Finite Group Databasebeta

← C2×#77434 #11429983

Subgroups — C2×#77434 #11429983

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×#898C211yesmaximal, characteristic, complemented
2C22×#882C211yesmaximal, characteristic
3C2×C3×#396C211yesmaximal, characteristic, complemented
4C2×#4993C211yesmaximal, characteristic, complemented
5C2×#4991C211yesmaximal, characteristic, complemented
6C2×#4991C211yesmaximal, characteristic, complemented
7C2×#4988C211yesmaximal, characteristic, complemented
8C2×#4990C211yesmaximal, characteristic, complemented
9C2×#4955C211yesmaximal, characteristic, complemented
10C2×#4955C211yesmaximal, characteristic, complemented
11C2×#4961C211yesmaximal, characteristic, complemented
12C2×#4957C211yesmaximal, characteristic, complemented
13C2×#4944C211yesmaximal, characteristic, complemented
14#77434C2116yesmaximal, direct product factor
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×C4⋊C4C2211yescharacteristic, complemented
24C22×C3×C4⋊C4C2211yescharacteristic, complemented
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×#217C2211yescharacteristic
29C22×#217C2211yescharacteristic
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
40C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
41C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
42C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
43C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C22×C4⋊Dic3C2211yescharacteristic, complemented
45C22×Dic3⋊C4C2211yescharacteristic, complemented
46C22×Dic3⋊C4C2211yescharacteristic, complemented
47C22×C4×Dic3C2211yescharacteristic, complemented
48C22×C4×Dic3C2211yescharacteristic, complemented
49C2×#898—28no—
50C2×#898C2218yescomplemented
51C2×#882—28no—
52C2×#882C2218yes—
53C3×#396C2218yescomplemented
54C2×C3×#95C2211yescharacteristic, complemented
55C2×C3⋊#95C2211yescharacteristic, complemented
56C2×C3⋊#95C2211yescharacteristic, complemented
57C2×C3⋊#95C2211yescharacteristic, complemented
58#4993C2218yescomplemented
59#4991C2218yescomplemented
60#4991C2218yescomplemented
61#4990C2218yescomplemented
62#4988C2218yescomplemented
63#4961C2218yescomplemented
64#4957C2218yescomplemented
65#4955C2218yescomplemented
66#4955C2218yescomplemented
67#4944C2218yescomplemented
68#4672C2218yescomplemented
69#4670C2218yescomplemented
70C22×#126—31no—
71C22×#120—31no—
72#2685—316no—
73C2×#399—31no—
74C2×#396D311yescharacteristic, complemented
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×#388—31no—
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—24no—
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—42no—
117C22×D12—42no—
118C22×D12—42no—
119C22×D12C2314yes—
120C22×D12C2314yes—
121C2×C3×C4⋊C4—24no—
122C2×C3×C4⋊C4—42no—
123C2×C3×C4⋊C4—42no—
124C2×C3×C4⋊C4C2314yescomplemented
125C2×C3×C4⋊C4C2314yescomplemented
126C2×C3×C4⋊C4C2314yescomplemented
127C2×C3×C22⋊C4—24no—
128C2×C3×C22⋊C4—42no—
129C2×C3×C22⋊C4—42no—
130C2×C3×C22⋊C4C2314yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C22⋊C4C2314yes—
133C2×#217—24no—
134C2×#217—42no—
135C2×#217C2314yes—
136C2×#217C2314yes—
137C2×(C2×D3)⋊C4—24no—
138C2×(C2×D3)⋊C4—24no—
139C2×(C2×D3)⋊C4—24no—
140C2×(C2×D3)⋊C4—24no—
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)⋊C4—42no—
150C2×(C2×D3)⋊C4D418yes—
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)⋊C4C2314yes—
160C2×(C2×D3)⋊C4C2314yes—
161C2×(C2×D3)⋊C4C2314yescomplemented
162C2×(C2×D3)⋊C4C2314yescomplemented
163C2×(C2×D3)⋊C4C2314yescomplemented
164C2×(C2×D3)⋊C4C2314yescomplemented
165C2×C4⋊Dic3—24no—
166C2×C4⋊Dic3C2314yescomplemented
167C2×Dic3⋊C4—24no—
168C2×Dic3⋊C4—42no—
169C2×Dic3⋊C4C2314yescomplemented
170C2×Dic3⋊C4C2314yescomplemented
171C2×C4×Dic3—24no—
172C2×C4×Dic3—42no—
173C2×C4×Dic3C2314yescomplemented
174C2×C4×Dic3C2314yescomplemented
175#898—232no—
176#882—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⋊C4C2×D311yescharacteristic, complemented
193C22×C4⋊C4C2×D311yescharacteristic, complemented
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×C42—31no—
216#399—38no—
217#396C2×D318yescomplemented
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#388—38no—
227#379—38no—
228#379—38no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95C2×D311yescharacteristic, complemented
233C24×C3—22no—
234C24×C3—22no—
235C24×C3—22no—
236C24×C3—22no—
237C24×C3—22no—
238C24×C3—22no—
239C24×C3#4114yes—
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—22no—
255C23×D3—22no—
256C23×D3—22no—
257C23×D3—28no—
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×D3C2×D414yes—
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×C4—22no—
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—28no—
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×Dic3C2×D414yes—
323C22×Dic3C2412yes—
324C22×Dic3C2412yes—
325C22×Dic3C2412yes—
326C22×Dic3C2412yes—
327C22×Dic3C2412yes—
328C2×D12—28no—
329C2×D12—28no—
330C2×D12—28no—
331C2×D12—44no—
332C2×D12—44no—
333C2×D12—44no—
334C2×D12—416no—
335C2×D12—416no—
336C3×C4⋊C4—28no—
337C3×C4⋊C4—44no—
338C3×C4⋊C4—44no—
339C3×C22⋊C4—28no—
340C3×C22⋊C4—44no—
341C3×C22⋊C4—44no—
342#217—28no—
343#217—44no—
344(C2×D3)⋊C4—28no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
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—
357(C2×D3)⋊C4C2×D4116yes—
358C4⋊Dic3—28no—
359Dic3⋊C4—28no—
360Dic3⋊C4—44no—
361C4×Dic3—28no—
362C4×Dic3—44no—
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—24no—
401C2×C4⋊C4—34no—
402C2×C4⋊C4—34no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—42no—
405C2×C4⋊C4—42no—
406C2×C4⋊C4—64no—
407C2×C4⋊C4—64no—
408C2×C4⋊C4—122no—
409C2×C4⋊C4C22×D314yescomplemented
410C2×C4⋊C4C22×D314yescomplemented
411C2×C4⋊C4C22×D314yescomplemented
412C2×C22⋊C4—24no—
413C2×C22⋊C4—38no—
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—34no—
429C2×C22⋊C4—34no—
430C2×C22⋊C4—42no—
431C2×C22⋊C4—42no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—64no—
435C2×C22⋊C4—64no—
436C2×C22⋊C4—64no—
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⋊C4—122no—
447C2×C22⋊C4C22×D314yes—
448C2×C22⋊C4C22×D314yes—
449C2×C22⋊C4C22×D314yes—
450C2×C42—34no—
451C2×C42—34no—
452C2×C42—64no—
453C2×C42—122no—
454#95—34no—
455#95—34no—
456#95—34no—
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×D412yes—
472C23×C3C2×#4114yes—
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×D3C22×D414yes—
529C22×D3C2×#4114yes—
530C2×C3×C4—28no—
531C2×C3×C4—22no—
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×C4—44no—
553C2×C3×C4C22×D414yes—
554#67—416no—
555C2×Dic3—28no—
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×Dic3C22×D414yes—
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—62no—
603C24—62no—
604C24—62no—
605C24—62no—
606C24—68no—
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—
621C24#23914yes—
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—124no—
632C2×D4—1216no—
633C2×D4—1216no—
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—22no—
653C22×C4—34no—
654C22×C4—32no—
655C22×C4—32no—
656C22×C4—32no—
657C22×C4—32no—
658C22×C4—32no—
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×C4—62no—
673C22×C4D3×D414yes—
674C22×C4C23×D312yes—
675C22×C4C23×D312yes—
676C22×C4C23×D312yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C4⋊C4—28no—
681C4⋊C4—44no—
682C4⋊C4—44no—
683C4⋊C4—68no—
684C4⋊C4—68no—
685C4⋊C4—124no—
686C22⋊C4—28no—
687C22⋊C4—316no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—68no—
691C22⋊C4—68no—
692C22⋊C4—68no—
693C22⋊C4—68no—
694C22⋊C4—68no—
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⋊C4—124no—
705C42—68no—
706C42—124no—
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—42no—
756C3×C4—42no—
757C3×C4—42no—
758C3×C4—42no—
759C3×C4—42no—
760Dic3—24no—
761Dic3—42no—
762Dic3—42no—
763Dic3—42no—
764Dic3—42no—
765C23—28no—
766C23—28no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—28no—
774C23—34no—
775C23—34no—
776C23—44no—
777C23—44no—
778C23—44no—
779C23—44no—
780C23—68no—
781C23—62no—
782C23—62no—
783C23—62no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—68no—
789C23—62no—
790C23—62no—
791C23—62no—
792C23—62no—
793C23—62no—
794C23—68no—
795C23—68no—
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—
828C23C2×D3×D412yes—
829C23#100412yes—
830C23#100412yes—
831C23C2×#23914yes—
832C23C2×#23912yes—
833C23D3×#4112yes—
834C23#100912yes—
835C23#100912yes—
836C23C24×D311yescharacteristic
837D4—1216no—
838D4—1216no—
839D4—1216no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—28no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
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—34no—
859C2×C4—44no—
860C2×C4—44no—
861C2×C4—44no—
862C2×C4—44no—
863C2×C4—44no—
864C2×C4—62no—
865C2×C4—62no—
866C2×C4—68no—
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—62no—
878C2×C4—62no—
879C2×C4—124no—
880C2×C4—124no—
881C2×C4—124no—
882C2×C4—124no—
883C2×C4C2×D3×D414yes—
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—416no—
901C22—42no—
902C22—42no—
903C22—42no—
904C22—64no—
905C22—64no—
906C22—64no—
907C22—64no—
908C22—64no—
909C22—64no—
910C22—1264no—
911C22—122no—
912C22—1216no—
913C22—1216no—
914C22—122no—
915C22—122no—
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#560714yes—
930C22#561014yes—
931C22#562014yes—
932C22#563014yes—
933C22#563714yes—
934C22#564414yes—
935C22#570414yes—
936C22C22×D3×D411yescharacteristic
937C22C2×#100411yescharacteristic
938C22C2×#100411yescharacteristic
939C22C22×#23911yescharacteristic
940C22C2×D3×#4111yescharacteristic
941C22C2×#100911yescharacteristic
942C22C2×#100911yescharacteristic
943C4—24no—
944C4—42no—
945C4—42no—
946C4—42no—
947C4—42no—
948C4—42no—
949C4—64no—
950C4—122no—
951C4—122no—
952C4—122no—
953C4—122no—
954C3C2×#268511yescharacteristic, complemented, Sylow
955C2—44no—
956C2—124no—
957C2—124no—
958C2—242no—
959C2#7743418yesdirect product factor
960C2C2×#560711yescharacteristic
961C2C2×#561011yescharacteristic
962C2C2×#562011yescharacteristic
963C2C2×#564411yescharacteristic
964C2C2×#563011yescharacteristic
965C2C2×#563711yescharacteristic
966C2C2×#570411yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#396C2
socleC24×C3C24
prime radicalC22×#882C2
hypercenterC2×#396D3
hypocenterC3C2×#2685
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#396

Complements

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

NH ≅ G/Ntype
1. C22×#898C2semidirect
3. C2×C3×#396C2semidirect
4. C2×#4993C2semidirect
5. C2×#4991C2semidirect
6. C2×#4991C2semidirect
7. C2×#4988C2semidirect
8. C2×#4990C2semidirect
9. C2×#4955C2semidirect
10. C2×#4955C2semidirect
11. C2×#4961C2semidirect
12. C2×#4957C2semidirect
13. C2×#4944C2semidirect
14. #77434C2direct (N × H)
15. C2×#4672C2semidirect
16. C2×#4670C2semidirect
22. C22×C3×C4⋊C4C22semidirect
23. C22×C3×C4⋊C4C22semidirect
24. C22×C3×C4⋊C4C22semidirect
40. C22×(C2×D3)⋊C4C22semidirect
41. C22×(C2×D3)⋊C4C22semidirect
42. C22×(C2×D3)⋊C4C22semidirect
43. C22×(C2×D3)⋊C4C22semidirect
44. C22×C4⋊Dic3C22semidirect
45. C22×Dic3⋊C4C22semidirect
46. C22×Dic3⋊C4C22semidirect
47. C22×C4×Dic3C22semidirect
48. C22×C4×Dic3C22semidirect
50. C2×#898C22semidirect
53. C3×#396C22semidirect
54. C2×C3×#95C22semidirect
55. C2×C3⋊#95C22semidirect
56. C2×C3⋊#95C22semidirect
57. C2×C3⋊#95C22semidirect
58. #4993C22semidirect
59. #4991C22semidirect
60. #4991C22semidirect
61. #4990C22semidirect
62. #4988C22semidirect
63. #4961C22semidirect
64. #4957C22semidirect
65. #4955C22semidirect
66. #4955C22semidirect
67. #4944C22semidirect
68. #4672C22semidirect
69. #4670C22semidirect
74. C2×#396D3semidirect
124. C2×C3×C4⋊C4C23semidirect
125. C2×C3×C4⋊C4C23semidirect
126. C2×C3×C4⋊C4C23semidirect
161. C2×(C2×D3)⋊C4C23semidirect
162. C2×(C2×D3)⋊C4C23semidirect
163. C2×(C2×D3)⋊C4C23semidirect
164. C2×(C2×D3)⋊C4C23semidirect
166. C2×C4⋊Dic3C23semidirect
169. C2×Dic3⋊C4C23semidirect
170. C2×Dic3⋊C4C23semidirect
173. C2×C4×Dic3C23semidirect
174. C2×C4×Dic3C23semidirect
177. C3×#95C23semidirect
178. C3⋊#95C23semidirect
179. C3⋊#95C23semidirect
180. C3⋊#95C23semidirect
192. C22×C4⋊C4C2×D3semidirect
193. C22×C4⋊C4C2×D3semidirect
194. C22×C4⋊C4C2×D3semidirect
217. #396C2×D3semidirect
232. C2×#95C2×D3semidirect
409. C2×C4⋊C4C22×D3semidirect
410. C2×C4⋊C4C22×D3semidirect
411. C2×C4⋊C4C22×D3semidirect
457. #95C22×D3semidirect
885. C2×C3#2685semidirect
954. C3C2×#2685semidirect
959. C2#77434direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#8982
C22×#8822
C2×C3×#3962
C2×#49932
C2×#49912
C2×#49882
C2×#49902
C2×#49552
C2×#49612
C2×#49572
C2×#49442
#774342
C2×#46722
C2×#46702
C2×#26853