Finite Group Databasebeta

← C3×#86736 #11904535

Subgroups — C3×#86736 #11904535

Order 1152.

3217 conjugacy classes of subgroups.

The subgroup lattice has 897 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×#5834C211yesmaximal, characteristic, complemented
5C3×#5817C211yesmaximal, characteristic, complemented
6C3×#5677C213yesmaximal, complemented
7C3×#5674C213yesmaximal, complemented
8C3×#5633C213yesmaximal, complemented
9C3×#5627C213yesmaximal, complemented
10C3×#5607C213yesmaximal, complemented
11C3×#5599C213yesmaximal, complemented
12C3×#5577C211yesmaximal, characteristic, complemented
13C3×#5572C211yesmaximal, characteristic, complemented
14C3×#5553C213yesmaximal, complemented
15C3×#5547C213yesmaximal, complemented
16C3×#3487—31nomaximal
17#86736C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C22×C32×Q8C2211yescharacteristic, complemented
20C3×D3×#41—28no—
21C3×#1007—28no—
22C2×C3×#239C2211yescharacteristic
23C2×C3×#239C2213yes—
24C2×C3×#239C2211yescharacteristic, complemented
25C2×C3×D3×Q8C2211yescharacteristic
26C2×C3×D3×Q8C2213yescomplemented
27C2×C3×#237C2213yes—
28C2×C3×D3×D4C2213yes—
29C2×C3×#235C2213yes—
30C2×C3×#235C2213yes—
31C2×C3×#235C2213yescomplemented
32C22×C3×C4×D3C2213yes—
33C32×#124C2213yescomplemented
34C32×C22⋊Q8C2213yescomplemented
35C32×#121C2213yescomplemented
36C32×C4×Q8C2211yescharacteristic, complemented
37C32×C4×D4C2213yescomplemented
38C3×#947C2213yescomplemented
39C3×#946C2213yescomplemented
40C3×Q8×Dic3C2211yescharacteristic, complemented
41C3×#940C2216yescomplemented
42C3×#940C2213yescomplemented
43C3×#939C2213yescomplemented
44C3×#938C2213yescomplemented
45C3×#937C2213yes—
46C3×#930C2213yescomplemented
47C3×#930C2213yescomplemented
48C3×C4×#67C2213yescomplemented
49C3×C4×#67C2213yescomplemented
50C3×#896C2213yescomplemented
51C3×#895C2213yescomplemented
52C3×#895C2213yescomplemented
53C3×#894C2213yes—
54C3×#893C2216yescomplemented
55C3×#892C2213yes—
56C3×#887C2213yescomplemented
57C3×#885C2216yescomplemented
58C3×#884C2213yescomplemented
59C3×#884C2216yescomplemented
60C3×#884C2216yescomplemented
61C3×#883C2211yescharacteristic
62C3×#882C2213yes—
63C3×#882C2216yes—
64C3×#67⋊C4C2216yescomplemented
65C3×#878C2213yescomplemented
66C3×#874C2213yescomplemented
67C3×C4×D12C2213yescomplemented
68C3×#872C2213yes—
69C3×C4×Dic6C2213yescomplemented
70C2×C3×2−1+4—31no—
71C22×C3×#41—31no—
72C2×D3×#41C2×C311yescharacteristic, complemented
73C2×#1007C2×C311yescharacteristic, complemented
74C3×#550—31no—
75C3×#550—33no—
76C3×#550—31no—
77C3×#550—33no—
78C3×#548—21no—
79C3×#548—31no—
80C3×#548—33no—
81C3×#548—33no—
82C3×#548D311yescharacteristic, complemented
83C3×#548C2×C311yescharacteristic, complemented
84C3×#535—33no—
85C3×#535—33no—
86C3×#525—33no—
87C3×#525—33no—
88C3×#519—31no—
89#5834C2×C311yescharacteristic, complemented
90#5817C2×C311yescharacteristic, complemented
91#5677C2×C313yescomplemented
92#5674C2×C313yescomplemented
93#5633C2×C313yescomplemented
94#5627C2×C313yescomplemented
95#5607C2×C313yescomplemented
96#5599C2×C313yescomplemented
97#5577C2×C311yescharacteristic, complemented
98#5572C2×C311yescharacteristic, complemented
99#5553C2×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×#67C2311yescharacteristic
111C2×C3×#67C2316yes—
112C2×C3×#67C2313yes—
113C2×C3×#67C2316yes—
114C2×C3×#67C2313yes—
115C2×C3×#67C2313yes—
116C22×C3×Dic3C2313yes—
117C3×#239—24no—
118C3×#239—24no—
119C3×#239—212no—
120C3×D3×Q8—212no—
121C3×D3×Q8D418yescomplemented
122C3×#237—212no—
123C3×D3×D4—212no—
124C3×#235—212no—
125C3×#235—212no—
126C3×#235—212no—
127C2×C3×D12C2313yes—
128C2×C3×D12C2313yes—
129C2×C3×D12C2313yes—
130C2×C3×D12C2313yes—
131C2×C3×D12C2316yes—
132C2×C3×C4×D3—212no—
133C2×C3×C4×D3C2316yes—
134C2×C3×C4×D3C2311yescharacteristic
135C2×C3×C4×D3C2313yes—
136C2×C3×C4×D3C2313yes—
137C2×C3×C4×D3C2313yes—
138C2×C3×C4×D3C2313yes—
139C2×C3×Dic6C2313yes—
140C2×C3×Dic6C2313yes—
141C32×C4⋊C4C2313yes—
142C32×C4⋊C4C2313yes—
143C32×C22⋊C4C2313yes—
144C32×C22⋊C4C2316yes—
145C32×C22⋊C4C2311yescharacteristic
146C32×C42C2313yes—
147C3×#217C2313yes—
148C3×#217C2311yescharacteristic
149C3×(C2×D3)⋊C4C2313yes—
150C3×(C2×D3)⋊C4C2311yescharacteristic
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2313yes—
153C3×(C2×D3)⋊C4C2316yes—
154C3×(C2×D3)⋊C4C2313yes—
155C3×(C2×D3)⋊C4C2313yes—
156C3×C4⋊Dic3C2311yescharacteristic
157C3×C4⋊Dic3C2313yes—
158C3×Dic3⋊C4C2313yes—
159C3×Dic3⋊C4C2313yes—
160C3×Dic3⋊C4C2311yescharacteristic
161C3×Dic3⋊C4C2313yes—
162C3×C4×Dic3C2316yes—
163C3×C4×Dic3C2313yes—
164#3487—31noSylow
165C3×2−1+4—68no—
166C2×C3×#41—21no—
167C2×C3×#41—31no—
168C2×C3×#41—33no—
169C2×C3×#41—31no—
170C2×C3×#41—33no—
171C2×C3×#41—33no—
172C2×C3×#41—33no—
173C2×C3×#41—33no—
174C2×C3×#41—68no—
175C2×C3×#41C2×D311yescharacteristic
176C2×C3×#41C22×C311yescharacteristic
177C22×C3×Q8—21no—
178C22×C3×Q8—31no—
179C22×C3×Q8—33no—
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×C313yes—
187C2×#239C22×C311yescharacteristic
188C2×#239C22×C311yescharacteristic, complemented
189C2×D3×Q8C22×C311yescharacteristic
190C2×D3×Q8C22×C313yescomplemented
191C2×#237C22×C313yes—
192C2×D3×D4C22×C313yes—
193C2×#235C22×C313yes—
194C2×#235C22×C313yes—
195C2×#235C22×C313yescomplemented
196C22×C4×D3C22×C313yes—
197C3×#127—36no—
198C3×#127—33no—
199C3×#127—33no—
200C3×#124—23no—
201C3×#124—33no—
202C3×#124—36no—
203C3×#124C2×D313yescomplemented
204C3×#124C22×C313yescomplemented
205C3×#123—33no—
206C3×#123—31no—
207C3×C22⋊Q8—23no—
208C3×C22⋊Q8—33no—
209C3×C22⋊Q8—33no—
210C3×C22⋊Q8—33no—
211C3×C22⋊Q8C2×D313yescomplemented
212C3×C22⋊Q8C22×C313yescomplemented
213C3×#121—23no—
214C3×#121—33no—
215C3×#121—33no—
216C3×#121—33no—
217C3×#121—33no—
218C3×#121—33no—
219C3×#121—33no—
220C3×#121—33no—
221C3×#121—36no—
222C3×#121—36no—
223C3×#121C2×D313yescomplemented
224C3×#121C22×C313yescomplemented
225C3×#120—33no—
226C3×#120—36no—
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×D313yescomplemented
241C3×C4×D4C22×C313yescomplemented
242C3×#117—33no—
243C3×#117—33no—
244#947C22×C313yescomplemented
245#946C22×C313yescomplemented
246Q8×Dic3C22×C311yescharacteristic, complemented
247#940C22×C313yescomplemented
248#940C22×C316yescomplemented
249#939C22×C313yescomplemented
250#938C22×C313yescomplemented
251#937C22×C313yes—
252#930C22×C313yescomplemented
253#930C22×C313yescomplemented
254C4×#67C22×C313yescomplemented
255C4×#67C22×C313yescomplemented
256#896C22×C313yescomplemented
257#895C22×C313yescomplemented
258#895C22×C313yescomplemented
259#894C22×C313yes—
260#893C22×C316yescomplemented
261#892C22×C313yes—
262#887C22×C313yescomplemented
263#885C22×C316yescomplemented
264#884C22×C316yescomplemented
265#884C22×C316yescomplemented
266#884C22×C313yescomplemented
267#883C22×C311yescharacteristic
268#882C22×C313yes—
269#882C22×C316yes—
270#67⋊C4C22×C316yescomplemented
271#878C22×C313yescomplemented
272#874C22×C313yescomplemented
273C4×D12C22×C313yescomplemented
274#872C22×C313yes—
275C4×Dic6C22×C313yescomplemented
276C23×C32C2413yes—
277C23×C32C2411yescharacteristic
278C22×C3×D3—26no—
279C22×C3×D3—43no—
280C22×C3×D3—43no—
281C22×C3×D3C2413yes—
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×C4C2413yes—
293C2×C32×C4C2411yescharacteristic
294C2×C32×C4C2413yes—
295C3×#67—22no—
296C3×#67—26no—
297C3×#67—212no—
298C3×#67—43no—
299C3×#67—46no—
300C3×#67—43no—
301C2×C3×Dic3—26no—
302C2×C3×Dic3C2411yescharacteristic
303C2×C3×Dic3C2413yes—
304C2×C3×Dic3C2411yescharacteristic
305C2×C3×Dic3C2411yescharacteristic
306C2×C3×Dic3C2413yes—
307C3×D12—26no—
308C3×D12—26no—
309C3×D12—26no—
310C3×D12—43no—
311C3×D12—46no—
312C3×C4×D3—22no—
313C3×C4×D3—26no—
314C3×C4×D3—26no—
315C3×C4×D3—26no—
316C3×C4×D3—212no—
317C3×C4×D3C2×D4112yes—
318C3×Dic6—26no—
319C3×Dic6C2×D4112yes—
320C2×2−1+4—31no—
321C22×#41—31no—
322#550—31no—
323#550—33no—
324#550—31no—
325#550—33no—
326#548—31no—
327#548—33no—
328#548—33no—
329#548C3×D311yescharacteristic, complemented
330#535—33no—
331#535—33no—
332#525—33no—
333#525—33no—
334#519—31no—
335C24×C3—33no—
336C23×D3C23×C313yes—
337C3×#41—24no—
338C3×#41—24no—
339C3×#41—44no—
340C3×#41—612no—
341C3×#41—612no—
342C3×#41—612no—
343C3×#41—612no—
344C3×#41—612no—
345C3×#41—64no—
346C3×#41—64no—
347C2×C3×Q8—24no—
348C2×C3×Q8—24no—
349C2×C3×Q8—21no—
350C2×C3×Q8—23no—
351C2×C3×Q8—38no—
352C2×C3×Q8—33no—
353C2×C3×Q8—33no—
354C2×C3×Q8—44no—
355C2×C3×Q8—612no—
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—36no—
364C2×C3×D4—33no—
365C2×C3×D4—33no—
366C2×C3×D4—33no—
367C2×C3×D4—36no—
368C2×C3×D4—33no—
369C2×C3×D4—33no—
370C2×C3×D4—33no—
371C2×C3×D4—36no—
372C2×C3×D4—33no—
373C2×C3×D4—612no—
374C2×C3×D4C22×D313yes—
375C2×C3×D4C22×D313yes—
376C2×C3×D4C23×C313yes—
377C2×C3×D4C23×C313yes—
378C22×C3×C4—23no—
379C22×C3×C4—23no—
380C22×C3×C4—33no—
381C22×C3×C4—33no—
382C22×C3×C4—36no—
383C22×C3×C4—33no—
384C22×C3×C4—33no—
385C22×C3×C4—33no—
386C22×C3×C4—31no—
387C22×C3×C4—612no—
388C22×C3×C4C22×D313yes—
389C22×C3×C4C22×D313yes—
390C22×C3×C4C23×C313yes—
391C22×C3×C4C23×C313yes—
392C2×#67C23×C311yescharacteristic
393C2×#67C23×C316yes—
394C2×#67C23×C313yes—
395C2×#67C23×C316yes—
396C2×#67C23×C313yes—
397C2×#67C23×C313yes—
398C22×Dic3C23×C313yes—
399#239—24no—
400#239—24no—
401#239—212no—
402D3×Q8—212no—
403D3×Q8C3×D418yescomplemented
404#237—212no—
405D3×D4—212no—
406#235—212no—
407#235—212no—
408#235—212no—
409C2×D12C23×C313yes—
410C2×D12C23×C313yes—
411C2×D12C23×C313yes—
412C2×D12C23×C313yes—
413C2×D12C23×C316yes—
414C2×C4×D3—212no—
415C2×C4×D3C23×C313yes—
416C2×C4×D3C23×C313yes—
417C2×C4×D3C23×C316yes—
418C2×C4×D3C23×C311yescharacteristic
419C2×C4×D3C23×C313yes—
420C2×C4×D3C23×C313yes—
421C2×Dic6C23×C313yes—
422C2×Dic6C23×C313yes—
423C3×C4⋊C4—23no—
424C3×C4⋊C4—23no—
425C3×C4⋊C4—33no—
426C3×C4⋊C4—33no—
427C3×C4⋊C4—31no—
428C3×C4⋊C4—33no—
429C3×C4⋊C4—33no—
430C3×C4⋊C4—31no—
431C3×C4⋊C4C22×D313yes—
432C3×C4⋊C4C22×D313yes—
433C3×C4⋊C4C23×C313yes—
434C3×C4⋊C4C23×C313yes—
435C3×C22⋊C4—21no—
436C3×C22⋊C4—23no—
437C3×C22⋊C4—26no—
438C3×C22⋊C4—31no—
439C3×C22⋊C4—33no—
440C3×C22⋊C4—33no—
441C3×C22⋊C4—31no—
442C3×C22⋊C4—33no—
443C3×C22⋊C4—33no—
444C3×C22⋊C4—33no—
445C3×C22⋊C4—36no—
446C3×C22⋊C4—33no—
447C3×C22⋊C4C22×D316yes—
448C3×C22⋊C4C22×D311yescharacteristic
449C3×C22⋊C4C22×D313yes—
450C3×C22⋊C4C23×C313yes—
451C3×C22⋊C4C23×C316yes—
452C3×C22⋊C4C23×C311yescharacteristic
453C3×C42—23no—
454C3×C42—36no—
455C3×C42—33no—
456C3×C42C22×D313yes—
457C3×C42C23×C313yes—
458#217C23×C313yes—
459#217C23×C311yescharacteristic
460(C2×D3)⋊C4C23×C311yescharacteristic
461(C2×D3)⋊C4C23×C313yes—
462(C2×D3)⋊C4C23×C313yes—
463(C2×D3)⋊C4C23×C313yes—
464(C2×D3)⋊C4C23×C313yes—
465(C2×D3)⋊C4C23×C316yes—
466(C2×D3)⋊C4C23×C313yes—
467C4⋊Dic3C23×C313yes—
468C4⋊Dic3C23×C311yescharacteristic
469Dic3⋊C4C23×C313yes—
470Dic3⋊C4C23×C313yes—
471Dic3⋊C4C23×C313yes—
472Dic3⋊C4C23×C311yescharacteristic
473C4×Dic3C23×C316yes—
474C4×Dic3C23×C313yes—
475C22×C32—21no—
476C22×C32—23no—
477C22×C32—21no—
478C22×C32—21no—
479C22×C32—23no—
480C22×C32—23no—
481C22×C32C2511yescharacteristic
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—23no—
485C2×C3×D3—23no—
486C2×C3×D3—23no—
487C2×C3×D3—23no—
488C2×C3×D3—23no—
489C2×C3×D3—23no—
490C2×C3×D3—412no—
491C2×C3×D3C22×D412yes—
492C32×C4—23no—
493C32×C4—21no—
494C32×C4—21no—
495C32×C4—23no—
496C32×C4C22×D416yes—
497C3×Dic3—21no—
498C3×Dic3—21no—
499C3×Dic3—21no—
500C3×Dic3—23no—
501C3×Dic3C22×D416yes—
5022−1+4—68no—
503C2×#41—33no—
504C2×#41—31no—
505C2×#41—31no—
506C2×#41—33no—
507C2×#41—33no—
508C2×#41—33no—
509C2×#41—33no—
510C2×#41—68no—
511C2×#41C2×C3×D311yescharacteristic
512C22×Q8—31no—
513C22×Q8—33no—
514C22×Q8C2×C3×D311yescharacteristic, complemented
515C22×D4—33no—
516C23×C4—33no—
517#127—36no—
518#127—33no—
519#127—33no—
520#124—33no—
521#124—36no—
522#124C2×C3×D313yescomplemented
523#123—33no—
524#123—31no—
525C22⋊Q8—33no—
526C22⋊Q8—33no—
527C22⋊Q8—33no—
528C22⋊Q8C2×C3×D313yescomplemented
529#121—33no—
530#121—33no—
531#121—33no—
532#121—33no—
533#121—33no—
534#121—33no—
535#121—33no—
536#121—36no—
537#121—36no—
538#121C2×C3×D313yescomplemented
539#120—33no—
540#120—36no—
541#120—33no—
542C4×Q8—31no—
543C4×Q8—33no—
544C4×Q8—33no—
545C4×Q8C2×C3×D311yescharacteristic, complemented
546C4×D4—33no—
547C4×D4—33no—
548C4×D4—36no—
549C4×D4—36no—
550C4×D4—33no—
551C4×D4C2×C3×D313yescomplemented
552#117—33no—
553#117—33no—
554C23×C3—21no—
555C23×C3—23no—
556C23×C3—31no—
557C23×C3—33no—
558C23×C3—33no—
559C23×C3—66no—
560C23×C3—123no—
561C23×C3—123no—
562C23×C3C23×D313yes—
563C23×C3C23×D311yescharacteristic
564C23×C3C24×C313yes—
565C23×C3C24×C311yescharacteristic
566C22×D3—26no—
567C22×D3—43no—
568C22×D3—43no—
569C22×D3C24×C313yes—
570C22×D3C24×C313yes—
571C22×D3C24×C311yescharacteristic
572C3×Q8—26no—
573C3×Q8—26no—
574C3×Q8—24no—
575C3×Q8—312no—
576C3×Q8—46no—
577C3×Q8—66no—
578C3×Q8D3×D414yes—
579C3×Q8C2×C3×D414yes—
580C3×D4—26no—
581C3×D4—26no—
582C3×D4—46no—
583C3×D4—43no—
584C3×D4—43no—
585C3×D4—46no—
586C3×D4—66no—
587C3×D4—612no—
588C3×D4—66no—
589C3×D4—62no—
590C3×D4—66no—
591C3×D4—66no—
592C3×D4—126no—
593C3×D4—123no—
594C3×D4—123no—
595C3×D4—123no—
596C3×D4—126no—
597C2×C3×C4—26no—
598C2×C3×C4—26no—
599C2×C3×C4—26no—
600C2×C3×C4—26no—
601C2×C3×C4—23no—
602C2×C3×C4—21no—
603C2×C3×C4—23no—
604C2×C3×C4—23no—
605C2×C3×C4—21no—
606C2×C3×C4—33no—
607C2×C3×C4—312no—
608C2×C3×C4—31no—
609C2×C3×C4—33no—
610C2×C3×C4—31no—
611C2×C3×C4—31no—
612C2×C3×C4—46no—
613C2×C3×C4—46no—
614C2×C3×C4—66no—
615C2×C3×C4—612no—
616C2×C3×C4—62no—
617C2×C3×C4—66no—
618C2×C3×C4—66no—
619C2×C3×C4—66no—
620C2×C3×C4C23×D313yes—
621C2×C3×C4C23×D311yescharacteristic
622C2×C3×C4C23×D313yes—
623C2×C3×C4C23×D311yescharacteristic
624C2×C3×C4C23×D313yes—
625C2×C3×C4C24×C313yes—
626C2×C3×C4C24×C311yescharacteristic
627C2×C3×C4C24×C313yes—
628C2×C3×C4C24×C311yescharacteristic
629C2×C3×C4C24×C313yes—
630#67—22no—
631#67—26no—
632#67—212no—
633#67—43no—
634#67—46no—
635#67—43no—
636C2×Dic3—26no—
637C2×Dic3C24×C311yescharacteristic
638C2×Dic3C24×C313yes—
639C2×Dic3C24×C311yescharacteristic
640C2×Dic3C24×C311yescharacteristic
641C2×Dic3C24×C313yes—
642D12—26no—
643D12—26no—
644D12—26no—
645D12—43no—
646D12—46no—
647C4×D3—22no—
648C4×D3—26no—
649C4×D3—26no—
650C4×D3—26no—
651C4×D3—212no—
652C4×D3C2×C3×D4112yes—
653Dic6—26no—
654Dic6C2×C3×D4112yes—
655C2×C32—41no—
656C2×C32—43no—
657C2×C32C23×D411yescharacteristic
658C2×C32#58511yescharacteristic
659C2×C32#58511yescharacteristic
660C3×D3—22no—
661C3×D3—43no—
662C3×D3—43no—
663C24—33no—
664#41—24no—
665#41—612no—
666#41—612no—
667#41—612no—
668#41—612no—
669#41—612no—
670#41—64no—
671#41—64no—
672C2×Q8—24no—
673C2×Q8—38no—
674C2×Q8—33no—
675C2×Q8—33no—
676C2×Q8—612no—
677C2×Q8C22×C3×D313yes—
678C2×Q8C22×C3×D311yescharacteristic
679C2×D4—31no—
680C2×D4—36no—
681C2×D4—33no—
682C2×D4—33no—
683C2×D4—33no—
684C2×D4—36no—
685C2×D4—33no—
686C2×D4—33no—
687C2×D4—33no—
688C2×D4—36no—
689C2×D4—33no—
690C2×D4—612no—
691C2×D4C22×C3×D313yes—
692C2×D4C22×C3×D313yes—
693C22×C4—33no—
694C22×C4—33no—
695C22×C4—36no—
696C22×C4—33no—
697C22×C4—33no—
698C22×C4—33no—
699C22×C4—31no—
700C22×C4—612no—
701C22×C4C22×C3×D313yes—
702C22×C4C22×C3×D313yes—
703C4⋊C4—33no—
704C4⋊C4—33no—
705C4⋊C4—33no—
706C4⋊C4—31no—
707C4⋊C4—33no—
708C4⋊C4—31no—
709C4⋊C4C22×C3×D313yes—
710C4⋊C4C22×C3×D313yes—
711C22⋊C4—31no—
712C22⋊C4—33no—
713C22⋊C4—33no—
714C22⋊C4—31no—
715C22⋊C4—33no—
716C22⋊C4—33no—
717C22⋊C4—33no—
718C22⋊C4—36no—
719C22⋊C4—33no—
720C22⋊C4C22×C3×D316yes—
721C22⋊C4C22×C3×D311yescharacteristic
722C22⋊C4C22×C3×D313yes—
723C42—36no—
724C42—33no—
725C42C22×C3×D313yes—
726C22×C3—22no—
727C22×C3—21no—
728C22×C3—23no—
729C22×C3—21no—
730C22×C3—23no—
731C22×C3—21no—
732C22×C3—23no—
733C22×C3—23no—
734C22×C3—21no—
735C22×C3—21no—
736C22×C3—23no—
737C22×C3—23no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—32no—
741C22×C3—41no—
742C22×C3—41no—
743C22×C3—43no—
744C22×C3—43no—
745C22×C3—43no—
746C22×C3—61no—
747C22×C3—61no—
748C22×C3—63no—
749C22×C3—63no—
750C22×C3—63no—
751C22×C3—63no—
752C22×C3—63no—
753C22×C3—63no—
754C22×C3—1212no—
755C22×C3C24×D311yescharacteristic
756C22×C3C25×C311yescharacteristic
757C2×D3—21no—
758C2×D3—21no—
759C2×D3—23no—
760C2×D3—23no—
761C2×D3—23no—
762C2×D3—23no—
763C2×D3—23no—
764C2×D3—23no—
765C2×D3—412no—
766C2×D3C22×C3×D412yes—
767C3×C4—21no—
768C3×C4—23no—
769C3×C4—23no—
770C3×C4—21no—
771C3×C4—23no—
772C3×C4—21no—
773C3×C4—21no—
774C3×C4—23no—
775C3×C4—26no—
776C3×C4—36no—
777C3×C4—41no—
778C3×C4—43no—
779C3×C4—43no—
780C3×C4—41no—
781C3×C4—61no—
782C3×C4—61no—
783C3×C4—61no—
784C3×C4—63no—
785C3×C4C2×D3×D416yes—
786C3×C4C22×C3×D416yes—
787Dic3—21no—
788Dic3—21no—
789Dic3—21no—
790Dic3—23no—
791Dic3C22×C3×D416yes—
792C32#348711yescharacteristic, complemented, Sylow
793C23—31no—
794C23—33no—
795C23—33no—
796C23—66no—
797C23—123no—
798C23—123no—
799C23C23×C3×D313yes—
800C23C23×C3×D311yescharacteristic
801Q8—26no—
802Q8—312no—
803Q8—66no—
804Q8C3×D3×D414yes—
805D4—26no—
806D4—43no—
807D4—66no—
808D4—612no—
809D4—66no—
810D4—62no—
811D4—66no—
812D4—66no—
813D4—126no—
814D4—123no—
815D4—123no—
816D4—123no—
817D4—126no—
818C2×C4—26no—
819C2×C4—26no—
820C2×C4—33no—
821C2×C4—312no—
822C2×C4—31no—
823C2×C4—33no—
824C2×C4—31no—
825C2×C4—31no—
826C2×C4—66no—
827C2×C4—612no—
828C2×C4—62no—
829C2×C4—66no—
830C2×C4—66no—
831C2×C4—66no—
832C2×C4C23×C3×D313yes—
833C2×C4C23×C3×D311yescharacteristic
834C2×C4C23×C3×D313yes—
835C2×C4C23×C3×D311yescharacteristic
836C2×C4C23×C3×D313yes—
837C2×C3—21no—
838C2×C3—21no—
839C2×C3—21no—
840C2×C3—42no—
841C2×C3—43no—
842C2×C3—41no—
843C2×C3—43no—
844C2×C3—41no—
845C2×C3—62no—
846C2×C3—83no—
847C2×C3—123no—
848C2×C3—123no—
849C2×C3C22×D3×D411yescharacteristic
850C2×C3#596411yescharacteristic
851C2×C3#596811yescharacteristic
852C2×C3C23×C3×D411yescharacteristic
853C2×C3C3×#58511yescharacteristic
854C2×C3C3×#58511yescharacteristic
855D3—22no—
856D3—43no—
857D3—43no—
858C22—21no—
859C22—23no—
860C22—21no—
861C22—23no—
862C22—21no—
863C22—23no—
864C22—32no—
865C22—61no—
866C22—61no—
867C22—63no—
868C22—63no—
869C22—63no—
870C22—63no—
871C22—63no—
872C22—63no—
873C22—1212no—
874C22C24×C3×D311yescharacteristic
875C4—21no—
876C4—23no—
877C4—23no—
878C4—21no—
879C4—36no—
880C4—61no—
881C4—61no—
882C4—61no—
883C4—63no—
884C4C2×C3×D3×D416yes—
885C3—21no—
886C3#8673611yescharacteristic, direct product factor
887C3C3×#348711yescharacteristic, complemented
888C2—43no—
889C2—41no—
890C2—62no—
891C2—123no—
892C2—123no—
893C2C22×C3×D3×D411yescharacteristic
894C2C3×#596411yescharacteristic
895C2C3×#596811yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#548C2
socleC22×C32C25
hypercenterC3×#548D3
hypocenterC3C3×#3487
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×#5834C2semidirect
5. C3×#5817C2semidirect
6. C3×#5677C2semidirect
7. C3×#5674C2semidirect
8. C3×#5633C2semidirect
9. C3×#5627C2semidirect
10. C3×#5607C2semidirect
11. C3×#5599C2semidirect
12. C3×#5577C2semidirect
13. C3×#5572C2semidirect
14. C3×#5553C2semidirect
15. C3×#5547C2semidirect
17. #86736C3direct (N × H)
19. C22×C32×Q8C22semidirect
24. C2×C3×#239C22semidirect
26. C2×C3×D3×Q8C22semidirect
31. C2×C3×#235C22semidirect
33. C32×#124C22semidirect
34. C32×C22⋊Q8C22semidirect
35. C32×#121C22semidirect
36. C32×C4×Q8C22semidirect
37. C32×C4×D4C22semidirect
38. C3×#947C22semidirect
39. C3×#946C22semidirect
40. C3×Q8×Dic3C22semidirect
41. C3×#940C22semidirect
42. C3×#940C22semidirect
43. C3×#939C22semidirect
44. C3×#938C22semidirect
46. C3×#930C22semidirect
47. C3×#930C22semidirect
48. C3×C4×#67C22semidirect
49. C3×C4×#67C22semidirect
50. C3×#896C22semidirect
51. C3×#895C22semidirect
52. C3×#895C22semidirect
54. C3×#893C22semidirect
56. C3×#887C22semidirect
57. C3×#885C22semidirect
58. C3×#884C22semidirect
59. C3×#884C22semidirect
60. C3×#884C22semidirect
64. C3×#67⋊C4C22semidirect
65. C3×#878C22semidirect
66. C3×#874C22semidirect
67. C3×C4×D12C22semidirect
69. C3×C4×Dic6C22semidirect
72. C2×D3×#41C2×C3semidirect
73. C2×#1007C2×C3semidirect
82. C3×#548D3semidirect
83. C3×#548C2×C3semidirect
89. #5834C2×C3semidirect
90. #5817C2×C3semidirect
91. #5677C2×C3semidirect
92. #5674C2×C3semidirect
93. #5633C2×C3semidirect
94. #5627C2×C3semidirect
95. #5607C2×C3semidirect
96. #5599C2×C3semidirect
97. #5577C2×C3semidirect
98. #5572C2×C3semidirect
99. #5553C2×C3semidirect
100. #5547C2×C3semidirect
121. C3×D3×Q8D4semidirect
180. C22×C3×Q8C2×D3semidirect
181. C22×C3×Q8C22×C3semidirect
188. C2×#239C22×C3semidirect
190. C2×D3×Q8C22×C3semidirect
195. C2×#235C22×C3semidirect
203. C3×#124C2×D3semidirect
204. C3×#124C22×C3semidirect
211. C3×C22⋊Q8C2×D3semidirect
212. C3×C22⋊Q8C22×C3semidirect
223. C3×#121C2×D3semidirect
224. C3×#121C22×C3semidirect
232. C3×C4×Q8C2×D3semidirect
233. C3×C4×Q8C22×C3semidirect
240. C3×C4×D4C2×D3semidirect
241. C3×C4×D4C22×C3semidirect
244. #947C22×C3semidirect
245. #946C22×C3semidirect
246. Q8×Dic3C22×C3semidirect
247. #940C22×C3semidirect
248. #940C22×C3semidirect
249. #939C22×C3semidirect
250. #938C22×C3semidirect
252. #930C22×C3semidirect
253. #930C22×C3semidirect
254. C4×#67C22×C3semidirect
255. C4×#67C22×C3semidirect
256. #896C22×C3semidirect
257. #895C22×C3semidirect
258. #895C22×C3semidirect
260. #893C22×C3semidirect
262. #887C22×C3semidirect
263. #885C22×C3semidirect
264. #884C22×C3semidirect
265. #884C22×C3semidirect
266. #884C22×C3semidirect
270. #67⋊C4C22×C3semidirect
271. #878C22×C3semidirect
272. #874C22×C3semidirect
273. C4×D12C22×C3semidirect
275. C4×Dic6C22×C3semidirect
329. #548C3×D3semidirect
403. D3×Q8C3×D4semidirect
514. C22×Q8C2×C3×D3semidirect
522. #124C2×C3×D3semidirect
528. C22⋊Q8C2×C3×D3semidirect
538. #121C2×C3×D3semidirect
545. C4×Q8C2×C3×D3semidirect
551. C4×D4C2×C3×D3semidirect
792. C32#3487semidirect
886. C3#86736direct (N × H)
887. C3C3×#3487semidirect

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×#58342
C3×#58172
C3×#56772
C3×#56742
C3×#56332
C3×#56272
C3×#56072
C3×#55992
C3×#55772
C3×#55722
C3×#55532
C3×#55472
C3×#34873
#867363