Finite Group Databasebeta

← D3×#4647 #11801596

Subgroups — D3×#4647 #11801596

Order 1152.

1685 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D3×C4⋊Dic3C211yesmaximal, characteristic
2C2×D3×Dic3⋊C4C211yesmaximal, characteristic
3C2×D3×Dic3⋊C4C211yesmaximal, characteristic
4C2×D3×Dic3⋊C4C211yesmaximal, characteristic
5C2×C4×D3×Dic3C211yesmaximal, characteristic
6#10592346C211yesmaximal, characteristic, complemented
7C3×D3×#95C211yesmaximal, characteristic
8C3×#4647C211yesmaximal, characteristic, complemented
9D3×C3⋊#95C211yesmaximal, characteristic
10#10591328C211yesmaximal, characteristic, complemented
11#10591327C211yesmaximal, characteristic, complemented
12#10591268C211yesmaximal, characteristic, complemented
13#10591264C211yesmaximal, characteristic, complemented
14#10591256C211yesmaximal, characteristic, complemented
15#10591234C211yesmaximal, characteristic, complemented
16D3×#389—31nomaximal
17C2×#4647—31nomaximal
18C22×C3×C4×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
26C2×#3750C2211yescharacteristic
27C2×#3750C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C4×C3⋊Dic3C2211yescharacteristic
30C2×C3×C4⋊Dic3C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×C3×Dic3⋊C4C2211yescharacteristic
34C2×C3×C4×Dic3C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×Dic32C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45D3×C4⋊Dic3—24no—
46D3×Dic3⋊C4—24no—
47D3×Dic3⋊C4—24no—
48D3×Dic3⋊C4C418yescomplemented
49C4×D3×Dic3—24no—
50C32×#95C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54C3×C3⋊#95C2211yescharacteristic
55C3×C3⋊#95C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C22×C4⋊Dic3—31no—
59C22×Dic3⋊C4—31no—
60C22×Dic3⋊C4—31no—
61C22×Dic3⋊C4—31no—
62C22×C4×Dic3—31no—
63C2×D3×C4⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C2×D3×C4⋊C4—31no—
66C2×D3×C4⋊C4—31no—
67C2×C42×D3—31no—
68C3×#389—31no—
69C2×C3×#95—31no—
70C2×C3⋊#95—31no—
71#4984—31no—
72#4976—31no—
73#4976—31no—
74#4972—31no—
75#4928—31no—
76D3×#95—31no—
77D3×#95D311yescharacteristic
78#4647—31no—
79#4647—31no—
80#4647—31no—
81#4647—31no—
82#4647—31no—
83#4647—31no—
84#4647—31no—
85#4647—31no—
86#4647—31no—
87#4647—61no—
88#4647D311yescharacteristic, direct product factor
89C23×C3×D3C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3×Dic3C2311yescharacteristic
98C22×C3×Dic3C2311yescharacteristic
99C22×C3×Dic3C2311yescharacteristic
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C2×C3×C4×D3—22no—
105C2×C3×C4×D3—22no—
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3C2×C414yes—
112C2×C3×C4×D3Q814yes—
113C2×D3×Dic3—22no—
114C2×D3×Dic3—22no—
115C2×D3×Dic3—22no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3C2×C414yes—
121C2×D3×Dic3C2×C414yes—
122C2×D3×Dic3D414yes—
123C2×D3×Dic3D414yes—
124C2×D3×Dic3Q814yes—
125C4⋊(C3⋊Dic3)—22no—
126#3750—22no—
127#3750—22no—
128#3750C2×C414yescomplemented
129C4×C3⋊Dic3—22no—
130C3×C4⋊Dic3—22no—
131C3×Dic3⋊C4—22no—
132C3×Dic3⋊C4—22no—
133C3×Dic3⋊C4C2×C414yescomplemented
134C3×C4×Dic3—22no—
135#3724—22no—
136#3724—22no—
137#3724C2×C414yescomplemented
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140Dic3⋊Dic3—22no—
141Dic3⋊Dic3—22no—
142Dic3⋊Dic3C2×C414yescomplemented
143Dic32—22no—
144Dic32—22no—
145C2×#389—91noSylow
146C23×C3×C4—31no—
147C23×C3×C4—31no—
148C23×C3×C4—31no—
149C23×Dic3—31no—
150C23×Dic3—31no—
151C23×Dic3—31no—
152C23×Dic3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3C2×D311yescharacteristic
158C22×C4×D3C2×D311yescharacteristic
159C22×C4×D3C2×D311yescharacteristic
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C42—31no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—31no—
167C2×C4⋊Dic3—31no—
168C2×C4⋊Dic3—31no—
169C2×C4⋊Dic3—31no—
170C2×C4⋊Dic3—31no—
171C2×C4⋊Dic3—31no—
172C2×C4⋊Dic3—61no—
173C2×C4⋊Dic3—64no—
174C2×C4⋊Dic3C2×D311yescharacteristic
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—38no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—31no—
187C2×Dic3⋊C4—31no—
188C2×Dic3⋊C4—31no—
189C2×Dic3⋊C4—31no—
190C2×Dic3⋊C4—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—61no—
194C2×Dic3⋊C4—61no—
195C2×Dic3⋊C4—61no—
196C2×Dic3⋊C4—64no—
197C2×Dic3⋊C4—64no—
198C2×Dic3⋊C4C2×D311yescharacteristic
199C2×Dic3⋊C4C2×D311yescharacteristic
200C2×Dic3⋊C4C2×D311yescharacteristic
201C2×C4×Dic3—31no—
202C2×C4×Dic3—31no—
203C2×C4×Dic3—31no—
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206C2×C4×Dic3—31no—
207C2×C4×Dic3—61no—
208C2×C4×Dic3—64no—
209C2×C4×Dic3C2×D311yescharacteristic
210D3×C4⋊C4—38no—
211D3×C4⋊C4—64no—
212D3×C4⋊C4—64no—
213D3×C4⋊C4—64no—
214C42×D3—64no—
215C3×#95—21no—
216C3×#95—31no—
217C3×#95—31no—
218C3×#95—31no—
219C3×#95—31no—
220C3×#95C2×D311yescharacteristic
221C3×#95C2×D311yescharacteristic
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—61no—
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C3⋊#95C2×D311yescharacteristic
232C3⋊#95C2×D311yescharacteristic
233C23×C32C2411yescharacteristic
234C22×C3×D3C22×C412yes—
235C22×C3×D3C2×D412yes—
236C22×C3×D3C2×D412yes—
237C22×C3×D3C2×Q812yes—
238C22×C3×D3C2×Q812yes—
239C22×C3×D3#4112yes—
240C22×C3×D3#4112yes—
241C2×C32×C4—21no—
242C2×C32×C4—21no—
243C2×C32×C4—21no—
244C2×C32×C4—21no—
245C2×C32×C4—21no—
246C2×C32×C4—21no—
247C2×C32×C4—21no—
248C2×C32×C4C22×C412yes—
249C2×C32×C4C2×Q812yes—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3—21no—
253C2×C3⋊Dic3—21no—
254C2×C3⋊Dic3—21no—
255C2×C3⋊Dic3—21no—
256C2×C3⋊Dic3—21no—
257C2×C3⋊Dic3C22×C412yes—
258C2×C3⋊Dic3C22×C412yes—
259C2×C3⋊Dic3C2×D412yes—
260C2×C3⋊Dic3C2×D412yes—
261C2×C3⋊Dic3C2×Q812yes—
262C2×C3×Dic3—21no—
263C2×C3×Dic3—21no—
264C2×C3×Dic3—21no—
265C2×C3×Dic3—21no—
266C2×C3×Dic3—21no—
267C2×C3×Dic3—21no—
268C2×C3×Dic3—21no—
269C2×C3×Dic3—21no—
270C2×C3×Dic3—21no—
271C2×C3×Dic3—21no—
272C2×C3×Dic3—21no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3C22×C412yes—
277C2×C3×Dic3C22×C412yes—
278C2×C3×Dic3C22×C412yes—
279C2×C3×Dic3C2×D412yes—
280C2×C3×Dic3C2×D412yes—
281C2×C3×Dic3C2×Q812yes—
282C2×C3×Dic3C2×Q812yes—
283C3×C4×D3—28no—
284C3×C4×D3—28no—
285C3×C4×D3—44no—
286D3×Dic3—28no—
287D3×Dic3—28no—
288D3×Dic3—44no—
289D3×Dic3C4⋊C4116yescomplemented
290C22×C4⋊C4—91no—
291C22×C4⋊C4—91no—
292C22×C4⋊C4—91no—
293C22×C4⋊C4—91no—
294C22×C42—91no—
295#389—31no—
296#389—91no—
297#389—91no—
298#389—91no—
299#389—91no—
300#389—91no—
301#389—91no—
302#389—91no—
303C2×#95—31no—
304C2×#95—91no—
305C24×C3—31no—
306C23×D3C22×D311yescharacteristic
307C22×C3×C4—21no—
308C22×C3×C4—21no—
309C22×C3×C4—21no—
310C22×C3×C4—31no—
311C22×C3×C4—31no—
312C22×C3×C4—31no—
313C22×C3×C4—31no—
314C22×C3×C4—31no—
315C22×C3×C4—34no—
316C22×C3×C4—34no—
317C22×C3×C4—31no—
318C22×C3×C4—31no—
319C22×C3×C4—62no—
320C22×C3×C4—62no—
321C22×C3×C4—62no—
322C22×C3×C4—62no—
323C22×C3×C4—62no—
324C22×C3×C4—62no—
325C22×C3×C4—62no—
326C22×C3×C4C22×D311yescharacteristic
327C22×C3×C4C22×D311yescharacteristic
328C22×C3×C4C22×D311yescharacteristic
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×Dic3—31no—
333C22×Dic3—31no—
334C22×Dic3—34no—
335C22×Dic3—34no—
336C22×Dic3—34no—
337C22×Dic3—31no—
338C22×Dic3—31no—
339C22×Dic3—31no—
340C22×Dic3—31no—
341C22×Dic3—34no—
342C22×Dic3—34no—
343C22×Dic3—31no—
344C22×Dic3—31no—
345C22×Dic3—61no—
346C22×Dic3—61no—
347C22×Dic3—61no—
348C22×Dic3—61no—
349C22×Dic3—62no—
350C22×Dic3—62no—
351C22×Dic3—62no—
352C22×Dic3—62no—
353C22×Dic3—62no—
354C22×Dic3—62no—
355C22×Dic3—62no—
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C22×Dic3C22×D311yescharacteristic
363C2×C4×D3—22no—
364C2×C4×D3—22no—
365C2×C4×D3—22no—
366C2×C4×D3—22no—
367C2×C4×D3—22no—
368C2×C4×D3—22no—
369C2×C4×D3—22no—
370C2×C4×D3—34no—
371C2×C4×D3—34no—
372C2×C4×D3—34no—
373C2×C4×D3—34no—
374C2×C4×D3—34no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3Dic614yes—
383C2×C4×D3C4×D314yes—
384C3×C4⋊C4—34no—
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C4⋊C4—62no—
388C3×C42—62no—
389C4⋊Dic3—22no—
390C4⋊Dic3—34no—
391C4⋊Dic3—62no—
392C4⋊Dic3—62no—
393C4⋊Dic3—62no—
394C4⋊Dic3—62no—
395C4⋊Dic3—62no—
396C4⋊Dic3—62no—
397C4⋊Dic3—122no—
398Dic3⋊C4—22no—
399Dic3⋊C4—22no—
400Dic3⋊C4—34no—
401Dic3⋊C4—34no—
402Dic3⋊C4—34no—
403Dic3⋊C4—34no—
404Dic3⋊C4—34no—
405Dic3⋊C4—64no—
406Dic3⋊C4—62no—
407Dic3⋊C4—62no—
408Dic3⋊C4—62no—
409Dic3⋊C4—62no—
410Dic3⋊C4—62no—
411Dic3⋊C4—62no—
412Dic3⋊C4—62no—
413Dic3⋊C4—62no—
414Dic3⋊C4—62no—
415Dic3⋊C4—62no—
416Dic3⋊C4—62no—
417Dic3⋊C4—62no—
418Dic3⋊C4—122no—
419Dic3⋊C4—122no—
420Dic3⋊C4C4×D314yescomplemented
421C4×Dic3—22no—
422C4×Dic3—62no—
423C4×Dic3—62no—
424C4×Dic3—62no—
425C4×Dic3—62no—
426C4×Dic3—62no—
427C4×Dic3—62no—
428C4×Dic3—122no—
429C22×C32C23×C411yescharacteristic
430C22×C32C22×D411yescharacteristic
431C22×C32C22×D411yescharacteristic
432C22×C32C22×Q811yescharacteristic
433C22×C32C22×Q811yescharacteristic
434C22×C32C2×#4111yescharacteristic
435C22×C32C2×#4111yescharacteristic
436C2×C3×D3C2×C4⋊C414yes—
437C2×C3×D3C4×D414yes—
438C2×C3×D3C4×Q814yes—
439C2×C3×D3#12114yes—
440C2×C3×D3C22⋊Q814yes—
441C2×C3×D3#12514yes—
442C2×C3×D3C4⋊Q814yes—
443C32×C4—22no—
444C32×C4—22no—
445C32×C4—41no—
446C3⋊Dic3—22no—
447C3⋊Dic3—22no—
448C3⋊Dic3—41no—
449C3⋊Dic3C2×C4⋊C414yescomplemented
450C3×Dic3—22no—
451C3×Dic3—22no—
452C3×Dic3—22no—
453C3×Dic3—22no—
454C3×Dic3—41no—
455C3×Dic3—41no—
456C3×Dic3C2×C4⋊C414yescomplemented
457C23×C4—31no—
458C23×C4—31no—
459C23×C4—31no—
460C23×C4—91no—
461C23×C4—91no—
462C23×C4—91no—
463C23×C4—91no—
464C2×C4⋊C4—31no—
465C2×C4⋊C4—31no—
466C2×C4⋊C4—31no—
467C2×C4⋊C4—31no—
468C2×C4⋊C4—98no—
469C2×C4⋊C4—91no—
470C2×C4⋊C4—91no—
471C2×C4⋊C4—91no—
472C2×C4⋊C4—91no—
473C2×C4⋊C4—91no—
474C2×C4⋊C4—91no—
475C2×C4⋊C4—91no—
476C2×C4⋊C4—91no—
477C2×C4⋊C4—91no—
478C2×C4⋊C4—91no—
479C2×C4⋊C4—91no—
480C2×C4⋊C4—91no—
481C2×C4⋊C4—184no—
482C2×C4⋊C4—184no—
483C2×C4⋊C4—184no—
484C2×C42—31no—
485C2×C42—91no—
486C2×C42—91no—
487C2×C42—91no—
488C2×C42—184no—
489#95—31no—
490#95—31no—
491#95—31no—
492#95—31no—
493#95—91no—
494#95—91no—
495#95—91no—
496#95D3211yescharacteristic
497C23×C3—21no—
498C23×C3—32no—
499C23×C3—32no—
500C23×C3—32no—
501C23×C3—32no—
502C23×C3—32no—
503C23×C3—32no—
504C23×C3—32no—
505C23×C3C23×D311yescharacteristic
506C23×C3C23×D311yescharacteristic
507C22×D3C2×Dic612yes—
508C22×D3C2×C4×D312yes—
509C22×D3#23512yes—
510C22×D3D3×D412yes—
511C22×D3D3×D412yes—
512C22×D3#23712yes—
513C22×D3D3×Q812yes—
514C2×C3×C4—21no—
515C2×C3×C4—21no—
516C2×C3×C4—21no—
517C2×C3×C4—21no—
518C2×C3×C4—21no—
519C2×C3×C4—21no—
520C2×C3×C4—21no—
521C2×C3×C4—21no—
522C2×C3×C4—21no—
523C2×C3×C4—21no—
524C2×C3×C4—21no—
525C2×C3×C4—21no—
526C2×C3×C4—21no—
527C2×C3×C4—21no—
528C2×C3×C4—22no—
529C2×C3×C4—22no—
530C2×C3×C4—32no—
531C2×C3×C4—32no—
532C2×C3×C4—32no—
533C2×C3×C4—32no—
534C2×C3×C4—32no—
535C2×C3×C4—32no—
536C2×C3×C4—32no—
537C2×C3×C4—41no—
538C2×C3×C4—41no—
539C2×C3×C4—41no—
540C2×C3×C4—41no—
541C2×C3×C4—41no—
542C2×C3×C4—41no—
543C2×C3×C4—41no—
544C2×C3×C4—68no—
545C2×C3×C4—68no—
546C2×C3×C4—61no—
547C2×C3×C4—61no—
548C2×C3×C4—61no—
549C2×C3×C4—61no—
550C2×C3×C4—61no—
551C2×C3×C4—61no—
552C2×C3×C4—61no—
553C2×C3×C4—61no—
554C2×C3×C4—61no—
555C2×C3×C4—61no—
556C2×C3×C4—61no—
557C2×C3×C4—61no—
558C2×C3×C4—61no—
559C2×C3×C4—61no—
560C2×C3×C4—124no—
561C2×C3×C4C2×Dic612yes—
562C2×C3×C4C2×C4×D312yes—
563C2×C3×C4C2×C4×D312yes—
564C2×C3×C4D3×Q812yes—
565C2×Dic3—21no—
566C2×Dic3—21no—
567C2×Dic3—21no—
568C2×Dic3—21no—
569C2×Dic3—21no—
570C2×Dic3—21no—
571C2×Dic3—21no—
572C2×Dic3—21no—
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—32no—
580C2×Dic3—32no—
581C2×Dic3—32no—
582C2×Dic3—32no—
583C2×Dic3—32no—
584C2×Dic3—32no—
585C2×Dic3—316no—
586C2×Dic3—32no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—62no—
591C2×Dic3—62no—
592C2×Dic3—62no—
593C2×Dic3—62no—
594C2×Dic3—62no—
595C2×Dic3—68no—
596C2×Dic3—68no—
597C2×Dic3—61no—
598C2×Dic3—61no—
599C2×Dic3—61no—
600C2×Dic3—61no—
601C2×Dic3—61no—
602C2×Dic3—61no—
603C2×Dic3—61no—
604C2×Dic3—61no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—121no—
612C2×Dic3—121no—
613C2×Dic3—121no—
614C2×Dic3—121no—
615C2×Dic3—121no—
616C2×Dic3—121no—
617C2×Dic3—121no—
618C2×Dic3—124no—
619C2×Dic3C2×Dic612yes—
620C2×Dic3C2×C4×D312yes—
621C2×Dic3C2×C4×D312yes—
622C2×Dic3C2×C4×D312yes—
623C2×Dic3D3×D412yes—
624C2×Dic3D3×D412yes—
625C2×Dic3D3×Q812yes—
626C4×D3—28no—
627C4×D3—28no—
628C4×D3—316no—
629C4×D3—44no—
630C4×D3—68no—
631C4×D3—68no—
632C4×D3—124no—
633C2×C32C22×C4⋊C411yescharacteristic
634C2×C32C2×C4×D411yescharacteristic
635C2×C32C2×C4×Q811yescharacteristic
636C2×C32C2×#12111yescharacteristic
637C2×C32C2×C22⋊Q811yescharacteristic
638C2×C32C2×#12511yescharacteristic
639C2×C32C2×C4⋊Q811yescharacteristic
640C3×D3#38918yescomplemented
641C24—31no—
642C22×C4—31no—
643C22×C4—31no—
644C22×C4—31no—
645C22×C4—31no—
646C22×C4—31no—
647C22×C4—34no—
648C22×C4—34no—
649C22×C4—31no—
650C22×C4—31no—
651C22×C4—62no—
652C22×C4—62no—
653C22×C4—62no—
654C22×C4—62no—
655C22×C4—62no—
656C22×C4—62no—
657C22×C4—62no—
658C22×C4—94no—
659C22×C4—94no—
660C22×C4—94no—
661C22×C4—94no—
662C22×C4—94no—
663C22×C4—91no—
664C22×C4—91no—
665C22×C4—91no—
666C22×C4—91no—
667C22×C4—182no—
668C22×C4—182no—
669C22×C4—182no—
670C22×C4—182no—
671C22×C4—182no—
672C22×C4—182no—
673C22×C4—182no—
674C22×C4C2×D3211yescharacteristic
675C22×C4C2×D3211yescharacteristic
676C22×C4C2×D3211yescharacteristic
677C4⋊C4—34no—
678C4⋊C4—62no—
679C4⋊C4—62no—
680C4⋊C4—62no—
681C4⋊C4—94no—
682C4⋊C4—94no—
683C4⋊C4—94no—
684C4⋊C4—182no—
685C4⋊C4—182no—
686C4⋊C4—182no—
687C4⋊C4—182no—
688C4⋊C4—182no—
689C4⋊C4—182no—
690C4⋊C4—182no—
691C4⋊C4—182no—
692C4⋊C4—182no—
693C42—62no—
694C42—182no—
695C42—182no—
696C42—182no—
697C22×C3—21no—
698C22×C3—21no—
699C22×C3—21no—
700C22×C3—21no—
701C22×C3—21no—
702C22×C3—21no—
703C22×C3—21no—
704C22×C3—34no—
705C22×C3—34no—
706C22×C3—34no—
707C22×C3—34no—
708C22×C3—34no—
709C22×C3—34no—
710C22×C3—34no—
711C22×C3C22×Dic611yescharacteristic
712C22×C3C22×C4×D311yescharacteristic
713C22×C3C22×C4×D311yescharacteristic
714C22×C3C2×#23511yescharacteristic
715C22×C3C2×D3×D411yescharacteristic
716C22×C3C2×D3×D411yescharacteristic
717C22×C3C2×D3×D411yescharacteristic
718C22×C3C2×D3×D411yescharacteristic
719C22×C3C2×#23711yescharacteristic
720C22×C3C2×D3×Q811yescharacteristic
721C22×C3C2×D3×Q811yescharacteristic
722C22×C3C2×D3×Q811yescharacteristic
723C22×C3D3×#4111yescharacteristic
724C22×C3D3×#4111yescharacteristic
725C2×D3C4×Dic614yes—
726C2×D3#87814yes—
727C2×D3#67⋊C414yes—
728C2×D3#88414yes—
729C2×D3#88814yes—
730C2×D3#88914yes—
731C2×D3D3×C4⋊C414yes—
732C3×C4—22no—
733C3×C4—22no—
734C3×C4—22no—
735C3×C4—22no—
736C3×C4—34no—
737C3×C4—42no—
738C3×C4—42no—
739C3×C4—41no—
740C3×C4—41no—
741C3×C4—62no—
742C3×C4—62no—
743C3×C4—62no—
744C3×C4—62no—
745C3×C4—81no—
746C3×C4—121no—
747C3×C4—121no—
748Dic3—22no—
749Dic3—22no—
750Dic3—22no—
751Dic3—22no—
752Dic3—34no—
753Dic3—34no—
754Dic3—41no—
755Dic3—41no—
756Dic3—64no—
757Dic3—62no—
758Dic3—62no—
759Dic3—62no—
760Dic3—62no—
761Dic3—122no—
762Dic3—122no—
763Dic3—121no—
764Dic3—121no—
765Dic3—241no—
766Dic3D3×C4⋊C414yescomplemented
767C32C2×#38911yescharacteristic, complemented, Sylow
768C23—32no—
769C23—32no—
770C23—32no—
771C23—32no—
772C23—32no—
773C23—32no—
774C23—32no—
775C23C22×D3211yescharacteristic
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—32no—
784C2×C4—32no—
785C2×C4—32no—
786C2×C4—32no—
787C2×C4—32no—
788C2×C4—32no—
789C2×C4—32no—
790C2×C4—68no—
791C2×C4—68no—
792C2×C4—61no—
793C2×C4—61no—
794C2×C4—61no—
795C2×C4—61no—
796C2×C4—61no—
797C2×C4—61no—
798C2×C4—61no—
799C2×C4—61no—
800C2×C4—61no—
801C2×C4—61no—
802C2×C4—61no—
803C2×C4—61no—
804C2×C4—61no—
805C2×C4—61no—
806C2×C4—916no—
807C2×C4—92no—
808C2×C4—92no—
809C2×C4—92no—
810C2×C4—92no—
811C2×C4—92no—
812C2×C4—124no—
813C2×C4—188no—
814C2×C4—188no—
815C2×C4—181no—
816C2×C4—181no—
817C2×C4—181no—
818C2×C4—181no—
819C2×C4—181no—
820C2×C4—181no—
821C2×C4—181no—
822C2×C4—364no—
823C2×C4D3×Dic612yes—
824C2×C4C4×D3212yes—
825C2×C3—21no—
826C2×C3—21no—
827C2×C3—21no—
828C2×C3—21no—
829C2×C3—21no—
830C2×C3—21no—
831C2×C3—21no—
832C2×C3—38no—
833C2×C3C2×C4×Dic611yescharacteristic
834C2×C3C2×#87811yescharacteristic
835C2×C3C2×#67⋊C411yescharacteristic
836C2×C3C2×#88411yescharacteristic
837C2×C3C2×#88811yescharacteristic
838C2×C3C2×#88911yescharacteristic
839C2×C3C2×D3×C4⋊C411yescharacteristic
840C2×C3C2×D3×C4⋊C411yescharacteristic
841C2×C3C4×D3×D411yescharacteristic
842C2×C3C4×D3×Q811yescharacteristic
843C2×C3D3×#12111yescharacteristic
844C2×C3D3×C22⋊Q811yescharacteristic
845C2×C3D3×#12511yescharacteristic
846C2×C3D3×C4⋊Q811yescharacteristic
847D3#464718yesdirect product factor
848C22—34no—
849C22—34no—
850C22—34no—
851C22—34no—
852C22—34no—
853C22—34no—
854C22—34no—
855C22C2×D3×Dic611yescharacteristic
856C22C2×C4×D3211yescharacteristic
857C22D3×#23511yescharacteristic
858C22D32×D411yescharacteristic
859C22D32×D411yescharacteristic
860C22D3×#23711yescharacteristic
861C22D32×Q811yescharacteristic
862C4—22no—
863C4—22no—
864C4—34no—
865C4—41no—
866C4—62no—
867C4—62no—
868C4—62no—
869C4—62no—
870C4—94no—
871C4—121no—
872C4—121no—
873C4—182no—
874C4—182no—
875C4—361no—
876C3—21no—
877C3C2×#464711yescharacteristic, complemented
878C3D3×#38911yescharacteristic, complemented
879C2—38no—
880C2C4×D3×Dic611yescharacteristic
881C2D3×#87811yescharacteristic
882C2D3×#67⋊C411yescharacteristic
883C2D3×#88411yescharacteristic
884C2D3×#88811yescharacteristic
885C2D3×#88911yescharacteristic
886C2D32×C4⋊C411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32C2×#389
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
6. #10592346C2semidirect
8. C3×#4647C2semidirect
10. #10591328C2semidirect
11. #10591327C2semidirect
12. #10591268C2semidirect
13. #10591264C2semidirect
14. #10591256C2semidirect
15. #10591234C2semidirect
48. D3×Dic3⋊C4C4semidirect
88. #4647D3direct (N × H)
128. #3750C2×C4semidirect
133. C3×Dic3⋊C4C2×C4semidirect
137. #3724C2×C4semidirect
142. Dic3⋊Dic3C2×C4semidirect
289. D3×Dic3C4⋊C4semidirect
420. Dic3⋊C4C4×D3semidirect
449. C3⋊Dic3C2×C4⋊C4semidirect
456. C3×Dic3C2×C4⋊C4semidirect
640. C3×D3#389semidirect
766. Dic3D3×C4⋊C4semidirect
767. C32C2×#389semidirect
847. D3#4647direct (N × H)
877. C3C2×#4647semidirect
878. C3D3×#389semidirect

Maximal subgroups

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

subgroupindex
C2×D3×C4⋊Dic32
C2×D3×Dic3⋊C42
C2×C4×D3×Dic32
#105923462
C3×D3×#952
C3×#46472
D3×C3⋊#952
#105913282
#105913272
#105912682
#105912642
#105912562
#105912342
D3×#3893
C2×#46473