Finite Group Databasebeta

← C2×#10595075 #11902422

Subgroups — C2×#10595075 #11902422

Order 1152.

4137 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3811C211yesmaximal, characteristic, complemented
2C22×#3805C211yesmaximal, characteristic, complemented
3C22×#3752C211yesmaximal, characteristic, complemented
4C2×C3×#930C211yesmaximal, characteristic, complemented
5C2×C3×C4×#67C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63962C211yesmaximal, characteristic, complemented
8#10595075C2116yesmaximal, direct product factor
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63906C211yesmaximal, characteristic, complemented
12C2×#63895C211yesmaximal, characteristic, complemented
13C2×#63890C211yesmaximal, characteristic, complemented
14C2×#63886C211yesmaximal, characteristic, complemented
15C2×#63880C211yesmaximal, characteristic, complemented
16C2×#63852C211yesmaximal, characteristic, complemented
17C2×#5610—31nomaximal
18C2×#5554—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C23×C32×C4C2211yescharacteristic, complemented
22C23×C3⋊Dic3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C2×#3811—28no—
29C2×#3811C2218yescomplemented
30C22×#627C2211yescharacteristic, complemented
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic, complemented
35C22×#625C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic
37C2×#3805—28no—
38C2×#3805C2218yescomplemented
39C22×D3×Dic3C2211yescharacteristic, complemented
40C22×D3×Dic3C2211yescharacteristic, complemented
41C2×#3752C2211yescharacteristic
42C2×#3752C2211yescharacteristic
43C2×#3752C2218yescomplemented
44C2×#3752C2211yescharacteristic, complemented
45C2×#3752C2211yescharacteristic, complemented
46C2×C3×#217C2211yescharacteristic, complemented
47C3×#930C2218yescomplemented
48C3×C4×#67C2218yescomplemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C2×C3×C4⋊Dic3C2211yescharacteristic, complemented
53C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
54C2×C3×C4×Dic3C2211yescharacteristic, complemented
55#63981C2218yescomplemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic
59C2×#3722C2211yescharacteristic, complemented
60#63962C2218yescomplemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63#63922C2218yescomplemented
64D3×(C2×D3)⋊C4C2218yescomplemented
65#63906C2218yescomplemented
66#63895C2218yescomplemented
67#63890C2218yescomplemented
68#63886C2218yescomplemented
69#63880C2218yescomplemented
70#63852C2218yescomplemented
71C22×#237—31no—
72C22×#237—31no—
73C22×D3×D4—31no—
74C22×D3×D4—31no—
75C2×C3×#121—31no—
76C2×C3×C4×D4—31no—
77C2×#939—31no—
78C2×#937—31no—
79C2×#937—31no—
80C2×#935—31no—
81C2×#930—31no—
82C2×#930D311yescharacteristic, complemented
83C2×C4×#67D311yescharacteristic, complemented
84C22×(C2×D3)⋊C4—31no—
85C22×(C2×D3)⋊C4—31no—
86C22×(C2×D3)⋊C4—31no—
87C22×(C2×D3)⋊C4—61no—
88#5610—316no—
89#5554—316no—
90C2×#897—31no—
91C2×#896—31no—
92C2×#895—31no—
93C2×#894—31no—
94C2×#886—31no—
95C2×#886—31no—
96C2×#885—31no—
97C2×#884—31no—
98C2×#882—31no—
99C2×#882—31no—
100C2×#67⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×#875—31no—
103C2×C4×D12—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3—24no—
106C23×C3⋊D3—24no—
107C23×C3⋊D3—42no—
108C23×C3⋊D3C2311yescharacteristic
109C23×C3⋊D3C2314yes—
110C23×C3⋊D3C2311yescharacteristic
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2311yescharacteristic
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C22×C32×C4—42no—
119C22×C32×C4C2311yescharacteristic
120C22×C32×C4C2311yescharacteristic
121C22×C32×C4C2314yescomplemented
122C22×C3⋊Dic3—24no—
123C22×C3⋊Dic3C2311yescharacteristic
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2314yescomplemented
126C2×C3×#67—24no—
127C2×C3×#67—24no—
128C2×C3×#67D418yescomplemented
129C2×C3×#67C2314yes—
130C2×C3×#67C2314yes—
131C2×C3×#67C2314yescomplemented
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C22×C3×Dic3C2311yescharacteristic
136C22×C3×Dic3C2311yescharacteristic
137C2×C3×D12—42no—
138C2×C3×D12C2314yescomplemented
139C2×C3×C4×D3—42no—
140C2×C3×C4×D3C2314yescomplemented
141#3811—232no—
142C2×#627—24no—
143C2×#627C2314yescomplemented
144C2×#626—24no—
145C2×#626—24no—
146C2×#626—24no—
147C2×#626—42no—
148C2×#626C2314yes—
149C2×#626C2314yes—
150C2×#626C2314yes—
151C2×#626C2314yescomplemented
152C2×#625—24no—
153C2×#625C2314yescomplemented
154C2×#624—24no—
155C2×#624C2314yes—
156#3805—232no—
157C2×D3×Dic3—24no—
158C2×D3×Dic3—24no—
159C2×D3×Dic3C2314yescomplemented
160C2×D3×Dic3C2314yescomplemented
161#3752C2314yes—
162#3752C2314yes—
163#3752C2314yescomplemented
164#3752C2314yescomplemented
165C3×#217C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×C4⋊Dic3C2314yescomplemented
170C3×Dic3⋊C4C2314yescomplemented
171C3×C4×Dic3C2314yescomplemented
172Dic3⋊Dic3C2314yescomplemented
173Dic3⋊Dic3C2314yescomplemented
174#3722C2314yes—
175#3722C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C24×D3—61no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C23×C3×C4—21no—
189C23×C3×C4—31no—
190C23×C3×C4C2×D311yescharacteristic, complemented
191C23×C3×C4C2×D311yescharacteristic, complemented
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67C2×D311yescharacteristic
199C22×#67C2×D311yescharacteristic
200C22×#67C2×D311yescharacteristic, complemented
201C23×Dic3—31no—
202C23×Dic3—31no—
203C23×Dic3—31no—
204C23×Dic3—31no—
205C23×Dic3—61no—
206C2×#237—38no—
207C2×#237—38no—
208C2×#237—68no—
209C2×#237—68no—
210C2×D3×D4—38no—
211C2×D3×D4—38no—
212C2×D3×D4—68no—
213C2×D3×D4—68no—
214C22×D12—31no—
215C22×D12—31no—
216C22×D12—31no—
217C22×D12—31no—
218C22×D12C2×D311yescharacteristic, complemented
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—31no—
223C22×C4×D3C2×D311yescharacteristic, complemented
224C22×Dic6—31no—
225C22×Dic6—31no—
226C3×#121—38no—
227C3×C4×D4—38no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C42—31no—
235C2×#217—31no—
236C2×#217—31no—
237C2×#217C2×D311yescharacteristic, complemented
238#939—38no—
239#937—38no—
240#937—38no—
241#935—38no—
242#930—38no—
243#930C2×D318yescomplemented
244C4×#67C2×D318yescomplemented
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—31no—
251C2×(C2×D3)⋊C4—31no—
252C2×(C2×D3)⋊C4—31no—
253C2×(C2×D3)⋊C4—31no—
254C2×(C2×D3)⋊C4—31no—
255C2×(C2×D3)⋊C4—38no—
256C2×(C2×D3)⋊C4—38no—
257C2×(C2×D3)⋊C4—31no—
258C2×(C2×D3)⋊C4—31no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—38no—
262C2×(C2×D3)⋊C4—61no—
263C2×(C2×D3)⋊C4—61no—
264C2×(C2×D3)⋊C4—61no—
265C2×(C2×D3)⋊C4—61no—
266C2×(C2×D3)⋊C4—68no—
267C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
268C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
269C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
270C2×C4⋊Dic3—31no—
271C2×C4⋊Dic3—31no—
272C2×C4⋊Dic3C2×D311yescharacteristic, complemented
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4C2×D311yescharacteristic, complemented
276C2×C4×Dic3C2×D311yescharacteristic, complemented
277#897—38no—
278#896—38no—
279#895—38no—
280#894—38no—
281#886—38no—
282#886—38no—
283#885—38no—
284#884—38no—
285#882—38no—
286#882—38no—
287#67⋊C4—38no—
288D3×C22⋊C4—38no—
289#875—38no—
290C4×D12—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32C2×D414yes—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—28no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—28no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3—44no—
304C22×C3⋊D3—416no—
305C22×C3⋊D3#4114yescomplemented
306C22×C3⋊D3C2412yes—
307C22×C3⋊D3C2412yes—
308C22×C3×D3—22no—
309C22×C3×D3—22no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—22no—
315C22×C3×D3—22no—
316C22×C3×D3C2×D414yes—
317C22×C3×D3C2412yes—
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C2×D32—28no—
321C2×D32—28no—
322C2×D32—44no—
323C2×D32—416no—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4—44no—
327C2×C32×C4C2412yes—
328C2×C32×C4C2412yes—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3—28no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C3×#67—28no—
335C3×#67—28no—
336C3×#67C2×D4116yescomplemented
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3C2×D414yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C3×D12—44no—
348C3×C4×D3—44no—
349#627—28no—
350#626—28no—
351#626—28no—
352#626—28no—
353#626—44no—
354#625—28no—
355#624—28no—
356D3×Dic3—28no—
357D3×Dic3—28no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—31no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—31no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—34no—
385C23×D3—34no—
386C23×D3—34no—
387C23×D3—34no—
388C23×D3—61no—
389C23×D3—61no—
390C23×D3—64no—
391C23×D3—64no—
392C23×D3—64no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—68no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—124no—
401C23×D3—122no—
402C23×D3—122no—
403C23×D3—122no—
404C23×D3—122no—
405C23×D3—124no—
406C23×D3C22×D311yescharacteristic
407C23×D3C22×D311yescharacteristic
408C23×D3C22×D311yescharacteristic
409C2×C3×D4—38no—
410C2×C3×D4—34no—
411C2×C3×D4—34no—
412C2×C3×D4—34no—
413C2×C3×D4—34no—
414C2×C3×D4—64no—
415C2×C3×D4—64no—
416C2×C3×D4—122no—
417C22×C3×C4—21no—
418C22×C3×C4—21no—
419C22×C3×C4—24no—
420C22×C3×C4—31no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—34no—
426C22×C3×C4—42no—
427C22×C3×C4—42no—
428C22×C3×C4—44no—
429C22×C3×C4—122no—
430C22×C3×C4C22×D311yescharacteristic
431C22×C3×C4C22×D311yescharacteristic
432C22×C3×C4C22×D311yescharacteristic
433C22×C3×C4C22×D311yescharacteristic
434C22×C3×C4C22×D314yescomplemented
435C22×C3×C4C22×D314yescomplemented
436C2×#67—24no—
437C2×#67—24no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—34no—
442C2×#67—34no—
443C2×#67—34no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—122no—
450C2×#67D1218yescomplemented
451C2×#67C22×D314yes—
452C2×#67C22×D314yes—
453C2×#67C22×D314yescomplemented
454C22×Dic3—34no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—34no—
460C22×Dic3—34no—
461C22×Dic3—34no—
462C22×Dic3—61no—
463C22×Dic3—61no—
464C22×Dic3—64no—
465C22×Dic3—64no—
466C22×Dic3—64no—
467C22×Dic3—64no—
468C22×Dic3—64no—
469C22×Dic3—124no—
470C22×Dic3C22×D311yescharacteristic
471C22×Dic3C22×D311yescharacteristic
472C22×Dic3C22×D311yescharacteristic
473C22×Dic3C22×D311yescharacteristic
474C22×Dic3C22×D311yescharacteristic
475#237—632no—
476#237—632no—
477D3×D4—632no—
478D3×D4—632no—
479C2×D12—34no—
480C2×D12—34no—
481C2×D12—34no—
482C2×D12—34no—
483C2×D12—42no—
484C2×D12—64no—
485C2×D12—64no—
486C2×D12—64no—
487C2×D12—122no—
488C2×D12C22×D314yescomplemented
489C2×C4×D3—34no—
490C2×C4×D3—34no—
491C2×C4×D3—34no—
492C2×C4×D3—34no—
493C2×C4×D3—42no—
494C2×C4×D3—64no—
495C2×C4×D3—64no—
496C2×C4×D3—64no—
497C2×C4×D3—64no—
498C2×C4×D3C22×D314yescomplemented
499C2×Dic6—34no—
500C2×Dic6—34no—
501C2×Dic6—64no—
502C2×Dic6—64no—
503C3×C4⋊C4—34no—
504C3×C4⋊C4—34no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4—34no—
509C3×C42—34no—
510#217—34no—
511#217—34no—
512#217C22×D314yescomplemented
513(C2×D3)⋊C4—34no—
514(C2×D3)⋊C4—34no—
515(C2×D3)⋊C4—34no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—64no—
528(C2×D3)⋊C4—64no—
529(C2×D3)⋊C4—64no—
530(C2×D3)⋊C4—64no—
531(C2×D3)⋊C4C22×D314yescomplemented
532(C2×D3)⋊C4C22×D314yescomplemented
533(C2×D3)⋊C4C22×D314yescomplemented
534C4⋊Dic3—34no—
535C4⋊Dic3—34no—
536C4⋊Dic3C22×D314yescomplemented
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4C22×D314yescomplemented
540C4×Dic3C22×D314yescomplemented
541C22×C32—28no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32C22×D414yes—
545C22×C32C22×D412yes—
546C22×C32C2×#4112yes—
547C22×C32H(5,𝔽2)12yes—
548C22×C32C2511yescharacteristic
549C2×C3⋊D3—22no—
550C2×C3⋊D3—28no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—22no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3—416no—
556C2×C3⋊D3—44no—
557C2×C3⋊D3C2×#4114yescomplemented
558C2×C3×D3—28no—
559C2×C3×D3—22no—
560C2×C3×D3—22no—
561C2×C3×D3—22no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—44no—
568C2×C3×D3—44no—
569C2×C3×D3C22×D414yes—
570D32—416no—
571C32×C4—22no—
572C32×C4—22no—
573C3⋊Dic3—22no—
574C3⋊Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3—22no—
579C3×Dic3C22×D414yes—
580C25—91no—
581C25—91no—
582C2×#41—98no—
583C2×#41—188no—
584C22×Q8—91no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—31no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—98no—
594C22×D4—91no—
595C22×D4—188no—
596C23×C4—31no—
597C23×C4—91no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601C23×C4D3211yescharacteristic, complemented
602#124—98no—
603#123—98no—
604#123—98no—
605C22⋊Q8—98no—
606#121—38no—
607#121—98no—
608#121—98no—
609#120—98no—
610#120—98no—
611C4×D4—38no—
612C4×D4—98no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4—31no—
615C2×C4⋊C4—91no—
616C2×C4⋊C4—91no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—31no—
619C2×C22⋊C4—31no—
620C2×C22⋊C4—31no—
621C2×C22⋊C4—98no—
622C2×C22⋊C4—91no—
623C2×C22⋊C4—91no—
624C2×C22⋊C4—91no—
625C2×C22⋊C4—91no—
626C2×C22⋊C4—91no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C22⋊C4—98no—
631C2×C42—31no—
632C23×C3—24no—
633C23×C3—24no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—21no—
640C23×C3—24no—
641C23×C3—34no—
642C23×C3—32no—
643C23×C3—32no—
644C23×C3—32no—
645C23×C3—62no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3C2×D1214yes—
654C23×C3D3×D414yes—
655C23×C3C23×D312yes—
656C23×C3C23×D312yes—
657C23×C3C23×D311yescharacteristic
658C23×C3C23×D311yescharacteristic
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—34no—
668C22×D3—34no—
669C22×D3—32no—
670C22×D3—32no—
671C22×D3—32no—
672C22×D3—32no—
673C22×D3—64no—
674C22×D3—62no—
675C22×D3—62no—
676C22×D3—68no—
677C22×D3—68no—
678C22×D3—68no—
679C22×D3—68no—
680C22×D3—68no—
681C22×D3—62no—
682C22×D3—62no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—616no—
686C22×D3—64no—
687C22×D3—62no—
688C22×D3—68no—
689C22×D3—62no—
690C22×D3—68no—
691C22×D3—62no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—68no—
696C22×D3—122no—
697C22×D3—122no—
698C22×D3—122no—
699C22×D3—128no—
700C22×D3—122no—
701C22×D3—124no—
702C22×D3—124no—
703C22×D3—1216no—
704C22×D3—1216no—
705C22×D3—124no—
706C22×D3—124no—
707C22×D3—1216no—
708C22×D3—1216no—
709C22×D3—128no—
710C22×D3—1232no—
711C22×D3C2×D1214yes—
712C22×D3C23×D312yes—
713C22×D3C23×D312yes—
714C22×D3C23×D312yes—
715C3×D4—316no—
716C3×D4—68no—
717C3×D4—68no—
718C3×D4—124no—
719C2×C3×C4—22no—
720C2×C3×C4—22no—
721C2×C3×C4—22no—
722C2×C3×C4—22no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—34no—
726C2×C3×C4—32no—
727C2×C3×C4—32no—
728C2×C3×C4—32no—
729C2×C3×C4—32no—
730C2×C3×C4—32no—
731C2×C3×C4—42no—
732C2×C3×C4—42no—
733C2×C3×C4—44no—
734C2×C3×C4—44no—
735C2×C3×C4—48no—
736C2×C3×C4—62no—
737C2×C3×C4—62no—
738C2×C3×C4—62no—
739C2×C3×C4—62no—
740C2×C3×C4—124no—
741C2×C3×C4C23×D312yes—
742C2×C3×C4C23×D312yes—
743C2×C3×C4C23×D312yes—
744C2×C3×C4C23×D312yes—
745#67—28no—
746#67—28no—
747#67—68no—
748#67—68no—
749#67—68no—
750#67—68no—
751#67—68no—
752#67—124no—
753#67C2×D12116yescomplemented
754C2×Dic3—22no—
755C2×Dic3—22no—
756C2×Dic3—22no—
757C2×Dic3—22no—
758C2×Dic3—32no—
759C2×Dic3—32no—
760C2×Dic3—32no—
761C2×Dic3—32no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—68no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—68no—
768C2×Dic3—62no—
769C2×Dic3—62no—
770C2×Dic3—68no—
771C2×Dic3—68no—
772C2×Dic3—122no—
773C2×Dic3—122no—
774C2×Dic3—128no—
775C2×Dic3C2×D1214yes—
776C2×Dic3C23×D312yes—
777C2×Dic3C23×D312yes—
778C2×Dic3C23×D312yes—
779C2×Dic3C23×D312yes—
780C2×Dic3C23×D312yes—
781D12—44no—
782D12—68no—
783D12—68no—
784D12—68no—
785D12—124no—
786C4×D3—44no—
787C4×D3—68no—
788C4×D3—68no—
789C4×D3—68no—
790C4×D3—68no—
791Dic6—68no—
792Dic6—68no—
793C2×C32—24no—
794C2×C32#54614yescomplemented
795C2×C32C23×D411yescharacteristic
796C2×C32C22×#4111yescharacteristic
797C2×C32C2×H(5,𝔽2)11yescharacteristic
798C3⋊D3—24no—
799C3⋊D3—42no—
800C3×D3—24no—
801C3×D3—42no—
802C3×D3—42no—
803C24—31no—
804C24—31no—
805C24—31no—
806C24—94no—
807C24—91no—
808C24—91no—
809C24—94no—
810C24—184no—
811C24—184no—
812C24—184no—
813C24—184no—
814C24—362no—
815C24—362no—
816C24C2×D3211yescharacteristic
817#41—1832no—
818C2×Q8—94no—
819C2×Q8—184no—
820C2×D4—34no—
821C2×D4—38no—
822C2×D4—34no—
823C2×D4—34no—
824C2×D4—34no—
825C2×D4—64no—
826C2×D4—64no—
827C2×D4—94no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—94no—
831C2×D4—94no—
832C2×D4—122no—
833C2×D4—184no—
834C2×D4—184no—
835C2×D4—184no—
836C2×D4—1832no—
837C2×D4—184no—
838C2×D4—362no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—31no—
844C22×C4—34no—
845C22×C4—42no—
846C22×C4—94no—
847C22×C4—94no—
848C22×C4—94no—
849C22×C4—94no—
850C22×C4—91no—
851C22×C4—91no—
852C22×C4—122no—
853C22×C4—184no—
854C22×C4—184no—
855C22×C4—184no—
856C22×C4—184no—
857C22×C4C2×D3211yescharacteristic
858C22×C4C2×D3211yescharacteristic
859C22×C4C2×D3214yescomplemented
860C4⋊C4—34no—
861C4⋊C4—34no—
862C4⋊C4—94no—
863C4⋊C4—94no—
864C22⋊C4—34no—
865C22⋊C4—34no—
866C22⋊C4—34no—
867C22⋊C4—34no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4—94no—
873C22⋊C4—94no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C42—34no—
877C22×C3—24no—
878C22×C3—24no—
879C22×C3—216no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—28no—
885C22×C3—28no—
886C22×C3—24no—
887C22×C3—22no—
888C22×C3—22no—
889C22×C3—22no—
890C22×C3—21no—
891C22×C3—34no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—68no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—124no—
902C22×C3—124no—
903C22×C3C22×D1214yes—
904C22×C3C22×D1212yes—
905C22×C3C2×D3×D414yes—
906C22×C3C2×D3×D412yes—
907C22×C3#100412yes—
908C22×C3#100412yes—
909C22×C3D3×#4112yes—
910C22×C3D3×#4112yes—
911C22×C3C24×D311yescharacteristic
912C22×C3C24×D311yescharacteristic
913C2×D3—22no—
914C2×D3—22no—
915C2×D3—28no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—34no—
923C2×D3—34no—
924C2×D3—44no—
925C2×D3—44no—
926C2×D3—64no—
927C2×D3—62no—
928C2×D3—62no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—68no—
932C2×D3—68no—
933C2×D3—64no—
934C2×D3—62no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—128no—
941C2×D3—122no—
942C2×D3—122no—
943C2×D3—122no—
944C2×D3—122no—
945C2×D3—1216no—
946C2×D3—1216no—
947C2×D3—1216no—
948C2×D3—1216no—
949C2×D3—1232no—
950C2×D3—128no—
951C2×D3—124no—
952C2×D3—124no—
953C2×D3C22×D1214yes—
954C3×C4—22no—
955C3×C4—22no—
956C3×C4—22no—
957C3×C4—22no—
958C3×C4—34no—
959C3×C4—42no—
960C3×C4—42no—
961C3×C4—62no—
962C3×C4—62no—
963C3×C4—62no—
964C3×C4—62no—
965Dic3—22no—
966Dic3—22no—
967Dic3—22no—
968Dic3—22no—
969Dic3—62no—
970Dic3—62no—
971Dic3—62no—
972Dic3—62no—
973Dic3—122no—
974Dic3—122no—
975Dic3C22×D1214yes—
976C32C2×#54611yescharacteristic, complemented, Sylow
977C23—22no—
978C23—22no—
979C23—34no—
980C23—32no—
981C23—32no—
982C23—32no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—94no—
992C23—92no—
993C23—92no—
994C23—188no—
995C23—188no—
996C23—188no—
997C23—182no—
998C23—182no—
999C23—188no—
1000C23—182no—
1001C23—182no—
1002C23—182no—
1003C23—364no—
1004C23—3616no—
1005C23—364no—
1006C23—3616no—
1007C23D3×D1214yes—
1008C23C22×D3212yes—
1009C23C22×D3211yescharacteristic
1010Q8—188no—
1011D4—316no—
1012D4—68no—
1013D4—68no—
1014D4—124no—
1015D4—188no—
1016D4—188no—
1017D4—188no—
1018D4—188no—
1019D4—364no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—34no—
1023C2×C4—32no—
1024C2×C4—32no—
1025C2×C4—32no—
1026C2×C4—32no—
1027C2×C4—32no—
1028C2×C4—44no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—92no—
1034C2×C4—92no—
1035C2×C4—124no—
1036C2×C4—188no—
1037C2×C4—188no—
1038C2×C4—188no—
1039C2×C4—182no—
1040C2×C4—182no—
1041C2×C4—188no—
1042C2×C4C22×D3212yes—
1043C2×C4C22×D3212yes—
1044C2×C3—28no—
1045C2×C3—24no—
1046C2×C3—24no—
1047C2×C3—24no—
1048C2×C3—21no—
1049C2×C3—21no—
1050C2×C3—21no—
1051C2×C3—64no—
1052C2×C3—122no—
1053C2×C3—122no—
1054C2×C3#555414yescomplemented
1055C2×C3#561014yescomplemented
1056C2×C3C23×D1211yescharacteristic
1057C2×C3C22×D3×D411yescharacteristic
1058C2×C3C2×#100411yescharacteristic
1059C2×C3C2×#100411yescharacteristic
1060C2×C3C2×D3×#4111yescharacteristic
1061C2×C3C2×D3×#4111yescharacteristic
1062D3—24no—
1063D3—42no—
1064D3—42no—
1065D3—64no—
1066D3—64no—
1067D3—124no—
1068D3—124no—
1069D3—122no—
1070D3—122no—
1071C22—28no—
1072C22—22no—
1073C22—22no—
1074C22—34no—
1075C22—68no—
1076C22—62no—
1077C22—62no—
1078C22—62no—
1079C22—62no—
1080C22—62no—
1081C22—62no—
1082C22—62no—
1083C22—62no—
1084C22—94no—
1085C22—124no—
1086C22—124no—
1087C22—188no—
1088C22—182no—
1089C22—182no—
1090C22—182no—
1091C22—182no—
1092C22—182no—
1093C22—3616no—
1094C22—3616no—
1095C22—364no—
1096C22C2×D3×D1214yes—
1097C22C2×D3×D1212yes—
1098C22#6430612yes—
1099C22#6433012yes—
1100C22C23×D3211yescharacteristic
1101C4—22no—
1102C4—22no—
1103C4—34no—
1104C4—62no—
1105C4—62no—
1106C4—62no—
1107C4—62no—
1108C4—182no—
1109C4—182no—
1110C3—21no—
1111C3C2×#555411yescharacteristic, complemented
1112C3C2×#561011yescharacteristic, complemented
1113C2—24no—
1114C2—64no—
1115C2—122no—
1116C2—122no—
1117C2—184no—
1118C2—362no—
1119C2#1059507514yesdirect product factor
1120C2C22×D3×D1211yescharacteristic
1121C2C2×#6430611yescharacteristic
1122C2C2×#6433011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC23×C32×C4C22
socleC23×C32C24
hypercenterC23×C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
1. C22×#3811C2semidirect
2. C22×#3805C2semidirect
3. C22×#3752C2semidirect
4. C2×C3×#930C2semidirect
5. C2×C3×C4×#67C2semidirect
6. C2×#63981C2semidirect
7. C2×#63962C2semidirect
8. #10595075C2direct (N × H)
9. C2×#63922C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63906C2semidirect
12. C2×#63895C2semidirect
13. C2×#63890C2semidirect
14. C2×#63886C2semidirect
15. C2×#63880C2semidirect
16. C2×#63852C2semidirect
21. C23×C32×C4C22semidirect
22. C23×C3⋊Dic3C22semidirect
25. C22×C3×#67C22semidirect
26. C22×C3×D12C22semidirect
27. C22×C3×C4×D3C22semidirect
29. C2×#3811C22semidirect
30. C22×#627C22semidirect
34. C22×#626C22semidirect
35. C22×#625C22semidirect
38. C2×#3805C22semidirect
39. C22×D3×Dic3C22semidirect
40. C22×D3×Dic3C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. C2×#3752C22semidirect
46. C2×C3×#217C22semidirect
47. C3×#930C22semidirect
48. C3×C4×#67C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×C4⋊Dic3C22semidirect
53. C2×C3×Dic3⋊C4C22semidirect
54. C2×C3×C4×Dic3C22semidirect
55. #63981C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
59. C2×#3722C22semidirect
60. #63962C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. #63922C22semidirect
64. D3×(C2×D3)⋊C4C22semidirect
65. #63906C22semidirect
66. #63895C22semidirect
67. #63890C22semidirect
68. #63886C22semidirect
69. #63880C22semidirect
70. #63852C22semidirect
82. C2×#930D3semidirect
83. C2×C4×#67D3semidirect
121. C22×C32×C4C23semidirect
125. C22×C3⋊Dic3C23semidirect
128. C2×C3×#67D4semidirect
131. C2×C3×#67C23semidirect
138. C2×C3×D12C23semidirect
140. C2×C3×C4×D3C23semidirect
143. C2×#627C23semidirect
151. C2×#626C23semidirect
153. C2×#625C23semidirect
159. C2×D3×Dic3C23semidirect
160. C2×D3×Dic3C23semidirect
163. #3752C23semidirect
164. #3752C23semidirect
165. C3×#217C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×C4⋊Dic3C23semidirect
170. C3×Dic3⋊C4C23semidirect
171. C3×C4×Dic3C23semidirect
172. Dic3⋊Dic3C23semidirect
173. Dic3⋊Dic3C23semidirect
175. #3722C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
190. C23×C3×C4C2×D3semidirect
191. C23×C3×C4C2×D3semidirect
200. C22×#67C2×D3semidirect
218. C22×D12C2×D3semidirect
223. C22×C4×D3C2×D3semidirect
237. C2×#217C2×D3semidirect
243. #930C2×D3semidirect
244. C4×#67C2×D3semidirect
267. C2×(C2×D3)⋊C4C2×D3semidirect
268. C2×(C2×D3)⋊C4C2×D3semidirect
269. C2×(C2×D3)⋊C4C2×D3semidirect
272. C2×C4⋊Dic3C2×D3semidirect
275. C2×Dic3⋊C4C2×D3semidirect
276. C2×C4×Dic3C2×D3semidirect
305. C22×C3⋊D3#41semidirect
336. C3×#67C2×D4semidirect
434. C22×C3×C4C22×D3semidirect
435. C22×C3×C4C22×D3semidirect
450. C2×#67D12semidirect
453. C2×#67C22×D3semidirect
488. C2×D12C22×D3semidirect
498. C2×C4×D3C22×D3semidirect
512. #217C22×D3semidirect
531. (C2×D3)⋊C4C22×D3semidirect
532. (C2×D3)⋊C4C22×D3semidirect
533. (C2×D3)⋊C4C22×D3semidirect
536. C4⋊Dic3C22×D3semidirect
539. Dic3⋊C4C22×D3semidirect
540. C4×Dic3C22×D3semidirect
557. C2×C3⋊D3C2×#41semidirect
601. C23×C4D32semidirect
753. #67C2×D12semidirect
794. C2×C32#546semidirect
859. C22×C4C2×D32semidirect
976. C32C2×#546semidirect
1054. C2×C3#5554semidirect
1055. C2×C3#5610semidirect
1111. C3C2×#5554semidirect
1112. C3C2×#5610semidirect
1119. C2#10595075direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38112
C22×#38052
C22×#37522
C2×C3×#9302
C2×C3×C4×#672
C2×#639812
C2×#639622
#105950752
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639062
C2×#638952
C2×#638902
C2×#638862
C2×#638802
C2×#638522
C2×#56103
C2×#55543