊C4C22×C316yescomplemented
265D3×C4⋊C4C22×C313yescomplemented
266#884C22×C313yescomplemented
267#884C22×C316yescomplemented
268#883C22×C313yescomplemented
269#882C22×C313yes—
270D3×C22⋊C4C22×C316yes—
271#878C22×C313yes—
272#875C22×C313yescomplemented
273C4×D12C22×C313yescomplemented
274C4×D12C22×C313yescomplemented
275#872C22×C313yescomplemented
276C23×C32C2411yescharacteristic
277C23×C32C2411yescharacteristic
278C22×C3×D3—26no—
279C22×C3×D3—26no—
280C22×C3×D3—43no—
281C22×C3×D3C2413yes—
282C22×C3×D3C2411yescharacteristic
283C22×C3×D3C2413yes—
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×C4C2413yes—
292C2×C32×C4C2411yescharacteristic
293C2×C32×C4C2413yes—
294C2×C32×C4C2413yes—
295C3×#67—22no—
296C3×#67—26no—
297C3×#67—22no—
298C3×#67—43no—
299C2×C3×Dic3—22no—
300C2×C3×Dic3C2411yescharacteristic
301C2×C3×Dic3C2413yes—
302C2×C3×Dic3C2411yescharacteristic
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2411yescharacteristic
305C3×D12—212no—
306C3×D12—26no—
307C3×D12—26no—
308C3×D12—43no—
309C3×D12C2×D4112yes—
310C3×C4×D3—26no—
311C3×C4×D3—212no—
312C3×C4×D3—26no—
313C3×C4×D3—26no—
314C3×C4×D3—26no—
315C3×C4×D3—46no—
316C3×C4×D3C2×D4112yes—
317C3×Dic6—26no—
318C3×Dic6—26no—
319C2×2−1+4—31no—
320C22×#41—31no—
321D4×Q8—31no—
322D4×Q8C3×D311yescharacteristic, complemented
323#548—31no—
324#548—31no—
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—38no—
337C3×#41—612no—
338C3×#41—612no—
339C3×#41—612no—
340C3×#41—612no—
341C3×#41—612no—
342C3×#41—64no—
343C2×C3×Q8—24no—
344C2×C3×Q8—24no—
345C2×C3×Q8—24no—
346C2×C3×Q8—24no—
347C2×C3×Q8—21no—
348C2×C3×Q8—23no—
349C2×C3×Q8—23no—
350C2×C3×Q8—33no—
351C2×C3×Q8—33no—
352C2×C3×Q8—44no—
353C2×C3×Q8—44no—
354C2×C3×Q8—612no—
355C2×C3×Q8—64no—
356C2×C3×Q8C22×D313yes—
357C2×C3×Q8C22×D313yes—
358C2×C3×Q8C22×D311yescharacteristic
359C2×C3×Q8C23×C313yes—
360C2×C3×Q8C23×C313yes—
361C2×C3×Q8C23×C311yescharacteristic
362C2×C3×D4—21no—
363C2×C3×D4—31no—
364C2×C3×D4—33no—
365C2×C3×D4—31no—
366C2×C3×D4—33no—
367C2×C3×D4—33no—
368C2×C3×D4—33no—
369C2×C3×D4—36no—
370C2×C3×D4—33no—
371C2×C3×D4—33no—
372C2×C3×D4—612no—
373C2×C3×D4C22×D311yescharacteristic
374C2×C3×D4C23×C311yescharacteristic
375C22×C3×C4—23no—
376C22×C3×C4—23no—
377C22×C3×C4—33no—
378C22×C3×C4—31no—
379C22×C3×C4—36no—
380C22×C3×C4—33no—
381C22×C3×C4—33no—
382C22×C3×C4—33no—
383C22×C3×C4—33no—
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×C311yescharacteristic
391C2×#67C23×C313yes—
392C2×#67C23×C311yescharacteristic
393C2×#67C23×C313yes—
394C22×Dic3C23×C311yescharacteristic
395#239—24no—
396#239—212no—
397#239—212no—
398#239—212no—
399#239C3×D418yescomplemented
400D3×Q8—24no—
401D3×Q8—212no—
402#235—212no—
403#235—212no—
404C2×D12—212no—
405C2×D12C23×C313yes—
406C2×D12C23×C313yes—
407C2×D12C23×C316yes—
408C2×D12C23×C313yes—
409C2×D12C23×C313yes—
410C2×C4×D3—212no—
411C2×C4×D3C23×C313yes—
412C2×C4×D3C23×C313yes—
413C2×C4×D3C23×C316yes—
414C2×C4×D3C23×C313yes—
415C2×C4×D3C23×C313yes—
416C2×C4×D3C23×C316yes—
417C2×C4×D3C23×C313yes—
418C2×Dic6C23×C313yes—
419C2×Dic6C23×C313yes—
420C3×C4⋊C4—23no—
421C3×C4⋊C4—23no—
422C3×C4⋊C4—26no—
423C3×C4⋊C4—33no—
424C3×C4⋊C4—33no—
425C3×C4⋊C4—36no—
426C3×C4⋊C4—31no—
427C3×C4⋊C4—33no—
428C3×C4⋊C4—33no—
429C3×C4⋊C4—33no—
430C3×C4⋊C4C22×D313yes—
431C3×C4⋊C4C22×D316yes—
432C3×C4⋊C4C22×D313yes—
433C3×C4⋊C4C23×C313yes—
434C3×C4⋊C4C23×C316yes—
435C3×C4⋊C4C23×C313yes—
436C3×C22⋊C4—23no—
437C3×C22⋊C4—23no—
438C3×C22⋊C4—33no—
439C3×C22⋊C4—31no—
440C3×C22⋊C4—36no—
441C3×C22⋊C4—36no—
442C3×C22⋊C4—33no—
443C3×C22⋊C4—33no—
444C3×C22⋊C4—31no—
445C3×C22⋊C4—33no—
446C3×C22⋊C4—33no—
447C3×C22⋊C4—33no—
448C3×C22⋊C4C22×D313yes—
449C3×C22⋊C4C22×D313yes—
450C3×C22⋊C4C23×C313yes—
451C3×C22⋊C4C23×C313yes—
452C3×C42—23no—
453C3×C42—33no—
454C3×C42C22×D313yes—
455C3×C42C23×C313yes—
456#217C23×C313yes—
457#217C23×C311yescharacteristic
458(C2×D3)⋊C4C23×C313yes—
459(C2×D3)⋊C4C23×C313yes—
460(C2×D3)⋊C4C23×C311yescharacteristic
461(C2×D3)⋊C4C23×C313yes—
462(C2×D3)⋊C4C23×C316yes—
463(C2×D3)⋊C4C23×C316yes—
464(C2×D3)⋊C4C23×C313yes—
465(C2×D3)⋊C4C23×C313yes—
466C4⋊Dic3C23×C313yes—
467C4⋊Dic3C23×C313yes—
468Dic3⋊C4C23×C311yescharacteristic
469Dic3⋊C4C23×C313yes—
470Dic3⋊C4C23×C313yes—
471Dic3⋊C4C23×C313yes—
472Dic3⋊C4C23×C316yes—
473C4×Dic3C23×C313yes—
474C22×C32—21no—
475C22×C32—21no—
476C22×C32—21no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C322−1+412yescomplemented
480C22×C32C2511yescharacteristic
481C2×C3×D3—23no—
482C2×C3×D3—23no—
483C2×C3×D3—21no—
484C2×C3×D3—23no—
485C2×C3×D3—21no—
486C2×C3×D3—23no—
487C2×C3×D3—21no—
488C2×C3×D3—23no—
489C2×C3×D3—412no—
490C2×C3×D3C22×D416yes—
491C32×C4—21no—
492C32×C4—23no—
493C32×C4—23no—
494C32×C4—23no—
495C32×C4C22×D416yes—
496C3×Dic3—23no—
497C3×Dic3—21no—
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—31no—
507C2×#41—33no—
508C2×#41—33no—
509C2×#41—68no—
510C22×Q8—33no—
511C22×Q8—31no—
512C22×Q8C2×C3×D311yescharacteristic
513C22×Q8C2×C3×D311yescharacteristic, complemented
514C22×D4—33no—
515C23×C4—33no—
516C4⋊Q8—33no—
517C4⋊Q8C2×C3×D313yescomplemented
518#124—33no—
519#124—33no—
520#123—33no—
521#123—36no—
522#123—36no—
523#123—33no—
524C22⋊Q8—33no—
525C22⋊Q8—33no—
526C22⋊Q8—33no—
527C22⋊Q8—36no—
528C22⋊Q8—33no—
529C22⋊Q8—33no—
530C22⋊Q8—33no—
531C22⋊Q8C2×C3×D313yes—
532C22⋊Q8C2×C3×D313yescomplemented
533#121—31no—
534#121—33no—
535#121—36no—
536#121—33no—
537#121—33no—
538#121—36no—
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×D313yes—
549#117—33no—
550C2×C4⋊C4—33no—
551C2×C4⋊C4—36no—
552C2×C22⋊C4—36no—
553C23×C3—21no—
554C23×C3—21no—
555C23×C3—33no—
556C23×C3—33no—
557C23×C3—31no—
558C23×C3—66no—
559C23×C3—66no—
560C23×C3—123no—
561C23×C3C23×D311yescharacteristic
562C23×C3C23×D311yescharacteristic
563C23×C3C24×C311yescharacteristic
564C23×C3C24×C311yescharacteristic
565C22×D3—26no—
566C22×D3—26no—
567C22×D3—43no—
568C22×D3C24×C313yes—
569C22×D3C24×C311yescharacteristic
570C22×D3C24×C313yes—
571C3×Q8—26no—
572C3×Q8—26no—
573C3×Q8—26no—
574C3×Q8—26no—
575C3×Q8—24no—
576C3×Q8—46no—
577C3×Q8—46no—
578C3×Q8—66no—
579C3×Q8—66no—
580C3×Q8D3×D414yes—
581C3×Q8C2×C3×D414yes—
582C3×D4—24no—
583C3×D4—22no—
584C3×D4—22no—
585C3×D4—312no—
586C3×D4—612no—
587C3×D4—66no—
588C3×D4—62no—
589C3×D4—66no—
590C3×D4—62no—
591C3×D4—66no—
592C3×D4—123no—
593C3×D4—123no—
594C2×C3×C4—26no—
595C2×C3×C4—26no—
596C2×C3×C4—26no—
597C2×C3×C4—26no—
598C2×C3×C4—21no—
599C2×C3×C4—23no—
600C2×C3×C4—23no—
601C2×C3×C4—23no—
602C2×C3×C4—23no—
603C2×C3×C4—31no—
604C2×C3×C4—312no—
605C2×C3×C4—31no—
606C2×C3×C4—33no—
607C2×C3×C4—33no—
608C2×C3×C4—31no—
609C2×C3×C4—46no—
610C2×C3×C4—46no—
611C2×C3×C4—66no—
612C2×C3×C4—66no—
613C2×C3×C4—612no—
614C2×C3×C4—62no—
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×D313yes—
622C2×C3×C4C23×D313yes—
623C2×C3×C4C24×C313yes—
624C2×C3×C4C24×C313yes—
625C2×C3×C4C24×C311yescharacteristic
626C2×C3×C4C24×C313yes—
627C2×C3×C4C24×C313yes—
628#67—22no—
629#67—26no—
630#67—22no—
631#67—43no—
632C2×Dic3—22no—
633C2×Dic3C24×C311yescharacteristic
634C2×Dic3C24×C313yes—
635C2×Dic3C24×C311yescharacteristic
636C2×Dic3C24×C313yes—
637C2×Dic3C24×C311yescharacteristic
638D12—212no—
639D12—26no—
640D12—26no—
641D12—43no—
642D12C2×C3×D4112yes—
643C4×D3—26no—
644C4×D3—212no—
645C4×D3—26no—
646C4×D3—26no—
647C4×D3—26no—
648C4×D3—46no—
649C4×D3C2×C3×D4112yes—
650Dic6—26no—
651Dic6—26no—
652C2×C32—22no—
653C2×C32—41no—
654C2×C32C23×D411yescharacteristic
655C2×C32C2×2−1+411yescharacteristic
656C2×C32#58511yescharacteristic
657C3×D3—26no—
658C3×D3—41no—
659C3×D3—43no—
660C24—33no—
661#41—38no—
662#41—612no—
663#41—612no—
664#41—612no—
665#41—612no—
666#41—612no—
667#41—64no—
668C2×Q8—24no—
669C2×Q8—24no—
670C2×Q8—33no—
671C2×Q8—33no—
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—36no—
684C2×D4—33no—
685C2×D4—33no—
686C2×D4—612no—
687C2×D4C22×C3×D311yescharacteristic
688C22×C4—33no—
689C22×C4—31no—
690C22×C4—36no—
691C22×C4—33no—
692C22×C4—33no—
693C22×C4—33no—
694C22×C4—33no—
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—33no—
703C4⋊C4—36no—
704C4⋊C4—31no—
705C4⋊C4—33no—
706C4⋊C4C22×C3×D313yes—
707C4⋊C4C22×C3×D316yes—
708C4⋊C4C22×C3×D313yes—
709C22⋊C4—33no—
710C22⋊C4—31no—
711C22⋊C4—36no—
712C22⋊C4—36no—
713C22⋊C4—33no—
714C22⋊C4—33no—
715C22⋊C4—31no—
716C22⋊C4—33no—
717C22⋊C4—33no—
718C22⋊C4—33no—
719C22⋊C4C22×C3×D313yes—
720C22⋊C4C22×C3×D313yes—
721C42—33no—
722C42C22×C3×D313yes—
723C22×C3—21no—
724C22×C3—21no—
725C22×C3—21no—
726C22×C3—21no—
727C22×C3—22no—
728C22×C3—21no—
729C22×C3—21no—
730C22×C3—21no—
731C22×C3—21no—
732C22×C3—21no—
733C22×C3—21no—
734C22×C3—22no—
735C22×C3—21no—
736C22×C3—36no—
737C22×C3—41no—
738C22×C3—41no—
739C22×C3—41no—
740C22×C3—41no—
741C22×C3—63no—
742C22×C3—63no—
743C22×C3—61no—
744C22×C3—63no—
745C22×C3—61no—
746C22×C3—63no—
747C22×C3—61no—
748C22×C3—63no—
749C22×C3—1212no—
750C22×C3#100712yescomplemented
751C22×C3C3×2−1+412yescomplemented
752C22×C3C24×D311yescharacteristic
753C22×C3C25×C311yescharacteristic
754C2×D3—23no—
755C2×D3—23no—
756C2×D3—21no—
757C2×D3—23no—
758C2×D3—21no—
759C2×D3—23no—
760C2×D3—21no—
761C2×D3—23no—
762C2×D3—412no—
763C2×D3C22×C3×D416yes—
764C3×C4—22no—
765C3×C4—23no—
766C3×C4—23no—
767C3×C4—21no—
768C3×C4—23no—
769C3×C4—23no—
770C3×C4—23no—
771C3×C4—21no—
772C3×C4—23no—
773C3×C4—26no—
774C3×C4—32no—
775C3×C4—43no—
776C3×C4—43no—
777C3×C4—43no—
778C3×C4—61no—
779C3×C4—63no—
780C3×C4—61no—
781C3×C4—63no—
782C3×C4C2×D3×D416yes—
783C3×C4C22×C3×D416yes—
784Dic3—23no—
785Dic3—21no—
786Dic3—21no—
787Dic3—23no—
788Dic3C22×C3×D412yes—
789C32#348911yescharacteristic, complemented, Sylow
790C23—33no—
791C23—33no—
792C23—31no—
793C23—66no—
794C23—66no—
795C23—123no—
796C23C23×C3×D311yescharacteristic
797C23C23×C3×D311yescharacteristic
798Q8—26no—
799Q8—26no—
800Q8—66no—
801Q8—66no—
802Q8C3×D3×D414yes—
803D4—22no—
804D4—312no—
805D4—612no—
806D4—66no—
807D4—62no—
808D4—66no—
809D4—62no—
810D4—66no—
811D4—123no—
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—31no—
821C2×C4—66no—
822C2×C4—66no—
823C2×C4—612no—
824C2×C4—62no—
825C2×C4—66no—
826C2×C4—66no—
827C2×C4—126no—
828C2×C4C23×C3×D311yescharacteristic
829C2×C4C23×C3×D313yes—
830C2×C4C23×C3×D313yes—
831C2×C4C23×C3×D313yes—
832C2×C4C23×C3×D313yes—
833C2×C3—22no—
834C2×C3—22no—
835C2×C3—21no—
836C2×C3—21no—
837C2×C3—21no—
838C2×C3—42no—
839C2×C3—42no—
840C2×C3—41no—
841C2×C3—41no—
842C2×C3—66no—
843C2×C3—123no—
844C2×C3—121no—
845C2×C3C22×D3×D411yescharacteristic
846C2×C3C2×#100711yescharacteristic
847C2×C3#596811yescharacteristic
848C2×C3C23×C3×D411yescharacteristic
849C2×C3C2×C3×2−1+411yescharacteristic
850C2×C3C3×#58511yescharacteristic
851D3—26no—
852D3—43no—
853D3—41no—
854C22—21no—
855C22—21no—
856C22—21no—
857C22—21no—
858C22—21no—
859C22—36no—
860C22—63no—
861C22—63no—
862C22—61no—
863C22—63no—
864C22—61no—
865C22—63no—
866C22—61no—
867C22—63no—
868C22—1212no—
869C22C3×#100712yescomplemented
870C22C24×C3×D311yescharacteristic
871C4—23no—
872C4—23no—
873C4—21no—
874C4—23no—
875C4—32no—
876C4—61no—
877C4—63no—
878C4—61no—
879C4—63no—
880C4C2×C3×D3×D416yes—
881C3—21no—
882C3#8674511yescharacteristic, direct product factor
883C3C3×#348911yescharacteristic, complemented
884C2—22no—
885C2—41no—
886C2—66no—
887C2—123no—
888C2—121no—
889C2C22×C3×D3×D411yescharacteristic
890C2C2×C3×#100711yescharacteristic
891C2C3×#596811yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×D4×Q8C2
socleC22×C32C25
hypercenterC3×D4×Q8D3
hypocenterC3C3×#3489
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×#239C2semidirect
3. C32×D4×Q8C2semidirect
4. C3×#5817C2semidirect
5. C3×Q8×#67C2semidirect
6. C3×#5726C2semidirect
7. C3×#5724C2semidirect
8. C3×#5631C2semidirect
9. C3×#5630C2semidirect
10. C3×#5629C2semidirect
11. C3×D3×C22⋊Q8C2semidirect
12. C3×#5576C2semidirect
13. C3×#5574C2semidirect
14. C3×#5550C2semidirect
15. C3×#5547C2semidirect
17. #86745C3direct (N × H)
19. C22×C32×Q8C22semidirect
26. C2×C3×#239C22semidirect
27. C2×C3×D3×Q8C22semidirect
28. C2×C3×D3×Q8C22semidirect
29. C2×C3×#235C22semidirect
30. C2×C3×#235C22semidirect
33. C32×C4⋊Q8C22semidirect
35. C32×C22⋊Q8C22semidirect
36. C32×C4×Q8C22semidirect
38. C3×#947C22semidirect
39. C3×#946C22semidirect
40. C3×#946C22semidirect
41. C3×Q8×Dic3C22semidirect
42. C3×#944C22semidirect
45. C3×#930C22semidirect
47. C3×C4×#67C22semidirect
49. C3×#897C22semidirect
50. C3×#896C22semidirect
51. C3×#896C22semidirect
52. C3×#895C22semidirect
53. C3×#895C22semidirect
54. C3×#894C22semidirect
55. C3×#894C22semidirect
56. C3×#894C22semidirect
57. C3×#893C22semidirect
58. C3×D3×C4⋊C4C22semidirect
59. C3×D3×C4⋊C4C22semidirect
60. C3×#884C22semidirect
61. C3×#884C22semidirect
62. C3×#883C22semidirect
66. C3×#875C22semidirect
67. C3×C4×D12C22semidirect
68. C3×C4×D12C22semidirect
69. C3×#872C22semidirect
72. C2×#1007C2×C3semidirect
73. C22×#239C2×C3semidirect
76. C3×D4×Q8D3semidirect
77. C3×D4×Q8C2×C3semidirect
89. #5817C2×C3semidirect
90. Q8×#67C2×C3semidirect
91. #5726C2×C3semidirect
92. #5724C2×C3semidirect
93. #5631C2×C3semidirect
94. #5630C2×C3semidirect
95. #5629C2×C3semidirect
96. D3×C22⋊Q8C2×C3semidirect
97. #5576C2×C3semidirect
98. #5574C2×C3semidirect
99. #5550C2×C3semidirect
100. #5547C2×C3semidirect
119. C3×#239D4semidirect
179. C22×C3×Q8C2×D3semidirect
181. C22×C3×Q8C22×C3semidirect
190. C2×#239C22×C3semidirect
191. C2×D3×Q8C22×C3semidirect
192. C2×D3×Q8C22×C3semidirect
193. C2×#235C22×C3semidirect
194. C2×#235C22×C3semidirect
199. C3×C4⋊Q8C2×D3semidirect
200. C3×C4⋊Q8C22×C3semidirect
217. C3×C22⋊Q8C2×D3semidirect
219. C3×C22⋊Q8C22×C3semidirect
230. C3×C4×Q8C2×D3semidirect
231. C3×C4×Q8C22×C3semidirect
244. #947C22×C3semidirect
245. #946C22×C3semidirect
246. #946C22×C3semidirect
247. Q8×Dic3C22×C3semidirect
248. #944C22×C3semidirect
251. #930C22×C3semidirect
253. C4×#67C22×C3semidirect
255. #897C22×C3semidirect
256. #896C22×C3semidirect
257. #896C22×C3semidirect
258. #895C22×C3semidirect
259. #895C22×C3semidirect
260. #894C22×C3semidirect
261. #894C22×C3semidirect
262. #894C22×C3semidirect
263. #893C22×C3semidirect
264. D3×C4⋊C4C22×C3semidirect
265. D3×C4⋊C4C22×C3semidirect
266. #884C22×C3semidirect
267. #884C22×C3semidirect
268. #883C22×C3semidirect
272. #875C22×C3semidirect
273. C4×D12C22×C3semidirect
274. C4×D12C22×C3semidirect
275. #872C22×C3semidirect
322. D4×Q8C3×D3semidirect
399. #239C3×D4semidirect
479. C22×C322−1+4semidirect
513. C22×Q8C2×C3×D3semidirect
517. C4⋊Q8C2×C3×D3semidirect
532. C22⋊Q8C2×C3×D3semidirect
542. C4×Q8C2×C3×D3semidirect
750. C22×C3#1007semidirect
751. C22×C3C3×2−1+4semidirect
789. C32#3489semidirect
869. C22C3×#1007semidirect
882. C3#86745direct (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×#10072
C22×C3×#2392
C32×D4×Q82
C3×#58172
C3×Q8×#672
C3×#57262
C3×#57242
C3×#56312
C3×#56302
C3×#56292
C3×D3×C22⋊Q82
C3×#55762
C3×#55742
C3×#55502
C3×#55472
C3×#34893
#867453