Finite Group Databasebeta

← #13172682

Subgroups — #13172682

Order 1728.

1708 conjugacy classes of subgroups.

The subgroup lattice has 1330 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#3804C211yesmaximal, characteristic, complemented
2C2×#88955C211yesmaximal, characteristic, complemented
3#11723729C211yesmaximal, characteristic, complemented
4#11723643C211yesmaximal, characteristic, complemented
5#11723632C211yesmaximal, characteristic, complemented
6#11723624C211yesmaximal, characteristic, complemented
7C3×#63971C211yesmaximal, characteristic, complemented
8C3×#63952C211yesmaximal, characteristic, complemented
9#11723003C211yesmaximal, characteristic, complemented
10#11722993C211yesmaximal, characteristic, complemented
11#11722986C211yesmaximal, characteristic, complemented
12#11722970C211yesmaximal, characteristic, complemented
13Dic3×#626C211yesmaximal, characteristic, complemented
14#11722905C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic, complemented
16#10595305—31nomaximal
17#10595067—31nomaximal
18#10594283—31nomaximal
19C22×#1113C2211yescharacteristic
20C22×D3×C3⋊D3C2211yescharacteristic
21C2×#6312C2211yescharacteristic, complemented
22C2×C3×#638C2211yescharacteristic
23C2×C3×#638C2211yescharacteristic, complemented
24C2×C3×#638C2211yescharacteristic, complemented
25C2×C32×#67C2211yescharacteristic, complemented
26C22×C32×Dic3C2211yescharacteristic, complemented
27C2×#6292C2211yescharacteristic
28C2×#6292C2211yescharacteristic
29C2×Dic3×C3⋊D3C2211yescharacteristic, complemented
30C2×C3×#627C2211yescharacteristic, complemented
31C2×C3×#626C2211yescharacteristic
32C2×C3×#626C2211yescharacteristic
33C2×C3×#624C2211yescharacteristic
34C2×C3×#624C2211yescharacteristic, complemented
35C3×#3804—24no—
36C2×C3×D3×Dic3C2211yescharacteristic, complemented
37C2×C3×D3×Dic3C2211yescharacteristic, complemented
38#88955—24no—
39C32×#217C2211yescharacteristic, complemented
40#88814C2211yescharacteristic
41#88814C2211yescharacteristic, complemented
42#88814C2211yescharacteristic, complemented
43#88806C2211yescharacteristic, complemented
44Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
45#88804C2211yescharacteristic, complemented
46#88804C2211yescharacteristic, complemented
47#88804C2211yescharacteristic, complemented
48#88803C2211yescharacteristic
49#88803C2211yescharacteristic, complemented
50(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic, complemented
51C3×#3724C2211yescharacteristic, complemented
52C3×#3724C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic
54C3×#3722C2211yescharacteristic, complemented
55C3×Dic32C2211yescharacteristic, complemented
56C2×C3×#237—31no—
57C2×C3×#235—31no—
58C2×#3811—31no—
59C2×#3804D311yescharacteristic, complemented
60C2×D3×D12—31no—
61C2×D3×D12—31no—
62#64146—31no—
63#64139—31no—
64#64093—31no—
65C3×#939—31no—
66C3×C4×#67—31no—
67C3×#884—31no—
68C3×#67⋊C4—31no—
69#63983—31no—
70#63983—31no—
71#63983—31no—
72#63983—31no—
73#63983—31no—
74#63983—61no—
75#63978—31no—
76#63978—31no—
77#63978—61no—
78Dic3×#67—31no—
79#63971—31no—
80#63971—31no—
81#63971—61no—
82#63971D311yescharacteristic, complemented
83C2×#3722—31no—
84#63961—31no—
85#63952D311yescharacteristic, complemented
86#63921—31no—
87D3×(C2×D3)⋊C4—31no—
88D3×(C2×D3)⋊C4—31no—
89D3×(C2×D3)⋊C4—31no—
90D3×(C2×D3)⋊C4—31no—
91#63907—31no—
92C4×#626—31no—
93#63897—31no—
94Dic3×D12—31no—
95#63888—31no—
96#63884—31no—
97#63864—31no—
98#63856—31no—
99#63852—31no—
100#63851—31no—
101#63850—31no—
102#63850—31no—
103#63850—31no—
104C23×C33C2311yescharacteristic
105C22×C3⋊(C3⋊D3)C2311yescharacteristic
106C22×C3×C3⋊D3C2311yescharacteristic
107C22×C3×C3⋊D3C2311yescharacteristic
108C22×C3×C3⋊D3C2311yescharacteristic
109C22×C32×D3C2311yescharacteristic
110C2×#1113—22no—
111C2×#1113—22no—
112C2×#1113—41no—
113C2×D3×C3⋊D3—22no—
114C2×D3×C3⋊D3—22no—
115C2×D3×C3⋊D3—41no—
116#6312—41no—
117C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
118C3×#638—22no—
119C3×#638—22no—
120C3×#638—41no—
121C2×C3×C3⋊Dic3C2311yescharacteristic
122C2×C3×C3⋊Dic3C2311yescharacteristic
123C2×C3×C3⋊Dic3C2311yescharacteristic
124C32×#67—22no—
125C2×C32×Dic3—22no—
126C2×C32×Dic3C2311yescharacteristic
127C2×C32×Dic3C2311yescharacteristic
128C2×C32×Dic3C2311yescharacteristic
129C2×C32×Dic3C2311yescharacteristic
130C2×C32×Dic3C2311yescharacteristic
131#6292—22no—
132#6292—22no—
133Dic3×C3⋊D3—41no—
134C3×#627—22no—
135C3×#626—22no—
136C3×#626D414yescomplemented
137C3×#624—22no—
138C3×#624—22no—
139C3×D3×Dic3—22no—
140C3×D3×Dic3—41no—
141#5829—91no—
142#5610—91no—
143#5550—91no—
144C23×C3⋊D3—31no—
145C22×D32—31no—
146C22×D32—31no—
147C22×D32—31no—
148C22×D32—31no—
149C22×D32—31no—
150C22×D32—61no—
151C2×C32×D4—31no—
152C22×C32×C4—31no—
153C2×#638—31no—
154C2×#638—31no—
155C2×#638—31no—
156C2×#638—61no—
157C2×#638—61no—
158C2×#638—61no—
159C2×#638—121no—
160C2×#638C2×D311yescharacteristic
161C2×#638C2×D311yescharacteristic, complemented
162C2×#638C2×D311yescharacteristic, complemented
163C2×C4⋊(C3⋊D3)—31no—
164C2×C4⋊(C3⋊D3)—31no—
165C2×C4×C3⋊D3—31no—
166C2×C3×#67—21no—
167C2×C3×#67—31no—
168C2×C3×#67—31no—
169C2×C3×#67—31no—
170C2×C3×#67—31no—
171C2×C3×#67—31no—
172C2×C3×#67—31no—
173C2×C3×#67—31no—
174C2×C3×#67—31no—
175C2×C3×#67—61no—
176C2×C3×#67—61no—
177C2×C3×#67—61no—
178C2×C3×#67C2×D311yescharacteristic, complemented
179C2×C3×#67C2×D311yescharacteristic, complemented
180C22×C3×Dic3—21no—
181C22×C3×Dic3—31no—
182C22×C3×Dic3—31no—
183C22×C3×Dic3C2×D311yescharacteristic, complemented
184C22×C3×Dic3C2×D311yescharacteristic, complemented
185C3×#237—64no—
186C3×#235—64no—
187C2×C3×D12—31no—
188C2×C3×D12—31no—
189C2×C3×C4×D3—31no—
190C2×C3×C4×D3—31no—
191C2×C3×C4×D3—31no—
192C2×C3×C4×D3—31no—
193C2×C3×C4×D3—31no—
194C2×C3×C4×D3—31no—
195C2×C3×Dic6—31no—
196C2×C3×Dic6—31no—
197#3811—64no—
198C2×#627C2×D311yescharacteristic, complemented
199C2×#626—31no—
200C2×#626—31no—
201C2×#626—31no—
202C2×#626—31no—
203C2×#626—61no—
204C2×#626—61no—
205C2×#626C2×D311yescharacteristic
206C2×#626C2×D311yescharacteristic
207C2×#624C2×D311yescharacteristic
208C2×#624C2×D311yescharacteristic, complemented
209#3804—24no—
210C2×D3×Dic3—31no—
211C2×D3×Dic3—31no—
212C2×D3×Dic3—61no—
213C2×D3×Dic3C2×D311yescharacteristic, complemented
214C2×D3×Dic3C2×D311yescharacteristic, complemented
215D3×D12—64no—
216D3×D12—64no—
217C32×C22⋊C4—31no—
218#3757—31no—
219#3752—31no—
220#3752—31no—
221#3752—31no—
222#3752—31no—
223#3752—31no—
224C4⋊(C3⋊Dic3)—31no—
225#3750—31no—
226C3×#217—21no—
227C3×#217C2×D311yescharacteristic, complemented
228C3×#217C2×D311yescharacteristic, complemented
229C3×(C2×D3)⋊C4—31no—
230C3×(C2×D3)⋊C4—31no—
231C3×(C2×D3)⋊C4—31no—
232C3×(C2×D3)⋊C4—31no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—31no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—31no—
237C3×C4×Dic3—31no—
238C3×C4×Dic3—31no—
239#3724—31no—
240#3724—31no—
241#3724—61no—
242#3724C2×D311yescharacteristic, complemented
243#3724C2×D311yescharacteristic, complemented
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—61no—
247#3722—31no—
248#3722—31no—
249#3722—31no—
250#3722—31no—
251#3722—31no—
252#3722—31no—
253#3722—31no—
254#3722—31no—
255#3722—31no—
256#3722—61no—
257#3722—61no—
258#3722—61no—
259#3722C2×D311yescharacteristic
260#3722C2×D311yescharacteristic, complemented
261(C2×D3)⋊Dic3—31no—
262(C2×D3)⋊Dic3—31no—
263(C2×D3)⋊Dic3—31no—
264(C2×D3)⋊Dic3—31no—
265(C2×D3)⋊Dic3—31no—
266(C2×D3)⋊Dic3—31no—
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—31no—
272(C2×D3)⋊Dic3—31no—
273(C2×D3)⋊Dic3—61no—
274(C2×D3)⋊Dic3—61no—
275(C2×D3)⋊Dic3—61no—
276Dic32C2×D311yescharacteristic, complemented
277C22×C33—21no—
278C22×C33—21no—
279C22×C33—21no—
280C22×C33C2411yescharacteristic
281C2×C3⋊(C3⋊D3)—21no—
282C2×C3⋊(C3⋊D3)—21no—
283C2×C3⋊(C3⋊D3)—21no—
284C2×C3×C3⋊D3—21no—
285C2×C3×C3⋊D3—21no—
286C2×C3×C3⋊D3—21no—
287C2×C3×C3⋊D3—21no—
288C2×C3×C3⋊D3—21no—
289C2×C3×C3⋊D3—21no—
290C2×C3×C3⋊D3—21no—
291C2×C3×C3⋊D3C2×D412yes—
292C2×C3×C3⋊D3#4112yescomplemented
293C2×C32×D3—21no—
294C2×C32×D3—21no—
295C2×C32×D3C2×D412yes—
296#1113—44no—
297D3×C3⋊D3—44no—
298C3⋊(C3⋊Dic3)—21no—
299C3×C3⋊Dic3—21no—
300C3×C3⋊Dic3—21no—
301C3×C3⋊Dic3—21no—
302C32×Dic3—21no—
303C32×Dic3—21no—
304C32×Dic3—21no—
305C32×Dic3—21no—
306C32×Dic3C2×D412yes—
307C2×C3×#41—91no—
308C2×#237—31no—
309C2×D3×D4—91no—
310C2×D3×D4—91no—
311C2×#235—31no—
312C22×D12—91no—
313C3×#121—91no—
314C3×C4×D4—91no—
315#947—91no—
316#946—91no—
317#939—31no—
318#939—91no—
319#939—91no—
320#937—91no—
321#937—91no—
322#937—91no—
323#937—91no—
324#937—91no—
325#937—91no—
326#937—181no—
327#935—91no—
328D4×Dic3—91no—
329#930—91no—
330#930—91no—
331#930—181no—
332#929—91no—
333#929—91no—
334C4×#67—31no—
335C4×#67—91no—
336C2×(C2×D3)⋊C4—91no—
337C2×(C2×D3)⋊C4—91no—
338C2×(C2×D3)⋊C4—91no—
339#924—91no—
340#896—91no—
341#894—91no—
342#894—91no—
343#894—91no—
344#885—91no—
345#884—31no—
346#884—91no—
347#884—91no—
348#884—181no—
349#67⋊C4—31no—
350D3×C22⋊C4—91no—
351D3×C22⋊C4—91no—
352D3×C22⋊C4—91no—
353#875—91no—
354C4×D12—91no—
355C23×C32—21no—
356C23×C32—21no—
357C23×C32—21no—
358C23×C32—31no—
359C23×C32—41no—
360C23×C32C22×D311yescharacteristic
361C23×C32C22×D311yescharacteristic
362C23×C32C22×D311yescharacteristic
363C22×C3⋊D3—31no—
364C22×C3⋊D3—31no—
365C22×C3⋊D3—31no—
366C22×C3⋊D3—61no—
367C22×C3⋊D3—61no—
368C22×C3⋊D3—61no—
369C22×C3⋊D3—62no—
370C22×C3⋊D3—62no—
371C22×C3⋊D3—121no—
372C22×C3⋊D3—121no—
373C22×C3⋊D3C22×D311yescharacteristic
374C22×C3⋊D3C22×D311yescharacteristic
375C22×C3⋊D3C22×D311yescharacteristic
376C22×C3×D3—21no—
377C22×C3×D3—31no—
378C22×C3×D3—31no—
379C22×C3×D3—31no—
380C22×C3×D3—31no—
381C22×C3×D3—31no—
382C22×C3×D3—31no—
383C22×C3×D3—61no—
384C22×C3×D3—61no—
385C22×C3×D3—61no—
386C22×C3×D3C22×D311yescharacteristic
387C22×C3×D3C22×D311yescharacteristic
388C2×D32—62no—
389C2×D32—62no—
390C2×D32—62no—
391C2×D32—62no—
392C2×D32—62no—
393C2×D32—62no—
394C2×D32—62no—
395C2×D32—62no—
396C2×D32—62no—
397C2×D32—62no—
398C2×D32—122no—
399C2×D32—122no—
400C2×D32—121no—
401C2×D32—121no—
402C2×D32—122no—
403C2×D32—121no—
404C2×D32—121no—
405C2×D32—121no—
406C32×D4—62no—
407C2×C32×C4—31no—
408C2×C32×C4—31no—
409C2×C32×C4—31no—
410C2×C32×C4—31no—
411C2×C32×C4—31no—
412C2×C32×C4—62no—
413#638—22no—
414#638—22no—
415#638—41no—
416#638—121no—
417#638—121no—
418#638—121no—
419#638—122no—
420#638—122no—
421#638—122no—
422#638—124no—
423C2×C3⋊Dic3—31no—
424C2×C3⋊Dic3—31no—
425C2×C3⋊Dic3—31no—
426C2×C3⋊Dic3—61no—
427C2×C3⋊Dic3—61no—
428C2×C3⋊Dic3—61no—
429C2×C3⋊Dic3—121no—
430C2×C3⋊Dic3C22×D311yescharacteristic
431C2×C3⋊Dic3C22×D311yescharacteristic
432C2×C3⋊Dic3C22×D311yescharacteristic
433C4⋊(C3⋊D3)—62no—
434C4⋊(C3⋊D3)—62no—
435C4×C3⋊D3—121no—
436C3×#67—22no—
437C3×#67—22no—
438C3×#67—34no—
439C3×#67—42no—
440C3×#67—62no—
441C3×#67—62no—
442C3×#67—62no—
443C3×#67—62no—
444C3×#67—62no—
445C3×#67—122no—
446C3×#67—122no—
447C3×#67—121no—
448C3×#67—121no—
449C3×#67—122no—
450C2×C3×Dic3—22no—
451C2×C3×Dic3—22no—
452C2×C3×Dic3—21no—
453C2×C3×Dic3—21no—
454C2×C3×Dic3—21no—
455C2×C3×Dic3—21no—
456C2×C3×Dic3—21no—
457C2×C3×Dic3—31no—
458C2×C3×Dic3—31no—
459C2×C3×Dic3—31no—
460C2×C3×Dic3—31no—
461C2×C3×Dic3—31no—
462C2×C3×Dic3—31no—
463C2×C3×Dic3—42no—
464C2×C3×Dic3—61no—
465C2×C3×Dic3—61no—
466C2×C3×Dic3—61no—
467C2×C3×Dic3—62no—
468C2×C3×Dic3—121no—
469C2×C3×Dic3C22×D311yescharacteristic
470C2×C3×Dic3C22×D311yescharacteristic
471C2×C3×Dic3C22×D311yescharacteristic
472C2×C3×Dic3C22×D311yescharacteristic
473C2×C3×Dic3C22×D311yescharacteristic
474C2×C3×Dic3C22×D311yescharacteristic
475C2×C3×Dic3C22×D311yescharacteristic
476C2×C3×Dic3C22×D311yescharacteristic
477C2×C3×Dic3C22×D311yescharacteristic
478C2×C3×Dic3C22×D311yescharacteristic
479C3×D12—34no—
480C3×D12—62no—
481C3×C4×D3—62no—
482C3×C4×D3—62no—
483C3×C4×D3—62no—
484C3×C4×D3—62no—
485C3×C4×D3—62no—
486C3×C4×D3—121no—
487C3×Dic6—62no—
488C3×Dic6—62no—
489#627—22no—
490#626—22no—
491#626—62no—
492#626—62no—
493#626—62no—
494#626—62no—
495#626—122no—
496#626—122no—
497#626#6714yescomplemented
498#624—22no—
499#624—22no—
500D3×Dic3—22no—
501D3×Dic3—41no—
502D3×Dic3—121no—
503D3×Dic3—121no—
504D3×Dic3—122no—
505#546—271noSylow
506C2×C33—41no—
507C2×C33C22×D411yescharacteristic
508C2×C33C2×#4111yescharacteristic
509C2×C33H(5,𝔽2)11yescharacteristic
510C3⋊(C3⋊D3)—41no—
511C3×C3⋊D3—22no—
512C3×C3⋊D3—22no—
513C3×C3⋊D3—41no—
514C32×D3—22no—
515C23×D3—91no—
516C23×D3—91no—
517C23×D3—91no—
518C23×D3—91no—
519C23×D3—91no—
520C23×D3—91no—
521C23×D3—181no—
522C3×#41—184no—
523C2×C3×Q8—91no—
524C2×C3×D4—31no—
525C2×C3×D4—31no—
526C2×C3×D4—61no—
527C2×C3×D4—91no—
528C2×C3×D4—91no—
529C2×C3×D4—91no—
530C2×C3×D4—91no—
531C2×C3×D4—91no—
532C22×C3×C4—31no—
533C22×C3×C4—31no—
534C22×C3×C4—61no—
535C22×C3×C4—91no—
536C22×C3×C4—91no—
537C22×C3×C4—91no—
538C22×C3×C4—91no—
539C2×#67—31no—
540C2×#67—31no—
541C2×#67—31no—
542C2×#67—31no—
543C2×#67—31no—
544C2×#67—31no—
545C2×#67—31no—
546C2×#67—31no—
547C2×#67—61no—
548C2×#67—61no—
549C2×#67—61no—
550C2×#67—91no—
551C2×#67—91no—
552C2×#67—91no—
553C2×#67—91no—
554C2×#67—91no—
555C2×#67—181no—
556C2×#67—181no—
557C2×#67—181no—
558C2×#67—361no—
559C2×#67D3211yescharacteristic, complemented
560C22×Dic3—31no—
561C22×Dic3—31no—
562C22×Dic3—91no—
563C22×Dic3D3211yescharacteristic, complemented
564#237—64no—
565D3×D4—184no—
566D3×D4—184no—
567#235—64no—
568C2×D12—31no—
569C2×D12—31no—
570C2×D12—91no—
571C2×D12—91no—
572C2×D12—91no—
573C2×D12—91no—
574C2×D12—181no—
575C2×D12—181no—
576C2×D12—184no—
577C2×C4×D3—31no—
578C2×C4×D3—31no—
579C2×C4×D3—31no—
580C2×C4×D3—31no—
581C2×C4×D3—31no—
582C2×C4×D3—31no—
583C2×C4×D3—91no—
584C2×C4×D3—91no—
585C2×C4×D3—181no—
586C2×Dic6—31no—
587C2×Dic6—31no—
588C3×C4⋊C4—91no—
589C3×C4⋊C4—91no—
590C3×C22⋊C4—31no—
591C3×C22⋊C4—31no—
592C3×C22⋊C4—61no—
593C3×C22⋊C4—91no—
594C3×C22⋊C4—91no—
595C3×C42—91no—
596#217—91no—
597#217—91no—
598#217—91no—
599#217—91no—
600#217—91no—
601#217—91no—
602#217—91no—
603#217—181no—
604#217D3211yescharacteristic, complemented
605(C2×D3)⋊C4—31no—
606(C2×D3)⋊C4—31no—
607(C2×D3)⋊C4—31no—
608(C2×D3)⋊C4—31no—
609(C2×D3)⋊C4—91no—
610(C2×D3)⋊C4—91no—
611(C2×D3)⋊C4—91no—
612(C2×D3)⋊C4—91no—
613(C2×D3)⋊C4—91no—
614(C2×D3)⋊C4—91no—
615(C2×D3)⋊C4—91no—
616(C2×D3)⋊C4—91no—
617(C2×D3)⋊C4—91no—
618(C2×D3)⋊C4—91no—
619(C2×D3)⋊C4—91no—
620(C2×D3)⋊C4—91no—
621(C2×D3)⋊C4—91no—
622(C2×D3)⋊C4—91no—
623(C2×D3)⋊C4—91no—
624(C2×D3)⋊C4—91no—
625(C2×D3)⋊C4—91no—
626(C2×D3)⋊C4—91no—
627(C2×D3)⋊C4—91no—
628(C2×D3)⋊C4—91no—
629(C2×D3)⋊C4—181no—
630(C2×D3)⋊C4—181no—
631(C2×D3)⋊C4—181no—
632(C2×D3)⋊C4—181no—
633(C2×D3)⋊C4—181no—
634C4⋊Dic3—91no—
635C4⋊Dic3—91no—
636C4⋊Dic3—181no—
637Dic3⋊C4—31no—
638Dic3⋊C4—31no—
639Dic3⋊C4—31no—
640Dic3⋊C4—31no—
641Dic3⋊C4—91no—
642Dic3⋊C4—91no—
643Dic3⋊C4—91no—
644Dic3⋊C4—91no—
645Dic3⋊C4—181no—
646C4×Dic3—31no—
647C4×Dic3—31no—
648C22×C32—21no—
649C22×C32—22no—
650C22×C32—21no—
651C22×C32—21no—
652C22×C32—21no—
653C22×C32—21no—
654C22×C32—21no—
655C22×C32—21no—
656C22×C32—21no—
657C22×C32—21no—
658C22×C32—21no—
659C22×C32—21no—
660C22×C32—21no—
661C22×C32—32no—
662C22×C32—41no—
663C22×C32—41no—
664C22×C32—41no—
665C22×C32—42no—
666C22×C32—41no—
667C22×C32—41no—
668C22×C32—41no—
669C22×C32—41no—
670C22×C32—41no—
671C22×C32—41no—
672C22×C32—61no—
673C22×C32—61no—
674C22×C32—81no—
675C22×C32—81no—
676C22×C32C23×D311yescharacteristic
677C22×C32C23×D311yescharacteristic
678C22×C32C23×D311yescharacteristic
679C2×C3⋊D3—21no—
680C2×C3⋊D3—21no—
681C2×C3⋊D3—21no—
682C2×C3⋊D3—21no—
683C2×C3⋊D3—21no—
684C2×C3⋊D3—21no—
685C2×C3⋊D3—21no—
686C2×C3⋊D3—61no—
687C2×C3⋊D3—62no—
688C2×C3⋊D3—61no—
689C2×C3⋊D3—61no—
690C2×C3⋊D3—61no—
691C2×C3⋊D3—61no—
692C2×C3⋊D3—61no—
693C2×C3⋊D3—61no—
694C2×C3⋊D3—61no—
695C2×C3⋊D3—61no—
696C2×C3⋊D3—121no—
697C2×C3⋊D3—121no—
698C2×C3⋊D3—122no—
699C2×C3⋊D3—121no—
700C2×C3⋊D3—121no—
701C2×C3⋊D3—121no—
702C2×C3⋊D3—121no—
703C2×C3⋊D3—121no—
704C2×C3⋊D3—121no—
705C2×C3⋊D3—124no—
706C2×C3⋊D3—241no—
707C2×C3⋊D3—241no—
708C2×C3⋊D3#23512yescomplemented
709C2×C3⋊D3C2×#6712yes—
710C2×C3×D3—21no—
711C2×C3×D3—21no—
712C2×C3×D3—21no—
713C2×C3×D3—21no—
714C2×C3×D3—22no—
715C2×C3×D3—32no—
716C2×C3×D3—32no—
717C2×C3×D3—32no—
718C2×C3×D3—32no—
719C2×C3×D3—41no—
720C2×C3×D3—41no—
721C2×C3×D3—62no—
722C2×C3×D3—62no—
723C2×C3×D3—61no—
724C2×C3×D3—61no—
725C2×C3×D3—61no—
726C2×C3×D3—61no—
727C2×C3×D3—61no—
728C2×C3×D3—61no—
729C2×C3×D3—61no—
730C2×C3×D3—61no—
731C2×C3×D3—61no—
732C2×C3×D3—61no—
733C2×C3×D3—61no—
734C2×C3×D3—61no—
735C2×C3×D3—61no—
736C2×C3×D3—61no—
737C2×C3×D3—121no—
738C2×C3×D3—121no—
739C2×C3×D3—121no—
740C2×C3×D3—121no—
741C2×C3×D3—121no—
742C2×C3×D3—121no—
743C2×C3×D3—121no—
744C2×C3×D3D3×D412yes—
745C2×C3×D3C2×#6712yes—
746D32—124no—
747D32—124no—
748D32—128no—
749D32—124no—
750D32—124no—
751D32—124no—
752C32×C4—32no—
753C32×C4—61no—
754C32×C4—61no—
755C32×C4—61no—
756C32×C4—61no—
757C3⋊Dic3—21no—
758C3⋊Dic3—21no—
759C3⋊Dic3—21no—
760C3⋊Dic3—61no—
761C3⋊Dic3—62no—
762C3⋊Dic3—61no—
763C3⋊Dic3—61no—
764C3⋊Dic3—121no—
765C3⋊Dic3—121no—
766C3⋊Dic3—122no—
767C3×Dic3—21no—
768C3×Dic3—21no—
769C3×Dic3—21no—
770C3×Dic3—21no—
771C3×Dic3—21no—
772C3×Dic3—21no—
773C3×Dic3—21no—
774C3×Dic3—21no—
775C3×Dic3—22no—
776C3×Dic3—41no—
777C3×Dic3—41no—
778C3×Dic3—41no—
779C3×Dic3—41no—
780C3×Dic3—61no—
781C3×Dic3—61no—
782C3×Dic3—61no—
783C3×Dic3—61no—
784C3×Dic3—61no—
785C3×Dic3—61no—
786C3×Dic3—121no—
787C3×Dic3—121no—
788C3×Dic3—121no—
789C3×Dic3D3×D412yes—
790C3×Dic3C2×#6712yes—
791C2×#41—91no—
792C22×D4—271no—
793#124—271no—
794#123—271no—
795#123—271no—
796C22⋊Q8—271no—
797#121—91no—
798#121—271no—
799#121—271no—
800#120—271no—
801#120—271no—
802C4×D4—91no—
803C4×D4—271no—
804C2×C22⋊C4—271no—
805C2×C22⋊C4—271no—
806C33#54611yescharacteristic, complemented, Sylow
807C23×C3—21no—
808C23×C3—21no—
809C23×C3—21no—
810C23×C3—31no—
811C23×C3—31no—
812C23×C3—41no—
813C23×C3—61no—
814C23×C3—91no—
815C23×C3—91no—
816C23×C3—91no—
817C23×C3C2×D3211yescharacteristic
818C23×C3C2×D3211yescharacteristic
819C23×C3C2×D3211yescharacteristic
820C22×D3—31no—
821C22×D3—31no—
822C22×D3—31no—
823C22×D3—31no—
824C22×D3—31no—
825C22×D3—31no—
826C22×D3—61no—
827C22×D3—61no—
828C22×D3—61no—
829C22×D3—91no—
830C22×D3—91no—
831C22×D3—91no—
832C22×D3—181no—
833C22×D3—181no—
834C22×D3—181no—
835C22×D3—182no—
836C22×D3—182no—
837C22×D3—182no—
838C22×D3—182no—
839C22×D3—182no—
840C22×D3—182no—
841C22×D3—182no—
842C22×D3—182no—
843C22×D3—182no—
844C22×D3—182no—
845C22×D3—182no—
846C22×D3—182no—
847C22×D3—361no—
848C22×D3—362no—
849C22×D3—362no—
850C22×D3—361no—
851C22×D3—361no—
852C22×D3—361no—
853C22×D3—361no—
854C22×D3—361no—
855C22×D3—361no—
856C22×D3—362no—
857C22×D3C2×D3211yescharacteristic
858C3×Q8—182no—
859C3×D4—62no—
860C3×D4—62no—
861C3×D4—94no—
862C3×D4—122no—
863C3×D4—182no—
864C3×D4—182no—
865C3×D4—182no—
866C3×D4—361no—
867C2×C3×C4—31no—
868C2×C3×C4—31no—
869C2×C3×C4—31no—
870C2×C3×C4—31no—
871C2×C3×C4—31no—
872C2×C3×C4—31no—
873C2×C3×C4—31no—
874C2×C3×C4—31no—
875C2×C3×C4—31no—
876C2×C3×C4—31no—
877C2×C3×C4—61no—
878C2×C3×C4—61no—
879C2×C3×C4—61no—
880C2×C3×C4—61no—
881C2×C3×C4—61no—
882C2×C3×C4—62no—
883C2×C3×C4—62no—
884C2×C3×C4—91no—
885C2×C3×C4—91no—
886C2×C3×C4—91no—
887C2×C3×C4—122no—
888C2×C3×C4—182no—
889C2×C3×C4—182no—
890C2×C3×C4—182no—
891C2×C3×C4—361no—
892#67—22no—
893#67—34no—
894#67—62no—
895#67—62no—
896#67—62no—
897#67—62no—
898#67—62no—
899#67—122no—
900#67—122no—
901#67—121no—
902#67—121no—
903#67—122no—
904#67—182no—
905#67—182no—
906#67—361no—
907#67—361no—
908#67—361no—
909#67—362no—
910#67—362no—
911#67—362no—
912#67—364no—
913C2×Dic3—22no—
914C2×Dic3—31no—
915C2×Dic3—31no—
916C2×Dic3—31no—
917C2×Dic3—31no—
918C2×Dic3—31no—
919C2×Dic3—31no—
920C2×Dic3—61no—
921C2×Dic3—61no—
922C2×Dic3—61no—
923C2×Dic3—62no—
924C2×Dic3—91no—
925C2×Dic3—91no—
926C2×Dic3—91no—
927C2×Dic3—121no—
928C2×Dic3—181no—
929C2×Dic3—181no—
930C2×Dic3—181no—
931C2×Dic3—361no—
932C2×Dic3—361no—
933C2×Dic3C2×D3211yescharacteristic
934C2×Dic3C2×D3211yescharacteristic
935C2×Dic3C2×D3211yescharacteristic
936C2×Dic3C2×D3211yescharacteristic
937C2×Dic3C2×D3211yescharacteristic
938D12—34no—
939D12—62no—
940D12—182no—
941D12—182no—
942D12—182no—
943D12—182no—
944D12—362no—
945D12—362no—
946C4×D3—62no—
947C4×D3—62no—
948C4×D3—62no—
949C4×D3—62no—
950C4×D3—62no—
951C4×D3—121no—
952C4×D3—361no—
953C4×D3—361no—
954C4×D3—362no—
955Dic6—62no—
956Dic6—62no—
957C2×C32—21no—
958C2×C32—21no—
959C2×C32—21no—
960C2×C32—21no—
961C2×C32—21no—
962C2×C32—21no—
963C2×C32—21no—
964C2×C32—21no—
965C2×C32—21no—
966C2×C32—41no—
967C2×C32—41no—
968C2×C32—41no—
969C2×C32—41no—
970C2×C32—42no—
971C2×C32—41no—
972C2×C32—41no—
973C2×C32—62no—
974C2×C32—81no—
975C2×C32—81no—
976C2×C32—82no—
977C2×C32C2×#23511yescharacteristic
978C2×C32C2×D3×D411yescharacteristic
979C2×C32C2×D3×D411yescharacteristic
980C2×C32#100411yescharacteristic
981C2×C32D3×#4111yescharacteristic
982C2×C32D3×#4111yescharacteristic
983C2×C32#100911yescharacteristic
984C2×C32#100911yescharacteristic
985C2×C32C22×#6711yescharacteristic
986C3⋊D3—22no—
987C3⋊D3—22no—
988C3⋊D3—41no—
989C3⋊D3—121no—
990C3⋊D3—122no—
991C3⋊D3—121no—
992C3⋊D3—121no—
993C3⋊D3—241no—
994C3⋊D3—241no—
995C3⋊D3—242no—
996C3×D3—22no—
997C3×D3—22no—
998C3×D3—42no—
999C3×D3—62no—
1000C3×D3—62no—
1001C3×D3—62no—
1002C3×D3—62no—
1003C3×D3—122no—
1004C3×D3—122no—
1005C3×D3—121no—
1006C3×D3—121no—
1007C3×D3—241no—
1008C24—271no—
1009C24—271no—
1010#41—184no—
1011C2×Q8—91no—
1012C2×D4—31no—
1013C2×D4—91no—
1014C2×D4—91no—
1015C2×D4—91no—
1016C2×D4—91no—
1017C2×D4—91no—
1018C2×D4—271no—
1019C2×D4—271no—
1020C2×D4—271no—
1021C2×D4—544no—
1022C22×C4—31no—
1023C22×C4—91no—
1024C22×C4—91no—
1025C22×C4—91no—
1026C22×C4—91no—
1027C22×C4—271no—
1028C4⋊C4—91no—
1029C4⋊C4—91no—
1030C4⋊C4—271no—
1031C4⋊C4—271no—
1032C22⋊C4—31no—
1033C22⋊C4—91no—
1034C22⋊C4—91no—
1035C22⋊C4—271no—
1036C22⋊C4—271no—
1037C22⋊C4—271no—
1038C22⋊C4—271no—
1039C22⋊C4—271no—
1040C22⋊C4—271no—
1041C22⋊C4—271no—
1042C22⋊C4—271no—
1043C22⋊C4—271no—
1044C42—91no—
1045C22×C3—22no—
1046C22×C3—21no—
1047C22×C3—21no—
1048C22×C3—21no—
1049C22×C3—21no—
1050C22×C3—21no—
1051C22×C3—21no—
1052C22×C3—21no—
1053C22×C3—21no—
1054C22×C3—21no—
1055C22×C3—21no—
1056C22×C3—21no—
1057C22×C3—21no—
1058C22×C3—32no—
1059C22×C3—32no—
1060C22×C3—41no—
1061C22×C3—41no—
1062C22×C3—41no—
1063C22×C3—41no—
1064C22×C3—41no—
1065C22×C3—41no—
1066C22×C3—41no—
1067C22×C3—41no—
1068C22×C3—42no—
1069C22×C3—41no—
1070C22×C3—62no—
1071C22×C3—61no—
1072C22×C3—61no—
1073C22×C3—61no—
1074C22×C3—61no—
1075C22×C3—81no—
1076C22×C3—81no—
1077C22×C3—92no—
1078C22×C3—92no—
1079C22×C3—121no—
1080C22×C3—121no—
1081C22×C3—181no—
1082C22×C3—181no—
1083C22×C3—181no—
1084C22×C3—181no—
1085C22×C3—181no—
1086C22×C3—181no—
1087C22×C3—181no—
1088C22×C3C22×D3211yescharacteristic
1089C22×C3C22×D3211yescharacteristic
1090C22×C3C22×D3211yescharacteristic
1091C2×D3—21no—
1092C2×D3—21no—
1093C2×D3—32no—
1094C2×D3—32no—
1095C2×D3—32no—
1096C2×D3—32no—
1097C2×D3—62no—
1098C2×D3—62no—
1099C2×D3—61no—
1100C2×D3—61no—
1101C2×D3—61no—
1102C2×D3—61no—
1103C2×D3—61no—
1104C2×D3—61no—
1105C2×D3—61no—
1106C2×D3—61no—
1107C2×D3—61no—
1108C2×D3—61no—
1109C2×D3—61no—
1110C2×D3—61no—
1111C2×D3—61no—
1112C2×D3—61no—
1113C2×D3—121no—
1114C2×D3—121no—
1115C2×D3—121no—
1116C2×D3—121no—
1117C2×D3—121no—
1118C2×D3—121no—
1119C2×D3—121no—
1120C2×D3—182no—
1121C2×D3—181no—
1122C2×D3—181no—
1123C2×D3—181no—
1124C2×D3—181no—
1125C2×D3—181no—
1126C2×D3—181no—
1127C2×D3—181no—
1128C2×D3—181no—
1129C2×D3—181no—
1130C2×D3—361no—
1131C2×D3—361no—
1132C2×D3—361no—
1133C2×D3—361no—
1134C2×D3—361no—
1135C2×D3—361no—
1136C2×D3—361no—
1137C2×D3—361no—
1138C2×D3—362no—
1139C2×D3—364no—
1140C2×D3—364no—
1141C2×D3—364no—
1142C2×D3—364no—
1143C2×D3—364no—
1144C2×D3—364no—
1145C2×D3—368no—
1146C2×D3—721no—
1147C2×D3—721no—
1148C2×D3D3×#6712yes—
1149C3×C4—32no—
1150C3×C4—32no—
1151C3×C4—62no—
1152C3×C4—61no—
1153C3×C4—61no—
1154C3×C4—61no—
1155C3×C4—61no—
1156C3×C4—61no—
1157C3×C4—61no—
1158C3×C4—61no—
1159C3×C4—61no—
1160C3×C4—121no—
1161C3×C4—121no—
1162C3×C4—121no—
1163C3×C4—121no—
1164C3×C4—181no—
1165C3×C4—181no—
1166C3×C4—181no—
1167Dic3—21no—
1168Dic3—21no—
1169Dic3—21no—
1170Dic3—21no—
1171Dic3—61no—
1172Dic3—61no—
1173Dic3—61no—
1174Dic3—61no—
1175Dic3—61no—
1176Dic3—61no—
1177Dic3—121no—
1178Dic3—121no—
1179Dic3—121no—
1180Dic3—182no—
1181Dic3—181no—
1182Dic3—181no—
1183Dic3—181no—
1184Dic3—361no—
1185Dic3—361no—
1186Dic3—362no—
1187Dic3D3×#6712yes—
1188C32—21no—
1189C32—21no—
1190C32—21no—
1191C32—41no—
1192C32#555011yescharacteristic, complemented
1193C32#561011yescharacteristic, complemented
1194C32#582911yescharacteristic, complemented
1195C23—31no—
1196C23—91no—
1197C23—91no—
1198C23—91no—
1199C23—271no—
1200C23—542no—
1201C23—542no—
1202C23—542no—
1203C23—542no—
1204C23—1081no—
1205C23—1081no—
1206C23D3311yescharacteristic
1207Q8—182no—
1208D4—62no—
1209D4—94no—
1210D4—182no—
1211D4—182no—
1212D4—182no—
1213D4—361no—
1214D4—542no—
1215D4—542no—
1216D4—1081no—
1217C2×C4—31no—
1218C2×C4—31no—
1219C2×C4—31no—
1220C2×C4—31no—
1221C2×C4—31no—
1222C2×C4—62no—
1223C2×C4—91no—
1224C2×C4—91no—
1225C2×C4—91no—
1226C2×C4—182no—
1227C2×C4—182no—
1228C2×C4—182no—
1229C2×C4—271no—
1230C2×C4—361no—
1231C2×C4—1081no—
1232C2×C3—21no—
1233C2×C3—21no—
1234C2×C3—21no—
1235C2×C3—21no—
1236C2×C3—21no—
1237C2×C3—21no—
1238C2×C3—21no—
1239C2×C3—21no—
1240C2×C3—21no—
1241C2×C3—42no—
1242C2×C3—41no—
1243C2×C3—41no—
1244C2×C3—41no—
1245C2×C3—41no—
1246C2×C3—41no—
1247C2×C3—41no—
1248C2×C3—62no—
1249C2×C3—62no—
1250C2×C3—81no—
1251C2×C3—81no—
1252C2×C3—82no—
1253C2×C3—122no—
1254C2×C3—182no—
1255C2×C3—182no—
1256C2×C3—361no—
1257C2×C3D3×#23511yescharacteristic
1258C2×C3D3×#23511yescharacteristic
1259C2×C3#6430811yescharacteristic
1260C2×C3D32×D411yescharacteristic
1261C2×C3#6431211yescharacteristic
1262C2×C3#6431411yescharacteristic
1263C2×C3#6431411yescharacteristic
1264C2×C3C2×D3×#6711yescharacteristic
1265C2×C3C2×D3×#6711yescharacteristic
1266D3—22no—
1267D3—62no—
1268D3—62no—
1269D3—62no—
1270D3—62no—
1271D3—122no—
1272D3—122no—
1273D3—121no—
1274D3—121no—
1275D3—241no—
1276D3—362no—
1277D3—361no—
1278D3—361no—
1279D3—361no—
1280D3—721no—
1281D3—721no—
1282D3—722no—
1283C22—21no—
1284C22—21no—
1285C22—21no—
1286C22—32no—
1287C22—61no—
1288C22—61no—
1289C22—92no—
1290C22—92no—
1291C22—181no—
1292C22—181no—
1293C22—181no—
1294C22—181no—
1295C22—181no—
1296C22—181no—
1297C22—181no—
1298C22—541no—
1299C22—541no—
1300C22—541no—
1301C22—1084no—
1302C22—1084no—
1303C22C2×D3311yescharacteristic
1304C4—32no—
1305C4—61no—
1306C4—61no—
1307C4—61no—
1308C4—61no—
1309C4—181no—
1310C4—181no—
1311C4—181no—
1312C4—541no—
1313C3—21no—
1314C3—21no—
1315C3—21no—
1316C3—41no—
1317C3#1059428311yescharacteristic, complemented
1318C3#1059506711yescharacteristic, complemented
1319C3#1059530511yescharacteristic, complemented
1320C2—41no—
1321C2—62no—
1322C2—182no—
1323C2—182no—
1324C2—361no—
1325C2—1081no—
1326C2#1172441011yescharacteristic
1327C2#1172442011yescharacteristic
1328C2D32×#6711yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC23×C33C23
hypercenterC23D33
hypocenterC33#546
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
1. C2×C3×#3804C2semidirect
2. C2×#88955C2semidirect
3. #11723729C2semidirect
4. #11723643C2semidirect
5. #11723632C2semidirect
6. #11723624C2semidirect
7. C3×#63971C2semidirect
8. C3×#63952C2semidirect
9. #11723003C2semidirect
10. #11722993C2semidirect
11. #11722986C2semidirect
12. #11722970C2semidirect
13. Dic3×#626C2semidirect
14. #11722905C2semidirect
15. D3×#3722C2semidirect
21. C2×#6312C22semidirect
23. C2×C3×#638C22semidirect
24. C2×C3×#638C22semidirect
25. C2×C32×#67C22semidirect
26. C22×C32×Dic3C22semidirect
29. C2×Dic3×C3⋊D3C22semidirect
30. C2×C3×#627C22semidirect
34. C2×C3×#624C22semidirect
36. C2×C3×D3×Dic3C22semidirect
37. C2×C3×D3×Dic3C22semidirect
39. C32×#217C22semidirect
41. #88814C22semidirect
42. #88814C22semidirect
43. #88806C22semidirect
44. Dic3⋊(C3⋊Dic3)C22semidirect
45. #88804C22semidirect
46. #88804C22semidirect
47. #88804C22semidirect
49. #88803C22semidirect
50. (C2×D3)⋊(C3⋊Dic3)C22semidirect
51. C3×#3724C22semidirect
52. C3×#3724C22semidirect
54. C3×#3722C22semidirect
55. C3×Dic32C22semidirect
59. C2×#3804D3semidirect
82. #63971D3semidirect
85. #63952D3semidirect
136. C3×#626D4semidirect
161. C2×#638C2×D3semidirect
162. C2×#638C2×D3semidirect
178. C2×C3×#67C2×D3semidirect
179. C2×C3×#67C2×D3semidirect
183. C22×C3×Dic3C2×D3semidirect
184. C22×C3×Dic3C2×D3semidirect
198. C2×#627C2×D3semidirect
208. C2×#624C2×D3semidirect
213. C2×D3×Dic3C2×D3semidirect
214. C2×D3×Dic3C2×D3semidirect
227. C3×#217C2×D3semidirect
228. C3×#217C2×D3semidirect
242. #3724C2×D3semidirect
243. #3724C2×D3semidirect
260. #3722C2×D3semidirect
276. Dic32C2×D3semidirect
292. C2×C3×C3⋊D3#41semidirect
497. #626#67semidirect
559. C2×#67D32semidirect
563. C22×Dic3D32semidirect
604. #217D32semidirect
708. C2×C3⋊D3#235semidirect
806. C33#546semidirect
1192. C32#5550semidirect
1193. C32#5610semidirect
1194. C32#5829semidirect
1317. C3#10594283semidirect
1318. C3#10595067semidirect
1319. C3#10595305semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#38042
C2×#889552
#117237292
#117236432
#117236322
#117236242
C3×#639712
C3×#639522
#117230032
#117229932
#117229862
#117229702
Dic3×#6262
#117229052
D3×#37222
#105953053
#105950673
#105942833