Finite Group Databasebeta

← D3×#63896 #13170756

Subgroups — D3×#63896 #13170756

Order 1728.

1630 conjugacy classes of subgroups.

The subgroup lattice has 1150 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#634C211yesmaximal, characteristic, complemented
2C2×D32×Dic3C211yesmaximal, characteristic
3#11723688C211yesmaximal, characteristic, complemented
4#11723497C211yesmaximal, characteristic, complemented
5#11723496C211yesmaximal, characteristic, complemented
6C3×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
7C3×#63896C211yesmaximal, characteristic, complemented
8C3×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
9#11722984C211yesmaximal, characteristic, complemented
10#11722983C211yesmaximal, characteristic, complemented
11#11722980C211yesmaximal, characteristic, complemented
12#11722975C211yesmaximal, characteristic, complemented
13D3×#3724C211yesmaximal, characteristic, complemented
14D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
16C2×#63896—31nomaximal
17D3×#896—31nomaximal
18D3×#878—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×#6308C2211yescharacteristic, complemented
21C2×C3×#634C2211yescharacteristic, complemented
22C2×C32×C4×D3C2211yescharacteristic
23C2×#6294C2211yescharacteristic
24C2×#6293C2211yescharacteristic, complemented
25C2×#6293C2211yescharacteristic, complemented
26C2×Dic3×C3⋊D3C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C2×D3×C3⋊Dic3C2211yescharacteristic
30D3×#634—24no—
31C2×C3×D3×Dic3C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34C2×C3×D3×Dic3C2211yescharacteristic
35D32×Dic3—24no—
36C3×#3752C2211yescharacteristic
37C3×#3750C2211yescharacteristic, complemented
38C32×(C2×D3)⋊C4C2211yescharacteristic
39C32×Dic3⋊C4C2211yescharacteristic, complemented
40#88815C2211yescharacteristic, complemented
41#88815C2211yescharacteristic, complemented
42#88814C2211yescharacteristic
43#88807C2211yescharacteristic, complemented
44#88806C2211yescharacteristic, complemented
45#88806C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47#88803C2211yescharacteristic
48(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
49C3×#3724C2211yescharacteristic, complemented
50C3×#3724C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic
56C22×#634—31no—
57C22×D3×Dic3—31no—
58C22×D3×Dic3—31no—
59C2×C4×D32—31no—
60C2×D3×Dic6—31no—
61C2×D3×Dic6—31no—
62C2×D3×Dic6—61no—
63#64105—31no—
64#64087—31no—
65C2×C3×(C2×D3)⋊C4—31no—
66C2×C3×Dic3⋊C4—31no—
67C3×#896—31no—
68C3×D3×C4⋊C4—31no—
69C3×D3×C22⋊C4—31no—
70C3×#878—31no—
71#63982—31no—
72D3×#217—31no—
73C2×#3724—31no—
74C2×Dic3⋊Dic3—31no—
75#63964—31no—
76C2×(C2×D3)⋊Dic3—31no—
77D3×(C2×D3)⋊C4—31no—
78D3×(C2×D3)⋊C4D311yescharacteristic
79#63899—31no—
80#63899—31no—
81#63896—31no—
82#63896—31no—
83#63896—31no—
84#63896—31no—
85#63896—31no—
86#63896—31no—
87#63896—31no—
88#63896—31no—
89#63896—31no—
90#63896—61no—
91#63896—61no—
92#63896D311yescharacteristic, direct product factor
93#63895—31no—
94#63893—31no—
95D3×C4⋊Dic3—31no—
96#63888—31no—
97#63887—31no—
98D3×Dic3⋊C4—31no—
99D3×Dic3⋊C4—31no—
100D3×Dic3⋊C4—31no—
101D3×Dic3⋊C4D311yescharacteristic, complemented
102#63865—31no—
103#63851—31no—
104C22×C3×C3⋊D3C2311yescharacteristic
105C22×C32×D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×C3×D32—22no—
108C2×C3×D32—22no—
109C2×C3×D32Q814yescomplemented
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
113#6308—22no—
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C3×C3⋊Dic3C2311yescharacteristic
119C3×#634—22no—
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C2×C32×Dic3C2311yescharacteristic
123C2×C32×Dic3C2311yescharacteristic
124C32×C4×D3—22no—
125#6294—22no—
126#6293—22no—
127#6293—22no—
128Dic3×C3⋊D3—22no—
129D3×C3⋊Dic3—22no—
130D3×C3⋊Dic3—22no—
131D3×C3⋊Dic3D414yes—
132C3×D3×Dic3—22no—
133C3×D3×Dic3—22no—
134C3×D3×Dic3—22no—
135C3×D3×Dic3—22no—
136D3×C22⋊Q8—91no—
137C2×#896—91no—
138C2×#878—91no—
139C23×C3×D3—31no—
140C23×C3×D3—31no—
141C22×D32C2×D311yescharacteristic
142C22×C32×C4—31no—
143C22×C3⋊Dic3—31no—
144C22×C3⋊Dic3—31no—
145C22×C3⋊Dic3—31no—
146C2×C4×C3⋊D3—31no—
147C2×#634—31no—
148C2×#634—31no—
149C2×#634—31no—
150C2×#634—31no—
151C2×#634—31no—
152C2×#634—64no—
153C2×#634—61no—
154C2×#634—61no—
155C2×#634—61no—
156C2×#634—121no—
157C2×#634C2×D311yescharacteristic, complemented
158C22×C3×Dic3—31no—
159C22×C3×Dic3—31no—
160C22×C3×Dic3—31no—
161C22×C3×Dic3—31no—
162C2×C3×C4×D3—21no—
163C2×C3×C4×D3—31no—
164C2×C3×C4×D3—31no—
165C2×C3×C4×D3—31no—
166C2×C3×C4×D3—31no—
167C2×C3×C4×D3C2×D311yescharacteristic
168C2×C3×C4×D3C2×D311yescharacteristic
169C2×C3×Dic6—31no—
170C2×C3×Dic6—31no—
171C2×C3×Dic6—61no—
172C2×#627—31no—
173C2×#627—31no—
174C2×#627—31no—
175C2×#627—31no—
176C2×#627—61no—
177C2×#627—61no—
178C2×#624—31no—
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—31no—
186C2×D3×Dic3—31no—
187C2×D3×Dic3—31no—
188C2×D3×Dic3—31no—
189C2×D3×Dic3—64no—
190C2×D3×Dic3—64no—
191C2×D3×Dic3—61no—
192C2×D3×Dic3—61no—
193C2×D3×Dic3—61no—
194C2×D3×Dic3—61no—
195C2×D3×Dic3C2×D311yescharacteristic
196C2×D3×Dic3C2×D311yescharacteristic
197C2×D3×Dic3C2×D311yescharacteristic
198C2×D3×Dic3C2×D311yescharacteristic
199C4×D32—64no—
200D3×Dic6—64no—
201D3×Dic6—64no—
202D3×Dic6—68no—
203C32×C4⋊C4—31no—
204C32×C22⋊C4—31no—
205#3757—31no—
206#3752—31no—
207#3752C2×D311yescharacteristic
208C4⋊(C3⋊Dic3)—31no—
209#3750—31no—
210#3750—31no—
211#3750—31no—
212#3750C2×D311yescharacteristic, complemented
213C3×#217—31no—
214C3×#217—31no—
215C3×(C2×D3)⋊C4—21no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—61no—
223C3×(C2×D3)⋊C4C2×D311yescharacteristic
224C3×(C2×D3)⋊C4C2×D311yescharacteristic
225C3×C4⋊Dic3—31no—
226C3×C4⋊Dic3—31no—
227C3×Dic3⋊C4—21no—
228C3×Dic3⋊C4—31no—
229C3×Dic3⋊C4—31no—
230C3×Dic3⋊C4—31no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—31no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—31no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—61no—
237C3×Dic3⋊C4C2×D311yescharacteristic, complemented
238C3×Dic3⋊C4C2×D311yescharacteristic, complemented
239#3724—31no—
240#3724—31no—
241#3724—31no—
242#3724—31no—
243#3724—31no—
244#3724—31no—
245#3724—61no—
246#3724—61no—
247#3724C2×D311yescharacteristic, complemented
248#3724C2×D311yescharacteristic, complemented
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—31no—
255Dic3⋊Dic3—31no—
256Dic3⋊Dic3—31no—
257Dic3⋊Dic3—61no—
258Dic3⋊Dic3—61no—
259Dic3⋊Dic3C2×D311yescharacteristic, complemented
260Dic3⋊Dic3C2×D311yescharacteristic, complemented
261#3722—31no—
262#3722C2×D311yescharacteristic
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—61no—
270(C2×D3)⋊Dic3—61no—
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272(C2×D3)⋊Dic3C2×D311yescharacteristic
273C22×C33C2411yescharacteristic
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3—21no—
276C2×C3×C3⋊D3C2×Q812yescomplemented
277C2×C32×D3—21no—
278C2×C32×D3—21no—
279C2×C32×D3C2×D412yes—
280C2×C32×D3C2×Q812yes—
281C2×C32×D3C2×Q812yescomplemented
282C2×C32×D3#4112yes—
283C3×D32—28no—
284C33×C4—21no—
285C3⋊(C3⋊Dic3)—21no—
286C3⋊(C3⋊Dic3)C2×D412yes—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C3×C3⋊Dic3—21no—
291C3×C3⋊Dic3C2×D412yes—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C32×Dic3—21no—
295C32×Dic3—21no—
296C23×Dic3—91no—
297C2×D3×Q8—91no—
298C22×C4×D3—91no—
299C22×C4×D3—91no—
300C22×Dic6—91no—
301C22×Dic6—91no—
302C22×Dic6—181no—
303C3×C22⋊Q8—91no—
304C2×C3×C4⋊C4—91no—
305C2×C3×C22⋊C4—91no—
306C2×#217—91no—
307#946—91no—
308C2×(C2×D3)⋊C4—31no—
309C2×(C2×D3)⋊C4—91no—
310C2×C4⋊Dic3—91no—
311#924—91no—
312C2×Dic3⋊C4—31no—
313C2×Dic3⋊C4—91no—
314C2×Dic3⋊C4—91no—
315C2×Dic3⋊C4—91no—
316#897—91no—
317#896—31no—
318#896—91no—
319#896—91no—
320#896—91no—
321#896—91no—
322#896—91no—
323#896—91no—
324#896—91no—
325#896—91no—
326#896—91no—
327#896—181no—
328D3×C4⋊C4—31no—
329D3×C4⋊C4—91no—
330D3×C4⋊C4—91no—
331D3×C22⋊C4—31no—
332D3×C22⋊C4—91no—
333#878—31no—
334#878—91no—
335#878—91no—
336#878—91no—
337#878—91no—
338#878—91no—
339#878—91no—
340#878—91no—
341#878—91no—
342#878—91no—
343#878—181no—
344C23×C32—31no—
345C23×C32—31no—
346C22×C3⋊D3C22×D311yescharacteristic
347C22×C3×D3—21no—
348C22×C3×D3—21no—
349C22×C3×D3—31no—
350C22×C3×D3—31no—
351C22×C3×D3—34no—
352C22×C3×D3—34no—
353C22×C3×D3—61no—
354C22×C3×D3—62no—
355C22×C3×D3—62no—
356C22×C3×D3—62no—
357C22×C3×D3—62no—
358C22×C3×D3C22×D311yescharacteristic
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C22×C3×D3C22×D311yescharacteristic
362C2×D32—22no—
363C2×D32—22no—
364C2×D32Dic614yescomplemented
365C2×C32×C4—21no—
366C2×C32×C4—21no—
367C2×C32×C4—21no—
368C2×C32×C4—31no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—31no—
372C2×C32×C4—41no—
373C2×C32×C4—62no—
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376C2×C32×C4C22×D311yescharacteristic
377C2×C3⋊Dic3—31no—
378C2×C3⋊Dic3—31no—
379C2×C3⋊Dic3—31no—
380C2×C3⋊Dic3—34no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—31no—
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—61no—
385C2×C3⋊Dic3—61no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—61no—
390C2×C3⋊Dic3—62no—
391C2×C3⋊Dic3—62no—
392C2×C3⋊Dic3—121no—
393C2×C3⋊Dic3—121no—
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C2×C3⋊Dic3C22×D311yescharacteristic
399C4×C3⋊D3—62no—
400#634—22no—
401#634—62no—
402#634—62no—
403#634—62no—
404#634—62no—
405#634—62no—
406#634—64no—
407#634—122no—
408#634—122no—
409#634—124no—
410C2×C3×Dic3—21no—
411C2×C3×Dic3—21no—
412C2×C3×Dic3—21no—
413C2×C3×Dic3—21no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—31no—
417C2×C3×Dic3—31no—
418C2×C3×Dic3—31no—
419C2×C3×Dic3—31no—
420C2×C3×Dic3—31no—
421C2×C3×Dic3—31no—
422C2×C3×Dic3—31no—
423C2×C3×Dic3—31no—
424C2×C3×Dic3—61no—
425C2×C3×Dic3—61no—
426C2×C3×Dic3—61no—
427C2×C3×Dic3—61no—
428C2×C3×Dic3—61no—
429C2×C3×Dic3—62no—
430C2×C3×Dic3—62no—
431C2×C3×Dic3—62no—
432C2×C3×Dic3—62no—
433C2×C3×Dic3C22×D311yescharacteristic
434C2×C3×Dic3C22×D311yescharacteristic
435C2×C3×Dic3C22×D311yescharacteristic
436C2×C3×Dic3C22×D311yescharacteristic
437C2×C3×Dic3C22×D311yescharacteristic
438C2×C3×Dic3C22×D311yescharacteristic
439C2×C3×Dic3C22×D311yescharacteristic
440C2×C3×Dic3C22×D311yescharacteristic
441C3×C4×D3—24no—
442C3×C4×D3—22no—
443C3×C4×D3—22no—
444C3×C4×D3—62no—
445C3×C4×D3—62no—
446C3×C4×D3—62no—
447C3×C4×D3—62no—
448C3×Dic6—62no—
449C3×Dic6—62no—
450C3×Dic6—64no—
451#627—62no—
452#627—62no—
453#627—62no—
454#627—62no—
455#627—64no—
456#627—64no—
457#624—62no—
458D3×Dic3—22no—
459D3×Dic3—22no—
460D3×Dic3—22no—
461D3×Dic3—22no—
462D3×Dic3—34no—
463D3×Dic3—34no—
464D3×Dic3—64no—
465D3×Dic3—62no—
466D3×Dic3—62no—
467D3×Dic3—62no—
468D3×Dic3—62no—
469D3×Dic3—62no—
470D3×Dic3—64no—
471D3×Dic3—62no—
472D3×Dic3—62no—
473D3×Dic3—62no—
474D3×Dic3—122no—
475D3×Dic3—122no—
476C2×C22⋊Q8—271noSylow
477C2×C33C22×D411yescharacteristic
478C2×C33C22×Q811yescharacteristic
479C2×C33C2×#4111yescharacteristic
480C3×C3⋊D3—22no—
481C32×D3—22no—
482C32×D3C22⋊Q814yescomplemented
483C24×C3—91no—
484C23×D3—31no—
485C23×D3—31no—
486C2×C3×Q8—91no—
487C22×C3×C4—31no—
488C22×C3×C4—31no—
489C22×C3×C4—61no—
490C22×C3×C4—91no—
491C22×C3×C4—91no—
492C22×C3×C4—91no—
493C22×C3×C4—91no—
494C22×Dic3—31no—
495C22×Dic3—31no—
496C22×Dic3—31no—
497C22×Dic3—31no—
498C22×Dic3—91no—
499C22×Dic3—91no—
500C22×Dic3—91no—
501C22×Dic3—91no—
502C22×Dic3—91no—
503C22×Dic3—91no—
504C22×Dic3—91no—
505C22×Dic3—91no—
506C22×Dic3—181no—
507C22×Dic3—181no—
508C22×Dic3—181no—
509C22×Dic3—184no—
510D3×Q8—184no—
511C2×C4×D3—31no—
512C2×C4×D3—31no—
513C2×C4×D3—31no—
514C2×C4×D3—31no—
515C2×C4×D3—91no—
516C2×C4×D3—91no—
517C2×C4×D3—91no—
518C2×C4×D3—91no—
519C2×C4×D3—91no—
520C2×C4×D3—91no—
521C2×C4×D3—91no—
522C2×C4×D3—181no—
523C2×C4×D3—184no—
524C2×C4×D3—184no—
525C2×C4×D3D3211yescharacteristic
526C2×Dic6—31no—
527C2×Dic6—31no—
528C2×Dic6—61no—
529C2×Dic6—91no—
530C2×Dic6—91no—
531C2×Dic6—91no—
532C2×Dic6—91no—
533C2×Dic6—91no—
534C2×Dic6—91no—
535C2×Dic6—91no—
536C2×Dic6—91no—
537C2×Dic6—91no—
538C2×Dic6—181no—
539C2×Dic6—181no—
540C2×Dic6—181no—
541C2×Dic6—181no—
542C2×Dic6—181no—
543C2×Dic6—184no—
544C2×Dic6—184no—
545C2×Dic6—188no—
546C2×Dic6—361no—
547C3×C4⋊C4—31no—
548C3×C4⋊C4—31no—
549C3×C4⋊C4—61no—
550C3×C4⋊C4—91no—
551C3×C4⋊C4—91no—
552C3×C4⋊C4—91no—
553C3×C4⋊C4—91no—
554C3×C4⋊C4—91no—
555C3×C22⋊C4—31no—
556C3×C22⋊C4—31no—
557C3×C22⋊C4—61no—
558C3×C22⋊C4—91no—
559C3×C22⋊C4—91no—
560C3×C22⋊C4—91no—
561C3×C22⋊C4—91no—
562#217—31no—
563#217—31no—
564#217—91no—
565#217—91no—
566#217—91no—
567#217—91no—
568#217—181no—
569(C2×D3)⋊C4—31no—
570(C2×D3)⋊C4—31no—
571(C2×D3)⋊C4—31no—
572(C2×D3)⋊C4—31no—
573(C2×D3)⋊C4—31no—
574(C2×D3)⋊C4—31no—
575(C2×D3)⋊C4—61no—
576(C2×D3)⋊C4—91no—
577(C2×D3)⋊C4—91no—
578(C2×D3)⋊C4—91no—
579(C2×D3)⋊C4—91no—
580(C2×D3)⋊C4—91no—
581(C2×D3)⋊C4—181no—
582(C2×D3)⋊C4D3211yescharacteristic
583C4⋊Dic3—31no—
584C4⋊Dic3—31no—
585C4⋊Dic3—91no—
586C4⋊Dic3—91no—
587C4⋊Dic3—91no—
588C4⋊Dic3—91no—
589C4⋊Dic3—91no—
590C4⋊Dic3—181no—
591Dic3⋊C4—31no—
592Dic3⋊C4—31no—
593Dic3⋊C4—31no—
594Dic3⋊C4—31no—
595Dic3⋊C4—31no—
596Dic3⋊C4—31no—
597Dic3⋊C4—31no—
598Dic3⋊C4—31no—
599Dic3⋊C4—61no—
600Dic3⋊C4—91no—
601Dic3⋊C4—91no—
602Dic3⋊C4—91no—
603Dic3⋊C4—91no—
604Dic3⋊C4—91no—
605Dic3⋊C4—91no—
606Dic3⋊C4—91no—
607Dic3⋊C4—91no—
608Dic3⋊C4—91no—
609Dic3⋊C4—91no—
610Dic3⋊C4—91no—
611Dic3⋊C4—91no—
612Dic3⋊C4—91no—
613Dic3⋊C4—181no—
614Dic3⋊C4—181no—
615Dic3⋊C4—181no—
616Dic3⋊C4D3211yescharacteristic, complemented
617C22×C32—21no—
618C22×C32—21no—
619C22×C32—21no—
620C22×C32—32no—
621C22×C32—32no—
622C22×C32—32no—
623C22×C32—32no—
624C22×C32—41no—
625C22×C32—61no—
626C22×C32—61no—
627C22×C32C23×D311yescharacteristic
628C22×C32C23×D311yescharacteristic
629C22×C32C23×D311yescharacteristic
630C2×C3⋊D3—21no—
631C2×C3⋊D3—21no—
632C2×C3⋊D3C2×Dic612yescomplemented
633C2×C3×D3—21no—
634C2×C3×D3—21no—
635C2×C3×D3—21no—
636C2×C3×D3—21no—
637C2×C3×D3—22no—
638C2×C3×D3—22no—
639C2×C3×D3—22no—
640C2×C3×D3—22no—
641C2×C3×D3—32no—
642C2×C3×D3—32no—
643C2×C3×D3—41no—
644C2×C3×D3—41no—
645C2×C3×D3—62no—
646C2×C3×D3—68no—
647C2×C3×D3—61no—
648C2×C3×D3—61no—
649C2×C3×D3—61no—
650C2×C3×D3—61no—
651C2×C3×D3—68no—
652C2×C3×D3—121no—
653C2×C3×D3—121no—
654C2×C3×D3C2×Dic612yes—
655C2×C3×D3C2×Dic612yescomplemented
656C2×C3×D3#23512yes—
657C2×C3×D3D3×D412yes—
658C2×C3×D3D3×D412yes—
659C2×C3×D3#23712yes—
660C2×C3×D3D3×Q812yes—
661C2×C3×D3D3×Q812yescomplemented
662D32—28no—
663C32×C4—21no—
664C32×C4—22no—
665C32×C4—21no—
666C32×C4—21no—
667C32×C4—41no—
668C32×C4—41no—
669C32×C4—42no—
670C32×C4—61no—
671C32×C4—61no—
672C32×C4—61no—
673C32×C4—61no—
674C3⋊Dic3—21no—
675C3⋊Dic3—21no—
676C3⋊Dic3—21no—
677C3⋊Dic3—21no—
678C3⋊Dic3—32no—
679C3⋊Dic3—32no—
680C3⋊Dic3—32no—
681C3⋊Dic3—62no—
682C3⋊Dic3—62no—
683C3⋊Dic3—62no—
684C3⋊Dic3—61no—
685C3⋊Dic3—62no—
686C3⋊Dic3—61no—
687C3⋊Dic3—61no—
688C3⋊Dic3—122no—
689C3⋊Dic3—121no—
690C3⋊Dic3—121no—
691C3⋊Dic3—122no—
692C3⋊Dic3D3×D412yes—
693C3×Dic3—22no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—21no—
701C3×Dic3—21no—
702C3×Dic3—32no—
703C3×Dic3—32no—
704C3×Dic3—41no—
705C3×Dic3—41no—
706C3×Dic3—41no—
707C3×Dic3—62no—
708C3×Dic3—62no—
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—
720C22×Q8—271no—
721C23×C4—271no—
722C22⋊Q8—91no—
723C22⋊Q8—271no—
724C22⋊Q8—271no—
725C22⋊Q8—271no—
726C22⋊Q8—271no—
727C22⋊Q8—271no—
728C22⋊Q8—271no—
729C22⋊Q8—271no—
730C2×C4⋊C4—91no—
731C2×C4⋊C4—271no—
732C2×C4⋊C4—271no—
733C2×C22⋊C4—91no—
734C2×C22⋊C4—271no—
735C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
736C23×C3—31no—
737C23×C3—31no—
738C23×C3—31no—
739C23×C3—31no—
740C23×C3—61no—
741C23×C3—61no—
742C23×C3—94no—
743C23×C3—91no—
744C23×C3—182no—
745C23×C3—182no—
746C22×D3—31no—
747C22×D3—31no—
748C22×D3—34no—
749C22×D3—34no—
750C22×D3—61no—
751C22×D3—62no—
752C22×D3—62no—
753C22×D3—62no—
754C22×D3—62no—
755C22×D3C2×D3211yescharacteristic
756C22×D3C2×D3211yescharacteristic
757C3×Q8—182no—
758C2×C3×C4—21no—
759C2×C3×C4—21no—
760C2×C3×C4—21no—
761C2×C3×C4—31no—
762C2×C3×C4—31no—
763C2×C3×C4—31no—
764C2×C3×C4—31no—
765C2×C3×C4—31no—
766C2×C3×C4—31no—
767C2×C3×C4—31no—
768C2×C3×C4—31no—
769C2×C3×C4—41no—
770C2×C3×C4—61no—
771C2×C3×C4—61no—
772C2×C3×C4—61no—
773C2×C3×C4—61no—
774C2×C3×C4—62no—
775C2×C3×C4—62no—
776C2×C3×C4—64no—
777C2×C3×C4—91no—
778C2×C3×C4—91no—
779C2×C3×C4—91no—
780C2×C3×C4—91no—
781C2×C3×C4—91no—
782C2×C3×C4—182no—
783C2×C3×C4—182no—
784C2×C3×C4—182no—
785C2×C3×C4—182no—
786C2×C3×C4C2×D3211yescharacteristic
787C2×C3×C4C2×D3211yescharacteristic
788C2×C3×C4C2×D3211yescharacteristic
789C2×Dic3—31no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—31no—
794C2×Dic3—31no—
795C2×Dic3—31no—
796C2×Dic3—31no—
797C2×Dic3—31no—
798C2×Dic3—31no—
799C2×Dic3—61no—
800C2×Dic3—61no—
801C2×Dic3—61no—
802C2×Dic3—61no—
803C2×Dic3—61no—
804C2×Dic3—62no—
805C2×Dic3—62no—
806C2×Dic3—62no—
807C2×Dic3—62no—
808C2×Dic3—94no—
809C2×Dic3—94no—
810C2×Dic3—91no—
811C2×Dic3—91no—
812C2×Dic3—91no—
813C2×Dic3—91no—
814C2×Dic3—91no—
815C2×Dic3—91no—
816C2×Dic3—184no—
817C2×Dic3—181no—
818C2×Dic3—181no—
819C2×Dic3—181no—
820C2×Dic3—181no—
821C2×Dic3—181no—
822C2×Dic3—181no—
823C2×Dic3—182no—
824C2×Dic3—182no—
825C2×Dic3—182no—
826C2×Dic3—182no—
827C2×Dic3—182no—
828C2×Dic3—182no—
829C2×Dic3—184no—
830C2×Dic3—361no—
831C2×Dic3—361no—
832C2×Dic3—362no—
833C2×Dic3C2×D3211yescharacteristic
834C2×Dic3C2×D3211yescharacteristic
835C2×Dic3C2×D3211yescharacteristic
836C2×Dic3C2×D3211yescharacteristic
837C4×D3—22no—
838C4×D3—62no—
839C4×D3—62no—
840C4×D3—62no—
841C4×D3—62no—
842C4×D3—94no—
843C4×D3—182no—
844C4×D3—182no—
845C4×D3—182no—
846C4×D3—182no—
847C4×D3—182no—
848C4×D3—182no—
849C4×D3—362no—
850Dic6—62no—
851Dic6—62no—
852Dic6—64no—
853Dic6—182no—
854Dic6—182no—
855Dic6—182no—
856Dic6—182no—
857Dic6—182no—
858Dic6—182no—
859Dic6—184no—
860Dic6—184no—
861Dic6—182no—
862Dic6—182no—
863Dic6—182no—
864Dic6—184no—
865Dic6—362no—
866Dic6—362no—
867Dic6—364no—
868C2×C32—21no—
869C2×C32—21no—
870C2×C32—21no—
871C2×C32—21no—
872C2×C32—21no—
873C2×C32—21no—
874C2×C32—21no—
875C2×C32—21no—
876C2×C32—21no—
877C2×C32—34no—
878C2×C32—41no—
879C2×C32—41no—
880C2×C32—41no—
881C2×C32—62no—
882C2×C32C22×Dic611yescharacteristic
883C2×C32C2×#23511yescharacteristic
884C2×C32C2×D3×D411yescharacteristic
885C2×C32C2×D3×D411yescharacteristic
886C2×C32C2×D3×D411yescharacteristic
887C2×C32C2×#23711yescharacteristic
888C2×C32C2×D3×Q811yescharacteristic
889C2×C32C2×D3×Q811yescharacteristic
890C2×C32D3×#4111yescharacteristic
891C3⋊D3—22no—
892C3×D3—22no—
893C3×D3—22no—
894C3×D3—24no—
895C3×D3—42no—
896C3×D3—62no—
897C3×D3—62no—
898C3×D3—122no—
899C3×D3#87814yescomplemented
900C3×D3#89614yescomplemented
901C24—91no—
902C2×Q8—91no—
903C2×Q8—271no—
904C2×Q8—271no—
905C2×Q8—271no—
906C2×Q8—544no—
907C22×C4—31no—
908C22×C4—91no—
909C22×C4—91no—
910C22×C4—91no—
911C22×C4—91no—
912C22×C4—271no—
913C22×C4—271no—
914C22×C4—271no—
915C22×C4—271no—
916C22×C4—271no—
917C22×C4—544no—
918C4⋊C4—31no—
919C4⋊C4—91no—
920C4⋊C4—91no—
921C4⋊C4—91no—
922C4⋊C4—91no—
923C4⋊C4—91no—
924C4⋊C4—271no—
925C4⋊C4—271no—
926C4⋊C4—271no—
927C4⋊C4—271no—
928C4⋊C4—271no—
929C4⋊C4—271no—
930C22⋊C4—31no—
931C22⋊C4—91no—
932C22⋊C4—91no—
933C22⋊C4—91no—
934C22⋊C4—91no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22×C3—21no—
939C22×C3—21no—
940C22×C3—21no—
941C22×C3—32no—
942C22×C3—32no—
943C22×C3—32no—
944C22×C3—32no—
945C22×C3—32no—
946C22×C3—32no—
947C22×C3—32no—
948C22×C3—32no—
949C22×C3—41no—
950C22×C3—62no—
951C22×C3—62no—
952C22×C3—62no—
953C22×C3—62no—
954C22×C3—61no—
955C22×C3—61no—
956C22×C3—61no—
957C22×C3—61no—
958C22×C3—92no—
959C22×C3—121no—
960C22×C3—121no—
961C22×C3—188no—
962C22×C3—181no—
963C22×C3—181no—
964C22×C3C22×D3211yescharacteristic
965C22×C3C22×D3211yescharacteristic
966C22×C3C22×D3211yescharacteristic
967C2×D3—21no—
968C2×D3—21no—
969C2×D3—32no—
970C2×D3—32no—
971C2×D3—62no—
972C2×D3—68no—
973C2×D3—61no—
974C2×D3—61no—
975C2×D3—61no—
976C2×D3—61no—
977C2×D3—68no—
978C2×D3—121no—
979C2×D3—121no—
980C2×D3D3×Dic612yes—
981C2×D3D3×Dic612yescomplemented
982C2×D3#379512yes—
983C2×D3#381112yes—
984C3×C4—22no—
985C3×C4—21no—
986C3×C4—21no—
987C3×C4—21no—
988C3×C4—41no—
989C3×C4—41no—
990C3×C4—42no—
991C3×C4—62no—
992C3×C4—61no—
993C3×C4—61no—
994C3×C4—61no—
995C3×C4—61no—
996C3×C4—61no—
997C3×C4—61no—
998C3×C4—61no—
999C3×C4—61no—
1000C3×C4—92no—
1001C3×C4—121no—
1002C3×C4—121no—
1003C3×C4—121no—
1004C3×C4—181no—
1005C3×C4—181no—
1006C3×C4—181no—
1007C3×C4—181no—
1008Dic3—21no—
1009Dic3—21no—
1010Dic3—21no—
1011Dic3—21no—
1012Dic3—32no—
1013Dic3—32no—
1014Dic3—62no—
1015Dic3—62no—
1016Dic3—61no—
1017Dic3—61no—
1018Dic3—61no—
1019Dic3—61no—
1020Dic3—61no—
1021Dic3—61no—
1022Dic3—61no—
1023Dic3—61no—
1024Dic3—92no—
1025Dic3—92no—
1026Dic3—92no—
1027Dic3—121no—
1028Dic3—121no—
1029Dic3—121no—
1030Dic3—182no—
1031Dic3—182no—
1032Dic3—182no—
1033Dic3—182no—
1034Dic3—181no—
1035Dic3—181no—
1036Dic3—181no—
1037Dic3—362no—
1038Dic3—361no—
1039Dic3—361no—
1040Dic3—362no—
1041C32—21no—
1042C32—21no—
1043C32—21no—
1044C32—41no—
1045C32C2×#87811yescharacteristic, complemented
1046C32C2×#89611yescharacteristic, complemented
1047C32D3×C22⋊Q811yescharacteristic, complemented
1048C23—31no—
1049C23—31no—
1050C23—94no—
1051C23—91no—
1052C23—182no—
1053C23—182no—
1054Q8—182no—
1055Q8—542no—
1056Q8—542no—
1057Q8—542no—
1058C2×C4—31no—
1059C2×C4—31no—
1060C2×C4—31no—
1061C2×C4—31no—
1062C2×C4—62no—
1063C2×C4—91no—
1064C2×C4—91no—
1065C2×C4—91no—
1066C2×C4—91no—
1067C2×C4—91no—
1068C2×C4—182no—
1069C2×C4—182no—
1070C2×C4—182no—
1071C2×C4—182no—
1072C2×C4—274no—
1073C2×C4—271no—
1074C2×C4—271no—
1075C2×C4—542no—
1076C2×C4—542no—
1077C2×C4—542no—
1078C2×C4—542no—
1079C2×C4D3311yescharacteristic
1080C2×C3—21no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—21no—
1085C2×C3—21no—
1086C2×C3—21no—
1087C2×C3—21no—
1088C2×C3—21no—
1089C2×C3—34no—
1090C2×C3—34no—
1091C2×C3—41no—
1092C2×C3—41no—
1093C2×C3—41no—
1094C2×C3—64no—
1095C2×C3—62no—
1096C2×C3—62no—
1097C2×C3—122no—
1098C2×C3—182no—
1099C2×C3C2×D3×Dic611yescharacteristic
1100C2×C3C2×D3×Dic611yescharacteristic
1101C2×C3C2×#379511yescharacteristic
1102C2×C3D3×#23511yescharacteristic
1103C2×C3D32×D411yescharacteristic
1104C2×C3D32×D411yescharacteristic
1105C2×C3D3×#23711yescharacteristic
1106C2×C3D32×Q811yescharacteristic
1107C2×C3C2×#381111yescharacteristic
1108D3—22no—
1109D3—62no—
1110D3—62no—
1111D3—122no—
1112D3#6389614yesdirect product factor
1113C22—32no—
1114C22—32no—
1115C22—32no—
1116C22—32no—
1117C22—61no—
1118C22—61no—
1119C22—92no—
1120C22—188no—
1121C22—181no—
1122C22—181no—
1123C22C2×D3311yescharacteristic
1124C4—21no—
1125C4—61no—
1126C4—61no—
1127C4—61no—
1128C4—61no—
1129C4—92no—
1130C4—181no—
1131C4—181no—
1132C4—181no—
1133C4—181no—
1134C4—272no—
1135C4—541no—
1136C3—21no—
1137C3—21no—
1138C3—21no—
1139C3—41no—
1140C3D3×#87811yescharacteristic, complemented
1141C3D3×#89611yescharacteristic, complemented
1142C3C2×#6389611yescharacteristic, complemented
1143C2—34no—
1144C2—62no—
1145C2—182no—
1146C2D32×Dic611yescharacteristic
1147C2D3×#379511yescharacteristic
1148C2D3×#381111yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×C3×D32C22
hypercenterC2×C4D33
hypocenterC33C2×C22⋊Q8
LCSG ▷ C22×C33 ▷ C33
UCSC1 ◁ C22 ◁ C2×C4

Complements

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

NH ≅ G/Ntype
1. C2×D3×#634C2semidirect
3. #11723688C2semidirect
4. #11723497C2semidirect
5. #11723496C2semidirect
7. C3×#63896C2semidirect
8. C3×D3×Dic3⋊C4C2semidirect
9. #11722984C2semidirect
10. #11722983C2semidirect
11. #11722980C2semidirect
12. #11722975C2semidirect
13. D3×#3724C2semidirect
14. D3×Dic3⋊Dic3C2semidirect
20. C2×#6308C22semidirect
21. C2×C3×#634C22semidirect
24. C2×#6293C22semidirect
25. C2×#6293C22semidirect
37. C3×#3750C22semidirect
39. C32×Dic3⋊C4C22semidirect
40. #88815C22semidirect
41. #88815C22semidirect
43. #88807C22semidirect
44. #88806C22semidirect
45. #88806C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
49. C3×#3724C22semidirect
50. C3×#3724C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
92. #63896D3direct (N × H)
101. D3×Dic3⋊C4D3semidirect
109. C2×C3×D32Q8semidirect
157. C2×#634C2×D3semidirect
212. #3750C2×D3semidirect
237. C3×Dic3⋊C4C2×D3semidirect
238. C3×Dic3⋊C4C2×D3semidirect
247. #3724C2×D3semidirect
248. #3724C2×D3semidirect
259. Dic3⋊Dic3C2×D3semidirect
260. Dic3⋊Dic3C2×D3semidirect
276. C2×C3×C3⋊D3C2×Q8semidirect
281. C2×C32×D3C2×Q8semidirect
364. C2×D32Dic6semidirect
482. C32×D3C22⋊Q8semidirect
616. Dic3⋊C4D32semidirect
632. C2×C3⋊D3C2×Dic6semidirect
655. C2×C3×D3C2×Dic6semidirect
661. C2×C3×D3D3×Q8semidirect
735. C33C2×C22⋊Q8semidirect
899. C3×D3#878semidirect
900. C3×D3#896semidirect
981. C2×D3D3×Dic6semidirect
1045. C32C2×#878semidirect
1046. C32C2×#896semidirect
1047. C32D3×C22⋊Q8semidirect
1112. D3#63896direct (N × H)
1140. C3D3×#878semidirect
1141. C3D3×#896semidirect
1142. C3C2×#63896semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6342
C2×D32×Dic32
#117236882
#117234972
#117234962
C3×D3×(C2×D3)⋊C42
C3×#638962
C3×D3×Dic3⋊C42
#117229842
#117229832
#117229802
#117229752
D3×#37242
D3×Dic3⋊Dic32
D3×(C2×D3)⋊Dic32
C2×#638963
D3×#8963
D3×#8783