Finite Group Databasebeta

← #11802019

Subgroups — #11802019

Order 1152.

2591 conjugacy classes of subgroups.

The subgroup lattice has 1160 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×D32C211yesmaximal, characteristic, complemented
2C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
3C2×#63983C211yesmaximal, characteristic
4C2×Dic3×#67C211yesmaximal, characteristic, complemented
5C2×#63952C211yesmaximal, characteristic, complemented
6#10592655C211yesmaximal, characteristic, complemented
7C3×#4956C211yesmaximal, characteristic, complemented
8#10591721C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591373C211yesmaximal, characteristic, complemented
11Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
12#10591290C211yesmaximal, characteristic, complemented
13#10591277C211yesmaximal, characteristic, complemented
14#10591237C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16C4×#937—31nomaximal
17#74659—31nomaximal
18C23×D32C2211yescharacteristic
19C22×#638C2211yescharacteristic
20C22×C4×C3⋊D3C2211yescharacteristic
21C22×C3×#67C2211yescharacteristic
22C22×C3×#67C2211yescharacteristic
23C23×C3×Dic3C2211yescharacteristic, complemented
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×#624C2211yescharacteristic
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×C4×D32—24no—
30C2×C4×D32—24no—
31C2×C4×D32—24no—
32C2×C32×C22⋊C4C2211yescharacteristic, complemented
33C2×#3757C2211yescharacteristic, complemented
34C2×#3752C2211yescharacteristic
35C2×C3×#217C2211yescharacteristic, complemented
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
39C2×C3×C4×Dic3C2211yescharacteristic, complemented
40C3×#67⋊C4—24no—
41#63983C418yescomplemented
42Dic3×#67—24no—
43C2×#3724C2211yescharacteristic, complemented
44C2×Dic3⋊Dic3C2211yescharacteristic, complemented
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic
50C2×(C2×D3)⋊Dic3C2211yescharacteristic
51C2×Dic32C2211yescharacteristic, complemented
52C2×Dic32C2211yescharacteristic, complemented
53#63952—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×#937—31no—
65C2×D4×Dic3—31no—
66C2×C4×#67—31no—
67C2×C4×#67—31no—
68C2×#67⋊C4—31no—
69C2×#67⋊C4D311yescharacteristic, complemented
70C3×#386—31no—
71#5220—31no—
72#5210—31no—
73C4×#217—31no—
74#4989—31no—
75#4989—31no—
76#4956—31no—
77#4956—31no—
78#4956—31no—
79#4956—61no—
80#4956D311yescharacteristic, complemented
81#4955—31no—
82#4955—31no—
83#4946—31no—
84Dic3×C22⋊C4—31no—
85C4×(C2×D3)⋊C4—31no—
86C4×(C2×D3)⋊C4—31no—
87#4668—31no—
88#4668—31no—
89#4666—31no—
90#4666—31no—
91C24×C32C2311yescharacteristic
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
104C2×#638—22no—
105C2×#638—22no—
106C2×#638C2×C414yescomplemented
107C22×C3⋊Dic3C2311yescharacteristic
108C22×C3⋊Dic3C2311yescharacteristic
109C22×C3⋊Dic3C2311yescharacteristic
110C2×C4×C3⋊D3—22no—
111C2×C4×C3⋊D3—22no—
112C2×C4×C3⋊D3—22no—
113C2×C3×#67—22no—
114C2×C3×#67—22no—
115C2×C3×#67—22no—
116C2×C3×#67—22no—
117C2×C3×#67C2×C414yescomplemented
118C2×C3×#67C2×C414yescomplemented
119C22×C3×Dic3—22no—
120C22×C3×Dic3—22no—
121C22×C3×Dic3—22no—
122C22×C3×Dic3C2311yescharacteristic
123C22×C3×Dic3C2311yescharacteristic
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C2×C3×C4×D3—22no—
129C2×C3×C4×D3—22no—
130C2×C3×C4×D3—22no—
131C2×C3×C4×D3—22no—
132C2×C3×C4×D3—22no—
133C2×C3×C4×D3D414yescomplemented
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×C22⋊C4—22no—
145#3757—22no—
146#3752—22no—
147C3×#217—22no—
148C3×(C2×D3)⋊C4—22no—
149C3×(C2×D3)⋊C4—22no—
150C3×Dic3⋊C4—22no—
151C3×C4×Dic3—22no—
152#3724—22no—
153Dic3⋊Dic3—22no—
154#3722—22no—
155#3722C2×C414yescomplemented
156(C2×D3)⋊Dic3—22no—
157(C2×D3)⋊Dic3—22no—
158(C2×D3)⋊Dic3C2×C414yescomplemented
159(C2×D3)⋊Dic3C2×C414yescomplemented
160Dic32—22no—
161Dic32—22no—
162C4×#120—91noSylow
163C24×D3—31no—
164C24×D3—31no—
165C22×C3×D4—31no—
166C22×C3×D4—31no—
167C23×C3×C4—31no—
168C23×C3×C4—31no—
169C23×C3×C4—31no—
170C22×#67—31no—
171C22×#67—31no—
172C22×#67—61no—
173C22×#67C2×D311yescharacteristic
174C22×#67C2×D311yescharacteristic
175C23×Dic3—31no—
176C23×Dic3—31no—
177C23×Dic3C2×D311yescharacteristic, complemented
178C22×C4×D3—31no—
179C22×C4×D3—31no—
180C22×C4×D3—31no—
181C22×C4×D3—31no—
182C22×C4×D3—31no—
183C22×C4×D3—31no—
184C22×C4×D3—61no—
185C22×C4×D3—64no—
186C22×C4×D3—64no—
187C22×C4×D3—64no—
188C22×C4×D3—64no—
189C22×C4×D3—64no—
190C22×C4×D3—64no—
191C22×C4×D3C2×D311yescharacteristic
192C22×C4×D3C2×D311yescharacteristic
193C3×C4×D4—64no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C22⋊C4—21no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
200C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
201C2×C3×C42—31no—
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207C2×#217—31no—
208C2×#217—61no—
209C2×#217C2×D311yescharacteristic, complemented
210#937—38no—
211#937—38no—
212D4×Dic3—64no—
213C4×#67—64no—
214C4×#67—64no—
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—31no—
222C2×(C2×D3)⋊C4—31no—
223C2×(C2×D3)⋊C4—31no—
224C2×(C2×D3)⋊C4—31no—
225C2×(C2×D3)⋊C4—61no—
226C2×(C2×D3)⋊C4C2×D311yescharacteristic
227C2×(C2×D3)⋊C4C2×D311yescharacteristic
228C2×C4⋊Dic3—31no—
229C2×Dic3⋊C4—31no—
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4C2×D311yescharacteristic, complemented
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3—31no—
236C2×C4×Dic3—31no—
237C2×C4×Dic3C2×D311yescharacteristic, complemented
238#67⋊C4—24no—
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×C32—21no—
255C23×C32—21no—
256C23×C32—21no—
257C23×C32—21no—
258C23×C32—21no—
259C23×C32—21no—
260C23×C32C22×C412yescomplemented
261C23×C32C2411yescharacteristic
262C22×C3⋊D3—21no—
263C22×C3⋊D3—21no—
264C22×C3⋊D3—21no—
265C22×C3⋊D3—21no—
266C22×C3⋊D3C22×C412yes—
267C22×C3⋊D3C2×D412yes—
268C22×C3⋊D3#4112yes—
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×D3—21no—
277C22×C3×D3C22×C412yes—
278C22×C3×D3C22×C412yes—
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×C4C2×D412yes—
296#638—28no—
297C2×C3⋊Dic3—21no—
298C2×C3⋊Dic3—21no—
299C2×C3⋊Dic3—21no—
300C2×C3⋊Dic3—21no—
301C2×C3⋊Dic3—21no—
302C2×C3⋊Dic3—21no—
303C2×C3⋊Dic3—21no—
304C2×C3⋊Dic3C22×C412yescomplemented
305C2×C3⋊Dic3C2×D412yes—
306C4×C3⋊D3—28no—
307C3×#67—28no—
308C3×#67—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×Dic3—44no—
322C2×C3×Dic3C22×C412yescomplemented
323C2×C3×Dic3C22×C412yescomplemented
324C2×C3×Dic3C2×D412yes—
325C2×C3×Dic3C2×D412yes—
326C2×C3×Dic3C2×D412yes—
327C2×C3×Dic3C2×D412yes—
328C3×C4×D3—28no—
329C3×C4×D3—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—31no—
339#386—91no—
340#386—91no—
341#385—91no—
342#385—91no—
343#385—91no—
344#379—91no—
345C4×C22⋊C4—91no—
346C4×C22⋊C4—91no—
347C4×C22⋊C4—91no—
348C24×C3—21no—
349C24×C3—31no—
350C24×C3—31no—
351C24×C3C22×D311yescharacteristic
352C24×C3C22×D311yescharacteristic
353C23×D3—31no—
354C23×D3—31no—
355C23×D3—34no—
356C23×D3—34no—
357C23×D3—61no—
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×D3—62no—
369C23×D3—62no—
370C23×D3C22×D311yescharacteristic
371C23×D3C22×D311yescharacteristic
372C2×C3×D4—34no—
373C2×C3×D4—34no—
374C2×C3×D4—62no—
375C2×C3×D4—62no—
376C2×C3×D4—62no—
377C2×C3×D4—62no—
378C22×C3×C4—21no—
379C22×C3×C4—21no—
380C22×C3×C4—31no—
381C22×C3×C4—31no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
384C22×C3×C4—34no—
385C22×C3×C4—31no—
386C22×C3×C4—31no—
387C22×C3×C4—62no—
388C22×C3×C4—62no—
389C22×C3×C4—62no—
390C22×C3×C4—62no—
391C22×C3×C4—62no—
392C22×C3×C4—62no—
393C22×C3×C4—62no—
394C22×C3×C4—62no—
395C22×C3×C4C22×D311yescharacteristic
396C22×C3×C4C22×D311yescharacteristic
397C22×C3×C4C22×D311yescharacteristic
398C22×C3×C4C22×D311yescharacteristic
399C2×#67—22no—
400C2×#67—22no—
401C2×#67—22no—
402C2×#67—22no—
403C2×#67—34no—
404C2×#67—34no—
405C2×#67—64no—
406C2×#67—62no—
407C2×#67—62no—
408C2×#67—62no—
409C2×#67—62no—
410C2×#67—122no—
411C2×#67—122no—
412C2×#67C4×D314yescomplemented
413C2×#67C4×D314yescomplemented
414C22×Dic3—22no—
415C22×Dic3—22no—
416C22×Dic3—22no—
417C22×Dic3—31no—
418C22×Dic3—31no—
419C22×Dic3—31no—
420C22×Dic3—31no—
421C22×Dic3—34no—
422C22×Dic3—31no—
423C22×Dic3—31no—
424C22×Dic3—61no—
425C22×Dic3—61no—
426C22×Dic3—61no—
427C22×Dic3—62no—
428C22×Dic3—62no—
429C22×Dic3—62no—
430C22×Dic3—62no—
431C22×Dic3—62no—
432C22×Dic3C22×D311yescharacteristic
433C22×Dic3C22×D311yescharacteristic
434C22×Dic3C22×D311yescharacteristic
435C22×Dic3C22×D311yescharacteristic
436C22×Dic3C22×D311yescharacteristic
437C22×Dic3C22×D311yescharacteristic
438C2×C4×D3—22no—
439C2×C4×D3—22no—
440C2×C4×D3—22no—
441C2×C4×D3—22no—
442C2×C4×D3—22no—
443C2×C4×D3—34no—
444C2×C4×D3—34no—
445C2×C4×D3—34no—
446C2×C4×D3—632no—
447C2×C4×D3—632no—
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—62no—
463C2×C4×D3—122no—
464C2×C4×D3—122no—
465C2×C4×D3—122no—
466C2×C4×D3#6714yescomplemented
467C3×C4⋊C4—62no—
468C3×C22⋊C4—22no—
469C3×C22⋊C4—22no—
470C3×C22⋊C4—42no—
471C3×C22⋊C4—62no—
472C3×C22⋊C4—62no—
473C3×C22⋊C4—62no—
474C3×C42—62no—
475#217—22no—
476#217—34no—
477#217—34no—
478#217—62no—
479#217—62no—
480#217—62no—
481#217—62no—
482#217—122no—
483(C2×D3)⋊C4—22no—
484(C2×D3)⋊C4—22no—
485(C2×D3)⋊C4—34no—
486(C2×D3)⋊C4—34no—
487(C2×D3)⋊C4—34no—
488(C2×D3)⋊C4—34no—
489(C2×D3)⋊C4—62no—
490(C2×D3)⋊C4—62no—
491(C2×D3)⋊C4—62no—
492(C2×D3)⋊C4—62no—
493(C2×D3)⋊C4—62no—
494(C2×D3)⋊C4—62no—
495(C2×D3)⋊C4—122no—
496C4⋊Dic3—62no—
497Dic3⋊C4—22no—
498Dic3⋊C4—62no—
499Dic3⋊C4—62no—
500Dic3⋊C4—62no—
501C4×Dic3—22no—
502C4×Dic3—62no—
503C4×Dic3—62no—
504C4×Dic3—62no—
505C4×Dic3—62no—
506C22×C32—22no—
507C22×C32—22no—
508C22×C32—22no—
509C22×C32—41no—
510C22×C32—41no—
511C22×C32—41no—
512C22×C32—41no—
513C22×C32C23×C411yescharacteristic
514C22×C32C22×D411yescharacteristic
515C22×C32C22×D411yescharacteristic
516C22×C32C22×D411yescharacteristic
517C22×C32C2×#4111yescharacteristic
518C22×C32C2×#4111yescharacteristic
519C22×C32C2×#4111yescharacteristic
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⋊D3C4×D414yescomplemented
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—22no—
534C2×C3×D3—22no—
535C2×C3×D3—22no—
536C2×C3×D3—22no—
537C2×C3×D3—22no—
538C2×C3×D3—22no—
539C2×C3×D3C4×D414yescomplemented
540C2×C3×D3C4×D414yescomplemented
541D32—232no—
542C32×C4—22no—
543C32×C4—41no—
544C3⋊Dic3—22no—
545C3⋊Dic3—22no—
546C3⋊Dic3—41no—
547C3×Dic3—22no—
548C3×Dic3—22no—
549C3×Dic3—22no—
550C3×Dic3—41no—
551C3×Dic3—41no—
552C3×Dic3#12014yescomplemented
553C25—91no—
554C22×D4—31no—
555C22×D4—31no—
556C22×D4—91no—
557C23×C4—31no—
558C23×C4—31no—
559C23×C4—31no—
560C23×C4—91no—
561C23×C4—91no—
562C23×C4—91no—
563C23×C4—91no—
564C23×C4—184no—
565C23×C4—184no—
566C23×C4—184no—
567#120—98no—
568C4×D4—64no—
569C4×D4—184no—
570C4×D4—184no—
571C2×C4⋊C4—31no—
572C2×C4⋊C4—91no—
573C2×C4⋊C4—91no—
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×C22⋊C4—91no—
585C2×C22⋊C4D3211yescharacteristic, complemented
586C2×C42—31no—
587C2×C42—91no—
588C2×C42—91no—
589#95—31no—
590#95—31no—
591#95—91no—
592#95—91no—
593#95—91no—
594#95—91no—
595C23×C3—21no—
596C23×C3—21no—
597C23×C3—21no—
598C23×C3—21no—
599C23×C3—21no—
600C23×C3—21no—
601C23×C3—21no—
602C23×C3—21no—
603C23×C3—21no—
604C23×C3—21no—
605C23×C3—21no—
606C23×C3—21no—
607C23×C3—21no—
608C23×C3—22no—
609C23×C3—32no—
610C23×C3—32no—
611C23×C3—32no—
612C23×C3—32no—
613C23×C3—32no—
614C23×C3—32no—
615C23×C3—41no—
616C23×C3—41no—
617C23×C3—41no—
618C23×C3—41no—
619C23×C3—41no—
620C23×C3—41no—
621C23×C3—61no—
622C23×C3—61no—
623C23×C3—61no—
624C23×C3—61no—
625C23×C3—61no—
626C23×C3—61no—
627C23×C3—61no—
628C23×C3—61no—
629C23×C3C2×C4×D312yescomplemented
630C23×C3C2×C4×D312yescomplemented
631C23×C3C23×D311yescharacteristic
632C23×C3C23×D311yescharacteristic
633C22×D3—21no—
634C22×D3—21no—
635C22×D3—21no—
636C22×D3—21no—
637C22×D3—21no—
638C22×D3—21no—
639C22×D3—21no—
640C22×D3—21no—
641C22×D3—32no—
642C22×D3—32no—
643C22×D3—32no—
644C22×D3—32no—
645C22×D3—32no—
646C22×D3—32no—
647C22×D3—62no—
648C22×D3—62no—
649C22×D3—62no—
650C22×D3—68no—
651C22×D3—68no—
652C22×D3—68no—
653C22×D3—68no—
654C22×D3—68no—
655C22×D3—68no—
656C22×D3—68no—
657C22×D3—68no—
658C22×D3—68no—
659C22×D3—68no—
660C22×D3—68no—
661C22×D3—68no—
662C22×D3—61no—
663C22×D3—61no—
664C22×D3—61no—
665C22×D3—61no—
666C22×D3—61no—
667C22×D3—61no—
668C22×D3—61no—
669C22×D3—61no—
670C22×D3—68no—
671C22×D3—68no—
672C22×D3—121no—
673C22×D3—121no—
674C22×D3—121no—
675C22×D3—121no—
676C22×D3C2×C4×D312yes—
677C22×D3C2×C4×D312yes—
678C22×D3#23512yes—
679C22×D3D3×D412yes—
680C22×D3#23712yes—
681C22×D3C2×#6712yes—
682C3×D4—68no—
683C3×D4—68no—
684C2×C3×C4—21no—
685C2×C3×C4—21no—
686C2×C3×C4—21no—
687C2×C3×C4—21no—
688C2×C3×C4—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—22no—
695C2×C3×C4—32no—
696C2×C3×C4—32no—
697C2×C3×C4—32no—
698C2×C3×C4—32no—
699C2×C3×C4—32no—
700C2×C3×C4—32no—
701C2×C3×C4—41no—
702C2×C3×C4—41no—
703C2×C3×C4—41no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—68no—
707C2×C3×C4—68no—
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—61no—
715C2×C3×C4—61no—
716C2×C3×C4—61no—
717C2×C3×C4—61no—
718C2×C3×C4—61no—
719C2×C3×C4—61no—
720C2×C3×C4—124no—
721C2×C3×C4D3×D412yes—
722C2×C3×C4C2×#6712yes—
723#67—28no—
724#67—28no—
725#67—68no—
726#67—68no—
727#67—128no—
728C2×Dic3—21no—
729C2×Dic3—21no—
730C2×Dic3—21no—
731C2×Dic3—21no—
732C2×Dic3—21no—
733C2×Dic3—21no—
734C2×Dic3—21no—
735C2×Dic3—21no—
736C2×Dic3—21no—
737C2×Dic3—21no—
738C2×Dic3—21no—
739C2×Dic3—21no—
740C2×Dic3—32no—
741C2×Dic3—32no—
742C2×Dic3—32no—
743C2×Dic3—32no—
744C2×Dic3—44no—
745C2×Dic3—62no—
746C2×Dic3—62no—
747C2×Dic3—68no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—68no—
757C2×Dic3—61no—
758C2×Dic3—61no—
759C2×Dic3—61no—
760C2×Dic3—61no—
761C2×Dic3—61no—
762C2×Dic3—61no—
763C2×Dic3—121no—
764C2×Dic3—121no—
765C2×Dic3—121no—
766C2×Dic3—121no—
767C2×Dic3—121no—
768C2×Dic3—121no—
769C2×Dic3—121no—
770C2×Dic3C2×C4×D312yescomplemented
771C2×Dic3C2×C4×D312yescomplemented
772C2×Dic3D3×D412yes—
773C2×Dic3D3×D412yes—
774C2×Dic3D3×D412yes—
775C2×Dic3C2×#6712yes—
776C4×D3—28no—
777C4×D3—28no—
778C4×D3—68no—
779C4×D3—68no—
780C4×D3—68no—
781C4×D3—68no—
782C4×D3—68no—
783C4×D3—68no—
784C4×D3—128no—
785C2×C32—42no—
786C2×C32C2×C4×D411yescharacteristic
787C2×C32C2×C4×D411yescharacteristic
788C2×C32C2×C4×D411yescharacteristic
789C2×C32C2×#12011yescharacteristic
790C2×C32#52511yescharacteristic
791C2×C32#52511yescharacteristic
792C2×C32#52511yescharacteristic
793C3⋊D3—24no—
794C3×D3—24no—
795C3×D3—24no—
796C24—31no—
797C24—31no—
798C24—94no—
799C24—91no—
800C24—182no—
801C24—182no—
802C24—182no—
803C24—182no—
804C24—182no—
805C24—182no—
806C24C2×D3211yescharacteristic
807C2×D4—34no—
808C2×D4—34no—
809C2×D4—62no—
810C2×D4—62no—
811C2×D4—62no—
812C2×D4—62no—
813C2×D4—94no—
814C2×D4—182no—
815C2×D4—182no—
816C22×C4—31no—
817C22×C4—31no—
818C22×C4—31no—
819C22×C4—31no—
820C22×C4—34no—
821C22×C4—31no—
822C22×C4—31no—
823C22×C4—62no—
824C22×C4—62no—
825C22×C4—62no—
826C22×C4—62no—
827C22×C4—62no—
828C22×C4—62no—
829C22×C4—62no—
830C22×C4—62no—
831C22×C4—94no—
832C22×C4—94no—
833C22×C4—91no—
834C22×C4—91no—
835C22×C4—91no—
836C22×C4—182no—
837C22×C4—182no—
838C22×C4—182no—
839C22×C4—182no—
840C22×C4—182no—
841C22×C4—182no—
842C22×C4—182no—
843C22×C4—1832no—
844C22×C4—182no—
845C22×C4—182no—
846C22×C4—182no—
847C22×C4C2×D3211yescharacteristic
848C22×C4C2×D3211yescharacteristic
849C4⋊C4—62no—
850C4⋊C4—182no—
851C4⋊C4—182no—
852C22⋊C4—22no—
853C22⋊C4—62no—
854C22⋊C4—62no—
855C22⋊C4—62no—
856C22⋊C4—94no—
857C22⋊C4—94no—
858C22⋊C4—94no—
859C22⋊C4—182no—
860C22⋊C4—182no—
861C22⋊C4—182no—
862C22⋊C4—182no—
863C22⋊C4—182no—
864C42—62no—
865C42—182no—
866C42—182no—
867C22×C3—22no—
868C22×C3—22no—
869C22×C3—22no—
870C22×C3—22no—
871C22×C3—22no—
872C22×C3—22no—
873C22×C3—21no—
874C22×C3—21no—
875C22×C3—21no—
876C22×C3—21no—
877C22×C3—21no—
878C22×C3—21no—
879C22×C3—21no—
880C22×C3—34no—
881C22×C3—34no—
882C22×C3—42no—
883C22×C3—42no—
884C22×C3—42no—
885C22×C3—41no—
886C22×C3—41no—
887C22×C3—41no—
888C22×C3—41no—
889C22×C3—41no—
890C22×C3—41no—
891C22×C3—41no—
892C22×C3—41no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—62no—
903C22×C3—62no—
904C22×C3—62no—
905C22×C3—81no—
906C22×C3—81no—
907C22×C3—81no—
908C22×C3—81no—
909C22×C3C22×C4×D311yescharacteristic
910C22×C3C22×C4×D311yescharacteristic
911C22×C3C2×#23511yescharacteristic
912C22×C3C2×D3×D411yescharacteristic
913C22×C3C2×D3×D411yescharacteristic
914C22×C3C2×D3×D411yescharacteristic
915C22×C3C2×D3×D411yescharacteristic
916C22×C3C2×D3×D411yescharacteristic
917C22×C3C2×#23711yescharacteristic
918C22×C3D3×#4111yescharacteristic
919C22×C3D3×#4111yescharacteristic
920C22×C3D3×#4111yescharacteristic
921C22×C3D3×#4111yescharacteristic
922C22×C3C22×#6711yescharacteristic
923C2×D3—22no—
924C2×D3—22no—
925C2×D3—22no—
926C2×D3—22no—
927C2×D3—22no—
928C2×D3—22no—
929C2×D3—22no—
930C2×D3—22no—
931C2×D3—22no—
932C2×D3—22no—
933C2×D3—22no—
934C2×D3—22no—
935C2×D3—34no—
936C2×D3—34no—
937C2×D3—64no—
938C2×D3—632no—
939C2×D3—632no—
940C2×D3—62no—
941C2×D3—62no—
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—62no—
946C2×D3—62no—
947C2×D3—62no—
948C2×D3—62no—
949C2×D3—62no—
950C2×D3—62no—
951C2×D3—62no—
952C2×D3—122no—
953C2×D3—122no—
954C2×D3—122no—
955C2×D3—122no—
956C2×D3—122no—
957C2×D3—122no—
958C2×D3#67⋊C414yescomplemented
959C2×D3C4×#6714yescomplemented
960C3×C4—22no—
961C3×C4—22no—
962C3×C4—34no—
963C3×C4—42no—
964C3×C4—41no—
965C3×C4—41no—
966C3×C4—62no—
967C3×C4—62no—
968C3×C4—62no—
969C3×C4—81no—
970C3×C4—121no—
971C3×C4—121no—
972Dic3—22no—
973Dic3—22no—
974Dic3—22no—
975Dic3—41no—
976Dic3—41no—
977Dic3—62no—
978Dic3—62no—
979Dic3—62no—
980Dic3—62no—
981Dic3—122no—
982Dic3—122no—
983Dic3—121no—
984Dic3—121no—
985Dic3—241no—
986Dic3#93714yescomplemented
987C32C4×#12011yescharacteristic, complemented, Sylow
988C23—21no—
989C23—21no—
990C23—21no—
991C23—21no—
992C23—21no—
993C23—21no—
994C23—32no—
995C23—32no—
996C23—32no—
997C23—32no—
998C23—32no—
999C23—32no—
1000C23—61no—
1001C23—61no—
1002C23—61no—
1003C23—61no—
1004C23—61no—
1005C23—61no—
1006C23—61no—
1007C23—61no—
1008C23—92no—
1009C23—92no—
1010C23—92no—
1011C23—188no—
1012C23—188no—
1013C23—188no—
1014C23—188no—
1015C23—188no—
1016C23—188no—
1017C23—188no—
1018C23—181no—
1019C23—181no—
1020C23—181no—
1021C23—181no—
1022C23C4×D3212yescomplemented
1023C23C22×D3211yescharacteristic
1024D4—68no—
1025D4—68no—
1026D4—188no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—32no—
1033C2×C4—32no—
1034C2×C4—32no—
1035C2×C4—32no—
1036C2×C4—32no—
1037C2×C4—32no—
1038C2×C4—68no—
1039C2×C4—68no—
1040C2×C4—61no—
1041C2×C4—61no—
1042C2×C4—61no—
1043C2×C4—61no—
1044C2×C4—61no—
1045C2×C4—61no—
1046C2×C4—61no—
1047C2×C4—61no—
1048C2×C4—61no—
1049C2×C4—61no—
1050C2×C4—61no—
1051C2×C4—61no—
1052C2×C4—92no—
1053C2×C4—92no—
1054C2×C4—124no—
1055C2×C4—188no—
1056C2×C4—188no—
1057C2×C4—188no—
1058C2×C4—188no—
1059C2×C4—181no—
1060C2×C4—181no—
1061C2×C4—181no—
1062C2×C4—181no—
1063C2×C4—181no—
1064C2×C4—181no—
1065C2×C4—181no—
1066C2×C4D3×#6712yes—
1067C2×C3—21no—
1068C2×C3—21no—
1069C2×C3—21no—
1070C2×C3—21no—
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—42no—
1075C2×C3—42no—
1076C2×C3—64no—
1077C2×C3—64no—
1078C2×C3—82no—
1079C2×C3C2×#67⋊C411yescharacteristic
1080C2×C3C4×D3×D411yescharacteristic
1081C2×C3C4×D3×D411yescharacteristic
1082C2×C3C4×D3×D411yescharacteristic
1083C2×C3C4×D3×D411yescharacteristic
1084C2×C3#554711yescharacteristic
1085C2×C3#554711yescharacteristic
1086C2×C3D3×#12011yescharacteristic
1087C2×C3#560611yescharacteristic
1088C2×C3#560611yescharacteristic
1089C2×C3#565611yescharacteristic
1090C2×C3C2×C4×#6711yescharacteristic
1091C2×C3C2×#93711yescharacteristic
1092C2×C3#582811yescharacteristic
1093D3—24no—
1094D3—24no—
1095D3—64no—
1096D3—64no—
1097D3—124no—
1098C22—22no—
1099C22—22no—
1100C22—22no—
1101C22—34no—
1102C22—34no—
1103C22—41no—
1104C22—41no—
1105C22—41no—
1106C22—41no—
1107C22—62no—
1108C22—62no—
1109C22—62no—
1110C22—62no—
1111C22—62no—
1112C22—62no—
1113C22—62no—
1114C22—62no—
1115C22—62no—
1116C22—62no—
1117C22—62no—
1118C22—62no—
1119C22—94no—
1120C22—1832no—
1121C22—182no—
1122C22—182no—
1123C22—182no—
1124C22—182no—
1125C22—182no—
1126C22—182no—
1127C22C2×C4×D3211yescharacteristic
1128C22D3×#23511yescharacteristic
1129C22D32×D411yescharacteristic
1130C22D32×D411yescharacteristic
1131C22D3×#23711yescharacteristic
1132C22#6431211yescharacteristic
1133C22C2×D3×#6711yescharacteristic
1134C4—22no—
1135C4—34no—
1136C4—41no—
1137C4—62no—
1138C4—62no—
1139C4—62no—
1140C4—121no—
1141C4—121no—
1142C4—182no—
1143C4—182no—
1144C4—361no—
1145C3—21no—
1146C3#7465911yescharacteristic, complemented
1147C3C4×#93711yescharacteristic, complemented
1148C2—42no—
1149C2—64no—
1150C2—64no—
1151C2—184no—
1152C2D3×#67⋊C411yescharacteristic
1153C2#1059425511yescharacteristic
1154C2#1059426611yescharacteristic
1155C2#1059428611yescharacteristic
1156C2C4×D3×#6711yescharacteristic
1157C2D3×#93711yescharacteristic
1158C2#1059530111yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C22⋊C4C22
socle, cosocleC23×C32C24
prime radicalC2×#63983C2
hypercenterC2×C22⋊C4D32
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C4×D32C2semidirect
2. C2×C3×#67⋊C4C2semidirect
4. C2×Dic3×#67C2semidirect
5. C2×#63952C2semidirect
6. #10592655C2semidirect
7. C3×#4956C2semidirect
8. #10591721C2semidirect
9. #10591399C2semidirect
10. #10591373C2semidirect
11. Dic3×(C2×D3)⋊C4C2semidirect
12. #10591290C2semidirect
13. #10591277C2semidirect
14. #10591237C2semidirect
15. #10591233C2semidirect
23. C23×C3×Dic3C22semidirect
32. C2×C32×C22⋊C4C22semidirect
33. C2×#3757C22semidirect
35. C2×C3×#217C22semidirect
38. C2×C3×Dic3⋊C4C22semidirect
39. C2×C3×C4×Dic3C22semidirect
41. #63983C4semidirect
43. C2×#3724C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
51. C2×Dic32C22semidirect
52. C2×Dic32C22semidirect
54. #63658C22semidirect
55. #63658C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
58. #63579C22semidirect
59. #63579C22semidirect
69. C2×#67⋊C4D3semidirect
80. #4956D3semidirect
101. C22×D32C2×C4semidirect
106. C2×#638C2×C4semidirect
117. C2×C3×#67C2×C4semidirect
118. C2×C3×#67C2×C4semidirect
133. C2×C3×C4×D3D4semidirect
136. C2×#624D4semidirect
142. C2×D3×Dic3D4semidirect
155. #3722C2×C4semidirect
158. (C2×D3)⋊Dic3C2×C4semidirect
159. (C2×D3)⋊Dic3C2×C4semidirect
177. C23×Dic3C2×D3semidirect
199. C2×C3×C22⋊C4C2×D3semidirect
200. C2×C3×C22⋊C4C2×D3semidirect
209. C2×#217C2×D3semidirect
232. C2×Dic3⋊C4C2×D3semidirect
237. C2×C4×Dic3C2×D3semidirect
252. C3⋊#95C2×D3semidirect
253. C3⋊#95C2×D3semidirect
260. C23×C32C22×C4semidirect
304. C2×C3⋊Dic3C22×C4semidirect
322. C2×C3×Dic3C22×C4semidirect
323. C2×C3×Dic3C22×C4semidirect
412. C2×#67C4×D3semidirect
413. C2×#67C4×D3semidirect
466. C2×C4×D3#67semidirect
526. C2×C3⋊D3C4×D4semidirect
539. C2×C3×D3C4×D4semidirect
540. C2×C3×D3C4×D4semidirect
552. C3×Dic3#120semidirect
585. C2×C22⋊C4D32semidirect
629. C23×C3C2×C4×D3semidirect
630. C23×C3C2×C4×D3semidirect
770. C2×Dic3C2×C4×D3semidirect
771. C2×Dic3C2×C4×D3semidirect
958. C2×D3#67⋊C4semidirect
959. C2×D3C4×#67semidirect
986. Dic3#937semidirect
987. C32C4×#120semidirect
1022. C23C4×D32semidirect
1146. C3#74659semidirect
1147. 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×#67⋊C42
C2×#639832
C2×Dic3×#672
C2×#639522
#105926552
C3×#49562
#105917212
#105913992
#105913732
Dic3×(C2×D3)⋊C42
#105912902
#105912772
#105912372
#105912332
C4×#9373
#746593