Finite Group Databasebeta

← C2×#10594283 #11902477

Subgroups — C2×#10594283 #11902477

Order 1152.

4013 conjugacy classes of subgroups.

The subgroup lattice has 1120 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#3804C211yesmaximal, characteristic, complemented
2C22×D3×D12C211yesmaximal, characteristic, complemented
3C2×#64093C211yesmaximal, characteristic, complemented
4C2×C3×#884C211yesmaximal, characteristic, complemented
5C2×C3×#67⋊C4C211yesmaximal, characteristic, complemented
6C2×#63983C211yesmaximal, characteristic, complemented
7C2×#63983C211yesmaximal, characteristic, complemented
8C2×#63978C211yesmaximal, characteristic, complemented
9C2×#63921C211yesmaximal, characteristic, complemented
10C2×D3×(C2×D3)⋊C4C211yesmaximal, characteristic, complemented
11C2×C4×#626C211yesmaximal, characteristic, complemented
12C2×#63897C211yesmaximal, characteristic, complemented
13C2×#63884C211yesmaximal, characteristic, complemented
14C2×#63852C211yesmaximal, characteristic, complemented
15C2×#63851C211yesmaximal, characteristic, complemented
16#10594283C2116yesmaximal, direct product factor
17C2×#5610—31nomaximal
18C2×#5550—31nomaximal
19C23×D32C2211yescharacteristic
20C23×D32C2211yescharacteristic
21C22×#638C2211yescharacteristic, complemented
22C22×#638C2211yescharacteristic, complemented
23C22×C4⋊(C3⋊D3)C2211yescharacteristic
24C22×C4×C3⋊D3C2211yescharacteristic, complemented
25C22×C3×#67C2211yescharacteristic
26C22×C3×#67C2211yescharacteristic, complemented
27C22×C3×#67C2211yescharacteristic, complemented
28C23×C3×Dic3C2211yescharacteristic, complemented
29C22×C3×D12C2211yescharacteristic
30C22×C3×C4×D3C2211yescharacteristic
31C22×C3×C4×D3C2211yescharacteristic, complemented
32C22×#627C2211yescharacteristic, complemented
33C22×#626C2211yescharacteristic
34C22×#626C2211yescharacteristic
35C22×#624C2211yescharacteristic, complemented
36C2×#3804—28no—
37C2×#3804C2218yescomplemented
38C22×D3×Dic3C2211yescharacteristic, complemented
39C2×D3×D12—28no—
40C2×D3×D12C2218yescomplemented
41C2×C32×C22⋊C4C2211yescharacteristic, complemented
42C2×#3752C2211yescharacteristic, complemented
43C2×#3750C2211yescharacteristic, complemented
44#64093C2218yescomplemented
45C2×C3×(C2×D3)⋊C4C2211yescharacteristic
46C2×C3×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
48C2×C3×Dic3⋊C4C2211yescharacteristic, complemented
49C2×C3×C4×Dic3C2211yescharacteristic, complemented
50C3×#884C2218yescomplemented
51C3×#67⋊C4C2218yescomplemented
52#63983C2218yescomplemented
53#63983C2218yescomplemented
54#63978C2218yescomplemented
55C2×Dic3⋊Dic3C2211yescharacteristic, complemented
56C2×#3722C2211yescharacteristic, complemented
57C2×#3722C2211yescharacteristic, complemented
58C2×#3722C2211yescharacteristic, complemented
59C2×(C2×D3)⋊Dic3C2211yescharacteristic
60C2×(C2×D3)⋊Dic3C2211yescharacteristic
61C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
62C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
63C2×(C2×D3)⋊Dic3C2211yescharacteristic, complemented
64#63921C2218yescomplemented
65D3×(C2×D3)⋊C4C2218yescomplemented
66C4×#626C2218yescomplemented
67#63897C2218yescomplemented
68#63884C2218yescomplemented
69#63852C2218yescomplemented
70#63851C2218yescomplemented
71C22×#237—31no—
72C22×D3×D4—31no—
73C22×#235—31no—
74C23×D12—31no—
75C2×C3×#121—31no—
76C2×C3×C4×D4—31no—
77C2×#939—31no—
78C2×#937—31no—
79C2×#937—31no—
80C2×#937—31no—
81C2×#937—31no—
82C2×#935—31no—
83C2×#930—31no—
84C2×C4×#67—31no—
85C22×(C2×D3)⋊C4—31no—
86C2×#924—31no—
87#5610—316no—
88#5550—316no—
89C2×#896—31no—
90C2×#894—31no—
91C2×#894—31no—
92C2×#894—31no—
93C2×#885—31no—
94C2×#884—31no—
95C2×#884—31no—
96C2×#884—61no—
97C2×#884D311yescharacteristic, complemented
98C2×#67⋊C4D311yescharacteristic, complemented
99C2×D3×C22⋊C4—31no—
100C2×D3×C22⋊C4—31no—
101C2×D3×C22⋊C4—31no—
102C2×#875—31no—
103C2×C4×D12—31no—
104C24×C32C2311yescharacteristic
105C23×C3⋊D3C2311yescharacteristic
106C23×C3⋊D3C2311yescharacteristic
107C23×C3×D3C2311yescharacteristic
108C23×C3×D3C2311yescharacteristic
109C23×C3×D3C2311yescharacteristic
110C22×D32—24no—
111C22×D32—24no—
112C22×D32—24no—
113C22×D32—24no—
114C22×D32—42no—
115C22×D32—42no—
116C22×D32C2314yes—
117C22×D32C2314yes—
118C22×C32×C4C2311yescharacteristic
119C22×C32×C4C2311yescharacteristic
120C2×#638—24no—
121C2×#638—42no—
122C2×#638C2314yescomplemented
123C2×#638C2314yescomplemented
124C22×C3⋊Dic3C2311yescharacteristic
125C22×C3⋊Dic3C2311yescharacteristic
126C2×C4⋊(C3⋊D3)—24no—
127C2×C4⋊(C3⋊D3)C2314yes—
128C2×C4×C3⋊D3—42no—
129C2×C4×C3⋊D3C2314yescomplemented
130C2×C3×#67—24no—
131C2×C3×#67—24no—
132C2×C3×#67—42no—
133C2×C3×#67C2314yes—
134C2×C3×#67C2314yescomplemented
135C2×C3×#67C2314yescomplemented
136C22×C3×Dic3—24no—
137C22×C3×Dic3C2311yescharacteristic
138C22×C3×Dic3C2311yescharacteristic
139C22×C3×Dic3C2311yescharacteristic
140C22×C3×Dic3C2311yescharacteristic
141C22×C3×Dic3C2311yescharacteristic
142C22×C3×Dic3C2314yescomplemented
143C2×C3×D12—24no—
144C2×C3×D12C2314yes—
145C2×C3×C4×D3—24no—
146C2×C3×C4×D3—42no—
147C2×C3×C4×D3C2314yes—
148C2×C3×C4×D3C2314yescomplemented
149C2×#627—24no—
150C2×#627C2314yescomplemented
151C2×#626—24no—
152C2×#626D418yescomplemented
153C2×#626C2314yes—
154C2×#626C2314yes—
155C2×#624—24no—
156C2×#624C2314yescomplemented
157#3804—232no—
158C2×D3×Dic3—24no—
159C2×D3×Dic3C2314yescomplemented
160D3×D12—232no—
161C32×C22⋊C4C2314yescomplemented
162#3752C2314yescomplemented
163#3750C2314yescomplemented
164C3×(C2×D3)⋊C4C2314yes—
165C3×(C2×D3)⋊C4C2314yescomplemented
166C3×Dic3⋊C4C2314yescomplemented
167C3×Dic3⋊C4C2314yescomplemented
168C3×C4×Dic3C2314yescomplemented
169Dic3⋊Dic3C2314yescomplemented
170#3722C2314yescomplemented
171#3722C2314yescomplemented
172#3722C2314yescomplemented
173(C2×D3)⋊Dic3C2314yes—
174(C2×D3)⋊Dic3C2314yes—
175(C2×D3)⋊Dic3C2314yescomplemented
176(C2×D3)⋊Dic3C2314yescomplemented
177(C2×D3)⋊Dic3C2314yescomplemented
178C2×#546—91noSylow
179C24×D3—31no—
180C24×D3—31no—
181C24×D3—31no—
182C24×D3—31no—
183C22×C3×D4—31no—
184C22×C3×D4—31no—
185C22×C3×D4—31no—
186C22×C3×D4—31no—
187C23×C3×C4—31no—
188C23×C3×C4—31no—
189C23×C3×C4—31no—
190C22×#67—31no—
191C22×#67—31no—
192C22×#67—31no—
193C22×#67—31no—
194C22×#67—31no—
195C22×#67—31no—
196C22×#67—61no—
197C22×#67—61no—
198C22×#67C2×D311yescharacteristic
199C22×#67C2×D311yescharacteristic, complemented
200C22×#67C2×D311yescharacteristic, complemented
201C23×Dic3—31no—
202C23×Dic3C2×D311yescharacteristic, complemented
203C2×#237—38no—
204C2×#237—68no—
205C2×D3×D4—38no—
206C2×D3×D4—68no—
207C2×#235—38no—
208C2×#235—68no—
209C22×D12—31no—
210C22×D12—31no—
211C22×D12—31no—
212C22×D12—31no—
213C22×D12—38no—
214C22×D12—61no—
215C22×D12—68no—
216C22×D12C2×D311yescharacteristic
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×D3C2×D311yescharacteristic
224C22×C4×D3C2×D311yescharacteristic, complemented
225C22×Dic6—31no—
226C22×Dic6—31no—
227C3×#121—38no—
228C3×C4×D4—38no—
229C2×C3×C4⋊C4—31no—
230C2×C3×C4⋊C4—31no—
231C2×C3×C22⋊C4—21no—
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—31no—
242#939—38no—
243#937—38no—
244#937—38no—
245#937—38no—
246#937—38no—
247#935—38no—
248#930—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—31no—
261C2×(C2×D3)⋊C4—31no—
262C2×(C2×D3)⋊C4—31no—
263C2×(C2×D3)⋊C4—38no—
264C2×(C2×D3)⋊C4—61no—
265C2×(C2×D3)⋊C4C2×D311yescharacteristic
266C2×(C2×D3)⋊C4C2×D311yescharacteristic, complemented
267C2×C4⋊Dic3—31no—
268#924—38no—
269C2×Dic3⋊C4—31no—
270C2×Dic3⋊C4—31no—
271C2×Dic3⋊C4—31no—
272C2×Dic3⋊C4—61no—
273C2×Dic3⋊C4C2×D311yescharacteristic, complemented
274C2×Dic3⋊C4C2×D311yescharacteristic, complemented
275C2×C4×Dic3C2×D311yescharacteristic, complemented
276#896—38no—
277#894—38no—
278#894—38no—
279#894—38no—
280#885—38no—
281#884—38no—
282#884—38no—
283#884—68no—
284#884C2×D318yescomplemented
285#67⋊C4C2×D318yescomplemented
286D3×C22⋊C4—38no—
287D3×C22⋊C4—38no—
288D3×C22⋊C4—38no—
289#875—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—22no—
299C22×C3⋊D3—22no—
300C22×C3⋊D3—22no—
301C22×C3⋊D3C2×D414yes—
302C22×C3⋊D3C2412yes—
303C22×C3⋊D3C2412yes—
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×D3C2×D414yes—
312C22×C3×D3#4114yescomplemented
313C22×C3×D3C2412yes—
314C22×C3×D3C2412yes—
315C22×C3×D3C2412yes—
316C2×D32—28no—
317C2×D32—28no—
318C2×D32—28no—
319C2×D32—28no—
320C2×D32—44no—
321C2×D32—44no—
322C2×D32—416no—
323C2×D32—416no—
324C2×C32×C4—22no—
325C2×C32×C4—22no—
326C2×C32×C4C2412yes—
327C2×C32×C4C2412yes—
328#638—28no—
329#638—44no—
330C2×C3⋊Dic3—22no—
331C2×C3⋊Dic3—22no—
332C2×C3⋊Dic3C2412yes—
333C2×C3⋊Dic3C2412yes—
334C4⋊(C3⋊D3)—28no—
335C4×C3⋊D3—44no—
336C3×#67—28no—
337C3×#67—28no—
338C3×#67—44no—
339C2×C3×Dic3—22no—
340C2×C3×Dic3—22no—
341C2×C3×Dic3—22no—
342C2×C3×Dic3—22no—
343C2×C3×Dic3—28no—
344C2×C3×Dic3C2×D414yes—
345C2×C3×Dic3C2412yes—
346C2×C3×Dic3C2412yes—
347C2×C3×Dic3C2412yes—
348C2×C3×Dic3C2412yes—
349C2×C3×Dic3C2412yes—
350C3×D12—28no—
351C3×C4×D3—28no—
352C3×C4×D3—44no—
353#627—28no—
354#626—28no—
355#626C2×D4116yescomplemented
356#624—28no—
357D3×Dic3—28no—
358C22×#41—91no—
359C23×D4—91no—
360#546—916no—
361C2×#124—91no—
362C2×#123—91no—
363C2×#123—91no—
364C2×C22⋊Q8—91no—
365C2×#121—31no—
366C2×#121—91no—
367C2×#121—91no—
368C2×#120—91no—
369C2×#120—91no—
370C2×C4×D4—31no—
371C2×C4×D4—91no—
372C22×C22⋊C4—91no—
373C22×C22⋊C4—91no—
374C24×C3—21no—
375C24×C3—31no—
376C24×C3—31no—
377C24×C3—31no—
378C24×C3C22×D311yescharacteristic
379C24×C3C22×D311yescharacteristic
380C23×D3—31no—
381C23×D3—31no—
382C23×D3—31no—
383C23×D3—31no—
384C23×D3—34no—
385C23×D3—34no—
386C23×D3—34no—
387C23×D3—34no—
388C23×D3—61no—
389C23×D3—61no—
390C23×D3—64no—
391C23×D3—64no—
392C23×D3—64no—
393C23×D3—64no—
394C23×D3—64no—
395C23×D3—64no—
396C23×D3—64no—
397C23×D3—64no—
398C23×D3—122no—
399C23×D3—122no—
400C23×D3—122no—
401C23×D3—122no—
402C23×D3C22×D311yescharacteristic
403C23×D3C22×D311yescharacteristic
404C23×D3C22×D311yescharacteristic
405C2×C3×D4—34no—
406C2×C3×D4—34no—
407C2×C3×D4—34no—
408C2×C3×D4—34no—
409C2×C3×D4—64no—
410C2×C3×D4—64no—
411C2×C3×D4—64no—
412C2×C3×D4—122no—
413C22×C3×C4—21no—
414C22×C3×C4—21no—
415C22×C3×C4—31no—
416C22×C3×C4—31no—
417C22×C3×C4—31no—
418C22×C3×C4—31no—
419C22×C3×C4—31no—
420C22×C3×C4—34no—
421C22×C3×C4—34no—
422C22×C3×C4—34no—
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—24no—
432C2×#67—34no—
433C2×#67—34no—
434C2×#67—34no—
435C2×#67—34no—
436C2×#67—38no—
437C2×#67—34no—
438C2×#67—34no—
439C2×#67—42no—
440C2×#67—64no—
441C2×#67—64no—
442C2×#67—64no—
443C2×#67—64no—
444C2×#67—64no—
445C2×#67—124no—
446C2×#67—122no—
447C2×#67—122no—
448C2×#67—124no—
449C2×#67C22×D314yes—
450C2×#67C22×D314yescomplemented
451C2×#67C22×D314yescomplemented
452C22×Dic3—24no—
453C22×Dic3—31no—
454C22×Dic3—31no—
455C22×Dic3—31no—
456C22×Dic3—31no—
457C22×Dic3—34no—
458C22×Dic3—61no—
459C22×Dic3—61no—
460C22×Dic3—64no—
461C22×Dic3C22×D311yescharacteristic
462C22×Dic3C22×D311yescharacteristic
463C22×Dic3C22×D311yescharacteristic
464C22×Dic3C22×D311yescharacteristic
465C22×Dic3C22×D311yescharacteristic
466C22×Dic3C22×D314yescomplemented
467#237—632no—
468D3×D4—632no—
469#235—632no—
470C2×D12—24no—
471C2×D12—38no—
472C2×D12—34no—
473C2×D12—34no—
474C2×D12—34no—
475C2×D12—34no—
476C2×D12—64no—
477C2×D12—632no—
478C2×D12—64no—
479C2×D12—64no—
480C2×D12—64no—
481C2×D12—124no—
482C2×D12C22×D314yes—
483C2×C4×D3—24no—
484C2×C4×D3—34no—
485C2×C4×D3—34no—
486C2×C4×D3—34no—
487C2×C4×D3—34no—
488C2×C4×D3—34no—
489C2×C4×D3—42no—
490C2×C4×D3—64no—
491C2×C4×D3—64no—
492C2×C4×D3—64no—
493C2×C4×D3—64no—
494C2×C4×D3—122no—
495C2×C4×D3—122no—
496C2×C4×D3—124no—
497C2×C4×D3C22×D314yes—
498C2×C4×D3C22×D314yescomplemented
499C2×Dic6—34no—
500C2×Dic6—34no—
501C2×Dic6—64no—
502C2×Dic6—64no—
503C3×C4⋊C4—34no—
504C3×C4⋊C4—34no—
505C3×C22⋊C4—24no—
506C3×C22⋊C4—34no—
507C3×C22⋊C4—34no—
508C3×C22⋊C4C22×D314yescomplemented
509C3×C22⋊C4C22×D314yescomplemented
510C3×C42—34no—
511#217—34no—
512#217—34no—
513#217—34no—
514#217—34no—
515#217—34no—
516(C2×D3)⋊C4—34no—
517(C2×D3)⋊C4—34no—
518(C2×D3)⋊C4—34no—
519(C2×D3)⋊C4—34no—
520(C2×D3)⋊C4—34no—
521(C2×D3)⋊C4—34no—
522(C2×D3)⋊C4—34no—
523(C2×D3)⋊C4—34no—
524(C2×D3)⋊C4—34no—
525(C2×D3)⋊C4—34no—
526(C2×D3)⋊C4—34no—
527(C2×D3)⋊C4—34no—
528(C2×D3)⋊C4—34no—
529(C2×D3)⋊C4—64no—
530(C2×D3)⋊C4C22×D314yes—
531(C2×D3)⋊C4C22×D314yescomplemented
532C4⋊Dic3—34no—
533Dic3⋊C4—34no—
534Dic3⋊C4—34no—
535Dic3⋊C4—34no—
536Dic3⋊C4—64no—
537Dic3⋊C4C22×D314yescomplemented
538Dic3⋊C4C22×D314yescomplemented
539C4×Dic3C22×D314yescomplemented
540C22×C32—22no—
541C22×C32—22no—
542C22×C32—22no—
543C22×C32—44no—
544C22×C32C22×D412yes—
545C22×C32C2×#4112yes—
546C22×C32H(5,𝔽2)12yes—
547C22×C32C2511yescharacteristic
548C2×C3⋊D3—28no—
549C2×C3⋊D3—22no—
550C2×C3⋊D3—22no—
551C2×C3⋊D3—22no—
552C2×C3⋊D3—22no—
553C2×C3⋊D3—22no—
554C2×C3⋊D3—44no—
555C2×C3⋊D3C22×D414yes—
556C2×C3×D3—28no—
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—22no—
564C2×C3×D3—22no—
565C2×C3×D3—44no—
566C2×C3×D3C22×D414yes—
567C2×C3×D3C2×#4114yescomplemented
568D32—416no—
569D32—416no—
570C32×C4—22no—
571C32×C4—22no—
572C3⋊Dic3—22no—
573C3⋊Dic3—22no—
574C3×Dic3—22no—
575C3×Dic3—22no—
576C3×Dic3—22no—
577C3×Dic3—22no—
578C3×Dic3C22×D414yes—
579C25—91no—
580C25—91no—
581C2×#41—98no—
582C2×#41—188no—
583C22×Q8—91no—
584C22×D4—31no—
585C22×D4—31no—
586C22×D4—31no—
587C22×D4—31no—
588C22×D4—98no—
589C22×D4—91no—
590C22×D4—91no—
591C22×D4—91no—
592C22×D4—91no—
593C22×D4—91no—
594C22×D4—188no—
595C23×C4—31no—
596C23×C4—31no—
597C23×C4—31no—
598C23×C4—91no—
599C23×C4—91no—
600C23×C4—91no—
601#124—98no—
602#123—98no—
603#123—98no—
604C22⋊Q8—98no—
605#121—38no—
606#121—98no—
607#121—98no—
608#120—98no—
609#120—98no—
610C4×D4—38no—
611C4×D4—98no—
612C2×C4⋊C4—31no—
613C2×C4⋊C4—31no—
614C2×C4⋊C4—91no—
615C2×C4⋊C4—91no—
616C2×C22⋊C4—31no—
617C2×C22⋊C4—31no—
618C2×C22⋊C4—98no—
619C2×C22⋊C4—98no—
620C2×C22⋊C4—91no—
621C2×C22⋊C4—91no—
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⋊C4D3211yescharacteristic, complemented
630C2×C42—31no—
631C23×C3—22no—
632C23×C3—22no—
633C23×C3—22no—
634C23×C3—22no—
635C23×C3—22no—
636C23×C3—22no—
637C23×C3—22no—
638C23×C3—21no—
639C23×C3—34no—
640C23×C3—34no—
641C23×C3—32no—
642C23×C3—32no—
643C23×C3—32no—
644C23×C3—42no—
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×C3C23×D312yes—
655C23×C3C23×D312yes—
656C23×C3C23×D311yescharacteristic
657C23×C3C23×D311yescharacteristic
658C22×D3—22no—
659C22×D3—22no—
660C22×D3—22no—
661C22×D3—22no—
662C22×D3—22no—
663C22×D3—22no—
664C22×D3—22no—
665C22×D3—34no—
666C22×D3—34no—
667C22×D3—32no—
668C22×D3—32no—
669C22×D3—32no—
670C22×D3—32no—
671C22×D3—64no—
672C22×D3—62no—
673C22×D3—62no—
674C22×D3—68no—
675C22×D3—68no—
676C22×D3—68no—
677C22×D3—68no—
678C22×D3—68no—
679C22×D3—62no—
680C22×D3—62no—
681C22×D3—62no—
682C22×D3—62no—
683C22×D3—62no—
684C22×D3—62no—
685C22×D3—62no—
686C22×D3—62no—
687C22×D3—62no—
688C22×D3—62no—
689C22×D3—68no—
690C22×D3—68no—
691C22×D3—68no—
692C22×D3—122no—
693C22×D3—122no—
694C22×D3—122no—
695C22×D3—122no—
696C22×D3—122no—
697C22×D3—124no—
698C22×D3—124no—
699C22×D3—124no—
700C22×D3—124no—
701C22×D3—1216no—
702C22×D3—1216no—
703C22×D3—1216no—
704C22×D3—1216no—
705C22×D3#23514yescomplemented
706C22×D3D3×D414yes—
707C22×D3C23×D312yes—
708C22×D3C23×D312yes—
709C22×D3C23×D312yes—
710C3×D4—68no—
711C3×D4—68no—
712C3×D4—68no—
713C3×D4—124no—
714C2×C3×C4—22no—
715C2×C3×C4—22no—
716C2×C3×C4—22no—
717C2×C3×C4—22no—
718C2×C3×C4—22no—
719C2×C3×C4—22no—
720C2×C3×C4—34no—
721C2×C3×C4—32no—
722C2×C3×C4—32no—
723C2×C3×C4—32no—
724C2×C3×C4—32no—
725C2×C3×C4—32no—
726C2×C3×C4—42no—
727C2×C3×C4—42no—
728C2×C3×C4—68no—
729C2×C3×C4—68no—
730C2×C3×C4—62no—
731C2×C3×C4—62no—
732C2×C3×C4—62no—
733C2×C3×C4—62no—
734C2×C3×C4—124no—
735C2×C3×C4C23×D312yes—
736C2×C3×C4C23×D312yes—
737C2×C3×C4C23×D312yes—
738C2×C3×C4C23×D312yes—
739#67—28no—
740#67—28no—
741#67—316no—
742#67—44no—
743#67—68no—
744#67—68no—
745#67—68no—
746#67—128no—
747#67—124no—
748#67—124no—
749#67—128no—
750C2×Dic3—22no—
751C2×Dic3—22no—
752C2×Dic3—22no—
753C2×Dic3—22no—
754C2×Dic3—28no—
755C2×Dic3—32no—
756C2×Dic3—32no—
757C2×Dic3—32no—
758C2×Dic3—32no—
759C2×Dic3—62no—
760C2×Dic3—62no—
761C2×Dic3—68no—
762C2×Dic3—64no—
763C2×Dic3—62no—
764C2×Dic3—62no—
765C2×Dic3—62no—
766C2×Dic3—62no—
767C2×Dic3—122no—
768C2×Dic3D3×D414yes—
769C2×Dic3C23×D312yes—
770C2×Dic3C23×D312yes—
771C2×Dic3C23×D312yes—
772C2×Dic3C23×D312yes—
773C2×Dic3C23×D312yes—
774D12—28no—
775D12—316no—
776D12—68no—
777D12—68no—
778D12—68no—
779D12—128no—
780C4×D3—28no—
781C4×D3—44no—
782C4×D3—68no—
783C4×D3—68no—
784C4×D3—68no—
785C4×D3—124no—
786C4×D3—124no—
787C4×D3—128no—
788Dic6—68no—
789Dic6—68no—
790C2×C32—42no—
791C2×C32#54614yescomplemented
792C2×C32C23×D411yescharacteristic
793C2×C32C22×#4111yescharacteristic
794C2×C32C2×H(5,𝔽2)11yescharacteristic
795C3⋊D3—24no—
796C3⋊D3—42no—
797C3×D3—24no—
798C3×D3—24no—
799C3×D3—42no—
800C24—31no—
801C24—31no—
802C24—31no—
803C24—94no—
804C24—94no—
805C24—91no—
806C24—91no—
807C24—184no—
808C24—184no—
809C24—184no—
810C24—184no—
811C24—362no—
812C24—362no—
813C24C2×D3211yescharacteristic
814#41—1832no—
815C2×Q8—94no—
816C2×Q8—184no—
817C2×D4—34no—
818C2×D4—34no—
819C2×D4—34no—
820C2×D4—34no—
821C2×D4—64no—
822C2×D4—64no—
823C2×D4—64no—
824C2×D4—94no—
825C2×D4—98no—
826C2×D4—94no—
827C2×D4—94no—
828C2×D4—94no—
829C2×D4—94no—
830C2×D4—122no—
831C2×D4—184no—
832C2×D4—184no—
833C2×D4—1832no—
834C2×D4—184no—
835C2×D4—362no—
836C22×C4—31no—
837C22×C4—34no—
838C22×C4—31no—
839C22×C4—31no—
840C22×C4—31no—
841C22×C4—31no—
842C22×C4—34no—
843C22×C4—34no—
844C22×C4—64no—
845C22×C4—64no—
846C22×C4—94no—
847C22×C4—94no—
848C22×C4—91no—
849C22×C4—91no—
850C22×C4—94no—
851C22×C4—122no—
852C22×C4—184no—
853C22×C4—184no—
854C22×C4—362no—
855C22×C4C2×D3211yescharacteristic
856C22×C4C2×D3211yescharacteristic
857C4⋊C4—34no—
858C4⋊C4—34no—
859C4⋊C4—94no—
860C4⋊C4—94no—
861C22⋊C4—34no—
862C22⋊C4—34no—
863C22⋊C4—94no—
864C22⋊C4—94no—
865C22⋊C4—94no—
866C22⋊C4—94no—
867C22⋊C4—94no—
868C22⋊C4—94no—
869C22⋊C4—94no—
870C22⋊C4—94no—
871C22⋊C4—94no—
872C22⋊C4C2×D3214yescomplemented
873C42—34no—
874C22×C3—22no—
875C22×C3—22no—
876C22×C3—22no—
877C22×C3—22no—
878C22×C3—22no—
879C22×C3—22no—
880C22×C3—22no—
881C22×C3—22no—
882C22×C3—22no—
883C22×C3—21no—
884C22×C3—34no—
885C22×C3—34no—
886C22×C3—42no—
887C22×C3—42no—
888C22×C3—42no—
889C22×C3—44no—
890C22×C3—44no—
891C22×C3—62no—
892C22×C3—62no—
893C22×C3—62no—
894C22×C3—62no—
895C22×C3—68no—
896C22×C3—68no—
897C22×C3—62no—
898C22×C3—62no—
899C22×C3—62no—
900C22×C3—84no—
901C22×C3—124no—
902C22×C3C2×#23512yes—
903C22×C3C2×D3×D412yes—
904C22×C3C2×D3×D412yes—
905C22×C3#100412yes—
906C22×C3D3×#4112yes—
907C22×C3#100912yes—
908C22×C3C24×D311yescharacteristic
909C22×C3C24×D311yescharacteristic
910C2×D3—22no—
911C2×D3—22no—
912C2×D3—22no—
913C2×D3—22no—
914C2×D3—28no—
915C2×D3—28no—
916C2×D3—22no—
917C2×D3—22no—
918C2×D3—22no—
919C2×D3—34no—
920C2×D3—34no—
921C2×D3—44no—
922C2×D3—64no—
923C2×D3—62no—
924C2×D3—62no—
925C2×D3—62no—
926C2×D3—62no—
927C2×D3—68no—
928C2×D3—68no—
929C2×D3—62no—
930C2×D3—62no—
931C2×D3—62no—
932C2×D3—62no—
933C2×D3—62no—
934C2×D3—62no—
935C2×D3—122no—
936C2×D3—122no—
937C2×D3—128no—
938C2×D3—122no—
939C2×D3—122no—
940C2×D3—122no—
941C2×D3—1216no—
942C2×D3—1216no—
943C2×D3—1216no—
944C2×D3—1216no—
945C2×D3—124no—
946C2×D3—124no—
947C2×D3—244no—
948C2×D3C2×#23514yescomplemented
949C2×D3C2×D3×D414yes—
950C3×C4—22no—
951C3×C4—22no—
952C3×C4—22no—
953C3×C4—22no—
954C3×C4—34no—
955C3×C4—42no—
956C3×C4—42no—
957C3×C4—62no—
958C3×C4—62no—
959C3×C4—62no—
960C3×C4—62no—
961Dic3—22no—
962Dic3—22no—
963Dic3—22no—
964Dic3—22no—
965Dic3—64no—
966Dic3—62no—
967Dic3—62no—
968Dic3—62no—
969Dic3—62no—
970Dic3—122no—
971Dic3C2×D3×D414yes—
972C32C2×#54611yescharacteristic, complemented, Sylow
973C23—22no—
974C23—22no—
975C23—22no—
976C23—34no—
977C23—34no—
978C23—32no—
979C23—32no—
980C23—32no—
981C23—62no—
982C23—62no—
983C23—62no—
984C23—62no—
985C23—62no—
986C23—62no—
987C23—62no—
988C23—94no—
989C23—92no—
990C23—92no—
991C23—188no—
992C23—188no—
993C23—188no—
994C23—188no—
995C23—182no—
996C23—182no—
997C23—182no—
998C23—182no—
999C23—182no—
1000C23—364no—
1001C23—364no—
1002C23—3616no—
1003C23—3616no—
1004C23C22×D3212yes—
1005C23C22×D3211yescharacteristic
1006Q8—188no—
1007D4—68no—
1008D4—68no—
1009D4—68no—
1010D4—916no—
1011D4—124no—
1012D4—188no—
1013D4—188no—
1014D4—188no—
1015D4—364no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—34no—
1019C2×C4—32no—
1020C2×C4—32no—
1021C2×C4—32no—
1022C2×C4—32no—
1023C2×C4—32no—
1024C2×C4—68no—
1025C2×C4—68no—
1026C2×C4—62no—
1027C2×C4—62no—
1028C2×C4—62no—
1029C2×C4—62no—
1030C2×C4—92no—
1031C2×C4—92no—
1032C2×C4—124no—
1033C2×C4—188no—
1034C2×C4—188no—
1035C2×C4—182no—
1036C2×C4—182no—
1037C2×C4—364no—
1038C2×C4C22×D3212yes—
1039C2×C4C22×D3212yes—
1040C2×C3—21no—
1041C2×C3—21no—
1042C2×C3—21no—
1043C2×C3—24no—
1044C2×C3—42no—
1045C2×C3—42no—
1046C2×C3—64no—
1047C2×C3—64no—
1048C2×C3—82no—
1049C2×C3—122no—
1050C2×C3#555014yescomplemented
1051C2×C3#561014yescomplemented
1052C2×C3C22×#23511yescharacteristic
1053C2×C3C22×D3×D411yescharacteristic
1054C2×C3C22×D3×D411yescharacteristic
1055C2×C3C2×#100411yescharacteristic
1056C2×C3C2×D3×#4111yescharacteristic
1057C2×C3C2×#100911yescharacteristic
1058D3—24no—
1059D3—24no—
1060D3—42no—
1061D3—64no—
1062D3—64no—
1063D3—124no—
1064D3—122no—
1065D3—122no—
1066D3—242no—
1067C22—22no—
1068C22—22no—
1069C22—22no—
1070C22—34no—
1071C22—34no—
1072C22—44no—
1073C22—62no—
1074C22—62no—
1075C22—62no—
1076C22—62no—
1077C22—68no—
1078C22—68no—
1079C22—62no—
1080C22—62no—
1081C22—62no—
1082C22—94no—
1083C22—124no—
1084C22—182no—
1085C22—182no—
1086C22—188no—
1087C22—182no—
1088C22—182no—
1089C22—182no—
1090C22—3616no—
1091C22—3616no—
1092C22—364no—
1093C22D3×#23512yes—
1094C22D32×D412yes—
1095C22#6431412yes—
1096C22C23×D3211yescharacteristic
1097C4—22no—
1098C4—22no—
1099C4—34no—
1100C4—62no—
1101C4—62no—
1102C4—62no—
1103C4—62no—
1104C4—182no—
1105C4—182no—
1106C3—21no—
1107C3C2×#555011yescharacteristic, complemented
1108C3C2×#561011yescharacteristic, complemented
1109C2—42no—
1110C2—64no—
1111C2—64no—
1112C2—122no—
1113C2—184no—
1114C2—362no—
1115C2#1059428314yesdirect product factor
1116C2C2×D3×#23511yescharacteristic
1117C2C2×D32×D411yescharacteristic
1118C2C2×#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×#3804C2semidirect
2. C22×D3×D12C2semidirect
3. C2×#64093C2semidirect
4. C2×C3×#884C2semidirect
5. C2×C3×#67⋊C4C2semidirect
6. C2×#63983C2semidirect
7. C2×#63983C2semidirect
8. C2×#63978C2semidirect
9. C2×#63921C2semidirect
10. C2×D3×(C2×D3)⋊C4C2semidirect
11. C2×C4×#626C2semidirect
12. C2×#63897C2semidirect
13. C2×#63884C2semidirect
14. C2×#63852C2semidirect
15. C2×#63851C2semidirect
16. #10594283C2direct (N × H)
21. C22×#638C22semidirect
22. C22×#638C22semidirect
24. C22×C4×C3⋊D3C22semidirect
26. C22×C3×#67C22semidirect
27. C22×C3×#67C22semidirect
28. C23×C3×Dic3C22semidirect
31. C22×C3×C4×D3C22semidirect
32. C22×#627C22semidirect
35. C22×#624C22semidirect
37. C2×#3804C22semidirect
38. C22×D3×Dic3C22semidirect
40. C2×D3×D12C22semidirect
41. C2×C32×C22⋊C4C22semidirect
42. C2×#3752C22semidirect
43. C2×#3750C22semidirect
44. #64093C22semidirect
46. C2×C3×(C2×D3)⋊C4C22semidirect
47. C2×C3×Dic3⋊C4C22semidirect
48. C2×C3×Dic3⋊C4C22semidirect
49. C2×C3×C4×Dic3C22semidirect
50. C3×#884C22semidirect
51. C3×#67⋊C4C22semidirect
52. #63983C22semidirect
53. #63983C22semidirect
54. #63978C22semidirect
55. C2×Dic3⋊Dic3C22semidirect
56. C2×#3722C22semidirect
57. C2×#3722C22semidirect
58. C2×#3722C22semidirect
61. C2×(C2×D3)⋊Dic3C22semidirect
62. C2×(C2×D3)⋊Dic3C22semidirect
63. C2×(C2×D3)⋊Dic3C22semidirect
64. #63921C22semidirect
65. D3×(C2×D3)⋊C4C22semidirect
66. C4×#626C22semidirect
67. #63897C22semidirect
68. #63884C22semidirect
69. #63852C22semidirect
70. #63851C22semidirect
97. C2×#884D3semidirect
98. C2×#67⋊C4D3semidirect
122. C2×#638C23semidirect
123. C2×#638C23semidirect
129. C2×C4×C3⋊D3C23semidirect
134. C2×C3×#67C23semidirect
135. C2×C3×#67C23semidirect
142. C22×C3×Dic3C23semidirect
148. C2×C3×C4×D3C23semidirect
150. C2×#627C23semidirect
152. C2×#626D4semidirect
156. C2×#624C23semidirect
159. C2×D3×Dic3C23semidirect
161. C32×C22⋊C4C23semidirect
162. #3752C23semidirect
163. #3750C23semidirect
165. C3×(C2×D3)⋊C4C23semidirect
166. C3×Dic3⋊C4C23semidirect
167. C3×Dic3⋊C4C23semidirect
168. C3×C4×Dic3C23semidirect
169. Dic3⋊Dic3C23semidirect
170. #3722C23semidirect
171. #3722C23semidirect
172. #3722C23semidirect
175. (C2×D3)⋊Dic3C23semidirect
176. (C2×D3)⋊Dic3C23semidirect
177. (C2×D3)⋊Dic3C23semidirect
199. C22×#67C2×D3semidirect
200. C22×#67C2×D3semidirect
202. C23×Dic3C2×D3semidirect
224. C22×C4×D3C2×D3semidirect
234. C2×C3×C22⋊C4C2×D3semidirect
235. C2×C3×C22⋊C4C2×D3semidirect
266. C2×(C2×D3)⋊C4C2×D3semidirect
273. C2×Dic3⋊C4C2×D3semidirect
274. C2×Dic3⋊C4C2×D3semidirect
275. C2×C4×Dic3C2×D3semidirect
284. #884C2×D3semidirect
285. #67⋊C4C2×D3semidirect
312. C22×C3×D3#41semidirect
355. #626C2×D4semidirect
450. C2×#67C22×D3semidirect
451. C2×#67C22×D3semidirect
466. C22×Dic3C22×D3semidirect
498. C2×C4×D3C22×D3semidirect
508. C3×C22⋊C4C22×D3semidirect
509. C3×C22⋊C4C22×D3semidirect
531. (C2×D3)⋊C4C22×D3semidirect
537. Dic3⋊C4C22×D3semidirect
538. Dic3⋊C4C22×D3semidirect
539. C4×Dic3C22×D3semidirect
567. C2×C3×D3C2×#41semidirect
629. C2×C22⋊C4D32semidirect
705. C22×D3#235semidirect
791. C2×C32#546semidirect
872. C22⋊C4C2×D32semidirect
948. C2×D3C2×#235semidirect
972. C32C2×#546semidirect
1050. C2×C3#5550semidirect
1051. C2×C3#5610semidirect
1107. C3C2×#5550semidirect
1108. C3C2×#5610semidirect
1115. C2#10594283direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#38042
C22×D3×D122
C2×#640932
C2×C3×#8842
C2×C3×#67⋊C42
C2×#639832
C2×#639782
C2×#639212
C2×D3×(C2×D3)⋊C42
C2×C4×#6262
C2×#638972
C2×#638842
C2×#638522
C2×#638512
#105942832
C2×#56103
C2×#55503