Finite Group Databasebeta

← C3×#41×#67 #11902748

Subgroups — C3×#41×#67 #11902748

Order 1152.

3741 conjugacy classes of subgroups.

The subgroup lattice has 935 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C32×#41C211yesmaximal, characteristic, complemented
2C2×C3×D3×#41C211yesmaximal, characteristic, complemented
3C3×#5834C211yesmaximal, characteristic, complemented
4C3×#5832C213yesmaximal, complemented
5C3×#5831C211yesmaximal, characteristic, complemented
6C3×#5829C213yesmaximal, complemented
7C3×#5828C213yesmaximal, complemented
8C3×Dic3×#41C211yesmaximal, characteristic, complemented
9C3×#5824C213yesmaximal, complemented
10C3×#5817C211yesmaximal, characteristic, complemented
11C3×Q8×#67C211yesmaximal, characteristic, complemented
12C3×#5806C213yesmaximal, complemented
13C3×D4×#67C213yesmaximal, complemented
14C3×#5791C213yesmaximal, complemented
15C2×C3×C4×#67C213yesmaximal, complemented
16C3×D4×#41—31nomaximal
17#41×#67C311yesmaximal, characteristic, direct product factor
18C2×C32×#41—28no—
19C2×C32×#41C2211yescharacteristic
20C2×C32×#41C2213yescomplemented
21C2×C32×#41C2213yescomplemented
22C2×C32×#41C2211yescharacteristic, complemented
23C22×C32×Q8C2211yescharacteristic, complemented
24C22×C32×D4C2213yescomplemented
25C23×C32×C4C2213yescomplemented
26C22×C3×#67C2213yes—
27C3×D3×#41—28no—
28C2×C3×#239C2211yescharacteristic, complemented
29C2×C3×D3×Q8C2211yescharacteristic, complemented
30C2×C3×#237C2213yescomplemented
31C2×C3×D3×D4C2213yescomplemented
32C2×C3×#235C2213yescomplemented
33C22×C3×C4×D3C2213yescomplemented
34C3×#953C2216yescomplemented
35C2×C3×#217C2213yescomplemented
36C3×#947C2213yescomplemented
37C3×#946C2213yescomplemented
38C3×#946C2213yescomplemented
39C3×Q8×Dic3C2211yescharacteristic, complemented
40C3×Q8×Dic3C2211yescharacteristic, complemented
41C3×#944C2213yescomplemented
42C3×#940C2213yescomplemented
43C3×#939C2216yescomplemented
44C3×#939C2216yescomplemented
45C3×#938C2213yescomplemented
46C3×#938C2213yescomplemented
47C3×#937C2216yescomplemented
48C3×#936C2213yescomplemented
49C3×#935C2216yescomplemented
50C3×D4×Dic3C2213yescomplemented
51C3×D4×Dic3C2213yescomplemented
52C3×#930C2213yescomplemented
53C3×#930C2213yescomplemented
54C3×#929C2216yescomplemented
55C3×C4×#67C2211yescharacteristic
56C3×C4×#67C2213yes—
57C3×C4×#67C2213yescomplemented
58C3×C4×#67C2213yescomplemented
59C3×C4×#67C2213yescomplemented
60C3×C4×#67C2213yescomplemented
61C3×C4×#67C2213yescomplemented
62C3×C4×#67C2213yescomplemented
63C3×C4×#67C2216yescomplemented
64C2×C3×(C2×D3)⋊C4C2213yescomplemented
65C3×#926C2213yescomplemented
66C3×#924C2213yescomplemented
67C3×#924C2213yescomplemented
68C2×C3×Dic3⋊C4C2213yescomplemented
69C2×C3×C4×Dic3C2213yescomplemented
70C22×C3×#41—21no—
71C22×C3×#41—31no—
72C22×C3×#41D311yescharacteristic, complemented
73C22×C3×#41C2×C311yescharacteristic, complemented
74C2×D3×#41C2×C311yescharacteristic, complemented
75C3×#550—31no—
76C3×D4×Q8—31no—
77C3×#548—31no—
78C3×#548—31no—
79C3×#547—33no—
80C3×#546—33no—
81C3×#546—33no—
82C3×D42—33no—
83C3×#532—33no—
84C3×#525—33no—
85C3×#525—33no—
86C3×C4×#41—31no—
87C2×C3×C4×D4—33no—
88#5834C2×C311yescharacteristic, complemented
89#5832C2×C313yescomplemented
90#5831C2×C311yescharacteristic, complemented
91#5829C2×C313yescomplemented
92#5828C2×C313yescomplemented
93Dic3×#41C2×C311yescharacteristic, complemented
94#5824C2×C313yescomplemented
95#5817C2×C311yescharacteristic, complemented
96Q8×#67C2×C311yescharacteristic, complemented
97#5806C2×C313yescomplemented
98D4×#67C2×C313yescomplemented
99#5791C2×C313yescomplemented
100C2×C4×#67C2×C313yescomplemented
101C24×C32C2313yes—
102C23×C3×D3C2313yes—
103C32×#41—24no—
104C32×#41—212no—
105C32×#41—212no—
106C32×#41D418yescomplemented
107C2×C32×Q8—24no—
108C2×C32×Q8C2313yes—
109C2×C32×Q8C2311yescharacteristic
110C2×C32×D4—212no—
111C2×C32×D4C2316yes—
112C2×C32×D4C2313yes—
113C2×C32×D4C2313yes—
114C22×C32×C4—212no—
115C22×C32×C4C2313yes—
116C22×C32×C4C2313yes—
117C22×C32×C4C2313yes—
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2313yes—
120C22×C32×C4C2313yes—
121C2×C3×#67—212no—
122C2×C3×#67C2313yes—
123C2×C3×#67C2313yes—
124C2×C3×#67C2313yes—
125C2×C3×#67C2316yes—
126C2×C3×#67C2316yes—
127C2×C3×#67C2311yescharacteristic
128C22×C3×Dic3C2313yes—
129C22×C3×Dic3C2313yes—
130C22×C3×Dic3C2313yes—
131C3×#239—24no—
132C3×D3×Q8—24no—
133C3×#237—212no—
134C3×D3×D4—212no—
135C3×#235—212no—
136C2×C3×D12C2313yes—
137C2×C3×C4×D3—212no—
138C2×C3×C4×D3C2311yescharacteristic
139C2×C3×C4×D3C2313yes—
140C2×C3×C4×D3C2313yes—
141C2×C3×C4×D3C2313yes—
142C2×C3×Dic6C2313yes—
143C3×#217C2313yes—
144C3×#217C2316yes—
145C3×#217C2316yes—
146C3×#217C2311yescharacteristic
147C3×#217C2313yes—
148C3×#217C2313yes—
149C3×(C2×D3)⋊C4C2311yescharacteristic
150C3×(C2×D3)⋊C4C2313yes—
151C3×(C2×D3)⋊C4C2313yes—
152C3×(C2×D3)⋊C4C2313yes—
153C3×(C2×D3)⋊C4C2316yes—
154C3×C4⋊Dic3C2313yes—
155C3×C4⋊Dic3C2313yes—
156C3×Dic3⋊C4C2311yescharacteristic
157C3×Dic3⋊C4C2313yes—
158C3×Dic3⋊C4C2313yes—
159C3×Dic3⋊C4C2313yes—
160C3×Dic3⋊C4C2316yes—
161C3×C4×Dic3C2311yescharacteristic
162C3×C4×Dic3C2313yes—
163C3×C4×Dic3C2313yes—
164C3×C4×Dic3C2313yes—
165D4×#41—31noSylow
166C2×C3×#41—216no—
167C2×C3×#41—28no—
168C2×C3×#41—28no—
169C2×C3×#41—21no—
170C2×C3×#41—23no—
171C2×C3×#41—23no—
172C2×C3×#41—21no—
173C2×C3×#41—31no—
174C2×C3×#41—33no—
175C2×C3×#41—33no—
176C2×C3×#41—68no—
177C2×C3×#41C2×D311yescharacteristic
178C2×C3×#41C2×D313yescomplemented
179C2×C3×#41C2×D313yescomplemented
180C2×C3×#41C2×D311yescharacteristic, complemented
181C2×C3×#41C22×C311yescharacteristic
182C2×C3×#41C22×C313yescomplemented
183C2×C3×#41C22×C313yescomplemented
184C2×C3×#41C22×C311yescharacteristic, complemented
185C22×C3×Q8—21no—
186C22×C3×Q8—31no—
187C22×C3×Q8C2×D311yescharacteristic, complemented
188C22×C3×Q8C22×C311yescharacteristic, complemented
189C22×C3×D4—23no—
190C22×C3×D4—33no—
191C22×C3×D4—33no—
192C22×C3×D4C2×D313yescomplemented
193C22×C3×D4C22×C313yescomplemented
194C23×C3×C4—23no—
195C23×C3×C4—33no—
196C23×C3×C4C2×D313yescomplemented
197C23×C3×C4C22×C313yescomplemented
198C22×#67C22×C313yes—
199D3×#41—28no—
200C2×#239C22×C311yescharacteristic, complemented
201C2×D3×Q8C22×C311yescharacteristic, complemented
202C2×#237C22×C313yescomplemented
203C2×D3×D4C22×C313yescomplemented
204C2×#235C22×C313yescomplemented
205C22×C4×D3C22×C313yescomplemented
206C3×C4⋊Q8—33no—
207C3×#127—33no—
208C3×#124—33no—
209C3×#124—33no—
210C3×#123—36no—
211C3×#123—36no—
212C3×C22⋊Q8—33no—
213C3×C22⋊Q8—33no—
214C3×C22⋊Q8—33no—
215C3×C22⋊Q8—33no—
216C3×#121—33no—
217C3×#121—33no—
218C3×#121—36no—
219C3×#121—36no—
220C3×#121—33no—
221C3×#121—33no—
222C3×#120—36no—
223C3×#120—36no—
224C3×C4×Q8—31no—
225C3×C4×Q8—31no—
226C3×C4×D4—33no—
227C3×C4×D4—33no—
228C3×C4×D4—31no—
229C3×C4×D4—33no—
230C3×C4×D4—33no—
231C3×C4×D4—33no—
232C3×C4×D4—33no—
233C3×C4×D4—33no—
234C3×C4×D4—33no—
235C3×C4×D4—33no—
236C3×C4×D4—36no—
237C3×#117—33no—
238C2×C3×C4⋊C4—33no—
239C2×C3×C22⋊C4—33no—
240C2×C3×C22⋊C4—33no—
241C2×C3×C42—33no—
242#953C22×C316yescomplemented
243C2×#217C22×C313yescomplemented
244#947C22×C313yescomplemented
245#946C22×C313yescomplemented
246#946C22×C313yescomplemented
247Q8×Dic3C22×C311yescharacteristic, complemented
248Q8×Dic3C22×C311yescharacteristic, complemented
249#944C22×C313yescomplemented
250#940C22×C313yescomplemented
251#939C22×C316yescomplemented
252#939C22×C316yescomplemented
253#938C22×C313yescomplemented
254#938C22×C313yescomplemented
255#937C22×C316yescomplemented
256#936C22×C313yescomplemented
257#935C22×C316yescomplemented
258D4×Dic3C22×C313yescomplemented
259D4×Dic3C22×C313yescomplemented
260#930C22×C313yescomplemented
261#930C22×C313yescomplemented
262#929C22×C316yescomplemented
263C4×#67C22×C311yescharacteristic
264C4×#67C22×C313yes—
265C4×#67C22×C313yescomplemented
266C4×#67C22×C313yescomplemented
267C4×#67C22×C313yescomplemented
268C4×#67C22×C313yescomplemented
269C4×#67C22×C313yescomplemented
270C4×#67C22×C313yescomplemented
271C4×#67C22×C316yescomplemented
272C2×(C2×D3)⋊C4C22×C313yescomplemented
273#926C22×C313yescomplemented
274#924C22×C313yescomplemented
275#924C22×C313yescomplemented
276C2×Dic3⋊C4C22×C313yescomplemented
277C2×C4×Dic3C22×C313yescomplemented
278C23×C32—26no—
279C23×C32—26no—
280C23×C32—43no—
281C23×C32C2413yes—
282C23×C32C2413yes—
283C23×C32C2411yescharacteristic
284C22×C3×D3—26no—
285C22×C3×D3—26no—
286C22×C3×D3—43no—
287C22×C3×D3C2413yes—
288C22×C3×D3C2411yescharacteristic
289C32×Q8—26no—
290C32×Q8C2×D414yescomplemented
291C32×D4—212no—
292C32×D4—26no—
293C32×D4C2×D4112yescomplemented
294C2×C32×C4—26no—
295C2×C32×C4—22no—
296C2×C32×C4—26no—
297C2×C32×C4—26no—
298C2×C32×C4—26no—
299C2×C32×C4C2×D4112yescomplemented
300C2×C32×C4C2411yescharacteristic
301C2×C32×C4C2413yes—
302C2×C32×C4C2413yes—
303C2×C32×C4C2411yescharacteristic
304C3×#67—212no—
305C3×#67—26no—
306C3×#67—26no—
307C3×#67—26no—
308C3×#67—46no—
309C3×#67#4114yesdirect product factor
310C2×C3×Dic3—26no—
311C2×C3×Dic3—26no—
312C2×C3×Dic3—43no—
313C2×C3×Dic3C2411yescharacteristic
314C2×C3×Dic3C2413yes—
315C2×C3×Dic3C2413yes—
316C2×C3×Dic3C2413yes—
317C2×C3×Dic3C2411yescharacteristic
318C2×C3×Dic3C2411yescharacteristic
319C3×D12—26no—
320C3×C4×D3—22no—
321C3×C4×D3—26no—
322C3×C4×D3—26no—
323C3×C4×D3—26no—
324C3×Dic6—26no—
325C22×#41—31no—
326C22×#41C3×D311yescharacteristic, complemented
327#550—31no—
328D4×Q8—31no—
329#548—31no—
330#548—31no—
331#547—33no—
332#546—33no—
333#546—33no—
334D42—33no—
335#532—33no—
336#525—33no—
337#525—33no—
338C4×#41—31no—
339C2×C4×D4—33no—
340C24×C3—23no—
341C24×C3—33no—
342C24×C3C22×D313yes—
343C24×C3C23×C313yes—
344C23×D3C23×C313yes—
345C3×#41—28no—
346C3×#41—224no—
347C3×#41—224no—
348C3×#41—24no—
349C3×#41—24no—
350C3×#41—212no—
351C3×#41—212no—
352C3×#41—212no—
353C3×#41—212no—
354C3×#41—28no—
355C3×#41—64no—
356C3×#41—612no—
357C3×#41—612no—
358C3×#41#6718yesdirect product factor
359C3×#41C3×D418yescomplemented
360C2×C3×Q8—28no—
361C2×C3×Q8—24no—
362C2×C3×Q8—24no—
363C2×C3×Q8—23no—
364C2×C3×Q8—21no—
365C2×C3×Q8—33no—
366C2×C3×Q8—64no—
367C2×C3×Q8C22×D313yes—
368C2×C3×Q8C22×D311yescharacteristic
369C2×C3×Q8C23×C313yes—
370C2×C3×Q8C23×C311yescharacteristic
371C2×C3×D4—224no—
372C2×C3×D4—212no—
373C2×C3×D4—212no—
374C2×C3×D4—26no—
375C2×C3×D4—23no—
376C2×C3×D4—23no—
377C2×C3×D4—31no—
378C2×C3×D4—33no—
379C2×C3×D4—33no—
380C2×C3×D4—33no—
381C2×C3×D4—36no—
382C2×C3×D4—36no—
383C2×C3×D4—33no—
384C2×C3×D4—612no—
385C2×C3×D4—612no—
386C2×C3×D4C22×D316yes—
387C2×C3×D4C22×D313yes—
388C2×C3×D4C22×D313yes—
389C2×C3×D4C23×C316yes—
390C2×C3×D4C23×C313yes—
391C2×C3×D4C23×C313yes—
392C22×C3×C4—224no—
393C22×C3×C4—212no—
394C22×C3×C4—212no—
395C22×C3×C4—21no—
396C22×C3×C4—23no—
397C22×C3×C4—23no—
398C22×C3×C4—23no—
399C22×C3×C4—23no—
400C22×C3×C4—23no—
401C22×C3×C4—33no—
402C22×C3×C4—33no—
403C22×C3×C4—33no—
404C22×C3×C4—33no—
405C22×C3×C4—33no—
406C22×C3×C4—31no—
407C22×C3×C4—33no—
408C22×C3×C4—612no—
409C22×C3×C4C22×D313yes—
410C22×C3×C4C22×D313yes—
411C22×C3×C4C22×D313yes—
412C22×C3×C4C22×D311yescharacteristic
413C22×C3×C4C22×D313yes—
414C22×C3×C4C22×D313yes—
415C22×C3×C4C23×C313yes—
416C22×C3×C4C23×C313yes—
417C22×C3×C4C23×C313yes—
418C22×C3×C4C23×C311yescharacteristic
419C22×C3×C4C23×C313yes—
420C22×C3×C4C23×C313yes—
421C2×#67—212no—
422C2×#67C23×C313yes—
423C2×#67C23×C313yes—
424C2×#67C23×C313yes—
425C2×#67C23×C316yes—
426C2×#67C23×C316yes—
427C2×#67C23×C311yescharacteristic
428C22×Dic3C23×C313yes—
429C22×Dic3C23×C313yes—
430C22×Dic3C23×C313yes—
431#239—24no—
432D3×Q8—24no—
433#237—212no—
434D3×D4—212no—
435#235—212no—
436C2×D12C23×C313yes—
437C2×C4×D3—212no—
438C2×C4×D3C23×C311yescharacteristic
439C2×C4×D3C23×C313yes—
440C2×C4×D3C23×C313yes—
441C2×C4×D3C23×C313yes—
442C2×Dic6C23×C313yes—
443C3×C4⋊C4—31no—
444C3×C4⋊C4—33no—
445C3×C4⋊C4—33no—
446C3×C4⋊C4—33no—
447C3×C4⋊C4—36no—
448C3×C4⋊C4—33no—
449C3×C4⋊C4—33no—
450C3×C22⋊C4—31no—
451C3×C22⋊C4—33no—
452C3×C22⋊C4—33no—
453C3×C22⋊C4—33no—
454C3×C22⋊C4—36no—
455C3×C22⋊C4—36no—
456C3×C22⋊C4—31no—
457C3×C22⋊C4—33no—
458C3×C22⋊C4—33no—
459C3×C22⋊C4—33no—
460C3×C22⋊C4—36no—
461C3×C42—33no—
462C3×C42—33no—
463C3×C42—31no—
464C3×C42—33no—
465#217C23×C313yes—
466#217C23×C316yes—
467#217C23×C316yes—
468#217C23×C311yescharacteristic
469#217C23×C313yes—
470#217C23×C313yes—
471(C2×D3)⋊C4C23×C311yescharacteristic
472(C2×D3)⋊C4C23×C313yes—
473(C2×D3)⋊C4C23×C313yes—
474(C2×D3)⋊C4C23×C313yes—
475(C2×D3)⋊C4C23×C316yes—
476C4⋊Dic3C23×C313yes—
477C4⋊Dic3C23×C313yes—
478Dic3⋊C4C23×C311yescharacteristic
479Dic3⋊C4C23×C313yes—
480Dic3⋊C4C23×C313yes—
481Dic3⋊C4C23×C313yes—
482Dic3⋊C4C23×C316yes—
483C4×Dic3C23×C311yescharacteristic
484C4×Dic3C23×C313yes—
485C4×Dic3C23×C313yes—
486C4×Dic3C23×C313yes—
487C22×C32—21no—
488C22×C32—21no—
489C22×C32—23no—
490C22×C32—23no—
491C22×C32—23no—
492C22×C32—23no—
493C22×C32—23no—
494C22×C32—412no—
495C22×C32C22×D416yes—
496C22×C32C2×#4112yescomplemented
497C22×C32C2511yescharacteristic
498C2×C3×D3—21no—
499C2×C3×D3—21no—
500C2×C3×D3—23no—
501C2×C3×D3—23no—
502C2×C3×D3—23no—
503C2×C3×D3—412no—
504C2×C3×D3C2×#4112yescomplemented
505C32×C4—21no—
506C32×C4—23no—
507C32×C4C22×D416yes—
508C32×C4C22×D412yes—
509C3×Dic3—23no—
510C3×Dic3—21no—
511C3×Dic3—23no—
512C3×Dic3—21no—
513C3×Dic3—23no—
514C3×Dic3C2×#4112yescomplemented
515C2×#41—28no—
516C2×#41—31no—
517C2×#41—33no—
518C2×#41—33no—
519C2×#41—68no—
520C2×#41C2×C3×D311yescharacteristic
521C2×#41C2×C3×D313yescomplemented
522C2×#41C2×C3×D313yescomplemented
523C2×#41C2×C3×D311yescharacteristic, complemented
524C22×Q8—31no—
525C22×Q8C2×C3×D311yescharacteristic, complemented
526C22×D4—33no—
527C22×D4—33no—
528C22×D4C2×C3×D313yescomplemented
529C23×C4—33no—
530C23×C4C2×C3×D313yescomplemented
531C4⋊Q8—33no—
532#127—33no—
533#124—33no—
534#124—33no—
535#123—36no—
536#123—36no—
537C22⋊Q8—33no—
538C22⋊Q8—33no—
539C22⋊Q8—33no—
540C22⋊Q8—33no—
541#121—33no—
542#121—33no—
543#121—36no—
544#121—36no—
545#121—33no—
546#121—33no—
547#120—36no—
548#120—36no—
549C4×Q8—31no—
550C4×Q8—31no—
551C4×D4—33no—
552C4×D4—33no—
553C4×D4—31no—
554C4×D4—33no—
555C4×D4—33no—
556C4×D4—33no—
557C4×D4—33no—
558C4×D4—33no—
559C4×D4—33no—
560C4×D4—33no—
561C4×D4—36no—
562#117—33no—
563C2×C4⋊C4—33no—
564C2×C22⋊C4—33no—
565C2×C22⋊C4—33no—
566C2×C42—33no—
567C23×C3—212no—
568C23×C3—26no—
569C23×C3—26no—
570C23×C3—26no—
571C23×C3—26no—
572C23×C3—21no—
573C23×C3—23no—
574C23×C3—23no—
575C23×C3—31no—
576C23×C3—33no—
577C23×C3—46no—
578C23×C3—43no—
579C23×C3—43no—
580C23×C3—46no—
581C23×C3—66no—
582C23×C3—66no—
583C23×C3—123no—
584C23×C3C23×D313yes—
585C23×C3C23×D311yescharacteristic
586C23×C3C23×D313yes—
587C23×C3C24×C313yes—
588C23×C3C24×C313yes—
589C23×C3C24×C311yescharacteristic
590C22×D3—26no—
591C22×D3—26no—
592C22×D3—43no—
593C22×D3C24×C313yes—
594C22×D3C24×C311yescharacteristic
595C3×Q8—212no—
596C3×Q8—26no—
597C3×Q8—26no—
598C3×Q8—24no—
599C3×Q8—66no—
600C3×Q8C2×#6714yescomplemented
601C3×Q8C2×C3×D414yescomplemented
602C3×D4—224no—
603C3×D4—212no—
604C3×D4—212no—
605C3×D4—212no—
606C3×D4—26no—
607C3×D4—26no—
608C3×D4—212no—
609C3×D4—34no—
610C3×D4—66no—
611C3×D4—66no—
612C3×D4—66no—
613C3×D4—612no—
614C3×D4—66no—
615C3×D4—126no—
616C3×D4C2×#67112yescomplemented
617C3×D4C2×C3×D4112yescomplemented
618C2×C3×C4—24no—
619C2×C3×C4—212no—
620C2×C3×C4—212no—
621C2×C3×C4—212no—
622C2×C3×C4—212no—
623C2×C3×C4—26no—
624C2×C3×C4—26no—
625C2×C3×C4—22no—
626C2×C3×C4—26no—
627C2×C3×C4—26no—
628C2×C3×C4—26no—
629C2×C3×C4—22no—
630C2×C3×C4—26no—
631C2×C3×C4—26no—
632C2×C3×C4—26no—
633C2×C3×C4—21no—
634C2×C3×C4—21no—
635C2×C3×C4—23no—
636C2×C3×C4—23no—
637C2×C3×C4—212no—
638C2×C3×C4—31no—
639C2×C3×C4—31no—
640C2×C3×C4—33no—
641C2×C3×C4—33no—
642C2×C3×C4—31no—
643C2×C3×C4—33no—
644C2×C3×C4—66no—
645C2×C3×C4—66no—
646C2×C3×C4—62no—
647C2×C3×C4—66no—
648C2×C3×C4—66no—
649C2×C3×C4—66no—
650C2×C3×C4—123no—
651C2×C3×C4C2×#67112yescomplemented
652C2×C3×C4C2×C3×D4112yescomplemented
653C2×C3×C4C23×D311yescharacteristic
654C2×C3×C4C23×D313yes—
655C2×C3×C4C23×D313yes—
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C24×C311yescharacteristic
658C2×C3×C4C24×C313yes—
659C2×C3×C4C24×C311yescharacteristic
660C2×C3×C4C24×C313yes—
661#67—212no—
662#67—26no—
663#67—26no—
664#67—26no—
665#67—46no—
666#67C3×#4114yesdirect product factor
667C2×Dic3—26no—
668C2×Dic3—26no—
669C2×Dic3—43no—
670C2×Dic3C24×C311yescharacteristic
671C2×Dic3C24×C313yes—
672C2×Dic3C24×C313yes—
673C2×Dic3C24×C313yes—
674C2×Dic3C24×C311yescharacteristic
675C2×Dic3C24×C311yescharacteristic
676D12—26no—
677C4×D3—22no—
678C4×D3—26no—
679C4×D3—26no—
680C4×D3—26no—
681Dic6—26no—
682C2×C32—22no—
683C2×C32—26no—
684C2×C32—43no—
685C2×C32C23×D411yescharacteristic
686C2×C32C22×#4111yescharacteristic
687C2×C32#58511yescharacteristic
688C3×D3—22no—
689C3×D3—43no—
690C24—33no—
691C24C22×C3×D313yes—
692#41—24no—
693#41—212no—
694#41—212no—
695#41—64no—
696#41—612no—
697#41—612no—
698#41C3×#6718yesdirect product factor
699C2×Q8—24no—
700C2×Q8—33no—
701C2×Q8—64no—
702C2×Q8C22×C3×D313yes—
703C2×Q8C22×C3×D311yescharacteristic
704C2×D4—212no—
705C2×D4—31no—
706C2×D4—33no—
707C2×D4—33no—
708C2×D4—33no—
709C2×D4—36no—
710C2×D4—36no—
711C2×D4—33no—
712C2×D4—612no—
713C2×D4—612no—
714C2×D4C22×C3×D316yes—
715C2×D4C22×C3×D313yes—
716C2×D4C22×C3×D313yes—
717C22×C4—212no—
718C22×C4—33no—
719C22×C4—33no—
720C22×C4—33no—
721C22×C4—31no—
722C22×C4—33no—
723C22×C4—33no—
724C22×C4—33no—
725C22×C4—612no—
726C22×C4C22×C3×D313yes—
727C22×C4C22×C3×D311yescharacteristic
728C22×C4C22×C3×D313yes—
729C22×C4C22×C3×D313yes—
730C22×C4C22×C3×D313yes—
731C22×C4C22×C3×D313yes—
732C4⋊C4—31no—
733C4⋊C4—33no—
734C4⋊C4—33no—
735C4⋊C4—33no—
736C4⋊C4—33no—
737C4⋊C4—33no—
738C4⋊C4—36no—
739C22⋊C4—31no—
740C22⋊C4—33no—
741C22⋊C4—33no—
742C22⋊C4—33no—
743C22⋊C4—36no—
744C22⋊C4—36no—
745C22⋊C4—31no—
746C22⋊C4—33no—
747C22⋊C4—33no—
748C22⋊C4—33no—
749C22⋊C4—36no—
750C42—31no—
751C42—33no—
752C42—33no—
753C42—33no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—23no—
757C22×C3—23no—
758C22×C3—21no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—23no—
762C22×C3—23no—
763C22×C3—21no—
764C22×C3—26no—
765C22×C3—23no—
766C22×C3—23no—
767C22×C3—23no—
768C22×C3—23no—
769C22×C3—23no—
770C22×C3—23no—
771C22×C3—22no—
772C22×C3—26no—
773C22×C3—21no—
774C22×C3—32no—
775C22×C3—43no—
776C22×C3—43no—
777C22×C3—43no—
778C22×C3—43no—
779C22×C3—412no—
780C22×C3—412no—
781C22×C3—424no—
782C22×C3—61no—
783C22×C3—61no—
784C22×C3—63no—
785C22×C3—63no—
786C22×C3—63no—
787C22×C3—1212no—
788C22×C3D3×#4112yescomplemented
789C22×C3C22×#6716yes—
790C22×C3C22×C3×D416yes—
791C22×C3C2×C3×#4112yescomplemented
792C22×C3C24×D311yescharacteristic
793C22×C3C25×C311yescharacteristic
794C2×D3—21no—
795C2×D3—21no—
796C2×D3—23no—
797C2×D3—23no—
798C2×D3—23no—
799C2×D3—412no—
800C2×D3C2×C3×#4112yescomplemented
801C3×C4—22no—
802C3×C4—26no—
803C3×C4—21no—
804C3×C4—23no—
805C3×C4—21no—
806C3×C4—23no—
807C3×C4—22no—
808C3×C4—26no—
809C3×C4—32no—
810C3×C4—63no—
811C3×C4—61no—
812C3×C4—63no—
813C3×C4—61no—
814C3×C4—63no—
815C3×C4C22×#6712yes—
816C3×C4C22×#6716yes—
817C3×C4C22×C3×D416yes—
818C3×C4C22×C3×D412yes—
819Dic3—23no—
820Dic3—21no—
821Dic3—23no—
822Dic3—21no—
823Dic3—23no—
824Dic3C2×C3×#4112yescomplemented
825C32D4×#4111yescharacteristic, complemented, Sylow
826C23—26no—
827C23—26no—
828C23—31no—
829C23—33no—
830C23—43no—
831C23—66no—
832C23—66no—
833C23—123no—
834C23C23×C3×D313yes—
835C23C23×C3×D311yescharacteristic
836C23C23×C3×D313yes—
837Q8—26no—
838Q8—66no—
839Q8C2×C3×#6714yescomplemented
840D4—212no—
841D4—26no—
842D4—34no—
843D4—66no—
844D4—66no—
845D4—66no—
846D4—612no—
847D4—66no—
848D4—126no—
849D4C2×C3×#67112yescomplemented
850C2×C4—26no—
851C2×C4—22no—
852C2×C4—26no—
853C2×C4—26no—
854C2×C4—26no—
855C2×C4—31no—
856C2×C4—31no—
857C2×C4—33no—
858C2×C4—33no—
859C2×C4—31no—
860C2×C4—33no—
861C2×C4—66no—
862C2×C4—66no—
863C2×C4—62no—
864C2×C4—66no—
865C2×C4—66no—
866C2×C4—66no—
867C2×C4—123no—
868C2×C4C2×C3×#67112yescomplemented
869C2×C4C23×C3×D311yescharacteristic
870C2×C4C23×C3×D313yes—
871C2×C4C23×C3×D311yescharacteristic
872C2×C4C23×C3×D313yes—
873C2×C3—24no—
874C2×C3—26no—
875C2×C3—22no—
876C2×C3—22no—
877C2×C3—26no—
878C2×C3—21no—
879C2×C3—21no—
880C2×C3—21no—
881C2×C3—46no—
882C2×C3—46no—
883C2×C3—43no—
884C2×C3—43no—
885C2×C3—62no—
886C2×C3—123no—
887C2×C3C2×D3×#4111yescharacteristic
888C2×C3#596411yescharacteristic
889C2×C3C23×#6711yescharacteristic
890C2×C3C23×C3×D411yescharacteristic
891C2×C3C22×C3×#4111yescharacteristic
892C2×C3C3×#58511yescharacteristic
893D3—22no—
894D3—43no—
895C22—23no—
896C22—23no—
897C22—21no—
898C22—21no—
899C22—23no—
900C22—23no—
901C22—23no—
902C22—32no—
903C22—412no—
904C22—61no—
905C22—61no—
906C22—63no—
907C22—63no—
908C22—63no—
909C22—1212no—
910C22C3×D3×#4112yescomplemented
911C22C22×C3×#6716yes—
912C22C24×C3×D311yescharacteristic
913C4—21no—
914C4—23no—
915C4—32no—
916C4—63no—
917C4—61no—
918C4—63no—
919C4—61no—
920C4—63no—
921C4C22×C3×#6712yes—
922C4C22×C3×#6716yes—
923C3—21no—
924C3#41×#6711yescharacteristic, direct product factor
925C3C3×D4×#4111yescharacteristic, complemented
926C2—22no—
927C2—26no—
928C2—43no—
929C2—62no—
930C2—123no—
931C2C2×C3×D3×#4111yescharacteristic
932C2C3×#596411yescharacteristic
933C2C23×C3×#6711yescharacteristic
subgroupG/H
centerC2×C3×C4C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC22×C32×#41C2
socleC22×C32C25
hypercenterC22×C3×#41D3
hypocenterC3C3×D4×#41
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C22×C3×#41

Complements

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

NH ≅ G/Ntype
1. C22×C32×#41C2semidirect
2. C2×C3×D3×#41C2semidirect
3. C3×#5834C2semidirect
4. C3×#5832C2semidirect
5. C3×#5831C2semidirect
6. C3×#5829C2semidirect
7. C3×#5828C2semidirect
8. C3×Dic3×#41C2semidirect
9. C3×#5824C2semidirect
10. C3×#5817C2semidirect
11. C3×Q8×#67C2semidirect
12. C3×#5806C2semidirect
13. C3×D4×#67C2semidirect
14. C3×#5791C2semidirect
15. C2×C3×C4×#67C2semidirect
17. #41×#67C3direct (N × H)
20. C2×C32×#41C22semidirect
21. C2×C32×#41C22semidirect
22. C2×C32×#41C22semidirect
23. C22×C32×Q8C22semidirect
24. C22×C32×D4C22semidirect
25. C23×C32×C4C22semidirect
28. C2×C3×#239C22semidirect
29. C2×C3×D3×Q8C22semidirect
30. C2×C3×#237C22semidirect
31. C2×C3×D3×D4C22semidirect
32. C2×C3×#235C22semidirect
33. C22×C3×C4×D3C22semidirect
34. C3×#953C22semidirect
35. C2×C3×#217C22semidirect
36. C3×#947C22semidirect
37. C3×#946C22semidirect
38. C3×#946C22semidirect
39. C3×Q8×Dic3C22semidirect
40. C3×Q8×Dic3C22semidirect
41. C3×#944C22semidirect
42. C3×#940C22semidirect
43. C3×#939C22semidirect
44. C3×#939C22semidirect
45. C3×#938C22semidirect
46. C3×#938C22semidirect
47. C3×#937C22semidirect
48. C3×#936C22semidirect
49. C3×#935C22semidirect
50. C3×D4×Dic3C22semidirect
51. C3×D4×Dic3C22semidirect
52. C3×#930C22semidirect
53. C3×#930C22semidirect
54. C3×#929C22semidirect
57. C3×C4×#67C22semidirect
58. C3×C4×#67C22semidirect
59. C3×C4×#67C22semidirect
60. C3×C4×#67C22semidirect
61. C3×C4×#67C22semidirect
62. C3×C4×#67C22semidirect
63. C3×C4×#67C22semidirect
64. C2×C3×(C2×D3)⋊C4C22semidirect
65. C3×#926C22semidirect
66. C3×#924C22semidirect
67. C3×#924C22semidirect
68. C2×C3×Dic3⋊C4C22semidirect
69. C2×C3×C4×Dic3C22semidirect
72. C22×C3×#41D3semidirect
73. C22×C3×#41C2×C3semidirect
74. C2×D3×#41C2×C3semidirect
88. #5834C2×C3semidirect
89. #5832C2×C3semidirect
90. #5831C2×C3semidirect
91. #5829C2×C3semidirect
92. #5828C2×C3semidirect
93. Dic3×#41C2×C3semidirect
94. #5824C2×C3semidirect
95. #5817C2×C3semidirect
96. Q8×#67C2×C3semidirect
97. #5806C2×C3semidirect
98. D4×#67C2×C3semidirect
99. #5791C2×C3semidirect
100. C2×C4×#67C2×C3semidirect
106. C32×#41D4semidirect
178. C2×C3×#41C2×D3semidirect
179. C2×C3×#41C2×D3semidirect
180. C2×C3×#41C2×D3semidirect
182. C2×C3×#41C22×C3semidirect
183. C2×C3×#41C22×C3semidirect
184. C2×C3×#41C22×C3semidirect
187. C22×C3×Q8C2×D3semidirect
188. C22×C3×Q8C22×C3semidirect
192. C22×C3×D4C2×D3semidirect
193. C22×C3×D4C22×C3semidirect
196. C23×C3×C4C2×D3semidirect
197. C23×C3×C4C22×C3semidirect
200. C2×#239C22×C3semidirect
201. C2×D3×Q8C22×C3semidirect
202. C2×#237C22×C3semidirect
203. C2×D3×D4C22×C3semidirect
204. C2×#235C22×C3semidirect
205. C22×C4×D3C22×C3semidirect
242. #953C22×C3semidirect
243. C2×#217C22×C3semidirect
244. #947C22×C3semidirect
245. #946C22×C3semidirect
246. #946C22×C3semidirect
247. Q8×Dic3C22×C3semidirect
248. Q8×Dic3C22×C3semidirect
249. #944C22×C3semidirect
250. #940C22×C3semidirect
251. #939C22×C3semidirect
252. #939C22×C3semidirect
253. #938C22×C3semidirect
254. #938C22×C3semidirect
255. #937C22×C3semidirect
256. #936C22×C3semidirect
257. #935C22×C3semidirect
258. D4×Dic3C22×C3semidirect
259. D4×Dic3C22×C3semidirect
260. #930C22×C3semidirect
261. #930C22×C3semidirect
262. #929C22×C3semidirect
265. C4×#67C22×C3semidirect
266. C4×#67C22×C3semidirect
267. C4×#67C22×C3semidirect
268. C4×#67C22×C3semidirect
269. C4×#67C22×C3semidirect
270. C4×#67C22×C3semidirect
271. C4×#67C22×C3semidirect
272. C2×(C2×D3)⋊C4C22×C3semidirect
273. #926C22×C3semidirect
274. #924C22×C3semidirect
275. #924C22×C3semidirect
276. C2×Dic3⋊C4C22×C3semidirect
277. C2×C4×Dic3C22×C3semidirect
290. C32×Q8C2×D4semidirect
293. C32×D4C2×D4semidirect
299. C2×C32×C4C2×D4semidirect
309. C3×#67#41direct (N × H)
326. C22×#41C3×D3semidirect
358. C3×#41#67direct (N × H)
359. C3×#41C3×D4semidirect
496. C22×C32C2×#41semidirect
504. C2×C3×D3C2×#41semidirect
514. C3×Dic3C2×#41semidirect
521. C2×#41C2×C3×D3semidirect
522. C2×#41C2×C3×D3semidirect
523. C2×#41C2×C3×D3semidirect
525. C22×Q8C2×C3×D3semidirect
528. C22×D4C2×C3×D3semidirect
530. C23×C4C2×C3×D3semidirect
600. C3×Q8C2×#67semidirect
601. C3×Q8C2×C3×D4semidirect
616. C3×D4C2×#67semidirect
617. C3×D4C2×C3×D4semidirect
651. C2×C3×C4C2×#67semidirect
652. C2×C3×C4C2×C3×D4semidirect
666. #67C3×#41direct (N × H)
698. #41C3×#67direct (N × H)
788. C22×C3D3×#41semidirect
791. C22×C3C2×C3×#41semidirect
800. C2×D3C2×C3×#41semidirect
824. Dic3C2×C3×#41semidirect
825. C32D4×#41semidirect
839. Q8C2×C3×#67semidirect
849. D4C2×C3×#67semidirect
868. C2×C4C2×C3×#67semidirect
910. C22C3×D3×#41semidirect
924. C3#41×#67direct (N × H)
925. C3C3×D4×#41semidirect

Maximal subgroups

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

subgroupindex
C22×C32×#412
C2×C3×D3×#412
C3×#58342
C3×#58322
C3×#58312
C3×#58292
C3×#58282
C3×Dic3×#412
C3×#58242
C3×#58172
C3×Q8×#672
C3×#58062
C3×D4×#672
C3×#57912
C2×C3×C4×#672
C3×D4×#413
#41×#673