Finite Group Databasebeta

← #11812930

Subgroups — #11812930

Order 1152.

1433 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×#886C211yesmaximal, characteristic, complemented
2C2×Dic3×#67C211yesmaximal, characteristic, complemented
3C2×#63970C211yesmaximal, characteristic
4C2×D3×C4⋊Dic3C211yesmaximal, characteristic, complemented
5#10592652C211yesmaximal, characteristic, complemented
6C3×#4956C211yesmaximal, characteristic, complemented
7#10591718C211yesmaximal, characteristic, complemented
8#10591709C211yesmaximal, characteristic, complemented
9#10591381C211yesmaximal, characteristic, complemented
10#10591377C211yesmaximal, characteristic, complemented
11#10591363C211yesmaximal, characteristic, complemented
12#10591348C211yesmaximal, characteristic, complemented
13#10591317C211yesmaximal, characteristic, complemented
14#10591284C211yesmaximal, characteristic, complemented
15#10591269C211yesmaximal, characteristic, complemented
16#82897—31nomaximal
17#74703—31nomaximal
18C22×C3×#67C2211yescharacteristic
19C22×C3×#67C2211yescharacteristic
20C23×C3×Dic3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×D3×Dic3C2211yescharacteristic
24C22×D3×Dic3C2211yescharacteristic
25C2×C32×C22⋊C4C2211yescharacteristic
26C2×#3757C2211yescharacteristic
27C2×#3757C2211yescharacteristic
28C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
29C2×C3×#217C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×C4⋊Dic3C2211yescharacteristic
34C2×C3×C4⋊Dic3C2211yescharacteristic
35C3×#886—24no—
36Dic3×#67—24no—
37#63970—24no—
38C2×Dic3⋊Dic3C2211yescharacteristic
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×Dic32C2211yescharacteristic
48D3×C4⋊Dic3—24no—
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51#63658C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×C3×#123—31no—
58C2×#939—31no—
59C2×#938—31no—
60C2×D4×Dic3—31no—
61C2×C4×#67—31no—
62C22×C4⋊Dic3—31no—
63C2×D3×C4⋊C4—31no—
64C2×#886D311yescharacteristic, complemented
65C3×#386—31no—
66#5222—31no—
67#5213—31no—
68#5210—31no—
69#4989—31no—
70#4982—31no—
71#4980—31no—
72#4961—31no—
73#4958—31no—
74#4956—31no—
75#4956—31no—
76#4956D311yescharacteristic, complemented
77#4953—31no—
78#4953—31no—
79#4953—61no—
80#4950—31no—
81#4950—31no—
82#4949—31no—
83#4945—31no—
84#4677—31no—
85#4670—31no—
86#4661—31no—
87#4653—31no—
88C24×C32C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C3⋊Dic3C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C3×#67—22no—
98C2×C3×#67—22no—
99C2×C3×#67—22no—
100C2×C3×#67—22no—
101C2×C3×#67—41no—
102C2×C3×#67D414yes—
103C22×C3×Dic3—22no—
104C22×C3×Dic3—22no—
105C22×C3×Dic3—41no—
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×#625—22no—
116C2×#625—22no—
117C2×#625—22no—
118C2×D3×Dic3—22no—
119C2×D3×Dic3—22no—
120C2×D3×Dic3—22no—
121C2×D3×Dic3—22no—
122C2×D3×Dic3—41no—
123C2×D3×Dic3—41no—
124C32×C22⋊C4—22no—
125#3757—22no—
126#3757—22no—
127C4⋊(C3⋊Dic3)—22no—
128C3×#217—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×C4⋊Dic3—22no—
133C3×C4⋊Dic3D414yescomplemented
134Dic3⋊Dic3—22no—
135Dic3⋊Dic3—22no—
136Dic3⋊Dic3—22no—
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3—41no—
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—41no—
143Dic32—22no—
144#2443—91noSylow
145C22×C3×D4—31no—
146C22×C3×D4—31no—
147C23×C3×C4—31no—
148C23×C3×C4—31no—
149C22×#67—31no—
150C22×#67—31no—
151C22×#67C2×D311yescharacteristic
152C22×#67C2×D311yescharacteristic
153C23×Dic3—31no—
154C23×Dic3—31no—
155C23×Dic3C2×D311yescharacteristic
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3C2×D311yescharacteristic
159C3×#123—64no—
160C2×C3×C4⋊C4—31no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C22⋊C4—21no—
163C2×C3×C22⋊C4—31no—
164C2×C3×C22⋊C4—31no—
165C2×C3×C22⋊C4—31no—
166C2×C3×C22⋊C4—31no—
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×#217C2×D311yescharacteristic
180#939—64no—
181#938—64no—
182D4×Dic3—64no—
183C4×#67—64no—
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×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×C4⋊Dic3—31no—
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×C4⋊Dic3—31no—
195C2×C4⋊Dic3—31no—
196C2×C4⋊Dic3—31no—
197C2×C4⋊Dic3—31no—
198C2×C4⋊Dic3—61no—
199C2×C4⋊Dic3—64no—
200C2×C4⋊Dic3C2×D311yescharacteristic
201C2×C4⋊Dic3C2×D311yescharacteristic
202C2×Dic3⋊C4—31no—
203C2×Dic3⋊C4—31no—
204C2×Dic3⋊C4—31no—
205C2×Dic3⋊C4—31no—
206C2×Dic3⋊C4—31no—
207C2×C4×Dic3—31no—
208C2×C4×Dic3—31no—
209D3×C4⋊C4—64no—
210#886—24no—
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
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—21no—
245C22×C3×D3—21no—
246C22×C3×D3—21no—
247C22×C3×D3—21no—
248C22×C3×D3—21no—
249C22×C3×D3C2×D412yes—
250C22×C3×D3#4112yes—
251C22×C3×D3#4112yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4C2×D412yes—
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—
270C3×#67—28no—
271C3×#67—44no—
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×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—44no—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3C2×D412yes—
289C2×C3×Dic3C2×D412yes—
290C2×C3×Dic3#4112yes—
291C3×C4×D3—28no—
292#625—44no—
293D3×Dic3—44no—
294D3×Dic3—44no—
295C2×#123—31no—
296C2×#121—91no—
297C2×C4×D4—91no—
298C22×C4⋊C4—91no—
299#399—91no—
300#398—91no—
301#397—91no—
302#394—91no—
303#388—91no—
304#387—91no—
305#386—31no—
306#386—91no—
307#386—91no—
308#385—91no—
309#385—91no—
310C24×C3—21no—
311C24×C3—31no—
312C24×C3—31no—
313C24×C3C22×D311yescharacteristic
314C24×C3C22×D311yescharacteristic
315C23×D3C22×D311yescharacteristic
316C23×D3C22×D311yescharacteristic
317C2×C3×D4—34no—
318C2×C3×D4—62no—
319C2×C3×D4—62no—
320C2×C3×D4—62no—
321C2×C3×D4—62no—
322C2×C3×D4—121no—
323C22×C3×C4—21no—
324C22×C3×C4—21no—
325C22×C3×C4—31no—
326C22×C3×C4—31no—
327C22×C3×C4—31no—
328C22×C3×C4—31no—
329C22×C3×C4—31no—
330C22×C3×C4—31no—
331C22×C3×C4—62no—
332C22×C3×C4—62no—
333C22×C3×C4—62no—
334C22×C3×C4—62no—
335C22×C3×C4—62no—
336C22×C3×C4—121no—
337C22×C3×C4C22×D311yescharacteristic
338C22×C3×C4C22×D311yescharacteristic
339C22×C3×C4C22×D311yescharacteristic
340C22×C3×C4C22×D311yescharacteristic
341C2×#67—22no—
342C2×#67—22no—
343C2×#67—22no—
344C2×#67—22no—
345C2×#67—41no—
346C2×#67—62no—
347C2×#67—62no—
348C2×#67—62no—
349C2×#67—62no—
350C2×#67—62no—
351C2×#67—62no—
352C2×#67D1214yes—
353C22×Dic3—22no—
354C22×Dic3—22no—
355C22×Dic3—31no—
356C22×Dic3—31no—
357C22×Dic3—31no—
358C22×Dic3—31no—
359C22×Dic3—31no—
360C22×Dic3—31no—
361C22×Dic3—31no—
362C22×Dic3—31no—
363C22×Dic3—41no—
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—121no—
373C22×Dic3—121no—
374C22×Dic3C22×D311yescharacteristic
375C22×Dic3C22×D311yescharacteristic
376C22×Dic3C22×D311yescharacteristic
377C22×Dic3C22×D311yescharacteristic
378C22×Dic3C22×D311yescharacteristic
379C22×Dic3C22×D311yescharacteristic
380C2×C4×D3—22no—
381C2×C4×D3—22no—
382C2×C4×D3—22no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—62no—
386C2×C4×D3—62no—
387C2×C4×D3—121no—
388C2×C4×D3—121no—
389C3×C4⋊C4—34no—
390C3×C4⋊C4—62no—
391C3×C22⋊C4—22no—
392C3×C22⋊C4—22no—
393C3×C22⋊C4—42no—
394C3×C22⋊C4—62no—
395C3×C22⋊C4—62no—
396C3×C22⋊C4—62no—
397C3×C22⋊C4—62no—
398#217—22no—
399#217—62no—
400#217—62no—
401#217—62no—
402#217—62no—
403#217—62no—
404#217—62no—
405#217—62no—
406#217—122no—
407#217—122no—
408#217—121no—
409(C2×D3)⋊C4—22no—
410(C2×D3)⋊C4—22no—
411(C2×D3)⋊C4—22no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—121no—
416C4⋊Dic3—22no—
417C4⋊Dic3—62no—
418C4⋊Dic3—62no—
419C4⋊Dic3—62no—
420C4⋊Dic3—62no—
421C4⋊Dic3—62no—
422C4⋊Dic3—62no—
423C4⋊Dic3—122no—
424C4⋊Dic3—121no—
425C4⋊Dic3#6714yescomplemented
426Dic3⋊C4—62no—
427Dic3⋊C4—62no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—121no—
431C4×Dic3—62no—
432C4×Dic3—62no—
433C22×C32—22no—
434C22×C32—22no—
435C22×C32—22no—
436C22×C32—41no—
437C22×C32—41no—
438C22×C32—41no—
439C22×C32—41no—
440C22×C32C22×D411yescharacteristic
441C22×C32C22×D411yescharacteristic
442C22×C32C2×#4111yescharacteristic
443C22×C32C2×#4111yescharacteristic
444C22×C32C2×#4111yescharacteristic
445C22×C32H(5,𝔽2)11yescharacteristic
446C22×C322−1+411yescharacteristic
447C2×C3×D3—22no—
448C2×C3×D3—22no—
449C2×C3×D3—22no—
450C2×C3×D3—22no—
451C2×C3×D3—22no—
452C2×C3×D3—22no—
453C2×C3×D3—41no—
454C2×C3×D3—41no—
455C2×C3×D3—41no—
456C2×C3×D3—41no—
457C2×C3×D3—41no—
458C2×C3×D3—41no—
459C2×C3×D3—41no—
460C2×C3×D3#12314yescomplemented
461C32×C4—22no—
462C32×C4—41no—
463C3⋊Dic3—41no—
464C3⋊Dic3—41no—
465C3⋊Dic3—41no—
466C3⋊Dic3—41no—
467C3×Dic3—22no—
468C3×Dic3—22no—
469C3×Dic3—22no—
470C3×Dic3—22no—
471C3×Dic3—41no—
472C3×Dic3—41no—
473C22×D4—31no—
474C22×D4—31no—
475C22×D4—91no—
476C23×C4—31no—
477C23×C4—31no—
478C23×C4—91no—
479C23×C4—91no—
480#123—64no—
481#121—184no—
482C4×D4—184no—
483C2×C4⋊C4—31no—
484C2×C4⋊C4—31no—
485C2×C4⋊C4—91no—
486C2×C4⋊C4—91no—
487C2×C4⋊C4—91no—
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—91no—
497C2×C22⋊C4—91no—
498C2×C22⋊C4—91no—
499C2×C22⋊C4—91no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4D3211yescharacteristic
503C2×C42—91no—
504#95—31no—
505#95—31no—
506#95—91no—
507#95—91no—
508#95—91no—
509#95—91no—
510#95—91no—
511#95—91no—
512C23×C3—21no—
513C23×C3—21no—
514C23×C3—21no—
515C23×C3—21no—
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—22no—
526C23×C3—32no—
527C23×C3—32no—
528C23×C3—32no—
529C23×C3—41no—
530C23×C3—41no—
531C23×C3—41no—
532C23×C3—41no—
533C23×C3—41no—
534C23×C3—41no—
535C23×C3—61no—
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×C3C2×D1212yes—
547C23×C3D3×D412yes—
548C23×C3C23×D311yescharacteristic
549C23×C3C23×D311yescharacteristic
550C22×D3—21no—
551C22×D3—21no—
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×D3C2×D1212yes—
562C22×D3#23712yes—
563C22×D3#23712yes—
564C3×D4—68no—
565C3×D4—124no—
566C2×C3×C4—21no—
567C2×C3×C4—21no—
568C2×C3×C4—21no—
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—21no—
576C2×C3×C4—22no—
577C2×C3×C4—32no—
578C2×C3×C4—32no—
579C2×C3×C4—32no—
580C2×C3×C4—32no—
581C2×C3×C4—41no—
582C2×C3×C4—41no—
583C2×C3×C4—41no—
584C2×C3×C4—41no—
585C2×C3×C4—41no—
586C2×C3×C4—68no—
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—61no—
596C2×C3×C4—61no—
597C2×C3×C4—61no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—124no—
602C2×C3×C4D3×D412yes—
603C2×C3×C4C2×#6712yes—
604#67—28no—
605#67—44no—
606#67—124no—
607#67—124no—
608C2×Dic3—21no—
609C2×Dic3—21no—
610C2×Dic3—21no—
611C2×Dic3—21no—
612C2×Dic3—21no—
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—44no—
623C2×Dic3—61no—
624C2×Dic3—61no—
625C2×Dic3—61no—
626C2×Dic3—61no—
627C2×Dic3—61no—
628C2×Dic3—61no—
629C2×Dic3—61no—
630C2×Dic3—61no—
631C2×Dic3—61no—
632C2×Dic3—61no—
633C2×Dic3—61no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
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—121no—
648C2×Dic3—121no—
649C2×Dic3—121no—
650C2×Dic3—121no—
651C2×Dic3—121no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3—121no—
656C2×Dic3—121no—
657C2×Dic3—121no—
658C2×Dic3—121no—
659C2×Dic3—124no—
660C2×Dic3—124no—
661C2×Dic3C2×D1212yes—
662C2×Dic3#23712yes—
663C2×Dic3C2×#6712yes—
664C2×Dic3C2×#6712yes—
665C4×D3—28no—
666C4×D3—124no—
667C4×D3—124no—
668C2×C32—42no—
669C2×C32C2×#12311yescharacteristic
670C2×C32#52511yescharacteristic
671C2×C32#53911yescharacteristic
672C2×C32D4211yescharacteristic
673C2×C32#54711yescharacteristic
674C2×C32#54811yescharacteristic
675C2×C32#55311yescharacteristic
676C3×D3—24no—
677C3×D3—81no—
678C24—31no—
679C24—31no—
680C24C2×D3211yescharacteristic
681C2×D4—34no—
682C2×D4—62no—
683C2×D4—62no—
684C2×D4—62no—
685C2×D4—62no—
686C2×D4—121no—
687C2×D4—182no—
688C2×D4—182no—
689C2×D4—182no—
690C22×C4—31no—
691C22×C4—31no—
692C22×C4—31no—
693C22×C4—31no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—62no—
697C22×C4—62no—
698C22×C4—62no—
699C22×C4—62no—
700C22×C4—62no—
701C22×C4—91no—
702C22×C4—91no—
703C22×C4—91no—
704C22×C4—91no—
705C22×C4—121no—
706C22×C4—182no—
707C22×C4—182no—
708C22×C4—182no—
709C22×C4—182no—
710C22×C4—361no—
711C22×C4—361no—
712C22×C4C2×D3211yescharacteristic
713C22×C4C2×D3211yescharacteristic
714C4⋊C4—34no—
715C4⋊C4—62no—
716C4⋊C4—182no—
717C4⋊C4—182no—
718C4⋊C4—182no—
719C4⋊C4—182no—
720C4⋊C4—182no—
721C4⋊C4—361no—
722C22⋊C4—22no—
723C22⋊C4—62no—
724C22⋊C4—62no—
725C22⋊C4—62no—
726C22⋊C4—62no—
727C22⋊C4—182no—
728C22⋊C4—182no—
729C22⋊C4—182no—
730C22⋊C4—182no—
731C22⋊C4—182no—
732C22⋊C4—361no—
733C42—182no—
734C22×C3—22no—
735C22×C3—22no—
736C22×C3—22no—
737C22×C3—22no—
738C22×C3—22no—
739C22×C3—22no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—21no—
746C22×C3—21no—
747C22×C3—34no—
748C22×C3—42no—
749C22×C3—42no—
750C22×C3—42no—
751C22×C3—41no—
752C22×C3—41no—
753C22×C3—41no—
754C22×C3—41no—
755C22×C3—41no—
756C22×C3—41no—
757C22×C3—41no—
758C22×C3—41no—
759C22×C3—62no—
760C22×C3—62no—
761C22×C3—62no—
762C22×C3—62no—
763C22×C3—62no—
764C22×C3—62no—
765C22×C3—81no—
766C22×C3—81no—
767C22×C3—81no—
768C22×C3—81no—
769C22×C3—121no—
770C22×C3—121no—
771C22×C3—121no—
772C22×C3—121no—
773C22×C3—121no—
774C22×C3—121no—
775C22×C3—121no—
776C22×C3C22×D1211yescharacteristic
777C22×C3C2×D3×D411yescharacteristic
778C22×C3C2×D3×D411yescharacteristic
779C22×C3C2×#23711yescharacteristic
780C22×C3C2×#23711yescharacteristic
781C22×C3C2×#23711yescharacteristic
782C22×C3#100411yescharacteristic
783C22×C3D3×#4111yescharacteristic
784C22×C3D3×#4111yescharacteristic
785C22×C3D3×#4111yescharacteristic
786C22×C3#100911yescharacteristic
787C22×C3#101011yescharacteristic
788C22×C3#101011yescharacteristic
789C22×C3C22×#6711yescharacteristic
790C2×D3—22no—
791C2×D3—22no—
792C2×D3—22no—
793C2×D3—22no—
794C2×D3—22no—
795C2×D3—22no—
796C2×D3—41no—
797C2×D3—41no—
798C2×D3—41no—
799C2×D3—41no—
800C2×D3—41no—
801C2×D3—41no—
802C2×D3—41no—
803C2×D3#88614yescomplemented
804C3×C4—22no—
805C3×C4—22no—
806C3×C4—42no—
807C3×C4—41no—
808C3×C4—41no—
809C3×C4—62no—
810C3×C4—62no—
811C3×C4—62no—
812C3×C4—62no—
813C3×C4—81no—
814C3×C4—121no—
815C3×C4—121no—
816Dic3—22no—
817Dic3—22no—
818Dic3—22no—
819Dic3—22no—
820Dic3—41no—
821Dic3—41no—
822Dic3—121no—
823Dic3—121no—
824Dic3—121no—
825Dic3—121no—
826Dic3—121no—
827Dic3—121no—
828Dic3—121no—
829Dic3—121no—
830Dic3—241no—
831Dic3—241no—
832Dic3—241no—
833Dic3—241no—
834C32#244311yescharacteristic, complemented, Sylow
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—32no—
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—
855C23D3×D1212yes—
856C23C22×D3211yescharacteristic
857D4—68no—
858D4—124no—
859D4—364no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—32no—
866C2×C4—32no—
867C2×C4—32no—
868C2×C4—32no—
869C2×C4—68no—
870C2×C4—61no—
871C2×C4—61no—
872C2×C4—61no—
873C2×C4—61no—
874C2×C4—61no—
875C2×C4—61no—
876C2×C4—61no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—124no—
885C2×C4—181no—
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—364no—
898C2×C4—364no—
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—42no—
908C2×C3—42no—
909C2×C3—64no—
910C2×C3—82no—
911C2×C3—241no—
912C2×C3C2×#88611yescharacteristic
913C2×C3D4×D1211yescharacteristic
914C2×C3#555511yescharacteristic
915C2×C3#558611yescharacteristic
916C2×C3#559811yescharacteristic
917C2×C3#561811yescharacteristic
918C2×C3D3×#12311yescharacteristic
919C2×C3#565511yescharacteristic
920C2×C3#566011yescharacteristic
921C2×C3#566111yescharacteristic
922C2×C3#566511yescharacteristic
923C2×C3D4×#6711yescharacteristic
924C2×C3#582811yescharacteristic
925C2×C3#583111yescharacteristic
926D3—24no—
927D3—81no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—34no—
932C22—41no—
933C22—41no—
934C22—41no—
935C22—41no—
936C22—62no—
937C22—62no—
938C22—62no—
939C22—62no—
940C22—62no—
941C22—62no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22—121no—
946C22—121no—
947C22—121no—
948C22—121no—
949C22C2×D3×D1211yescharacteristic
950C22#6430711yescharacteristic
951C22#6430911yescharacteristic
952C22D3×#23711yescharacteristic
953C22D3×#23711yescharacteristic
954C22D3×#23711yescharacteristic
955C22C2×D3×#6711yescharacteristic
956C4—22no—
957C4—41no—
958C4—62no—
959C4—62no—
960C4—62no—
961C4—62no—
962C4—121no—
963C4—121no—
964C4—361no—
965C4—361no—
966C4—361no—
967C4—361no—
968C3—21no—
969C3#7470311yescharacteristic, complemented
970C3#8289711yescharacteristic, complemented
971C2—42no—
972C2—64no—
973C2—241no—
974C2#1059407711yescharacteristic
975C2#1059412311yescharacteristic
976C2#1059421211yescharacteristic
977C2D3×#88611yescharacteristic
978C2D12×#6711yescharacteristic
979C2#1059515411yescharacteristic
980C2#1059515711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C22⋊C4C22
prime radicalC2×#63970C2
hypercenterC2×C22⋊C4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#886C2semidirect
2. C2×Dic3×#67C2semidirect
4. C2×D3×C4⋊Dic3C2semidirect
5. #10592652C2semidirect
6. C3×#4956C2semidirect
7. #10591718C2semidirect
8. #10591709C2semidirect
9. #10591381C2semidirect
10. #10591377C2semidirect
11. #10591363C2semidirect
12. #10591348C2semidirect
13. #10591317C2semidirect
14. #10591284C2semidirect
15. #10591269C2semidirect
64. C2×#886D3semidirect
76. #4956D3semidirect
133. C3×C4⋊Dic3D4semidirect
425. C4⋊Dic3#67semidirect
460. C2×C3×D3#123semidirect
803. C2×D3#886semidirect
834. C32#2443semidirect
969. C3#74703semidirect
970. C3#82897semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8862
C2×Dic3×#672
C2×#639702
C2×D3×C4⋊Dic32
#105926522
C3×#49562
#105917182
#105917092
#105913812
#105913772
#105913632
#105913482
#105913172
#105912842
#105912692
#828973
#747033