Finite Group Databasebeta

← C3×D3×#548 #11902570

Subgroups — C3×D3×#548 #11902570

Order 1152.

3385 conjugacy classes of subgroups.

The subgroup lattice has 913 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×#41C211yesmaximal, characteristic, complemented
2C22×C3×D3×Q8C211yesmaximal, characteristic, complemented
3C32×#548C211yesmaximal, characteristic, complemented
4C3×#5831C211yesmaximal, characteristic, complemented
5C3×#5817C211yesmaximal, characteristic, complemented
6C3×#5677C213yesmaximal, complemented
7C3×D3×#124C213yesmaximal, complemented
8C3×#5633C213yesmaximal, complemented
9C3×D3×C22⋊Q8C213yesmaximal, complemented
10C3×D3×#121C213yesmaximal, complemented
11C3×#5598C213yesmaximal, complemented
12C3×#5576C211yesmaximal, characteristic, complemented
13C3×C4×D3×Q8C211yesmaximal, characteristic, complemented
14C3×#5552C213yesmaximal, complemented
15C3×C4×D3×D4C213yesmaximal, complemented
16C2×C3×#548—31nomaximal
17D3×#548C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic, complemented
19C22×C32×Q8C2211yescharacteristic, complemented
20C3×D3×#41—28no—
21C2×C3×#239C2211yescharacteristic, complemented
22C2×C3×D3×Q8—28no—
23C2×C3×D3×Q8C2213yes—
24C2×C3×D3×Q8C2211yescharacteristic
25C2×C3×D3×Q8C2211yescharacteristic, complemented
26C2×C3×D3×Q8C2213yescomplemented
27C2×C3×#237C2213yescomplemented
28C2×C3×D3×D4C2213yes—
29C2×C3×D3×D4C2213yes—
30C2×C3×#235C2213yescomplemented
31C22×C3×C4×D3C2213yes—
32C22×C3×C4×D3C2213yes—
33C22×C3×Dic6C2213yescomplemented
34C32×#124C2213yescomplemented
35C32×C22⋊Q8C2213yescomplemented
36C32×#121C2213yescomplemented
37C32×C4×Q8C2211yescharacteristic, complemented
38C32×C4×D4C2213yescomplemented
39C3×#947C2213yescomplemented
40C3×#946C2213yescomplemented
41C3×Q8×Dic3C2211yescharacteristic, complemented
42C3×#939C2216yescomplemented
43C3×#938C2213yescomplemented
44C3×#936C2213yescomplemented
45C3×D4×Dic3C2213yescomplemented
46C3×#930C2213yescomplemented
47C3×C4×#67C2213yescomplemented
48C3×C4×#67C2213yescomplemented
49C3×#924C2213yescomplemented
50C3×#897C2213yescomplemented
51C3×#896C2216yescomplemented
52C3×#895C2213yescomplemented
53C3×#893C2213yescomplemented
54C3×D3×C4⋊C4C2213yes—
55C3×D3×C4⋊C4C2213yes—
56C3×#887C2213yescomplemented
57C3×#885C2216yescomplemented
58C3×#885C2216yescomplemented
59C3×#884C2216yescomplemented
60C3×#67⋊C4C2213yescomplemented
61C3×#67⋊C4C2213yescomplemented
62C3×D3×C22⋊C4C2211yescharacteristic
63C3×D3×C22⋊C4C2213yes—
64C3×D3×C22⋊C4C2216yes—
65C3×#878C2216yescomplemented
66C3×#875C2213yescomplemented
67C3×C4×D12C2213yescomplemented
68C3×C42×D3C2213yes—
69C3×C4×Dic6C2213yescomplemented
70C22×C3×#41—31no—
71C23×C3×Q8—31no—
72C2×D3×#41C2×C311yescharacteristic, complemented
73C22×D3×Q8C2×C311yescharacteristic, complemented
74C3×#548—21no—
75C3×#548—31no—
76C3×#548—31no—
77C3×#548—33no—
78C3×#548—33no—
79C3×#548—33no—
80C3×#548—31no—
81C3×#548—33no—
82C3×#548D311yescharacteristic, direct product factor
83C3×#548C2×C311yescharacteristic, complemented
84C2×C3×#124—33no—
85C2×C3×C22⋊Q8—33no—
86C2×C3×#121—33no—
87C2×C3×C4×Q8—31no—
88C2×C3×C4×D4—33no—
89#5831C2×C311yescharacteristic, complemented
90#5817C2×C311yescharacteristic, complemented
91#5677C2×C313yescomplemented
92D3×#124C2×C313yescomplemented
93#5633C2×C313yescomplemented
94D3×C22⋊Q8C2×C313yescomplemented
95D3×#121C2×C313yescomplemented
96#5598C2×C313yescomplemented
97#5576C2×C311yescharacteristic, complemented
98C4×D3×Q8C2×C311yescharacteristic, complemented
99#5552C2×C313yescomplemented
100C4×D3×D4C2×C313yescomplemented
101C23×C3×D3C2313yes—
102C23×C3×D3C2311yescharacteristic
103C32×#41—24no—
104C2×C32×Q8—24no—
105C2×C32×Q8C2313yes—
106C2×C32×Q8C2311yescharacteristic
107C2×C32×D4C2313yes—
108C2×C32×D4C2313yes—
109C22×C32×C4C2313yes—
110C22×C32×C4C2313yes—
111C2×C3×#67C2313yes—
112C2×C3×#67C2313yes—
113C2×C3×#67C2316yes—
114C22×C3×Dic3C2313yes—
115C22×C3×Dic3C2313yes—
116C3×#239—24no—
117C3×D3×Q8—24no—
118C3×D3×Q8—212no—
119C3×D3×Q8—212no—
120C3×D3×Q8D418yescomplemented
121C3×#237—212no—
122C3×D3×D4—212no—
123C3×D3×D4—212no—
124C3×#235—212no—
125C2×C3×D12C2313yes—
126C2×C3×D12C2313yes—
127C2×C3×C4×D3—212no—
128C2×C3×C4×D3—212no—
129C2×C3×C4×D3C2311yescharacteristic
130C2×C3×C4×D3C2313yes—
131C2×C3×C4×D3C2313yes—
132C2×C3×C4×D3C2311yescharacteristic
133C2×C3×C4×D3C2313yes—
134C2×C3×C4×D3C2313yes—
135C2×C3×C4×D3C2313yes—
136C2×C3×C4×D3C2313yes—
137C2×C3×C4×D3C2313yes—
138C2×C3×Dic6—212no—
139C2×C3×Dic6C2316yes—
140C2×C3×Dic6C2313yes—
141C2×C3×Dic6C2313yes—
142C32×C4⋊C4C2313yes—
143C32×C4⋊C4C2313yes—
144C32×C22⋊C4C2316yes—
145C32×C22⋊C4C2311yescharacteristic
146C32×C22⋊C4C2313yes—
147C32×C42C2313yes—
148C3×#217C2316yes—
149C3×#217C2313yes—
150C3×#217C2311yescharacteristic
151C3×(C2×D3)⋊C4C2311yescharacteristic
152C3×(C2×D3)⋊C4C2313yes—
153C3×(C2×D3)⋊C4C2316yes—
154C3×(C2×D3)⋊C4C2313yes—
155C3×(C2×D3)⋊C4C2316yes—
156C3×(C2×D3)⋊C4C2311yescharacteristic
157C3×C4⋊Dic3C2313yes—
158C3×C4⋊Dic3C2313yes—
159C3×Dic3⋊C4C2313yes—
160C3×Dic3⋊C4C2316yes—
161C3×Dic3⋊C4C2313yes—
162C3×C4×Dic3C2313yes—
163C3×C4×Dic3C2313yes—
164C3×C4×Dic3C2313yes—
165C2×#548—31noSylow
166C2×C3×#41—21no—
167C2×C3×#41—31no—
168C2×C3×#41—33no—
169C2×C3×#41—33no—
170C2×C3×#41—68no—
171C2×C3×#41C2×D311yescharacteristic, complemented
172C2×C3×#41C22×C311yescharacteristic, complemented
173C22×C3×Q8—21no—
174C22×C3×Q8—31no—
175C22×C3×Q8—33no—
176C22×C3×Q8—33no—
177C22×C3×Q8—31no—
178C22×C3×Q8—33no—
179C22×C3×Q8—68no—
180C22×C3×Q8C2×D311yescharacteristic, complemented
181C22×C3×Q8C22×C311yescharacteristic, complemented
182C22×C3×D4—33no—
183C22×C3×D4—33no—
184C23×C3×C4—33no—
185C23×C3×C4—33no—
186D3×#41—28no—
187C2×#239C22×C311yescharacteristic, complemented
188C2×D3×Q8—28no—
189C2×D3×Q8C22×C313yes—
190C2×D3×Q8C22×C311yescharacteristic
191C2×D3×Q8C22×C313yescomplemented
192C2×D3×Q8C22×C311yescharacteristic, complemented
193C2×#237C22×C313yescomplemented
194C2×D3×D4C22×C313yes—
195C2×D3×D4C22×C313yes—
196C2×#235C22×C313yescomplemented
197C22×C4×D3C22×C313yes—
198C22×C4×D3C22×C313yes—
199C22×Dic6C22×C313yescomplemented
200C3×#124—23no—
201C3×#124—33no—
202C3×#124—33no—
203C3×#124—36no—
204C3×#124—36no—
205C3×#124—33no—
206C3×#124C2×D313yescomplemented
207C3×#124C22×C313yescomplemented
208C3×C22⋊Q8—23no—
209C3×C22⋊Q8—33no—
210C3×C22⋊Q8—33no—
211C3×C22⋊Q8—36no—
212C3×C22⋊Q8—33no—
213C3×C22⋊Q8—36no—
214C3×C22⋊Q8C2×D313yescomplemented
215C3×C22⋊Q8C22×C313yescomplemented
216C3×#121—23no—
217C3×#121—33no—
218C3×#121—36no—
219C3×#121—33no—
220C3×#121—33no—
221C3×#121—36no—
222C3×#121C2×D313yescomplemented
223C3×#121C22×C313yescomplemented
224C3×C4×Q8—21no—
225C3×C4×Q8—31no—
226C3×C4×Q8—33no—
227C3×C4×Q8—33no—
228C3×C4×Q8C2×D311yescharacteristic, complemented
229C3×C4×Q8C22×C311yescharacteristic, complemented
230C3×C4×D4—23no—
231C3×C4×D4—33no—
232C3×C4×D4—33no—
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
240C2×C3×C4⋊C4—33no—
241C2×C3×C4⋊C4—33no—
242C2×C3×C22⋊C4—31no—
243C2×C3×C22⋊C4—33no—
244C2×C3×C22⋊C4—36no—
245C2×C3×C42—33no—
246#947C22×C313yescomplemented
247#946C22×C313yescomplemented
248Q8×Dic3C22×C311yescharacteristic, complemented
249#939C22×C316yescomplemented
250#938C22×C313yescomplemented
251#936C22×C313yescomplemented
252D4×Dic3C22×C313yescomplemented
253#930C22×C313yescomplemented
254C4×#67C22×C313yescomplemented
255C4×#67C22×C313yescomplemented
256#924C22×C313yescomplemented
257#897C22×C313yescomplemented
258#896C22×C316yescomplemented
259#895C22×C313yescomplemented
260#893C22×C313yescomplemented
261D3×C4⋊C4C22×C313yes—
262D3×C4⋊C4C22×C313yes—
263#887C22×C313yescomplemented
264#885C22×C316yescomplemented
265#885C22×C316yescomplemented
266#884C22×C316yescomplemented
267#67⋊C4C22×C313yescomplemented
268#67⋊C4C22×C313yescomplemented
269D3×C22⋊C4C22×C313yes—
270D3×C22⋊C4C22×C316yes—
271D3×C22⋊C4C22×C311yescharacteristic
272#878C22×C316yescomplemented
273#875C22×C313yescomplemented
274C4×D12C22×C313yescomplemented
275C42×D3C22×C313yes—
276C4×Dic6C22×C313yescomplemented
277C23×C32C2413yes—
278C23×C32C2411yescharacteristic
279C22×C3×D3—22no—
280C22×C3×D3—22no—
281C22×C3×D3—26no—
282C22×C3×D3—26no—
283C22×C3×D3—26no—
284C22×C3×D3#4114yescomplemented
285C22×C3×D3C2413yes—
286C22×C3×D3C2411yescharacteristic
287C22×C3×D3C2411yescharacteristic
288C32×Q8—26no—
289C32×Q8C2×D414yescomplemented
290C32×D4—26no—
291C32×D4—26no—
292C2×C32×C4—26no—
293C2×C32×C4—26no—
294C2×C32×C4C2411yescharacteristic
295C2×C32×C4C2413yes—
296C2×C32×C4C2411yescharacteristic
297C2×C32×C4C2413yes—
298C2×C32×C4C2413yes—
299C3×#67—26no—
300C3×#67—26no—
301C3×#67—212no—
302C2×C3×Dic3—26no—
303C2×C3×Dic3—26no—
304C2×C3×Dic3C2411yescharacteristic
305C2×C3×Dic3C2413yes—
306C2×C3×Dic3C2411yescharacteristic
307C2×C3×Dic3C2413yes—
308C2×C3×Dic3C2413yes—
309C3×D12—26no—
310C3×D12—26no—
311C3×C4×D3—22no—
312C3×C4×D3—26no—
313C3×C4×D3—26no—
314C3×C4×D3—22no—
315C3×C4×D3—26no—
316C3×C4×D3—26no—
317C3×C4×D3—26no—
318C3×C4×D3—26no—
319C3×C4×D3C2×D4112yes—
320C3×Dic6—26no—
321C3×Dic6—212no—
322C3×Dic6C2×D4112yescomplemented
323C22×#41—31no—
324C23×Q8—31no—
325#548—31no—
326#548—31no—
327#548—33no—
328#548—33no—
329#548—33no—
330#548—31no—
331#548—33no—
332#548C3×D311yescharacteristic, direct product factor
333C2×#124—33no—
334C2×C22⋊Q8—33no—
335C2×#121—33no—
336C2×C4×Q8—31no—
337C2×C4×D4—33no—
338C24×C3—31no—
339C24×C3—33no—
340C23×D3C23×C313yes—
341C23×D3C23×C311yescharacteristic
342C3×#41—24no—
343C3×#41—24no—
344C3×#41—44no—
345C3×#41—612no—
346C3×#41—612no—
347C3×#41—64no—
348C2×C3×Q8—24no—
349C2×C3×Q8—24no—
350C2×C3×Q8—21no—
351C2×C3×Q8—23no—
352C2×C3×Q8—38no—
353C2×C3×Q8—33no—
354C2×C3×Q8—36no—
355C2×C3×Q8—33no—
356C2×C3×Q8—44no—
357C2×C3×Q8—612no—
358C2×C3×Q8—612no—
359C2×C3×Q8—612no—
360C2×C3×Q8—64no—
361C2×C3×Q8C22×D313yes—
362C2×C3×Q8C22×D311yescharacteristic
363C2×C3×Q8C23×C313yes—
364C2×C3×Q8C23×C311yescharacteristic
365C2×C3×D4—23no—
366C2×C3×D4—23no—
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×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—33no—
383C22×C3×C4—31no—
384C22×C3×C4—33no—
385C22×C3×C4—33no—
386C22×C3×C4—31no—
387C22×C3×C4—33no—
388C22×C3×C4—33no—
389C22×C3×C4—33no—
390C22×C3×C4—33no—
391C22×C3×C4—612no—
392C22×C3×C4—612no—
393C22×C3×C4C22×D313yes—
394C22×C3×C4C22×D313yes—
395C22×C3×C4C23×C313yes—
396C22×C3×C4C23×C313yes—
397C2×#67C23×C313yes—
398C2×#67C23×C313yes—
399C2×#67C23×C316yes—
400C22×Dic3C23×C313yes—
401C22×Dic3C23×C313yes—
402#239—24no—
403D3×Q8—24no—
404D3×Q8—212no—
405D3×Q8—212no—
406D3×Q8C3×D418yescomplemented
407#237—212no—
408D3×D4—212no—
409D3×D4—212no—
410#235—212no—
411C2×D12C23×C313yes—
412C2×D12C23×C313yes—
413C2×C4×D3—212no—
414C2×C4×D3—212no—
415C2×C4×D3C23×C311yescharacteristic
416C2×C4×D3C23×C313yes—
417C2×C4×D3C23×C313yes—
418C2×C4×D3C23×C313yes—
419C2×C4×D3C23×C313yes—
420C2×C4×D3C23×C311yescharacteristic
421C2×C4×D3C23×C313yes—
422C2×C4×D3C23×C313yes—
423C2×C4×D3C23×C313yes—
424C2×Dic6—212no—
425C2×Dic6C23×C313yes—
426C2×Dic6C23×C316yes—
427C2×Dic6C23×C313yes—
428C3×C4⋊C4—23no—
429C3×C4⋊C4—23no—
430C3×C4⋊C4—33no—
431C3×C4⋊C4—33no—
432C3×C4⋊C4—36no—
433C3×C4⋊C4—33no—
434C3×C4⋊C4—33no—
435C3×C4⋊C4C22×D313yes—
436C3×C4⋊C4C22×D313yes—
437C3×C4⋊C4C23×C313yes—
438C3×C4⋊C4C23×C313yes—
439C3×C22⋊C4—21no—
440C3×C22⋊C4—23no—
441C3×C22⋊C4—26no—
442C3×C22⋊C4—31no—
443C3×C22⋊C4—33no—
444C3×C22⋊C4—36no—
445C3×C22⋊C4—31no—
446C3×C22⋊C4—31no—
447C3×C22⋊C4—33no—
448C3×C22⋊C4—33no—
449C3×C22⋊C4—36no—
450C3×C22⋊C4—36no—
451C3×C22⋊C4C22×D311yescharacteristic
452C3×C22⋊C4C22×D313yes—
453C3×C22⋊C4C22×D316yes—
454C3×C22⋊C4C23×C316yes—
455C3×C22⋊C4C23×C311yescharacteristic
456C3×C22⋊C4C23×C313yes—
457C3×C42—23no—
458C3×C42—33no—
459C3×C42—33no—
460C3×C42—33no—
461C3×C42C22×D313yes—
462C3×C42C23×C313yes—
463#217C23×C316yes—
464#217C23×C313yes—
465#217C23×C311yescharacteristic
466(C2×D3)⋊C4C23×C311yescharacteristic
467(C2×D3)⋊C4C23×C313yes—
468(C2×D3)⋊C4C23×C316yes—
469(C2×D3)⋊C4C23×C316yes—
470(C2×D3)⋊C4C23×C313yes—
471(C2×D3)⋊C4C23×C311yescharacteristic
472C4⋊Dic3C23×C313yes—
473C4⋊Dic3C23×C313yes—
474Dic3⋊C4C23×C316yes—
475Dic3⋊C4C23×C313yes—
476Dic3⋊C4C23×C313yes—
477C4×Dic3C23×C313yes—
478C4×Dic3C23×C313yes—
479C4×Dic3C23×C313yes—
480C22×C32—21no—
481C22×C32—21no—
482C22×C32—23no—
483C22×C32—23no—
484C22×C32—23no—
485C22×C32C2×#4112yescomplemented
486C22×C32C2511yescharacteristic
487C2×C3×D3—21no—
488C2×C3×D3—21no—
489C2×C3×D3—28no—
490C2×C3×D3—23no—
491C2×C3×D3—23no—
492C2×C3×D3—23no—
493C2×C3×D3—412no—
494C2×C3×D3C22×D412yes—
495C2×C3×D3C2×#4112yes—
496C2×C3×D3C2×#4112yescomplemented
497C2×C3×D32−1+412yes—
498C32×C4—23no—
499C32×C4—21no—
500C32×C4—23no—
501C32×C4—21no—
502C32×C4C22×D416yes—
503C3×Dic3—23no—
504C3×Dic3—21no—
505C3×Dic3—23no—
506C3×Dic3—21no—
507C3×Dic3C22×D416yes—
508C2×#41—31no—
509C2×#41—33no—
510C2×#41—33no—
511C2×#41—68no—
512C2×#41C2×C3×D311yescharacteristic, complemented
513C22×Q8—31no—
514C22×Q8—33no—
515C22×Q8—33no—
516C22×Q8—31no—
517C22×Q8—33no—
518C22×Q8—68no—
519C22×Q8C2×C3×D311yescharacteristic, complemented
520C22×D4—33no—
521C22×D4—33no—
522C23×C4—33no—
523C23×C4—33no—
524#124—33no—
525#124—33no—
526#124—36no—
527#124—36no—
528#124—33no—
529#124C2×C3×D313yescomplemented
530C22⋊Q8—33no—
531C22⋊Q8—33no—
532C22⋊Q8—36no—
533C22⋊Q8—33no—
534C22⋊Q8—36no—
535C22⋊Q8C2×C3×D313yescomplemented
536#121—33no—
537#121—36no—
538#121—33no—
539#121—33no—
540#121—36no—
541#121C2×C3×D313yescomplemented
542C4×Q8—31no—
543C4×Q8—33no—
544C4×Q8—33no—
545C4×Q8C2×C3×D311yescharacteristic, complemented
546C4×D4—33no—
547C4×D4—33no—
548C4×D4—33no—
549C4×D4—33no—
550C4×D4—33no—
551C4×D4—33no—
552C4×D4—33no—
553C4×D4C2×C3×D313yescomplemented
554C2×C4⋊C4—33no—
555C2×C4⋊C4—33no—
556C2×C22⋊C4—31no—
557C2×C22⋊C4—33no—
558C2×C22⋊C4—36no—
559C2×C42—33no—
560C23×C3—21no—
561C23×C3—23no—
562C23×C3—31no—
563C23×C3—34no—
564C23×C3—31no—
565C23×C3—33no—
566C23×C3—62no—
567C23×C3—62no—
568C23×C3—66no—
569C23×C3—66no—
570C23×C3—66no—
571C23×C3C23×D313yes—
572C23×C3C23×D311yescharacteristic
573C23×C3C24×C313yes—
574C23×C3C24×C311yescharacteristic
575C22×D3—22no—
576C22×D3—22no—
577C22×D3—26no—
578C22×D3—26no—
579C22×D3—26no—
580C22×D3C3×#4114yescomplemented
581C22×D3C24×C313yes—
582C22×D3C24×C311yescharacteristic
583C22×D3C24×C311yescharacteristic
584C3×Q8—26no—
585C3×Q8—26no—
586C3×Q8—24no—
587C3×Q8—312no—
588C3×Q8—46no—
589C3×Q8—612no—
590C3×Q8—66no—
591C3×Q8D3×D414yescomplemented
592C3×Q8C2×C3×D414yescomplemented
593C3×D4—26no—
594C3×D4—26no—
595C3×D4—26no—
596C3×D4—26no—
597C3×D4—46no—
598C3×D4—46no—
599C3×D4—66no—
600C3×D4—612no—
601C3×D4—66no—
602C3×D4—66no—
603C3×D4—66no—
604C2×C3×C4—26no—
605C2×C3×C4—26no—
606C2×C3×C4—26no—
607C2×C3×C4—26no—
608C2×C3×C4—23no—
609C2×C3×C4—21no—
610C2×C3×C4—23no—
611C2×C3×C4—23no—
612C2×C3×C4—21no—
613C2×C3×C4—33no—
614C2×C3×C4—312no—
615C2×C3×C4—31no—
616C2×C3×C4—33no—
617C2×C3×C4—33no—
618C2×C3×C4—31no—
619C2×C3×C4—46no—
620C2×C3×C4—46no—
621C2×C3×C4—66no—
622C2×C3×C4—66no—
623C2×C3×C4—62no—
624C2×C3×C4—62no—
625C2×C3×C4—66no—
626C2×C3×C4—66no—
627C2×C3×C4—66no—
628C2×C3×C4—66no—
629C2×C3×C4—66no—
630C2×C3×C4—66no—
631C2×C3×C4C23×D311yescharacteristic
632C2×C3×C4C23×D313yes—
633C2×C3×C4C23×D313yes—
634C2×C3×C4C23×D311yescharacteristic
635C2×C3×C4C23×D313yes—
636C2×C3×C4C24×C311yescharacteristic
637C2×C3×C4C24×C313yes—
638C2×C3×C4C24×C311yescharacteristic
639C2×C3×C4C24×C313yes—
640C2×C3×C4C24×C313yes—
641#67—26no—
642#67—26no—
643#67—212no—
644C2×Dic3—26no—
645C2×Dic3—26no—
646C2×Dic3C24×C311yescharacteristic
647C2×Dic3C24×C313yes—
648C2×Dic3C24×C311yescharacteristic
649C2×Dic3C24×C313yes—
650C2×Dic3C24×C313yes—
651D12—26no—
652D12—26no—
653C4×D3—22no—
654C4×D3—26no—
655C4×D3—26no—
656C4×D3—22no—
657C4×D3—26no—
658C4×D3—26no—
659C4×D3—26no—
660C4×D3—26no—
661C4×D3C2×C3×D4112yes—
662Dic6—26no—
663Dic6—212no—
664Dic6C2×C3×D4112yescomplemented
665C2×C32—22no—
666C2×C32—43no—
667C2×C32C23×D411yescharacteristic
668C2×C32C22×#4111yescharacteristic
669C2×C32C2×2−1+411yescharacteristic
670C3×D3—22no—
671C3×D3—43no—
672C3×D3#54814yesdirect product factor
673C24—31no—
674C24—33no—
675#41—24no—
676#41—612no—
677#41—612no—
678#41—64no—
679C2×Q8—24no—
680C2×Q8—38no—
681C2×Q8—33no—
682C2×Q8—36no—
683C2×Q8—33no—
684C2×Q8—612no—
685C2×Q8—612no—
686C2×Q8—612no—
687C2×Q8—64no—
688C2×Q8C22×C3×D313yes—
689C2×Q8C22×C3×D311yescharacteristic
690C2×D4—33no—
691C2×D4—33no—
692C2×D4—36no—
693C2×D4—33no—
694C2×D4—33no—
695C2×D4—612no—
696C2×D4—612no—
697C2×D4C22×C3×D313yes—
698C2×D4C22×C3×D313yes—
699C22×C4—33no—
700C22×C4—33no—
701C22×C4—33no—
702C22×C4—31no—
703C22×C4—33no—
704C22×C4—33no—
705C22×C4—31no—
706C22×C4—33no—
707C22×C4—33no—
708C22×C4—33no—
709C22×C4—33no—
710C22×C4—612no—
711C22×C4—612no—
712C22×C4C22×C3×D313yes—
713C22×C4C22×C3×D313yes—
714C4⋊C4—33no—
715C4⋊C4—33no—
716C4⋊C4—33no—
717C4⋊C4—36no—
718C4⋊C4—33no—
719C4⋊C4C22×C3×D313yes—
720C4⋊C4C22×C3×D313yes—
721C22⋊C4—31no—
722C22⋊C4—33no—
723C22⋊C4—36no—
724C22⋊C4—31no—
725C22⋊C4—31no—
726C22⋊C4—33no—
727C22⋊C4—33no—
728C22⋊C4—36no—
729C22⋊C4—36no—
730C22⋊C4C22×C3×D311yescharacteristic
731C22⋊C4C22×C3×D313yes—
732C22⋊C4C22×C3×D316yes—
733C42—33no—
734C42—33no—
735C42—33no—
736C42C22×C3×D313yes—
737C22×C3—21no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—23no—
742C22×C3—23no—
743C22×C3—23no—
744C22×C3—23no—
745C22×C3—23no—
746C22×C3—23no—
747C22×C3—22no—
748C22×C3—21no—
749C22×C3—32no—
750C22×C3—32no—
751C22×C3—32no—
752C22×C3—32no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—43no—
756C22×C3—43no—
757C22×C3—43no—
758C22×C3—68no—
759C22×C3—61no—
760C22×C3—61no—
761C22×C3—63no—
762C22×C3—63no—
763C22×C3—63no—
764C22×C3—1212no—
765C22×C3D3×#4112yescomplemented
766C22×C3C2×C3×#4112yescomplemented
767C22×C3C24×D311yescharacteristic
768C22×C3C25×C311yescharacteristic
769C2×D3—21no—
770C2×D3—21no—
771C2×D3—28no—
772C2×D3—23no—
773C2×D3—23no—
774C2×D3—23no—
775C2×D3—412no—
776C2×D3C22×C3×D412yes—
777C2×D3C2×C3×#4112yes—
778C2×D3C2×C3×#4112yescomplemented
779C2×D3C3×2−1+412yes—
780C3×C4—21no—
781C3×C4—23no—
782C3×C4—23no—
783C3×C4—21no—
784C3×C4—23no—
785C3×C4—21no—
786C3×C4—23no—
787C3×C4—21no—
788C3×C4—26no—
789C3×C4—36no—
790C3×C4—41no—
791C3×C4—43no—
792C3×C4—43no—
793C3×C4—41no—
794C3×C4—61no—
795C3×C4—63no—
796C3×C4—63no—
797C3×C4—61no—
798C3×C4C2×D3×D416yes—
799C3×C4C22×C3×D416yes—
800Dic3—23no—
801Dic3—21no—
802Dic3—23no—
803Dic3—21no—
804Dic3C22×C3×D416yes—
805C32C2×#54811yescharacteristic, complemented, Sylow
806C23—31no—
807C23—34no—
808C23—31no—
809C23—33no—
810C23—62no—
811C23—62no—
812C23—66no—
813C23—66no—
814C23—66no—
815C23C23×C3×D313yes—
816C23C23×C3×D311yescharacteristic
817Q8—26no—
818Q8—312no—
819Q8—612no—
820Q8—66no—
821Q8C3×D3×D414yescomplemented
822D4—26no—
823D4—26no—
824D4—66no—
825D4—612no—
826D4—66no—
827D4—66no—
828D4—66no—
829C2×C4—26no—
830C2×C4—26no—
831C2×C4—33no—
832C2×C4—312no—
833C2×C4—31no—
834C2×C4—33no—
835C2×C4—33no—
836C2×C4—31no—
837C2×C4—66no—
838C2×C4—66no—
839C2×C4—62no—
840C2×C4—66no—
841C2×C4—66no—
842C2×C4—62no—
843C2×C4—66no—
844C2×C4—66no—
845C2×C4—66no—
846C2×C4—66no—
847C2×C4C23×C3×D311yescharacteristic
848C2×C4C23×C3×D313yes—
849C2×C4C23×C3×D313yes—
850C2×C4C23×C3×D311yescharacteristic
851C2×C4C23×C3×D313yes—
852C2×C3—22no—
853C2×C3—22no—
854C2×C3—21no—
855C2×C3—21no—
856C2×C3—21no—
857C2×C3—34no—
858C2×C3—42no—
859C2×C3—43no—
860C2×C3—43no—
861C2×C3—62no—
862C2×C3—83no—
863C2×C3—123no—
864C2×C3C22×D3×D411yescharacteristic
865C2×C3C2×D3×#4111yescharacteristic
866C2×C3D3×2−1+411yescharacteristic
867C2×C3C23×C3×D411yescharacteristic
868C2×C3C22×C3×#4111yescharacteristic
869C2×C3C2×C3×2−1+411yescharacteristic
870D3—22no—
871D3—43no—
872D3C3×#54814yesdirect product factor
873C22—21no—
874C22—21no—
875C22—23no—
876C22—23no—
877C22—23no—
878C22—32no—
879C22—32no—
880C22—32no—
881C22—32no—
882C22—68no—
883C22—61no—
884C22—61no—
885C22—63no—
886C22—63no—
887C22—63no—
888C22—1212no—
889C22C3×D3×#4112yescomplemented
890C22C24×C3×D311yescharacteristic
891C4—21no—
892C4—23no—
893C4—23no—
894C4—21no—
895C4—36no—
896C4—61no—
897C4—63no—
898C4—63no—
899C4—61no—
900C4C2×C3×D3×D416yes—
901C3—21no—
902C3D3×#54811yescharacteristic, direct product factor
903C3C2×C3×#54811yescharacteristic, complemented
904C2—22no—
905C2—34no—
906C2—43no—
907C2—62no—
908C2—123no—
909C2C22×C3×D3×D411yescharacteristic
910C2C2×C3×D3×#4111yescharacteristic
911C2C3×D3×2−1+411yescharacteristic
subgroupG/H
centerC22×C3C24×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#548C2
socleC22×C32C25
hypercenterC3×#548D3
hypocenterC3C2×C3×#548
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. C22×C3×D3×Q8C2semidirect
3. C32×#548C2semidirect
4. C3×#5831C2semidirect
5. C3×#5817C2semidirect
6. C3×#5677C2semidirect
7. C3×D3×#124C2semidirect
8. C3×#5633C2semidirect
9. C3×D3×C22⋊Q8C2semidirect
10. C3×D3×#121C2semidirect
11. C3×#5598C2semidirect
12. C3×#5576C2semidirect
13. C3×C4×D3×Q8C2semidirect
14. C3×#5552C2semidirect
15. C3×C4×D3×D4C2semidirect
17. D3×#548C3direct (N × H)
18. C2×C32×#41C22semidirect
19. C22×C32×Q8C22semidirect
21. C2×C3×#239C22semidirect
25. C2×C3×D3×Q8C22semidirect
26. C2×C3×D3×Q8C22semidirect
27. C2×C3×#237C22semidirect
30. C2×C3×#235C22semidirect
33. C22×C3×Dic6C22semidirect
34. C32×#124C22semidirect
35. C32×C22⋊Q8C22semidirect
36. C32×#121C22semidirect
37. C32×C4×Q8C22semidirect
38. C32×C4×D4C22semidirect
39. C3×#947C22semidirect
40. C3×#946C22semidirect
41. C3×Q8×Dic3C22semidirect
42. C3×#939C22semidirect
43. C3×#938C22semidirect
44. C3×#936C22semidirect
45. C3×D4×Dic3C22semidirect
46. C3×#930C22semidirect
47. C3×C4×#67C22semidirect
48. C3×C4×#67C22semidirect
49. C3×#924C22semidirect
50. C3×#897C22semidirect
51. C3×#896C22semidirect
52. C3×#895C22semidirect
53. C3×#893C22semidirect
56. C3×#887C22semidirect
57. C3×#885C22semidirect
58. C3×#885C22semidirect
59. C3×#884C22semidirect
60. C3×#67⋊C4C22semidirect
61. C3×#67⋊C4C22semidirect
65. C3×#878C22semidirect
66. C3×#875C22semidirect
67. C3×C4×D12C22semidirect
69. C3×C4×Dic6C22semidirect
72. C2×D3×#41C2×C3semidirect
73. C22×D3×Q8C2×C3semidirect
82. C3×#548D3direct (N × H)
83. C3×#548C2×C3semidirect
89. #5831C2×C3semidirect
90. #5817C2×C3semidirect
91. #5677C2×C3semidirect
92. D3×#124C2×C3semidirect
93. #5633C2×C3semidirect
94. D3×C22⋊Q8C2×C3semidirect
95. D3×#121C2×C3semidirect
96. #5598C2×C3semidirect
97. #5576C2×C3semidirect
98. C4×D3×Q8C2×C3semidirect
99. #5552C2×C3semidirect
100. C4×D3×D4C2×C3semidirect
120. C3×D3×Q8D4semidirect
171. C2×C3×#41C2×D3semidirect
172. C2×C3×#41C22×C3semidirect
180. C22×C3×Q8C2×D3semidirect
181. C22×C3×Q8C22×C3semidirect
187. C2×#239C22×C3semidirect
191. C2×D3×Q8C22×C3semidirect
192. C2×D3×Q8C22×C3semidirect
193. C2×#237C22×C3semidirect
196. C2×#235C22×C3semidirect
199. C22×Dic6C22×C3semidirect
206. C3×#124C2×D3semidirect
207. C3×#124C22×C3semidirect
214. C3×C22⋊Q8C2×D3semidirect
215. C3×C22⋊Q8C22×C3semidirect
222. C3×#121C2×D3semidirect
223. C3×#121C22×C3semidirect
228. C3×C4×Q8C2×D3semidirect
229. C3×C4×Q8C22×C3semidirect
238. C3×C4×D4C2×D3semidirect
239. C3×C4×D4C22×C3semidirect
246. #947C22×C3semidirect
247. #946C22×C3semidirect
248. Q8×Dic3C22×C3semidirect
249. #939C22×C3semidirect
250. #938C22×C3semidirect
251. #936C22×C3semidirect
252. D4×Dic3C22×C3semidirect
253. #930C22×C3semidirect
254. C4×#67C22×C3semidirect
255. C4×#67C22×C3semidirect
256. #924C22×C3semidirect
257. #897C22×C3semidirect
258. #896C22×C3semidirect
259. #895C22×C3semidirect
260. #893C22×C3semidirect
263. #887C22×C3semidirect
264. #885C22×C3semidirect
265. #885C22×C3semidirect
266. #884C22×C3semidirect
267. #67⋊C4C22×C3semidirect
268. #67⋊C4C22×C3semidirect
272. #878C22×C3semidirect
273. #875C22×C3semidirect
274. C4×D12C22×C3semidirect
276. C4×Dic6C22×C3semidirect
284. C22×C3×D3#41semidirect
289. C32×Q8C2×D4semidirect
322. C3×Dic6C2×D4semidirect
332. #548C3×D3direct (N × H)
406. D3×Q8C3×D4semidirect
485. C22×C32C2×#41semidirect
496. C2×C3×D3C2×#41semidirect
512. C2×#41C2×C3×D3semidirect
519. C22×Q8C2×C3×D3semidirect
529. #124C2×C3×D3semidirect
535. C22⋊Q8C2×C3×D3semidirect
541. #121C2×C3×D3semidirect
545. C4×Q8C2×C3×D3semidirect
553. C4×D4C2×C3×D3semidirect
580. C22×D3C3×#41semidirect
591. C3×Q8D3×D4semidirect
592. C3×Q8C2×C3×D4semidirect
664. Dic6C2×C3×D4semidirect
672. C3×D3#548direct (N × H)
765. C22×C3D3×#41semidirect
766. C22×C3C2×C3×#41semidirect
778. C2×D3C2×C3×#41semidirect
805. C32C2×#548semidirect
821. Q8C3×D3×D4semidirect
872. D3C3×#548direct (N × H)
889. C22C3×D3×#41semidirect
902. C3D3×#548direct (N × H)
903. C3C2×C3×#548semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×#412
C22×C3×D3×Q82
C32×#5482
C3×#58312
C3×#58172
C3×#56772
C3×D3×#1242
C3×#56332
C3×D3×C22⋊Q82
C3×D3×#1212
C3×#55982
C3×#55762
C3×C4×D3×Q82
C3×#55522
C3×C4×D3×D42
C2×C3×#5483
D3×#5483