Finite Group Databasebeta

← D3×#63893 #13170734

Subgroups — D3×#63893 #13170734

Order 1728.

1554 conjugacy classes of subgroups.

The subgroup lattice has 1138 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#627C211yesmaximal, characteristic, complemented
2C2×D32×Dic3C211yesmaximal, characteristic
3#11723692C211yesmaximal, characteristic, complemented
4#11723491C211yesmaximal, characteristic, complemented
5#11723483C211yesmaximal, characteristic, complemented
6D3×C4⋊(C3⋊Dic3)C211yesmaximal, characteristic, complemented
7C3×D3×(C2×D3)⋊C4C211yesmaximal, characteristic
8C3×#63893C211yesmaximal, characteristic, complemented
9C3×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
10#11722984C211yesmaximal, characteristic, complemented
11#11722981C211yesmaximal, characteristic, complemented
12#11722974C211yesmaximal, characteristic, complemented
13#11722971C211yesmaximal, characteristic, complemented
14D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
15D3×(C2×D3)⋊Dic3C211yesmaximal, characteristic
16C2×#63893—31nomaximal
17D3×#897—31nomaximal
18D3×#878—31nomaximal
19C22×C3×D32C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6296C2211yescharacteristic, complemented
22C2×#6294C2211yescharacteristic
23C2×#6293C2211yescharacteristic, complemented
24C2×#6293C2211yescharacteristic, complemented
25C2×Dic3×C3⋊D3C2211yescharacteristic
26C2×D3×C3⋊Dic3C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C2×D3×C3⋊Dic3C2211yescharacteristic
29C2×C3×#627C2211yescharacteristic, complemented
30C2×C3×D3×Dic3C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34D3×#627—24no—
35D32×Dic3—24no—
36C4⋊(C3⋊(C3⋊Dic3))C2211yescharacteristic, complemented
37C3×#3752C2211yescharacteristic
38C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C32×(C2×D3)⋊C4C2211yescharacteristic
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88814C2211yescharacteristic
44#88807C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
47Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
48#88803C2211yescharacteristic
49(C2×D3)⋊(C3⋊Dic3)C2211yescharacteristic
50C3×#3724C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×#3722C2211yescharacteristic
54C3×(C2×D3)⋊Dic3C2211yescharacteristic
55C3×(C2×D3)⋊Dic3C2211yescharacteristic
56C22×#627—31no—
57C22×D3×Dic3—31no—
58C22×D3×Dic3—31no—
59C2×C4×D32—31no—
60C2×D3×Dic6—31no—
61C2×D3×Dic6—31no—
62C2×C4⋊(C3⋊Dic3)—31no—
63#64106—31no—
64#64087—31no—
65C2×C3×(C2×D3)⋊C4—31no—
66C2×C3×Dic3⋊C4—31no—
67C3×#897—31no—
68C3×D3×C4⋊C4—31no—
69C3×D3×C22⋊C4—31no—
70C3×#878—31no—
71#63982—31no—
72D3×#217—31no—
73C2×Dic3⋊Dic3—31no—
74#63964—31no—
75C2×(C2×D3)⋊Dic3—31no—
76D3×(C2×D3)⋊C4—31no—
77D3×(C2×D3)⋊C4D311yescharacteristic
78#63899—31no—
79#63896—31no—
80#63895—31no—
81#63895—31no—
82#63893—31no—
83#63893—31no—
84#63893—31no—
85#63893—31no—
86#63893—31no—
87#63893—31no—
88#63893—31no—
89#63893—31no—
90#63893—31no—
91#63893—31no—
92#63893—61no—
93#63893—61no—
94#63893D311yescharacteristic, direct product factor
95D3×C4⋊Dic3—31no—
96D3×C4⋊Dic3—31no—
97D3×C4⋊Dic3—31no—
98D3×C4⋊Dic3—61no—
99#63887—31no—
100D3×Dic3⋊C4—31no—
101D3×Dic3⋊C4D311yescharacteristic, complemented
102#63871—31no—
103#63857—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
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C3×C3⋊Dic3C2311yescharacteristic
118C2×C32×Dic3C2311yescharacteristic
119C2×C32×Dic3C2311yescharacteristic
120C2×C32×Dic3C2311yescharacteristic
121C2×C32×Dic3C2311yescharacteristic
122C32×C4×D3—22no—
123#6296—22no—
124#6294—22no—
125#6293—22no—
126#6293—22no—
127Dic3×C3⋊D3—22no—
128D3×C3⋊Dic3—22no—
129D3×C3⋊Dic3—22no—
130D3×C3⋊Dic3—22no—
131C3×#627—22no—
132C3×D3×Dic3—22no—
133C3×D3×Dic3—22no—
134C3×D3×Dic3—22no—
135C3×D3×Dic3D414yes—
136D3×C22⋊Q8—91no—
137C2×#897—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—
149C22×C3×Dic3—31no—
150C22×C3×Dic3—31no—
151C22×C3×Dic3—31no—
152C22×C3×Dic3—31no—
153C2×C3×C4×D3—21no—
154C2×C3×C4×D3—31no—
155C2×C3×C4×D3—31no—
156C2×C3×C4×D3—31no—
157C2×C3×C4×D3—31no—
158C2×C3×C4×D3C2×D311yescharacteristic
159C2×C3×C4×D3C2×D311yescharacteristic
160C2×C3×Dic6—31no—
161C2×C3×Dic6—31no—
162C2×#627—31no—
163C2×#627—31no—
164C2×#627—31no—
165C2×#627—31no—
166C2×#627—31no—
167C2×#627—31no—
168C2×#627—31no—
169C2×#627—64no—
170C2×#627—61no—
171C2×#627—61no—
172C2×#627C2×D311yescharacteristic, complemented
173C2×#624—31no—
174C2×D3×Dic3—31no—
175C2×D3×Dic3—31no—
176C2×D3×Dic3—31no—
177C2×D3×Dic3—31no—
178C2×D3×Dic3—31no—
179C2×D3×Dic3—31no—
180C2×D3×Dic3—31no—
181C2×D3×Dic3—31no—
182C2×D3×Dic3—31no—
183C2×D3×Dic3—31no—
184C2×D3×Dic3—64no—
185C2×D3×Dic3—64no—
186C2×D3×Dic3—61no—
187C2×D3×Dic3—61no—
188C2×D3×Dic3—61no—
189C2×D3×Dic3—61no—
190C2×D3×Dic3C2×D311yescharacteristic
191C2×D3×Dic3C2×D311yescharacteristic
192C2×D3×Dic3C2×D311yescharacteristic
193C2×D3×Dic3C2×D311yescharacteristic
194C4×D32—64no—
195D3×Dic6—64no—
196D3×Dic6—64no—
197C32×C4⋊C4—31no—
198C32×C22⋊C4—31no—
199#3757—31no—
200#3752—31no—
201#3752C2×D311yescharacteristic
202C4⋊(C3⋊Dic3)—31no—
203C4⋊(C3⋊Dic3)—31no—
204C4⋊(C3⋊Dic3)—31no—
205C4⋊(C3⋊Dic3)—31no—
206C4⋊(C3⋊Dic3)—31no—
207C4⋊(C3⋊Dic3)—31no—
208C4⋊(C3⋊Dic3)—61no—
209C4⋊(C3⋊Dic3)—61no—
210C4⋊(C3⋊Dic3)—61no—
211C4⋊(C3⋊Dic3)—121no—
212C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
213#3750—31no—
214#3750C2×D311yescharacteristic, complemented
215C3×#217—31no—
216C3×#217—31no—
217C3×(C2×D3)⋊C4—21no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—31no—
220C3×(C2×D3)⋊C4—31no—
221C3×(C2×D3)⋊C4—31no—
222C3×(C2×D3)⋊C4—31no—
223C3×(C2×D3)⋊C4—31no—
224C3×(C2×D3)⋊C4—61no—
225C3×(C2×D3)⋊C4C2×D311yescharacteristic
226C3×(C2×D3)⋊C4C2×D311yescharacteristic
227C3×C4⋊Dic3—31no—
228C3×C4⋊Dic3—31no—
229C3×C4⋊Dic3—31no—
230C3×C4⋊Dic3—31no—
231C3×C4⋊Dic3—61no—
232C3×Dic3⋊C4—21no—
233C3×Dic3⋊C4—31no—
234C3×Dic3⋊C4—31no—
235C3×Dic3⋊C4—31no—
236C3×Dic3⋊C4—31no—
237C3×Dic3⋊C4—31no—
238C3×Dic3⋊C4—31no—
239C3×Dic3⋊C4—61no—
240C3×Dic3⋊C4C2×D311yescharacteristic, complemented
241C3×Dic3⋊C4C2×D311yescharacteristic, complemented
242#3724—31no—
243#3724C2×D311yescharacteristic, complemented
244Dic3⋊Dic3—31no—
245Dic3⋊Dic3—31no—
246Dic3⋊Dic3—31no—
247Dic3⋊Dic3—31no—
248Dic3⋊Dic3—31no—
249Dic3⋊Dic3—31no—
250Dic3⋊Dic3—31no—
251Dic3⋊Dic3—31no—
252Dic3⋊Dic3—31no—
253Dic3⋊Dic3—31no—
254Dic3⋊Dic3—61no—
255Dic3⋊Dic3—61no—
256Dic3⋊Dic3—61no—
257Dic3⋊Dic3—61no—
258Dic3⋊Dic3C2×D311yescharacteristic, complemented
259Dic3⋊Dic3C2×D311yescharacteristic, complemented
260#3722—31no—
261#3722C2×D311yescharacteristic
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—61no—
269(C2×D3)⋊Dic3—61no—
270(C2×D3)⋊Dic3C2×D311yescharacteristic
271(C2×D3)⋊Dic3C2×D311yescharacteristic
272C22×C33C2411yescharacteristic
273C2×C3×C3⋊D3—21no—
274C2×C3×C3⋊D3—21no—
275C2×C3×C3⋊D3C2×Q812yescomplemented
276C2×C32×D3—21no—
277C2×C32×D3—21no—
278C2×C32×D3C2×D412yes—
279C2×C32×D3C2×Q812yes—
280C2×C32×D3C2×Q812yescomplemented
281C2×C32×D3#4112yes—
282C3×D32—28no—
283C33×C4—21no—
284C3⋊(C3⋊Dic3)—21no—
285C3⋊(C3⋊Dic3)—21no—
286C3×C3⋊Dic3—21no—
287C3×C3⋊Dic3—21no—
288C3×C3⋊Dic3—21no—
289C3×C3⋊Dic3—21no—
290C3×C3⋊Dic3C2×D412yes—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C32×Dic3C2×D412yes—
295C23×Dic3—91no—
296C2×D3×Q8—91no—
297C22×C4×D3—91no—
298C22×C4×D3—91no—
299C22×Dic6—91no—
300C22×Dic6—91no—
301C3×C22⋊Q8—91no—
302C2×C3×C4⋊C4—91no—
303C2×C3×C22⋊C4—91no—
304C2×#217—91no—
305#946—91no—
306C2×(C2×D3)⋊C4—31no—
307C2×(C2×D3)⋊C4—91no—
308C2×C4⋊Dic3—91no—
309C2×C4⋊Dic3—91no—
310C2×C4⋊Dic3—91no—
311C2×C4⋊Dic3—181no—
312#924—91no—
313C2×Dic3⋊C4—31no—
314C2×Dic3⋊C4—91no—
315#897—31no—
316#897—91no—
317#897—91no—
318#897—91no—
319#897—91no—
320#897—91no—
321#897—91no—
322#897—91no—
323#897—91no—
324#897—181no—
325#896—91no—
326#896—91no—
327D3×C4⋊C4—31no—
328D3×C4⋊C4—91no—
329D3×C4⋊C4—91no—
330D3×C22⋊C4—31no—
331D3×C22⋊C4—91no—
332#878—31no—
333#878—91no—
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—181no—
343C23×C32—31no—
344C23×C32—31no—
345C22×C3⋊D3C22×D311yescharacteristic
346C22×C3×D3—21no—
347C22×C3×D3—21no—
348C22×C3×D3—31no—
349C22×C3×D3—31no—
350C22×C3×D3—34no—
351C22×C3×D3—34no—
352C22×C3×D3—61no—
353C22×C3×D3—62no—
354C22×C3×D3—62no—
355C22×C3×D3—62no—
356C22×C3×D3—62no—
357C22×C3×D3C22×D311yescharacteristic
358C22×C3×D3C22×D311yescharacteristic
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C2×D32—22no—
362C2×D32—22no—
363C2×D32Dic614yescomplemented
364C2×C32×C4—21no—
365C2×C32×C4—21no—
366C2×C32×C4—21no—
367C2×C32×C4—31no—
368C2×C32×C4—31no—
369C2×C32×C4—31no—
370C2×C32×C4—31no—
371C2×C32×C4—41no—
372C2×C32×C4—62no—
373C2×C32×C4C22×D311yescharacteristic
374C2×C32×C4C22×D311yescharacteristic
375C2×C32×C4C22×D311yescharacteristic
376C2×C3⋊Dic3—31no—
377C2×C3⋊Dic3—31no—
378C2×C3⋊Dic3—31no—
379C2×C3⋊Dic3—31no—
380C2×C3⋊Dic3—31no—
381C2×C3⋊Dic3—31no—
382C2×C3⋊Dic3—61no—
383C2×C3⋊Dic3—61no—
384C2×C3⋊Dic3—61no—
385C2×C3⋊Dic3—61no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—62no—
389C2×C3⋊Dic3—62no—
390C2×C3⋊Dic3—62no—
391C2×C3⋊Dic3—121no—
392C2×C3⋊Dic3—121no—
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C2×C3⋊Dic3C22×D311yescharacteristic
397C2×C3⋊Dic3C22×D311yescharacteristic
398C4×C3⋊D3—62no—
399#634—62no—
400#634—62no—
401C2×C3×Dic3—21no—
402C2×C3×Dic3—21no—
403C2×C3×Dic3—21no—
404C2×C3×Dic3—21no—
405C2×C3×Dic3—31no—
406C2×C3×Dic3—31no—
407C2×C3×Dic3—34no—
408C2×C3×Dic3—31no—
409C2×C3×Dic3—31no—
410C2×C3×Dic3—31no—
411C2×C3×Dic3—31no—
412C2×C3×Dic3—31no—
413C2×C3×Dic3—31no—
414C2×C3×Dic3—31no—
415C2×C3×Dic3—31no—
416C2×C3×Dic3—61no—
417C2×C3×Dic3—61no—
418C2×C3×Dic3—61no—
419C2×C3×Dic3—61no—
420C2×C3×Dic3—61no—
421C2×C3×Dic3—62no—
422C2×C3×Dic3—62no—
423C2×C3×Dic3—62no—
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
432C3×C4×D3—24no—
433C3×C4×D3—22no—
434C3×C4×D3—22no—
435C3×C4×D3—34no—
436C3×C4×D3—62no—
437C3×C4×D3—62no—
438C3×C4×D3—62no—
439C3×Dic6—62no—
440C3×Dic6—62no—
441#627—22no—
442#627—62no—
443#627—62no—
444#627—62no—
445#627—62no—
446#627—62no—
447#627—62no—
448#627—62no—
449#627—122no—
450#627—122no—
451#624—62no—
452D3×Dic3—22no—
453D3×Dic3—22no—
454D3×Dic3—22no—
455D3×Dic3—62no—
456D3×Dic3—62no—
457D3×Dic3—62no—
458D3×Dic3—62no—
459D3×Dic3—62no—
460D3×Dic3—62no—
461D3×Dic3—62no—
462D3×Dic3—62no—
463D3×Dic3—62no—
464D3×Dic3—62no—
465D3×Dic3—122no—
466D3×Dic3—122no—
467D3×Dic3—122no—
468D3×Dic3—122no—
469D3×Dic3D1214yes—
470C2×C22⋊Q8—271noSylow
471C2×C33C22×D411yescharacteristic
472C2×C33C22×Q811yescharacteristic
473C2×C33C2×#4111yescharacteristic
474C3×C3⋊D3—22no—
475C32×D3—22no—
476C32×D3C22⋊Q814yescomplemented
477C24×C3—91no—
478C23×D3—31no—
479C23×D3—31no—
480C2×C3×Q8—91no—
481C22×C3×C4—31no—
482C22×C3×C4—31no—
483C22×C3×C4—61no—
484C22×C3×C4—91no—
485C22×C3×C4—91no—
486C22×C3×C4—91no—
487C22×C3×C4—91no—
488C22×Dic3—31no—
489C22×Dic3—31no—
490C22×Dic3—31no—
491C22×Dic3—31no—
492C22×Dic3—91no—
493C22×Dic3—91no—
494C22×Dic3—91no—
495C22×Dic3—91no—
496C22×Dic3—91no—
497C22×Dic3—91no—
498C22×Dic3—91no—
499C22×Dic3—91no—
500C22×Dic3—181no—
501C22×Dic3—181no—
502C22×Dic3—181no—
503C22×Dic3—184no—
504D3×Q8—184no—
505C2×C4×D3—31no—
506C2×C4×D3—31no—
507C2×C4×D3—31no—
508C2×C4×D3—31no—
509C2×C4×D3—91no—
510C2×C4×D3—91no—
511C2×C4×D3—91no—
512C2×C4×D3—91no—
513C2×C4×D3—91no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—181no—
517C2×C4×D3—184no—
518C2×C4×D3—184no—
519C2×C4×D3D3211yescharacteristic
520C2×Dic6—31no—
521C2×Dic6—31no—
522C2×Dic6—91no—
523C2×Dic6—91no—
524C2×Dic6—91no—
525C2×Dic6—91no—
526C2×Dic6—91no—
527C2×Dic6—91no—
528C2×Dic6—91no—
529C2×Dic6—91no—
530C2×Dic6—91no—
531C2×Dic6—181no—
532C2×Dic6—181no—
533C2×Dic6—184no—
534C2×Dic6—184no—
535C3×C4⋊C4—31no—
536C3×C4⋊C4—31no—
537C3×C4⋊C4—61no—
538C3×C4⋊C4—91no—
539C3×C4⋊C4—91no—
540C3×C4⋊C4—91no—
541C3×C4⋊C4—91no—
542C3×C4⋊C4—91no—
543C3×C22⋊C4—31no—
544C3×C22⋊C4—31no—
545C3×C22⋊C4—61no—
546C3×C22⋊C4—91no—
547C3×C22⋊C4—91no—
548C3×C22⋊C4—91no—
549C3×C22⋊C4—91no—
550#217—31no—
551#217—31no—
552#217—91no—
553#217—91no—
554#217—91no—
555#217—91no—
556#217—181no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—31no—
559(C2×D3)⋊C4—31no—
560(C2×D3)⋊C4—31no—
561(C2×D3)⋊C4—31no—
562(C2×D3)⋊C4—31no—
563(C2×D3)⋊C4—61no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—181no—
570(C2×D3)⋊C4D3211yescharacteristic
571C4⋊Dic3—31no—
572C4⋊Dic3—31no—
573C4⋊Dic3—31no—
574C4⋊Dic3—31no—
575C4⋊Dic3—61no—
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—
593C4⋊Dic3—361no—
594Dic3⋊C4—31no—
595Dic3⋊C4—31no—
596Dic3⋊C4—31no—
597Dic3⋊C4—31no—
598Dic3⋊C4—31no—
599Dic3⋊C4—31no—
600Dic3⋊C4—61no—
601Dic3⋊C4—91no—
602Dic3⋊C4—91no—
603Dic3⋊C4—91no—
604Dic3⋊C4—91no—
605Dic3⋊C4—91no—
606Dic3⋊C4—91no—
607Dic3⋊C4—91no—
608Dic3⋊C4—181no—
609Dic3⋊C4D3211yescharacteristic, complemented
610C22×C32—21no—
611C22×C32—21no—
612C22×C32—21no—
613C22×C32—32no—
614C22×C32—32no—
615C22×C32—32no—
616C22×C32—32no—
617C22×C32—41no—
618C22×C32—61no—
619C22×C32—61no—
620C22×C32C23×D311yescharacteristic
621C22×C32C23×D311yescharacteristic
622C22×C32C23×D311yescharacteristic
623C2×C3⋊D3—21no—
624C2×C3⋊D3—21no—
625C2×C3⋊D3C2×Dic612yescomplemented
626C2×C3×D3—21no—
627C2×C3×D3—21no—
628C2×C3×D3—21no—
629C2×C3×D3—21no—
630C2×C3×D3—22no—
631C2×C3×D3—22no—
632C2×C3×D3—22no—
633C2×C3×D3—22no—
634C2×C3×D3—32no—
635C2×C3×D3—32no—
636C2×C3×D3—41no—
637C2×C3×D3—41no—
638C2×C3×D3—62no—
639C2×C3×D3—68no—
640C2×C3×D3—61no—
641C2×C3×D3—61no—
642C2×C3×D3—61no—
643C2×C3×D3—61no—
644C2×C3×D3—68no—
645C2×C3×D3—121no—
646C2×C3×D3—121no—
647C2×C3×D3C2×Dic612yes—
648C2×C3×D3C2×Dic612yescomplemented
649C2×C3×D3C2×D1212yes—
650C2×C3×D3D3×D412yes—
651C2×C3×D3#23712yes—
652C2×C3×D3#23712yes—
653C2×C3×D3D3×Q812yes—
654C2×C3×D3D3×Q812yescomplemented
655D32—28no—
656C32×C4—21no—
657C32×C4—22no—
658C32×C4—21no—
659C32×C4—21no—
660C32×C4—32no—
661C32×C4—41no—
662C32×C4—41no—
663C32×C4—42no—
664C32×C4—61no—
665C32×C4—61no—
666C32×C4—61no—
667C3⋊Dic3—21no—
668C3⋊Dic3—21no—
669C3⋊Dic3—21no—
670C3⋊Dic3—21no—
671C3⋊Dic3—61no—
672C3⋊Dic3—61no—
673C3⋊Dic3—61no—
674C3⋊Dic3—61no—
675C3⋊Dic3—61no—
676C3⋊Dic3—61no—
677C3⋊Dic3—121no—
678C3⋊Dic3—121no—
679C3⋊Dic3—121no—
680C3⋊Dic3—121no—
681C3⋊Dic3—121no—
682C3⋊Dic3—121no—
683C3⋊Dic3—241no—
684C3⋊Dic3—241no—
685C3⋊Dic3C2×D1212yes—
686C3×Dic3—22no—
687C3×Dic3—21no—
688C3×Dic3—21no—
689C3×Dic3—21no—
690C3×Dic3—21no—
691C3×Dic3—21no—
692C3×Dic3—21no—
693C3×Dic3—22no—
694C3×Dic3—32no—
695C3×Dic3—32no—
696C3×Dic3—41no—
697C3×Dic3—41no—
698C3×Dic3—62no—
699C3×Dic3—61no—
700C3×Dic3—61no—
701C3×Dic3—61no—
702C3×Dic3—61no—
703C3×Dic3—61no—
704C3×Dic3—61no—
705C3×Dic3—61no—
706C3×Dic3—61no—
707C3×Dic3—121no—
708C3×Dic3—121no—
709C3×Dic3—121no—
710C3×Dic3—121no—
711C3×Dic3C2×D1212yes—
712C3×Dic3D3×D412yes—
713C22×Q8—271no—
714C23×C4—271no—
715C22⋊Q8—91no—
716C22⋊Q8—271no—
717C22⋊Q8—271no—
718C22⋊Q8—271no—
719C22⋊Q8—271no—
720C22⋊Q8—271no—
721C22⋊Q8—271no—
722C22⋊Q8—271no—
723C2×C4⋊C4—91no—
724C2×C4⋊C4—271no—
725C2×C4⋊C4—271no—
726C2×C22⋊C4—91no—
727C2×C22⋊C4—271no—
728C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
729C23×C3—31no—
730C23×C3—31no—
731C23×C3—31no—
732C23×C3—31no—
733C23×C3—61no—
734C23×C3—61no—
735C23×C3—94no—
736C23×C3—91no—
737C23×C3—182no—
738C23×C3—182no—
739C22×D3—31no—
740C22×D3—31no—
741C22×D3—34no—
742C22×D3—34no—
743C22×D3—61no—
744C22×D3—62no—
745C22×D3—62no—
746C22×D3—62no—
747C22×D3—62no—
748C22×D3C2×D3211yescharacteristic
749C22×D3C2×D3211yescharacteristic
750C3×Q8—182no—
751C2×C3×C4—21no—
752C2×C3×C4—21no—
753C2×C3×C4—21no—
754C2×C3×C4—31no—
755C2×C3×C4—31no—
756C2×C3×C4—31no—
757C2×C3×C4—31no—
758C2×C3×C4—31no—
759C2×C3×C4—31no—
760C2×C3×C4—31no—
761C2×C3×C4—31no—
762C2×C3×C4—41no—
763C2×C3×C4—61no—
764C2×C3×C4—61no—
765C2×C3×C4—61no—
766C2×C3×C4—61no—
767C2×C3×C4—62no—
768C2×C3×C4—62no—
769C2×C3×C4—64no—
770C2×C3×C4—94no—
771C2×C3×C4—91no—
772C2×C3×C4—91no—
773C2×C3×C4—91no—
774C2×C3×C4—91no—
775C2×C3×C4—91no—
776C2×C3×C4—182no—
777C2×C3×C4—182no—
778C2×C3×C4—182no—
779C2×C3×C4C2×D3211yescharacteristic
780C2×C3×C4C2×D3211yescharacteristic
781C2×C3×C4C2×D3211yescharacteristic
782C2×Dic3—31no—
783C2×Dic3—31no—
784C2×Dic3—34no—
785C2×Dic3—31no—
786C2×Dic3—31no—
787C2×Dic3—31no—
788C2×Dic3—31no—
789C2×Dic3—31no—
790C2×Dic3—31no—
791C2×Dic3—31no—
792C2×Dic3—31no—
793C2×Dic3—61no—
794C2×Dic3—61no—
795C2×Dic3—61no—
796C2×Dic3—61no—
797C2×Dic3—61no—
798C2×Dic3—62no—
799C2×Dic3—62no—
800C2×Dic3—62no—
801C2×Dic3—91no—
802C2×Dic3—91no—
803C2×Dic3—91no—
804C2×Dic3—91no—
805C2×Dic3—91no—
806C2×Dic3—91no—
807C2×Dic3—181no—
808C2×Dic3—181no—
809C2×Dic3—181no—
810C2×Dic3—181no—
811C2×Dic3—181no—
812C2×Dic3—181no—
813C2×Dic3—182no—
814C2×Dic3—182no—
815C2×Dic3—182no—
816C2×Dic3—182no—
817C2×Dic3—182no—
818C2×Dic3—182no—
819C2×Dic3—182no—
820C2×Dic3—182no—
821C2×Dic3—361no—
822C2×Dic3—361no—
823C2×Dic3—362no—
824C2×Dic3—362no—
825C2×Dic3—362no—
826C2×Dic3C2×D3211yescharacteristic
827C2×Dic3C2×D3211yescharacteristic
828C2×Dic3C2×D3211yescharacteristic
829C2×Dic3C2×D3211yescharacteristic
830C4×D3—22no—
831C4×D3—34no—
832C4×D3—62no—
833C4×D3—62no—
834C4×D3—62no—
835C4×D3—182no—
836C4×D3—182no—
837C4×D3—182no—
838C4×D3—182no—
839C4×D3—182no—
840C4×D3—182no—
841C4×D3—182no—
842C4×D3—362no—
843Dic6—62no—
844Dic6—62no—
845Dic6—182no—
846Dic6—182no—
847Dic6—182no—
848Dic6—182no—
849Dic6—182no—
850Dic6—182no—
851Dic6—182no—
852Dic6—182no—
853Dic6—182no—
854Dic6—362no—
855Dic6—362no—
856C2×C32—21no—
857C2×C32—21no—
858C2×C32—21no—
859C2×C32—21no—
860C2×C32—21no—
861C2×C32—21no—
862C2×C32—21no—
863C2×C32—21no—
864C2×C32—21no—
865C2×C32—34no—
866C2×C32—41no—
867C2×C32—41no—
868C2×C32—41no—
869C2×C32—62no—
870C2×C32C22×Dic611yescharacteristic
871C2×C32C22×D1211yescharacteristic
872C2×C32C2×D3×D411yescharacteristic
873C2×C32C2×D3×D411yescharacteristic
874C2×C32C2×#23711yescharacteristic
875C2×C32C2×#23711yescharacteristic
876C2×C32C2×D3×Q811yescharacteristic
877C2×C32C2×D3×Q811yescharacteristic
878C2×C32D3×#4111yescharacteristic
879C3⋊D3—22no—
880C3×D3—22no—
881C3×D3—22no—
882C3×D3—24no—
883C3×D3—42no—
884C3×D3—62no—
885C3×D3—62no—
886C3×D3—122no—
887C3×D3#87814yescomplemented
888C3×D3#89714yescomplemented
889C24—91no—
890C2×Q8—91no—
891C2×Q8—271no—
892C2×Q8—271no—
893C2×Q8—271no—
894C2×Q8—544no—
895C22×C4—31no—
896C22×C4—91no—
897C22×C4—91no—
898C22×C4—91no—
899C22×C4—91no—
900C22×C4—271no—
901C22×C4—271no—
902C22×C4—271no—
903C22×C4—271no—
904C22×C4—271no—
905C22×C4—544no—
906C4⋊C4—31no—
907C4⋊C4—91no—
908C4⋊C4—91no—
909C4⋊C4—91no—
910C4⋊C4—91no—
911C4⋊C4—91no—
912C4⋊C4—271no—
913C4⋊C4—271no—
914C4⋊C4—271no—
915C4⋊C4—271no—
916C4⋊C4—271no—
917C4⋊C4—271no—
918C22⋊C4—31no—
919C22⋊C4—91no—
920C22⋊C4—91no—
921C22⋊C4—91no—
922C22⋊C4—91no—
923C22⋊C4—271no—
924C22⋊C4—271no—
925C22⋊C4—271no—
926C22×C3—21no—
927C22×C3—21no—
928C22×C3—21no—
929C22×C3—32no—
930C22×C3—32no—
931C22×C3—32no—
932C22×C3—32no—
933C22×C3—32no—
934C22×C3—32no—
935C22×C3—32no—
936C22×C3—32no—
937C22×C3—41no—
938C22×C3—62no—
939C22×C3—62no—
940C22×C3—62no—
941C22×C3—62no—
942C22×C3—61no—
943C22×C3—61no—
944C22×C3—61no—
945C22×C3—61no—
946C22×C3—92no—
947C22×C3—121no—
948C22×C3—121no—
949C22×C3—188no—
950C22×C3—181no—
951C22×C3—181no—
952C22×C3C22×D3211yescharacteristic
953C22×C3C22×D3211yescharacteristic
954C22×C3C22×D3211yescharacteristic
955C2×D3—21no—
956C2×D3—21no—
957C2×D3—32no—
958C2×D3—32no—
959C2×D3—62no—
960C2×D3—68no—
961C2×D3—61no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—68no—
966C2×D3—121no—
967C2×D3—121no—
968C2×D3D3×Dic612yes—
969C2×D3D3×Dic612yescomplemented
970C2×D3D3×D1212yes—
971C2×D3#380512yes—
972C3×C4—22no—
973C3×C4—21no—
974C3×C4—21no—
975C3×C4—21no—
976C3×C4—32no—
977C3×C4—32no—
978C3×C4—41no—
979C3×C4—41no—
980C3×C4—42no—
981C3×C4—62no—
982C3×C4—62no—
983C3×C4—61no—
984C3×C4—61no—
985C3×C4—61no—
986C3×C4—61no—
987C3×C4—61no—
988C3×C4—61no—
989C3×C4—92no—
990C3×C4—121no—
991C3×C4—121no—
992C3×C4—181no—
993C3×C4—181no—
994C3×C4—181no—
995C3×C4—181no—
996Dic3—21no—
997Dic3—21no—
998Dic3—21no—
999Dic3—32no—
1000Dic3—32no—
1001Dic3—62no—
1002Dic3—61no—
1003Dic3—61no—
1004Dic3—61no—
1005Dic3—61no—
1006Dic3—61no—
1007Dic3—61no—
1008Dic3—61no—
1009Dic3—61no—
1010Dic3—121no—
1011Dic3—121no—
1012Dic3—121no—
1013Dic3—121no—
1014Dic3—181no—
1015Dic3—181no—
1016Dic3—181no—
1017Dic3—181no—
1018Dic3—181no—
1019Dic3—181no—
1020Dic3—361no—
1021Dic3—361no—
1022Dic3—361no—
1023Dic3—361no—
1024Dic3—361no—
1025Dic3—361no—
1026Dic3—721no—
1027Dic3—721no—
1028Dic3D3×D1212yes—
1029C32—21no—
1030C32—21no—
1031C32—21no—
1032C32—41no—
1033C32C2×#87811yescharacteristic, complemented
1034C32C2×#89711yescharacteristic, complemented
1035C32D3×C22⋊Q811yescharacteristic, complemented
1036C23—31no—
1037C23—31no—
1038C23—94no—
1039C23—91no—
1040C23—182no—
1041C23—182no—
1042Q8—182no—
1043Q8—542no—
1044Q8—542no—
1045Q8—542no—
1046C2×C4—31no—
1047C2×C4—31no—
1048C2×C4—31no—
1049C2×C4—31no—
1050C2×C4—62no—
1051C2×C4—94no—
1052C2×C4—91no—
1053C2×C4—91no—
1054C2×C4—91no—
1055C2×C4—91no—
1056C2×C4—91no—
1057C2×C4—182no—
1058C2×C4—182no—
1059C2×C4—182no—
1060C2×C4—271no—
1061C2×C4—271no—
1062C2×C4—542no—
1063C2×C4—542no—
1064C2×C4—542no—
1065C2×C4—542no—
1066C2×C4—542no—
1067C2×C4D3311yescharacteristic
1068C2×C3—21no—
1069C2×C3—21no—
1070C2×C3—21no—
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—21no—
1075C2×C3—21no—
1076C2×C3—21no—
1077C2×C3—34no—
1078C2×C3—34no—
1079C2×C3—41no—
1080C2×C3—41no—
1081C2×C3—41no—
1082C2×C3—64no—
1083C2×C3—62no—
1084C2×C3—62no—
1085C2×C3—122no—
1086C2×C3—182no—
1087C2×C3C2×D3×Dic611yescharacteristic
1088C2×C3C2×D3×Dic611yescharacteristic
1089C2×C3C2×D3×D1211yescharacteristic
1090C2×C3C2×D3×D1211yescharacteristic
1091C2×C3D32×D411yescharacteristic
1092C2×C3D3×#23711yescharacteristic
1093C2×C3D3×#23711yescharacteristic
1094C2×C3D32×Q811yescharacteristic
1095C2×C3C2×#380511yescharacteristic
1096D3—22no—
1097D3—62no—
1098D3—62no—
1099D3—122no—
1100D3#6389314yesdirect product factor
1101C22—32no—
1102C22—32no—
1103C22—32no—
1104C22—32no—
1105C22—61no—
1106C22—61no—
1107C22—92no—
1108C22—188no—
1109C22—181no—
1110C22—181no—
1111C22C2×D3311yescharacteristic
1112C4—21no—
1113C4—32no—
1114C4—61no—
1115C4—61no—
1116C4—61no—
1117C4—92no—
1118C4—181no—
1119C4—181no—
1120C4—181no—
1121C4—181no—
1122C4—541no—
1123C4—541no—
1124C3—21no—
1125C3—21no—
1126C3—21no—
1127C3—41no—
1128C3D3×#87811yescharacteristic, complemented
1129C3D3×#89711yescharacteristic, complemented
1130C3C2×#6389311yescharacteristic, complemented
1131C2—34no—
1132C2—62no—
1133C2—182no—
1134C2D32×Dic611yescharacteristic
1135C2D32×D1211yescharacteristic
1136C2D3×#380511yescharacteristic
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×#627C2semidirect
3. #11723692C2semidirect
4. #11723491C2semidirect
5. #11723483C2semidirect
6. D3×C4⋊(C3⋊Dic3)C2semidirect
8. C3×#63893C2semidirect
9. C3×D3×Dic3⋊C4C2semidirect
10. #11722984C2semidirect
11. #11722981C2semidirect
12. #11722974C2semidirect
13. #11722971C2semidirect
14. D3×Dic3⋊Dic3C2semidirect
21. C2×#6296C22semidirect
23. C2×#6293C22semidirect
24. C2×#6293C22semidirect
29. C2×C3×#627C22semidirect
36. C4⋊(C3⋊(C3⋊Dic3))C22semidirect
38. C3×C4⋊(C3⋊Dic3)C22semidirect
39. C3×#3750C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88815C22semidirect
44. #88807C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
46. Dic3⋊(C3⋊Dic3)C22semidirect
47. Dic3⋊(C3⋊Dic3)C22semidirect
50. C3×#3724C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
94. #63893D3direct (N × H)
101. D3×Dic3⋊C4D3semidirect
109. C2×C3×D32Q8semidirect
172. C2×#627C2×D3semidirect
212. C4⋊(C3⋊Dic3)C2×D3semidirect
214. #3750C2×D3semidirect
240. C3×Dic3⋊C4C2×D3semidirect
241. C3×Dic3⋊C4C2×D3semidirect
243. #3724C2×D3semidirect
258. Dic3⋊Dic3C2×D3semidirect
259. Dic3⋊Dic3C2×D3semidirect
275. C2×C3×C3⋊D3C2×Q8semidirect
280. C2×C32×D3C2×Q8semidirect
363. C2×D32Dic6semidirect
476. C32×D3C22⋊Q8semidirect
609. Dic3⋊C4D32semidirect
625. C2×C3⋊D3C2×Dic6semidirect
648. C2×C3×D3C2×Dic6semidirect
654. C2×C3×D3D3×Q8semidirect
728. C33C2×C22⋊Q8semidirect
887. C3×D3#878semidirect
888. C3×D3#897semidirect
969. C2×D3D3×Dic6semidirect
1033. C32C2×#878semidirect
1034. C32C2×#897semidirect
1035. C32D3×C22⋊Q8semidirect
1100. D3#63893direct (N × H)
1128. C3D3×#878semidirect
1129. C3D3×#897semidirect
1130. C3C2×#63893semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6272
C2×D32×Dic32
#117236922
#117234912
#117234832
D3×C4⋊(C3⋊Dic3)2
C3×D3×(C2×D3)⋊C42
C3×#638932
C3×D3×Dic3⋊C42
#117229842
#117229812
#117229742
#117229712
D3×Dic3⋊Dic32
D3×(C2×D3)⋊Dic32
C2×#638933
D3×#8973
D3×#8783