Finite Group Databasebeta

← #13172885

Subgroups — #13172885

Order 1728.

1558 conjugacy classes of subgroups.

The subgroup lattice has 1188 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#6293C211yesmaximal, characteristic, complemented
2C2×#88961C211yesmaximal, characteristic, complemented
3#11723726C211yesmaximal, characteristic, complemented
4#11723637C211yesmaximal, characteristic, complemented
5#67⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
6C3×#63980C211yesmaximal, characteristic, complemented
7C3×#63978C211yesmaximal, characteristic, complemented
8C3×Dic3×#67C211yesmaximal, characteristic, complemented
9#11723009C211yesmaximal, characteristic, complemented
10#11723004C211yesmaximal, characteristic, complemented
11#11723002C211yesmaximal, characteristic, complemented
12#11722984C211yesmaximal, characteristic, complemented
13#11722980C211yesmaximal, characteristic, complemented
14#11722971C211yesmaximal, characteristic, complemented
15#11722943C211yesmaximal, characteristic, complemented
16#10595142—31nomaximal
17#10595141—31nomaximal
18#10594918—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C2×C32×#67C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×#6294C2211yescharacteristic
26C2×#6293—24no—
27C2×#6293C2211yescharacteristic
28C2×#6293C2211yescharacteristic
29C2×#6293C2211yescharacteristic
30C2×#6293C2211yescharacteristic
31C2×#6290C2211yescharacteristic
32C2×D3×C3⋊Dic3C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic
34C2×C3×#625C2211yescharacteristic
35C2×C3×D3×Dic3C2211yescharacteristic
36#88961—24no—
37C3×#3757C2211yescharacteristic
38#88815C2211yescharacteristic
39#88814C2211yescharacteristic
40#88813C2211yescharacteristic
41#88806C2211yescharacteristic
42Dic3⋊(C3⋊Dic3)C2211yescharacteristic
43#88803C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
45(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
46Dic3×C3⋊Dic3C2211yescharacteristic
47C3×#3724C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×#3722C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×Dic32C2211yescharacteristic
56C22×#634—31no—
57C22×#627—31no—
58C22×#627—31no—
59C22×#627—61no—
60C2×#3805—31no—
61C2×#3804—31no—
62C2×#3795—31no—
63#64148—31no—
64D4×C3⋊Dic3—31no—
65C3×#939—31no—
66C3×#939—31no—
67C3×#939—31no—
68C3×D4×Dic3—31no—
69C3×#930—31no—
70C3×C4×#67—31no—
71#63982—31no—
72#63980—31no—
73#63980—31no—
74#63980—61no—
75#63980D311yescharacteristic, complemented
76#63978D311yescharacteristic, complemented
77#67⋊Dic3—31no—
78#67⋊Dic3—31no—
79#67⋊Dic3—31no—
80#67⋊Dic3—61no—
81Dic3×#67—31no—
82Dic3×#67D311yescharacteristic, complemented
83#63964—31no—
84#63959—31no—
85#63959—31no—
86#63959—31no—
87#63953—31no—
88#63952—31no—
89#63915—31no—
90#63913—31no—
91#63913—31no—
92#63899—31no—
93#63896—31no—
94#63896—31no—
95#63895—31no—
96#63893—31no—
97#63893—31no—
98#63860—31no—
99#63857—31no—
100#63852—31no—
101#63844—31no—
102#63838—31no—
103#63837—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)—22no—
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C3×#638—22no—
112C2×C3×C3⋊Dic3—22no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C32×#67—22no—
119C32×#67—22no—
120C2×C32×Dic3—22no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6294—22no—
126#6293—22no—
127#6293—22no—
128#6293—22no—
129#6293D414yescomplemented
130#6290—22no—
131D3×C3⋊Dic3—22no—
132C3×#626—22no—
133C3×#625—22no—
134C3×D3×Dic3—22no—
135#5598—91no—
136#5598—91no—
137#5552—91no—
138C2×C32×D4—31no—
139C2×C32×D4—31no—
140C22×C32×C4—31no—
141C2×#638—31no—
142C2×#638C2×D311yescharacteristic
143C22×C3⋊Dic3—31no—
144C22×C3⋊Dic3—31no—
145C22×C3⋊Dic3—31no—
146C22×C3⋊Dic3—31no—
147C22×C3⋊Dic3—61no—
148C22×C3⋊Dic3—61no—
149C22×C3⋊Dic3—61no—
150C22×C3⋊Dic3—121no—
151C22×C3⋊Dic3C2×D311yescharacteristic
152C2×#634—31no—
153C2×#634—31no—
154C2×#634—31no—
155C2×#634—31no—
156C2×#634—64no—
157C2×C3×#67—21no—
158C2×C3×#67—21no—
159C2×C3×#67—31no—
160C2×C3×#67—31no—
161C2×C3×#67—31no—
162C2×C3×#67—31no—
163C2×C3×#67—31no—
164C2×C3×#67—61no—
165C2×C3×#67C2×D311yescharacteristic
166C2×C3×#67C2×D311yescharacteristic
167C2×C3×#67C2×D311yescharacteristic
168C2×C3×#67C2×D311yescharacteristic
169C22×C3×Dic3—21no—
170C22×C3×Dic3—31no—
171C22×C3×Dic3—31no—
172C22×C3×Dic3—31no—
173C22×C3×Dic3—61no—
174C22×C3×Dic3C2×D311yescharacteristic
175C22×C3×Dic3C2×D311yescharacteristic
176C2×C3×D12—31no—
177C2×C3×C4×D3—31no—
178C2×#627—31no—
179C2×#627—31no—
180C2×#627—31no—
181C2×#627—31no—
182C2×#627—31no—
183C2×#627—31no—
184C2×#627—31no—
185C2×#627—31no—
186C2×#627—64no—
187C2×#627—64no—
188C2×#627—61no—
189C2×#627—61no—
190C2×#627—61no—
191C2×#627—61no—
192C2×#627—68no—
193C2×#626C2×D311yescharacteristic
194C2×#625—31no—
195C2×#625—31no—
196C2×#625—61no—
197C2×#625C2×D311yescharacteristic
198C2×#624—31no—
199#3805—64no—
200#3804—64no—
201C2×D3×Dic3—31no—
202C2×D3×Dic3—31no—
203C2×D3×Dic3—31no—
204C2×D3×Dic3—31no—
205C2×D3×Dic3—61no—
206C2×D3×Dic3C2×D311yescharacteristic
207#3795—64no—
208#3757—31no—
209#3757—31no—
210#3757C2×D311yescharacteristic
211#3752—31no—
212C4⋊(C3⋊Dic3)—31no—
213#3750—31no—
214C4×C3⋊Dic3—31no—
215C3×#217—31no—
216C3×#217—31no—
217C3×#217—31no—
218C3×#217—31no—
219C3×#217—31no—
220C3×#217—31no—
221C3×#217—61no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—31no—
225C3×(C2×D3)⋊C4—31no—
226C3×(C2×D3)⋊C4—31no—
227C3×(C2×D3)⋊C4—31no—
228C3×C4⋊Dic3—31no—
229C3×C4⋊Dic3—31no—
230C3×Dic3⋊C4—31no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—31no—
233C3×Dic3⋊C4—31no—
234C3×C4×Dic3—31no—
235C3×C4×Dic3—31no—
236#3724—31no—
237#3724—31no—
238#3724—31no—
239#3724—61no—
240#3724C2×D311yescharacteristic
241Dic3⋊Dic3—31no—
242Dic3⋊Dic3—31no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—61no—
246Dic3⋊Dic3C2×D311yescharacteristic
247Dic3⋊Dic3C2×D311yescharacteristic
248#3722—31no—
249#3722C2×D311yescharacteristic
250(C2×D3)⋊Dic3—31no—
251(C2×D3)⋊Dic3—31no—
252(C2×D3)⋊Dic3—31no—
253(C2×D3)⋊Dic3—31no—
254(C2×D3)⋊Dic3—31no—
255(C2×D3)⋊Dic3—31no—
256(C2×D3)⋊Dic3—31no—
257(C2×D3)⋊Dic3—31no—
258(C2×D3)⋊Dic3—61no—
259(C2×D3)⋊Dic3—61no—
260(C2×D3)⋊Dic3—61no—
261(C2×D3)⋊Dic3C2×D311yescharacteristic
262(C2×D3)⋊Dic3C2×D311yescharacteristic
263(C2×D3)⋊Dic3C2×D311yescharacteristic
264(C2×D3)⋊Dic3C2×D311yescharacteristic
265Dic32—31no—
266Dic32—31no—
267Dic32—31no—
268Dic32—31no—
269Dic32—31no—
270Dic32—61no—
271Dic32C2×D311yescharacteristic
272C22×C33—21no—
273C22×C33—21no—
274C22×C33#4112yescomplemented
275C22×C33C2411yescharacteristic
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3—21no—
279C2×C32×D3—21no—
280C2×C32×D3—21no—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C2×C32×D3—21no—
285C3⋊(C3⋊Dic3)—21no—
286C3⋊(C3⋊Dic3)C2×D412yes—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C3×C3⋊Dic3—21no—
291C3×C3⋊Dic3C2×D412yes—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C32×Dic3—21no—
295C32×Dic3C2×D412yes—
296C2×#237—91no—
297C2×#237—91no—
298C2×#235—91no—
299C22×Dic6—91no—
300C22×Dic6—91no—
301C22×Dic6—91no—
302C22×Dic6—181no—
303C3×#121—91no—
304C3×#121—91no—
305C3×C4×D4—91no—
306#939—31no—
307#939—31no—
308#939—31no—
309#939—91no—
310#939—91no—
311#939—91no—
312#939—181no—
313#936—91no—
314#936—91no—
315D4×Dic3—31no—
316D4×Dic3—91no—
317D4×Dic3—91no—
318D4×Dic3—91no—
319D4×Dic3—181no—
320#930—31no—
321C4×#67—31no—
322C4×#67—91no—
323#924—91no—
324#897—91no—
325#897—91no—
326#896—91no—
327#896—91no—
328#887—91no—
329#887—91no—
330#885—91no—
331#885—91no—
332#885—91no—
333#885—91no—
334#885—91no—
335#885—91no—
336#67⋊C4—91no—
337#67⋊C4—91no—
338#878—91no—
339#878—91no—
340#878—91no—
341#878—91no—
342#875—91no—
343C4×Dic6—91no—
344C23×C32—21no—
345C23×C32—21no—
346C23×C32—21no—
347C23×C32—31no—
348C23×C32—31no—
349C23×C32—41no—
350C23×C32C22×D311yescharacteristic
351C23×C32C22×D311yescharacteristic
352C23×C32C22×D311yescharacteristic
353C22×C3⋊D3C22×D311yescharacteristic
354C22×C3×D3—21no—
355C22×C3×D3—21no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—61no—
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C22×C3×D3C22×D311yescharacteristic
363C32×D4—62no—
364C32×D4—62no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—62no—
370#638—22no—
371#638—62no—
372C2×C3⋊Dic3—22no—
373C2×C3⋊Dic3—31no—
374C2×C3⋊Dic3—31no—
375C2×C3⋊Dic3—31no—
376C2×C3⋊Dic3—31no—
377C2×C3⋊Dic3—31no—
378C2×C3⋊Dic3—31no—
379C2×C3⋊Dic3—61no—
380C2×C3⋊Dic3—61no—
381C2×C3⋊Dic3—61no—
382C2×C3⋊Dic3—61no—
383C2×C3⋊Dic3—61no—
384C2×C3⋊Dic3—61no—
385C2×C3⋊Dic3—62no—
386C2×C3⋊Dic3—62no—
387C2×C3⋊Dic3—62no—
388C2×C3⋊Dic3—62no—
389C2×C3⋊Dic3—64no—
390C2×C3⋊Dic3—121no—
391C2×C3⋊Dic3—121no—
392C2×C3⋊Dic3—122no—
393C2×C3⋊Dic3—122no—
394C2×C3⋊Dic3—124no—
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400#634—34no—
401#634—62no—
402#634—62no—
403#634—62no—
404C3×#67—24no—
405C3×#67—22no—
406C3×#67—22no—
407C3×#67—22no—
408C3×#67—22no—
409C3×#67—42no—
410C3×#67—62no—
411C3×#67—62no—
412C3×#67—62no—
413C3×#67—62no—
414C3×#67—62no—
415C3×#67—122no—
416C2×C3×Dic3—24no—
417C2×C3×Dic3—22no—
418C2×C3×Dic3—22no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—21no—
421C2×C3×Dic3—21no—
422C2×C3×Dic3—21no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—31no—
425C2×C3×Dic3—31no—
426C2×C3×Dic3—31no—
427C2×C3×Dic3—31no—
428C2×C3×Dic3—31no—
429C2×C3×Dic3—31no—
430C2×C3×Dic3—31no—
431C2×C3×Dic3—31no—
432C2×C3×Dic3—31no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—61no—
436C2×C3×Dic3—61no—
437C2×C3×Dic3—61no—
438C2×C3×Dic3—62no—
439C2×C3×Dic3—62no—
440C2×C3×Dic3—64no—
441C2×C3×Dic3—62no—
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C2×C3×Dic3C22×D311yescharacteristic
448C2×C3×Dic3C22×D311yescharacteristic
449C2×C3×Dic3C22×D311yescharacteristic
450C3×D12—62no—
451C3×C4×D3—62no—
452#627—34no—
453#627—34no—
454#627—64no—
455#627—62no—
456#627—62no—
457#627—62no—
458#627—62no—
459#627—64no—
460#627—64no—
461#627—64no—
462#627—62no—
463#627—62no—
464#626—22no—
465#625—22no—
466#625—62no—
467#625—62no—
468#625—122no—
469#624—62no—
470D3×Dic3—22no—
471D3×Dic3—62no—
472D3×Dic3—62no—
473D3×Dic3—62no—
474D3×Dic3—62no—
475D3×Dic3—122no—
476#548—271noSylow
477C2×C33—22no—
478C2×C33C22×D411yescharacteristic
479C2×C33C2×#4111yescharacteristic
480C2×C332−1+411yescharacteristic
481C3×C3⋊D3—41no—
482C32×D3—41no—
483C32×D3—41no—
484C2×C3×D4—31no—
485C2×C3×D4—31no—
486C2×C3×D4—31no—
487C2×C3×D4—31no—
488C2×C3×D4—61no—
489C2×C3×D4—61no—
490C2×C3×D4—91no—
491C2×C3×D4—91no—
492C2×C3×D4—91no—
493C22×C3×C4—31no—
494C22×C3×C4—31no—
495C22×C3×C4—61no—
496C22×C3×C4—91no—
497C22×C3×C4—91no—
498C2×#67—31no—
499C2×#67—31no—
500C2×#67—31no—
501C2×#67—31no—
502C2×#67—31no—
503C2×#67—61no—
504C2×#67—91no—
505C2×#67—91no—
506C2×#67—91no—
507C2×#67—181no—
508C2×#67D3211yescharacteristic
509C2×#67D3211yescharacteristic
510C22×Dic3—31no—
511C22×Dic3—31no—
512C22×Dic3—31no—
513C22×Dic3—61no—
514C22×Dic3—91no—
515C22×Dic3—91no—
516C22×Dic3—91no—
517C22×Dic3—91no—
518C22×Dic3—91no—
519C22×Dic3—91no—
520C22×Dic3—181no—
521C22×Dic3—181no—
522C22×Dic3—181no—
523C22×Dic3—181no—
524C22×Dic3—361no—
525C22×Dic3D3211yescharacteristic
526#237—184no—
527#237—184no—
528#235—184no—
529C2×D12—31no—
530C2×C4×D3—31no—
531C2×C4×D3—91no—
532C2×C4×D3—91no—
533C2×C4×D3—91no—
534C2×Dic6—91no—
535C2×Dic6—91no—
536C2×Dic6—91no—
537C2×Dic6—91no—
538C2×Dic6—91no—
539C2×Dic6—91no—
540C2×Dic6—91no—
541C2×Dic6—91no—
542C2×Dic6—91no—
543C2×Dic6—91no—
544C2×Dic6—91no—
545C2×Dic6—91no—
546C2×Dic6—181no—
547C2×Dic6—181no—
548C2×Dic6—181no—
549C2×Dic6—181no—
550C2×Dic6—184no—
551C2×Dic6—184no—
552C2×Dic6—184no—
553C2×Dic6—188no—
554C3×C4⋊C4—91no—
555C3×C4⋊C4—91no—
556C3×C4⋊C4—91no—
557C3×C22⋊C4—91no—
558C3×C22⋊C4—91no—
559C3×C22⋊C4—91no—
560C3×C22⋊C4—91no—
561C3×C22⋊C4—91no—
562C3×C22⋊C4—91no—
563C3×C42—91no—
564#217—31no—
565#217—31no—
566#217—31no—
567#217—31no—
568#217—31no—
569#217—31no—
570#217—61no—
571#217—91no—
572#217—91no—
573#217—91no—
574#217—91no—
575#217—91no—
576#217—91no—
577#217—181no—
578#217—181no—
579(C2×D3)⋊C4—31no—
580(C2×D3)⋊C4—31no—
581(C2×D3)⋊C4—31no—
582(C2×D3)⋊C4—31no—
583(C2×D3)⋊C4—31no—
584(C2×D3)⋊C4—31no—
585(C2×D3)⋊C4—91no—
586(C2×D3)⋊C4—91no—
587(C2×D3)⋊C4—91no—
588(C2×D3)⋊C4—91no—
589(C2×D3)⋊C4—91no—
590(C2×D3)⋊C4—91no—
591(C2×D3)⋊C4—181no—
592C4⋊Dic3—31no—
593C4⋊Dic3—31no—
594C4⋊Dic3—91no—
595C4⋊Dic3—91no—
596C4⋊Dic3—91no—
597C4⋊Dic3—181no—
598Dic3⋊C4—31no—
599Dic3⋊C4—31no—
600Dic3⋊C4—31no—
601Dic3⋊C4—31no—
602Dic3⋊C4—91no—
603Dic3⋊C4—91no—
604Dic3⋊C4—91no—
605Dic3⋊C4—91no—
606Dic3⋊C4—91no—
607Dic3⋊C4—91no—
608Dic3⋊C4—181no—
609C4×Dic3—31no—
610C4×Dic3—31no—
611C4×Dic3—91no—
612C4×Dic3—91no—
613C4×Dic3—91no—
614C4×Dic3—91no—
615C4×Dic3—91no—
616C4×Dic3—91no—
617C4×Dic3—181no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—22no—
621C22×C32—22no—
622C22×C32—21no—
623C22×C32—21no—
624C22×C32—21no—
625C22×C32—21no—
626C22×C32—21no—
627C22×C32—21no—
628C22×C32—21no—
629C22×C32—22no—
630C22×C32—22no—
631C22×C32—22no—
632C22×C32—42no—
633C22×C32—41no—
634C22×C32—41no—
635C22×C32—41no—
636C22×C32—41no—
637C22×C32—41no—
638C22×C32—42no—
639C22×C32—42no—
640C22×C32—61no—
641C22×C32—61no—
642C22×C32—61no—
643C22×C32—61no—
644C22×C32—61no—
645C22×C32—61no—
646C22×C32#23512yescomplemented
647C22×C32#23712yescomplemented
648C22×C32#23712yescomplemented
649C22×C32C23×D311yescharacteristic
650C22×C32C23×D311yescharacteristic
651C22×C32C23×D311yescharacteristic
652C2×C3⋊D3—21no—
653C2×C3⋊D3—21no—
654C2×C3⋊D3—21no—
655C2×C3×D3—22no—
656C2×C3×D3—21no—
657C2×C3×D3—21no—
658C2×C3×D3—21no—
659C2×C3×D3—21no—
660C2×C3×D3—21no—
661C2×C3×D3—21no—
662C2×C3×D3—21no—
663C2×C3×D3—21no—
664C2×C3×D3—21no—
665C2×C3×D3—21no—
666C2×C3×D3—21no—
667C2×C3×D3—21no—
668C2×C3×D3—41no—
669C2×C3×D3—41no—
670C2×C3×D3—41no—
671C2×C3×D3—41no—
672C2×C3×D3—41no—
673C2×C3×D3—61no—
674C2×C3×D3—61no—
675C2×C3×D3—61no—
676C2×C3×D3—61no—
677C2×C3×D3—61no—
678C2×C3×D3—61no—
679C2×C3×D3—121no—
680C2×C3×D3—121no—
681C2×C3×D3—121no—
682C32×C4—32no—
683C32×C4—61no—
684C32×C4—61no—
685C32×C4—61no—
686C3⋊Dic3—21no—
687C3⋊Dic3—21no—
688C3⋊Dic3—21no—
689C3⋊Dic3—21no—
690C3⋊Dic3—32no—
691C3⋊Dic3—32no—
692C3⋊Dic3—32no—
693C3⋊Dic3—62no—
694C3⋊Dic3—62no—
695C3⋊Dic3—62no—
696C3⋊Dic3—61no—
697C3⋊Dic3—62no—
698C3⋊Dic3—61no—
699C3⋊Dic3—61no—
700C3⋊Dic3—122no—
701C3⋊Dic3—121no—
702C3⋊Dic3—121no—
703C3⋊Dic3—122no—
704C3⋊Dic3D3×D412yes—
705C3×Dic3—22no—
706C3×Dic3—22no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—21no—
713C3×Dic3—22no—
714C3×Dic3—32no—
715C3×Dic3—32no—
716C3×Dic3—41no—
717C3×Dic3—62no—
718C3×Dic3—62no—
719C3×Dic3—61no—
720C3×Dic3—61no—
721C3×Dic3—61no—
722C3×Dic3—61no—
723C3×Dic3—61no—
724C3×Dic3—61no—
725C3×Dic3—61no—
726C3×Dic3—61no—
727C3×Dic3—121no—
728C3×Dic3—121no—
729C3×Dic3—121no—
730C3×Dic3D3×D412yes—
731C3×Dic3D3×D412yes—
732C2×#41—271no—
733C22×Q8—271no—
734#124—271no—
735#124—271no—
736#124—271no—
737C22⋊Q8—271no—
738C22⋊Q8—271no—
739C22⋊Q8—271no—
740#121—91no—
741#121—91no—
742#121—271no—
743C4×Q8—271no—
744C4×D4—91no—
745C4×D4—271no—
746C4×D4—271no—
747C33#54811yescharacteristic, complemented, Sylow
748C23×C3—21no—
749C23×C3—21no—
750C23×C3—21no—
751C23×C3—31no—
752C23×C3—31no—
753C23×C3—31no—
754C23×C3—31no—
755C23×C3—41no—
756C23×C3—61no—
757C23×C3—61no—
758C23×C3—91no—
759C23×C3C2×D3211yescharacteristic
760C23×C3C2×D3211yescharacteristic
761C23×C3C2×D3211yescharacteristic
762C22×D3—31no—
763C22×D3—31no—
764C22×D3—61no—
765C22×D3C2×D3211yescharacteristic
766C22×D3C2×D3211yescharacteristic
767C3×D4—64no—
768C3×D4—62no—
769C3×D4—62no—
770C3×D4—62no—
771C3×D4—62no—
772C3×D4—122no—
773C3×D4—182no—
774C3×D4—182no—
775C3×D4—182no—
776C2×C3×C4—31no—
777C2×C3×C4—31no—
778C2×C3×C4—31no—
779C2×C3×C4—31no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—61no—
785C2×C3×C4—61no—
786C2×C3×C4—61no—
787C2×C3×C4—61no—
788C2×C3×C4—62no—
789C2×C3×C4—62no—
790C2×C3×C4—64no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796C2×C3×C4—182no—
797C2×C3×C4—182no—
798#67—22no—
799#67—22no—
800#67—62no—
801#67—62no—
802#67—62no—
803#67—62no—
804#67—62no—
805#67—122no—
806#67—182no—
807#67—182no—
808#67—182no—
809#67—362no—
810C2×Dic3—22no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—31no—
815C2×Dic3—31no—
816C2×Dic3—31no—
817C2×Dic3—31no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—61no—
822C2×Dic3—61no—
823C2×Dic3—61no—
824C2×Dic3—61no—
825C2×Dic3—61no—
826C2×Dic3—62no—
827C2×Dic3—62no—
828C2×Dic3—64no—
829C2×Dic3—62no—
830C2×Dic3—91no—
831C2×Dic3—91no—
832C2×Dic3—91no—
833C2×Dic3—91no—
834C2×Dic3—91no—
835C2×Dic3—91no—
836C2×Dic3—181no—
837C2×Dic3—181no—
838C2×Dic3—181no—
839C2×Dic3—181no—
840C2×Dic3—181no—
841C2×Dic3—181no—
842C2×Dic3—182no—
843C2×Dic3—182no—
844C2×Dic3—182no—
845C2×Dic3—182no—
846C2×Dic3—182no—
847C2×Dic3—182no—
848C2×Dic3—184no—
849C2×Dic3—361no—
850C2×Dic3—361no—
851C2×Dic3—362no—
852C2×Dic3—362no—
853C2×Dic3—362no—
854C2×Dic3—364no—
855C2×Dic3C2×D3211yescharacteristic
856C2×Dic3C2×D3211yescharacteristic
857C2×Dic3C2×D3211yescharacteristic
858C2×Dic3C2×D3211yescharacteristic
859D12—62no—
860C4×D3—62no—
861C4×D3—182no—
862C4×D3—182no—
863C4×D3—182no—
864Dic6—94no—
865Dic6—94no—
866Dic6—94no—
867Dic6—184no—
868Dic6—182no—
869Dic6—182no—
870Dic6—182no—
871Dic6—182no—
872Dic6—182no—
873Dic6—182no—
874Dic6—182no—
875Dic6—182no—
876Dic6—184no—
877Dic6—184no—
878Dic6—184no—
879Dic6—182no—
880C2×C32—22no—
881C2×C32—24no—
882C2×C32—22no—
883C2×C32—22no—
884C2×C32—21no—
885C2×C32—21no—
886C2×C32—21no—
887C2×C32—21no—
888C2×C32—21no—
889C2×C32—21no—
890C2×C32—21no—
891C2×C32—21no—
892C2×C32—21no—
893C2×C32—41no—
894C2×C32—41no—
895C2×C32—41no—
896C2×C32—42no—
897C2×C32—42no—
898C2×C32—44no—
899C2×C32—121no—
900C2×C32—121no—
901C2×C32C2×#23511yescharacteristic
902C2×C32C2×D3×D411yescharacteristic
903C2×C32C2×D3×D411yescharacteristic
904C2×C32C2×D3×D411yescharacteristic
905C2×C32C2×#23711yescharacteristic
906C2×C32C2×#23711yescharacteristic
907C2×C32#101011yescharacteristic
908C2×C32#101011yescharacteristic
909C2×C32#101011yescharacteristic
910C3⋊D3—41no—
911C3×D3—42no—
912C3×D3—41no—
913C3×D3—41no—
914C3×D3—41no—
915C3×D3—41no—
916C3×D3—81no—
917C3×D3—121no—
918C3×D3—121no—
919C3×D3—241no—
920#41—544no—
921C2×Q8—271no—
922C2×Q8—271no—
923C2×Q8—271no—
924C2×Q8—271no—
925C2×Q8—544no—
926C2×D4—31no—
927C2×D4—31no—
928C2×D4—91no—
929C2×D4—91no—
930C2×D4—91no—
931C2×D4—271no—
932C22×C4—31no—
933C22×C4—91no—
934C22×C4—91no—
935C22×C4—271no—
936C22×C4—271no—
937C22×C4—271no—
938C4⋊C4—91no—
939C4⋊C4—91no—
940C4⋊C4—91no—
941C4⋊C4—271no—
942C4⋊C4—271no—
943C4⋊C4—271no—
944C22⋊C4—91no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—91no—
948C22⋊C4—91no—
949C22⋊C4—91no—
950C22⋊C4—271no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C42—91no—
955C42—271no—
956C42—271no—
957C22×C3—22no—
958C22×C3—22no—
959C22×C3—21no—
960C22×C3—21no—
961C22×C3—21no—
962C22×C3—21no—
963C22×C3—21no—
964C22×C3—21no—
965C22×C3—21no—
966C22×C3—21no—
967C22×C3—21no—
968C22×C3—22no—
969C22×C3—22no—
970C22×C3—22no—
971C22×C3—41no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—42no—
976C22×C3—42no—
977C22×C3—41no—
978C22×C3—42no—
979C22×C3—62no—
980C22×C3—61no—
981C22×C3—61no—
982C22×C3—61no—
983C22×C3—61no—
984C22×C3—61no—
985C22×C3—61no—
986C22×C3—61no—
987C22×C3—61no—
988C22×C3—61no—
989C22×C3—61no—
990C22×C3—61no—
991C22×C3—61no—
992C22×C3—121no—
993C22×C3—121no—
994C22×C3—121no—
995C22×C3—121no—
996C22×C3—121no—
997C22×C3—181no—
998C22×C3—181no—
999C22×C3—181no—
1000C22×C3#379512yescomplemented
1001C22×C3#380412yescomplemented
1002C22×C3#380512yescomplemented
1003C22×C3C22×D3211yescharacteristic
1004C22×C3C22×D3211yescharacteristic
1005C22×C3C22×D3211yescharacteristic
1006C2×D3—21no—
1007C2×D3—21no—
1008C2×D3—21no—
1009C2×D3—21no—
1010C2×D3—21no—
1011C2×D3—21no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—121no—
1019C2×D3—121no—
1020C2×D3—121no—
1021C3×C4—32no—
1022C3×C4—32no—
1023C3×C4—62no—
1024C3×C4—62no—
1025C3×C4—62no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—61no—
1032C3×C4—92no—
1033C3×C4—121no—
1034C3×C4—181no—
1035C3×C4—181no—
1036C3×C4—181no—
1037C3×C4—181no—
1038Dic3—21no—
1039Dic3—21no—
1040Dic3—21no—
1041Dic3—32no—
1042Dic3—32no—
1043Dic3—62no—
1044Dic3—62no—
1045Dic3—61no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—92no—
1054Dic3—92no—
1055Dic3—92no—
1056Dic3—121no—
1057Dic3—121no—
1058Dic3—121no—
1059Dic3—182no—
1060Dic3—182no—
1061Dic3—182no—
1062Dic3—182no—
1063Dic3—181no—
1064Dic3—181no—
1065Dic3—181no—
1066Dic3—362no—
1067Dic3—361no—
1068Dic3—361no—
1069Dic3—362no—
1070Dic3#381112yes—
1071C32—21no—
1072C32—21no—
1073C32—21no—
1074C32—41no—
1075C32#555211yescharacteristic, complemented
1076C32#559811yescharacteristic, complemented
1077C32#559811yescharacteristic, complemented
1078C23—31no—
1079C23—31no—
1080C23—91no—
1081C23D3311yescharacteristic
1082Q8—274no—
1083Q8—542no—
1084Q8—542no—
1085Q8—542no—
1086D4—62no—
1087D4—62no—
1088D4—182no—
1089D4—182no—
1090D4—182no—
1091D4—542no—
1092C2×C4—31no—
1093C2×C4—31no—
1094C2×C4—31no—
1095C2×C4—31no—
1096C2×C4—62no—
1097C2×C4—91no—
1098C2×C4—91no—
1099C2×C4—91no—
1100C2×C4—91no—
1101C2×C4—91no—
1102C2×C4—182no—
1103C2×C4—182no—
1104C2×C4—271no—
1105C2×C4—271no—
1106C2×C4—542no—
1107C2×C4—542no—
1108C2×C4—542no—
1109C2×C3—24no—
1110C2×C3—22no—
1111C2×C3—22no—
1112C2×C3—22no—
1113C2×C3—21no—
1114C2×C3—21no—
1115C2×C3—21no—
1116C2×C3—21no—
1117C2×C3—21no—
1118C2×C3—21no—
1119C2×C3—21no—
1120C2×C3—21no—
1121C2×C3—21no—
1122C2×C3—42no—
1123C2×C3—42no—
1124C2×C3—44no—
1125C2×C3—41no—
1126C2×C3—41no—
1127C2×C3—41no—
1128C2×C3—122no—
1129C2×C3—121no—
1130C2×C3—121no—
1131C2×C3—121no—
1132C2×C3—121no—
1133C2×C3—241no—
1134C2×C3—361no—
1135C2×C3C2×#379511yescharacteristic
1136C2×C3#6429811yescharacteristic
1137C2×C3#6430911yescharacteristic
1138C2×C3#6430911yescharacteristic
1139C2×C3D32×D411yescharacteristic
1140C2×C3D32×D411yescharacteristic
1141C2×C3C2×#380411yescharacteristic
1142C2×C3C2×#380511yescharacteristic
1143C2×C3C2×#381111yescharacteristic
1144D3—41no—
1145D3—41no—
1146D3—121no—
1147D3—121no—
1148D3—241no—
1149C22—21no—
1150C22—21no—
1151C22—61no—
1152C22—61no—
1153C22—61no—
1154C22—61no—
1155C22—61no—
1156C22—61no—
1157C22—181no—
1158C22—181no—
1159C22—181no—
1160C22#8896112yescomplemented
1161C22C2×D3311yescharacteristic
1162C4—32no—
1163C4—61no—
1164C4—61no—
1165C4—61no—
1166C4—92no—
1167C4—181no—
1168C4—181no—
1169C4—181no—
1170C4—181no—
1171C4—272no—
1172C4—541no—
1173C3—21no—
1174C3—21no—
1175C3—21no—
1176C3—41no—
1177C3#1059491811yescharacteristic, complemented
1178C3#1059514111yescharacteristic, complemented
1179C3#1059514211yescharacteristic, complemented
1180C2—22no—
1181C2—121no—
1182C2—121no—
1183C2—361no—
1184C2#1172442711yescharacteristic
1185C2C2×#8896111yescharacteristic
1186C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#548
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C22×#6293C2semidirect
2. C2×#88961C2semidirect
3. #11723726C2semidirect
4. #11723637C2semidirect
5. #67⋊(C3⋊Dic3)C2semidirect
6. C3×#63980C2semidirect
7. C3×#63978C2semidirect
8. C3×Dic3×#67C2semidirect
9. #11723009C2semidirect
10. #11723004C2semidirect
11. #11723002C2semidirect
12. #11722984C2semidirect
13. #11722980C2semidirect
14. #11722971C2semidirect
15. #11722943C2semidirect
75. #63980D3semidirect
76. #63978D3semidirect
82. Dic3×#67D3semidirect
129. #6293D4semidirect
274. C22×C33#41semidirect
646. C22×C32#235semidirect
647. C22×C32#237semidirect
648. C22×C32#237semidirect
747. C33#548semidirect
1000. C22×C3#3795semidirect
1001. C22×C3#3804semidirect
1002. C22×C3#3805semidirect
1075. C32#5552semidirect
1076. C32#5598semidirect
1077. C32#5598semidirect
1160. C22#88961semidirect
1177. C3#10594918semidirect
1178. C3#10595141semidirect
1179. C3#10595142semidirect

Maximal subgroups

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

subgroupindex
C22×#62932
C2×#889612
#117237262
#117236372
#67⋊(C3⋊Dic3)2
C3×#639802
C3×#639782
C3×Dic3×#672
#117230092
#117230042
#117230022
#117229842
#117229802
#117229712
#117229432
#105951423
#105951413
#105949183