Finite Group Databasebeta

← C2×#10595060 #11900454

Subgroups — C2×#10595060 #11900454

Order 1152.

3973 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×#235C211yesmaximal, characteristic, complemented
2C22×C4×D32C211yesmaximal, characteristic, complemented
3C2×C4×#638C211yesmaximal, characteristic, complemented
4C2×C3×C4×#67C211yesmaximal, characteristic, complemented
5C2×#63983C211yesmaximal, characteristic, complemented
6C2×#63970C211yesmaximal, characteristic, complemented
7C2×#63969C211yesmaximal, characteristic, complemented
8C2×#63958C211yesmaximal, characteristic, complemented
9#10595060C2116yesmaximal, direct product factor
10C2×#63922C211yesmaximal, characteristic, complemented
11C2×C4×#626C211yesmaximal, characteristic, complemented
12C2×C4×#625C211yesmaximal, characteristic, complemented
13C2×#63888C211yesmaximal, characteristic, complemented
14C2×#63887C211yesmaximal, characteristic, complemented
15C2×#63884C211yesmaximal, characteristic, complemented
16C2×#63855C211yesmaximal, characteristic, complemented
17C2×#5828—31nomaximal
18C2×#5547—31nomaximal
19C23×D32C2211yescharacteristic
20C23×C32×C4C2211yescharacteristic, complemented
21C22×#638C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic, complemented
26C2×C3×#235—28no—
27C2×C3×#235C2218yescomplemented
28C22×C3×D12C2211yescharacteristic
29C22×C3×C4×D3C2211yescharacteristic
30C22×C3×C4×D3C2211yescharacteristic
31C22×C3×C4×D3C2211yescharacteristic, complemented
32C22×C3×Dic6C2211yescharacteristic, complemented
33C22×#626C2211yescharacteristic
34C22×#625C2211yescharacteristic
35C22×#624C2211yescharacteristic
36C22×D3×Dic3C2211yescharacteristic
37C22×D3×Dic3C2211yescharacteristic
38C2×C4×D32—28no—
39C2×C4×D32C2218yescomplemented
40C2×#3757C2211yescharacteristic, complemented
41C4×#638C2218yescomplemented
42C2×#3752C2211yescharacteristic
43C2×#3750C2211yescharacteristic, complemented
44C2×C4×C3⋊Dic3C2211yescharacteristic, complemented
45C2×C3×#217C2211yescharacteristic, complemented
46C3×C4×#67C2218yescomplemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×C4×Dic3C2211yescharacteristic, complemented
50#63983C2218yescomplemented
51#63970C2218yescomplemented
52#63969C2218yescomplemented
53C2×#3724C2211yescharacteristic, complemented
54C2×Dic3⋊Dic3C2211yescharacteristic, complemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63958C2218yescomplemented
64#63922C2218yescomplemented
65C4×#626C2218yescomplemented
66C4×#625C2218yescomplemented
67#63888C2218yescomplemented
68#63887C2218yescomplemented
69#63884C2218yescomplemented
70#63855C2218yescomplemented
71C22×C3×#41—31no—
72C22×#235D311yescharacteristic, complemented
73C23×C4×D3—31no—
74C23×C4×D3—31no—
75C2×C3×C4×D4—31no—
76#5828—316no—
77C2×#946—31no—
78C2×#946—31no—
79C2×#939—31no—
80C2×#938—31no—
81C2×#938—31no—
82C2×#937—31no—
83C2×#937—31no—
84C2×#937—31no—
85C2×#935—31no—
86C2×#935—31no—
87C2×C4×#67—31no—
88C2×C4×#67—31no—
89C2×C4×#67—31no—
90C2×C4×#67—31no—
91C2×C4×#67—31no—
92C2×C4×#67—61no—
93C2×C4×#67D311yescharacteristic, complemented
94C2×#926—31no—
95#5547—316no—
96C2×#896—31no—
97C2×#894—31no—
98C2×#884—31no—
99C2×#883—31no—
100C2×#882—31no—
101C2×#878—31no—
102C2×C4×D12—31no—
103C2×#872—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C22×D32—24no—
110C22×D32—24no—
111C22×D32—24no—
112C22×D32C2314yes—
113C22×C32×C4—24no—
114C22×C32×C4C2311yescharacteristic
115C22×C32×C4C2311yescharacteristic
116C22×C32×C4C2314yescomplemented
117C2×#638—24no—
118C2×#638C2314yes—
119C22×C3⋊Dic3C2311yescharacteristic
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C2×C4×C3⋊D3—24no—
123C2×C4×C3⋊D3C2314yes—
124C2×C3×#67—24no—
125C2×C3×#67—24no—
126C2×C3×#67—24no—
127C2×C3×#67C2314yes—
128C2×C3×#67C2314yes—
129C2×C3×#67C2314yescomplemented
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C3×#235—232no—
136C2×C3×D12—24no—
137C2×C3×D12C2314yes—
138C2×C3×C4×D3—24no—
139C2×C3×C4×D3—24no—
140C2×C3×C4×D3D418yescomplemented
141C2×C3×C4×D3C2314yes—
142C2×C3×C4×D3C2314yes—
143C2×C3×C4×D3C2314yescomplemented
144C2×C3×Dic6—24no—
145C2×C3×Dic6C2314yescomplemented
146C2×#626—24no—
147C2×#626C2314yes—
148C2×#625—24no—
149C2×#625C2314yes—
150C2×#624—24no—
151C2×#624C2314yes—
152C2×D3×Dic3—24no—
153C2×D3×Dic3—24no—
154C2×D3×Dic3C2314yes—
155C2×D3×Dic3C2314yes—
156C4×D32—232no—
157#3757C2314yescomplemented
158#3752C2314yes—
159#3750C2314yescomplemented
160C4×C3⋊Dic3C2314yescomplemented
161C3×#217C2314yescomplemented
162C3×(C2×D3)⋊C4C2314yes—
163C3×Dic3⋊C4C2314yescomplemented
164C3×C4×Dic3C2314yescomplemented
165#3724C2314yescomplemented
166Dic3⋊Dic3C2314yescomplemented
167Dic3⋊Dic3C2314yescomplemented
168Dic3⋊Dic3C2314yescomplemented
169#3722C2314yes—
170(C2×D3)⋊Dic3C2314yes—
171(C2×D3)⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175C2×#525—91noSylow
176C24×D3—31no—
177C24×D3—31no—
178C2×C3×#41—38no—
179C2×C3×#41—68no—
180C22×C3×Q8—31no—
181C22×C3×D4—31no—
182C22×C3×D4—31no—
183C22×C3×D4—31no—
184C22×C3×D4—31no—
185C23×C3×C4—21no—
186C23×C3×C4—31no—
187C23×C3×C4—31no—
188C23×C3×C4—31no—
189C23×C3×C4C2×D311yescharacteristic, complemented
190C23×C3×C4C2×D311yescharacteristic, complemented
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—61no—
197C22×#67C2×D311yescharacteristic
198C22×#67C2×D311yescharacteristic
199C22×#67C2×D311yescharacteristic, complemented
200C23×Dic3—31no—
201C23×Dic3—31no—
202C2×#235—28no—
203C2×#235C2×D318yescomplemented
204C22×D12—31no—
205C22×D12C2×D311yescharacteristic
206C22×C4×D3—31no—
207C22×C4×D3—31no—
208C22×C4×D3—31no—
209C22×C4×D3—31no—
210C22×C4×D3—31no—
211C22×C4×D3—31no—
212C22×C4×D3—38no—
213C22×C4×D3—38no—
214C22×C4×D3—61no—
215C22×C4×D3—68no—
216C22×C4×D3—68no—
217C22×C4×D3C2×D311yescharacteristic
218C22×C4×D3C2×D311yescharacteristic
219C22×C4×D3C2×D311yescharacteristic, complemented
220C22×Dic6C2×D311yescharacteristic, complemented
221C3×C4×D4—38no—
222C2×C3×C4⋊C4—31no—
223C2×C3×C22⋊C4—31no—
224C2×C3×C22⋊C4—31no—
225C2×C3×C42—31no—
226C2×#217—31no—
227C2×#217—31no—
228C2×#217—31no—
229C2×#217—31no—
230C2×#217—31no—
231C2×#217—31no—
232C2×#217—31no—
233C2×#217—61no—
234C2×#217C2×D311yescharacteristic, complemented
235#946—38no—
236#946—38no—
237#939—38no—
238#938—38no—
239#938—38no—
240#937—38no—
241#937—38no—
242#937—38no—
243#935—38no—
244#935—38no—
245C4×#67—38no—
246C4×#67—38no—
247C4×#67—38no—
248C4×#67—38no—
249C4×#67—38no—
250C4×#67—68no—
251C4×#67C2×D318yescomplemented
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—31no—
256C2×(C2×D3)⋊C4—31no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—61no—
262C2×(C2×D3)⋊C4C2×D311yescharacteristic
263#926—38no—
264C2×C4⋊Dic3—31no—
265C2×C4⋊Dic3—31no—
266C2×C4⋊Dic3—31no—
267C2×Dic3⋊C4—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—31no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4—31no—
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—61no—
275C2×Dic3⋊C4C2×D311yescharacteristic, complemented
276C2×C4×Dic3—31no—
277C2×C4×Dic3—31no—
278C2×C4×Dic3—61no—
279C2×C4×Dic3C2×D311yescharacteristic, complemented
280#896—38no—
281#894—38no—
282#884—38no—
283#883—38no—
284#882—38no—
285#878—38no—
286C4×D12—38no—
287#872—38no—
288C23×C32—22no—
289C23×C32—22no—
290C23×C32—22no—
291C23×C32C2412yes—
292C23×C32C2411yescharacteristic
293C22×C3⋊D3—22no—
294C22×C3⋊D3—22no—
295C22×C3⋊D3#4114yescomplemented
296C22×C3⋊D3C2412yes—
297C22×C3×D3—22no—
298C22×C3×D3—22no—
299C22×C3×D3—22no—
300C22×C3×D3—22no—
301C22×C3×D3—22no—
302C22×C3×D3—22no—
303C22×C3×D3—22no—
304C22×C3×D3C2×D414yes—
305C22×C3×D3#4114yescomplemented
306C22×C3×D3C2412yes—
307C22×C3×D3C2412yes—
308C22×C3×D3C2412yes—
309C2×D32—232no—
310C2×D32—28no—
311C2×D32—28no—
312C2×D32—28no—
313C2×C32×C4—22no—
314C2×C32×C4—28no—
315C2×C32×C4C2×D414yes—
316C2×C32×C4C2412yes—
317C2×C32×C4C2412yes—
318#638—28no—
319C2×C3⋊Dic3—22no—
320C2×C3⋊Dic3—22no—
321C2×C3⋊Dic3—22no—
322C2×C3⋊Dic3C2412yes—
323C2×C3⋊Dic3C2412yes—
324C2×C3⋊Dic3C2412yes—
325C4×C3⋊D3—28no—
326C3×#67—28no—
327C3×#67—28no—
328C3×#67—28no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3—22no—
331C2×C3×Dic3—22no—
332C2×C3×Dic3—22no—
333C2×C3×Dic3C2×D414yes—
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C2×C3×Dic3C2412yes—
337C2×C3×Dic3C2412yes—
338C2×C3×Dic3C2412yes—
339C3×D12—28no—
340C3×C4×D3—28no—
341C3×C4×D3—28no—
342C3×C4×D3C2×D4116yescomplemented
343C3×Dic6—28no—
344#626—28no—
345#625—28no—
346#624—28no—
347D3×Dic3—28no—
348D3×Dic3—28no—
349C22×#41—31no—
350C24×C4—91no—
351#525—916no—
352C2×#123—91no—
353C2×#123—91no—
354C2×C22⋊Q8—91no—
355C2×C22⋊Q8—91no—
356C2×#121—91no—
357C2×#121—91no—
358C2×#120—91no—
359C2×#120—91no—
360C2×C4×D4—31no—
361C2×C4×D4—91no—
362C2×C4×D4—91no—
363C2×C4×D4—91no—
364C2×#117—91no—
365C24×C3—21no—
366C24×C3—31no—
367C24×C3—31no—
368C24×C3—31no—
369C24×C3C22×D311yescharacteristic
370C24×C3C22×D311yescharacteristic
371C23×D3—31no—
372C23×D3—31no—
373C23×D3—34no—
374C23×D3—34no—
375C23×D3—61no—
376C23×D3—64no—
377C23×D3—64no—
378C23×D3—64no—
379C23×D3—64no—
380C23×D3—64no—
381C23×D3—64no—
382C23×D3C22×D311yescharacteristic
383C23×D3C22×D311yescharacteristic
384C23×D3C22×D311yescharacteristic
385C3×#41—632no—
386C2×C3×Q8—34no—
387C2×C3×Q8—64no—
388C2×C3×D4—34no—
389C2×C3×D4—34no—
390C2×C3×D4—34no—
391C2×C3×D4—34no—
392C2×C3×D4—64no—
393C2×C3×D4—64no—
394C2×C3×D4—64no—
395C2×C3×D4—64no—
396C22×C3×C4—24no—
397C22×C3×C4—24no—
398C22×C3×C4—21no—
399C22×C3×C4—21no—
400C22×C3×C4—24no—
401C22×C3×C4—31no—
402C22×C3×C4—38no—
403C22×C3×C4—34no—
404C22×C3×C4—31no—
405C22×C3×C4—31no—
406C22×C3×C4—31no—
407C22×C3×C4—31no—
408C22×C3×C4—34no—
409C22×C3×C4—34no—
410C22×C3×C4—44no—
411C22×C3×C4—64no—
412C22×C3×C4—64no—
413C22×C3×C4C22×D311yescharacteristic
414C22×C3×C4C22×D311yescharacteristic
415C22×C3×C4C22×D311yescharacteristic
416C22×C3×C4C22×D311yescharacteristic
417C22×C3×C4C22×D314yescomplemented
418C22×C3×C4C22×D314yescomplemented
419C2×#67—24no—
420C2×#67—24no—
421C2×#67—24no—
422C2×#67—34no—
423C2×#67—34no—
424C2×#67—34no—
425C2×#67—34no—
426C2×#67—34no—
427C2×#67—64no—
428C2×#67—64no—
429C2×#67—64no—
430C2×#67—64no—
431C2×#67—64no—
432C2×#67—68no—
433C2×#67—64no—
434C2×#67C22×D314yes—
435C2×#67C22×D314yes—
436C2×#67C22×D314yescomplemented
437C22×Dic3—31no—
438C22×Dic3—31no—
439C22×Dic3—31no—
440C22×Dic3—31no—
441C22×Dic3—31no—
442C22×Dic3—31no—
443C22×Dic3—34no—
444C22×Dic3—34no—
445C22×Dic3—61no—
446C22×Dic3—61no—
447C22×Dic3—61no—
448C22×Dic3—64no—
449C22×Dic3—64no—
450C22×Dic3C22×D311yescharacteristic
451C22×Dic3C22×D311yescharacteristic
452C22×Dic3C22×D311yescharacteristic
453C22×Dic3C22×D311yescharacteristic
454C22×Dic3C22×D311yescharacteristic
455#235—232no—
456C2×D12—24no—
457C2×D12—34no—
458C2×D12—64no—
459C2×D12C22×D314yes—
460C2×C4×D3—24no—
461C2×C4×D3—24no—
462C2×C4×D3—34no—
463C2×C4×D3—34no—
464C2×C4×D3—34no—
465C2×C4×D3—34no—
466C2×C4×D3—34no—
467C2×C4×D3—34no—
468C2×C4×D3—64no—
469C2×C4×D3—632no—
470C2×C4×D3—64no—
471C2×C4×D3—64no—
472C2×C4×D3—64no—
473C2×C4×D3—64no—
474C2×C4×D3—64no—
475C2×C4×D3—64no—
476C2×C4×D3—632no—
477C2×C4×D3—124no—
478C2×C4×D3#6718yescomplemented
479C2×C4×D3C22×D314yes—
480C2×C4×D3C22×D314yes—
481C2×C4×D3C22×D314yescomplemented
482C2×Dic6—24no—
483C2×Dic6C22×D314yescomplemented
484C3×C4⋊C4—34no—
485C3×C22⋊C4—34no—
486C3×C22⋊C4—34no—
487C3×C42—34no—
488#217—34no—
489#217—34no—
490#217—34no—
491#217—34no—
492#217—34no—
493#217—34no—
494#217—34no—
495#217—64no—
496#217C22×D314yescomplemented
497(C2×D3)⋊C4—34no—
498(C2×D3)⋊C4—34no—
499(C2×D3)⋊C4—34no—
500(C2×D3)⋊C4—34no—
501(C2×D3)⋊C4—34no—
502(C2×D3)⋊C4—34no—
503(C2×D3)⋊C4—34no—
504(C2×D3)⋊C4—34no—
505(C2×D3)⋊C4—34no—
506(C2×D3)⋊C4—64no—
507(C2×D3)⋊C4C22×D314yes—
508C4⋊Dic3—34no—
509C4⋊Dic3—34no—
510C4⋊Dic3—34no—
511Dic3⋊C4—34no—
512Dic3⋊C4—34no—
513Dic3⋊C4—34no—
514Dic3⋊C4—34no—
515Dic3⋊C4—34no—
516Dic3⋊C4—34no—
517Dic3⋊C4—34no—
518Dic3⋊C4—64no—
519Dic3⋊C4C22×D314yescomplemented
520C4×Dic3—34no—
521C4×Dic3—34no—
522C4×Dic3—64no—
523C4×Dic3C22×D314yescomplemented
524C22×C32—22no—
525C22×C32—22no—
526C22×C32—22no—
527C22×C32—44no—
528C22×C32C22×D412yes—
529C22×C32C2×#4112yes—
530C22×C32C2×#4112yes—
531C22×C32C2511yescharacteristic
532C2×C3⋊D3—28no—
533C2×C3⋊D3—22no—
534C2×C3⋊D3—22no—
535C2×C3⋊D3C2×#4114yescomplemented
536C2×C3×D3—28no—
537C2×C3×D3—28no—
538C2×C3×D3—22no—
539C2×C3×D3—22no—
540C2×C3×D3—22no—
541C2×C3×D3—22no—
542C2×C3×D3—22no—
543C2×C3×D3—22no—
544C2×C3×D3—22no—
545C2×C3×D3—44no—
546C2×C3×D3C22×D414yes—
547C2×C3×D3C2×#4114yescomplemented
548D32—232no—
549C32×C4—22no—
550C32×C4C22×D414yes—
551C3⋊Dic3—22no—
552C3⋊Dic3—22no—
553C3⋊Dic3—22no—
554C3×Dic3—22no—
555C3×Dic3—22no—
556C3×Dic3—22no—
557C3×Dic3—22no—
558C3×Dic3C22×D414yes—
559C25—91no—
560C2×#41—38no—
561C2×#41—68no—
562C22×Q8—31no—
563C22×D4—31no—
564C22×D4—31no—
565C22×D4—31no—
566C22×D4—31no—
567C22×D4—91no—
568C22×D4—91no—
569C22×D4—91no—
570C23×C4—31no—
571C23×C4—31no—
572C23×C4—31no—
573C23×C4—91no—
574C23×C4—98no—
575C23×C4—91no—
576C23×C4—91no—
577C23×C4—91no—
578C23×C4—188no—
579C23×C4D3211yescharacteristic, complemented
580#123—98no—
581#123—98no—
582C22⋊Q8—98no—
583C22⋊Q8—98no—
584#121—98no—
585#121—98no—
586#120—98no—
587#120—98no—
588C4×D4—38no—
589C4×D4—98no—
590C4×D4—98no—
591C4×D4—98no—
592#117—98no—
593C2×C4⋊C4—31no—
594C2×C4⋊C4—91no—
595C2×C4⋊C4—91no—
596C2×C4⋊C4—91no—
597C2×C4⋊C4—91no—
598C2×C4⋊C4—91no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—91no—
602C2×C22⋊C4—91no—
603C2×C22⋊C4—91no—
604C2×C22⋊C4—91no—
605C2×C22⋊C4—91no—
606C2×C22⋊C4—91no—
607C2×C22⋊C4—91no—
608C2×C22⋊C4—91no—
609C2×C42—31no—
610C2×C42—91no—
611C23×C3—24no—
612C23×C3—22no—
613C23×C3—22no—
614C23×C3—22no—
615C23×C3—22no—
616C23×C3—22no—
617C23×C3—22no—
618C23×C3—21no—
619C23×C3—22no—
620C23×C3—34no—
621C23×C3—34no—
622C23×C3—32no—
623C23×C3—32no—
624C23×C3—32no—
625C23×C3—42no—
626C23×C3—42no—
627C23×C3—62no—
628C23×C3—62no—
629C23×C3—62no—
630C23×C3—62no—
631C23×C3—62no—
632C23×C3—62no—
633C23×C3—62no—
634C23×C3C23×D312yes—
635C23×C3C23×D312yes—
636C23×C3C23×D311yescharacteristic
637C23×C3C23×D311yescharacteristic
638C22×D3—22no—
639C22×D3—22no—
640C22×D3—22no—
641C22×D3—22no—
642C22×D3—22no—
643C22×D3—22no—
644C22×D3—22no—
645C22×D3—34no—
646C22×D3—34no—
647C22×D3—32no—
648C22×D3—32no—
649C22×D3—64no—
650C22×D3—62no—
651C22×D3—68no—
652C22×D3—68no—
653C22×D3—68no—
654C22×D3—68no—
655C22×D3—632no—
656C22×D3—632no—
657C22×D3—62no—
658C22×D3—62no—
659C22×D3—62no—
660C22×D3—62no—
661C22×D3—68no—
662C22×D3—68no—
663C22×D3—122no—
664C22×D3—122no—
665C22×D3#23514yescomplemented
666C22×D3C2×#6714yes—
667C22×D3C23×D312yes—
668C22×D3C23×D312yes—
669C22×D3C23×D312yes—
670C3×Q8—68no—
671C3×D4—68no—
672C3×D4—68no—
673C3×D4—68no—
674C3×D4—68no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—28no—
678C2×C3×C4—28no—
679C2×C3×C4—22no—
680C2×C3×C4—22no—
681C2×C3×C4—24no—
682C2×C3×C4—34no—
683C2×C3×C4—32no—
684C2×C3×C4—316no—
685C2×C3×C4—32no—
686C2×C3×C4—32no—
687C2×C3×C4—32no—
688C2×C3×C4—32no—
689C2×C3×C4—48no—
690C2×C3×C4—42no—
691C2×C3×C4—62no—
692C2×C3×C4—62no—
693C2×C3×C4—62no—
694C2×C3×C4—62no—
695C2×C3×C4—68no—
696C2×C3×C4—68no—
697C2×C3×C4D3×D414yes—
698C2×C3×C4C2×#6714yes—
699C2×C3×C4C23×D312yes—
700C2×C3×C4C23×D312yes—
701C2×C3×C4C23×D312yes—
702C2×C3×C4C23×D312yes—
703#67—28no—
704#67—28no—
705#67—28no—
706#67—68no—
707#67—68no—
708#67—68no—
709#67—68no—
710#67—616no—
711#67—68no—
712C2×Dic3—22no—
713C2×Dic3—22no—
714C2×Dic3—22no—
715C2×Dic3—22no—
716C2×Dic3—32no—
717C2×Dic3—32no—
718C2×Dic3—32no—
719C2×Dic3—32no—
720C2×Dic3—32no—
721C2×Dic3—32no—
722C2×Dic3—62no—
723C2×Dic3—62no—
724C2×Dic3—62no—
725C2×Dic3—68no—
726C2×Dic3—64no—
727C2×Dic3—62no—
728C2×Dic3—62no—
729C2×Dic3—62no—
730C2×Dic3—62no—
731C2×Dic3—62no—
732C2×Dic3—62no—
733C2×Dic3—68no—
734C2×Dic3—122no—
735C2×Dic3—122no—
736C2×Dic3C2×#6714yes—
737C2×Dic3C23×D312yes—
738C2×Dic3C23×D312yes—
739C2×Dic3C23×D312yes—
740C2×Dic3C23×D312yes—
741C2×Dic3C23×D312yes—
742D12—28no—
743D12—68no—
744C4×D3—28no—
745C4×D3—28no—
746C4×D3—68no—
747C4×D3—68no—
748C4×D3—68no—
749C4×D3—68no—
750C4×D3—68no—
751C4×D3—68no—
752C4×D3—128no—
753C4×D3C2×#67116yescomplemented
754Dic6—28no—
755C2×C32—42no—
756C2×C32#52514yescomplemented
757C2×C32C23×D411yescharacteristic
758C2×C32C22×#4111yescharacteristic
759C2×C32C22×#4111yescharacteristic
760C3⋊D3—24no—
761C3×D3—24no—
762C3×D3—24no—
763C3×D3—42no—
764C24—31no—
765C24—31no—
766C24—31no—
767C24—94no—
768C24—91no—
769C24—184no—
770C24—184no—
771C24—184no—
772C24C2×D3211yescharacteristic
773#41—632no—
774C2×Q8—34no—
775C2×Q8—64no—
776C2×D4—34no—
777C2×D4—34no—
778C2×D4—34no—
779C2×D4—34no—
780C2×D4—64no—
781C2×D4—64no—
782C2×D4—64no—
783C2×D4—64no—
784C2×D4—94no—
785C2×D4—94no—
786C2×D4—94no—
787C2×D4—184no—
788C2×D4—184no—
789C2×D4—184no—
790C22×C4—24no—
791C22×C4—31no—
792C22×C4—34no—
793C22×C4—38no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—31no—
798C22×C4—34no—
799C22×C4—34no—
800C22×C4—64no—
801C22×C4—64no—
802C22×C4—94no—
803C22×C4—94no—
804C22×C4—94no—
805C22×C4—91no—
806C22×C4—91no—
807C22×C4—91no—
808C22×C4—94no—
809C22×C4—184no—
810C22×C4—1832no—
811C22×C4—184no—
812C22×C4—184no—
813C22×C4—184no—
814C22×C4C2×D3211yescharacteristic
815C22×C4C2×D3211yescharacteristic
816C22×C4C2×D3214yescomplemented
817C4⋊C4—34no—
818C4⋊C4—94no—
819C4⋊C4—94no—
820C4⋊C4—94no—
821C4⋊C4—94no—
822C4⋊C4—94no—
823C22⋊C4—34no—
824C22⋊C4—34no—
825C22⋊C4—94no—
826C22⋊C4—94no—
827C22⋊C4—94no—
828C22⋊C4—94no—
829C22⋊C4—94no—
830C22⋊C4—94no—
831C22⋊C4—94no—
832C22⋊C4—94no—
833C42—34no—
834C42—94no—
835C22×C3—24no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—22no—
839C22×C3—22no—
840C22×C3—22no—
841C22×C3—22no—
842C22×C3—22no—
843C22×C3—22no—
844C22×C3—22no—
845C22×C3—21no—
846C22×C3—34no—
847C22×C3—34no—
848C22×C3—42no—
849C22×C3—42no—
850C22×C3—48no—
851C22×C3—44no—
852C22×C3—44no—
853C22×C3—62no—
854C22×C3—62no—
855C22×C3—62no—
856C22×C3—62no—
857C22×C3—68no—
858C22×C3—68no—
859C22×C3—62no—
860C22×C3—62no—
861C22×C3—62no—
862C22×C3—124no—
863C22×C3C2×#23512yes—
864C22×C3C2×D3×D412yes—
865C22×C3D3×#4112yes—
866C22×C3D3×#4112yes—
867C22×C3D3×#4112yes—
868C22×C3C22×#6712yes—
869C22×C3C24×D311yescharacteristic
870C22×C3C24×D311yescharacteristic
871C2×D3—22no—
872C2×D3—22no—
873C2×D3—22no—
874C2×D3—22no—
875C2×D3—28no—
876C2×D3—28no—
877C2×D3—22no—
878C2×D3—22no—
879C2×D3—22no—
880C2×D3—34no—
881C2×D3—34no—
882C2×D3—44no—
883C2×D3—64no—
884C2×D3—632no—
885C2×D3—632no—
886C2×D3—62no—
887C2×D3—62no—
888C2×D3—62no—
889C2×D3—62no—
890C2×D3—68no—
891C2×D3—68no—
892C2×D3—122no—
893C2×D3—122no—
894C2×D3—128no—
895C2×D3C2×#23514yescomplemented
896C2×D3C22×#6714yes—
897C3×C4—22no—
898C3×C4—22no—
899C3×C4—24no—
900C3×C4—34no—
901C3×C4—42no—
902C3×C4—62no—
903C3×C4—62no—
904C3×C4—62no—
905C3×C4—62no—
906C3×C4C2×D3×D414yes—
907C3×C4C22×#6714yes—
908Dic3—22no—
909Dic3—22no—
910Dic3—22no—
911Dic3—22no—
912Dic3—64no—
913Dic3—62no—
914Dic3—62no—
915Dic3—62no—
916Dic3—62no—
917Dic3—62no—
918Dic3—62no—
919Dic3—122no—
920Dic3—122no—
921Dic3C22×#6714yes—
922C32C2×#52511yescharacteristic, complemented, Sylow
923C23—22no—
924C23—22no—
925C23—22no—
926C23—34no—
927C23—34no—
928C23—32no—
929C23—32no—
930C23—32no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—62no—
936C23—62no—
937C23—62no—
938C23—94no—
939C23—92no—
940C23—188no—
941C23—188no—
942C23—188no—
943C23—1832no—
944C23—182no—
945C23—182no—
946C23C22×D3212yes—
947C23C22×D3211yescharacteristic
948Q8—68no—
949D4—68no—
950D4—68no—
951D4—68no—
952D4—68no—
953D4—188no—
954D4—188no—
955D4—188no—
956C2×C4—22no—
957C2×C4—28no—
958C2×C4—34no—
959C2×C4—32no—
960C2×C4—316no—
961C2×C4—32no—
962C2×C4—32no—
963C2×C4—32no—
964C2×C4—32no—
965C2×C4—62no—
966C2×C4—62no—
967C2×C4—62no—
968C2×C4—62no—
969C2×C4—68no—
970C2×C4—68no—
971C2×C4—92no—
972C2×C4—92no—
973C2×C4—92no—
974C2×C4—188no—
975C2×C4—188no—
976C2×C4—188no—
977C2×C4—182no—
978C2×C4—182no—
979C2×C4—182no—
980C2×C4—188no—
981C2×C4D3×#6714yes—
982C2×C4C22×D3212yes—
983C2×C4C22×D3212yes—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—24no—
988C2×C3—44no—
989C2×C3—42no—
990C2×C3—42no—
991C2×C3—64no—
992C2×C3—64no—
993C2×C3—122no—
994C2×C3#554714yescomplemented
995C2×C3#582814yescomplemented
996C2×C3C22×#23511yescharacteristic
997C2×C3C22×D3×D411yescharacteristic
998C2×C3C2×D3×#4111yescharacteristic
999C2×C3C2×D3×#4111yescharacteristic
1000C2×C3C2×D3×#4111yescharacteristic
1001C2×C3C23×#6711yescharacteristic
1002D3—24no—
1003D3—24no—
1004D3—42no—
1005D3—64no—
1006D3—64no—
1007D3—124no—
1008C22—22no—
1009C22—22no—
1010C22—22no—
1011C22—34no—
1012C22—34no—
1013C22—44no—
1014C22—62no—
1015C22—62no—
1016C22—62no—
1017C22—62no—
1018C22—68no—
1019C22—68no—
1020C22—62no—
1021C22—62no—
1022C22—62no—
1023C22—94no—
1024C22—124no—
1025C22—1832no—
1026C22—182no—
1027C22—182no—
1028C22—188no—
1029C22D3×#23512yes—
1030C22#6430612yes—
1031C22C2×D3×#6712yes—
1032C22C23×D3211yescharacteristic
1033C4—22no—
1034C4—34no—
1035C4—62no—
1036C4—62no—
1037C4—62no—
1038C4—62no—
1039C4—182no—
1040C4—182no—
1041C4—182no—
1042C4C2×D3×#6714yes—
1043C3—21no—
1044C3C2×#554711yescharacteristic, complemented
1045C3C2×#582811yescharacteristic, complemented
1046C2—42no—
1047C2—64no—
1048C2—64no—
1049C2—122no—
1050C2—184no—
1051C2#1059506014yesdirect product factor
1052C2C2×D3×#23511yescharacteristic
1053C2C2×#6430611yescharacteristic
1054C2C22×D3×#6711yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#525
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×C3×#235C2semidirect
2. C22×C4×D32C2semidirect
3. C2×C4×#638C2semidirect
4. C2×C3×C4×#67C2semidirect
5. C2×#63983C2semidirect
6. C2×#63970C2semidirect
7. C2×#63969C2semidirect
8. C2×#63958C2semidirect
9. #10595060C2direct (N × H)
10. C2×#63922C2semidirect
11. C2×C4×#626C2semidirect
12. C2×C4×#625C2semidirect
13. C2×#63888C2semidirect
14. C2×#63887C2semidirect
15. C2×#63884C2semidirect
16. C2×#63855C2semidirect
20. C23×C32×C4C22semidirect
25. C22×C3×#67C22semidirect
27. C2×C3×#235C22semidirect
31. C22×C3×C4×D3C22semidirect
32. C22×C3×Dic6C22semidirect
39. C2×C4×D32C22semidirect
40. C2×#3757C22semidirect
41. C4×#638C22semidirect
43. C2×#3750C22semidirect
44. C2×C4×C3⋊Dic3C22semidirect
45. C2×C3×#217C22semidirect
46. C3×C4×#67C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. C2×C3×C4×Dic3C22semidirect
50. #63983C22semidirect
51. #63970C22semidirect
52. #63969C22semidirect
53. C2×#3724C22semidirect
54. C2×Dic3⋊Dic3C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63958C22semidirect
64. #63922C22semidirect
65. C4×#626C22semidirect
66. C4×#625C22semidirect
67. #63888C22semidirect
68. #63887C22semidirect
69. #63884C22semidirect
70. #63855C22semidirect
72. C22×#235D3semidirect
93. C2×C4×#67D3semidirect
116. C22×C32×C4C23semidirect
129. C2×C3×#67C23semidirect
140. C2×C3×C4×D3D4semidirect
143. C2×C3×C4×D3C23semidirect
145. C2×C3×Dic6C23semidirect
157. #3757C23semidirect
159. #3750C23semidirect
160. C4×C3⋊Dic3C23semidirect
161. C3×#217C23semidirect
163. C3×Dic3⋊C4C23semidirect
164. C3×C4×Dic3C23semidirect
165. #3724C23semidirect
166. Dic3⋊Dic3C23semidirect
167. Dic3⋊Dic3C23semidirect
168. Dic3⋊Dic3C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
189. C23×C3×C4C2×D3semidirect
190. C23×C3×C4C2×D3semidirect
199. C22×#67C2×D3semidirect
203. C2×#235C2×D3semidirect
219. C22×C4×D3C2×D3semidirect
220. C22×Dic6C2×D3semidirect
234. C2×#217C2×D3semidirect
251. C4×#67C2×D3semidirect
275. C2×Dic3⋊C4C2×D3semidirect
279. C2×C4×Dic3C2×D3semidirect
295. C22×C3⋊D3#41semidirect
305. C22×C3×D3#41semidirect
342. C3×C4×D3C2×D4semidirect
417. C22×C3×C4C22×D3semidirect
418. C22×C3×C4C22×D3semidirect
436. C2×#67C22×D3semidirect
478. C2×C4×D3#67semidirect
481. C2×C4×D3C22×D3semidirect
483. C2×Dic6C22×D3semidirect
496. #217C22×D3semidirect
519. Dic3⋊C4C22×D3semidirect
523. C4×Dic3C22×D3semidirect
535. C2×C3⋊D3C2×#41semidirect
547. C2×C3×D3C2×#41semidirect
579. C23×C4D32semidirect
665. C22×D3#235semidirect
753. C4×D3C2×#67semidirect
756. C2×C32#525semidirect
816. C22×C4C2×D32semidirect
895. C2×D3C2×#235semidirect
922. C32C2×#525semidirect
994. C2×C3#5547semidirect
995. C2×C3#5828semidirect
1044. C3C2×#5547semidirect
1045. C3C2×#5828semidirect
1051. C2#10595060direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#2352
C22×C4×D322
C2×C4×#6382
C2×C3×C4×#672
C2×#639832
C2×#639702
C2×#639692
C2×#639582
#105950602
C2×#639222
C2×C4×#6262
C2×C4×#6252
C2×#638882
C2×#638872
C2×#638842
C2×#638552
C2×#58283
C2×#55473