Finite Group Databasebeta

← C3×#86019 #11901748

Subgroups — C3×#86019 #11901748

Order 1152.

2245 conjugacy classes of subgroups.

The subgroup lattice has 878 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
5C2×C3×#926C211yesmaximal, characteristic, complemented
6C3×#5665C214yesmaximal, complemented
7C3×#5643C212yesmaximal, complemented
8C3×#5625C212yesmaximal, complemented
9C3×#5619C212yesmaximal, complemented
10C3×#5603C212yesmaximal, complemented
11C3×#5593C214yesmaximal, complemented
12C3×#5557C214yesmaximal, complemented
13C3×#5538C214yesmaximal, complemented
14C3×#5522C211yesmaximal, characteristic, complemented
15C3×#5517C211yesmaximal, characteristic, complemented
16C3×#3455—31nomaximal
17#86019C311yesmaximal, characteristic, direct product factor
18C2×C32×#41C2211yescharacteristic
19C23×C32×C4C2211yescharacteristic
20C2×C3×#235C2211yescharacteristic
21C32×#123C2212yes—
22C32×C22⋊Q8C2212yes—
23C32×#121C2212yes—
24C32×#120C2212yes—
25C32×C4×D4C2214yes—
26C32×#117C2211yescharacteristic
27C3×#953C2212yes—
28C2×C3×#217C2212yes—
29C3×#947C2211yescharacteristic, complemented
30C3×Q8×Dic3C2212yescomplemented
31C3×#944C2211yescharacteristic, complemented
32C3×#940C2211yescharacteristic, complemented
33C3×#939C2214yes—
34C3×#939C2214yes—
35C3×#938C2214yes—
36C3×#936C2214yes—
37C3×#936C2211yescharacteristic, complemented
38C3×#935C2214yes—
39C3×D4×Dic3C2214yes—
40C3×D4×Dic3C2212yescomplemented
41C3×#930C2212yes—
42C3×#929C2212yes—
43C3×C4×#67C2214yes—
44C3×C4×#67C2214yescomplemented
45C3×#926C2211yescharacteristic
46C3×#926C2212yes—
47C3×#926C2212yes—
48C3×#926C2212yes—
49C3×#926C2212yes—
50C3×#926C2212yescomplemented
51C2×C3×C4⋊Dic3C2212yes—
52C3×#924C2212yes—
53C2×C3×C4×Dic3C2211yescharacteristic
54C2×C3×C4×Dic3C2211yescharacteristic
55C2×C3×C4×Dic3C2212yescomplemented
56C3×#898C2214yescomplemented
57C3×#897C2214yescomplemented
58C3×#893C2212yescomplemented
59C3×#890C2212yescomplemented
60C3×#890C2214yescomplemented
61C3×#889C2214yescomplemented
62C3×#888C2212yescomplemented
63C3×#887C2212yescomplemented
64C3×#886C2214yescomplemented
65C3×#885C2214yes—
66C3×#883C2214yes—
67C3×#883C2214yescomplemented
68C3×#67⋊C4C2214yes—
69C3×#879C2214yes—
70C3×#879C2214yes—
71C3×#879C2214yescomplemented
72C3×#878C2214yes—
73C3×#878C2214yescomplemented
74C3×#872C2212yescomplemented
75C3×C42×D3C2212yescomplemented
76C3×C4×Dic6C2214yescomplemented
77C3×#542—32no—
78C3×#542—32no—
79C3×#541—32no—
80C3×#540—32no—
81C3×#539—34no—
82C3×#538—34no—
83C3×#533—31no—
84C3×#532—31no—
85C3×#529—34no—
86C3×#529—34no—
87C3×#525—21no—
88C3×#525—31no—
89C3×#525D311yescharacteristic, complemented
90C3×#525C2×C311yescharacteristic, complemented
91C3×C4×#41—31no—
92C3×C4×#41—31no—
93C2×C3×#117—31no—
94#5832C2×C311yescharacteristic, complemented
95Dic3×#41C2×C311yescharacteristic, complemented
96#5791C2×C311yescharacteristic, complemented
97C2×#926C2×C311yescharacteristic, complemented
98#5665C2×C314yescomplemented
99#5643C2×C312yescomplemented
100#5625C2×C312yescomplemented
101#5619C2×C312yescomplemented
102#5603C2×C312yescomplemented
103#5593C2×C314yescomplemented
104#5557C2×C314yescomplemented
105#5538C2×C314yescomplemented
106#5522C2×C311yescharacteristic, complemented
107#5517C2×C311yescharacteristic, complemented
108C24×C32C2311yescharacteristic
109C32×#41—24no—
110C2×C32×Q8C2311yescharacteristic
111C2×C32×D4C2312yes—
112C2×C32×D4C2311yescharacteristic
113C2×C32×D4C2314yes—
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×Dic3C2312yes—
124C22×C3×Dic3C2314yes—
125C22×C3×Dic3C2312yes—
126C3×#235—24no—
127C2×C3×D12C2311yescharacteristic
128C2×C3×C4×D3C2312yes—
129C2×C3×C4×D3C2314yes—
130C2×C3×Dic6C2311yescharacteristic
131C2×C3×Dic6C2314yes—
132C32×C4⋊C4C2312yes—
133C32×C4⋊C4C2314yes—
134C32×C22⋊C4C2312yes—
135C32×C22⋊C4C2314yes—
136C32×C22⋊C4C2314yes—
137C32×C42C2312yes—
138C3×#217C2312yes—
139C3×#217C2314yes—
140C3×#217C2314yes—
141C3×#217C2312yes—
142C3×#217C2312yes—
143C3×#217C2314yes—
144C3×#217C2312yes—
145C3×#217C2312yes—
146C3×(C2×D3)⋊C4C2314yes—
147C3×(C2×D3)⋊C4C2314yes—
148C3×(C2×D3)⋊C4C2314yes—
149C3×C4⋊Dic3C2314yes—
150C3×C4⋊Dic3C2312yes—
151C3×C4⋊Dic3C2314yes—
152C3×C4⋊Dic3C2312yes—
153C3×C4⋊Dic3C2312yes—
154C3×C4⋊Dic3C2312yes—
155C3×C4⋊Dic3C2312yes—
156C3×Dic3⋊C4C2314yes—
157C3×Dic3⋊C4C2314yes—
158C3×Dic3⋊C4C2314yes—
159C3×Dic3⋊C4C2314yes—
160C3×Dic3⋊C4C2314yes—
161C3×C4×Dic3C2314yes—
162C3×C4×Dic3C2314yes—
163C3×C4×Dic3C2312yes—
164C3×C4×Dic3C2311yescharacteristic
165C3×C4×Dic3C2311yescharacteristic
166C3×C4×Dic3C2311yescharacteristic
167C3×C4×Dic3C2311yescharacteristic
168C3×C4×Dic3C2312yes—
169C3×C4×Dic3C2312yes—
170#3455—31noSylow
171C2×C3×#41—21no—
172C2×C3×#41—31no—
173C2×C3×#41C2×D311yescharacteristic
174C2×C3×#41C22×C311yescharacteristic
175C23×C3×C4—21no—
176C23×C3×C4C2×D311yescharacteristic
177C23×C3×C4C22×C311yescharacteristic
178C2×#235C22×C311yescharacteristic
179C3×C4⋊Q8—31no—
180C3×C4⋊Q8—32no—
181C3×#127—31no—
182C3×#126—34no—
183C3×#126—34no—
184C3×#126—34no—
185C3×#126—34no—
186C3×#125—34no—
187C3×#125—34no—
188C3×#125—32no—
189C3×#124—31no—
190C3×#124—34no—
191C3×#124—31no—
192C3×#124—34no—
193C3×#123—22no—
194C3×#123—34no—
195C3×#123—32no—
196C3×#123—34no—
197C3×#123—34no—
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⋊Q8—34no—
206C3×C22⋊Q8C2×D312yes—
207C3×C22⋊Q8C22×C312yes—
208C3×#121—22no—
209C3×#121—34no—
210C3×#121—34no—
211C3×#121—34no—
212C3×#121—32no—
213C3×#121C2×D312yes—
214C3×#121C22×C312yes—
215C3×#120—22no—
216C3×#120—32no—
217C3×#120C2×D312yes—
218C3×#120C22×C312yes—
219C3×C4×Q8—32no—
220C3×C4×Q8—32no—
221C3×C4×Q8—34no—
222C3×C4×D4—24no—
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×D4C2×D314yes—
230C3×C4×D4C22×C314yes—
231C3×#117—21no—
232C3×#117—32no—
233C3×#117—32no—
234C3×#117—32no—
235C3×#117—32no—
236C3×#117—31no—
237C3×#117—32no—
238C3×#117—32no—
239C3×#117C2×D311yescharacteristic
240C3×#117C22×C311yescharacteristic
241C2×C3×C4⋊C4—32no—
242C2×C3×C22⋊C4—32no—
243C2×C3×C42—31no—
244C2×C3×C42—31no—
245C2×C3×C42—32no—
246C2×C3×C42—32no—
247#953C22×C312yes—
248C2×#217C22×C312yes—
249#947C22×C311yescharacteristic, complemented
250Q8×Dic3C22×C312yescomplemented
251#944C22×C311yescharacteristic, complemented
252#940C22×C311yescharacteristic, complemented
253#939C22×C314yes—
254#939C22×C314yes—
255#938C22×C314yes—
256#936C22×C314yes—
257#936C22×C311yescharacteristic, complemented
258#935C22×C314yes—
259D4×Dic3C22×C314yes—
260D4×Dic3C22×C312yescomplemented
261#930C22×C312yes—
262#929C22×C312yes—
263C4×#67C22×C314yes—
264C4×#67C22×C314yescomplemented
265#926C22×C312yes—
266#926C22×C311yescharacteristic
267#926C22×C312yes—
268#926C22×C312yes—
269#926C22×C312yes—
270#926C22×C312yescomplemented
271C2×C4⋊Dic3C22×C312yes—
272#924C22×C312yes—
273C2×C4×Dic3C22×C311yescharacteristic
274C2×C4×Dic3C22×C311yescharacteristic
275C2×C4×Dic3C22×C312yescomplemented
276#898C22×C314yescomplemented
277#897C22×C314yescomplemented
278#893C22×C312yescomplemented
279#890C22×C314yescomplemented
280#890C22×C312yescomplemented
281#889C22×C314yescomplemented
282#888C22×C312yescomplemented
283#887C22×C312yescomplemented
284#886C22×C314yescomplemented
285#885C22×C314yes—
286#883C22×C314yes—
287#883C22×C314yescomplemented
288#67⋊C4C22×C314yes—
289#879C22×C314yes—
290#879C22×C314yes—
291#879C22×C314yescomplemented
292#878C22×C314yes—
293#878C22×C314yescomplemented
294#872C22×C312yescomplemented
295C42×D3C22×C312yescomplemented
296C4×Dic6C22×C314yescomplemented
297C23×C32—22no—
298C23×C32—42no—
299C23×C32C2412yes—
300C23×C32C2412yes—
301C23×C32C2411yescharacteristic
302C22×C3×D3C2412yes—
303C32×Q8—22no—
304C32×D4—24no—
305C32×D4—22no—
306C32×D4—44no—
307C2×C32×C4—22no—
308C2×C32×C4—24no—
309C2×C32×C4—24no—
310C2×C32×C4—24no—
311C2×C32×C4#4114yes—
312C2×C32×C4C2412yes—
313C2×C32×C4C2414yes—
314C2×C32×C4C2412yes—
315C2×C32×C4C2411yescharacteristic
316C2×C32×C4C2411yescharacteristic
317C3×#67—24no—
318C3×#67—44no—
319C3×#67—44no—
320C2×C3×Dic3—42no—
321C2×C3×Dic3—44no—
322C2×C3×Dic3—42no—
323C2×C3×Dic3C2412yes—
324C2×C3×Dic3C2412yes—
325C2×C3×Dic3C2412yes—
326C2×C3×Dic3C2412yes—
327C2×C3×Dic3C2414yes—
328C2×C3×Dic3C2412yes—
329C3×D12—22no—
330C3×C4×D3—24no—
331C3×C4×D3—44no—
332C3×Dic6—22no—
333C3×Dic6—44no—
334#542—32no—
335#542—32no—
336#541—32no—
337#540—32no—
338#539—34no—
339#538—34no—
340#533—31no—
341#532—31no—
342#529—34no—
343#529—34no—
344#525—31no—
345#525C3×D311yescharacteristic, complemented
346C4×#41—31no—
347C4×#41—31no—
348C2×#117—31no—
349C24×C3—21no—
350C24×C3C22×D311yescharacteristic
351C24×C3C23×C311yescharacteristic
352C3×#41—24no—
353C3×#41—24no—
354C3×#41—44no—
355C3×#41—64no—
356C2×C3×Q8—21no—
357C2×C3×Q8—31no—
358C2×C3×Q8—34no—
359C2×C3×Q8C22×D311yescharacteristic
360C2×C3×Q8C23×C311yescharacteristic
361C2×C3×D4—24no—
362C2×C3×D4—22no—
363C2×C3×D4—21no—
364C2×C3×D4—32no—
365C2×C3×D4—34no—
366C2×C3×D4—34no—
367C2×C3×D4—31no—
368C2×C3×D4C22×D312yes—
369C2×C3×D4C22×D311yescharacteristic
370C2×C3×D4C22×D314yes—
371C2×C3×D4C23×C312yes—
372C2×C3×D4C23×C311yescharacteristic
373C2×C3×D4C23×C314yes—
374C22×C3×C4—24no—
375C22×C3×C4—24no—
376C22×C3×C4—21no—
377C22×C3×C4—22no—
378C22×C3×C4—22no—
379C22×C3×C4—22no—
380C22×C3×C4—21no—
381C22×C3×C4—32no—
382C22×C3×C4—32no—
383C22×C3×C4—34no—
384C22×C3×C4—32no—
385C22×C3×C4—34no—
386C22×C3×C4—44no—
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D312yes—
389C22×C3×C4C22×D312yes—
390C22×C3×C4C22×D312yes—
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C23×C312yes—
393C22×C3×C4C23×C312yes—
394C22×C3×C4C23×C311yescharacteristic
395C22×C3×C4C23×C312yes—
396C22×C3×C4C23×C311yescharacteristic
397C2×#67C23×C312yes—
398C2×#67C23×C314yes—
399C2×#67C23×C314yes—
400C22×Dic3C23×C312yes—
401C22×Dic3C23×C314yes—
402C22×Dic3C23×C312yes—
403#235—24no—
404C2×D12C23×C311yescharacteristic
405C2×C4×D3C23×C312yes—
406C2×C4×D3C23×C314yes—
407C2×Dic6C23×C311yescharacteristic
408C2×Dic6C23×C314yes—
409C3×C4⋊C4—22no—
410C3×C4⋊C4—24no—
411C3×C4⋊C4—34no—
412C3×C4⋊C4—34no—
413C3×C4⋊C4—34no—
414C3×C4⋊C4—34no—
415C3×C4⋊C4—34no—
416C3×C4⋊C4—32no—
417C3×C4⋊C4—32no—
418C3×C4⋊C4—32no—
419C3×C4⋊C4—32no—
420C3×C4⋊C4—32no—
421C3×C4⋊C4—34no—
422C3×C4⋊C4—34no—
423C3×C4⋊C4C22×D312yes—
424C3×C4⋊C4C22×D314yes—
425C3×C4⋊C4C23×C312yes—
426C3×C4⋊C4C23×C314yes—
427C3×C22⋊C4—22no—
428C3×C22⋊C4—24no—
429C3×C22⋊C4—24no—
430C3×C22⋊C4—32no—
431C3×C22⋊C4—32no—
432C3×C22⋊C4—32no—
433C3×C22⋊C4—32no—
434C3×C22⋊C4—32no—
435C3×C22⋊C4—34no—
436C3×C22⋊C4—34no—
437C3×C22⋊C4—34no—
438C3×C22⋊C4—34no—
439C3×C22⋊C4—34no—
440C3×C22⋊C4—34no—
441C3×C22⋊C4C22×D312yes—
442C3×C22⋊C4C22×D314yes—
443C3×C22⋊C4C22×D314yes—
444C3×C22⋊C4C23×C312yes—
445C3×C22⋊C4C23×C314yes—
446C3×C22⋊C4C23×C314yes—
447C3×C42—22no—
448C3×C42—32no—
449C3×C42—31no—
450C3×C42—31no—
451C3×C42—34no—
452C3×C42—34no—
453C3×C42—31no—
454C3×C42—31no—
455C3×C42—32no—
456C3×C42—32no—
457C3×C42C22×D312yes—
458C3×C42C23×C312yes—
459#217C23×C312yes—
460#217C23×C314yes—
461#217C23×C314yes—
462#217C23×C312yes—
463#217C23×C312yes—
464#217C23×C314yes—
465#217C23×C312yes—
466#217C23×C312yes—
467(C2×D3)⋊C4C23×C314yes—
468(C2×D3)⋊C4C23×C314yes—
469(C2×D3)⋊C4C23×C314yes—
470C4⋊Dic3C23×C314yes—
471C4⋊Dic3C23×C312yes—
472C4⋊Dic3C23×C314yes—
473C4⋊Dic3C23×C312yes—
474C4⋊Dic3C23×C312yes—
475C4⋊Dic3C23×C312yes—
476C4⋊Dic3C23×C312yes—
477Dic3⋊C4C23×C314yes—
478Dic3⋊C4C23×C314yes—
479Dic3⋊C4C23×C314yes—
480Dic3⋊C4C23×C314yes—
481Dic3⋊C4C23×C314yes—
482C4×Dic3C23×C312yes—
483C4×Dic3C23×C312yes—
484C4×Dic3C23×C311yescharacteristic
485C4×Dic3C23×C314yes—
486C4×Dic3C23×C311yescharacteristic
487C4×Dic3C23×C314yes—
488C4×Dic3C23×C312yes—
489C4×Dic3C23×C311yescharacteristic
490C4×Dic3C23×C311yescharacteristic
491C22×C32—22no—
492C22×C32—22no—
493C22×C32—22no—
494C22×C32—22no—
495C22×C32—24no—
496C22×C32—22no—
497C22×C32—44no—
498C22×C32C2×#4112yes—
499C22×C32C2511yescharacteristic
500C2×C3×D3—22no—
501C2×C3×D3—24no—
502C32×C4—22no—
503C32×C4—22no—
504C32×C4—24no—
505C32×C4C2×#4112yes—
506C32×C4C2×#4112yes—
507C3×Dic3—22no—
508C3×Dic3—22no—
509C3×Dic3—24no—
510C3×Dic3—22no—
511C3×Dic3—22no—
512C3×Dic3—22no—
513C2×#41—31no—
514C2×#41C2×C3×D311yescharacteristic
515C23×C4C2×C3×D311yescharacteristic
516C4⋊Q8—31no—
517C4⋊Q8—32no—
518#127—31no—
519#126—34no—
520#126—34no—
521#126—34no—
522#126—34no—
523#125—34no—
524#125—34no—
525#125—32no—
526#124—31no—
527#124—34no—
528#124—31no—
529#124—34no—
530#123—34no—
531#123—32no—
532#123—34no—
533#123—34no—
534#123—34no—
535#123C2×C3×D312yes—
536C22⋊Q8—32no—
537C22⋊Q8—34no—
538C22⋊Q8—34no—
539C22⋊Q8—34no—
540C22⋊Q8C2×C3×D312yes—
541#121—34no—
542#121—34no—
543#121—34no—
544#121—32no—
545#121C2×C3×D312yes—
546#120—32no—
547#120C2×C3×D312yes—
548C4×Q8—32no—
549C4×Q8—32no—
550C4×Q8—34no—
551C4×D4—34no—
552C4×D4—32no—
553C4×D4—34no—
554C4×D4—34no—
555C4×D4—32no—
556C4×D4—34no—
557C4×D4C2×C3×D314yes—
558#117—32no—
559#117—32no—
560#117—32no—
561#117—32no—
562#117—31no—
563#117—32no—
564#117—32no—
565#117C2×C3×D311yescharacteristic
566C2×C4⋊C4—32no—
567C2×C22⋊C4—32no—
568C2×C42—31no—
569C2×C42—31no—
570C2×C42—32no—
571C2×C42—32no—
572C23×C3—22no—
573C23×C3—22no—
574C23×C3—22no—
575C23×C3—21no—
576C23×C3—22no—
577C23×C3—32no—
578C23×C3—42no—
579C23×C3—42no—
580C23×C3—42no—
581C23×C3—44no—
582C23×C3C23×D312yes—
583C23×C3C23×D312yes—
584C23×C3C23×D311yescharacteristic
585C23×C3C24×C312yes—
586C23×C3C24×C312yes—
587C23×C3C24×C311yescharacteristic
588C22×D3C24×C312yes—
589C3×Q8—22no—
590C3×Q8—22no—
591C3×Q8—42no—
592C3×Q8—62no—
593C3×Q8—124no—
594C3×D4—24no—
595C3×D4—24no—
596C3×D4—22no—
597C3×D4—22no—
598C3×D4—42no—
599C3×D4—44no—
600C3×D4—44no—
601C3×D4—44no—
602C3×D4—48no—
603C3×D4—64no—
604C3×D4—62no—
605C3×D4—124no—
606C3×D4—124no—
607C2×C3×C4—22no—
608C2×C3×C4—22no—
609C2×C3×C4—24no—
610C2×C3×C4—24no—
611C2×C3×C4—24no—
612C2×C3×C4—24no—
613C2×C3×C4—24no—
614C2×C3×C4—24no—
615C2×C3×C4—21no—
616C2×C3×C4—21no—
617C2×C3×C4—24no—
618C2×C3×C4—22no—
619C2×C3×C4—22no—
620C2×C3×C4—24no—
621C2×C3×C4—32no—
622C2×C3×C4—32no—
623C2×C3×C4—32no—
624C2×C3×C4—32no—
625C2×C3×C4—34no—
626C2×C3×C4—32no—
627C2×C3×C4—44no—
628C2×C3×C4—44no—
629C2×C3×C4—44no—
630C2×C3×C4—42no—
631C2×C3×C4—64no—
632C2×C3×C4—124no—
633C2×C3×C4—122no—
634C2×C3×C4—124no—
635C2×C3×C4—122no—
636C2×C3×C4#23714yes—
637C2×C3×C4C3×#4114yes—
638C2×C3×C4C23×D312yes—
639C2×C3×C4C23×D314yes—
640C2×C3×C4C23×D312yes—
641C2×C3×C4C23×D311yescharacteristic
642C2×C3×C4C23×D311yescharacteristic
643C2×C3×C4C24×C312yes—
644C2×C3×C4C24×C314yes—
645C2×C3×C4C24×C312yes—
646C2×C3×C4C24×C311yescharacteristic
647C2×C3×C4C24×C311yescharacteristic
648#67—24no—
649#67—44no—
650#67—44no—
651C2×Dic3—42no—
652C2×Dic3—44no—
653C2×Dic3—42no—
654C2×Dic3C24×C312yes—
655C2×Dic3C24×C312yes—
656C2×Dic3C24×C312yes—
657C2×Dic3C24×C312yes—
658C2×Dic3C24×C314yes—
659C2×Dic3C24×C312yes—
660D12—22no—
661C4×D3—24no—
662C4×D3—44no—
663Dic6—22no—
664Dic6—44no—
665C2×C32—22no—
666C2×C32—42no—
667C2×C32—42no—
668C2×C32C22×#4111yescharacteristic
669C2×C32#58512yes—
670C3×D3—42no—
671C24C22×C3×D311yescharacteristic
672#41—24no—
673#41—64no—
674C2×Q8—31no—
675C2×Q8—34no—
676C2×Q8C22×C3×D311yescharacteristic
677C2×D4—32no—
678C2×D4—34no—
679C2×D4—34no—
680C2×D4—31no—
681C2×D4C22×C3×D312yes—
682C2×D4C22×C3×D311yescharacteristic
683C2×D4C22×C3×D314yes—
684C22×C4—24no—
685C22×C4—32no—
686C22×C4—32no—
687C22×C4—34no—
688C22×C4—32no—
689C22×C4—34no—
690C22×C4C22×C3×D312yes—
691C22×C4C22×C3×D311yescharacteristic
692C22×C4C22×C3×D312yes—
693C22×C4C22×C3×D312yes—
694C22×C4C22×C3×D311yescharacteristic
695C4⋊C4—32no—
696C4⋊C4—32no—
697C4⋊C4—32no—
698C4⋊C4—32no—
699C4⋊C4—32no—
700C4⋊C4—34no—
701C4⋊C4—34no—
702C4⋊C4—34no—
703C4⋊C4—34no—
704C4⋊C4—34no—
705C4⋊C4—34no—
706C4⋊C4—34no—
707C4⋊C4C22×C3×D312yes—
708C4⋊C4C22×C3×D314yes—
709C22⋊C4—32no—
710C22⋊C4—32no—
711C22⋊C4—32no—
712C22⋊C4—32no—
713C22⋊C4—32no—
714C22⋊C4—34no—
715C22⋊C4—34no—
716C22⋊C4—34no—
717C22⋊C4—34no—
718C22⋊C4—34no—
719C22⋊C4—34no—
720C22⋊C4C22×C3×D312yes—
721C22⋊C4C22×C3×D314yes—
722C22⋊C4C22×C3×D314yes—
723C42—31no—
724C42—31no—
725C42—32no—
726C42—32no—
727C42—32no—
728C42—31no—
729C42—31no—
730C42—34no—
731C42—34no—
732C42C22×C3×D312yes—
733C22×C3—22no—
734C22×C3—22no—
735C22×C3—24no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—24no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—22no—
743C22×C3—24no—
744C22×C3—22no—
745C22×C3—22no—
746C22×C3—22no—
747C22×C3—21no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—44no—
753C22×C3—44no—
754C22×C3—44no—
755C22×C3—48no—
756C22×C3—62no—
757C22×C3—64no—
758C22×C3C2×#23712yes—
759C22×C3C2×C3×#4112yes—
760C22×C3C24×D311yescharacteristic
761C22×C3C25×C311yescharacteristic
762C2×D3—22no—
763C2×D3—24no—
764C3×C4—22no—
765C3×C4—22no—
766C3×C4—24no—
767C3×C4—22no—
768C3×C4—22no—
769C3×C4—24no—
770C3×C4—22no—
771C3×C4—22no—
772C3×C4—42no—
773C3×C4—42no—
774C3×C4—44no—
775C3×C4—62no—
776C3×C4—62no—
777C3×C4—62no—
778C3×C4—62no—
779C3×C4—64no—
780C3×C4—62no—
781C3×C4C2×#23712yes—
782C3×C4C2×#23712yes—
783C3×C4C2×C3×#4112yes—
784C3×C4C2×C3×#4112yes—
785Dic3—22no—
786Dic3—22no—
787Dic3—24no—
788Dic3—22no—
789Dic3—22no—
790Dic3—22no—
791C32#345511yescharacteristic, complemented, Sylow
792C23—22no—
793C23—32no—
794C23—42no—
795C23C23×C3×D312yes—
796C23C23×C3×D312yes—
797C23C23×C3×D311yescharacteristic
798Q8—22no—
799Q8—62no—
800Q8—124no—
801D4—24no—
802D4—22no—
803D4—44no—
804D4—64no—
805D4—62no—
806D4—124no—
807D4—124no—
808C2×C4—22no—
809C2×C4—24no—
810C2×C4—24no—
811C2×C4—24no—
812C2×C4—32no—
813C2×C4—32no—
814C2×C4—32no—
815C2×C4—32no—
816C2×C4—34no—
817C2×C4—32no—
818C2×C4—64no—
819C2×C4—124no—
820C2×C4—122no—
821C2×C4—124no—
822C2×C4—122no—
823C2×C4C3×#23714yes—
824C2×C4C23×C3×D312yes—
825C2×C4C23×C3×D314yes—
826C2×C4C23×C3×D312yes—
827C2×C4C23×C3×D311yescharacteristic
828C2×C4C23×C3×D311yescharacteristic
829C2×C3—22no—
830C2×C3—22no—
831C2×C3—21no—
832C2×C3—22no—
833C2×C3—42no—
834C2×C3—44no—
835C2×C3—42no—
836C2×C3—42no—
837C2×C3—42no—
838C2×C3—42no—
839C2×C3—82no—
840C2×C3—122no—
841C2×C3C22×#23711yescharacteristic
842C2×C3#596412yes—
843C2×C3C22×C3×#4111yescharacteristic
844C2×C3C3×#58512yes—
845D3—42no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—24no—
850C22—22no—
851C22—22no—
852C22—44no—
853C22—62no—
854C22—64no—
855C22C2×C3×#23712yes—
856C22C24×C3×D311yescharacteristic
857C4—22no—
858C4—22no—
859C4—24no—
860C4—62no—
861C4—62no—
862C4—62no—
863C4—62no—
864C4—64no—
865C4—62no—
866C4C2×C3×#23712yes—
867C4C2×C3×#23712yes—
868C3—21no—
869C3#8601911yescharacteristic, direct product factor
870C3C3×#345511yescharacteristic, complemented
871C2—22no—
872C2—42no—
873C2—42no—
874C2—122no—
875C2C22×C3×#23711yescharacteristic
876C2C3×#596412yes—
subgroupG/H
centerC2×C3×C4C23×D3
commutator, cosocleC22×C3C25×C3
FrattiniC22C24×C3×D3
FittingC32×#525C2
socleC22×C32C25
hypercenterC3×#525D3
hypocenterC3C3×#3455
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. C2×C3×#926C2semidirect
6. C3×#5665C2semidirect
7. C3×#5643C2semidirect
8. C3×#5625C2semidirect
9. C3×#5619C2semidirect
10. C3×#5603C2semidirect
11. C3×#5593C2semidirect
12. C3×#5557C2semidirect
13. C3×#5538C2semidirect
14. C3×#5522C2semidirect
15. C3×#5517C2semidirect
17. #86019C3direct (N × H)
29. C3×#947C22semidirect
30. C3×Q8×Dic3C22semidirect
31. C3×#944C22semidirect
32. C3×#940C22semidirect
37. C3×#936C22semidirect
40. C3×D4×Dic3C22semidirect
44. C3×C4×#67C22semidirect
50. C3×#926C22semidirect
55. C2×C3×C4×Dic3C22semidirect
56. C3×#898C22semidirect
57. C3×#897C22semidirect
58. C3×#893C22semidirect
59. C3×#890C22semidirect
60. C3×#890C22semidirect
61. C3×#889C22semidirect
62. C3×#888C22semidirect
63. C3×#887C22semidirect
64. C3×#886C22semidirect
67. C3×#883C22semidirect
71. C3×#879C22semidirect
73. C3×#878C22semidirect
74. C3×#872C22semidirect
75. C3×C42×D3C22semidirect
76. C3×C4×Dic6C22semidirect
89. C3×#525D3semidirect
90. C3×#525C2×C3semidirect
94. #5832C2×C3semidirect
95. Dic3×#41C2×C3semidirect
96. #5791C2×C3semidirect
97. C2×#926C2×C3semidirect
98. #5665C2×C3semidirect
99. #5643C2×C3semidirect
100. #5625C2×C3semidirect
101. #5619C2×C3semidirect
102. #5603C2×C3semidirect
103. #5593C2×C3semidirect
104. #5557C2×C3semidirect
105. #5538C2×C3semidirect
106. #5522C2×C3semidirect
107. #5517C2×C3semidirect
249. #947C22×C3semidirect
250. Q8×Dic3C22×C3semidirect
251. #944C22×C3semidirect
252. #940C22×C3semidirect
257. #936C22×C3semidirect
260. D4×Dic3C22×C3semidirect
264. C4×#67C22×C3semidirect
270. #926C22×C3semidirect
275. C2×C4×Dic3C22×C3semidirect
276. #898C22×C3semidirect
277. #897C22×C3semidirect
278. #893C22×C3semidirect
279. #890C22×C3semidirect
280. #890C22×C3semidirect
281. #889C22×C3semidirect
282. #888C22×C3semidirect
283. #887C22×C3semidirect
284. #886C22×C3semidirect
287. #883C22×C3semidirect
291. #879C22×C3semidirect
293. #878C22×C3semidirect
294. #872C22×C3semidirect
295. C42×D3C22×C3semidirect
296. C4×Dic6C22×C3semidirect
345. #525C3×D3semidirect
791. C32#3455semidirect
869. C3#86019direct (N × H)
870. C3C3×#3455semidirect

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
C2×C3×#9262
C3×#56652
C3×#56432
C3×#56252
C3×#56192
C3×#56032
C3×#55932
C3×#55572
C3×#55382
C3×#55222
C3×#55172
C3×#34553
#860193