Finite Group Databasebeta

← D3×#63895 #13170740

Subgroups — D3×#63895 #13170740

Order 1728.

1602 conjugacy classes of subgroups.

The subgroup lattice has 1162 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×#627C211yesmaximal, characteristic, complemented
2C2×D3×#624C211yesmaximal, characteristic
3#11723692C211yesmaximal, characteristic, complemented
4D3×#3752C211yesmaximal, characteristic
5#11723495C211yesmaximal, characteristic, complemented
6#11723485C211yesmaximal, characteristic, complemented
7C3×#63895C211yesmaximal, characteristic, complemented
8C3×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
9C3×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
10#11722984C211yesmaximal, characteristic, complemented
11#11722982C211yesmaximal, characteristic, complemented
12#11722973C211yesmaximal, characteristic, complemented
13#11722972C211yesmaximal, characteristic, complemented
14D3×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
15D3×#3722C211yesmaximal, characteristic
16C2×#63895—31nomaximal
17D3×#897—31nomaximal
18D3×#896—31nomaximal
19C22×D3×C3⋊D3C2211yescharacteristic
20C2×C32×C4×D3C2211yescharacteristic
21C2×#6296C2211yescharacteristic, complemented
22C2×#6294C2211yescharacteristic
23C2×#6293C2211yescharacteristic, complemented
24C2×#6293C2211yescharacteristic, complemented
25C2×#6289C2211yescharacteristic
26C2×#6289C2211yescharacteristic
27C2×D3×C3⋊Dic3C2211yescharacteristic
28C2×C3×#627C2211yescharacteristic, complemented
29C2×C3×#624C2211yescharacteristic
30C2×C3×D3×Dic3C2211yescharacteristic
31C2×C3×D3×Dic3C2211yescharacteristic
32C2×C3×D3×Dic3C2211yescharacteristic
33C2×C3×D3×Dic3C2211yescharacteristic
34D3×#627—24no—
35D3×#624—24no—
36#88859C2211yescharacteristic
37C3×#3752C2211yescharacteristic
38C3×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
39C3×#3750C2211yescharacteristic, complemented
40C32×C4⋊Dic3C2211yescharacteristic, complemented
41C32×Dic3⋊C4C2211yescharacteristic, complemented
42#88815C2211yescharacteristic, complemented
43#88814C2211yescharacteristic
44#88807C2211yescharacteristic, complemented
45Dic3⋊(C3⋊Dic3)C2211yescharacteristic, complemented
46#88804C2211yescharacteristic
47#88804C2211yescharacteristic
48#88804C2211yescharacteristic
49#88803C2211yescharacteristic
50C3×#3724C2211yescharacteristic, complemented
51C3×Dic3⋊Dic3C2211yescharacteristic, complemented
52C3×Dic3⋊Dic3C2211yescharacteristic, complemented
53C3×Dic3⋊Dic3C2211yescharacteristic, complemented
54C3×Dic3⋊Dic3C2211yescharacteristic, complemented
55C3×#3722C2211yescharacteristic
56C22×#627—31no—
57C22×#624—31no—
58C2×C4×D32—31no—
59C2×C4×D32—31no—
60C2×D3×Dic6—31no—
61C2×D3×Dic6—31no—
62C2×#3752—31no—
63#64106—31no—
64#64105—31no—
65C2×C3×C4⋊Dic3—31no—
66C2×C3×Dic3⋊C4—31no—
67C3×#897—31no—
68C3×#896—31no—
69C3×D3×C4⋊C4—31no—
70C3×D3×C4⋊C4—31no—
71C2×Dic3⋊Dic3—31no—
72C2×#3722—31no—
73D3×(C2×D3)⋊C4—31no—
74D3×(C2×D3)⋊C4—31no—
75D3×(C2×D3)⋊C4—31no—
76D3×(C2×D3)⋊C4—31no—
77D3×(C2×D3)⋊C4—61no—
78#63899—31no—
79#63896—31no—
80#63895—31no—
81#63895—31no—
82#63895—31no—
83#63895—31no—
84#63895—31no—
85#63895—31no—
86#63895—31no—
87#63895—31no—
88#63895—31no—
89#63895—31no—
90#63895—61no—
91#63895—61no—
92#63895D311yescharacteristic, direct product factor
93#63893—31no—
94#63893—31no—
95D3×C4⋊Dic3—31no—
96D3×C4⋊Dic3D311yescharacteristic, complemented
97#63888—31no—
98D3×Dic3⋊C4—31no—
99D3×Dic3⋊C4D311yescharacteristic, complemented
100#63871—31no—
101#63865—31no—
102#63857—31no—
103#63851—31no—
104C22×C3⋊(C3⋊D3)C2311yescharacteristic
105C22×C3×C3⋊D3C2311yescharacteristic
106C22×C32×D3C2311yescharacteristic
107C2×D3×C3⋊D3—22no—
108C2×D3×C3⋊D3—22no—
109C2×D3×C3⋊D3Q814yescomplemented
110C2×C33×C4C2311yescharacteristic
111C2×C3⋊(C3⋊Dic3)C2311yescharacteristic
112C2×C3×C3⋊Dic3C2311yescharacteristic
113C2×C3×C3⋊Dic3C2311yescharacteristic
114C2×C3×C3⋊Dic3C2311yescharacteristic
115C2×C3×C3⋊Dic3C2311yescharacteristic
116C2×C3×C3⋊Dic3C2311yescharacteristic
117C2×C32×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—
127#6289—22no—
128#6289—22no—
129D3×C3⋊Dic3—22no—
130C3×#627—22no—
131C3×#624—22no—
132C3×D3×Dic3—22no—
133C3×D3×Dic3—22no—
134C3×D3×Dic3—22no—
135C3×D3×Dic3D414yes—
136D3×C22⋊Q8—91no—
137C2×#897—91no—
138C2×#896—91no—
139C23×C3⋊D3—31no—
140C22×D32—31no—
141C22×D32—31no—
142C22×D32—61no—
143C22×C32×C4—31no—
144C22×C3⋊Dic3—31no—
145C2×C4×C3⋊D3—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×D3—31no—
159C2×C3×C4×D3—31no—
160C2×C3×C4×D3C2×D311yescharacteristic
161C2×C3×C4×D3C2×D311yescharacteristic
162C2×C3×Dic6—31no—
163C2×C3×Dic6—31no—
164C2×#627—31no—
165C2×#627—31no—
166C2×#627—31no—
167C2×#627—31no—
168C2×#627—31no—
169C2×#627—31no—
170C2×#627—31no—
171C2×#627—64no—
172C2×#627—61no—
173C2×#627—61no—
174C2×#627C2×D311yescharacteristic, complemented
175C2×#624—31no—
176C2×#624—31no—
177C2×#624—31no—
178C2×#624—31no—
179C2×#624—31no—
180C2×#624—64no—
181C2×#624—61no—
182C2×#624—61no—
183C2×#624C2×D311yescharacteristic
184C2×D3×Dic3—31no—
185C2×D3×Dic3—31no—
186C2×D3×Dic3—31no—
187C2×D3×Dic3—31no—
188C2×D3×Dic3—61no—
189C2×D3×Dic3C2×D311yescharacteristic
190C2×D3×Dic3C2×D311yescharacteristic
191C2×D3×Dic3C2×D311yescharacteristic
192C2×D3×Dic3C2×D311yescharacteristic
193C4×D32—64no—
194C4×D32—64no—
195D3×Dic6—64no—
196D3×Dic6—64no—
197C32×C4⋊C4—31no—
198C32×C4⋊C4—31no—
199#3752—31no—
200#3752—31no—
201#3752—31no—
202#3752—31no—
203#3752—31no—
204#3752—31no—
205#3752—31no—
206#3752—61no—
207#3752—61no—
208#3752—61no—
209#3752—121no—
210#3752C2×D311yescharacteristic
211C4⋊(C3⋊Dic3)—31no—
212C4⋊(C3⋊Dic3)C2×D311yescharacteristic, complemented
213#3750—31no—
214#3750C2×D311yescharacteristic, complemented
215C3×(C2×D3)⋊C4—31no—
216C3×(C2×D3)⋊C4—31no—
217C3×(C2×D3)⋊C4—31no—
218C3×(C2×D3)⋊C4—31no—
219C3×(C2×D3)⋊C4—61no—
220C3×C4⋊Dic3—21no—
221C3×C4⋊Dic3—31no—
222C3×C4⋊Dic3—31no—
223C3×C4⋊Dic3—31no—
224C3×C4⋊Dic3—31no—
225C3×C4⋊Dic3—31no—
226C3×C4⋊Dic3—31no—
227C3×C4⋊Dic3—61no—
228C3×C4⋊Dic3C2×D311yescharacteristic, complemented
229C3×C4⋊Dic3C2×D311yescharacteristic, complemented
230C3×Dic3⋊C4—21no—
231C3×Dic3⋊C4—31no—
232C3×Dic3⋊C4—31no—
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—61no—
251Dic3⋊Dic3—61no—
252Dic3⋊Dic3C2×D311yescharacteristic, complemented
253Dic3⋊Dic3C2×D311yescharacteristic, complemented
254Dic3⋊Dic3C2×D311yescharacteristic, complemented
255Dic3⋊Dic3C2×D311yescharacteristic, complemented
256#3722—31no—
257#3722—31no—
258#3722—31no—
259#3722—31no—
260#3722—31no—
261#3722—31no—
262#3722—31no—
263#3722—61no—
264#3722—61no—
265#3722—61no—
266#3722C2×D311yescharacteristic
267(C2×D3)⋊Dic3—31no—
268(C2×D3)⋊Dic3—31no—
269(C2×D3)⋊Dic3—31no—
270(C2×D3)⋊Dic3—31no—
271(C2×D3)⋊Dic3—61no—
272C22×C33C2411yescharacteristic
273C2×C3⋊(C3⋊D3)—21no—
274C2×C3⋊(C3⋊D3)—21no—
275C2×C3⋊(C3⋊D3)C2×Q812yescomplemented
276C2×C3×C3⋊D3—21no—
277C2×C3×C3⋊D3—21no—
278C2×C3×C3⋊D3C2×Q812yescomplemented
279C2×C32×D3C2×D412yes—
280C2×C32×D3C2×Q812yes—
281C2×C32×D3#4112yes—
282D3×C3⋊D3—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⋊Dic3C2×D412yes—
290C32×Dic3—21no—
291C32×Dic3—21no—
292C32×Dic3—21no—
293C32×Dic3—21no—
294C32×Dic3C2×D412yes—
295C2×D3×Q8—91no—
296C22×C4×D3—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×C4⋊C4—91no—
304#946—91no—
305C2×(C2×D3)⋊C4—91no—
306C2×(C2×D3)⋊C4—91no—
307C2×(C2×D3)⋊C4—91no—
308C2×(C2×D3)⋊C4—91no—
309C2×(C2×D3)⋊C4—181no—
310C2×C4⋊Dic3—31no—
311C2×C4⋊Dic3—91no—
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—31no—
326#896—91no—
327#896—91no—
328#896—91no—
329#896—91no—
330#896—91no—
331#896—91no—
332#896—91no—
333#896—91no—
334#896—91no—
335#896—181no—
336D3×C4⋊C4—31no—
337D3×C4⋊C4—31no—
338D3×C4⋊C4—91no—
339D3×C22⋊C4—91no—
340D3×C22⋊C4—91no—
341#878—91no—
342#878—91no—
343C23×C32—31no—
344C22×C3⋊D3—31no—
345C22×C3⋊D3—31no—
346C22×C3⋊D3—31no—
347C22×C3⋊D3—34no—
348C22×C3⋊D3—61no—
349C22×C3⋊D3—61no—
350C22×C3⋊D3—61no—
351C22×C3⋊D3—62no—
352C22×C3⋊D3—62no—
353C22×C3⋊D3—121no—
354C22×C3⋊D3C22×D311yescharacteristic
355C22×C3×D3—21no—
356C22×C3×D3—31no—
357C22×C3×D3—31no—
358C22×C3×D3—61no—
359C22×C3×D3C22×D311yescharacteristic
360C22×C3×D3C22×D311yescharacteristic
361C2×D32—34no—
362C2×D32—34no—
363C2×D32—64no—
364C2×D32—62no—
365C2×D32—62no—
366C2×D32—62no—
367C2×D32—62no—
368C2×D32—122no—
369C2×D32—122no—
370C2×C32×C4—21no—
371C2×C32×C4—21no—
372C2×C32×C4—21no—
373C2×C32×C4—31no—
374C2×C32×C4—31no—
375C2×C32×C4—31no—
376C2×C32×C4—31no—
377C2×C32×C4—31no—
378C2×C32×C4—41no—
379C2×C32×C4—62no—
380C2×C32×C4C22×D311yescharacteristic
381C2×C32×C4C22×D311yescharacteristic
382C2×C32×C4C22×D311yescharacteristic
383C2×C3⋊Dic3—31no—
384C2×C3⋊Dic3—31no—
385C2×C3⋊Dic3—31no—
386C2×C3⋊Dic3—61no—
387C2×C3⋊Dic3—61no—
388C2×C3⋊Dic3—61no—
389C2×C3⋊Dic3—62no—
390C2×C3⋊Dic3—121no—
391C2×C3⋊Dic3C22×D311yescharacteristic
392C2×C3⋊Dic3C22×D311yescharacteristic
393C2×C3⋊Dic3C22×D311yescharacteristic
394C2×C3⋊Dic3C22×D311yescharacteristic
395C2×C3⋊Dic3C22×D311yescharacteristic
396C4×C3⋊D3—62no—
397C4×C3⋊D3—62no—
398#634—62no—
399#634—62no—
400C2×C3×Dic3—21no—
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
432C2×C3×Dic3C22×D311yescharacteristic
433C2×C3×Dic3C22×D311yescharacteristic
434C3×C4×D3—22no—
435C3×C4×D3—22no—
436C3×C4×D3—34no—
437C3×C4×D3—42no—
438C3×C4×D3—62no—
439C3×C4×D3—62no—
440C3×C4×D3—62no—
441C3×C4×D3—62no—
442C3×C4×D3—62no—
443C3×Dic6—62no—
444C3×Dic6—62no—
445#627—22no—
446#627—62no—
447#627—62no—
448#627—62no—
449#627—62no—
450#627—62no—
451#627—62no—
452#627—62no—
453#627—122no—
454#627—122no—
455#624—22no—
456#624—62no—
457#624—62no—
458#624—62no—
459#624—62no—
460#624—62no—
461#624—122no—
462#624—122no—
463D3×Dic3—22no—
464D3×Dic3—22no—
465D3×Dic3—22no—
466D3×Dic3—62no—
467D3×Dic3—62no—
468D3×Dic3—62no—
469D3×Dic3—62no—
470D3×Dic3—122no—
471D3×Dic3D1214yes—
472C2×C22⋊Q8—271noSylow
473C2×C33C22×D411yescharacteristic
474C2×C33C22×Q811yescharacteristic
475C2×C33C2×#4111yescharacteristic
476C3⋊(C3⋊D3)—22no—
477C3×C3⋊D3—22no—
478C32×D3C22⋊Q814yescomplemented
479C23×D3—91no—
480C23×D3—91no—
481C23×D3—91no—
482C23×D3—181no—
483C2×C3×Q8—91no—
484C22×C3×C4—31no—
485C22×C3×C4—31no—
486C22×C3×C4—61no—
487C22×C3×C4—91no—
488C22×C3×C4—91no—
489C22×C3×C4—91no—
490C22×C3×C4—91no—
491C22×C3×C4—91no—
492C22×Dic3—31no—
493C22×Dic3—31no—
494C22×Dic3—31no—
495C22×Dic3—31no—
496C22×Dic3—91no—
497C22×Dic3—91no—
498C22×Dic3—91no—
499C22×Dic3—181no—
500D3×Q8—184no—
501C2×C4×D3—31no—
502C2×C4×D3—31no—
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—91no—
513C2×C4×D3—91no—
514C2×C4×D3—91no—
515C2×C4×D3—91no—
516C2×C4×D3—181no—
517C2×C4×D3—181no—
518C2×C4×D3—184no—
519C2×C4×D3—184no—
520C2×C4×D3—184no—
521C2×C4×D3D3211yescharacteristic
522C2×Dic6—31no—
523C2×Dic6—31no—
524C2×Dic6—91no—
525C2×Dic6—91no—
526C2×Dic6—91no—
527C2×Dic6—91no—
528C2×Dic6—91no—
529C2×Dic6—91no—
530C2×Dic6—91no—
531C2×Dic6—91no—
532C2×Dic6—91no—
533C2×Dic6—181no—
534C2×Dic6—181no—
535C2×Dic6—184no—
536C2×Dic6—184no—
537C3×C4⋊C4—31no—
538C3×C4⋊C4—31no—
539C3×C4⋊C4—31no—
540C3×C4⋊C4—31no—
541C3×C4⋊C4—61no—
542C3×C4⋊C4—61no—
543C3×C4⋊C4—91no—
544C3×C4⋊C4—91no—
545C3×C4⋊C4—91no—
546C3×C4⋊C4—91no—
547C3×C4⋊C4—91no—
548C3×C4⋊C4—91no—
549C3×C4⋊C4—91no—
550C3×C22⋊C4—91no—
551C3×C22⋊C4—91no—
552#217—91no—
553#217—91no—
554(C2×D3)⋊C4—31no—
555(C2×D3)⋊C4—31no—
556(C2×D3)⋊C4—31no—
557(C2×D3)⋊C4—31no—
558(C2×D3)⋊C4—61no—
559(C2×D3)⋊C4—91no—
560(C2×D3)⋊C4—91no—
561(C2×D3)⋊C4—91no—
562(C2×D3)⋊C4—91no—
563(C2×D3)⋊C4—91no—
564(C2×D3)⋊C4—91no—
565(C2×D3)⋊C4—91no—
566(C2×D3)⋊C4—91no—
567(C2×D3)⋊C4—91no—
568(C2×D3)⋊C4—91no—
569(C2×D3)⋊C4—91no—
570(C2×D3)⋊C4—91no—
571(C2×D3)⋊C4—91no—
572(C2×D3)⋊C4—91no—
573(C2×D3)⋊C4—91no—
574(C2×D3)⋊C4—91no—
575(C2×D3)⋊C4—181no—
576(C2×D3)⋊C4—181no—
577(C2×D3)⋊C4—181no—
578(C2×D3)⋊C4—181no—
579(C2×D3)⋊C4—181no—
580(C2×D3)⋊C4—181no—
581(C2×D3)⋊C4—181no—
582(C2×D3)⋊C4—361no—
583C4⋊Dic3—31no—
584C4⋊Dic3—31no—
585C4⋊Dic3—31no—
586C4⋊Dic3—31no—
587C4⋊Dic3—31no—
588C4⋊Dic3—31no—
589C4⋊Dic3—61no—
590C4⋊Dic3—91no—
591C4⋊Dic3—91no—
592C4⋊Dic3—91no—
593C4⋊Dic3—91no—
594C4⋊Dic3—181no—
595C4⋊Dic3D3211yescharacteristic, complemented
596Dic3⋊C4—31no—
597Dic3⋊C4—31no—
598Dic3⋊C4—31no—
599Dic3⋊C4—31no—
600Dic3⋊C4—31no—
601Dic3⋊C4—31no—
602Dic3⋊C4—31no—
603Dic3⋊C4—31no—
604Dic3⋊C4—61no—
605Dic3⋊C4—91no—
606Dic3⋊C4—91no—
607Dic3⋊C4—91no—
608Dic3⋊C4—91no—
609Dic3⋊C4—91no—
610Dic3⋊C4—181no—
611Dic3⋊C4D3211yescharacteristic, complemented
612C22×C32—21no—
613C22×C32—21no—
614C22×C32—21no—
615C22×C32—32no—
616C22×C32—32no—
617C22×C32—32no—
618C22×C32—41no—
619C22×C32C23×D311yescharacteristic
620C22×C32C23×D311yescharacteristic
621C22×C32C23×D311yescharacteristic
622C2×C3⋊D3—21no—
623C2×C3⋊D3—21no—
624C2×C3⋊D3—32no—
625C2×C3⋊D3—32no—
626C2×C3⋊D3—32no—
627C2×C3⋊D3—62no—
628C2×C3⋊D3—62no—
629C2×C3⋊D3—62no—
630C2×C3⋊D3—68no—
631C2×C3⋊D3—61no—
632C2×C3⋊D3—61no—
633C2×C3⋊D3—61no—
634C2×C3⋊D3—61no—
635C2×C3⋊D3—61no—
636C2×C3⋊D3—61no—
637C2×C3⋊D3—122no—
638C2×C3⋊D3—121no—
639C2×C3⋊D3—121no—
640C2×C3⋊D3—121no—
641C2×C3⋊D3—121no—
642C2×C3⋊D3—121no—
643C2×C3⋊D3—121no—
644C2×C3⋊D3—241no—
645C2×C3⋊D3—241no—
646C2×C3⋊D3D3×Q812yescomplemented
647C2×C3×D3—22no—
648C2×C3×D3—22no—
649C2×C3×D3—22no—
650C2×C3×D3—32no—
651C2×C3×D3—32no—
652C2×C3×D3—62no—
653C2×C3×D3—61no—
654C2×C3×D3—61no—
655C2×C3×D3—61no—
656C2×C3×D3—61no—
657C2×C3×D3—121no—
658C2×C3×D3—121no—
659C2×C3×D3C2×D1212yes—
660C2×C3×D3#23512yes—
661C2×C3×D3D3×D412yes—
662C2×C3×D3#23712yes—
663C2×C3×D3D3×Q812yes—
664C2×C3×D3D3×Q812yes—
665D32—68no—
666D32—68no—
667D32—128no—
668C32×C4—21no—
669C32×C4—21no—
670C32×C4—21no—
671C32×C4—32no—
672C32×C4—41no—
673C32×C4—41no—
674C32×C4—41no—
675C32×C4—61no—
676C32×C4—61no—
677C32×C4—61no—
678C32×C4—61no—
679C32×C4—81no—
680C3⋊Dic3—21no—
681C3⋊Dic3—21no—
682C3⋊Dic3—21no—
683C3⋊Dic3—21no—
684C3⋊Dic3—61no—
685C3⋊Dic3—61no—
686C3⋊Dic3—61no—
687C3⋊Dic3—121no—
688C3⋊Dic3—121no—
689C3⋊Dic3—121no—
690C3⋊Dic3—241no—
691C3⋊Dic3C2×D1212yes—
692C3×Dic3—21no—
693C3×Dic3—21no—
694C3×Dic3—21no—
695C3×Dic3—21no—
696C3×Dic3—21no—
697C3×Dic3—21no—
698C3×Dic3—21no—
699C3×Dic3—21no—
700C3×Dic3—22no—
701C3×Dic3—32no—
702C3×Dic3—32no—
703C3×Dic3—41no—
704C3×Dic3—41no—
705C3×Dic3—41no—
706C3×Dic3—41no—
707C3×Dic3—62no—
708C3×Dic3—61no—
709C3×Dic3—61no—
710C3×Dic3—61no—
711C3×Dic3—61no—
712C3×Dic3—61no—
713C3×Dic3—61no—
714C3×Dic3—61no—
715C3×Dic3—61no—
716C3×Dic3—121no—
717C3×Dic3—121no—
718C3×Dic3—121no—
719C3×Dic3—121no—
720C3×Dic3C2×D1212yes—
721C3×Dic3D3×D412yes—
722C22×Q8—271no—
723C23×C4—271no—
724C22⋊Q8—91no—
725C22⋊Q8—271no—
726C22⋊Q8—271no—
727C22⋊Q8—271no—
728C22⋊Q8—271no—
729C22⋊Q8—271no—
730C22⋊Q8—271no—
731C22⋊Q8—271no—
732C2×C4⋊C4—91no—
733C2×C4⋊C4—91no—
734C2×C4⋊C4—271no—
735C2×C22⋊C4—271no—
736C2×C22⋊C4—271no—
737C33C2×C22⋊Q811yescharacteristic, complemented, Sylow
738C23×C3—31no—
739C23×C3—31no—
740C23×C3—61no—
741C23×C3—91no—
742C22×D3—31no—
743C22×D3—31no—
744C22×D3—61no—
745C22×D3—94no—
746C22×D3—94no—
747C22×D3—91no—
748C22×D3—91no—
749C22×D3—91no—
750C22×D3—94no—
751C22×D3—184no—
752C22×D3—181no—
753C22×D3—181no—
754C22×D3—181no—
755C22×D3—182no—
756C22×D3—182no—
757C22×D3—182no—
758C22×D3—182no—
759C22×D3—182no—
760C22×D3—182no—
761C22×D3—361no—
762C22×D3—362no—
763C22×D3—362no—
764C22×D3C2×D3211yescharacteristic
765C3×Q8—182no—
766C2×C3×C4—21no—
767C2×C3×C4—21no—
768C2×C3×C4—21no—
769C2×C3×C4—31no—
770C2×C3×C4—31no—
771C2×C3×C4—31no—
772C2×C3×C4—31no—
773C2×C3×C4—31no—
774C2×C3×C4—31no—
775C2×C3×C4—31no—
776C2×C3×C4—31no—
777C2×C3×C4—31no—
778C2×C3×C4—31no—
779C2×C3×C4—41no—
780C2×C3×C4—61no—
781C2×C3×C4—61no—
782C2×C3×C4—61no—
783C2×C3×C4—61no—
784C2×C3×C4—61no—
785C2×C3×C4—62no—
786C2×C3×C4—62no—
787C2×C3×C4—94no—
788C2×C3×C4—91no—
789C2×C3×C4—91no—
790C2×C3×C4—91no—
791C2×C3×C4—91no—
792C2×C3×C4—91no—
793C2×C3×C4—122no—
794C2×C3×C4—182no—
795C2×C3×C4—182no—
796C2×C3×C4—182no—
797C2×C3×C4—182no—
798C2×C3×C4C2×D3211yescharacteristic
799C2×C3×C4C2×D3211yescharacteristic
800C2×C3×C4C2×D3211yescharacteristic
801C2×Dic3—31no—
802C2×Dic3—31no—
803C2×Dic3—34no—
804C2×Dic3—31no—
805C2×Dic3—31no—
806C2×Dic3—31no—
807C2×Dic3—31no—
808C2×Dic3—31no—
809C2×Dic3—31no—
810C2×Dic3—31no—
811C2×Dic3—31no—
812C2×Dic3—61no—
813C2×Dic3—61no—
814C2×Dic3—61no—
815C2×Dic3—61no—
816C2×Dic3—61no—
817C2×Dic3—62no—
818C2×Dic3—62no—
819C2×Dic3—62no—
820C2×Dic3—91no—
821C2×Dic3—91no—
822C2×Dic3—91no—
823C2×Dic3—181no—
824C2×Dic3—181no—
825C2×Dic3—181no—
826C2×Dic3—182no—
827C2×Dic3—182no—
828C2×Dic3—182no—
829C2×Dic3—361no—
830C2×Dic3—362no—
831C2×Dic3C2×D3211yescharacteristic
832C2×Dic3C2×D3211yescharacteristic
833C2×Dic3C2×D3211yescharacteristic
834C2×Dic3C2×D3211yescharacteristic
835C2×Dic3C2×D3211yescharacteristic
836C4×D3—22no—
837C4×D3—34no—
838C4×D3—62no—
839C4×D3—62no—
840C4×D3—62no—
841C4×D3—62no—
842C4×D3—62no—
843C4×D3—182no—
844C4×D3—182no—
845C4×D3—182no—
846C4×D3—182no—
847C4×D3—182no—
848C4×D3—182no—
849C4×D3—182no—
850C4×D3—182no—
851C4×D3—182no—
852C4×D3—362no—
853C4×D3—362no—
854Dic6—62no—
855Dic6—62no—
856Dic6—182no—
857Dic6—182no—
858Dic6—182no—
859Dic6—182no—
860Dic6—182no—
861Dic6—182no—
862Dic6—182no—
863Dic6—182no—
864Dic6—182no—
865Dic6—362no—
866Dic6—362no—
867C2×C32—21no—
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—34no—
877C2×C32—41no—
878C2×C32—41no—
879C2×C32—41no—
880C2×C32C22×D1211yescharacteristic
881C2×C32C2×#23511yescharacteristic
882C2×C32C2×D3×D411yescharacteristic
883C2×C32C2×D3×D411yescharacteristic
884C2×C32C2×#23711yescharacteristic
885C2×C32C2×D3×Q811yescharacteristic
886C2×C32C2×D3×Q811yescharacteristic
887C2×C32C2×D3×Q811yescharacteristic
888C2×C32D3×#4111yescharacteristic
889C3⋊D3—22no—
890C3⋊D3—62no—
891C3⋊D3—62no—
892C3⋊D3—62no—
893C3⋊D3—122no—
894C3⋊D3—122no—
895C3⋊D3—122no—
896C3⋊D3—242no—
897C3×D3—24no—
898C3×D3—62no—
899C3×D3—62no—
900C3×D3—122no—
901C3×D3#89614yescomplemented
902C3×D3#89714yescomplemented
903C24—271no—
904C2×Q8—91no—
905C2×Q8—271no—
906C2×Q8—271no—
907C2×Q8—271no—
908C2×Q8—544no—
909C22×C4—31no—
910C22×C4—91no—
911C22×C4—91no—
912C22×C4—91no—
913C22×C4—91no—
914C22×C4—91no—
915C22×C4—271no—
916C22×C4—271no—
917C22×C4—271no—
918C22×C4—271no—
919C22×C4—544no—
920C4⋊C4—31no—
921C4⋊C4—31no—
922C4⋊C4—91no—
923C4⋊C4—91no—
924C4⋊C4—91no—
925C4⋊C4—91no—
926C4⋊C4—91no—
927C4⋊C4—91no—
928C4⋊C4—91no—
929C4⋊C4—271no—
930C4⋊C4—271no—
931C4⋊C4—271no—
932C22⋊C4—91no—
933C22⋊C4—91no—
934C22⋊C4—271no—
935C22⋊C4—271no—
936C22⋊C4—271no—
937C22⋊C4—271no—
938C22⋊C4—271no—
939C22⋊C4—271no—
940C22×C3—21no—
941C22×C3—21no—
942C22×C3—21no—
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—92no—
954C22×C3—181no—
955C22×C3—181no—
956C22×C3C22×D3211yescharacteristic
957C22×C3C22×D3211yescharacteristic
958C22×C3C22×D3211yescharacteristic
959C2×D3—32no—
960C2×D3—32no—
961C2×D3—62no—
962C2×D3—61no—
963C2×D3—61no—
964C2×D3—61no—
965C2×D3—61no—
966C2×D3—92no—
967C2×D3—92no—
968C2×D3—92no—
969C2×D3—121no—
970C2×D3—121no—
971C2×D3—182no—
972C2×D3—182no—
973C2×D3—182no—
974C2×D3—188no—
975C2×D3—188no—
976C2×D3—181no—
977C2×D3—181no—
978C2×D3—181no—
979C2×D3—181no—
980C2×D3—181no—
981C2×D3—181no—
982C2×D3—188no—
983C2×D3—362no—
984C2×D3—368no—
985C2×D3—361no—
986C2×D3—361no—
987C2×D3—361no—
988C2×D3—361no—
989C2×D3—361no—
990C2×D3—361no—
991C2×D3—721no—
992C2×D3—721no—
993C2×D3#379712yes—
994C2×D3D3×D1212yes—
995C2×D3#380412yes—
996C3×C4—21no—
997C3×C4—21no—
998C3×C4—21no—
999C3×C4—32no—
1000C3×C4—32no—
1001C3×C4—41no—
1002C3×C4—41no—
1003C3×C4—41no—
1004C3×C4—62no—
1005C3×C4—61no—
1006C3×C4—61no—
1007C3×C4—61no—
1008C3×C4—61no—
1009C3×C4—61no—
1010C3×C4—61no—
1011C3×C4—61no—
1012C3×C4—61no—
1013C3×C4—81no—
1014C3×C4—92no—
1015C3×C4—121no—
1016C3×C4—121no—
1017C3×C4—121no—
1018C3×C4—121no—
1019C3×C4—181no—
1020C3×C4—181no—
1021C3×C4—181no—
1022C3×C4—181no—
1023Dic3—21no—
1024Dic3—21no—
1025Dic3—21no—
1026Dic3—21no—
1027Dic3—32no—
1028Dic3—32no—
1029Dic3—62no—
1030Dic3—61no—
1031Dic3—61no—
1032Dic3—61no—
1033Dic3—61no—
1034Dic3—61no—
1035Dic3—61no—
1036Dic3—61no—
1037Dic3—61no—
1038Dic3—121no—
1039Dic3—121no—
1040Dic3—121no—
1041Dic3—121no—
1042Dic3—181no—
1043Dic3—181no—
1044Dic3—181no—
1045Dic3—361no—
1046Dic3—361no—
1047Dic3—361no—
1048Dic3—721no—
1049Dic3D3×D1212yes—
1050C32—21no—
1051C32—21no—
1052C32—21no—
1053C32—41no—
1054C32C2×#89611yescharacteristic, complemented
1055C32C2×#89711yescharacteristic, complemented
1056C32D3×C22⋊Q811yescharacteristic, complemented
1057C23—31no—
1058C23—91no—
1059C23—274no—
1060C23—271no—
1061C23—542no—
1062C23—542no—
1063Q8—182no—
1064Q8—542no—
1065Q8—542no—
1066Q8—542no—
1067C2×C4—31no—
1068C2×C4—31no—
1069C2×C4—31no—
1070C2×C4—31no—
1071C2×C4—31no—
1072C2×C4—62no—
1073C2×C4—94no—
1074C2×C4—91no—
1075C2×C4—91no—
1076C2×C4—91no—
1077C2×C4—91no—
1078C2×C4—91no—
1079C2×C4—182no—
1080C2×C4—182no—
1081C2×C4—182no—
1082C2×C4—182no—
1083C2×C4—271no—
1084C2×C4—542no—
1085C2×C4—542no—
1086C2×C4—542no—
1087C2×C4—542no—
1088C2×C4D3311yescharacteristic
1089C2×C3—21no—
1090C2×C3—21no—
1091C2×C3—21no—
1092C2×C3—21no—
1093C2×C3—21no—
1094C2×C3—21no—
1095C2×C3—21no—
1096C2×C3—21no—
1097C2×C3—21no—
1098C2×C3—34no—
1099C2×C3—34no—
1100C2×C3—41no—
1101C2×C3—41no—
1102C2×C3—41no—
1103C2×C3—64no—
1104C2×C3—182no—
1105C2×C3C2×#379711yescharacteristic
1106C2×C3C2×D3×D1211yescharacteristic
1107C2×C3C2×D3×D1211yescharacteristic
1108C2×C3D3×#23511yescharacteristic
1109C2×C3D32×D411yescharacteristic
1110C2×C3D3×#23711yescharacteristic
1111C2×C3D32×Q811yescharacteristic
1112C2×C3D32×Q811yescharacteristic
1113C2×C3C2×#380411yescharacteristic
1114D3—62no—
1115D3—62no—
1116D3—122no—
1117D3—182no—
1118D3—182no—
1119D3—182no—
1120D3—362no—
1121D3—362no—
1122D3—362no—
1123D3—722no—
1124D3#6389514yesdirect product factor
1125C22—32no—
1126C22—32no—
1127C22—32no—
1128C22—92no—
1129C22—181no—
1130C22—181no—
1131C22—272no—
1132C22—548no—
1133C22—541no—
1134C22—541no—
1135C22C2×D3311yescharacteristic
1136C4—21no—
1137C4—32no—
1138C4—61no—
1139C4—61no—
1140C4—61no—
1141C4—61no—
1142C4—92no—
1143C4—181no—
1144C4—181no—
1145C4—181no—
1146C4—181no—
1147C4—541no—
1148C3—21no—
1149C3—21no—
1150C3—21no—
1151C3—41no—
1152C3D3×#89611yescharacteristic, complemented
1153C3D3×#89711yescharacteristic, complemented
1154C3C2×#6389511yescharacteristic, complemented
1155C2—34no—
1156C2—182no—
1157C2—542no—
1158C2D3×#379711yescharacteristic
1159C2D32×D1211yescharacteristic
1160C2D3×#380411yescharacteristic
subgroupG/H
center, FrattiniC22C2×D33
commutator, socle, cosocleC22×C33C24
FittingC2×C33×C4C23
prime radicalC22×D3×C3⋊D3C22
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
5. #11723495C2semidirect
6. #11723485C2semidirect
7. C3×#63895C2semidirect
8. C3×D3×C4⋊Dic3C2semidirect
9. C3×D3×Dic3⋊C4C2semidirect
10. #11722984C2semidirect
11. #11722982C2semidirect
12. #11722973C2semidirect
13. #11722972C2semidirect
14. D3×Dic3⋊Dic3C2semidirect
21. C2×#6296C22semidirect
23. C2×#6293C22semidirect
24. C2×#6293C22semidirect
28. C2×C3×#627C22semidirect
38. C3×C4⋊(C3⋊Dic3)C22semidirect
39. C3×#3750C22semidirect
40. C32×C4⋊Dic3C22semidirect
41. C32×Dic3⋊C4C22semidirect
42. #88815C22semidirect
44. #88807C22semidirect
45. Dic3⋊(C3⋊Dic3)C22semidirect
50. C3×#3724C22semidirect
51. C3×Dic3⋊Dic3C22semidirect
52. C3×Dic3⋊Dic3C22semidirect
53. C3×Dic3⋊Dic3C22semidirect
54. C3×Dic3⋊Dic3C22semidirect
92. #63895D3direct (N × H)
96. D3×C4⋊Dic3D3semidirect
99. D3×Dic3⋊C4D3semidirect
109. C2×D3×C3⋊D3Q8semidirect
174. C2×#627C2×D3semidirect
212. C4⋊(C3⋊Dic3)C2×D3semidirect
214. #3750C2×D3semidirect
228. C3×C4⋊Dic3C2×D3semidirect
229. C3×C4⋊Dic3C2×D3semidirect
240. C3×Dic3⋊C4C2×D3semidirect
241. C3×Dic3⋊C4C2×D3semidirect
243. #3724C2×D3semidirect
252. Dic3⋊Dic3C2×D3semidirect
253. Dic3⋊Dic3C2×D3semidirect
254. Dic3⋊Dic3C2×D3semidirect
255. Dic3⋊Dic3C2×D3semidirect
275. C2×C3⋊(C3⋊D3)C2×Q8semidirect
278. C2×C3×C3⋊D3C2×Q8semidirect
478. C32×D3C22⋊Q8semidirect
595. C4⋊Dic3D32semidirect
611. Dic3⋊C4D32semidirect
646. C2×C3⋊D3D3×Q8semidirect
737. C33C2×C22⋊Q8semidirect
901. C3×D3#896semidirect
902. C3×D3#897semidirect
1054. C32C2×#896semidirect
1055. C32C2×#897semidirect
1056. C32D3×C22⋊Q8semidirect
1124. D3#63895direct (N × H)
1152. C3D3×#896semidirect
1153. C3D3×#897semidirect
1154. C3C2×#63895semidirect

Maximal subgroups

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

subgroupindex
C2×D3×#6272
C2×D3×#6242
#117236922
D3×#37522
#117234952
#117234852
C3×#638952
C3×D3×C4⋊Dic32
C3×D3×Dic3⋊C42
#117229842
#117229822
#117229732
#117229722
D3×Dic3⋊Dic32
D3×#37222
C2×#638953
D3×#8973
D3×#8963