Finite Group Databasebeta

← C2×#10594186 #11902433

Subgroups — C2×#10594186 #11902433

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
1C23×#626C211yesmaximal, characteristic, complemented
2C22×#3798C211yesmaximal, characteristic, complemented
3C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic, complemented
4C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
5C2×C3×D3×C22⋊C4C211yesmaximal, characteristic, complemented
6C2×#63981C211yesmaximal, characteristic, complemented
7C2×#63976C211yesmaximal, characteristic, complemented
8C2×#63964C211yesmaximal, characteristic, complemented
9C2×#63912C211yesmaximal, characteristic, complemented
10C2×#63906C211yesmaximal, characteristic, complemented
11C2×#63906C211yesmaximal, characteristic, complemented
12C2×C4×#626C211yesmaximal, characteristic, complemented
13C2×#63853C211yesmaximal, characteristic, complemented
14C2×#63852C211yesmaximal, characteristic, complemented
15C2×#63850C211yesmaximal, characteristic, complemented
16#10594186C2116yesmaximal, direct product factor
17C2×#5550—31nomaximal
18C2×#5490—31nomaximal
19C24×C3⋊D3C2211yescharacteristic
20C24×C3×D3C2211yescharacteristic
21C22×C4×C3⋊D3C2211yescharacteristic, complemented
22C22×C4×C3⋊D3C2211yescharacteristic, complemented
23C22×C3×#67C2211yescharacteristic
24C23×C3×Dic3C2211yescharacteristic
25C22×C3×C4×D3C2211yescharacteristic, complemented
26C22×C3×C4×D3C2211yescharacteristic, complemented
27C22×C3×C4×D3C2211yescharacteristic, complemented
28C22×#627C2211yescharacteristic, complemented
29C22×#626—28no—
30C22×#626C2211yescharacteristic
31C22×#626C2211yescharacteristic
32C22×#626C2211yescharacteristic
33C22×#626C2211yescharacteristic
34C22×#626C2218yescomplemented
35C22×#626C2211yescharacteristic, complemented
36C22×#626C2211yescharacteristic, complemented
37C22×#625C2211yescharacteristic, complemented
38C22×#625C2211yescharacteristic, complemented
39C2×#3798—28no—
40C2×#3798C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic
42C2×#3757C2211yescharacteristic
43C2×#3752C2211yescharacteristic, complemented
44C2×#3752C2211yescharacteristic, complemented
45C22⋊C4×C3⋊D3C2218yescomplemented
46C2×C3×#217C2211yescharacteristic
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×#67⋊C4C2218yescomplemented
53C3×D3×C22⋊C4C2218yescomplemented
54#63981C2218yescomplemented
55#63976C2218yescomplemented
56C2×#3724C2211yescharacteristic, complemented
57C2×Dic3⋊Dic3C2211yescharacteristic, complemented
58C2×Dic3⋊Dic3C2211yescharacteristic, complemented
59#63964C2218yescomplemented
60C2×#3722C2211yescharacteristic, complemented
61C2×#3722C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64#63912C2218yescomplemented
65#63906C2218yescomplemented
66#63906C2218yescomplemented
67C4×#626C2218yescomplemented
68#63853C2218yescomplemented
69#63852C2218yescomplemented
70#63850C2218yescomplemented
71C23×#67—31no—
72C22×#235—31no—
73C22×#235—31no—
74C23×D12—31no—
75C2×C3×C4×D4—31no—
76C22×C3×C22⋊C4—31no—
77C2×#953—31no—
78C2×#937—31no—
79C2×#937—31no—
80C2×#930—31no—
81C2×#930—31no—
82C2×#929—31no—
83C2×C4×#67—31no—
84C2×#924—31no—
85#5550—316no—
86C2×#894—31no—
87C2×#894—31no—
88C2×#885—31no—
89#5490—316no—
90C2×#884—31no—
91C2×#884—31no—
92C2×#884—31no—
93C2×#884—31no—
94C2×#883—31no—
95C2×#882—31no—
96C2×#67⋊C4D311yescharacteristic, complemented
97C2×D3×C22⋊C4—31no—
98C2×D3×C22⋊C4—31no—
99C2×D3×C22⋊C4—61no—
100C2×D3×C22⋊C4D311yescharacteristic, complemented
101C2×#878—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×D3—24no—
112C23×C3×D3—24no—
113C23×C3×D3—42no—
114C23×C3×D3C2311yescharacteristic
115C23×C3×D3C2311yescharacteristic
116C23×C3×D3C2314yes—
117C23×C3×D3C2311yescharacteristic
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×#67C2314yes—
128C22×C3×Dic3—24no—
129C22×C3×Dic3C2314yes—
130C22×C3×Dic3C2311yescharacteristic
131C22×C3×Dic3C2311yescharacteristic
132C22×C3×Dic3C2311yescharacteristic
133C22×C3×Dic3C2311yescharacteristic
134C22×C3×Dic3C2311yescharacteristic
135C2×C3×C4×D3—24no—
136C2×C3×C4×D3—24no—
137C2×C3×C4×D3—42no—
138C2×C3×C4×D3C2314yescomplemented
139C2×C3×C4×D3C2314yescomplemented
140C2×C3×C4×D3C2314yescomplemented
141C2×#627—24no—
142C2×#627C2314yescomplemented
143C2×#626—24no—
144C2×#626—24no—
145C2×#626—24no—
146C2×#626—24no—
147C2×#626—232no—
148C2×#626—42no—
149C2×#626D418yescomplemented
150C2×#626C2314yes—
151C2×#626C2314yes—
152C2×#626C2314yes—
153C2×#626C2314yes—
154C2×#626C2314yescomplemented
155C2×#626C2314yescomplemented
156C2×#625—24no—
157C2×#625—42no—
158C2×#625C2314yescomplemented
159C2×#625C2314yescomplemented
160#3798—232no—
161C32×C22⋊C4C2314yes—
162#3757C2314yes—
163#3752C2314yescomplemented
164#3752C2314yescomplemented
165C3×#217C2314yes—
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#3722C2314yescomplemented
175#3722C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—61no—
183C24×D3C2×D311yescharacteristic
184C22×C3×D4—31no—
185C23×C3×C4—31no—
186C23×C3×C4—31no—
187C23×C3×C4—31no—
188C23×C3×C4—31no—
189C22×#67—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—31no—
198C22×#67—38no—
199C22×#67—31no—
200C22×#67—68no—
201C22×#67C2×D311yescharacteristic
202C23×Dic3C2×D311yescharacteristic
203C2×#235—38no—
204C2×#235—38no—
205C2×#235—68no—
206C2×#235—68no—
207C22×D12—31no—
208C22×D12—31no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12—38no—
212C22×D12—31no—
213C22×D12—31no—
214C22×D12—68no—
215C22×C4×D3—31no—
216C22×C4×D3—31no—
217C22×C4×D3—31no—
218C22×C4×D3—31no—
219C22×C4×D3—61no—
220C22×C4×D3—61no—
221C22×C4×D3C2×D311yescharacteristic, complemented
222C22×C4×D3C2×D311yescharacteristic, complemented
223C22×C4×D3C2×D311yescharacteristic, complemented
224C22×Dic6—31no—
225C22×Dic6—31no—
226C3×C4×D4—38no—
227C2×C3×C4⋊C4—31no—
228C2×C3×C22⋊C4—21no—
229C2×C3×C22⋊C4—31no—
230C2×C3×C22⋊C4—31no—
231C2×C3×C22⋊C4—31no—
232C2×C3×C22⋊C4—31no—
233C2×C3×C22⋊C4—38no—
234C2×C3×C22⋊C4C2×D311yescharacteristic
235C2×C3×C22⋊C4C2×D311yescharacteristic
236C2×C3×C42—31no—
237#953—38no—
238C2×#217—31no—
239C2×#217—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—61no—
243C2×#217C2×D311yescharacteristic
244#937—38no—
245#937—38no—
246#930—38no—
247#930—38no—
248#929—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—61no—
261C2×(C2×D3)⋊C4—61no—
262C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
263C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
264C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
265C2×C4⋊Dic3—31no—
266C2×C4⋊Dic3—31no—
267#924—38no—
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#894—38no—
275#894—38no—
276#885—38no—
277#884—38no—
278#884—38no—
279#884—38no—
280#884—38no—
281#883—38no—
282#882—38no—
283#67⋊C4C2×D318yescomplemented
284D3×C22⋊C4—38no—
285D3×C22⋊C4—38no—
286D3×C22⋊C4—68no—
287D3×C22⋊C4C2×D318yescomplemented
288#878—38no—
289#875—38no—
290C4×D12—38no—
291C23×C32—22no—
292C23×C32—22no—
293C23×C32#4114yescomplemented
294C23×C32C2412yes—
295C23×C32C2411yescharacteristic
296C22×C3⋊D3—22no—
297C22×C3⋊D3—22no—
298C22×C3⋊D3—22no—
299C22×C3⋊D3—28no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3—22no—
302C22×C3⋊D3—28no—
303C22×C3⋊D3—44no—
304C22×C3⋊D3—416no—
305C22×C3⋊D3C2×D414yes—
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—28no—
315C22×C3×D3—22no—
316C22×C3×D3—22no—
317C22×C3×D3—28no—
318C22×C3×D3—44no—
319C22×C3×D3—416no—
320C22×C3×D3C2×D414yes—
321C22×C3×D3C2412yes—
322C22×C3×D3C2412yes—
323C22×C3×D3C2412yes—
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—
335C2×C3×Dic3—22no—
336C2×C3×Dic3—22no—
337C2×C3×Dic3—22no—
338C2×C3×Dic3—22no—
339C2×C3×Dic3—28no—
340C2×C3×Dic3C2×D414yes—
341C2×C3×Dic3C2412yes—
342C2×C3×Dic3C2412yes—
343C2×C3×Dic3C2412yes—
344C2×C3×Dic3C2412yes—
345C2×C3×Dic3C2412yes—
346C3×C4×D3—28no—
347C3×C4×D3—28no—
348C3×C4×D3—44no—
349#627—28no—
350#626—28no—
351#626—28no—
352#626—28no—
353#626—28no—
354#626—44no—
355#626C2×D4116yescomplemented
356#625—28no—
357#625—44no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—91no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—31no—
371C2×C4×D4—91no—
372C22×C22⋊C4—31no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3—34no—
379C24×C3—64no—
380C24×C3—64no—
381C24×C3—122no—
382C24×C3C22×D311yescharacteristic
383C24×C3C22×D311yescharacteristic
384C23×D3—24no—
385C23×D3—24no—
386C23×D3—31no—
387C23×D3—31no—
388C23×D3—31no—
389C23×D3—31no—
390C23×D3—34no—
391C23×D3—34no—
392C23×D3—42no—
393C23×D3—61no—
394C23×D3—64no—
395C23×D3—61no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—68no—
399C23×D3—64no—
400C23×D3—64no—
401C23×D3—124no—
402C23×D3—122no—
403C23×D3—122no—
404C23×D3—124no—
405C23×D3C22×D311yescharacteristic
406C23×D3C22×D311yescharacteristic
407C23×D3C22×D314yes—
408C23×D3C22×D311yescharacteristic
409C2×C3×D4—34no—
410C2×C3×D4—64no—
411C22×C3×C4—21no—
412C22×C3×C4—21no—
413C22×C3×C4—31no—
414C22×C3×C4—31no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—34no—
418C22×C3×C4—31no—
419C22×C3×C4—34no—
420C22×C3×C4—34no—
421C22×C3×C4—34no—
422C22×C3×C4—64no—
423C22×C3×C4—64no—
424C22×C3×C4—64no—
425C22×C3×C4—122no—
426C22×C3×C4C22×D311yescharacteristic
427C22×C3×C4C22×D311yescharacteristic
428C22×C3×C4C22×D311yescharacteristic
429C22×C3×C4C22×D311yescharacteristic
430C2×#67—24no—
431C2×#67—34no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—38no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—34no—
442C2×#67—632no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—122no—
450C2×#67—122no—
451C2×#67—122no—
452C2×#67C22×D314yes—
453C22×Dic3—24no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—31no—
458C22×Dic3—61no—
459C22×Dic3—61no—
460C22×Dic3C22×D314yes—
461C22×Dic3C22×D311yescharacteristic
462C22×Dic3C22×D311yescharacteristic
463C22×Dic3C22×D311yescharacteristic
464C22×Dic3C22×D311yescharacteristic
465C22×Dic3C22×D311yescharacteristic
466#235—632no—
467#235—632no—
468C2×D12—38no—
469C2×D12—34no—
470C2×D12—34no—
471C2×D12—34no—
472C2×D12—34no—
473C2×D12—34no—
474C2×D12—34no—
475C2×D12—632no—
476C2×D12—64no—
477C2×D12—64no—
478C2×D12—64no—
479C2×D12—64no—
480C2×D12—122no—
481C2×C4×D3—24no—
482C2×C4×D3—24no—
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—124no—
493C2×C4×D3—122no—
494C2×C4×D3—122no—
495C2×C4×D3—124no—
496C2×C4×D3C22×D314yescomplemented
497C2×C4×D3C22×D314yescomplemented
498C2×C4×D3C22×D314yescomplemented
499C2×Dic6—34no—
500C2×Dic6—34no—
501C2×Dic6—64no—
502C2×Dic6—64no—
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×D314yes—
510C3×C22⋊C4C22×D314yes—
511C3×C42—34no—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516#217—64no—
517#217C22×D314yes—
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—28no—
542C22×C32—22no—
543C22×C32—22no—
544C22×C32C22×D412yes—
545C22×C32C2×#4112yes—
546C22×C32C2×#4114yescomplemented
547C22×C32H(5,𝔽2)12yes—
548C22×C32C2511yescharacteristic
549C2×C3⋊D3—28no—
550C2×C3⋊D3—22no—
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⋊D3C22×D414yes—
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—416no—
568C2×C3×D3—44no—
569C2×C3×D3—44no—
570C2×C3×D3C22×D414yes—
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—31no—
581C25—91no—
582C2×#41—98no—
583C2×#41—188no—
584C22×Q8—91no—
585C22×D4—31no—
586C22×D4—91no—
587C22×D4—91no—
588C22×D4—91no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—98no—
592C22×D4—91no—
593C22×D4—91no—
594C22×D4—91no—
595C22×D4—188no—
596C23×C4—31no—
597C23×C4—31no—
598C23×C4—31no—
599C23×C4—31no—
600C23×C4—91no—
601C23×C4—91no—
602#124—98no—
603#123—98no—
604#123—98no—
605C22⋊Q8—98no—
606#121—98no—
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—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—38no—
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
631C2×C42—31no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—21no—
638C23×C3—24no—
639C23×C3—34no—
640C23×C3—32no—
641C23×C3—32no—
642C23×C3—32no—
643C23×C3—42no—
644C23×C3—42no—
645C23×C3—68no—
646C23×C3—62no—
647C23×C3—62no—
648C23×C3—62no—
649C23×C3—62no—
650C23×C3—68no—
651C23×C3—62no—
652C23×C3—62no—
653C23×C3—62no—
654C23×C3—62no—
655C23×C3—124no—
656C23×C3—1216no—
657C23×C3#23514yescomplemented
658C23×C3#23514yescomplemented
659C23×C3C23×D312yes—
660C23×C3C23×D312yes—
661C23×C3C23×D311yescharacteristic
662C23×C3C23×D311yescharacteristic
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—22no—
666C22×D3—22no—
667C22×D3—28no—
668C22×D3—22no—
669C22×D3—22no—
670C22×D3—22no—
671C22×D3—22no—
672C22×D3—28no—
673C22×D3—34no—
674C22×D3—34no—
675C22×D3—32no—
676C22×D3—32no—
677C22×D3—32no—
678C22×D3—32no—
679C22×D3—44no—
680C22×D3—416no—
681C22×D3—64no—
682C22×D3—62no—
683C22×D3—62no—
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—64no—
693C22×D3—616no—
694C22×D3—62no—
695C22×D3—62no—
696C22×D3—68no—
697C22×D3—68no—
698C22×D3—62no—
699C22×D3—62no—
700C22×D3—62no—
701C22×D3—62no—
702C22×D3—128no—
703C22×D3—122no—
704C22×D3—122no—
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×D4—68no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—22no—
720C2×C3×C4—22no—
721C2×C3×C4—22no—
722C2×C3×C4—34no—
723C2×C3×C4—32no—
724C2×C3×C4—32no—
725C2×C3×C4—32no—
726C2×C3×C4—32no—
727C2×C3×C4—32no—
728C2×C3×C4—42no—
729C2×C3×C4—42no—
730C2×C3×C4—68no—
731C2×C3×C4—68no—
732C2×C3×C4—68no—
733C2×C3×C4—62no—
734C2×C3×C4—62no—
735C2×C3×C4—62no—
736C2×C3×C4—62no—
737C2×C3×C4—124no—
738C2×C3×C4C23×D312yes—
739C2×C3×C4C23×D312yes—
740C2×C3×C4C23×D312yes—
741C2×C3×C4C23×D312yes—
742#67—28no—
743#67—316no—
744#67—68no—
745#67—68no—
746#67—68no—
747#67—68no—
748#67—68no—
749#67—68no—
750#67—124no—
751#67—124no—
752#67—124no—
753C2×Dic3—22no—
754C2×Dic3—22no—
755C2×Dic3—22no—
756C2×Dic3—22no—
757C2×Dic3—28no—
758C2×Dic3—32no—
759C2×Dic3—32no—
760C2×Dic3—32no—
761C2×Dic3—32no—
762C2×Dic3—62no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—62no—
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—316no—
777D12—68no—
778D12—68no—
779D12—68no—
780D12—68no—
781D12—124no—
782C4×D3—28no—
783C4×D3—28no—
784C4×D3—44no—
785C4×D3—68no—
786C4×D3—68no—
787C4×D3—128no—
788C4×D3—124no—
789C4×D3—124no—
790C4×D3—128no—
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—34no—
807C24—64no—
808C24—64no—
809C24—91no—
810C24—91no—
811C24—94no—
812C24—122no—
813C24—184no—
814C24—184no—
815C24—362no—
816C24C2×D3211yescharacteristic
817#41—1832no—
818C2×Q8—94no—
819C2×Q8—184no—
820C2×D4—34no—
821C2×D4—64no—
822C2×D4—94no—
823C2×D4—98no—
824C2×D4—94no—
825C2×D4—94no—
826C2×D4—94no—
827C2×D4—94no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—94no—
831C2×D4—184no—
832C2×D4—1832no—
833C2×D4—184no—
834C2×D4—184no—
835C2×D4—184no—
836C2×D4—184no—
837C2×D4—362no—
838C2×D4—362no—
839C22×C4—31no—
840C22×C4—34no—
841C22×C4—31no—
842C22×C4—31no—
843C22×C4—31no—
844C22×C4—31no—
845C22×C4—34no—
846C22×C4—34no—
847C22×C4—34no—
848C22×C4—64no—
849C22×C4—64no—
850C22×C4—64no—
851C22×C4—91no—
852C22×C4—91no—
853C22×C4—94no—
854C22×C4—94no—
855C22×C4—122no—
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×D3214yes—
876C42—34no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—28no—
882C22×C3—28no—
883C22×C3—22no—
884C22×C3—24no—
885C22×C3—22no—
886C22×C3—22no—
887C22×C3—21no—
888C22×C3—34no—
889C22×C3—42no—
890C22×C3—42no—
891C22×C3—48no—
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—1216no—
902C22×C3—124no—
903C22×C3—124no—
904C22×C3C2×#23512yes—
905C22×C3C2×#23512yes—
906C22×C3C2×#23514yescomplemented
907C22×C3C2×#23514yescomplemented
908C22×C3C2×D3×D412yes—
909C22×C3C2×D3×D412yes—
910C22×C3#100412yes—
911C22×C3#100912yes—
912C22×C3C24×D311yescharacteristic
913C22×C3C24×D311yescharacteristic
914C2×D3—22no—
915C2×D3—22no—
916C2×D3—28no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—22no—
920C2×D3—22no—
921C2×D3—22no—
922C2×D3—22no—
923C2×D3—34no—
924C2×D3—34no—
925C2×D3—416no—
926C2×D3—44no—
927C2×D3—44no—
928C2×D3—64no—
929C2×D3—64no—
930C2×D3—64no—
931C2×D3—616no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—62no—
935C2×D3—62no—
936C2×D3—68no—
937C2×D3—68no—
938C2×D3—64no—
939C2×D3—62no—
940C2×D3—62no—
941C2×D3—62no—
942C2×D3—62no—
943C2×D3—62no—
944C2×D3—62no—
945C2×D3—122no—
946C2×D3—122no—
947C2×D3—1216no—
948C2×D3—1216no—
949C2×D3—1232no—
950C2×D3—128no—
951C2×D3—124no—
952C2×D3—124no—
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—34no—
980C23—32no—
981C23—32no—
982C23—32no—
983C23—68no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—68no—
989C23—62no—
990C23—62no—
991C23—62no—
992C23—62no—
993C23—94no—
994C23—92no—
995C23—92no—
996C23—124no—
997C23—1216no—
998C23—188no—
999C23—182no—
1000C23—182no—
1001C23—182no—
1002C23—188no—
1003C23—182no—
1004C23—182no—
1005C23—364no—
1006C23—3616no—
1007C23#379814yescomplemented
1008C23C22×D3212yes—
1009C23C22×D3211yescharacteristic
1010Q8—188no—
1011D4—68no—
1012D4—916no—
1013D4—188no—
1014D4—188no—
1015D4—188no—
1016D4—188no—
1017D4—188no—
1018D4—364no—
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—68no—
1029C2×C4—68no—
1030C2×C4—68no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—92no—
1036C2×C4—92no—
1037C2×C4—124no—
1038C2×C4—188no—
1039C2×C4—182no—
1040C2×C4—182no—
1041C2×C4—364no—
1042C2×C4C22×D3212yes—
1043C2×C4C22×D3212yes—
1044C2×C3—24no—
1045C2×C3—24no—
1046C2×C3—21no—
1047C2×C3—21no—
1048C2×C3—21no—
1049C2×C3—24no—
1050C2×C3—44no—
1051C2×C3—64no—
1052C2×C3—122no—
1053C2×C3—122no—
1054C2×C3#549014yescomplemented
1055C2×C3#555014yescomplemented
1056C2×C3C22×#23511yescharacteristic
1057C2×C3C22×#23511yescharacteristic
1058C2×C3C22×D3×D411yescharacteristic
1059C2×C3C22×D3×D411yescharacteristic
1060C2×C3C2×#100411yescharacteristic
1061C2×C3C2×#100911yescharacteristic
1062D3—24no—
1063D3—42no—
1064D3—42no—
1065D3—68no—
1066D3—64no—
1067D3—64no—
1068D3—124no—
1069D3—122no—
1070D3—122no—
1071C22—22no—
1072C22—22no—
1073C22—28no—
1074C22—34no—
1075C22—62no—
1076C22—62no—
1077C22—68no—
1078C22—62no—
1079C22—62no—
1080C22—62no—
1081C22—62no—
1082C22—62no—
1083C22—62no—
1084C22—94no—
1085C22—1216no—
1086C22—124no—
1087C22—124no—
1088C22—182no—
1089C22—182no—
1090C22—188no—
1091C22—182no—
1092C22—182no—
1093C22—182no—
1094C22—3616no—
1095C22—364no—
1096C22C2×#379812yes—
1097C22C2×#379814yescomplemented
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×#549011yescharacteristic, complemented
1112C3C2×#555011yescharacteristic, complemented
1113C2—24no—
1114C2—64no—
1115C2—122no—
1116C2—122no—
1117C2—184no—
1118C2—362no—
1119C2#1059418614yesdirect product factor
1120C2C22×#379811yescharacteristic
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. C23×#626C2semidirect
2. C22×#3798C2semidirect
3. C2×C22⋊C4×C3⋊D3C2semidirect
4. C2×C3×#67⋊C4C2semidirect
5. C2×C3×D3×C22⋊C4C2semidirect
6. C2×#63981C2semidirect
7. C2×#63976C2semidirect
8. C2×#63964C2semidirect
9. C2×#63912C2semidirect
10. C2×#63906C2semidirect
11. C2×#63906C2semidirect
12. C2×C4×#626C2semidirect
13. C2×#63853C2semidirect
14. C2×#63852C2semidirect
15. C2×#63850C2semidirect
16. #10594186C2direct (N × H)
21. C22×C4×C3⋊D3C22semidirect
22. C22×C4×C3⋊D3C22semidirect
25. C22×C3×C4×D3C22semidirect
26. C22×C3×C4×D3C22semidirect
27. C22×C3×C4×D3C22semidirect
28. C22×#627C22semidirect
34. C22×#626C22semidirect
35. C22×#626C22semidirect
36. C22×#626C22semidirect
37. C22×#625C22semidirect
38. C22×#625C22semidirect
40. C2×#3798C22semidirect
43. C2×#3752C22semidirect
44. C2×#3752C22semidirect
45. C22⋊C4×C3⋊D3C22semidirect
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×#67⋊C4C22semidirect
53. C3×D3×C22⋊C4C22semidirect
54. #63981C22semidirect
55. #63976C22semidirect
56. C2×#3724C22semidirect
57. C2×Dic3⋊Dic3C22semidirect
58. C2×Dic3⋊Dic3C22semidirect
59. #63964C22semidirect
60. C2×#3722C22semidirect
61. C2×#3722C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63912C22semidirect
65. #63906C22semidirect
66. #63906C22semidirect
67. C4×#626C22semidirect
68. #63853C22semidirect
69. #63852C22semidirect
70. #63850C22semidirect
96. C2×#67⋊C4D3semidirect
100. C2×D3×C22⋊C4D3semidirect
124. C2×C4×C3⋊D3C23semidirect
125. C2×C4×C3⋊D3C23semidirect
138. C2×C3×C4×D3C23semidirect
139. C2×C3×C4×D3C23semidirect
140. C2×C3×C4×D3C23semidirect
142. C2×#627C23semidirect
149. C2×#626D4semidirect
154. C2×#626C23semidirect
155. C2×#626C23semidirect
158. C2×#625C23semidirect
159. C2×#625C23semidirect
163. #3752C23semidirect
164. #3752C23semidirect
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
174. #3722C23semidirect
175. #3722C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
221. C22×C4×D3C2×D3semidirect
222. C22×C4×D3C2×D3semidirect
223. C22×C4×D3C2×D3semidirect
262. C2×(C2×D3)⋊C4C2×D3semidirect
263. C2×(C2×D3)⋊C4C2×D3semidirect
264. C2×(C2×D3)⋊C4C2×D3semidirect
272. C2×Dic3⋊C4C2×D3semidirect
273. C2×C4×Dic3C2×D3semidirect
283. #67⋊C4C2×D3semidirect
287. D3×C22⋊C4C2×D3semidirect
293. C23×C32#41semidirect
355. #626C2×D4semidirect
496. C2×C4×D3C22×D3semidirect
497. C2×C4×D3C22×D3semidirect
498. C2×C4×D3C22×D3semidirect
530. (C2×D3)⋊C4C22×D3semidirect
531. (C2×D3)⋊C4C22×D3semidirect
532. (C2×D3)⋊C4C22×D3semidirect
539. Dic3⋊C4C22×D3semidirect
540. C4×Dic3C22×D3semidirect
546. C22×C32C2×#41semidirect
657. C23×C3#235semidirect
658. C23×C3#235semidirect
794. C2×C32#546semidirect
906. C22×C3C2×#235semidirect
907. C22×C3C2×#235semidirect
976. C32C2×#546semidirect
1007. C23#3798semidirect
1054. C2×C3#5490semidirect
1055. C2×C3#5550semidirect
1097. C22C2×#3798semidirect
1111. C3C2×#5490semidirect
1112. C3C2×#5550semidirect
1119. C2#10594186direct (N × H)

Maximal subgroups

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

subgroupindex
C23×#6262
C22×#37982
C2×C22⋊C4×C3⋊D32
C2×C3×#67⋊C42
C2×C3×D3×C22⋊C42
C2×#639812
C2×#639762
C2×#639642
C2×#639122
C2×#639062
C2×C4×#6262
C2×#638532
C2×#638522
C2×#638502
#105941862
C2×#55503
C2×#54903