Finite Group Databasebeta

← #13172060

Subgroups — #13172060

Order 1728.

1452 conjugacy classes of subgroups.

The subgroup lattice has 1170 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89046C211yesmaximal, characteristic, complemented
2C2×C3×#3804C211yesmaximal, characteristic, complemented
3Dic3×#638C211yesmaximal, characteristic, complemented
4#11723605C211yesmaximal, characteristic, complemented
5#11723602C211yesmaximal, characteristic, complemented
6C3×#63978C211yesmaximal, characteristic, complemented
7C2×C3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
8#11723035C211yesmaximal, characteristic, complemented
9#11722995C211yesmaximal, characteristic, complemented
10#11722994C211yesmaximal, characteristic, complemented
11#11722979C211yesmaximal, characteristic, complemented
12#11722978C211yesmaximal, characteristic, complemented
13#11722962C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15#11722911C211yesmaximal, characteristic, complemented
16#10595151—31nomaximal
17#10594928—31nomaximal
18#10594885—31nomaximal
19C2×C3×#638C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C22×C32×Dic3C2211yescharacteristic
25C2×#6296C2211yescharacteristic
26C2×#6295C2211yescharacteristic
27#89046—24no—
28C2×#6294C2211yescharacteristic
29C2×#6294C2211yescharacteristic
30C2×Dic3×C3⋊D3C2211yescharacteristic
31C2×C3×#627C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic
33C2×C3×#626C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic
35C3×#3804—24no—
36C2×C3×D3×Dic3C2211yescharacteristic
37#88864C2211yescharacteristic
38#88807C2211yescharacteristic
39#88806C2211yescharacteristic
40#88806C2211yescharacteristic
41#88806C2211yescharacteristic
42#88806C2211yescharacteristic
43#88803C2211yescharacteristic
44#88803C2211yescharacteristic
45#88803C2211yescharacteristic
46(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
47(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
48Dic3×C3⋊Dic3C2211yescharacteristic
49C3×Dic3⋊Dic3C2211yescharacteristic
50C3×Dic3⋊Dic3C2211yescharacteristic
51C3×Dic3⋊Dic3C2211yescharacteristic
52C3×Dic3⋊Dic3C2211yescharacteristic
53C3×Dic3⋊Dic3C2211yescharacteristic
54C3×#3722C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic
56C2×C3×#237—31no—
57C2×C3×#235—31no—
58C2×#3805—31no—
59C2×#3804—31no—
60C2×#3804—31no—
61C2×#3804D311yescharacteristic, complemented
62#64144—31no—
63#64138—31no—
64C4×#638—31no—
65C3×#939—31no—
66C3×#930—31no—
67C2×C3×C4⋊Dic3—31no—
68C2×C3×Dic3⋊C4—31no—
69#63978D311yescharacteristic, complemented
70Dic3×#67—31no—
71Dic3×#67—31no—
72Dic3×#67—31no—
73Dic3×#67—61no—
74#63970—31no—
75#63969—31no—
76C2×Dic3⋊Dic3D311yescharacteristic, complemented
77#63964—31no—
78#63961—31no—
79#63961—31no—
80#63961—31no—
81#63961—31no—
82#63961—61no—
83#63961—61no—
84#63919—31no—
85#63916—31no—
86#63905—31no—
87#63904—31no—
88#63900—31no—
89#63899—31no—
90#63899—31no—
91#63898—31no—
92#63888—31no—
93#63887—31no—
94#63886—31no—
95#63884—31no—
96D3×Dic3⋊C4—31no—
97D3×Dic3⋊C4—31no—
98#63854—31no—
99#63854—31no—
100#63851—31no—
101#63850—31no—
102#63839—31no—
103#63839—31no—
104C23×C33C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C32×D3C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
110C3×#638—22no—
111C3×#638D414yescomplemented
112C2×C3×C3⋊Dic3—22no—
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C32×#67—22no—
118C2×C32×Dic3—22no—
119C2×C32×Dic3—22no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6296—22no—
126#6295—22no—
127#6294—22no—
128#6294—22no—
129Dic3×C3⋊D3—22no—
130C3×#627—22no—
131C3×#626—22no—
132C3×#626—22no—
133C3×#624—22no—
134C3×D3×Dic3—22no—
135#5824—91no—
136#5611—91no—
137#5507—91no—
138C2×C32×D4—31no—
139C22×C32×C4—31no—
140C22×C32×C4—31no—
141C2×#638C2×D311yescharacteristic
142C2×#638C2×D311yescharacteristic
143C22×C3⋊Dic3C2×D311yescharacteristic
144C2×C4×C3⋊D3—31no—
145C2×C3×#67—21no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—61no—
153C2×C3×#67—61no—
154C2×C3×#67C2×D311yescharacteristic
155C2×C3×#67C2×D311yescharacteristic
156C22×C3×Dic3—21no—
157C22×C3×Dic3—21no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—31no—
160C22×C3×Dic3—31no—
161C22×C3×Dic3—61no—
162C22×C3×Dic3C2×D311yescharacteristic
163C22×C3×Dic3C2×D311yescharacteristic
164C22×C3×Dic3C2×D311yescharacteristic
165C22×C3×Dic3C2×D311yescharacteristic
166C3×#237—64no—
167C3×#235—64no—
168C2×C3×D12—31no—
169C2×C3×D12—31no—
170C2×C3×C4×D3—31no—
171C2×C3×C4×D3—31no—
172C2×C3×C4×D3—31no—
173C2×C3×Dic6—31no—
174C2×C3×Dic6—31no—
175C2×#627—31no—
176C2×#627—31no—
177C2×#627—31no—
178C2×#627C2×D311yescharacteristic
179C2×#626—31no—
180C2×#626—31no—
181C2×#626C2×D311yescharacteristic
182C2×#626C2×D311yescharacteristic
183C2×#625—31no—
184C2×#624—31no—
185C2×#624—31no—
186C2×#624C2×D311yescharacteristic
187#3805—64no—
188#3804—24no—
189#3804—64no—
190#3804—64no—
191C2×D3×Dic3—31no—
192C2×D3×Dic3—31no—
193C2×D3×Dic3—31no—
194C2×D3×Dic3—31no—
195C2×D3×Dic3—31no—
196C2×D3×Dic3—31no—
197C2×D3×Dic3—61no—
198C2×D3×Dic3C2×D311yescharacteristic
199#3757—31no—
200#3757—31no—
201#3757—31no—
202#3757—31no—
203#3757—31no—
204#3757—61no—
205#3757—61no—
206#3757—61no—
207#3757—121no—
208#3752—31no—
209#3752—31no—
210#3752—31no—
211#3750—31no—
212#3750—31no—
213#3750—31no—
214#3750—31no—
215#3750—31no—
216C4×C3⋊Dic3—31no—
217C3×#217—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×C4⋊Dic3—31no—
222C3×C4⋊Dic3—31no—
223C3×C4⋊Dic3—31no—
224C3×C4⋊Dic3—31no—
225C3×C4⋊Dic3—31no—
226C3×Dic3⋊C4—31no—
227C3×Dic3⋊C4—31no—
228C3×Dic3⋊C4—31no—
229C3×Dic3⋊C4—31no—
230C3×Dic3⋊C4—31no—
231#3724—31no—
232#3724—31no—
233#3724—31no—
234#3724—31no—
235#3724—31no—
236#3724—31no—
237#3724—31no—
238#3724—31no—
239#3724—61no—
240#3724—61no—
241#3724—61no—
242#3724—61no—
243Dic3⋊Dic3—31no—
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—61no—
246Dic3⋊Dic3C2×D311yescharacteristic
247Dic3⋊Dic3C2×D311yescharacteristic
248Dic3⋊Dic3C2×D311yescharacteristic
249Dic3⋊Dic3C2×D311yescharacteristic
250Dic3⋊Dic3C2×D311yescharacteristic
251#3722C2×D311yescharacteristic
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—31no—
259(C2×D3)⋊Dic3—31no—
260(C2×D3)⋊Dic3—31no—
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—61no—
263(C2×D3)⋊Dic3—61no—
264(C2×D3)⋊Dic3—61no—
265(C2×D3)⋊Dic3—61no—
266(C2×D3)⋊Dic3—61no—
267(C2×D3)⋊Dic3C2×D311yescharacteristic
268Dic32—31no—
269Dic32—31no—
270Dic32—61no—
271C22×C33—21no—
272C22×C33—21no—
273C22×C33C2×D412yes—
274C22×C33C2411yescharacteristic
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3—21no—
279C2×C3×C3⋊D3—21no—
280C2×C3×C3⋊D3C2×D412yes—
281C2×C32×D3—21no—
282C2×C32×D3—21no—
283C2×C32×D3—21no—
284C3⋊(C3⋊Dic3)—21no—
285C3⋊(C3⋊Dic3)—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3C2×D412yes—
290C32×Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C32×Dic3#4112yescomplemented
295C2×C3×#41—91no—
296C2×#237—31no—
297C2×#237—91no—
298C2×#237—91no—
299C2×#235—31no—
300C2×#235—91no—
301C3×#121—91no—
302C2×C3×C4⋊C4—91no—
303#946—91no—
304#944—91no—
305#939—31no—
306#939—91no—
307#938—91no—
308#935—91no—
309#935—91no—
310#935—91no—
311#935—91no—
312#935—181no—
313D4×Dic3—91no—
314D4×Dic3—91no—
315#930—31no—
316#929—91no—
317#929—91no—
318#929—91no—
319#929—91no—
320#929—181no—
321C4×#67—91no—
322C4×#67—91no—
323C4×#67—91no—
324C4×#67—181no—
325C2×C4⋊Dic3—31no—
326#924—91no—
327C2×Dic3⋊C4—31no—
328C2×Dic3⋊C4—91no—
329#896—91no—
330#896—91no—
331#895—91no—
332#894—91no—
333#894—91no—
334#893—91no—
335D3×C4⋊C4—91no—
336D3×C4⋊C4—91no—
337#888—91no—
338#888—91no—
339#883—91no—
340#883—91no—
341#878—91no—
342#878—91no—
343C23×C32—21no—
344C23×C32—21no—
345C23×C32—21no—
346C23×C32—31no—
347C23×C32—41no—
348C23×C32C22×D311yescharacteristic
349C23×C32C22×D311yescharacteristic
350C23×C32C22×D311yescharacteristic
351C22×C3⋊D3C22×D311yescharacteristic
352C22×C3⋊D3C22×D311yescharacteristic
353C22×C3×D3—21no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—61no—
359C22×C3×D3—61no—
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C32×D4—62no—
363C2×C32×C4—31no—
364C2×C32×C4—31no—
365C2×C32×C4—31no—
366C2×C32×C4—31no—
367C2×C32×C4—31no—
368C2×C32×C4—62no—
369C2×C32×C4—62no—
370#638—22no—
371#638#6714yescomplemented
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—121no—
386C2×C3⋊Dic3—121no—
387C2×C3⋊Dic3C22×D311yescharacteristic
388C2×C3⋊Dic3C22×D311yescharacteristic
389C2×C3⋊Dic3C22×D311yescharacteristic
390C2×C3⋊Dic3C22×D311yescharacteristic
391C4×C3⋊D3—62no—
392C3×#67—22no—
393C3×#67—22no—
394C3×#67—34no—
395C3×#67—34no—
396C3×#67—42no—
397C3×#67—64no—
398C3×#67—62no—
399C3×#67—62no—
400C3×#67—62no—
401C3×#67—62no—
402C3×#67—122no—
403C2×C3×Dic3—22no—
404C2×C3×Dic3—22no—
405C2×C3×Dic3—22no—
406C2×C3×Dic3—22no—
407C2×C3×Dic3—21no—
408C2×C3×Dic3—21no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—42no—
421C2×C3×Dic3—42no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—62no—
427C2×C3×Dic3—62no—
428C2×C3×Dic3—62no—
429C2×C3×Dic3—122no—
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C3×D12—62no—
441C3×D12—62no—
442C3×C4×D3—62no—
443C3×C4×D3—62no—
444C3×C4×D3—62no—
445C3×Dic6—62no—
446C3×Dic6—62no—
447#627—22no—
448#627—62no—
449#627—62no—
450#627—62no—
451#626—22no—
452#626—22no—
453#626—62no—
454#626—62no—
455#625—62no—
456#624—22no—
457#624—62no—
458#624—62no—
459D3×Dic3—22no—
460D3×Dic3—62no—
461D3×Dic3—62no—
462D3×Dic3—62no—
463D3×Dic3—62no—
464D3×Dic3—62no—
465D3×Dic3—62no—
466D3×Dic3—122no—
467#547—271noSylow
468C2×C33—22no—
469C2×C33C22×D411yescharacteristic
470C2×C33C2×#4111yescharacteristic
471C2×C332−1+411yescharacteristic
472C3×C3⋊D3—22no—
473C3×C3⋊D3—41no—
474C32×D3—41no—
475C3×#41—184no—
476C2×C3×Q8—91no—
477C2×C3×D4—31no—
478C2×C3×D4—31no—
479C2×C3×D4—61no—
480C2×C3×D4—91no—
481C2×C3×D4—91no—
482C2×C3×D4—91no—
483C2×C3×D4—91no—
484C22×C3×C4—31no—
485C22×C3×C4—31no—
486C22×C3×C4—31no—
487C22×C3×C4—31no—
488C22×C3×C4—61no—
489C22×C3×C4—61no—
490C22×C3×C4—91no—
491C22×C3×C4—91no—
492C22×C3×C4—91no—
493C2×#67—31no—
494C2×#67—31no—
495C2×#67—31no—
496C2×#67—31no—
497C2×#67—31no—
498C2×#67—31no—
499C2×#67—61no—
500C2×#67—61no—
501C2×#67—91no—
502C2×#67—91no—
503C2×#67D3211yescharacteristic
504C22×Dic3—31no—
505C22×Dic3—31no—
506C22×Dic3—31no—
507C22×Dic3—61no—
508C22×Dic3—91no—
509C22×Dic3—91no—
510C22×Dic3—91no—
511C22×Dic3D3211yescharacteristic
512C22×Dic3D3211yescharacteristic
513#237—64no—
514#237—184no—
515#237—184no—
516#235—64no—
517#235—184no—
518C2×D12—31no—
519C2×D12—31no—
520C2×D12—91no—
521C2×C4×D3—31no—
522C2×C4×D3—31no—
523C2×C4×D3—31no—
524C2×C4×D3—91no—
525C2×C4×D3—91no—
526C2×C4×D3—91no—
527C2×C4×D3—91no—
528C2×C4×D3—91no—
529C2×C4×D3—91no—
530C2×C4×D3—181no—
531C2×Dic6—31no—
532C2×Dic6—31no—
533C2×Dic6—91no—
534C2×Dic6—91no—
535C2×Dic6—91no—
536C3×C4⋊C4—91no—
537C3×C4⋊C4—91no—
538C3×C4⋊C4—91no—
539C3×C4⋊C4—91no—
540C3×C4⋊C4—91no—
541C3×C22⋊C4—91no—
542C3×C22⋊C4—91no—
543#217—31no—
544#217—91no—
545#217—91no—
546#217—91no—
547#217—91no—
548#217—91no—
549#217—91no—
550#217—91no—
551#217—91no—
552#217—91no—
553#217—91no—
554#217—181no—
555#217—181no—
556#217—181no—
557#217—181no—
558#217—181no—
559#217—361no—
560(C2×D3)⋊C4—31no—
561(C2×D3)⋊C4—31no—
562(C2×D3)⋊C4—31no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—181no—
572(C2×D3)⋊C4—181no—
573(C2×D3)⋊C4—181no—
574C4⋊Dic3—31no—
575C4⋊Dic3—31no—
576C4⋊Dic3—31no—
577C4⋊Dic3—31no—
578C4⋊Dic3—31no—
579C4⋊Dic3—91no—
580Dic3⋊C4—31no—
581Dic3⋊C4—31no—
582Dic3⋊C4—31no—
583Dic3⋊C4—31no—
584Dic3⋊C4—31no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—91no—
591Dic3⋊C4—91no—
592Dic3⋊C4—91no—
593Dic3⋊C4—91no—
594Dic3⋊C4—91no—
595Dic3⋊C4—91no—
596Dic3⋊C4—91no—
597Dic3⋊C4—91no—
598Dic3⋊C4—91no—
599Dic3⋊C4—181no—
600Dic3⋊C4—181no—
601Dic3⋊C4—181no—
602Dic3⋊C4—181no—
603Dic3⋊C4—181no—
604C4×Dic3—91no—
605C4×Dic3—91no—
606C4×Dic3—91no—
607C4×Dic3—181no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32—21no—
614C22×C32—21no—
615C22×C32—21no—
616C22×C32—21no—
617C22×C32—22no—
618C22×C32—22no—
619C22×C32—22no—
620C22×C32—41no—
621C22×C32—42no—
622C22×C32—41no—
623C22×C32—41no—
624C22×C32—41no—
625C22×C32—41no—
626C22×C32—41no—
627C22×C32—41no—
628C22×C32—61no—
629C22×C32—61no—
630C22×C32—61no—
631C22×C32—81no—
632C22×C32—81no—
633C22×C32D3×D412yes—
634C22×C32D3×D412yes—
635C22×C32C2×#6712yes—
636C22×C32C23×D311yescharacteristic
637C22×C32C23×D311yescharacteristic
638C22×C32C23×D311yescharacteristic
639C2×C3⋊D3—21no—
640C2×C3⋊D3—21no—
641C2×C3⋊D3—21no—
642C2×C3⋊D3—21no—
643C2×C3⋊D3—21no—
644C2×C3⋊D3C2×#6712yes—
645C2×C3×D3—21no—
646C2×C3×D3—21no—
647C2×C3×D3—21no—
648C2×C3×D3—21no—
649C2×C3×D3—21no—
650C2×C3×D3—21no—
651C2×C3×D3—32no—
652C2×C3×D3—32no—
653C2×C3×D3—41no—
654C2×C3×D3—41no—
655C2×C3×D3—41no—
656C2×C3×D3—62no—
657C2×C3×D3—61no—
658C2×C3×D3—61no—
659C2×C3×D3—61no—
660C2×C3×D3—61no—
661C2×C3×D3—61no—
662C2×C3×D3—61no—
663C2×C3×D3—61no—
664C2×C3×D3—61no—
665C2×C3×D3—61no—
666C2×C3×D3—61no—
667C2×C3×D3—121no—
668C2×C3×D3—121no—
669C2×C3×D3—121no—
670C2×C3×D3—121no—
671C2×C3×D3—121no—
672C32×C4—32no—
673C32×C4—61no—
674C32×C4—61no—
675C32×C4—61no—
676C32×C4—61no—
677C3⋊Dic3—21no—
678C3⋊Dic3—21no—
679C3⋊Dic3—21no—
680C3⋊Dic3—61no—
681C3⋊Dic3—61no—
682C3⋊Dic3—61no—
683C3⋊Dic3—61no—
684C3⋊Dic3—61no—
685C3⋊Dic3—61no—
686C3⋊Dic3—121no—
687C3⋊Dic3—121no—
688C3⋊Dic3—121no—
689C3⋊Dic3—121no—
690C3⋊Dic3—121no—
691C3⋊Dic3—121no—
692C3⋊Dic3—241no—
693C3⋊Dic3—241no—
694C3⋊Dic3C2×#6712yes—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—22no—
704C3×Dic3—32no—
705C3×Dic3—32no—
706C3×Dic3—41no—
707C3×Dic3—41no—
708C3×Dic3—41no—
709C3×Dic3—41no—
710C3×Dic3—62no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—121no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3#23512yescomplemented
721C3×Dic3#23712yescomplemented
722C2×#41—91no—
723C2×#41—271no—
724C4⋊Q8—271no—
725#123—271no—
726#123—271no—
727#123—271no—
728#123—271no—
729C22⋊Q8—271no—
730C22⋊Q8—271no—
731#121—91no—
732#121—271no—
733C4×D4—271no—
734C4×D4—271no—
735C2×C4⋊C4—91no—
736C2×C4⋊C4—271no—
737C33#54711yescharacteristic, complemented, Sylow
738C23×C3—21no—
739C23×C3—21no—
740C23×C3—21no—
741C23×C3—31no—
742C23×C3—31no—
743C23×C3—41no—
744C23×C3—61no—
745C23×C3—91no—
746C23×C3—91no—
747C23×C3C2×D3211yescharacteristic
748C23×C3C2×D3211yescharacteristic
749C23×C3C2×D3211yescharacteristic
750C22×D3—31no—
751C22×D3—31no—
752C22×D3—31no—
753C22×D3—31no—
754C22×D3—61no—
755C22×D3—61no—
756C22×D3C2×D3211yescharacteristic
757C3×Q8—182no—
758C3×D4—62no—
759C3×D4—62no—
760C3×D4—94no—
761C3×D4—122no—
762C3×D4—182no—
763C3×D4—182no—
764C3×D4—182no—
765C2×C3×C4—31no—
766C2×C3×C4—31no—
767C2×C3×C4—31no—
768C2×C3×C4—31no—
769C2×C3×C4—31no—
770C2×C3×C4—31no—
771C2×C3×C4—31no—
772C2×C3×C4—31no—
773C2×C3×C4—31no—
774C2×C3×C4—31no—
775C2×C3×C4—61no—
776C2×C3×C4—61no—
777C2×C3×C4—61no—
778C2×C3×C4—61no—
779C2×C3×C4—61no—
780C2×C3×C4—62no—
781C2×C3×C4—62no—
782C2×C3×C4—62no—
783C2×C3×C4—62no—
784C2×C3×C4—91no—
785C2×C3×C4—91no—
786C2×C3×C4—91no—
787C2×C3×C4—91no—
788C2×C3×C4—122no—
789C2×C3×C4—122no—
790C2×C3×C4—182no—
791C2×C3×C4—182no—
792C2×C3×C4—182no—
793#67—22no—
794#67—34no—
795#67—34no—
796#67—64no—
797#67—62no—
798#67—62no—
799#67—62no—
800#67—62no—
801#67—122no—
802#67—182no—
803#67—182no—
804C2×Dic3—22no—
805C2×Dic3—22no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—31no—
813C2×Dic3—31no—
814C2×Dic3—61no—
815C2×Dic3—61no—
816C2×Dic3—61no—
817C2×Dic3—61no—
818C2×Dic3—62no—
819C2×Dic3—62no—
820C2×Dic3—62no—
821C2×Dic3—91no—
822C2×Dic3—91no—
823C2×Dic3—91no—
824C2×Dic3—91no—
825C2×Dic3—91no—
826C2×Dic3—91no—
827C2×Dic3—122no—
828C2×Dic3—181no—
829C2×Dic3—181no—
830C2×Dic3—181no—
831C2×Dic3—181no—
832C2×Dic3—181no—
833C2×Dic3—181no—
834C2×Dic3—182no—
835C2×Dic3—182no—
836C2×Dic3—182no—
837C2×Dic3—361no—
838C2×Dic3—361no—
839C2×Dic3C2×D3211yescharacteristic
840C2×Dic3C2×D3211yescharacteristic
841C2×Dic3C2×D3211yescharacteristic
842C2×Dic3C2×D3211yescharacteristic
843C2×Dic3C2×D3211yescharacteristic
844D12—62no—
845D12—62no—
846D12—182no—
847C4×D3—62no—
848C4×D3—62no—
849C4×D3—62no—
850C4×D3—182no—
851C4×D3—182no—
852C4×D3—182no—
853C4×D3—182no—
854C4×D3—182no—
855C4×D3—182no—
856C4×D3—362no—
857Dic6—62no—
858Dic6—62no—
859Dic6—182no—
860Dic6—182no—
861Dic6—182no—
862C2×C32—22no—
863C2×C32—22no—
864C2×C32—22no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—21no—
872C2×C32—21no—
873C2×C32—21no—
874C2×C32—41no—
875C2×C32—41no—
876C2×C32—41no—
877C2×C32—42no—
878C2×C32—42no—
879C2×C32—42no—
880C2×C32—82no—
881C2×C32—121no—
882C2×C32C2×#23511yescharacteristic
883C2×C32C2×D3×D411yescharacteristic
884C2×C32C2×D3×D411yescharacteristic
885C2×C32C2×#23711yescharacteristic
886C2×C32#100711yescharacteristic
887C2×C32D3×#4111yescharacteristic
888C2×C32#101011yescharacteristic
889C2×C32#101011yescharacteristic
890C2×C32C22×#6711yescharacteristic
891C3⋊D3—22no—
892C3⋊D3—41no—
893C3×D3—41no—
894C3×D3—41no—
895C3×D3—62no—
896C3×D3—62no—
897C3×D3—81no—
898C3×D3—122no—
899C3×D3—121no—
900C3×D3—121no—
901C3×D3—241no—
902#41—184no—
903#41—544no—
904C2×Q8—91no—
905C2×Q8—271no—
906C2×D4—31no—
907C2×D4—91no—
908C2×D4—91no—
909C2×D4—91no—
910C2×D4—91no—
911C2×D4—271no—
912C22×C4—31no—
913C22×C4—31no—
914C22×C4—91no—
915C22×C4—91no—
916C22×C4—91no—
917C22×C4—271no—
918C22×C4—271no—
919C22×C4—271no—
920C4⋊C4—91no—
921C4⋊C4—91no—
922C4⋊C4—91no—
923C4⋊C4—91no—
924C4⋊C4—91no—
925C4⋊C4—271no—
926C4⋊C4—271no—
927C4⋊C4—271no—
928C4⋊C4—271no—
929C4⋊C4—271no—
930C22⋊C4—91no—
931C22⋊C4—91no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C42—271no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—21no—
943C22×C3—21no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—22no—
949C22×C3—22no—
950C22×C3—22no—
951C22×C3—41no—
952C22×C3—41no—
953C22×C3—41no—
954C22×C3—41no—
955C22×C3—41no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—42no—
959C22×C3—61no—
960C22×C3—61no—
961C22×C3—61no—
962C22×C3—61no—
963C22×C3—61no—
964C22×C3—61no—
965C22×C3—81no—
966C22×C3—81no—
967C22×C3—92no—
968C22×C3—121no—
969C22×C3—121no—
970C22×C3—121no—
971C22×C3—181no—
972C22×C3—181no—
973C22×C3—181no—
974C22×C3—181no—
975C22×C3—181no—
976C22×C3#380212yes—
977C22×C3D3×#6712yes—
978C22×C3D3×#6712yes—
979C22×C3C22×D3211yescharacteristic
980C22×C3C22×D3211yescharacteristic
981C22×C3C22×D3211yescharacteristic
982C2×D3—21no—
983C2×D3—21no—
984C2×D3—21no—
985C2×D3—32no—
986C2×D3—32no—
987C2×D3—62no—
988C2×D3—61no—
989C2×D3—61no—
990C2×D3—61no—
991C2×D3—61no—
992C2×D3—61no—
993C2×D3—61no—
994C2×D3—61no—
995C2×D3—61no—
996C2×D3—61no—
997C2×D3—61no—
998C2×D3—121no—
999C2×D3—121no—
1000C2×D3—121no—
1001C2×D3—121no—
1002C2×D3—121no—
1003C3×C4—32no—
1004C3×C4—32no—
1005C3×C4—62no—
1006C3×C4—61no—
1007C3×C4—61no—
1008C3×C4—61no—
1009C3×C4—61no—
1010C3×C4—61no—
1011C3×C4—61no—
1012C3×C4—61no—
1013C3×C4—61no—
1014C3×C4—92no—
1015C3×C4—121no—
1016C3×C4—121no—
1017C3×C4—121no—
1018C3×C4—121no—
1019C3×C4—181no—
1020C3×C4—181no—
1021C3×C4—181no—
1022Dic3—21no—
1023Dic3—21no—
1024Dic3—21no—
1025Dic3—21no—
1026Dic3—32no—
1027Dic3—32no—
1028Dic3—62no—
1029Dic3—61no—
1030Dic3—61no—
1031Dic3—61no—
1032Dic3—61no—
1033Dic3—61no—
1034Dic3—61no—
1035Dic3—121no—
1036Dic3—121no—
1037Dic3—121no—
1038Dic3—181no—
1039Dic3—181no—
1040Dic3—181no—
1041Dic3—181no—
1042Dic3—181no—
1043Dic3—181no—
1044Dic3—361no—
1045Dic3—361no—
1046Dic3—361no—
1047Dic3—361no—
1048Dic3—361no—
1049Dic3—361no—
1050Dic3—721no—
1051Dic3—721no—
1052Dic3#380412yescomplemented
1053C32—21no—
1054C32—21no—
1055C32—21no—
1056C32—41no—
1057C32#550711yescharacteristic, complemented
1058C32#561111yescharacteristic, complemented
1059C32#582411yescharacteristic, complemented
1060C23—31no—
1061C23—91no—
1062C23—91no—
1063C23D3311yescharacteristic
1064Q8—182no—
1065Q8—542no—
1066D4—62no—
1067D4—94no—
1068D4—182no—
1069D4—182no—
1070D4—182no—
1071D4—542no—
1072C2×C4—31no—
1073C2×C4—31no—
1074C2×C4—31no—
1075C2×C4—31no—
1076C2×C4—31no—
1077C2×C4—62no—
1078C2×C4—62no—
1079C2×C4—91no—
1080C2×C4—91no—
1081C2×C4—91no—
1082C2×C4—91no—
1083C2×C4—182no—
1084C2×C4—182no—
1085C2×C4—182no—
1086C2×C4—271no—
1087C2×C4—271no—
1088C2×C4—542no—
1089C2×C4—542no—
1090C2×C4—542no—
1091C2×C3—22no—
1092C2×C3—22no—
1093C2×C3—22no—
1094C2×C3—21no—
1095C2×C3—21no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—21no—
1099C2×C3—21no—
1100C2×C3—21no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—42no—
1104C2×C3—42no—
1105C2×C3—42no—
1106C2×C3—41no—
1107C2×C3—41no—
1108C2×C3—41no—
1109C2×C3—82no—
1110C2×C3—121no—
1111C2×C3—121no—
1112C2×C3—182no—
1113C2×C3—241no—
1114C2×C3—361no—
1115C2×C3#6429711yescharacteristic
1116C2×C3#6429711yescharacteristic
1117C2×C3C2×#380211yescharacteristic
1118C2×C3D3×#23511yescharacteristic
1119C2×C3#6430911yescharacteristic
1120C2×C3D3×#23711yescharacteristic
1121C2×C3C2×#380411yescharacteristic
1122C2×C3C2×D3×#6711yescharacteristic
1123C2×C3C2×D3×#6711yescharacteristic
1124D3—41no—
1125D3—62no—
1126D3—62no—
1127D3—122no—
1128D3—121no—
1129D3—121no—
1130D3—241no—
1131C22—21no—
1132C22—21no—
1133C22—61no—
1134C22—61no—
1135C22—61no—
1136C22—92no—
1137C22—181no—
1138C22—181no—
1139C22—181no—
1140C22—181no—
1141C22—181no—
1142C22#8895312yes—
1143C22C2×D3311yescharacteristic
1144C4—32no—
1145C4—61no—
1146C4—61no—
1147C4—61no—
1148C4—61no—
1149C4—92no—
1150C4—181no—
1151C4—181no—
1152C4—181no—
1153C4—541no—
1154C4—541no—
1155C3—21no—
1156C3—21no—
1157C3—21no—
1158C3—41no—
1159C3#1059488511yescharacteristic, complemented
1160C3#1059492811yescharacteristic, complemented
1161C3#1059515111yescharacteristic, complemented
1162C2—22no—
1163C2—121no—
1164C2—182no—
1165C2—361no—
1166C2D3×#380411yescharacteristic
1167C2C2×#8895311yescharacteristic
1168C2#1172442611yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#547
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×#89046C2semidirect
2. C2×C3×#3804C2semidirect
3. Dic3×#638C2semidirect
4. #11723605C2semidirect
5. #11723602C2semidirect
6. C3×#63978C2semidirect
7. C2×C3×Dic3⋊Dic3C2semidirect
8. #11723035C2semidirect
9. #11722995C2semidirect
10. #11722994C2semidirect
11. #11722979C2semidirect
12. #11722978C2semidirect
13. #11722962C2semidirect
14. #11722927C2semidirect
15. #11722911C2semidirect
61. C2×#3804D3semidirect
69. #63978D3semidirect
76. C2×Dic3⋊Dic3D3semidirect
111. C3×#638D4semidirect
294. C32×Dic3#41semidirect
371. #638#67semidirect
720. C3×Dic3#235semidirect
721. C3×Dic3#237semidirect
737. C33#547semidirect
1052. Dic3#3804semidirect
1057. C32#5507semidirect
1058. C32#5611semidirect
1059. C32#5824semidirect
1159. C3#10594885semidirect
1160. C3#10594928semidirect
1161. C3#10595151semidirect

Maximal subgroups

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

subgroupindex
C2×#890462
C2×C3×#38042
Dic3×#6382
#117236052
#117236022
C3×#639782
C2×C3×Dic3⋊Dic32
#117230352
#117229952
#117229942
#117229792
#117229782
#117229622
#117229272
#117229112
#105951513
#105949283
#105948853