Finite Group Databasebeta

← #11802014

Subgroups — #11802014

Order 1152.

2565 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×C3×#893C211yesmaximal, characteristic, complemented
3C2×#63922C211yesmaximal, characteristic
4C2×#63904C211yesmaximal, characteristic, complemented
5C2×#63879C211yesmaximal, characteristic, complemented
6#10592688C211yesmaximal, characteristic, complemented
7C3×#4989C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591387C211yesmaximal, characteristic, complemented
10#10591381C211yesmaximal, characteristic, complemented
11#10591376C211yesmaximal, characteristic, complemented
12#10591372C211yesmaximal, characteristic, complemented
13Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
14#10591237C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16C4×#937—31nomaximal
17#74379—31nomaximal
18C23×D32C2211yescharacteristic
19C22×C4×C3⋊D3C2211yescharacteristic
20C22×C3×D12C2211yescharacteristic
21C22×C3×C4×D3C2211yescharacteristic
22C22×C3×C4×D3C2211yescharacteristic
23C22×C3×C4×D3C2211yescharacteristic, complemented
24C22×#626C2211yescharacteristic
25C22×#625C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×C4×D32—24no—
30C2×C4×D32—24no—
31C2×C4×D32—24no—
32C2×C32×C4⋊C4C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
35C2×#3750C2211yescharacteristic, complemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C3×C4×Dic3C2211yescharacteristic, complemented
42C3×#893—24no—
43C2×#3722C2211yescharacteristic
44C2×(C2×D3)⋊Dic3C2211yescharacteristic
45C2×(C2×D3)⋊Dic3C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
48C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
49C2×Dic32C2211yescharacteristic, complemented
50C2×Dic32C2211yescharacteristic, complemented
51#63922C418yescomplemented
52#63904—24no—
53#63879—24no—
54#63658C2211yescharacteristic, 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×C3×C4×D4—31no—
63C2×#937—31no—
64C2×C4×#67—31no—
65C2×C4×#67—31no—
66C2×#893—31no—
67C2×#893D311yescharacteristic, complemented
68C2×#882—31no—
69C2×#67⋊C4—31no—
70C3×#385—31no—
71#5220—31no—
72#5213—31no—
73C4×#217—31no—
74#4989—31no—
75#4989—31no—
76#4989—31no—
77#4989—61no—
78#4989D311yescharacteristic, complemented
79#4956—31no—
80#4956—31no—
81#4955—31no—
82#4955—31no—
83#4946—31no—
84Dic3×C22⋊C4—31no—
85C4×(C2×D3)⋊C4—31no—
86C4×(C2×D3)⋊C4—31no—
87#4666—31no—
88#4666—31no—
89#4665—31no—
90#4665—31no—
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⋊D3—22no—
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×C3×C4×D3—22no—
126C2×C3×C4×D3—22no—
127C2×C3×C4×D3D414yescomplemented
128C2×#626—22no—
129C2×#626—22no—
130C2×#626C2×C414yescomplemented
131C2×#625—22no—
132C2×#625—22no—
133C2×#625C2×C414yescomplemented
134C2×#624—22no—
135C2×#624—22no—
136C2×#624D414yescomplemented
137C2×D3×Dic3—22no—
138C2×D3×Dic3—22no—
139C2×D3×Dic3—22no—
140C2×D3×Dic3—22no—
141C2×D3×Dic3—22no—
142C2×D3×Dic3D414yescomplemented
143C4×D32—232no—
144C32×C4⋊C4—22no—
145#3752—22no—
146#3752C2×C414yescomplemented
147#3750—22no—
148C3×(C2×D3)⋊C4—22no—
149C3×(C2×D3)⋊C4—22no—
150C3×(C2×D3)⋊C4—22no—
151C3×(C2×D3)⋊C4C2×C414yescomplemented
152C3×Dic3⋊C4—22no—
153C3×C4×Dic3—22no—
154#3722—22no—
155(C2×D3)⋊Dic3—22no—
156(C2×D3)⋊Dic3—22no—
157(C2×D3)⋊Dic3—22no—
158(C2×D3)⋊Dic3—22no—
159(C2×D3)⋊Dic3C2×C414yescomplemented
160Dic32—22no—
161Dic32—22no—
162C4×#120—91noSylow
163C24×D3—31no—
164C24×D3—31no—
165C22×C3×D4—31no—
166C23×C3×C4—31no—
167C23×C3×C4—31no—
168C23×C3×C4—31no—
169C22×#67—31no—
170C22×#67—31no—
171C22×#67—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—61no—
183C22×C4×D3—64no—
184C22×C4×D3—64no—
185C22×C4×D3—64no—
186C22×C4×D3—64no—
187C22×C4×D3—64no—
188C22×C4×D3—64no—
189C22×C4×D3C2×D311yescharacteristic
190C22×C4×D3C2×D311yescharacteristic
191C22×C4×D3C2×D311yescharacteristic, complemented
192C3×C4×D4—64no—
193C2×C3×C4⋊C4—21no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
196C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4—31no—
200C2×C3×C22⋊C4—31no—
201C2×C3×C42—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207#937—38no—
208C4×#67—64no—
209C4×#67—64no—
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—31no—
216C2×(C2×D3)⋊C4—31no—
217C2×(C2×D3)⋊C4—31no—
218C2×(C2×D3)⋊C4—31no—
219C2×(C2×D3)⋊C4—31no—
220C2×(C2×D3)⋊C4—31no—
221C2×(C2×D3)⋊C4—61no—
222C2×(C2×D3)⋊C4—61no—
223C2×(C2×D3)⋊C4C2×D311yescharacteristic
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225C2×(C2×D3)⋊C4C2×D311yescharacteristic
226C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4—31no—
229C2×Dic3⋊C4—61no—
230C2×Dic3⋊C4C2×D311yescharacteristic, complemented
231C2×C4×Dic3—31no—
232C2×C4×Dic3—31no—
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3C2×D311yescharacteristic, complemented
236#893—24no—
237#893—64no—
238#882—38no—
239#67⋊C4—64no—
240C3×#95—31no—
241C3×#95—31no—
242C3⋊#95—31no—
243C3⋊#95—31no—
244C3⋊#95—31no—
245C3⋊#95—31no—
246C3⋊#95—31no—
247C3⋊#95—31no—
248C3⋊#95—31no—
249C3⋊#95—31no—
250C3⋊#95—61no—
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⋊Dic3—21no—
305C2×C3⋊Dic3—21no—
306C2×C3⋊Dic3C22×C412yescomplemented
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×Dic3C22×C412yescomplemented
320C2×C3×Dic3C2×D412yes—
321C2×C3×Dic3C2×D412yes—
322C2×C3×Dic3C2×D412yes—
323C2×C3×Dic3C2×D412yes—
324C3×D12—28no—
325C3×C4×D3—28no—
326C3×C4×D3—28no—
327C3×C4×D3—44no—
328#626—28no—
329#625—28no—
330#624—28no—
331D3×Dic3—28no—
332D3×Dic3—28no—
333C24×C4—91no—
334C2×#120—91no—
335C2×C4×D4—31no—
336C2×C4×D4—91no—
337C2×C4×D4—91no—
338#386—91no—
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—34no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—62no—
384C22×C3×C4—62no—
385C22×C3×C4—62no—
386C22×C3×C4—62no—
387C22×C3×C4—62no—
388C22×C3×C4—62no—
389C22×C3×C4—62no—
390C22×C3×C4—62no—
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C22×C3×C4C22×D311yescharacteristic
394C22×C3×C4C22×D311yescharacteristic
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C2×#67—34no—
398C2×#67—34no—
399C2×#67—34no—
400C2×#67—62no—
401C2×#67—62no—
402C2×#67—62no—
403C2×#67—62no—
404C2×#67—62no—
405C2×#67—62no—
406C22×Dic3—31no—
407C22×Dic3—31no—
408C22×Dic3—31no—
409C22×Dic3—31no—
410C22×Dic3—34no—
411C22×Dic3—31no—
412C22×Dic3—31no—
413C22×Dic3—61no—
414C22×Dic3—61no—
415C22×Dic3—61no—
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—22no—
439C2×C4×D3—22no—
440C2×C4×D3—34no—
441C2×C4×D3—34no—
442C2×C4×D3—34no—
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—122no—
461C2×C4×D3—122no—
462C2×C4×D3—122no—
463C2×C4×D3#6714yescomplemented
464C3×C4⋊C4—22no—
465C3×C4⋊C4—22no—
466C3×C4⋊C4—42no—
467C3×C4⋊C4—62no—
468C3×C22⋊C4—34no—
469C3×C22⋊C4—62no—
470C3×C22⋊C4—62no—
471C3×C22⋊C4—62no—
472C3×C42—62no—
473#217—34no—
474#217—62no—
475#217—62no—
476#217—62no—
477#217—62no—
478(C2×D3)⋊C4—22no—
479(C2×D3)⋊C4—22no—
480(C2×D3)⋊C4—22no—
481(C2×D3)⋊C4—34no—
482(C2×D3)⋊C4—34no—
483(C2×D3)⋊C4—34no—
484(C2×D3)⋊C4—64no—
485(C2×D3)⋊C4—62no—
486(C2×D3)⋊C4—62no—
487(C2×D3)⋊C4—62no—
488(C2×D3)⋊C4—62no—
489(C2×D3)⋊C4—62no—
490(C2×D3)⋊C4—62no—
491(C2×D3)⋊C4—62no—
492(C2×D3)⋊C4—62no—
493(C2×D3)⋊C4—122no—
494(C2×D3)⋊C4C4×D314yescomplemented
495Dic3⋊C4—22no—
496Dic3⋊C4—62no—
497Dic3⋊C4—62no—
498Dic3⋊C4—122no—
499C4×Dic3—22no—
500C4×Dic3—62no—
501C4×Dic3—62no—
502C4×Dic3—62no—
503C4×Dic3—62no—
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—22no—
545C3⋊Dic3—41no—
546C3×Dic3—22no—
547C3×Dic3—22no—
548C3×Dic3—41no—
549C3×Dic3—41no—
550C3×Dic3#12014yescomplemented
551C25—91no—
552C22×D4—31no—
553C22×D4—91no—
554C22×D4—91no—
555C23×C4—31no—
556C23×C4—31no—
557C23×C4—31no—
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—64no—
567C4×D4—184no—
568C4×D4—184no—
569C2×C4⋊C4—31no—
570C2×C4⋊C4—91no—
571C2×C4⋊C4D3211yescharacteristic, complemented
572C2×C22⋊C4—31no—
573C2×C22⋊C4—31no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4—91no—
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—31no—
585C2×C42—91no—
586C2×C42—91no—
587#95—31no—
588#95—31no—
589#95—91no—
590#95—91no—
591#95—91no—
592#95—91no—
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×D3#23512yes—
670C22×D3D3×D412yes—
671C22×D3#23912yes—
672C22×D3C2×#6712yes—
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—21no—
683C2×C3×C4—21no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—22no—
689C2×C3×C4—22no—
690C2×C3×C4—32no—
691C2×C3×C4—32no—
692C2×C3×C4—32no—
693C2×C3×C4—32no—
694C2×C3×C4—32no—
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—41no—
702C2×C3×C4—68no—
703C2×C3×C4—68no—
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×C4—124no—
715C2×C3×C4C2×C4×D312yescomplemented
716C2×C3×C4C2×C4×D312yescomplemented
717C2×C3×C4D3×D412yes—
718C2×C3×C4C2×#6712yes—
719#67—68no—
720#67—68no—
721#67—68no—
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—32no—
733C2×Dic3—32no—
734C2×Dic3—32no—
735C2×Dic3—32no—
736C2×Dic3—62no—
737C2×Dic3—62no—
738C2×Dic3—68no—
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—68no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—121no—
755C2×Dic3—121no—
756C2×Dic3—121no—
757C2×Dic3—121no—
758C2×Dic3—121no—
759C2×Dic3—121no—
760C2×Dic3—121no—
761C2×Dic3C2×C4×D312yescomplemented
762C2×Dic3D3×D412yes—
763C2×Dic3D3×D412yes—
764C2×Dic3D3×D412yes—
765C2×Dic3C2×#6712yes—
766D12—28no—
767D12—68no—
768C4×D3—28no—
769C4×D3—28no—
770C4×D3—44no—
771C4×D3—68no—
772C4×D3—68no—
773C4×D3—68no—
774C4×D3—68no—
775C4×D3—68no—
776C4×D3—68no—
777C4×D3—128no—
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—34no—
813C22×C4—31no—
814C22×C4—31no—
815C22×C4—62no—
816C22×C4—62no—
817C22×C4—62no—
818C22×C4—62no—
819C22×C4—62no—
820C22×C4—62no—
821C22×C4—62no—
822C22×C4—62no—
823C22×C4—94no—
824C22×C4—94no—
825C22×C4—91no—
826C22×C4—91no—
827C22×C4—91no—
828C22×C4—182no—
829C22×C4—182no—
830C22×C4—182no—
831C22×C4—182no—
832C22×C4—182no—
833C22×C4—182no—
834C22×C4—182no—
835C22×C4—1832no—
836C22×C4—182no—
837C22×C4—182no—
838C22×C4—182no—
839C22×C4C2×D3211yescharacteristic
840C22×C4C2×D3211yescharacteristic
841C22×C4C2×D3211yescharacteristic
842C4⋊C4—22no—
843C4⋊C4—62no—
844C4⋊C4—182no—
845C22⋊C4—34no—
846C22⋊C4—62no—
847C22⋊C4—62no—
848C22⋊C4—62no—
849C22⋊C4—94no—
850C22⋊C4—94no—
851C22⋊C4—182no—
852C22⋊C4—182no—
853C22⋊C4—182no—
854C22⋊C4—182no—
855C22⋊C4—182no—
856C22⋊C4—182no—
857C42—62no—
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×#23511yescharacteristic
891C22×C3C2×D3×D411yescharacteristic
892C22×C3C2×D3×D411yescharacteristic
893C22×C3C2×D3×D411yescharacteristic
894C22×C3C2×D3×D411yescharacteristic
895C22×C3C2×D3×D411yescharacteristic
896C22×C3C2×#23911yescharacteristic
897C22×C3D3×#4111yescharacteristic
898C22×C3D3×#4111yescharacteristic
899C22×C3D3×#4111yescharacteristic
900C22×C3D3×#4111yescharacteristic
901C22×C3C22×#6711yescharacteristic
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#89314yescomplemented
945C2×D3C4×#6714yescomplemented
946C3×C4—22no—
947C3×C4—22no—
948C3×C4—22no—
949C3×C4—22no—
950C3×C4—34no—
951C3×C4—42no—
952C3×C4—42no—
953C3×C4—41no—
954C3×C4—41no—
955C3×C4—62no—
956C3×C4—62no—
957C3×C4—81no—
958C3×C4—121no—
959C3×C4—121no—
960Dic3—22no—
961Dic3—22no—
962Dic3—41no—
963Dic3—41no—
964Dic3—62no—
965Dic3—62no—
966Dic3—62no—
967Dic3—62no—
968Dic3—122no—
969Dic3—122no—
970Dic3—121no—
971Dic3—121no—
972Dic3—241no—
973Dic3#93714yescomplemented
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—32no—
1025C2×C4—32no—
1026C2×C4—68no—
1027C2×C4—68no—
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—124no—
1041C2×C4—188no—
1042C2×C4—188no—
1043C2×C4—188no—
1044C2×C4—188no—
1045C2×C4—181no—
1046C2×C4—181no—
1047C2×C4—181no—
1048C2×C4—181no—
1049C2×C4—181no—
1050C2×C4—181no—
1051C2×C4—181no—
1052C2×C4C4×D3212yescomplemented
1053C2×C4D3×#6712yes—
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×#89311yescharacteristic
1065C2×C3C4×D3×D411yescharacteristic
1066C2×C3C4×D3×D411yescharacteristic
1067C2×C3C4×D3×D411yescharacteristic
1068C2×C3C4×D3×D411yescharacteristic
1069C2×C3#554711yescharacteristic
1070C2×C3#554711yescharacteristic
1071C2×C3D3×#12011yescharacteristic
1072C2×C3#562711yescharacteristic
1073C2×C3#562711yescharacteristic
1074C2×C3#565611yescharacteristic
1075C2×C3C2×C4×#6711yescharacteristic
1076C2×C3C2×#93711yescharacteristic
1077C2×C3#582811yescharacteristic
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
1114C22D3×#23511yescharacteristic
1115C22D32×D411yescharacteristic
1116C22D32×D411yescharacteristic
1117C22D3×#23911yescharacteristic
1118C22#6431911yescharacteristic
1119C22C2×D3×#6711yescharacteristic
1120C4—22no—
1121C4—22no—
1122C4—34no—
1123C4—41no—
1124C4—62no—
1125C4—62no—
1126C4—121no—
1127C4—121no—
1128C4—182no—
1129C4—182no—
1130C4—361no—
1131C3—21no—
1132C3#7437911yescharacteristic, complemented
1133C3C4×#93711yescharacteristic, complemented
1134C2—64no—
1135C2—64no—
1136C2—122no—
1137C2—184no—
1138C2D3×#89311yescharacteristic
1139C2#1059460511yescharacteristic
1140C2#1059461411yescharacteristic
1141C2#1059462311yescharacteristic
1142C2C4×D3×#6711yescharacteristic
1143C2D3×#93711yescharacteristic
1144C2#1059542411yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C4⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63922C2
hypercenterC2×C4⋊C4D32
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D32C2semidirect
2. C2×C3×#893C2semidirect
4. C2×#63904C2semidirect
5. C2×#63879C2semidirect
6. #10592688C2semidirect
7. C3×#4989C2semidirect
8. #10591399C2semidirect
9. #10591387C2semidirect
10. #10591381C2semidirect
11. #10591376C2semidirect
12. #10591372C2semidirect
13. Dic3×(C2×D3)⋊C4C2semidirect
14. #10591237C2semidirect
15. #10591233C2semidirect
23. C22×C3×C4×D3C22semidirect
32. C2×C32×C4⋊C4C22semidirect
35. C2×#3750C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×C4×Dic3C22semidirect
47. C2×(C2×D3)⋊Dic3C22semidirect
48. C2×(C2×D3)⋊Dic3C22semidirect
49. C2×Dic32C22semidirect
50. C2×Dic32C22semidirect
51. #63922C4semidirect
54. #63658C22semidirect
55. #63658C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
58. #63579C22semidirect
59. #63579C22semidirect
67. C2×#893D3semidirect
78. #4989D3semidirect
101. C22×D32C2×C4semidirect
118. C2×C3×D12C2×C4semidirect
127. C2×C3×C4×D3D4semidirect
130. C2×#626C2×C4semidirect
133. C2×#625C2×C4semidirect
136. C2×#624D4semidirect
142. C2×D3×Dic3D4semidirect
146. #3752C2×C4semidirect
151. C3×(C2×D3)⋊C4C2×C4semidirect
159. (C2×D3)⋊Dic3C2×C4semidirect
191. C22×C4×D3C2×D3semidirect
195. C2×C3×C4⋊C4C2×D3semidirect
196. C2×C3×C4⋊C4C2×D3semidirect
226. C2×(C2×D3)⋊C4C2×D3semidirect
230. C2×Dic3⋊C4C2×D3semidirect
235. C2×C4×Dic3C2×D3semidirect
252. C3⋊#95C2×D3semidirect
253. C3⋊#95C2×D3semidirect
278. C22×C3×D3C22×C4semidirect
297. C2×C32×C4C22×C4semidirect
306. C2×C3⋊Dic3C22×C4semidirect
319. C2×C3×Dic3C22×C4semidirect
431. C2×D12C4×D3semidirect
463. C2×C4×D3#67semidirect
494. (C2×D3)⋊C4C4×D3semidirect
517. C2×C3⋊D3C4×D4semidirect
537. C2×C3×D3C4×D4semidirect
538. C2×C3×D3C4×D4semidirect
550. C3×Dic3#120semidirect
571. C2×C4⋊C4D32semidirect
668. C22×D3C2×C4×D3semidirect
715. C2×C3×C4C2×C4×D3semidirect
716. C2×C3×C4C2×C4×D3semidirect
761. C2×Dic3C2×C4×D3semidirect
944. C2×D3#893semidirect
945. C2×D3C4×#67semidirect
973. Dic3#937semidirect
974. C32C4×#120semidirect
1052. C2×C4C4×D32semidirect
1132. C3#74379semidirect
1133. C3C4×#937semidirect

Maximal subgroups

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

subgroupindex
C22×C4×D322
C2×C3×#8932
C2×#639222
C2×#639042
C2×#638792
#105926882
C3×#49892
#105913992
#105913872
#105913812
#105913762
#105913722
Dic3×(C2×D3)⋊C42
#105912372
#105912332
C4×#9373
#743793