Finite Group Databasebeta

← C2×#10593997 #11900461

Subgroups — C2×#10593997 #11900461

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×C4×D32C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic, complemented
4C2×C3×C4×D12C211yesmaximal, characteristic, complemented
5C2×C3×#872C211yesmaximal, characteristic, complemented
6C2×#63923C211yesmaximal, characteristic, complemented
7C2×#63922C211yesmaximal, characteristic, complemented
8C2×#63910C211yesmaximal, characteristic, complemented
9C2×C4×#626C211yesmaximal, characteristic, complemented
10C2×C4×#626C211yesmaximal, characteristic, complemented
11C2×#63895C211yesmaximal, characteristic, complemented
12C2×#63893C211yesmaximal, characteristic, complemented
13C2×#63891C211yesmaximal, characteristic, complemented
14C2×#63890C211yesmaximal, characteristic, complemented
15C2×#63886C211yesmaximal, characteristic, complemented
16#10593997C2116yesmaximal, direct product factor
17C2×#5547—31nomaximal
18C2×#5524—31nomaximal
19C23×D32C2211yescharacteristic
20C22×C4⋊(C3⋊D3)C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×D12C2211yescharacteristic
24C22×C3×C4×D3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×#627C2211yescharacteristic, complemented
28C22×#626C2211yescharacteristic
29C22×#626C2211yescharacteristic
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic, complemented
32C22×#625C2211yescharacteristic
33C22×#624C2211yescharacteristic
34C22×D3×Dic3C2211yescharacteristic
35C22×D3×Dic3C2211yescharacteristic
36C2×C4×D32—28no—
37C2×C4×D32C2218yescomplemented
38C2×#3798—28no—
39C2×#3798C2218yescomplemented
40C2×C32×C42C2211yescharacteristic, complemented
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic, complemented
43C2×C4⋊(C3⋊Dic3)C2211yescharacteristic, complemented
44C4×C4⋊(C3⋊D3)C2218yescomplemented
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
52C2×C3×C4×Dic3C2211yescharacteristic, complemented
53C3×C4×D12C2218yescomplemented
54C3×#872C2218yescomplemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic
58C2×#3722C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61#63923C2218yescomplemented
62#63922C2218yescomplemented
63#63910C2218yescomplemented
64C4×#626C2218yescomplemented
65C4×#626C2218yescomplemented
66#63895C2218yescomplemented
67#63893C2218yescomplemented
68#63891C2218yescomplemented
69#63890C2218yescomplemented
70#63886C2218yescomplemented
71C22×#235—31no—
72C22×#235—31no—
73C23×C4×D3—31no—
74C23×C4×D3—31no—
75C2×C3×C4×D4—31no—
76C2×C3×#117—31no—
77C2×#939—31no—
78C2×#937—31no—
79C2×C4×#67—31no—
80C2×C4×#67—31no—
81#5547—316no—
82#5524—316no—
83C2×#897—31no—
84C2×#897—31no—
85C2×#896—31no—
86C2×#895—31no—
87C2×#895—31no—
88C2×#894—31no—
89C2×#886—31no—
90C2×#886—31no—
91C2×#884—31no—
92C2×#883—31no—
93C2×#882—31no—
94C2×#882—31no—
95C2×#882—31no—
96C2×#878—31no—
97C2×C4×D12—31no—
98C2×C4×D12—31no—
99C2×C4×D12—31no—
100C2×C4×D12—31no—
101C2×C4×D12—61no—
102C2×C4×D12D311yescharacteristic, complemented
103C2×#872D311yescharacteristic, complemented
104C23×C3⋊D3C2311yescharacteristic
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×C4C2311yescharacteristic
114C22×C32×C4C2311yescharacteristic
115C22×C32×C4C2311yescharacteristic
116C22×C3⋊Dic3C2311yescharacteristic
117C22×C3⋊Dic3C2311yescharacteristic
118C2×C4⋊(C3⋊D3)—24no—
119C2×C4⋊(C3⋊D3)C2314yes—
120C2×C4×C3⋊D3—24no—
121C2×C4×C3⋊D3—24no—
122C2×C4×C3⋊D3C2314yes—
123C2×C4×C3⋊D3C2314yescomplemented
124C22×C3×Dic3C2311yescharacteristic
125C22×C3×Dic3C2311yescharacteristic
126C22×C3×Dic3C2311yescharacteristic
127C22×C3×Dic3C2311yescharacteristic
128C22×C3×Dic3C2311yescharacteristic
129C2×C3×D12—24no—
130C2×C3×D12C2314yes—
131C2×C3×C4×D3—24no—
132C2×C3×C4×D3—24no—
133C2×C3×C4×D3D418yescomplemented
134C2×C3×C4×D3C2314yes—
135C2×C3×C4×D3C2314yes—
136C2×C3×C4×D3C2314yescomplemented
137C2×#627—24no—
138C2×#627C2314yescomplemented
139C2×#626—24no—
140C2×#626—24no—
141C2×#626—24no—
142C2×#626—24no—
143C2×#626C2314yes—
144C2×#626C2314yes—
145C2×#626C2314yes—
146C2×#626C2314yescomplemented
147C2×#625—24no—
148C2×#625C2314yes—
149C2×#624—24no—
150C2×#624C2314yes—
151C2×D3×Dic3—24no—
152C2×D3×Dic3—24no—
153C2×D3×Dic3C2314yes—
154C2×D3×Dic3C2314yes—
155C4×D32—232no—
156#3798—232no—
157C32×C42C2314yescomplemented
158#3752C2314yes—
159#3752C2314yescomplemented
160C4⋊(C3⋊Dic3)C2314yescomplemented
161C3×(C2×D3)⋊C4C2314yes—
162C3×(C2×D3)⋊C4C2314yes—
163C3×(C2×D3)⋊C4C2314yes—
164C3×(C2×D3)⋊C4C2314yescomplemented
165C3×C4⋊Dic3C2314yescomplemented
166C3×Dic3⋊C4C2314yescomplemented
167C3×Dic3⋊C4C2314yescomplemented
168C3×C4×Dic3C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170Dic3⋊Dic3C2314yescomplemented
171#3722C2314yes—
172#3722C2314yescomplemented
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yescomplemented
175C2×#525—91noSylow
176C24×D3—31no—
177C24×D3—31no—
178C22×C3×D4—31no—
179C23×C3×C4—31no—
180C23×C3×C4—31no—
181C23×C3×C4—31no—
182C22×#67—31no—
183C22×#67—31no—
184C22×#67—31no—
185C22×#67—31no—
186C22×#67—31no—
187C22×#67—31no—
188C23×Dic3—31no—
189C23×Dic3—31no—
190C2×#235—38no—
191C2×#235—38no—
192C2×#235—68no—
193C2×#235—68no—
194C22×D12—31no—
195C22×D12—31no—
196C22×D12—31no—
197C22×D12—31no—
198C22×D12—31no—
199C22×D12—31no—
200C22×D12—61no—
201C22×D12C2×D311yescharacteristic
202C22×C4×D3—31no—
203C22×C4×D3—31no—
204C22×C4×D3—31no—
205C22×C4×D3—31no—
206C22×C4×D3—31no—
207C22×C4×D3—31no—
208C22×C4×D3—31no—
209C22×C4×D3—31no—
210C22×C4×D3—38no—
211C22×C4×D3—38no—
212C22×C4×D3—61no—
213C22×C4×D3—61no—
214C22×C4×D3—68no—
215C22×C4×D3—68no—
216C22×C4×D3C2×D311yescharacteristic
217C22×C4×D3C2×D311yescharacteristic
218C22×C4×D3C2×D311yescharacteristic, complemented
219C22×Dic6—31no—
220C22×Dic6—31no—
221C3×C4×D4—38no—
222C3×#117—38no—
223C2×C3×C4⋊C4—31no—
224C2×C3×C4⋊C4—31no—
225C2×C3×C4⋊C4—31no—
226C2×C3×C22⋊C4—31no—
227C2×C3×C22⋊C4—31no—
228C2×C3×C22⋊C4—31no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C42—21no—
231C2×C3×C42—31no—
232C2×C3×C42C2×D311yescharacteristic, complemented
233C2×C3×C42C2×D311yescharacteristic, complemented
234C2×#217—31no—
235C2×#217—31no—
236#939—38no—
237#937—38no—
238C4×#67—38no—
239C4×#67—38no—
240C2×(C2×D3)⋊C4—31no—
241C2×(C2×D3)⋊C4—31no—
242C2×(C2×D3)⋊C4—31no—
243C2×(C2×D3)⋊C4—31no—
244C2×(C2×D3)⋊C4—31no—
245C2×(C2×D3)⋊C4—31no—
246C2×(C2×D3)⋊C4—31no—
247C2×(C2×D3)⋊C4—31no—
248C2×(C2×D3)⋊C4—31no—
249C2×(C2×D3)⋊C4—31no—
250C2×(C2×D3)⋊C4—61no—
251C2×(C2×D3)⋊C4—61no—
252C2×(C2×D3)⋊C4C2×D311yescharacteristic
253C2×(C2×D3)⋊C4C2×D311yescharacteristic
254C2×(C2×D3)⋊C4C2×D311yescharacteristic
255C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
256C2×C4⋊Dic3—31no—
257C2×C4⋊Dic3—31no—
258C2×C4⋊Dic3—31no—
259C2×C4⋊Dic3—31no—
260C2×C4⋊Dic3—61no—
261C2×C4⋊Dic3C2×D311yescharacteristic, complemented
262C2×Dic3⋊C4—31no—
263C2×Dic3⋊C4—31no—
264C2×Dic3⋊C4C2×D311yescharacteristic, complemented
265C2×Dic3⋊C4C2×D311yescharacteristic, complemented
266C2×C4×Dic3C2×D311yescharacteristic, complemented
267#897—38no—
268#897—38no—
269#896—38no—
270#895—38no—
271#895—38no—
272#894—38no—
273#886—38no—
274#886—38no—
275#884—38no—
276#883—38no—
277#882—38no—
278#882—38no—
279#882—38no—
280#878—38no—
281C4×D12—38no—
282C4×D12—38no—
283C4×D12—38no—
284C4×D12—38no—
285C4×D12—68no—
286C4×D12C2×D318yescomplemented
287#872C2×D318yescomplemented
288C23×C32C2411yescharacteristic
289C22×C3⋊D3—22no—
290C22×C3⋊D3—22no—
291C22×C3⋊D3—22no—
292C22×C3⋊D3—22no—
293C22×C3⋊D3—22no—
294C22×C3⋊D3#4114yescomplemented
295C22×C3⋊D3C2412yes—
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—22no—
315C2×C32×C4C2×D414yes—
316C2×C32×C4C2412yes—
317C2×C32×C4C2412yes—
318C2×C32×C4C2412yes—
319C2×C3⋊Dic3—22no—
320C2×C3⋊Dic3—22no—
321C2×C3⋊Dic3C2412yes—
322C2×C3⋊Dic3C2412yes—
323C4⋊(C3⋊D3)—28no—
324C4×C3⋊D3—28no—
325C4×C3⋊D3—28no—
326C2×C3×Dic3—22no—
327C2×C3×Dic3—22no—
328C2×C3×Dic3—22no—
329C2×C3×Dic3—22no—
330C2×C3×Dic3C2×D414yes—
331C2×C3×Dic3C2412yes—
332C2×C3×Dic3C2412yes—
333C2×C3×Dic3C2412yes—
334C2×C3×Dic3C2412yes—
335C2×C3×Dic3C2412yes—
336C3×D12—28no—
337C3×C4×D3—28no—
338C3×C4×D3—28no—
339C3×C4×D3C2×D4116yescomplemented
340#627—28no—
341#626—28no—
342#626—28no—
343#626—28no—
344#626—28no—
345#625—28no—
346#624—28no—
347D3×Dic3—28no—
348D3×Dic3—28no—
349C22×#41—91no—
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—31no—
365C24×C3—31no—
366C24×C3—31no—
367C24×C3—31no—
368C23×D3—31no—
369C23×D3—31no—
370C23×D3—31no—
371C23×D3—31no—
372C23×D3—34no—
373C23×D3—34no—
374C23×D3—61no—
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
385C2×C3×D4—34no—
386C2×C3×D4—64no—
387C22×C3×C4—21no—
388C22×C3×C4—21no—
389C22×C3×C4—21no—
390C22×C3×C4—31no—
391C22×C3×C4—38no—
392C22×C3×C4—34no—
393C22×C3×C4—31no—
394C22×C3×C4—31no—
395C22×C3×C4—31no—
396C22×C3×C4—31no—
397C22×C3×C4—34no—
398C22×C3×C4—34no—
399C22×C3×C4—64no—
400C22×C3×C4—64no—
401C22×C3×C4C22×D311yescharacteristic
402C22×C3×C4C22×D311yescharacteristic
403C22×C3×C4C22×D311yescharacteristic
404C22×C3×C4C22×D311yescharacteristic
405C22×C3×C4C22×D311yescharacteristic
406C22×C3×C4C22×D311yescharacteristic
407C2×#67—34no—
408C2×#67—34no—
409C2×#67—34no—
410C2×#67—34no—
411C2×#67—34no—
412C2×#67—34no—
413C2×#67—64no—
414C2×#67—64no—
415C2×#67—64no—
416C2×#67—64no—
417C2×#67—64no—
418C2×#67—64no—
419C22×Dic3—31no—
420C22×Dic3—31no—
421C22×Dic3—31no—
422C22×Dic3—31no—
423C22×Dic3—34no—
424C22×Dic3—34no—
425C22×Dic3—61no—
426C22×Dic3—61no—
427C22×Dic3—64no—
428C22×Dic3—64no—
429C22×Dic3C22×D311yescharacteristic
430C22×Dic3C22×D311yescharacteristic
431C22×Dic3C22×D311yescharacteristic
432C22×Dic3C22×D311yescharacteristic
433C22×Dic3C22×D311yescharacteristic
434#235—632no—
435#235—632no—
436C2×D12—24no—
437C2×D12—34no—
438C2×D12—34no—
439C2×D12—34no—
440C2×D12—34no—
441C2×D12—34no—
442C2×D12—34no—
443C2×D12—64no—
444C2×D12—64no—
445C2×D12—64no—
446C2×D12—68no—
447C2×D12—64no—
448C2×D12—64no—
449C2×D12—64no—
450C2×D12—64no—
451C2×D12C22×D314yes—
452C2×C4×D3—24no—
453C2×C4×D3—24no—
454C2×C4×D3—34no—
455C2×C4×D3—34no—
456C2×C4×D3—34no—
457C2×C4×D3—34no—
458C2×C4×D3—34no—
459C2×C4×D3—34no—
460C2×C4×D3—34no—
461C2×C4×D3—34no—
462C2×C4×D3—64no—
463C2×C4×D3—64no—
464C2×C4×D3—632no—
465C2×C4×D3—64no—
466C2×C4×D3—64no—
467C2×C4×D3—64no—
468C2×C4×D3—64no—
469C2×C4×D3—64no—
470C2×C4×D3—64no—
471C2×C4×D3—64no—
472C2×C4×D3—64no—
473C2×C4×D3—632no—
474C2×C4×D3—124no—
475C2×C4×D3—124no—
476C2×C4×D3D1218yescomplemented
477C2×C4×D3C22×D314yes—
478C2×C4×D3C22×D314yes—
479C2×C4×D3C22×D314yescomplemented
480C2×Dic6—34no—
481C2×Dic6—34no—
482C2×Dic6—64no—
483C2×Dic6—64no—
484C3×C4⋊C4—34no—
485C3×C4⋊C4—34no—
486C3×C4⋊C4—34no—
487C3×C22⋊C4—34no—
488C3×C22⋊C4—34no—
489C3×C22⋊C4—34no—
490C3×C22⋊C4—34no—
491C3×C42—24no—
492C3×C42—34no—
493C3×C42C22×D314yescomplemented
494C3×C42C22×D314yescomplemented
495#217—34no—
496#217—34no—
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—34no—
507(C2×D3)⋊C4—64no—
508(C2×D3)⋊C4—64no—
509(C2×D3)⋊C4C22×D314yes—
510(C2×D3)⋊C4C22×D314yes—
511(C2×D3)⋊C4C22×D314yes—
512(C2×D3)⋊C4C22×D314yescomplemented
513C4⋊Dic3—34no—
514C4⋊Dic3—34no—
515C4⋊Dic3—34no—
516C4⋊Dic3—34no—
517C4⋊Dic3—64no—
518C4⋊Dic3C22×D314yescomplemented
519Dic3⋊C4—34no—
520Dic3⋊C4—34no—
521Dic3⋊C4C22×D314yescomplemented
522Dic3⋊C4C22×D314yescomplemented
523C4×Dic3C22×D314yescomplemented
524C22×C32C22×D412yes—
525C22×C32C2×#4112yes—
526C22×C32C2×#4112yes—
527C22×C32C2511yescharacteristic
528C2×C3⋊D3—22no—
529C2×C3⋊D3—28no—
530C2×C3⋊D3—22no—
531C2×C3⋊D3—22no—
532C2×C3⋊D3—22no—
533C2×C3⋊D3—22no—
534C2×C3⋊D3—44no—
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×C4—22no—
551C32×C4C22×D414yes—
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—98no—
561C2×#41—188no—
562C22×Q8—91no—
563C22×D4—31no—
564C22×D4—91no—
565C22×D4—91no—
566C22×D4—91no—
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—91no—
579C23×C4—188no—
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—38no—
593C2×C4⋊C4—31no—
594C2×C4⋊C4—31no—
595C2×C4⋊C4—31no—
596C2×C4⋊C4—91no—
597C2×C4⋊C4—91no—
598C2×C4⋊C4—91no—
599C2×C22⋊C4—31no—
600C2×C22⋊C4—31no—
601C2×C22⋊C4—31no—
602C2×C22⋊C4—31no—
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×C42D3211yescharacteristic, complemented
611C23×C3—21no—
612C23×C3—34no—
613C23×C3—34no—
614C23×C3—32no—
615C23×C3—32no—
616C23×C3—32no—
617C23×C3—62no—
618C23×C3—62no—
619C23×C3—62no—
620C23×C3—62no—
621C23×C3—62no—
622C23×C3—62no—
623C23×C3—62no—
624C23×C3C23×D311yescharacteristic
625C23×C3C23×D311yescharacteristic
626C22×D3—22no—
627C22×D3—22no—
628C22×D3—22no—
629C22×D3—22no—
630C22×D3—22no—
631C22×D3—22no—
632C22×D3—22no—
633C22×D3—34no—
634C22×D3—34no—
635C22×D3—32no—
636C22×D3—32no—
637C22×D3—32no—
638C22×D3—32no—
639C22×D3—64no—
640C22×D3—62no—
641C22×D3—62no—
642C22×D3—68no—
643C22×D3—68no—
644C22×D3—68no—
645C22×D3—68no—
646C22×D3—632no—
647C22×D3—632no—
648C22×D3—62no—
649C22×D3—62no—
650C22×D3—62no—
651C22×D3—62no—
652C22×D3—68no—
653C22×D3—68no—
654C22×D3—64no—
655C22×D3—62no—
656C22×D3—62no—
657C22×D3—62no—
658C22×D3—62no—
659C22×D3—62no—
660C22×D3—62no—
661C22×D3—122no—
662C22×D3—122no—
663C22×D3—122no—
664C22×D3—122no—
665C22×D3C2×D1214yes—
666C22×D3#23514yescomplemented
667C22×D3C23×D312yes—
668C22×D3C23×D312yes—
669C22×D3C23×D312yes—
670C3×D4—68no—
671C2×C3×C4—24no—
672C2×C3×C4—22no—
673C2×C3×C4—22no—
674C2×C3×C4—22no—
675C2×C3×C4—22no—
676C2×C3×C4—22no—
677C2×C3×C4—22no—
678C2×C3×C4—22no—
679C2×C3×C4—24no—
680C2×C3×C4—34no—
681C2×C3×C4—32no—
682C2×C3×C4—316no—
683C2×C3×C4—32no—
684C2×C3×C4—32no—
685C2×C3×C4—32no—
686C2×C3×C4—32no—
687C2×C3×C4—42no—
688C2×C3×C4—62no—
689C2×C3×C4—62no—
690C2×C3×C4—62no—
691C2×C3×C4—62no—
692C2×C3×C4—68no—
693C2×C3×C4—68no—
694C2×C3×C4C2×D1214yes—
695C2×C3×C4D3×D414yes—
696C2×C3×C4C23×D312yes—
697C2×C3×C4C23×D312yes—
698C2×C3×C4C23×D312yes—
699C2×C3×C4C23×D312yes—
700C2×C3×C4C23×D312yes—
701C2×C3×C4C23×D312yes—
702#67—68no—
703#67—68no—
704#67—68no—
705#67—68no—
706#67—68no—
707#67—68no—
708C2×Dic3—22no—
709C2×Dic3—22no—
710C2×Dic3—22no—
711C2×Dic3—22no—
712C2×Dic3—32no—
713C2×Dic3—32no—
714C2×Dic3—32no—
715C2×Dic3—32no—
716C2×Dic3—62no—
717C2×Dic3—62no—
718C2×Dic3—68no—
719C2×Dic3—62no—
720C2×Dic3—62no—
721C2×Dic3—62no—
722C2×Dic3—62no—
723C2×Dic3—68no—
724C2×Dic3—122no—
725C2×Dic3—122no—
726C2×Dic3C2×D1214yes—
727C2×Dic3C23×D312yes—
728C2×Dic3C23×D312yes—
729C2×Dic3C23×D312yes—
730C2×Dic3C23×D312yes—
731C2×Dic3C23×D312yes—
732D12—28no—
733D12—68no—
734D12—68no—
735D12—616no—
736D12—68no—
737D12—68no—
738D12—68no—
739D12—68no—
740C4×D3—28no—
741C4×D3—28no—
742C4×D3—68no—
743C4×D3—68no—
744C4×D3—68no—
745C4×D3—68no—
746C4×D3—68no—
747C4×D3—68no—
748C4×D3—68no—
749C4×D3—68no—
750C4×D3—128no—
751C4×D3—128no—
752C4×D3C2×D12116yescomplemented
753Dic6—68no—
754Dic6—68no—
755C2×C32#52514yescomplemented
756C2×C32C23×D411yescharacteristic
757C2×C32C22×#4111yescharacteristic
758C2×C32C22×#4111yescharacteristic
759C3⋊D3—24no—
760C3⋊D3—42no—
761C3×D3—24no—
762C3×D3—24no—
763C3×D3—42no—
764C24—31no—
765C24—31no—
766C24—31no—
767C24—94no—
768C24—91no—
769C24—91no—
770C24—184no—
771C24—184no—
772C24—184no—
773#41—1832no—
774C2×Q8—94no—
775C2×Q8—184no—
776C2×D4—34no—
777C2×D4—64no—
778C2×D4—94no—
779C2×D4—94no—
780C2×D4—94no—
781C2×D4—94no—
782C2×D4—94no—
783C2×D4—94no—
784C2×D4—184no—
785C2×D4—184no—
786C2×D4—184no—
787C2×D4—184no—
788C2×D4—184no—
789C2×D4—184no—
790C22×C4—31no—
791C22×C4—34no—
792C22×C4—38no—
793C22×C4—31no—
794C22×C4—31no—
795C22×C4—31no—
796C22×C4—31no—
797C22×C4—34no—
798C22×C4—34no—
799C22×C4—64no—
800C22×C4—64no—
801C22×C4—94no—
802C22×C4—94no—
803C22×C4—94no—
804C22×C4—91no—
805C22×C4—91no—
806C22×C4—94no—
807C22×C4—94no—
808C22×C4—184no—
809C22×C4—1832no—
810C22×C4—184no—
811C22×C4—184no—
812C22×C4—184no—
813C22×C4—184no—
814C22×C4C2×D3211yescharacteristic
815C22×C4C2×D3211yescharacteristic
816C22×C4C2×D3211yescharacteristic
817C4⋊C4—34no—
818C4⋊C4—34no—
819C4⋊C4—34no—
820C4⋊C4—94no—
821C4⋊C4—94no—
822C4⋊C4—94no—
823C22⋊C4—34no—
824C22⋊C4—34no—
825C22⋊C4—34no—
826C22⋊C4—34no—
827C22⋊C4—94no—
828C22⋊C4—94no—
829C22⋊C4—94no—
830C22⋊C4—94no—
831C22⋊C4—94no—
832C22⋊C4—94no—
833C42—34no—
834C42C2×D3214yescomplemented
835C22×C3—22no—
836C22×C3—22no—
837C22×C3—22no—
838C22×C3—21no—
839C22×C3—34no—
840C22×C3—34no—
841C22×C3—62no—
842C22×C3—62no—
843C22×C3—62no—
844C22×C3—62no—
845C22×C3—68no—
846C22×C3—68no—
847C22×C3—62no—
848C22×C3—62no—
849C22×C3—62no—
850C22×C3—124no—
851C22×C3C22×D1212yes—
852C22×C3C2×#23512yes—
853C22×C3C2×D3×D412yes—
854C22×C3D3×#4112yes—
855C22×C3D3×#4112yes—
856C22×C3D3×#4112yes—
857C22×C3C24×D311yescharacteristic
858C22×C3C24×D311yescharacteristic
859C2×D3—22no—
860C2×D3—22no—
861C2×D3—22no—
862C2×D3—22no—
863C2×D3—28no—
864C2×D3—28no—
865C2×D3—22no—
866C2×D3—22no—
867C2×D3—22no—
868C2×D3—34no—
869C2×D3—34no—
870C2×D3—44no—
871C2×D3—64no—
872C2×D3—632no—
873C2×D3—632no—
874C2×D3—62no—
875C2×D3—62no—
876C2×D3—62no—
877C2×D3—62no—
878C2×D3—68no—
879C2×D3—68no—
880C2×D3—64no—
881C2×D3—62no—
882C2×D3—62no—
883C2×D3—62no—
884C2×D3—62no—
885C2×D3—62no—
886C2×D3—62no—
887C2×D3—122no—
888C2×D3—122no—
889C2×D3—122no—
890C2×D3—128no—
891C2×D3—122no—
892C2×D3—128no—
893C2×D3—124no—
894C2×D3—124no—
895C2×D3C22×D1214yes—
896C2×D3C2×#23514yescomplemented
897C3×C4—24no—
898C3×C4—22no—
899C3×C4—22no—
900C3×C4—22no—
901C3×C4—22no—
902C3×C4—24no—
903C3×C4—34no—
904C3×C4—42no—
905C3×C4—62no—
906C3×C4—62no—
907C3×C4—62no—
908C3×C4—62no—
909C3×C4C22×D1214yes—
910C3×C4C2×D3×D414yes—
911Dic3—22no—
912Dic3—22no—
913Dic3—22no—
914Dic3—22no—
915Dic3—62no—
916Dic3—62no—
917Dic3—62no—
918Dic3—62no—
919Dic3—122no—
920Dic3—122no—
921Dic3C22×D1214yes—
922C32C2×#52511yescharacteristic, complemented, Sylow
923C23—34no—
924C23—34no—
925C23—32no—
926C23—32no—
927C23—32no—
928C23—62no—
929C23—62no—
930C23—62no—
931C23—62no—
932C23—62no—
933C23—62no—
934C23—62no—
935C23—94no—
936C23—92no—
937C23—92no—
938C23—188no—
939C23—188no—
940C23—188no—
941C23—1832no—
942C23—182no—
943C23—182no—
944C23—182no—
945C23—182no—
946C23—182no—
947C23C22×D3211yescharacteristic
948Q8—188no—
949D4—68no—
950D4—188no—
951D4—188no—
952D4—188no—
953D4—188no—
954D4—188no—
955D4—188no—
956C2×C4—22no—
957C2×C4—22no—
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—188no—
974C2×C4—188no—
975C2×C4—188no—
976C2×C4—182no—
977C2×C4—182no—
978C2×C4—188no—
979C2×C4—188no—
980C2×C4D3×D1214yes—
981C2×C4C22×D3212yes—
982C2×C4C22×D3212yes—
983C2×C4C22×D3212yes—
984C2×C3—21no—
985C2×C3—21no—
986C2×C3—21no—
987C2×C3—24no—
988C2×C3—64no—
989C2×C3—64no—
990C2×C3—122no—
991C2×C3#552414yescomplemented
992C2×C3#554714yescomplemented
993C2×C3C23×D1211yescharacteristic
994C2×C3C22×#23511yescharacteristic
995C2×C3C22×D3×D411yescharacteristic
996C2×C3C2×D3×#4111yescharacteristic
997C2×C3C2×D3×#4111yescharacteristic
998C2×C3C2×D3×#4111yescharacteristic
999D3—24no—
1000D3—24no—
1001D3—42no—
1002D3—64no—
1003D3—64no—
1004D3—124no—
1005D3—124no—
1006D3—122no—
1007D3—122no—
1008C22—34no—
1009C22—34no—
1010C22—62no—
1011C22—62no—
1012C22—62no—
1013C22—62no—
1014C22—68no—
1015C22—68no—
1016C22—62no—
1017C22—62no—
1018C22—62no—
1019C22—94no—
1020C22—124no—
1021C22—1832no—
1022C22—182no—
1023C22—182no—
1024C22—188no—
1025C22—182no—
1026C22—182no—
1027C22—182no—
1028C22—364no—
1029C22C2×D3×D1212yes—
1030C22D3×#23512yes—
1031C22#6430612yes—
1032C22C23×D3211yescharacteristic
1033C4—22no—
1034C4—22no—
1035C4—34no—
1036C4—62no—
1037C4—62no—
1038C4—62no—
1039C4—62no—
1040C4—182no—
1041C4—182no—
1042C4C2×D3×D1214yes—
1043C3—21no—
1044C3C2×#552411yescharacteristic, complemented
1045C3C2×#554711yescharacteristic, complemented
1046C2—64no—
1047C2—64no—
1048C2—122no—
1049C2—184no—
1050C2—362no—
1051C2#1059399714yesdirect product factor
1052C2C22×D3×D1211yescharacteristic
1053C2C2×D3×#23511yescharacteristic
1054C2C2×#6430611yescharacteristic
subgroupG/H
centerC22×C4C2×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#525
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. C22×#3798C2semidirect
3. C2×C4×C4⋊(C3⋊D3)C2semidirect
4. C2×C3×C4×D12C2semidirect
5. C2×C3×#872C2semidirect
6. C2×#63923C2semidirect
7. C2×#63922C2semidirect
8. C2×#63910C2semidirect
9. C2×C4×#626C2semidirect
10. C2×C4×#626C2semidirect
11. C2×#63895C2semidirect
12. C2×#63893C2semidirect
13. C2×#63891C2semidirect
14. C2×#63890C2semidirect
15. C2×#63886C2semidirect
16. #10593997C2direct (N × H)
22. C22×C4×C3⋊D3C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×#627C22semidirect
31. C22×#626C22semidirect
37. C2×C4×D32C22semidirect
39. C2×#3798C22semidirect
40. C2×C32×C42C22semidirect
42. C2×#3752C22semidirect
43. C2×C4⋊(C3⋊Dic3)C22semidirect
44. C4×C4⋊(C3⋊D3)C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×C4⋊Dic3C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×Dic3⋊C4C22semidirect
52. C2×C3×C4×Dic3C22semidirect
53. C3×C4×D12C22semidirect
54. C3×#872C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
58. C2×#3722C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. #63923C22semidirect
62. #63922C22semidirect
63. #63910C22semidirect
64. C4×#626C22semidirect
65. C4×#626C22semidirect
66. #63895C22semidirect
67. #63893C22semidirect
68. #63891C22semidirect
69. #63890C22semidirect
70. #63886C22semidirect
102. C2×C4×D12D3semidirect
103. C2×#872D3semidirect
123. C2×C4×C3⋊D3C23semidirect
133. C2×C3×C4×D3D4semidirect
136. C2×C3×C4×D3C23semidirect
138. C2×#627C23semidirect
146. C2×#626C23semidirect
157. C32×C42C23semidirect
159. #3752C23semidirect
160. C4⋊(C3⋊Dic3)C23semidirect
164. C3×(C2×D3)⋊C4C23semidirect
165. C3×C4⋊Dic3C23semidirect
166. C3×Dic3⋊C4C23semidirect
167. C3×Dic3⋊C4C23semidirect
168. C3×C4×Dic3C23semidirect
169. Dic3⋊Dic3C23semidirect
170. Dic3⋊Dic3C23semidirect
172. #3722C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
218. C22×C4×D3C2×D3semidirect
232. C2×C3×C42C2×D3semidirect
233. C2×C3×C42C2×D3semidirect
255. C2×(C2×D3)⋊C4C2×D3semidirect
261. C2×C4⋊Dic3C2×D3semidirect
264. C2×Dic3⋊C4C2×D3semidirect
265. C2×Dic3⋊C4C2×D3semidirect
266. C2×C4×Dic3C2×D3semidirect
286. C4×D12C2×D3semidirect
287. #872C2×D3semidirect
294. C22×C3⋊D3#41semidirect
305. C22×C3×D3#41semidirect
339. C3×C4×D3C2×D4semidirect
476. C2×C4×D3D12semidirect
479. C2×C4×D3C22×D3semidirect
493. C3×C42C22×D3semidirect
494. C3×C42C22×D3semidirect
512. (C2×D3)⋊C4C22×D3semidirect
518. C4⋊Dic3C22×D3semidirect
521. Dic3⋊C4C22×D3semidirect
522. Dic3⋊C4C22×D3semidirect
523. C4×Dic3C22×D3semidirect
535. C2×C3⋊D3C2×#41semidirect
547. C2×C3×D3C2×#41semidirect
610. C2×C42D32semidirect
666. C22×D3#235semidirect
752. C4×D3C2×D12semidirect
755. C2×C32#525semidirect
834. C42C2×D32semidirect
896. C2×D3C2×#235semidirect
922. C32C2×#525semidirect
991. C2×C3#5524semidirect
992. C2×C3#5547semidirect
1044. C3C2×#5524semidirect
1045. C3C2×#5547semidirect
1051. C2#10593997direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×D322
C22×#37982
C2×C4×C4⋊(C3⋊D3)2
C2×C3×C4×D122
C2×C3×#8722
C2×#639232
C2×#639222
C2×#639102
C2×C4×#6262
C2×#638952
C2×#638932
C2×#638912
C2×#638902
C2×#638862
#105939972
C2×#55473
C2×#55243