Finite Group Databasebeta

← #11856279

Subgroups — #11856279

Order 1152.

2313 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic, complemented
2C2×#63922C211yesmaximal, characteristic
3C2×#63854C211yesmaximal, characteristic, complemented
4C2×#63853C211yesmaximal, characteristic, complemented
5#10592363C211yesmaximal, characteristic, complemented
6C3×#4668C211yesmaximal, characteristic, complemented
7C3×#4665C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591381C211yesmaximal, characteristic, complemented
10#10591377C211yesmaximal, characteristic, complemented
11#10591376C211yesmaximal, characteristic, complemented
12#10591373C211yesmaximal, characteristic, complemented
13#10591371C211yesmaximal, characteristic, complemented
14#10591363C211yesmaximal, characteristic, complemented
15#10591277C211yesmaximal, characteristic, complemented
16#74936—31nomaximal
17#74656—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#625C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C4×D32—24no—
29C2×C4×D32—24no—
30C2×C4×D32—24no—
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic
33C2×C3×(C2×D3)⋊C4C2211yescharacteristic
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
40C2×#3724C2211yescharacteristic, complemented
41C2×Dic3⋊Dic3C2211yescharacteristic, complemented
42C2×#3722C2211yescharacteristic
43C2×(C2×D3)⋊Dic3C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48#63922—24no—
49#63854—24no—
50#63853—24no—
51C32×#95C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53#63658C2211yescharacteristic, complemented
54#63658C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57#63579C2211yescharacteristic, complemented
58#63579C2211yescharacteristic, complemented
59C23×C4×D3—31no—
60C23×C4×D3—31no—
61C2×#937—31no—
62C2×#894—31no—
63C2×#894—31no—
64C2×#883—31no—
65C2×#883—31no—
66C2×#882—31no—
67C3×#386—31no—
68C3×#385—31no—
69#5220—31no—
70#5213—31no—
71#5210—31no—
72#4989—31no—
73#4989—31no—
74#4958—31no—
75#4956—31no—
76#4956—31no—
77#4955—31no—
78#4955—31no—
79#4950—31no—
80#4946—31no—
81#4668—31no—
82#4668D311yescharacteristic, complemented
83#4665—31no—
84#4665D311yescharacteristic, complemented
85#4664—31no—
86#4664—31no—
87#4664—31no—
88#4664—31no—
89#4664—61no—
90C23×C3⋊D3C2311yescharacteristic
91C23×C3×D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C23×C3×D3C2311yescharacteristic
94C22×D32—22no—
95C22×D32—22no—
96C22×D32—22no—
97C22×D32—22no—
98C22×D32—22no—
99C22×D32—22no—
100C22×D32D414yes—
101C22×C32×C4C2311yescharacteristic
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C3⋊Dic3C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C2×C4×C3⋊D3—22no—
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3D414yescomplemented
110C22×C3×Dic3C2311yescharacteristic
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C2×C3×D12—22no—
116C2×C3×D12—22no—
117C2×C3×D12—22no—
118C2×C3×C4×D3—22no—
119C2×C3×C4×D3—22no—
120C2×C3×C4×D3—22no—
121C2×C3×C4×D3—22no—
122C2×C3×C4×D3—22no—
123C2×C3×C4×D3—22no—
124C2×#626—22no—
125C2×#626—22no—
126C2×#626—22no—
127C2×#625—22no—
128C2×#625—22no—
129C2×#625—22no—
130C2×#624—22no—
131C2×#624—22no—
132C2×#624D414yescomplemented
133C2×D3×Dic3—22no—
134C2×D3×Dic3—22no—
135C2×D3×Dic3—22no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3—22no—
138C2×D3×Dic3—22no—
139C4×D32—232no—
140#3752—22no—
141#3752—22no—
142C3×(C2×D3)⋊C4—22no—
143C3×(C2×D3)⋊C4—22no—
144C3×(C2×D3)⋊C4—22no—
145C3×(C2×D3)⋊C4—22no—
146C3×(C2×D3)⋊C4—22no—
147C3×C4⋊Dic3—22no—
148C3×Dic3⋊C4—22no—
149#3724—22no—
150Dic3⋊Dic3—22no—
151#3722—22no—
152(C2×D3)⋊Dic3—22no—
153(C2×D3)⋊Dic3—22no—
154(C2×D3)⋊Dic3—22no—
155(C2×D3)⋊Dic3—22no—
156(C2×D3)⋊Dic3—22no—
157#2849—91noSylow
158C24×D3—31no—
159C24×D3—31no—
160C22×C3×D4—31no—
161C23×C3×C4—31no—
162C23×C3×C4—31no—
163C22×#67—31no—
164C22×#67—31no—
165C22×#67—31no—
166C23×Dic3—31no—
167C23×Dic3—31no—
168C22×D12—31no—
169C22×D12C2×D311yescharacteristic
170C22×C4×D3—31no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—61no—
177C22×C4×D3—64no—
178C22×C4×D3—64no—
179C22×C4×D3—64no—
180C22×C4×D3—64no—
181C22×C4×D3—64no—
182C22×C4×D3—64no—
183C22×C4×D3C2×D311yescharacteristic
184C22×C4×D3C2×D311yescharacteristic
185C2×C3×C4⋊C4—31no—
186C2×C3×C4⋊C4—31no—
187C2×C3×C22⋊C4—31no—
188C2×C3×C22⋊C4—31no—
189C2×C3×C22⋊C4—31no—
190C2×C3×C22⋊C4—31no—
191C2×C3×C22⋊C4—31no—
192C2×#217—31no—
193C2×#217—31no—
194C2×#217—31no—
195C2×#217—31no—
196C2×#217—31no—
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—61no—
210C2×(C2×D3)⋊C4—61no—
211C2×(C2×D3)⋊C4C2×D311yescharacteristic
212C2×(C2×D3)⋊C4C2×D311yescharacteristic
213C2×(C2×D3)⋊C4C2×D311yescharacteristic
214C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
215C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
216C2×C4⋊Dic3—31no—
217C2×C4⋊Dic3C2×D311yescharacteristic, complemented
218C2×Dic3⋊C4—31no—
219C2×Dic3⋊C4—31no—
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4C2×D311yescharacteristic, complemented
222#894—64no—
223#894—64no—
224#883—64no—
225#883—64no—
226#882—64no—
227C3×#95—21no—
228C3×#95—31no—
229C3×#95—31no—
230C3×#95C2×D311yescharacteristic, complemented
231C3×#95C2×D311yescharacteristic, complemented
232C3⋊#95—31no—
233C3⋊#95—31no—
234C3⋊#95—31no—
235C3⋊#95—31no—
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—31no—
241C3⋊#95—31no—
242C3⋊#95—61no—
243C3⋊#95—61no—
244C3⋊#95—61no—
245C3⋊#95C2×D311yescharacteristic, complemented
246C3⋊#95C2×D311yescharacteristic, complemented
247C23×C32C2411yescharacteristic
248C22×C3⋊D3—21no—
249C22×C3⋊D3—21no—
250C22×C3⋊D3—21no—
251C22×C3⋊D3—21no—
252C22×C3⋊D3C2×D412yes—
253C22×C3⋊D3C2×D412yes—
254C22×C3⋊D3C2×D412yes—
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×D3C2×D412yes—
271C22×C3×D3C2×D412yes—
272C22×C3×D3#4112yes—
273C22×C3×D3#4112yes—
274C22×C3×D3#4112yes—
275C22×C3×D3#4112yes—
276C2×D32—28no—
277C2×D32—28no—
278C2×D32—28no—
279C2×D32—28no—
280C2×D32—28no—
281C2×D32—28no—
282C2×D32—28no—
283C2×C32×C4—21no—
284C2×C32×C4—21no—
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×C4C2×D412yes—
292C2×C3⋊Dic3—21no—
293C2×C3⋊Dic3—21no—
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⋊Dic3C2×D412yes—
301C4×C3⋊D3—28no—
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×Dic3—21no—
315C2×C3×Dic3C2×D412yes—
316C2×C3×Dic3C2×D412yes—
317C3×D12—44no—
318C3×C4×D3—28no—
319C3×C4×D3—28no—
320#626—44no—
321#625—44no—
322#624—28no—
323D3×Dic3—28no—
324D3×Dic3—28no—
325C24×C4—91no—
326C2×#123—91no—
327C2×#123—91no—
328C2×#120—91no—
329#386—31no—
330#386—91no—
331#386—91no—
332#386—91no—
333#385—31no—
334#385—91no—
335#385—91no—
336#385—91no—
337#381—91no—
338#381—91no—
339#379—91no—
340C24×C3—31no—
341C24×C3—31no—
342C24×C3—31no—
343C23×D3—31no—
344C23×D3—31no—
345C23×D3—34no—
346C23×D3—34no—
347C23×D3—61no—
348C23×D3—62no—
349C23×D3—62no—
350C23×D3—62no—
351C23×D3—62no—
352C23×D3—62no—
353C23×D3—62no—
354C23×D3—62no—
355C23×D3—62no—
356C23×D3—62no—
357C23×D3—62no—
358C23×D3—62no—
359C23×D3—62no—
360C23×D3C22×D311yescharacteristic
361C23×D3C22×D311yescharacteristic
362C23×D3C22×D311yescharacteristic
363C2×C3×D4—62no—
364C2×C3×D4—62no—
365C2×C3×D4—62no—
366C22×C3×C4—21no—
367C22×C3×C4—21no—
368C22×C3×C4—21no—
369C22×C3×C4—31no—
370C22×C3×C4—31no—
371C22×C3×C4—31no—
372C22×C3×C4—31no—
373C22×C3×C4—31no—
374C22×C3×C4—62no—
375C22×C3×C4—62no—
376C22×C3×C4—62no—
377C22×C3×C4—62no—
378C22×C3×C4—62no—
379C22×C3×C4—62no—
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C22×C3×C4C22×D311yescharacteristic
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67—62no—
391C2×#67—62no—
392C2×#67—62no—
393C2×#67—62no—
394C2×#67—62no—
395C22×Dic3—31no—
396C22×Dic3—31no—
397C22×Dic3—31no—
398C22×Dic3—31no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—61no—
402C22×Dic3—61no—
403C22×Dic3—61no—
404C22×Dic3—62no—
405C22×Dic3—62no—
406C22×Dic3—62no—
407C22×Dic3—62no—
408C22×Dic3—62no—
409C22×Dic3—62no—
410C22×Dic3C22×D311yescharacteristic
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C2×D12—22no—
416C2×D12—22no—
417C2×D12—22no—
418C2×D12—62no—
419C2×D12—62no—
420C2×D12—62no—
421C2×C4×D3—22no—
422C2×C4×D3—22no—
423C2×C4×D3—22no—
424C2×C4×D3—22no—
425C2×C4×D3—22no—
426C2×C4×D3—22no—
427C2×C4×D3—34no—
428C2×C4×D3—34no—
429C2×C4×D3—34no—
430C2×C4×D3—34no—
431C2×C4×D3—64no—
432C2×C4×D3—632no—
433C2×C4×D3—632no—
434C2×C4×D3—62no—
435C2×C4×D3—62no—
436C2×C4×D3—62no—
437C2×C4×D3—62no—
438C2×C4×D3—62no—
439C2×C4×D3—62no—
440C2×C4×D3—62no—
441C2×C4×D3—62no—
442C2×C4×D3—62no—
443C2×C4×D3—62no—
444C2×C4×D3—62no—
445C2×C4×D3—62no—
446C2×C4×D3—62no—
447C2×C4×D3—62no—
448C2×C4×D3—122no—
449C2×C4×D3—122no—
450C3×C4⋊C4—62no—
451C3×C4⋊C4—62no—
452C3×C22⋊C4—62no—
453C3×C22⋊C4—62no—
454C3×C22⋊C4—62no—
455C3×C22⋊C4—62no—
456C3×C22⋊C4—62no—
457#217—62no—
458#217—62no—
459#217—62no—
460#217—62no—
461#217—62no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—22no—
466(C2×D3)⋊C4—22no—
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—62no—
476(C2×D3)⋊C4—62no—
477(C2×D3)⋊C4—62no—
478(C2×D3)⋊C4—122no—
479(C2×D3)⋊C4—122no—
480C4⋊Dic3—22no—
481C4⋊Dic3—62no—
482Dic3⋊C4—22no—
483Dic3⋊C4—62no—
484Dic3⋊C4—62no—
485Dic3⋊C4—62no—
486C22×C32C22×D411yescharacteristic
487C22×C32C22×D411yescharacteristic
488C22×C32C22×D411yescharacteristic
489C22×C32C2×#4111yescharacteristic
490C22×C32C2×#4111yescharacteristic
491C22×C32C2×#4111yescharacteristic
492C22×C32C2×#4111yescharacteristic
493C2×C3⋊D3—22no—
494C2×C3⋊D3—22no—
495C2×C3⋊D3—22no—
496C2×C3⋊D3—22no—
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3#12014yes—
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#12314yescomplemented
520C2×C3×D3#12314yescomplemented
521D32—232no—
522C32×C4—22no—
523C32×C4—41no—
524C32×C4—41no—
525C3⋊Dic3—22no—
526C3⋊Dic3—41no—
527C3⋊Dic3—41no—
528C3×Dic3—22no—
529C3×Dic3—22no—
530C3×Dic3—41no—
531C3×Dic3—41no—
532C3×Dic3—41no—
533C25—91no—
534C22×D4—31no—
535C22×D4—91no—
536C22×D4—91no—
537C23×C4—31no—
538C23×C4—31no—
539C23×C4—91no—
540C23×C4—91no—
541C23×C4—91no—
542C23×C4—91no—
543C23×C4—184no—
544C23×C4—184no—
545C23×C4—184no—
546#123—184no—
547#123—184no—
548#120—184no—
549C2×C4⋊C4—31no—
550C2×C4⋊C4—31no—
551C2×C4⋊C4—91no—
552C2×C4⋊C4—91no—
553C2×C22⋊C4—31no—
554C2×C22⋊C4—31no—
555C2×C22⋊C4—31no—
556C2×C22⋊C4—31no—
557C2×C22⋊C4—31no—
558C2×C22⋊C4—91no—
559C2×C22⋊C4—91no—
560C2×C22⋊C4—91no—
561C2×C22⋊C4—91no—
562C2×C22⋊C4—91no—
563C2×C22⋊C4—91no—
564C2×C22⋊C4—91no—
565C2×C22⋊C4—91no—
566#95—31no—
567#95—31no—
568#95—91no—
569#95—91no—
570#95—91no—
571#95—91no—
572#95—91no—
573#95D3211yescharacteristic, complemented
574C23×C3—21no—
575C23×C3—32no—
576C23×C3—32no—
577C23×C3—32no—
578C23×C3—32no—
579C23×C3—32no—
580C23×C3—32no—
581C23×C3—61no—
582C23×C3—61no—
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×C3C23×D311yescharacteristic
597C23×C3C23×D311yescharacteristic
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—21no—
604C22×D3—21no—
605C22×D3—21no—
606C22×D3—21no—
607C22×D3—21no—
608C22×D3—21no—
609C22×D3—21no—
610C22×D3—21no—
611C22×D3—21no—
612C22×D3—21no—
613C22×D3—32no—
614C22×D3—32no—
615C22×D3—32no—
616C22×D3—32no—
617C22×D3—32no—
618C22×D3—32no—
619C22×D3—62no—
620C22×D3—62no—
621C22×D3—62no—
622C22×D3—68no—
623C22×D3—68no—
624C22×D3—68no—
625C22×D3—68no—
626C22×D3—68no—
627C22×D3—68no—
628C22×D3—68no—
629C22×D3—68no—
630C22×D3—68no—
631C22×D3—68no—
632C22×D3—68no—
633C22×D3—68no—
634C22×D3—61no—
635C22×D3—61no—
636C22×D3—61no—
637C22×D3—61no—
638C22×D3—61no—
639C22×D3—61no—
640C22×D3—61no—
641C22×D3—61no—
642C22×D3—68no—
643C22×D3—68no—
644C22×D3—121no—
645C22×D3—121no—
646C22×D3—121no—
647C22×D3—121no—
648C22×D3#23512yes—
649C22×D3#23512yes—
650C22×D3D3×D412yes—
651C22×D3D3×D412yes—
652C22×D3#23712yes—
653C22×D3#23912yes—
654C3×D4—124no—
655C2×C3×C4—21no—
656C2×C3×C4—21no—
657C2×C3×C4—21no—
658C2×C3×C4—21no—
659C2×C3×C4—21no—
660C2×C3×C4—21no—
661C2×C3×C4—21no—
662C2×C3×C4—21no—
663C2×C3×C4—21no—
664C2×C3×C4—21no—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—21no—
670C2×C3×C4—21no—
671C2×C3×C4—22no—
672C2×C3×C4—32no—
673C2×C3×C4—32no—
674C2×C3×C4—41no—
675C2×C3×C4—41no—
676C2×C3×C4—41no—
677C2×C3×C4—41no—
678C2×C3×C4—41no—
679C2×C3×C4—41no—
680C2×C3×C4—41no—
681C2×C3×C4—41no—
682C2×C3×C4—68no—
683C2×C3×C4—68no—
684C2×C3×C4—61no—
685C2×C3×C4—61no—
686C2×C3×C4—61no—
687C2×C3×C4—61no—
688C2×C3×C4—61no—
689C2×C3×C4—61no—
690C2×C3×C4—61no—
691C2×C3×C4—61no—
692C2×C3×C4—61no—
693C2×C3×C4—61no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4D3×D412yes—
698C2×C3×C4D3×D412yes—
699#67—124no—
700#67—124no—
701#67—124no—
702C2×Dic3—21no—
703C2×Dic3—21no—
704C2×Dic3—21no—
705C2×Dic3—21no—
706C2×Dic3—21no—
707C2×Dic3—21no—
708C2×Dic3—21no—
709C2×Dic3—21no—
710C2×Dic3—21no—
711C2×Dic3—21no—
712C2×Dic3—21no—
713C2×Dic3—21no—
714C2×Dic3—21no—
715C2×Dic3—32no—
716C2×Dic3—32no—
717C2×Dic3—62no—
718C2×Dic3—68no—
719C2×Dic3—68no—
720C2×Dic3—61no—
721C2×Dic3—61no—
722C2×Dic3—61no—
723C2×Dic3—61no—
724C2×Dic3—61no—
725C2×Dic3—61no—
726C2×Dic3—61no—
727C2×Dic3—61no—
728C2×Dic3—61no—
729C2×Dic3—61no—
730C2×Dic3—61no—
731C2×Dic3—61no—
732C2×Dic3—61no—
733C2×Dic3—61no—
734C2×Dic3—61no—
735C2×Dic3—61no—
736C2×Dic3—121no—
737C2×Dic3—121no—
738C2×Dic3—121no—
739C2×Dic3—121no—
740C2×Dic3—121no—
741C2×Dic3—121no—
742C2×Dic3—121no—
743C2×Dic3—121no—
744C2×Dic3D3×D412yes—
745C2×Dic3D3×D412yes—
746D12—44no—
747D12—124no—
748C4×D3—28no—
749C4×D3—28no—
750C4×D3—68no—
751C4×D3—68no—
752C4×D3—68no—
753C4×D3—68no—
754C4×D3—68no—
755C4×D3—68no—
756C4×D3—128no—
757C2×C32C2×#12011yescharacteristic
758C2×C32C2×#12311yescharacteristic
759C2×C32C2×#12311yescharacteristic
760C2×C32#52511yescharacteristic
761C2×C32#52511yescharacteristic
762C2×C32#52511yescharacteristic
763C2×C32#52511yescharacteristic
764C3⋊D3—24no—
765C3×D3—24no—
766C3×D3—24no—
767C3×D3—81no—
768C24—31no—
769C24—31no—
770C24—31no—
771C24—94no—
772C24—91no—
773C24—182no—
774C24—182no—
775C24—182no—
776C24—182no—
777C24—182no—
778C24—182no—
779C2×D4—62no—
780C2×D4—62no—
781C2×D4—62no—
782C2×D4—182no—
783C2×D4—182no—
784C2×D4—182no—
785C2×D4—182no—
786C2×D4—182no—
787C2×D4—182no—
788C22×C4—31no—
789C22×C4—31no—
790C22×C4—31no—
791C22×C4—31no—
792C22×C4—31no—
793C22×C4—62no—
794C22×C4—62no—
795C22×C4—62no—
796C22×C4—62no—
797C22×C4—62no—
798C22×C4—62no—
799C22×C4—94no—
800C22×C4—91no—
801C22×C4—94no—
802C22×C4—91no—
803C22×C4—91no—
804C22×C4—182no—
805C22×C4—182no—
806C22×C4—182no—
807C22×C4—182no—
808C22×C4—182no—
809C22×C4—182no—
810C22×C4—1832no—
811C22×C4—182no—
812C22×C4—182no—
813C22×C4—182no—
814C22×C4—182no—
815C22×C4C2×D3211yescharacteristic
816C22×C4C2×D3211yescharacteristic
817C22×C4C2×D3211yescharacteristic
818C4⋊C4—62no—
819C4⋊C4—62no—
820C4⋊C4—182no—
821C4⋊C4—182no—
822C22⋊C4—62no—
823C22⋊C4—62no—
824C22⋊C4—62no—
825C22⋊C4—62no—
826C22⋊C4—62no—
827C22⋊C4—182no—
828C22⋊C4—182no—
829C22⋊C4—182no—
830C22⋊C4—182no—
831C22⋊C4—182no—
832C22⋊C4—182no—
833C22⋊C4—182no—
834C22⋊C4—182no—
835C22×C3—21no—
836C22×C3—21no—
837C22×C3—21no—
838C22×C3—21no—
839C22×C3—21no—
840C22×C3—21no—
841C22×C3—21no—
842C22×C3—34no—
843C22×C3—34no—
844C22×C3—62no—
845C22×C3—62no—
846C22×C3—62no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—62no—
851C22×C3—62no—
852C22×C3—62no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—121no—
857C22×C3—121no—
858C22×C3—121no—
859C22×C3—121no—
860C22×C3—121no—
861C22×C3—121no—
862C22×C3—121no—
863C22×C3C2×#23511yescharacteristic
864C22×C3C2×#23511yescharacteristic
865C22×C3C2×D3×D411yescharacteristic
866C22×C3C2×D3×D411yescharacteristic
867C22×C3C2×D3×D411yescharacteristic
868C22×C3C2×D3×D411yescharacteristic
869C22×C3C2×D3×D411yescharacteristic
870C22×C3C2×D3×D411yescharacteristic
871C22×C3C2×#23711yescharacteristic
872C22×C3C2×#23911yescharacteristic
873C22×C3D3×#4111yescharacteristic
874C22×C3D3×#4111yescharacteristic
875C22×C3D3×#4111yescharacteristic
876C22×C3D3×#4111yescharacteristic
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—22no—
881C2×D3—22no—
882C2×D3—22no—
883C2×D3—22no—
884C2×D3—22no—
885C2×D3—22no—
886C2×D3—22no—
887C2×D3—22no—
888C2×D3—22no—
889C2×D3—34no—
890C2×D3—34no—
891C2×D3—41no—
892C2×D3—41no—
893C2×D3—41no—
894C2×D3—41no—
895C2×D3—41no—
896C2×D3—41no—
897C2×D3—41no—
898C2×D3—64no—
899C2×D3—632no—
900C2×D3—632no—
901C2×D3—62no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—62no—
905C2×D3—62no—
906C2×D3—62no—
907C2×D3—62no—
908C2×D3—62no—
909C2×D3—62no—
910C2×D3—62no—
911C2×D3—62no—
912C2×D3—62no—
913C2×D3—122no—
914C2×D3—122no—
915C2×D3—122no—
916C2×D3—122no—
917C2×D3—122no—
918C2×D3—122no—
919C2×D3#88314yescomplemented
920C2×D3#89414yescomplemented
921C3×C4—22no—
922C3×C4—22no—
923C3×C4—42no—
924C3×C4—41no—
925C3×C4—41no—
926C3×C4—41no—
927C3×C4—41no—
928C3×C4—62no—
929C3×C4—62no—
930C3×C4—81no—
931C3×C4—81no—
932C3×C4—121no—
933C3×C4—121no—
934C3×C4—121no—
935Dic3—22no—
936Dic3—22no—
937Dic3—41no—
938Dic3—41no—
939Dic3—41no—
940Dic3—62no—
941Dic3—62no—
942Dic3—122no—
943Dic3—121no—
944Dic3—121no—
945Dic3—121no—
946Dic3—121no—
947Dic3—241no—
948Dic3—241no—
949C32#284911yescharacteristic, complemented, Sylow
950C23—32no—
951C23—32no—
952C23—32no—
953C23—32no—
954C23—32no—
955C23—32no—
956C23—61no—
957C23—61no—
958C23—61no—
959C23—61no—
960C23—61no—
961C23—61no—
962C23—61no—
963C23—61no—
964C23—61no—
965C23—61no—
966C23—61no—
967C23—61no—
968C23—61no—
969C23—61no—
970C23—61no—
971C23—92no—
972C23—92no—
973C23—92no—
974C23—188no—
975C23—188no—
976C23—188no—
977C23—188no—
978C23—188no—
979C23—188no—
980C23—188no—
981C23—181no—
982C23—181no—
983C23—181no—
984C23—181no—
985C23C22×D3211yescharacteristic
986D4—124no—
987D4—364no—
988D4—364no—
989C2×C4—21no—
990C2×C4—21no—
991C2×C4—21no—
992C2×C4—21no—
993C2×C4—21no—
994C2×C4—21no—
995C2×C4—21no—
996C2×C4—21no—
997C2×C4—32no—
998C2×C4—32no—
999C2×C4—68no—
1000C2×C4—68no—
1001C2×C4—61no—
1002C2×C4—61no—
1003C2×C4—61no—
1004C2×C4—61no—
1005C2×C4—61no—
1006C2×C4—61no—
1007C2×C4—61no—
1008C2×C4—61no—
1009C2×C4—61no—
1010C2×C4—61no—
1011C2×C4—61no—
1012C2×C4—61no—
1013C2×C4—61no—
1014C2×C4—92no—
1015C2×C4—188no—
1016C2×C4—188no—
1017C2×C4—188no—
1018C2×C4—188no—
1019C2×C4—181no—
1020C2×C4—181no—
1021C2×C4—181no—
1022C2×C4—181no—
1023C2×C4—181no—
1024C2×C4—181no—
1025C2×C4—181no—
1026C2×C4—181no—
1027C2×C4#380212yes—
1028C2×C3—21no—
1029C2×C3—21no—
1030C2×C3—21no—
1031C2×C3—21no—
1032C2×C3—21no—
1033C2×C3—21no—
1034C2×C3—21no—
1035C2×C3—64no—
1036C2×C3—64no—
1037C2×C3—241no—
1038C2×C3C2×#88311yescharacteristic
1039C2×C3C2×#89411yescharacteristic
1040C2×C3#554711yescharacteristic
1041C2×C3#554711yescharacteristic
1042C2×C3#554711yescharacteristic
1043C2×C3#554711yescharacteristic
1044C2×C3D3×#12011yescharacteristic
1045C2×C3D3×#12011yescharacteristic
1046C2×C3#560611yescharacteristic
1047C2×C3#560611yescharacteristic
1048C2×C3#562711yescharacteristic
1049C2×C3#562711yescharacteristic
1050C2×C3D3×#12311yescharacteristic
1051C2×C3D3×#12311yescharacteristic
1052D3—24no—
1053D3—24no—
1054D3—64no—
1055D3—64no—
1056D3—81no—
1057D3—124no—
1058C22—34no—
1059C22—34no—
1060C22—62no—
1061C22—62no—
1062C22—62no—
1063C22—62no—
1064C22—62no—
1065C22—62no—
1066C22—62no—
1067C22—62no—
1068C22—62no—
1069C22—62no—
1070C22—62no—
1071C22—62no—
1072C22—94no—
1073C22—121no—
1074C22—121no—
1075C22—121no—
1076C22—121no—
1077C22—121no—
1078C22—121no—
1079C22—121no—
1080C22—1832no—
1081C22—182no—
1082C22—182no—
1083C22—182no—
1084C22—182no—
1085C22—182no—
1086C22—182no—
1087C22C2×#380211yescharacteristic
1088C22D3×#23511yescharacteristic
1089C22D3×#23511yescharacteristic
1090C22D32×D411yescharacteristic
1091C22D32×D411yescharacteristic
1092C22D3×#23711yescharacteristic
1093C22D3×#23911yescharacteristic
1094C4—22no—
1095C4—41no—
1096C4—41no—
1097C4—62no—
1098C4—62no—
1099C4—121no—
1100C4—121no—
1101C4—121no—
1102C4—182no—
1103C4—361no—
1104C4—361no—
1105C3—21no—
1106C3#7465611yescharacteristic, complemented
1107C3#7493611yescharacteristic, complemented
1108C2—64no—
1109C2—64no—
1110C2—184no—
1111C2—241no—
1112C2#1059400611yescharacteristic
1113C2#1059425811yescharacteristic
1114C2D3×#88311yescharacteristic
1115C2#1059428611yescharacteristic
1116C2D3×#89411yescharacteristic
1117C2#1059462311yescharacteristic
1118C2#1059463211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC2×#63922C2
hypercenter#95D32
hypocenterC32#2849
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #95

Complements

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

NH ≅ G/Ntype
1. C22×C4×D32C2semidirect
3. C2×#63854C2semidirect
4. C2×#63853C2semidirect
5. #10592363C2semidirect
6. C3×#4668C2semidirect
7. C3×#4665C2semidirect
8. #10591399C2semidirect
9. #10591381C2semidirect
10. #10591377C2semidirect
11. #10591376C2semidirect
12. #10591373C2semidirect
13. #10591371C2semidirect
14. #10591363C2semidirect
15. #10591277C2semidirect
36. C2×C3×(C2×D3)⋊C4C22semidirect
37. C2×C3×(C2×D3)⋊C4C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
40. C2×#3724C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
46. C2×(C2×D3)⋊Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
51. C32×#95C22semidirect
52. #63658C22semidirect
53. #63658C22semidirect
54. #63658C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
57. #63579C22semidirect
58. #63579C22semidirect
82. #4668D3semidirect
84. #4665D3semidirect
109. C2×C4×C3⋊D3D4semidirect
132. C2×#624D4semidirect
214. C2×(C2×D3)⋊C4C2×D3semidirect
215. C2×(C2×D3)⋊C4C2×D3semidirect
217. C2×C4⋊Dic3C2×D3semidirect
221. C2×Dic3⋊C4C2×D3semidirect
230. C3×#95C2×D3semidirect
231. C3×#95C2×D3semidirect
245. C3⋊#95C2×D3semidirect
246. C3⋊#95C2×D3semidirect
519. C2×C3×D3#123semidirect
520. C2×C3×D3#123semidirect
573. #95D32semidirect
919. C2×D3#883semidirect
920. C2×D3#894semidirect
949. C32#2849semidirect
1106. C3#74656semidirect
1107. C3#74936semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×#639222
C2×#638542
C2×#638532
#105923632
C3×#46682
C3×#46652
#105913992
#105913812
#105913772
#105913762
#105913732
#105913712
#105913632
#105912772
#749363
#746563