Finite Group Databasebeta

← C3×#10595157 #13174718

Subgroups — C3×#10595157 #13174718

Order 1728.

1548 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
1C2×C32×#237C211yesmaximal, characteristic, complemented
2C2×C3×D3×Dic6C211yesmaximal, characteristic, complemented
3C3×#64145C211yesmaximal, characteristic, complemented
4C32×#938C211yesmaximal, characteristic, complemented
5C3×Dic3×#67C212yesmaximal, complemented
6C3×#63970C212yesmaximal, complemented
7C3×#63964C212yesmaximal, complemented
8C3×#63959C212yesmaximal, complemented
9C3×C4×#625C211yesmaximal, characteristic, complemented
10C3×#63857C211yesmaximal, characteristic, complemented
11C3×#63843C211yesmaximal, characteristic, complemented
12C3×#5831—31nomaximal
13C3×#5598—31nomaximal
14#10595157C311yesmaximal, characteristic, direct product factor
15C2×C33×D4C2211yescharacteristic
16C2×C3×#634C2211yescharacteristic
17C2×C32×#67C2212yes—
18C2×C32×#67C2212yes—
19C22×C32×Dic3C2212yes—
20C32×#237—24no—
21C2×C32×C4×D3C2211yescharacteristic
22C2×C32×C4×D3C2211yescharacteristic
23C2×C32×Dic6C2211yescharacteristic
24C2×C3×#627C2212yes—
25C2×C3×#625C2211yescharacteristic
26C2×C3×D3×Dic3C2212yes—
27C3×D3×Dic6—24no—
28C3×#3757C2212yes—
29C3×#3757C2212yes—
30C3×C4×C3⋊Dic3C2211yescharacteristic
31C32×#217C2212yes—
32C32×C4⋊Dic3C2211yescharacteristic
33C3×#3724C2211yescharacteristic
34C3×Dic3⋊Dic3C2212yes—
35C3×Dic3⋊Dic3C2212yes—
36C3×(C2×D3)⋊Dic3C2211yescharacteristic
37C3×(C2×D3)⋊Dic3C2212yes—
38C3×(C2×D3)⋊Dic3C2211yescharacteristic
39C3×Dic32C2212yes—
40C2×C32×#41—31no—
41C2×C3×D3×Q8—31no—
42C2×C3×#237—21no—
43C2×C3×#237D311yescharacteristic, complemented
44C2×C3×#237C2×C311yescharacteristic, complemented
45C22×C3×Dic6—31no—
46C2×D3×Dic6C2×C311yescharacteristic, complemented
47C32×#121—31no—
48#64145C2×C311yescharacteristic, complemented
49C3×Q8×Dic3—31no—
50C3×#939—32no—
51C3×#938—21no—
52C3×#938—32no—
53C3×#938D311yescharacteristic, complemented
54C3×#938C2×C311yescharacteristic, complemented
55C3×#936—31no—
56C3×#936—31no—
57C3×#936—32no—
58C3×#936—61no—
59C3×D4×Dic3—32no—
60C3×C4×#67—32no—
61C3×C4×#67—31no—
62C3×C4×#67—31no—
63C3×#924—32no—
64C3×#924—31no—
65C3×#897—31no—
66C3×#887—31no—
67C3×#885—32no—
68C3×#878—32no—
69Dic3×#67C2×C312yescomplemented
70#63970C2×C312yescomplemented
71#63964C2×C312yescomplemented
72#63959C2×C312yescomplemented
73C4×#625C2×C311yescharacteristic, complemented
74#63857C2×C311yescharacteristic, complemented
75#63843C2×C311yescharacteristic, complemented
76C23×C33C2312yes—
77C22×C32×D3C2311yescharacteristic
78C22×C32×D3C2311yescharacteristic
79C33×D4—22no—
80C2×C33×C4C2311yescharacteristic
81C2×C3×C3⋊Dic3C2311yescharacteristic
82C2×C3×C3⋊Dic3C2311yescharacteristic
83C2×C3×C3⋊Dic3C2312yes—
84C3×#634—22no—
85C32×#67—24no—
86C32×#67—24no—
87C2×C32×Dic3—24no—
88C2×C32×Dic3C2311yescharacteristic
89C2×C32×Dic3C2312yes—
90C2×C32×Dic3C2311yescharacteristic
91C2×C32×Dic3C2312yes—
92C32×C4×D3—22no—
93C32×C4×D3—22no—
94C32×Dic6D414yescomplemented
95C3×#627—24no—
96C3×#625—22no—
97C3×D3×Dic3—24no—
98C3×#548—91no—
99#5831—31no—
100#5598—31no—
101C32×#41—64no—
102C2×C32×Q8—31no—
103C2×C32×D4—21no—
104C2×C32×D4—21no—
105C2×C32×D4—21no—
106C2×C32×D4—32no—
107C2×C32×D4—32no—
108C2×C32×D4—41no—
109C2×C32×D4C2×D311yescharacteristic
110C2×C32×D4C2×D311yescharacteristic
111C2×C32×D4C22×C311yescharacteristic
112C22×C32×C4—32no—
113C22×C32×C4—31no—
114C22×C32×C4—31no—
115C2×#634C22×C311yescharacteristic
116C2×C3×#67—22no—
117C2×C3×#67—22no—
118C2×C3×#67—31no—
119C2×C3×#67—31no—
120C2×C3×#67C2×D312yes—
121C2×C3×#67C2×D312yes—
122C2×C3×#67C22×C312yes—
123C2×C3×#67C22×C312yes—
124C22×C3×Dic3—22no—
125C22×C3×Dic3—32no—
126C22×C3×Dic3C2×D312yes—
127C22×C3×Dic3C22×C312yes—
128C3×D3×Q8—64no—
129C3×#237—28no—
130C3×#237—24no—
131C3×#237—24no—
132C2×C3×C4×D3—21no—
133C2×C3×C4×D3—21no—
134C2×C3×C4×D3—32no—
135C2×C3×C4×D3C2×D311yescharacteristic
136C2×C3×C4×D3C2×D311yescharacteristic
137C2×C3×C4×D3C22×C311yescharacteristic
138C2×C3×C4×D3C22×C311yescharacteristic
139C2×C3×Dic6—21no—
140C2×C3×Dic6—31no—
141C2×C3×Dic6—31no—
142C2×C3×Dic6—32no—
143C2×C3×Dic6—32no—
144C2×C3×Dic6—64no—
145C2×C3×Dic6—61no—
146C2×C3×Dic6C2×D311yescharacteristic
147C2×C3×Dic6C22×C311yescharacteristic
148C2×#627C22×C312yes—
149C2×#625C22×C311yescharacteristic
150C2×D3×Dic3C22×C312yes—
151D3×Dic6—24no—
152C32×C4⋊C4—31no—
153C32×C22⋊C4—32no—
154#3757C22×C312yes—
155#3757C22×C312yes—
156C4×C3⋊Dic3C22×C311yescharacteristic
157C3×#217—22no—
158C3×#217—32no—
159C3×#217—32no—
160C3×#217—32no—
161C3×#217—32no—
162C3×#217—32no—
163C3×#217—31no—
164C3×#217—31no—
165C3×#217—62no—
166C3×#217—62no—
167C3×#217C2×D312yes—
168C3×#217C22×C312yes—
169C3×(C2×D3)⋊C4—31no—
170C3×(C2×D3)⋊C4—32no—
171C3×(C2×D3)⋊C4—31no—
172C3×C4⋊Dic3—21no—
173C3×C4⋊Dic3—32no—
174C3×C4⋊Dic3—32no—
175C3×C4⋊Dic3C2×D311yescharacteristic
176C3×C4⋊Dic3C22×C311yescharacteristic
177C3×Dic3⋊C4—31no—
178C3×Dic3⋊C4—32no—
179C3×Dic3⋊C4—32no—
180C3×Dic3⋊C4—31no—
181C3×C4×Dic3—31no—
182C3×C4×Dic3—31no—
183C3×C4×Dic3—32no—
184C3×C4×Dic3—32no—
185C3×C4×Dic3—61no—
186#3724C22×C311yescharacteristic
187Dic3⋊Dic3C22×C312yes—
188Dic3⋊Dic3C22×C312yes—
189(C2×D3)⋊Dic3C22×C312yes—
190(C2×D3)⋊Dic3C22×C311yescharacteristic
191(C2×D3)⋊Dic3C22×C311yescharacteristic
192Dic32C22×C312yes—
193C22×C33—22no—
194C22×C33—22no—
195C22×C33—22no—
196C22×C33C2411yescharacteristic
197C2×C32×D3—21no—
198C2×C32×D3—21no—
199C2×C32×D3—21no—
200C2×C32×D3—21no—
201C2×C32×D3—21no—
202C2×C32×D3#4112yescomplemented
203C33×C4C2×D412yes—
204C3×C3⋊Dic3—22no—
205C3×C3⋊Dic3—21no—
206C3×C3⋊Dic3—21no—
207C32×Dic3—21no—
208C32×Dic3—21no—
209C32×Dic3—22no—
210C32×Dic3C2×D414yes—
211C2×C3×#41—31no—
212C2×C3×#41—31no—
213C2×C3×#41—61no—
214C22×C3×Q8—91no—
215C2×D3×Q8—31no—
216C2×#237C3×D311yescharacteristic, complemented
217C22×Dic6—31no—
218C3×#124—92no—
219C3×#124—91no—
220C3×C22⋊Q8—92no—
221C3×C22⋊Q8—91no—
222C3×#121—31no—
223C3×#121—31no—
224C3×#121—61no—
225C3×#121—92no—
226C3×C4×Q8—91no—
227C3×C4×D4—91no—
228C3×C4×D4—92no—
229Q8×Dic3—31no—
230#939—32no—
231#938—32no—
232#938C3×D311yescharacteristic, complemented
233#936—31no—
234#936—31no—
235#936—32no—
236#936—61no—
237D4×Dic3—32no—
238C4×#67—32no—
239C4×#67—31no—
240C4×#67—31no—
241#924—32no—
242#924—31no—
243#897—31no—
244#887—31no—
245#885—32no—
246#878—32no—
247C23×C32—22no—
248C23×C32—22no—
249C23×C32—22no—
250C23×C32—31no—
251C23×C32—31no—
252C23×C32—42no—
253C23×C32C22×D312yes—
254C23×C32C22×D312yes—
255C23×C32C23×C312yes—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3C22×D311yescharacteristic
259C22×C3×D3C22×D311yescharacteristic
260C22×C3×D3C23×C311yescharacteristic
261C22×C3×D3C23×C311yescharacteristic
262C32×Q8—34no—
263C32×D4—22no—
264C32×D4—24no—
265C32×D4—22no—
266C32×D4—22no—
267C32×D4—42no—
268C32×D4—42no—
269C32×D4—44no—
270C32×D4—64no—
271C32×D4—64no—
272C2×C32×C4—21no—
273C2×C32×C4—21no—
274C2×C32×C4—21no—
275C2×C32×C4—32no—
276C2×C32×C4—32no—
277C2×C32×C4—31no—
278C2×C32×C4—31no—
279C2×C32×C4—41no—
280C2×C32×C4—64no—
281C2×C32×C4—62no—
282C2×C32×C4—62no—
283C2×C32×C4C22×D311yescharacteristic
284C2×C32×C4C22×D311yescharacteristic
285C2×C32×C4C23×C311yescharacteristic
286C2×C3⋊Dic3C23×C311yescharacteristic
287C2×C3⋊Dic3C23×C312yes—
288C2×C3⋊Dic3C23×C311yescharacteristic
289#634—22no—
290C3×#67—28no—
291C3×#67—24no—
292C3×#67—24no—
293C3×#67—24no—
294C3×#67—24no—
295C3×#67—44no—
296C3×#67—62no—
297C3×#67—62no—
298C2×C3×Dic3—28no—
299C2×C3×Dic3—24no—
300C2×C3×Dic3—24no—
301C2×C3×Dic3—22no—
302C2×C3×Dic3—21no—
303C2×C3×Dic3—22no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—31no—
306C2×C3×Dic3—31no—
307C2×C3×Dic3—31no—
308C2×C3×Dic3—31no—
309C2×C3×Dic3—32no—
310C2×C3×Dic3—32no—
311C2×C3×Dic3—61no—
312C2×C3×Dic3—61no—
313C2×C3×Dic3—62no—
314C2×C3×Dic3—64no—
315C2×C3×Dic3C22×D312yes—
316C2×C3×Dic3C22×D311yescharacteristic
317C2×C3×Dic3C22×D311yescharacteristic
318C2×C3×Dic3C22×D312yes—
319C2×C3×Dic3C23×C312yes—
320C2×C3×Dic3C23×C311yescharacteristic
321C2×C3×Dic3C23×C311yescharacteristic
322C2×C3×Dic3C23×C312yes—
323C3×C4×D3—24no—
324C3×C4×D3—22no—
325C3×C4×D3—22no—
326C3×C4×D3—22no—
327C3×C4×D3—22no—
328C3×C4×D3—42no—
329C3×C4×D3—64no—
330C3×Dic6—24no—
331C3×Dic6—64no—
332C3×Dic6—62no—
333C3×Dic6—62no—
334C3×Dic6—64no—
335C3×Dic6—122no—
336C3×Dic6#6714yescomplemented
337C3×Dic6C3×D414yescomplemented
338#627—24no—
339#625—22no—
340D3×Dic3—24no—
341#548—91noSylow
342C2×C33—42no—
343C2×C33C22×D411yescharacteristic
344C2×C33C2×#4111yescharacteristic
345C2×C332−1+411yescharacteristic
346C32×D3—22no—
347C32×D3—41no—
348C3×#41—64no—
349C3×#41—64no—
350C3×#41—68no—
351C2×C3×Q8—31no—
352C2×C3×Q8—31no—
353C2×C3×Q8—61no—
354C2×C3×Q8—92no—
355C2×C3×Q8—91no—
356C2×C3×Q8—184no—
357C2×C3×D4—21no—
358C2×C3×D4—21no—
359C2×C3×D4—21no—
360C2×C3×D4—32no—
361C2×C3×D4—32no—
362C2×C3×D4—32no—
363C2×C3×D4—32no—
364C2×C3×D4—41no—
365C2×C3×D4—62no—
366C2×C3×D4—62no—
367C2×C3×D4—91no—
368C2×C3×D4D3211yescharacteristic
369C2×C3×D4C2×C3×D311yescharacteristic
370C2×C3×D4C2×C3×D311yescharacteristic
371C22×C3×C4—32no—
372C22×C3×C4—32no—
373C22×C3×C4—31no—
374C22×C3×C4—31no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—61no—
378C22×C3×C4—61no—
379C22×C3×C4—62no—
380C22×C3×C4—92no—
381C2×#67—31no—
382C2×#67—31no—
383C2×#67C2×C3×D312yes—
384C2×#67C2×C3×D312yes—
385C22×Dic3—32no—
386C22×Dic3C2×C3×D312yes—
387D3×Q8—64no—
388#237—24no—
389C2×C4×D3—32no—
390C2×C4×D3C2×C3×D311yescharacteristic
391C2×C4×D3C2×C3×D311yescharacteristic
392C2×Dic6—31no—
393C2×Dic6—31no—
394C2×Dic6—32no—
395C2×Dic6—32no—
396C2×Dic6—61no—
397C2×Dic6—64no—
398C2×Dic6C2×C3×D311yescharacteristic
399C3×C4⋊C4—31no—
400C3×C4⋊C4—31no—
401C3×C4⋊C4—61no—
402C3×C4⋊C4—91no—
403C3×C4⋊C4—92no—
404C3×C4⋊C4—92no—
405C3×C22⋊C4—32no—
406C3×C22⋊C4—32no—
407C3×C22⋊C4—62no—
408C3×C22⋊C4—91no—
409C3×C22⋊C4—91no—
410C3×C22⋊C4—92no—
411C3×C22⋊C4—92no—
412C3×C22⋊C4—92no—
413C3×C42—92no—
414C3×C42—91no—
415#217—32no—
416#217—32no—
417#217—32no—
418#217—32no—
419#217—32no—
420#217—31no—
421#217—31no—
422#217—62no—
423#217—62no—
424#217C2×C3×D312yes—
425(C2×D3)⋊C4—31no—
426(C2×D3)⋊C4—32no—
427(C2×D3)⋊C4—31no—
428C4⋊Dic3—32no—
429C4⋊Dic3—32no—
430C4⋊Dic3C2×C3×D311yescharacteristic
431Dic3⋊C4—31no—
432Dic3⋊C4—32no—
433Dic3⋊C4—32no—
434Dic3⋊C4—31no—
435C4×Dic3—31no—
436C4×Dic3—31no—
437C4×Dic3—32no—
438C4×Dic3—32no—
439C4×Dic3—61no—
440C22×C32—22no—
441C22×C32—24no—
442C22×C32—22no—
443C22×C32—22no—
444C22×C32—22no—
445C22×C32—22no—
446C22×C32—22no—
447C22×C32—22no—
448C22×C32—22no—
449C22×C32—22no—
450C22×C32—21no—
451C22×C32—21no—
452C22×C32—21no—
453C22×C32—32no—
454C22×C32—41no—
455C22×C32—42no—
456C22×C32—42no—
457C22×C32—44no—
458C22×C32—42no—
459C22×C32—42no—
460C22×C32—42no—
461C22×C32—42no—
462C22×C32—42no—
463C22×C32—42no—
464C22×C32—61no—
465C22×C32—61no—
466C22×C32—61no—
467C22×C32—61no—
468C22×C32—61no—
469C22×C32—82no—
470C22×C32—82no—
471C22×C32C23×D311yescharacteristic
472C22×C32C23×D311yescharacteristic
473C22×C32C24×C311yescharacteristic
474C2×C3×D3—21no—
475C2×C3×D3—21no—
476C2×C3×D3—21no—
477C2×C3×D3—21no—
478C2×C3×D3—22no—
479C2×C3×D3—21no—
480C2×C3×D3—21no—
481C2×C3×D3—21no—
482C2×C3×D3—21no—
483C2×C3×D3—21no—
484C2×C3×D3—21no—
485C2×C3×D3—22no—
486C2×C3×D3—41no—
487C2×C3×D3—41no—
488C2×C3×D3—41no—
489C2×C3×D3—41no—
490C2×C3×D3#23712yescomplemented
491C2×C3×D3C3×#4112yescomplemented
492C32×C4—22no—
493C32×C4—22no—
494C32×C4—22no—
495C32×C4—34no—
496C32×C4—42no—
497C32×C4—61no—
498C32×C4—62no—
499C32×C4—61no—
500C32×C4D3×D412yes—
501C32×C4C2×#6712yes—
502C32×C4C2×C3×D412yes—
503C3⋊Dic3—22no—
504C3⋊Dic3—21no—
505C3⋊Dic3—21no—
506C3×Dic3—22no—
507C3×Dic3—21no—
508C3×Dic3—22no—
509C3×Dic3—21no—
510C3×Dic3—21no—
511C3×Dic3—21no—
512C3×Dic3—22no—
513C3×Dic3—24no—
514C3×Dic3—41no—
515C3×Dic3—42no—
516C3×Dic3—62no—
517C3×Dic3—61no—
518C3×Dic3—61no—
519C3×Dic3—61no—
520C3×Dic3—61no—
521C3×Dic3—62no—
522C3×Dic3—122no—
523C3×Dic3—121no—
524C3×Dic3—121no—
525C3×Dic3C2×#6714yes—
526C3×Dic3C2×C3×D414yes—
527C2×#41—31no—
528C22×Q8—91no—
529#124—92no—
530#124—91no—
531C22⋊Q8—92no—
532C22⋊Q8—91no—
533#121—31no—
534#121—92no—
535C4×Q8—91no—
536C4×D4—91no—
537C4×D4—92no—
538C33#54811yescharacteristic, complemented, Sylow
539C23×C3—22no—
540C23×C3—22no—
541C23×C3—22no—
542C23×C3—31no—
543C23×C3—31no—
544C23×C3—31no—
545C23×C3—31no—
546C23×C3—42no—
547C23×C3—61no—
548C23×C3—61no—
549C23×C3C2×D3212yes—
550C23×C3C22×C3×D312yes—
551C23×C3C22×C3×D312yes—
552C22×D3C22×C3×D311yescharacteristic
553C22×D3C22×C3×D311yescharacteristic
554C3×Q8—34no—
555C3×Q8—34no—
556C3×Q8—64no—
557C3×Q8—184no—
558C3×Q8—182no—
559C3×D4—24no—
560C3×D4—22no—
561C3×D4—22no—
562C3×D4—22no—
563C3×D4—42no—
564C3×D4—42no—
565C3×D4—44no—
566C3×D4—64no—
567C3×D4—64no—
568C3×D4—64no—
569C3×D4—64no—
570C3×D4—68no—
571C3×D4—124no—
572C3×D4—182no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—21no—
576C2×C3×C4—32no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—31no—
580C2×C3×C4—31no—
581C2×C3×C4—32no—
582C2×C3×C4—31no—
583C2×C3×C4—31no—
584C2×C3×C4—41no—
585C2×C3×C4—61no—
586C2×C3×C4—62no—
587C2×C3×C4—61no—
588C2×C3×C4—62no—
589C2×C3×C4—64no—
590C2×C3×C4—64no—
591C2×C3×C4—64no—
592C2×C3×C4—68no—
593C2×C3×C4—62no—
594C2×C3×C4—62no—
595C2×C3×C4—62no—
596C2×C3×C4—62no—
597C2×C3×C4—91no—
598C2×C3×C4—91no—
599C2×C3×C4—92no—
600C2×C3×C4—122no—
601C2×C3×C4—184no—
602C2×C3×C4C2×D3211yescharacteristic
603C2×C3×C4C22×C3×D311yescharacteristic
604C2×C3×C4C22×C3×D311yescharacteristic
605#67—24no—
606#67—24no—
607#67—62no—
608#67—62no—
609C2×Dic3—24no—
610C2×Dic3—31no—
611C2×Dic3—31no—
612C2×Dic3—31no—
613C2×Dic3—31no—
614C2×Dic3—32no—
615C2×Dic3—32no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—62no—
619C2×Dic3—64no—
620C2×Dic3C22×C3×D312yes—
621C2×Dic3C22×C3×D311yescharacteristic
622C2×Dic3C22×C3×D311yescharacteristic
623C2×Dic3C22×C3×D312yes—
624C4×D3—22no—
625C4×D3—22no—
626C4×D3—64no—
627Dic6—64no—
628Dic6—62no—
629Dic6—62no—
630Dic6—64no—
631Dic6—122no—
632Dic6C3×#6714yescomplemented
633C2×C32—21no—
634C2×C32—21no—
635C2×C32—21no—
636C2×C32—21no—
637C2×C32—21no—
638C2×C32—21no—
639C2×C32—21no—
640C2×C32—21no—
641C2×C32—21no—
642C2×C32—41no—
643C2×C32—41no—
644C2×C32—41no—
645C2×C32—42no—
646C2×C32—44no—
647C2×C32—42no—
648C2×C32—42no—
649C2×C32—62no—
650C2×C32—82no—
651C2×C32—82no—
652C2×C32—84no—
653C2×C32—121no—
654C2×C32C2×D3×D411yescharacteristic
655C2×C32C2×#23711yescharacteristic
656C2×C32D3×#4111yescharacteristic
657C2×C32#101011yescharacteristic
658C2×C32#101011yescharacteristic
659C2×C32C22×#6711yescharacteristic
660C2×C32C22×C3×D411yescharacteristic
661C2×C32C2×C3×#4111yescharacteristic
662C2×C32C3×2−1+411yescharacteristic
663C3×D3—22no—
664C3×D3—22no—
665C3×D3—42no—
666C3×D3—42no—
667C3×D3—41no—
668C3×D3—41no—
669#41—64no—
670C2×Q8—31no—
671C2×Q8—92no—
672C2×Q8—91no—
673C2×Q8—184no—
674C2×D4—32no—
675C2×D4—32no—
676C2×D4—91no—
677C2×D4C3×D3211yescharacteristic
678C22×C4—32no—
679C22×C4—31no—
680C22×C4—31no—
681C22×C4—92no—
682C4⋊C4—31no—
683C4⋊C4—91no—
684C4⋊C4—92no—
685C4⋊C4—92no—
686C22⋊C4—32no—
687C22⋊C4—91no—
688C22⋊C4—91no—
689C22⋊C4—92no—
690C22⋊C4—92no—
691C22⋊C4—92no—
692C42—92no—
693C42—91no—
694C22×C3—24no—
695C22×C3—22no—
696C22×C3—22no—
697C22×C3—22no—
698C22×C3—22no—
699C22×C3—22no—
700C22×C3—22no—
701C22×C3—22no—
702C22×C3—22no—
703C22×C3—22no—
704C22×C3—21no—
705C22×C3—21no—
706C22×C3—21no—
707C22×C3—32no—
708C22×C3—32no—
709C22×C3—42no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—42no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3—42no—
716C22×C3—42no—
717C22×C3—44no—
718C22×C3—41no—
719C22×C3—62no—
720C22×C3—62no—
721C22×C3—61no—
722C22×C3—61no—
723C22×C3—61no—
724C22×C3—61no—
725C22×C3—61no—
726C22×C3—61no—
727C22×C3—61no—
728C22×C3—61no—
729C22×C3—61no—
730C22×C3—61no—
731C22×C3—82no—
732C22×C3—82no—
733C22×C3—121no—
734C22×C3—121no—
735C22×C3—121no—
736C22×C3—121no—
737C22×C3C22×D3211yescharacteristic
738C22×C3C23×C3×D311yescharacteristic
739C22×C3C23×C3×D311yescharacteristic
740C2×D3—21no—
741C2×D3—21no—
742C2×D3—21no—
743C2×D3—21no—
744C2×D3—21no—
745C2×D3C3×#23712yescomplemented
746C3×C4—22no—
747C3×C4—22no—
748C3×C4—22no—
749C3×C4—34no—
750C3×C4—34no—
751C3×C4—42no—
752C3×C4—64no—
753C3×C4—62no—
754C3×C4—62no—
755C3×C4—61no—
756C3×C4—61no—
757C3×C4—61no—
758C3×C4—62no—
759C3×C4—61no—
760C3×C4—121no—
761C3×C4—122no—
762C3×C4—181no—
763C3×C4—181no—
764C3×C4—182no—
765C3×C4D3×#6712yes—
766C3×C4C3×D3×D412yes—
767C3×C4C2×C3×#6712yes—
768Dic3—21no—
769Dic3—22no—
770Dic3—21no—
771Dic3—62no—
772Dic3—61no—
773Dic3—61no—
774Dic3—61no—
775Dic3—61no—
776Dic3—62no—
777Dic3—122no—
778Dic3—121no—
779Dic3—121no—
780Dic3C2×C3×#6714yes—
781C32—21no—
782C32—21no—
783C32—21no—
784C32—41no—
785C32#559811yescharacteristic, complemented
786C32#583111yescharacteristic, complemented
787C32C3×#54811yescharacteristic, complemented
788C23—31no—
789C23—31no—
790C23C2×C3×D3212yes—
791Q8—34no—
792Q8—184no—
793Q8—182no—
794D4—22no—
795D4—64no—
796D4—64no—
797D4—182no—
798C2×C4—32no—
799C2×C4—32no—
800C2×C4—31no—
801C2×C4—31no—
802C2×C4—64no—
803C2×C4—62no—
804C2×C4—62no—
805C2×C4—91no—
806C2×C4—91no—
807C2×C4—92no—
808C2×C4—184no—
809C2×C4C2×C3×D3211yescharacteristic
810C2×C3—21no—
811C2×C3—21no—
812C2×C3—21no—
813C2×C3—21no—
814C2×C3—21no—
815C2×C3—21no—
816C2×C3—21no—
817C2×C3—21no—
818C2×C3—21no—
819C2×C3—44no—
820C2×C3—42no—
821C2×C3—42no—
822C2×C3—42no—
823C2×C3—41no—
824C2×C3—41no—
825C2×C3—41no—
826C2×C3—62no—
827C2×C3—62no—
828C2×C3—82no—
829C2×C3—82no—
830C2×C3—84no—
831C2×C3—122no—
832C2×C3—122no—
833C2×C3—121no—
834C2×C3—121no—
835C2×C3#6430911yescharacteristic
836C2×C3D3×#23711yescharacteristic
837C2×C3C2×D3×#6711yescharacteristic
838C2×C3C2×C3×D3×D411yescharacteristic
839C2×C3C2×C3×#23711yescharacteristic
840C2×C3C3×D3×#4111yescharacteristic
841C2×C3C3×#101011yescharacteristic
842C2×C3C3×#101011yescharacteristic
843C2×C3C22×C3×#6711yescharacteristic
844D3—22no—
845D3—41no—
846C22—22no—
847C22—22no—
848C22—22no—
849C22—32no—
850C22—61no—
851C22—61no—
852C22—61no—
853C22—61no—
854C22—61no—
855C22C22×C3×D3211yescharacteristic
856C4—34no—
857C4—61no—
858C4—61no—
859C4—62no—
860C4—182no—
861C4—181no—
862C4—181no—
863C4C3×D3×#6712yes—
864C3—21no—
865C3—21no—
866C3—21no—
867C3—41no—
868C3#1059515711yescharacteristic, direct product factor
869C3C3×#559811yescharacteristic, complemented
870C3C3×#583111yescharacteristic, complemented
871C2—42no—
872C2—62no—
873C2—121no—
874C2C3×#6430911yescharacteristic
875C2C3×D3×#23711yescharacteristic
876C2C2×C3×D3×#6711yescharacteristic
subgroupG/H
centerC22×C3C22×D32
commutator, cosocleC22×C32C24×C3
FrattiniC22C22×C3×D32
FittingC2×C33×D4C22
socleC22×C33C24
hypercenterC2×C3×D4D32
hypocenterC32C3×#548
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C3 ◁ C2×C3×D4

Complements

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

NH ≅ G/Ntype
1. C2×C32×#237C2semidirect
2. C2×C3×D3×Dic6C2semidirect
3. C3×#64145C2semidirect
4. C32×#938C2semidirect
5. C3×Dic3×#67C2semidirect
6. C3×#63970C2semidirect
7. C3×#63964C2semidirect
8. C3×#63959C2semidirect
9. C3×C4×#625C2semidirect
10. C3×#63857C2semidirect
11. C3×#63843C2semidirect
14. #10595157C3direct (N × H)
43. C2×C3×#237D3semidirect
44. C2×C3×#237C2×C3semidirect
46. C2×D3×Dic6C2×C3semidirect
48. #64145C2×C3semidirect
53. C3×#938D3semidirect
54. C3×#938C2×C3semidirect
69. Dic3×#67C2×C3semidirect
70. #63970C2×C3semidirect
71. #63964C2×C3semidirect
72. #63959C2×C3semidirect
73. C4×#625C2×C3semidirect
74. #63857C2×C3semidirect
75. #63843C2×C3semidirect
94. C32×Dic6D4semidirect
202. C2×C32×D3#41semidirect
216. C2×#237C3×D3semidirect
232. #938C3×D3semidirect
336. C3×Dic6#67semidirect
337. C3×Dic6C3×D4semidirect
490. C2×C3×D3#237semidirect
491. C2×C3×D3C3×#41semidirect
538. C33#548semidirect
632. Dic6C3×#67semidirect
745. C2×D3C3×#237semidirect
785. C32#5598semidirect
786. C32#5831semidirect
787. C32C3×#548semidirect
868. C3#10595157direct (N × H)
869. C3C3×#5598semidirect
870. C3C3×#5831semidirect

Maximal subgroups

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

subgroupindex
C2×C32×#2372
C2×C3×D3×Dic62
C3×#641452
C32×#9382
C3×Dic3×#672
C3×#639702
C3×#639642
C3×#639592
C3×C4×#6252
C3×#638572
C3×#638432
C3×#58313
C3×#55983
#105951573