Finite Group Databasebeta

← C2×#83114 #11429970

Subgroups — C2×#83114 #11429970

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×C3×#126C211yesmaximal, characteristic, complemented
2C22×#882C211yesmaximal, characteristic
3#83114C2116yesmaximal, direct product factor
4C2×#4993C211yesmaximal, characteristic, complemented
5C2×#4994C211yesmaximal, characteristic, complemented
6C2×#4991C211yesmaximal, characteristic, complemented
7C2×#4991C211yesmaximal, characteristic, complemented
8C2×#4988C211yesmaximal, characteristic, complemented
9C2×#4990C211yesmaximal, characteristic, complemented
10C2×#4959C211yesmaximal, characteristic, complemented
11C2×#4959C211yesmaximal, characteristic, complemented
12C2×#4955C211yesmaximal, characteristic, complemented
13C2×#4955C211yesmaximal, characteristic, complemented
14C2×#4951C211yesmaximal, characteristic, complemented
15C2×#4939C211yesmaximal, characteristic, complemented
16C2×#4940C211yesmaximal, characteristic, complemented
17C2×#2685—31nomaximal, Sylow
18C25×D3C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×D12C2211yescharacteristic
21C23×D12C2211yescharacteristic
22C2×C3×#126—28no—
23C2×C3×#126C2218yescomplemented
24C22×C3×C4⋊C4C2211yescharacteristic, complemented
25C22×C3×C4⋊C4C2211yescharacteristic, complemented
26C22×C3×C4⋊C4C2211yescharacteristic, complemented
27C22×C3×C22⋊C4C2211yescharacteristic
28C22×C3×C22⋊C4C2211yescharacteristic
29C22×C3×C22⋊C4C2211yescharacteristic
30C22×C3×C42C2211yescharacteristic, complemented
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
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
41C22×(C2×D3)⋊C4C2211yescharacteristic
42C22×(C2×D3)⋊C4C2211yescharacteristic
43C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
44C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
45C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
46C22×(C2×D3)⋊C4C2211yescharacteristic, complemented
47C22×C4⋊Dic3C2211yescharacteristic, complemented
48C22×Dic3⋊C4C2211yescharacteristic, complemented
49C22×Dic3⋊C4C2211yescharacteristic, complemented
50C22×C4×Dic3C2211yescharacteristic, complemented
51C2×#882—28no—
52C2×#882C2218yes—
53C2×C3⋊#95C2211yescharacteristic, complemented
54C2×C3⋊#95C2211yescharacteristic, complemented
55C2×C3⋊#95C2211yescharacteristic, complemented
56C2×C3⋊#95C2211yescharacteristic, complemented
57#4994C2218yescomplemented
58#4993C2218yescomplemented
59#4991C2218yescomplemented
60#4991C2218yescomplemented
61#4990C2218yescomplemented
62#4988C2218yescomplemented
63#4959C2218yescomplemented
64#4959C2218yescomplemented
65#4955C2218yescomplemented
66#4955C2218yescomplemented
67#4951C2218yescomplemented
68#4940C2218yescomplemented
69#4939C2218yescomplemented
70C22×#126D311yescharacteristic, complemented
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×#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—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—
121C3×#126—232no—
122C2×C3×C4⋊C4—24no—
123C2×C3×C4⋊C4—24no—
124C2×C3×C4⋊C4—24no—
125C2×C3×C4⋊C4C2314yescomplemented
126C2×C3×C4⋊C4C2314yescomplemented
127C2×C3×C4⋊C4C2314yescomplemented
128C2×C3×C22⋊C4—24no—
129C2×C3×C22⋊C4—24no—
130C2×C3×C22⋊C4D418yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C22⋊C4C2314yes—
133C2×C3×C22⋊C4C2314yes—
134C2×C3×C42—24no—
135C2×C3×C42C2314yescomplemented
136C2×#217—42no—
137C2×#217—42no—
138C2×#217C2314yes—
139C2×#217C2314yes—
140C2×(C2×D3)⋊C4—24no—
141C2×(C2×D3)⋊C4—24no—
142C2×(C2×D3)⋊C4—24no—
143C2×(C2×D3)⋊C4—24no—
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)⋊C4—42no—
151C2×(C2×D3)⋊C4—42no—
152C2×(C2×D3)⋊C4—42no—
153C2×(C2×D3)⋊C4—42no—
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)⋊C4C2314yes—
162C2×(C2×D3)⋊C4C2314yes—
163C2×(C2×D3)⋊C4C2314yes—
164C2×(C2×D3)⋊C4C2314yescomplemented
165C2×(C2×D3)⋊C4C2314yescomplemented
166C2×(C2×D3)⋊C4C2314yescomplemented
167C2×(C2×D3)⋊C4C2314yescomplemented
168C2×C4⋊Dic3—42no—
169C2×C4⋊Dic3C2314yescomplemented
170C2×Dic3⋊C4—42no—
171C2×Dic3⋊C4—42no—
172C2×Dic3⋊C4C2314yescomplemented
173C2×Dic3⋊C4C2314yescomplemented
174C2×C4×Dic3—42no—
175C2×C4×Dic3C2314yescomplemented
176#882—232no—
177C3⋊#95C2314yescomplemented
178C3⋊#95C2314yescomplemented
179C3⋊#95C2314yescomplemented
180C3⋊#95C2314yescomplemented
181C26—31no—
182C23×D4—31no—
183C23×D4—31no—
184C23×D4—31no—
185C2×#126—28no—
186C2×#126C2×D318yescomplemented
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×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#388—38no—
227#379—38no—
228#379—38no—
229C2×#95—31no—
230C2×#95—31no—
231C2×#95—31no—
232C2×#95—31no—
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—28no—
337C3×C4⋊C4—28no—
338C3×C4⋊C4—28no—
339C3×C22⋊C4—28no—
340C3×C22⋊C4—28no—
341C3×C22⋊C4C2×D4116yes—
342C3×C42—28no—
343#217—44no—
344#217—44no—
345(C2×D3)⋊C4—28no—
346(C2×D3)⋊C4—28no—
347(C2×D3)⋊C4—28no—
348(C2×D3)⋊C4—28no—
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)⋊C4—44no—
358(C2×D3)⋊C4—44no—
359C4⋊Dic3—44no—
360Dic3⋊C4—44no—
361Dic3⋊C4—44no—
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—232no—
399#120—632no—
400C2×C4⋊C4—24no—
401C2×C4⋊C4—24no—
402C2×C4⋊C4—24no—
403C2×C4⋊C4—34no—
404C2×C4⋊C4—34no—
405C2×C4⋊C4—34no—
406C2×C4⋊C4—122no—
407C2×C4⋊C4—122no—
408C2×C4⋊C4—122no—
409C2×C4⋊C4C22×D314yescomplemented
410C2×C4⋊C4C22×D314yescomplemented
411C2×C4⋊C4C22×D314yescomplemented
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
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—64no—
431C2×C22⋊C4—64no—
432C2×C22⋊C4—64no—
433C2×C22⋊C4—64no—
434C2×C22⋊C4—122no—
435C2×C22⋊C4—122no—
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⋊C4#6718yes—
447C2×C22⋊C4C22×D314yes—
448C2×C22⋊C4C22×D314yes—
449C2×C22⋊C4C22×D314yes—
450C2×C42—24no—
451C2×C42—34no—
452C2×C42—122no—
453C2×C42C22×D314yescomplemented
454#95—34no—
455#95—34no—
456#95—34no—
457#95—34no—
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—62no—
603C24—62no—
604C24—62no—
605C24—62no—
606C24—62no—
607C24—62no—
608C24—68no—
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×#6714yes—
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×#6714yes—
673C22×C4C2×#6714yes—
674C22×C4C23×D312yes—
675C22×C4C23×D312yes—
676C22×C4C23×D312yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C4⋊C4—28no—
681C4⋊C4—28no—
682C4⋊C4—28no—
683C4⋊C4—124no—
684C4⋊C4—124no—
685C4⋊C4—124no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—68no—
689C22⋊C4—68no—
690C22⋊C4—68no—
691C22⋊C4—68no—
692C22⋊C4—124no—
693C22⋊C4—124no—
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×#67116yes—
705C42—28no—
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—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—68no—
783C23—68no—
784C23—62no—
785C23—62no—
786C23—62no—
787C23—62no—
788C23—62no—
789C23—62no—
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—1216no—
812C23—12128no—
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—
828C23D3×#4112yes—
829C23D3×#4112yes—
830C23#100912yes—
831C23#100912yes—
832C23#100912yes—
833C23#100912yes—
834C23C22×#6714yes—
835C23C22×#6712yes—
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×#6714yes—
883C2×C4C22×#6714yes—
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—42no—
902C22—42no—
903C22—416no—
904C22—64no—
905C22—64no—
906C22—64no—
907C22—64no—
908C22—64no—
909C22—64no—
910C22—1264no—
911C22—122no—
912C22—122no—
913C22—122no—
914C22—122no—
915C22—1216no—
916C22—1216no—
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#570414yes—
930C22#570414yes—
931C22#570514yes—
932C22#571114yes—
933C22#582914yes—
934C22#582914yes—
935C22#583014yes—
936C22C2×D3×#4111yescharacteristic
937C22C2×D3×#4111yescharacteristic
938C22C2×#100911yescharacteristic
939C22C2×#100911yescharacteristic
940C22C2×#100911yescharacteristic
941C22C2×#100911yescharacteristic
942C22C23×#6711yescharacteristic
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#8311418yesdirect product factor
960C2C2×#570411yescharacteristic
961C2C2×#570411yescharacteristic
962C2C2×#570511yescharacteristic
963C2C2×#571111yescharacteristic
964C2C2×#583011yescharacteristic
965C2C2×#582911yescharacteristic
966C2C2×#582911yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC22×C3×#126C2
socleC24×C3C24
prime radicalC22×#882C2
hypercenterC22×#126D3
hypocenterC3C2×#2685
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C22×#126

Complements

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

NH ≅ G/Ntype
1. C22×C3×#126C2semidirect
3. #83114C2direct (N × H)
4. C2×#4993C2semidirect
5. C2×#4994C2semidirect
6. C2×#4991C2semidirect
7. C2×#4991C2semidirect
8. C2×#4988C2semidirect
9. C2×#4990C2semidirect
10. C2×#4959C2semidirect
11. C2×#4959C2semidirect
12. C2×#4955C2semidirect
13. C2×#4955C2semidirect
14. C2×#4951C2semidirect
15. C2×#4939C2semidirect
16. C2×#4940C2semidirect
23. C2×C3×#126C22semidirect
24. C22×C3×C4⋊C4C22semidirect
25. C22×C3×C4⋊C4C22semidirect
26. C22×C3×C4⋊C4C22semidirect
30. C22×C3×C42C22semidirect
43. C22×(C2×D3)⋊C4C22semidirect
44. C22×(C2×D3)⋊C4C22semidirect
45. C22×(C2×D3)⋊C4C22semidirect
46. C22×(C2×D3)⋊C4C22semidirect
47. C22×C4⋊Dic3C22semidirect
48. C22×Dic3⋊C4C22semidirect
49. C22×Dic3⋊C4C22semidirect
50. C22×C4×Dic3C22semidirect
53. C2×C3⋊#95C22semidirect
54. C2×C3⋊#95C22semidirect
55. C2×C3⋊#95C22semidirect
56. C2×C3⋊#95C22semidirect
57. #4994C22semidirect
58. #4993C22semidirect
59. #4991C22semidirect
60. #4991C22semidirect
61. #4990C22semidirect
62. #4988C22semidirect
63. #4959C22semidirect
64. #4959C22semidirect
65. #4955C22semidirect
66. #4955C22semidirect
67. #4951C22semidirect
68. #4940C22semidirect
69. #4939C22semidirect
70. C22×#126D3semidirect
125. C2×C3×C4⋊C4C23semidirect
126. C2×C3×C4⋊C4C23semidirect
127. C2×C3×C4⋊C4C23semidirect
135. C2×C3×C42C23semidirect
164. C2×(C2×D3)⋊C4C23semidirect
165. C2×(C2×D3)⋊C4C23semidirect
166. C2×(C2×D3)⋊C4C23semidirect
167. C2×(C2×D3)⋊C4C23semidirect
169. C2×C4⋊Dic3C23semidirect
172. C2×Dic3⋊C4C23semidirect
173. C2×Dic3⋊C4C23semidirect
175. C2×C4×Dic3C23semidirect
177. C3⋊#95C23semidirect
178. C3⋊#95C23semidirect
179. C3⋊#95C23semidirect
180. C3⋊#95C23semidirect
186. C2×#126C2×D3semidirect
192. C22×C4⋊C4C2×D3semidirect
193. C22×C4⋊C4C2×D3semidirect
194. C22×C4⋊C4C2×D3semidirect
215. C22×C42C2×D3semidirect
409. C2×C4⋊C4C22×D3semidirect
410. C2×C4⋊C4C22×D3semidirect
411. C2×C4⋊C4C22×D3semidirect
453. C2×C42C22×D3semidirect
885. C2×C3#2685semidirect
954. C3C2×#2685semidirect
959. C2#83114direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×#1262
C22×#8822
#831142
C2×#49932
C2×#49942
C2×#49912
C2×#49882
C2×#49902
C2×#49592
C2×#49552
C2×#49512
C2×#49392
C2×#49402
C2×#26853