Finite Group Databasebeta

← #11856280

Subgroups — #11856280

Order 1152.

2347 conjugacy classes of subgroups.

The subgroup lattice has 1136 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic, complemented
2C2×#63923C211yesmaximal, characteristic
3C2×#63890C211yesmaximal, characteristic, complemented
4C2×#63850C211yesmaximal, characteristic, complemented
5#10592364C211yesmaximal, characteristic, complemented
6C3×#4668C211yesmaximal, characteristic, complemented
7C3×#4664C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591382C211yesmaximal, characteristic, complemented
10#10591380C211yesmaximal, characteristic, complemented
11#10591378C211yesmaximal, characteristic, complemented
12#10591373C211yesmaximal, characteristic, complemented
13#10591364C211yesmaximal, characteristic, complemented
14#10591362C211yesmaximal, characteristic, complemented
15#10591290C211yesmaximal, characteristic, complemented
16#74656—31nomaximal
17#74146—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4⋊(C3⋊D3)C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×#626C2211yescharacteristic
24C22×#626C2211yescharacteristic
25C22×#624C2211yescharacteristic
26C22×D3×Dic3C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C2×C4×D32—24no—
29C2×C4×D32—24no—
30C2×C4×D32—24no—
31C2×#3752C2211yescharacteristic
32C2×#3752C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic, complemented
34C2×C3×(C2×D3)⋊C4C2211yescharacteristic
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
39C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
40C2×#3724C2211yescharacteristic, complemented
41C2×Dic3⋊Dic3C2211yescharacteristic, complemented
42C2×#3722C2211yescharacteristic
43C2×#3722C2211yescharacteristic
44C2×#3722C2211yescharacteristic, complemented
45C2×#3722C2211yescharacteristic, complemented
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48#63923—24no—
49#63890—24no—
50#63850—24no—
51C32×#95C2211yescharacteristic, complemented
52#63658C2211yescharacteristic, complemented
53C3×C3⋊#95C2211yescharacteristic, complemented
54C3×C3⋊#95C2211yescharacteristic, complemented
55C3×C3⋊#95C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57#63579C2211yescharacteristic, complemented
58#63579C2211yescharacteristic, complemented
59C23×C4×D3—31no—
60C23×C4×D3—31no—
61C2×#929—31no—
62C2×#894—31no—
63C2×#894—31no—
64C2×#886—31no—
65C2×#882—31no—
66C2×#882—31no—
67C3×#385—31no—
68C3×#381—31no—
69#5213—31no—
70#4989—31no—
71#4989—31no—
72#4958—31no—
73#4955—31no—
74#4955—31no—
75#4946—31no—
76#4943—31no—
77#4668—31no—
78#4668—31no—
79#4668—31no—
80#4668D311yescharacteristic, complemented
81#4665—31no—
82#4665—31no—
83#4665—31no—
84#4665—31no—
85#4665—31no—
86#4665—31no—
87#4665—61no—
88#4664—31no—
89#4664D311yescharacteristic, complemented
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
106C2×C4⋊(C3⋊D3)—22no—
107C2×C4⋊(C3⋊D3)—22no—
108C2×C4⋊(C3⋊D3)—22no—
109C2×C4×C3⋊D3—22no—
110C2×C4×C3⋊D3—22no—
111C2×C4×C3⋊D3—22no—
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
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×D3D414yescomplemented
124C2×#626—22no—
125C2×#626—22no—
126C2×#626—22no—
127C2×#626—22no—
128C2×#626—22no—
129C2×#626—22no—
130C2×#624—22no—
131C2×#624—22no—
132C2×#624—22no—
133C2×D3×Dic3—22no—
134C2×D3×Dic3—22no—
135C2×D3×Dic3—22no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3—22no—
138C2×D3×Dic3D414yescomplemented
139C4×D32—232no—
140#3752—22no—
141#3752—22no—
142#3752—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#3722—22no—
153#3722—22no—
154#3722—22no—
155(C2×D3)⋊Dic3—22no—
156(C2×D3)⋊Dic3—22no—
157#2849—91noSylow
158C24×D3—31no—
159C24×D3—31no—
160C23×C3×C4—31no—
161C23×C3×C4—31no—
162C22×#67—31no—
163C22×#67—31no—
164C23×Dic3—31no—
165C23×Dic3—31no—
166C22×D12—31no—
167C22×D12—31no—
168C22×D12—31no—
169C22×D12—31no—
170C22×D12—61no—
171C22×C4×D3—31no—
172C22×C4×D3—31no—
173C22×C4×D3—31no—
174C22×C4×D3—31no—
175C22×C4×D3—31no—
176C22×C4×D3—31no—
177C22×C4×D3—61no—
178C22×C4×D3—64no—
179C22×C4×D3—64no—
180C22×C4×D3—64no—
181C22×C4×D3—64no—
182C22×C4×D3—64no—
183C22×C4×D3—64no—
184C22×C4×D3C2×D311yescharacteristic
185C22×C4×D3C2×D311yescharacteristic
186C2×C3×C4⋊C4—31no—
187C2×C3×C4⋊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—
194#929—64no—
195C2×(C2×D3)⋊C4—31no—
196C2×(C2×D3)⋊C4—31no—
197C2×(C2×D3)⋊C4—31no—
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—61no—
212C2×(C2×D3)⋊C4—61no—
213C2×(C2×D3)⋊C4—61no—
214C2×(C2×D3)⋊C4C2×D311yescharacteristic
215C2×(C2×D3)⋊C4C2×D311yescharacteristic
216C2×(C2×D3)⋊C4C2×D311yescharacteristic
217C2×(C2×D3)⋊C4C2×D311yescharacteristic
218C2×C4⋊Dic3—31no—
219C2×C4⋊Dic3C2×D311yescharacteristic, complemented
220C2×Dic3⋊C4—31no—
221C2×Dic3⋊C4—31no—
222C2×Dic3⋊C4—31no—
223C2×Dic3⋊C4C2×D311yescharacteristic, complemented
224#894—64no—
225#894—64no—
226#886—64no—
227#882—64no—
228#882—64no—
229C3×#95—21no—
230C3×#95—31no—
231C3×#95—31no—
232C3×#95—31no—
233C3×#95—31no—
234C3×#95C2×D311yescharacteristic, complemented
235C3×#95C2×D311yescharacteristic, complemented
236C3⋊#95—31no—
237C3⋊#95—31no—
238C3⋊#95—31no—
239C3⋊#95—31no—
240C3⋊#95—31no—
241C3⋊#95—31no—
242C3⋊#95—61no—
243C3⋊#95C2×D311yescharacteristic, complemented
244C3⋊#95C2×D311yescharacteristic, complemented
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⋊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⋊D3C2×D412yes—
260C22×C3⋊D3#4112yes—
261C22×C3⋊D3#4112yes—
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×D3C2×D412yes—
273C22×C3×D3C2×D412yes—
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⋊Dic3C2×D412yes—
298C4⋊(C3⋊D3)—44no—
299C4×C3⋊D3—28no—
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×Dic3—21no—
315C2×C3×Dic3—21no—
316C2×C3×Dic3C2×D412yes—
317C2×C3×Dic3C2×D412yes—
318C3×C4×D3—28no—
319C3×C4×D3—28no—
320#626—44no—
321#626—44no—
322#624—28no—
323D3×Dic3—28no—
324D3×Dic3—28no—
325C24×C4—91no—
326C2×#123—91no—
327C2×#123—91no—
328C2×#120—91no—
329#386—91no—
330#386—91no—
331#386—91no—
332#386—91no—
333#385—31no—
334#385—91no—
335#385—91no—
336#385—91no—
337#381—31no—
338#381—91no—
339#379—91no—
340C24×C3—31no—
341C24×C3—31no—
342C23×D3—31no—
343C23×D3—31no—
344C23×D3—34no—
345C23×D3—34no—
346C23×D3—31no—
347C23×D3—31no—
348C23×D3—61no—
349C23×D3—61no—
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×D3—62no—
361C23×D3—62no—
362C23×D3C22×D311yescharacteristic
363C23×D3C22×D311yescharacteristic
364C22×C3×C4—21no—
365C22×C3×C4—21no—
366C22×C3×C4—21no—
367C22×C3×C4—31no—
368C22×C3×C4—31no—
369C22×C3×C4—34no—
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×C4C22×D311yescharacteristic
380C22×C3×C4C22×D311yescharacteristic
381C22×C3×C4C22×D311yescharacteristic
382C22×C3×C4C22×D311yescharacteristic
383C22×C3×C4C22×D311yescharacteristic
384C22×C3×C4C22×D311yescharacteristic
385C2×#67—62no—
386C2×#67—62no—
387C2×#67—62no—
388C2×#67—62no—
389C2×#67—62no—
390C2×#67—62no—
391C22×Dic3—31no—
392C22×Dic3—31no—
393C22×Dic3—34no—
394C22×Dic3—31no—
395C22×Dic3—31no—
396C22×Dic3—61no—
397C22×Dic3—61no—
398C22×Dic3—62no—
399C22×Dic3—62no—
400C22×Dic3—62no—
401C22×Dic3—62no—
402C22×Dic3—62no—
403C22×Dic3C22×D311yescharacteristic
404C22×Dic3C22×D311yescharacteristic
405C22×Dic3C22×D311yescharacteristic
406C22×Dic3C22×D311yescharacteristic
407C22×Dic3C22×D311yescharacteristic
408C22×Dic3C22×D311yescharacteristic
409C2×D12—62no—
410C2×D12—62no—
411C2×D12—62no—
412C2×D12—62no—
413C2×D12—62no—
414C2×D12—62no—
415C2×D12—64no—
416C2×D12—62no—
417C2×D12—62no—
418C2×D12—62no—
419C2×D12—62no—
420C2×D12—62no—
421C2×D12—62no—
422C2×D12—122no—
423C2×D12—122no—
424C2×C4×D3—22no—
425C2×C4×D3—22no—
426C2×C4×D3—22no—
427C2×C4×D3—22no—
428C2×C4×D3—22no—
429C2×C4×D3—34no—
430C2×C4×D3—632no—
431C2×C4×D3—632no—
432C2×C4×D3—62no—
433C2×C4×D3—62no—
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—62no—
449C2×C4×D3—122no—
450C2×C4×D3—122no—
451C2×C4×D3—122no—
452C2×C4×D3D1214yescomplemented
453C3×C4⋊C4—62no—
454C3×C4⋊C4—62no—
455C3×C22⋊C4—62no—
456C3×C22⋊C4—62no—
457C3×C22⋊C4—62no—
458C3×C22⋊C4—62no—
459#217—62no—
460#217—62no—
461(C2×D3)⋊C4—22no—
462(C2×D3)⋊C4—22no—
463(C2×D3)⋊C4—22no—
464(C2×D3)⋊C4—22no—
465(C2×D3)⋊C4—62no—
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—62no—
476(C2×D3)⋊C4—62no—
477(C2×D3)⋊C4—62no—
478(C2×D3)⋊C4—62no—
479(C2×D3)⋊C4—62no—
480(C2×D3)⋊C4—62no—
481(C2×D3)⋊C4—122no—
482(C2×D3)⋊C4—122no—
483(C2×D3)⋊C4—122no—
484C4⋊Dic3—22no—
485C4⋊Dic3—62no—
486Dic3⋊C4—22no—
487Dic3⋊C4—62no—
488Dic3⋊C4—62no—
489Dic3⋊C4—62no—
490C22×C32C22×D411yescharacteristic
491C22×C32C22×D411yescharacteristic
492C22×C32C22×D411yescharacteristic
493C22×C32C2×#4111yescharacteristic
494C22×C32C2×#4111yescharacteristic
495C22×C32C2×#4111yescharacteristic
496C22×C32C2×#4111yescharacteristic
497C2×C3⋊D3—22no—
498C2×C3⋊D3—22no—
499C2×C3⋊D3—22no—
500C2×C3⋊D3—22no—
501C2×C3⋊D3—22no—
502C2×C3⋊D3—22no—
503C2×C3⋊D3—41no—
504C2×C3⋊D3—41no—
505C2×C3⋊D3—41no—
506C2×C3⋊D3—41no—
507C2×C3⋊D3—41no—
508C2×C3⋊D3—41no—
509C2×C3⋊D3—41no—
510C2×C3⋊D3#12314yescomplemented
511C2×C3×D3—22no—
512C2×C3×D3—22no—
513C2×C3×D3—22no—
514C2×C3×D3—22no—
515C2×C3×D3—22no—
516C2×C3×D3—22no—
517C2×C3×D3—22no—
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3#12014yes—
524C2×C3×D3#12314yescomplemented
525D32—232no—
526C32×C4—22no—
527C32×C4—41no—
528C32×C4—41no—
529C3⋊Dic3—22no—
530C3⋊Dic3—41no—
531C3×Dic3—22no—
532C3×Dic3—22no—
533C3×Dic3—41no—
534C3×Dic3—41no—
535C3×Dic3—41no—
536C3×Dic3—41no—
537C25—91no—
538C22×D4—91no—
539C22×D4—91no—
540C22×D4—91no—
541C23×C4—31no—
542C23×C4—31no—
543C23×C4—91no—
544C23×C4—91no—
545C23×C4—91no—
546C23×C4—91no—
547C23×C4—184no—
548C23×C4—184no—
549C23×C4—184no—
550#123—184no—
551#123—184no—
552#120—184no—
553C2×C4⋊C4—31no—
554C2×C4⋊C4—31no—
555C2×C4⋊C4—91no—
556C2×C4⋊C4—91no—
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—
570#95—31no—
571#95—31no—
572#95—31no—
573#95—31no—
574#95—91no—
575#95—91no—
576#95—91no—
577#95D3211yescharacteristic, complemented
578C23×C3—21no—
579C23×C3—32no—
580C23×C3—32no—
581C23×C3—32no—
582C23×C3—32no—
583C23×C3—32no—
584C23×C3—32no—
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×C3C23×D311yescharacteristic
594C23×C3C23×D311yescharacteristic
595C22×D3—21no—
596C22×D3—21no—
597C22×D3—21no—
598C22×D3—21no—
599C22×D3—21no—
600C22×D3—21no—
601C22×D3—21no—
602C22×D3—21no—
603C22×D3—32no—
604C22×D3—32no—
605C22×D3—32no—
606C22×D3—32no—
607C22×D3—32no—
608C22×D3—32no—
609C22×D3—62no—
610C22×D3—62no—
611C22×D3—62no—
612C22×D3—68no—
613C22×D3—68no—
614C22×D3—68no—
615C22×D3—68no—
616C22×D3—68no—
617C22×D3—68no—
618C22×D3—68no—
619C22×D3—68no—
620C22×D3—68no—
621C22×D3—68no—
622C22×D3—68no—
623C22×D3—68no—
624C22×D3—61no—
625C22×D3—61no—
626C22×D3—61no—
627C22×D3—61no—
628C22×D3—61no—
629C22×D3—61no—
630C22×D3—61no—
631C22×D3—61no—
632C22×D3—68no—
633C22×D3—68no—
634C22×D3—62no—
635C22×D3—61no—
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—61no—
649C22×D3—121no—
650C22×D3—121no—
651C22×D3—121no—
652C22×D3—121no—
653C22×D3—121no—
654C22×D3—121no—
655C22×D3—121no—
656C22×D3—121no—
657C22×D3—121no—
658C22×D3—121no—
659C22×D3C2×D1212yes—
660C22×D3#23512yes—
661C22×D3D3×D412yes—
662C22×D3D3×D412yes—
663C22×D3D3×D412yes—
664C22×D3#23912yes—
665C2×C3×C4—21no—
666C2×C3×C4—21no—
667C2×C3×C4—21no—
668C2×C3×C4—21no—
669C2×C3×C4—22no—
670C2×C3×C4—21no—
671C2×C3×C4—21no—
672C2×C3×C4—21no—
673C2×C3×C4—21no—
674C2×C3×C4—21no—
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—22no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—41no—
686C2×C3×C4—41no—
687C2×C3×C4—41no—
688C2×C3×C4—41no—
689C2×C3×C4—41no—
690C2×C3×C4—41no—
691C2×C3×C4—41no—
692C2×C3×C4—68no—
693C2×C3×C4—68no—
694C2×C3×C4—61no—
695C2×C3×C4—61no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
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×C4C2×D1212yes—
711C2×C3×C4D3×D412yes—
712#67—124no—
713#67—124no—
714C2×Dic3—21no—
715C2×Dic3—21no—
716C2×Dic3—21no—
717C2×Dic3—21no—
718C2×Dic3—21no—
719C2×Dic3—21no—
720C2×Dic3—21no—
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—32no—
731C2×Dic3—32no—
732C2×Dic3—62no—
733C2×Dic3—68no—
734C2×Dic3—68no—
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—121no—
746C2×Dic3—121no—
747C2×Dic3—121no—
748C2×Dic3—121no—
749C2×Dic3—121no—
750C2×Dic3C2×D1212yes—
751C2×Dic3D3×D412yes—
752D12—124no—
753D12—124no—
754D12—128no—
755D12—124no—
756D12—124no—
757C4×D3—28no—
758C4×D3—28no—
759C4×D3—68no—
760C4×D3—68no—
761C4×D3—68no—
762C4×D3—68no—
763C4×D3—68no—
764C4×D3—68no—
765C4×D3—128no—
766C2×C32C2×#12011yescharacteristic
767C2×C32C2×#12311yescharacteristic
768C2×C32C2×#12311yescharacteristic
769C2×C32#52511yescharacteristic
770C2×C32#52511yescharacteristic
771C2×C32#52511yescharacteristic
772C2×C32#52511yescharacteristic
773C3⋊D3—24no—
774C3⋊D3—81no—
775C3×D3—24no—
776C3×D3—24no—
777C24—31no—
778C24—31no—
779C24—94no—
780C24—91no—
781C24—91no—
782C24—182no—
783C24—182no—
784C24—182no—
785C24—182no—
786C24—182no—
787C24—182no—
788C2×D4—182no—
789C2×D4—182no—
790C2×D4—182no—
791C2×D4—182no—
792C2×D4—182no—
793C2×D4—182no—
794C2×D4—182no—
795C2×D4—182no—
796C2×D4—182no—
797C22×C4—31no—
798C22×C4—31no—
799C22×C4—34no—
800C22×C4—31no—
801C22×C4—31no—
802C22×C4—31no—
803C22×C4—31no—
804C22×C4—62no—
805C22×C4—62no—
806C22×C4—62no—
807C22×C4—62no—
808C22×C4—62no—
809C22×C4—94no—
810C22×C4—91no—
811C22×C4—91no—
812C22×C4—182no—
813C22×C4—182no—
814C22×C4—182no—
815C22×C4—182no—
816C22×C4—182no—
817C22×C4—182no—
818C22×C4—1832no—
819C22×C4—182no—
820C22×C4—182no—
821C22×C4—182no—
822C22×C4—182no—
823C22×C4—182no—
824C22×C4C2×D3211yescharacteristic
825C22×C4C2×D3211yescharacteristic
826C22×C4C2×D3211yescharacteristic
827C4⋊C4—62no—
828C4⋊C4—62no—
829C4⋊C4—182no—
830C4⋊C4—182no—
831C22⋊C4—62no—
832C22⋊C4—62no—
833C22⋊C4—62no—
834C22⋊C4—62no—
835C22⋊C4—182no—
836C22⋊C4—182no—
837C22⋊C4—182no—
838C22⋊C4—182no—
839C22⋊C4—182no—
840C22⋊C4—182no—
841C22⋊C4—182no—
842C22⋊C4—182no—
843C22⋊C4—182no—
844C22×C3—21no—
845C22×C3—21no—
846C22×C3—21no—
847C22×C3—21no—
848C22×C3—21no—
849C22×C3—21no—
850C22×C3—21no—
851C22×C3—34no—
852C22×C3—34no—
853C22×C3—62no—
854C22×C3—62no—
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×C3C22×D1211yescharacteristic
866C22×C3C2×#23511yescharacteristic
867C22×C3C2×D3×D411yescharacteristic
868C22×C3C2×D3×D411yescharacteristic
869C22×C3C2×D3×D411yescharacteristic
870C22×C3C2×D3×D411yescharacteristic
871C22×C3C2×D3×D411yescharacteristic
872C22×C3C2×#23911yescharacteristic
873C22×C3D3×#4111yescharacteristic
874C22×C3D3×#4111yescharacteristic
875C22×C3D3×#4111yescharacteristic
876C22×C3D3×#4111yescharacteristic
877C22×C3D3×#4111yescharacteristic
878C22×C3D3×#4111yescharacteristic
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—22no—
890C2×D3—22no—
891C2×D3—34no—
892C2×D3—34no—
893C2×D3—64no—
894C2×D3—632no—
895C2×D3—632no—
896C2×D3—62no—
897C2×D3—62no—
898C2×D3—62no—
899C2×D3—62no—
900C2×D3—62no—
901C2×D3—62no—
902C2×D3—62no—
903C2×D3—62no—
904C2×D3—62no—
905C2×D3—62no—
906C2×D3—62no—
907C2×D3—62no—
908C2×D3—122no—
909C2×D3—122no—
910C2×D3—122no—
911C2×D3—122no—
912C2×D3—122no—
913C2×D3—122no—
914C2×D3—122no—
915C2×D3—122no—
916C2×D3—122no—
917C2×D3—121no—
918C2×D3—121no—
919C2×D3—121no—
920C2×D3—121no—
921C2×D3—121no—
922C2×D3—121no—
923C2×D3—121no—
924C2×D3—121no—
925C2×D3—121no—
926C2×D3—121no—
927C2×D3—121no—
928C2×D3—121no—
929C2×D3—121no—
930C2×D3—121no—
931C2×D3—241no—
932C2×D3—241no—
933C2×D3—241no—
934C2×D3—241no—
935C2×D3#88214yes—
936C2×D3#89414yescomplemented
937C3×C4—22no—
938C3×C4—22no—
939C3×C4—42no—
940C3×C4—42no—
941C3×C4—41no—
942C3×C4—41no—
943C3×C4—41no—
944C3×C4—41no—
945C3×C4—62no—
946C3×C4—62no—
947C3×C4—81no—
948C3×C4—121no—
949C3×C4—121no—
950C3×C4—121no—
951C3×C4—121no—
952Dic3—22no—
953Dic3—22no—
954Dic3—41no—
955Dic3—41no—
956Dic3—41no—
957Dic3—41no—
958Dic3—62no—
959Dic3—62no—
960Dic3—122no—
961Dic3—121no—
962Dic3—121no—
963Dic3—241no—
964C32#284911yescharacteristic, complemented, Sylow
965C23—32no—
966C23—32no—
967C23—32no—
968C23—32no—
969C23—32no—
970C23—32no—
971C23—61no—
972C23—61no—
973C23—61no—
974C23—61no—
975C23—61no—
976C23—61no—
977C23—61no—
978C23—61no—
979C23—92no—
980C23—92no—
981C23—92no—
982C23—188no—
983C23—188no—
984C23—188no—
985C23—188no—
986C23—188no—
987C23—188no—
988C23—188no—
989C23—181no—
990C23—181no—
991C23—181no—
992C23—181no—
993C23—181no—
994C23—181no—
995C23—181no—
996C23—181no—
997C23—181no—
998C23—181no—
999C23—181no—
1000C23C22×D3211yescharacteristic
1001D4—364no—
1002D4—364no—
1003D4—364no—
1004C2×C4—21no—
1005C2×C4—21no—
1006C2×C4—21no—
1007C2×C4—21no—
1008C2×C4—21no—
1009C2×C4—21no—
1010C2×C4—21no—
1011C2×C4—21no—
1012C2×C4—32no—
1013C2×C4—32no—
1014C2×C4—68no—
1015C2×C4—68no—
1016C2×C4—61no—
1017C2×C4—61no—
1018C2×C4—61no—
1019C2×C4—61no—
1020C2×C4—61no—
1021C2×C4—61no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—61no—
1029C2×C4—61no—
1030C2×C4—61no—
1031C2×C4—61no—
1032C2×C4—92no—
1033C2×C4—188no—
1034C2×C4—188no—
1035C2×C4—188no—
1036C2×C4—188no—
1037C2×C4—181no—
1038C2×C4—181no—
1039C2×C4—181no—
1040C2×C4—181no—
1041C2×C4—181no—
1042C2×C4D3×D1212yes—
1043C2×C3—21no—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—64no—
1051C2×C3—64no—
1052C2×C3C2×#88211yescharacteristic
1053C2×C3C2×#89411yescharacteristic
1054C2×C3#552411yescharacteristic
1055C2×C3#552411yescharacteristic
1056C2×C3#554711yescharacteristic
1057C2×C3#554711yescharacteristic
1058C2×C3D3×#12011yescharacteristic
1059C2×C3#562711yescharacteristic
1060C2×C3#562711yescharacteristic
1061C2×C3D3×#12311yescharacteristic
1062C2×C3D3×#12311yescharacteristic
1063C2×C3D3×#12311yescharacteristic
1064C2×C3#565611yescharacteristic
1065C2×C3#565611yescharacteristic
1066D3—24no—
1067D3—24no—
1068D3—64no—
1069D3—64no—
1070D3—124no—
1071D3—242no—
1072D3—241no—
1073D3—241no—
1074C22—34no—
1075C22—34no—
1076C22—62no—
1077C22—62no—
1078C22—62no—
1079C22—62no—
1080C22—62no—
1081C22—62no—
1082C22—62no—
1083C22—62no—
1084C22—62no—
1085C22—62no—
1086C22—62no—
1087C22—62no—
1088C22—94no—
1089C22—1832no—
1090C22—182no—
1091C22—182no—
1092C22—182no—
1093C22—182no—
1094C22—182no—
1095C22—182no—
1096C22—361no—
1097C22—361no—
1098C22—361no—
1099C22—361no—
1100C22—361no—
1101C22—361no—
1102C22—361no—
1103C22C2×D3×D1211yescharacteristic
1104C22D3×#23511yescharacteristic
1105C22#6430611yescharacteristic
1106C22D32×D411yescharacteristic
1107C22D32×D411yescharacteristic
1108C22#6431211yescharacteristic
1109C22D3×#23911yescharacteristic
1110C4—22no—
1111C4—41no—
1112C4—41no—
1113C4—62no—
1114C4—62no—
1115C4—121no—
1116C4—121no—
1117C4—121no—
1118C4—121no—
1119C4—182no—
1120C4—361no—
1121C3—21no—
1122C3#7414611yescharacteristic, complemented
1123C3#7465611yescharacteristic, complemented
1124C2—64no—
1125C2—64no—
1126C2—184no—
1127C2—721no—
1128C2#1059399711yescharacteristic
1129C2D3×#88211yescharacteristic
1130C2#1059426011yescharacteristic
1131C2#1059426611yescharacteristic
1132C2D3×#89411yescharacteristic
1133C2#1059461511yescharacteristic
1134C2#1059462711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutator, socle, cosocleC23×C32C24
FittingC32×#95C22
prime radicalC2×#63923C2
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×#63890C2semidirect
4. C2×#63850C2semidirect
5. #10592364C2semidirect
6. C3×#4668C2semidirect
7. C3×#4664C2semidirect
8. #10591399C2semidirect
9. #10591382C2semidirect
10. #10591380C2semidirect
11. #10591378C2semidirect
12. #10591373C2semidirect
13. #10591364C2semidirect
14. #10591362C2semidirect
15. #10591290C2semidirect
32. C2×#3752C22semidirect
33. C2×#3752C22semidirect
38. C2×C3×C4⋊Dic3C22semidirect
39. C2×C3×Dic3⋊C4C22semidirect
40. C2×#3724C22semidirect
41. C2×Dic3⋊Dic3C22semidirect
44. C2×#3722C22semidirect
45. C2×#3722C22semidirect
51. C32×#95C22semidirect
52. #63658C22semidirect
53. C3×C3⋊#95C22semidirect
54. C3×C3⋊#95C22semidirect
55. C3×C3⋊#95C22semidirect
56. C3×C3⋊#95C22semidirect
57. #63579C22semidirect
58. #63579C22semidirect
80. #4668D3semidirect
89. #4664D3semidirect
123. C2×C3×C4×D3D4semidirect
138. C2×D3×Dic3D4semidirect
219. C2×C4⋊Dic3C2×D3semidirect
223. C2×Dic3⋊C4C2×D3semidirect
234. C3×#95C2×D3semidirect
235. C3×#95C2×D3semidirect
243. C3⋊#95C2×D3semidirect
244. C3⋊#95C2×D3semidirect
245. C3⋊#95C2×D3semidirect
246. C3⋊#95C2×D3semidirect
452. C2×C4×D3D12semidirect
510. C2×C3⋊D3#123semidirect
524. C2×C3×D3#123semidirect
577. #95D32semidirect
936. C2×D3#894semidirect
964. C32#2849semidirect
1122. C3#74146semidirect
1123. C3#74656semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×#639232
C2×#638902
C2×#638502
#105923642
C3×#46682
C3×#46642
#105913992
#105913822
#105913802
#105913782
#105913732
#105913642
#105913622
#105912902
#746563
#741463