Finite Group Databasebeta

← D3×#4952 #11808300

Subgroups — D3×#4952 #11808300

Order 1152.

1725 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×D3×C22⋊C4C211yesmaximal, characteristic
2C2×D3×#217C211yesmaximal, characteristic
3C2×D3×#217C211yesmaximal, characteristic
4C2×D3×Dic3⋊C4C211yesmaximal, characteristic, complemented
5#10592651C211yesmaximal, characteristic, complemented
6C3×#4952C211yesmaximal, characteristic, complemented
7#10591717C211yesmaximal, characteristic, complemented
8#10591694C211yesmaximal, characteristic, complemented
9D3×C3⋊#95C211yesmaximal, characteristic, complemented
10D3×C3⋊#95C211yesmaximal, characteristic, complemented
11D3×C3⋊#95C211yesmaximal, characteristic, complemented
12#10591301C211yesmaximal, characteristic, complemented
13#10591299C211yesmaximal, characteristic, complemented
14#10591298C211yesmaximal, characteristic, complemented
15#10591296C211yesmaximal, characteristic, complemented
16C2×#4952—31nomaximal
17D3×#397—31nomaximal
18C24×C3×D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×C3×C4×D3C2211yescharacteristic
21C22×D3×Dic3C2211yescharacteristic
22C22×D3×Dic3C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×#3750C2211yescharacteristic, complemented
29C2×C3×#217C2211yescharacteristic
30C2×C3×#217C2211yescharacteristic
31C2×C3×#217C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
35C3×D3×C22⋊C4—24no—
36D3×#217—24no—
37D3×#217—24no—
38C2×#3724C2211yescharacteristic, complemented
39C2×Dic3⋊Dic3C2211yescharacteristic, complemented
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44D3×Dic3⋊C4—24no—
45#63658C2211yescharacteristic, complemented
46#63658C2211yescharacteristic, complemented
47#63658C2211yescharacteristic, complemented
48C3×C3⋊#95C2211yescharacteristic, complemented
49C3×C3⋊#95C2211yescharacteristic, complemented
50C3×C3⋊#95C2211yescharacteristic, complemented
51#63579C2211yescharacteristic, complemented
52#63579C2211yescharacteristic, complemented
53#63579C2211yescharacteristic, complemented
54#63579C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C22×C3×C22⋊C4—31no—
58C22×#217—31no—
59C22×#217—31no—
60C22×Dic3⋊C4—31no—
61C2×D3×C4⋊C4—31no—
62C2×D3×C22⋊C4—31no—
63C2×D3×C22⋊C4—31no—
64C2×D3×C22⋊C4D311yescharacteristic
65C3×#397—31no—
66C2×C3⋊#95—31no—
67C2×C3⋊#95—31no—
68C2×C3⋊#95—31no—
69#4992—31no—
70#4953—31no—
71#4952—31no—
72#4952—31no—
73#4952—31no—
74#4952—31no—
75#4952—31no—
76#4952—31no—
77#4952—31no—
78#4952—31no—
79#4952—31no—
80#4952—61no—
81#4952D311yescharacteristic, direct product factor
82#4675—31no—
83#4675—31no—
84#4674—31no—
85D3×#95—31no—
86D3×#95—31no—
87D3×#95—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3—22no—
90C23×C3×D3—22no—
91C23×C3×D3—22no—
92C23×C3×D3—22no—
93C23×C3×D3—22no—
94C23×C3×D3—22no—
95C23×C3×D3D414yes—
96C23×C3×D3C2311yescharacteristic
97C23×C3×D3C2311yescharacteristic
98C22×C32×C4C2311yescharacteristic
99C22×C32×C4C2311yescharacteristic
100C22×C3⋊Dic3C2311yescharacteristic
101C22×C3⋊Dic3C2311yescharacteristic
102C22×C3⋊Dic3C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×C3×C4×D3—22no—
111C2×C3×C4×D3—22no—
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×D3×Dic3—22no—
117C2×D3×Dic3—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—22no—
123C2×D3×Dic3—22no—
124C2×D3×Dic3—22no—
125C2×D3×Dic3—22no—
126C2×D3×Dic3—22no—
127C2×D3×Dic3D414yes—
128C32×C22⋊C4—22no—
129#3757—22no—
130#3757—22no—
131#3750—22no—
132C3×#217—22no—
133C3×#217—22no—
134C3×#217—22no—
135C3×(C2×D3)⋊C4—22no—
136C3×(C2×D3)⋊C4—22no—
137C3×Dic3⋊C4—22no—
138#3724—22no—
139Dic3⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144C2×#397—91noSylow
145C25×C3—31no—
146C24×D3C2×D311yescharacteristic
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
159C2×C3×C4⋊C4—31no—
160C2×C3×C22⋊C4—21no—
161C2×C3×C22⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—64no—
167C2×C3×C22⋊C4C2×D311yescharacteristic
168C2×C3×C22⋊C4C2×D311yescharacteristic
169C2×#217—31no—
170C2×#217—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175C2×#217—31no—
176C2×#217—31no—
177C2×#217—61no—
178C2×#217—61no—
179C2×#217—64no—
180C2×#217—64no—
181C2×#217C2×D311yescharacteristic
182C2×#217C2×D311yescharacteristic
183C2×#217C2×D311yescharacteristic
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—31no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×C4⋊Dic3—31no—
191C2×Dic3⋊C4—31no—
192C2×Dic3⋊C4—31no—
193C2×Dic3⋊C4—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—61no—
197C2×Dic3⋊C4—64no—
198C2×Dic3⋊C4C2×D311yescharacteristic, complemented
199D3×C4⋊C4—64no—
200D3×C22⋊C4—24no—
201D3×C22⋊C4—64no—
202D3×C22⋊C4—64no—
203C3×#95—31no—
204C3×#95—31no—
205C3×#95—31no—
206C3⋊#95—31no—
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—61no—
225C3⋊#95—61no—
226C3⋊#95—61no—
227C3⋊#95C2×D311yescharacteristic, complemented
228C3⋊#95C2×D311yescharacteristic, complemented
229C3⋊#95C2×D311yescharacteristic, complemented
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32C2×D412yes—
237C23×C32C2411yescharacteristic
238C22×C3×D3—21no—
239C22×C3×D3—21no—
240C22×C3×D3—21no—
241C22×C3×D3—21no—
242C22×C3×D3—21no—
243C22×C3×D3—21no—
244C22×C3×D3—28no—
245C22×C3×D3—28no—
246C22×C3×D3—28no—
247C22×C3×D3—44no—
248C22×C3×D3—44no—
249C22×C3×D3—44no—
250C22×C3×D3—44no—
251C22×C3×D3C2×D412yes—
252C22×C3×D3C2×D412yes—
253C22×C3×D3C2×D412yes—
254C22×C3×D3#4112yes—
255C22×C3×D3#4112yes—
256C22×C3×D3#4112yes—
257C22×C3×D3#4112yes—
258C22×C3×D3#4112yes—
259C2×C32×C4—21no—
260C2×C32×C4—21no—
261C2×C32×C4—21no—
262C2×C32×C4—21no—
263C2×C32×C4—21no—
264C2×C32×C4—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⋊Dic3C2×D412yes—
277C2×C3×Dic3—21no—
278C2×C3×Dic3—21no—
279C2×C3×Dic3—21no—
280C2×C3×Dic3—21no—
281C2×C3×Dic3—21no—
282C2×C3×Dic3—21no—
283C2×C3×Dic3—21no—
284C2×C3×Dic3—21no—
285C2×C3×Dic3—21no—
286C2×C3×Dic3—21no—
287C2×C3×Dic3—21no—
288C2×C3×Dic3—21no—
289C2×C3×Dic3—21no—
290C2×C3×Dic3—21no—
291C2×C3×Dic3—21no—
292C2×C3×Dic3—21no—
293C2×C3×Dic3—21no—
294C2×C3×Dic3C2×D412yes—
295C3×C4×D3—44no—
296C3×C4×D3—44no—
297D3×Dic3—28no—
298D3×Dic3—44no—
299D3×Dic3—44no—
300D3×Dic3—44no—
301C22×C4⋊C4—91no—
302C22×C22⋊C4—31no—
303C22×C22⋊C4—91no—
304C22×C22⋊C4—91no—
305#397—31no—
306#397—91no—
307#397—91no—
308#397—91no—
309#397—91no—
310#397—91no—
311#397—91no—
312#397—91no—
313C2×#95—91no—
314C2×#95—91no—
315C2×#95—91no—
316C24×C3—21no—
317C24×C3—31no—
318C24×C3—34no—
319C24×C3—31no—
320C24×C3—62no—
321C24×C3—62no—
322C24×C3—62no—
323C24×C3—62no—
324C24×C3—62no—
325C24×C3—62no—
326C24×C3C22×D311yescharacteristic
327C24×C3C22×D311yescharacteristic
328C23×D3—22no—
329C23×D3—22no—
330C23×D3—22no—
331C23×D3—22no—
332C23×D3—22no—
333C23×D3—22no—
334C23×D3#6714yes—
335C23×D3C22×D311yescharacteristic
336C23×D3C22×D311yescharacteristic
337C22×C3×C4—21no—
338C22×C3×C4—21no—
339C22×C3×C4—31no—
340C22×C3×C4—31no—
341C22×C3×C4—31no—
342C22×C3×C4—31no—
343C22×C3×C4—31no—
344C22×C3×C4—31no—
345C22×C3×C4—62no—
346C22×C3×C4—62no—
347C22×C3×C4—62no—
348C22×C3×C4—62no—
349C22×C3×C4—62no—
350C22×C3×C4—62no—
351C22×C3×C4C22×D311yescharacteristic
352C22×C3×C4C22×D311yescharacteristic
353C22×C3×C4C22×D311yescharacteristic
354C22×C3×C4C22×D311yescharacteristic
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—34no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—61no—
365C22×Dic3—61no—
366C22×Dic3—61no—
367C22×Dic3—61no—
368C22×Dic3—62no—
369C22×Dic3—62no—
370C22×Dic3—62no—
371C22×Dic3—62no—
372C22×Dic3—62no—
373C22×Dic3—62no—
374C22×Dic3—62no—
375C22×Dic3—62no—
376C22×Dic3—62no—
377C22×Dic3—62no—
378C22×Dic3—62no—
379C22×Dic3C22×D311yescharacteristic
380C22×Dic3C22×D311yescharacteristic
381C22×Dic3C22×D311yescharacteristic
382C22×Dic3C22×D311yescharacteristic
383C22×Dic3C22×D311yescharacteristic
384C22×Dic3C22×D311yescharacteristic
385C2×C4×D3—22no—
386C2×C4×D3—22no—
387C2×C4×D3—22no—
388C2×C4×D3—22no—
389C2×C4×D3—22no—
390C2×C4×D3—22no—
391C2×C4×D3—34no—
392C2×C4×D3—62no—
393C2×C4×D3—62no—
394C2×C4×D3—62no—
395C2×C4×D3—62no—
396C2×C4×D3—62no—
397C2×C4×D3—62no—
398C2×C4×D3—62no—
399C2×C4×D3—62no—
400C2×C4×D3—62no—
401C2×C4×D3—62no—
402C2×C4×D3—62no—
403C3×C4⋊C4—62no—
404C3×C22⋊C4—22no—
405C3×C22⋊C4—22no—
406C3×C22⋊C4—42no—
407C3×C22⋊C4—62no—
408C3×C22⋊C4—62no—
409C3×C22⋊C4—62no—
410C3×C22⋊C4—62no—
411C3×C22⋊C4—62no—
412#217—22no—
413#217—22no—
414#217—22no—
415#217—62no—
416#217—62no—
417#217—62no—
418#217—62no—
419#217—62no—
420#217—62no—
421#217—62no—
422#217—62no—
423#217—122no—
424#217—122no—
425(C2×D3)⋊C4—22no—
426(C2×D3)⋊C4—22no—
427(C2×D3)⋊C4—62no—
428(C2×D3)⋊C4—62no—
429(C2×D3)⋊C4—62no—
430(C2×D3)⋊C4—62no—
431C4⋊Dic3—62no—
432Dic3⋊C4—22no—
433Dic3⋊C4—62no—
434Dic3⋊C4—62no—
435Dic3⋊C4—62no—
436Dic3⋊C4—62no—
437Dic3⋊C4—62no—
438Dic3⋊C4—122no—
439C22×C32—22no—
440C22×C32—22no—
441C22×C32—22no—
442C22×C32—41no—
443C22×C32—41no—
444C22×C32—41no—
445C22×C32—41no—
446C22×C32C22×D411yescharacteristic
447C22×C32C22×D411yescharacteristic
448C22×C32C2×#4111yescharacteristic
449C22×C32C2×#4111yescharacteristic
450C22×C32C2×#4111yescharacteristic
451C22×C32C2×#4111yescharacteristic
452C22×C32C2×#4111yescharacteristic
453C2×C3×D3—22no—
454C2×C3×D3—22no—
455C2×C3×D3—22no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—416no—
461C2×C3×D3#12114yes—
462C2×C3×D3#12314yes—
463C2×C3×D3#12314yes—
464C2×C3×D3#12314yes—
465C2×C3×D3#12414yes—
466C2×C3×D3#12614yes—
467C2×C3×D3#12614yes—
468C32×C4—41no—
469C32×C4—41no—
470C3⋊Dic3—22no—
471C3⋊Dic3—41no—
472C3⋊Dic3—41no—
473C3⋊Dic3—41no—
474C3×Dic3—22no—
475C3×Dic3—41no—
476C3×Dic3—41no—
477C3×Dic3—41no—
478C3×Dic3—41no—
479C3×Dic3—41no—
480C25—31no—
481C23×C4—31no—
482C23×C4—31no—
483C23×C4—91no—
484C23×C4—91no—
485C23×C4—91no—
486C23×C4—91no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—184no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—64no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—184no—
505C2×C22⋊C4—184no—
506C2×C22⋊C4D3211yescharacteristic
507#95—31no—
508#95—31no—
509#95—31no—
510#95—91no—
511#95—91no—
512#95—91no—
513#95—91no—
514#95—91no—
515#95—91no—
516#95—91no—
517#95—91no—
518#95—91no—
519C23×C3—21no—
520C23×C3—21no—
521C23×C3—21no—
522C23×C3—21no—
523C23×C3—21no—
524C23×C3—21no—
525C23×C3—21no—
526C23×C3—21no—
527C23×C3—21no—
528C23×C3—21no—
529C23×C3—21no—
530C23×C3—21no—
531C23×C3—21no—
532C23×C3—22no—
533C23×C3—32no—
534C23×C3—32no—
535C23×C3—32no—
536C23×C3—32no—
537C23×C3—32no—
538C23×C3—32no—
539C23×C3—32no—
540C23×C3—32no—
541C23×C3—41no—
542C23×C3—41no—
543C23×C3—41no—
544C23×C3—41no—
545C23×C3—41no—
546C23×C3—41no—
547C23×C3—68no—
548C23×C3—68no—
549C23×C3—68no—
550C23×C3—61no—
551C23×C3—61no—
552C23×C3—61no—
553C23×C3—61no—
554C23×C3—61no—
555C23×C3—61no—
556C23×C3—124no—
557C23×C3—124no—
558C23×C3—124no—
559C23×C3—124no—
560C23×C3D3×D412yes—
561C23×C3C2×#6712yes—
562C23×C3C23×D311yescharacteristic
563C23×C3C23×D311yescharacteristic
564C22×D3—21no—
565C22×D3—21no—
566C22×D3—21no—
567C22×D3—21no—
568C22×D3—21no—
569C22×D3—21no—
570C22×D3—28no—
571C22×D3—28no—
572C22×D3—28no—
573C22×D3—44no—
574C22×D3—44no—
575C22×D3—44no—
576C22×D3—44no—
577C22×D3#23512yes—
578C22×D3#23512yes—
579C22×D3D3×D412yes—
580C22×D3#23712yes—
581C22×D3#23712yes—
582C22×D3#23712yes—
583C22×D3C2×#6712yes—
584C22×D3C2×#6712yes—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—21no—
588C2×C3×C4—21no—
589C2×C3×C4—21no—
590C2×C3×C4—21no—
591C2×C3×C4—21no—
592C2×C3×C4—21no—
593C2×C3×C4—21no—
594C2×C3×C4—21no—
595C2×C3×C4—21no—
596C2×C3×C4—21no—
597C2×C3×C4—32no—
598C2×C3×C4—41no—
599C2×C3×C4—41no—
600C2×C3×C4—41no—
601C2×C3×C4—41no—
602C2×C3×C4—41no—
603C2×C3×C4—41no—
604C2×C3×C4—61no—
605C2×C3×C4—61no—
606C2×C3×C4—61no—
607C2×C3×C4—61no—
608C2×C3×C4—61no—
609C2×C3×C4—61no—
610C2×C3×C4—61no—
611C2×C3×C4—61no—
612C2×C3×C4—61no—
613C2×C3×C4—61no—
614C2×C3×C4—61no—
615C2×C3×C4—61no—
616C2×C3×C4—61no—
617C2×C3×C4—61no—
618C2×C3×C4—61no—
619C2×C3×C4—61no—
620C2×C3×C4—61no—
621C2×C3×C4—124no—
622C2×C3×C4—124no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—21no—
632C2×Dic3—21no—
633C2×Dic3—21no—
634C2×Dic3—21no—
635C2×Dic3—21no—
636C2×Dic3—21no—
637C2×Dic3—21no—
638C2×Dic3—21no—
639C2×Dic3—21no—
640C2×Dic3—32no—
641C2×Dic3—32no—
642C2×Dic3—62no—
643C2×Dic3—68no—
644C2×Dic3—61no—
645C2×Dic3—61no—
646C2×Dic3—61no—
647C2×Dic3—61no—
648C2×Dic3—61no—
649C2×Dic3—61no—
650C2×Dic3—61no—
651C2×Dic3—61no—
652C2×Dic3—61no—
653C2×Dic3—61no—
654C2×Dic3—61no—
655C2×Dic3—61no—
656C2×Dic3—61no—
657C2×Dic3—61no—
658C2×Dic3—61no—
659C2×Dic3—61no—
660C2×Dic3—61no—
661C2×Dic3—61no—
662C2×Dic3—61no—
663C2×Dic3—61no—
664C2×Dic3—61no—
665C2×Dic3—61no—
666C2×Dic3—121no—
667C2×Dic3—121no—
668C2×Dic3—121no—
669C2×Dic3—121no—
670C2×Dic3—121no—
671C2×Dic3—121no—
672C2×Dic3—121no—
673C2×Dic3—121no—
674C2×Dic3—121no—
675C2×Dic3—121no—
676C2×Dic3—121no—
677C2×Dic3—124no—
678C2×Dic3—124no—
679C2×Dic3—124no—
680C2×Dic3D3×D412yes—
681C4×D3—44no—
682C4×D3—44no—
683C4×D3—68no—
684C4×D3—124no—
685C4×D3—124no—
686C4×D3—124no—
687C2×C32—42no—
688C2×C32C2×#12111yescharacteristic
689C2×C32C2×#12311yescharacteristic
690C2×C32C2×#12311yescharacteristic
691C2×C32C2×#12311yescharacteristic
692C2×C32C2×#12411yescharacteristic
693C2×C32C2×#12611yescharacteristic
694C2×C32C2×#12611yescharacteristic
695C3×D3—42no—
696C3×D3#39718yescomplemented
697C24—31no—
698C24—31no—
699C24—34no—
700C24—62no—
701C24—62no—
702C24—62no—
703C24—62no—
704C24—62no—
705C24—62no—
706C24C2×D3211yescharacteristic
707C22×C4—31no—
708C22×C4—31no—
709C22×C4—31no—
710C22×C4—31no—
711C22×C4—31no—
712C22×C4—31no—
713C22×C4—62no—
714C22×C4—62no—
715C22×C4—62no—
716C22×C4—62no—
717C22×C4—62no—
718C22×C4—62no—
719C22×C4—94no—
720C22×C4—91no—
721C22×C4—91no—
722C22×C4—91no—
723C22×C4—91no—
724C22×C4—182no—
725C22×C4—182no—
726C22×C4—182no—
727C22×C4—182no—
728C22×C4—182no—
729C22×C4—182no—
730C22×C4—182no—
731C22×C4—182no—
732C22×C4—182no—
733C22×C4—182no—
734C22×C4—182no—
735C22×C4C2×D3211yescharacteristic
736C22×C4C2×D3211yescharacteristic
737C4⋊C4—62no—
738C4⋊C4—182no—
739C4⋊C4—182no—
740C4⋊C4—182no—
741C22⋊C4—22no—
742C22⋊C4—62no—
743C22⋊C4—62no—
744C22⋊C4—62no—
745C22⋊C4—62no—
746C22⋊C4—62no—
747C22⋊C4—182no—
748C22⋊C4—182no—
749C22⋊C4—182no—
750C22⋊C4—182no—
751C22⋊C4—182no—
752C22⋊C4—182no—
753C22×C3—22no—
754C22×C3—22no—
755C22×C3—22no—
756C22×C3—22no—
757C22×C3—22no—
758C22×C3—22no—
759C22×C3—21no—
760C22×C3—21no—
761C22×C3—21no—
762C22×C3—21no—
763C22×C3—21no—
764C22×C3—21no—
765C22×C3—21no—
766C22×C3—34no—
767C22×C3—34no—
768C22×C3—34no—
769C22×C3—34no—
770C22×C3—34no—
771C22×C3—34no—
772C22×C3—34no—
773C22×C3—42no—
774C22×C3—42no—
775C22×C3—42no—
776C22×C3—41no—
777C22×C3—41no—
778C22×C3—41no—
779C22×C3—41no—
780C22×C3—41no—
781C22×C3—41no—
782C22×C3—41no—
783C22×C3—41no—
784C22×C3—62no—
785C22×C3—62no—
786C22×C3—62no—
787C22×C3—81no—
788C22×C3—81no—
789C22×C3—81no—
790C22×C3—81no—
791C22×C3—1216no—
792C22×C3—121no—
793C22×C3—121no—
794C22×C3—121no—
795C22×C3—121no—
796C22×C3C2×#23511yescharacteristic
797C22×C3C2×#23511yescharacteristic
798C22×C3C2×D3×D411yescharacteristic
799C22×C3C2×D3×D411yescharacteristic
800C22×C3C2×D3×D411yescharacteristic
801C22×C3C2×#23711yescharacteristic
802C22×C3C2×#23711yescharacteristic
803C22×C3C2×#23711yescharacteristic
804C22×C3D3×#4111yescharacteristic
805C22×C3D3×#4111yescharacteristic
806C22×C3D3×#4111yescharacteristic
807C22×C3D3×#4111yescharacteristic
808C22×C3D3×#4111yescharacteristic
809C22×C3C22×#6711yescharacteristic
810C2×D3—22no—
811C2×D3—22no—
812C2×D3—22no—
813C2×D3—41no—
814C2×D3—41no—
815C2×D3—41no—
816C2×D3—41no—
817C2×D3—416no—
818C2×D3#87914yes—
819C2×D3#87914yes—
820C2×D3#88314yes—
821C2×D3#88514yes—
822C2×D3#92914yes—
823C2×D3#93514yes—
824C2×D3#93914yes—
825C3×C4—41no—
826C3×C4—41no—
827C3×C4—41no—
828C3×C4—41no—
829C3×C4—62no—
830C3×C4—81no—
831C3×C4—81no—
832C3×C4—121no—
833C3×C4—121no—
834C3×C4—121no—
835C3×C4—121no—
836C3×C4—121no—
837Dic3—22no—
838Dic3—41no—
839Dic3—41no—
840Dic3—41no—
841Dic3—41no—
842Dic3—41no—
843Dic3—62no—
844Dic3—62no—
845Dic3—122no—
846Dic3—121no—
847Dic3—121no—
848Dic3—121no—
849Dic3—121no—
850Dic3—121no—
851Dic3—121no—
852Dic3—241no—
853Dic3—241no—
854Dic3—241no—
855C32C2×#39711yescharacteristic, complemented, Sylow
856C23—21no—
857C23—21no—
858C23—21no—
859C23—21no—
860C23—21no—
861C23—21no—
862C23—32no—
863C23—32no—
864C23—32no—
865C23—32no—
866C23—32no—
867C23—32no—
868C23—32no—
869C23—32no—
870C23—68no—
871C23—68no—
872C23—68no—
873C23—61no—
874C23—61no—
875C23—61no—
876C23—61no—
877C23—61no—
878C23—61no—
879C23—124no—
880C23—124no—
881C23—124no—
882C23—124no—
883C23D3×#6712yes—
884C23C22×D3211yescharacteristic
885C2×C4—21no—
886C2×C4—21no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—21no—
890C2×C4—21no—
891C2×C4—32no—
892C2×C4—61no—
893C2×C4—61no—
894C2×C4—61no—
895C2×C4—61no—
896C2×C4—61no—
897C2×C4—61no—
898C2×C4—61no—
899C2×C4—61no—
900C2×C4—61no—
901C2×C4—61no—
902C2×C4—61no—
903C2×C4—61no—
904C2×C4—61no—
905C2×C4—61no—
906C2×C4—61no—
907C2×C4—61no—
908C2×C4—61no—
909C2×C4—92no—
910C2×C4—124no—
911C2×C4—124no—
912C2×C4—188no—
913C2×C4—181no—
914C2×C4—181no—
915C2×C4—181no—
916C2×C4—181no—
917C2×C4—181no—
918C2×C4—181no—
919C2×C4—181no—
920C2×C4—181no—
921C2×C4—181no—
922C2×C4—181no—
923C2×C4—181no—
924C2×C4—364no—
925C2×C4—364no—
926C2×C4—364no—
927C2×C3—21no—
928C2×C3—21no—
929C2×C3—21no—
930C2×C3—21no—
931C2×C3—21no—
932C2×C3—21no—
933C2×C3—21no—
934C2×C3—38no—
935C2×C3—42no—
936C2×C3—42no—
937C2×C3—82no—
938C2×C3—122no—
939C2×C3C2×#87911yescharacteristic
940C2×C3C2×#87911yescharacteristic
941C2×C3C2×#88311yescharacteristic
942C2×C3C2×#88511yescharacteristic
943C2×C3D3×#12111yescharacteristic
944C2×C3D3×#12311yescharacteristic
945C2×C3D3×#12311yescharacteristic
946C2×C3D3×#12311yescharacteristic
947C2×C3D3×#12411yescharacteristic
948C2×C3D3×#12611yescharacteristic
949C2×C3D3×#12611yescharacteristic
950C2×C3C2×#92911yescharacteristic
951C2×C3C2×#93511yescharacteristic
952C2×C3C2×#93911yescharacteristic
953D3—42no—
954D3#495218yesdirect product factor
955C22—22no—
956C22—22no—
957C22—22no—
958C22—34no—
959C22—34no—
960C22—34no—
961C22—34no—
962C22—34no—
963C22—34no—
964C22—34no—
965C22—41no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—62no—
970C22—62no—
971C22—62no—
972C22—1216no—
973C22—121no—
974C22—121no—
975C22—121no—
976C22—121no—
977C22D3×#23511yescharacteristic
978C22D3×#23511yescharacteristic
979C22D32×D411yescharacteristic
980C22D3×#23711yescharacteristic
981C22D3×#23711yescharacteristic
982C22D3×#23711yescharacteristic
983C22C2×D3×#6711yescharacteristic
984C4—41no—
985C4—41no—
986C4—62no—
987C4—121no—
988C4—121no—
989C4—121no—
990C4—121no—
991C4—121no—
992C4—182no—
993C4—361no—
994C4—361no—
995C4—361no—
996C3—21no—
997C3D3×#39711yescharacteristic, complemented
998C3C2×#495211yescharacteristic, complemented
999C2—38no—
1000C2—42no—
1001C2—122no—
1002C2D3×#87911yescharacteristic
1003C2D3×#87911yescharacteristic
1004C2D3×#88311yescharacteristic
1005C2D3×#88511yescharacteristic
1006C2D3×#92911yescharacteristic
1007C2D3×#93511yescharacteristic
1008C2D3×#93911yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC24×C3×D3C22
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#397
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. C2×D3×Dic3⋊C4C2semidirect
5. #10592651C2semidirect
6. C3×#4952C2semidirect
7. #10591717C2semidirect
8. #10591694C2semidirect
9. D3×C3⋊#95C2semidirect
10. D3×C3⋊#95C2semidirect
11. D3×C3⋊#95C2semidirect
12. #10591301C2semidirect
13. #10591299C2semidirect
14. #10591298C2semidirect
15. #10591296C2semidirect
28. C2×#3750C22semidirect
34. C2×C3×Dic3⋊C4C22semidirect
38. C2×#3724C22semidirect
39. C2×Dic3⋊Dic3C22semidirect
45. #63658C22semidirect
46. #63658C22semidirect
47. #63658C22semidirect
48. C3×C3⋊#95C22semidirect
49. C3×C3⋊#95C22semidirect
50. C3×C3⋊#95C22semidirect
51. #63579C22semidirect
52. #63579C22semidirect
53. #63579C22semidirect
54. #63579C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
81. #4952D3direct (N × H)
198. C2×Dic3⋊C4C2×D3semidirect
227. C3⋊#95C2×D3semidirect
228. C3⋊#95C2×D3semidirect
229. C3⋊#95C2×D3semidirect
696. C3×D3#397semidirect
855. C32C2×#397semidirect
954. D3#4952direct (N × H)
997. C3D3×#397semidirect
998. C3C2×#4952semidirect

Maximal subgroups

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

subgroupindex
C2×C3×D3×C22⋊C42
C2×D3×#2172
C2×D3×Dic3⋊C42
#105926512
C3×#49522
#105917172
#105916942
D3×C3⋊#952
#105913012
#105912992
#105912982
#105912962
C2×#49523
D3×#3973