Finite Group Databasebeta

← C2×#10595307 #11902414

Subgroups — C2×#10595307 #11902414

Order 1152.

4245 conjugacy classes of subgroups.

The subgroup lattice has 1128 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3830C211yesmaximal, characteristic, complemented
2C22×D3×#67C211yesmaximal, characteristic, complemented
3C2×C3×#939C211yesmaximal, characteristic, complemented
4C2×C3×#937C211yesmaximal, characteristic, complemented
5C2×#63983C211yesmaximal, characteristic, complemented
6C2×#63980C211yesmaximal, characteristic, complemented
7C2×#67⋊Dic3C211yesmaximal, characteristic, complemented
8C2×#63962C211yesmaximal, characteristic, complemented
9C22×(C2×D3)⋊Dic3C211yesmaximal, characteristic, complemented
10C2×#63958C211yesmaximal, characteristic, complemented
11C2×#63952C211yesmaximal, characteristic, complemented
12#10595307C2116yesmaximal, direct product factor
13C2×#63921C211yesmaximal, characteristic, complemented
14C2×#63913C211yesmaximal, characteristic, complemented
15C2×#63896C211yesmaximal, characteristic, complemented
16C2×#63853C211yesmaximal, characteristic, complemented
17C2×#5610—31nomaximal
18C2×#5591—31nomaximal
19C24×C3×D3C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×C32×D4C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic
23C22×#638C2211yescharacteristic, complemented
24C23×C3⋊Dic3C2211yescharacteristic, complemented
25C23×C3⋊Dic3C2211yescharacteristic, complemented
26C2×#3830—28no—
27C2×#3830C2218yescomplemented
28C22×C4×C3⋊D3C2211yescharacteristic, complemented
29C22×#634C2211yescharacteristic, complemented
30C22×C3×#67C2211yescharacteristic
31C22×C3×#67C2211yescharacteristic
32C22×C3×#67C2211yescharacteristic, complemented
33C22×C3×#67C2211yescharacteristic, complemented
34C23×C3×Dic3C2211yescharacteristic, complemented
35C2×D3×#67—28no—
36C2×D3×#67C2218yescomplemented
37C22×#626C2211yescharacteristic
38C22×#625C2211yescharacteristic
39C22×#624C2211yescharacteristic, complemented
40C22×D3×Dic3C2211yescharacteristic
41C2×C3×#217C2211yescharacteristic, complemented
42C2×C3×#217C2211yescharacteristic, complemented
43C3×#939C2218yescomplemented
44C3×#937C2218yescomplemented
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49#63983C2218yescomplemented
50#63980C2218yescomplemented
51#67⋊Dic3C2218yescomplemented
52C2×#3724C2211yescharacteristic, complemented
53C2×Dic3⋊Dic3C2211yescharacteristic, complemented
54C2×Dic3⋊Dic3C2211yescharacteristic, complemented
55C2×#3722C2211yescharacteristic, complemented
56#63962C2218yescomplemented
57C2×(C2×D3)⋊Dic3C2211yescharacteristic
58C2×(C2×D3)⋊Dic3C2211yescharacteristic
59C2×(C2×D3)⋊Dic3C2218yescomplemented
60C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64#63958C2218yescomplemented
65C2×Dic32C2211yescharacteristic, complemented
66#63952C2218yescomplemented
67#63921C2218yescomplemented
68#63913C2218yescomplemented
69#63896C2218yescomplemented
70#63853C2218yescomplemented
71C23×#67—31no—
72C22×#237—31no—
73C22×#237—31no—
74C22×#237—61no—
75C22×D3×D4—31no—
76C2×C3×#121—31no—
77C2×C3×#120—31no—
78C22×#217—31no—
79C2×#939—31no—
80C2×#939—31no—
81C2×#939D311yescharacteristic, complemented
82C2×#938—31no—
83C2×#937—31no—
84C2×#937—31no—
85C2×#937D311yescharacteristic, complemented
86C2×#935—31no—
87C2×D4×Dic3—31no—
88C2×C4×#67—31no—
89C22×(C2×D3)⋊C4—31no—
90#5610—316no—
91#5591—316no—
92C2×#896—31no—
93C2×#894—31no—
94C2×#886—31no—
95C2×#885—31no—
96C2×#885—31no—
97C2×#884—31no—
98C2×#883—31no—
99C2×#67⋊C4—31no—
100C2×#67⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×D3×C22⋊C4—31no—
103C2×#878—31no—
104C24×C32C2311yescharacteristic
105C24×C32C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3—24no—
108C23×C3×D3—24no—
109C23×C3×D3—42no—
110C23×C3×D3C2311yescharacteristic
111C23×C3×D3C2311yescharacteristic
112C23×C3×D3C2314yes—
113C23×C3×D3C2311yescharacteristic
114C22×D32—24no—
115C22×D32—24no—
116C22×D32—42no—
117C22×D32C2314yes—
118C2×C32×D4—24no—
119C2×C32×D4C2314yescomplemented
120C22×C32×C4C2311yescharacteristic
121C2×#638—24no—
122C2×#638D418yescomplemented
123C2×#638C2314yes—
124C2×#638C2314yescomplemented
125C22×C3⋊Dic3—24no—
126C22×C3⋊Dic3—24no—
127C22×C3⋊Dic3C2311yescharacteristic
128C22×C3⋊Dic3C2311yescharacteristic
129C22×C3⋊Dic3C2311yescharacteristic
130C22×C3⋊Dic3C2314yescomplemented
131C22×C3⋊Dic3C2314yescomplemented
132#3830—232no—
133C2×C4×C3⋊D3—24no—
134C2×C4×C3⋊D3C2314yescomplemented
135C2×#634—24no—
136C2×#634C2314yescomplemented
137C2×C3×#67—24no—
138C2×C3×#67—24no—
139C2×C3×#67—42no—
140C2×C3×#67—42no—
141C2×C3×#67C2314yes—
142C2×C3×#67C2314yes—
143C2×C3×#67C2314yescomplemented
144C2×C3×#67C2314yescomplemented
145C22×C3×Dic3—42no—
146C22×C3×Dic3C2311yescharacteristic
147C22×C3×Dic3C2311yescharacteristic
148C22×C3×Dic3C2311yescharacteristic
149C22×C3×Dic3C2311yescharacteristic
150C22×C3×Dic3C2311yescharacteristic
151C22×C3×Dic3C2314yescomplemented
152D3×#67—232no—
153C2×#626—24no—
154C2×#626C2314yes—
155C2×#625—24no—
156C2×#625C2314yes—
157C2×#624—42no—
158C2×#624C2314yescomplemented
159C2×D3×Dic3—24no—
160C2×D3×Dic3C2314yes—
161C3×#217C2314yescomplemented
162C3×#217C2314yescomplemented
163C3×(C2×D3)⋊C4C2314yes—
164C3×(C2×D3)⋊C4C2314yescomplemented
165C3×(C2×D3)⋊C4C2314yescomplemented
166C3×Dic3⋊C4C2314yescomplemented
167#3724C2314yescomplemented
168Dic3⋊Dic3C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170#3722C2314yescomplemented
171(C2×D3)⋊Dic3C2314yes—
172(C2×D3)⋊Dic3C2314yes—
173(C2×D3)⋊Dic3C2314yescomplemented
174(C2×D3)⋊Dic3C2314yescomplemented
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177Dic32C2314yescomplemented
178C2×#546—91noSylow
179C25×C3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3C2×D311yescharacteristic
183C22×C3×D4—21no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C22×C3×D4—31no—
188C22×C3×D4C2×D311yescharacteristic, complemented
189C22×C3×D4C2×D311yescharacteristic, complemented
190C23×C3×C4—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—31no—
197C22×#67—38no—
198C22×#67—31no—
199C22×#67—61no—
200C22×#67—61no—
201C22×#67—68no—
202C22×#67C2×D311yescharacteristic
203C22×#67C2×D311yescharacteristic
204C22×#67C2×D311yescharacteristic, complemented
205C22×#67C2×D311yescharacteristic, complemented
206C23×Dic3—31no—
207C23×Dic3—31no—
208C23×Dic3—31no—
209C23×Dic3—31no—
210C23×Dic3—31no—
211C23×Dic3—61no—
212C23×Dic3—61no—
213C23×Dic3C2×D311yescharacteristic, complemented
214C2×#237—38no—
215C2×#237—38no—
216C2×#237—68no—
217C2×#237—68no—
218C2×#237—68no—
219C2×#237—616no—
220C2×D3×D4—38no—
221C2×D3×D4—68no—
222C22×D12—31no—
223C22×C4×D3—31no—
224C22×C4×D3—31no—
225C22×C4×D3—31no—
226C22×C4×D3—31no—
227C22×C4×D3—31no—
228C22×C4×D3—61no—
229C22×Dic6—31no—
230C22×Dic6—31no—
231C22×Dic6—61no—
232C3×#121—38no—
233C3×#120—38no—
234C2×C3×C4⋊C4—31no—
235C2×C3×C22⋊C4—31no—
236C2×C3×C22⋊C4—31no—
237C2×C3×C22⋊C4—31no—
238C2×C3×C22⋊C4—31no—
239C2×C3×C22⋊C4—31no—
240C2×#217—31no—
241C2×#217—31no—
242C2×#217—31no—
243C2×#217—31no—
244C2×#217—31no—
245C2×#217—31no—
246C2×#217—38no—
247C2×#217C2×D311yescharacteristic, complemented
248C2×#217C2×D311yescharacteristic, complemented
249#939—38no—
250#939—38no—
251#939C2×D318yescomplemented
252#938—38no—
253#937—38no—
254#937—38no—
255#937C2×D318yescomplemented
256#935—38no—
257D4×Dic3—38no—
258C4×#67—38no—
259C2×(C2×D3)⋊C4—31no—
260C2×(C2×D3)⋊C4—31no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—31no—
264C2×(C2×D3)⋊C4—31no—
265C2×(C2×D3)⋊C4—38no—
266C2×(C2×D3)⋊C4—31no—
267C2×(C2×D3)⋊C4—31no—
268C2×(C2×D3)⋊C4C2×D311yescharacteristic
269C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
270C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
271C2×C4⋊Dic3—31no—
272C2×C4⋊Dic3—31no—
273C2×Dic3⋊C4—31no—
274C2×Dic3⋊C4—31no—
275C2×Dic3⋊C4—31no—
276C2×Dic3⋊C4—31no—
277C2×Dic3⋊C4C2×D311yescharacteristic, complemented
278C2×C4×Dic3—31no—
279C2×C4×Dic3—31no—
280#896—38no—
281#894—38no—
282#886—38no—
283#885—38no—
284#885—38no—
285#884—38no—
286#883—38no—
287#67⋊C4—38no—
288#67⋊C4—38no—
289D3×C22⋊C4—38no—
290D3×C22⋊C4—38no—
291#878—38no—
292C23×C32—22no—
293C23×C32—22no—
294C23×C32—22no—
295C23×C32—22no—
296C23×C32—22no—
297C23×C32C2×D414yes—
298C23×C32C2412yes—
299C23×C32C2412yes—
300C23×C32C2411yescharacteristic
301C22×C3⋊D3—22no—
302C22×C3⋊D3—22no—
303C22×C3⋊D3C2×D414yes—
304C22×C3⋊D3C2412yes—
305C22×C3×D3—22no—
306C22×C3×D3—22no—
307C22×C3×D3—22no—
308C22×C3×D3—22no—
309C22×C3×D3—28no—
310C22×C3×D3—22no—
311C22×C3×D3—22no—
312C22×C3×D3—22no—
313C22×C3×D3—22no—
314C22×C3×D3—28no—
315C22×C3×D3—44no—
316C22×C3×D3—416no—
317C22×C3×D3#4114yescomplemented
318C22×C3×D3C2412yes—
319C22×C3×D3C2412yes—
320C22×C3×D3C2412yes—
321C2×D32—28no—
322C2×D32—28no—
323C2×D32—44no—
324C2×D32—416no—
325C32×D4—28no—
326C2×C32×C4—22no—
327C2×C32×C4C2412yes—
328#638—28no—
329#638C2×D4116yescomplemented
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3—28no—
333C2×C3⋊Dic3—28no—
334C2×C3⋊Dic3C2×D414yes—
335C2×C3⋊Dic3C2412yes—
336C2×C3⋊Dic3C2412yes—
337C2×C3⋊Dic3C2412yes—
338C4×C3⋊D3—28no—
339#634—28no—
340C3×#67—28no—
341C3×#67—28no—
342C3×#67—44no—
343C3×#67—44no—
344C2×C3×Dic3—22no—
345C2×C3×Dic3—22no—
346C2×C3×Dic3—22no—
347C2×C3×Dic3—22no—
348C2×C3×Dic3—22no—
349C2×C3×Dic3—44no—
350C2×C3×Dic3C2412yes—
351C2×C3×Dic3C2412yes—
352C2×C3×Dic3C2412yes—
353C2×C3×Dic3C2412yes—
354C2×C3×Dic3C2412yes—
355#626—28no—
356#625—28no—
357#624—44no—
358D3×Dic3—28no—
359C22×#41—91no—
360C23×D4—91no—
361#546—916no—
362C2×#124—91no—
363C2×#123—91no—
364C2×#123—91no—
365C2×C22⋊Q8—91no—
366C2×#121—31no—
367C2×#121—91no—
368C2×#121—91no—
369C2×#120—31no—
370C2×#120—91no—
371C2×C4×D4—91no—
372C2×C4×D4—91no—
373C22×C22⋊C4—91no—
374C22×C22⋊C4—91no—
375C24×C3—21no—
376C24×C3—21no—
377C24×C3—31no—
378C24×C3—31no—
379C24×C3—31no—
380C24×C3—34no—
381C24×C3—64no—
382C24×C3—64no—
383C24×C3—122no—
384C24×C3C22×D311yescharacteristic
385C24×C3C22×D311yescharacteristic
386C24×C3C22×D311yescharacteristic
387C24×C3C22×D311yescharacteristic
388C23×D3—24no—
389C23×D3—24no—
390C23×D3—31no—
391C23×D3—31no—
392C23×D3—34no—
393C23×D3—34no—
394C23×D3—42no—
395C23×D3—61no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—64no—
399C23×D3—64no—
400C23×D3—122no—
401C23×D3—122no—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C23×D3C22×D314yes—
405C23×D3C22×D311yescharacteristic
406C2×C3×D4—28no—
407C2×C3×D4—24no—
408C2×C3×D4—24no—
409C2×C3×D4—24no—
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—
417C2×C3×D4—122no—
418C2×C3×D4C22×D314yescomplemented
419C2×C3×D4C22×D314yescomplemented
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
430C2×#67—24no—
431C2×#67—24no—
432C2×#67—38no—
433C2×#67—38no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—34no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—34no—
440C2×#67—34no—
441C2×#67—42no—
442C2×#67—42no—
443C2×#67—68no—
444C2×#67—64no—
445C2×#67—64no—
446C2×#67—64no—
447C2×#67—64no—
448C2×#67—64no—
449C2×#67—632no—
450C2×#67—64no—
451C2×#67—64no—
452C2×#67—68no—
453C2×#67C22×D314yes—
454C2×#67C22×D314yes—
455C2×#67C22×D314yescomplemented
456C2×#67C22×D314yescomplemented
457C22×Dic3—31no—
458C22×Dic3—31no—
459C22×Dic3—34no—
460C22×Dic3—34no—
461C22×Dic3—31no—
462C22×Dic3—31no—
463C22×Dic3—31no—
464C22×Dic3—31no—
465C22×Dic3—34no—
466C22×Dic3—34no—
467C22×Dic3—34no—
468C22×Dic3—42no—
469C22×Dic3—61no—
470C22×Dic3—61no—
471C22×Dic3—61no—
472C22×Dic3—64no—
473C22×Dic3—64no—
474C22×Dic3—64no—
475C22×Dic3—64no—
476C22×Dic3—64no—
477C22×Dic3—68no—
478C22×Dic3—68no—
479C22×Dic3—64no—
480C22×Dic3—64no—
481C22×Dic3C22×D311yescharacteristic
482C22×Dic3C22×D311yescharacteristic
483C22×Dic3C22×D311yescharacteristic
484C22×Dic3C22×D311yescharacteristic
485C22×Dic3C22×D311yescharacteristic
486C22×Dic3C22×D314yescomplemented
487#237—632no—
488#237—632no—
489#237—664no—
490D3×D4—632no—
491C2×D12—34no—
492C2×D12—64no—
493C2×C4×D3—34no—
494C2×C4×D3—34no—
495C2×C4×D3—34no—
496C2×C4×D3—34no—
497C2×C4×D3—34no—
498C2×C4×D3—64no—
499C2×C4×D3—64no—
500C2×C4×D3—64no—
501C2×C4×D3—64no—
502C2×C4×D3—68no—
503C2×C4×D3—122no—
504C2×C4×D3—122no—
505C2×Dic6—34no—
506C2×Dic6—34no—
507C2×Dic6—64no—
508C2×Dic6—64no—
509C2×Dic6—64no—
510C2×Dic6—68no—
511C3×C4⋊C4—34no—
512C3×C22⋊C4—34no—
513C3×C22⋊C4—34no—
514C3×C22⋊C4—34no—
515C3×C22⋊C4—34no—
516C3×C22⋊C4—34no—
517#217—34no—
518#217—34no—
519#217—34no—
520#217—34no—
521#217—34no—
522#217—34no—
523#217C22×D314yescomplemented
524#217C22×D314yescomplemented
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—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)⋊C4C22×D314yes—
534(C2×D3)⋊C4C22×D314yescomplemented
535(C2×D3)⋊C4C22×D314yescomplemented
536C4⋊Dic3—34no—
537C4⋊Dic3—34no—
538Dic3⋊C4—34no—
539Dic3⋊C4—34no—
540Dic3⋊C4—34no—
541Dic3⋊C4—34no—
542Dic3⋊C4C22×D314yescomplemented
543C4×Dic3—34no—
544C4×Dic3—34no—
545C22×C32—22no—
546C22×C32—28no—
547C22×C32—22no—
548C22×C32—22no—
549C22×C32—22no—
550C22×C32—22no—
551C22×C32—44no—
552C22×C32C22×D414yes—
553C22×C32C22×D412yes—
554C22×C32C2×#4112yes—
555C22×C32H(5,𝔽2)12yes—
556C22×C32C2511yescharacteristic
557C2×C3⋊D3—28no—
558C2×C3⋊D3—22no—
559C2×C3⋊D3—22no—
560C2×C3⋊D3C22×D414yes—
561C2×C3×D3—28no—
562C2×C3×D3—22no—
563C2×C3×D3—22no—
564C2×C3×D3—22no—
565C2×C3×D3—22no—
566C2×C3×D3—22no—
567C2×C3×D3—22no—
568C2×C3×D3—22no—
569C2×C3×D3—22no—
570C2×C3×D3—416no—
571C2×C3×D3—44no—
572C2×C3×D3—44no—
573C2×C3×D3C2×#4114yescomplemented
574D32—416no—
575C32×C4—22no—
576C3⋊Dic3—22no—
577C3⋊Dic3—22no—
578C3⋊Dic3C22×D414yes—
579C3×Dic3—22no—
580C3×Dic3—22no—
581C3×Dic3—22no—
582C3×Dic3—22no—
583C3×Dic3—22no—
584C25—31no—
585C25—91no—
586C2×#41—98no—
587C2×#41—188no—
588C22×Q8—91no—
589C22×D4—31no—
590C22×D4—31no—
591C22×D4—31no—
592C22×D4—31no—
593C22×D4—91no—
594C22×D4—98no—
595C22×D4—91no—
596C22×D4—91no—
597C22×D4—91no—
598C22×D4—188no—
599C22×D4D3211yescharacteristic, complemented
600C23×C4—31no—
601C23×C4—91no—
602C23×C4—91no—
603C23×C4—91no—
604C23×C4—91no—
605C23×C4—91no—
606#124—98no—
607#123—98no—
608#123—98no—
609C22⋊Q8—98no—
610#121—38no—
611#121—98no—
612#121—98no—
613#120—38no—
614#120—98no—
615C4×D4—98no—
616C4×D4—98no—
617C2×C4⋊C4—31no—
618C2×C4⋊C4—91no—
619C2×C4⋊C4—91no—
620C2×C4⋊C4—91no—
621C2×C22⋊C4—31no—
622C2×C22⋊C4—31no—
623C2×C22⋊C4—31no—
624C2×C22⋊C4—31no—
625C2×C22⋊C4—31no—
626C2×C22⋊C4—98no—
627C2×C22⋊C4—91no—
628C2×C22⋊C4—91no—
629C2×C22⋊C4—91no—
630C2×C22⋊C4—91no—
631C2×C22⋊C4—91no—
632C2×C22⋊C4—91no—
633C2×C22⋊C4—98no—
634C2×C22⋊C4—91no—
635C2×C42—91no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—22no—
639C23×C3—22no—
640C23×C3—24no—
641C23×C3—22no—
642C23×C3—22no—
643C23×C3—22no—
644C23×C3—22no—
645C23×C3—22no—
646C23×C3—22no—
647C23×C3—22no—
648C23×C3—22no—
649C23×C3—21no—
650C23×C3—24no—
651C23×C3—34no—
652C23×C3—32no—
653C23×C3—32no—
654C23×C3—32no—
655C23×C3—42no—
656C23×C3—42no—
657C23×C3—42no—
658C23×C3—42no—
659C23×C3—68no—
660C23×C3—62no—
661C23×C3—62no—
662C23×C3—68no—
663C23×C3—62no—
664C23×C3—62no—
665C23×C3—62no—
666C23×C3—62no—
667C23×C3—62no—
668C23×C3—62no—
669C23×C3—124no—
670C23×C3—1216no—
671C23×C3D3×D414yes—
672C23×C3D3×D414yes—
673C23×C3C23×D312yes—
674C23×C3C23×D312yes—
675C23×C3C23×D312yes—
676C23×C3C23×D312yes—
677C23×C3C23×D311yescharacteristic
678C23×C3C23×D311yescharacteristic
679C22×D3—22no—
680C22×D3—22no—
681C22×D3—22no—
682C22×D3—28no—
683C22×D3—22no—
684C22×D3—22no—
685C22×D3—22no—
686C22×D3—22no—
687C22×D3—22no—
688C22×D3—28no—
689C22×D3—34no—
690C22×D3—34no—
691C22×D3—32no—
692C22×D3—32no—
693C22×D3—44no—
694C22×D3—416no—
695C22×D3—64no—
696C22×D3—62no—
697C22×D3—68no—
698C22×D3—68no—
699C22×D3—68no—
700C22×D3—62no—
701C22×D3—62no—
702C22×D3—62no—
703C22×D3—62no—
704C22×D3—68no—
705C22×D3—122no—
706C22×D3—122no—
707C22×D3—124no—
708C22×D3—124no—
709C22×D3—1216no—
710C22×D3—1216no—
711C22×D3#23714yescomplemented
712C22×D3C23×D312yes—
713C22×D3C23×D312yes—
714C22×D3C23×D312yes—
715C3×D4—216no—
716C3×D4—28no—
717C3×D4—28no—
718C3×D4—68no—
719C3×D4—68no—
720C3×D4—124no—
721C3×D4—124no—
722C2×C3×C4—24no—
723C2×C3×C4—22no—
724C2×C3×C4—22no—
725C2×C3×C4—22no—
726C2×C3×C4—32no—
727C2×C3×C4—32no—
728C2×C3×C4—32no—
729C2×C3×C4—32no—
730C2×C3×C4—32no—
731C2×C3×C4—62no—
732C2×C3×C4—62no—
733C2×C3×C4—62no—
734C2×C3×C4—62no—
735C2×C3×C4—62no—
736C2×C3×C4—124no—
737C2×C3×C4C23×D312yes—
738C2×C3×C4C23×D312yes—
739#67—28no—
740#67—28no—
741#67—316no—
742#67—316no—
743#67—44no—
744#67—44no—
745#67—616no—
746#67—68no—
747#67—68no—
748#67—68no—
749#67—68no—
750#67—68no—
751#67—616no—
752C2×Dic3—22no—
753C2×Dic3—22no—
754C2×Dic3—22no—
755C2×Dic3—22no—
756C2×Dic3—22no—
757C2×Dic3—34no—
758C2×Dic3—34no—
759C2×Dic3—32no—
760C2×Dic3—32no—
761C2×Dic3—32no—
762C2×Dic3—32no—
763C2×Dic3—32no—
764C2×Dic3—32no—
765C2×Dic3—44no—
766C2×Dic3—64no—
767C2×Dic3—62no—
768C2×Dic3—62no—
769C2×Dic3—62no—
770C2×Dic3—68no—
771C2×Dic3—68no—
772C2×Dic3—68no—
773C2×Dic3—64no—
774C2×Dic3—64no—
775C2×Dic3—616no—
776C2×Dic3—616no—
777C2×Dic3—62no—
778C2×Dic3—62no—
779C2×Dic3—62no—
780C2×Dic3—62no—
781C2×Dic3—68no—
782C2×Dic3—68no—
783C2×Dic3C23×D312yes—
784C2×Dic3C23×D312yes—
785C2×Dic3C23×D312yes—
786C2×Dic3C23×D312yes—
787C2×Dic3C23×D312yes—
788D12—68no—
789C4×D3—68no—
790C4×D3—68no—
791C4×D3—68no—
792C4×D3—616no—
793C4×D3—124no—
794C4×D3—124no—
795Dic6—68no—
796Dic6—68no—
797Dic6—616no—
798C2×C32—24no—
799C2×C32—42no—
800C2×C32#54614yescomplemented
801C2×C32C23×D411yescharacteristic
802C2×C32C22×#4111yescharacteristic
803C2×C32C2×H(5,𝔽2)11yescharacteristic
804C3⋊D3—24no—
805C3×D3—24no—
806C3×D3—42no—
807C3×D3—42no—
808C24—31no—
809C24—31no—
810C24—31no—
811C24—34no—
812C24—64no—
813C24—64no—
814C24—94no—
815C24—91no—
816C24—122no—
817C24—184no—
818C24—184no—
819C24—362no—
820C24C2×D3211yescharacteristic
821C24C2×D3211yescharacteristic
822#41—1832no—
823C2×Q8—94no—
824C2×Q8—184no—
825C2×D4—24no—
826C2×D4—34no—
827C2×D4—34no—
828C2×D4—34no—
829C2×D4—34no—
830C2×D4—64no—
831C2×D4—64no—
832C2×D4—94no—
833C2×D4—94no—
834C2×D4—98no—
835C2×D4—94no—
836C2×D4—94no—
837C2×D4—122no—
838C2×D4—122no—
839C2×D4—184no—
840C2×D4—184no—
841C2×D4—1832no—
842C2×D4—184no—
843C2×D4C2×D3214yescomplemented
844C22×C4—31no—
845C22×C4—31no—
846C22×C4—31no—
847C22×C4—31no—
848C22×C4—31no—
849C22×C4—34no—
850C22×C4—94no—
851C22×C4—94no—
852C22×C4—91no—
853C22×C4—94no—
854C22×C4—94no—
855C22×C4—91no—
856C22×C4—91no—
857C22×C4—94no—
858C22×C4—122no—
859C22×C4—184no—
860C22×C4—184no—
861C22×C4—184no—
862C22×C4—184no—
863C22×C4—362no—
864C22×C4C2×D3211yescharacteristic
865C4⋊C4—34no—
866C4⋊C4—94no—
867C4⋊C4—94no—
868C4⋊C4—94no—
869C22⋊C4—34no—
870C22⋊C4—34no—
871C22⋊C4—34no—
872C22⋊C4—34no—
873C22⋊C4—34no—
874C22⋊C4—94no—
875C22⋊C4—94no—
876C22⋊C4—94no—
877C22⋊C4—94no—
878C22⋊C4—94no—
879C22⋊C4—94no—
880C22⋊C4—94no—
881C42—94no—
882C22×C3—22no—
883C22×C3—22no—
884C22×C3—22no—
885C22×C3—22no—
886C22×C3—28no—
887C22×C3—28no—
888C22×C3—24no—
889C22×C3—22no—
890C22×C3—22no—
891C22×C3—22no—
892C22×C3—22no—
893C22×C3—22no—
894C22×C3—22no—
895C22×C3—22no—
896C22×C3—22no—
897C22×C3—22no—
898C22×C3—24no—
899C22×C3—21no—
900C22×C3—34no—
901C22×C3—42no—
902C22×C3—42no—
903C22×C3—48no—
904C22×C3—42no—
905C22×C3—42no—
906C22×C3—48no—
907C22×C3—44no—
908C22×C3—44no—
909C22×C3—62no—
910C22×C3—62no—
911C22×C3—68no—
912C22×C3—62no—
913C22×C3—62no—
914C22×C3—62no—
915C22×C3—62no—
916C22×C3—62no—
917C22×C3—62no—
918C22×C3—1216no—
919C22×C3—124no—
920C22×C3—124no—
921C22×C3C2×D3×D414yes—
922C22×C3C2×D3×D414yes—
923C22×C3C2×D3×D412yes—
924C22×C3C2×D3×D412yes—
925C22×C3C2×#23712yes—
926C22×C3#100412yes—
927C22×C3#100412yes—
928C22×C3D3×#4112yes—
929C22×C3C24×D311yescharacteristic
930C22×C3C24×D311yescharacteristic
931C2×D3—22no—
932C2×D3—22no—
933C2×D3—28no—
934C2×D3—22no—
935C2×D3—22no—
936C2×D3—22no—
937C2×D3—22no—
938C2×D3—22no—
939C2×D3—22no—
940C2×D3—34no—
941C2×D3—34no—
942C2×D3—416no—
943C2×D3—44no—
944C2×D3—44no—
945C2×D3—64no—
946C2×D3—62no—
947C2×D3—62no—
948C2×D3—62no—
949C2×D3—62no—
950C2×D3—68no—
951C2×D3—68no—
952C2×D3—122no—
953C2×D3—122no—
954C2×D3—128no—
955C2×D3—1216no—
956C2×D3—1216no—
957C2×D3C2×#23714yescomplemented
958C3×C4—24no—
959C3×C4—22no—
960C3×C4—22no—
961C3×C4—62no—
962C3×C4—62no—
963C3×C4—62no—
964C3×C4—62no—
965C3×C4—62no—
966Dic3—22no—
967Dic3—22no—
968Dic3—22no—
969Dic3—22no—
970Dic3—22no—
971Dic3—34no—
972Dic3—34no—
973Dic3—64no—
974Dic3—64no—
975Dic3—64no—
976Dic3—62no—
977Dic3—62no—
978Dic3—62no—
979Dic3—62no—
980C32C2×#54611yescharacteristic, complemented, Sylow
981C23—22no—
982C23—22no—
983C23—22no—
984C23—22no—
985C23—22no—
986C23—34no—
987C23—32no—
988C23—32no—
989C23—32no—
990C23—68no—
991C23—62no—
992C23—62no—
993C23—62no—
994C23—62no—
995C23—62no—
996C23—62no—
997C23—62no—
998C23—68no—
999C23—62no—
1000C23—94no—
1001C23—92no—
1002C23—124no—
1003C23—1216no—
1004C23—188no—
1005C23—188no—
1006C23—182no—
1007C23—182no—
1008C23—364no—
1009C23—3616no—
1010C23#381114yes—
1011C23C22×D3212yes—
1012C23C22×D3212yes—
1013C23C22×D3211yescharacteristic
1014Q8—188no—
1015D4—28no—
1016D4—68no—
1017D4—68no—
1018D4—916no—
1019D4—124no—
1020D4—124no—
1021D4—188no—
1022D4—188no—
1023D4—188no—
1024C2×C4—22no—
1025C2×C4—32no—
1026C2×C4—32no—
1027C2×C4—32no—
1028C2×C4—32no—
1029C2×C4—32no—
1030C2×C4—62no—
1031C2×C4—62no—
1032C2×C4—62no—
1033C2×C4—62no—
1034C2×C4—62no—
1035C2×C4—94no—
1036C2×C4—92no—
1037C2×C4—92no—
1038C2×C4—92no—
1039C2×C4—124no—
1040C2×C4—188no—
1041C2×C4—188no—
1042C2×C4—188no—
1043C2×C4—182no—
1044C2×C4—182no—
1045C2×C4—188no—
1046C2×C4—364no—
1047C2×C4C22×D3212yes—
1048C2×C3—24no—
1049C2×C3—24no—
1050C2×C3—21no—
1051C2×C3—21no—
1052C2×C3—21no—
1053C2×C3—24no—
1054C2×C3—44no—
1055C2×C3—44no—
1056C2×C3—42no—
1057C2×C3—42no—
1058C2×C3—64no—
1059C2×C3—122no—
1060C2×C3—122no—
1061C2×C3#559114yescomplemented
1062C2×C3#561014yescomplemented
1063C2×C3C22×D3×D411yescharacteristic
1064C2×C3C22×D3×D411yescharacteristic
1065C2×C3C22×#23711yescharacteristic
1066C2×C3C2×#100411yescharacteristic
1067C2×C3C2×#100411yescharacteristic
1068C2×C3C2×D3×#4111yescharacteristic
1069D3—24no—
1070D3—42no—
1071D3—42no—
1072D3—64no—
1073D3—64no—
1074D3—124no—
1075C22—22no—
1076C22—22no—
1077C22—28no—
1078C22—22no—
1079C22—22no—
1080C22—22no—
1081C22—34no—
1082C22—44no—
1083C22—62no—
1084C22—62no—
1085C22—68no—
1086C22—62no—
1087C22—62no—
1088C22—62no—
1089C22—62no—
1090C22—62no—
1091C22—62no—
1092C22—94no—
1093C22—1216no—
1094C22—124no—
1095C22—124no—
1096C22—182no—
1097C22—182no—
1098C22—188no—
1099C22—3616no—
1100C22D3×#23712yes—
1101C22#6431312yes—
1102C22C2×#381114yes—
1103C22C2×#381112yes—
1104C22C23×D3211yescharacteristic
1105C4—22no—
1106C4—62no—
1107C4—62no—
1108C4—62no—
1109C4—62no—
1110C4—62no—
1111C4—94no—
1112C4—182no—
1113C4—182no—
1114C3—21no—
1115C3C2×#559111yescharacteristic, complemented
1116C3C2×#561011yescharacteristic, complemented
1117C2—24no—
1118C2—42no—
1119C2—64no—
1120C2—122no—
1121C2—122no—
1122C2—184no—
1123C2#1059530714yesdirect product factor
1124C2C2×D3×#23711yescharacteristic
1125C2C2×#6431311yescharacteristic
1126C2C22×#381111yescharacteristic
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC22×C32×D4C22
socleC23×C32C24
hypercenterC22×D4D32
hypocenterC32C2×#546
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C22×D4

Complements

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

NH ≅ G/Ntype
1. C22×#3830C2semidirect
2. C22×D3×#67C2semidirect
3. C2×C3×#939C2semidirect
4. C2×C3×#937C2semidirect
5. C2×#63983C2semidirect
6. C2×#63980C2semidirect
7. C2×#67⋊Dic3C2semidirect
8. C2×#63962C2semidirect
9. C22×(C2×D3)⋊Dic3C2semidirect
10. C2×#63958C2semidirect
11. C2×#63952C2semidirect
12. #10595307C2direct (N × H)
13. C2×#63921C2semidirect
14. C2×#63913C2semidirect
15. C2×#63896C2semidirect
16. C2×#63853C2semidirect
21. C22×C32×D4C22semidirect
23. C22×#638C22semidirect
24. C23×C3⋊Dic3C22semidirect
25. C23×C3⋊Dic3C22semidirect
27. C2×#3830C22semidirect
28. C22×C4×C3⋊D3C22semidirect
29. C22×#634C22semidirect
32. C22×C3×#67C22semidirect
33. C22×C3×#67C22semidirect
34. C23×C3×Dic3C22semidirect
36. C2×D3×#67C22semidirect
39. C22×#624C22semidirect
41. C2×C3×#217C22semidirect
42. C2×C3×#217C22semidirect
43. C3×#939C22semidirect
44. C3×#937C22semidirect
46. C2×C3×(C2×D3)⋊C4C22semidirect
47. C2×C3×(C2×D3)⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. #63983C22semidirect
50. #63980C22semidirect
51. #67⋊Dic3C22semidirect
52. C2×#3724C22semidirect
53. C2×Dic3⋊Dic3C22semidirect
54. C2×Dic3⋊Dic3C22semidirect
55. C2×#3722C22semidirect
56. #63962C22semidirect
59. C2×(C2×D3)⋊Dic3C22semidirect
60. C2×(C2×D3)⋊Dic3C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63958C22semidirect
65. C2×Dic32C22semidirect
66. #63952C22semidirect
67. #63921C22semidirect
68. #63913C22semidirect
69. #63896C22semidirect
70. #63853C22semidirect
81. C2×#939D3semidirect
85. C2×#937D3semidirect
119. C2×C32×D4C23semidirect
122. C2×#638D4semidirect
124. C2×#638C23semidirect
130. C22×C3⋊Dic3C23semidirect
131. C22×C3⋊Dic3C23semidirect
134. C2×C4×C3⋊D3C23semidirect
136. C2×#634C23semidirect
143. C2×C3×#67C23semidirect
144. C2×C3×#67C23semidirect
151. C22×C3×Dic3C23semidirect
158. C2×#624C23semidirect
161. C3×#217C23semidirect
162. C3×#217C23semidirect
164. C3×(C2×D3)⋊C4C23semidirect
165. C3×(C2×D3)⋊C4C23semidirect
166. C3×Dic3⋊C4C23semidirect
167. #3724C23semidirect
168. Dic3⋊Dic3C23semidirect
169. Dic3⋊Dic3C23semidirect
170. #3722C23semidirect
173. (C2×D3)⋊Dic3C23semidirect
174. (C2×D3)⋊Dic3C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. Dic32C23semidirect
188. C22×C3×D4C2×D3semidirect
189. C22×C3×D4C2×D3semidirect
204. C22×#67C2×D3semidirect
205. C22×#67C2×D3semidirect
213. C23×Dic3C2×D3semidirect
247. C2×#217C2×D3semidirect
248. C2×#217C2×D3semidirect
251. #939C2×D3semidirect
255. #937C2×D3semidirect
269. C2×(C2×D3)⋊C4C2×D3semidirect
270. C2×(C2×D3)⋊C4C2×D3semidirect
277. C2×Dic3⋊C4C2×D3semidirect
317. C22×C3×D3#41semidirect
329. #638C2×D4semidirect
418. C2×C3×D4C22×D3semidirect
419. C2×C3×D4C22×D3semidirect
455. C2×#67C22×D3semidirect
456. C2×#67C22×D3semidirect
486. C22×Dic3C22×D3semidirect
523. #217C22×D3semidirect
524. #217C22×D3semidirect
534. (C2×D3)⋊C4C22×D3semidirect
535. (C2×D3)⋊C4C22×D3semidirect
542. Dic3⋊C4C22×D3semidirect
573. C2×C3×D3C2×#41semidirect
599. C22×D4D32semidirect
711. C22×D3#237semidirect
800. C2×C32#546semidirect
843. C2×D4C2×D32semidirect
957. C2×D3C2×#237semidirect
980. C32C2×#546semidirect
1061. C2×C3#5591semidirect
1062. C2×C3#5610semidirect
1115. C3C2×#5591semidirect
1116. C3C2×#5610semidirect
1123. C2#10595307direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38302
C22×D3×#672
C2×C3×#9392
C2×C3×#9372
C2×#639832
C2×#639802
C2×#67⋊Dic32
C2×#639622
C22×(C2×D3)⋊Dic32
C2×#639582
C2×#639522
#105953072
C2×#639212
C2×#639132
C2×#638962
C2×#638532
C2×#56103
C2×#55913