Finite Group Databasebeta

← #11836004

Subgroups — #11836004

Order 1152.

1717 conjugacy classes of subgroups.

The subgroup lattice has 1158 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C3×#895C211yesmaximal, characteristic, complemented
2C2×#63922C211yesmaximal, characteristic, complemented
3C2×#63922C211yesmaximal, characteristic, complemented
4C2×#63886C211yesmaximal, characteristic, complemented
5#10592691C211yesmaximal, characteristic, complemented
6C3×#4993C211yesmaximal, characteristic, complemented
7#10591399C211yesmaximal, characteristic, complemented
8#10591389C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591376C211yesmaximal, characteristic, complemented
12#10591363C211yesmaximal, characteristic, complemented
13#10591301C211yesmaximal, characteristic, complemented
14#10591300C211yesmaximal, characteristic, complemented
15#10591291C211yesmaximal, characteristic, complemented
16#82713—31nomaximal
17#78112—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C3×D12C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×D12C2211yescharacteristic, complemented
22C22×C3×C4×D3C2211yescharacteristic, complemented
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×#625C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic, complemented
28C2×C32×C4⋊C4C2211yescharacteristic, complemented
29C2×#3752C2211yescharacteristic
30C2×#3752C2211yescharacteristic
31C2×#3752C2211yescharacteristic
32C2×C3×(C2×D3)⋊C4C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39C3×#895—24no—
40C2×#3722C2211yescharacteristic
41C2×(C2×D3)⋊Dic3C2211yescharacteristic
42C2×(C2×D3)⋊Dic3C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48#63922—24no—
49#63922—24no—
50#63886—24no—
51#63658C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55#63579C2211yescharacteristic, complemented
56#63579C2211yescharacteristic, complemented
57C2×C3×#121—31no—
58C2×#939—31no—
59C2×#937—31no—
60C2×#937—31no—
61C2×#895—31no—
62C2×#895D311yescharacteristic, complemented
63C2×#882—31no—
64C2×#882—31no—
65C3×#399—31no—
66#5223—31no—
67#5222—31no—
68#5220—31no—
69#5213—31no—
70#5213—31no—
71#4993D311yescharacteristic, complemented
72#4992—31no—
73#4992—31no—
74#4992—31no—
75#4992—61no—
76#4991—31no—
77#4991—31no—
78#4960—31no—
79#4959—31no—
80#4958—31no—
81#4956—31no—
82#4956—31no—
83#4955—31no—
84#4955—31no—
85#4952—31no—
86#4665—31no—
87#4665—31no—
88C23×C3⋊D3C2311yescharacteristic
89C23×C3×D3C2311yescharacteristic
90C23×C3×D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C22×D32—22no—
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—41no—
97C22×D32—41no—
98C22×D32—41no—
99C22×D32—41no—
100C22×C32×C4C2311yescharacteristic
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C3⋊Dic3C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3×Dic3C2311yescharacteristic
107C22×C3×Dic3C2311yescharacteristic
108C22×C3×Dic3C2311yescharacteristic
109C22×C3×Dic3C2311yescharacteristic
110C2×C3×D12—22no—
111C2×C3×D12—22no—
112C2×C3×D12—22no—
113C2×C3×D12—22no—
114C2×C3×D12—41no—
115C2×C3×D12—41no—
116C2×C3×D12—41no—
117C2×C3×D12—41no—
118C2×C3×D12D414yescomplemented
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—41no—
121C2×C3×C4×D3—41no—
122C2×#626—22no—
123C2×#626—22no—
124C2×#626—41no—
125C2×#626—41no—
126C2×#626—41no—
127C2×#626D414yescomplemented
128C2×#625—22no—
129C2×#625—22no—
130C2×#625—22no—
131C2×#625—22no—
132C2×#625—41no—
133C2×#625—41no—
134C2×D3×Dic3—22no—
135C2×D3×Dic3—41no—
136C2×D3×Dic3—41no—
137C32×C4⋊C4—22no—
138#3752—22no—
139#3752—22no—
140#3752—22no—
141C3×(C2×D3)⋊C4—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—41no—
146C3×Dic3⋊C4—22no—
147C3×Dic3⋊C4—41no—
148#3722—41no—
149(C2×D3)⋊Dic3—22no—
150(C2×D3)⋊Dic3—22no—
151(C2×D3)⋊Dic3—22no—
152(C2×D3)⋊Dic3—41no—
153(C2×D3)⋊Dic3—41no—
154(C2×D3)⋊Dic3—41no—
155(C2×D3)⋊Dic3—41no—
156#2668—91noSylow
157C24×D3—31no—
158C24×D3—31no—
159C22×C3×D4—31no—
160C22×C3×D4—31no—
161C22×C3×D4—31no—
162C23×C3×C4—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C22×#67—31no—
167C22×#67—31no—
168C22×#67—31no—
169C23×Dic3—31no—
170C22×D12—31no—
171C22×D12—31no—
172C22×D12C2×D311yescharacteristic
173C22×D12C2×D311yescharacteristic
174C22×D12C2×D311yescharacteristic, complemented
175C22×C4×D3—31no—
176C22×C4×D3C2×D311yescharacteristic, complemented
177C3×#121—64no—
178C2×C3×C4⋊C4—21no—
179C2×C3×C4⋊C4—31no—
180C2×C3×C4⋊C4—31no—
181C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
182C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
183C2×C3×C22⋊C4—31no—
184C2×C3×C22⋊C4—31no—
185C2×C3×C22⋊C4—31no—
186C2×C3×C22⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×#217—31no—
189C2×#217—31no—
190C2×#217—31no—
191C2×#217—31no—
192C2×#217—31no—
193C2×#217—31no—
194C2×#217—31no—
195#939—64no—
196#937—64no—
197#937—64no—
198C2×(C2×D3)⋊C4—31no—
199C2×(C2×D3)⋊C4—31no—
200C2×(C2×D3)⋊C4—31no—
201C2×(C2×D3)⋊C4—31no—
202C2×(C2×D3)⋊C4—31no—
203C2×(C2×D3)⋊C4—31no—
204C2×(C2×D3)⋊C4—31no—
205C2×(C2×D3)⋊C4—31no—
206C2×(C2×D3)⋊C4—31no—
207C2×(C2×D3)⋊C4—31no—
208C2×(C2×D3)⋊C4—31no—
209C2×(C2×D3)⋊C4—31no—
210C2×(C2×D3)⋊C4—31no—
211C2×(C2×D3)⋊C4—31no—
212C2×(C2×D3)⋊C4—31no—
213C2×(C2×D3)⋊C4—61no—
214C2×(C2×D3)⋊C4—61no—
215C2×(C2×D3)⋊C4—61no—
216C2×(C2×D3)⋊C4C2×D311yescharacteristic
217C2×(C2×D3)⋊C4C2×D311yescharacteristic
218C2×(C2×D3)⋊C4C2×D311yescharacteristic
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
221C2×Dic3⋊C4C2×D311yescharacteristic, complemented
222C2×Dic3⋊C4C2×D311yescharacteristic, complemented
223#895—24no—
224#895—64no—
225#882—64no—
226#882—64no—
227C3×#95—31no—
228C3⋊#95—31no—
229C3⋊#95—31no—
230C3⋊#95—31no—
231C3⋊#95—31no—
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—61no—
239C3⋊#95—61no—
240C3⋊#95—61no—
241C3⋊#95C2×D311yescharacteristic, complemented
242C23×C32C2411yescharacteristic
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—21no—
251C22×C3×D3—21no—
252C22×C3×D3—21no—
253C22×C3×D3—21no—
254C22×C3×D3—21no—
255C22×C3×D3—21no—
256C22×C3×D3—21no—
257C22×C3×D3—21no—
258C22×C3×D3—21no—
259C22×C3×D3—21no—
260C22×C3×D3—21no—
261C22×C3×D3—21no—
262C22×C3×D3—21no—
263C22×C3×D3—21no—
264C22×C3×D3—21no—
265C22×C3×D3—21no—
266C22×C3×D3—21no—
267C22×C3×D3—21no—
268C22×C3×D3—21no—
269C22×C3×D3—21no—
270C22×C3×D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3C2×D412yes—
275C22×C3×D3C2×D412yes—
276C22×C3×D3C2×D412yes—
277C22×C3×D3#4112yes—
278C2×D32—44no—
279C2×D32—44no—
280C2×D32—44no—
281C2×D32—44no—
282C2×D32—44no—
283C2×D32—44no—
284C2×D32—44no—
285C2×C32×C4—21no—
286C2×C32×C4—21no—
287C2×C32×C4—21no—
288C2×C32×C4—21no—
289C2×C32×C4—21no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4C2×D412yes—
294C2×C3⋊Dic3—21no—
295C2×C3⋊Dic3—21no—
296C2×C3⋊Dic3—21no—
297C2×C3⋊Dic3—21no—
298C2×C3⋊Dic3—21no—
299C2×C3⋊Dic3—21no—
300C2×C3⋊Dic3—21no—
301C2×C3⋊Dic3—21no—
302C2×C3⋊Dic3—21no—
303C2×C3×Dic3—21no—
304C2×C3×Dic3—21no—
305C2×C3×Dic3—21no—
306C2×C3×Dic3—21no—
307C2×C3×Dic3—21no—
308C2×C3×Dic3—21no—
309C2×C3×Dic3—21no—
310C2×C3×Dic3—21no—
311C2×C3×Dic3—21no—
312C2×C3×Dic3—21no—
313C2×C3×Dic3—21no—
314C2×C3×Dic3C2×D412yes—
315C3×D12—44no—
316C3×D12—44no—
317C3×D12—44no—
318C3×C4×D3—44no—
319#626—44no—
320#626—44no—
321#625—44no—
322#625—44no—
323D3×Dic3—44no—
324C2×#121—31no—
325C2×#121—91no—
326C2×#120—91no—
327C2×#120—91no—
328#399—31no—
329#397—91no—
330#397—91no—
331#394—91no—
332#394—91no—
333#392—91no—
334#386—91no—
335#386—91no—
336#386—91no—
337#386—91no—
338#379—91no—
339C24×C3—31no—
340C24×C3—31no—
341C24×C3—31no—
342C24×C3—31no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—61no—
346C23×D3—62no—
347C23×D3—62no—
348C23×D3—62no—
349C23×D3—62no—
350C23×D3—62no—
351C23×D3—62no—
352C23×D3—121no—
353C23×D3—121no—
354C23×D3—121no—
355C23×D3—121no—
356C23×D3—121no—
357C23×D3—121no—
358C23×D3—121no—
359C23×D3—121no—
360C23×D3C22×D311yescharacteristic
361C23×D3C22×D311yescharacteristic
362C23×D3C22×D311yescharacteristic
363C23×D3C22×D311yescharacteristic
364C2×C3×D4—34no—
365C2×C3×D4—62no—
366C2×C3×D4—62no—
367C2×C3×D4—62no—
368C2×C3×D4—62no—
369C2×C3×D4—121no—
370C2×C3×D4—121no—
371C2×C3×D4—121no—
372C2×C3×D4—121no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—62no—
381C22×C3×C4—121no—
382C22×C3×C4—121no—
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C22×C3×C4C22×D311yescharacteristic
387C22×C3×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C2×#67—34no—
390C2×#67—62no—
391C2×#67—62no—
392C2×#67—62no—
393C2×#67—62no—
394C2×#67—62no—
395C2×#67—62no—
396C2×#67—62no—
397C2×#67—62no—
398C2×#67—62no—
399C2×#67—62no—
400C2×#67—121no—
401C2×#67—121no—
402C2×#67—121no—
403C2×#67—121no—
404C2×#67—121no—
405C2×#67—121no—
406C2×#67—121no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—61no—
414C22×Dic3—61no—
415C22×Dic3—61no—
416C22×Dic3—62no—
417C22×Dic3—121no—
418C22×Dic3—121no—
419C22×Dic3C22×D311yescharacteristic
420C22×Dic3C22×D311yescharacteristic
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C2×D12—22no—
424C2×D12—22no—
425C2×D12—22no—
426C2×D12—22no—
427C2×D12—34no—
428C2×D12—41no—
429C2×D12—41no—
430C2×D12—41no—
431C2×D12—41no—
432C2×D12—62no—
433C2×D12—62no—
434C2×D12—121no—
435C2×D12—121no—
436C2×D12—121no—
437C2×D12#6714yescomplemented
438C2×C4×D3—22no—
439C2×C4×D3—41no—
440C2×C4×D3—41no—
441C2×C4×D3—62no—
442C2×C4×D3—121no—
443C2×C4×D3—121no—
444C3×C4⋊C4—22no—
445C3×C4⋊C4—22no—
446C3×C4⋊C4—42no—
447C3×C4⋊C4—62no—
448C3×C4⋊C4—121no—
449C3×C22⋊C4—62no—
450C3×C22⋊C4—62no—
451C3×C22⋊C4—62no—
452C3×C22⋊C4—62no—
453C3×C22⋊C4—121no—
454#217—62no—
455#217—62no—
456#217—62no—
457#217—121no—
458#217—121no—
459#217—121no—
460#217—121no—
461(C2×D3)⋊C4—22no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—41no—
466(C2×D3)⋊C4—62no—
467(C2×D3)⋊C4—62no—
468(C2×D3)⋊C4—62no—
469(C2×D3)⋊C4—62no—
470(C2×D3)⋊C4—62no—
471(C2×D3)⋊C4—62no—
472(C2×D3)⋊C4—62no—
473(C2×D3)⋊C4—62no—
474(C2×D3)⋊C4—62no—
475(C2×D3)⋊C4—122no—
476(C2×D3)⋊C4—122no—
477(C2×D3)⋊C4—122no—
478(C2×D3)⋊C4—121no—
479(C2×D3)⋊C4—121no—
480(C2×D3)⋊C4—121no—
481(C2×D3)⋊C4—121no—
482(C2×D3)⋊C4—121no—
483(C2×D3)⋊C4—121no—
484Dic3⋊C4—22no—
485Dic3⋊C4—41no—
486C22×C32C22×D411yescharacteristic
487C22×C32C22×D411yescharacteristic
488C22×C32C2×#4111yescharacteristic
489C22×C32H(5,𝔽2)11yescharacteristic
490C22×C32H(5,𝔽2)11yescharacteristic
491C22×C32H(5,𝔽2)11yescharacteristic
492C22×C32H(5,𝔽2)11yescharacteristic
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—41no—
497C2×C3⋊D3—41no—
498C2×C3⋊D3—41no—
499C2×C3⋊D3—41no—
500C2×C3×D3—22no—
501C2×C3×D3—22no—
502C2×C3×D3—22no—
503C2×C3×D3—22no—
504C2×C3×D3—22no—
505C2×C3×D3—22no—
506C2×C3×D3—22no—
507C2×C3×D3—22no—
508C2×C3×D3—22no—
509C2×C3×D3—22no—
510C2×C3×D3—22no—
511C2×C3×D3—22no—
512C2×C3×D3—41no—
513C2×C3×D3—41no—
514C2×C3×D3—41no—
515C2×C3×D3—41no—
516C2×C3×D3—41no—
517C2×C3×D3—41no—
518C2×C3×D3—41no—
519C2×C3×D3—41no—
520C2×C3×D3—41no—
521C2×C3×D3—41no—
522C2×C3×D3—41no—
523C2×C3×D3—41no—
524C2×C3×D3—41no—
525C2×C3×D3—41no—
526C2×C3×D3—41no—
527C2×C3×D3—41no—
528D32—416no—
529C32×C4—22no—
530C32×C4—41no—
531C32×C4—41no—
532C3⋊Dic3—41no—
533C3⋊Dic3—41no—
534C3⋊Dic3—41no—
535C3×Dic3—22no—
536C3×Dic3—41no—
537C3×Dic3—41no—
538C3×Dic3—41no—
539C25—91no—
540C22×D4—31no—
541C22×D4—31no—
542C22×D4—31no—
543C22×D4—91no—
544C22×D4—91no—
545C22×D4—91no—
546C22×D4—91no—
547C23×C4—31no—
548C23×C4—91no—
549#121—64no—
550#121—184no—
551#120—184no—
552#120—184no—
553C2×C4⋊C4—31no—
554C2×C4⋊C4—31no—
555C2×C4⋊C4D3211yescharacteristic, complemented
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—31no—
559C2×C22⋊C4—31no—
560C2×C22⋊C4—31no—
561C2×C22⋊C4—91no—
562C2×C22⋊C4—91no—
563C2×C22⋊C4—91no—
564C2×C22⋊C4—91no—
565C2×C22⋊C4—91no—
566C2×C22⋊C4—91no—
567C2×C22⋊C4—91no—
568C2×C22⋊C4—91no—
569C2×C22⋊C4—91no—
570C2×C22⋊C4—91no—
571C2×C22⋊C4—91no—
572#95—31no—
573#95—91no—
574#95—91no—
575#95—91no—
576#95—91no—
577#95—91no—
578C23×C3—21no—
579C23×C3—32no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—32no—
583C23×C3—61no—
584C23×C3—61no—
585C23×C3—61no—
586C23×C3—61no—
587C23×C3—61no—
588C23×C3—61no—
589C23×C3—61no—
590C23×C3—61no—
591C23×C3—61no—
592C23×C3—61no—
593C23×C3—61no—
594C23×C3—61no—
595C23×C3—61no—
596C23×C3—61no—
597C23×C3—61no—
598C23×C3—61no—
599C23×C3—61no—
600C23×C3—61no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3C23×D311yescharacteristic
608C23×C3C23×D311yescharacteristic
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—21no—
621C22×D3—21no—
622C22×D3—21no—
623C22×D3—21no—
624C22×D3—21no—
625C22×D3—21no—
626C22×D3—21no—
627C22×D3—21no—
628C22×D3—21no—
629C22×D3—21no—
630C22×D3—21no—
631C22×D3—21no—
632C22×D3—21no—
633C22×D3—32no—
634C22×D3—32no—
635C22×D3—62no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—61no—
640C22×D3—61no—
641C22×D3—61no—
642C22×D3—61no—
643C22×D3—61no—
644C22×D3—61no—
645C22×D3—61no—
646C22×D3—61no—
647C22×D3—61no—
648C22×D3—121no—
649C22×D3—121no—
650C22×D3—121no—
651C22×D3—121no—
652C22×D3—121no—
653C22×D3—121no—
654C22×D3—124no—
655C22×D3—124no—
656C22×D3—124no—
657C22×D3—124no—
658C22×D3—124no—
659C22×D3—124no—
660C22×D3—124no—
661C22×D3—124no—
662C22×D3—124no—
663C22×D3—124no—
664C22×D3—124no—
665C22×D3—124no—
666C22×D3—124no—
667C22×D3—124no—
668C22×D3D3×D412yes—
669C22×D3#23912yes—
670C22×D3C2×#6712yes—
671C22×D3C2×#6712yes—
672C3×D4—124no—
673C3×D4—124no—
674C3×D4—124no—
675C2×C3×C4—21no—
676C2×C3×C4—21no—
677C2×C3×C4—21no—
678C2×C3×C4—21no—
679C2×C3×C4—21no—
680C2×C3×C4—21no—
681C2×C3×C4—21no—
682C2×C3×C4—21no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—22no—
692C2×C3×C4—32no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—41no—
697C2×C3×C4—41no—
698C2×C3×C4—41no—
699C2×C3×C4—41no—
700C2×C3×C4—41no—
701C2×C3×C4—61no—
702C2×C3×C4—61no—
703C2×C3×C4—61no—
704C2×C3×C4—61no—
705C2×C3×C4—61no—
706C2×C3×C4—61no—
707C2×C3×C4—61no—
708C2×C3×C4—61no—
709C2×C3×C4—61no—
710C2×C3×C4—61no—
711C2×C3×C4—61no—
712C2×C3×C4—124no—
713C2×C3×C4D3×D412yes—
714C2×C3×C4C2×#6712yes—
715#67—124no—
716#67—124no—
717#67—124no—
718#67—124no—
719#67—124no—
720#67—124no—
721C2×Dic3—21no—
722C2×Dic3—21no—
723C2×Dic3—21no—
724C2×Dic3—21no—
725C2×Dic3—21no—
726C2×Dic3—21no—
727C2×Dic3—21no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—61no—
733C2×Dic3—61no—
734C2×Dic3—61no—
735C2×Dic3—61no—
736C2×Dic3—61no—
737C2×Dic3—61no—
738C2×Dic3—61no—
739C2×Dic3—61no—
740C2×Dic3—61no—
741C2×Dic3—61no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—121no—
751C2×Dic3—121no—
752C2×Dic3—121no—
753C2×Dic3—121no—
754C2×Dic3—121no—
755C2×Dic3—121no—
756C2×Dic3—121no—
757C2×Dic3—121no—
758C2×Dic3—121no—
759C2×Dic3—124no—
760C2×Dic3D3×D412yes—
761D12—44no—
762D12—44no—
763D12—44no—
764D12—124no—
765D12—124no—
766C4×D3—44no—
767C4×D3—124no—
768C2×C32#53411yescharacteristic
769C2×C32#53411yescharacteristic
770C2×C32#53811yescharacteristic
771C2×C32D4211yescharacteristic
772C2×C32#54611yescharacteristic
773C2×C32#54611yescharacteristic
774C2×C32#56011yescharacteristic
775C3⋊D3—42no—
776C3×D3—42no—
777C3×D3—42no—
778C3×D3—42no—
779C3×D3—42no—
780C24—31no—
781C24—31no—
782C24—31no—
783C24—31no—
784C24—91no—
785C24—182no—
786C24—182no—
787C24—182no—
788C24—361no—
789C24—361no—
790C24—361no—
791C24—361no—
792C2×D4—34no—
793C2×D4—62no—
794C2×D4—62no—
795C2×D4—62no—
796C2×D4—62no—
797C2×D4—94no—
798C2×D4—121no—
799C2×D4—121no—
800C2×D4—121no—
801C2×D4—121no—
802C2×D4—182no—
803C2×D4—182no—
804C2×D4—182no—
805C2×D4—182no—
806C2×D4—182no—
807C2×D4—182no—
808C2×D4—361no—
809C2×D4—361no—
810C2×D4—361no—
811C2×D4—361no—
812C2×D4—361no—
813C22×C4—31no—
814C22×C4—31no—
815C22×C4—31no—
816C22×C4—31no—
817C22×C4—62no—
818C22×C4—91no—
819C22×C4—91no—
820C22×C4—91no—
821C22×C4—121no—
822C22×C4—121no—
823C22×C4—182no—
824C22×C4—361no—
825C22×C4—361no—
826C22×C4C2×D3211yescharacteristic
827C22×C4C2×D3211yescharacteristic
828C22×C4C2×D3211yescharacteristic
829C4⋊C4—22no—
830C4⋊C4—62no—
831C4⋊C4—121no—
832C22⋊C4—62no—
833C22⋊C4—62no—
834C22⋊C4—62no—
835C22⋊C4—62no—
836C22⋊C4—121no—
837C22⋊C4—182no—
838C22⋊C4—182no—
839C22⋊C4—182no—
840C22⋊C4—182no—
841C22⋊C4—182no—
842C22⋊C4—182no—
843C22⋊C4—361no—
844C22⋊C4—361no—
845C22⋊C4—361no—
846C22⋊C4—361no—
847C22⋊C4—361no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—21no—
852C22×C3—21no—
853C22×C3—21no—
854C22×C3—21no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—62no—
858C22×C3—62no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—62no—
863C22×C3—62no—
864C22×C3—62no—
865C22×C3—62no—
866C22×C3—62no—
867C22×C3—121no—
868C22×C3—121no—
869C22×C3—121no—
870C22×C3—121no—
871C22×C3—121no—
872C22×C3—121no—
873C22×C3—121no—
874C22×C3—121no—
875C22×C3—121no—
876C22×C3—121no—
877C22×C3—121no—
878C22×C3—121no—
879C22×C3—121no—
880C22×C3—121no—
881C22×C3—121no—
882C22×C3—121no—
883C22×C3C2×D3×D411yescharacteristic
884C22×C3C2×D3×D411yescharacteristic
885C22×C3C2×D3×D411yescharacteristic
886C22×C3#100411yescharacteristic
887C22×C3#100411yescharacteristic
888C22×C3#100411yescharacteristic
889C22×C3#100411yescharacteristic
890C22×C3C2×#23911yescharacteristic
891C22×C3D3×#4111yescharacteristic
892C22×C3#100911yescharacteristic
893C22×C3#100911yescharacteristic
894C22×C3#100911yescharacteristic
895C22×C3#100911yescharacteristic
896C22×C3C22×#6711yescharacteristic
897C2×D3—22no—
898C2×D3—22no—
899C2×D3—22no—
900C2×D3—22no—
901C2×D3—22no—
902C2×D3—22no—
903C2×D3—22no—
904C2×D3—22no—
905C2×D3—22no—
906C2×D3—22no—
907C2×D3—22no—
908C2×D3—22no—
909C2×D3—41no—
910C2×D3—41no—
911C2×D3—41no—
912C2×D3—41no—
913C2×D3—41no—
914C2×D3—41no—
915C2×D3—41no—
916C2×D3—41no—
917C2×D3—41no—
918C2×D3—41no—
919C2×D3—41no—
920C2×D3—41no—
921C2×D3—41no—
922C2×D3—41no—
923C2×D3—41no—
924C2×D3—41no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—122no—
932C2×D3—122no—
933C2×D3—122no—
934C2×D3—1216no—
935C2×D3—1216no—
936C2×D3—121no—
937C2×D3—121no—
938C2×D3—121no—
939C2×D3—121no—
940C2×D3—121no—
941C2×D3—121no—
942C2×D3—121no—
943C2×D3—121no—
944C2×D3—241no—
945C2×D3—241no—
946C2×D3—241no—
947C2×D3—241no—
948C3×C4—22no—
949C3×C4—22no—
950C3×C4—42no—
951C3×C4—41no—
952C3×C4—41no—
953C3×C4—41no—
954C3×C4—41no—
955C3×C4—62no—
956C3×C4—81no—
957C3×C4—81no—
958C3×C4—121no—
959C3×C4—121no—
960C3×C4—121no—
961Dic3—22no—
962Dic3—41no—
963Dic3—41no—
964Dic3—41no—
965Dic3—121no—
966Dic3—121no—
967Dic3—121no—
968Dic3—121no—
969Dic3—121no—
970Dic3—121no—
971Dic3—241no—
972Dic3—241no—
973Dic3—241no—
974C32#266811yescharacteristic, complemented, Sylow
975C23—32no—
976C23—32no—
977C23—32no—
978C23—32no—
979C23—61no—
980C23—61no—
981C23—61no—
982C23—61no—
983C23—61no—
984C23—61no—
985C23—61no—
986C23—61no—
987C23—61no—
988C23—61no—
989C23—61no—
990C23—61no—
991C23—61no—
992C23—61no—
993C23—61no—
994C23—61no—
995C23—61no—
996C23—61no—
997C23—61no—
998C23—61no—
999C23—61no—
1000C23—61no—
1001C23—61no—
1002C23—61no—
1003C23—92no—
1004C23—181no—
1005C23—181no—
1006C23—181no—
1007C23—181no—
1008C23—181no—
1009C23—181no—
1010C23—364no—
1011C23—364no—
1012C23—364no—
1013C23—364no—
1014C23—364no—
1015C23—364no—
1016C23—364no—
1017C23C22×D3211yescharacteristic
1018D4—124no—
1019D4—124no—
1020D4—124no—
1021D4—364no—
1022D4—364no—
1023D4—364no—
1024D4—364no—
1025C2×C4—21no—
1026C2×C4—21no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—32no—
1034C2×C4—61no—
1035C2×C4—61no—
1036C2×C4—61no—
1037C2×C4—61no—
1038C2×C4—61no—
1039C2×C4—61no—
1040C2×C4—61no—
1041C2×C4—61no—
1042C2×C4—61no—
1043C2×C4—61no—
1044C2×C4—61no—
1045C2×C4—124no—
1046C2×C4—181no—
1047C2×C4—181no—
1048C2×C4—181no—
1049C2×C4—181no—
1050C2×C4—181no—
1051C2×C4—181no—
1052C2×C4—181no—
1053C2×C4—181no—
1054C2×C4—181no—
1055C2×C4—364no—
1056C2×C4D3×#6712yes—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—21no—
1062C2×C3—21no—
1063C2×C3—21no—
1064C2×C3—122no—
1065C2×C3—122no—
1066C2×C3—122no—
1067C2×C3—122no—
1068C2×C3#560511yescharacteristic
1069C2×C3#561011yescharacteristic
1070C2×C3#561311yescharacteristic
1071C2×C3#562011yescharacteristic
1072C2×C3#563011yescharacteristic
1073C2×C3#563011yescharacteristic
1074C2×C3#564411yescharacteristic
1075C2×C3#565311yescharacteristic
1076C2×C3#565311yescharacteristic
1077C2×C3#566611yescharacteristic
1078C2×C3#571711yescharacteristic
1079C2×C3D4×#6711yescharacteristic
1080C2×C3#580411yescharacteristic
1081C2×C3#582911yescharacteristic
1082D3—42no—
1083D3—42no—
1084D3—42no—
1085D3—42no—
1086D3—122no—
1087D3—122no—
1088D3—242no—
1089C22—62no—
1090C22—62no—
1091C22—62no—
1092C22—62no—
1093C22—62no—
1094C22—62no—
1095C22—62no—
1096C22—62no—
1097C22—62no—
1098C22—62no—
1099C22—62no—
1100C22—62no—
1101C22—121no—
1102C22—121no—
1103C22—121no—
1104C22—121no—
1105C22—121no—
1106C22—121no—
1107C22—121no—
1108C22—121no—
1109C22—121no—
1110C22—121no—
1111C22—121no—
1112C22—121no—
1113C22—121no—
1114C22—121no—
1115C22—121no—
1116C22—121no—
1117C22—182no—
1118C22—182no—
1119C22—182no—
1120C22—3616no—
1121C22—361no—
1122C22—361no—
1123C22—361no—
1124C22—361no—
1125C22#6430711yescharacteristic
1126C22#6430711yescharacteristic
1127C22D32×D411yescharacteristic
1128C22#6431311yescharacteristic
1129C22D3×#23911yescharacteristic
1130C22#6432011yescharacteristic
1131C22C2×D3×#6711yescharacteristic
1132C4—22no—
1133C4—41no—
1134C4—41no—
1135C4—62no—
1136C4—121no—
1137C4—121no—
1138C4—121no—
1139C4—361no—
1140C4—361no—
1141C4—361no—
1142C3—21no—
1143C3#7811211yescharacteristic, complemented
1144C3#8271311yescharacteristic, complemented
1145C2—122no—
1146C2—122no—
1147C2—122no—
1148C2—122no—
1149C2—362no—
1150C2#1059461111yescharacteristic
1151C2#1059462211yescharacteristic
1152C2#1059465111yescharacteristic
1153C2#1059466211yescharacteristic
1154C2#1059506211yescharacteristic
1155C2#1059529311yescharacteristic
1156C2#1059542711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC2×C32×C4⋊C4C22
hypercenterC2×C4⋊C4D32
hypocenterC32#2668
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×C3×#895C2semidirect
2. C2×#63922C2semidirect
3. C2×#63922C2semidirect
4. C2×#63886C2semidirect
5. #10592691C2semidirect
6. C3×#4993C2semidirect
7. #10591399C2semidirect
8. #10591389C2semidirect
9. #10591382C2semidirect
10. #10591381C2semidirect
11. #10591376C2semidirect
12. #10591363C2semidirect
13. #10591301C2semidirect
14. #10591300C2semidirect
15. #10591291C2semidirect
21. C22×C3×D12C22semidirect
22. C22×C3×C4×D3C22semidirect
27. C22×D3×Dic3C22semidirect
28. C2×C32×C4⋊C4C22semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×Dic3⋊C4C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
45. C2×(C2×D3)⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
51. #63658C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. C3×C3⋊#95C22semidirect
55. #63579C22semidirect
56. #63579C22semidirect
62. C2×#895D3semidirect
71. #4993D3semidirect
118. C2×C3×D12D4semidirect
127. C2×#626D4semidirect
174. C22×D12C2×D3semidirect
176. C22×C4×D3C2×D3semidirect
181. C2×C3×C4⋊C4C2×D3semidirect
182. C2×C3×C4⋊C4C2×D3semidirect
220. C2×(C2×D3)⋊C4C2×D3semidirect
221. C2×Dic3⋊C4C2×D3semidirect
222. C2×Dic3⋊C4C2×D3semidirect
241. C3⋊#95C2×D3semidirect
437. C2×D12#67semidirect
555. C2×C4⋊C4D32semidirect
974. C32#2668semidirect
1143. C3#78112semidirect
1144. C3#82713semidirect

Maximal subgroups

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

subgroupindex
C2×C3×#8952
C2×#639222
C2×#638862
#105926912
C3×#49932
#105913992
#105913892
#105913822
#105913812
#105913762
#105913632
#105913012
#105913002
#105912912
#827133
#781123