Finite Group Databasebeta

← C2×#10594611 #11900976

Subgroups — C2×#10594611 #11900976

Order 1152.

4139 conjugacy classes of subgroups.

The subgroup lattice has 1166 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3802C211yesmaximal, characteristic, complemented
2C22×D3×D12C211yesmaximal, characteristic, complemented
3C2×#64103C211yesmaximal, characteristic, complemented
4C2×C3×#895C211yesmaximal, characteristic, complemented
5C2×C3×#894C211yesmaximal, characteristic, complemented
6C2×#63923C211yesmaximal, characteristic, complemented
7C2×#63922C211yesmaximal, characteristic, complemented
8C2×#63922C211yesmaximal, characteristic, complemented
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63906C211yesmaximal, characteristic, complemented
12C2×#63905C211yesmaximal, characteristic, complemented
13C2×#63886C211yesmaximal, characteristic, complemented
14C2×#63885C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594611C2116yesmaximal, direct product factor
17C2×#5653—31nomaximal
18C2×#5605—31nomaximal
19C23×D32C2211yescharacteristic
20C23×D32C2211yescharacteristic, complemented
21C23×D32C2211yescharacteristic, complemented
22C22×C4⋊(C3⋊D3)C2211yescharacteristic
23C22×C4×C3⋊D3C2211yescharacteristic, complemented
24C22×C3×D12C2211yescharacteristic
25C22×C3×D12C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic, complemented
27C22×C3×D12C2211yescharacteristic, complemented
28C22×C3×C4×D3C2211yescharacteristic, complemented
29C22×C3×C4×D3C2211yescharacteristic, complemented
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic, complemented
32C22×#626C2211yescharacteristic, complemented
33C22×#626C2211yescharacteristic, complemented
34C22×#625C2211yescharacteristic
35C22×#625C2211yescharacteristic, complemented
36C22×#625C2211yescharacteristic, complemented
37C22×D3×Dic3C2211yescharacteristic, complemented
38C2×#3802—28no—
39C2×#3802C2218yescomplemented
40C2×D3×D12—28no—
41C2×D3×D12C2218yescomplemented
42C2×C32×C4⋊C4C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C2×#3752C2211yescharacteristic, complemented
46C2×#3750C2211yescharacteristic, complemented
47#64103C2218yescomplemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
51C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
52C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
53C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
54C3×#895C2218yescomplemented
55C3×#894C2218yescomplemented
56C2×Dic3⋊Dic3C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61#63923C2218yescomplemented
62#63922C2218yescomplemented
63#63922C2218yescomplemented
64#63922C2218yescomplemented
65D3×(C2×D3)⋊C4C2218yescomplemented
66#63906C2218yescomplemented
67#63905C2218yescomplemented
68#63886C2218yescomplemented
69#63885C2218yescomplemented
70#63853C2218yescomplemented
71C22×D3×D4—31no—
72C22×D3×D4—31no—
73C22×D3×D4—31no—
74C23×D12—31no—
75C2×C3×#123—31no—
76C2×C3×#121—31no—
77C2×#939—31no—
78C2×#939—31no—
79C2×#937—31no—
80C2×#937—31no—
81C2×#937—31no—
82C2×#930—31no—
83C2×#929—31no—
84C22×(C2×D3)⋊C4—31no—
85#5653—316no—
86#5605—316no—
87C2×#895—31no—
88C2×#895D311yescharacteristic, complemented
89C2×#894—31no—
90C2×#894—31no—
91C2×#894—31no—
92C2×#894—61no—
93C2×#894D311yescharacteristic, complemented
94C2×#884—31no—
95C2×#884—31no—
96C2×#883—31no—
97C2×#883—31no—
98C2×#882—31no—
99C2×#882—31no—
100C2×#882—31no—
101C2×#882—31no—
102C2×#882—31no—
103C2×D3×C22⋊C4—31no—
104C23×C3⋊D3C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3×D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C23×C3×D3C2311yescharacteristic
111C22×D32—24no—
112C22×D32—24no—
113C22×D32—42no—
114C22×D32—42no—
115C22×D32—42no—
116C22×D32—42no—
117C22×D32—42no—
118C22×D32—42no—
119C22×D32D418yescomplemented
120C22×D32C2314yes—
121C22×D32C2314yescomplemented
122C22×D32C2314yescomplemented
123C22×C32×C4C2311yescharacteristic
124C22×C32×C4C2311yescharacteristic
125C22×C32×C4C2311yescharacteristic
126C22×C3⋊Dic3C2311yescharacteristic
127C22×C3⋊Dic3C2311yescharacteristic
128C2×C4⋊(C3⋊D3)—24no—
129C2×C4⋊(C3⋊D3)C2314yes—
130C2×C4×C3⋊D3—24no—
131C2×C4×C3⋊D3C2314yescomplemented
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×D12—24no—
136C2×C3×D12—24no—
137C2×C3×D12—24no—
138C2×C3×D12—42no—
139C2×C3×D12C2314yes—
140C2×C3×D12C2314yescomplemented
141C2×C3×D12C2314yescomplemented
142C2×C3×D12C2314yescomplemented
143C2×C3×C4×D3—24no—
144C2×C3×C4×D3—42no—
145C2×C3×C4×D3C2314yescomplemented
146C2×C3×C4×D3C2314yescomplemented
147C2×#626—24no—
148C2×#626—24no—
149C2×#626—42no—
150C2×#626—42no—
151C2×#626C2314yes—
152C2×#626C2314yescomplemented
153C2×#626C2314yescomplemented
154C2×#626C2314yescomplemented
155C2×#625—24no—
156C2×#625—24no—
157C2×#625—42no—
158C2×#625C2314yes—
159C2×#625C2314yescomplemented
160C2×#625C2314yescomplemented
161C2×D3×Dic3—42no—
162C2×D3×Dic3C2314yescomplemented
163#3802—232no—
164D3×D12—232no—
165C32×C4⋊C4C2314yescomplemented
166#3752C2314yescomplemented
167#3752C2314yescomplemented
168#3752C2314yescomplemented
169#3750C2314yescomplemented
170C3×(C2×D3)⋊C4C2314yescomplemented
171C3×(C2×D3)⋊C4C2314yescomplemented
172C3×(C2×D3)⋊C4C2314yescomplemented
173C3×(C2×D3)⋊C4C2314yescomplemented
174C3×(C2×D3)⋊C4C2314yescomplemented
175C3×Dic3⋊C4C2314yescomplemented
176Dic3⋊Dic3C2314yescomplemented
177#3722C2314yescomplemented
178(C2×D3)⋊Dic3C2314yescomplemented
179(C2×D3)⋊Dic3C2314yescomplemented
180(C2×D3)⋊Dic3C2314yescomplemented
181C2×#534—91noSylow
182C24×D3—31no—
183C24×D3—31no—
184C24×D3—31no—
185C24×D3—31no—
186C24×D3—31no—
187C24×D3—31no—
188C22×C3×D4—31no—
189C22×C3×D4—31no—
190C22×C3×D4—31no—
191C22×C3×D4—31no—
192C23×C3×C4—31no—
193C23×C3×C4—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—31no—
199C22×#67—31no—
200C22×#67—31no—
201C22×#67—31no—
202C22×#67—31no—
203C22×#67—31no—
204C23×Dic3—31no—
205C2×D3×D4—38no—
206C2×D3×D4—38no—
207C2×D3×D4—38no—
208C2×D3×D4—68no—
209C2×D3×D4—68no—
210C2×D3×D4—68no—
211C22×D12—31no—
212C22×D12—31no—
213C22×D12—31no—
214C22×D12—31no—
215C22×D12—31no—
216C22×D12—31no—
217C22×D12—38no—
218C22×D12—61no—
219C22×D12—68no—
220C22×D12C2×D311yescharacteristic
221C22×D12C2×D311yescharacteristic, complemented
222C22×D12C2×D311yescharacteristic, complemented
223C22×D12C2×D311yescharacteristic, complemented
224C22×C4×D3—31no—
225C22×C4×D3—31no—
226C22×C4×D3—31no—
227C22×C4×D3—61no—
228C22×C4×D3C2×D311yescharacteristic, complemented
229C22×C4×D3C2×D311yescharacteristic, complemented
230C3×#123—38no—
231C3×#121—38no—
232C2×C3×C4⋊C4—21no—
233C2×C3×C4⋊C4—31no—
234C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
235C2×C3×C4⋊C4C2×D311yescharacteristic, complemented
236C2×C3×C22⋊C4—31no—
237C2×C3×C22⋊C4—31no—
238C2×C3×C22⋊C4—31no—
239C2×C3×C22⋊C4—31no—
240C2×C3×C22⋊C4—31no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—31no—
244#939—38no—
245#939—38no—
246#937—38no—
247#937—38no—
248#937—38no—
249#930—38no—
250#929—38no—
251C2×(C2×D3)⋊C4—31no—
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—31no—
262C2×(C2×D3)⋊C4—38no—
263C2×(C2×D3)⋊C4—61no—
264C2×(C2×D3)⋊C4—61no—
265C2×(C2×D3)⋊C4—61no—
266C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
267C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
268C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
269C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
270C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
271C2×C4⋊Dic3—31no—
272C2×Dic3⋊C4—31no—
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—61no—
276C2×Dic3⋊C4C2×D311yescharacteristic, complemented
277#895—38no—
278#895C2×D318yescomplemented
279#894—38no—
280#894—38no—
281#894—38no—
282#894—68no—
283#894C2×D318yescomplemented
284#884—38no—
285#884—38no—
286#883—38no—
287#883—38no—
288#882—38no—
289#882—38no—
290#882—38no—
291#882—38no—
292#882—38no—
293D3×C22⋊C4—38no—
294C23×C32C2411yescharacteristic
295C22×C3⋊D3—22no—
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3C2×D414yes—
301C22×C3⋊D3C2412yes—
302C22×C3⋊D3C2412yes—
303C22×C3×D3—22no—
304C22×C3×D3—22no—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
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×D3C2×D414yes—
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C22×C3×D3C2412yes—
321C22×C3×D3C2412yes—
322C22×C3×D3C2412yes—
323C2×D32—28no—
324C2×D32—28no—
325C2×D32—416no—
326C2×D32—44no—
327C2×D32—44no—
328C2×D32—44no—
329C2×D32—44no—
330C2×D32—44no—
331C2×D32—44no—
332C2×D32—416no—
333C2×D32—416no—
334C2×D32C2×D4116yescomplemented
335C2×C32×C4—22no—
336C2×C32×C4—22no—
337C2×C32×C4—22no—
338C2×C32×C4C2412yes—
339C2×C32×C4C2412yes—
340C2×C32×C4C2412yes—
341C2×C3⋊Dic3—22no—
342C2×C3⋊Dic3—22no—
343C2×C3⋊Dic3C2412yes—
344C2×C3⋊Dic3C2412yes—
345C4⋊(C3⋊D3)—28no—
346C4×C3⋊D3—28no—
347C2×C3×Dic3—22no—
348C2×C3×Dic3—22no—
349C2×C3×Dic3—22no—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C3×D12—28no—
354C3×D12—28no—
355C3×D12—28no—
356C3×D12—44no—
357C3×C4×D3—28no—
358C3×C4×D3—44no—
359#626—28no—
360#626—28no—
361#626—44no—
362#626—44no—
363#625—28no—
364#625—28no—
365#625—44no—
366D3×Dic3—44no—
367C23×D4—91no—
368C23×D4—91no—
369#534—916no—
370C2×#123—31no—
371C2×#123—91no—
372C2×#123—91no—
373C2×#123—91no—
374C2×#121—31no—
375C2×#121—91no—
376C2×#121—91no—
377C2×#121—91no—
378C2×#120—91no—
379C2×#120—91no—
380C2×#120—91no—
381C2×#120—91no—
382C22×C22⋊C4—91no—
383C24×C3—31no—
384C24×C3—31no—
385C24×C3—31no—
386C24×C3—31no—
387C24×C3—31no—
388C23×D3—31no—
389C23×D3—31no—
390C23×D3—38no—
391C23×D3—38no—
392C23×D3—34no—
393C23×D3—34no—
394C23×D3—31no—
395C23×D3—31no—
396C23×D3—34no—
397C23×D3—34no—
398C23×D3—34no—
399C23×D3—34no—
400C23×D3—61no—
401C23×D3—61no—
402C23×D3—64no—
403C23×D3—64no—
404C23×D3—64no—
405C23×D3—64no—
406C23×D3—122no—
407C23×D3—122no—
408C23×D3—122no—
409C23×D3—122no—
410C23×D3—122no—
411C23×D3—122no—
412C23×D3—122no—
413C23×D3—122no—
414C23×D3—122no—
415C23×D3—122no—
416C23×D3—122no—
417C23×D3—122no—
418C23×D3C22×D311yescharacteristic
419C23×D3C22×D311yescharacteristic
420C23×D3C22×D311yescharacteristic
421C23×D3C22×D311yescharacteristic
422C23×D3C22×D311yescharacteristic
423C2×C3×D4—34no—
424C2×C3×D4—34no—
425C2×C3×D4—34no—
426C2×C3×D4—34no—
427C2×C3×D4—64no—
428C2×C3×D4—64no—
429C2×C3×D4—64no—
430C2×C3×D4—122no—
431C22×C3×C4—21no—
432C22×C3×C4—21no—
433C22×C3×C4—21no—
434C22×C3×C4—31no—
435C22×C3×C4—31no—
436C22×C3×C4—31no—
437C22×C3×C4—34no—
438C22×C3×C4—34no—
439C22×C3×C4—64no—
440C22×C3×C4—122no—
441C22×C3×C4C22×D311yescharacteristic
442C22×C3×C4C22×D311yescharacteristic
443C22×C3×C4C22×D311yescharacteristic
444C22×C3×C4C22×D311yescharacteristic
445C22×C3×C4C22×D311yescharacteristic
446C22×C3×C4C22×D311yescharacteristic
447C2×#67—34no—
448C2×#67—34no—
449C2×#67—34no—
450C2×#67—34no—
451C2×#67—34no—
452C2×#67—34no—
453C2×#67—34no—
454C2×#67—34no—
455C2×#67—34no—
456C2×#67—34no—
457C2×#67—64no—
458C2×#67—64no—
459C2×#67—64no—
460C2×#67—64no—
461C2×#67—64no—
462C2×#67—64no—
463C2×#67—122no—
464C2×#67—122no—
465C2×#67—122no—
466C2×#67—122no—
467C22×Dic3—31no—
468C22×Dic3—31no—
469C22×Dic3—31no—
470C22×Dic3—31no—
471C22×Dic3—34no—
472C22×Dic3—61no—
473C22×Dic3—61no—
474C22×Dic3—122no—
475C22×Dic3C22×D311yescharacteristic
476C22×Dic3C22×D311yescharacteristic
477C22×Dic3C22×D311yescharacteristic
478D3×D4—632no—
479D3×D4—632no—
480D3×D4—632no—
481C2×D12—24no—
482C2×D12—24no—
483C2×D12—24no—
484C2×D12—34no—
485C2×D12—34no—
486C2×D12—34no—
487C2×D12—34no—
488C2×D12—34no—
489C2×D12—34no—
490C2×D12—42no—
491C2×D12—64no—
492C2×D12—632no—
493C2×D12—64no—
494C2×D12—64no—
495C2×D12—64no—
496C2×D12—64no—
497C2×D12—124no—
498C2×D12—122no—
499C2×D12—122no—
500C2×D12C22×D314yes—
501C2×D12C22×D314yescomplemented
502C2×D12C22×D314yescomplemented
503C2×D12C22×D314yescomplemented
504C2×C4×D3—24no—
505C2×C4×D3—34no—
506C2×C4×D3—34no—
507C2×C4×D3—34no—
508C2×C4×D3—42no—
509C2×C4×D3—64no—
510C2×C4×D3—64no—
511C2×C4×D3—64no—
512C2×C4×D3—124no—
513C2×C4×D3—122no—
514C2×C4×D3C22×D314yescomplemented
515C2×C4×D3C22×D314yescomplemented
516C3×C4⋊C4—24no—
517C3×C4⋊C4—34no—
518C3×C4⋊C4C22×D314yescomplemented
519C3×C4⋊C4C22×D314yescomplemented
520C3×C22⋊C4—34no—
521C3×C22⋊C4—34no—
522C3×C22⋊C4—34no—
523C3×C22⋊C4—34no—
524C3×C22⋊C4—34no—
525#217—34no—
526#217—34no—
527#217—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—34no—
530(C2×D3)⋊C4—34no—
531(C2×D3)⋊C4—34no—
532(C2×D3)⋊C4—34no—
533(C2×D3)⋊C4—34no—
534(C2×D3)⋊C4—34no—
535(C2×D3)⋊C4—34no—
536(C2×D3)⋊C4—34no—
537(C2×D3)⋊C4—34no—
538(C2×D3)⋊C4—34no—
539(C2×D3)⋊C4—64no—
540(C2×D3)⋊C4—64no—
541(C2×D3)⋊C4—64no—
542(C2×D3)⋊C4C22×D314yescomplemented
543(C2×D3)⋊C4C22×D314yescomplemented
544(C2×D3)⋊C4C22×D314yescomplemented
545(C2×D3)⋊C4C22×D314yescomplemented
546(C2×D3)⋊C4C22×D314yescomplemented
547C4⋊Dic3—34no—
548Dic3⋊C4—34no—
549Dic3⋊C4—34no—
550Dic3⋊C4—34no—
551Dic3⋊C4—64no—
552Dic3⋊C4C22×D314yescomplemented
553C22×C32C22×D412yes—
554C22×C32H(5,𝔽2)12yes—
555C22×C32H(5,𝔽2)12yes—
556C22×C32C2511yescharacteristic
557C2×C3⋊D3—28no—
558C2×C3⋊D3—22no—
559C2×C3⋊D3—22no—
560C2×C3⋊D3—22no—
561C2×C3⋊D3—22no—
562C2×C3⋊D3—22no—
563C2×C3⋊D3—44no—
564C2×C3⋊D3C22×D414yes—
565C2×C3×D3—28no—
566C2×C3×D3—28no—
567C2×C3×D3—22no—
568C2×C3×D3—22no—
569C2×C3×D3—22no—
570C2×C3×D3—22no—
571C2×C3×D3—22no—
572C2×C3×D3—22no—
573C2×C3×D3—22no—
574C2×C3×D3—22no—
575C2×C3×D3—22no—
576C2×C3×D3—22no—
577C2×C3×D3—22no—
578C2×C3×D3—22no—
579C2×C3×D3—22no—
580C2×C3×D3—44no—
581C2×C3×D3—44no—
582C2×C3×D3—44no—
583C2×C3×D3C22×D414yes—
584C2×C3×D3C22×D414yes—
585D32—416no—
586D32—416no—
587D32—416no—
588C32×C4—22no—
589C32×C4—22no—
590C32×C4—22no—
591C3⋊Dic3—22no—
592C3⋊Dic3—22no—
593C3×Dic3—22no—
594C3×Dic3—22no—
595C3×Dic3—22no—
596C25—91no—
597C25—91no—
598C25—91no—
599C22×D4—31no—
600C22×D4—31no—
601C22×D4—31no—
602C22×D4—31no—
603C22×D4—98no—
604C22×D4—91no—
605C22×D4—91no—
606C22×D4—91no—
607C22×D4—91no—
608C22×D4—98no—
609C22×D4—91no—
610C22×D4—91no—
611C22×D4—91no—
612C22×D4—91no—
613C22×D4—188no—
614C22×D4—188no—
615C23×C4—31no—
616C23×C4—31no—
617C23×C4—91no—
618C23×C4—91no—
619#123—38no—
620#123—98no—
621#123—98no—
622#123—98no—
623#121—38no—
624#121—98no—
625#121—98no—
626#121—98no—
627#120—98no—
628#120—98no—
629#120—98no—
630#120—98no—
631C2×C4⋊C4—31no—
632C2×C4⋊C4—91no—
633C2×C4⋊C4—91no—
634C2×C4⋊C4D3211yescharacteristic, complemented
635C2×C22⋊C4—31no—
636C2×C22⋊C4—31no—
637C2×C22⋊C4—31no—
638C2×C22⋊C4—31no—
639C2×C22⋊C4—31no—
640C2×C22⋊C4—98no—
641C2×C22⋊C4—91no—
642C2×C22⋊C4—91no—
643C2×C22⋊C4—91no—
644C2×C22⋊C4—91no—
645C2×C22⋊C4—91no—
646C2×C22⋊C4—91no—
647C2×C22⋊C4—91no—
648C23×C3—21no—
649C23×C3—34no—
650C23×C3—34no—
651C23×C3—32no—
652C23×C3—32no—
653C23×C3—32no—
654C23×C3—32no—
655C23×C3—32no—
656C23×C3—62no—
657C23×C3—62no—
658C23×C3—62no—
659C23×C3—62no—
660C23×C3—62no—
661C23×C3—62no—
662C23×C3—62no—
663C23×C3—62no—
664C23×C3—62no—
665C23×C3—62no—
666C23×C3—62no—
667C23×C3—62no—
668C23×C3—62no—
669C23×C3C23×D311yescharacteristic
670C23×C3C23×D311yescharacteristic
671C22×D3—22no—
672C22×D3—22no—
673C22×D3—22no—
674C22×D3—22no—
675C22×D3—22no—
676C22×D3—22no—
677C22×D3—22no—
678C22×D3—22no—
679C22×D3—22no—
680C22×D3—22no—
681C22×D3—22no—
682C22×D3—22no—
683C22×D3—22no—
684C22×D3—34no—
685C22×D3—34no—
686C22×D3—32no—
687C22×D3—32no—
688C22×D3—316no—
689C22×D3—316no—
690C22×D3—32no—
691C22×D3—32no—
692C22×D3—64no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—68no—
696C22×D3—68no—
697C22×D3—68no—
698C22×D3—62no—
699C22×D3—62no—
700C22×D3—62no—
701C22×D3—62no—
702C22×D3—62no—
703C22×D3—62no—
704C22×D3—62no—
705C22×D3—62no—
706C22×D3—62no—
707C22×D3—62no—
708C22×D3—68no—
709C22×D3—122no—
710C22×D3—122no—
711C22×D3—122no—
712C22×D3—122no—
713C22×D3—122no—
714C22×D3—1216no—
715C22×D3—124no—
716C22×D3—124no—
717C22×D3—124no—
718C22×D3—124no—
719C22×D3—124no—
720C22×D3—124no—
721C22×D3—1216no—
722C22×D3—124no—
723C22×D3—124no—
724C22×D3—124no—
725C22×D3—124no—
726C22×D3—124no—
727C22×D3—124no—
728C22×D3—1216no—
729C22×D3—1216no—
730C22×D3—1216no—
731C22×D3—1216no—
732C22×D3D3×D414yes—
733C22×D3D3×D414yes—
734C22×D3C23×D312yes—
735C22×D3C23×D312yes—
736C22×D3C23×D312yes—
737C22×D3C23×D312yes—
738C22×D3C23×D312yes—
739C3×D4—68no—
740C3×D4—68no—
741C3×D4—68no—
742C3×D4—124no—
743C2×C3×C4—22no—
744C2×C3×C4—22no—
745C2×C3×C4—22no—
746C2×C3×C4—22no—
747C2×C3×C4—22no—
748C2×C3×C4—22no—
749C2×C3×C4—22no—
750C2×C3×C4—22no—
751C2×C3×C4—22no—
752C2×C3×C4—32no—
753C2×C3×C4—32no—
754C2×C3×C4—32no—
755C2×C3×C4—42no—
756C2×C3×C4—42no—
757C2×C3×C4—42no—
758C2×C3×C4—68no—
759C2×C3×C4—62no—
760C2×C3×C4—62no—
761C2×C3×C4—62no—
762C2×C3×C4—124no—
763C2×C3×C4C23×D312yes—
764C2×C3×C4C23×D312yes—
765C2×C3×C4C23×D312yes—
766C2×C3×C4C23×D312yes—
767C2×C3×C4C23×D312yes—
768C2×C3×C4C23×D312yes—
769#67—68no—
770#67—68no—
771#67—68no—
772#67—68no—
773#67—68no—
774#67—68no—
775#67—124no—
776#67—124no—
777#67—124no—
778#67—124no—
779C2×Dic3—22no—
780C2×Dic3—22no—
781C2×Dic3—22no—
782C2×Dic3—32no—
783C2×Dic3—32no—
784C2×Dic3—32no—
785C2×Dic3—32no—
786C2×Dic3—62no—
787C2×Dic3—62no—
788C2×Dic3—62no—
789C2×Dic3—62no—
790C2×Dic3—62no—
791C2×Dic3—62no—
792C2×Dic3—122no—
793C2×Dic3—122no—
794C2×Dic3—124no—
795C2×Dic3C23×D312yes—
796C2×Dic3C23×D312yes—
797C2×Dic3C23×D312yes—
798D12—28no—
799D12—28no—
800D12—28no—
801D12—44no—
802D12—68no—
803D12—68no—
804D12—68no—
805D12—68no—
806D12—128no—
807D12—124no—
808D12—124no—
809C4×D3—28no—
810C4×D3—44no—
811C4×D3—68no—
812C4×D3—68no—
813C4×D3—128no—
814C4×D3—124no—
815C2×C32#53414yescomplemented
816C2×C32C23×D411yescharacteristic
817C2×C32C2×H(5,𝔽2)11yescharacteristic
818C2×C32C2×H(5,𝔽2)11yescharacteristic
819C3⋊D3—24no—
820C3⋊D3—42no—
821C3×D3—24no—
822C3×D3—24no—
823C3×D3—42no—
824C3×D3—42no—
825C3×D3—42no—
826C24—31no—
827C24—31no—
828C24—31no—
829C24—31no—
830C24—31no—
831C24—94no—
832C24—98no—
833C24—94no—
834C24—94no—
835C24—91no—
836C24—91no—
837C24—184no—
838C24—184no—
839C24—362no—
840C24—362no—
841C24—362no—
842C24—362no—
843C24—362no—
844C24—362no—
845C2×D4—34no—
846C2×D4—34no—
847C2×D4—34no—
848C2×D4—34no—
849C2×D4—64no—
850C2×D4—64no—
851C2×D4—64no—
852C2×D4—94no—
853C2×D4—94no—
854C2×D4—94no—
855C2×D4—94no—
856C2×D4—94no—
857C2×D4—94no—
858C2×D4—94no—
859C2×D4—94no—
860C2×D4—122no—
861C2×D4—184no—
862C2×D4—1832no—
863C2×D4—184no—
864C2×D4—184no—
865C2×D4—1832no—
866C2×D4—184no—
867C2×D4—184no—
868C2×D4—362no—
869C2×D4—362no—
870C2×D4—362no—
871C22×C4—31no—
872C22×C4—31no—
873C22×C4—31no—
874C22×C4—34no—
875C22×C4—34no—
876C22×C4—64no—
877C22×C4—94no—
878C22×C4—91no—
879C22×C4—91no—
880C22×C4—94no—
881C22×C4—122no—
882C22×C4—184no—
883C22×C4—362no—
884C22×C4C2×D3211yescharacteristic
885C22×C4C2×D3211yescharacteristic
886C22×C4C2×D3211yescharacteristic
887C4⋊C4—34no—
888C4⋊C4—94no—
889C4⋊C4—94no—
890C4⋊C4C2×D3214yescomplemented
891C22⋊C4—34no—
892C22⋊C4—34no—
893C22⋊C4—34no—
894C22⋊C4—34no—
895C22⋊C4—34no—
896C22⋊C4—94no—
897C22⋊C4—94no—
898C22⋊C4—94no—
899C22⋊C4—94no—
900C22⋊C4—94no—
901C22⋊C4—94no—
902C22⋊C4—94no—
903C22×C3—22no—
904C22×C3—22no—
905C22×C3—22no—
906C22×C3—21no—
907C22×C3—34no—
908C22×C3—34no—
909C22×C3—68no—
910C22×C3—62no—
911C22×C3—62no—
912C22×C3—62no—
913C22×C3—62no—
914C22×C3—68no—
915C22×C3—62no—
916C22×C3—62no—
917C22×C3—62no—
918C22×C3—62no—
919C22×C3—62no—
920C22×C3—62no—
921C22×C3—62no—
922C22×C3—62no—
923C22×C3—62no—
924C22×C3—124no—
925C22×C3—124no—
926C22×C3—124no—
927C22×C3C2×D3×D412yes—
928C22×C3C2×D3×D412yes—
929C22×C3#100412yes—
930C22×C3#100912yes—
931C22×C3#100912yes—
932C22×C3#100912yes—
933C22×C3C24×D311yescharacteristic
934C22×C3C24×D311yescharacteristic
935C2×D3—28no—
936C2×D3—22no—
937C2×D3—22no—
938C2×D3—22no—
939C2×D3—22no—
940C2×D3—28no—
941C2×D3—22no—
942C2×D3—22no—
943C2×D3—22no—
944C2×D3—22no—
945C2×D3—22no—
946C2×D3—22no—
947C2×D3—22no—
948C2×D3—22no—
949C2×D3—22no—
950C2×D3—34no—
951C2×D3—34no—
952C2×D3—44no—
953C2×D3—44no—
954C2×D3—44no—
955C2×D3—64no—
956C2×D3—68no—
957C2×D3—62no—
958C2×D3—62no—
959C2×D3—62no—
960C2×D3—62no—
961C2×D3—68no—
962C2×D3—62no—
963C2×D3—62no—
964C2×D3—62no—
965C2×D3—62no—
966C2×D3—62no—
967C2×D3—62no—
968C2×D3—128no—
969C2×D3—122no—
970C2×D3—122no—
971C2×D3—122no—
972C2×D3—122no—
973C2×D3—122no—
974C2×D3—1216no—
975C2×D3—1216no—
976C2×D3—1216no—
977C2×D3—1216no—
978C2×D3—1216no—
979C2×D3—1216no—
980C2×D3—124no—
981C2×D3—124no—
982C2×D3—244no—
983C2×D3C2×D3×D414yes—
984C2×D3C2×D3×D414yes—
985C3×C4—22no—
986C3×C4—22no—
987C3×C4—22no—
988C3×C4—22no—
989C3×C4—22no—
990C3×C4—22no—
991C3×C4—42no—
992C3×C4—42no—
993C3×C4—42no—
994C3×C4—62no—
995C3×C4—62no—
996C3×C4—62no—
997Dic3—22no—
998Dic3—22no—
999Dic3—22no—
1000Dic3—62no—
1001Dic3—62no—
1002Dic3—62no—
1003Dic3—62no—
1004Dic3—122no—
1005Dic3—122no—
1006C32C2×#53411yescharacteristic, complemented, Sylow
1007C23—34no—
1008C23—34no—
1009C23—32no—
1010C23—32no—
1011C23—32no—
1012C23—32no—
1013C23—32no—
1014C23—62no—
1015C23—62no—
1016C23—62no—
1017C23—62no—
1018C23—62no—
1019C23—62no—
1020C23—62no—
1021C23—62no—
1022C23—62no—
1023C23—62no—
1024C23—62no—
1025C23—62no—
1026C23—62no—
1027C23—916no—
1028C23—94no—
1029C23—92no—
1030C23—92no—
1031C23—188no—
1032C23—188no—
1033C23—182no—
1034C23—182no—
1035C23—182no—
1036C23—182no—
1037C23—182no—
1038C23—3616no—
1039C23—364no—
1040C23—364no—
1041C23—364no—
1042C23—364no—
1043C23—364no—
1044C23—364no—
1045C23—3616no—
1046C23—3616no—
1047C23C22×D3211yescharacteristic
1048D4—68no—
1049D4—68no—
1050D4—68no—
1051D4—124no—
1052D4—188no—
1053D4—188no—
1054D4—188no—
1055D4—188no—
1056D4—188no—
1057D4—364no—
1058D4—364no—
1059D4—364no—
1060C2×C4—22no—
1061C2×C4—22no—
1062C2×C4—22no—
1063C2×C4—32no—
1064C2×C4—32no—
1065C2×C4—32no—
1066C2×C4—68no—
1067C2×C4—62no—
1068C2×C4—62no—
1069C2×C4—62no—
1070C2×C4—92no—
1071C2×C4—92no—
1072C2×C4—124no—
1073C2×C4—188no—
1074C2×C4—182no—
1075C2×C4—182no—
1076C2×C4—364no—
1077C2×C4C22×D3212yes—
1078C2×C4C22×D3212yes—
1079C2×C4C22×D3212yes—
1080C2×C3—24no—
1081C2×C3—21no—
1082C2×C3—21no—
1083C2×C3—21no—
1084C2×C3—64no—
1085C2×C3—64no—
1086C2×C3—122no—
1087C2×C3—122no—
1088C2×C3—122no—
1089C2×C3#560514yescomplemented
1090C2×C3#565314yescomplemented
1091C2×C3C22×D3×D411yescharacteristic
1092C2×C3C22×D3×D411yescharacteristic
1093C2×C3C2×#100411yescharacteristic
1094C2×C3C2×#100911yescharacteristic
1095C2×C3C2×#100911yescharacteristic
1096C2×C3C2×#100911yescharacteristic
1097D3—24no—
1098D3—24no—
1099D3—42no—
1100D3—42no—
1101D3—42no—
1102D3—64no—
1103D3—64no—
1104D3—124no—
1105D3—122no—
1106D3—122no—
1107D3—242no—
1108C22—34no—
1109C22—34no—
1110C22—68no—
1111C22—68no—
1112C22—62no—
1113C22—62no—
1114C22—62no—
1115C22—62no—
1116C22—62no—
1117C22—62no—
1118C22—62no—
1119C22—62no—
1120C22—62no—
1121C22—62no—
1122C22—62no—
1123C22—62no—
1124C22—62no—
1125C22—94no—
1126C22—124no—
1127C22—124no—
1128C22—124no—
1129C22—188no—
1130C22—182no—
1131C22—182no—
1132C22—182no—
1133C22—182no—
1134C22—182no—
1135C22—3616no—
1136C22—3616no—
1137C22—3616no—
1138C22—364no—
1139C22#6430712yes—
1140C22D32×D412yes—
1141C22#6432012yes—
1142C22C23×D3211yescharacteristic
1143C4—22no—
1144C4—22no—
1145C4—22no—
1146C4—62no—
1147C4—62no—
1148C4—62no—
1149C4—182no—
1150C4—182no—
1151C3—21no—
1152C3C2×#560511yescharacteristic, complemented
1153C3C2×#565311yescharacteristic, complemented
1154C2—64no—
1155C2—64no—
1156C2—122no—
1157C2—122no—
1158C2—122no—
1159C2—184no—
1160C2—362no—
1161C2#1059461114yesdirect product factor
1162C2C2×#6430711yescharacteristic
1163C2C2×D32×D411yescharacteristic
1164C2C2×#6432011yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C4⋊C4C22
socleC23×C32C24
hypercenterC2×C4⋊C4D32
hypocenterC32C2×#534
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3802C2semidirect
2. C22×D3×D12C2semidirect
3. C2×#64103C2semidirect
4. C2×C3×#895C2semidirect
5. C2×C3×#894C2semidirect
6. C2×#63923C2semidirect
7. C2×#63922C2semidirect
8. C2×#63922C2semidirect
9. C2×#63922C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63906C2semidirect
12. C2×#63905C2semidirect
13. C2×#63886C2semidirect
14. C2×#63885C2semidirect
15. C2×#63853C2semidirect
16. #10594611C2direct (N × H)
20. C23×D32C22semidirect
21. C23×D32C22semidirect
23. C22×C4×C3⋊D3C22semidirect
25. C22×C3×D12C22semidirect
26. C22×C3×D12C22semidirect
27. C22×C3×D12C22semidirect
28. C22×C3×C4×D3C22semidirect
29. C22×C3×C4×D3C22semidirect
31. C22×#626C22semidirect
32. C22×#626C22semidirect
33. C22×#626C22semidirect
35. C22×#625C22semidirect
36. C22×#625C22semidirect
37. C22×D3×Dic3C22semidirect
39. C2×#3802C22semidirect
41. C2×D3×D12C22semidirect
42. C2×C32×C4⋊C4C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. C2×#3752C22semidirect
46. C2×#3750C22semidirect
47. #64103C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×(C2×D3)⋊C4C22semidirect
51. C2×C3×(C2×D3)⋊C4C22semidirect
52. C2×C3×(C2×D3)⋊C4C22semidirect
53. C2×C3×Dic3⋊C4C22semidirect
54. C3×#895C22semidirect
55. C3×#894C22semidirect
56. C2×Dic3⋊Dic3C22semidirect
57. C2×#3722C22semidirect
58. C2×(C2×D3)⋊Dic3C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. #63923C22semidirect
62. #63922C22semidirect
63. #63922C22semidirect
64. #63922C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. #63906C22semidirect
67. #63905C22semidirect
68. #63886C22semidirect
69. #63885C22semidirect
70. #63853C22semidirect
88. C2×#895D3semidirect
93. C2×#894D3semidirect
119. C22×D32D4semidirect
121. C22×D32C23semidirect
122. C22×D32C23semidirect
131. C2×C4×C3⋊D3C23semidirect
140. C2×C3×D12C23semidirect
141. C2×C3×D12C23semidirect
142. C2×C3×D12C23semidirect
145. C2×C3×C4×D3C23semidirect
146. C2×C3×C4×D3C23semidirect
152. C2×#626C23semidirect
153. C2×#626C23semidirect
154. C2×#626C23semidirect
159. C2×#625C23semidirect
160. C2×#625C23semidirect
162. C2×D3×Dic3C23semidirect
165. C32×C4⋊C4C23semidirect
166. #3752C23semidirect
167. #3752C23semidirect
168. #3752C23semidirect
169. #3750C23semidirect
170. C3×(C2×D3)⋊C4C23semidirect
171. C3×(C2×D3)⋊C4C23semidirect
172. C3×(C2×D3)⋊C4C23semidirect
173. C3×(C2×D3)⋊C4C23semidirect
174. C3×(C2×D3)⋊C4C23semidirect
175. C3×Dic3⋊C4C23semidirect
176. Dic3⋊Dic3C23semidirect
177. #3722C23semidirect
178. (C2×D3)⋊Dic3C23semidirect
179. (C2×D3)⋊Dic3C23semidirect
180. (C2×D3)⋊Dic3C23semidirect
221. C22×D12C2×D3semidirect
222. C22×D12C2×D3semidirect
223. C22×D12C2×D3semidirect
228. C22×C4×D3C2×D3semidirect
229. C22×C4×D3C2×D3semidirect
234. C2×C3×C4⋊C4C2×D3semidirect
235. C2×C3×C4⋊C4C2×D3semidirect
266. C2×(C2×D3)⋊C4C2×D3semidirect
267. C2×(C2×D3)⋊C4C2×D3semidirect
268. C2×(C2×D3)⋊C4C2×D3semidirect
269. C2×(C2×D3)⋊C4C2×D3semidirect
270. C2×(C2×D3)⋊C4C2×D3semidirect
276. C2×Dic3⋊C4C2×D3semidirect
278. #895C2×D3semidirect
283. #894C2×D3semidirect
334. C2×D32C2×D4semidirect
501. C2×D12C22×D3semidirect
502. C2×D12C22×D3semidirect
503. C2×D12C22×D3semidirect
514. C2×C4×D3C22×D3semidirect
515. C2×C4×D3C22×D3semidirect
518. C3×C4⋊C4C22×D3semidirect
519. C3×C4⋊C4C22×D3semidirect
542. (C2×D3)⋊C4C22×D3semidirect
543. (C2×D3)⋊C4C22×D3semidirect
544. (C2×D3)⋊C4C22×D3semidirect
545. (C2×D3)⋊C4C22×D3semidirect
546. (C2×D3)⋊C4C22×D3semidirect
552. Dic3⋊C4C22×D3semidirect
634. C2×C4⋊C4D32semidirect
815. C2×C32#534semidirect
890. C4⋊C4C2×D32semidirect
1006. C32C2×#534semidirect
1089. C2×C3#5605semidirect
1090. C2×C3#5653semidirect
1152. C3C2×#5605semidirect
1153. C3C2×#5653semidirect
1161. C2#10594611direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38022
C22×D3×D122
C2×#641032
C2×C3×#8952
C2×C3×#8942
C2×#639232
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639062
C2×#639052
C2×#638862
C2×#638852
C2×#638532
#105946112
C2×#56533
C2×#56053