Finite Group Databasebeta

← C3×#86018 #11900866

Subgroups — C3×#86018 #11900866

Order 1152.

2589 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C32×#525C211yesmaximal, characteristic, complemented
2C3×#5832C211yesmaximal, characteristic, complemented
3C3×Dic3×#41C211yesmaximal, characteristic, complemented
4C3×#5791C211yesmaximal, characteristic, complemented
5C22×C3×C4×Dic3C211yesmaximal, characteristic, complemented
6C3×#5649C214yesmaximal, complemented
7C3×#5624C212yesmaximal, complemented
8C3×#5622C212yesmaximal, complemented
9C3×#5600C212yesmaximal, complemented
10C3×#5596C212yesmaximal, complemented
11C3×#5586C214yesmaximal, complemented
12C3×#5538C214yesmaximal, complemented
13C3×C4×#237C214yesmaximal, complemented
14C3×#5522C211yesmaximal, characteristic, complemented
15C3×#5517C211yesmaximal, characteristic, complemented
16C3×#3444—31nomaximal
17#86018C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C23×C3×Dic3C2212yes—
21C2×C3×#237C2214yes—
22C2×C3×#235C2211yescharacteristic
23C32×#123C2212yes—
24C32×C22⋊Q8C2212yes—
25C32×#121C2212yes—
26C32×#120C2212yes—
27C32×C4×D4C2214yes—
28C32×#117C2211yescharacteristic
29C3×#953C2212yes—
30C3×#947C2211yescharacteristic, complemented
31C3×Q8×Dic3C2212yescomplemented
32C3×#944C2211yescharacteristic, complemented
33C3×#940C2211yescharacteristic, complemented
34C3×#939C2214yes—
35C3×#939C2214yes—
36C3×#936C2211yescharacteristic, complemented
37C3×#935C2214yes—
38C3×D4×Dic3C2214yes—
39C3×D4×Dic3C2214yes—
40C3×D4×Dic3C2212yescomplemented
41C3×#930C2212yes—
42C3×#929C2212yes—
43C3×C4×#67C2214yes—
44C3×C4×#67C2214yescomplemented
45C3×#926C2211yescharacteristic
46C3×#926C2212yescomplemented
47C3×#924C2212yes—
48C2×C3×C4×Dic3C2211yescharacteristic
49C2×C3×C4×Dic3C2211yescharacteristic
50C2×C3×C4×Dic3C2212yes—
51C2×C3×C4×Dic3C2212yes—
52C2×C3×C4×Dic3C2212yes—
53C2×C3×C4×Dic3C2212yes—
54C2×C3×C4×Dic3C2212yes—
55C2×C3×C4×Dic3C2212yescomplemented
56C3×#898C2214yescomplemented
57C3×#893C2212yescomplemented
58C3×#892C2214yescomplemented
59C3×#890C2212yescomplemented
60C3×#889C2214yescomplemented
61C3×#888C2212yescomplemented
62C3×#887C2212yescomplemented
63C3×#887C2214yescomplemented
64C3×#886C2214yes—
65C3×#885C2214yescomplemented
66C3×#67⋊C4C2214yes—
67C3×#67⋊C4C2214yes—
68C3×#67⋊C4C2214yescomplemented
69C3×#879C2214yescomplemented
70C3×#878C2214yes—
71C3×#878C2214yes—
72C3×#877C2214yes—
73C3×#877C2214yescomplemented
74C3×#872C2212yescomplemented
75C3×C42×D3C2212yescomplemented
76C3×C4×Dic6C2214yescomplemented
77C3×#533—32no—
78C3×#533—31no—
79C3×#532—31no—
80C3×#532—32no—
81C3×#529—34no—
82C3×#529—32no—
83C3×#529—32no—
84C3×#529—34no—
85C3×#525—21no—
86C3×#525—31no—
87C3×#525—34no—
88C3×#525D311yescharacteristic, complemented
89C3×#525C2×C311yescharacteristic, complemented
90C3×C4×#41—31no—
91C3×C4×#41—34no—
92C3×C4×#41—31no—
93C22×C3×C42—31no—
94#5832C2×C311yescharacteristic, complemented
95Dic3×#41C2×C311yescharacteristic, complemented
96#5791C2×C311yescharacteristic, complemented
97C22×C4×Dic3C2×C311yescharacteristic, complemented
98#5649C2×C314yescomplemented
99#5624C2×C312yescomplemented
100#5622C2×C312yescomplemented
101#5600C2×C312yescomplemented
102#5596C2×C312yescomplemented
103#5586C2×C314yescomplemented
104#5538C2×C314yescomplemented
105C4×#237C2×C314yescomplemented
106#5522C2×C311yescharacteristic, complemented
107#5517C2×C311yescharacteristic, complemented
108C24×C32C2311yescharacteristic
109C32×#41—24no—
110C2×C32×Q8C2311yescharacteristic
111C2×C32×D4C2312yes—
112C2×C32×D4C2314yes—
113C2×C32×D4C2311yescharacteristic
114C22×C32×C4—24no—
115C22×C32×C4C2312yes—
116C22×C32×C4C2312yes—
117C22×C32×C4C2311yescharacteristic
118C22×C32×C4C2312yes—
119C22×C32×C4C2311yescharacteristic
120C2×C3×#67C2312yes—
121C2×C3×#67C2314yes—
122C2×C3×#67C2314yes—
123C22×C3×Dic3—28no—
124C22×C3×Dic3C2314yes—
125C22×C3×Dic3C2312yes—
126C22×C3×Dic3C2312yes—
127C22×C3×Dic3C2312yes—
128C22×C3×Dic3C2312yes—
129C22×C3×Dic3C2312yes—
130C22×C3×Dic3C2312yes—
131C3×#237—216no—
132C3×#235—24no—
133C2×C3×D12C2311yescharacteristic
134C2×C3×C4×D3C2314yes—
135C2×C3×C4×D3C2312yes—
136C2×C3×Dic6C2314yes—
137C2×C3×Dic6C2311yescharacteristic
138C32×C4⋊C4C2312yes—
139C32×C4⋊C4C2314yes—
140C32×C22⋊C4C2314yes—
141C32×C22⋊C4C2314yes—
142C32×C22⋊C4C2312yes—
143C32×C42C2312yes—
144C3×#217C2314yes—
145C3×#217C2314yes—
146C3×#217C2312yes—
147C3×#217C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×(C2×D3)⋊C4C2314yes—
150C3×(C2×D3)⋊C4C2314yes—
151C3×C4⋊Dic3C2314yes—
152C3×C4⋊Dic3C2314yes—
153C3×C4⋊Dic3C2312yes—
154C3×Dic3⋊C4C2314yes—
155C3×Dic3⋊C4C2314yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×C4×Dic3C2314yes—
160C3×C4×Dic3C2314yes—
161C3×C4×Dic3C2312yes—
162C3×C4×Dic3C2312yes—
163C3×C4×Dic3C2312yes—
164C3×C4×Dic3C2312yes—
165C3×C4×Dic3C2312yes—
166C3×C4×Dic3C2311yescharacteristic
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2311yescharacteristic
169C3×C4×Dic3C2311yescharacteristic
170C3×C4×Dic3C2312yes—
171C3×C4×Dic3C2312yes—
172#3444—31noSylow
173C2×C3×#41—21no—
174C2×C3×#41—34no—
175C2×C3×#41—31no—
176C2×C3×#41C2×D311yescharacteristic
177C2×C3×#41C22×C311yescharacteristic
178C23×C3×C4—21no—
179C23×C3×C4—32no—
180C23×C3×C4C2×D311yescharacteristic
181C23×C3×C4C22×C311yescharacteristic
182C23×Dic3C22×C312yes—
183C2×#237C22×C314yes—
184C2×#235C22×C311yescharacteristic
185C3×C4⋊Q8—31no—
186C3×C4⋊Q8—32no—
187C3×#127—31no—
188C3×#126—34no—
189C3×#126—34no—
190C3×#125—34no—
191C3×#125—32no—
192C3×#124—31no—
193C3×#124—31no—
194C3×#124—34no—
195C3×#123—22no—
196C3×#123—34no—
197C3×#123—32no—
198C3×#123—34no—
199C3×#123C2×D312yes—
200C3×#123C22×C312yes—
201C3×C22⋊Q8—22no—
202C3×C22⋊Q8—32no—
203C3×C22⋊Q8—34no—
204C3×C22⋊Q8—34no—
205C3×C22⋊Q8C2×D312yes—
206C3×C22⋊Q8C22×C312yes—
207C3×#121—22no—
208C3×#121—34no—
209C3×#121—34no—
210C3×#121—32no—
211C3×#121C2×D312yes—
212C3×#121C22×C312yes—
213C3×#120—22no—
214C3×#120—32no—
215C3×#120C2×D312yes—
216C3×#120C22×C312yes—
217C3×C4×Q8—32no—
218C3×C4×Q8—34no—
219C3×C4×Q8—32no—
220C3×C4×Q8—34no—
221C3×C4×D4—24no—
222C3×C4×D4—34no—
223C3×C4×D4—34no—
224C3×C4×D4—32no—
225C3×C4×D4—34no—
226C3×C4×D4—34no—
227C3×C4×D4—32no—
228C3×C4×D4—34no—
229C3×C4×D4—34no—
230C3×C4×D4—34no—
231C3×C4×D4C2×D314yes—
232C3×C4×D4C22×C314yes—
233C3×#117—21no—
234C3×#117—31no—
235C3×#117—32no—
236C3×#117—34no—
237C3×#117—34no—
238C3×#117—34no—
239C3×#117—32no—
240C3×#117C2×D311yescharacteristic
241C3×#117C22×C311yescharacteristic
242C2×C3×C42—32no—
243C2×C3×C42—31no—
244C2×C3×C42—32no—
245C2×C3×C42—32no—
246C2×C3×C42—32no—
247C2×C3×C42—32no—
248C2×C3×C42—31no—
249C2×C3×C42—32no—
250C2×C3×C42—32no—
251#953C22×C312yes—
252#947C22×C311yescharacteristic, complemented
253Q8×Dic3C22×C312yescomplemented
254#944C22×C311yescharacteristic, complemented
255#940C22×C311yescharacteristic, complemented
256#939C22×C314yes—
257#939C22×C314yes—
258#936C22×C311yescharacteristic, complemented
259#935C22×C314yes—
260D4×Dic3C22×C314yes—
261D4×Dic3C22×C314yes—
262D4×Dic3C22×C312yescomplemented
263#930C22×C312yes—
264#929C22×C312yes—
265C4×#67C22×C314yes—
266C4×#67C22×C314yescomplemented
267#926C22×C311yescharacteristic
268#926C22×C312yescomplemented
269#924C22×C312yes—
270C2×C4×Dic3C22×C312yes—
271C2×C4×Dic3C22×C311yescharacteristic
272C2×C4×Dic3C22×C311yescharacteristic
273C2×C4×Dic3C22×C312yes—
274C2×C4×Dic3C22×C312yes—
275C2×C4×Dic3C22×C312yes—
276C2×C4×Dic3C22×C312yes—
277C2×C4×Dic3C22×C312yescomplemented
278#898C22×C314yescomplemented
279#893C22×C312yescomplemented
280#892C22×C314yescomplemented
281#890C22×C312yescomplemented
282#889C22×C314yescomplemented
283#888C22×C312yescomplemented
284#887C22×C314yescomplemented
285#887C22×C312yescomplemented
286#886C22×C314yes—
287#885C22×C314yescomplemented
288#67⋊C4C22×C314yes—
289#67⋊C4C22×C314yes—
290#67⋊C4C22×C314yescomplemented
291#879C22×C314yescomplemented
292#878C22×C314yes—
293#878C22×C314yes—
294#877C22×C314yes—
295#877C22×C314yescomplemented
296#872C22×C312yescomplemented
297C42×D3C22×C312yescomplemented
298C4×Dic6C22×C314yescomplemented
299C23×C32—24no—
300C23×C32—22no—
301C23×C32C2412yes—
302C23×C32C2411yescharacteristic
303C23×C32C2412yes—
304C22×C3×D3C2412yes—
305C32×Q8—22no—
306C32×D4—28no—
307C32×D4—24no—
308C32×D4—22no—
309C2×C32×C4—22no—
310C2×C32×C4—24no—
311C2×C32×C4—24no—
312C2×C32×C4—24no—
313C2×C32×C4#4114yescomplemented
314C2×C32×C4C2412yes—
315C2×C32×C4C2412yes—
316C2×C32×C4C2414yes—
317C2×C32×C4C2411yescharacteristic
318C2×C32×C4C2411yescharacteristic
319C3×#67—24no—
320C3×#67—28no—
321C3×#67—28no—
322C2×C3×Dic3—24no—
323C2×C3×Dic3—28no—
324C2×C3×Dic3—24no—
325C2×C3×Dic3—24no—
326C2×C3×Dic3—24no—
327C2×C3×Dic3—24no—
328C2×C3×Dic3#4118yescomplemented
329C2×C3×Dic3C2412yes—
330C2×C3×Dic3C2412yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2414yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335C3×D12—22no—
336C3×C4×D3—24no—
337C3×C4×D3—28no—
338C3×Dic6—22no—
339C3×Dic6—28no—
340#533—32no—
341#533—31no—
342#532—31no—
343#532—32no—
344#529—34no—
345#529—32no—
346#529—32no—
347#529—34no—
348#525—31no—
349#525—34no—
350#525C3×D311yescharacteristic, complemented
351C4×#41—31no—
352C4×#41—34no—
353C4×#41—31no—
354C22×C42—31no—
355C24×C3—21no—
356C24×C3C22×D311yescharacteristic
357C24×C3C23×C311yescharacteristic
358C3×#41—24no—
359C3×#41—24no—
360C3×#41—44no—
361C3×#41—616no—
362C3×#41—64no—
363C2×C3×Q8—21no—
364C2×C3×Q8—34no—
365C2×C3×Q8—31no—
366C2×C3×Q8C22×D311yescharacteristic
367C2×C3×Q8C23×C311yescharacteristic
368C2×C3×D4—24no—
369C2×C3×D4—22no—
370C2×C3×D4—21no—
371C2×C3×D4—32no—
372C2×C3×D4—34no—
373C2×C3×D4—34no—
374C2×C3×D4—31no—
375C2×C3×D4C22×D312yes—
376C2×C3×D4C22×D311yescharacteristic
377C2×C3×D4C22×D314yes—
378C2×C3×D4C23×C312yes—
379C2×C3×D4C23×C314yes—
380C2×C3×D4C23×C311yescharacteristic
381C22×C3×C4—24no—
382C22×C3×C4—24no—
383C22×C3×C4—21no—
384C22×C3×C4—22no—
385C22×C3×C4—22no—
386C22×C3×C4—22no—
387C22×C3×C4—21no—
388C22×C3×C4—32no—
389C22×C3×C4—32no—
390C22×C3×C4—32no—
391C22×C3×C4—32no—
392C22×C3×C4—32no—
393C22×C3×C4—32no—
394C22×C3×C4—34no—
395C22×C3×C4—34no—
396C22×C3×C4—32no—
397C22×C3×C4—44no—
398C22×C3×C4—68no—
399C22×C3×C4C22×D312yes—
400C22×C3×C4C22×D311yescharacteristic
401C22×C3×C4C22×D312yes—
402C22×C3×C4C22×D312yes—
403C22×C3×C4C22×D311yescharacteristic
404C22×C3×C4C23×C312yes—
405C22×C3×C4C23×C312yes—
406C22×C3×C4C23×C311yescharacteristic
407C22×C3×C4C23×C312yes—
408C22×C3×C4C23×C311yescharacteristic
409C2×#67C23×C312yes—
410C2×#67C23×C314yes—
411C2×#67C23×C314yes—
412C22×Dic3—28no—
413C22×Dic3C23×C314yes—
414C22×Dic3C23×C312yes—
415C22×Dic3C23×C312yes—
416C22×Dic3C23×C312yes—
417C22×Dic3C23×C312yes—
418C22×Dic3C23×C312yes—
419C22×Dic3C23×C312yes—
420#237—216no—
421#235—24no—
422C2×D12C23×C311yescharacteristic
423C2×C4×D3C23×C312yes—
424C2×C4×D3C23×C314yes—
425C2×Dic6C23×C314yes—
426C2×Dic6C23×C311yescharacteristic
427C3×C4⋊C4—22no—
428C3×C4⋊C4—24no—
429C3×C4⋊C4—34no—
430C3×C4⋊C4—34no—
431C3×C4⋊C4—34no—
432C3×C4⋊C4—34no—
433C3×C4⋊C4—34no—
434C3×C4⋊C4—32no—
435C3×C4⋊C4—34no—
436C3×C4⋊C4—34no—
437C3×C4⋊C4C22×D314yes—
438C3×C4⋊C4C22×D312yes—
439C3×C4⋊C4C23×C312yes—
440C3×C4⋊C4C23×C314yes—
441C3×C22⋊C4—22no—
442C3×C22⋊C4—24no—
443C3×C22⋊C4—24no—
444C3×C22⋊C4—32no—
445C3×C22⋊C4—34no—
446C3×C22⋊C4—34no—
447C3×C22⋊C4—34no—
448C3×C22⋊C4—34no—
449C3×C22⋊C4—34no—
450C3×C22⋊C4—34no—
451C3×C22⋊C4C22×D314yes—
452C3×C22⋊C4C22×D314yes—
453C3×C22⋊C4C22×D312yes—
454C3×C22⋊C4C23×C314yes—
455C3×C22⋊C4C23×C314yes—
456C3×C22⋊C4C23×C312yes—
457C3×C42—22no—
458C3×C42—32no—
459C3×C42—32no—
460C3×C42—32no—
461C3×C42—32no—
462C3×C42—31no—
463C3×C42—32no—
464C3×C42—31no—
465C3×C42—34no—
466C3×C42—34no—
467C3×C42—31no—
468C3×C42—31no—
469C3×C42—32no—
470C3×C42—32no—
471C3×C42C22×D312yes—
472C3×C42C23×C312yes—
473#217C23×C314yes—
474#217C23×C314yes—
475#217C23×C312yes—
476#217C23×C314yes—
477(C2×D3)⋊C4C23×C314yes—
478(C2×D3)⋊C4C23×C314yes—
479(C2×D3)⋊C4C23×C314yes—
480C4⋊Dic3C23×C314yes—
481C4⋊Dic3C23×C314yes—
482C4⋊Dic3C23×C312yes—
483Dic3⋊C4C23×C314yes—
484Dic3⋊C4C23×C314yes—
485Dic3⋊C4C23×C314yes—
486Dic3⋊C4C23×C314yes—
487Dic3⋊C4C23×C314yes—
488C4×Dic3C23×C312yes—
489C4×Dic3C23×C312yes—
490C4×Dic3C23×C311yescharacteristic
491C4×Dic3C23×C314yes—
492C4×Dic3C23×C311yescharacteristic
493C4×Dic3C23×C314yes—
494C4×Dic3C23×C312yes—
495C4×Dic3C23×C312yes—
496C4×Dic3C23×C312yes—
497C4×Dic3C23×C312yes—
498C4×Dic3C23×C312yes—
499C4×Dic3C23×C311yescharacteristic
500C4×Dic3C23×C311yescharacteristic
501C22×C32—28no—
502C22×C32—22no—
503C22×C32—22no—
504C22×C32—22no—
505C22×C32—24no—
506C22×C32—22no—
507C22×C32C2×#4112yes—
508C22×C32C2×#4114yes—
509C22×C32C2511yescharacteristic
510C2×C3×D3—22no—
511C2×C3×D3—24no—
512C32×C4—24no—
513C32×C4—22no—
514C32×C4—22no—
515C32×C4C2×#4112yes—
516C32×C4C2×#4112yes—
517C3×Dic3—22no—
518C3×Dic3—24no—
519C3×Dic3—22no—
520C3×Dic3—22no—
521C3×Dic3C2×#4114yes—
522C3×Dic3C2×#4114yes—
523C2×#41—34no—
524C2×#41—31no—
525C2×#41C2×C3×D311yescharacteristic
526C23×C4—32no—
527C23×C4C2×C3×D311yescharacteristic
528C4⋊Q8—31no—
529C4⋊Q8—32no—
530#127—31no—
531#126—34no—
532#126—34no—
533#125—34no—
534#125—32no—
535#124—31no—
536#124—31no—
537#124—34no—
538#123—34no—
539#123—32no—
540#123—34no—
541#123C2×C3×D312yes—
542C22⋊Q8—32no—
543C22⋊Q8—34no—
544C22⋊Q8—34no—
545C22⋊Q8C2×C3×D312yes—
546#121—34no—
547#121—34no—
548#121—32no—
549#121C2×C3×D312yes—
550#120—32no—
551#120C2×C3×D312yes—
552C4×Q8—32no—
553C4×Q8—34no—
554C4×Q8—32no—
555C4×Q8—34no—
556C4×D4—34no—
557C4×D4—34no—
558C4×D4—32no—
559C4×D4—34no—
560C4×D4—34no—
561C4×D4—32no—
562C4×D4—34no—
563C4×D4—34no—
564C4×D4—34no—
565C4×D4C2×C3×D314yes—
566#117—31no—
567#117—32no—
568#117—34no—
569#117—34no—
570#117—34no—
571#117—32no—
572#117C2×C3×D311yescharacteristic
573C2×C42—32no—
574C2×C42—32no—
575C2×C42—31no—
576C2×C42—32no—
577C2×C42—32no—
578C2×C42—32no—
579C2×C42—32no—
580C2×C42—31no—
581C2×C42—32no—
582C23×C3—22no—
583C23×C3—24no—
584C23×C3—24no—
585C23×C3—22no—
586C23×C3—21no—
587C23×C3—22no—
588C23×C3—22no—
589C23×C3—32no—
590C23×C3—42no—
591C23×C3—44no—
592C23×C3C23×D312yes—
593C23×C3C23×D311yescharacteristic
594C23×C3C23×D312yes—
595C23×C3C24×C312yes—
596C23×C3C24×C311yescharacteristic
597C23×C3C24×C312yes—
598C22×D3C24×C312yes—
599C3×Q8—22no—
600C3×Q8—22no—
601C3×Q8—42no—
602C3×Q8—68no—
603C3×Q8—62no—
604C3×D4—24no—
605C3×D4—28no—
606C3×D4—28no—
607C3×D4—24no—
608C3×D4—22no—
609C3×D4—22no—
610C3×D4—42no—
611C3×D4—48no—
612C3×D4—44no—
613C3×D4—68no—
614C3×D4—64no—
615C3×D4—68no—
616C3×D4—62no—
617C2×C3×C4—22no—
618C2×C3×C4—22no—
619C2×C3×C4—24no—
620C2×C3×C4—24no—
621C2×C3×C4—24no—
622C2×C3×C4—24no—
623C2×C3×C4—24no—
624C2×C3×C4—24no—
625C2×C3×C4—21no—
626C2×C3×C4—21no—
627C2×C3×C4—24no—
628C2×C3×C4—22no—
629C2×C3×C4—22no—
630C2×C3×C4—24no—
631C2×C3×C4—38no—
632C2×C3×C4—32no—
633C2×C3×C4—32no—
634C2×C3×C4—32no—
635C2×C3×C4—32no—
636C2×C3×C4—32no—
637C2×C3×C4—34no—
638C2×C3×C4—44no—
639C2×C3×C4—44no—
640C2×C3×C4—44no—
641C2×C3×C4—42no—
642C2×C3×C4—68no—
643C2×C3×C4—64no—
644C2×C3×C4—64no—
645C2×C3×C4—64no—
646C2×C3×C4—64no—
647C2×C3×C4—68no—
648C2×C3×C4—64no—
649C2×C3×C4—64no—
650C2×C3×C4#23714yescomplemented
651C2×C3×C4C3×#4114yescomplemented
652C2×C3×C4C23×D312yes—
653C2×C3×C4C23×D312yes—
654C2×C3×C4C23×D314yes—
655C2×C3×C4C23×D311yescharacteristic
656C2×C3×C4C23×D311yescharacteristic
657C2×C3×C4C24×C312yes—
658C2×C3×C4C24×C312yes—
659C2×C3×C4C24×C314yes—
660C2×C3×C4C24×C311yescharacteristic
661C2×C3×C4C24×C311yescharacteristic
662#67—24no—
663#67—28no—
664#67—28no—
665C2×Dic3—24no—
666C2×Dic3—28no—
667C2×Dic3—24no—
668C2×Dic3—24no—
669C2×Dic3—24no—
670C2×Dic3—24no—
671C2×Dic3C3×#4118yescomplemented
672C2×Dic3C24×C312yes—
673C2×Dic3C24×C312yes—
674C2×Dic3C24×C312yes—
675C2×Dic3C24×C314yes—
676C2×Dic3C24×C312yes—
677C2×Dic3C24×C312yes—
678D12—22no—
679C4×D3—24no—
680C4×D3—28no—
681Dic6—22no—
682Dic6—28no—
683C2×C32—22no—
684C2×C32—24no—
685C2×C32—42no—
686C2×C32C22×#4111yescharacteristic
687C2×C32C22×#4112yes—
688C3×D3—42no—
689C24C22×C3×D311yescharacteristic
690#41—24no—
691#41—616no—
692#41—64no—
693C2×Q8—34no—
694C2×Q8—31no—
695C2×Q8C22×C3×D311yescharacteristic
696C2×D4—32no—
697C2×D4—34no—
698C2×D4—34no—
699C2×D4—31no—
700C2×D4C22×C3×D312yes—
701C2×D4C22×C3×D311yescharacteristic
702C2×D4C22×C3×D314yes—
703C22×C4—24no—
704C22×C4—32no—
705C22×C4—32no—
706C22×C4—32no—
707C22×C4—32no—
708C22×C4—32no—
709C22×C4—32no—
710C22×C4—34no—
711C22×C4—34no—
712C22×C4—32no—
713C22×C4—68no—
714C22×C4C22×C3×D312yes—
715C22×C4C22×C3×D312yes—
716C22×C4C22×C3×D311yescharacteristic
717C22×C4C22×C3×D312yes—
718C22×C4C22×C3×D311yescharacteristic
719C4⋊C4—34no—
720C4⋊C4—34no—
721C4⋊C4—32no—
722C4⋊C4—34no—
723C4⋊C4—34no—
724C4⋊C4—34no—
725C4⋊C4—34no—
726C4⋊C4—34no—
727C4⋊C4C22×C3×D314yes—
728C4⋊C4C22×C3×D312yes—
729C22⋊C4—32no—
730C22⋊C4—34no—
731C22⋊C4—34no—
732C22⋊C4—34no—
733C22⋊C4—34no—
734C22⋊C4—34no—
735C22⋊C4—34no—
736C22⋊C4C22×C3×D314yes—
737C22⋊C4C22×C3×D314yes—
738C22⋊C4C22×C3×D312yes—
739C42—31no—
740C42—32no—
741C42—31no—
742C42—32no—
743C42—32no—
744C42—32no—
745C42—32no—
746C42—31no—
747C42—32no—
748C42—31no—
749C42—34no—
750C42—34no—
751C42—32no—
752C42C22×C3×D312yes—
753C22×C3—28no—
754C22×C3—28no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—22no—
760C22×C3—22no—
761C22×C3—22no—
762C22×C3—24no—
763C22×C3—24no—
764C22×C3—22no—
765C22×C3—22no—
766C22×C3—24no—
767C22×C3—21no—
768C22×C3—42no—
769C22×C3—42no—
770C22×C3—42no—
771C22×C3—42no—
772C22×C3—44no—
773C22×C3—48no—
774C22×C3—62no—
775C22×C3—64no—
776C22×C3C2×#23712yes—
777C22×C3D3×#4114yes—
778C22×C3C2×C3×#4112yes—
779C22×C3C2×C3×#4114yes—
780C22×C3C24×D311yescharacteristic
781C22×C3C25×C311yescharacteristic
782C2×D3—22no—
783C2×D3—24no—
784C3×C4—22no—
785C3×C4—22no—
786C3×C4—24no—
787C3×C4—24no—
788C3×C4—22no—
789C3×C4—22no—
790C3×C4—22no—
791C3×C4—22no—
792C3×C4—34no—
793C3×C4—34no—
794C3×C4—42no—
795C3×C4—42no—
796C3×C4—44no—
797C3×C4—62no—
798C3×C4—62no—
799C3×C4—62no—
800C3×C4—64no—
801C3×C4C2×#23712yes—
802C3×C4C2×#23712yes—
803C3×C4C2×C3×#4112yes—
804C3×C4C2×C3×#4112yes—
805Dic3—22no—
806Dic3—24no—
807Dic3—22no—
808Dic3—22no—
809Dic3C2×C3×#4114yes—
810Dic3C2×C3×#4114yes—
811C32#344411yescharacteristic, complemented, Sylow
812C23—22no—
813C23—24no—
814C23—32no—
815C23C23×C3×D312yes—
816C23C23×C3×D311yescharacteristic
817C23C23×C3×D312yes—
818Q8—22no—
819Q8—68no—
820Q8—62no—
821D4—24no—
822D4—28no—
823D4—22no—
824D4—68no—
825D4—64no—
826D4—68no—
827D4—62no—
828C2×C4—22no—
829C2×C4—24no—
830C2×C4—24no—
831C2×C4—24no—
832C2×C4—38no—
833C2×C4—32no—
834C2×C4—32no—
835C2×C4—32no—
836C2×C4—32no—
837C2×C4—32no—
838C2×C4—34no—
839C2×C4—68no—
840C2×C4—64no—
841C2×C4—64no—
842C2×C4—64no—
843C2×C4—64no—
844C2×C4—68no—
845C2×C4—64no—
846C2×C4—64no—
847C2×C4C3×#23714yescomplemented
848C2×C4C23×C3×D312yes—
849C2×C4C23×C3×D312yes—
850C2×C4C23×C3×D314yes—
851C2×C4C23×C3×D311yescharacteristic
852C2×C4C23×C3×D311yescharacteristic
853C2×C3—22no—
854C2×C3—24no—
855C2×C3—22no—
856C2×C3—24no—
857C2×C3—21no—
858C2×C3—22no—
859C2×C3—42no—
860C2×C3—44no—
861C2×C3—42no—
862C2×C3—42no—
863C2×C3—82no—
864C2×C3—122no—
865C2×C3C22×#23711yescharacteristic
866C2×C3C2×D3×#4112yes—
867C2×C3C22×C3×#4111yescharacteristic
868C2×C3C22×C3×#4112yes—
869D3—42no—
870C22—28no—
871C22—22no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—24no—
876C22—62no—
877C22—64no—
878C22C2×C3×#23712yes—
879C22C3×D3×#4114yes—
880C22C24×C3×D311yescharacteristic
881C4—22no—
882C4—22no—
883C4—24no—
884C4—34no—
885C4—34no—
886C4—62no—
887C4—62no—
888C4—62no—
889C4—64no—
890C4C2×C3×#23712yes—
891C4C2×C3×#23712yes—
892C3—21no—
893C3#8601811yescharacteristic, direct product factor
894C3C3×#344411yescharacteristic, complemented
895C2—22no—
896C2—24no—
897C2—42no—
898C2—122no—
899C2C22×C3×#23711yescharacteristic
900C2C2×C3×D3×#4112yes—
subgroupG/H
centerC2×C3×C4C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#525C2
socleC22×C32C25
hypercenterC3×#525D3
hypocenterC3C3×#3444
LCSG ▷ C22×C3 ▷ C3
UCSC1 ◁ C2×C3×C4 ◁ C3×#525

Complements

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

NH ≅ G/Ntype
1. C32×#525C2semidirect
2. C3×#5832C2semidirect
3. C3×Dic3×#41C2semidirect
4. C3×#5791C2semidirect
5. C22×C3×C4×Dic3C2semidirect
6. C3×#5649C2semidirect
7. C3×#5624C2semidirect
8. C3×#5622C2semidirect
9. C3×#5600C2semidirect
10. C3×#5596C2semidirect
11. C3×#5586C2semidirect
12. C3×#5538C2semidirect
13. C3×C4×#237C2semidirect
14. C3×#5522C2semidirect
15. C3×#5517C2semidirect
17. #86018C3direct (N × H)
30. C3×#947C22semidirect
31. C3×Q8×Dic3C22semidirect
32. C3×#944C22semidirect
33. C3×#940C22semidirect
36. C3×#936C22semidirect
40. C3×D4×Dic3C22semidirect
44. C3×C4×#67C22semidirect
46. C3×#926C22semidirect
55. C2×C3×C4×Dic3C22semidirect
56. C3×#898C22semidirect
57. C3×#893C22semidirect
58. C3×#892C22semidirect
59. C3×#890C22semidirect
60. C3×#889C22semidirect
61. C3×#888C22semidirect
62. C3×#887C22semidirect
63. C3×#887C22semidirect
65. C3×#885C22semidirect
68. C3×#67⋊C4C22semidirect
69. C3×#879C22semidirect
73. C3×#877C22semidirect
74. C3×#872C22semidirect
75. C3×C42×D3C22semidirect
76. C3×C4×Dic6C22semidirect
88. C3×#525D3semidirect
89. C3×#525C2×C3semidirect
94. #5832C2×C3semidirect
95. Dic3×#41C2×C3semidirect
96. #5791C2×C3semidirect
97. C22×C4×Dic3C2×C3semidirect
98. #5649C2×C3semidirect
99. #5624C2×C3semidirect
100. #5622C2×C3semidirect
101. #5600C2×C3semidirect
102. #5596C2×C3semidirect
103. #5586C2×C3semidirect
104. #5538C2×C3semidirect
105. C4×#237C2×C3semidirect
106. #5522C2×C3semidirect
107. #5517C2×C3semidirect
252. #947C22×C3semidirect
253. Q8×Dic3C22×C3semidirect
254. #944C22×C3semidirect
255. #940C22×C3semidirect
258. #936C22×C3semidirect
262. D4×Dic3C22×C3semidirect
266. C4×#67C22×C3semidirect
268. #926C22×C3semidirect
277. C2×C4×Dic3C22×C3semidirect
278. #898C22×C3semidirect
279. #893C22×C3semidirect
280. #892C22×C3semidirect
281. #890C22×C3semidirect
282. #889C22×C3semidirect
283. #888C22×C3semidirect
284. #887C22×C3semidirect
285. #887C22×C3semidirect
287. #885C22×C3semidirect
290. #67⋊C4C22×C3semidirect
291. #879C22×C3semidirect
295. #877C22×C3semidirect
296. #872C22×C3semidirect
297. C42×D3C22×C3semidirect
298. C4×Dic6C22×C3semidirect
313. C2×C32×C4#41semidirect
328. C2×C3×Dic3#41semidirect
350. #525C3×D3semidirect
650. C2×C3×C4#237semidirect
651. C2×C3×C4C3×#41semidirect
671. C2×Dic3C3×#41semidirect
811. C32#3444semidirect
847. C2×C4C3×#237semidirect
893. C3#86018direct (N × H)
894. C3C3×#3444semidirect

Maximal subgroups

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

subgroupindex
C32×#5252
C3×#58322
C3×Dic3×#412
C3×#57912
C22×C3×C4×Dic32
C3×#56492
C3×#56242
C3×#56222
C3×#56002
C3×#55962
C3×#55862
C3×#55382
C3×C4×#2372
C3×#55222
C3×#55172
C3×#34443
#860183