Finite Group Databasebeta

← C2×#75918 #11429974

Subgroups — C2×#75918 #11429974

Order 768.

4098 conjugacy classes of subgroups.

The subgroup lattice has 968 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#882C211yesmaximal, characteristic
2C22×#879C211yesmaximal, characteristic, complemented
3C2×C3×#388C211yesmaximal, characteristic, complemented
4C2×#4994C211yesmaximal, characteristic, complemented
5C2×#4988C211yesmaximal, characteristic, complemented
6C2×#4955C211yesmaximal, characteristic, complemented
7C2×#4955C211yesmaximal, characteristic, complemented
8C2×#4961C211yesmaximal, characteristic, complemented
9C2×#4961C211yesmaximal, characteristic, complemented
10C2×#4939C211yesmaximal, characteristic, complemented
11C2×#4940C211yesmaximal, characteristic, complemented
12#75918C2116yesmaximal, direct product factor
13C2×#4677C211yesmaximal, characteristic, complemented
14C2×#4672C211yesmaximal, characteristic, complemented
15C2×#4672C211yesmaximal, characteristic, complemented
16C2×#4670C211yesmaximal, characteristic, complemented
17C2×#2685—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C22×C3×C4⋊C4C2211yescharacteristic, complemented
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C42C2211yescharacteristic, complemented
27C22×#217C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×(C2×D3)⋊C4C2211yescharacteristic
30C22×(C2×D3)⋊C4C2211yescharacteristic
31C22×(C2×D3)⋊C4C2211yescharacteristic
32C22×(C2×D3)⋊C4C2211yescharacteristic
33C22×(C2×D3)⋊C4C2211yescharacteristic
34C22×(C2×D3)⋊C4C2211yescharacteristic
35C22×(C2×D3)⋊C4C2211yescharacteristic
36C22×(C2×D3)⋊C4C2211yescharacteristic
37C22×(C2×D3)⋊C4C2211yescharacteristic
38C22×(C2×D3)⋊C4C2211yescharacteristic
39C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
40C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C22×C4⋊Dic3C2211yescharacteristic, complemented
44C22×C4⋊Dic3C2211yescharacteristic, complemented
45C22×C4⋊Dic3C2211yescharacteristic, complemented
46C22×Dic3⋊C4C2211yescharacteristic, complemented
47C22×Dic3⋊C4C2211yescharacteristic, complemented
48C22×C4×Dic3C2211yescharacteristic, complemented
49C2×#882—28no—
50C2×#882C2218yes—
51C2×#879—28no—
52C2×#879C2218yescomplemented
53C3×#388C2218yescomplemented
54C2×C3×#95C2211yescharacteristic, complemented
55C2×C3×#95C2211yescharacteristic, complemented
56C2×C3⋊#95C2211yescharacteristic, complemented
57C2×C3⋊#95C2211yescharacteristic, complemented
58#4994C2218yescomplemented
59#4988C2218yescomplemented
60#4961C2218yescomplemented
61#4961C2218yescomplemented
62#4955C2218yescomplemented
63#4955C2218yescomplemented
64#4940C2218yescomplemented
65#4939C2218yescomplemented
66#4677C2218yescomplemented
67#4672C2218yescomplemented
68#4672C2218yescomplemented
69#4670C2218yescomplemented
70C22×#126—31no—
71C22×#120—31no—
72#2685—316no—
73C2×#399—31no—
74C2×#396—31no—
75C2×#394—31no—
76C2×#394—31no—
77C2×#394—31no—
78C2×#394—31no—
79C2×#390—31no—
80C2×#390—31no—
81C2×#388—31no—
82C2×#388—31no—
83C2×#388D311yescharacteristic, complemented
84C2×#379—31no—
85C2×#379—31no—
86C25×C3C2311yescharacteristic
87C24×D3—24no—
88C24×D3—24no—
89C24×D3—24no—
90C24×D3—42no—
91C24×D3—42no—
92C24×D3—42no—
93C24×D3—42no—
94C24×D3C2311yescharacteristic
95C24×D3C2311yescharacteristic
96C24×D3C2311yescharacteristic
97C24×D3C2314yes—
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C23×C3×C4C2311yescharacteristic
103C23×C3×C4C2311yescharacteristic
104C22×#67—24no—
105C22×#67—42no—
106C22×#67—42no—
107C22×#67C2314yes—
108C23×Dic3C2311yescharacteristic
109C23×Dic3C2311yescharacteristic
110C23×Dic3C2311yescharacteristic
111C23×Dic3C2311yescharacteristic
112C23×Dic3C2311yescharacteristic
113C22×D12—24no—
114C22×D12—24no—
115C22×D12—24no—
116C22×D12—24no—
117C22×D12—42no—
118C22×D12—42no—
119C22×D12C2314yes—
120C22×D12C2314yes—
121C2×C3×C4⋊C4—42no—
122C2×C3×C4⋊C4C2314yescomplemented
123C2×C3×C22⋊C4—42no—
124C2×C3×C22⋊C4—42no—
125C2×C3×C22⋊C4D418yes—
126C2×C3×C22⋊C4C2314yes—
127C2×C3×C22⋊C4C2314yes—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C42—42no—
130C2×C3×C42C2314yescomplemented
131C2×#217—24no—
132C2×#217—24no—
133C2×#217C2314yes—
134C2×#217C2314yes—
135C2×(C2×D3)⋊C4—24no—
136C2×(C2×D3)⋊C4—24no—
137C2×(C2×D3)⋊C4—24no—
138C2×(C2×D3)⋊C4—24no—
139C2×(C2×D3)⋊C4—42no—
140C2×(C2×D3)⋊C4—42no—
141C2×(C2×D3)⋊C4—42no—
142C2×(C2×D3)⋊C4—42no—
143C2×(C2×D3)⋊C4—42no—
144C2×(C2×D3)⋊C4—42no—
145C2×(C2×D3)⋊C4—42no—
146C2×(C2×D3)⋊C4—42no—
147C2×(C2×D3)⋊C4—42no—
148C2×(C2×D3)⋊C4—42no—
149C2×(C2×D3)⋊C4C2314yes—
150C2×(C2×D3)⋊C4C2314yes—
151C2×(C2×D3)⋊C4C2314yes—
152C2×(C2×D3)⋊C4C2314yes—
153C2×(C2×D3)⋊C4C2314yes—
154C2×(C2×D3)⋊C4C2314yes—
155C2×(C2×D3)⋊C4C2314yes—
156C2×(C2×D3)⋊C4C2314yes—
157C2×(C2×D3)⋊C4C2314yes—
158C2×(C2×D3)⋊C4C2314yes—
159C2×(C2×D3)⋊C4C2314yescomplemented
160C2×(C2×D3)⋊C4C2314yescomplemented
161C2×(C2×D3)⋊C4C2314yescomplemented
162C2×(C2×D3)⋊C4C2314yescomplemented
163C2×C4⋊Dic3—24no—
164C2×C4⋊Dic3—42no—
165C2×C4⋊Dic3—42no—
166C2×C4⋊Dic3C2314yescomplemented
167C2×C4⋊Dic3C2314yescomplemented
168C2×C4⋊Dic3C2314yescomplemented
169C2×Dic3⋊C4—24no—
170C2×Dic3⋊C4—24no—
171C2×Dic3⋊C4C2314yescomplemented
172C2×Dic3⋊C4C2314yescomplemented
173C2×C4×Dic3—24no—
174C2×C4×Dic3C2314yescomplemented
175#882—232no—
176#879—232no—
177C3×#95C2314yescomplemented
178C3×#95C2314yescomplemented
179C3⋊#95C2314yescomplemented
180C3⋊#95C2314yescomplemented
181C26—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4—31no—
185C2×#126—38no—
186C2×#126—68no—
187C2×#120—38no—
188C2×#120—68no—
189C22×C4⋊C4—31no—
190C22×C4⋊C4—31no—
191C22×C4⋊C4—31no—
192C22×C4⋊C4—31no—
193C22×C4⋊C4—31no—
194C22×C4⋊C4C2×D311yescharacteristic, complemented
195C22×C22⋊C4—31no—
196C22×C22⋊C4—31no—
197C22×C22⋊C4—31no—
198C22×C22⋊C4—31no—
199C22×C22⋊C4—31no—
200C22×C22⋊C4—31no—
201C22×C22⋊C4—31no—
202C22×C22⋊C4—31no—
203C22×C22⋊C4—31no—
204C22×C22⋊C4—31no—
205C22×C22⋊C4—31no—
206C22×C22⋊C4—31no—
207C22×C22⋊C4—31no—
208C22×C22⋊C4—31no—
209C22×C22⋊C4—31no—
210C22×C22⋊C4—31no—
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C22⋊C4C2×D311yescharacteristic
213C22×C22⋊C4C2×D311yescharacteristic
214C22×C42—31no—
215C22×C42C2×D311yescharacteristic, complemented
216#399—38no—
217#396—38no—
218#394—38no—
219#394—38no—
220#394—38no—
221#394—38no—
222#390—38no—
223#390—38no—
224#388—38no—
225#388—38no—
226#388C2×D318yescomplemented
227#379—38no—
228#379—38no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95C2×D311yescharacteristic, complemented
232C2×#95C2×D311yescharacteristic, complemented
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3C2×D414yes—
240C24×C3C2412yes—
241C24×C3C2411yescharacteristic
242C23×D3—22no—
243C23×D3—22no—
244C23×D3—22no—
245C23×D3—22no—
246C23×D3—22no—
247C23×D3—22no—
248C23×D3—22no—
249C23×D3—22no—
250C23×D3—22no—
251C23×D3—22no—
252C23×D3—22no—
253C23×D3—22no—
254C23×D3—28no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—22no—
258C23×D3—22no—
259C23×D3—22no—
260C23×D3—22no—
261C23×D3—22no—
262C23×D3—28no—
263C23×D3—28no—
264C23×D3—44no—
265C23×D3—44no—
266C23×D3—44no—
267C23×D3—44no—
268C23×D3—416no—
269C23×D3—416no—
270C23×D3—416no—
271C23×D3—416no—
272C23×D3—416no—
273C23×D3—416no—
274C23×D3—416no—
275C23×D3#4114yes—
276C23×D3#4114yes—
277C23×D3C2412yes—
278C23×D3C2412yes—
279C23×D3C2412yes—
280C22×C3×C4—22no—
281C22×C3×C4—22no—
282C22×C3×C4—22no—
283C22×C3×C4—22no—
284C22×C3×C4—22no—
285C22×C3×C4—22no—
286C22×C3×C4—22no—
287C22×C3×C4—22no—
288C22×C3×C4—22no—
289C22×C3×C4—22no—
290C22×C3×C4—22no—
291C22×C3×C4—22no—
292C22×C3×C4—22no—
293C22×C3×C4—22no—
294C22×C3×C4—22no—
295C22×C3×C4—22no—
296C22×C3×C4C2×D414yes—
297C22×C3×C4C2×D414yes—
298C22×C3×C4C2412yes—
299C22×C3×C4C2412yes—
300C22×C3×C4C2412yes—
301C22×C3×C4C2412yes—
302C22×C3×C4C2412yes—
303C22×C3×C4C2412yes—
304C2×#67—28no—
305C2×#67—44no—
306C2×#67—44no—
307C2×#67—416no—
308C22×Dic3—22no—
309C22×Dic3—22no—
310C22×Dic3—22no—
311C22×Dic3—22no—
312C22×Dic3—22no—
313C22×Dic3—22no—
314C22×Dic3—22no—
315C22×Dic3—22no—
316C22×Dic3—22no—
317C22×Dic3—22no—
318C22×Dic3—22no—
319C22×Dic3—22no—
320C22×Dic3—22no—
321C22×Dic3—22no—
322C22×Dic3—22no—
323C22×Dic3C2412yes—
324C22×Dic3C2412yes—
325C22×Dic3C2412yes—
326C22×Dic3C2412yes—
327C22×Dic3C2412yes—
328C2×D12—28no—
329C2×D12—28no—
330C2×D12—28no—
331C2×D12—28no—
332C2×D12—44no—
333C2×D12—44no—
334C2×D12—416no—
335C2×D12—416no—
336C3×C4⋊C4—44no—
337C3×C22⋊C4—44no—
338C3×C22⋊C4—44no—
339C3×C22⋊C4C2×D4116yes—
340C3×C42—44no—
341#217—28no—
342#217—28no—
343(C2×D3)⋊C4—28no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—44no—
348(C2×D3)⋊C4—44no—
349(C2×D3)⋊C4—44no—
350(C2×D3)⋊C4—44no—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355(C2×D3)⋊C4—44no—
356(C2×D3)⋊C4—44no—
357C4⋊Dic3—28no—
358C4⋊Dic3—44no—
359C4⋊Dic3—44no—
360Dic3⋊C4—28no—
361Dic3⋊C4—28no—
362C4×Dic3—28no—
363C25—31no—
364C25—31no—
365C25—31no—
366C25—34no—
367C25—64no—
368C25—64no—
369C25—64no—
370C25—122no—
371C25—122no—
372C25—122no—
373C25—122no—
374C25C22×D311yescharacteristic
375C22×D4—34no—
376C22×D4—34no—
377C22×D4—34no—
378C22×D4—64no—
379C22×D4—64no—
380C22×D4—64no—
381C22×D4—64no—
382C22×D4—64no—
383C22×D4—122no—
384C22×D4—122no—
385C22×D4—122no—
386C22×D4—122no—
387C23×C4—31no—
388C23×C4—31no—
389C23×C4—31no—
390C23×C4—31no—
391C23×C4—31no—
392C23×C4C22×D311yescharacteristic
393C23×C4C22×D311yescharacteristic
394C23×C4C22×D311yescharacteristic
395C23×C4C22×D311yescharacteristic
396C23×C4C22×D311yescharacteristic
397C23×C4C22×D311yescharacteristic
398#126—632no—
399#120—632no—
400C2×C4⋊C4—34no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—64no—
407C2×C4⋊C4—64no—
408C2×C4⋊C4—64no—
409C2×C4⋊C4—122no—
410C2×C4⋊C4—122no—
411C2×C4⋊C4C22×D314yescomplemented
412C2×C22⋊C4—34no—
413C2×C22⋊C4—34no—
414C2×C22⋊C4—34no—
415C2×C22⋊C4—34no—
416C2×C22⋊C4—34no—
417C2×C22⋊C4—34no—
418C2×C22⋊C4—34no—
419C2×C22⋊C4—34no—
420C2×C22⋊C4—34no—
421C2×C22⋊C4—34no—
422C2×C22⋊C4—34no—
423C2×C22⋊C4—34no—
424C2×C22⋊C4—34no—
425C2×C22⋊C4—34no—
426C2×C22⋊C4—34no—
427C2×C22⋊C4—34no—
428C2×C22⋊C4—42no—
429C2×C22⋊C4—42no—
430C2×C22⋊C4—64no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—122no—
437C2×C22⋊C4—122no—
438C2×C22⋊C4—122no—
439C2×C22⋊C4—122no—
440C2×C22⋊C4—122no—
441C2×C22⋊C4—122no—
442C2×C22⋊C4—122no—
443C2×C22⋊C4—122no—
444C2×C22⋊C4—122no—
445C2×C22⋊C4—122no—
446C2×C22⋊C4D1218yes—
447C2×C22⋊C4C22×D314yes—
448C2×C22⋊C4C22×D314yes—
449C2×C22⋊C4C22×D314yes—
450C2×C42—34no—
451C2×C42—42no—
452C2×C42—64no—
453C2×C42C22×D314yescomplemented
454#95—34no—
455#95—34no—
456#95C22×D314yescomplemented
457#95C22×D314yescomplemented
458C23×C3—28no—
459C23×C3—28no—
460C23×C3—28no—
461C23×C3—22no—
462C23×C3—22no—
463C23×C3—22no—
464C23×C3—22no—
465C23×C3—22no—
466C23×C3—22no—
467C23×C3—44no—
468C23×C3—44no—
469C23×C3—44no—
470C23×C3—44no—
471C23×C3C22×D414yes—
472C23×C3C22×D412yes—
473C23×C3C2×#4112yes—
474C23×C3C2×#4112yes—
475C23×C3H(5,𝔽2)12yes—
476C23×C3H(5,𝔽2)12yes—
477C23×C3H(5,𝔽2)12yes—
478C23×C3H(5,𝔽2)12yes—
479C23×C3C2511yescharacteristic
480C22×D3—28no—
481C22×D3—28no—
482C22×D3—28no—
483C22×D3—28no—
484C22×D3—28no—
485C22×D3—28no—
486C22×D3—22no—
487C22×D3—22no—
488C22×D3—22no—
489C22×D3—22no—
490C22×D3—22no—
491C22×D3—22no—
492C22×D3—22no—
493C22×D3—22no—
494C22×D3—22no—
495C22×D3—22no—
496C22×D3—22no—
497C22×D3—22no—
498C22×D3—22no—
499C22×D3—22no—
500C22×D3—22no—
501C22×D3—22no—
502C22×D3—22no—
503C22×D3—22no—
504C22×D3—22no—
505C22×D3—416no—
506C22×D3—416no—
507C22×D3—416no—
508C22×D3—416no—
509C22×D3—416no—
510C22×D3—416no—
511C22×D3—4128no—
512C22×D3—416no—
513C22×D3—44no—
514C22×D3—44no—
515C22×D3—44no—
516C22×D3—44no—
517C22×D3—44no—
518C22×D3—44no—
519C22×D3—44no—
520C22×D3—44no—
521C22×D3—44no—
522C22×D3—44no—
523C22×D3—44no—
524C22×D3—44no—
525C22×D3—44no—
526C22×D3—44no—
527C22×D3—44no—
528C22×D3C2×#4114yes—
529C22×D3C2×#4114yes—
530C2×C3×C4—28no—
531C2×C3×C4—28no—
532C2×C3×C4—22no—
533C2×C3×C4—22no—
534C2×C3×C4—22no—
535C2×C3×C4—22no—
536C2×C3×C4—22no—
537C2×C3×C4—22no—
538C2×C3×C4—22no—
539C2×C3×C4—22no—
540C2×C3×C4—22no—
541C2×C3×C4—22no—
542C2×C3×C4—22no—
543C2×C3×C4—22no—
544C2×C3×C4—22no—
545C2×C3×C4—22no—
546C2×C3×C4—22no—
547C2×C3×C4—22no—
548C2×C3×C4—44no—
549C2×C3×C4—44no—
550C2×C3×C4—44no—
551C2×C3×C4—44no—
552C2×C3×C4C22×D414yes—
553C2×C3×C4C22×D414yes—
554#67—416no—
555C2×Dic3—22no—
556C2×Dic3—22no—
557C2×Dic3—22no—
558C2×Dic3—22no—
559C2×Dic3—22no—
560C2×Dic3—22no—
561C2×Dic3—22no—
562C2×Dic3—22no—
563C2×Dic3—22no—
564C2×Dic3—22no—
565C2×Dic3—22no—
566C2×Dic3—22no—
567C2×Dic3—22no—
568C2×Dic3—22no—
569C2×Dic3—22no—
570C2×Dic3—44no—
571C2×Dic3—44no—
572C2×Dic3—44no—
573C2×Dic3—44no—
574C2×Dic3—44no—
575D12—416no—
576D12—416no—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—34no—
584C24—34no—
585C24—32no—
586C24—32no—
587C24—32no—
588C24—68no—
589C24—68no—
590C24—62no—
591C24—62no—
592C24—62no—
593C24—62no—
594C24—62no—
595C24—62no—
596C24—62no—
597C24—62no—
598C24—62no—
599C24—62no—
600C24—62no—
601C24—62no—
602C24—68no—
603C24—62no—
604C24—62no—
605C24—62no—
606C24—62no—
607C24—62no—
608C24—62no—
609C24—62no—
610C24—124no—
611C24—124no—
612C24—124no—
613C24—124no—
614C24—1216no—
615C24—1216no—
616C24—1216no—
617C24—1216no—
618C24—1216no—
619C24—1216no—
620C24—1216no—
621C24C2×D1214yes—
622C24C23×D312yes—
623C24C23×D311yescharacteristic
624C2×D4—68no—
625C2×D4—68no—
626C2×D4—68no—
627C2×D4—68no—
628C2×D4—68no—
629C2×D4—124no—
630C2×D4—124no—
631C2×D4—1216no—
632C2×D4—1216no—
633C2×D4—124no—
634C2×D4—124no—
635C2×D4—1216no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—22no—
639C22×C4—22no—
640C22×C4—22no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—22no—
645C22×C4—22no—
646C22×C4—22no—
647C22×C4—22no—
648C22×C4—22no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—22no—
652C22×C4—32no—
653C22×C4—32no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—32no—
657C22×C4—62no—
658C22×C4—62no—
659C22×C4—62no—
660C22×C4—62no—
661C22×C4—62no—
662C22×C4—62no—
663C22×C4—62no—
664C22×C4—62no—
665C22×C4—62no—
666C22×C4—62no—
667C22×C4—62no—
668C22×C4—62no—
669C22×C4—62no—
670C22×C4—62no—
671C22×C4—62no—
672C22×C4C2×D1214yes—
673C22×C4C2×D1214yes—
674C22×C4C23×D312yes—
675C22×C4C23×D312yes—
676C22×C4C23×D312yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C4⋊C4—44no—
681C4⋊C4—68no—
682C4⋊C4—68no—
683C4⋊C4—68no—
684C4⋊C4—124no—
685C4⋊C4—124no—
686C22⋊C4—44no—
687C22⋊C4—44no—
688C22⋊C4—68no—
689C22⋊C4—68no—
690C22⋊C4—68no—
691C22⋊C4—68no—
692C22⋊C4—68no—
693C22⋊C4—68no—
694C22⋊C4—124no—
695C22⋊C4—124no—
696C22⋊C4—124no—
697C22⋊C4—124no—
698C22⋊C4—124no—
699C22⋊C4—124no—
700C22⋊C4—124no—
701C22⋊C4—124no—
702C22⋊C4—124no—
703C22⋊C4—124no—
704C22⋊C4C2×D12116yes—
705C42—44no—
706C42—68no—
707C22×C3—24no—
708C22×C3—24no—
709C22×C3—24no—
710C22×C3—42no—
711C22×C3—42no—
712C22×C3—416no—
713C22×C3—42no—
714C22×C3—42no—
715C22×C3#53514yes—
716C22×C3#53814yes—
717C22×C3#53814yes—
718C22×C3#54614yes—
719C22×C3#54614yes—
720C22×C3#55114yes—
721C22×C3#56014yes—
722C22×C3C23×D411yescharacteristic
723C22×C3C22×#4111yescharacteristic
724C22×C3C22×#4111yescharacteristic
725C22×C3C2×H(5,𝔽2)11yescharacteristic
726C22×C3C2×H(5,𝔽2)11yescharacteristic
727C22×C3C2×H(5,𝔽2)11yescharacteristic
728C22×C3C2×H(5,𝔽2)11yescharacteristic
729C2×D3—24no—
730C2×D3—24no—
731C2×D3—24no—
732C2×D3—24no—
733C2×D3—24no—
734C2×D3—24no—
735C2×D3—464no—
736C2×D3—42no—
737C2×D3—42no—
738C2×D3—42no—
739C2×D3—42no—
740C2×D3—416no—
741C2×D3—416no—
742C2×D3—42no—
743C2×D3—42no—
744C2×D3—42no—
745C2×D3—42no—
746C2×D3—42no—
747C2×D3—42no—
748C2×D3—42no—
749C2×D3—42no—
750C2×D3—42no—
751C2×D3—42no—
752C2×D3—42no—
753C2×D3—88no—
754C3×C4—24no—
755C3×C4—24no—
756C3×C4—42no—
757C3×C4—42no—
758C3×C4—42no—
759C3×C4—42no—
760Dic3—42no—
761Dic3—42no—
762Dic3—42no—
763Dic3—42no—
764Dic3—42no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—28no—
772C23—28no—
773C23—28no—
774C23—34no—
775C23—34no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—68no—
781C23—68no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—68no—
789C23—68no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—62no—
795C23—62no—
796C23—68no—
797C23—68no—
798C23—62no—
799C23—62no—
800C23—62no—
801C23—62no—
802C23—62no—
803C23—62no—
804C23—62no—
805C23—1216no—
806C23—1216no—
807C23—1216no—
808C23—1216no—
809C23—1216no—
810C23—1216no—
811C23—12128no—
812C23—1216no—
813C23—124no—
814C23—124no—
815C23—124no—
816C23—124no—
817C23—124no—
818C23—124no—
819C23—124no—
820C23—124no—
821C23—124no—
822C23—124no—
823C23—124no—
824C23—124no—
825C23—124no—
826C23—124no—
827C23—124no—
828C23C22×D1214yes—
829C23C22×D1212yes—
830C23#100412yes—
831C23#100412yes—
832C23D3×#4112yes—
833C23D3×#4112yes—
834C23#100912yes—
835C23#100912yes—
836C23C24×D311yescharacteristic
837D4—1216no—
838D4—1216no—
839D4—1216no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—28no—
845C2×C4—28no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—44no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—62no—
863C2×C4—62no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—62no—
867C2×C4—62no—
868C2×C4—62no—
869C2×C4—62no—
870C2×C4—62no—
871C2×C4—62no—
872C2×C4—62no—
873C2×C4—62no—
874C2×C4—62no—
875C2×C4—62no—
876C2×C4—62no—
877C2×C4—124no—
878C2×C4—124no—
879C2×C4—124no—
880C2×C4—124no—
881C2×C4—124no—
882C2×C4C22×D1214yes—
883C2×C4C22×D1214yes—
884C2×C3—44no—
885C2×C3#268518yescomplemented
886C2×C3C2×#53511yescharacteristic
887C2×C3C2×#53811yescharacteristic
888C2×C3C2×#53811yescharacteristic
889C2×C3C2×#54611yescharacteristic
890C2×C3C2×#54611yescharacteristic
891C2×C3C2×#55111yescharacteristic
892C2×C3C2×#56011yescharacteristic
893D3—44no—
894D3—44no—
895D3—82no—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—42no—
900C22—42no—
901C22—416no—
902C22—42no—
903C22—42no—
904C22—64no—
905C22—64no—
906C22—64no—
907C22—64no—
908C22—64no—
909C22—64no—
910C22—1264no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—1216no—
915C22—1216no—
916C22—122no—
917C22—122no—
918C22—122no—
919C22—122no—
920C22—122no—
921C22—122no—
922C22—122no—
923C22—122no—
924C22—122no—
925C22—122no—
926C22—122no—
927C22—122no—
928C22—248no—
929C22#552514yes—
930C22#555414yes—
931C22#555414yes—
932C22#562014yes—
933C22#565714yes—
934C22#567814yes—
935C22#570514yes—
936C22C23×D1211yescharacteristic
937C22C2×#100411yescharacteristic
938C22C2×#100411yescharacteristic
939C22C2×D3×#4111yescharacteristic
940C22C2×D3×#4111yescharacteristic
941C22C2×#100911yescharacteristic
942C22C2×#100911yescharacteristic
943C4—24no—
944C4—24no—
945C4—42no—
946C4—42no—
947C4—42no—
948C4—42no—
949C4—122no—
950C4—122no—
951C4—122no—
952C4—122no—
953C4—122no—
954C3C2×#268511yescharacteristic, complemented, Sylow
955C2—44no—
956C2—124no—
957C2—124no—
958C2—242no—
959C2#7591818yesdirect product factor
960C2C2×#552511yescharacteristic
961C2C2×#555411yescharacteristic
962C2C2×#555411yescharacteristic
963C2C2×#562011yescharacteristic
964C2C2×#565711yescharacteristic
965C2C2×#567811yescharacteristic
966C2C2×#570511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#388C2
socleC24×C3C24
prime radicalC22×#882C2
hypercenterC2×#388D3
hypocenterC3C2×#2685
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#388

Complements

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

NH ≅ G/Ntype
2. C22×#879C2semidirect
3. C2×C3×#388C2semidirect
4. C2×#4994C2semidirect
5. C2×#4988C2semidirect
6. C2×#4955C2semidirect
7. C2×#4955C2semidirect
8. C2×#4961C2semidirect
9. C2×#4961C2semidirect
10. C2×#4939C2semidirect
11. C2×#4940C2semidirect
12. #75918C2direct (N × H)
13. C2×#4677C2semidirect
14. C2×#4672C2semidirect
15. C2×#4672C2semidirect
16. C2×#4670C2semidirect
22. C22×C3×C4⋊C4C22semidirect
26. C22×C3×C42C22semidirect
39. C22×(C2×D3)⋊C4C22semidirect
40. C22×(C2×D3)⋊C4C22semidirect
41. C22×(C2×D3)⋊C4C22semidirect
42. C22×(C2×D3)⋊C4C22semidirect
43. C22×C4⋊Dic3C22semidirect
44. C22×C4⋊Dic3C22semidirect
45. C22×C4⋊Dic3C22semidirect
46. C22×Dic3⋊C4C22semidirect
47. C22×Dic3⋊C4C22semidirect
48. C22×C4×Dic3C22semidirect
52. C2×#879C22semidirect
53. C3×#388C22semidirect
54. C2×C3×#95C22semidirect
55. C2×C3×#95C22semidirect
56. C2×C3⋊#95C22semidirect
57. C2×C3⋊#95C22semidirect
58. #4994C22semidirect
59. #4988C22semidirect
60. #4961C22semidirect
61. #4961C22semidirect
62. #4955C22semidirect
63. #4955C22semidirect
64. #4940C22semidirect
65. #4939C22semidirect
66. #4677C22semidirect
67. #4672C22semidirect
68. #4672C22semidirect
69. #4670C22semidirect
83. C2×#388D3semidirect
122. C2×C3×C4⋊C4C23semidirect
130. C2×C3×C42C23semidirect
159. C2×(C2×D3)⋊C4C23semidirect
160. C2×(C2×D3)⋊C4C23semidirect
161. C2×(C2×D3)⋊C4C23semidirect
162. C2×(C2×D3)⋊C4C23semidirect
166. C2×C4⋊Dic3C23semidirect
167. C2×C4⋊Dic3C23semidirect
168. C2×C4⋊Dic3C23semidirect
171. C2×Dic3⋊C4C23semidirect
172. C2×Dic3⋊C4C23semidirect
174. C2×C4×Dic3C23semidirect
177. C3×#95C23semidirect
178. C3×#95C23semidirect
179. C3⋊#95C23semidirect
180. C3⋊#95C23semidirect
194. C22×C4⋊C4C2×D3semidirect
215. C22×C42C2×D3semidirect
226. #388C2×D3semidirect
231. C2×#95C2×D3semidirect
232. C2×#95C2×D3semidirect
411. C2×C4⋊C4C22×D3semidirect
453. C2×C42C22×D3semidirect
456. #95C22×D3semidirect
457. #95C22×D3semidirect
885. C2×C3#2685semidirect
954. C3C2×#2685semidirect
959. C2#75918direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8822
C22×#8792
C2×C3×#3882
C2×#49942
C2×#49882
C2×#49552
C2×#49612
C2×#49392
C2×#49402
#759182
C2×#46772
C2×#46722
C2×#46702
C2×#26853