Finite Group Databasebeta

← C2×#73838 #11429976

Subgroups — C2×#73838 #11429976

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×#953C211yesmaximal, characteristic
2C22×#879C211yesmaximal, characteristic, complemented
3C2×C3×#379C211yesmaximal, characteristic, complemented
4C2×#5247C211yesmaximal, characteristic, complemented
5C2×#4959C211yesmaximal, characteristic, complemented
6C2×#4959C211yesmaximal, characteristic, complemented
7C2×#4949C211yesmaximal, characteristic, complemented
8C2×#4948C211yesmaximal, characteristic, complemented
9C2×#4961C211yesmaximal, characteristic, complemented
10C2×#4961C211yesmaximal, characteristic, complemented
11C2×#4957C211yesmaximal, characteristic, complemented
12C2×#4957C211yesmaximal, characteristic, complemented
13C2×#4945C211yesmaximal, characteristic, complemented
14C2×#4944C211yesmaximal, characteristic, complemented
15C2×#4951C211yesmaximal, characteristic, complemented
16#73838C2116yesmaximal, direct product factor
17C2×#2685—31nomaximal, Sylow
18C26×C3C2211yescharacteristic
19C23×#67C2211yescharacteristic
20C23×#67C2211yescharacteristic
21C23×#67C2211yescharacteristic
22C22×C3×C22⋊C4C2211yescharacteristic
23C22×C3×C22⋊C4C2211yescharacteristic
24C22×C3×C22⋊C4C2211yescharacteristic
25C22×C3×C22⋊C4C2211yescharacteristic
26C22×C3×C22⋊C4C2211yescharacteristic
27C22×C3×C22⋊C4C2211yescharacteristic
28C2×#953—28no—
29C2×#953C2218yes—
30C22×#217C2211yescharacteristic
31C22×#217C2211yescharacteristic
32C22×#217C2211yescharacteristic
33C22×#217C2211yescharacteristic
34C22×#217C2211yescharacteristic
35C22×#217C2211yescharacteristic
36C22×#217C2211yescharacteristic
37C22×#217C2211yescharacteristic
38C22×#217C2211yescharacteristic
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×Dic3⋊C4C2211yescharacteristic, complemented
46C22×Dic3⋊C4C2211yescharacteristic, complemented
47C22×Dic3⋊C4C2211yescharacteristic, complemented
48C22×Dic3⋊C4C2211yescharacteristic, complemented
49C22×C4×Dic3C2211yescharacteristic, complemented
50C22×C4×Dic3C2211yescharacteristic, complemented
51C2×#879—28no—
52C2×#879C2218yescomplemented
53C3×#379C2218yescomplemented
54#5247C2218yescomplemented
55C2×C3⋊#95C2211yescharacteristic, complemented
56C2×C3⋊#95C2211yescharacteristic, complemented
57C2×C3⋊#95C2211yescharacteristic, complemented
58C2×C3⋊#95C2211yescharacteristic, complemented
59#4961C2218yescomplemented
60#4961C2218yescomplemented
61#4959C2218yescomplemented
62#4959C2218yescomplemented
63#4957C2218yescomplemented
64#4957C2218yescomplemented
65#4951C2218yescomplemented
66#4949C2218yescomplemented
67#4948C2218yescomplemented
68#4945C2218yescomplemented
69#4944C2218yescomplemented
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×#388—31no—
84C2×#379—31no—
85C2×#379D311yescharacteristic, complemented
86C25×C3—24no—
87C25×C3—24no—
88C25×C3—24no—
89C25×C3—42no—
90C25×C3—42no—
91C25×C3—42no—
92C25×C3—42no—
93C25×C3C2311yescharacteristic
94C25×C3C2311yescharacteristic
95C25×C3C2311yescharacteristic
96C25×C3C2314yes—
97C24×D3C2311yescharacteristic
98C23×C3×C4C2311yescharacteristic
99C23×C3×C4C2311yescharacteristic
100C23×C3×C4C2311yescharacteristic
101C23×C3×C4C2311yescharacteristic
102C22×#67—24no—
103C22×#67—24no—
104C22×#67—24no—
105C22×#67—24no—
106C22×#67—24no—
107C22×#67—42no—
108C22×#67—42no—
109C22×#67—42no—
110C22×#67—42no—
111C22×#67C2314yes—
112C22×#67C2314yes—
113C22×#67C2314yes—
114C23×Dic3C2311yescharacteristic
115C23×Dic3C2311yescharacteristic
116C23×Dic3C2311yescharacteristic
117C23×Dic3C2311yescharacteristic
118C23×Dic3C2311yescharacteristic
119C23×Dic3C2311yescharacteristic
120C23×Dic3C2311yescharacteristic
121C2×C3×C22⋊C4—24no—
122C2×C3×C22⋊C4—24no—
123C2×C3×C22⋊C4—42no—
124C2×C3×C22⋊C4—42no—
125C2×C3×C22⋊C4—42no—
126C2×C3×C22⋊C4—42no—
127C2×C3×C22⋊C4C2314yes—
128C2×C3×C22⋊C4C2314yes—
129C2×C3×C22⋊C4C2314yes—
130C2×C3×C22⋊C4C2314yes—
131C2×C3×C22⋊C4C2314yes—
132C2×C3×C22⋊C4C2314yes—
133#953—232no—
134C2×#217—24no—
135C2×#217—24no—
136C2×#217—24no—
137C2×#217—24no—
138C2×#217—42no—
139C2×#217—42no—
140C2×#217—42no—
141C2×#217—42no—
142C2×#217D418yes—
143C2×#217C2314yes—
144C2×#217C2314yes—
145C2×#217C2314yes—
146C2×#217C2314yes—
147C2×#217C2314yes—
148C2×#217C2314yes—
149C2×#217C2314yes—
150C2×#217C2314yes—
151C2×#217C2314yes—
152C2×(C2×D3)⋊C4—42no—
153C2×(C2×D3)⋊C4—42no—
154C2×(C2×D3)⋊C4—42no—
155C2×(C2×D3)⋊C4—42no—
156C2×(C2×D3)⋊C4C2314yescomplemented
157C2×(C2×D3)⋊C4C2314yescomplemented
158C2×(C2×D3)⋊C4C2314yescomplemented
159C2×(C2×D3)⋊C4C2314yescomplemented
160C2×C4⋊Dic3—24no—
161C2×C4⋊Dic3—42no—
162C2×C4⋊Dic3C2314yescomplemented
163C2×C4⋊Dic3C2314yescomplemented
164C2×Dic3⋊C4—24no—
165C2×Dic3⋊C4—24no—
166C2×Dic3⋊C4—42no—
167C2×Dic3⋊C4—42no—
168C2×Dic3⋊C4C2314yescomplemented
169C2×Dic3⋊C4C2314yescomplemented
170C2×Dic3⋊C4C2314yescomplemented
171C2×Dic3⋊C4C2314yescomplemented
172C2×C4×Dic3—24no—
173C2×C4×Dic3—42no—
174C2×C4×Dic3C2314yescomplemented
175C2×C4×Dic3C2314yescomplemented
176#879—232no—
177C3⋊#95C2314yescomplemented
178C3⋊#95C2314yescomplemented
179C3⋊#95C2314yescomplemented
180C3⋊#95C2314yescomplemented
181C26C2×D311yescharacteristic
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⋊C4—31no—
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⋊C4C2×D311yescharacteristic
209C22×C22⋊C4C2×D311yescharacteristic
210C22×C22⋊C4C2×D311yescharacteristic
211C22×C22⋊C4C2×D311yescharacteristic
212C22×C22⋊C4C2×D311yescharacteristic
213C22×C22⋊C4C2×D311yescharacteristic
214C22×C42—31no—
215C22×C42—31no—
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#379C2×D318yescomplemented
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×C3—22no—
240C24×C3—22no—
241C24×C3—22no—
242C24×C3—22no—
243C24×C3—22no—
244C24×C3—22no—
245C24×C3—22no—
246C24×C3—22no—
247C24×C3—22no—
248C24×C3—22no—
249C24×C3—22no—
250C24×C3—22no—
251C24×C3—28no—
252C24×C3—28no—
253C24×C3—28no—
254C24×C3—44no—
255C24×C3—44no—
256C24×C3—44no—
257C24×C3—44no—
258C24×C3—416no—
259C24×C3—416no—
260C24×C3—416no—
261C24×C3—416no—
262C24×C3—416no—
263C24×C3—416no—
264C24×C3—416no—
265C24×C3C2×D414yes—
266C24×C3#4114yes—
267C24×C3#4114yes—
268C24×C3C2412yes—
269C24×C3C2412yes—
270C24×C3C2412yes—
271C24×C3C2411yescharacteristic
272C23×D3—22no—
273C23×D3—22no—
274C23×D3—22no—
275C23×D3—22no—
276C23×D3—22no—
277C23×D3—22no—
278C23×D3—22no—
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×C4C2412yes—
293C22×C3×C4C2412yes—
294C22×C3×C4C2412yes—
295C22×C3×C4C2412yes—
296C2×#67—28no—
297C2×#67—28no—
298C2×#67—28no—
299C2×#67—28no—
300C2×#67—28no—
301C2×#67—44no—
302C2×#67—44no—
303C2×#67—44no—
304C2×#67—44no—
305C2×#67—416no—
306C2×#67—416no—
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×Dic3—22no—
324C22×Dic3—22no—
325C22×Dic3—22no—
326C22×Dic3—22no—
327C22×Dic3C2×D414yes—
328C22×Dic3C2×D414yes—
329C22×Dic3C2412yes—
330C22×Dic3C2412yes—
331C22×Dic3C2412yes—
332C22×Dic3C2412yes—
333C22×Dic3C2412yes—
334C22×Dic3C2412yes—
335C22×Dic3C2412yes—
336C3×C22⋊C4—28no—
337C3×C22⋊C4—28no—
338C3×C22⋊C4—44no—
339C3×C22⋊C4—44no—
340C3×C22⋊C4—44no—
341C3×C22⋊C4—44no—
342#217—28no—
343#217—28no—
344#217—28no—
345#217—28no—
346#217—44no—
347#217—44no—
348#217—44no—
349#217—44no—
350#217C2×D4116yes—
351(C2×D3)⋊C4—44no—
352(C2×D3)⋊C4—44no—
353(C2×D3)⋊C4—44no—
354(C2×D3)⋊C4—44no—
355C4⋊Dic3—28no—
356C4⋊Dic3—44no—
357Dic3⋊C4—28no—
358Dic3⋊C4—28no—
359Dic3⋊C4—44no—
360Dic3⋊C4—44no—
361C4×Dic3—28no—
362C4×Dic3—44no—
363C25—24no—
364C25—24no—
365C25—24no—
366C25—31no—
367C25—42no—
368C25—42no—
369C25—42no—
370C25—42no—
371C25C22×D311yescharacteristic
372C25C22×D311yescharacteristic
373C25C22×D311yescharacteristic
374C25C22×D314yes—
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×C4—31no—
393C23×C4—31no—
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—34no—
406C2×C4⋊C4—64no—
407C2×C4⋊C4—64no—
408C2×C4⋊C4—64no—
409C2×C4⋊C4—122no—
410C2×C4⋊C4—122no—
411C2×C4⋊C4—122no—
412C2×C22⋊C4—24no—
413C2×C22⋊C4—24no—
414C2×C22⋊C4—38no—
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—42no—
431C2×C22⋊C4—42no—
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⋊C4C22×D314yes—
445C2×C22⋊C4C22×D314yes—
446C2×C22⋊C4C22×D314yes—
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#95—34no—
458C23×C3—28no—
459C23×C3—28no—
460C23×C3—28no—
461C23×C3—28no—
462C23×C3—28no—
463C23×C3—28no—
464C23×C3—28no—
465C23×C3—28no—
466C23×C3—28no—
467C23×C3—22no—
468C23×C3—22no—
469C23×C3—22no—
470C23×C3—22no—
471C23×C3—22no—
472C23×C3—22no—
473C23×C3—22no—
474C23×C3—22no—
475C23×C3—22no—
476C23×C3—22no—
477C23×C3—22no—
478C23×C3—22no—
479C23×C3—22no—
480C23×C3—22no—
481C23×C3—22no—
482C23×C3—22no—
483C23×C3—22no—
484C23×C3—22no—
485C23×C3—416no—
486C23×C3—416no—
487C23×C3—416no—
488C23×C3—416no—
489C23×C3—416no—
490C23×C3—416no—
491C23×C3—4128no—
492C23×C3—416no—
493C23×C3—44no—
494C23×C3—44no—
495C23×C3—44no—
496C23×C3—44no—
497C23×C3—44no—
498C23×C3—44no—
499C23×C3—44no—
500C23×C3—44no—
501C23×C3—44no—
502C23×C3—44no—
503C23×C3—44no—
504C23×C3—44no—
505C23×C3C22×D414yes—
506C23×C3C22×D412yes—
507C23×C3C2×#4114yes—
508C23×C3C2×#4112yes—
509C23×C3C2×#4114yes—
510C23×C3C2×#4112yes—
511C23×C3H(5,𝔽2)12yes—
512C23×C3H(5,𝔽2)12yes—
513C23×C3H(5,𝔽2)12yes—
514C23×C3H(5,𝔽2)12yes—
515C23×C3C2511yescharacteristic
516C22×D3—22no—
517C22×D3—22no—
518C22×D3—22no—
519C22×D3—22no—
520C22×D3—22no—
521C22×D3—22no—
522C22×D3—22no—
523C22×D3—44no—
524C22×D3—44no—
525C22×D3—44no—
526C22×D3—44no—
527C22×D3—44no—
528C22×D3—44no—
529C22×D3—44no—
530C2×C3×C4—22no—
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—44no—
543C2×C3×C4—44no—
544C2×C3×C4—44no—
545C2×C3×C4—44no—
546#67—416no—
547#67—416no—
548#67—416no—
549C2×Dic3—28no—
550C2×Dic3—28no—
551C2×Dic3—22no—
552C2×Dic3—22no—
553C2×Dic3—22no—
554C2×Dic3—22no—
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—
575C2×Dic3C22×D414yes—
576C2×Dic3C22×D414yes—
577C24—22no—
578C24—22no—
579C24—22no—
580C24—22no—
581C24—22no—
582C24—22no—
583C24—22no—
584C24—22no—
585C24—22no—
586C24—22no—
587C24—22no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—22no—
593C24—22no—
594C24—22no—
595C24—28no—
596C24—28no—
597C24—28no—
598C24—32no—
599C24—44no—
600C24—44no—
601C24—44no—
602C24—44no—
603C24—416no—
604C24—416no—
605C24—416no—
606C24—416no—
607C24—416no—
608C24—416no—
609C24—416no—
610C24—62no—
611C24—62no—
612C24—62no—
613C24—62no—
614C24—62no—
615C24—62no—
616C24—62no—
617C24#23514yes—
618C24D3×D414yes—
619C24#23714yes—
620C24C23×D312yes—
621C24C23×D312yes—
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—124no—
633C2×D4—1216no—
634C2×D4—1216no—
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—34no—
649C22×C4—34no—
650C22×C4—32no—
651C22×C4—32no—
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×C4—62no—
673C22×C4—62no—
674C22×C4—62no—
675C22×C4—62no—
676C22×C4C23×D312yes—
677C22×C4C23×D312yes—
678C22×C4C23×D312yes—
679C22×C4C23×D312yes—
680C4⋊C4—68no—
681C4⋊C4—68no—
682C4⋊C4—68no—
683C4⋊C4—124no—
684C4⋊C4—124no—
685C4⋊C4—124no—
686C22⋊C4—28no—
687C22⋊C4—28no—
688C22⋊C4—316no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—44no—
692C22⋊C4—44no—
693C22⋊C4—68no—
694C22⋊C4—68no—
695C22⋊C4—68no—
696C22⋊C4—68no—
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—24no—
711C22×C3—24no—
712C22×C3—24no—
713C22×C3—24no—
714C22×C3—24no—
715C22×C3—24no—
716C22×C3—464no—
717C22×C3—42no—
718C22×C3—42no—
719C22×C3—42no—
720C22×C3—42no—
721C22×C3—42no—
722C22×C3—42no—
723C22×C3—416no—
724C22×C3—416no—
725C22×C3—416no—
726C22×C3—42no—
727C22×C3—42no—
728C22×C3—42no—
729C22×C3—42no—
730C22×C3—42no—
731C22×C3—42no—
732C22×C3#53514yes—
733C22×C3#53814yes—
734C22×C3#53814yes—
735C22×C3#54614yes—
736C22×C3#54614yes—
737C22×C3#55114yes—
738C22×C3#56014yes—
739C22×C3C23×D411yescharacteristic
740C22×C3C22×#4111yescharacteristic
741C22×C3C22×#4111yescharacteristic
742C22×C3C2×H(5,𝔽2)11yescharacteristic
743C22×C3C2×H(5,𝔽2)11yescharacteristic
744C22×C3C2×H(5,𝔽2)11yescharacteristic
745C22×C3C2×H(5,𝔽2)11yescharacteristic
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—42no—
755C3×C4—42no—
756C3×C4—42no—
757C3×C4—42no—
758Dic3—24no—
759Dic3—24no—
760Dic3—42no—
761Dic3—42no—
762Dic3—42no—
763Dic3—42no—
764Dic3—42no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—28no—
784C23—28no—
785C23—28no—
786C23—28no—
787C23—28no—
788C23—28no—
789C23—28no—
790C23—28no—
791C23—28no—
792C23—416no—
793C23—416no—
794C23—416no—
795C23—416no—
796C23—416no—
797C23—416no—
798C23—4128no—
799C23—416no—
800C23—44no—
801C23—44no—
802C23—44no—
803C23—44no—
804C23—44no—
805C23—44no—
806C23—44no—
807C23—44no—
808C23—44no—
809C23—44no—
810C23—44no—
811C23—44no—
812C23—62no—
813C23—62no—
814C23—62no—
815C23—62no—
816C23—62no—
817C23—62no—
818C23—62no—
819C23—124no—
820C23—124no—
821C23—124no—
822C23—124no—
823C23—124no—
824C23—124no—
825C23—124no—
826C23C2×#23514yes—
827C23C2×#23512yes—
828C23C2×D3×D414yes—
829C23C2×D3×D412yes—
830C23C2×#23714yes—
831C23C2×#23712yes—
832C23#100412yes—
833C23#100412yes—
834C23#100412yes—
835C23#100412yes—
836C23C24×D311yescharacteristic
837D4—1216no—
838D4—1216no—
839D4—1216no—
840C2×C4—22no—
841C2×C4—22no—
842C2×C4—22no—
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—34no—
853C2×C4—34no—
854C2×C4—44no—
855C2×C4—44no—
856C2×C4—44no—
857C2×C4—44no—
858C2×C4—62no—
859C2×C4—62no—
860C2×C4—62no—
861C2×C4—62no—
862C2×C4—68no—
863C2×C4—68no—
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—62no—
878C2×C4—62no—
879C2×C4—124no—
880C2×C4—124no—
881C2×C4—124no—
882C2×C4—124no—
883C2×C4—124no—
884C2×C3—44no—
885C2×C3—44no—
886C2×C3—44no—
887C2×C3#268518yescomplemented
888C2×C3C2×#53511yescharacteristic
889C2×C3C2×#53811yescharacteristic
890C2×C3C2×#53811yescharacteristic
891C2×C3C2×#54611yescharacteristic
892C2×C3C2×#54611yescharacteristic
893C2×C3C2×#55111yescharacteristic
894C2×C3C2×#56011yescharacteristic
895D3—82no—
896C22—24no—
897C22—24no—
898C22—24no—
899C22—24no—
900C22—24no—
901C22—24no—
902C22—24no—
903C22—24no—
904C22—24no—
905C22—464no—
906C22—416no—
907C22—416no—
908C22—416no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—122no—
922C22—122no—
923C22—122no—
924C22—122no—
925C22—122no—
926C22—122no—
927C22—122no—
928C22—248no—
929C22#549014yes—
930C22#549414yes—
931C22#549514yes—
932C22#559114yes—
933C22#559214yes—
934C22#559314yes—
935C22#559514yes—
936C22C22×#23511yescharacteristic
937C22C22×D3×D411yescharacteristic
938C22C22×#23711yescharacteristic
939C22C2×#100411yescharacteristic
940C22C2×#100411yescharacteristic
941C22C2×#100411yescharacteristic
942C22C2×#100411yescharacteristic
943C4—42no—
944C4—42no—
945C4—42no—
946C4—42no—
947C4—64no—
948C4—64no—
949C4—122no—
950C4—122no—
951C4—122no—
952C4—122no—
953C4—122no—
954C3C2×#268511yescharacteristic, complemented, Sylow
955C2—44no—
956C2—44no—
957C2—44no—
958C2—242no—
959C2#7383818yesdirect product factor
960C2C2×#549511yescharacteristic
961C2C2×#549411yescharacteristic
962C2C2×#549011yescharacteristic
963C2C2×#559211yescharacteristic
964C2C2×#559311yescharacteristic
965C2C2×#559111yescharacteristic
966C2C2×#559511yescharacteristic
subgroupG/H
centerC24C23×D3
commutator, cosocleC23×C3C25
FrattiniC23C24×D3
FittingC2×C3×#379C2
socleC24×C3C24
prime radicalC22×#953C2
hypercenterC2×#379D3
hypocenterC3C2×#2685
LCSG ▷ C23×C3 ▷ C3
UCSC1 ◁ C24 ◁ C2×#379

Complements

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

NH ≅ G/Ntype
2. C22×#879C2semidirect
3. C2×C3×#379C2semidirect
4. C2×#5247C2semidirect
5. C2×#4959C2semidirect
6. C2×#4959C2semidirect
7. C2×#4949C2semidirect
8. C2×#4948C2semidirect
9. C2×#4961C2semidirect
10. C2×#4961C2semidirect
11. C2×#4957C2semidirect
12. C2×#4957C2semidirect
13. C2×#4945C2semidirect
14. C2×#4944C2semidirect
15. C2×#4951C2semidirect
16. #73838C2direct (N × H)
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×Dic3⋊C4C22semidirect
46. C22×Dic3⋊C4C22semidirect
47. C22×Dic3⋊C4C22semidirect
48. C22×Dic3⋊C4C22semidirect
49. C22×C4×Dic3C22semidirect
50. C22×C4×Dic3C22semidirect
52. C2×#879C22semidirect
53. C3×#379C22semidirect
54. #5247C22semidirect
55. C2×C3⋊#95C22semidirect
56. C2×C3⋊#95C22semidirect
57. C2×C3⋊#95C22semidirect
58. C2×C3⋊#95C22semidirect
59. #4961C22semidirect
60. #4961C22semidirect
61. #4959C22semidirect
62. #4959C22semidirect
63. #4957C22semidirect
64. #4957C22semidirect
65. #4951C22semidirect
66. #4949C22semidirect
67. #4948C22semidirect
68. #4945C22semidirect
69. #4944C22semidirect
85. C2×#379D3semidirect
156. C2×(C2×D3)⋊C4C23semidirect
157. C2×(C2×D3)⋊C4C23semidirect
158. C2×(C2×D3)⋊C4C23semidirect
159. C2×(C2×D3)⋊C4C23semidirect
162. C2×C4⋊Dic3C23semidirect
163. C2×C4⋊Dic3C23semidirect
168. C2×Dic3⋊C4C23semidirect
169. C2×Dic3⋊C4C23semidirect
170. C2×Dic3⋊C4C23semidirect
171. C2×Dic3⋊C4C23semidirect
174. C2×C4×Dic3C23semidirect
175. C2×C4×Dic3C23semidirect
177. C3⋊#95C23semidirect
178. C3⋊#95C23semidirect
179. C3⋊#95C23semidirect
180. C3⋊#95C23semidirect
228. #379C2×D3semidirect
887. C2×C3#2685semidirect
954. C3C2×#2685semidirect
959. C2#73838direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#9532
C22×#8792
C2×C3×#3792
C2×#52472
C2×#49592
C2×#49492
C2×#49482
C2×#49612
C2×#49572
C2×#49452
C2×#49442
C2×#49512
#738382
C2×#26853