Finite Group Databasebeta

← #11802018

Subgroups — #11802018

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×#63923C211yesmaximal, characteristic
3C2×#63904C211yesmaximal, characteristic, complemented
4C2×#63894C211yesmaximal, characteristic, complemented
5C2×#63880C211yesmaximal, characteristic, complemented
6#10592364C211yesmaximal, characteristic, complemented
7C3×#4668C211yesmaximal, characteristic, complemented
8C3×#4666C211yesmaximal, characteristic, complemented
9#10591399C211yesmaximal, characteristic, complemented
10#10591382C211yesmaximal, characteristic, complemented
11#10591377C211yesmaximal, characteristic, complemented
12Dic3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
13#10591364C211yesmaximal, characteristic, complemented
14#10591290C211yesmaximal, characteristic, complemented
15#10591233C211yesmaximal, characteristic, complemented
16#74379—31nomaximal
17C4×#882—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×#624C2211yescharacteristic, complemented
27C22×D3×Dic3C2211yescharacteristic
28C22×D3×Dic3C2211yescharacteristic
29C2×C4×D32—24no—
30C2×C4×D32—24no—
31C2×C4×D32—24no—
32C2×#3752C2211yescharacteristic
33C2×#3752C2211yescharacteristic, complemented
34C2×#3752C2211yescharacteristic, complemented
35C2×C3×(C2×D3)⋊C4C2211yescharacteristic
36C2×C3×(C2×D3)⋊C4C2211yescharacteristic
37C2×C3×(C2×D3)⋊C4C2211yescharacteristic
38C2×C3×(C2×D3)⋊C4C2211yescharacteristic
39C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
40C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
41C2×C3×C4×Dic3C2211yescharacteristic, complemented
42C2×C3×C4×Dic3C2211yescharacteristic, complemented
43C2×Dic3⋊Dic3C2211yescharacteristic, complemented
44C2×#3722C2211yescharacteristic
45C2×#3722C2211yescharacteristic
46C2×#3722C2211yescharacteristic, complemented
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×Dic32C2211yescharacteristic, complemented
50#63923C418yescomplemented
51#63904—24no—
52#63894—24no—
53#63880—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×C4×#67—31no—
63C2×#893—31no—
64C2×#893—31no—
65C2×#882—31no—
66C2×#882—31no—
67C2×#67⋊C4—31no—
68C2×C4×D12—31no—
69C2×C4×D12—31no—
70C3×#385—31no—
71C3×C4×C22⋊C4—31no—
72#5213—31no—
73#4989—31no—
74#4989—31no—
75#4958—31no—
76#4955—31no—
77#4955—31no—
78#4950—31no—
79Dic3×C22⋊C4—31no—
80C4×(C2×D3)⋊C4—31no—
81C4×(C2×D3)⋊C4—31no—
82#4668—31no—
83#4668D311yescharacteristic, complemented
84#4666—31no—
85#4666D311yescharacteristic, complemented
86#4665—31no—
87#4665—31no—
88#4665—31no—
89#4665—31no—
90#4665—61no—
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
107C2×C4⋊(C3⋊D3)—22no—
108C2×C4⋊(C3⋊D3)—22no—
109C2×C4⋊(C3⋊D3)C2×C414yescomplemented
110C2×C4×C3⋊D3—22no—
111C2×C4×C3⋊D3—22no—
112C2×C4×C3⋊D3—22no—
113C22×C3×Dic3C2311yescharacteristic
114C22×C3×Dic3C2311yescharacteristic
115C22×C3×Dic3C2311yescharacteristic
116C22×C3×Dic3C2311yescharacteristic
117C22×C3×Dic3C2311yescharacteristic
118C22×C3×Dic3C2311yescharacteristic
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×D3D414yescomplemented
125C2×#626—22no—
126C2×#626—22no—
127C2×#626—22no—
128C2×#626—22no—
129C2×#626C2×C414yescomplemented
130C2×#626C2×C414yescomplemented
131C2×#624—22no—
132C2×#624—22no—
133C2×#624—22no—
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—
144#3752—22no—
145#3752—22no—
146#3752—22no—
147C3×(C2×D3)⋊C4—22no—
148C3×(C2×D3)⋊C4—22no—
149C3×(C2×D3)⋊C4C2×C414yescomplemented
150C3×(C2×D3)⋊C4C2×C414yescomplemented
151C3×C4⋊Dic3—22no—
152C3×Dic3⋊C4—22no—
153C3×C4×Dic3—22no—
154C3×C4×Dic3—22no—
155Dic3⋊Dic3—22no—
156#3722—22no—
157#3722—22no—
158#3722C2×C414yescomplemented
159(C2×D3)⋊Dic3—22no—
160(C2×D3)⋊Dic3—22no—
161Dic32—22no—
162C4×#120—91noSylow
163C24×D3—31no—
164C24×D3—31no—
165C23×C3×C4—31no—
166C23×C3×C4—31no—
167C22×#67—31no—
168C22×#67—31no—
169C23×Dic3—31no—
170C23×Dic3—31no—
171C22×D12—31no—
172C22×D12—31no—
173C22×D12—31no—
174C22×D12—31no—
175C22×D12—61no—
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—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
193C2×C3×C4⋊C4—31no—
194C2×C3×C4⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C22⋊C4—31no—
199C2×C3×C42—31no—
200C2×C3×C42—31no—
201C2×#217—31no—
202C2×#217—31no—
203C4×#67—64no—
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—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—61no—
219C2×(C2×D3)⋊C4—61no—
220C2×(C2×D3)⋊C4—61no—
221C2×(C2×D3)⋊C4C2×D311yescharacteristic
222C2×(C2×D3)⋊C4C2×D311yescharacteristic
223C2×(C2×D3)⋊C4C2×D311yescharacteristic
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225C2×C4⋊Dic3—31no—
226C2×C4⋊Dic3C2×D311yescharacteristic, complemented
227C2×Dic3⋊C4—31no—
228C2×Dic3⋊C4C2×D311yescharacteristic, complemented
229C2×C4×Dic3—31no—
230C2×C4×Dic3—31no—
231C2×C4×Dic3C2×D311yescharacteristic, complemented
232C2×C4×Dic3C2×D311yescharacteristic, complemented
233#893—64no—
234#893—64no—
235#882—38no—
236#882—38no—
237#67⋊C4—64no—
238C4×D12—64no—
239C4×D12—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⋊D3—21no—
260C22×C3⋊D3—21no—
261C22×C3⋊D3—21no—
262C22×C3⋊D3—21no—
263C22×C3⋊D3—21no—
264C22×C3⋊D3—21no—
265C22×C3⋊D3C22×C412yes—
266C22×C3⋊D3C22×C412yescomplemented
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×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⋊Dic3C2×D412yes—
305C4⋊(C3⋊D3)—28no—
306C4×C3⋊D3—28no—
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×Dic3—21no—
317C2×C3×Dic3—21no—
318C2×C3×Dic3—21no—
319C2×C3×Dic3C22×C412yescomplemented
320C2×C3×Dic3C22×C412yescomplemented
321C2×C3×Dic3C2×D412yes—
322C2×C3×Dic3C2×D412yes—
323C2×C3×Dic3C2×D412yes—
324C2×C3×Dic3C2×D412yes—
325C3×C4×D3—28no—
326C3×C4×D3—28no—
327#626—28no—
328#626—28no—
329#624—28no—
330#624—44no—
331D3×Dic3—28no—
332D3×Dic3—28no—
333C24×C4—91no—
334C2×#120—91no—
335C2×C4×D4—91no—
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—31no—
346C4×C22⋊C4—91no—
347C4×C22⋊C4—91no—
348C24×C3—31no—
349C24×C3—31no—
350C23×D3—31no—
351C23×D3—31no—
352C23×D3—31no—
353C23×D3—31no—
354C23×D3—34no—
355C23×D3—34no—
356C23×D3—61no—
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
372C22×C3×C4—21no—
373C22×C3×C4—21no—
374C22×C3×C4—21no—
375C22×C3×C4—31no—
376C22×C3×C4—31no—
377C22×C3×C4—31no—
378C22×C3×C4—31no—
379C22×C3×C4—34no—
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×C4C22×D311yescharacteristic
388C22×C3×C4C22×D311yescharacteristic
389C22×C3×C4C22×D311yescharacteristic
390C22×C3×C4C22×D311yescharacteristic
391C22×C3×C4C22×D311yescharacteristic
392C22×C3×C4C22×D311yescharacteristic
393C2×#67—34no—
394C2×#67—34no—
395C2×#67—62no—
396C2×#67—62no—
397C2×#67—62no—
398C2×#67—62no—
399C22×Dic3—31no—
400C22×Dic3—31no—
401C22×Dic3—34no—
402C22×Dic3—31no—
403C22×Dic3—31no—
404C22×Dic3—61no—
405C22×Dic3—61no—
406C22×Dic3—62no—
407C22×Dic3—62no—
408C22×Dic3—62no—
409C22×Dic3—62no—
410C22×Dic3—62no—
411C22×Dic3C22×D311yescharacteristic
412C22×Dic3C22×D311yescharacteristic
413C22×Dic3C22×D311yescharacteristic
414C22×Dic3C22×D311yescharacteristic
415C22×Dic3C22×D311yescharacteristic
416C22×Dic3C22×D311yescharacteristic
417C2×D12—34no—
418C2×D12—34no—
419C2×D12—34no—
420C2×D12—34no—
421C2×D12—64no—
422C2×D12—62no—
423C2×D12—62no—
424C2×D12—62no—
425C2×D12—62no—
426C2×D12—62no—
427C2×D12—62no—
428C2×D12—62no—
429C2×D12—62no—
430C2×D12—122no—
431C2×D12—122no—
432C2×C4×D3—22no—
433C2×C4×D3—22no—
434C2×C4×D3—22no—
435C2×C4×D3—22no—
436C2×C4×D3—22no—
437C2×C4×D3—34no—
438C2×C4×D3—34no—
439C2×C4×D3—34no—
440C2×C4×D3—632no—
441C2×C4×D3—632no—
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—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×D3D1214yescomplemented
467C3×C4⋊C4—62no—
468C3×C4⋊C4—62no—
469C3×C22⋊C4—34no—
470C3×C22⋊C4—34no—
471C3×C22⋊C4—62no—
472C3×C22⋊C4—62no—
473C3×C42—62no—
474C3×C42—62no—
475#217—62no—
476#217—62no—
477(C2×D3)⋊C4—22no—
478(C2×D3)⋊C4—22no—
479(C2×D3)⋊C4—34no—
480(C2×D3)⋊C4—34no—
481(C2×D3)⋊C4—62no—
482(C2×D3)⋊C4—62no—
483(C2×D3)⋊C4—62no—
484(C2×D3)⋊C4—62no—
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)⋊C4—122no—
495(C2×D3)⋊C4—122no—
496(C2×D3)⋊C4C4×D314yescomplemented
497(C2×D3)⋊C4C4×D314yescomplemented
498C4⋊Dic3—22no—
499C4⋊Dic3—62no—
500Dic3⋊C4—22no—
501Dic3⋊C4—62no—
502C4×Dic3—22no—
503C4×Dic3—22no—
504C4×Dic3—62no—
505C4×Dic3—62no—
506C22×C32C23×C411yescharacteristic
507C22×C32C22×D411yescharacteristic
508C22×C32C22×D411yescharacteristic
509C22×C32C22×D411yescharacteristic
510C22×C32C2×#4111yescharacteristic
511C22×C32C2×#4111yescharacteristic
512C22×C32C2×#4111yescharacteristic
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—41no—
523C2×C3⋊D3—41no—
524C2×C3⋊D3—41no—
525C2×C3⋊D3—41no—
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—22no—
544C32×C4—41no—
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—91no—
555C22×D4—91no—
556C22×D4—91no—
557C23×C4—31no—
558C23×C4—31no—
559C23×C4—91no—
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—184no—
569C4×D4—184no—
570C4×D4—184no—
571C2×C4⋊C4—31no—
572C2×C4⋊C4—31no—
573C2×C4⋊C4—91no—
574C2×C22⋊C4—31no—
575C2×C22⋊C4—31no—
576C2×C22⋊C4—31no—
577C2×C22⋊C4—31no—
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⋊C4—91no—
586C2×C42—31no—
587C2×C42—31no—
588C2×C42—91no—
589#95—31no—
590#95—31no—
591#95—91no—
592#95—91no—
593#95—91no—
594#95D3211yescharacteristic, complemented
595C23×C3—21no—
596C23×C3—32no—
597C23×C3—32no—
598C23×C3—32no—
599C23×C3—32no—
600C23×C3—32no—
601C23×C3—32no—
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×C3C23×D311yescharacteristic
611C23×C3C23×D311yescharacteristic
612C22×D3—21no—
613C22×D3—21no—
614C22×D3—21no—
615C22×D3—21no—
616C22×D3—21no—
617C22×D3—21no—
618C22×D3—21no—
619C22×D3—21no—
620C22×D3—32no—
621C22×D3—32no—
622C22×D3—32no—
623C22×D3—32no—
624C22×D3—32no—
625C22×D3—32no—
626C22×D3—32no—
627C22×D3—32no—
628C22×D3—62no—
629C22×D3—62no—
630C22×D3—62no—
631C22×D3—62no—
632C22×D3—68no—
633C22×D3—68no—
634C22×D3—68no—
635C22×D3—68no—
636C22×D3—68no—
637C22×D3—68no—
638C22×D3—68no—
639C22×D3—68no—
640C22×D3—68no—
641C22×D3—68no—
642C22×D3—68no—
643C22×D3—68no—
644C22×D3—61no—
645C22×D3—61no—
646C22×D3—61no—
647C22×D3—61no—
648C22×D3—61no—
649C22×D3—61no—
650C22×D3—61no—
651C22×D3—61no—
652C22×D3—68no—
653C22×D3—68no—
654C22×D3—61no—
655C22×D3—61no—
656C22×D3—61no—
657C22×D3—61no—
658C22×D3—61no—
659C22×D3—61no—
660C22×D3—61no—
661C22×D3—61no—
662C22×D3—61no—
663C22×D3—61no—
664C22×D3—61no—
665C22×D3—61no—
666C22×D3—121no—
667C22×D3—121no—
668C22×D3—121no—
669C22×D3—121no—
670C22×D3—121no—
671C22×D3—121no—
672C22×D3—121no—
673C22×D3—121no—
674C22×D3—121no—
675C22×D3—121no—
676C22×D3C2×C4×D312yes—
677C22×D3C2×C4×D312yes—
678C22×D3C2×D1212yes—
679C22×D3#23512yes—
680C22×D3D3×D412yes—
681C22×D3#23912yes—
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—21no—
689C2×C3×C4—21no—
690C2×C3×C4—21no—
691C2×C3×C4—21no—
692C2×C3×C4—21no—
693C2×C3×C4—21no—
694C2×C3×C4—21no—
695C2×C3×C4—21no—
696C2×C3×C4—22no—
697C2×C3×C4—22no—
698C2×C3×C4—32no—
699C2×C3×C4—32no—
700C2×C3×C4—32no—
701C2×C3×C4—32no—
702C2×C3×C4—32no—
703C2×C3×C4—32no—
704C2×C3×C4—41no—
705C2×C3×C4—41no—
706C2×C3×C4—41no—
707C2×C3×C4—41no—
708C2×C3×C4—41no—
709C2×C3×C4—41no—
710C2×C3×C4—41no—
711C2×C3×C4—68no—
712C2×C3×C4—68no—
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—61no—
721C2×C3×C4—61no—
722C2×C3×C4—61no—
723C2×C3×C4—61no—
724C2×C3×C4—61no—
725C2×C3×C4C2×C4×D312yescomplemented
726C2×C3×C4C2×C4×D312yescomplemented
727C2×C3×C4C2×D1212yes—
728C2×C3×C4D3×D412yes—
729#67—68no—
730#67—68no—
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—21no—
741C2×Dic3—21no—
742C2×Dic3—21no—
743C2×Dic3—32no—
744C2×Dic3—32no—
745C2×Dic3—62no—
746C2×Dic3—68no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—61no—
751C2×Dic3—68no—
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—121no—
763C2×Dic3C2×C4×D312yescomplemented
764C2×Dic3C2×C4×D312yescomplemented
765C2×Dic3C2×D1212yes—
766C2×Dic3D3×D412yes—
767C2×Dic3D3×D412yes—
768C2×Dic3D3×D412yes—
769D12—68no—
770D12—68no—
771D12—68no—
772D12—68no—
773D12—128no—
774C4×D3—28no—
775C4×D3—28no—
776C4×D3—68no—
777C4×D3—68no—
778C4×D3—68no—
779C4×D3—68no—
780C4×D3—68no—
781C4×D3—68no—
782C4×D3—128no—
783C4×D3—124no—
784C4×D3—124no—
785C2×C32C2×C4×D411yescharacteristic
786C2×C32C2×C4×D411yescharacteristic
787C2×C32C2×C4×D411yescharacteristic
788C2×C32C2×#12011yescharacteristic
789C2×C32#52511yescharacteristic
790C2×C32#52511yescharacteristic
791C2×C32#52511yescharacteristic
792C3⋊D3—24no—
793C3⋊D3—42no—
794C3×D3—24no—
795C3×D3—24no—
796C24—31no—
797C24—31no—
798C24—94no—
799C24—91no—
800C24—91no—
801C24—182no—
802C24—182no—
803C24—182no—
804C24—182no—
805C24—182no—
806C24—182no—
807C2×D4—94no—
808C2×D4—94no—
809C2×D4—94no—
810C2×D4—182no—
811C2×D4—182no—
812C2×D4—182no—
813C2×D4—182no—
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—94no—
829C22×C4—94no—
830C22×C4—91no—
831C22×C4—91no—
832C22×C4—182no—
833C22×C4—182no—
834C22×C4—182no—
835C22×C4—182no—
836C22×C4—182no—
837C22×C4—182no—
838C22×C4—182no—
839C22×C4—182no—
840C22×C4—182no—
841C22×C4—182no—
842C22×C4—1832no—
843C22×C4—182no—
844C22×C4—182no—
845C22×C4—182no—
846C22×C4C2×D3211yescharacteristic
847C22×C4C2×D3211yescharacteristic
848C22×C4C2×D3211yescharacteristic
849C4⋊C4—62no—
850C4⋊C4—62no—
851C4⋊C4—182no—
852C22⋊C4—34no—
853C22⋊C4—34no—
854C22⋊C4—62no—
855C22⋊C4—62no—
856C22⋊C4—94no—
857C22⋊C4—182no—
858C22⋊C4—182no—
859C22⋊C4—182no—
860C22⋊C4—182no—
861C22⋊C4—182no—
862C22⋊C4—182no—
863C22⋊C4—182no—
864C42—62no—
865C42—62no—
866C42—182no—
867C22×C3—21no—
868C22×C3—21no—
869C22×C3—21no—
870C22×C3—21no—
871C22×C3—21no—
872C22×C3—21no—
873C22×C3—21no—
874C22×C3—34no—
875C22×C3—34no—
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—62no—
885C22×C3—62no—
886C22×C3—62no—
887C22×C3—62no—
888C22×C3C22×C4×D311yescharacteristic
889C22×C3C22×C4×D311yescharacteristic
890C22×C3C22×D1211yescharacteristic
891C22×C3C2×#23511yescharacteristic
892C22×C3C2×D3×D411yescharacteristic
893C22×C3C2×D3×D411yescharacteristic
894C22×C3C2×D3×D411yescharacteristic
895C22×C3C2×D3×D411yescharacteristic
896C22×C3C2×D3×D411yescharacteristic
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—34no—
915C2×D3—34no—
916C2×D3—64no—
917C2×D3—632no—
918C2×D3—632no—
919C2×D3—62no—
920C2×D3—62no—
921C2×D3—62no—
922C2×D3—62no—
923C2×D3—62no—
924C2×D3—62no—
925C2×D3—62no—
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—122no—
938C2×D3—122no—
939C2×D3—122no—
940C2×D3—122no—
941C2×D3—122no—
942C2×D3—122no—
943C2×D3—122no—
944C2×D3—122no—
945C2×D3—122no—
946C2×D3—121no—
947C2×D3—121no—
948C2×D3—121no—
949C2×D3—121no—
950C2×D3—121no—
951C2×D3—121no—
952C2×D3—121no—
953C2×D3—121no—
954C2×D3—241no—
955C2×D3—241no—
956C2×D3—241no—
957C2×D3—241no—
958C2×D3C4×D1214yescomplemented
959C2×D3#89314yescomplemented
960C3×C4—22no—
961C3×C4—22no—
962C3×C4—22no—
963C3×C4—22no—
964C3×C4—34no—
965C3×C4—42no—
966C3×C4—42no—
967C3×C4—41no—
968C3×C4—41no—
969C3×C4—62no—
970C3×C4—62no—
971C3×C4—62no—
972C3×C4—81no—
973C3×C4—121no—
974C3×C4—121no—
975Dic3—22no—
976Dic3—22no—
977Dic3—22no—
978Dic3—41no—
979Dic3—41no—
980Dic3—62no—
981Dic3—62no—
982Dic3—122no—
983Dic3—121no—
984Dic3—121no—
985Dic3—241no—
986Dic3#88214yescomplemented
987C32C4×#12011yescharacteristic, complemented, Sylow
988C23—32no—
989C23—32no—
990C23—32no—
991C23—32no—
992C23—32no—
993C23—32no—
994C23—61no—
995C23—61no—
996C23—61no—
997C23—61no—
998C23—61no—
999C23—61no—
1000C23—61no—
1001C23—61no—
1002C23—92no—
1003C23—92no—
1004C23—92no—
1005C23—92no—
1006C23—188no—
1007C23—188no—
1008C23—188no—
1009C23—188no—
1010C23—188no—
1011C23—188no—
1012C23—188no—
1013C23—181no—
1014C23—181no—
1015C23—181no—
1016C23—181no—
1017C23—181no—
1018C23—181no—
1019C23—181no—
1020C23—181no—
1021C23—181no—
1022C23—181no—
1023C23C22×D3211yescharacteristic
1024D4—188no—
1025D4—188no—
1026D4—188no—
1027C2×C4—21no—
1028C2×C4—21no—
1029C2×C4—21no—
1030C2×C4—21no—
1031C2×C4—21no—
1032C2×C4—21no—
1033C2×C4—21no—
1034C2×C4—32no—
1035C2×C4—32no—
1036C2×C4—32no—
1037C2×C4—32no—
1038C2×C4—32no—
1039C2×C4—32no—
1040C2×C4—68no—
1041C2×C4—68no—
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—61no—
1053C2×C4—61no—
1054C2×C4—92no—
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—364no—
1065C2×C4C4×D3212yescomplemented
1066C2×C4D3×D1212yes—
1067C2×C3—21no—
1068C2×C3—21no—
1069C2×C3—21no—
1070C2×C3—21no—
1071C2×C3—21no—
1072C2×C3—21no—
1073C2×C3—21no—
1074C2×C3—64no—
1075C2×C3—64no—
1076C2×C3C2×C4×D1211yescharacteristic
1077C2×C3C2×#88211yescharacteristic
1078C2×C3C2×#89311yescharacteristic
1079C2×C3#552411yescharacteristic
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#562711yescharacteristic
1088C2×C3#562711yescharacteristic
1089C2×C3#565611yescharacteristic
1090D3—24no—
1091D3—24no—
1092D3—64no—
1093D3—64no—
1094D3—124no—
1095D3—122no—
1096D3—122no—
1097D3—242no—
1098C22—34no—
1099C22—34no—
1100C22—62no—
1101C22—62no—
1102C22—62no—
1103C22—62no—
1104C22—62no—
1105C22—62no—
1106C22—62no—
1107C22—62no—
1108C22—62no—
1109C22—62no—
1110C22—62no—
1111C22—62no—
1112C22—94no—
1113C22—1832no—
1114C22—182no—
1115C22—182no—
1116C22—182no—
1117C22—182no—
1118C22—182no—
1119C22—182no—
1120C22—182no—
1121C22—182no—
1122C22—182no—
1123C22—361no—
1124C22—361no—
1125C22—361no—
1126C22—361no—
1127C22C2×C4×D3211yescharacteristic
1128C22C2×D3×D1211yescharacteristic
1129C22D3×#23511yescharacteristic
1130C22D32×D411yescharacteristic
1131C22D32×D411yescharacteristic
1132C22#6431211yescharacteristic
1133C22D3×#23911yescharacteristic
1134C4—22no—
1135C4—22no—
1136C4—34no—
1137C4—41no—
1138C4—62no—
1139C4—62no—
1140C4—62no—
1141C4—121no—
1142C4—121no—
1143C4—182no—
1144C4—361no—
1145C3—21no—
1146C3C4×#88211yescharacteristic, complemented
1147C3#7437911yescharacteristic, complemented
1148C2—64no—
1149C2—64no—
1150C2—184no—
1151C2—362no—
1152C2C4×D3×D1211yescharacteristic
1153C2#1059425511yescharacteristic
1154C2D3×#88211yescharacteristic
1155C2#1059426611yescharacteristic
1156C2D3×#89311yescharacteristic
1157C2#1059462311yescharacteristic
1158C2#1059462711yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC32×#95C22
socle, cosocleC23×C32C24
prime radicalC2×#63923C2
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×#63904C2semidirect
4. C2×#63894C2semidirect
5. C2×#63880C2semidirect
6. #10592364C2semidirect
7. C3×#4668C2semidirect
8. C3×#4666C2semidirect
9. #10591399C2semidirect
10. #10591382C2semidirect
11. #10591377C2semidirect
12. Dic3×(C2×D3)⋊C4C2semidirect
13. #10591364C2semidirect
14. #10591290C2semidirect
15. #10591233C2semidirect
26. C22×#624C22semidirect
33. C2×#3752C22semidirect
34. C2×#3752C22semidirect
39. C2×C3×C4⋊Dic3C22semidirect
40. C2×C3×Dic3⋊C4C22semidirect
41. C2×C3×C4×Dic3C22semidirect
42. C2×C3×C4×Dic3C22semidirect
43. C2×Dic3⋊Dic3C22semidirect
46. C2×#3722C22semidirect
49. C2×Dic32C22semidirect
50. #63923C4semidirect
54. C32×#95C22semidirect
55. #63658C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
58. #63579C22semidirect
59. #63579C22semidirect
83. #4668D3semidirect
85. #4666D3semidirect
101. C22×D32C2×C4semidirect
109. C2×C4⋊(C3⋊D3)C2×C4semidirect
124. C2×C3×C4×D3D4semidirect
129. C2×#626C2×C4semidirect
130. C2×#626C2×C4semidirect
136. C2×#624D4semidirect
142. C2×D3×Dic3D4semidirect
149. C3×(C2×D3)⋊C4C2×C4semidirect
150. C3×(C2×D3)⋊C4C2×C4semidirect
158. #3722C2×C4semidirect
226. C2×C4⋊Dic3C2×D3semidirect
228. C2×Dic3⋊C4C2×D3semidirect
231. C2×C4×Dic3C2×D3semidirect
232. C2×C4×Dic3C2×D3semidirect
243. C3×#95C2×D3semidirect
244. C3×#95C2×D3semidirect
252. C3⋊#95C2×D3semidirect
253. C3⋊#95C2×D3semidirect
266. C22×C3⋊D3C22×C4semidirect
297. C2×C32×C4C22×C4semidirect
319. C2×C3×Dic3C22×C4semidirect
320. C2×C3×Dic3C22×C4semidirect
466. C2×C4×D3D12semidirect
496. (C2×D3)⋊C4C4×D3semidirect
497. (C2×D3)⋊C4C4×D3semidirect
526. C2×C3⋊D3C4×D4semidirect
539. C2×C3×D3C4×D4semidirect
540. C2×C3×D3C4×D4semidirect
552. C3×Dic3#120semidirect
594. #95D32semidirect
725. C2×C3×C4C2×C4×D3semidirect
726. C2×C3×C4C2×C4×D3semidirect
763. C2×Dic3C2×C4×D3semidirect
764. C2×Dic3C2×C4×D3semidirect
958. C2×D3C4×D12semidirect
959. C2×D3#893semidirect
986. Dic3#882semidirect
987. C32C4×#120semidirect
1065. C2×C4C4×D32semidirect
1146. C3C4×#882semidirect
1147. C3#74379semidirect

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×#639042
C2×#638942
C2×#638802
#105923642
C3×#46682
C3×#46662
#105913992
#105913822
#105913772
Dic3×(C2×D3)⋊C42
#105913642
#105912902
#105912332
#743793
C4×#8823