Finite Group Databasebeta

← #11802017

Subgroups — #11802017

Order 1152.

2577 conjugacy classes of subgroups.

The subgroup lattice has 1146 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×#63902C211yesmaximal, characteristic, complemented
4C2×#63898C211yesmaximal, characteristic, complemented
5C2×#63881C211yesmaximal, characteristic, complemented
6#10592365C211yesmaximal, characteristic, complemented
7C3×#4668C211yesmaximal, characteristic, complemented
8C3×#4665C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591378C211yesmaximal, characteristic, complemented
12#10591368C211yesmaximal, characteristic, complemented
13#10591368C211yesmaximal, characteristic, complemented
14#10591277C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16#74659—31nomaximal
17#74379—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
28C22×D3×Dic3C2211yescharacteristic, complemented
29C2×C4×D32—24no—
30C2×C4×D32—24no—
31C2×C4×D32—24no—
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic
34C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
35C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
42C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
43C2×#3724C2211yescharacteristic, complemented
44C2×#3722C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
49C2×Dic32C2211yescharacteristic, complemented
50#63922C418yescomplemented
51#63902—24no—
52#63898—24no—
53#63881—24no—
54C32×#95C2211yescharacteristic, complemented
55#63658C2211yescharacteristic, complemented
56C3×C3⋊#95C2211yescharacteristic, complemented
57C3×C3⋊#95C2211yescharacteristic, complemented
58#63579C2211yescharacteristic, complemented
59#63579C2211yescharacteristic, complemented
60C23×C4×D3—31no—
61C23×C4×D3—31no—
62C2×#937—31no—
63C2×D4×Dic3—31no—
64C2×#893—31no—
65C2×#893—31no—
66C2×#882—31no—
67C2×#67⋊C4—31no—
68C2×#67⋊C4—31no—
69C2×#67⋊C4—31no—
70C3×#386—31no—
71C3×#385—31no—
72#5213—31no—
73#5210—31no—
74#4989—31no—
75#4989—31no—
76#4956—31no—
77#4956—31no—
78#4955—31no—
79#4955—31no—
80Dic3×C22⋊C4—31no—
81Dic3×C22⋊C4—31no—
82#4668—31no—
83#4668D311yescharacteristic, complemented
84#4666—31no—
85#4666—31no—
86#4666—31no—
87#4666—31no—
88#4666—61no—
89#4665—31no—
90#4665D311yescharacteristic, complemented
91C23×C3⋊D3C2311yescharacteristic
92C23×C3×D3C2311yescharacteristic
93C23×C3×D3C2311yescharacteristic
94C23×C3×D3C2311yescharacteristic
95C22×D32—22no—
96C22×D32—22no—
97C22×D32—22no—
98C22×D32—22no—
99C22×D32—22no—
100C22×D32—22no—
101C22×D32C2×C414yescomplemented
102C22×C32×C4C2311yescharacteristic
103C22×C32×C4C2311yescharacteristic
104C22×C32×C4C2311yescharacteristic
105C22×C3⋊Dic3C2311yescharacteristic
106C22×C3⋊Dic3C2311yescharacteristic
107C22×C3⋊Dic3C2311yescharacteristic
108C2×C4×C3⋊D3—22no—
109C2×C4×C3⋊D3—22no—
110C2×C4×C3⋊D3D414yescomplemented
111C22×C3×Dic3C2311yescharacteristic
112C22×C3×Dic3C2311yescharacteristic
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C2×C3×D12—22no—
117C2×C3×D12—22no—
118C2×C3×D12C2×C414yescomplemented
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×C3×C4×D3—22no—
125C2×#626—22no—
126C2×#626—22no—
127C2×#626C2×C414yescomplemented
128C2×#625—22no—
129C2×#625—22no—
130C2×#625C2×C414yescomplemented
131C2×#624—22no—
132C2×#624—22no—
133C2×#624—22no—
134C2×D3×Dic3—22no—
135C2×D3×Dic3—22no—
136C2×D3×Dic3—22no—
137C2×D3×Dic3—22no—
138C2×D3×Dic3—22no—
139C2×D3×Dic3—22no—
140C2×D3×Dic3—22no—
141C2×D3×Dic3D414yescomplemented
142C2×D3×Dic3D414yescomplemented
143C4×D32—232no—
144#3752—22no—
145#3752C2×C414yescomplemented
146C4×C3⋊Dic3—22no—
147C4×C3⋊Dic3—22no—
148C3×(C2×D3)⋊C4—22no—
149C3×(C2×D3)⋊C4—22no—
150C3×(C2×D3)⋊C4—22no—
151C3×(C2×D3)⋊C4—22no—
152C3×(C2×D3)⋊C4C2×C414yescomplemented
153C3×C4⋊Dic3—22no—
154C3×Dic3⋊C4—22no—
155#3724—22no—
156#3722—22no—
157(C2×D3)⋊Dic3—22no—
158(C2×D3)⋊Dic3—22no—
159(C2×D3)⋊Dic3—22no—
160(C2×D3)⋊Dic3C2×C414yescomplemented
161Dic32—22no—
162C4×#120—91noSylow
163C24×D3—31no—
164C24×D3—31no—
165C22×C3×D4—31no—
166C23×C3×C4—31no—
167C23×C3×C4—31no—
168C22×#67—31no—
169C22×#67—31no—
170C22×#67—31no—
171C23×Dic3—31no—
172C23×Dic3—31no—
173C23×Dic3—31no—
174C22×D12—31no—
175C22×D12C2×D311yescharacteristic
176C22×C4×D3—31no—
177C22×C4×D3—31no—
178C22×C4×D3—31no—
179C22×C4×D3—31no—
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—31no—
183C22×C4×D3—61no—
184C22×C4×D3—64no—
185C22×C4×D3—64no—
186C22×C4×D3—64no—
187C22×C4×D3—64no—
188C22×C4×D3—64no—
189C22×C4×D3—64no—
190C22×C4×D3C2×D311yescharacteristic
191C22×C4×D3C2×D311yescharacteristic
192C2×C3×C4⋊C4—31no—
193C2×C3×C4⋊C4—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×#217—31no—
200C2×#217—31no—
201C2×#217—31no—
202C2×#217—31no—
203#937—38no—
204D4×Dic3—64no—
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—31no—
214C2×(C2×D3)⋊C4—31no—
215C2×(C2×D3)⋊C4—61no—
216C2×(C2×D3)⋊C4—61no—
217C2×(C2×D3)⋊C4C2×D311yescharacteristic
218C2×(C2×D3)⋊C4C2×D311yescharacteristic
219C2×(C2×D3)⋊C4C2×D311yescharacteristic
220C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
221C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
222C2×C4⋊Dic3C2×D311yescharacteristic, complemented
223C2×Dic3⋊C4—31no—
224C2×Dic3⋊C4—31no—
225C2×Dic3⋊C4C2×D311yescharacteristic, complemented
226C2×C4×Dic3—31no—
227C2×C4×Dic3—31no—
228C2×C4×Dic3—31no—
229C2×C4×Dic3—31no—
230C2×C4×Dic3—31no—
231C2×C4×Dic3—31no—
232C2×C4×Dic3—61no—
233C2×C4×Dic3—61no—
234#893—64no—
235#893—64no—
236#882—38no—
237#67⋊C4—64no—
238#67⋊C4—64no—
239#67⋊C4—64no—
240C3×#95—21no—
241C3×#95—31no—
242C3×#95—31no—
243C3×#95C2×D311yescharacteristic, complemented
244C3×#95C2×D311yescharacteristic, complemented
245C3⋊#95—31no—
246C3⋊#95—31no—
247C3⋊#95—31no—
248C3⋊#95—31no—
249C3⋊#95—31no—
250C3⋊#95—31no—
251C3⋊#95—61no—
252C3⋊#95C2×D311yescharacteristic, complemented
253C3⋊#95C2×D311yescharacteristic, complemented
254C23×C32C2411yescharacteristic
255C22×C3⋊D3—21no—
256C22×C3⋊D3—21no—
257C22×C3⋊D3—21no—
258C22×C3⋊D3—21no—
259C22×C3⋊D3C22×C412yes—
260C22×C3⋊D3C2×D412yes—
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×D3—21no—
271C22×C3×D3—21no—
272C22×C3×D3—21no—
273C22×C3×D3—21no—
274C22×C3×D3—21no—
275C22×C3×D3—21no—
276C22×C3×D3C22×C412yes—
277C22×C3×D3C22×C412yes—
278C22×C3×D3C22×C412yescomplemented
279C22×C3×D3C2×D412yes—
280C22×C3×D3C2×D412yes—
281C22×C3×D3#4112yes—
282C22×C3×D3#4112yes—
283C2×D32—28no—
284C2×D32—28no—
285C2×D32—28no—
286C2×D32—28no—
287C2×D32—28no—
288C2×D32—28no—
289C2×D32—28no—
290C2×C32×C4—21no—
291C2×C32×C4—21no—
292C2×C32×C4—21no—
293C2×C32×C4—21no—
294C2×C32×C4—21no—
295C2×C32×C4—21no—
296C2×C32×C4—21no—
297C2×C32×C4C22×C412yescomplemented
298C2×C32×C4C2×D412yes—
299C2×C3⋊Dic3—21no—
300C2×C3⋊Dic3—21no—
301C2×C3⋊Dic3—21no—
302C2×C3⋊Dic3—21no—
303C2×C3⋊Dic3—21no—
304C2×C3⋊Dic3C22×C412yescomplemented
305C2×C3⋊Dic3C2×D412yes—
306C2×C3⋊Dic3C2×D412yes—
307C2×C3⋊Dic3C2×D412yes—
308C4×C3⋊D3—28no—
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×Dic3—21no—
317C2×C3×Dic3—21no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3—21no—
320C2×C3×Dic3—21no—
321C2×C3×Dic3C22×C412yescomplemented
322C2×C3×Dic3C2×D412yes—
323C2×C3×Dic3C2×D412yes—
324C3×D12—28no—
325C3×C4×D3—28no—
326C3×C4×D3—28no—
327#626—28no—
328#625—28no—
329#624—28no—
330D3×Dic3—28no—
331D3×Dic3—28no—
332D3×Dic3—44no—
333C24×C4—91no—
334C2×#120—91no—
335C2×C4×D4—91no—
336C2×C4×D4—91no—
337C2×C4×D4—91no—
338#386—31no—
339#386—91no—
340#386—91no—
341#385—31no—
342#385—91no—
343#385—91no—
344#379—91no—
345C4×C22⋊C4—91no—
346C4×C22⋊C4—91no—
347C4×C22⋊C4—91no—
348C24×C3—31no—
349C24×C3—31no—
350C24×C3—31no—
351C23×D3—31no—
352C23×D3—31no—
353C23×D3—34no—
354C23×D3—34no—
355C23×D3—61no—
356C23×D3—62no—
357C23×D3—62no—
358C23×D3—62no—
359C23×D3—62no—
360C23×D3—62no—
361C23×D3—62no—
362C23×D3—62no—
363C23×D3—62no—
364C23×D3—62no—
365C23×D3—62no—
366C23×D3—62no—
367C23×D3—62no—
368C23×D3C22×D311yescharacteristic
369C23×D3C22×D311yescharacteristic
370C23×D3C22×D311yescharacteristic
371C2×C3×D4—34no—
372C2×C3×D4—62no—
373C2×C3×D4—62no—
374C22×C3×C4—21no—
375C22×C3×C4—21no—
376C22×C3×C4—21no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—31no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—62no—
383C22×C3×C4—62no—
384C22×C3×C4—62no—
385C22×C3×C4—62no—
386C22×C3×C4—62no—
387C22×C3×C4—62no—
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C2×#67—34no—
395C2×#67—34no—
396C2×#67—34no—
397C2×#67—62no—
398C2×#67—62no—
399C2×#67—62no—
400C2×#67—62no—
401C2×#67—62no—
402C2×#67—62no—
403C22×Dic3—31no—
404C22×Dic3—31no—
405C22×Dic3—31no—
406C22×Dic3—31no—
407C22×Dic3—34no—
408C22×Dic3—34no—
409C22×Dic3—31no—
410C22×Dic3—31no—
411C22×Dic3—61no—
412C22×Dic3—61no—
413C22×Dic3—61no—
414C22×Dic3—62no—
415C22×Dic3—62no—
416C22×Dic3—62no—
417C22×Dic3—62no—
418C22×Dic3—62no—
419C22×Dic3—62no—
420C22×Dic3—62no—
421C22×Dic3C22×D311yescharacteristic
422C22×Dic3C22×D311yescharacteristic
423C22×Dic3C22×D311yescharacteristic
424C22×Dic3C22×D311yescharacteristic
425C22×Dic3C22×D311yescharacteristic
426C2×D12—22no—
427C2×D12—22no—
428C2×D12—34no—
429C2×D12—62no—
430C2×D12—62no—
431C2×D12C4×D314yescomplemented
432C2×C4×D3—22no—
433C2×C4×D3—22no—
434C2×C4×D3—22no—
435C2×C4×D3—22no—
436C2×C4×D3—22no—
437C2×C4×D3—22no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—64no—
443C2×C4×D3—632no—
444C2×C4×D3—632no—
445C2×C4×D3—62no—
446C2×C4×D3—62no—
447C2×C4×D3—62no—
448C2×C4×D3—62no—
449C2×C4×D3—62no—
450C2×C4×D3—62no—
451C2×C4×D3—62no—
452C2×C4×D3—62no—
453C2×C4×D3—62no—
454C2×C4×D3—62no—
455C2×C4×D3—62no—
456C2×C4×D3—62no—
457C2×C4×D3—62no—
458C2×C4×D3—62no—
459C2×C4×D3—62no—
460C2×C4×D3—62no—
461C2×C4×D3—62no—
462C2×C4×D3—122no—
463C2×C4×D3—122no—
464C3×C4⋊C4—62no—
465C3×C4⋊C4—62no—
466C3×C22⋊C4—34no—
467C3×C22⋊C4—62no—
468C3×C22⋊C4—62no—
469C3×C22⋊C4—62no—
470C3×C22⋊C4—62no—
471#217—34no—
472#217—62no—
473#217—62no—
474#217—62no—
475(C2×D3)⋊C4—22no—
476(C2×D3)⋊C4—22no—
477(C2×D3)⋊C4—22no—
478(C2×D3)⋊C4—22no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—64no—
483(C2×D3)⋊C4—62no—
484(C2×D3)⋊C4—62no—
485(C2×D3)⋊C4—62no—
486(C2×D3)⋊C4—62no—
487(C2×D3)⋊C4—64no—
488(C2×D3)⋊C4—62no—
489(C2×D3)⋊C4—62no—
490(C2×D3)⋊C4—62no—
491(C2×D3)⋊C4C4×D314yescomplemented
492C4⋊Dic3—22no—
493Dic3⋊C4—22no—
494Dic3⋊C4—62no—
495Dic3⋊C4—62no—
496C4×Dic3—62no—
497C4×Dic3—62no—
498C4×Dic3—62no—
499C4×Dic3—62no—
500C4×Dic3—62no—
501C4×Dic3—62no—
502C4×Dic3—122no—
503C4×Dic3—122no—
504C22×C32C23×C411yescharacteristic
505C22×C32C22×D411yescharacteristic
506C22×C32C22×D411yescharacteristic
507C22×C32C22×D411yescharacteristic
508C22×C32C2×#4111yescharacteristic
509C22×C32C2×#4111yescharacteristic
510C22×C32C2×#4111yescharacteristic
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⋊D3C4×D414yescomplemented
518C2×C3×D3—22no—
519C2×C3×D3—22no—
520C2×C3×D3—22no—
521C2×C3×D3—22no—
522C2×C3×D3—22no—
523C2×C3×D3—22no—
524C2×C3×D3—22no—
525C2×C3×D3—22no—
526C2×C3×D3—22no—
527C2×C3×D3—22no—
528C2×C3×D3—22no—
529C2×C3×D3—22no—
530C2×C3×D3—22no—
531C2×C3×D3—22no—
532C2×C3×D3—22no—
533C2×C3×D3—41no—
534C2×C3×D3—41no—
535C2×C3×D3—41no—
536C2×C3×D3—41no—
537C2×C3×D3C4×D414yescomplemented
538C2×C3×D3C4×D414yescomplemented
539D32—232no—
540C32×C4—22no—
541C32×C4—22no—
542C32×C4—41no—
543C3⋊Dic3—22no—
544C3⋊Dic3—41no—
545C3⋊Dic3#12014yescomplemented
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C3×Dic3—41no—
550C3×Dic3—41no—
551C25—91no—
552C22×D4—31no—
553C22×D4—91no—
554C22×D4—91no—
555C23×C4—31no—
556C23×C4—31no—
557C23×C4—91no—
558C23×C4—91no—
559C23×C4—91no—
560C23×C4—91no—
561C23×C4—91no—
562C23×C4—184no—
563C23×C4—184no—
564C23×C4—184no—
565#120—98no—
566C4×D4—184no—
567C4×D4—184no—
568C4×D4—184no—
569C2×C4⋊C4—31no—
570C2×C4⋊C4—31no—
571C2×C4⋊C4—91no—
572C2×C22⋊C4—31no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4—31no—
577C2×C22⋊C4—91no—
578C2×C22⋊C4—91no—
579C2×C22⋊C4—91no—
580C2×C22⋊C4—91no—
581C2×C22⋊C4—91no—
582C2×C22⋊C4—91no—
583C2×C22⋊C4—91no—
584C2×C42—91no—
585C2×C42—91no—
586C2×C42—91no—
587#95—31no—
588#95—31no—
589#95—91no—
590#95—91no—
591#95—91no—
592#95D3211yescharacteristic, complemented
593C23×C3—21no—
594C23×C3—32no—
595C23×C3—32no—
596C23×C3—32no—
597C23×C3—32no—
598C23×C3—32no—
599C23×C3—32no—
600C23×C3—32no—
601C23×C3—61no—
602C23×C3—61no—
603C23×C3—61no—
604C23×C3—61no—
605C23×C3—61no—
606C23×C3—61no—
607C23×C3—61no—
608C23×C3—61no—
609C23×C3—61no—
610C23×C3—61no—
611C23×C3—61no—
612C23×C3—61no—
613C23×C3—61no—
614C23×C3—61no—
615C23×C3C23×D311yescharacteristic
616C23×C3C23×D311yescharacteristic
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—32no—
632C22×D3—32no—
633C22×D3—32no—
634C22×D3—32no—
635C22×D3—32no—
636C22×D3—32no—
637C22×D3—62no—
638C22×D3—62no—
639C22×D3—62no—
640C22×D3—68no—
641C22×D3—68no—
642C22×D3—68no—
643C22×D3—68no—
644C22×D3—68no—
645C22×D3—68no—
646C22×D3—68no—
647C22×D3—68no—
648C22×D3—68no—
649C22×D3—68no—
650C22×D3—68no—
651C22×D3—68no—
652C22×D3—61no—
653C22×D3—61no—
654C22×D3—61no—
655C22×D3—61no—
656C22×D3—61no—
657C22×D3—61no—
658C22×D3—61no—
659C22×D3—61no—
660C22×D3—68no—
661C22×D3—68no—
662C22×D3—121no—
663C22×D3—121no—
664C22×D3—121no—
665C22×D3—121no—
666C22×D3C2×C4×D312yes—
667C22×D3C2×C4×D312yes—
668C22×D3C2×C4×D312yescomplemented
669C22×D3D3×D412yes—
670C22×D3D3×D412yes—
671C22×D3#23712yes—
672C22×D3#23912yes—
673C3×D4—68no—
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—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—22no—
690C2×C3×C4—22no—
691C2×C3×C4—32no—
692C2×C3×C4—32no—
693C2×C3×C4—32no—
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—68no—
701C2×C3×C4—68no—
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—61no—
713C2×C3×C4—61no—
714C2×C3×C4C2×C4×D312yescomplemented
715C2×C3×C4C2×C4×D312yescomplemented
716C2×C3×C4D3×D412yes—
717C2×C3×C4D3×D412yes—
718#67—68no—
719#67—68no—
720#67—68no—
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—21no—
733C2×Dic3—32no—
734C2×Dic3—32no—
735C2×Dic3—32no—
736C2×Dic3—32no—
737C2×Dic3—32no—
738C2×Dic3—32no—
739C2×Dic3—32no—
740C2×Dic3—32no—
741C2×Dic3—62no—
742C2×Dic3—62no—
743C2×Dic3—62no—
744C2×Dic3—62no—
745C2×Dic3—68no—
746C2×Dic3—68no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—62no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—61no—
758C2×Dic3—121no—
759C2×Dic3—121no—
760C2×Dic3—121no—
761C2×Dic3—121no—
762C2×Dic3—124no—
763C2×Dic3C2×C4×D312yescomplemented
764C2×Dic3D3×D412yes—
765C2×Dic3D3×D412yes—
766D12—28no—
767D12—68no—
768C4×D3—28no—
769C4×D3—28no—
770C4×D3—68no—
771C4×D3—68no—
772C4×D3—68no—
773C4×D3—68no—
774C4×D3—68no—
775C4×D3—68no—
776C4×D3—128no—
777C4×D3—124no—
778C2×C32C2×C4×D411yescharacteristic
779C2×C32C2×C4×D411yescharacteristic
780C2×C32C2×C4×D411yescharacteristic
781C2×C32C2×#12011yescharacteristic
782C2×C32#52511yescharacteristic
783C2×C32#52511yescharacteristic
784C2×C32#52511yescharacteristic
785C3⋊D3—24no—
786C3×D3—24no—
787C3×D3—24no—
788C3×D3—42no—
789C24—31no—
790C24—31no—
791C24—31no—
792C24—94no—
793C24—91no—
794C24—182no—
795C24—182no—
796C24—182no—
797C24—182no—
798C24—182no—
799C24—182no—
800C2×D4—34no—
801C2×D4—62no—
802C2×D4—62no—
803C2×D4—94no—
804C2×D4—94no—
805C2×D4—182no—
806C2×D4—182no—
807C2×D4—182no—
808C2×D4—182no—
809C22×C4—31no—
810C22×C4—31no—
811C22×C4—31no—
812C22×C4—31no—
813C22×C4—31no—
814C22×C4—62no—
815C22×C4—62no—
816C22×C4—62no—
817C22×C4—62no—
818C22×C4—62no—
819C22×C4—62no—
820C22×C4—94no—
821C22×C4—94no—
822C22×C4—91no—
823C22×C4—91no—
824C22×C4—94no—
825C22×C4—91no—
826C22×C4—182no—
827C22×C4—182no—
828C22×C4—182no—
829C22×C4—182no—
830C22×C4—182no—
831C22×C4—1832no—
832C22×C4—182no—
833C22×C4—182no—
834C22×C4—182no—
835C22×C4—182no—
836C22×C4—182no—
837C22×C4—182no—
838C22×C4—182no—
839C22×C4C2×D3211yescharacteristic
840C22×C4C2×D3211yescharacteristic
841C22×C4C2×D3211yescharacteristic
842C4⋊C4—62no—
843C4⋊C4—62no—
844C4⋊C4—182no—
845C22⋊C4—34no—
846C22⋊C4—62no—
847C22⋊C4—62no—
848C22⋊C4—62no—
849C22⋊C4—62no—
850C22⋊C4—94no—
851C22⋊C4—94no—
852C22⋊C4—182no—
853C22⋊C4—182no—
854C22⋊C4—182no—
855C22⋊C4—182no—
856C22⋊C4—182no—
857C42—182no—
858C42—182no—
859C42—182no—
860C22×C3—21no—
861C22×C3—21no—
862C22×C3—21no—
863C22×C3—21no—
864C22×C3—21no—
865C22×C3—21no—
866C22×C3—21no—
867C22×C3—34no—
868C22×C3—34no—
869C22×C3—62no—
870C22×C3—62no—
871C22×C3—62no—
872C22×C3—62no—
873C22×C3—62no—
874C22×C3—62no—
875C22×C3—62no—
876C22×C3—62no—
877C22×C3—62no—
878C22×C3—62no—
879C22×C3—62no—
880C22×C3—62no—
881C22×C3—62no—
882C22×C3—62no—
883C22×C3—62no—
884C22×C3—121no—
885C22×C3—121no—
886C22×C3—121no—
887C22×C3—121no—
888C22×C3C22×C4×D311yescharacteristic
889C22×C3C22×C4×D311yescharacteristic
890C22×C3C2×D3×D411yescharacteristic
891C22×C3C2×D3×D411yescharacteristic
892C22×C3C2×D3×D411yescharacteristic
893C22×C3C2×D3×D411yescharacteristic
894C22×C3C2×D3×D411yescharacteristic
895C22×C3C2×D3×D411yescharacteristic
896C22×C3C2×#23711yescharacteristic
897C22×C3C2×#23911yescharacteristic
898C22×C3D3×#4111yescharacteristic
899C22×C3D3×#4111yescharacteristic
900C22×C3D3×#4111yescharacteristic
901C22×C3D3×#4111yescharacteristic
902C2×D3—22no—
903C2×D3—22no—
904C2×D3—22no—
905C2×D3—22no—
906C2×D3—22no—
907C2×D3—22no—
908C2×D3—22no—
909C2×D3—22no—
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—22no—
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—22no—
917C2×D3—34no—
918C2×D3—34no—
919C2×D3—41no—
920C2×D3—41no—
921C2×D3—41no—
922C2×D3—41no—
923C2×D3—64no—
924C2×D3—632no—
925C2×D3—632no—
926C2×D3—62no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—62no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—122no—
939C2×D3—122no—
940C2×D3—122no—
941C2×D3—122no—
942C2×D3—122no—
943C2×D3—122no—
944C2×D3#67⋊C414yescomplemented
945C2×D3#89314yescomplemented
946C3×C4—22no—
947C3×C4—22no—
948C3×C4—22no—
949C3×C4—22no—
950C3×C4—42no—
951C3×C4—42no—
952C3×C4—42no—
953C3×C4—41no—
954C3×C4—41no—
955C3×C4—62no—
956C3×C4—62no—
957C3×C4—62no—
958C3×C4—121no—
959C3×C4—121no—
960Dic3—22no—
961Dic3—22no—
962Dic3—22no—
963Dic3—34no—
964Dic3—34no—
965Dic3—41no—
966Dic3—41no—
967Dic3—64no—
968Dic3—62no—
969Dic3—62no—
970Dic3—122no—
971Dic3—122no—
972Dic3—121no—
973Dic3—121no—
974C32C4×#12011yescharacteristic, complemented, Sylow
975C23—32no—
976C23—32no—
977C23—32no—
978C23—32no—
979C23—32no—
980C23—32no—
981C23—32no—
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—92no—
997C23—92no—
998C23—92no—
999C23—188no—
1000C23—188no—
1001C23—188no—
1002C23—188no—
1003C23—188no—
1004C23—188no—
1005C23—188no—
1006C23—181no—
1007C23—181no—
1008C23—181no—
1009C23—181no—
1010C23C22×D3211yescharacteristic
1011D4—68no—
1012D4—188no—
1013D4—188no—
1014C2×C4—21no—
1015C2×C4—21no—
1016C2×C4—21no—
1017C2×C4—21no—
1018C2×C4—21no—
1019C2×C4—21no—
1020C2×C4—21no—
1021C2×C4—32no—
1022C2×C4—32no—
1023C2×C4—32no—
1024C2×C4—68no—
1025C2×C4—68no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—61no—
1029C2×C4—61no—
1030C2×C4—61no—
1031C2×C4—61no—
1032C2×C4—61no—
1033C2×C4—61no—
1034C2×C4—61no—
1035C2×C4—61no—
1036C2×C4—61no—
1037C2×C4—61no—
1038C2×C4—92no—
1039C2×C4—92no—
1040C2×C4—92no—
1041C2×C4—92no—
1042C2×C4—188no—
1043C2×C4—188no—
1044C2×C4—188no—
1045C2×C4—188no—
1046C2×C4—181no—
1047C2×C4—181no—
1048C2×C4—181no—
1049C2×C4—181no—
1050C2×C4—181no—
1051C2×C4—364no—
1052C2×C4C4×D3212yescomplemented
1053C2×C4#380212yes—
1054C2×C3—21no—
1055C2×C3—21no—
1056C2×C3—21no—
1057C2×C3—21no—
1058C2×C3—21no—
1059C2×C3—21no—
1060C2×C3—21no—
1061C2×C3—64no—
1062C2×C3—64no—
1063C2×C3—122no—
1064C2×C3C2×#67⋊C411yescharacteristic
1065C2×C3C2×#89311yescharacteristic
1066C2×C3C4×D3×D411yescharacteristic
1067C2×C3C4×D3×D411yescharacteristic
1068C2×C3C4×D3×D411yescharacteristic
1069C2×C3C4×D3×D411yescharacteristic
1070C2×C3D3×#12011yescharacteristic
1071C2×C3D3×#12011yescharacteristic
1072C2×C3#560611yescharacteristic
1073C2×C3#560611yescharacteristic
1074C2×C3#562711yescharacteristic
1075C2×C3#562711yescharacteristic
1076C2×C3#565611yescharacteristic
1077C2×C3#565611yescharacteristic
1078D3—24no—
1079D3—24no—
1080D3—42no—
1081D3—64no—
1082D3—64no—
1083D3—124no—
1084C22—34no—
1085C22—34no—
1086C22—62no—
1087C22—62no—
1088C22—62no—
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—94no—
1102C22—121no—
1103C22—121no—
1104C22—121no—
1105C22—121no—
1106C22—1832no—
1107C22—182no—
1108C22—182no—
1109C22—182no—
1110C22—182no—
1111C22—182no—
1112C22—182no—
1113C22C2×C4×D3211yescharacteristic
1114C22C2×#380211yescharacteristic
1115C22#6430611yescharacteristic
1116C22D32×D411yescharacteristic
1117C22D32×D411yescharacteristic
1118C22D3×#23711yescharacteristic
1119C22D3×#23911yescharacteristic
1120C4—22no—
1121C4—22no—
1122C4—41no—
1123C4—62no—
1124C4—62no—
1125C4—62no—
1126C4—94no—
1127C4—121no—
1128C4—121no—
1129C4—182no—
1130C4—361no—
1131C3—21no—
1132C3#7437911yescharacteristic, complemented
1133C3#7465911yescharacteristic, complemented
1134C2—64no—
1135C2—64no—
1136C2—122no—
1137C2—184no—
1138C2C4×#380211yescharacteristic
1139C2D3×#67⋊C411yescharacteristic
1140C2#1059425811yescharacteristic
1141C2#1059426711yescharacteristic
1142C2D3×#89311yescharacteristic
1143C2#1059461511yescharacteristic
1144C2#1059463211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63922C2
hypercenter#95D32
hypocenterC32C4×#120
LCSG ▷ C22×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×#63902C2semidirect
4. C2×#63898C2semidirect
5. C2×#63881C2semidirect
6. #10592365C2semidirect
7. C3×#4668C2semidirect
8. C3×#4665C2semidirect
9. #10591399C2semidirect
10. #10591381C2semidirect
11. #10591378C2semidirect
12. #10591368C2semidirect
13. #10591368C2semidirect
14. #10591277C2semidirect
15. #10591275C2semidirect
28. C22×D3×Dic3C22semidirect
34. C2×C4×C3⋊Dic3C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×(C2×D3)⋊C4C22semidirect
41. C2×C3×C4⋊Dic3C22semidirect
42. C2×C3×Dic3⋊C4C22semidirect
43. C2×#3724C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. C2×Dic32C22semidirect
50. #63922C4semidirect
54. C32×#95C22semidirect
55. #63658C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
58. #63579C22semidirect
59. #63579C22semidirect
83. #4668D3semidirect
90. #4665D3semidirect
101. C22×D32C2×C4semidirect
110. C2×C4×C3⋊D3D4semidirect
118. C2×C3×D12C2×C4semidirect
127. C2×#626C2×C4semidirect
130. C2×#625C2×C4semidirect
141. C2×D3×Dic3D4semidirect
142. C2×D3×Dic3D4semidirect
145. #3752C2×C4semidirect
152. C3×(C2×D3)⋊C4C2×C4semidirect
160. (C2×D3)⋊Dic3C2×C4semidirect
220. C2×(C2×D3)⋊C4C2×D3semidirect
221. C2×(C2×D3)⋊C4C2×D3semidirect
222. C2×C4⋊Dic3C2×D3semidirect
225. C2×Dic3⋊C4C2×D3semidirect
243. C3×#95C2×D3semidirect
244. C3×#95C2×D3semidirect
252. C3⋊#95C2×D3semidirect
253. C3⋊#95C2×D3semidirect
278. C22×C3×D3C22×C4semidirect
297. C2×C32×C4C22×C4semidirect
304. C2×C3⋊Dic3C22×C4semidirect
321. C2×C3×Dic3C22×C4semidirect
431. C2×D12C4×D3semidirect
491. (C2×D3)⋊C4C4×D3semidirect
517. C2×C3⋊D3C4×D4semidirect
537. C2×C3×D3C4×D4semidirect
538. C2×C3×D3C4×D4semidirect
545. C3⋊Dic3#120semidirect
592. #95D32semidirect
668. C22×D3C2×C4×D3semidirect
714. C2×C3×C4C2×C4×D3semidirect
715. C2×C3×C4C2×C4×D3semidirect
763. C2×Dic3C2×C4×D3semidirect
944. C2×D3#67⋊C4semidirect
945. C2×D3#893semidirect
974. C32C4×#120semidirect
1052. C2×C4C4×D32semidirect
1132. C3#74379semidirect
1133. C3#74659semidirect

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×#639022
C2×#638982
C2×#638812
#105923652
C3×#46682
C3×#46652
#105913992
#105913812
#105913782
#105913682
#105912772
#105912752
#746593
#743793