Finite Group Databasebeta

← C2×#10594285 #11902453

Subgroups — C2×#10594285 #11902453

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×#3796C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#885C211yesmaximal, characteristic, complemented
5C2×C3×#884C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63970C211yesmaximal, characteristic, complemented
8C2×#63969C211yesmaximal, characteristic, complemented
9C2×#63922C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×#63912C211yesmaximal, characteristic, complemented
12C2×C4×#626C211yesmaximal, characteristic, complemented
13C2×#63888C211yesmaximal, characteristic, complemented
14C2×#63880C211yesmaximal, characteristic, complemented
15C2×#63853C211yesmaximal, characteristic, complemented
16#10594285C2116yesmaximal, direct product factor
17C2×#5676—31nomaximal
18C2×#5610—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic, complemented
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C22×C3×#67C2211yescharacteristic
25C22×C3×#67C2211yescharacteristic, complemented
26C22×C3×D12C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×C3×Dic6C2211yescharacteristic, complemented
29C2×#3811—28no—
30C2×#3811C2218yescomplemented
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic, complemented
35C22×#625C2211yescharacteristic, complemented
36C22×#624C2211yescharacteristic
37C22×D3×Dic3C2211yescharacteristic, complemented
38C22×D3×Dic3C2211yescharacteristic, complemented
39C2×#3796—28no—
40C2×#3796C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3757C2211yescharacteristic, complemented
43C2×#3752C2211yescharacteristic
44C2×#3752C2211yescharacteristic
45C22⋊C4×C3⋊D3C2218yescomplemented
46C2×C3×#217C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
49C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
50C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
51C2×C3×C4×Dic3C2211yescharacteristic, complemented
52C3×#885C2218yescomplemented
53C3×#884C2218yescomplemented
54#63981C2218yescomplemented
55#63970C2218yescomplemented
56#63969C2218yescomplemented
57C2×#3724C2211yescharacteristic, complemented
58C2×Dic3⋊Dic3C2211yescharacteristic, complemented
59C2×Dic3⋊Dic3C2211yescharacteristic, complemented
60C2×#3722C2211yescharacteristic
61C2×#3722C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64#63922C2218yescomplemented
65D3×(C2×D3)⋊C4C2218yescomplemented
66#63912C2218yescomplemented
67C4×#626C2218yescomplemented
68#63888C2218yescomplemented
69#63880C2218yescomplemented
70#63853C2218yescomplemented
71C22×#239—31no—
72C22×#237—31no—
73C22×D3×D4—31no—
74C22×D3×D4—31no—
75C2×C3×#124—31no—
76C2×C3×#121—31no—
77C2×#946—31no—
78C2×#939—31no—
79C2×#938—31no—
80C2×#937—31no—
81C2×#937—31no—
82C2×#935—31no—
83C2×C4×#67—31no—
84C22×(C2×D3)⋊C4—31no—
85#5676—316no—
86#5610—316no—
87C2×#896—31no—
88C2×#894—31no—
89C2×#885D311yescharacteristic, complemented
90C2×#884—31no—
91C2×#884—31no—
92C2×#884D311yescharacteristic, complemented
93C2×#883—31no—
94C2×#883—31no—
95C2×#882—31no—
96C2×#882—31no—
97C2×#67⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×D3×C22⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×D3×C22⋊C4—61no—
102C2×C4×D12—31no—
103C2×C4×D12—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3—24no—
106C23×C3⋊D3—24no—
107C23×C3⋊D3—42no—
108C23×C3⋊D3C2314yes—
109C23×C3⋊D3C2311yescharacteristic
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×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C22×C3⋊Dic3C2311yescharacteristic
121C22×C3⋊Dic3C2311yescharacteristic
122C2×C4×C3⋊D3—24no—
123C2×C4×C3⋊D3—42no—
124C2×C4×C3⋊D3C2314yescomplemented
125C2×C4×C3⋊D3C2314yescomplemented
126C2×C3×#67—24no—
127C2×C3×#67—24no—
128C2×C3×#67—42no—
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—24no—
138C2×C3×D12C2314yescomplemented
139C2×C3×C4×D3—42no—
140C2×C3×C4×D3C2314yescomplemented
141C2×C3×Dic6—24no—
142C2×C3×Dic6C2314yescomplemented
143#3811—232no—
144C2×#626—24no—
145C2×#626—24no—
146C2×#626—24no—
147C2×#626D418yescomplemented
148C2×#626C2314yes—
149C2×#626C2314yes—
150C2×#626C2314yes—
151C2×#626C2314yescomplemented
152C2×#625—42no—
153C2×#625C2314yescomplemented
154C2×#624—24no—
155C2×#624C2314yes—
156C2×D3×Dic3—24no—
157C2×D3×Dic3—24no—
158C2×D3×Dic3C2314yescomplemented
159C2×D3×Dic3C2314yescomplemented
160#3796—232no—
161C32×C22⋊C4C2314yescomplemented
162#3757C2314yescomplemented
163#3752C2314yes—
164#3752C2314yes—
165C3×#217C2314yescomplemented
166C3×(C2×D3)⋊C4C2314yescomplemented
167C3×(C2×D3)⋊C4C2314yescomplemented
168C3×(C2×D3)⋊C4C2314yescomplemented
169C3×Dic3⋊C4C2314yescomplemented
170C3×C4×Dic3C2314yescomplemented
171#3724C2314yescomplemented
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×Q8—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C22×C3×D4—31no—
189C23×C3×C4—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67C2×D311yescharacteristic
197C22×#67C2×D311yescharacteristic
198C22×#67C2×D311yescharacteristic, complemented
199C23×Dic3—31no—
200C23×Dic3—31no—
201C2×#239—38no—
202C2×#239—68no—
203C2×#237—38no—
204C2×#237—68no—
205C2×D3×D4—38no—
206C2×D3×D4—38no—
207C2×D3×D4—68no—
208C2×D3×D4—68no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12—31no—
212C22×D12—31no—
213C22×D12C2×D311yescharacteristic, complemented
214C22×C4×D3—31no—
215C22×C4×D3—31no—
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—31no—
220C22×C4×D3—31no—
221C22×C4×D3—31no—
222C22×C4×D3—61no—
223C22×C4×D3—61no—
224C22×C4×D3C2×D311yescharacteristic, complemented
225C22×Dic6C2×D311yescharacteristic, complemented
226C3×#124—38no—
227C3×#121—38no—
228C2×C3×C4⋊C4—31no—
229C2×C3×C22⋊C4—21no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—31no—
234C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
235C2×C3×C22⋊C4C2×D311yescharacteristic, complemented
236C2×C3×C42—31no—
237C2×#217—31no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—61no—
242C2×#217C2×D311yescharacteristic, complemented
243#946—38no—
244#939—38no—
245#938—38no—
246#937—38no—
247#937—38no—
248#935—38no—
249C4×#67—38no—
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—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—38no—
261C2×(C2×D3)⋊C4—61no—
262C2×(C2×D3)⋊C4—61no—
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
266C2×C4⋊Dic3—31no—
267C2×C4⋊Dic3—31no—
268C2×Dic3⋊C4—31no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—31no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4C2×D311yescharacteristic, complemented
273C2×C4×Dic3C2×D311yescharacteristic, complemented
274#896—38no—
275#894—38no—
276#885C2×D318yescomplemented
277#884—38no—
278#884—38no—
279#884C2×D318yescomplemented
280#883—38no—
281#883—38no—
282#882—38no—
283#882—38no—
284#67⋊C4—38no—
285D3×C22⋊C4—38no—
286D3×C22⋊C4—38no—
287D3×C22⋊C4—38no—
288D3×C22⋊C4—68no—
289C4×D12—38no—
290C4×D12—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—28no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—28no—
302C22×C3⋊D3—44no—
303C22×C3⋊D3—416no—
304C22×C3⋊D3C2×D414yes—
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×C4C2412yes—
327C2×C32×C4C2412yes—
328C2×C3⋊Dic3—22no—
329C2×C3⋊Dic3—22no—
330C2×C3⋊Dic3C2412yes—
331C2×C3⋊Dic3C2412yes—
332C4×C3⋊D3—28no—
333C4×C3⋊D3—44no—
334C3×#67—28no—
335C3×#67—28no—
336C3×#67—44no—
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—28no—
348C3×C4×D3—44no—
349C3×Dic6—28no—
350#626—28no—
351#626—28no—
352#626—28no—
353#626C2×D4116yescomplemented
354#625—44no—
355#624—28no—
356D3×Dic3—28no—
357D3×Dic3—28no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—31no—
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—91no—
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—64no—
390C23×D3—61no—
391C23×D3—64no—
392C23×D3—64no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—68no—
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×Q8—34no—
410C2×C3×Q8—64no—
411C2×C3×D4—34no—
412C2×C3×D4—34no—
413C2×C3×D4—34no—
414C2×C3×D4—34no—
415C2×C3×D4—64no—
416C2×C3×D4—64no—
417C2×C3×D4—64no—
418C2×C3×D4—122no—
419C22×C3×C4—21no—
420C22×C3×C4—21no—
421C22×C3×C4—31no—
422C22×C3×C4—31no—
423C22×C3×C4—31no—
424C22×C3×C4—31no—
425C22×C3×C4—31no—
426C22×C3×C4—34no—
427C22×C3×C4—122no—
428C22×C3×C4C22×D311yescharacteristic
429C22×C3×C4C22×D311yescharacteristic
430C22×C3×C4C22×D311yescharacteristic
431C22×C3×C4C22×D311yescharacteristic
432C2×#67—24no—
433C2×#67—24no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—38no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—42no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—122no—
446C2×#67—122no—
447C2×#67C22×D314yes—
448C2×#67C22×D314yes—
449C2×#67C22×D314yescomplemented
450C22×Dic3—31no—
451C22×Dic3—31no—
452C22×Dic3—31no—
453C22×Dic3—31no—
454C22×Dic3—34no—
455C22×Dic3—34no—
456C22×Dic3—61no—
457C22×Dic3—61no—
458C22×Dic3—64no—
459C22×Dic3—64no—
460C22×Dic3C22×D311yescharacteristic
461C22×Dic3C22×D311yescharacteristic
462C22×Dic3C22×D311yescharacteristic
463C22×Dic3C22×D311yescharacteristic
464C22×Dic3C22×D311yescharacteristic
465#239—632no—
466#237—632no—
467D3×D4—632no—
468D3×D4—632no—
469C2×D12—24no—
470C2×D12—38no—
471C2×D12—34no—
472C2×D12—34no—
473C2×D12—34no—
474C2×D12—34no—
475C2×D12—64no—
476C2×D12—64no—
477C2×D12—64no—
478C2×D12C22×D314yescomplemented
479C2×C4×D3—34no—
480C2×C4×D3—34no—
481C2×C4×D3—34no—
482C2×C4×D3—34no—
483C2×C4×D3—34no—
484C2×C4×D3—34no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—42no—
488C2×C4×D3—64no—
489C2×C4×D3—64no—
490C2×C4×D3—64no—
491C2×C4×D3—64no—
492C2×C4×D3—64no—
493C2×C4×D3—64no—
494C2×C4×D3—64no—
495C2×C4×D3—64no—
496C2×C4×D3—124no—
497C2×C4×D3—122no—
498C2×C4×D3—122no—
499C2×C4×D3—124no—
500C2×C4×D3C22×D314yescomplemented
501C2×Dic6—24no—
502C2×Dic6C22×D314yescomplemented
503C3×C4⋊C4—34no—
504C3×C22⋊C4—24no—
505C3×C22⋊C4—34no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4—34no—
509C3×C22⋊C4C22×D314yescomplemented
510C3×C22⋊C4C22×D314yescomplemented
511C3×C42—34no—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516#217—64no—
517#217C22×D314yescomplemented
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—34no—
528(C2×D3)⋊C4—64no—
529(C2×D3)⋊C4—64no—
530(C2×D3)⋊C4C22×D314yescomplemented
531(C2×D3)⋊C4C22×D314yescomplemented
532(C2×D3)⋊C4C22×D314yescomplemented
533C4⋊Dic3—34no—
534C4⋊Dic3—34no—
535Dic3⋊C4—34no—
536Dic3⋊C4—34no—
537Dic3⋊C4—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4C22×D314yescomplemented
540C4×Dic3C22×D314yescomplemented
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32—44no—
545C22×C32C22×D412yes—
546C22×C32C2×#4112yes—
547C22×C32H(5,𝔽2)12yes—
548C22×C32C2511yescharacteristic
549C2×C3⋊D3—28no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—28no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—22no—
555C2×C3⋊D3—416no—
556C2×C3⋊D3C22×D414yes—
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—31no—
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×C4—91no—
602#124—38no—
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—98no—
612C4×D4—98no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4—91no—
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—98no—
630C2×C22⋊C4D3211yescharacteristic, complemented
631C2×C42—31no—
632C23×C3—24no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—21no—
641C23×C3—34no—
642C23×C3—32no—
643C23×C3—32no—
644C23×C3—32no—
645C23×C3—42no—
646C23×C3—42no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—62no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—62no—
654C23×C3—62no—
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—34no—
670C22×D3—34no—
671C22×D3—32no—
672C22×D3—32no—
673C22×D3—32no—
674C22×D3—32no—
675C22×D3—64no—
676C22×D3—62no—
677C22×D3—64no—
678C22×D3—62no—
679C22×D3—68no—
680C22×D3—68no—
681C22×D3—68no—
682C22×D3—68no—
683C22×D3—68no—
684C22×D3—68no—
685C22×D3—68no—
686C22×D3—64no—
687C22×D3—64no—
688C22×D3—62no—
689C22×D3—62no—
690C22×D3—62no—
691C22×D3—62no—
692C22×D3—62no—
693C22×D3—62no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—616no—
697C22×D3—68no—
698C22×D3—128no—
699C22×D3—122no—
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×D3D3×D414yes—
712C22×D3C23×D312yes—
713C22×D3C23×D312yes—
714C22×D3C23×D312yes—
715C3×Q8—68no—
716C3×D4—68no—
717C3×D4—68no—
718C3×D4—68no—
719C3×D4—124no—
720C2×C3×C4—22no—
721C2×C3×C4—22no—
722C2×C3×C4—22no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—22no—
726C2×C3×C4—34no—
727C2×C3×C4—32no—
728C2×C3×C4—32no—
729C2×C3×C4—32no—
730C2×C3×C4—32no—
731C2×C3×C4—32no—
732C2×C3×C4—42no—
733C2×C3×C4—42no—
734C2×C3×C4—62no—
735C2×C3×C4—62no—
736C2×C3×C4—62no—
737C2×C3×C4—62no—
738C2×C3×C4—124no—
739C2×C3×C4C23×D312yes—
740C2×C3×C4C23×D312yes—
741C2×C3×C4C23×D312yes—
742C2×C3×C4C23×D312yes—
743#67—28no—
744#67—28no—
745#67—316no—
746#67—44no—
747#67—68no—
748#67—68no—
749#67—68no—
750#67—124no—
751#67—124no—
752C2×Dic3—22no—
753C2×Dic3—22no—
754C2×Dic3—22no—
755C2×Dic3—22no—
756C2×Dic3—32no—
757C2×Dic3—32no—
758C2×Dic3—32no—
759C2×Dic3—32no—
760C2×Dic3—62no—
761C2×Dic3—62no—
762C2×Dic3—68no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—68no—
768C2×Dic3—122no—
769C2×Dic3—122no—
770C2×Dic3D3×D414yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774C2×Dic3C23×D312yes—
775C2×Dic3C23×D312yes—
776D12—28no—
777D12—316no—
778D12—68no—
779D12—68no—
780D12—68no—
781C4×D3—44no—
782C4×D3—68no—
783C4×D3—68no—
784C4×D3—68no—
785C4×D3—68no—
786C4×D3—68no—
787C4×D3—68no—
788C4×D3—128no—
789C4×D3—124no—
790C4×D3—124no—
791C4×D3—128no—
792Dic6—28no—
793C2×C32—42no—
794C2×C32#54614yescomplemented
795C2×C32C23×D411yescharacteristic
796C2×C32C22×#4111yescharacteristic
797C2×C32C2×H(5,𝔽2)11yescharacteristic
798C3⋊D3—24no—
799C3⋊D3—24no—
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—34no—
819C2×Q8—64no—
820C2×D4—34no—
821C2×D4—34no—
822C2×D4—34no—
823C2×D4—34no—
824C2×D4—64no—
825C2×D4—64no—
826C2×D4—64no—
827C2×D4—94no—
828C2×D4—98no—
829C2×D4—94no—
830C2×D4—94no—
831C2×D4—94no—
832C2×D4—94no—
833C2×D4—122no—
834C2×D4—184no—
835C2×D4—184no—
836C2×D4—184no—
837C2×D4—1832no—
838C2×D4—362no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—31no—
844C22×C4—34no—
845C22×C4—94no—
846C22×C4—94no—
847C22×C4—94no—
848C22×C4—91no—
849C22×C4—91no—
850C22×C4—94no—
851C22×C4—94no—
852C22×C4—122no—
853C22×C4—184no—
854C22×C4—184no—
855C22×C4—184no—
856C22×C4—184no—
857C22×C4—362no—
858C22×C4C2×D3211yescharacteristic
859C22×C4C2×D3211yescharacteristic
860C4⋊C4—34no—
861C4⋊C4—94no—
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⋊C4C2×D3214yescomplemented
876C42—34no—
877C22×C3—24no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—21no—
888C22×C3—34no—
889C22×C3—42no—
890C22×C3—42no—
891C22×C3—48no—
892C22×C3—44no—
893C22×C3—44no—
894C22×C3—68no—
895C22×C3—62no—
896C22×C3—62no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—62no—
901C22×C3—62no—
902C22×C3—62no—
903C22×C3—124no—
904C22×C3—124no—
905C22×C3C2×D3×D412yes—
906C22×C3C2×D3×D412yes—
907C22×C3#100412yes—
908C22×C3D3×#4112yes—
909C22×C3D3×#4112yes—
910C22×C3#100912yes—
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—34no—
925C2×D3—34no—
926C2×D3—44no—
927C2×D3—44no—
928C2×D3—64no—
929C2×D3—64no—
930C2×D3—64no—
931C2×D3—64no—
932C2×D3—616no—
933C2×D3—68no—
934C2×D3—68no—
935C2×D3—62no—
936C2×D3—62no—
937C2×D3—62no—
938C2×D3—62no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—62no—
942C2×D3—62no—
943C2×D3—68no—
944C2×D3—68no—
945C2×D3—122no—
946C2×D3—122no—
947C2×D3—128no—
948C2×D3—1216no—
949C2×D3—1216no—
950C2×D3—1216no—
951C2×D3—1216no—
952C2×D3—1232no—
953C2×D3C2×D3×D414yes—
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—
975Dic3C2×D3×D414yes—
976C32C2×#54611yescharacteristic, complemented, Sylow
977C23—22no—
978C23—22no—
979C23—22no—
980C23—34no—
981C23—32no—
982C23—32no—
983C23—32no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—62no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—94no—
993C23—94no—
994C23—92no—
995C23—92no—
996C23—188no—
997C23—188no—
998C23—188no—
999C23—188no—
1000C23—182no—
1001C23—182no—
1002C23—182no—
1003C23—182no—
1004C23—364no—
1005C23—3616no—
1006C23—364no—
1007C23—3616no—
1008C23C22×D3212yes—
1009C23C22×D3211yescharacteristic
1010Q8—68no—
1011D4—68no—
1012D4—68no—
1013D4—68no—
1014D4—916no—
1015D4—124no—
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—62no—
1029C2×C4—62no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—92no—
1033C2×C4—92no—
1034C2×C4—124no—
1035C2×C4—188no—
1036C2×C4—188no—
1037C2×C4—188no—
1038C2×C4—188no—
1039C2×C4—182no—
1040C2×C4—182no—
1041C2×C4—364no—
1042C2×C4C22×D3212yes—
1043C2×C4C22×D3212yes—
1044C2×C3—21no—
1045C2×C3—21no—
1046C2×C3—21no—
1047C2×C3—24no—
1048C2×C3—44no—
1049C2×C3—42no—
1050C2×C3—42no—
1051C2×C3—64no—
1052C2×C3—122no—
1053C2×C3—122no—
1054C2×C3#561014yescomplemented
1055C2×C3#567614yescomplemented
1056C2×C3C22×D3×D411yescharacteristic
1057C2×C3C22×D3×D411yescharacteristic
1058C2×C3C2×#100411yescharacteristic
1059C2×C3C2×D3×#4111yescharacteristic
1060C2×C3C2×D3×#4111yescharacteristic
1061C2×C3C2×#100911yescharacteristic
1062D3—24no—
1063D3—42no—
1064D3—42no—
1065D3—68no—
1066D3—64no—
1067D3—64no—
1068D3—64no—
1069D3—64no—
1070D3—124no—
1071C22—22no—
1072C22—22no—
1073C22—22no—
1074C22—34no—
1075C22—44no—
1076C22—62no—
1077C22—62no—
1078C22—68no—
1079C22—62no—
1080C22—62no—
1081C22—62no—
1082C22—62no—
1083C22—62no—
1084C22—62no—
1085C22—94no—
1086C22—94no—
1087C22—124no—
1088C22—124no—
1089C22—182no—
1090C22—182no—
1091C22—182no—
1092C22—182no—
1093C22—188no—
1094C22—188no—
1095C22—3616no—
1096C22—3616no—
1097C22#6430612yes—
1098C22D32×D412yes—
1099C22#6431412yes—
1100C22C23×D3211yescharacteristic
1101C4—22no—
1102C4—22no—
1103C4—34no—
1104C4—62no—
1105C4—62no—
1106C4—62no—
1107C4—62no—
1108C4—182no—
1109C4—182no—
1110C3—21no—
1111C3C2×#561011yescharacteristic, complemented
1112C3C2×#567611yescharacteristic, complemented
1113C2—42no—
1114C2—64no—
1115C2—122no—
1116C2—122no—
1117C2—184no—
1118C2—184no—
1119C2#1059428514yesdirect product factor
1120C2C2×#6430611yescharacteristic
1121C2C2×D32×D411yescharacteristic
1122C2C2×#6431411yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C22⋊C4C22
socleC23×C32C24
hypercenterC2×C22⋊C4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#3811C2semidirect
2. C22×#3796C2semidirect
3. C2×C22⋊C4×C3⋊D3C2semidirect
4. C2×C3×#885C2semidirect
5. C2×C3×#884C2semidirect
6. C2×#63981C2semidirect
7. C2×#63970C2semidirect
8. C2×#63969C2semidirect
9. C2×#63922C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×#63912C2semidirect
12. C2×C4×#626C2semidirect
13. C2×#63888C2semidirect
14. C2×#63880C2semidirect
15. C2×#63853C2semidirect
16. #10594285C2direct (N × H)
21. C22×C4×C3⋊D3C22semidirect
22. C22×C4×C3⋊D3C22semidirect
25. C22×C3×#67C22semidirect
26. C22×C3×D12C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×C3×Dic6C22semidirect
30. C2×#3811C22semidirect
34. C22×#626C22semidirect
35. C22×#625C22semidirect
37. C22×D3×Dic3C22semidirect
38. C22×D3×Dic3C22semidirect
40. C2×#3796C22semidirect
41. C2×C32×C22⋊C4C22semidirect
42. C2×#3757C22semidirect
45. C22⋊C4×C3⋊D3C22semidirect
46. C2×C3×#217C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×(C2×D3)⋊C4C22semidirect
49. C2×C3×(C2×D3)⋊C4C22semidirect
50. C2×C3×Dic3⋊C4C22semidirect
51. C2×C3×C4×Dic3C22semidirect
52. C3×#885C22semidirect
53. C3×#884C22semidirect
54. #63981C22semidirect
55. #63970C22semidirect
56. #63969C22semidirect
57. C2×#3724C22semidirect
58. C2×Dic3⋊Dic3C22semidirect
59. C2×Dic3⋊Dic3C22semidirect
61. C2×#3722C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63922C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. #63912C22semidirect
67. C4×#626C22semidirect
68. #63888C22semidirect
69. #63880C22semidirect
70. #63853C22semidirect
89. C2×#885D3semidirect
92. C2×#884D3semidirect
124. C2×C4×C3⋊D3C23semidirect
125. C2×C4×C3⋊D3C23semidirect
131. C2×C3×#67C23semidirect
138. C2×C3×D12C23semidirect
140. C2×C3×C4×D3C23semidirect
142. C2×C3×Dic6C23semidirect
147. C2×#626D4semidirect
151. C2×#626C23semidirect
153. C2×#625C23semidirect
158. C2×D3×Dic3C23semidirect
159. C2×D3×Dic3C23semidirect
161. C32×C22⋊C4C23semidirect
162. #3757C23semidirect
165. C3×#217C23semidirect
166. C3×(C2×D3)⋊C4C23semidirect
167. C3×(C2×D3)⋊C4C23semidirect
168. C3×(C2×D3)⋊C4C23semidirect
169. C3×Dic3⋊C4C23semidirect
170. C3×C4×Dic3C23semidirect
171. #3724C23semidirect
172. Dic3⋊Dic3C23semidirect
173. Dic3⋊Dic3C23semidirect
175. #3722C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
198. C22×#67C2×D3semidirect
213. C22×D12C2×D3semidirect
224. C22×C4×D3C2×D3semidirect
225. C22×Dic6C2×D3semidirect
234. C2×C3×C22⋊C4C2×D3semidirect
235. C2×C3×C22⋊C4C2×D3semidirect
242. C2×#217C2×D3semidirect
263. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×(C2×D3)⋊C4C2×D3semidirect
265. C2×(C2×D3)⋊C4C2×D3semidirect
272. C2×Dic3⋊C4C2×D3semidirect
273. C2×C4×Dic3C2×D3semidirect
276. #885C2×D3semidirect
279. #884C2×D3semidirect
305. C22×C3⋊D3#41semidirect
353. #626C2×D4semidirect
449. C2×#67C22×D3semidirect
478. C2×D12C22×D3semidirect
500. C2×C4×D3C22×D3semidirect
502. C2×Dic6C22×D3semidirect
509. C3×C22⋊C4C22×D3semidirect
510. C3×C22⋊C4C22×D3semidirect
517. #217C22×D3semidirect
530. (C2×D3)⋊C4C22×D3semidirect
531. (C2×D3)⋊C4C22×D3semidirect
532. (C2×D3)⋊C4C22×D3semidirect
539. Dic3⋊C4C22×D3semidirect
540. C4×Dic3C22×D3semidirect
557. C2×C3⋊D3C2×#41semidirect
630. C2×C22⋊C4D32semidirect
794. C2×C32#546semidirect
875. C22⋊C4C2×D32semidirect
976. C32C2×#546semidirect
1054. C2×C3#5610semidirect
1055. C2×C3#5676semidirect
1111. C3C2×#5610semidirect
1112. C3C2×#5676semidirect
1119. C2#10594285direct (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×#37962
C2×C22⋊C4×C3⋊D32
C2×C3×#8852
C2×C3×#8842
C2×#639812
C2×#639702
C2×#639692
C2×#639222
C2×D3×(C2×D3)⋊C42
C2×#639122
C2×C4×#6262
C2×#638882
C2×#638802
C2×#638532
#105942852
C2×#56763
C2×#56103