Finite Group Databasebeta

← C2×C3×#5631 #11902500

Subgroups — C2×C3×#5631 #11902500

Order 1152.

3425 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#239C211yesmaximal, characteristic, complemented
2C22×C3×#235C211yesmaximal, characteristic, complemented
3C2×C32×C22⋊Q8C211yesmaximal, characteristic, complemented
4C2×C3×#944C211yesmaximal, characteristic, complemented
5C2×C3×C4×#67C211yesmaximal, characteristic, complemented
6C3×#5631C2116yesmaximal, direct product factor
7C2×C3×#897C211yesmaximal, characteristic, complemented
8C2×C3×#894C212yesmaximal, complemented
9C2×C3×#893C211yesmaximal, characteristic, complemented
10C2×C3×D3×C4⋊C4C212yesmaximal, complemented
11C2×C3×#884C212yesmaximal, complemented
12C2×C3×#883C212yesmaximal, complemented
13C2×C3×#547—31nomaximal
14C2×#5631C311yesmaximal, characteristic, direct product factor
15C22×C32×Q8C2211yescharacteristic
16C23×C32×C4C2211yescharacteristic
17C22×C3×#67C2212yes—
18C22×C3×#67C2211yescharacteristic
19C2×C3×#239—28no—
20C2×C3×#239C2218yescomplemented
21C2×C3×#235—28no—
22C2×C3×#235C2218yescomplemented
23C22×C3×D12C2212yes—
24C22×C3×D12C2211yescharacteristic
25C22×C3×C4×D3C2212yes—
26C22×C3×C4×D3C2212yes—
27C22×C3×C4×D3C2212yes—
28C22×C3×C4×D3C2211yescharacteristic
29C22×C3×Dic6C2211yescharacteristic
30C32×C22⋊Q8C2218yescomplemented
31C2×C32×C4⋊C4C2212yes—
32C2×C32×C4⋊C4C2211yescharacteristic
33C2×C32×C22⋊C4C2212yes—
34C2×C3×#217C2211yescharacteristic
35C3×#944C2218yescomplemented
36C3×C4×#67C2218yescomplemented
37C2×C3×(C2×D3)⋊C4C2212yes—
38C2×C3×(C2×D3)⋊C4C2212yes—
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic
40C2×C3×C4⋊Dic3C2212yes—
41C2×C3×Dic3⋊C4C2212yes—
42C2×C3×Dic3⋊C4C2212yes—
43C2×C3×Dic3⋊C4C2211yescharacteristic
44C2×C3×C4×Dic3C2211yescharacteristic
45C3×#897C2218yescomplemented
46C3×#894C22116yescomplemented
47C3×#893C2218yescomplemented
48C3×D3×C4⋊C4C22116yescomplemented
49C3×#884C22116yescomplemented
50C3×#883C22116yescomplemented
51C22×C3×#41—31no—
52C22×C3×#41—31no—
53C22×#239C2×C311yescharacteristic, complemented
54C22×#235C2×C311yescharacteristic, complemented
55C3×#547—316no—
56C2×C3×C4⋊Q8—31no—
57C2×C3×#123—32no—
58C2×C3×#123—32no—
59C2×C3×C22⋊Q8—21no—
60C2×C3×C22⋊Q8—31no—
61C2×C3×C22⋊Q8D311yescharacteristic, complemented
62C2×C3×C22⋊Q8C2×C311yescharacteristic, complemented
63C2×C3×#121—32no—
64C2×C3×C4×D4—31no—
65C2×C3×C4×D4—31no—
66C22×C3×C4⋊C4—32no—
67C2×#944C2×C311yescharacteristic, complemented
68C2×C4×#67C2×C311yescharacteristic, complemented
69#5631C2×C3116yesdirect product factor
70C2×#897C2×C311yescharacteristic, complemented
71C2×#894C2×C312yescomplemented
72C2×#893C2×C311yescharacteristic, complemented
73C2×D3×C4⋊C4C2×C312yescomplemented
74C2×#884C2×C312yescomplemented
75C2×#883C2×C312yescomplemented
76C24×C32C2311yescharacteristic
77C23×C3×D3C2311yescharacteristic
78C23×C3×D3C2312yes—
79C2×C32×Q8—24no—
80C2×C32×Q8C2314yes—
81C22×C32×C4—24no—
82C22×C32×C4C2312yes—
83C22×C32×C4C2311yescharacteristic
84C22×C32×C4C2312yes—
85C22×C32×C4C2314yes—
86C22×C32×C4C2311yescharacteristic
87C2×C3×#67—28no—
88C2×C3×#67—24no—
89C2×C3×#67C2318yes—
90C2×C3×#67C2314yes—
91C22×C3×Dic3C2311yescharacteristic
92C22×C3×Dic3C2312yes—
93C22×C3×Dic3C2311yescharacteristic
94C22×C3×Dic3C2311yescharacteristic
95C3×#239—232no—
96C3×#235—232no—
97C2×C3×D12—28no—
98C2×C3×D12D418yescomplemented
99C2×C3×D12C2318yes—
100C2×C3×D12C2314yes—
101C2×C3×C4×D3—28no—
102C2×C3×C4×D3—28no—
103C2×C3×C4×D3—24no—
104C2×C3×C4×D3—28no—
105C2×C3×C4×D3C2318yes—
106C2×C3×C4×D3C2318yes—
107C2×C3×C4×D3C2318yes—
108C2×C3×C4×D3C2314yes—
109C2×C3×Dic6—24no—
110C2×C3×Dic6C2314yes—
111C32×C4⋊C4C2318yes—
112C32×C4⋊C4C2314yes—
113C32×C22⋊C4C2318yes—
114C3×#217C2314yes—
115C3×(C2×D3)⋊C4C2318yes—
116C3×(C2×D3)⋊C4C2318yes—
117C3×(C2×D3)⋊C4C2314yes—
118C3×C4⋊Dic3C2318yes—
119C3×Dic3⋊C4C2318yes—
120C3×Dic3⋊C4C2318yes—
121C3×Dic3⋊C4C2314yes—
122C3×C4×Dic3C2314yes—
123C2×#547—31noSylow
124C2×C3×#41—38no—
125C2×C3×#41—38no—
126C2×C3×#41—68no—
127C2×C3×#41—68no—
128C22×C3×Q8—21no—
129C22×C3×Q8—31no—
130C22×C3×Q8C2×D311yescharacteristic
131C22×C3×Q8C22×C311yescharacteristic
132C22×C3×D4—32no—
133C22×C3×D4—31no—
134C22×C3×D4—31no—
135C22×C3×D4—32no—
136C23×C3×C4—21no—
137C23×C3×C4—32no—
138C23×C3×C4—32no—
139C23×C3×C4—31no—
140C23×C3×C4—32no—
141C23×C3×C4C2×D311yescharacteristic
142C23×C3×C4C22×C311yescharacteristic
143C22×#67C22×C312yes—
144C22×#67C22×C311yescharacteristic
145C2×#239—28no—
146C2×#239C22×C318yescomplemented
147C2×#235—28no—
148C2×#235C22×C318yescomplemented
149C22×D12C22×C312yes—
150C22×D12C22×C311yescharacteristic
151C22×C4×D3C22×C312yes—
152C22×C4×D3C22×C312yes—
153C22×C4×D3C22×C311yescharacteristic
154C22×C4×D3C22×C312yes—
155C22×Dic6C22×C311yescharacteristic
156C3×C4⋊Q8—38no—
157C3×#123—316no—
158C3×#123—316no—
159C3×C22⋊Q8—28no—
160C3×C22⋊Q8—38no—
161C3×C22⋊Q8C2×D318yescomplemented
162C3×C22⋊Q8C22×C318yescomplemented
163C3×#121—316no—
164C3×C4×D4—38no—
165C3×C4×D4—38no—
166C2×C3×C4⋊C4—22no—
167C2×C3×C4⋊C4—21no—
168C2×C3×C4⋊C4—31no—
169C2×C3×C4⋊C4—32no—
170C2×C3×C4⋊C4—32no—
171C2×C3×C4⋊C4—32no—
172C2×C3×C4⋊C4—316no—
173C2×C3×C4⋊C4C2×D312yes—
174C2×C3×C4⋊C4C2×D311yescharacteristic
175C2×C3×C4⋊C4C22×C312yes—
176C2×C3×C4⋊C4C22×C311yescharacteristic
177C2×C3×C22⋊C4—22no—
178C2×C3×C22⋊C4—31no—
179C2×C3×C22⋊C4—32no—
180C2×C3×C22⋊C4—31no—
181C2×C3×C22⋊C4—32no—
182C2×C3×C22⋊C4C2×D312yes—
183C2×C3×C22⋊C4C22×C312yes—
184C2×C3×C42—31no—
185C2×#217C22×C311yescharacteristic
186#944C22×C318yescomplemented
187C4×#67C22×C318yescomplemented
188C2×(C2×D3)⋊C4C22×C312yes—
189C2×(C2×D3)⋊C4C22×C312yes—
190C2×(C2×D3)⋊C4C22×C311yescharacteristic
191C2×C4⋊Dic3C22×C312yes—
192C2×Dic3⋊C4C22×C312yes—
193C2×Dic3⋊C4C22×C312yes—
194C2×Dic3⋊C4C22×C311yescharacteristic
195C2×C4×Dic3C22×C311yescharacteristic
196#897C22×C318yescomplemented
197#894C22×C3116yescomplemented
198#893C22×C318yescomplemented
199D3×C4⋊C4C22×C3116yescomplemented
200#884C22×C3116yescomplemented
201#883C22×C3116yescomplemented
202C23×C32—22no—
203C23×C32—22no—
204C23×C32—22no—
205C23×C32C2412yes—
206C23×C32C2411yescharacteristic
207C22×C3×D3—24no—
208C22×C3×D3—24no—
209C22×C3×D3—22no—
210C22×C3×D3—22no—
211C22×C3×D3—22no—
212C22×C3×D3C2×D418yes—
213C22×C3×D3C2412yes—
214C22×C3×D3C2414yes—
215C32×Q8—28no—
216C2×C32×C4—22no—
217C2×C32×C4—24no—
218C2×C32×C4—24no—
219C2×C32×C4—28no—
220C2×C32×C4C2×D414yes—
221C2×C32×C4C2414yes—
222C2×C32×C4C2412yes—
223C2×C32×C4C2414yes—
224C2×C32×C4C2412yes—
225C3×#67—216no—
226C3×#67—28no—
227C2×C3×Dic3—24no—
228C2×C3×Dic3—22no—
229C2×C3×Dic3—22no—
230C2×C3×Dic3#4114yescomplemented
231C2×C3×Dic3C2412yes—
232C2×C3×Dic3C2414yes—
233C2×C3×Dic3C2412yes—
234C2×C3×Dic3C2412yes—
235C3×D12—216no—
236C3×D12C2×D4116yescomplemented
237C3×C4×D3—216no—
238C3×C4×D3—216no—
239C3×C4×D3—28no—
240C3×C4×D3—216no—
241C3×Dic6—28no—
242C22×#41—31no—
243C22×#41—31no—
244#547—316no—
245C2×C4⋊Q8—31no—
246C2×#123—32no—
247C2×#123—32no—
248C2×C22⋊Q8—31no—
249C2×C22⋊Q8C3×D311yescharacteristic, complemented
250C2×#121—32no—
251C2×C4×D4—31no—
252C2×C4×D4—31no—
253C22×C4⋊C4—32no—
254C24×C3—21no—
255C24×C3—32no—
256C24×C3—31no—
257C24×C3C22×D311yescharacteristic
258C24×C3C23×C311yescharacteristic
259C23×D3C23×C311yescharacteristic
260C23×D3C23×C312yes—
261C3×#41—632no—
262C3×#41—632no—
263C2×C3×Q8—24no—
264C2×C3×Q8—24no—
265C2×C3×Q8—24no—
266C2×C3×Q8—34no—
267C2×C3×Q8—44no—
268C2×C3×Q8—64no—
269C2×C3×Q8C22×D314yes—
270C2×C3×Q8C23×C314yes—
271C2×C3×D4—34no—
272C2×C3×D4—38no—
273C2×C3×D4—38no—
274C2×C3×D4—34no—
275C2×C3×D4—38no—
276C2×C3×D4—68no—
277C2×C3×D4—64no—
278C2×C3×D4—68no—
279C22×C3×C4—24no—
280C22×C3×C4—24no—
281C22×C3×C4—21no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—21no—
285C22×C3×C4—24no—
286C22×C3×C4—31no—
287C22×C3×C4—31no—
288C22×C3×C4—31no—
289C22×C3×C4—32no—
290C22×C3×C4—38no—
291C22×C3×C4—38no—
292C22×C3×C4—38no—
293C22×C3×C4—34no—
294C22×C3×C4—44no—
295C22×C3×C4—68no—
296C22×C3×C4—68no—
297C22×C3×C4—68no—
298C22×C3×C4—64no—
299C22×C3×C4C22×D314yes—
300C22×C3×C4C22×D312yes—
301C22×C3×C4C22×D311yescharacteristic
302C22×C3×C4C22×D312yes—
303C22×C3×C4C22×D311yescharacteristic
304C22×C3×C4C23×C312yes—
305C22×C3×C4C23×C311yescharacteristic
306C22×C3×C4C23×C312yes—
307C22×C3×C4C23×C314yes—
308C22×C3×C4C23×C311yescharacteristic
309C2×#67—28no—
310C2×#67—24no—
311C2×#67C23×C318yes—
312C2×#67C23×C314yes—
313C22×Dic3C23×C311yescharacteristic
314C22×Dic3C23×C312yes—
315C22×Dic3C23×C311yescharacteristic
316C22×Dic3C23×C311yescharacteristic
317#239—232no—
318#235—232no—
319C2×D12—28no—
320C2×D12C3×D418yescomplemented
321C2×D12C23×C318yes—
322C2×D12C23×C314yes—
323C2×C4×D3—28no—
324C2×C4×D3—28no—
325C2×C4×D3—24no—
326C2×C4×D3—28no—
327C2×C4×D3C23×C318yes—
328C2×C4×D3C23×C318yes—
329C2×C4×D3C23×C318yes—
330C2×C4×D3C23×C314yes—
331C2×Dic6—24no—
332C2×Dic6C23×C314yes—
333C3×C4⋊C4—28no—
334C3×C4⋊C4—24no—
335C3×C4⋊C4—34no—
336C3×C4⋊C4—38no—
337C3×C4⋊C4—38no—
338C3×C4⋊C4—38no—
339C3×C4⋊C4C22×D318yes—
340C3×C4⋊C4C22×D314yes—
341C3×C4⋊C4C23×C318yes—
342C3×C4⋊C4C23×C314yes—
343C3×C22⋊C4—28no—
344C3×C22⋊C4—34no—
345C3×C22⋊C4—38no—
346C3×C22⋊C4—34no—
347C3×C22⋊C4—38no—
348C3×C22⋊C4C22×D318yes—
349C3×C22⋊C4C23×C318yes—
350C3×C42—34no—
351#217C23×C314yes—
352(C2×D3)⋊C4C23×C318yes—
353(C2×D3)⋊C4C23×C318yes—
354(C2×D3)⋊C4C23×C314yes—
355C4⋊Dic3C23×C318yes—
356Dic3⋊C4C23×C318yes—
357Dic3⋊C4C23×C318yes—
358Dic3⋊C4C23×C314yes—
359C4×Dic3C23×C314yes—
360C22×C32—22no—
361C22×C32—22no—
362C22×C32—22no—
363C22×C32—44no—
364C22×C32C22×D412yes—
365C22×C32C2×#4112yes—
366C22×C322−1+412yes—
367C22×C32C2511yescharacteristic
368C2×C3×D3—216no—
369C2×C3×D3—24no—
370C2×C3×D3—24no—
371C2×C3×D3—22no—
372C2×C3×D3—22no—
373C2×C3×D3—22no—
374C2×C3×D3—44no—
375C2×C3×D3C22×D418yes—
376C32×C4—22no—
377C32×C4—24no—
378C32×C4—24no—
379C32×C4C22×D414yes—
380C3×Dic3—24no—
381C3×Dic3—22no—
382C3×Dic3—22no—
383C3×Dic3C2×#4114yescomplemented
384C2×#41—38no—
385C2×#41—38no—
386C2×#41—68no—
387C2×#41—68no—
388C22×Q8—31no—
389C22×Q8C2×C3×D311yescharacteristic
390C22×D4—31no—
391C22×D4—32no—
392C22×D4—31no—
393C22×D4—32no—
394C23×C4—32no—
395C23×C4—32no—
396C23×C4—32no—
397C23×C4—31no—
398C23×C4C2×C3×D311yescharacteristic
399C4⋊Q8—38no—
400#123—316no—
401#123—316no—
402C22⋊Q8—38no—
403C22⋊Q8C2×C3×D318yescomplemented
404#121—316no—
405C4×D4—38no—
406C4×D4—38no—
407C2×C4⋊C4—31no—
408C2×C4⋊C4—32no—
409C2×C4⋊C4—32no—
410C2×C4⋊C4—32no—
411C2×C4⋊C4—316no—
412C2×C4⋊C4C2×C3×D312yes—
413C2×C4⋊C4C2×C3×D311yescharacteristic
414C2×C22⋊C4—31no—
415C2×C22⋊C4—32no—
416C2×C22⋊C4—31no—
417C2×C22⋊C4—32no—
418C2×C22⋊C4C2×C3×D312yes—
419C2×C42—31no—
420C23×C3—24no—
421C23×C3—22no—
422C23×C3—22no—
423C23×C3—22no—
424C23×C3—22no—
425C23×C3—22no—
426C23×C3—22no—
427C23×C3—21no—
428C23×C3—22no—
429C23×C3—38no—
430C23×C3—34no—
431C23×C3—32no—
432C23×C3—42no—
433C23×C3—42no—
434C23×C3—64no—
435C23×C3—64no—
436C23×C3—62no—
437C23×C3—62no—
438C23×C3—62no—
439C23×C3C23×D312yes—
440C23×C3C23×D311yescharacteristic
441C23×C3C24×C312yes—
442C23×C3C24×C311yescharacteristic
443C22×D3—24no—
444C22×D3—24no—
445C22×D3—22no—
446C22×D3—22no—
447C22×D3—22no—
448C22×D3C2×C3×D418yes—
449C22×D3C24×C312yes—
450C22×D3C24×C314yes—
451C3×Q8—28no—
452C3×Q8—28no—
453C3×Q8—48no—
454C3×Q8—68no—
455C3×D4—316no—
456C3×D4—616no—
457C3×D4—68no—
458C3×D4—616no—
459C2×C3×C4—22no—
460C2×C3×C4—24no—
461C2×C3×C4—24no—
462C2×C3×C4—22no—
463C2×C3×C4—24no—
464C2×C3×C4—24no—
465C2×C3×C4—28no—
466C2×C3×C4—28no—
467C2×C3×C4—22no—
468C2×C3×C4—24no—
469C2×C3×C4—24no—
470C2×C3×C4—22no—
471C2×C3×C4—24no—
472C2×C3×C4—34no—
473C2×C3×C4—32no—
474C2×C3×C4—32no—
475C2×C3×C4—32no—
476C2×C3×C4—34no—
477C2×C3×C4—48no—
478C2×C3×C4—44no—
479C2×C3×C4—42no—
480C2×C3×C4—44no—
481C2×C3×C4—616no—
482C2×C3×C4—616no—
483C2×C3×C4—616no—
484C2×C3×C4—62no—
485C2×C3×C4—64no—
486C2×C3×C4—62no—
487C2×C3×C4—68no—
488C2×C3×C4D3×D414yes—
489C2×C3×C4C2×C3×D414yes—
490C2×C3×C4C23×D314yes—
491C2×C3×C4C23×D312yes—
492C2×C3×C4C23×D314yes—
493C2×C3×C4C23×D312yes—
494C2×C3×C4C24×C314yes—
495C2×C3×C4C24×C312yes—
496C2×C3×C4C24×C314yes—
497C2×C3×C4C24×C312yes—
498#67—216no—
499#67—28no—
500C2×Dic3—24no—
501C2×Dic3—22no—
502C2×Dic3—22no—
503C2×Dic3C3×#4114yescomplemented
504C2×Dic3C24×C312yes—
505C2×Dic3C24×C314yes—
506C2×Dic3C24×C312yes—
507C2×Dic3C24×C312yes—
508D12—216no—
509D12C2×C3×D4116yescomplemented
510C4×D3—216no—
511C4×D3—216no—
512C4×D3—28no—
513C4×D3—216no—
514Dic6—28no—
515C2×C32—42no—
516C2×C32#54714yescomplemented
517C2×C32C23×D411yescharacteristic
518C2×C32C22×#4111yescharacteristic
519C2×C32C2×2−1+411yescharacteristic
520C3×D3—28no—
521C3×D3—42no—
522C24—32no—
523C24—31no—
524C24C22×C3×D311yescharacteristic
525#41—632no—
526#41—632no—
527C2×Q8—24no—
528C2×Q8—34no—
529C2×Q8—64no—
530C2×Q8C22×C3×D314yes—
531C2×D4—34no—
532C2×D4—38no—
533C2×D4—34no—
534C2×D4—38no—
535C2×D4—38no—
536C2×D4—68no—
537C2×D4—64no—
538C2×D4—68no—
539C22×C4—24no—
540C22×C4—31no—
541C22×C4—31no—
542C22×C4—31no—
543C22×C4—32no—
544C22×C4—38no—
545C22×C4—38no—
546C22×C4—38no—
547C22×C4—34no—
548C22×C4—68no—
549C22×C4—68no—
550C22×C4—68no—
551C22×C4—64no—
552C22×C4C22×C3×D312yes—
553C22×C4C22×C3×D311yescharacteristic
554C22×C4C22×C3×D312yes—
555C22×C4C22×C3×D314yes—
556C22×C4C22×C3×D311yescharacteristic
557C4⋊C4—34no—
558C4⋊C4—38no—
559C4⋊C4—38no—
560C4⋊C4—38no—
561C4⋊C4C22×C3×D318yes—
562C4⋊C4C22×C3×D314yes—
563C22⋊C4—34no—
564C22⋊C4—38no—
565C22⋊C4—34no—
566C22⋊C4—38no—
567C22⋊C4C22×C3×D318yes—
568C42—34no—
569C22×C3—24no—
570C22×C3—22no—
571C22×C3—22no—
572C22×C3—22no—
573C22×C3—22no—
574C22×C3—22no—
575C22×C3—22no—
576C22×C3—22no—
577C22×C3—22no—
578C22×C3—22no—
579C22×C3—21no—
580C22×C3—38no—
581C22×C3—42no—
582C22×C3—42no—
583C22×C3—48no—
584C22×C3—44no—
585C22×C3—44no—
586C22×C3—64no—
587C22×C3—64no—
588C22×C3—616no—
589C22×C3—62no—
590C22×C3—62no—
591C22×C3—62no—
592C22×C3—124no—
593C22×C3C2×D3×D412yes—
594C22×C3#100712yes—
595C22×C3D3×#4112yes—
596C22×C3C22×C3×D412yes—
597C22×C3C2×C3×#4112yes—
598C22×C3C3×2−1+412yes—
599C22×C3C24×D311yescharacteristic
600C22×C3C25×C311yescharacteristic
601C2×D3—24no—
602C2×D3—24no—
603C2×D3—216no—
604C2×D3—22no—
605C2×D3—22no—
606C2×D3—22no—
607C2×D3—44no—
608C2×D3C22×C3×D418yes—
609C3×C4—22no—
610C3×C4—24no—
611C3×C4—24no—
612C3×C4—22no—
613C3×C4—24no—
614C3×C4—24no—
615C3×C4—24no—
616C3×C4—34no—
617C3×C4—42no—
618C3×C4—44no—
619C3×C4—44no—
620C3×C4—62no—
621C3×C4—64no—
622C3×C4—62no—
623C3×C4C2×D3×D414yes—
624C3×C4C22×C3×D414yes—
625Dic3—24no—
626Dic3—22no—
627Dic3—22no—
628Dic3C2×C3×#4114yescomplemented
629C32C2×#54711yescharacteristic, complemented, Sylow
630C23—22no—
631C23—22no—
632C23—22no—
633C23—38no—
634C23—34no—
635C23—32no—
636C23—64no—
637C23—64no—
638C23—62no—
639C23—62no—
640C23—62no—
641C23C23×C3×D312yes—
642C23C23×C3×D311yescharacteristic
643Q8—28no—
644Q8—68no—
645D4—316no—
646D4—616no—
647D4—68no—
648D4—616no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—28no—
653C2×C4—34no—
654C2×C4—32no—
655C2×C4—32no—
656C2×C4—32no—
657C2×C4—34no—
658C2×C4—616no—
659C2×C4—616no—
660C2×C4—616no—
661C2×C4—62no—
662C2×C4—64no—
663C2×C4—62no—
664C2×C4—68no—
665C2×C4C3×D3×D414yes—
666C2×C4C23×C3×D314yes—
667C2×C4C23×C3×D312yes—
668C2×C4C23×C3×D314yes—
669C2×C4C23×C3×D312yes—
670C2×C3—21no—
671C2×C3—21no—
672C2×C3—21no—
673C2×C3—24no—
674C2×C3—44no—
675C2×C3—42no—
676C2×C3—42no—
677C2×C3—68no—
678C2×C3—122no—
679C2×C3#563114yesdirect product factor
680C2×C3C3×#54714yescomplemented
681C2×C3C22×D3×D411yescharacteristic
682C2×C3C2×#100711yescharacteristic
683C2×C3C2×D3×#4111yescharacteristic
684C2×C3C23×C3×D411yescharacteristic
685C2×C3C22×C3×#4111yescharacteristic
686C2×C3C2×C3×2−1+411yescharacteristic
687D3—28no—
688D3—42no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—38no—
693C22—44no—
694C22—64no—
695C22—64no—
696C22—616no—
697C22—62no—
698C22—62no—
699C22—62no—
700C22—124no—
701C22C2×C3×D3×D412yes—
702C22C3×#100712yes—
703C22C3×D3×#4112yes—
704C22C24×C3×D311yescharacteristic
705C4—22no—
706C4—24no—
707C4—24no—
708C4—34no—
709C4—62no—
710C4—64no—
711C4—62no—
712C4C2×C3×D3×D414yes—
713C3—21no—
714C3C2×#563111yescharacteristic, direct product factor
715C3C2×C3×#54711yescharacteristic, complemented
716C2—42no—
717C2—68no—
718C2—122no—
719C2C3×#563114yesdirect product factor
720C2C22×C3×D3×D411yescharacteristic
721C2C2×C3×#100711yescharacteristic
722C2C2×C3×D3×#4111yescharacteristic
subgroupG/H
centerC23×C3C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC2×C32×C22⋊Q8C2
socleC23×C32C24
hypercenterC2×C3×C22⋊Q8D3
hypocenterC3C2×C3×#547
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C23×C3 ◁ C2×C3×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×C3×#239C2semidirect
2. C22×C3×#235C2semidirect
3. C2×C32×C22⋊Q8C2semidirect
4. C2×C3×#944C2semidirect
5. C2×C3×C4×#67C2semidirect
6. C3×#5631C2direct (N × H)
7. C2×C3×#897C2semidirect
8. C2×C3×#894C2semidirect
9. C2×C3×#893C2semidirect
10. C2×C3×D3×C4⋊C4C2semidirect
11. C2×C3×#884C2semidirect
12. C2×C3×#883C2semidirect
14. C2×#5631C3direct (N × H)
20. C2×C3×#239C22semidirect
22. C2×C3×#235C22semidirect
30. C32×C22⋊Q8C22semidirect
35. C3×#944C22semidirect
36. C3×C4×#67C22semidirect
45. C3×#897C22semidirect
46. C3×#894C22semidirect
47. C3×#893C22semidirect
48. C3×D3×C4⋊C4C22semidirect
49. C3×#884C22semidirect
50. C3×#883C22semidirect
53. C22×#239C2×C3semidirect
54. C22×#235C2×C3semidirect
61. C2×C3×C22⋊Q8D3semidirect
62. C2×C3×C22⋊Q8C2×C3semidirect
67. C2×#944C2×C3semidirect
68. C2×C4×#67C2×C3semidirect
69. #5631C2×C3direct (N × H)
70. C2×#897C2×C3semidirect
71. C2×#894C2×C3semidirect
72. C2×#893C2×C3semidirect
73. C2×D3×C4⋊C4C2×C3semidirect
74. C2×#884C2×C3semidirect
75. C2×#883C2×C3semidirect
98. C2×C3×D12D4semidirect
146. C2×#239C22×C3semidirect
148. C2×#235C22×C3semidirect
161. C3×C22⋊Q8C2×D3semidirect
162. C3×C22⋊Q8C22×C3semidirect
186. #944C22×C3semidirect
187. C4×#67C22×C3semidirect
196. #897C22×C3semidirect
197. #894C22×C3semidirect
198. #893C22×C3semidirect
199. D3×C4⋊C4C22×C3semidirect
200. #884C22×C3semidirect
201. #883C22×C3semidirect
230. C2×C3×Dic3#41semidirect
236. C3×D12C2×D4semidirect
249. C2×C22⋊Q8C3×D3semidirect
320. C2×D12C3×D4semidirect
383. C3×Dic3C2×#41semidirect
403. C22⋊Q8C2×C3×D3semidirect
503. C2×Dic3C3×#41semidirect
509. D12C2×C3×D4semidirect
516. C2×C32#547semidirect
628. Dic3C2×C3×#41semidirect
629. C32C2×#547semidirect
679. C2×C3#5631direct (N × H)
680. C2×C3C3×#547semidirect
714. C3C2×#5631direct (N × H)
715. C3C2×C3×#547semidirect
719. C2C3×#5631direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2392
C22×C3×#2352
C2×C32×C22⋊Q82
C2×C3×#9442
C2×C3×C4×#672
C3×#56312
C2×C3×#8972
C2×C3×#8942
C2×C3×#8932
C2×C3×D3×C4⋊C42
C2×C3×#8842
C2×C3×#8832
C2×C3×#5473
C2×#56313