Finite Group Databasebeta

← #13172137

Subgroups — #13172137

Order 1728.

1300 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
1#11723723C211yesmaximal, characteristic, complemented
2#11723634C211yesmaximal, characteristic, complemented
3#11723600C211yesmaximal, characteristic, complemented
4#11723596C211yesmaximal, characteristic, complemented
5C3×#63981C211yesmaximal, characteristic, complemented
6C3×#63970C211yesmaximal, characteristic, complemented
7C3×#63969C211yesmaximal, characteristic, complemented
8#11723025C211yesmaximal, characteristic, complemented
9#11723009C211yesmaximal, characteristic, complemented
10#11722986C211yesmaximal, characteristic, complemented
11#11722984C211yesmaximal, characteristic, complemented
12#11722965C211yesmaximal, characteristic, complemented
13#11722956C211yesmaximal, characteristic, complemented
14#11722936C211yesmaximal, characteristic, complemented
15#11722927C211yesmaximal, characteristic, complemented
16#10595255—31nomaximal
17#10595181—31nomaximal
18#10594213—31nomaximal
19C23×C3×C3⋊D3C2211yescharacteristic
20C2×C32×#67C2211yescharacteristic
21C2×C32×#67C2211yescharacteristic
22C2×#6294C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6293C2211yescharacteristic, complemented
25C2×#6290C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×C3×#626C2211yescharacteristic
28C2×C3×#626C2211yescharacteristic
29C2×C3×#625C2211yescharacteristic, complemented
30C2×C3×D3×Dic3C2211yescharacteristic, complemented
31C2×C3×D3×Dic3C2211yescharacteristic, complemented
32#88864C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C3×#3757C2211yescharacteristic
35C32×#217C2211yescharacteristic
36#88814C2211yescharacteristic
37#88814C2211yescharacteristic
38#88807C2211yescharacteristic, complemented
39#88806C2211yescharacteristic, complemented
40Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
41#88803C2211yescharacteristic
42#88803C2211yescharacteristic
43(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45Dic3×C3⋊Dic3C2211yescharacteristic, complemented
46Dic3×C3⋊Dic3C2211yescharacteristic, complemented
47C3×#3724C2211yescharacteristic, complemented
48C3×Dic3⋊Dic3C2211yescharacteristic, complemented
49C3×Dic3⋊Dic3C2211yescharacteristic, complemented
50C3×#3722C2211yescharacteristic
51C3×#3722C2211yescharacteristic
52C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
53C3×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
54#64146—31no—
55#64145—31no—
56#64088—31no—
57C3×#939—31no—
58C3×#938—31no—
59C3×#937—31no—
60C3×#935—31no—
61C3×#883—31no—
62C3×#882—31no—
63#63981D311yescharacteristic, complemented
64#63978—31no—
65#63976—31no—
66#63976—31no—
67#63976—61no—
68#63974—31no—
69Dic3×#67—31no—
70#63970—31no—
71#63970—31no—
72#63970D311yescharacteristic, complemented
73#63969D311yescharacteristic, complemented
74D3×#217—31no—
75D3×#217—31no—
76#63961—31no—
77#63959—31no—
78#63959—31no—
79#63959—61no—
80#63958—31no—
81#63956—31no—
82#63956—31no—
83#63956—61no—
84#63953—31no—
85#63952—31no—
86#63915—31no—
87#63913—31no—
88#63908—31no—
89#63904—31no—
90#63902—31no—
91#63898—31no—
92#63896—31no—
93#63895—31no—
94#63893—31no—
95#63885—31no—
96#63884—31no—
97#63879—31no—
98#63862—31no—
99#63858—31no—
100#63850—31no—
101#63848—31no—
102C23×C33C2311yescharacteristic
103C22×C3×C3⋊D3—22no—
104C22×C3×C3⋊D3—41no—
105C22×C3×C3⋊D3—41no—
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C32×D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C32×#67—41no—
117C32×#67—41no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122#6294—41no—
123#6294—41no—
124#6293—41no—
125#6290—22no—
126#6290—41no—
127C3×#626—22no—
128C3×#626—41no—
129C3×#625—41no—
130C3×D3×Dic3—41no—
131C3×D3×Dic3—41no—
132#5657—91no—
133#5613—91no—
134#5593—91no—
135C23×C3⋊D3C2×D311yescharacteristic
136C23×C3×D3—31no—
137C23×C3×D3—31no—
138C23×C3×D3—61no—
139C2×C32×D4—31no—
140C2×C32×D4—31no—
141C2×#638—31no—
142C2×#638—31no—
143C2×#634—31no—
144C2×C3×#67—21no—
145C2×C3×#67—21no—
146C2×C3×#67—31no—
147C2×C3×#67—31no—
148C2×C3×#67—31no—
149C2×C3×#67—31no—
150C2×C3×#67C2×D311yescharacteristic
151C2×C3×#67C2×D311yescharacteristic
152C2×C3×#67C2×D311yescharacteristic
153C2×C3×#67C2×D311yescharacteristic
154C22×C3×Dic3—31no—
155C22×C3×Dic3—31no—
156C2×C3×D12—31no—
157C2×C3×D12—31no—
158C2×C3×C4×D3—31no—
159C2×C3×C4×D3—31no—
160C2×#627—31no—
161C2×#627—31no—
162C2×#627—61no—
163C2×#626C2×D311yescharacteristic
164C2×#626C2×D311yescharacteristic
165C2×#625—31no—
166C2×#625—31no—
167C2×#625—31no—
168C2×#625—31no—
169C2×#625—61no—
170C2×#625—61no—
171C2×#625C2×D311yescharacteristic, complemented
172C2×#624—31no—
173C2×#624—31no—
174C2×D3×Dic3—31no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3C2×D311yescharacteristic, complemented
179C2×D3×Dic3C2×D311yescharacteristic, complemented
180C32×C22⋊C4—31no—
181#3757—31no—
182#3757—31no—
183#3757—31no—
184#3757—31no—
185#3757—31no—
186#3757—61no—
187#3757—61no—
188#3757—61no—
189#3757—121no—
190#3757C2×D311yescharacteristic
191#3757C2×D311yescharacteristic
192#3752—31no—
193#3752—31no—
194C4⋊(C3⋊Dic3)—31no—
195#3750—31no—
196#3750—31no—
197C4×C3⋊Dic3—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×#217—61no—
207C3×#217—61no—
208C3×#217C2×D311yescharacteristic
209C3×#217C2×D311yescharacteristic
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×C4⋊Dic3—31no—
217C3×C4⋊Dic3—31no—
218C3×Dic3⋊C4—31no—
219C3×Dic3⋊C4—31no—
220C3×Dic3⋊C4—31no—
221C3×Dic3⋊C4—31no—
222#3724—31no—
223#3724—31no—
224#3724—61no—
225#3724C2×D311yescharacteristic, complemented
226Dic3⋊Dic3—31no—
227Dic3⋊Dic3—31no—
228Dic3⋊Dic3—31no—
229Dic3⋊Dic3—31no—
230Dic3⋊Dic3—61no—
231Dic3⋊Dic3—61no—
232Dic3⋊Dic3C2×D311yescharacteristic, complemented
233Dic3⋊Dic3C2×D311yescharacteristic, complemented
234#3722—31no—
235#3722—31no—
236#3722C2×D311yescharacteristic
237#3722C2×D311yescharacteristic
238(C2×D3)⋊Dic3—31no—
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—31no—
250(C2×D3)⋊Dic3—61no—
251(C2×D3)⋊Dic3—61no—
252(C2×D3)⋊Dic3—61no—
253(C2×D3)⋊Dic3—61no—
254(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
255(C2×D3)⋊Dic3C2×D311yescharacteristic, complemented
256Dic32—31no—
257Dic32—31no—
258Dic32—31no—
259Dic32—31no—
260Dic32—61no—
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—44no—
272C2×C3×C3⋊D3#4112yes—
273C2×C32×D3—21no—
274C2×C32×D3—21no—
275C2×C32×D3—21no—
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C2×C32×D3—21no—
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×#120—91no—
292#953—91no—
293C2×#217—91no—
294#939—31no—
295#939—91no—
296#939—91no—
297#938—31no—
298#938—91no—
299#938—91no—
300#937—31no—
301#937—91no—
302#937—91no—
303#937—181no—
304#936—91no—
305#936—91no—
306#936—181no—
307#935—31no—
308#935—91no—
309D4×Dic3—91no—
310#930—91no—
311#929—91no—
312C4×#67—91no—
313C4×#67—91no—
314#898—91no—
315#898—91no—
316#897—91no—
317#896—91no—
318#894—91no—
319#893—91no—
320#885—91no—
321#885—91no—
322#885—91no—
323#885—91no—
324#884—91no—
325#883—31no—
326#882—31no—
327#67⋊C4—91no—
328#67⋊C4—91no—
329D3×C22⋊C4—91no—
330D3×C22⋊C4—91no—
331#879—91no—
332#879—91no—
333#879—91no—
334#879—91no—
335#879—181no—
336#878—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—22no—
347C22×C3⋊D3—41no—
348C22×C3⋊D3—41no—
349C22×C3⋊D3C22×D311yescharacteristic
350C22×C3⋊D3C22×D311yescharacteristic
351C22×C3×D3—21no—
352C22×C3×D3—21no—
353C22×C3×D3—31no—
354C22×C3×D3—31no—
355C22×C3×D3—31no—
356C22×C3×D3—31no—
357C22×C3×D3—61no—
358C22×C3×D3—61no—
359C22×C3×D3—62no—
360C22×C3×D3—62no—
361C22×C3×D3—122no—
362C22×C3×D3—121no—
363C22×C3×D3—121no—
364C22×C3×D3—121no—
365C22×C3×D3—121no—
366C22×C3×D3—122no—
367C22×C3×D3—122no—
368C22×C3×D3C22×D311yescharacteristic
369C22×C3×D3C22×D311yescharacteristic
370C22×C3×D3C22×D311yescharacteristic
371C22×C3×D3C22×D311yescharacteristic
372C32×D4—121no—
373C32×D4—121no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378#638—62no—
379#638—121no—
380C2×C3⋊Dic3—31no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—61no—
391C2×C3⋊Dic3—61no—
392C2×C3⋊Dic3—121no—
393C2×C3⋊Dic3—121no—
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398#634—121no—
399C3×#67—41no—
400C3×#67—41no—
401C3×#67—41no—
402C3×#67—41no—
403C3×#67—42no—
404C3×#67—42no—
405C3×#67—62no—
406C3×#67—121no—
407C3×#67—121no—
408C3×#67—121no—
409C2×C3×Dic3—21no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—21no—
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—31no—
421C2×C3×Dic3—61no—
422C2×C3×Dic3—61no—
423C2×C3×Dic3—61no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—121no—
426C2×C3×Dic3—121no—
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C3×D12—62no—
436C3×D12—121no—
437C3×C4×D3—121no—
438C3×C4×D3—121no—
439#627—121no—
440#627—121no—
441#627—122no—
442#626—22no—
443#626—41no—
444#625—41no—
445#625—62no—
446#625—62no—
447#625—122no—
448#625—121no—
449#625—121no—
450#625—122no—
451#624—121no—
452#624—121no—
453D3×Dic3—41no—
454D3×Dic3—41no—
455D3×Dic3—121no—
456D3×Dic3—121no—
457D3×Dic3—121no—
458D3×Dic3—121no—
459#538—271noSylow
460C2×C33—41no—
461C2×C33C2×#4111yescharacteristic
462C2×C33H(5,𝔽2)11yescharacteristic
463C2×C33H(5,𝔽2)11yescharacteristic
464C3×C3⋊D3—22no—
465C3×C3⋊D3—41no—
466C32×D3—41no—
467C32×D3—41no—
468C24×C3—91no—
469C23×D3—31no—
470C23×D3—31no—
471C23×D3—61no—
472C2×C3×D4—31no—
473C2×C3×D4—31no—
474C2×C3×D4—31no—
475C2×C3×D4—31no—
476C2×C3×D4—61no—
477C2×C3×D4—61no—
478C2×C3×D4—91no—
479C2×C3×D4—91no—
480C2×C3×D4—91no—
481C22×C3×C4—91no—
482C22×C3×C4—91no—
483C2×#67—31no—
484C2×#67—31no—
485C2×#67—31no—
486C2×#67—31no—
487C2×#67—91no—
488C2×#67—91no—
489C2×#67—91no—
490C2×#67—91no—
491C2×#67—91no—
492C2×#67—91no—
493C2×#67—181no—
494C2×#67—181no—
495C2×#67D3211yescharacteristic
496C2×#67D3211yescharacteristic
497C22×Dic3—31no—
498C22×Dic3—31no—
499C22×Dic3—91no—
500C22×Dic3—91no—
501C2×D12—31no—
502C2×D12—31no—
503C2×C4×D3—31no—
504C2×C4×D3—31no—
505C2×C4×D3—91no—
506C2×C4×D3—91no—
507C2×C4×D3—91no—
508C2×C4×D3—91no—
509C2×Dic6—91no—
510C2×Dic6—91no—
511C2×Dic6—91no—
512C2×Dic6—181no—
513C3×C4⋊C4—91no—
514C3×C4⋊C4—91no—
515C3×C4⋊C4—91no—
516C3×C22⋊C4—31no—
517C3×C22⋊C4—31no—
518C3×C22⋊C4—61no—
519C3×C22⋊C4—91no—
520C3×C22⋊C4—91no—
521C3×C22⋊C4—91no—
522C3×C22⋊C4—91no—
523C3×C22⋊C4—91no—
524C3×C22⋊C4—91no—
525#217—31no—
526#217—31no—
527#217—31no—
528#217—31no—
529#217—31no—
530#217—31no—
531#217—61no—
532#217—61no—
533#217—91no—
534#217—91no—
535#217—91no—
536#217—91no—
537#217—91no—
538#217—91no—
539#217—91no—
540#217—91no—
541#217—91no—
542#217—91no—
543#217—91no—
544#217—181no—
545#217—181no—
546#217—181no—
547#217—181no—
548#217—181no—
549#217—361no—
550#217D3211yescharacteristic
551(C2×D3)⋊C4—31no—
552(C2×D3)⋊C4—31no—
553(C2×D3)⋊C4—31no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
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—181no—
568(C2×D3)⋊C4—181no—
569C4⋊Dic3—31no—
570C4⋊Dic3—31no—
571C4⋊Dic3—91no—
572C4⋊Dic3—91no—
573C4⋊Dic3—91no—
574C4⋊Dic3—181no—
575Dic3⋊C4—31no—
576Dic3⋊C4—31no—
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—181no—
586Dic3⋊C4—181no—
587C4×Dic3—91no—
588C4×Dic3—91no—
589C4×Dic3—91no—
590C4×Dic3—91no—
591C4×Dic3—91no—
592C4×Dic3—91no—
593C4×Dic3—181no—
594C4×Dic3—181no—
595C22×C32—21no—
596C22×C32—22no—
597C22×C32—21no—
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—21no—
608C22×C32—41no—
609C22×C32—41no—
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×C32C23×D311yescharacteristic
627C22×C32C23×D311yescharacteristic
628C22×C32C23×D311yescharacteristic
629C2×C3⋊D3—21no—
630C2×C3⋊D3—21no—
631C2×C3⋊D3—21no—
632C2×C3⋊D3—21no—
633C2×C3⋊D3—21no—
634C2×C3⋊D3—44no—
635C2×C3⋊D3#23712yes—
636C2×C3×D3—21no—
637C2×C3×D3—21no—
638C2×C3×D3—21no—
639C2×C3×D3—21no—
640C2×C3×D3—21no—
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—32no—
649C2×C3×D3—32no—
650C2×C3×D3—41no—
651C2×C3×D3—41no—
652C2×C3×D3—41no—
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—62no—
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—121no—
669C2×C3×D3—121no—
670C2×C3×D3—121no—
671C2×C3×D3—121no—
672C2×C3×D3—124no—
673C2×C3×D3—124no—
674C2×C3×D3—128no—
675C32×C4—61no—
676C32×C4—61no—
677C32×C4—61no—
678C32×C4—61no—
679C3⋊Dic3—21no—
680C3⋊Dic3—21no—
681C3⋊Dic3—21no—
682C3⋊Dic3—21no—
683C3⋊Dic3—61no—
684C3⋊Dic3—61no—
685C3⋊Dic3—61no—
686C3⋊Dic3—61no—
687C3⋊Dic3—61no—
688C3⋊Dic3—61no—
689C3⋊Dic3—121no—
690C3⋊Dic3—121no—
691C3⋊Dic3—121no—
692C3⋊Dic3—121no—
693C3⋊Dic3—121no—
694C3⋊Dic3—121no—
695C3⋊Dic3—241no—
696C3⋊Dic3—241no—
697C3×Dic3—22no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—21no—
703C3×Dic3—21no—
704C3×Dic3—21no—
705C3×Dic3—21no—
706C3×Dic3—41no—
707C3×Dic3—41no—
708C3×Dic3—41no—
709C3×Dic3—61no—
710C3×Dic3—61no—
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—121no—
721#126—271no—
722#126—271no—
723#124—271no—
724#124—271no—
725#123—91no—
726#123—271no—
727C22⋊Q8—271no—
728#121—91no—
729#121—271no—
730#121—271no—
731#120—91no—
732#120—271no—
733C4×D4—271no—
734C4×D4—271no—
735C2×C22⋊C4—271no—
736C33#53811yescharacteristic, complemented, Sylow
737C23×C3—21no—
738C23×C3—21no—
739C23×C3—21no—
740C23×C3—31no—
741C23×C3—31no—
742C23×C3—31no—
743C23×C3—31no—
744C23×C3—41no—
745C23×C3—61no—
746C23×C3—61no—
747C23×C3—91no—
748C23×C3—91no—
749C23×C3—182no—
750C23×C3—361no—
751C23×C3—361no—
752C23×C3C2×D3211yescharacteristic
753C23×C3C2×D3211yescharacteristic
754C23×C3C2×D3211yescharacteristic
755C22×D3—31no—
756C22×D3—31no—
757C22×D3—31no—
758C22×D3—31no—
759C22×D3—61no—
760C22×D3—61no—
761C22×D3—62no—
762C22×D3—62no—
763C22×D3—122no—
764C22×D3—121no—
765C22×D3—121no—
766C22×D3—121no—
767C22×D3—121no—
768C22×D3—122no—
769C22×D3—122no—
770C22×D3C2×D3211yescharacteristic
771C22×D3C2×D3211yescharacteristic
772C3×D4—121no—
773C3×D4—121no—
774C3×D4—121no—
775C3×D4—121no—
776C3×D4—122no—
777C3×D4—122no—
778C3×D4—182no—
779C3×D4—361no—
780C3×D4—361no—
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—31no—
788C2×C3×C4—31no—
789C2×C3×C4—61no—
790C2×C3×C4—61no—
791C2×C3×C4—61no—
792C2×C3×C4—61no—
793C2×C3×C4—91no—
794C2×C3×C4—91no—
795C2×C3×C4—91no—
796C2×C3×C4—91no—
797C2×C3×C4—361no—
798C2×C3×C4—361no—
799#67—41no—
800#67—41no—
801#67—62no—
802#67—121no—
803#67—121no—
804#67—121no—
805#67—182no—
806#67—182no—
807#67—182no—
808#67—362no—
809#67—361no—
810#67—361no—
811#67—361no—
812#67—362no—
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—91no—
826C2×Dic3—91no—
827C2×Dic3—91no—
828C2×Dic3—91no—
829C2×Dic3—91no—
830C2×Dic3—91no—
831C2×Dic3—121no—
832C2×Dic3—121no—
833C2×Dic3—181no—
834C2×Dic3—181no—
835C2×Dic3—181no—
836C2×Dic3—181no—
837C2×Dic3—181no—
838C2×Dic3—181no—
839C2×Dic3—361no—
840C2×Dic3—361no—
841C2×Dic3—361no—
842C2×Dic3—361no—
843C2×Dic3C2×D3211yescharacteristic
844C2×Dic3C2×D3211yescharacteristic
845C2×Dic3C2×D3211yescharacteristic
846C2×Dic3C2×D3211yescharacteristic
847D12—62no—
848D12—121no—
849C4×D3—121no—
850C4×D3—121no—
851C4×D3—361no—
852C4×D3—361no—
853C4×D3—361no—
854C4×D3—361no—
855Dic6—361no—
856Dic6—361no—
857Dic6—361no—
858Dic6—362no—
859C2×C32—21no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—21no—
866C2×C32—21no—
867C2×C32—21no—
868C2×C32—41no—
869C2×C32—41no—
870C2×C32—41no—
871C2×C32—41no—
872C2×C32—42no—
873C2×C32—41no—
874C2×C32—41no—
875C2×C32—81no—
876C2×C32—81no—
877C2×C32—82no—
878C2×C32—121no—
879C2×C32—121no—
880C2×C32C2×#23711yescharacteristic
881C2×C32#100411yescharacteristic
882C2×C32#100411yescharacteristic
883C2×C32#100411yescharacteristic
884C2×C32#100411yescharacteristic
885C2×C32#100411yescharacteristic
886C2×C32D3×#4111yescharacteristic
887C2×C32D3×#4111yescharacteristic
888C2×C32#100911yescharacteristic
889C3⋊D3—22no—
890C3⋊D3—41no—
891C3×D3—41no—
892C3×D3—41no—
893C3×D3—41no—
894C3×D3—41no—
895C3×D3—62no—
896C3×D3—62no—
897C3×D3—81no—
898C3×D3—81no—
899C3×D3—122no—
900C3×D3—122no—
901C3×D3—121no—
902C3×D3—121no—
903C24—91no—
904C2×Q8—271no—
905C2×D4—31no—
906C2×D4—31no—
907C2×D4—91no—
908C2×D4—91no—
909C2×D4—91no—
910C2×D4—271no—
911C2×D4—271no—
912C22×C4—91no—
913C22×C4—91no—
914C22×C4—271no—
915C22×C4—271no—
916C4⋊C4—91no—
917C4⋊C4—91no—
918C4⋊C4—91no—
919C4⋊C4—271no—
920C4⋊C4—271no—
921C4⋊C4—271no—
922C22⋊C4—31no—
923C22⋊C4—91no—
924C22⋊C4—91no—
925C22⋊C4—91no—
926C22⋊C4—91no—
927C22⋊C4—91no—
928C22⋊C4—91no—
929C22⋊C4—271no—
930C22⋊C4—271no—
931C22⋊C4—271no—
932C22⋊C4—271no—
933C22⋊C4—271no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C42—271no—
937C42—271no—
938C22×C3—22no—
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—21no—
949C22×C3—21no—
950C22×C3—21no—
951C22×C3—41no—
952C22×C3—41no—
953C22×C3—41no—
954C22×C3—41no—
955C22×C3—41no—
956C22×C3—41no—
957C22×C3—41no—
958C22×C3—41no—
959C22×C3—42no—
960C22×C3—41no—
961C22×C3—61no—
962C22×C3—61no—
963C22×C3—61no—
964C22×C3—61no—
965C22×C3—61no—
966C22×C3—61no—
967C22×C3—61no—
968C22×C3—61no—
969C22×C3—61no—
970C22×C3—61no—
971C22×C3—61no—
972C22×C3—61no—
973C22×C3—81no—
974C22×C3—81no—
975C22×C3—92no—
976C22×C3—121no—
977C22×C3—121no—
978C22×C3—121no—
979C22×C3—121no—
980C22×C3—121no—
981C22×C3—121no—
982C22×C3—181no—
983C22×C3—181no—
984C22×C3—181no—
985C22×C3—181no—
986C22×C3—181no—
987C22×C3—364no—
988C22×C3C22×D3211yescharacteristic
989C22×C3C22×D3211yescharacteristic
990C22×C3C22×D3211yescharacteristic
991C2×D3—21no—
992C2×D3—21no—
993C2×D3—21no—
994C2×D3—21no—
995C2×D3—21no—
996C2×D3—21no—
997C2×D3—32no—
998C2×D3—32no—
999C2×D3—62no—
1000C2×D3—61no—
1001C2×D3—61no—
1002C2×D3—61no—
1003C2×D3—61no—
1004C2×D3—62no—
1005C2×D3—61no—
1006C2×D3—61no—
1007C2×D3—61no—
1008C2×D3—61no—
1009C2×D3—61no—
1010C2×D3—61no—
1011C2×D3—121no—
1012C2×D3—121no—
1013C2×D3—121no—
1014C2×D3—121no—
1015C2×D3—124no—
1016C2×D3—124no—
1017C2×D3—128no—
1018C3×C4—62no—
1019C3×C4—61no—
1020C3×C4—61no—
1021C3×C4—61no—
1022C3×C4—61no—
1023C3×C4—61no—
1024C3×C4—61no—
1025C3×C4—61no—
1026C3×C4—61no—
1027C3×C4—121no—
1028C3×C4—121no—
1029C3×C4—121no—
1030C3×C4—181no—
1031C3×C4—181no—
1032C3×C4—181no—
1033C3×C4—181no—
1034Dic3—21no—
1035Dic3—21no—
1036Dic3—21no—
1037Dic3—21no—
1038Dic3—61no—
1039Dic3—61no—
1040Dic3—61no—
1041Dic3—61no—
1042Dic3—61no—
1043Dic3—61no—
1044Dic3—61no—
1045Dic3—61no—
1046Dic3—121no—
1047Dic3—121no—
1048Dic3—121no—
1049Dic3—121no—
1050Dic3—181no—
1051Dic3—181no—
1052Dic3—181no—
1053Dic3—181no—
1054Dic3—181no—
1055Dic3—181no—
1056Dic3—361no—
1057Dic3—361no—
1058Dic3—361no—
1059Dic3—361no—
1060Dic3—361no—
1061Dic3—361no—
1062Dic3—721no—
1063Dic3—721no—
1064C32—21no—
1065C32—21no—
1066C32—21no—
1067C32—41no—
1068C32#559311yescharacteristic, complemented
1069C32#561311yescharacteristic, complemented
1070C32#565711yescharacteristic, complemented
1071C23—31no—
1072C23—31no—
1073C23—91no—
1074C23—91no—
1075C23—182no—
1076C23—361no—
1077C23—361no—
1078C23D3311yescharacteristic
1079Q8—1081no—
1080D4—121no—
1081D4—121no—
1082D4—182no—
1083D4—361no—
1084D4—361no—
1085D4—542no—
1086D4—1081no—
1087C2×C4—31no—
1088C2×C4—31no—
1089C2×C4—31no—
1090C2×C4—31no—
1091C2×C4—91no—
1092C2×C4—91no—
1093C2×C4—91no—
1094C2×C4—91no—
1095C2×C4—271no—
1096C2×C4—271no—
1097C2×C4—361no—
1098C2×C4—361no—
1099C2×C4—1081no—
1100C2×C4—1081no—
1101C2×C3—21no—
1102C2×C3—21no—
1103C2×C3—21no—
1104C2×C3—21no—
1105C2×C3—21no—
1106C2×C3—21no—
1107C2×C3—21no—
1108C2×C3—21no—
1109C2×C3—21no—
1110C2×C3—42no—
1111C2×C3—41no—
1112C2×C3—41no—
1113C2×C3—41no—
1114C2×C3—41no—
1115C2×C3—41no—
1116C2×C3—41no—
1117C2×C3—81no—
1118C2×C3—81no—
1119C2×C3—82no—
1120C2×C3—121no—
1121C2×C3—121no—
1122C2×C3—121no—
1123C2×C3—121no—
1124C2×C3—182no—
1125C2×C3—241no—
1126C2×C3—241no—
1127C2×C3—361no—
1128C2×C3#6430711yescharacteristic
1129C2×C3D3×#23711yescharacteristic
1130C2×C3D3×#23711yescharacteristic
1131C2×C3#6431211yescharacteristic
1132C2×C3#6431311yescharacteristic
1133C2×C3#6431311yescharacteristic
1134C2×C3#6431411yescharacteristic
1135C2×C3#6433011yescharacteristic
1136C2×C3#6433011yescharacteristic
1137D3—41no—
1138D3—41no—
1139D3—62no—
1140D3—62no—
1141D3—122no—
1142D3—122no—
1143D3—121no—
1144D3—121no—
1145C22—21no—
1146C22—21no—
1147C22—21no—
1148C22—61no—
1149C22—61no—
1150C22—61no—
1151C22—61no—
1152C22—61no—
1153C22—61no—
1154C22—92no—
1155C22—181no—
1156C22—181no—
1157C22—181no—
1158C22—181no—
1159C22—181no—
1160C22—364no—
1161C22C2×D3311yescharacteristic
1162C4—61no—
1163C4—61no—
1164C4—61no—
1165C4—61no—
1166C4—181no—
1167C4—181no—
1168C4—181no—
1169C4—181no—
1170C4—541no—
1171C4—541no—
1172C3—21no—
1173C3—21no—
1174C3—21no—
1175C3—41no—
1176C3#1059421311yescharacteristic, complemented
1177C3#1059518111yescharacteristic, complemented
1178C3#1059525511yescharacteristic, complemented
1179C2—41no—
1180C2—121no—
1181C2—121no—
1182C2—182no—
1183C2—361no—
1184C2#1172440811yescharacteristic
1185C2#1172441511yescharacteristic
1186C2#1172441811yescharacteristic
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. #11723723C2semidirect
2. #11723634C2semidirect
3. #11723600C2semidirect
4. #11723596C2semidirect
5. C3×#63981C2semidirect
6. C3×#63970C2semidirect
7. C3×#63969C2semidirect
8. #11723025C2semidirect
9. #11723009C2semidirect
10. #11722986C2semidirect
11. #11722984C2semidirect
12. #11722965C2semidirect
13. #11722956C2semidirect
14. #11722936C2semidirect
15. #11722927C2semidirect
24. C2×#6293C22semidirect
29. C2×C3×#625C22semidirect
30. C2×C3×D3×Dic3C22semidirect
31. C2×C3×D3×Dic3C22semidirect
38. #88807C22semidirect
39. #88806C22semidirect
40. Dic3⋊(C3⋊Dic3)C22semidirect
43. (C2×D3)⋊(C3⋊Dic3)C22semidirect
44. (C2×D3)⋊(C3⋊Dic3)C22semidirect
45. Dic3×C3⋊Dic3C22semidirect
46. Dic3×C3⋊Dic3C22semidirect
47. C3×#3724C22semidirect
48. C3×Dic3⋊Dic3C22semidirect
49. C3×Dic3⋊Dic3C22semidirect
52. C3×(C2×D3)⋊Dic3C22semidirect
53. C3×(C2×D3)⋊Dic3C22semidirect
63. #63981D3semidirect
72. #63970D3semidirect
73. #63969D3semidirect
171. C2×#625C2×D3semidirect
178. C2×D3×Dic3C2×D3semidirect
179. C2×D3×Dic3C2×D3semidirect
225. #3724C2×D3semidirect
232. Dic3⋊Dic3C2×D3semidirect
233. Dic3⋊Dic3C2×D3semidirect
254. (C2×D3)⋊Dic3C2×D3semidirect
255. (C2×D3)⋊Dic3C2×D3semidirect
736. C33#538semidirect
1068. C32#5593semidirect
1069. C32#5613semidirect
1070. C32#5657semidirect
1176. C3#10594213semidirect
1177. C3#10595181semidirect
1178. C3#10595255semidirect

Maximal subgroups

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

subgroupindex
#117237232
#117236342
#117236002
#117235962
C3×#639812
C3×#639702
C3×#639692
#117230252
#117230092
#117229862
#117229842
#117229652
#117229562
#117229362
#117229272
#105952553
#105951813
#105942133