Finite Group Databasebeta

← C4×#63922 #11802013

Subgroups — C4×#63922 #11802013

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×C3×C4×D12C211yesmaximal, characteristic, complemented
3C2×#63922C211yesmaximal, characteristic
4C2×C4×#626C211yesmaximal, characteristic, complemented
5C2×C4×#625C211yesmaximal, characteristic, complemented
6C4×#3752C211yesmaximal, characteristic, complemented
7C3×C4×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
8#10591399C211yesmaximal, characteristic, complemented
9#10591378C211yesmaximal, characteristic, complemented
10#10591377C211yesmaximal, characteristic, complemented
11#10591376C211yesmaximal, characteristic, complemented
12#10591373C211yesmaximal, characteristic, complemented
13#10591363C211yesmaximal, characteristic, complemented
14C4×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
15#10591275C211yesmaximal, characteristic, complemented
16C4×#937—31nomaximal
17C4×#882—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×C42C2211yescharacteristic, complemented
33C2×#3752C2211yescharacteristic
34C2×#3752C2211yescharacteristic
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×C4⋊Dic3C2211yescharacteristic, complemented
41C2×C3×C4×Dic3C2211yescharacteristic, complemented
42C3×C4×D12—24no—
43C2×#3724C2211yescharacteristic, complemented
44C2×Dic3⋊Dic3C2211yescharacteristic, complemented
45C2×#3722C2211yescharacteristic
46C2×(C2×D3)⋊Dic3C2211yescharacteristic
47C2×(C2×D3)⋊Dic3C2211yescharacteristic
48C2×(C2×D3)⋊Dic3C2211yescharacteristic
49C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
50C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
51#63922C418yesdirect product factor
52C4×#626—24no—
53C4×#625—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×C4×#67—31no—
67C2×#882—31no—
68C2×C4×D12—31no—
69C2×C4×D12D311yescharacteristic, complemented
70C3×C4×C22⋊C4—31no—
71#5220—31no—
72C4×#217—31no—
73#4989—31no—
74#4989—31no—
75#4958—31no—
76#4956—31no—
77#4956—31no—
78#4955—31no—
79#4955—31no—
80#4950—31no—
81#4946—31no—
82C4×(C2×D3)⋊C4—31no—
83C4×(C2×D3)⋊C4—31no—
84C4×(C2×D3)⋊C4—31no—
85C4×(C2×D3)⋊C4—61no—
86C4×(C2×D3)⋊C4D311yescharacteristic, complemented
87#4668—31no—
88#4668—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⋊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×C3×C4×D3—22no—
126C2×C3×C4×D3D414yescomplemented
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×#624—22no—
137C2×D3×Dic3—22no—
138C2×D3×Dic3—22no—
139C2×D3×Dic3—22no—
140C2×D3×Dic3—22no—
141C2×D3×Dic3—22no—
142C2×D3×Dic3—22no—
143C4×D32—232no—
144C32×C42—22no—
145#3752—22no—
146#3752C2×C414yescomplemented
147C4×C3⋊Dic3—22no—
148C3×(C2×D3)⋊C4—22no—
149C3×(C2×D3)⋊C4—22no—
150C3×(C2×D3)⋊C4—22no—
151C3×(C2×D3)⋊C4C2×C414yescomplemented
152C3×C4⋊Dic3—22no—
153C3×C4×Dic3—22no—
154#3724—22no—
155Dic3⋊Dic3—22no—
156#3722—22no—
157(C2×D3)⋊Dic3—22no—
158(C2×D3)⋊Dic3—22no—
159(C2×D3)⋊Dic3—22no—
160(C2×D3)⋊Dic3—22no—
161(C2×D3)⋊Dic3C2×C414yescomplemented
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—31no—
194C2×C3×C22⋊C4—31no—
195C2×C3×C22⋊C4—31no—
196C2×C3×C22⋊C4—31no—
197C2×C3×C22⋊C4—31no—
198C2×C3×C42—21no—
199C2×C3×C42—31no—
200C2×C3×C42C2×D311yescharacteristic, complemented
201C2×C3×C42C2×D311yescharacteristic, complemented
202C2×#217—31no—
203C2×#217—31no—
204C2×#217—31no—
205C2×#217—31no—
206C2×#217—31no—
207#937—38no—
208C4×#67—64no—
209C4×#67—64no—
210C4×#67—64no—
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—31no—
222C2×(C2×D3)⋊C4—61no—
223C2×(C2×D3)⋊C4—61no—
224C2×(C2×D3)⋊C4C2×D311yescharacteristic
225C2×(C2×D3)⋊C4C2×D311yescharacteristic
226C2×(C2×D3)⋊C4C2×D311yescharacteristic
227C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
228C2×C4⋊Dic3—31no—
229C2×C4⋊Dic3C2×D311yescharacteristic, complemented
230C2×Dic3⋊C4—31no—
231C2×Dic3⋊C4—31no—
232C2×Dic3⋊C4—31no—
233C2×C4×Dic3—31no—
234C2×C4×Dic3—31no—
235C2×C4×Dic3—61no—
236C2×C4×Dic3C2×D311yescharacteristic, complemented
237#882—38no—
238C4×D12—24no—
239C4×D12—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×C4C22×C412yescomplemented
296C2×C32×C4C2×D412yes—
297C2×C32×C4C2×D412yes—
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×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—
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—91no—
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—
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—34no—
382C22×C3×C4—31no—
383C22×C3×C4—31no—
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—31no—
411C22×Dic3—31no—
412C22×Dic3—61no—
413C22×Dic3—61no—
414C22×Dic3—61no—
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—22no—
439C2×C4×D3—34no—
440C2×C4×D3—34no—
441C2×C4×D3—64no—
442C2×C4×D3—632no—
443C2×C4×D3—632no—
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—122no—
461C2×C4×D3—122no—
462C2×C4×D3D1214yescomplemented
463C2×C4×D3#6714yescomplemented
464C3×C4⋊C4—62no—
465C3×C22⋊C4—34no—
466C3×C22⋊C4—62no—
467C3×C22⋊C4—62no—
468C3×C22⋊C4—62no—
469C3×C42—22no—
470C3×C42—22no—
471C3×C42—42no—
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—64no—
491(C2×D3)⋊C4—62no—
492(C2×D3)⋊C4—62no—
493(C2×D3)⋊C4—62no—
494(C2×D3)⋊C4C4×D314yescomplemented
495C4⋊Dic3—22no—
496C4⋊Dic3—62no—
497Dic3⋊C4—62no—
498Dic3⋊C4—62no—
499Dic3⋊C4—62no—
500C4×Dic3—22no—
501C4×Dic3—62no—
502C4×Dic3—62no—
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—41no—
542C32×C4#12014yescomplemented
543C3⋊Dic3—22no—
544C3⋊Dic3—22no—
545C3⋊Dic3—41no—
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—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⋊C4—91no—
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×C42D3211yescharacteristic, complemented
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×D3C2×D1212yes—
670C22×D3#23512yes—
671C22×D3#23512yes—
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—22no—
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—22no—
686C2×C3×C4—22no—
687C2×C3×C4—22no—
688C2×C3×C4—22no—
689C2×C3×C4—32no—
690C2×C3×C4—32no—
691C2×C3×C4—32no—
692C2×C3×C4—41no—
693C2×C3×C4—41no—
694C2×C3×C4—41no—
695C2×C3×C4—41no—
696C2×C3×C4—61no—
697C2×C3×C4—61no—
698C2×C3×C4—61no—
699C2×C3×C4—61no—
700C2×C3×C4—61no—
701C2×C3×C4—61no—
702C2×C3×C4—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—124no—
711C2×C3×C4C2×C4×D312yescomplemented
712C2×C3×C4C2×C4×D312yescomplemented
713C2×C3×C4C2×D1212yes—
714C2×C3×C4D3×D412yes—
715C2×C3×C4D3×D412yes—
716C2×C3×C4D3×D412yes—
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—21no—
733C2×Dic3—21no—
734C2×Dic3—32no—
735C2×Dic3—32no—
736C2×Dic3—32no—
737C2×Dic3—32no—
738C2×Dic3—62no—
739C2×Dic3—62no—
740C2×Dic3—68no—
741C2×Dic3—68no—
742C2×Dic3—61no—
743C2×Dic3—61no—
744C2×Dic3—61no—
745C2×Dic3—61no—
746C2×Dic3—61no—
747C2×Dic3—61no—
748C2×Dic3—61no—
749C2×Dic3—61no—
750C2×Dic3—62no—
751C2×Dic3—61no—
752C2×Dic3—61no—
753C2×Dic3—61no—
754C2×Dic3—61no—
755C2×Dic3—61no—
756C2×Dic3—61no—
757C2×Dic3—121no—
758C2×Dic3—121no—
759C2×Dic3—121no—
760C2×Dic3—121no—
761C2×Dic3—121no—
762C2×Dic3—121no—
763C2×Dic3C2×C4×D312yescomplemented
764C2×Dic3C2×D1212yes—
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—34no—
814C22×C4—31no—
815C22×C4—31no—
816C22×C4—62no—
817C22×C4—62no—
818C22×C4—62no—
819C22×C4—62no—
820C22×C4—62no—
821C22×C4—62no—
822C22×C4—62no—
823C22×C4—91no—
824C22×C4—91no—
825C22×C4—94no—
826C22×C4—91no—
827C22×C4—182no—
828C22×C4—182no—
829C22×C4—182no—
830C22×C4—182no—
831C22×C4—182no—
832C22×C4—1832no—
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—182no—
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—22no—
858C42—62no—
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×C3C22×D1211yescharacteristic
891C22×C3C2×#23511yescharacteristic
892C22×C3C2×#23511yescharacteristic
893C22×C3C2×D3×D411yescharacteristic
894C22×C3C2×D3×D411yescharacteristic
895C22×C3C2×D3×D411yescharacteristic
896C22×C3C2×D3×D411yescharacteristic
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×D3C4×D1214yescomplemented
945C2×D3C4×#6714yescomplemented
946C3×C4—22no—
947C3×C4—22no—
948C3×C4—24no—
949C3×C4—42no—
950C3×C4—42no—
951C3×C4—41no—
952C3×C4—41no—
953C3×C4—62no—
954C3×C4—62no—
955C3×C4—62no—
956C3×C4—121no—
957C3×C4—121no—
958C3×C4#88214yescomplemented
959C3×C4#93714yescomplemented
960Dic3—22no—
961Dic3—22no—
962Dic3—22no—
963Dic3—41no—
964Dic3—41no—
965Dic3—62no—
966Dic3—62no—
967Dic3—62no—
968Dic3—62no—
969Dic3—122no—
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—32no—
1020C2×C4—32no—
1021C2×C4—32no—
1022C2×C4—61no—
1023C2×C4—61no—
1024C2×C4—61no—
1025C2×C4—61no—
1026C2×C4—61no—
1027C2×C4—61no—
1028C2×C4—68no—
1029C2×C4—68no—
1030C2×C4—61no—
1031C2×C4—61no—
1032C2×C4—61no—
1033C2×C4—61no—
1034C2×C4—61no—
1035C2×C4—61no—
1036C2×C4—92no—
1037C2×C4—92no—
1038C2×C4—124no—
1039C2×C4—188no—
1040C2×C4—188no—
1041C2×C4—188no—
1042C2×C4—181no—
1043C2×C4—181no—
1044C2×C4—181no—
1045C2×C4—181no—
1046C2×C4—188no—
1047C2×C4—181no—
1048C2×C4—181no—
1049C2×C4—181no—
1050C2×C4C4×D3212yescomplemented
1051C2×C4D3×D1212yes—
1052C2×C4#380212yes—
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×C4×D1211yescharacteristic
1065C2×C3C2×#88211yescharacteristic
1066C2×C3#552411yescharacteristic
1067C2×C3C4×D3×D411yescharacteristic
1068C2×C3C4×D3×D411yescharacteristic
1069C2×C3C4×D3×D411yescharacteristic
1070C2×C3C4×D3×D411yescharacteristic
1071C2×C3#554711yescharacteristic
1072C2×C3#554711yescharacteristic
1073C2×C3#554711yescharacteristic
1074C2×C3#554711yescharacteristic
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
1114C22C2×D3×D1211yescharacteristic
1115C22C2×#380211yescharacteristic
1116C22D3×#23511yescharacteristic
1117C22D3×#23511yescharacteristic
1118C22#6430611yescharacteristic
1119C22C2×D3×#6711yescharacteristic
1120C4—22no—
1121C4—41no—
1122C4—62no—
1123C4—62no—
1124C4—62no—
1125C4—121no—
1126C4—121no—
1127C4—182no—
1128C4—182no—
1129C4—361no—
1130C4#6392214yesdirect product factor
1131C3—21no—
1132C3C4×#88211yescharacteristic, complemented
1133C3C4×#93711yescharacteristic, complemented
1134C2—64no—
1135C2—64no—
1136C2—122no—
1137C2—184no—
1138C2C4×D3×D1211yescharacteristic
1139C2C4×#380211yescharacteristic
1140C2#1059399711yescharacteristic
1141C2#1059400611yescharacteristic
1142C2C4×D3×#6711yescharacteristic
1143C2C2×#6392211yescharacteristic
1144C2#1059506011yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutatorC22×C32C23×C4
FrattiniC23C22×D32
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#63922C2
hypercenterC2×C42D32
hypocenterC32C4×#120
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C22×C4×D32C2semidirect
2. C2×C3×C4×D12C2semidirect
4. C2×C4×#626C2semidirect
5. C2×C4×#625C2semidirect
6. C4×#3752C2semidirect
7. C3×C4×(C2×D3)⋊C4C2semidirect
8. #10591399C2semidirect
9. #10591378C2semidirect
10. #10591377C2semidirect
11. #10591376C2semidirect
12. #10591373C2semidirect
13. #10591363C2semidirect
14. C4×(C2×D3)⋊Dic3C2semidirect
15. #10591275C2semidirect
23. C22×C3×C4×D3C22semidirect
32. C2×C32×C42C22semidirect
35. C2×C4×C3⋊Dic3C22semidirect
39. C2×C3×(C2×D3)⋊C4C22semidirect
40. C2×C3×C4⋊Dic3C22semidirect
41. C2×C3×C4×Dic3C22semidirect
43. C2×#3724C22semidirect
44. C2×Dic3⋊Dic3C22semidirect
49. C2×(C2×D3)⋊Dic3C22semidirect
50. C2×(C2×D3)⋊Dic3C22semidirect
51. #63922C4direct (N × H)
54. #63658C22semidirect
55. #63658C22semidirect
56. C3×C3⋊#95C22semidirect
57. C3×C3⋊#95C22semidirect
58. #63579C22semidirect
59. #63579C22semidirect
69. C2×C4×D12D3semidirect
86. C4×(C2×D3)⋊C4D3semidirect
101. C22×D32C2×C4semidirect
110. C2×C4×C3⋊D3D4semidirect
118. C2×C3×D12C2×C4semidirect
126. C2×C3×C4×D3D4semidirect
127. C2×C3×C4×D3D4semidirect
130. C2×#626C2×C4semidirect
133. C2×#625C2×C4semidirect
146. #3752C2×C4semidirect
151. C3×(C2×D3)⋊C4C2×C4semidirect
161. (C2×D3)⋊Dic3C2×C4semidirect
191. C22×C4×D3C2×D3semidirect
200. C2×C3×C42C2×D3semidirect
201. C2×C3×C42C2×D3semidirect
227. C2×(C2×D3)⋊C4C2×D3semidirect
229. C2×C4⋊Dic3C2×D3semidirect
236. C2×C4×Dic3C2×D3semidirect
252. C3⋊#95C2×D3semidirect
253. C3⋊#95C2×D3semidirect
278. C22×C3×D3C22×C4semidirect
295. C2×C32×C4C22×C4semidirect
306. C2×C3⋊Dic3C22×C4semidirect
321. C2×C3×Dic3C22×C4semidirect
431. C2×D12C4×D3semidirect
462. C2×C4×D3D12semidirect
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
542. C32×C4#120semidirect
586. C2×C42D32semidirect
668. C22×D3C2×C4×D3semidirect
711. C2×C3×C4C2×C4×D3semidirect
712. C2×C3×C4C2×C4×D3semidirect
763. C2×Dic3C2×C4×D3semidirect
944. C2×D3C4×D12semidirect
945. C2×D3C4×#67semidirect
958. C3×C4#882semidirect
959. C3×C4#937semidirect
974. C32C4×#120semidirect
1050. C2×C4C4×D32semidirect
1130. C4#63922direct (N × H)
1132. C3C4×#882semidirect
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×C4×D122
C2×#639222
C2×C4×#6262
C2×C4×#6252
C4×#37522
C3×C4×(C2×D3)⋊C42
#105913992
#105913782
#105913772
#105913762
#105913732
#105913632
C4×(C2×D3)⋊Dic32
#105912752
C4×#9373
C4×#8823