Finite Group Databasebeta

← #13172337

Subgroups — #13172337

Order 1728.

1332 conjugacy classes of subgroups.

The subgroup lattice has 1194 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723717C211yesmaximal, characteristic, complemented
2#11723641C211yesmaximal, characteristic, complemented
3#11723629C211yesmaximal, characteristic, complemented
4Dic3×#638C211yesmaximal, characteristic, complemented
5C3×#63977C211yesmaximal, characteristic, complemented
6C2×C3×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11723022C211yesmaximal, characteristic, complemented
9#11723020C211yesmaximal, characteristic, complemented
10#11723009C211yesmaximal, characteristic, complemented
11#11723002C211yesmaximal, characteristic, complemented
12#11722992C211yesmaximal, characteristic, complemented
13#11722991C211yesmaximal, characteristic, complemented
14#11722967C211yesmaximal, characteristic, complemented
15#11722957C211yesmaximal, characteristic, complemented
16#10595507—31nomaximal
17#10595036—31nomaximal
18#10594238—31nomaximal
19C23×C32×D3C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6295C2211yescharacteristic, complemented
25C2×#6293C2211yescharacteristic, complemented
26C2×#6290C2211yescharacteristic
27C2×#6290C2211yescharacteristic
28C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
29C2×C3×#626C2211yescharacteristic
30C2×C3×#626C2211yescharacteristic
31C2×C3×#624C2211yescharacteristic, complemented
32#88864C2211yescharacteristic
33C32×#217C2211yescharacteristic
34#88815C2211yescharacteristic, complemented
35#88814C2211yescharacteristic, complemented
36#88814C2211yescharacteristic, complemented
37#88807C2211yescharacteristic, complemented
38#88807C2211yescharacteristic, complemented
39#88806C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88803C2211yescharacteristic, complemented
42(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic, complemented
45C3×#3724C2211yescharacteristic, complemented
46C3×#3722C2211yescharacteristic, complemented
47C3×(C2×D3)⋊Dic3C2211yescharacteristic
48C3×(C2×D3)⋊Dic3C2211yescharacteristic
49C3×(C2×D3)⋊Dic3C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×Dic32C2211yescharacteristic, complemented
54#64162—31no—
55C4×#638—31no—
56#64087—31no—
57C3×#953—31no—
58C2×C3×#217—31no—
59C3×C4×#67—31no—
60C2×C3×(C2×D3)⋊C4—31no—
61C3×#882—31no—
62C3×#67⋊C4—31no—
63#63980—31no—
64#63978—31no—
65#63978—31no—
66#63977D311yescharacteristic, complemented
67#63976—31no—
68#63976—31no—
69#63976—61no—
70#63975—31no—
71Dic3×#67—31no—
72Dic3×#67—31no—
73Dic3×#67—61no—
74#63971—31no—
75#63969—31no—
76#63964—31no—
77#63964—31no—
78#63964—61no—
79C2×(C2×D3)⋊Dic3D311yescharacteristic, complemented
80#63959—31no—
81#63958—31no—
82#63956—31no—
83#63956—31no—
84#63953—31no—
85#63952D311yescharacteristic, complemented
86#63915—31no—
87#63913—31no—
88#63912—31no—
89#63908—31no—
90#63906—31no—
91#63905—31no—
92#63905—31no—
93#63885—31no—
94#63884—31no—
95#63862—31no—
96#63861—31no—
97#63860—31no—
98#63859—31no—
99#63859—31no—
100#63853—31no—
101#63852—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3—22no—
106C22×C32×D3—41no—
107C22×C32×D3—41no—
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C3×#638—22no—
113C3×#638—22no—
114C2×C3×C3⋊Dic3—41no—
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C2×C32×Dic3—41no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124#6295—41no—
125#6293—41no—
126#6290—41no—
127#6290—41no—
128Dic3×C3⋊D3—41no—
129C3×#626—41no—
130C3×#626—41no—
131C3×#624—41no—
132#5593—91no—
133#5560—91no—
134#5494—91no—
135C24×C32—31no—
136C23×C3×D3—21no—
137C23×C3×D3C2×D311yescharacteristic
138C23×C3×D3C2×D311yescharacteristic
139C22×C32×C4—31no—
140C2×#638—31no—
141C2×#638—31no—
142C2×#638C2×D311yescharacteristic
143C2×#638C2×D311yescharacteristic
144C22×C3⋊Dic3C2×D311yescharacteristic
145C2×C4×C3⋊D3—31no—
146C2×#634—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67—31no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—61no—
154C2×C3×#67—61no—
155C22×C3×Dic3—21no—
156C22×C3×Dic3—31no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—61no—
159C22×C3×Dic3C2×D311yescharacteristic
160C22×C3×Dic3C2×D311yescharacteristic
161C2×C3×D12—31no—
162C2×C3×D12—31no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×#627—31no—
166C2×#627—31no—
167C2×#627—61no—
168C2×#626—31no—
169C2×#626—31no—
170C2×#626C2×D311yescharacteristic
171C2×#626C2×D311yescharacteristic
172C2×#625—31no—
173C2×#625—31no—
174C2×#625—31no—
175C2×#625—31no—
176C2×#625—31no—
177C2×#625—61no—
178C2×#625—61no—
179C2×#624C2×D311yescharacteristic, complemented
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—61no—
183C32×C22⋊C4—31no—
184#3757—31no—
185#3757—31no—
186#3757—31no—
187#3757—31no—
188#3757—31no—
189#3757—61no—
190#3757—61no—
191#3757—61no—
192#3757—121no—
193#3752—31no—
194C4⋊(C3⋊Dic3)—31no—
195#3750—31no—
196#3750—31no—
197#3750—31no—
198C4×C3⋊Dic3—31no—
199C3×#217—21no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×#217—31no—
204C3×#217—31no—
205C3×#217—31no—
206C3×#217C2×D311yescharacteristic
207C3×#217C2×D311yescharacteristic
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×(C2×D3)⋊C4—31no—
212C3×(C2×D3)⋊C4—31no—
213C3×(C2×D3)⋊C4—31no—
214C3×(C2×D3)⋊C4—31no—
215C3×(C2×D3)⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218C3×C4×Dic3—31no—
219C3×C4×Dic3—31no—
220#3724—31no—
221#3724—31no—
222#3724—31no—
223#3724—61no—
224#3724C2×D311yescharacteristic, complemented
225Dic3⋊Dic3—31no—
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—31no—
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3—61no—
234Dic3⋊Dic3—61no—
235Dic3⋊Dic3—61no—
236#3722—31no—
237#3722—31no—
238#3722C2×D311yescharacteristic, complemented
239(C2×D3)⋊Dic3—31no—
240(C2×D3)⋊Dic3—31no—
241(C2×D3)⋊Dic3—31no—
242(C2×D3)⋊Dic3—31no—
243(C2×D3)⋊Dic3—31no—
244(C2×D3)⋊Dic3—31no—
245(C2×D3)⋊Dic3—31no—
246(C2×D3)⋊Dic3—31no—
247(C2×D3)⋊Dic3—31no—
248(C2×D3)⋊Dic3—31no—
249(C2×D3)⋊Dic3—61no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3C2×D311yescharacteristic
253(C2×D3)⋊Dic3C2×D311yescharacteristic
254(C2×D3)⋊Dic3C2×D311yescharacteristic
255(C2×D3)⋊Dic3C2×D311yescharacteristic
256(C2×D3)⋊Dic3C2×D311yescharacteristic
257(C2×D3)⋊Dic3C2×D311yescharacteristic
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
261Dic32C2×D311yescharacteristic, complemented
262C22×C33—21no—
263C22×C33—21no—
264C22×C33#4112yes—
265C22×C33C2411yescharacteristic
266C2×C3×C3⋊D3—21no—
267C2×C3×C3⋊D3—21no—
268C2×C3×C3⋊D3—21no—
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3—21no—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C2×C32×D3—44no—
279C3⋊(C3⋊Dic3)—21no—
280C3⋊(C3⋊Dic3)—21no—
281C3×C3⋊Dic3—21no—
282C3×C3⋊Dic3—21no—
283C3×C3⋊Dic3—21no—
284C3×C3⋊Dic3—21no—
285C32×Dic3—21no—
286C32×Dic3—21no—
287C32×Dic3—21no—
288C32×Dic3—21no—
289C3×#120—91no—
290C3×C4×D4—91no—
291C2×C3×C22⋊C4—91no—
292#953—31no—
293#953—91no—
294#953—91no—
295#953—181no—
296C2×#217—31no—
297#939—91no—
298#939—91no—
299#939—91no—
300#938—91no—
301#937—91no—
302#936—91no—
303#935—91no—
304D4×Dic3—91no—
305#930—91no—
306#930—91no—
307#929—91no—
308C4×#67—31no—
309C4×#67—91no—
310C4×#67—91no—
311C4×#67—181no—
312C2×(C2×D3)⋊C4—31no—
313#924—91no—
314#898—91no—
315#894—91no—
316#885—91no—
317#885—91no—
318#885—91no—
319#885—91no—
320#884—91no—
321#884—91no—
322#884—91no—
323#883—91no—
324#883—91no—
325#883—91no—
326#882—31no—
327#67⋊C4—31no—
328#879—91no—
329#879—91no—
330#879—91no—
331#879—91no—
332#878—91no—
333#878—91no—
334#878—181no—
335#876—91no—
336#875—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—31no—
341C23×C32—31no—
342C23×C32—41no—
343C23×C32—62no—
344C23×C32—121no—
345C23×C32—121no—
346C23×C32C22×D311yescharacteristic
347C23×C32C22×D311yescharacteristic
348C23×C32C22×D311yescharacteristic
349C22×C3⋊D3C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—22no—
352C22×C3×D3—22no—
353C22×C3×D3—21no—
354C22×C3×D3—21no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—31no—
359C22×C3×D3—42no—
360C22×C3×D3—41no—
361C22×C3×D3—41no—
362C22×C3×D3—41no—
363C22×C3×D3—41no—
364C22×C3×D3—42no—
365C22×C3×D3—42no—
366C22×C3×D3—61no—
367C22×C3×D3—61no—
368C22×C3×D3C22×D311yescharacteristic
369C22×C3×D3C22×D311yescharacteristic
370C22×C3×D3C22×D311yescharacteristic
371C22×C3×D3C22×D311yescharacteristic
372C2×C32×C4—31no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—121no—
377#638—22no—
378#638—22no—
379#638—121no—
380#638—121no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—31no—
387C2×C3⋊Dic3—41no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—61no—
392C2×C3⋊Dic3—61no—
393C2×C3⋊Dic3—61no—
394C2×C3⋊Dic3—121no—
395C2×C3⋊Dic3—121no—
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C4×C3⋊D3—121no—
401#634—121no—
402C3×#67—64no—
403C3×#67—62no—
404C3×#67—62no—
405C3×#67—62no—
406C3×#67—62no—
407C3×#67—122no—
408C3×#67—121no—
409C3×#67—121no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—21no—
413C2×C3×Dic3—21no—
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—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—41no—
423C2×C3×Dic3—41no—
424C2×C3×Dic3—42no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—121no—
430C2×C3×Dic3—121no—
431C2×C3×Dic3—122no—
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—121no—
441C3×D12—121no—
442C3×C4×D3—121no—
443C3×C4×D3—121no—
444#627—121no—
445#627—121no—
446#627—122no—
447#626—41no—
448#626—41no—
449#626—121no—
450#626—121no—
451#625—121no—
452#625—121no—
453#625—121no—
454#625—121no—
455#625—121no—
456#625—122no—
457#625—122no—
458#624—41no—
459D3×Dic3—121no—
460D3×Dic3—121no—
461D3×Dic3—122no—
462#538—271noSylow
463C2×C33—22no—
464C2×C33C2×#4111yescharacteristic
465C2×C33H(5,𝔽2)11yescharacteristic
466C2×C33H(5,𝔽2)11yescharacteristic
467C3×C3⋊D3—41no—
468C3×C3⋊D3—41no—
469C32×D3—41no—
470C32×D3—41no—
471C24×C3—31no—
472C24×C3—31no—
473C24×C3—61no—
474C23×D3D3211yescharacteristic
475C2×C3×D4—91no—
476C2×C3×D4—91no—
477C2×C3×D4—91no—
478C2×C3×D4—91no—
479C22×C3×C4—31no—
480C22×C3×C4—31no—
481C22×C3×C4—61no—
482C22×C3×C4—91no—
483C22×C3×C4—91no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—31no—
488C2×#67—31no—
489C2×#67—31no—
490C2×#67—61no—
491C2×#67—61no—
492C2×#67—91no—
493C2×#67—91no—
494C2×#67—91no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—91no—
499C2×#67—91no—
500C2×#67—181no—
501C2×#67—181no—
502C22×Dic3—31no—
503C22×Dic3—31no—
504C22×Dic3—61no—
505C22×Dic3—91no—
506C22×Dic3D3211yescharacteristic
507C2×D12—31no—
508C2×D12—31no—
509C2×D12—91no—
510C2×C4×D3—31no—
511C2×C4×D3—31no—
512C2×C4×D3—91no—
513C2×C4×D3—91no—
514C2×C4×D3—181no—
515C2×Dic6—91no—
516C2×Dic6—91no—
517C2×Dic6—91no—
518C2×Dic6—181no—
519C3×C4⋊C4—91no—
520C3×C22⋊C4—31no—
521C3×C22⋊C4—31no—
522C3×C22⋊C4—61no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525C3×C22⋊C4—91no—
526C3×C22⋊C4—91no—
527C3×C22⋊C4—91no—
528C3×C22⋊C4—91no—
529C3×C22⋊C4—91no—
530C3×C42—91no—
531#217—31no—
532#217—31no—
533#217—31no—
534#217—31no—
535#217—31no—
536#217—31no—
537#217—91no—
538#217—91no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—91no—
547#217—181no—
548#217—181no—
549#217—181no—
550#217—181no—
551#217—181no—
552#217—361no—
553#217D3211yescharacteristic
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—31no—
560(C2×D3)⋊C4—31no—
561(C2×D3)⋊C4—31no—
562(C2×D3)⋊C4—91no—
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—181no—
571C4⋊Dic3—91no—
572C4⋊Dic3—91no—
573C4⋊Dic3—91no—
574C4⋊Dic3—91no—
575C4⋊Dic3—91no—
576C4⋊Dic3—181no—
577Dic3⋊C4—31no—
578Dic3⋊C4—31no—
579Dic3⋊C4—91no—
580Dic3⋊C4—91no—
581Dic3⋊C4—91no—
582Dic3⋊C4—91no—
583Dic3⋊C4—91no—
584Dic3⋊C4—91no—
585Dic3⋊C4—91no—
586Dic3⋊C4—91no—
587Dic3⋊C4—91no—
588Dic3⋊C4—91no—
589Dic3⋊C4—181no—
590Dic3⋊C4—181no—
591Dic3⋊C4—181no—
592C4×Dic3—31no—
593C4×Dic3—31no—
594C4×Dic3—91no—
595C4×Dic3—91no—
596C4×Dic3—91no—
597C4×Dic3—181no—
598C22×C32—21no—
599C22×C32—21no—
600C22×C32—21no—
601C22×C32—21no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—22no—
608C22×C32—22no—
609C22×C32—22no—
610C22×C32—41no—
611C22×C32—42no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—41no—
617C22×C32—41no—
618C22×C32—61no—
619C22×C32—61no—
620C22×C32—61no—
621C22×C32—61no—
622C22×C32—61no—
623C22×C32—61no—
624C22×C32—81no—
625C22×C32—81no—
626C22×C32—124no—
627C22×C32#23512yes—
628C22×C32#23512yes—
629C22×C32#23712yes—
630C22×C32C23×D311yescharacteristic
631C22×C32C23×D311yescharacteristic
632C22×C32C23×D311yescharacteristic
633C2×C3⋊D3—21no—
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—21no—
637C2×C3⋊D3—21no—
638C2×C3⋊D3—21no—
639C2×C3×D3—22no—
640C2×C3×D3—22no—
641C2×C3×D3—21no—
642C2×C3×D3—21no—
643C2×C3×D3—21no—
644C2×C3×D3—21no—
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—21no—
652C2×C3×D3—21no—
653C2×C3×D3—41no—
654C2×C3×D3—41no—
655C2×C3×D3—41no—
656C2×C3×D3—41no—
657C2×C3×D3—44no—
658C2×C3×D3—44no—
659C2×C3×D3—48no—
660C2×C3×D3—62no—
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—61no—
668C2×C3×D3—61no—
669C2×C3×D3—61no—
670C2×C3×D3—61no—
671C2×C3×D3—61no—
672C2×C3×D3—61no—
673C2×C3×D3—121no—
674C2×C3×D3—121no—
675C2×C3×D3—121no—
676C2×C3×D3—121no—
677C2×C3×D3—121no—
678C32×C4—61no—
679C32×C4—61no—
680C32×C4—61no—
681C32×C4—61no—
682C3⋊Dic3—21no—
683C3⋊Dic3—21no—
684C3⋊Dic3—21no—
685C3⋊Dic3—21no—
686C3⋊Dic3—61no—
687C3⋊Dic3—61no—
688C3⋊Dic3—61no—
689C3⋊Dic3—61no—
690C3⋊Dic3—61no—
691C3⋊Dic3—61no—
692C3⋊Dic3—121no—
693C3⋊Dic3—121no—
694C3⋊Dic3—121no—
695C3⋊Dic3—121no—
696C3⋊Dic3—121no—
697C3⋊Dic3—121no—
698C3⋊Dic3—241no—
699C3⋊Dic3—241no—
700C3×Dic3—22no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—41no—
710C3×Dic3—41no—
711C3×Dic3—41no—
712C3×Dic3—62no—
713C3×Dic3—62no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—61no—
717C3×Dic3—61no—
718C3×Dic3—61no—
719C3×Dic3—61no—
720C3×Dic3—61no—
721C3×Dic3—61no—
722C3×Dic3—121no—
723C3×Dic3—121no—
724#126—271no—
725#126—271no—
726#124—271no—
727#124—271no—
728#123—271no—
729#123—271no—
730C22⋊Q8—271no—
731#121—271no—
732#121—271no—
733#121—271no—
734#120—91no—
735#120—271no—
736C4×D4—91no—
737C4×D4—271no—
738C2×C22⋊C4—91no—
739C33#53811yescharacteristic, complemented, Sylow
740C23×C3—21no—
741C23×C3—21no—
742C23×C3—21no—
743C23×C3—31no—
744C23×C3—31no—
745C23×C3—31no—
746C23×C3—31no—
747C23×C3—41no—
748C23×C3—61no—
749C23×C3—61no—
750C23×C3—62no—
751C23×C3—62no—
752C23×C3—91no—
753C23×C3—91no—
754C23×C3—122no—
755C23×C3—121no—
756C23×C3—121no—
757C23×C3—121no—
758C23×C3—121no—
759C23×C3—122no—
760C23×C3—122no—
761C23×C3C2×D3211yescharacteristic
762C23×C3C2×D3211yescharacteristic
763C23×C3C2×D3211yescharacteristic
764C22×D3—22no—
765C22×D3—31no—
766C22×D3—31no—
767C22×D3—31no—
768C22×D3—31no—
769C22×D3—41no—
770C22×D3—41no—
771C22×D3—61no—
772C22×D3—61no—
773C22×D3C2×D3211yescharacteristic
774C22×D3C2×D3211yescharacteristic
775C3×D4—182no—
776C3×D4—182no—
777C3×D4—361no—
778C3×D4—361no—
779C2×C3×C4—31no—
780C2×C3×C4—31no—
781C2×C3×C4—31no—
782C2×C3×C4—31no—
783C2×C3×C4—31no—
784C2×C3×C4—31no—
785C2×C3×C4—31no—
786C2×C3×C4—31no—
787C2×C3×C4—61no—
788C2×C3×C4—61no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—121no—
796C2×C3×C4—121no—
797C2×C3×C4—122no—
798C2×C3×C4—361no—
799C2×C3×C4—361no—
800#67—64no—
801#67—62no—
802#67—62no—
803#67—62no—
804#67—62no—
805#67—122no—
806#67—121no—
807#67—121no—
808#67—361no—
809#67—361no—
810#67—361no—
811#67—361no—
812#67—361no—
813#67—361no—
814#67—361no—
815#67—361no—
816#67—362no—
817#67—362no—
818C2×Dic3—31no—
819C2×Dic3—31no—
820C2×Dic3—31no—
821C2×Dic3—31no—
822C2×Dic3—31no—
823C2×Dic3—31no—
824C2×Dic3—31no—
825C2×Dic3—31no—
826C2×Dic3—41no—
827C2×Dic3—61no—
828C2×Dic3—61no—
829C2×Dic3—61no—
830C2×Dic3—61no—
831C2×Dic3—91no—
832C2×Dic3—91no—
833C2×Dic3—91no—
834C2×Dic3—91no—
835C2×Dic3—91no—
836C2×Dic3—91no—
837C2×Dic3—121no—
838C2×Dic3—121no—
839C2×Dic3—122no—
840C2×Dic3—181no—
841C2×Dic3—181no—
842C2×Dic3—181no—
843C2×Dic3—181no—
844C2×Dic3—181no—
845C2×Dic3—181no—
846C2×Dic3—361no—
847C2×Dic3—361no—
848C2×Dic3—361no—
849C2×Dic3C2×D3211yescharacteristic
850C2×Dic3C2×D3211yescharacteristic
851C2×Dic3C2×D3211yescharacteristic
852C2×Dic3C2×D3211yescharacteristic
853D12—121no—
854D12—121no—
855D12—361no—
856C4×D3—121no—
857C4×D3—121no—
858C4×D3—361no—
859C4×D3—361no—
860C4×D3—362no—
861Dic6—361no—
862Dic6—361no—
863Dic6—361no—
864Dic6—362no—
865C2×C32—22no—
866C2×C32—22no—
867C2×C32—22no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—21no—
872C2×C32—21no—
873C2×C32—21no—
874C2×C32—21no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—41no—
878C2×C32—41no—
879C2×C32—41no—
880C2×C32—42no—
881C2×C32—42no—
882C2×C32—42no—
883C2×C32—82no—
884C2×C32—121no—
885C2×C32—121no—
886C2×C32C2×#23511yescharacteristic
887C2×C32C2×#23511yescharacteristic
888C2×C32C2×#23711yescharacteristic
889C2×C32#100411yescharacteristic
890C2×C32#100411yescharacteristic
891C2×C32#100411yescharacteristic
892C2×C32#100411yescharacteristic
893C2×C32#100411yescharacteristic
894C2×C32#100911yescharacteristic
895C3⋊D3—41no—
896C3⋊D3—41no—
897C3×D3—42no—
898C3×D3—42no—
899C3×D3—41no—
900C3×D3—41no—
901C3×D3—41no—
902C3×D3—41no—
903C3×D3—122no—
904C3×D3—121no—
905C3×D3—121no—
906C3×D3—121no—
907C3×D3—121no—
908C3×D3—241no—
909C24—31no—
910C2×Q8—271no—
911C2×D4—91no—
912C2×D4—91no—
913C2×D4—91no—
914C2×D4—91no—
915C2×D4—271no—
916C2×D4—271no—
917C2×D4—271no—
918C22×C4—31no—
919C22×C4—91no—
920C22×C4—91no—
921C22×C4—271no—
922C4⋊C4—91no—
923C4⋊C4—271no—
924C4⋊C4—271no—
925C4⋊C4—271no—
926C4⋊C4—271no—
927C4⋊C4—271no—
928C22⋊C4—31no—
929C22⋊C4—91no—
930C22⋊C4—91no—
931C22⋊C4—91no—
932C22⋊C4—91no—
933C22⋊C4—91no—
934C22⋊C4—91no—
935C22⋊C4—91no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22⋊C4—271no—
939C22⋊C4—271no—
940C22⋊C4—271no—
941C22⋊C4—271no—
942C42—91no—
943C42—271no—
944C22×C3—21no—
945C22×C3—21no—
946C22×C3—21no—
947C22×C3—21no—
948C22×C3—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—21no—
952C22×C3—21no—
953C22×C3—22no—
954C22×C3—22no—
955C22×C3—22no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—41no—
960C22×C3—41no—
961C22×C3—41no—
962C22×C3—41no—
963C22×C3—42no—
964C22×C3—62no—
965C22×C3—62no—
966C22×C3—61no—
967C22×C3—61no—
968C22×C3—61no—
969C22×C3—61no—
970C22×C3—61no—
971C22×C3—61no—
972C22×C3—61no—
973C22×C3—61no—
974C22×C3—61no—
975C22×C3—61no—
976C22×C3—61no—
977C22×C3—61no—
978C22×C3—81no—
979C22×C3—81no—
980C22×C3—121no—
981C22×C3—121no—
982C22×C3—121no—
983C22×C3—121no—
984C22×C3—124no—
985C22×C3—124no—
986C22×C3—128no—
987C22×C3—181no—
988C22×C3—181no—
989C22×C3—181no—
990C22×C3—181no—
991C22×C3—181no—
992C22×C3—181no—
993C22×C3#379512yes—
994C22×C3#379812yes—
995C22×C3#380412yes—
996C22×C3C22×D3211yescharacteristic
997C22×C3C22×D3211yescharacteristic
998C22×C3C22×D3211yescharacteristic
999C2×D3—21no—
1000C2×D3—21no—
1001C2×D3—21no—
1002C2×D3—21no—
1003C2×D3—21no—
1004C2×D3—21no—
1005C2×D3—44no—
1006C2×D3—62no—
1007C2×D3—61no—
1008C2×D3—61no—
1009C2×D3—61no—
1010C2×D3—61no—
1011C2×D3—61no—
1012C2×D3—61no—
1013C2×D3—61no—
1014C2×D3—61no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—61no—
1019C2×D3—121no—
1020C2×D3—121no—
1021C2×D3—121no—
1022C2×D3—121no—
1023C2×D3—121no—
1024C3×C4—62no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—61no—
1028C3×C4—61no—
1029C3×C4—61no—
1030C3×C4—61no—
1031C3×C4—61no—
1032C3×C4—61no—
1033C3×C4—121no—
1034C3×C4—121no—
1035C3×C4—121no—
1036C3×C4—181no—
1037C3×C4—181no—
1038C3×C4—181no—
1039C3×C4—181no—
1040Dic3—21no—
1041Dic3—21no—
1042Dic3—21no—
1043Dic3—21no—
1044Dic3—62no—
1045Dic3—62no—
1046Dic3—61no—
1047Dic3—61no—
1048Dic3—61no—
1049Dic3—61no—
1050Dic3—61no—
1051Dic3—61no—
1052Dic3—61no—
1053Dic3—61no—
1054Dic3—121no—
1055Dic3—121no—
1056Dic3—181no—
1057Dic3—181no—
1058Dic3—181no—
1059Dic3—181no—
1060Dic3—181no—
1061Dic3—181no—
1062Dic3—361no—
1063Dic3—361no—
1064Dic3—361no—
1065Dic3—361no—
1066Dic3—361no—
1067Dic3—361no—
1068Dic3—721no—
1069Dic3—721no—
1070C32—21no—
1071C32—21no—
1072C32—21no—
1073C32—41no—
1074C32#549411yescharacteristic, complemented
1075C32#556011yescharacteristic, complemented
1076C32#559311yescharacteristic, complemented
1077C23—31no—
1078C23—31no—
1079C23—62no—
1080C23—91no—
1081C23—91no—
1082C23—121no—
1083C23—121no—
1084C23D3311yescharacteristic
1085Q8—1081no—
1086D4—182no—
1087D4—182no—
1088D4—361no—
1089D4—361no—
1090D4—1081no—
1091D4—1081no—
1092D4—1081no—
1093C2×C4—31no—
1094C2×C4—31no—
1095C2×C4—31no—
1096C2×C4—31no—
1097C2×C4—91no—
1098C2×C4—91no—
1099C2×C4—91no—
1100C2×C4—91no—
1101C2×C4—121no—
1102C2×C4—271no—
1103C2×C4—271no—
1104C2×C4—361no—
1105C2×C4—361no—
1106C2×C4—1081no—
1107C2×C3—22no—
1108C2×C3—22no—
1109C2×C3—22no—
1110C2×C3—21no—
1111C2×C3—21no—
1112C2×C3—21no—
1113C2×C3—21no—
1114C2×C3—21no—
1115C2×C3—21no—
1116C2×C3—21no—
1117C2×C3—21no—
1118C2×C3—21no—
1119C2×C3—42no—
1120C2×C3—42no—
1121C2×C3—42no—
1122C2×C3—41no—
1123C2×C3—41no—
1124C2×C3—41no—
1125C2×C3—82no—
1126C2×C3—122no—
1127C2×C3—122no—
1128C2×C3—121no—
1129C2×C3—121no—
1130C2×C3—121no—
1131C2×C3—121no—
1132C2×C3—361no—
1133C2×C3—361no—
1134C2×C3C2×#379511yescharacteristic
1135C2×C3C2×#379811yescharacteristic
1136C2×C3#6430711yescharacteristic
1137C2×C3#6431311yescharacteristic
1138C2×C3#6431411yescharacteristic
1139C2×C3C2×#380411yescharacteristic
1140C2×C3#6433011yescharacteristic
1141C2×C3#6433011yescharacteristic
1142C2×C3#6433011yescharacteristic
1143D3—41no—
1144D3—41no—
1145D3—122no—
1146D3—121no—
1147D3—121no—
1148D3—121no—
1149D3—121no—
1150D3—241no—
1151C22—21no—
1152C22—21no—
1153C22—61no—
1154C22—61no—
1155C22—61no—
1156C22—61no—
1157C22—61no—
1158C22—61no—
1159C22—124no—
1160C22—181no—
1161C22—181no—
1162C22—181no—
1163C22—181no—
1164C22—181no—
1165C22—181no—
1166C22#8896012yes—
1167C22C2×D3311yescharacteristic
1168C4—61no—
1169C4—61no—
1170C4—61no—
1171C4—61no—
1172C4—181no—
1173C4—181no—
1174C4—181no—
1175C4—181no—
1176C4—541no—
1177C4—541no—
1178C3—21no—
1179C3—21no—
1180C3—21no—
1181C3—41no—
1182C3#1059423811yescharacteristic, complemented
1183C3#1059503611yescharacteristic, complemented
1184C3#1059550711yescharacteristic, complemented
1185C2—22no—
1186C2—121no—
1187C2—121no—
1188C2—361no—
1189C2—361no—
1190C2#1172441411yescharacteristic
1191C2#1172441811yescharacteristic
1192C2C2×#8896011yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#538
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. #11723717C2semidirect
2. #11723641C2semidirect
3. #11723629C2semidirect
4. Dic3×#638C2semidirect
5. C3×#63977C2semidirect
6. C2×C3×(C2×D3)⋊Dic3C2semidirect
7. C3×#63952C2semidirect
8. #11723022C2semidirect
9. #11723020C2semidirect
10. #11723009C2semidirect
11. #11723002C2semidirect
12. #11722992C2semidirect
13. #11722991C2semidirect
14. #11722967C2semidirect
15. #11722957C2semidirect
24. C2×#6295C22semidirect
25. C2×#6293C22semidirect
28. C2×Dic3×C3⋊D3C22semidirect
31. C2×C3×#624C22semidirect
34. #88815C22semidirect
35. #88814C22semidirect
36. #88814C22semidirect
37. #88807C22semidirect
38. #88807C22semidirect
39. #88806C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
41. #88803C22semidirect
44. Dic3×C3⋊Dic3C22semidirect
45. C3×#3724C22semidirect
46. C3×#3722C22semidirect
53. C3×Dic32C22semidirect
66. #63977D3semidirect
79. C2×(C2×D3)⋊Dic3D3semidirect
85. #63952D3semidirect
179. C2×#624C2×D3semidirect
224. #3724C2×D3semidirect
238. #3722C2×D3semidirect
261. Dic32C2×D3semidirect
739. C33#538semidirect
1074. C32#5494semidirect
1075. C32#5560semidirect
1076. C32#5593semidirect
1182. C3#10594238semidirect
1183. C3#10595036semidirect
1184. C3#10595507semidirect

Maximal subgroups

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

subgroupindex
#117237172
#117236412
#117236292
Dic3×#6382
C3×#639772
C2×C3×(C2×D3)⋊Dic32
C3×#639522
#117230222
#117230202
#117230092
#117230022
#117229922
#117229912
#117229672
#117229572
#105955073
#105950363
#105942383