Finite Group Databasebeta

← D3×#4646 #11801721

Subgroups — D3×#4646 #11801721

Order 1152.

1949 conjugacy classes of subgroups.

The subgroup lattice has 909 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D3×Dic6C211yesmaximal, characteristic
2C2×D3×Dic3⋊C4C211yesmaximal, characteristic
3C2×C4×D3×Dic3C211yesmaximal, characteristic
4#10592345C211yesmaximal, characteristic, complemented
5C3×D3×#95C211yesmaximal, characteristic
6C3×#4646C211yesmaximal, characteristic, complemented
7#10591396C211yesmaximal, characteristic, complemented
8D3×C3⋊#95C211yesmaximal, characteristic
9D3×C3⋊#95C211yesmaximal, characteristic
10D3×C3⋊#95C211yesmaximal, characteristic
11#10591273C211yesmaximal, characteristic, complemented
12#10591261C211yesmaximal, characteristic, complemented
13#10591236C211yesmaximal, characteristic, complemented
14#10591235C211yesmaximal, characteristic, complemented
15#10591191C211yesmaximal, characteristic, complemented
16D3×#391—31nomaximal
17C2×#4646—31nomaximal
18C22×#634C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×Dic6C2211yescharacteristic
23C22×#627C2211yescharacteristic
24C22×#627C2211yescharacteristic
25C22×D3×Dic3C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×D3×Dic6—24no—
30C2×D3×Dic6—24no—
31C2×D3×Dic6C418yescomplemented
32C2×#3750C2211yescharacteristic
33C2×C4×C3⋊Dic3C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×C4×Dic3C2211yescharacteristic
36C2×#3724C2211yescharacteristic
37C2×Dic3⋊Dic3C2211yescharacteristic
38C2×Dic32C2211yescharacteristic
39C2×Dic32C2211yescharacteristic
40D3×Dic3⋊C4—24no—
41C4×D3×Dic3—24no—
42C32×#95C2211yescharacteristic
43#63658C2211yescharacteristic
44#63658C2211yescharacteristic
45#63658C2211yescharacteristic
46C3×C3⋊#95C2211yescharacteristic
47C3×C3⋊#95C2211yescharacteristic
48C3×C3⋊#95C2211yescharacteristic
49C3×C3⋊#95C2211yescharacteristic
50C3×C3⋊#95C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52#63579C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57#63579C2211yescharacteristic
58C22×D3×Q8—31no—
59C23×Dic6—31no—
60C22×Dic3⋊C4—31no—
61C22×C4×Dic3—31no—
62C2×D3×C4⋊C4—31no—
63C2×C42×D3—31no—
64C3×#391—31no—
65C2×C3×#95—31no—
66#5229—31no—
67C2×C3⋊#95—31no—
68C2×C3⋊#95—31no—
69C2×C3⋊#95—31no—
70#4973—31no—
71#4929—31no—
72D3×#95—31no—
73D3×#95—31no—
74D3×#95—31no—
75D3×#95D311yescharacteristic
76#4646—31no—
77#4646—31no—
78#4646—31no—
79#4646—31no—
80#4646—31no—
81#4646—31no—
82#4646—31no—
83#4646—31no—
84#4646—31no—
85#4646—31no—
86#4646—31no—
87#4646—61no—
88#4646D311yescharacteristic, 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
97C2×#634—22no—
98C2×#634—22no—
99C2×#634C2×C414yescomplemented
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—22no—
109C2×C3×C4×D3—22no—
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3C2×C414yes—
115C2×C3×C4×D3Q814yescomplemented
116C2×C3×Dic6—22no—
117C2×C3×Dic6—22no—
118C2×C3×Dic6C2×C414yescomplemented
119C2×#627—22no—
120C2×#627—22no—
121C2×#627—22no—
122C2×#627—22no—
123C2×#627C2×C414yescomplemented
124C2×#627C2×C414yescomplemented
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3—22no—
128C2×D3×Dic3—22no—
129C2×D3×Dic3—22no—
130C2×D3×Dic3—22no—
131C2×D3×Dic3—22no—
132C2×D3×Dic3C2×C414yes—
133C2×D3×Dic3C2×C414yes—
134C2×D3×Dic3D414yes—
135C2×D3×Dic3D414yes—
136C2×D3×Dic3Q814yescomplemented
137D3×Dic6—232no—
138#3750—22no—
139C4×C3⋊Dic3—22no—
140C3×Dic3⋊C4—22no—
141C3×C4×Dic3—22no—
142#3724—22no—
143Dic3⋊Dic3—22no—
144Dic32—22no—
145Dic32—22no—
146C2×#391—91noSylow
147C22×C3×Q8—31no—
148C23×C3×C4—31no—
149C23×C3×C4—31no—
150C23×C3×C4—31no—
151C23×Dic3—31no—
152C23×Dic3—31no—
153C23×Dic3—31no—
154C23×Dic3—31no—
155C2×D3×Q8—38no—
156C2×D3×Q8—64no—
157C2×D3×Q8—64no—
158C22×C4×D3—31no—
159C22×C4×D3—31no—
160C22×C4×D3—31no—
161C22×C4×D3—31no—
162C22×C4×D3C2×D311yescharacteristic
163C22×C4×D3C2×D311yescharacteristic
164C22×C4×D3C2×D311yescharacteristic
165C22×Dic6—31no—
166C22×Dic6—31no—
167C22×Dic6—31no—
168C22×Dic6—31no—
169C22×Dic6—31no—
170C22×Dic6—31no—
171C22×Dic6—38no—
172C22×Dic6—61no—
173C22×Dic6—64no—
174C22×Dic6—64no—
175C22×Dic6C2×D311yescharacteristic
176C2×C3×C4⋊C4—31no—
177C2×C3×C42—31no—
178C2×C4⋊Dic3—31no—
179C2×Dic3⋊C4—31no—
180C2×Dic3⋊C4—31no—
181C2×Dic3⋊C4—31no—
182C2×Dic3⋊C4—31no—
183C2×Dic3⋊C4—31no—
184C2×Dic3⋊C4—61no—
185C2×Dic3⋊C4—64no—
186C2×Dic3⋊C4C2×D311yescharacteristic
187C2×C4×Dic3—31no—
188C2×C4×Dic3—31no—
189C2×C4×Dic3—31no—
190C2×C4×Dic3—31no—
191C2×C4×Dic3—31no—
192C2×C4×Dic3—31no—
193C2×C4×Dic3—61no—
194C2×C4×Dic3—64no—
195C2×C4×Dic3C2×D311yescharacteristic
196D3×C4⋊C4—64no—
197C42×D3—64no—
198C3×#95—21no—
199C3×#95—31no—
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—31no—
220C3⋊#95—31no—
221C3⋊#95—31no—
222C3⋊#95—31no—
223C3⋊#95—31no—
224C3⋊#95—31no—
225C3⋊#95—61no—
226C3⋊#95—61no—
227C3⋊#95—61no—
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C3⋊#95C2×D311yescharacteristic
231C3⋊#95C2×D311yescharacteristic
232C3⋊#95C2×D311yescharacteristic
233C3⋊#95C2×D311yescharacteristic
234C23×C32C2411yescharacteristic
235C22×C3×D3C22×C412yes—
236C22×C3×D3C2×D412yes—
237C22×C3×D3C2×D412yes—
238C22×C3×D3C2×Q812yes—
239C22×C3×D3C2×Q812yes—
240C22×C3×D3#4112yes—
241C22×C3×D3#4112yes—
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×C4—21no—
249C2×C32×C4C22×C412yes—
250C2×C32×C4C2×Q812yescomplemented
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⋊Dic3—21no—
258C2×C3⋊Dic3C22×C412yes—
259C2×C3⋊Dic3C22×C412yes—
260C2×C3⋊Dic3C2×D412yes—
261C2×C3⋊Dic3C2×D412yes—
262C2×C3⋊Dic3C2×Q812yescomplemented
263#634—28no—
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×Dic3—21no—
277C2×C3×Dic3—21no—
278C2×C3×Dic3C22×C412yes—
279C2×C3×Dic3C22×C412yes—
280C2×C3×Dic3C22×C412yes—
281C2×C3×Dic3C2×D412yes—
282C2×C3×Dic3C2×D412yes—
283C2×C3×Dic3C2×Q812yescomplemented
284C2×C3×Dic3C2×Q812yescomplemented
285C3×C4×D3—28no—
286C3×C4×D3—28no—
287C3×C4×D3—44no—
288C3×Dic6—28no—
289#627—28no—
290#627—28no—
291D3×Dic3—28no—
292D3×Dic3—28no—
293D3×Dic3—44no—
294D3×Dic3C22⋊C4116yes—
295C23×Q8—91no—
296C22×C4⋊C4—91no—
297C22×C42—91no—
298#391—31no—
299#391—91no—
300#391—91no—
301#391—91no—
302#391—91no—
303#391—91no—
304#391—91no—
305#391—91no—
306C2×#95—31no—
307C2×#95—91no—
308C2×#95—91no—
309C2×#95—91no—
310C24×C3—31no—
311C23×D3C22×D311yescharacteristic
312C2×C3×Q8—34no—
313C2×C3×Q8—62no—
314C2×C3×Q8—62no—
315C22×C3×C4—21no—
316C22×C3×C4—21no—
317C22×C3×C4—21no—
318C22×C3×C4—31no—
319C22×C3×C4—31no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—34no—
324C22×C3×C4—34no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—62no—
328C22×C3×C4—62no—
329C22×C3×C4—62no—
330C22×C3×C4—62no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4C22×D311yescharacteristic
335C22×C3×C4C22×D311yescharacteristic
336C22×C3×C4C22×D311yescharacteristic
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×Dic3—31no—
341C22×Dic3—31no—
342C22×Dic3—34no—
343C22×Dic3—34no—
344C22×Dic3—34no—
345C22×Dic3—31no—
346C22×Dic3—31no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—34no—
350C22×Dic3—34no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3—61no—
357C22×Dic3—62no—
358C22×Dic3—62no—
359C22×Dic3—62no—
360C22×Dic3—62no—
361C22×Dic3—62no—
362C22×Dic3—62no—
363C22×Dic3—62no—
364C22×Dic3C22×D311yescharacteristic
365C22×Dic3C22×D311yescharacteristic
366C22×Dic3C22×D311yescharacteristic
367C22×Dic3C22×D311yescharacteristic
368C22×Dic3C22×D311yescharacteristic
369C22×Dic3C22×D311yescharacteristic
370C22×Dic3C22×D311yescharacteristic
371D3×Q8—632no—
372C2×C4×D3—22no—
373C2×C4×D3—22no—
374C2×C4×D3—22no—
375C2×C4×D3—22no—
376C2×C4×D3—22no—
377C2×C4×D3—22no—
378C2×C4×D3—22no—
379C2×C4×D3—34no—
380C2×C4×D3—34no—
381C2×C4×D3—34no—
382C2×C4×D3—34no—
383C2×C4×D3—34no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—62no—
388C2×C4×D3—62no—
389C2×C4×D3—62no—
390C2×C4×D3—62no—
391C2×C4×D3Dic614yescomplemented
392C2×C4×D3C4×D314yes—
393C2×Dic6—22no—
394C2×Dic6—22no—
395C2×Dic6—34no—
396C2×Dic6—34no—
397C2×Dic6—34no—
398C2×Dic6—34no—
399C2×Dic6—34no—
400C2×Dic6—34no—
401C2×Dic6—64no—
402C2×Dic6—632no—
403C2×Dic6—62no—
404C2×Dic6—62no—
405C2×Dic6—62no—
406C2×Dic6—62no—
407C2×Dic6—62no—
408C2×Dic6—62no—
409C2×Dic6—62no—
410C2×Dic6—62no—
411C2×Dic6—62no—
412C2×Dic6—62no—
413C2×Dic6—62no—
414C2×Dic6—62no—
415C2×Dic6—122no—
416C2×Dic6—122no—
417C2×Dic6C4×D314yescomplemented
418C3×C4⋊C4—62no—
419C3×C42—62no—
420C4⋊Dic3—62no—
421Dic3⋊C4—22no—
422Dic3⋊C4—62no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427Dic3⋊C4—122no—
428C4×Dic3—22no—
429C4×Dic3—62no—
430C4×Dic3—62no—
431C4×Dic3—62no—
432C4×Dic3—62no—
433C4×Dic3—62no—
434C4×Dic3—62no—
435C4×Dic3—122no—
436C22×C32C23×C411yescharacteristic
437C22×C32C22×D411yescharacteristic
438C22×C32C22×D411yescharacteristic
439C22×C32C22×Q811yescharacteristic
440C22×C32C22×Q811yescharacteristic
441C22×C32C2×#4111yescharacteristic
442C22×C32C2×#4111yescharacteristic
443C2×C3×D3C2×C22⋊C414yes—
444C2×C3×D3C4×Q814yes—
445C2×C3×D3C4×Q814yes—
446C2×C3×D3C22⋊Q814yes—
447C2×C3×D3C22⋊Q814yes—
448C2×C3×D3#12414yes—
449C2×C3×D3C4⋊Q814yes—
450C32×C4—22no—
451C32×C4—22no—
452C32×C4—41no—
453C3⋊Dic3—22no—
454C3⋊Dic3—22no—
455C3⋊Dic3—41no—
456C3⋊Dic3C2×C22⋊C414yes—
457C3×Dic3—22no—
458C3×Dic3—22no—
459C3×Dic3—22no—
460C3×Dic3—22no—
461C3×Dic3—41no—
462C3×Dic3—41no—
463C3×Dic3C2×C22⋊C414yes—
464C22×Q8—31no—
465C22×Q8—91no—
466C22×Q8—91no—
467C22×Q8—98no—
468C22×Q8—91no—
469C22×Q8—184no—
470C22×Q8—184no—
471C23×C4—31no—
472C23×C4—31no—
473C23×C4—31no—
474C23×C4—91no—
475C23×C4—91no—
476C23×C4—91no—
477C23×C4—91no—
478C2×C4⋊C4—31no—
479C2×C4⋊C4—91no—
480C2×C4⋊C4—91no—
481C2×C4⋊C4—91no—
482C2×C4⋊C4—184no—
483C2×C42—31no—
484C2×C42—91no—
485C2×C42—91no—
486C2×C42—91no—
487C2×C42—184no—
488#95—31no—
489#95—31no—
490#95—31no—
491#95—31no—
492#95—31no—
493#95—31no—
494#95—91no—
495#95—91no—
496#95—91no—
497#95—91no—
498#95—91no—
499#95—91no—
500#95—91no—
501#95—91no—
502#95—91no—
503#95D3211yescharacteristic
504C23×C3—21no—
505C23×C3—32no—
506C23×C3—32no—
507C23×C3—32no—
508C23×C3—32no—
509C23×C3—32no—
510C23×C3—32no—
511C23×C3—32no—
512C23×C3C23×D311yescharacteristic
513C23×C3C23×D311yescharacteristic
514C22×D3C2×Dic612yes—
515C22×D3C2×C4×D312yes—
516C22×D3#23512yes—
517C22×D3D3×D412yes—
518C22×D3D3×D412yes—
519C22×D3#23712yes—
520C22×D3D3×Q812yes—
521C3×Q8—68no—
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—21no—
529C2×C3×C4—21no—
530C2×C3×C4—21no—
531C2×C3×C4—21no—
532C2×C3×C4—21no—
533C2×C3×C4—21no—
534C2×C3×C4—21no—
535C2×C3×C4—21no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—32no—
539C2×C3×C4—32no—
540C2×C3×C4—32no—
541C2×C3×C4—32no—
542C2×C3×C4—32no—
543C2×C3×C4—32no—
544C2×C3×C4—32no—
545C2×C3×C4—41no—
546C2×C3×C4—41no—
547C2×C3×C4—41no—
548C2×C3×C4—41no—
549C2×C3×C4—41no—
550C2×C3×C4—41no—
551C2×C3×C4—41no—
552C2×C3×C4—68no—
553C2×C3×C4—68no—
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—61no—
561C2×C3×C4—61no—
562C2×C3×C4—61no—
563C2×C3×C4—61no—
564C2×C3×C4—61no—
565C2×C3×C4—61no—
566C2×C3×C4—61no—
567C2×C3×C4—61no—
568C2×C3×C4—124no—
569C2×C3×C4C2×Dic612yescomplemented
570C2×C3×C4C2×C4×D312yes—
571C2×C3×C4C2×C4×D312yes—
572C2×C3×C4D3×Q812yescomplemented
573C2×Dic3—21no—
574C2×Dic3—21no—
575C2×Dic3—21no—
576C2×Dic3—21no—
577C2×Dic3—21no—
578C2×Dic3—21no—
579C2×Dic3—21no—
580C2×Dic3—21no—
581C2×Dic3—21no—
582C2×Dic3—21no—
583C2×Dic3—21no—
584C2×Dic3—21no—
585C2×Dic3—21no—
586C2×Dic3—21no—
587C2×Dic3—32no—
588C2×Dic3—32no—
589C2×Dic3—32no—
590C2×Dic3—32no—
591C2×Dic3—32no—
592C2×Dic3—32no—
593C2×Dic3—316no—
594C2×Dic3—32no—
595C2×Dic3—32no—
596C2×Dic3—32no—
597C2×Dic3—32no—
598C2×Dic3—62no—
599C2×Dic3—62no—
600C2×Dic3—62no—
601C2×Dic3—62no—
602C2×Dic3—62no—
603C2×Dic3—68no—
604C2×Dic3—68no—
605C2×Dic3—61no—
606C2×Dic3—61no—
607C2×Dic3—61no—
608C2×Dic3—61no—
609C2×Dic3—61no—
610C2×Dic3—61no—
611C2×Dic3—61no—
612C2×Dic3—61no—
613C2×Dic3—61no—
614C2×Dic3—61no—
615C2×Dic3—61no—
616C2×Dic3—61no—
617C2×Dic3—61no—
618C2×Dic3—61no—
619C2×Dic3—121no—
620C2×Dic3—121no—
621C2×Dic3—121no—
622C2×Dic3—121no—
623C2×Dic3—121no—
624C2×Dic3—121no—
625C2×Dic3—121no—
626C2×Dic3—124no—
627C2×Dic3C2×Dic612yescomplemented
628C2×Dic3C2×C4×D312yes—
629C2×Dic3C2×C4×D312yes—
630C2×Dic3C2×C4×D312yes—
631C2×Dic3D3×D412yes—
632C2×Dic3D3×D412yes—
633C2×Dic3D3×Q812yescomplemented
634C4×D3—28no—
635C4×D3—28no—
636C4×D3—316no—
637C4×D3—44no—
638C4×D3—68no—
639C4×D3—68no—
640C4×D3—124no—
641Dic6—28no—
642Dic6—68no—
643Dic6—68no—
644Dic6—68no—
645Dic6—68no—
646Dic6—68no—
647Dic6—68no—
648Dic6—128no—
649C2×C32C22×C22⋊C411yescharacteristic
650C2×C32C2×C4×Q811yescharacteristic
651C2×C32C2×C4×Q811yescharacteristic
652C2×C32C2×C22⋊Q811yescharacteristic
653C2×C32C2×C22⋊Q811yescharacteristic
654C2×C32C2×#12411yescharacteristic
655C2×C32C2×C4⋊Q811yescharacteristic
656C3×D3#39118yescomplemented
657C24—31no—
658C2×Q8—34no—
659C2×Q8—62no—
660C2×Q8—62no—
661C2×Q8—94no—
662C2×Q8—94no—
663C2×Q8—94no—
664C2×Q8—182no—
665C2×Q8—182no—
666C2×Q8—182no—
667C2×Q8—182no—
668C2×Q8—182no—
669C2×Q8—182no—
670C2×Q8—1832no—
671C22×C4—31no—
672C22×C4—31no—
673C22×C4—31no—
674C22×C4—31no—
675C22×C4—31no—
676C22×C4—34no—
677C22×C4—34no—
678C22×C4—31no—
679C22×C4—31no—
680C22×C4—62no—
681C22×C4—62no—
682C22×C4—62no—
683C22×C4—62no—
684C22×C4—62no—
685C22×C4—62no—
686C22×C4—62no—
687C22×C4—94no—
688C22×C4—94no—
689C22×C4—94no—
690C22×C4—94no—
691C22×C4—94no—
692C22×C4—91no—
693C22×C4—91no—
694C22×C4—91no—
695C22×C4—91no—
696C22×C4—182no—
697C22×C4—182no—
698C22×C4—182no—
699C22×C4—182no—
700C22×C4—182no—
701C22×C4—182no—
702C22×C4—182no—
703C22×C4C2×D3211yescharacteristic
704C22×C4C2×D3211yescharacteristic
705C22×C4C2×D3211yescharacteristic
706C4⋊C4—62no—
707C4⋊C4—182no—
708C4⋊C4—182no—
709C4⋊C4—182no—
710C42—62no—
711C42—182no—
712C42—182no—
713C42—182no—
714C22×C3—21no—
715C22×C3—21no—
716C22×C3—21no—
717C22×C3—21no—
718C22×C3—21no—
719C22×C3—21no—
720C22×C3—21no—
721C22×C3—34no—
722C22×C3—34no—
723C22×C3—34no—
724C22×C3—34no—
725C22×C3—34no—
726C22×C3—34no—
727C22×C3—34no—
728C22×C3C22×Dic611yescharacteristic
729C22×C3C22×C4×D311yescharacteristic
730C22×C3C22×C4×D311yescharacteristic
731C22×C3C2×#23511yescharacteristic
732C22×C3C2×D3×D411yescharacteristic
733C22×C3C2×D3×D411yescharacteristic
734C22×C3C2×D3×D411yescharacteristic
735C22×C3C2×D3×D411yescharacteristic
736C22×C3C2×#23711yescharacteristic
737C22×C3C2×D3×Q811yescharacteristic
738C22×C3C2×D3×Q811yescharacteristic
739C22×C3C2×D3×Q811yescharacteristic
740C22×C3D3×#4111yescharacteristic
741C22×C3D3×#4111yescharacteristic
742C2×D3C4×Dic614yes—
743C2×D3#87814yes—
744C2×D3D3×C22⋊C414yes—
745C2×D3#88514yes—
746C2×D3#88714yes—
747C2×D3#88814yes—
748C2×D3#89614yes—
749C3×C4—22no—
750C3×C4—22no—
751C3×C4—22no—
752C3×C4—22no—
753C3×C4—34no—
754C3×C4—42no—
755C3×C4—42no—
756C3×C4—41no—
757C3×C4—41no—
758C3×C4—62no—
759C3×C4—62no—
760C3×C4—62no—
761C3×C4—62no—
762C3×C4—81no—
763C3×C4—121no—
764C3×C4—121no—
765Dic3—22no—
766Dic3—22no—
767Dic3—22no—
768Dic3—22no—
769Dic3—34no—
770Dic3—34no—
771Dic3—41no—
772Dic3—41no—
773Dic3—64no—
774Dic3—62no—
775Dic3—62no—
776Dic3—62no—
777Dic3—62no—
778Dic3—122no—
779Dic3—122no—
780Dic3—121no—
781Dic3—121no—
782Dic3—241no—
783Dic3D3×C22⋊C414yes—
784C32C2×#39111yescharacteristic, complemented, Sylow
785C23—32no—
786C23—32no—
787C23—32no—
788C23—32no—
789C23—32no—
790C23—32no—
791C23—32no—
792C23C22×D3211yescharacteristic
793Q8—68no—
794Q8—188no—
795Q8—188no—
796Q8—188no—
797C2×C4—21no—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—32no—
805C2×C4—32no—
806C2×C4—32no—
807C2×C4—32no—
808C2×C4—32no—
809C2×C4—32no—
810C2×C4—32no—
811C2×C4—68no—
812C2×C4—68no—
813C2×C4—61no—
814C2×C4—61no—
815C2×C4—61no—
816C2×C4—61no—
817C2×C4—61no—
818C2×C4—61no—
819C2×C4—61no—
820C2×C4—61no—
821C2×C4—61no—
822C2×C4—61no—
823C2×C4—61no—
824C2×C4—61no—
825C2×C4—61no—
826C2×C4—61no—
827C2×C4—916no—
828C2×C4—92no—
829C2×C4—92no—
830C2×C4—92no—
831C2×C4—92no—
832C2×C4—92no—
833C2×C4—124no—
834C2×C4—188no—
835C2×C4—188no—
836C2×C4—181no—
837C2×C4—181no—
838C2×C4—181no—
839C2×C4—181no—
840C2×C4—181no—
841C2×C4—181no—
842C2×C4—181no—
843C2×C4—364no—
844C2×C4D3×Dic612yescomplemented
845C2×C4C4×D3212yes—
846C2×C3—21no—
847C2×C3—21no—
848C2×C3—21no—
849C2×C3—21no—
850C2×C3—21no—
851C2×C3—21no—
852C2×C3—21no—
853C2×C3—38no—
854C2×C3C2×C4×Dic611yescharacteristic
855C2×C3C2×#87811yescharacteristic
856C2×C3C2×D3×C22⋊C411yescharacteristic
857C2×C3C2×D3×C22⋊C411yescharacteristic
858C2×C3C2×#88511yescharacteristic
859C2×C3C2×#88711yescharacteristic
860C2×C3C2×#88811yescharacteristic
861C2×C3C2×#89611yescharacteristic
862C2×C3C4×D3×Q811yescharacteristic
863C2×C3C4×D3×Q811yescharacteristic
864C2×C3D3×C22⋊Q811yescharacteristic
865C2×C3D3×C22⋊Q811yescharacteristic
866C2×C3D3×#12411yescharacteristic
867C2×C3D3×C4⋊Q811yescharacteristic
868D3#464618yesdirect product factor
869C22—34no—
870C22—34no—
871C22—34no—
872C22—34no—
873C22—34no—
874C22—34no—
875C22—34no—
876C22C2×D3×Dic611yescharacteristic
877C22C2×C4×D3211yescharacteristic
878C22D3×#23511yescharacteristic
879C22D32×D411yescharacteristic
880C22D32×D411yescharacteristic
881C22D3×#23711yescharacteristic
882C22D32×Q811yescharacteristic
883C4—22no—
884C4—22no—
885C4—34no—
886C4—41no—
887C4—62no—
888C4—62no—
889C4—62no—
890C4—62no—
891C4—94no—
892C4—121no—
893C4—121no—
894C4—182no—
895C4—182no—
896C4—361no—
897C3—21no—
898C3C2×#464611yescharacteristic, complemented
899C3D3×#39111yescharacteristic, complemented
900C2—38no—
901C2C4×D3×Dic611yescharacteristic
902C2D3×#87811yescharacteristic
903C2D32×C22⋊C411yescharacteristic
904C2D3×#88511yescharacteristic
905C2D3×#88711yescharacteristic
906C2D3×#88811yescharacteristic
907C2D3×#89611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC23×C3×D3C23
hypercenter#95D32
hypocenterC32C2×#391
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
4. #10592345C2semidirect
6. C3×#4646C2semidirect
7. #10591396C2semidirect
11. #10591273C2semidirect
12. #10591261C2semidirect
13. #10591236C2semidirect
14. #10591235C2semidirect
15. #10591191C2semidirect
31. C2×D3×Dic6C4semidirect
88. #4646D3direct (N × H)
99. C2×#634C2×C4semidirect
115. C2×C3×C4×D3Q8semidirect
118. C2×C3×Dic6C2×C4semidirect
123. C2×#627C2×C4semidirect
124. C2×#627C2×C4semidirect
136. C2×D3×Dic3Q8semidirect
250. C2×C32×C4C2×Q8semidirect
262. C2×C3⋊Dic3C2×Q8semidirect
283. C2×C3×Dic3C2×Q8semidirect
284. C2×C3×Dic3C2×Q8semidirect
391. C2×C4×D3Dic6semidirect
417. C2×Dic6C4×D3semidirect
569. C2×C3×C4C2×Dic6semidirect
572. C2×C3×C4D3×Q8semidirect
627. C2×Dic3C2×Dic6semidirect
633. C2×Dic3D3×Q8semidirect
656. C3×D3#391semidirect
784. C32C2×#391semidirect
844. C2×C4D3×Dic6semidirect
868. D3#4646direct (N × H)
898. C3C2×#4646semidirect
899. C3D3×#391semidirect

Maximal subgroups

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

subgroupindex
C22×D3×Dic62
C2×D3×Dic3⋊C42
C2×C4×D3×Dic32
#105923452
C3×D3×#952
C3×#46462
#105913962
D3×C3⋊#952
#105912732
#105912612
#105912362
#105912352
#105911912
D3×#3913
C2×#46463