Finite Group Databasebeta

← #14926167

Subgroups — #14926167

Order 2816.

2630 conjugacy classes of subgroups.

The subgroup lattice has 1048 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×#4341C211yesmaximal, characteristic
2C22×C4×Dic22C211yesmaximal, characteristic, complemented
3#13074192C212yesmaximal, complemented
4#13074190C212yesmaximal, complemented
5#13073981C212yesmaximal, complemented
6#13073524C212yesmaximal, complemented
7#13072923C211yesmaximal, characteristic, complemented
8#13072921C211yesmaximal, characteristic, complemented
9#13072902C211yesmaximal, characteristic, complemented
10#13072900C211yesmaximal, characteristic, complemented
11#13071980C211yesmaximal, characteristic, complemented
12#13071978C211yesmaximal, characteristic, complemented
13#13071950C211yesmaximal, characteristic
14#13071948C211yesmaximal, characteristic
15#13071910C212yesmaximal, complemented
16#13071903C212yesmaximal, complemented
17C4×#66949C212yesmaximal, complemented
18C4×#66931C212yesmaximal, complemented
19C4×#66939C211yesmaximal, characteristic, complemented
20C4×#66982C211yesmaximal, characteristic, complemented
21C4×#66988C211yesmaximal, characteristic, complemented
22#13071010C211yesmaximal, characteristic, complemented
23C4×C11×#123C211yesmaximal, characteristic, complemented
24C22×#4341C2211yescharacteristic
25C23×Dic22C2211yescharacteristic
26C2×C11×#123C2211yescharacteristic
27C2×C4×D4×C11C2211yescharacteristic
28C22×C42×C11C2211yescharacteristic
29C2×#66988C2211yescharacteristic
30C2×D4×Dic11C2211yescharacteristic
31C2×#66982C2211yescharacteristic
32C2×C4×C22⋊D11C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C22×C4⋊Dic11C2211yescharacteristic
35C22×Dic11⋊C4C2211yescharacteristic
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39C22×C4×Dic11C2211yescharacteristic
40C4×#4341—28no—
41C2×#66949C2212yes—
42C2×#66945C2211yescharacteristic
43C2×#66940C2211yescharacteristic
44C2×#66939C2211yescharacteristic
45C2×(C22⋊D11)⋊C4C2211yescharacteristic
46C2×(C22⋊D11)⋊C4C2211yescharacteristic
47C2×#66931C2212yes—
48C2×#66930C2211yescharacteristic
49C2×#66930C2211yescharacteristic
50C2×C42×D11C2211yescharacteristic
51C2×C4×Dic22—28no—
52C2×C4×Dic22C2212yes—
53C2×C4×Dic22C2212yes—
54C2×C4×Dic22C2211yescharacteristic
55C2×C4×Dic22C2212yes—
56C2×C4×Dic22C2212yes—
57C11×#388C2212yes—
58C11×#387C2212yes—
59C11×#386C2211yescharacteristic
60C11×#385C2211yescharacteristic
61C11×#381C2211yescharacteristic
62C4×C11×C4⋊C4C2212yes—
63C4×C11×C22⋊C4C2212yes—
64C4×C11×C22⋊C4C2211yescharacteristic
65#10622833C2211yescharacteristic
66#10622826C2211yescharacteristic
67#10622824C2211yescharacteristic
68#10622823C2211yescharacteristic
69C4×C22⋊Dic11C2212yes—
70C4×C22⋊Dic11C2211yescharacteristic
71#10622602C2212yes—
72#10622597C2212yes—
73#10622597C2212yes—
74#10622594C2212yes—
75#10622592C2212yes—
76#10622592C2212yes—
77#10622591C2212yes—
78#10622585C2212yes—
79#10622574C2212yes—
80#10622572C2212yes—
81#10622571C2211yescharacteristic
82#10622565C2212yes—
83#10622563C2211yescharacteristic
84#10622563C2212yes—
85#10622560C2212yes—
86#10622559C2211yescharacteristic
87#10622559C2212yes—
88#10622557C2212yes—
89#10622556C2211yescharacteristic
90#10622556C2211yescharacteristic
91#10622556C2211yescharacteristic
92#10622556C2211yescharacteristic
93#10622555C2212yes—
94#10622555C2211yescharacteristic
95#10622555C2211yescharacteristic
96#10622553C2212yes—
97C4×(C2×D11)⋊C4C2212yes—
98C4×(C2×D11)⋊C4C2212yes—
99C4×C4⋊Dic11C2212yes—
100#10622546C2212yes—
101#10622545C2212yes—
102C4×Dic11⋊C4C2212yes—
103C4×Dic11⋊C4C2212yes—
104C4×Dic11⋊C4C2212yes—
105#10622288C2212yes—
106#10622286C2212yes—
107#10622283C2212yes—
108#10622281C2212yes—
109#10622280C2212yes—
110#10622273C2212yes—
111#10622271C2212yes—
112#10622270C2212yes—
113#10622270C2212yes—
114#10622269C2212yes—
115#10622269C2212yes—
116#10622268C2212yes—
117#10622267C2212yes—
118#10622266C2212yes—
119#10622265C2212yes—
120#10622264C2212yes—
121#10622263C2212yes—
122#10622260C2212yes—
123#10622259C2212yes—
124#10622259C2212yes—
125C22×D4×C11C2311yescharacteristic
126C23×C4×C11C2311yescharacteristic
127C23×C4×C11C2311yescharacteristic
128C23×C4×C11C2311yescharacteristic
129C23×C4×C11C2311yescharacteristic
130C22×C22⋊D11C2311yescharacteristic
131C22×C22⋊D11C2311yescharacteristic
132C23×Dic11C2311yescharacteristic
133C23×Dic11C2311yescharacteristic
134C23×Dic11C2311yescharacteristic
135C23×Dic11C2311yescharacteristic
136C23×Dic11C2311yescharacteristic
137C23×Dic11C2311yescharacteristic
138C2×#4341—24no—
139C2×#4341—24no—
140C2×#4341—24no—
141C22×C4×D11C2311yescharacteristic
142C22×C4×D11C2311yescharacteristic
143C22×C4×D11C2311yescharacteristic
144C22×Dic22—24no—
145C22×Dic22—28no—
146C22×Dic22C2312yes—
147C22×Dic22C2311yescharacteristic
148C22×Dic22C2312yes—
149C11×#123—24no—
150C4×D4×C11—24no—
151C2×C11×C4⋊C4C2311yescharacteristic
152C2×C11×C4⋊C4C2312yes—
153C2×C11×C4⋊C4C2312yes—
154C2×C11×C22⋊C4C2311yescharacteristic
155C2×C11×C22⋊C4C2311yescharacteristic
156C2×C11×C22⋊C4C2312yes—
157C2×C11×C22⋊C4C2311yescharacteristic
158C2×C11×C22⋊C4C2311yescharacteristic
159C2×C11×C22⋊C4C2312yes—
160C2×C42×C11—24no—
161C2×C42×C11C2312yes—
162C2×C42×C11C2312yes—
163C2×C42×C11C2311yescharacteristic
164C2×C42×C11C2312yes—
165C2×C22⋊Dic11C2311yescharacteristic
166C2×C22⋊Dic11C2311yescharacteristic
167C2×C22⋊Dic11C2312yes—
168C2×C22⋊Dic11C2311yescharacteristic
169C2×C22⋊Dic11C2311yescharacteristic
170C2×C22⋊Dic11C2312yes—
171#66988—24no—
172D4×Dic11—24no—
173#66982—24no—
174C4×C22⋊D11—24no—
175C4×C22⋊D11—24no—
176C2×(C2×D11)⋊C4C2311yescharacteristic
177C2×(C2×D11)⋊C4C2311yescharacteristic
178C2×(C2×D11)⋊C4C2312yes—
179C2×(C2×D11)⋊C4C2312yes—
180C2×(C2×D11)⋊C4C2312yes—
181C2×(C2×D11)⋊C4C2312yes—
182C2×C4⋊Dic11—24no—
183C2×C4⋊Dic11C2312yes—
184C2×C4⋊Dic11C2312yes—
185C2×C4⋊Dic11C2311yescharacteristic
186C2×C4⋊Dic11C2312yes—
187C2×C4⋊Dic11C2312yes—
188C2×Dic11⋊C4—24no—
189C2×Dic11⋊C4—24no—
190C2×Dic11⋊C4C2312yes—
191C2×Dic11⋊C4C2312yes—
192C2×Dic11⋊C4C2312yes—
193C2×Dic11⋊C4C2312yes—
194C2×Dic11⋊C4C2311yescharacteristic
195C2×Dic11⋊C4C2311yescharacteristic
196C2×Dic11⋊C4C2311yescharacteristic
197C2×Dic11⋊C4C2311yescharacteristic
198C2×Dic11⋊C4C2312yes—
199C2×Dic11⋊C4C2312yes—
200C2×Dic11⋊C4C2312yes—
201C2×Dic11⋊C4C2312yes—
202C2×Dic11⋊C4C2312yes—
203C2×Dic11⋊C4C2312yes—
204C2×C4×Dic11—24no—
205C2×C4×Dic11—24no—
206C2×C4×Dic11D418yes—
207C2×C4×Dic11C2312yes—
208C2×C4×Dic11C2312yes—
209C2×C4×Dic11C2311yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211C2×C4×Dic11C2311yescharacteristic
212C2×C4×Dic11C2311yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2312yes—
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219#66949—28no—
220#66945—24no—
221#66940—24no—
222#66939—24no—
223(C22⋊D11)⋊C4—24no—
224(C22⋊D11)⋊C4—24no—
225#66931—28no—
226#66930—24no—
227#66930—24no—
228C42×D11—24no—
229C4×Dic22—28no—
230C4×Dic22—28no—
231C4×Dic22—28no—
232C4×Dic22—28no—
233C4×Dic22—24no—
234C11×#95C2312yes—
235C11×#95C2312yes—
236C11×#95C2312yes—
237C11×#95C2312yes—
238C11×#95C2312yes—
239C11⋊#95C2312yes—
240C11⋊#95C2312yes—
241C11⋊#95C2312yes—
242C11⋊#95C2312yes—
243C11⋊#95C2312yes—
244C11⋊#95C2312yes—
245C11⋊#95C2312yes—
246C11⋊#95C2312yes—
247C11⋊#95C2312yes—
248C11⋊#95C2312yes—
249C11⋊#95C2312yes—
250C11⋊#95C2312yes—
251C11⋊#95C2312yes—
252C11⋊#95C2312yes—
253C11⋊#95C2312yes—
254C11⋊#95C2312yes—
255C11⋊#95C2312yes—
256C11⋊#95C2312yes—
257C11⋊#95C2312yes—
258#34971—111nomaximal, Sylow
259C24×C11C2411yescharacteristic
260C24×C11C2411yescharacteristic
261C23×D11C2411yescharacteristic
262C2×D4×C11—22no—
263C2×D4×C11—22no—
264C2×D4×C11#4114yes—
265C22×C4×C11—22no—
266C22×C4×C11—24no—
267C22×C4×C11—24no—
268C22×C4×C11—22no—
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—22no—
272C22×C4×C11—24no—
273C22×C4×C11C2×D414yes—
274C22×C4×C11C2412yes—
275C22×C4×C11C2411yescharacteristic
276C22×C4×C11C2412yes—
277C22×C4×C11C2411yescharacteristic
278C22×C4×C11C2412yes—
279C22×C4×C11C2411yescharacteristic
280C22×C4×C11C2411yescharacteristic
281C22×C4×C11C2412yes—
282C22×C4×C11C2411yescharacteristic
283C2×C22⋊D11—22no—
284C2×C22⋊D11—22no—
285C2×C22⋊D11—22no—
286C2×C22⋊D11—22no—
287C2×C22⋊D11—22no—
288C2×C22⋊D11#4114yes—
289C22×Dic11—22no—
290C22×Dic11—24no—
291C22×Dic11—24no—
292C22×Dic11—22no—
293C22×Dic11—22no—
294C22×Dic11—24no—
295C22×Dic11—22no—
296C22×Dic11—22no—
297C22×Dic11—22no—
298C22×Dic11—22no—
299C22×Dic11—22no—
300C22×Dic11—22no—
301C22×Dic11—22no—
302C22×Dic11C2×D414yes—
303C22×Dic11C2×D414yes—
304C22×Dic11C2411yescharacteristic
305C22×Dic11C2412yes—
306C22×Dic11C2412yes—
307C22×Dic11C2412yes—
308C22×Dic11C2411yescharacteristic
309C22×Dic11C2411yescharacteristic
310C22×Dic11C2411yescharacteristic
311C22×Dic11C2411yescharacteristic
312C22×Dic11C2411yescharacteristic
313C22×Dic11C2412yes—
314C22×Dic11C2411yescharacteristic
315#4341—232no—
316C2×C4×D11—22no—
317C2×C4×D11—22no—
318C2×C4×D11—24no—
319C2×C4×D11—22no—
320C2×C4×D11—22no—
321C2×C4×D11—22no—
322C2×C4×D11—24no—
323C2×Dic22—232no—
324C2×Dic22—24no—
325C2×Dic22—24no—
326C2×Dic22—22no—
327C2×Dic22—24no—
328C2×Dic22—24no—
329C2×Dic22—22no—
330C2×Dic22—24no—
331C2×Dic22—22no—
332C2×Dic22#4118yescomplemented
333C11×C4⋊C4—22no—
334C11×C4⋊C4—24no—
335C11×C4⋊C4—24no—
336C11×C22⋊C4—22no—
337C11×C22⋊C4—22no—
338C11×C22⋊C4—22no—
339C11×C22⋊C4—24no—
340C11×C22⋊C4—22no—
341C11×C22⋊C4—24no—
342C42×C11—24no—
343C42×C11—24no—
344C42×C11—22no—
345C42×C11—24no—
346C22⋊Dic11—22no—
347C22⋊Dic11—24no—
348C22⋊Dic11—22no—
349C22⋊Dic11—22no—
350C22⋊Dic11—24no—
351C22⋊Dic11—22no—
352(C2×D11)⋊C4—22no—
353(C2×D11)⋊C4—24no—
354(C2×D11)⋊C4—24no—
355(C2×D11)⋊C4—24no—
356(C2×D11)⋊C4—22no—
357(C2×D11)⋊C4—24no—
358C4⋊Dic11—24no—
359C4⋊Dic11—24no—
360C4⋊Dic11—22no—
361C4⋊Dic11—24no—
362C4⋊Dic11—24no—
363Dic11⋊C4—24no—
364Dic11⋊C4—24no—
365Dic11⋊C4—24no—
366Dic11⋊C4—24no—
367Dic11⋊C4—22no—
368Dic11⋊C4—22no—
369Dic11⋊C4—22no—
370Dic11⋊C4—24no—
371Dic11⋊C4—24no—
372Dic11⋊C4—24no—
373Dic11⋊C4—24no—
374Dic11⋊C4—22no—
375Dic11⋊C4—24no—
376Dic11⋊C4—24no—
377C4×Dic11—22no—
378C4×Dic11—22no—
379C4×Dic11—22no—
380C4×Dic11—22no—
381C4×Dic11—24no—
382C4×Dic11—24no—
383C4×Dic11—22no—
384C4×Dic11—24no—
385C4×Dic11C2×D414yes—
386C4×Dic11C2×D414yes—
387C4×Dic11C2×D414yes—
388C4×Dic11C2×D414yes—
389C2×C4×#41—111no—
390C22×C4×Q8—111no—
391#2599—112no—
392#2599—112no—
393#2581—112no—
394#2536—112no—
395#2486—111no—
396#2486—111no—
397#2484—111no—
398#2484—111no—
399#2409—111no—
400#2409—111no—
401#2406—111no—
402#2406—111no—
403#2399—112no—
404#2398—112no—
405C4×C22⋊Q8—112no—
406C4×C22⋊Q8—112no—
407C4×#123—111no—
408C4×#123—111no—
409C4×#123—111no—
410C4×#123D1111yescharacteristic, complemented
411#2283—111no—
412C23×C11—22no—
413C23×C11—22no—
414C23×C11—21no—
415C23×C11—22no—
416C23×C11—21no—
417C23×C11—22no—
418C23×C11C22×D412yes—
419C23×C11C2×#4112yes—
420C23×C11C2×#4112yes—
421C23×C11C2×#4112yes—
422C23×C11C2511yescharacteristic
423C22×D11—21no—
424C22×D11—22no—
425C22×D11—21no—
426C22×D11—22no—
427C22×D11C2×#4112yes—
428D4×C11—28no—
429C2×C4×C11—28no—
430C2×C4×C11—21no—
431C2×C4×C11—22no—
432C2×C4×C11—22no—
433C2×C4×C11—21no—
434C2×C4×C11—22no—
435C2×C4×C11—28no—
436C2×C4×C11—21no—
437C2×C4×C11—21no—
438C2×C4×C11—22no—
439C2×C4×C11—22no—
440C2×C4×C11—22no—
441C2×C4×C11—22no—
442C2×C4×C11—22no—
443C2×C4×C11—22no—
444C2×C4×C11—22no—
445C2×C4×C11—22no—
446C2×C4×C11—22no—
447C2×C4×C11—22no—
448C2×C4×C11—22no—
449C2×C4×C11—44no—
450C2×C4×C11—44no—
451C2×C4×C11C22×D412yes—
452C2×C4×C11C22×D412yes—
453C2×C4×C11C2×#4112yes—
454C2×C4×C11C2×#4114yes—
455C2×C4×C112−1+414yes—
456C22⋊D11—28no—
457C22⋊D11—28no—
458C2×Dic11—28no—
459C2×Dic11—28no—
460C2×Dic11—28no—
461C2×Dic11—22no—
462C2×Dic11—21no—
463C2×Dic11—22no—
464C2×Dic11—22no—
465C2×Dic11—21no—
466C2×Dic11—21no—
467C2×Dic11—21no—
468C2×Dic11—21no—
469C2×Dic11—21no—
470C2×Dic11—28no—
471C2×Dic11—22no—
472C2×Dic11—21no—
473C2×Dic11—21no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—22no—
481C2×Dic11—22no—
482C2×Dic11—22no—
483C2×Dic11—22no—
484C2×Dic11—44no—
485C2×Dic11—44no—
486C2×Dic11C22×D412yes—
487C2×Dic11C22×D412yes—
488C2×Dic11C22×D412yes—
489C2×Dic11C22×D412yes—
490C2×Dic11C2×#4112yes—
491C2×Dic11C2×#4114yes—
492C2×Dic11C2×#4114yes—
493C4×D11—28no—
494C4×D11—44no—
495C4×D11—44no—
496Dic22—216no—
497Dic22—28no—
498Dic22—216no—
499C22×#41—111no—
500C23×Q8—111no—
501C2×#123—111no—
502C2×#123—111no—
503C2×#123—111no—
504C2×#123C2×D1111yescharacteristic
505C2×C22⋊Q8—112no—
506C2×C22⋊Q8—112no—
507C4×#41—228no—
508C2×C4×Q8—111no—
509C2×C4×Q8—112no—
510C2×C4×Q8—112no—
511C2×C4×Q8—112no—
512C2×C4×Q8—111no—
513C2×C4×Q8—112no—
514C2×C4×Q8—228no—
515C2×C4×D4—111no—
516C2×C4×D4—111no—
517C2×C4×D4—111no—
518C2×C4×D4—111no—
519C2×C4×D4—111no—
520C2×C4×D4C2×D1111yescharacteristic
521C2×#117—111no—
522C2×#117—111no—
523C2×#117—111no—
524C22×C4⋊C4—111no—
525C22×C4⋊C4—111no—
526C22×C4⋊C4—111no—
527C22×C42—111no—
528C22×C42—111no—
529C22×C42—111no—
530C22×C42—111no—
531C22×C42C2×D1111yescharacteristic
532#400—112no—
533#400—112no—
534#398—112no—
535#398—112no—
536#398—112no—
537#398—112no—
538#397—112no—
539#397—112no—
540#395—112no—
541#395—112no—
542#395—112no—
543#395—112no—
544#394—112no—
545#394—112no—
546#393—112no—
547#393—112no—
548#391—112no—
549#391—112no—
550#389—112no—
551#389—112no—
552#388—112no—
553#388—112no—
554#388—112no—
555#388C2×D1112yes—
556#387—112no—
557#387—112no—
558#387—112no—
559#387—112no—
560#387—112no—
561#387—112no—
562#387—112no—
563#387C2×D1112yes—
564#386—111no—
565#386—111no—
566#386—111no—
567#386C2×D1111yescharacteristic
568#385—111no—
569#385—112no—
570#385—112no—
571#385—112no—
572#385—111no—
573#385—111no—
574#385—112no—
575#385C2×D1111yescharacteristic
576#383—112no—
577#382—112no—
578#381—111no—
579#381—111no—
580#381—111no—
581#381—111no—
582#381—111no—
583#381C2×D1111yescharacteristic
584#380—111no—
585#380—111no—
586#380—112no—
587#380—112no—
588C4×C4⋊C4—112no—
589C4×C4⋊C4—112no—
590C4×C4⋊C4—112no—
591C4×C4⋊C4—112no—
592C4×C4⋊C4C2×D1112yes—
593C4×C22⋊C4—112no—
594C4×C22⋊C4—111no—
595C4×C22⋊C4—112no—
596C4×C22⋊C4—112no—
597C4×C22⋊C4C2×D1112yes—
598C4×C22⋊C4C2×D1111yescharacteristic
599#376—112no—
600C22×C11—22no—
601C22×C11—22no—
602C22×C11—24no—
603C22×C11—24no—
604C22×C11—22no—
605C22×C11—24no—
606C22×C11—41no—
607C22×C11—41no—
608C22×C11—42no—
609C22×C11#52514yes—
610C22×C11C23×D411yescharacteristic
611C22×C11C22×#4111yescharacteristic
612C22×C11C22×#4111yescharacteristic
613C22×C11C22×#4112yes—
614C22×C11C2×2−1+412yes—
615C2×D11—22no—
616C2×D11—24no—
617C2×D11—41no—
618C2×D11—41no—
619C2×D11—42no—
620C4×C11—24no—
621C4×C11—22no—
622C4×C11—22no—
623C4×C11—42no—
624C4×C11—41no—
625C4×C11—41no—
626C4×C11—42no—
627C4×C11—42no—
628C4×C11#53614yes—
629Dic11—22no—
630Dic11—24no—
631Dic11—22no—
632Dic11—22no—
633Dic11—22no—
634Dic11—42no—
635Dic11—41no—
636Dic11—41no—
637Dic11—42no—
638Dic11—42no—
639Dic11#52514yes—
640C2×#41—224no—
641C2×#41—224no—
642C2×#41—224no—
643C22×Q8—112no—
644C22×Q8—112no—
645C22×Q8—111no—
646C22×Q8—224no—
647C22×Q8—228no—
648C22×D4—111no—
649C22×D4—111no—
650C22×D4C22×D1111yescharacteristic
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—111no—
654C23×C4—111no—
655C23×C4—111no—
656C23×C4—111no—
657C23×C4—111no—
658C23×C4—111no—
659C23×C4—111no—
660C23×C4C22×D1111yescharacteristic
661C23×C4C22×D1111yescharacteristic
662C23×C4C22×D1111yescharacteristic
663C23×C4C22×D1111yescharacteristic
664#123—24no—
665#123—224no—
666#123—224no—
667#123—224no—
668C22⋊Q8—228no—
669C22⋊Q8—228no—
670C4×Q8—228no—
671C4×Q8—228no—
672C4×Q8—228no—
673C4×Q8—228no—
674C4×Q8—224no—
675C4×Q8—224no—
676C4×D4—24no—
677C4×D4—224no—
678C4×D4—224no—
679C4×D4—224no—
680C4×D4—224no—
681C4×D4—224no—
682#117—224no—
683#117—224no—
684#117—224no—
685C2×C4⋊C4—112no—
686C2×C4⋊C4—112no—
687C2×C4⋊C4—112no—
688C2×C4⋊C4—112no—
689C2×C4⋊C4—112no—
690C2×C4⋊C4—112no—
691C2×C4⋊C4—111no—
692C2×C4⋊C4—111no—
693C2×C4⋊C4—111no—
694C2×C4⋊C4—111no—
695C2×C4⋊C4—111no—
696C2×C4⋊C4—112no—
697C2×C4⋊C4—112no—
698C2×C4⋊C4—112no—
699C2×C4⋊C4—112no—
700C2×C4⋊C4—112no—
701C2×C4⋊C4—112no—
702C2×C4⋊C4—112no—
703C2×C4⋊C4—112no—
704C2×C4⋊C4—224no—
705C2×C4⋊C4—224no—
706C2×C4⋊C4—224no—
707C2×C4⋊C4C22×D1111yescharacteristic
708C2×C4⋊C4C22×D1112yes—
709C2×C4⋊C4C22×D1112yes—
710C2×C22⋊C4—111no—
711C2×C22⋊C4—111no—
712C2×C22⋊C4—112no—
713C2×C22⋊C4—111no—
714C2×C22⋊C4—111no—
715C2×C22⋊C4—112no—
716C2×C22⋊C4—111no—
717C2×C22⋊C4—111no—
718C2×C22⋊C4—112no—
719C2×C22⋊C4—112no—
720C2×C22⋊C4—112no—
721C2×C22⋊C4—112no—
722C2×C22⋊C4C22×D1111yescharacteristic
723C2×C22⋊C4C22×D1111yescharacteristic
724C2×C22⋊C4C22×D1112yes—
725C2×C22⋊C4C22×D1111yescharacteristic
726C2×C22⋊C4C22×D1111yescharacteristic
727C2×C22⋊C4C22×D1112yes—
728C2×C42—24no—
729C2×C42—118no—
730C2×C42—111no—
731C2×C42—111no—
732C2×C42—111no—
733C2×C42—111no—
734C2×C42—111no—
735C2×C42—111no—
736C2×C42—111no—
737C2×C42—111no—
738C2×C42—112no—
739C2×C42—111no—
740C2×C42—112no—
741C2×C42—112no—
742C2×C42—224no—
743C2×C42—224no—
744C2×C42—224no—
745C2×C42C22×D1112yes—
746C2×C42C22×D1111yescharacteristic
747C2×C42C22×D1112yes—
748C2×C42C22×D1112yes—
749#95—112no—
750#95—112no—
751#95—112no—
752#95—112no—
753#95—112no—
754#95—112no—
755#95—112no—
756#95—112no—
757#95—112no—
758#95—112no—
759#95—112no—
760#95—112no—
761#95—112no—
762#95—112no—
763#95—112no—
764#95—112no—
765#95—112no—
766#95—112no—
767#95—112no—
768#95C22×D1112yes—
769#95C22×D1112yes—
770#95C22×D1112yes—
771#95C22×D1112yes—
772#95C22×D1112yes—
773C2×C11—24no—
774C2×C11—42no—
775C2×C11C2×#52511yescharacteristic
776C2×C11C2×#52511yescharacteristic
777C2×C11C2×#53611yescharacteristic
778C2×C11#348212yes—
779C2×C11#348212yes—
780D11—42no—
781C24—111no—
782C24C23×D1111yescharacteristic
783C24C23×D1111yescharacteristic
784#41—2232no—
785C2×Q8—118no—
786C2×Q8—224no—
787C2×Q8—224no—
788C2×Q8—222no—
789C2×Q8—224no—
790C2×Q8—224no—
791C2×Q8—222no—
792C2×Q8—2232no—
793C2×Q8—222no—
794C2×Q8—224no—
795C2×D4—22no—
796C2×D4—22no—
797C2×D4—114no—
798C2×D4—222no—
799C2×D4—222no—
800C2×D4—222no—
801C2×D4—222no—
802C2×D4—222no—
803C2×D4#433914yes—
804C22×C4—22no—
805C22×C4—24no—
806C22×C4—24no—
807C22×C4—22no—
808C22×C4—22no—
809C22×C4—22no—
810C22×C4—22no—
811C22×C4—24no—
812C22×C4—111no—
813C22×C4—114no—
814C22×C4—114no—
815C22×C4—111no—
816C22×C4—111no—
817C22×C4—112no—
818C22×C4—111no—
819C22×C4—111no—
820C22×C4—111no—
821C22×C4—112no—
822C22×C4—112no—
823C22×C4—112no—
824C22×C4—111no—
825C22×C4—222no—
826C22×C4—222no—
827C22×C4—224no—
828C22×C4—222no—
829C22×C4—222no—
830C22×C4—224no—
831C22×C4—224no—
832C22×C4—222no—
833C22×C4—222no—
834C22×C4—224no—
835C22×C4—222no—
836C22×C4—222no—
837C22×C4—222no—
838C22×C4—222no—
839C22×C4—222no—
840C22×C4—222no—
841C22×C4—222no—
842C22×C4—222no—
843C22×C4—222no—
844C22×C4—224no—
845C22×C4D4×D1114yes—
846C22×C4C23×D1112yes—
847C22×C4C23×D1111yescharacteristic
848C22×C4C23×D1112yes—
849C22×C4C23×D1111yescharacteristic
850C22×C4C23×D1112yes—
851C22×C4C23×D1111yescharacteristic
852C22×C4C23×D1111yescharacteristic
853C22×C4C23×D1112yes—
854C22×C4C23×D1111yescharacteristic
855C4⋊C4—24no—
856C4⋊C4—22no—
857C4⋊C4—24no—
858C4⋊C4—224no—
859C4⋊C4—224no—
860C4⋊C4—224no—
861C4⋊C4—224no—
862C4⋊C4—224no—
863C4⋊C4—224no—
864C4⋊C4—222no—
865C4⋊C4—222no—
866C4⋊C4—222no—
867C4⋊C4—222no—
868C4⋊C4—224no—
869C4⋊C4—224no—
870C4⋊C4—224no—
871C4⋊C4—224no—
872C4⋊C4—224no—
873C4⋊C4—224no—
874C4⋊C4—224no—
875C4⋊C4—222no—
876C4⋊C4—224no—
877C22⋊C4—22no—
878C22⋊C4—24no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—22no—
882C22⋊C4—24no—
883C22⋊C4—222no—
884C22⋊C4—224no—
885C22⋊C4—224no—
886C22⋊C4—224no—
887C22⋊C4—222no—
888C22⋊C4—224no—
889C22⋊C4—222no—
890C22⋊C4—224no—
891C22⋊C4—222no—
892C22⋊C4—222no—
893C22⋊C4—222no—
894C22⋊C4—224no—
895C42—24no—
896C42—24no—
897C42—22no—
898C42—24no—
899C42—114no—
900C42—114no—
901C42—114no—
902C42—114no—
903C42—222no—
904C42—222no—
905C42—222no—
906C42—222no—
907C42—222no—
908C42—224no—
909C42—224no—
910C42—224no—
911C11#3497111yescharacteristic, complemented, Sylow
912C23—22no—
913C23—22no—
914C23—21no—
915C23—22no—
916C23—21no—
917C23—22no—
918C23—112no—
919C23—221no—
920C23—221no—
921C23—222no—
922C23—222no—
923C23C2×#433912yes—
924C23C2×#433912yes—
925C23C2×D4×D1112yes—
926C23#41×D1112yes—
927C23C24×D1111yescharacteristic
928Q8—2216no—
929Q8—2216no—
930Q8—228no—
931D4—28no—
932D4—228no—
933D4—228no—
934C2×C4—28no—
935C2×C4—22no—
936C2×C4—21no—
937C2×C4—22no—
938C2×C4—21no—
939C2×C4—22no—
940C2×C4—28no—
941C2×C4—22no—
942C2×C4—22no—
943C2×C4—22no—
944C2×C4—21no—
945C2×C4—21no—
946C2×C4—22no—
947C2×C4—22no—
948C2×C4—22no—
949C2×C4—22no—
950C2×C4—22no—
951C2×C4—22no—
952C2×C4—22no—
953C2×C4—22no—
954C2×C4—44no—
955C2×C4—44no—
956C2×C4—112no—
957C2×C4—114no—
958C2×C4—112no—
959C2×C4—112no—
960C2×C4—112no—
961C2×C4—114no—
962C2×C4—112no—
963C2×C4—228no—
964C2×C4—228no—
965C2×C4—228no—
966C2×C4—228no—
967C2×C4—228no—
968C2×C4—221no—
969C2×C4—221no—
970C2×C4—221no—
971C2×C4—221no—
972C2×C4—222no—
973C2×C4—221no—
974C2×C4—221no—
975C2×C4—222no—
976C2×C4—222no—
977C2×C4—222no—
978C2×C4—222no—
979C2×C4—221no—
980C2×C4—221no—
981C2×C4—222no—
982C2×C4—222no—
983C2×C4—222no—
984C2×C4—222no—
985C2×C4—222no—
986C2×C4—222no—
987C2×C4—222no—
988C2×C4—222no—
989C2×C4—222no—
990C2×C4—444no—
991C2×C4—444no—
992C2×C4—444no—
993C2×C4—444no—
994C2×C4C2×#433912yes—
995C2×C4C2×D4×D1112yes—
996C2×C4C2×D4×D1112yes—
997C2×C4#41×D1114yes—
998C2×C4#6704314yes—
999C22—22no—
1000C22—24no—
1001C22—24no—
1002C22—22no—
1003C22—22no—
1004C22—24no—
1005C22—41no—
1006C22—42no—
1007C22—41no—
1008C22—222no—
1009C22—224no—
1010C22—441no—
1011C22—442no—
1012C22—441no—
1013C22#1062307814yes—
1014C22C22×#433911yescharacteristic
1015C22C22×D4×D1111yescharacteristic
1016C22C2×#41×D1111yescharacteristic
1017C22C2×#41×D1112yes—
1018C22C2×#6704312yes—
1019C4—22no—
1020C4—22no—
1021C4—24no—
1022C4—42no—
1023C4—41no—
1024C4—42no—
1025C4—42no—
1026C4—41no—
1027C4—114no—
1028C4—222no—
1029C4—222no—
1030C4—222no—
1031C4—222no—
1032C4—224no—
1033C4—442no—
1034C4—441no—
1035C4—442no—
1036C4—442no—
1037C4—441no—
1038C4#1062317914yes—
1039C2—24no—
1040C2—42no—
1041C2—442no—
1042C2D11×#52511yescharacteristic
1043C2C2×#1062307811yescharacteristic
1044C2C2×#1062317911yescharacteristic
1045C2#1308222912yes—
1046C2#1308223112yes—
subgroupG/H
centerC22×C4C23×D11
commutator, socle, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC4×C11×#123C2
prime radicalC22×#4341C22
hypercenterC4×#123D11
hypocenterC11#34971
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C22×C4 ◁ C4×#123

Complements

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

NH ≅ G/Ntype
2. C22×C4×Dic22C2semidirect
3. #13074192C2semidirect
4. #13074190C2semidirect
5. #13073981C2semidirect
6. #13073524C2semidirect
7. #13072923C2semidirect
8. #13072921C2semidirect
9. #13072902C2semidirect
10. #13072900C2semidirect
11. #13071980C2semidirect
12. #13071978C2semidirect
15. #13071910C2semidirect
16. #13071903C2semidirect
17. C4×#66949C2semidirect
18. C4×#66931C2semidirect
19. C4×#66939C2semidirect
20. C4×#66982C2semidirect
21. C4×#66988C2semidirect
22. #13071010C2semidirect
23. C4×C11×#123C2semidirect
332. C2×Dic22#41semidirect
410. C4×#123D11semidirect
911. C11#34971semidirect

Maximal subgroups

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

subgroupindex
C2×C4×#43412
C22×C4×Dic222
#130741922
#130741902
#130739812
#130735242
#130729232
#130729212
#130729022
#130729002
#130719802
#130719782
#130719502
#130719482
#130719102
#130719032
C4×#669492
C4×#669312
C4×#669392
C4×#669822
C4×#669882
#130710102
C4×C11×#1232
#3497111