Finite Group Databasebeta

← #11812926

Subgroups — #11812926

Order 1152.

1465 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#63912C211yesmaximal, characteristic
2C2×#63905C211yesmaximal, characteristic, complemented
3C2×#63904C211yesmaximal, characteristic, complemented
4C2×#63883C211yesmaximal, characteristic, complemented
5#10592688C211yesmaximal, characteristic, complemented
6C3×#4993C211yesmaximal, characteristic, complemented
7C3×#4989C211yesmaximal, characteristic, complemented
8#10591390C211yesmaximal, characteristic, complemented
9#10591301C211yesmaximal, characteristic, complemented
10#10591285C211yesmaximal, characteristic, complemented
11#10591275C211yesmaximal, characteristic, complemented
12#10591275C211yesmaximal, characteristic, complemented
13#10591275C211yesmaximal, characteristic, complemented
14#10591250C211yesmaximal, characteristic, complemented
15#10591198C211yesmaximal, characteristic, complemented
16#78103—31nomaximal
17#74608—31nomaximal
18C22×C4×C3⋊D3C2211yescharacteristic
19C22×C3×C4×D3C2211yescharacteristic
20C22×#626C2211yescharacteristic
21C22×#626C2211yescharacteristic
22C22×#625C2211yescharacteristic
23C22×#624C2211yescharacteristic
24C22×#624C2211yescharacteristic
25C2×C32×C4⋊C4C2211yescharacteristic
26C2×#3752C2211yescharacteristic
27C2×#3752C2211yescharacteristic
28C2×#3750C2211yescharacteristic
29C2×C3×(C2×D3)⋊C4C2211yescharacteristic
30C2×C3×(C2×D3)⋊C4C2211yescharacteristic
31C2×C3×(C2×D3)⋊C4C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×Dic3⋊C4C2211yescharacteristic
35C2×C3×Dic3⋊C4C2211yescharacteristic
36C2×C3×Dic3⋊C4C2211yescharacteristic
37C2×#3724C2211yescharacteristic
38C2×Dic3⋊Dic3C2211yescharacteristic
39C2×Dic3⋊Dic3C2211yescharacteristic
40C2×(C2×D3)⋊Dic3C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×Dic32C2211yescharacteristic
45#63912—24no—
46#63905—24no—
47#63904—24no—
48#63883—24no—
49#63658C2211yescharacteristic
50#63658C2211yescharacteristic
51C3×C3⋊#95C2211yescharacteristic
52C3×C3⋊#95C2211yescharacteristic
53C3×C3⋊#95C2211yescharacteristic
54#63579C2211yescharacteristic
55#63579C2211yescharacteristic
56#63579C2211yescharacteristic
57C2×#929—31no—
58C2×C4×#67—31no—
59C2×#893—31no—
60C2×D3×C4⋊C4—31no—
61C2×D3×C4⋊C4—31no—
62C2×#884—31no—
63C2×#884—31no—
64C2×#883—31no—
65C3×#399—31no—
66C3×#385—31no—
67#4993D311yescharacteristic, complemented
68#4992—31no—
69#4990—31no—
70#4989—31no—
71#4989—31no—
72#4989—61no—
73#4989D311yescharacteristic, complemented
74#4983—31no—
75#4961—31no—
76#4959—31no—
77#4956—31no—
78#4956—31no—
79#4956—31no—
80#4952—31no—
81#4944—31no—
82#4665—31no—
83#4665—31no—
84#4665—31no—
85#4657—31no—
86#4653—31no—
87#4652—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C22×C32×C4C2311yescharacteristic
92C22×C32×C4C2311yescharacteristic
93C22×C32×C4C2311yescharacteristic
94C22×C3⋊Dic3C2311yescharacteristic
95C22×C3⋊Dic3C2311yescharacteristic
96C22×C3⋊Dic3C2311yescharacteristic
97C2×C4×C3⋊D3—22no—
98C2×C4×C3⋊D3—22no—
99C2×C4×C3⋊D3—41no—
100C22×C3×Dic3C2311yescharacteristic
101C22×C3×Dic3C2311yescharacteristic
102C22×C3×Dic3C2311yescharacteristic
103C22×C3×Dic3C2311yescharacteristic
104C22×C3×Dic3C2311yescharacteristic
105C22×C3×Dic3C2311yescharacteristic
106C2×C3×C4×D3—22no—
107C2×C3×C4×D3—22no—
108C2×C3×C4×D3—41no—
109C2×#626—22no—
110C2×#626—22no—
111C2×#626—22no—
112C2×#626—22no—
113C2×#626—22no—
114C2×#626D414yes—
115C2×#625—22no—
116C2×#625—22no—
117C2×#625—41no—
118C2×#624—22no—
119C2×#624—22no—
120C2×#624—22no—
121C2×#624—22no—
122C2×#624—22no—
123C2×#624—41no—
124C32×C4⋊C4—41no—
125#3752—22no—
126#3752—22no—
127#3750—22no—
128C3×(C2×D3)⋊C4—22no—
129C3×(C2×D3)⋊C4—22no—
130C3×(C2×D3)⋊C4—22no—
131C3×(C2×D3)⋊C4—22no—
132C3×(C2×D3)⋊C4—41no—
133C3×Dic3⋊C4—22no—
134C3×Dic3⋊C4—22no—
135C3×Dic3⋊C4—22no—
136#3724—22no—
137Dic3⋊Dic3—22no—
138Dic3⋊Dic3D414yescomplemented
139(C2×D3)⋊Dic3—22no—
140(C2×D3)⋊Dic3—22no—
141(C2×D3)⋊Dic3—22no—
142(C2×D3)⋊Dic3—22no—
143Dic32—22no—
144#2443—91noSylow
145C23×C3×C4—31no—
146C22×#67—31no—
147C22×#67—31no—
148C22×#67—31no—
149C22×#67—31no—
150C22×D12—31no—
151C22×D12—31no—
152C22×C4×D3—31no—
153C22×C4×D3—31no—
154C22×C4×D3—31no—
155C22×C4×D3—31no—
156C22×C4×D3—31no—
157C22×C4×D3—31no—
158C22×C4×D3—61no—
159C22×C4×D3C2×D311yescharacteristic
160C2×C3×C4⋊C4—21no—
161C2×C3×C4⋊C4—31no—
162C2×C3×C4⋊C4—31no—
163C2×C3×C4⋊C4—31no—
164C2×C3×C4⋊C4C2×D311yescharacteristic
165C2×C3×C4⋊C4C2×D311yescharacteristic
166C2×C3×C22⋊C4—31no—
167C2×C3×C22⋊C4—31no—
168C2×C3×C22⋊C4—31no—
169C2×C3×C22⋊C4—31no—
170C2×C3×C22⋊C4—31no—
171C2×#217—31no—
172C2×#217—31no—
173C2×#217—31no—
174C2×#217—31no—
175#929—64no—
176C4×#67—64no—
177C2×(C2×D3)⋊C4—31no—
178C2×(C2×D3)⋊C4—31no—
179C2×(C2×D3)⋊C4—31no—
180C2×(C2×D3)⋊C4—31no—
181C2×(C2×D3)⋊C4—31no—
182C2×(C2×D3)⋊C4—31no—
183C2×(C2×D3)⋊C4—31no—
184C2×(C2×D3)⋊C4—31no—
185C2×(C2×D3)⋊C4—61no—
186C2×(C2×D3)⋊C4—61no—
187C2×(C2×D3)⋊C4C2×D311yescharacteristic
188C2×(C2×D3)⋊C4C2×D311yescharacteristic
189C2×(C2×D3)⋊C4C2×D311yescharacteristic
190C2×(C2×D3)⋊C4C2×D311yescharacteristic
191C2×(C2×D3)⋊C4C2×D311yescharacteristic
192C2×C4⋊Dic3—31no—
193C2×C4⋊Dic3—31no—
194C2×Dic3⋊C4—31no—
195C2×Dic3⋊C4—31no—
196C2×Dic3⋊C4—31no—
197C2×Dic3⋊C4—31no—
198C2×Dic3⋊C4—31no—
199C2×Dic3⋊C4—31no—
200C2×Dic3⋊C4—61no—
201C2×Dic3⋊C4C2×D311yescharacteristic
202C2×Dic3⋊C4C2×D311yescharacteristic
203C2×Dic3⋊C4C2×D311yescharacteristic
204C2×C4×Dic3—31no—
205C2×C4×Dic3—31no—
206#893—64no—
207D3×C4⋊C4—64no—
208D3×C4⋊C4—64no—
209#884—64no—
210#884—64no—
211#883—64no—
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⋊#95C2×D311yescharacteristic
228C3⋊#95C2×D311yescharacteristic
229C3⋊#95C2×D311yescharacteristic
230C23×C32C2411yescharacteristic
231C22×C3⋊D3—21no—
232C22×C3⋊D3—21no—
233C22×C3⋊D3—21no—
234C22×C3⋊D3—21no—
235C22×C3⋊D3C2×D412yes—
236C22×C3⋊D3#4112yes—
237C22×C3⋊D3#4112yes—
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×D3—21no—
251C22×C3×D3C2×D412yes—
252C2×C32×C4—21no—
253C2×C32×C4—21no—
254C2×C32×C4—21no—
255C2×C32×C4—21no—
256C2×C32×C4—21no—
257C2×C32×C4—21no—
258C2×C32×C4—21no—
259C2×C32×C4—21no—
260C2×C32×C4—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⋊Dic3C2×D412yes—
270C4×C3⋊D3—44no—
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×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×Dic3C2×D412yes—
286C2×C3×Dic3C2×D412yes—
287C2×C3×Dic3C2×D412yes—
288C2×C3×Dic3#4112yes—
289C3×C4×D3—44no—
290#626—28no—
291#626—44no—
292#625—44no—
293#624—28no—
294#624—44no—
295C2×#123—91no—
296C2×#121—91no—
297C2×C4×D4—91no—
298C22×C4⋊C4—91no—
299#399—31no—
300#398—91no—
301#397—91no—
302#394—91no—
303#388—91no—
304#387—91no—
305#386—91no—
306#386—91no—
307#386—91no—
308#385—31no—
309#385—91no—
310C24×C3—31no—
311C24×C3—31no—
312C23×D3—31no—
313C23×D3—31no—
314C23×D3—61no—
315C23×D3C22×D311yescharacteristic
316C23×D3C22×D311yescharacteristic
317C22×C3×C4—21no—
318C22×C3×C4—21no—
319C22×C3×C4—21no—
320C22×C3×C4—31no—
321C22×C3×C4—31no—
322C22×C3×C4—31no—
323C22×C3×C4—31no—
324C22×C3×C4—31no—
325C22×C3×C4—31no—
326C22×C3×C4—62no—
327C22×C3×C4—62no—
328C22×C3×C4—121no—
329C22×C3×C4C22×D311yescharacteristic
330C22×C3×C4C22×D311yescharacteristic
331C22×C3×C4C22×D311yescharacteristic
332C22×C3×C4C22×D311yescharacteristic
333C22×C3×C4C22×D311yescharacteristic
334C22×C3×C4C22×D311yescharacteristic
335C2×#67—34no—
336C2×#67—62no—
337C2×#67—62no—
338C2×#67—62no—
339C2×#67—62no—
340C2×#67—62no—
341C2×#67—62no—
342C2×#67—62no—
343C2×#67—62no—
344C2×#67—62no—
345C2×#67—121no—
346C2×#67—121no—
347C22×Dic3—31no—
348C22×Dic3—31no—
349C22×Dic3—31no—
350C22×Dic3—31no—
351C22×Dic3—31no—
352C22×Dic3—31no—
353C22×Dic3—61no—
354C22×Dic3—61no—
355C22×Dic3—61no—
356C22×Dic3C22×D311yescharacteristic
357C22×Dic3C22×D311yescharacteristic
358C22×Dic3C22×D311yescharacteristic
359C22×Dic3C22×D311yescharacteristic
360C22×Dic3C22×D311yescharacteristic
361C22×Dic3C22×D311yescharacteristic
362C2×D12—34no—
363C2×D12—62no—
364C2×D12—62no—
365C2×D12—62no—
366C2×D12—62no—
367C2×D12—62no—
368C2×C4×D3—22no—
369C2×C4×D3—22no—
370C2×C4×D3—41no—
371C2×C4×D3—62no—
372C2×C4×D3—62no—
373C2×C4×D3—62no—
374C2×C4×D3—62no—
375C2×C4×D3—62no—
376C2×C4×D3—62no—
377C2×C4×D3—62no—
378C2×C4×D3—62no—
379C2×C4×D3—62no—
380C2×C4×D3—62no—
381C2×C4×D3—62no—
382C2×C4×D3—62no—
383C2×C4×D3—62no—
384C2×C4×D3—62no—
385C2×C4×D3—122no—
386C2×C4×D3—122no—
387C2×C4×D3—121no—
388C2×C4×D3—121no—
389C2×C4×D3—121no—
390C2×C4×D3—121no—
391C2×C4×D3—122no—
392C3×C4⋊C4—41no—
393C3×C4⋊C4—41no—
394C3×C4⋊C4—42no—
395C3×C4⋊C4—62no—
396C3×C4⋊C4—62no—
397C3×C4⋊C4—62no—
398C3×C22⋊C4—62no—
399C3×C22⋊C4—62no—
400C3×C22⋊C4—62no—
401C3×C22⋊C4—62no—
402C3×C22⋊C4—121no—
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—22no—
410(C2×D3)⋊C4—22no—
411(C2×D3)⋊C4—41no—
412(C2×D3)⋊C4—62no—
413(C2×D3)⋊C4—62no—
414(C2×D3)⋊C4—62no—
415(C2×D3)⋊C4—62no—
416(C2×D3)⋊C4—64no—
417(C2×D3)⋊C4—62no—
418(C2×D3)⋊C4—62no—
419(C2×D3)⋊C4—62no—
420(C2×D3)⋊C4—62no—
421(C2×D3)⋊C4—122no—
422C4⋊Dic3—34no—
423C4⋊Dic3—62no—
424Dic3⋊C4—22no—
425Dic3⋊C4—22no—
426Dic3⋊C4—22no—
427Dic3⋊C4—34no—
428Dic3⋊C4—62no—
429Dic3⋊C4—62no—
430Dic3⋊C4—62no—
431Dic3⋊C4—62no—
432Dic3⋊C4—62no—
433Dic3⋊C4—122no—
434C4×Dic3—62no—
435C4×Dic3—62no—
436C22×C32C22×D411yescharacteristic
437C22×C32C22×D411yescharacteristic
438C22×C32C2×#4111yescharacteristic
439C22×C32C2×#4111yescharacteristic
440C22×C32C2×#4111yescharacteristic
441C22×C32H(5,𝔽2)11yescharacteristic
442C22×C322−1+411yescharacteristic
443C2×C3⋊D3—22no—
444C2×C3⋊D3—22no—
445C2×C3⋊D3—22no—
446C2×C3⋊D3—22no—
447C2×C3⋊D3—22no—
448C2×C3⋊D3—22no—
449C2×C3⋊D3#12314yescomplemented
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—41no—
461C2×C3×D3—41no—
462C2×C3×D3—41no—
463C2×C3×D3—41no—
464C32×C4—41no—
465C32×C4—41no—
466C32×C4—41no—
467C3⋊Dic3—22no—
468C3⋊Dic3—41no—
469C3⋊Dic3—41no—
470C3×Dic3—22no—
471C3×Dic3—22no—
472C3×Dic3—22no—
473C3×Dic3—22no—
474C3×Dic3—41no—
475C3×Dic3—41no—
476C22×D4—91no—
477C22×D4—91no—
478C22×D4—91no—
479C23×C4—31no—
480C23×C4—91no—
481C23×C4—91no—
482C23×C4—91no—
483#123—184no—
484#121—184no—
485C4×D4—184no—
486C2×C4⋊C4—31no—
487C2×C4⋊C4—31no—
488C2×C4⋊C4—31no—
489C2×C4⋊C4—91no—
490C2×C4⋊C4—91no—
491C2×C4⋊C4—91no—
492C2×C4⋊C4—91no—
493C2×C4⋊C4—184no—
494C2×C4⋊C4D3211yescharacteristic
495C2×C22⋊C4—31no—
496C2×C22⋊C4—31no—
497C2×C22⋊C4—31no—
498C2×C22⋊C4—31no—
499C2×C22⋊C4—31no—
500C2×C22⋊C4—91no—
501C2×C22⋊C4—91no—
502C2×C22⋊C4—91no—
503C2×C22⋊C4—91no—
504C2×C22⋊C4—91no—
505C2×C22⋊C4—91no—
506C2×C42—91no—
507#95—31no—
508#95—31no—
509#95—31no—
510#95—91no—
511#95—91no—
512#95—91no—
513#95—91no—
514#95—91no—
515C23×C3—21no—
516C23×C3—32no—
517C23×C3—61no—
518C23×C3—61no—
519C23×C3—61no—
520C23×C3—61no—
521C23×C3—61no—
522C23×C3—61no—
523C23×C3—61no—
524C23×C3—61no—
525C23×C3—61no—
526C23×C3—61no—
527C23×C3—61no—
528C23×C3—61no—
529C23×C3—61no—
530C23×C3C23×D311yescharacteristic
531C23×C3C23×D311yescharacteristic
532C22×D3—21no—
533C22×D3—21no—
534C22×D3—21no—
535C22×D3—21no—
536C22×D3—21no—
537C22×D3—21no—
538C22×D3—21no—
539C22×D3—21no—
540C22×D3—21no—
541C22×D3—21no—
542C22×D3—21no—
543C22×D3—21no—
544C22×D3—21no—
545C22×D3—32no—
546C22×D3—32no—
547C22×D3—32no—
548C22×D3—32no—
549C22×D3—32no—
550C22×D3—32no—
551C22×D3—62no—
552C22×D3—62no—
553C22×D3—62no—
554C22×D3—61no—
555C22×D3—61no—
556C22×D3—61no—
557C22×D3—61no—
558C22×D3—61no—
559C22×D3—61no—
560C22×D3—61no—
561C22×D3—61no—
562C22×D3—121no—
563C22×D3—121no—
564C22×D3—121no—
565C22×D3—121no—
566C22×D3D3×D412yes—
567C2×C3×C4—22no—
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—21no—
576C2×C3×C4—21no—
577C2×C3×C4—21no—
578C2×C3×C4—21no—
579C2×C3×C4—21no—
580C2×C3×C4—21no—
581C2×C3×C4—21no—
582C2×C3×C4—21no—
583C2×C3×C4—21no—
584C2×C3×C4—21no—
585C2×C3×C4—21no—
586C2×C3×C4—21no—
587C2×C3×C4—32no—
588C2×C3×C4—32no—
589C2×C3×C4—32no—
590C2×C3×C4—32no—
591C2×C3×C4—41no—
592C2×C3×C4—41no—
593C2×C3×C4—41no—
594C2×C3×C4—41no—
595C2×C3×C4—41no—
596C2×C3×C4—41no—
597C2×C3×C4—41no—
598C2×C3×C4—61no—
599C2×C3×C4—61no—
600C2×C3×C4—61no—
601C2×C3×C4—61no—
602C2×C3×C4—61no—
603C2×C3×C4—61no—
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—124no—
613#67—68no—
614#67—124no—
615#67—124no—
616#67—124no—
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—21no—
628C2×Dic3—21no—
629C2×Dic3—21no—
630C2×Dic3—21no—
631C2×Dic3—32no—
632C2×Dic3—32no—
633C2×Dic3—62no—
634C2×Dic3—61no—
635C2×Dic3—61no—
636C2×Dic3—61no—
637C2×Dic3—61no—
638C2×Dic3—62no—
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—121no—
652C2×Dic3—121no—
653C2×Dic3—121no—
654C2×Dic3—121no—
655C2×Dic3—121no—
656C2×Dic3—121no—
657C2×Dic3—121no—
658C2×Dic3#23512yes—
659C2×Dic3D3×D412yes—
660C2×Dic3D3×D412yes—
661C2×Dic3D3×D412yes—
662D12—68no—
663D12—124no—
664C4×D3—44no—
665C4×D3—68no—
666C4×D3—68no—
667C4×D3—124no—
668C4×D3—124no—
669C4×D3—124no—
670C4×D3—124no—
671C4×D3—128no—
672C2×C32C2×#12311yescharacteristic
673C2×C32#52511yescharacteristic
674C2×C32#53911yescharacteristic
675C2×C32D4211yescharacteristic
676C2×C32#54711yescharacteristic
677C2×C32#54811yescharacteristic
678C2×C32#55311yescharacteristic
679C3⋊D3—24no—
680C3×D3—42no—
681C3×D3—81no—
682C24—31no—
683C24—31no—
684C24—91no—
685C2×D4—94no—
686C2×D4—182no—
687C2×D4—182no—
688C2×D4—182no—
689C2×D4—182no—
690C2×D4—182no—
691C2×D4—182no—
692C2×D4—182no—
693C2×D4—361no—
694C22×C4—31no—
695C22×C4—31no—
696C22×C4—31no—
697C22×C4—31no—
698C22×C4—31no—
699C22×C4—31no—
700C22×C4—62no—
701C22×C4—62no—
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—182no—
711C22×C4—182no—
712C22×C4—182no—
713C22×C4—361no—
714C22×C4—361no—
715C22×C4C2×D3211yescharacteristic
716C22×C4C2×D3211yescharacteristic
717C22×C4C2×D3211yescharacteristic
718C4⋊C4—41no—
719C4⋊C4—62no—
720C4⋊C4—62no—
721C4⋊C4—62no—
722C4⋊C4—94no—
723C4⋊C4—182no—
724C4⋊C4—182no—
725C4⋊C4—182no—
726C22⋊C4—62no—
727C22⋊C4—62no—
728C22⋊C4—62no—
729C22⋊C4—62no—
730C22⋊C4—121no—
731C22⋊C4—182no—
732C22⋊C4—182no—
733C22⋊C4—182no—
734C22⋊C4—182no—
735C22⋊C4—182no—
736C22⋊C4—182no—
737C42—182no—
738C22×C3—21no—
739C22×C3—21no—
740C22×C3—21no—
741C22×C3—21no—
742C22×C3—21no—
743C22×C3—21no—
744C22×C3—21no—
745C22×C3—62no—
746C22×C3—62no—
747C22×C3—62no—
748C22×C3—121no—
749C22×C3—121no—
750C22×C3—121no—
751C22×C3—121no—
752C22×C3—121no—
753C22×C3—121no—
754C22×C3—121no—
755C22×C3—121no—
756C22×C3—121no—
757C22×C3—121no—
758C22×C3—121no—
759C22×C3C2×#23511yescharacteristic
760C22×C3C2×D3×D411yescharacteristic
761C22×C3C2×D3×D411yescharacteristic
762C22×C3C2×D3×D411yescharacteristic
763C22×C3C2×D3×D411yescharacteristic
764C22×C3#100411yescharacteristic
765C22×C3#100411yescharacteristic
766C22×C3#100711yescharacteristic
767C22×C3#100711yescharacteristic
768C22×C3D3×#4111yescharacteristic
769C22×C3D3×#4111yescharacteristic
770C22×C3D3×#4111yescharacteristic
771C22×C3D3×#4111yescharacteristic
772C22×C3D3×#4111yescharacteristic
773C2×D3—22no—
774C2×D3—22no—
775C2×D3—22no—
776C2×D3—34no—
777C2×D3—34no—
778C2×D3—41no—
779C2×D3—41no—
780C2×D3—41no—
781C2×D3—41no—
782C2×D3—41no—
783C2×D3—41no—
784C2×D3—41no—
785C2×D3—41no—
786C2×D3—41no—
787C2×D3—41no—
788C2×D3—41no—
789C2×D3—64no—
790C2×D3—62no—
791C2×D3—62no—
792C2×D3—62no—
793C2×D3—62no—
794C2×D3—62no—
795C2×D3—62no—
796C2×D3—62no—
797C2×D3—62no—
798C2×D3—62no—
799C2×D3—62no—
800C2×D3—62no—
801C2×D3—62no—
802C2×D3—122no—
803C2×D3—122no—
804C2×D3—122no—
805C2×D3—122no—
806C2×D3—122no—
807C2×D3—122no—
808C3×C4—42no—
809C3×C4—42no—
810C3×C4—41no—
811C3×C4—41no—
812C3×C4—41no—
813C3×C4—41no—
814C3×C4—41no—
815C3×C4—41no—
816C3×C4—62no—
817C3×C4—62no—
818C3×C4—62no—
819C3×C4—62no—
820C3×C4—81no—
821C3×C4—121no—
822C3×C4—121no—
823Dic3—22no—
824Dic3—22no—
825Dic3—22no—
826Dic3—22no—
827Dic3—41no—
828Dic3—41no—
829Dic3—62no—
830Dic3—62no—
831Dic3—122no—
832Dic3—122no—
833Dic3—121no—
834Dic3—121no—
835Dic3—121no—
836Dic3—121no—
837Dic3—241no—
838C32#244311yescharacteristic, complemented, Sylow
839C23—32no—
840C23—61no—
841C23—61no—
842C23—61no—
843C23—61no—
844C23—61no—
845C23—61no—
846C23—61no—
847C23—61no—
848C23—61no—
849C23—61no—
850C23—61no—
851C23—61no—
852C23—61no—
853C23—92no—
854C23—92no—
855C23—92no—
856C23—181no—
857C23—181no—
858C23—181no—
859C23—181no—
860C23C22×D3211yescharacteristic
861D4—188no—
862D4—364no—
863D4—364no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—21no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—32no—
874C2×C4—32no—
875C2×C4—32no—
876C2×C4—32no—
877C2×C4—61no—
878C2×C4—61no—
879C2×C4—61no—
880C2×C4—61no—
881C2×C4—61no—
882C2×C4—61no—
883C2×C4—61no—
884C2×C4—61no—
885C2×C4—61no—
886C2×C4—61no—
887C2×C4—61no—
888C2×C4—61no—
889C2×C4—61no—
890C2×C4—61no—
891C2×C4—92no—
892C2×C4—124no—
893C2×C4—188no—
894C2×C4—181no—
895C2×C4—181no—
896C2×C4—181no—
897C2×C4—181no—
898C2×C4—181no—
899C2×C4—181no—
900C2×C4—181no—
901C2×C4—181no—
902C2×C4—364no—
903C2×C4—364no—
904C2×C3—21no—
905C2×C3—21no—
906C2×C3—21no—
907C2×C3—21no—
908C2×C3—21no—
909C2×C3—21no—
910C2×C3—21no—
911C2×C3—122no—
912C2×C3—241no—
913C2×C3#550711yescharacteristic
914C2×C3#554711yescharacteristic
915C2×C3#555811yescharacteristic
916C2×C3#559011yescharacteristic
917C2×C3#563111yescharacteristic
918C2×C3#563311yescharacteristic
919C2×C3#563311yescharacteristic
920C2×C3#563811yescharacteristic
921C2×C3#563811yescharacteristic
922C2×C3D3×#12311yescharacteristic
923C2×C3D3×#12311yescharacteristic
924C2×C3#565611yescharacteristic
925C2×C3#566111yescharacteristic
926C2×C3#571711yescharacteristic
927D3—42no—
928D3—64no—
929D3—64no—
930D3—81no—
931D3—124no—
932C22—62no—
933C22—62no—
934C22—62no—
935C22—94no—
936C22—121no—
937C22—121no—
938C22—121no—
939C22—121no—
940C22—121no—
941C22—121no—
942C22—121no—
943C22—121no—
944C22—121no—
945C22—121no—
946C22—121no—
947C22—182no—
948C22—182no—
949C22—182no—
950C22—182no—
951C22—182no—
952C22—182no—
953C22D3×#23511yescharacteristic
954C22#6430611yescharacteristic
955C22D32×D411yescharacteristic
956C22D32×D411yescharacteristic
957C22#6431611yescharacteristic
958C22#6431911yescharacteristic
959C22#6433011yescharacteristic
960C4—41no—
961C4—41no—
962C4—41no—
963C4—62no—
964C4—62no—
965C4—62no—
966C4—62no—
967C4—121no—
968C4—121no—
969C4—182no—
970C4—361no—
971C4—361no—
972C3—21no—
973C3#7460811yescharacteristic, complemented
974C3#7810311yescharacteristic, complemented
975C2—122no—
976C2—184no—
977C2—241no—
978C2#1059451611yescharacteristic
979C2#1059452111yescharacteristic
980C2#1059460811yescharacteristic
981C2#1059461411yescharacteristic
982C2#1059502511yescharacteristic
983C2#1059529511yescharacteristic
984C2#1059541511yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
prime radicalC2×#63912C2
hypercenterC2×C4⋊C4D32
hypocenterC32#2443
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#63905C2semidirect
3. C2×#63904C2semidirect
4. C2×#63883C2semidirect
5. #10592688C2semidirect
6. C3×#4993C2semidirect
7. C3×#4989C2semidirect
8. #10591390C2semidirect
9. #10591301C2semidirect
10. #10591285C2semidirect
11. #10591275C2semidirect
12. #10591275C2semidirect
13. #10591275C2semidirect
14. #10591250C2semidirect
15. #10591198C2semidirect
67. #4993D3semidirect
73. #4989D3semidirect
138. Dic3⋊Dic3D4semidirect
449. C2×C3⋊D3#123semidirect
838. C32#2443semidirect
973. C3#74608semidirect
974. C3#78103semidirect

Maximal subgroups

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

subgroupindex
C2×#639122
C2×#639052
C2×#639042
C2×#638832
#105926882
C3×#49932
C3×#49892
#105913902
#105913012
#105912852
#105912752
#105912502
#105911982
#781033
#746083