Finite Group Databasebeta

← D3×#4657 #11808347

Subgroups — D3×#4657 #11808347

Order 1152.

1459 conjugacy classes of subgroups.

The subgroup lattice has 867 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
5#10592356C211yesmaximal, characteristic, complemented
6C3×D3×#95C211yesmaximal, characteristic
7C3×#4657C211yesmaximal, characteristic, complemented
8D3×C3⋊#95C211yesmaximal, characteristic
9D3×C3⋊#95C211yesmaximal, characteristic
10#10591356C211yesmaximal, characteristic, complemented
11#10591351C211yesmaximal, characteristic, complemented
12#10591345C211yesmaximal, characteristic, complemented
13#10591340C211yesmaximal, characteristic, complemented
14#10591339C211yesmaximal, characteristic, complemented
15#10591198C211yesmaximal, characteristic, complemented
16D3×#398—31nomaximal
17C2×#4657—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×C3×C4⋊Dic3C2211yescharacteristic
30C2×C3×Dic3⋊C4C2211yescharacteristic
31C2×C3×Dic3⋊C4C2211yescharacteristic
32C2×C3×Dic3⋊C4C2211yescharacteristic
33C2×#3724C2211yescharacteristic
34C2×#3724C2211yescharacteristic
35C2×#3724C2211yescharacteristic
36C2×Dic3⋊Dic3C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41D3×C4⋊Dic3—24no—
42D3×Dic3⋊C4—24no—
43D3×Dic3⋊C4—24no—
44D3×Dic3⋊C4—24no—
45C32×#95C2211yescharacteristic
46#63658C2211yescharacteristic
47#63658C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C22×C4⋊Dic3—31no—
58C22×Dic3⋊C4—31no—
59C22×Dic3⋊C4—31no—
60C22×Dic3⋊C4—31no—
61C2×D3×C4⋊C4—31no—
62C2×D3×C4⋊C4—31no—
63C2×D3×C4⋊C4—31no—
64C2×D3×C4⋊C4—31no—
65C3×#398—31no—
66C2×C3×#95—31no—
67C2×C3⋊#95—31no—
68C2×C3⋊#95—31no—
69#4983—31no—
70#4982—31no—
71#4982—31no—
72#4981—31no—
73D3×#95—31no—
74D3×#95—31no—
75D3×#95D311yescharacteristic
76#4661—31no—
77#4657—31no—
78#4657—31no—
79#4657—31no—
80#4657—31no—
81#4657—31no—
82#4657—31no—
83#4657—31no—
84#4657—31no—
85#4657—31no—
86#4657—61no—
87#4657D311yescharacteristic, direct product factor
88C23×C3×D3C2311yescharacteristic
89C22×C32×C4C2311yescharacteristic
90C22×C32×C4C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C3⋊Dic3C2311yescharacteristic
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
103C2×C3×C4×D3—22no—
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×D3Q814yes—
112C2×D3×Dic3—22no—
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×Dic3—22no—
121C2×D3×Dic3D414yes—
122C2×D3×Dic3D414yes—
123C2×D3×Dic3Q814yes—
124C4⋊(C3⋊Dic3)—22no—
125#3750—22no—
126#3750—22no—
127#3750—22no—
128C3×C4⋊Dic3—22no—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—22no—
131C3×Dic3⋊C4—22no—
132#3724—22no—
133#3724—22no—
134#3724—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3—22no—
139Dic3⋊Dic3—22no—
140C2×#398—91noSylow
141C23×C3×C4—31no—
142C23×C3×C4—31no—
143C23×C3×C4—31no—
144C23×Dic3—31no—
145C23×Dic3—31no—
146C23×Dic3—31no—
147C23×Dic3—31no—
148C22×C4×D3—31no—
149C22×C4×D3—31no—
150C22×C4×D3—31no—
151C22×C4×D3—31no—
152C22×C4×D3C2×D311yescharacteristic
153C22×C4×D3C2×D311yescharacteristic
154C22×C4×D3C2×D311yescharacteristic
155C2×C3×C4⋊C4—31no—
156C2×C3×C4⋊C4—31no—
157C2×C3×C4⋊C4—31no—
158C2×C3×C4⋊C4—31no—
159C2×C4⋊Dic3—31no—
160C2×C4⋊Dic3—31no—
161C2×C4⋊Dic3—31no—
162C2×C4⋊Dic3—31no—
163C2×C4⋊Dic3—31no—
164C2×C4⋊Dic3—31no—
165C2×C4⋊Dic3—31no—
166C2×C4⋊Dic3—61no—
167C2×C4⋊Dic3—64no—
168C2×C4⋊Dic3C2×D311yescharacteristic
169C2×Dic3⋊C4—31no—
170C2×Dic3⋊C4—31no—
171C2×Dic3⋊C4—31no—
172C2×Dic3⋊C4—31no—
173C2×Dic3⋊C4—31no—
174C2×Dic3⋊C4—31no—
175C2×Dic3⋊C4—31no—
176C2×Dic3⋊C4—31no—
177C2×Dic3⋊C4—31no—
178C2×Dic3⋊C4—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—31no—
185C2×Dic3⋊C4—31no—
186C2×Dic3⋊C4—61no—
187C2×Dic3⋊C4—61no—
188C2×Dic3⋊C4—61no—
189C2×Dic3⋊C4—64no—
190C2×Dic3⋊C4—64no—
191C2×Dic3⋊C4—64no—
192C2×Dic3⋊C4C2×D311yescharacteristic
193C2×Dic3⋊C4C2×D311yescharacteristic
194C2×Dic3⋊C4C2×D311yescharacteristic
195D3×C4⋊C4—64no—
196D3×C4⋊C4—64no—
197D3×C4⋊C4—64no—
198D3×C4⋊C4—64no—
199C3×#95—21no—
200C3×#95—31no—
201C3×#95—31no—
202C3×#95—31no—
203C3×#95—31no—
204C3×#95—31no—
205C3×#95C2×D311yescharacteristic
206C3×#95C2×D311yescharacteristic
207C3⋊#95—31no—
208C3⋊#95—31no—
209C3⋊#95—31no—
210C3⋊#95—31no—
211C3⋊#95—31no—
212C3⋊#95—31no—
213C3⋊#95—31no—
214C3⋊#95—31no—
215C3⋊#95—31no—
216C3⋊#95—31no—
217C3⋊#95—31no—
218C3⋊#95—31no—
219C3⋊#95—61no—
220C3⋊#95—61no—
221C3⋊#95C2×D311yescharacteristic
222C3⋊#95C2×D311yescharacteristic
223C3⋊#95C2×D311yescharacteristic
224C3⋊#95C2×D311yescharacteristic
225C3⋊#95C2×D311yescharacteristic
226C23×C32C2411yescharacteristic
227C22×C3×D3C2×D412yes—
228C22×C3×D3C2×D412yes—
229C22×C3×D3C2×Q812yes—
230C22×C3×D3C2×Q812yes—
231C22×C3×D3#4112yes—
232C22×C3×D3#4112yes—
233C22×C3×D3#4112yes—
234C2×C32×C4—21no—
235C2×C32×C4—21no—
236C2×C32×C4—21no—
237C2×C32×C4—21no—
238C2×C32×C4—21no—
239C2×C32×C4—21no—
240C2×C32×C4—21no—
241C2×C32×C4—21no—
242C2×C32×C4C2×Q812yes—
243C2×C3⋊Dic3—21no—
244C2×C3⋊Dic3—21no—
245C2×C3⋊Dic3—21no—
246C2×C3⋊Dic3—21no—
247C2×C3⋊Dic3—21no—
248C2×C3⋊Dic3—21no—
249C2×C3⋊Dic3—21no—
250C2×C3⋊Dic3—21no—
251C2×C3⋊Dic3—21no—
252C2×C3⋊Dic3C2×D412yes—
253C2×C3⋊Dic3C2×D412yes—
254C2×C3⋊Dic3C2×Q812yes—
255C2×C3×Dic3—21no—
256C2×C3×Dic3—21no—
257C2×C3×Dic3—21no—
258C2×C3×Dic3—21no—
259C2×C3×Dic3—21no—
260C2×C3×Dic3—21no—
261C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
273C2×C3×Dic3C2×D412yes—
274C2×C3×Dic3C2×Q812yes—
275C2×C3×Dic3C2×Q812yes—
276C3×C4×D3—28no—
277C3×C4×D3—44no—
278C3×C4×D3—44no—
279D3×Dic3—28no—
280D3×Dic3—28no—
281D3×Dic3—28no—
282D3×Dic3—44no—
283C22×C4⋊C4—91no—
284C22×C4⋊C4—91no—
285C22×C4⋊C4—91no—
286C22×C4⋊C4—91no—
287#398—31no—
288#398—91no—
289#398—91no—
290#398—91no—
291#398—91no—
292#398—91no—
293#398—91no—
294#398—91no—
295C2×#95—31no—
296C2×#95—91no—
297C2×#95—91no—
298C24×C3—31no—
299C23×D3C22×D311yescharacteristic
300C22×C3×C4—21no—
301C22×C3×C4—21no—
302C22×C3×C4—21no—
303C22×C3×C4—31no—
304C22×C3×C4—31no—
305C22×C3×C4—31no—
306C22×C3×C4—31no—
307C22×C3×C4—34no—
308C22×C3×C4—31no—
309C22×C3×C4—31no—
310C22×C3×C4—31no—
311C22×C3×C4—62no—
312C22×C3×C4—62no—
313C22×C3×C4—62no—
314C22×C3×C4—62no—
315C22×C3×C4—62no—
316C22×C3×C4—62no—
317C22×C3×C4—62no—
318C22×C3×C4—62no—
319C22×C3×C4C22×D311yescharacteristic
320C22×C3×C4C22×D311yescharacteristic
321C22×C3×C4C22×D311yescharacteristic
322C22×C3×C4C22×D311yescharacteristic
323C22×C3×C4C22×D311yescharacteristic
324C22×C3×C4C22×D311yescharacteristic
325C22×Dic3—31no—
326C22×Dic3—31no—
327C22×Dic3—31no—
328C22×Dic3—31no—
329C22×Dic3—31no—
330C22×Dic3—31no—
331C22×Dic3—34no—
332C22×Dic3—34no—
333C22×Dic3—34no—
334C22×Dic3—31no—
335C22×Dic3—31no—
336C22×Dic3—61no—
337C22×Dic3—61no—
338C22×Dic3—61no—
339C22×Dic3—61no—
340C22×Dic3—62no—
341C22×Dic3—62no—
342C22×Dic3—62no—
343C22×Dic3—62no—
344C22×Dic3—62no—
345C22×Dic3—62no—
346C22×Dic3—62no—
347C22×Dic3—62no—
348C22×Dic3—62no—
349C22×Dic3C22×D311yescharacteristic
350C22×Dic3C22×D311yescharacteristic
351C22×Dic3C22×D311yescharacteristic
352C22×Dic3C22×D311yescharacteristic
353C22×Dic3C22×D311yescharacteristic
354C22×Dic3C22×D311yescharacteristic
355C22×Dic3C22×D311yescharacteristic
356C2×C4×D3—22no—
357C2×C4×D3—22no—
358C2×C4×D3—22no—
359C2×C4×D3—22no—
360C2×C4×D3—22no—
361C2×C4×D3—22no—
362C2×C4×D3—22no—
363C2×C4×D3—22no—
364C2×C4×D3—34no—
365C2×C4×D3—34no—
366C2×C4×D3—34no—
367C2×C4×D3—62no—
368C2×C4×D3—62no—
369C2×C4×D3—62no—
370C2×C4×D3—62no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3Dic614yes—
377C3×C4⋊C4—62no—
378C3×C4⋊C4—62no—
379C3×C4⋊C4—62no—
380C3×C4⋊C4—62no—
381C4⋊Dic3—22no—
382C4⋊Dic3—62no—
383C4⋊Dic3—62no—
384C4⋊Dic3—62no—
385C4⋊Dic3—62no—
386C4⋊Dic3—62no—
387C4⋊Dic3—62no—
388C4⋊Dic3—62no—
389C4⋊Dic3—122no—
390Dic3⋊C4—22no—
391Dic3⋊C4—22no—
392Dic3⋊C4—22no—
393Dic3⋊C4—62no—
394Dic3⋊C4—62no—
395Dic3⋊C4—62no—
396Dic3⋊C4—62no—
397Dic3⋊C4—62no—
398Dic3⋊C4—62no—
399Dic3⋊C4—62no—
400Dic3⋊C4—62no—
401Dic3⋊C4—62no—
402Dic3⋊C4—62no—
403Dic3⋊C4—62no—
404Dic3⋊C4—62no—
405Dic3⋊C4—62no—
406Dic3⋊C4—62no—
407Dic3⋊C4—62no—
408Dic3⋊C4—62no—
409Dic3⋊C4—62no—
410Dic3⋊C4—122no—
411Dic3⋊C4—122no—
412Dic3⋊C4—122no—
413C22×C32C22×D411yescharacteristic
414C22×C32C22×D411yescharacteristic
415C22×C32C22×Q811yescharacteristic
416C22×C32C22×Q811yescharacteristic
417C22×C32C2×#4111yescharacteristic
418C22×C32C2×#4111yescharacteristic
419C22×C32C2×#4111yescharacteristic
420C2×C3×D3#12114yes—
421C2×C3×D3C22⋊Q814yes—
422C2×C3×D3C22⋊Q814yes—
423C2×C3×D3#12314yes—
424C2×C3×D3#12514yes—
425C2×C3×D3#12514yes—
426C2×C3×D3C4⋊Q814yes—
427C32×C4—22no—
428C32×C4—41no—
429C32×C4—41no—
430C3⋊Dic3—22no—
431C3⋊Dic3—22no—
432C3⋊Dic3—22no—
433C3⋊Dic3—41no—
434C3×Dic3—22no—
435C3×Dic3—22no—
436C3×Dic3—22no—
437C3×Dic3—22no—
438C3×Dic3—41no—
439C3×Dic3—41no—
440C3×Dic3—41no—
441C23×C4—31no—
442C23×C4—31no—
443C23×C4—31no—
444C23×C4—91no—
445C23×C4—91no—
446C23×C4—91no—
447C23×C4—91no—
448C2×C4⋊C4—31no—
449C2×C4⋊C4—31no—
450C2×C4⋊C4—31no—
451C2×C4⋊C4—31no—
452C2×C4⋊C4—91no—
453C2×C4⋊C4—91no—
454C2×C4⋊C4—91no—
455C2×C4⋊C4—91no—
456C2×C4⋊C4—91no—
457C2×C4⋊C4—91no—
458C2×C4⋊C4—91no—
459C2×C4⋊C4—91no—
460C2×C4⋊C4—91no—
461C2×C4⋊C4—91no—
462C2×C4⋊C4—91no—
463C2×C4⋊C4—91no—
464C2×C4⋊C4—184no—
465C2×C4⋊C4—184no—
466C2×C4⋊C4—184no—
467C2×C4⋊C4—184no—
468#95—31no—
469#95—31no—
470#95—31no—
471#95—31no—
472#95—31no—
473#95—91no—
474#95—91no—
475#95—91no—
476#95—91no—
477#95—91no—
478#95—91no—
479#95D3211yescharacteristic
480C23×C3—21no—
481C23×C3—32no—
482C23×C3—32no—
483C23×C3—32no—
484C23×C3—32no—
485C23×C3—32no—
486C23×C3—32no—
487C23×C3—32no—
488C23×C3C23×D311yescharacteristic
489C23×C3C23×D311yescharacteristic
490C22×D3C2×Dic612yes—
491C22×D3#23512yes—
492C22×D3#23512yes—
493C22×D3D3×D412yes—
494C22×D3D3×D412yes—
495C22×D3#23712yes—
496C22×D3D3×Q812yes—
497C2×C3×C4—21no—
498C2×C3×C4—21no—
499C2×C3×C4—21no—
500C2×C3×C4—21no—
501C2×C3×C4—21no—
502C2×C3×C4—21no—
503C2×C3×C4—21no—
504C2×C3×C4—21no—
505C2×C3×C4—21no—
506C2×C3×C4—21no—
507C2×C3×C4—21no—
508C2×C3×C4—21no—
509C2×C3×C4—21no—
510C2×C3×C4—21no—
511C2×C3×C4—21no—
512C2×C3×C4—21no—
513C2×C3×C4—22no—
514C2×C3×C4—32no—
515C2×C3×C4—32no—
516C2×C3×C4—32no—
517C2×C3×C4—32no—
518C2×C3×C4—41no—
519C2×C3×C4—41no—
520C2×C3×C4—41no—
521C2×C3×C4—41no—
522C2×C3×C4—41no—
523C2×C3×C4—41no—
524C2×C3×C4—41no—
525C2×C3×C4—41no—
526C2×C3×C4—68no—
527C2×C3×C4—61no—
528C2×C3×C4—61no—
529C2×C3×C4—61no—
530C2×C3×C4—61no—
531C2×C3×C4—61no—
532C2×C3×C4—61no—
533C2×C3×C4—61no—
534C2×C3×C4—61no—
535C2×C3×C4—61no—
536C2×C3×C4—61no—
537C2×C3×C4—61no—
538C2×C3×C4—61no—
539C2×C3×C4—61no—
540C2×C3×C4—61no—
541C2×C3×C4—61no—
542C2×C3×C4—61no—
543C2×C3×C4—61no—
544C2×C3×C4—124no—
545C2×C3×C4—124no—
546C2×C3×C4C2×Dic612yes—
547C2×C3×C4D3×Q812yes—
548C2×Dic3—21no—
549C2×Dic3—21no—
550C2×Dic3—21no—
551C2×Dic3—21no—
552C2×Dic3—21no—
553C2×Dic3—21no—
554C2×Dic3—21no—
555C2×Dic3—21no—
556C2×Dic3—21no—
557C2×Dic3—21no—
558C2×Dic3—21no—
559C2×Dic3—21no—
560C2×Dic3—21no—
561C2×Dic3—21no—
562C2×Dic3—21no—
563C2×Dic3—21no—
564C2×Dic3—21no—
565C2×Dic3—32no—
566C2×Dic3—32no—
567C2×Dic3—32no—
568C2×Dic3—32no—
569C2×Dic3—32no—
570C2×Dic3—32no—
571C2×Dic3—62no—
572C2×Dic3—62no—
573C2×Dic3—62no—
574C2×Dic3—68no—
575C2×Dic3—68no—
576C2×Dic3—68no—
577C2×Dic3—61no—
578C2×Dic3—61no—
579C2×Dic3—61no—
580C2×Dic3—61no—
581C2×Dic3—61no—
582C2×Dic3—61no—
583C2×Dic3—61no—
584C2×Dic3—61no—
585C2×Dic3—61no—
586C2×Dic3—61no—
587C2×Dic3—61no—
588C2×Dic3—61no—
589C2×Dic3—61no—
590C2×Dic3—61no—
591C2×Dic3—61no—
592C2×Dic3—61no—
593C2×Dic3—61no—
594C2×Dic3—61no—
595C2×Dic3—121no—
596C2×Dic3—121no—
597C2×Dic3—121no—
598C2×Dic3—121no—
599C2×Dic3—121no—
600C2×Dic3—121no—
601C2×Dic3—121no—
602C2×Dic3—121no—
603C2×Dic3—121no—
604C2×Dic3—124no—
605C2×Dic3C2×Dic612yes—
606C2×Dic3D3×D412yes—
607C2×Dic3D3×D412yes—
608C2×Dic3D3×Q812yes—
609C4×D3—28no—
610C4×D3—44no—
611C4×D3—44no—
612C4×D3—68no—
613C4×D3—68no—
614C4×D3—68no—
615C4×D3—124no—
616C2×C32C2×#12111yescharacteristic
617C2×C32C2×C22⋊Q811yescharacteristic
618C2×C32C2×C22⋊Q811yescharacteristic
619C2×C32C2×#12311yescharacteristic
620C2×C32C2×#12511yescharacteristic
621C2×C32C2×#12511yescharacteristic
622C2×C32C2×C4⋊Q811yescharacteristic
623C3×D3#39818yescomplemented
624C24—31no—
625C22×C4—31no—
626C22×C4—31no—
627C22×C4—31no—
628C22×C4—31no—
629C22×C4—34no—
630C22×C4—31no—
631C22×C4—31no—
632C22×C4—31no—
633C22×C4—62no—
634C22×C4—62no—
635C22×C4—62no—
636C22×C4—62no—
637C22×C4—62no—
638C22×C4—62no—
639C22×C4—62no—
640C22×C4—62no—
641C22×C4—94no—
642C22×C4—94no—
643C22×C4—94no—
644C22×C4—91no—
645C22×C4—91no—
646C22×C4—91no—
647C22×C4—91no—
648C22×C4—182no—
649C22×C4—182no—
650C22×C4—182no—
651C22×C4—182no—
652C22×C4—182no—
653C22×C4—182no—
654C22×C4—182no—
655C22×C4—182no—
656C22×C4—182no—
657C22×C4C2×D3211yescharacteristic
658C22×C4C2×D3211yescharacteristic
659C22×C4C2×D3211yescharacteristic
660C4⋊C4—62no—
661C4⋊C4—62no—
662C4⋊C4—62no—
663C4⋊C4—62no—
664C4⋊C4—182no—
665C4⋊C4—182no—
666C4⋊C4—182no—
667C4⋊C4—182no—
668C4⋊C4—182no—
669C4⋊C4—182no—
670C4⋊C4—182no—
671C4⋊C4—182no—
672C4⋊C4—182no—
673C4⋊C4—182no—
674C4⋊C4—182no—
675C4⋊C4—182no—
676C22×C3—21no—
677C22×C3—21no—
678C22×C3—21no—
679C22×C3—21no—
680C22×C3—21no—
681C22×C3—21no—
682C22×C3—21no—
683C22×C3—34no—
684C22×C3—34no—
685C22×C3—34no—
686C22×C3—34no—
687C22×C3—34no—
688C22×C3—34no—
689C22×C3—34no—
690C22×C3C22×Dic611yescharacteristic
691C22×C3C2×#23511yescharacteristic
692C22×C3C2×#23511yescharacteristic
693C22×C3C2×D3×D411yescharacteristic
694C22×C3C2×D3×D411yescharacteristic
695C22×C3C2×D3×D411yescharacteristic
696C22×C3C2×D3×D411yescharacteristic
697C22×C3C2×#23711yescharacteristic
698C22×C3C2×D3×Q811yescharacteristic
699C22×C3C2×D3×Q811yescharacteristic
700C22×C3C2×D3×Q811yescharacteristic
701C22×C3D3×#4111yescharacteristic
702C22×C3D3×#4111yescharacteristic
703C22×C3D3×#4111yescharacteristic
704C2×D3#87014yes—
705C2×D3#87814yes—
706C2×D3#88314yes—
707C2×D3#88414yes—
708C2×D3#88814yes—
709C2×D3#88914yes—
710C2×D3#89614yes—
711C3×C4—22no—
712C3×C4—22no—
713C3×C4—42no—
714C3×C4—41no—
715C3×C4—41no—
716C3×C4—41no—
717C3×C4—41no—
718C3×C4—62no—
719C3×C4—62no—
720C3×C4—62no—
721C3×C4—62no—
722C3×C4—81no—
723C3×C4—81no—
724C3×C4—121no—
725C3×C4—121no—
726C3×C4—121no—
727Dic3—22no—
728Dic3—22no—
729Dic3—22no—
730Dic3—22no—
731Dic3—41no—
732Dic3—41no—
733Dic3—41no—
734Dic3—62no—
735Dic3—62no—
736Dic3—62no—
737Dic3—62no—
738Dic3—62no—
739Dic3—62no—
740Dic3—122no—
741Dic3—122no—
742Dic3—122no—
743Dic3—121no—
744Dic3—121no—
745Dic3—241no—
746C32C2×#39811yescharacteristic, complemented, Sylow
747C23—32no—
748C23—32no—
749C23—32no—
750C23—32no—
751C23—32no—
752C23—32no—
753C23—32no—
754C23C22×D3211yescharacteristic
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—32no—
764C2×C4—32no—
765C2×C4—32no—
766C2×C4—32no—
767C2×C4—68no—
768C2×C4—61no—
769C2×C4—61no—
770C2×C4—61no—
771C2×C4—61no—
772C2×C4—61no—
773C2×C4—61no—
774C2×C4—61no—
775C2×C4—61no—
776C2×C4—61no—
777C2×C4—61no—
778C2×C4—61no—
779C2×C4—61no—
780C2×C4—61no—
781C2×C4—61no—
782C2×C4—61no—
783C2×C4—61no—
784C2×C4—61no—
785C2×C4—92no—
786C2×C4—92no—
787C2×C4—92no—
788C2×C4—124no—
789C2×C4—124no—
790C2×C4—188no—
791C2×C4—188no—
792C2×C4—188no—
793C2×C4—181no—
794C2×C4—181no—
795C2×C4—181no—
796C2×C4—181no—
797C2×C4—181no—
798C2×C4—181no—
799C2×C4—181no—
800C2×C4—181no—
801C2×C4—181no—
802C2×C4—364no—
803C2×C4D3×Dic612yes—
804C2×C3—21no—
805C2×C3—21no—
806C2×C3—21no—
807C2×C3—21no—
808C2×C3—21no—
809C2×C3—21no—
810C2×C3—21no—
811C2×C3—38no—
812C2×C3C2×#87011yescharacteristic
813C2×C3C2×#87811yescharacteristic
814C2×C3C2×#88311yescharacteristic
815C2×C3C2×#88411yescharacteristic
816C2×C3C2×#88811yescharacteristic
817C2×C3C2×#88911yescharacteristic
818C2×C3C2×#89611yescharacteristic
819C2×C3D3×#12111yescharacteristic
820C2×C3D3×C22⋊Q811yescharacteristic
821C2×C3D3×C22⋊Q811yescharacteristic
822C2×C3D3×#12311yescharacteristic
823C2×C3D3×#12511yescharacteristic
824C2×C3D3×#12511yescharacteristic
825C2×C3D3×C4⋊Q811yescharacteristic
826D3#465718yesdirect product factor
827C22—34no—
828C22—34no—
829C22—34no—
830C22—34no—
831C22—34no—
832C22—34no—
833C22—34no—
834C22C2×D3×Dic611yescharacteristic
835C22D3×#23511yescharacteristic
836C22D3×#23511yescharacteristic
837C22D32×D411yescharacteristic
838C22D32×D411yescharacteristic
839C22D3×#23711yescharacteristic
840C22D32×Q811yescharacteristic
841C4—22no—
842C4—41no—
843C4—41no—
844C4—62no—
845C4—62no—
846C4—62no—
847C4—62no—
848C4—121no—
849C4—121no—
850C4—121no—
851C4—182no—
852C4—182no—
853C4—182no—
854C4—361no—
855C3—21no—
856C3C2×#465711yescharacteristic, complemented
857C3D3×#39811yescharacteristic, complemented
858C2—38no—
859C2D3×#87011yescharacteristic
860C2D3×#87811yescharacteristic
861C2D3×#88311yescharacteristic
862C2D3×#88411yescharacteristic
863C2D3×#88811yescharacteristic
864C2D3×#88911yescharacteristic
865C2D3×#89611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32C2×#398
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
5. #10592356C2semidirect
7. C3×#4657C2semidirect
10. #10591356C2semidirect
11. #10591351C2semidirect
12. #10591345C2semidirect
13. #10591340C2semidirect
14. #10591339C2semidirect
15. #10591198C2semidirect
87. #4657D3direct (N × H)
623. C3×D3#398semidirect
746. C32C2×#398semidirect
826. D3#4657direct (N × H)
856. C3C2×#4657semidirect
857. C3D3×#398semidirect

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
#105923562
C3×D3×#952
C3×#46572
D3×C3⋊#952
#105913562
#105913512
#105913452
#105913402
#105913392
#105911982
D3×#3983
C2×#46573