Finite Group Databasebeta

← #13172136

Subgroups — #13172136

Order 1728.

1354 conjugacy classes of subgroups.

The subgroup lattice has 1216 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#11723726C211yesmaximal, characteristic, complemented
2#11723643C211yesmaximal, characteristic, complemented
3#11723635C211yesmaximal, characteristic, complemented
4#11723592C211yesmaximal, characteristic, complemented
5C3×#63970C211yesmaximal, characteristic, complemented
6C3×#63962C211yesmaximal, characteristic, complemented
7C3×#63958C211yesmaximal, characteristic, complemented
8#11723028C211yesmaximal, characteristic, complemented
9#11723019C211yesmaximal, characteristic, complemented
10#11723004C211yesmaximal, characteristic, complemented
11#11722987C211yesmaximal, characteristic, complemented
12#11722972C211yesmaximal, characteristic, complemented
13#11722949C211yesmaximal, characteristic, complemented
14#11722927C211yesmaximal, characteristic, complemented
15#11722904C211yesmaximal, characteristic, complemented
16#10595310—31nomaximal
17#10595255—31nomaximal
18#10594302—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×#6312C2211yescharacteristic
21C2×C3×#638C2211yescharacteristic
22C22×C3×C3⋊Dic3C2211yescharacteristic, complemented
23C2×C32×#67C2211yescharacteristic
24C2×C32×#67C2211yescharacteristic, complemented
25C2×#6294C2211yescharacteristic
26C2×#6293C2211yescharacteristic, complemented
27C2×#6291C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#625C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32C3×#3757C2211yescharacteristic, complemented
33C32×#217C2211yescharacteristic, complemented
34#88815C2211yescharacteristic, complemented
35#88814C2211yescharacteristic
36#88813C2211yescharacteristic, complemented
37#88807C2211yescharacteristic, complemented
38#88804C2211yescharacteristic
39#88804C2211yescharacteristic
40#88804C2211yescharacteristic
41#88804C2211yescharacteristic
42#88803C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46C3×Dic3⋊Dic3C2211yescharacteristic, complemented
47C3×Dic3⋊Dic3C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64148—31no—
55#64146—31no—
56#64094—31no—
57C3×#939—31no—
58C3×#938—31no—
59C3×#938—31no—
60C3×#935—31no—
61C3×#886—31no—
62C3×#884—31no—
63#63983—31no—
64#63983—31no—
65#63983—31no—
66#63983—61no—
67#63981—31no—
68#63978—31no—
69#63978—31no—
70#63978—61no—
71#63974—31no—
72#67⋊Dic3—31no—
73Dic3×#67—31no—
74Dic3×#67—31no—
75#63970D311yescharacteristic, complemented
76#63966—31no—
77#63962D311yescharacteristic, complemented
78#63959—31no—
79#63959—31no—
80#63958D311yescharacteristic, complemented
81#63956—31no—
82#63953—31no—
83#63953—31no—
84#63953—61no—
85#63952—31no—
86#63922—31no—
87D3×(C2×D3)⋊C4—31no—
88D3×(C2×D3)⋊C4—31no—
89#63913—31no—
90#63904—31no—
91#63898—31no—
92#63895—31no—
93#63890—31no—
94#63862—31no—
95#63858—31no—
96#63857—31no—
97#63851—31no—
98#63850—31no—
99#63848—31no—
100#63848—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3⋊(C3⋊D3)C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—41no—
109C2×D3×C3⋊D3—41no—
110#6312—41no—
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C3×#638—22no—
113C2×C3×C3⋊Dic3—41no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C32×#67—41no—
120C32×#67—41no—
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C2×C32×Dic3C2311yescharacteristic
125#6294—41no—
126#6293—41no—
127#6291—41no—
128C3×#626—22no—
129C3×#625—41no—
130C3×#624—41no—
131C3×D3×Dic3—41no—
132#5657—91no—
133#5617—91no—
134#5613—91no—
135C23×C3⋊D3—31no—
136C22×D32—31no—
137C22×D32—31no—
138C22×D32—61no—
139C2×C32×D4—31no—
140C2×C32×D4—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#638—31no—
144C2×#638—31no—
145C2×#638—61no—
146C2×#638—61no—
147C2×#638—61no—
148C2×#638—121no—
149C2×#638C2×D311yescharacteristic
150C22×C3⋊Dic3C2×D311yescharacteristic, complemented
151C2×#634—31no—
152C2×C3×#67—21no—
153C2×C3×#67—21no—
154C2×C3×#67—31no—
155C2×C3×#67—31no—
156C2×C3×#67—31no—
157C2×C3×#67—31no—
158C2×C3×#67—31no—
159C2×C3×#67—61no—
160C2×C3×#67C2×D311yescharacteristic
161C2×C3×#67C2×D311yescharacteristic
162C2×C3×#67C2×D311yescharacteristic, complemented
163C2×C3×#67C2×D311yescharacteristic, complemented
164C22×C3×Dic3—31no—
165C22×C3×Dic3—31no—
166C22×C3×Dic3—31no—
167C22×C3×Dic3—61no—
168C2×C3×D12—31no—
169C2×C3×C4×D3—31no—
170C2×C3×C4×D3—31no—
171C2×C3×C4×D3—31no—
172C2×#627—31no—
173C2×#627—31no—
174C2×#627—61no—
175C2×#626—31no—
176C2×#626—31no—
177C2×#626—61no—
178C2×#626C2×D311yescharacteristic
179C2×#625C2×D311yescharacteristic
180C2×#624—31no—
181C2×#624C2×D311yescharacteristic
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3C2×D311yescharacteristic, complemented
185C32×C22⋊C4—31no—
186#3757—31no—
187#3757—31no—
188#3757C2×D311yescharacteristic, complemented
189#3752—31no—
190#3752—31no—
191#3752—31no—
192#3752—31no—
193#3752—31no—
194#3750—31no—
195C4×C3⋊Dic3—31no—
196C3×#217—21no—
197C3×#217—31no—
198C3×#217—31no—
199C3×#217—31no—
200C3×#217—31no—
201C3×#217—31no—
202C3×#217—31no—
203C3×#217—61no—
204C3×#217C2×D311yescharacteristic, complemented
205C3×#217C2×D311yescharacteristic, complemented
206C3×(C2×D3)⋊C4—31no—
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×C4⋊Dic3—31no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3—31no—
213C3×C4⋊Dic3—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×Dic3⋊C4—31no—
218#3724—31no—
219Dic3⋊Dic3—31no—
220Dic3⋊Dic3—31no—
221Dic3⋊Dic3—31no—
222Dic3⋊Dic3—31no—
223Dic3⋊Dic3—61no—
224Dic3⋊Dic3C2×D311yescharacteristic, complemented
225Dic3⋊Dic3C2×D311yescharacteristic, complemented
226Dic3⋊Dic3C2×D311yescharacteristic, complemented
227Dic3⋊Dic3C2×D311yescharacteristic, complemented
228#3722—31no—
229#3722—31no—
230#3722—31no—
231#3722—31no—
232#3722—31no—
233#3722—31no—
234#3722—31no—
235#3722—31no—
236#3722—31no—
237#3722—61no—
238#3722—61no—
239#3722—61no—
240#3722—61no—
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, complemented
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259Dic32—31no—
260Dic32—31no—
261Dic32—61no—
262C22×C33—21no—
263C22×C33—21no—
264C22×C33—21no—
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#4112yes—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278D3×C3⋊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×#123—91no—
290C3×#121—91no—
291C3×#121—91no—
292#939—31no—
293#939—91no—
294#939—91no—
295#939—181no—
296#938—31no—
297#938—31no—
298#937—91no—
299#937—91no—
300#937—91no—
301#937—91no—
302#937—91no—
303#937—181no—
304#936—91no—
305#935—31no—
306D4×Dic3—91no—
307D4×Dic3—91no—
308#930—91no—
309#929—91no—
310C4×#67—91no—
311C4×#67—91no—
312C2×(C2×D3)⋊C4—91no—
313#924—91no—
314#898—91no—
315#898—91no—
316#898—91no—
317#898—91no—
318#897—91no—
319#896—91no—
320#894—91no—
321#893—91no—
322#886—31no—
323#886—91no—
324#885—91no—
325#885—91no—
326#885—91no—
327#885—91no—
328#885—91no—
329#885—181no—
330#884—31no—
331#882—91no—
332#67⋊C4—91no—
333D3×C22⋊C4—91no—
334D3×C22⋊C4—91no—
335#879—91no—
336#879—91no—
337C23×C32—21no—
338C23×C32—21no—
339C23×C32—21no—
340C23×C32—31no—
341C23×C32—31no—
342C23×C32—41no—
343C23×C32C22×D311yescharacteristic
344C23×C32C22×D311yescharacteristic
345C23×C32C22×D311yescharacteristic
346C22×C3⋊D3—31no—
347C22×C3⋊D3—31no—
348C22×C3⋊D3—31no—
349C22×C3⋊D3—61no—
350C22×C3⋊D3—61no—
351C22×C3⋊D3—61no—
352C22×C3⋊D3—62no—
353C22×C3⋊D3—121no—
354C22×C3⋊D3—121no—
355C22×C3⋊D3—121no—
356C22×C3⋊D3C22×D311yescharacteristic
357C22×C3×D3—21no—
358C22×C3×D3—21no—
359C22×C3×D3—31no—
360C22×C3×D3—31no—
361C22×C3×D3—61no—
362C22×C3×D3C22×D311yescharacteristic
363C22×C3×D3C22×D311yescharacteristic
364C22×C3×D3C22×D311yescharacteristic
365C22×C3×D3C22×D311yescharacteristic
366C2×D32—62no—
367C2×D32—62no—
368C2×D32—122no—
369C2×D32—121no—
370C2×D32—121no—
371C2×D32—121no—
372C2×D32—121no—
373C2×D32—122no—
374C2×D32—122no—
375C32×D4—121no—
376C32×D4—121no—
377C2×C32×C4—31no—
378C2×C32×C4—31no—
379C2×C32×C4—31no—
380C2×C32×C4—31no—
381#638—22no—
382#638—121no—
383#638—121no—
384#638—121no—
385#638—121no—
386#638—122no—
387#638—122no—
388#638—122no—
389#638—124no—
390C2×C3⋊Dic3—31no—
391C2×C3⋊Dic3—31no—
392C2×C3⋊Dic3—31no—
393C2×C3⋊Dic3—41no—
394C2×C3⋊Dic3—61no—
395C2×C3⋊Dic3—61no—
396C2×C3⋊Dic3—61no—
397C2×C3⋊Dic3—121no—
398C2×C3⋊Dic3C22×D311yescharacteristic
399C2×C3⋊Dic3C22×D311yescharacteristic
400C2×C3⋊Dic3C22×D311yescharacteristic
401C2×C3⋊Dic3C22×D311yescharacteristic
402C2×C3⋊Dic3C22×D311yescharacteristic
403#634—121no—
404C3×#67—41no—
405C3×#67—41no—
406C3×#67—41no—
407C3×#67—41no—
408C3×#67—42no—
409C3×#67—42no—
410C3×#67—62no—
411C3×#67—62no—
412C3×#67—62no—
413C3×#67—122no—
414C3×#67—121no—
415C3×#67—121no—
416C2×C3×Dic3—21no—
417C2×C3×Dic3—21no—
418C2×C3×Dic3—21no—
419C2×C3×Dic3—21no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
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—61no—
431C2×C3×Dic3—61no—
432C2×C3×Dic3—61no—
433C2×C3×Dic3—61no—
434C2×C3×Dic3—61no—
435C2×C3×Dic3—121no—
436C2×C3×Dic3—121no—
437C2×C3×Dic3—121no—
438C2×C3×Dic3—122no—
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C2×C3×Dic3C22×D311yescharacteristic
442C2×C3×Dic3C22×D311yescharacteristic
443C2×C3×Dic3C22×D311yescharacteristic
444C2×C3×Dic3C22×D311yescharacteristic
445C2×C3×Dic3C22×D311yescharacteristic
446C2×C3×Dic3C22×D311yescharacteristic
447C3×D12—62no—
448C3×C4×D3—121no—
449C3×C4×D3—121no—
450C3×C4×D3—121no—
451#627—121no—
452#627—121no—
453#627—122no—
454#626—22no—
455#626—121no—
456#626—121no—
457#626—122no—
458#625—41no—
459#624—41no—
460#624—121no—
461D3×Dic3—41no—
462D3×Dic3—121no—
463D3×Dic3—121no—
464#538—271noSylow
465C2×C33—41no—
466C2×C33C2×#4111yescharacteristic
467C2×C33H(5,𝔽2)11yescharacteristic
468C2×C33H(5,𝔽2)11yescharacteristic
469C3⋊(C3⋊D3)—41no—
470C3×C3⋊D3—22no—
471C32×D3—41no—
472C32×D3—41no—
473C23×D3—91no—
474C23×D3—91no—
475C23×D3—91no—
476C23×D3—181no—
477C2×C3×D4—31no—
478C2×C3×D4—31no—
479C2×C3×D4—31no—
480C2×C3×D4—31no—
481C2×C3×D4—61no—
482C2×C3×D4—61no—
483C2×C3×D4—91no—
484C2×C3×D4—91no—
485C2×C3×D4—91no—
486C22×C3×C4—91no—
487C22×C3×C4—91no—
488C22×C3×C4—91no—
489C2×#67—31no—
490C2×#67—31no—
491C2×#67—31no—
492C2×#67—31no—
493C2×#67—31no—
494C2×#67—61no—
495C2×#67—91no—
496C2×#67—91no—
497C2×#67—91no—
498C2×#67—91no—
499C2×#67—91no—
500C2×#67—181no—
501C2×#67—181no—
502C2×#67—181no—
503C2×#67—181no—
504C2×#67—361no—
505C2×#67D3211yescharacteristic
506C2×#67D3211yescharacteristic, complemented
507C22×Dic3—31no—
508C22×Dic3—31no—
509C22×Dic3—31no—
510C22×Dic3—61no—
511C22×Dic3—91no—
512C2×D12—31no—
513C2×D12—91no—
514C2×C4×D3—31no—
515C2×C4×D3—31no—
516C2×C4×D3—31no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×Dic6—91no—
520C2×Dic6—91no—
521C2×Dic6—91no—
522C2×Dic6—181no—
523C3×C4⋊C4—91no—
524C3×C4⋊C4—91no—
525C3×C4⋊C4—91no—
526C3×C4⋊C4—91no—
527C3×C22⋊C4—31no—
528C3×C22⋊C4—31no—
529C3×C22⋊C4—61no—
530C3×C22⋊C4—91no—
531C3×C22⋊C4—91no—
532C3×C22⋊C4—91no—
533C3×C22⋊C4—91no—
534C3×C22⋊C4—91no—
535#217—31no—
536#217—31no—
537#217—31no—
538#217—31no—
539#217—31no—
540#217—31no—
541#217—61no—
542#217—91no—
543#217—91no—
544#217—91no—
545#217—91no—
546#217—91no—
547#217—91no—
548#217—181no—
549#217—181no—
550#217D3211yescharacteristic, complemented
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—91no—
556(C2×D3)⋊C4—91no—
557(C2×D3)⋊C4—91no—
558(C2×D3)⋊C4—91no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
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—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—91no—
573(C2×D3)⋊C4—181no—
574(C2×D3)⋊C4—181no—
575(C2×D3)⋊C4—181no—
576(C2×D3)⋊C4—181no—
577(C2×D3)⋊C4—181no—
578C4⋊Dic3—31no—
579C4⋊Dic3—31no—
580C4⋊Dic3—31no—
581C4⋊Dic3—31no—
582C4⋊Dic3—91no—
583C4⋊Dic3—91no—
584Dic3⋊C4—31no—
585Dic3⋊C4—31no—
586Dic3⋊C4—31no—
587Dic3⋊C4—31no—
588Dic3⋊C4—91no—
589Dic3⋊C4—91no—
590Dic3⋊C4—91no—
591Dic3⋊C4—91no—
592Dic3⋊C4—181no—
593C4×Dic3—91no—
594C4×Dic3—91no—
595C4×Dic3—91no—
596C4×Dic3—91no—
597C4×Dic3—91no—
598C4×Dic3—91no—
599C4×Dic3—181no—
600C22×C32—21no—
601C22×C32—22no—
602C22×C32—21no—
603C22×C32—21no—
604C22×C32—21no—
605C22×C32—21no—
606C22×C32—21no—
607C22×C32—21no—
608C22×C32—21no—
609C22×C32—21no—
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32—41no—
614C22×C32—41no—
615C22×C32—41no—
616C22×C32—42no—
617C22×C32—41no—
618C22×C32—41no—
619C22×C32—41no—
620C22×C32—41no—
621C22×C32—41no—
622C22×C32—41no—
623C22×C32—61no—
624C22×C32—61no—
625C22×C32—61no—
626C22×C32—61no—
627C22×C32—61no—
628C22×C32—61no—
629C22×C32—81no—
630C22×C32—81no—
631C22×C32C23×D311yescharacteristic
632C22×C32C23×D311yescharacteristic
633C22×C32C23×D311yescharacteristic
634C2×C3⋊D3—21no—
635C2×C3⋊D3—21no—
636C2×C3⋊D3—61no—
637C2×C3⋊D3—62no—
638C2×C3⋊D3—61no—
639C2×C3⋊D3—61no—
640C2×C3⋊D3—61no—
641C2×C3⋊D3—61no—
642C2×C3⋊D3—61no—
643C2×C3⋊D3—61no—
644C2×C3⋊D3—61no—
645C2×C3⋊D3—61no—
646C2×C3⋊D3—121no—
647C2×C3⋊D3—121no—
648C2×C3⋊D3—122no—
649C2×C3⋊D3—121no—
650C2×C3⋊D3—121no—
651C2×C3⋊D3—121no—
652C2×C3⋊D3—121no—
653C2×C3⋊D3—121no—
654C2×C3⋊D3—121no—
655C2×C3⋊D3—124no—
656C2×C3⋊D3—241no—
657C2×C3⋊D3—241no—
658C2×C3⋊D3#23712yes—
659C2×C3×D3—22no—
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—21no—
669C2×C3×D3—21no—
670C2×C3×D3—21no—
671C2×C3×D3—21no—
672C2×C3×D3—32no—
673C2×C3×D3—32no—
674C2×C3×D3—41no—
675C2×C3×D3—41no—
676C2×C3×D3—41no—
677C2×C3×D3—41no—
678C2×C3×D3—41no—
679C2×C3×D3—62no—
680C2×C3×D3—61no—
681C2×C3×D3—61no—
682C2×C3×D3—61no—
683C2×C3×D3—61no—
684C2×C3×D3—121no—
685C2×C3×D3—121no—
686D32—124no—
687D32—124no—
688D32—128no—
689C32×C4—61no—
690C32×C4—61no—
691C32×C4—61no—
692C32×C4—61no—
693C3⋊Dic3—21no—
694C3⋊Dic3—21no—
695C3⋊Dic3—21no—
696C3⋊Dic3—21no—
697C3⋊Dic3—21no—
698C3⋊Dic3—61no—
699C3⋊Dic3—62no—
700C3⋊Dic3—61no—
701C3⋊Dic3—61no—
702C3⋊Dic3—121no—
703C3⋊Dic3—121no—
704C3⋊Dic3—122no—
705C3×Dic3—21no—
706C3×Dic3—21no—
707C3×Dic3—21no—
708C3×Dic3—21no—
709C3×Dic3—21no—
710C3×Dic3—21no—
711C3×Dic3—21no—
712C3×Dic3—21no—
713C3×Dic3—41no—
714C3×Dic3—41no—
715C3×Dic3—41no—
716C3×Dic3—41no—
717C3×Dic3—62no—
718C3×Dic3—61no—
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—61no—
728C3×Dic3—121no—
729C3×Dic3—121no—
730C3×Dic3—121no—
731C3×Dic3—121no—
732#126—271no—
733#126—271no—
734#124—271no—
735#124—271no—
736#123—91no—
737#123—271no—
738C22⋊Q8—271no—
739#121—91no—
740#121—91no—
741#121—271no—
742#120—271no—
743#120—271no—
744C4×D4—271no—
745C4×D4—271no—
746C2×C22⋊C4—271no—
747C33#53811yescharacteristic, 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×D3—91no—
766C22×D3—91no—
767C22×D3—91no—
768C22×D3—181no—
769C22×D3—181no—
770C22×D3—181no—
771C22×D3—182no—
772C22×D3—182no—
773C22×D3—182no—
774C22×D3—361no—
775C22×D3—362no—
776C22×D3—361no—
777C22×D3—361no—
778C22×D3—361no—
779C22×D3—361no—
780C22×D3—361no—
781C22×D3—361no—
782C22×D3—362no—
783C22×D3—362no—
784C22×D3C2×D3211yescharacteristic
785C22×D3C2×D3211yescharacteristic
786C3×D4—121no—
787C3×D4—121no—
788C3×D4—121no—
789C3×D4—121no—
790C3×D4—122no—
791C3×D4—122no—
792C3×D4—182no—
793C3×D4—182no—
794C3×D4—361no—
795C2×C3×C4—31no—
796C2×C3×C4—31no—
797C2×C3×C4—31no—
798C2×C3×C4—31no—
799C2×C3×C4—31no—
800C2×C3×C4—31no—
801C2×C3×C4—31no—
802C2×C3×C4—31no—
803C2×C3×C4—61no—
804C2×C3×C4—61no—
805C2×C3×C4—61no—
806C2×C3×C4—61no—
807C2×C3×C4—91no—
808C2×C3×C4—91no—
809C2×C3×C4—91no—
810C2×C3×C4—91no—
811C2×C3×C4—91no—
812C2×C3×C4—361no—
813C2×C3×C4—361no—
814C2×C3×C4—361no—
815#67—41no—
816#67—41no—
817#67—62no—
818#67—62no—
819#67—62no—
820#67—122no—
821#67—121no—
822#67—121no—
823#67—361no—
824#67—361no—
825#67—362no—
826#67—361no—
827#67—361no—
828#67—361no—
829#67—362no—
830#67—362no—
831#67—362no—
832#67—364no—
833C2×Dic3—31no—
834C2×Dic3—31no—
835C2×Dic3—31no—
836C2×Dic3—31no—
837C2×Dic3—31no—
838C2×Dic3—31no—
839C2×Dic3—31no—
840C2×Dic3—31no—
841C2×Dic3—31no—
842C2×Dic3—31no—
843C2×Dic3—61no—
844C2×Dic3—61no—
845C2×Dic3—61no—
846C2×Dic3—61no—
847C2×Dic3—61no—
848C2×Dic3—91no—
849C2×Dic3—91no—
850C2×Dic3—91no—
851C2×Dic3—121no—
852C2×Dic3—121no—
853C2×Dic3—121no—
854C2×Dic3—122no—
855C2×Dic3—181no—
856C2×Dic3—181no—
857C2×Dic3—181no—
858C2×Dic3—361no—
859C2×Dic3—361no—
860C2×Dic3C2×D3211yescharacteristic
861C2×Dic3C2×D3211yescharacteristic
862C2×Dic3C2×D3211yescharacteristic
863C2×Dic3C2×D3211yescharacteristic
864D12—62no—
865D12—361no—
866C4×D3—121no—
867C4×D3—121no—
868C4×D3—121no—
869C4×D3—361no—
870C4×D3—361no—
871Dic6—361no—
872Dic6—361no—
873Dic6—361no—
874Dic6—362no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—21no—
878C2×C32—21no—
879C2×C32—21no—
880C2×C32—21no—
881C2×C32—21no—
882C2×C32—21no—
883C2×C32—21no—
884C2×C32—41no—
885C2×C32—41no—
886C2×C32—41no—
887C2×C32—41no—
888C2×C32—42no—
889C2×C32—41no—
890C2×C32—41no—
891C2×C32—81no—
892C2×C32—81no—
893C2×C32—82no—
894C2×C32—121no—
895C2×C32—121no—
896C2×C32C2×#23711yescharacteristic
897C2×C32#100411yescharacteristic
898C2×C32#100411yescharacteristic
899C2×C32#100411yescharacteristic
900C2×C32#100411yescharacteristic
901C2×C32D3×#4111yescharacteristic
902C2×C32D3×#4111yescharacteristic
903C2×C32#100911yescharacteristic
904C2×C32#100911yescharacteristic
905C3⋊D3—22no—
906C3⋊D3—121no—
907C3⋊D3—122no—
908C3⋊D3—121no—
909C3⋊D3—121no—
910C3⋊D3—241no—
911C3⋊D3—241no—
912C3⋊D3—242no—
913C3×D3—42no—
914C3×D3—41no—
915C3×D3—41no—
916C3×D3—41no—
917C3×D3—41no—
918C3×D3—62no—
919C3×D3—62no—
920C3×D3—81no—
921C3×D3—122no—
922C24—271no—
923C2×Q8—271no—
924C2×D4—31no—
925C2×D4—31no—
926C2×D4—91no—
927C2×D4—91no—
928C2×D4—91no—
929C2×D4—271no—
930C2×D4—271no—
931C22×C4—91no—
932C22×C4—91no—
933C22×C4—91no—
934C22×C4—271no—
935C4⋊C4—91no—
936C4⋊C4—91no—
937C4⋊C4—91no—
938C4⋊C4—91no—
939C4⋊C4—271no—
940C4⋊C4—271no—
941C22⋊C4—31no—
942C22⋊C4—91no—
943C22⋊C4—91no—
944C22⋊C4—91no—
945C22⋊C4—91no—
946C22⋊C4—91no—
947C22⋊C4—271no—
948C22⋊C4—271no—
949C22⋊C4—271no—
950C22⋊C4—271no—
951C22⋊C4—271no—
952C22⋊C4—271no—
953C22⋊C4—271no—
954C22⋊C4—271no—
955C42—271no—
956C42—271no—
957C22×C3—22no—
958C22×C3—21no—
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—21no—
969C22×C3—21no—
970C22×C3—41no—
971C22×C3—41no—
972C22×C3—41no—
973C22×C3—41no—
974C22×C3—41no—
975C22×C3—41no—
976C22×C3—41no—
977C22×C3—41no—
978C22×C3—42no—
979C22×C3—41no—
980C22×C3—62no—
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—61no—
993C22×C3—81no—
994C22×C3—81no—
995C22×C3—92no—
996C22×C3—121no—
997C22×C3—121no—
998C22×C3—121no—
999C22×C3—121no—
1000C22×C3—121no—
1001C22×C3—181no—
1002C22×C3—181no—
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—32no—
1013C2×D3—32no—
1014C2×D3—62no—
1015C2×D3—61no—
1016C2×D3—61no—
1017C2×D3—61no—
1018C2×D3—61no—
1019C2×D3—121no—
1020C2×D3—121no—
1021C2×D3—182no—
1022C2×D3—181no—
1023C2×D3—181no—
1024C2×D3—181no—
1025C2×D3—181no—
1026C2×D3—181no—
1027C2×D3—181no—
1028C2×D3—181no—
1029C2×D3—181no—
1030C2×D3—181no—
1031C2×D3—361no—
1032C2×D3—361no—
1033C2×D3—361no—
1034C2×D3—361no—
1035C2×D3—361no—
1036C2×D3—361no—
1037C2×D3—361no—
1038C2×D3—361no—
1039C2×D3—362no—
1040C2×D3—364no—
1041C2×D3—364no—
1042C2×D3—364no—
1043C2×D3—368no—
1044C2×D3—721no—
1045C2×D3—721no—
1046C3×C4—61no—
1047C3×C4—61no—
1048C3×C4—61no—
1049C3×C4—61no—
1050C3×C4—61no—
1051C3×C4—61no—
1052C3×C4—61no—
1053C3×C4—61no—
1054C3×C4—121no—
1055C3×C4—121no—
1056C3×C4—121no—
1057C3×C4—121no—
1058C3×C4—181no—
1059C3×C4—181no—
1060C3×C4—181no—
1061C3×C4—181no—
1062C3×C4—181no—
1063Dic3—21no—
1064Dic3—21no—
1065Dic3—21no—
1066Dic3—21no—
1067Dic3—62no—
1068Dic3—61no—
1069Dic3—61no—
1070Dic3—61no—
1071Dic3—61no—
1072Dic3—61no—
1073Dic3—61no—
1074Dic3—61no—
1075Dic3—61no—
1076Dic3—61no—
1077Dic3—61no—
1078Dic3—121no—
1079Dic3—121no—
1080Dic3—121no—
1081Dic3—121no—
1082Dic3—182no—
1083Dic3—181no—
1084Dic3—181no—
1085Dic3—181no—
1086Dic3—361no—
1087Dic3—361no—
1088Dic3—362no—
1089C32—21no—
1090C32—21no—
1091C32—21no—
1092C32—41no—
1093C32#561311yescharacteristic, complemented
1094C32#561711yescharacteristic, complemented
1095C32#565711yescharacteristic, complemented
1096C23—31no—
1097C23—31no—
1098C23—91no—
1099C23—271no—
1100C23—542no—
1101C23—1081no—
1102C23—1081no—
1103C23D3311yescharacteristic
1104Q8—1081no—
1105D4—121no—
1106D4—121no—
1107D4—182no—
1108D4—182no—
1109D4—361no—
1110D4—1081no—
1111D4—1081no—
1112C2×C4—31no—
1113C2×C4—31no—
1114C2×C4—31no—
1115C2×C4—31no—
1116C2×C4—91no—
1117C2×C4—91no—
1118C2×C4—91no—
1119C2×C4—91no—
1120C2×C4—91no—
1121C2×C4—271no—
1122C2×C4—361no—
1123C2×C4—361no—
1124C2×C4—361no—
1125C2×C4—1081no—
1126C2×C3—21no—
1127C2×C3—21no—
1128C2×C3—21no—
1129C2×C3—21no—
1130C2×C3—21no—
1131C2×C3—21no—
1132C2×C3—21no—
1133C2×C3—21no—
1134C2×C3—21no—
1135C2×C3—42no—
1136C2×C3—41no—
1137C2×C3—41no—
1138C2×C3—41no—
1139C2×C3—41no—
1140C2×C3—41no—
1141C2×C3—41no—
1142C2×C3—81no—
1143C2×C3—81no—
1144C2×C3—82no—
1145C2×C3—122no—
1146C2×C3—121no—
1147C2×C3—121no—
1148C2×C3—121no—
1149C2×C3—121no—
1150C2×C3—182no—
1151C2×C3—241no—
1152C2×C3#6430711yescharacteristic
1153C2×C3D3×#23711yescharacteristic
1154C2×C3D3×#23711yescharacteristic
1155C2×C3#6431211yescharacteristic
1156C2×C3#6431411yescharacteristic
1157C2×C3#6431411yescharacteristic
1158C2×C3#6431411yescharacteristic
1159C2×C3#6433011yescharacteristic
1160C2×C3#6433011yescharacteristic
1161D3—41no—
1162D3—41no—
1163D3—62no—
1164D3—62no—
1165D3—122no—
1166D3—362no—
1167D3—361no—
1168D3—361no—
1169D3—361no—
1170D3—721no—
1171D3—721no—
1172D3—722no—
1173C22—21no—
1174C22—21no—
1175C22—21no—
1176C22—61no—
1177C22—61no—
1178C22—61no—
1179C22—61no—
1180C22—61no—
1181C22—61no—
1182C22—92no—
1183C22—181no—
1184C22—181no—
1185C22—541no—
1186C22—541no—
1187C22—541no—
1188C22—1084no—
1189C22C2×D3311yescharacteristic
1190C4—61no—
1191C4—61no—
1192C4—61no—
1193C4—61no—
1194C4—181no—
1195C4—181no—
1196C4—181no—
1197C4—181no—
1198C4—181no—
1199C4—541no—
1200C3—21no—
1201C3—21no—
1202C3—21no—
1203C3—41no—
1204C3#1059430211yescharacteristic, complemented
1205C3#1059525511yescharacteristic, complemented
1206C3#1059531011yescharacteristic, complemented
1207C2—41no—
1208C2—121no—
1209C2—121no—
1210C2—182no—
1211C2—1081no—
1212C2#1172440811yescharacteristic
1213C2#1172441811yescharacteristic
1214C2#1172441911yescharacteristic
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. #11723726C2semidirect
2. #11723643C2semidirect
3. #11723635C2semidirect
4. #11723592C2semidirect
5. C3×#63970C2semidirect
6. C3×#63962C2semidirect
7. C3×#63958C2semidirect
8. #11723028C2semidirect
9. #11723019C2semidirect
10. #11723004C2semidirect
11. #11722987C2semidirect
12. #11722972C2semidirect
13. #11722949C2semidirect
14. #11722927C2semidirect
15. #11722904C2semidirect
22. C22×C3×C3⋊Dic3C22semidirect
24. C2×C32×#67C22semidirect
26. C2×#6293C22semidirect
31. C2×C3×D3×Dic3C22semidirect
32. C3×#3757C22semidirect
33. C32×#217C22semidirect
34. #88815C22semidirect
36. #88813C22semidirect
37. #88807C22semidirect
44. (C2×D3)⋊(C3⋊Dic3)C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. C3×Dic3⋊Dic3C22semidirect
47. C3×Dic3⋊Dic3C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
75. #63970D3semidirect
77. #63962D3semidirect
80. #63958D3semidirect
150. C22×C3⋊Dic3C2×D3semidirect
162. C2×C3×#67C2×D3semidirect
163. C2×C3×#67C2×D3semidirect
184. C2×D3×Dic3C2×D3semidirect
188. #3757C2×D3semidirect
204. C3×#217C2×D3semidirect
205. C3×#217C2×D3semidirect
224. Dic3⋊Dic3C2×D3semidirect
225. Dic3⋊Dic3C2×D3semidirect
226. Dic3⋊Dic3C2×D3semidirect
227. Dic3⋊Dic3C2×D3semidirect
255. (C2×D3)⋊Dic3C2×D3semidirect
506. C2×#67D32semidirect
550. #217D32semidirect
747. C33#538semidirect
1093. C32#5613semidirect
1094. C32#5617semidirect
1095. C32#5657semidirect
1204. C3#10594302semidirect
1205. C3#10595255semidirect
1206. C3#10595310semidirect

Maximal subgroups

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

subgroupindex
#117237262
#117236432
#117236352
#117235922
C3×#639702
C3×#639622
C3×#639582
#117230282
#117230192
#117230042
#117229872
#117229722
#117229492
#117229272
#117229042
#105953103
#105952553
#105943023