Finite Group Databasebeta

← #13171749

Subgroups — #13171749

Order 1728.

1642 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#89029C211yesmaximal, characteristic
2#11723726C211yesmaximal, characteristic, complemented
3#11723598C211yesmaximal, characteristic, complemented
4C2×Dic3×C3⋊Dic3C211yesmaximal, characteristic, complemented
5C3×#67⋊Dic3C211yesmaximal, characteristic, complemented
6C3×Dic3×#67C211yesmaximal, characteristic, complemented
7C3×#63952C211yesmaximal, characteristic, complemented
8#11722943C211yesmaximal, characteristic, complemented
9#11722942C211yesmaximal, characteristic, complemented
10#11722936C211yesmaximal, characteristic, complemented
11#11722930C211yesmaximal, characteristic, complemented
12#11722921C211yesmaximal, characteristic, complemented
13#11722917C211yesmaximal, characteristic, complemented
14Dic3×#624C211yesmaximal, characteristic, complemented
15D3×Dic32C211yesmaximal, characteristic, complemented
16#10595190—31nomaximal
17C4×#3805—31nomaximal
18#10594050—31nomaximal
19C22×C3⋊(C3⋊Dic3)C2211yescharacteristic
20C2×C3×#638C2211yescharacteristic
21C22×C3×C3⋊Dic3C2211yescharacteristic
22C2×C32×#67C2211yescharacteristic
23C22×C32×Dic3C2211yescharacteristic
24C2×#6294C2211yescharacteristic
25C2×#6293C2211yescharacteristic
26C2×#6290C2211yescharacteristic
27C2×Dic3×C3⋊D3C2211yescharacteristic
28#89029C418yescomplemented
29C2×D3×C3⋊Dic3C2211yescharacteristic
30C2×C3×#624C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C3×#3757C2211yescharacteristic
34C32×#217C2211yescharacteristic
35#88815C2211yescharacteristic
36#88814C2211yescharacteristic
37#88813C2211yescharacteristic
38#88806C2211yescharacteristic
39#88806C2211yescharacteristic
40Dic3×C3⋊Dic3C2211yescharacteristic
41Dic3×C3⋊Dic3C2211yescharacteristic
42Dic3×C3⋊Dic3C2211yescharacteristic
43Dic3×C3⋊Dic3C2211yescharacteristic
44Dic3×C3⋊Dic3C2211yescharacteristic
45Dic3×C3⋊Dic3C2211yescharacteristic
46C3×#3724C2211yescharacteristic
47C3×Dic3⋊Dic3C2211yescharacteristic
48C3×Dic3⋊Dic3C2211yescharacteristic
49C3×#3722C2211yescharacteristic
50C3×(C2×D3)⋊Dic3C2211yescharacteristic
51C3×(C2×D3)⋊Dic3C2211yescharacteristic
52C3×Dic32C2211yescharacteristic
53C3×Dic32C2211yescharacteristic
54C3×Dic32C2211yescharacteristic
55C2×#3830—31no—
56C2×#3805—31no—
57C2×#3805—31no—
58C2×#3805—61no—
59C2×C4×C3⋊Dic3—31no—
60#64086—31no—
61C3×D4×Dic3—31no—
62C3×D4×Dic3—31no—
63C3×C4×#67—31no—
64C3×C4×#67—31no—
65C3×#67⋊C4—31no—
66C3×#67⋊C4—31no—
67#67⋊Dic3—31no—
68#67⋊Dic3D311yescharacteristic, complemented
69Dic3×#67—31no—
70Dic3×#67D311yescharacteristic, complemented
71#63957—31no—
72#63957—31no—
73#63957—31no—
74#63957—61no—
75C2×Dic32—31no—
76C2×Dic32—31no—
77C2×Dic32—31no—
78C2×Dic32—61no—
79#63952—31no—
80#63952—31no—
81#63952—31no—
82#63952D311yescharacteristic, complemented
83C4×#627—31no—
84#63902—31no—
85C4×#625—31no—
86C4×#624—31no—
87#63879—31no—
88#63879—31no—
89#63878—31no—
90#63878—31no—
91#63878—31no—
92#63878—31no—
93C4×D3×Dic3—31no—
94C4×D3×Dic3—31no—
95C4×D3×Dic3—31no—
96C4×D3×Dic3—31no—
97#63849—31no—
98#63844—31no—
99#63844—31no—
100#63838—31no—
101#63837—31no—
102#63837—31no—
103C23×C33C2311yescharacteristic
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C2×C3⋊(C3⋊Dic3)C2×C414yescomplemented
107C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
108C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
109C3×#638C2×C414yescomplemented
110C2×C3×C3⋊Dic3—22no—
111C2×C3×C3⋊Dic3C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C32×#67C2×C414yescomplemented
117C2×C32×Dic3—22no—
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123#6294—22no—
124#6293C2×C414yescomplemented
125#6290C2×C414yescomplemented
126Dic3×C3⋊D3C2×C414yescomplemented
127D3×C3⋊Dic3C2×C414yescomplemented
128C3×#624—22no—
129C3×D3×Dic3—22no—
130C3×D3×Dic3—22no—
131C4×#237—91no—
132C4×#237—91no—
133C4×#237—91no—
134C2×C32×D4—31no—
135C22×C32×C4—31no—
136C2×#638—31no—
137C2×#638C2×D311yescharacteristic
138C22×C3⋊Dic3—31no—
139C22×C3⋊Dic3—31no—
140C22×C3⋊Dic3—31no—
141C22×C3⋊Dic3—31no—
142C22×C3⋊Dic3—61no—
143C22×C3⋊Dic3—61no—
144C22×C3⋊Dic3—61no—
145C22×C3⋊Dic3—121no—
146C22×C3⋊Dic3C2×D311yescharacteristic
147#3830—38no—
148C2×C4×C3⋊D3—31no—
149C2×#634—31no—
150C2×C3×#67—21no—
151C2×C3×#67—31no—
152C2×C3×#67—31no—
153C2×C3×#67—61no—
154C2×C3×#67C2×D311yescharacteristic
155C2×C3×#67C2×D311yescharacteristic
156C22×C3×Dic3—21no—
157C22×C3×Dic3—31no—
158C22×C3×Dic3—31no—
159C22×C3×Dic3—31no—
160C22×C3×Dic3—31no—
161C22×C3×Dic3—61no—
162C22×C3×Dic3C2×D311yescharacteristic
163C22×C3×Dic3C2×D311yescharacteristic
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3—31no—
168C2×#627—31no—
169C2×#627—31no—
170C2×#627—61no—
171C2×#625—31no—
172C2×#625—31no—
173C2×#625—61no—
174C2×#624—31no—
175C2×#624C2×D311yescharacteristic
176#3805—38no—
177#3805—38no—
178#3805—68no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—31no—
185C2×D3×Dic3—61no—
186C2×D3×Dic3—61no—
187C2×D3×Dic3C2×D311yescharacteristic
188C2×D3×Dic3C2×D311yescharacteristic
189C32×C22⋊C4—31no—
190#3757C2×D311yescharacteristic
191#3750—31no—
192#3750—31no—
193C4×C3⋊Dic3—31no—
194C4×C3⋊Dic3—31no—
195C4×C3⋊Dic3—31no—
196C4×C3⋊Dic3—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—61no—
205C3×#217C2×D311yescharacteristic
206C3×#217C2×D311yescharacteristic
207C3×(C2×D3)⋊C4—31no—
208C3×(C2×D3)⋊C4—31no—
209C3×(C2×D3)⋊C4—31no—
210C3×(C2×D3)⋊C4—31no—
211C3×C4⋊Dic3—31no—
212C3×C4⋊Dic3—31no—
213C3×Dic3⋊C4—31no—
214C3×Dic3⋊C4—31no—
215C3×Dic3⋊C4—31no—
216C3×Dic3⋊C4—31no—
217C3×C4×Dic3—31no—
218C3×C4×Dic3—31no—
219C3×C4×Dic3—31no—
220C3×C4×Dic3—31no—
221C3×C4×Dic3—31no—
222C3×C4×Dic3—31no—
223#3724—31no—
224#3724—31no—
225#3724—31no—
226#3724—31no—
227#3724—31no—
228#3724—61no—
229#3724—61no—
230#3724C2×D311yescharacteristic
231Dic3⋊Dic3—31no—
232Dic3⋊Dic3—31no—
233Dic3⋊Dic3C2×D311yescharacteristic
234Dic3⋊Dic3C2×D311yescharacteristic
235#3722—31no—
236#3722C2×D311yescharacteristic
237(C2×D3)⋊Dic3—31no—
238(C2×D3)⋊Dic3—31no—
239(C2×D3)⋊Dic3C2×D311yescharacteristic
240(C2×D3)⋊Dic3C2×D311yescharacteristic
241Dic32—31no—
242Dic32—31no—
243Dic32—31no—
244Dic32—31no—
245Dic32—31no—
246Dic32—31no—
247Dic32—31no—
248Dic32—31no—
249Dic32—31no—
250Dic32—31no—
251Dic32—31no—
252Dic32—31no—
253Dic32—31no—
254Dic32—31no—
255Dic32—31no—
256Dic32—61no—
257Dic32—61no—
258Dic32—61no—
259Dic32—61no—
260Dic32—61no—
261Dic32—61no—
262Dic32C2×D311yescharacteristic
263Dic32C2×D311yescharacteristic
264Dic32C2×D311yescharacteristic
265C22×C33—21no—
266C22×C33—21no—
267C22×C33C22×C412yes—
268C22×C33C2411yescharacteristic
269C2×C3×C3⋊D3—21no—
270C2×C3×C3⋊D3—21no—
271C2×C3×C3⋊D3C22×C412yes—
272C2×C32×D3—21no—
273C2×C32×D3—21no—
274C2×C32×D3C22×C412yes—
275C3⋊(C3⋊Dic3)C22×C412yes—
276C3⋊(C3⋊Dic3)C22×C412yes—
277C3×C3⋊Dic3—21no—
278C3×C3⋊Dic3—21no—
279C3×C3⋊Dic3—21no—
280C3×C3⋊Dic3C22×C412yes—
281C3×C3⋊Dic3#4112yescomplemented
282C32×Dic3—21no—
283C32×Dic3—21no—
284C32×Dic3—21no—
285C32×Dic3C22×C412yes—
286C32×Dic3#4112yescomplemented
287C2×#237—91no—
288C2×#237—91no—
289C2×#237—91no—
290C2×#237—181no—
291C3×C4×D4—91no—
292C3×C4×D4—91no—
293C3×C4×D4—91no—
294D4×Dic3—31no—
295D4×Dic3—31no—
296D4×Dic3—91no—
297C4×#67—31no—
298C4×#67—31no—
299C4×#67—91no—
300C4×#67—91no—
301C4×#67—91no—
302C4×#67—91no—
303C2×C4×Dic3—91no—
304C2×C4×Dic3—91no—
305C2×C4×Dic3—91no—
306C2×C4×Dic3—91no—
307C2×C4×Dic3—91no—
308C2×C4×Dic3—91no—
309C2×C4×Dic3—181no—
310#892—91no—
311#892—91no—
312#892—91no—
313#887—91no—
314#887—91no—
315#887—91no—
316#67⋊C4—31no—
317#67⋊C4—31no—
318#67⋊C4—91no—
319#67⋊C4—91no—
320#67⋊C4—91no—
321#67⋊C4—91no—
322#877—91no—
323#877—91no—
324#877—91no—
325#877—91no—
326#877—91no—
327#877—91no—
328#877—181no—
329C42×D3—91no—
330C42×D3—91no—
331C42×D3—91no—
332C4×Dic6—91no—
333C4×Dic6—91no—
334C4×Dic6—91no—
335C23×C32—21no—
336C23×C32—21no—
337C23×C32—21no—
338C23×C32—31no—
339C23×C32—41no—
340C23×C32C22×D311yescharacteristic
341C23×C32C22×D311yescharacteristic
342C23×C32C22×D311yescharacteristic
343C22×C3⋊D3C22×D311yescharacteristic
344C22×C3×D3—21no—
345C22×C3×D3—31no—
346C22×C3×D3—31no—
347C22×C3×D3—61no—
348C22×C3×D3C22×D311yescharacteristic
349C22×C3×D3C22×D311yescharacteristic
350C32×D4—34no—
351C2×C32×C4—31no—
352C2×C32×C4—31no—
353C2×C32×C4—31no—
354C2×C32×C4—31no—
355C2×C32×C4—31no—
356C2×C32×C4—62no—
357#638—34no—
358#638C4×D314yescomplemented
359C2×C3⋊Dic3—22no—
360C2×C3⋊Dic3—34no—
361C2×C3⋊Dic3—34no—
362C2×C3⋊Dic3—34no—
363C2×C3⋊Dic3—31no—
364C2×C3⋊Dic3—31no—
365C2×C3⋊Dic3—31no—
366C2×C3⋊Dic3—31no—
367C2×C3⋊Dic3—31no—
368C2×C3⋊Dic3—31no—
369C2×C3⋊Dic3—34no—
370C2×C3⋊Dic3—61no—
371C2×C3⋊Dic3—61no—
372C2×C3⋊Dic3—61no—
373C2×C3⋊Dic3—61no—
374C2×C3⋊Dic3—64no—
375C2×C3⋊Dic3—64no—
376C2×C3⋊Dic3—64no—
377C2×C3⋊Dic3—61no—
378C2×C3⋊Dic3—61no—
379C2×C3⋊Dic3—124no—
380C2×C3⋊Dic3—121no—
381C2×C3⋊Dic3—121no—
382C2×C3⋊Dic3C22×D311yescharacteristic
383C2×C3⋊Dic3C22×D311yescharacteristic
384C2×C3⋊Dic3C22×D311yescharacteristic
385C2×C3⋊Dic3C22×D311yescharacteristic
386C2×C3⋊Dic3C22×D311yescharacteristic
387C4×C3⋊D3—34no—
388#634—34no—
389C3×#67—24no—
390C3×#67—34no—
391C3×#67—34no—
392C3×#67—64no—
393C3×#67C4×D314yescomplemented
394C3×#67C4×D314yescomplemented
395C2×C3×Dic3—24no—
396C2×C3×Dic3—22no—
397C2×C3×Dic3—22no—
398C2×C3×Dic3—21no—
399C2×C3×Dic3—21no—
400C2×C3×Dic3—21no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—31no—
404C2×C3×Dic3—31no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—31no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—61no—
414C2×C3×Dic3—61no—
415C2×C3×Dic3—61no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—62no—
419C2×C3×Dic3—62no—
420C2×C3×Dic3—62no—
421C2×C3×Dic3—64no—
422C2×C3×Dic3—62no—
423C2×C3×Dic3C22×D311yescharacteristic
424C2×C3×Dic3C22×D311yescharacteristic
425C2×C3×Dic3C22×D311yescharacteristic
426C2×C3×Dic3C22×D311yescharacteristic
427C2×C3×Dic3C22×D311yescharacteristic
428C2×C3×Dic3C22×D311yescharacteristic
429C2×C3×Dic3C22×D311yescharacteristic
430C2×C3×Dic3C22×D311yescharacteristic
431C2×C3×Dic3C22×D311yescharacteristic
432C2×C3×Dic3C22×D311yescharacteristic
433C3×C4×D3—62no—
434C3×C4×D3—62no—
435C3×C4×D3—62no—
436C3×C4×D3—62no—
437#627—34no—
438#627—34no—
439#627—64no—
440#625—34no—
441#625—34no—
442#625—64no—
443#624—22no—
444#624—62no—
445D3×Dic3—22no—
446D3×Dic3—22no—
447D3×Dic3—34no—
448D3×Dic3—34no—
449D3×Dic3—34no—
450D3×Dic3—34no—
451D3×Dic3—64no—
452D3×Dic3—64no—
453D3×Dic3—62no—
454D3×Dic3—62no—
455C4×#41—271noSylow
456C2×C33—22no—
457C2×C33C23×C411yescharacteristic
458C2×C33C2×#4111yescharacteristic
459C2×C33C2×#4111yescharacteristic
460C3×C3⋊D3—22no—
461C32×D3—22no—
462C2×C3×D4—31no—
463C2×C3×D4—31no—
464C2×C3×D4—61no—
465C2×C3×D4—91no—
466C22×C3×C4—31no—
467C22×C3×C4—31no—
468C22×C3×C4—61no—
469C22×C3×C4—91no—
470C22×C3×C4—91no—
471C22×C3×C4—91no—
472C22×C3×C4—91no—
473C2×#67—31no—
474C2×#67—31no—
475C2×#67—61no—
476C2×#67—91no—
477C2×#67—91no—
478C2×#67—91no—
479C2×#67—181no—
480C2×#67D3211yescharacteristic
481C22×Dic3—31no—
482C22×Dic3—31no—
483C22×Dic3—31no—
484C22×Dic3—31no—
485C22×Dic3—61no—
486C22×Dic3—91no—
487C22×Dic3—91no—
488C22×Dic3—91no—
489C22×Dic3—91no—
490C22×Dic3—91no—
491C22×Dic3—91no—
492C22×Dic3—91no—
493C22×Dic3—181no—
494C22×Dic3—181no—
495C22×Dic3—181no—
496C22×Dic3—181no—
497C22×Dic3—361no—
498C22×Dic3D3211yescharacteristic
499#237—98no—
500#237—98no—
501#237—98no—
502#237—188no—
503C2×C4×D3—31no—
504C2×C4×D3—31no—
505C2×C4×D3—31no—
506C2×C4×D3—31no—
507C2×C4×D3—91no—
508C2×C4×D3—91no—
509C2×C4×D3—91no—
510C2×C4×D3—91no—
511C2×C4×D3—91no—
512C2×C4×D3—181no—
513C2×Dic6—91no—
514C2×Dic6—91no—
515C2×Dic6—91no—
516C2×Dic6—181no—
517C3×C4⋊C4—91no—
518C3×C4⋊C4—91no—
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×C42—91no—
528C3×C42—91no—
529C3×C42—91no—
530#217—31no—
531#217—31no—
532#217—31no—
533#217—31no—
534#217—61no—
535#217—91no—
536#217D3211yescharacteristic
537(C2×D3)⋊C4—31no—
538(C2×D3)⋊C4—31no—
539(C2×D3)⋊C4—31no—
540(C2×D3)⋊C4—31no—
541(C2×D3)⋊C4—91no—
542(C2×D3)⋊C4—91no—
543C4⋊Dic3—31no—
544C4⋊Dic3—31no—
545C4⋊Dic3—91no—
546Dic3⋊C4—31no—
547Dic3⋊C4—31no—
548Dic3⋊C4—31no—
549Dic3⋊C4—31no—
550Dic3⋊C4—91no—
551Dic3⋊C4—91no—
552Dic3⋊C4—91no—
553Dic3⋊C4—91no—
554Dic3⋊C4—91no—
555Dic3⋊C4—91no—
556Dic3⋊C4—91no—
557Dic3⋊C4—91no—
558Dic3⋊C4—181no—
559Dic3⋊C4—181no—
560C4×Dic3—31no—
561C4×Dic3—31no—
562C4×Dic3—31no—
563C4×Dic3—31no—
564C4×Dic3—31no—
565C4×Dic3—31no—
566C4×Dic3—91no—
567C4×Dic3—91no—
568C4×Dic3—91no—
569C4×Dic3—91no—
570C4×Dic3—91no—
571C4×Dic3—91no—
572C4×Dic3—91no—
573C4×Dic3—91no—
574C4×Dic3—91no—
575C4×Dic3—91no—
576C4×Dic3—91no—
577C4×Dic3—91no—
578C4×Dic3—91no—
579C4×Dic3—91no—
580C4×Dic3—91no—
581C4×Dic3—91no—
582C4×Dic3—91no—
583C4×Dic3—91no—
584C4×Dic3—91no—
585C4×Dic3—91no—
586C4×Dic3—91no—
587C4×Dic3—181no—
588C4×Dic3—181no—
589C4×Dic3—181no—
590C4×Dic3—181no—
591C4×Dic3—181no—
592C4×Dic3—181no—
593C22×C32—21no—
594C22×C32—21no—
595C22×C32—22no—
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—22no—
605C22×C32—22no—
606C22×C32—22no—
607C22×C32—32no—
608C22×C32—42no—
609C22×C32—41no—
610C22×C32—41no—
611C22×C32—41no—
612C22×C32—41no—
613C22×C32—41no—
614C22×C32—42no—
615C22×C32—42no—
616C22×C32—61no—
617C22×C32—61no—
618C22×C32C2×C4×D312yes—
619C22×C32C2×C4×D312yes—
620C22×C32C2×C4×D312yes—
621C22×C32C23×D311yescharacteristic
622C22×C32C23×D311yescharacteristic
623C22×C32C23×D311yescharacteristic
624C2×C3⋊D3—21no—
625C2×C3⋊D3—21no—
626C2×C3⋊D3C2×C4×D312yes—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—21no—
631C2×C3×D3—22no—
632C2×C3×D3—32no—
633C2×C3×D3—32no—
634C2×C3×D3—41no—
635C2×C3×D3—41no—
636C2×C3×D3—62no—
637C2×C3×D3—61no—
638C2×C3×D3—61no—
639C2×C3×D3—61no—
640C2×C3×D3—61no—
641C2×C3×D3—121no—
642C2×C3×D3—121no—
643C2×C3×D3C2×C4×D312yes—
644C2×C3×D3C2×C4×D312yes—
645C32×C4—32no—
646C32×C4—32no—
647C32×C4—61no—
648C32×C4—61no—
649C32×C4—61no—
650C3⋊Dic3—21no—
651C3⋊Dic3—21no—
652C3⋊Dic3—21no—
653C3⋊Dic3—32no—
654C3⋊Dic3—32no—
655C3⋊Dic3—32no—
656C3⋊Dic3—32no—
657C3⋊Dic3—32no—
658C3⋊Dic3—32no—
659C3⋊Dic3—62no—
660C3⋊Dic3—62no—
661C3⋊Dic3—62no—
662C3⋊Dic3—62no—
663C3⋊Dic3—62no—
664C3⋊Dic3—62no—
665C3⋊Dic3—122no—
666C3⋊Dic3—122no—
667C3⋊Dic3C2×C4×D312yes—
668C3⋊Dic3#23712yescomplemented
669C3×Dic3—22no—
670C3×Dic3—21no—
671C3×Dic3—21no—
672C3×Dic3—21no—
673C3×Dic3—21no—
674C3×Dic3—21no—
675C3×Dic3—21no—
676C3×Dic3—22no—
677C3×Dic3—22no—
678C3×Dic3—32no—
679C3×Dic3—32no—
680C3×Dic3—32no—
681C3×Dic3—32no—
682C3×Dic3—41no—
683C3×Dic3—41no—
684C3×Dic3—62no—
685C3×Dic3—62no—
686C3×Dic3—62no—
687C3×Dic3—61no—
688C3×Dic3—61no—
689C3×Dic3—61no—
690C3×Dic3—61no—
691C3×Dic3—61no—
692C3×Dic3—61no—
693C3×Dic3—121no—
694C3×Dic3—121no—
695C3×Dic3C2×C4×D312yes—
696C3×Dic3C2×C4×D312yes—
697C3×Dic3#23712yescomplemented
698C3×Dic3#23712yescomplemented
699C2×#41—271no—
700C4×Q8—271no—
701C4×Q8—271no—
702C4×D4—91no—
703C4×D4—91no—
704C4×D4—91no—
705C4×D4—271no—
706C4×D4—271no—
707C4×D4—271no—
708#117—271no—
709#117—271no—
710#117—271no—
711C2×C42—271no—
712C2×C42—271no—
713C2×C42—271no—
714C33C4×#4111yescharacteristic, complemented, Sylow
715C23×C3—21no—
716C23×C3—21no—
717C23×C3—21no—
718C23×C3—31no—
719C23×C3—31no—
720C23×C3—41no—
721C23×C3—61no—
722C23×C3—91no—
723C23×C3C2×D3211yescharacteristic
724C23×C3C2×D3211yescharacteristic
725C23×C3C2×D3211yescharacteristic
726C22×D3—31no—
727C22×D3—31no—
728C22×D3—61no—
729C22×D3C2×D3211yescharacteristic
730C3×D4—34no—
731C3×D4—34no—
732C3×D4—64no—
733C3×D4—94no—
734C2×C3×C4—31no—
735C2×C3×C4—31no—
736C2×C3×C4—31no—
737C2×C3×C4—31no—
738C2×C3×C4—31no—
739C2×C3×C4—31no—
740C2×C3×C4—31no—
741C2×C3×C4—31no—
742C2×C3×C4—31no—
743C2×C3×C4—31no—
744C2×C3×C4—61no—
745C2×C3×C4—61no—
746C2×C3×C4—61no—
747C2×C3×C4—61no—
748C2×C3×C4—61no—
749C2×C3×C4—62no—
750C2×C3×C4—62no—
751C2×C3×C4—64no—
752C2×C3×C4—91no—
753C2×C3×C4—91no—
754C2×C3×C4—91no—
755C2×C3×C4—91no—
756C2×C3×C4—91no—
757C2×C3×C4—182no—
758C2×C3×C4—182no—
759C2×C3×C4—182no—
760C2×C3×C4—182no—
761#67—34no—
762#67—34no—
763#67—64no—
764#67—94no—
765#67—94no—
766#67—94no—
767#67—184no—
768#67#62414yescomplemented
769C2×Dic3—22no—
770C2×Dic3—31no—
771C2×Dic3—31no—
772C2×Dic3—31no—
773C2×Dic3—31no—
774C2×Dic3—31no—
775C2×Dic3—31no—
776C2×Dic3—31no—
777C2×Dic3—31no—
778C2×Dic3—31no—
779C2×Dic3—31no—
780C2×Dic3—61no—
781C2×Dic3—61no—
782C2×Dic3—61no—
783C2×Dic3—61no—
784C2×Dic3—61no—
785C2×Dic3—62no—
786C2×Dic3—62no—
787C2×Dic3—62no—
788C2×Dic3—64no—
789C2×Dic3—62no—
790C2×Dic3—94no—
791C2×Dic3—94no—
792C2×Dic3—91no—
793C2×Dic3—91no—
794C2×Dic3—91no—
795C2×Dic3—91no—
796C2×Dic3—91no—
797C2×Dic3—91no—
798C2×Dic3—94no—
799C2×Dic3—94no—
800C2×Dic3—94no—
801C2×Dic3—94no—
802C2×Dic3—184no—
803C2×Dic3—181no—
804C2×Dic3—181no—
805C2×Dic3—181no—
806C2×Dic3—181no—
807C2×Dic3—181no—
808C2×Dic3—181no—
809C2×Dic3—184no—
810C2×Dic3—184no—
811C2×Dic3—184no—
812C2×Dic3—182no—
813C2×Dic3—361no—
814C2×Dic3—361no—
815C2×Dic3—364no—
816C2×Dic3C2×D3211yescharacteristic
817C2×Dic3C2×D3211yescharacteristic
818C2×Dic3C2×D3211yescharacteristic
819C2×Dic3C2×D3211yescharacteristic
820C2×Dic3C2×D3211yescharacteristic
821C4×D3—62no—
822C4×D3—62no—
823C4×D3—62no—
824C4×D3—62no—
825C4×D3—94no—
826C4×D3—94no—
827C4×D3—94no—
828C4×D3—184no—
829C4×D3—182no—
830C4×D3—182no—
831Dic6—94no—
832Dic6—94no—
833Dic6—94no—
834Dic6—184no—
835C2×C32—22no—
836C2×C32—24no—
837C2×C32—22no—
838C2×C32—22no—
839C2×C32—21no—
840C2×C32—21no—
841C2×C32—21no—
842C2×C32—21no—
843C2×C32—21no—
844C2×C32—21no—
845C2×C32—21no—
846C2×C32—21no—
847C2×C32—21no—
848C2×C32—41no—
849C2×C32—41no—
850C2×C32—41no—
851C2×C32—42no—
852C2×C32—42no—
853C2×C32—44no—
854C2×C32—62no—
855C2×C32C22×C4×D311yescharacteristic
856C2×C32C22×C4×D311yescharacteristic
857C2×C32C22×C4×D311yescharacteristic
858C2×C32C2×#23711yescharacteristic
859C2×C32C2×#23711yescharacteristic
860C2×C32C2×#23711yescharacteristic
861C2×C32D3×#4111yescharacteristic
862C2×C32D3×#4111yescharacteristic
863C2×C32D3×#4111yescharacteristic
864C3⋊D3—22no—
865C3×D3—22no—
866C3×D3—22no—
867C3×D3—42no—
868C3×D3—62no—
869C3×D3—62no—
870C3×D3—122no—
871#41—278no—
872C2×Q8—271no—
873C2×D4—31no—
874C2×D4—91no—
875C2×D4—271no—
876C22×C4—31no—
877C22×C4—91no—
878C22×C4—91no—
879C22×C4—91no—
880C22×C4—91no—
881C22×C4—271no—
882C22×C4—271no—
883C22×C4—271no—
884C22×C4—271no—
885C4⋊C4—91no—
886C4⋊C4—91no—
887C4⋊C4—91no—
888C4⋊C4—271no—
889C4⋊C4—271no—
890C4⋊C4—271no—
891C22⋊C4—31no—
892C22⋊C4—91no—
893C22⋊C4—91no—
894C22⋊C4—91no—
895C22⋊C4—91no—
896C22⋊C4—271no—
897C42—91no—
898C42—91no—
899C42—91no—
900C42—271no—
901C42—271no—
902C42—271no—
903C42—271no—
904C42—271no—
905C42—271no—
906C42—271no—
907C22×C3—22no—
908C22×C3—22no—
909C22×C3—21no—
910C22×C3—21no—
911C22×C3—21no—
912C22×C3—21no—
913C22×C3—21no—
914C22×C3—21no—
915C22×C3—21no—
916C22×C3—21no—
917C22×C3—21no—
918C22×C3—22no—
919C22×C3—22no—
920C22×C3—22no—
921C22×C3—32no—
922C22×C3—32no—
923C22×C3—41no—
924C22×C3—41no—
925C22×C3—41no—
926C22×C3—41no—
927C22×C3—42no—
928C22×C3—42no—
929C22×C3—41no—
930C22×C3—42no—
931C22×C3—62no—
932C22×C3—61no—
933C22×C3—61no—
934C22×C3—61no—
935C22×C3—61no—
936C22×C3—92no—
937C22×C3—121no—
938C22×C3—121no—
939C22×C3—181no—
940C22×C3—181no—
941C22×C3C4×D3212yes—
942C22×C3C4×D3212yes—
943C22×C3C2×#62412yes—
944C22×C3C22×D3211yescharacteristic
945C22×C3C22×D3211yescharacteristic
946C22×C3C22×D3211yescharacteristic
947C2×D3—21no—
948C2×D3—21no—
949C2×D3—32no—
950C2×D3—32no—
951C2×D3—62no—
952C2×D3—61no—
953C2×D3—61no—
954C2×D3—61no—
955C2×D3—61no—
956C2×D3—121no—
957C2×D3—121no—
958C2×D3C2×#62412yes—
959C3×C4—32no—
960C3×C4—32no—
961C3×C4—32no—
962C3×C4—32no—
963C3×C4—62no—
964C3×C4—62no—
965C3×C4—62no—
966C3×C4—61no—
967C3×C4—61no—
968C3×C4—61no—
969C3×C4—61no—
970C3×C4—61no—
971C3×C4—61no—
972C3×C4—92no—
973C3×C4—92no—
974C3×C4—121no—
975C3×C4—121no—
976C3×C4—181no—
977C3×C4—181no—
978C3×C4—181no—
979Dic3—21no—
980Dic3—21no—
981Dic3—21no—
982Dic3—32no—
983Dic3—32no—
984Dic3—32no—
985Dic3—32no—
986Dic3—62no—
987Dic3—62no—
988Dic3—62no—
989Dic3—61no—
990Dic3—61no—
991Dic3—61no—
992Dic3—61no—
993Dic3—61no—
994Dic3—61no—
995Dic3—92no—
996Dic3—92no—
997Dic3—92no—
998Dic3—92no—
999Dic3—92no—
1000Dic3—92no—
1001Dic3—121no—
1002Dic3—121no—
1003Dic3—182no—
1004Dic3—182no—
1005Dic3—182no—
1006Dic3—182no—
1007Dic3—182no—
1008Dic3—182no—
1009Dic3—362no—
1010Dic3—362no—
1011Dic3#380512yescomplemented
1012Dic3C2×#62412yes—
1013C32—21no—
1014C32—21no—
1015C32—21no—
1016C32—41no—
1017C32C4×#23711yescharacteristic, complemented
1018C32C4×#23711yescharacteristic, complemented
1019C32C4×#23711yescharacteristic, complemented
1020C23—31no—
1021C23—91no—
1022C23D3311yescharacteristic
1023Q8—274no—
1024D4—34no—
1025D4—94no—
1026D4—274no—
1027C2×C4—31no—
1028C2×C4—31no—
1029C2×C4—31no—
1030C2×C4—31no—
1031C2×C4—31no—
1032C2×C4—62no—
1033C2×C4—91no—
1034C2×C4—91no—
1035C2×C4—91no—
1036C2×C4—91no—
1037C2×C4—91no—
1038C2×C4—182no—
1039C2×C4—182no—
1040C2×C4—182no—
1041C2×C4—182no—
1042C2×C4—274no—
1043C2×C4—274no—
1044C2×C4—271no—
1045C2×C4—271no—
1046C2×C4—274no—
1047C2×C4—542no—
1048C2×C3—24no—
1049C2×C3—22no—
1050C2×C3—22no—
1051C2×C3—22no—
1052C2×C3—21no—
1053C2×C3—21no—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—42no—
1062C2×C3—42no—
1063C2×C3—44no—
1064C2×C3—41no—
1065C2×C3—41no—
1066C2×C3—41no—
1067C2×C3—62no—
1068C2×C3—62no—
1069C2×C3—122no—
1070C2×C3—182no—
1071C2×C3C2×C4×D3211yescharacteristic
1072C2×C3C2×C4×D3211yescharacteristic
1073C2×C3#6430611yescharacteristic
1074C2×C3D3×#23711yescharacteristic
1075C2×C3D3×#23711yescharacteristic
1076C2×C3D3×#23711yescharacteristic
1077C2×C3D3×#23711yescharacteristic
1078C2×C3C2×#380511yescharacteristic
1079C2×C3C22×#62411yescharacteristic
1080D3—22no—
1081D3—62no—
1082D3—62no—
1083D3—122no—
1084C22—21no—
1085C22—21no—
1086C22—32no—
1087C22—61no—
1088C22—61no—
1089C22—92no—
1090C22—181no—
1091C22—181no—
1092C22D3×#62412yes—
1093C22C2×D3311yescharacteristic
1094C4—32no—
1095C4—32no—
1096C4—61no—
1097C4—61no—
1098C4—61no—
1099C4—92no—
1100C4—92no—
1101C4—181no—
1102C4—181no—
1103C4—181no—
1104C4—272no—
1105C4—272no—
1106C3—21no—
1107C3—21no—
1108C3—21no—
1109C3—41no—
1110C3#1059405011yescharacteristic, complemented
1111C3C4×#380511yescharacteristic, complemented
1112C3#1059519011yescharacteristic, complemented
1113C2—22no—
1114C2—62no—
1115C2—182no—
1116C2D3×#380511yescharacteristic
1117C2#1172440711yescharacteristic
1118C2C2×D3×#62411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutatorC2×C33C23×C4
FittingC23×C33C23
socle, cosocleC22×C33C24
prime radicalC2×#89029C2
hypercenterC23D33
hypocenterC33C4×#41
LCSG ▷ C2×C33 ▷ C33
UCSC1 ◁ C22 ◁ C23

Complements

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

NH ≅ G/Ntype
2. #11723726C2semidirect
3. #11723598C2semidirect
4. C2×Dic3×C3⋊Dic3C2semidirect
5. C3×#67⋊Dic3C2semidirect
6. C3×Dic3×#67C2semidirect
7. C3×#63952C2semidirect
8. #11722943C2semidirect
9. #11722942C2semidirect
10. #11722936C2semidirect
11. #11722930C2semidirect
12. #11722921C2semidirect
13. #11722917C2semidirect
14. Dic3×#624C2semidirect
15. D3×Dic32C2semidirect
28. #89029C4semidirect
68. #67⋊Dic3D3semidirect
70. Dic3×#67D3semidirect
82. #63952D3semidirect
106. C2×C3⋊(C3⋊Dic3)C2×C4semidirect
109. C3×#638C2×C4semidirect
116. C32×#67C2×C4semidirect
124. #6293C2×C4semidirect
125. #6290C2×C4semidirect
126. Dic3×C3⋊D3C2×C4semidirect
127. D3×C3⋊Dic3C2×C4semidirect
281. C3×C3⋊Dic3#41semidirect
286. C32×Dic3#41semidirect
358. #638C4×D3semidirect
393. C3×#67C4×D3semidirect
394. C3×#67C4×D3semidirect
668. C3⋊Dic3#237semidirect
697. C3×Dic3#237semidirect
698. C3×Dic3#237semidirect
714. C33C4×#41semidirect
768. #67#624semidirect
1011. Dic3#3805semidirect
1017. C32C4×#237semidirect
1018. C32C4×#237semidirect
1019. C32C4×#237semidirect
1110. C3#10594050semidirect
1111. C3C4×#3805semidirect
1112. C3#10595190semidirect

Maximal subgroups

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

subgroupindex
C2×#890292
#117237262
#117235982
C2×Dic3×C3⋊Dic32
C3×#67⋊Dic32
C3×Dic3×#672
C3×#639522
#117229432
#117229422
#117229362
#117229302
#117229212
#117229172
Dic3×#6242
D3×Dic322
#105951903
C4×#38053
#105940503