Finite Group Databasebeta

← #11808433

Subgroups — #11808433

Order 1152.

1521 conjugacy classes of subgroups.

The subgroup lattice has 982 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×C4×#67C211yesmaximal, characteristic, complemented
2C2×C3×C4×#67C211yesmaximal, characteristic, complemented
3C2×C4×#625C211yesmaximal, characteristic, complemented
4C2×#63855C211yesmaximal, characteristic, complemented
5C4×#3757C211yesmaximal, characteristic, complemented
6#10591723C211yesmaximal, characteristic
7#10591709C211yesmaximal, characteristic, complemented
8#10591709C211yesmaximal, characteristic, complemented
9#10591691C211yesmaximal, characteristic, complemented
10#10591390C211yesmaximal, characteristic, complemented
11C4×Dic3⋊Dic3C211yesmaximal, characteristic, complemented
12#10591306C211yesmaximal, characteristic, complemented
13#10591301C211yesmaximal, characteristic, complemented
14C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
15#10591200C211yesmaximal, characteristic, complemented
16#82401—31nomaximal
17#82345—31nomaximal
18C23×C32×C4C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C22×C3×#67C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#625C2211yescharacteristic
24C2×#3757C2211yescharacteristic
25C2×#3757C2211yescharacteristic
26C2×C4×C3⋊Dic3C2211yescharacteristic
27C2×C4×C3⋊Dic3C2211yescharacteristic
28C2×C3×#217C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C3×C4×#67—24no—
31C3×C4×#67—24no—
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×C4×Dic3C2211yescharacteristic
37C2×C3×C4×Dic3C2211yescharacteristic
38C2×#3724C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×Dic3⋊Dic3C2211yescharacteristic
41C2×Dic3⋊Dic3C2211yescharacteristic
42C2×Dic3⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C4×#625—24no—
50#63855—24no—
51#63658C2211yescharacteristic
52#63658C2211yescharacteristic
53#63579C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×C4×D4—31no—
58C2×C3×C4×D4—31no—
59C2×C4×#67—31no—
60C2×C4×#67—31no—
61C2×C4×#67D311yescharacteristic, complemented
62C2×C4×#67D311yescharacteristic, complemented
63C2×#926—31no—
64C2×#872—31no—
65#5223—31no—
66#5223—31no—
67#5222—31no—
68#5222—31no—
69C4×#217—31no—
70C4×#217—31no—
71C4×#217—31no—
72C4×#217—61no—
73#4994—31no—
74#4992—31no—
75#4983—31no—
76#4982—31no—
77#4961—31no—
78#4961—31no—
79#4961—31no—
80#4959—31no—
81#4952—31no—
82#4948—31no—
83#4948—31no—
84#4948—31no—
85C4×(C2×D3)⋊C4—31no—
86C4×C4⋊Dic3—31no—
87C4×Dic3⋊C4—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4—22no—
92C22×C32×C4—22no—
93C22×C32×C4—22no—
94C22×C32×C4C2311yescharacteristic
95C22×C32×C4C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C22×C3⋊Dic3C2311yescharacteristic
98C22×C3⋊Dic3C2311yescharacteristic
99C22×C3⋊Dic3C2311yescharacteristic
100C2×C3×#67—22no—
101C2×C3×#67—22no—
102C2×C3×#67—22no—
103C2×C3×#67—22no—
104C2×C3×#67—22no—
105C2×C3×#67—22no—
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C2×C3×C4×D3—22no—
113C2×C3×C4×D3—22no—
114C2×C3×C4×D3—22no—
115C2×C3×C4×D3—22no—
116C2×C3×C4×D3—22no—
117C2×C3×C4×D3D414yescomplemented
118C2×#625—22no—
119C2×#625—22no—
120C2×#625—22no—
121#3757—22no—
122#3757—22no—
123C4×C3⋊Dic3—22no—
124C4×C3⋊Dic3—22no—
125C3×#217—22no—
126C3×#217—22no—
127C3×(C2×D3)⋊C4—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×Dic3⋊C4—22no—
130C3×Dic3⋊C4—22no—
131C3×C4×Dic3—22no—
132C3×C4×Dic3D414yescomplemented
133#3724—22no—
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138(C2×D3)⋊Dic3—22no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143(C2×D3)⋊Dic3—22no—
144#2392—91noSylow
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C23×C3×C4—21no—
148C23×C3×C4—31no—
149C23×C3×C4—31no—
150C23×C3×C4C2×D311yescharacteristic
151C23×C3×C4C2×D311yescharacteristic
152C22×#67—31no—
153C22×#67—31no—
154C22×#67C2×D311yescharacteristic
155C22×#67C2×D311yescharacteristic
156C22×C4×D3C2×D311yescharacteristic
157C22×C4×D3C2×D311yescharacteristic
158C3×C4×D4—64no—
159C3×C4×D4—64no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C22⋊C4—31no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C42—31no—
167C2×C3×C42—31no—
168C2×#217—31no—
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—31no—
178C2×#217—61no—
179C2×#217—61no—
180C2×#217C2×D311yescharacteristic
181C2×#217C2×D311yescharacteristic
182C4×#67—24no—
183C4×#67—24no—
184C4×#67—64no—
185C4×#67—64no—
186C2×(C2×D3)⋊C4—31no—
187C2×(C2×D3)⋊C4—31no—
188C2×(C2×D3)⋊C4—31no—
189C2×(C2×D3)⋊C4—31no—
190C2×(C2×D3)⋊C4—31no—
191C2×(C2×D3)⋊C4—31no—
192C2×(C2×D3)⋊C4C2×D311yescharacteristic
193C2×(C2×D3)⋊C4C2×D311yescharacteristic
194#926—64no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—31no—
201C2×Dic3⋊C4—31no—
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4C2×D311yescharacteristic
206C2×Dic3⋊C4C2×D311yescharacteristic
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209C2×C4×Dic3—31no—
210C2×C4×Dic3—31no—
211C2×C4×Dic3—61no—
212C2×C4×Dic3—61no—
213C2×C4×Dic3C2×D311yescharacteristic
214C2×C4×Dic3C2×D311yescharacteristic
215#872—64no—
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—31no—
226C3⋊#95—31no—
227C3⋊#95—31no—
228C3⋊#95—61no—
229C3⋊#95—61no—
230C23×C32—21no—
231C23×C32—21no—
232C23×C32—21no—
233C23×C32—21no—
234C23×C32—21no—
235C23×C32—21no—
236C23×C32#4112yes—
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—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3—21no—
250C22×C3×D3C2×D412yes—
251C22×C3×D3#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—44no—
256C2×C32×C4C2×D412yes—
257C2×C32×C4C2×D412yes—
258C2×C32×C4#4112yes—
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#4112yes—
271C3×#67—28no—
272C3×#67—28no—
273C2×C3×Dic3—21no—
274C2×C3×Dic3—21no—
275C2×C3×Dic3—21no—
276C2×C3×Dic3—21no—
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×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3#4112yes—
291C3×C4×D3—28no—
292C3×C4×D3—44no—
293#625—28no—
294C2×C4×D4—31no—
295C2×C4×D4—31no—
296C2×C4×D4—91no—
297C2×#117—91no—
298#398—91no—
299#397—91no—
300#396—91no—
301#396—91no—
302#394—91no—
303#394—91no—
304#394—91no—
305#392—91no—
306C4×C4⋊C4—91no—
307C4×C22⋊C4—91no—
308C4×C22⋊C4—91no—
309C24×C3—21no—
310C24×C3—31no—
311C24×C3—31no—
312C24×C3C22×D311yescharacteristic
313C24×C3C22×D311yescharacteristic
314C23×D3C22×D311yescharacteristic
315C23×D3C22×D311yescharacteristic
316C2×C3×D4—62no—
317C2×C3×D4—62no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—62no—
322C22×C3×C4—24no—
323C22×C3×C4—22no—
324C22×C3×C4—22no—
325C22×C3×C4—22no—
326C22×C3×C4—22no—
327C22×C3×C4—22no—
328C22×C3×C4—22no—
329C22×C3×C4—21no—
330C22×C3×C4—21no—
331C22×C3×C4—31no—
332C22×C3×C4—31no—
333C22×C3×C4—31no—
334C22×C3×C4—31no—
335C22×C3×C4—34no—
336C22×C3×C4—31no—
337C22×C3×C4—31no—
338C22×C3×C4—42no—
339C22×C3×C4—42no—
340C22×C3×C4—62no—
341C22×C3×C4—62no—
342C22×C3×C4—62no—
343C22×C3×C4—62no—
344C22×C3×C4—62no—
345C22×C3×C4C22×D311yescharacteristic
346C22×C3×C4C22×D311yescharacteristic
347C22×C3×C4C22×D311yescharacteristic
348C22×C3×C4C22×D311yescharacteristic
349C2×#67—22no—
350C2×#67—22no—
351C2×#67—22no—
352C2×#67—22no—
353C2×#67—22no—
354C2×#67—22no—
355C2×#67—62no—
356C2×#67—62no—
357C2×#67—62no—
358C2×#67—62no—
359C2×#67—62no—
360C2×#67—62no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—31no—
364C22×Dic3—31no—
365C22×Dic3—31no—
366C22×Dic3—31no—
367C22×Dic3—31no—
368C22×Dic3—31no—
369C22×Dic3—61no—
370C22×Dic3—61no—
371C22×Dic3—61no—
372C22×Dic3—61no—
373C22×Dic3C22×D311yescharacteristic
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C2×C4×D3—22no—
380C2×C4×D3—22no—
381C2×C4×D3—22no—
382C2×C4×D3—22no—
383C2×C4×D3—22no—
384C2×C4×D3#6714yescomplemented
385C3×C4⋊C4—62no—
386C3×C4⋊C4—62no—
387C3×C22⋊C4—62no—
388C3×C22⋊C4—62no—
389C3×C22⋊C4—62no—
390C3×C22⋊C4—62no—
391C3×C42—34no—
392C3×C42—62no—
393#217—22no—
394#217—22no—
395#217—62no—
396#217—62no—
397#217—62no—
398#217—62no—
399#217—64no—
400#217—64no—
401#217—62no—
402#217—62no—
403#217—62no—
404#217—62no—
405#217—62no—
406#217—62no—
407(C2×D3)⋊C4—22no—
408(C2×D3)⋊C4—22no—
409(C2×D3)⋊C4—62no—
410(C2×D3)⋊C4—62no—
411(C2×D3)⋊C4—62no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415C4⋊Dic3—62no—
416C4⋊Dic3—62no—
417C4⋊Dic3—62no—
418C4⋊Dic3—62no—
419Dic3⋊C4—22no—
420Dic3⋊C4—22no—
421Dic3⋊C4—62no—
422Dic3⋊C4—62no—
423Dic3⋊C4—62no—
424Dic3⋊C4—62no—
425Dic3⋊C4—62no—
426Dic3⋊C4—62no—
427C4×Dic3—22no—
428C4×Dic3—62no—
429C4×Dic3—62no—
430C4×Dic3—62no—
431C4×Dic3—62no—
432C4×Dic3—122no—
433C4×Dic3—122no—
434C4×Dic3#6714yescomplemented
435C22×C32—22no—
436C22×C32—22no—
437C22×C32—22no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32—41no—
441C22×C32—41no—
442C22×C32C22×D411yescharacteristic
443C22×C32C22×D411yescharacteristic
444C22×C32C2×#4111yescharacteristic
445C22×C32C2×#4111yescharacteristic
446C22×C32C2×#4111yescharacteristic
447C22×C32C2×#4111yescharacteristic
448C22×C32C2×#4111yescharacteristic
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—22no—
454C2×C3×D3—22no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C32×C4—41no—
464C32×C4#12114yes—
465C3⋊Dic3—22no—
466C3⋊Dic3—41no—
467C3⋊Dic3—41no—
468C3⋊Dic3—41no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—41no—
474C3×Dic3—41no—
475C22×D4—31no—
476C22×D4—31no—
477C22×D4—91no—
478C23×C4—31no—
479C23×C4—31no—
480C23×C4D3211yescharacteristic
481C4×D4—64no—
482C4×D4—64no—
483C4×D4—184no—
484#117—184no—
485C2×C4⋊C4—31no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—91no—
488C2×C4⋊C4—91no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C22⋊C4—31no—
493C2×C22⋊C4—31no—
494C2×C22⋊C4—31no—
495C2×C22⋊C4—31no—
496C2×C22⋊C4—91no—
497C2×C22⋊C4—91no—
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×C42—31no—
505C2×C42—31no—
506C2×C42—91no—
507C2×C42—91no—
508#95—91no—
509#95—91no—
510#95—91no—
511#95—91no—
512#95—91no—
513#95—91no—
514C23×C3—22no—
515C23×C3—22no—
516C23×C3—21no—
517C23×C3—21no—
518C23×C3—21no—
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—22no—
530C23×C3—32no—
531C23×C3—32no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—41no—
536C23×C3—61no—
537C23×C3—61no—
538C23×C3—61no—
539C23×C3—61no—
540C23×C3—61no—
541C23×C3—61no—
542C23×C3—61no—
543C23×C3—61no—
544C23×C3—61no—
545C23×C3—61no—
546C23×C3—61no—
547C23×C3—61no—
548C23×C3#23512yes—
549C23×C3#23512yes—
550C23×C3C23×D311yescharacteristic
551C23×C3C23×D311yescharacteristic
552C22×D3—21no—
553C22×D3—21no—
554C22×D3—21no—
555C22×D3—21no—
556C22×D3—21no—
557C22×D3—21no—
558C22×D3—21no—
559C22×D3—21no—
560C22×D3—21no—
561C22×D3—21no—
562C22×D3—21no—
563C22×D3—21no—
564C22×D3#23512yes—
565C22×D3C2×#6712yes—
566C3×D4—68no—
567C3×D4—68no—
568C2×C3×C4—22no—
569C2×C3×C4—21no—
570C2×C3×C4—21no—
571C2×C3×C4—21no—
572C2×C3×C4—21no—
573C2×C3×C4—21no—
574C2×C3×C4—21no—
575C2×C3×C4—22no—
576C2×C3×C4—22no—
577C2×C3×C4—22no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—32no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—48no—
585C2×C3×C4—44no—
586C2×C3×C4—44no—
587C2×C3×C4—61no—
588C2×C3×C4—61no—
589C2×C3×C4—61no—
590C2×C3×C4—61no—
591C2×C3×C4—61no—
592C2×C3×C4—61no—
593C2×C3×C4—61no—
594C2×C3×C4—61no—
595C2×C3×C4—68no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—124no—
603C2×C3×C4D3×D412yes—
604C2×C3×C4D3×D412yes—
605C2×C3×C4#23712yes—
606C2×C3×C4#23712yes—
607C2×C3×C4C2×#6712yes—
608C2×C3×C4C2×#6712yes—
609#67—28no—
610#67—28no—
611#67—68no—
612#67—68no—
613C2×Dic3—21no—
614C2×Dic3—21no—
615C2×Dic3—21no—
616C2×Dic3—21no—
617C2×Dic3—21no—
618C2×Dic3—21no—
619C2×Dic3—21no—
620C2×Dic3—21no—
621C2×Dic3—21no—
622C2×Dic3—21no—
623C2×Dic3—21no—
624C2×Dic3—21no—
625C2×Dic3—21no—
626C2×Dic3—21no—
627C2×Dic3—32no—
628C2×Dic3—32no—
629C2×Dic3—62no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—62no—
635C2×Dic3—62no—
636C2×Dic3—62no—
637C2×Dic3—61no—
638C2×Dic3—61no—
639C2×Dic3—61no—
640C2×Dic3—61no—
641C2×Dic3—61no—
642C2×Dic3—61no—
643C2×Dic3—61no—
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—121no—
656C2×Dic3—121no—
657C2×Dic3—121no—
658C2×Dic3—121no—
659C2×Dic3—121no—
660C2×Dic3—121no—
661C2×Dic3—121no—
662C2×Dic3—121no—
663C2×Dic3#23512yes—
664C2×Dic3C2×#6712yes—
665C2×Dic3C2×#6712yes—
666C2×Dic3C2×#6712yes—
667C4×D3—28no—
668C4×D3—44no—
669C2×C32—42no—
670C2×C32C2×#12111yescharacteristic
671C2×C32#52511yescharacteristic
672C2×C32#52511yescharacteristic
673C2×C32#52511yescharacteristic
674C2×C32#52911yescharacteristic
675C2×C32#52911yescharacteristic
676C2×C32#53211yescharacteristic
677C3×D3—42no—
678C3×D3—42no—
679C24—31no—
680C24—31no—
681C24C2×D3211yescharacteristic
682C2×D4—62no—
683C2×D4—62no—
684C2×D4—62no—
685C2×D4—62no—
686C2×D4—62no—
687C2×D4—62no—
688C2×D4—182no—
689C2×D4—182no—
690C2×D4—182no—
691C22×C4—22no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—34no—
699C22×C4—31no—
700C22×C4—31no—
701C22×C4—62no—
702C22×C4—62no—
703C22×C4—62no—
704C22×C4—62no—
705C22×C4—62no—
706C22×C4—91no—
707C22×C4—91no—
708C22×C4—91no—
709C22×C4—91no—
710C22×C4C2×D3211yescharacteristic
711C22×C4C2×D3211yescharacteristic
712C4⋊C4—62no—
713C4⋊C4—62no—
714C4⋊C4—182no—
715C4⋊C4—182no—
716C4⋊C4—182no—
717C4⋊C4—182no—
718C4⋊C4—182no—
719C22⋊C4—62no—
720C22⋊C4—62no—
721C22⋊C4—62no—
722C22⋊C4—62no—
723C22⋊C4—182no—
724C22⋊C4—182no—
725C22⋊C4—182no—
726C22⋊C4—182no—
727C22⋊C4—182no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—182no—
731C42—34no—
732C42—62no—
733C42—182no—
734C42—182no—
735C22×C3—24no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—22no—
741C22×C3—22no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—21no—
748C22×C3—21no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—42no—
752C22×C3—42no—
753C22×C3—42no—
754C22×C3—42no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—41no—
760C22×C3—41no—
761C22×C3—41no—
762C22×C3—41no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—62no—
766C22×C3—62no—
767C22×C3—62no—
768C22×C3—62no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3—121no—
777C22×C3C2×#23511yescharacteristic
778C22×C3C2×#23511yescharacteristic
779C22×C3C2×#23511yescharacteristic
780C22×C3C2×#23511yescharacteristic
781C22×C3C2×D3×D411yescharacteristic
782C22×C3C2×D3×D411yescharacteristic
783C22×C3C2×#23711yescharacteristic
784C22×C3C2×#23711yescharacteristic
785C22×C3D3×#4111yescharacteristic
786C22×C3D3×#4111yescharacteristic
787C22×C3D3×#4111yescharacteristic
788C22×C3D3×#4111yescharacteristic
789C22×C3C22×#6711yescharacteristic
790C22×C3C22×#6711yescharacteristic
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—22no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C2×D3—41no—
802C2×D3—41no—
803C2×D3—41no—
804C2×D3—41no—
805C3×C4—24no—
806C3×C4—42no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—121no—
814C3×C4—121no—
815C3×C4#93814yes—
816C3×C4#93914yes—
817Dic3—22no—
818Dic3—22no—
819Dic3—22no—
820Dic3—22no—
821Dic3—41no—
822Dic3—41no—
823Dic3—62no—
824Dic3—62no—
825Dic3—122no—
826Dic3—122no—
827Dic3—122no—
828Dic3—122no—
829Dic3—121no—
830Dic3—121no—
831Dic3—121no—
832Dic3—121no—
833Dic3—121no—
834Dic3—121no—
835C32#239211yescharacteristic, complemented, Sylow
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—21no—
842C23—32no—
843C23—32no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—61no—
854C23—61no—
855C23—61no—
856C23#379812yes—
857C23C22×D3211yescharacteristic
858D4—68no—
859D4—68no—
860D4—188no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—32no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—44no—
869C2×C4—61no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—68no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—92no—
885C2×C4—124no—
886C2×C4—181no—
887C2×C4—181no—
888C2×C4—181no—
889C2×C4—181no—
890C2×C4—181no—
891C2×C4—181no—
892C2×C4—181no—
893C2×C4—181no—
894C2×C4—181no—
895C2×C4—181no—
896C2×C4—181no—
897C2×C4#380512yes—
898C2×C4D3×#6712yes—
899C2×C4D3×#6712yes—
900C2×C3—21no—
901C2×C3—21no—
902C2×C3—21no—
903C2×C3—21no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—44no—
908C2×C3—42no—
909C2×C3—42no—
910C2×C3—122no—
911C2×C3—122no—
912C2×C3#553811yescharacteristic
913C2×C3#553811yescharacteristic
914C2×C3#553811yescharacteristic
915C2×C3#554711yescharacteristic
916C2×C3#554711yescharacteristic
917C2×C3#554711yescharacteristic
918C2×C3#554811yescharacteristic
919C2×C3#555711yescharacteristic
920C2×C3#579111yescharacteristic
921C2×C3#579111yescharacteristic
922C2×C3C2×#93811yescharacteristic
923C2×C3C2×#93911yescharacteristic
924C2×C3#582811yescharacteristic
925C2×C3#583211yescharacteristic
926D3—42no—
927D3—42no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—41no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—62no—
936C22—62no—
937C22—62no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22—121no—
946C22—121no—
947C22—121no—
948C22—121no—
949C22C2×#379811yescharacteristic
950C22D3×#23511yescharacteristic
951C22D3×#23511yescharacteristic
952C22#6430611yescharacteristic
953C22C2×#380511yescharacteristic
954C22C2×D3×#6711yescharacteristic
955C22C2×D3×#6711yescharacteristic
956C4—41no—
957C4—62no—
958C4—62no—
959C4—62no—
960C4—62no—
961C4—121no—
962C4—121no—
963C4—182no—
964C4—361no—
965C4—361no—
966C4—361no—
967C4#6397014yes—
968C3—21no—
969C3#8234511yescharacteristic, complemented
970C3#8240111yescharacteristic, complemented
971C2—42no—
972C2—122no—
973C2—122no—
974C2#1059493411yescharacteristic
975C2#1059500211yescharacteristic
976C2#1059500211yescharacteristic
977C2#1059500311yescharacteristic
978C2#1059503311yescharacteristic
979C2#1059506011yescharacteristic
980C2C2×#6397011yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, socle, cosocleC23×C32C24
FrattiniC23C22×D32
FittingC23×C32×C4C22
prime radical#10591723C2
hypercenterC23×C4D32
hypocenterC32#2392
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×C4×#67C2semidirect
2. C2×C3×C4×#67C2semidirect
3. C2×C4×#625C2semidirect
4. C2×#63855C2semidirect
5. C4×#3757C2semidirect
7. #10591709C2semidirect
8. #10591709C2semidirect
9. #10591691C2semidirect
10. #10591390C2semidirect
11. C4×Dic3⋊Dic3C2semidirect
12. #10591306C2semidirect
13. #10591301C2semidirect
14. C4×(C2×D3)⋊Dic3C2semidirect
15. #10591200C2semidirect
61. C2×C4×#67D3semidirect
62. C2×C4×#67D3semidirect
117. C2×C3×C4×D3D4semidirect
132. C3×C4×Dic3D4semidirect
384. C2×C4×D3#67semidirect
434. C4×Dic3#67semidirect
835. C32#2392semidirect
969. C3#82345semidirect
970. C3#82401semidirect

Maximal subgroups

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

subgroupindex
C2×C3×C4×#672
C2×C4×#6252
C2×#638552
C4×#37572
#105917232
#105917092
#105916912
#105913902
C4×Dic3⋊Dic32
#105913062
#105913012
C4×(C2×D3)⋊Dic32
#105912002
#824013
#823453