Finite Group Databasebeta

← C4×#388×C113 #43281783

Subgroups — C4×#388×C113 #43281783

Order 28928.

2134 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#388×C113C212yesmaximal
2C2×C4×C4⋊C4×C113C211yesmaximal, characteristic, complemented
3C2×C4×C22⋊C4×C113C211yesmaximal, characteristic
4C2×C4×C22⋊C4×C113C211yesmaximal, characteristic
5C2×C4×C22⋊C4×C113C211yesmaximal, characteristic
6C2×C43×C113C211yesmaximal, characteristic, complemented
7C113×#1437C212yesmaximal
8C113×#1436C212yesmaximal, complemented
9C113×#1434C212yesmaximal, complemented
10C4×#95×C113C211yesmaximal, characteristic, complemented
11C4×#95×C113C211yesmaximal, characteristic, complemented
12C24×C4×C113C2211yescharacteristic
13C22×C4⋊C4×C113C2212yes—
14C22×C22⋊C4×C113C2212yes—
15C22×C22⋊C4×C113C2212yes—
16C22×C22⋊C4×C113C2211yescharacteristic
17C22×C22⋊C4×C113C2211yescharacteristic
18C22×C42×C113C2212yes—
19C22×C42×C113C2211yescharacteristic
20C22×C42×C113C2211yescharacteristic
21C22×C42×C113C2211yescharacteristic
22C22×C42×C113C2211yescharacteristic
23C22×C42×C113C2212yes—
24C22×C42×C113C2211yescharacteristic
25C22×C42×C113C2211yescharacteristic
26#388×C113C4116yesdirect product factor
27C4×C4⋊C4×C113—24no—
28C4×C22⋊C4×C113—24no—
29C4×C22⋊C4×C113—24no—
30C4×C22⋊C4×C113C418yescomplemented
31C2×#95×C113C2212yes—
32C2×#95×C113C2212yes—
33C2×#95×C113C2212yes—
34C2×#95×C113C2212yes—
35C2×#95×C113C2212yes—
36C2×#95×C113C2211yescharacteristic
37C2×#95×C113C2211yescharacteristic
38C2×#95×C113C2212yes—
39C2×#95×C113C2212yes—
40C43×C113—24no—
41C25×C113C2311yescharacteristic
42C23×C4×C113—22no—
43C23×C4×C113—22no—
44C23×C4×C113—22no—
45C23×C4×C113—22no—
46C23×C4×C113—22no—
47C23×C4×C113—22no—
48C23×C4×C113C2×C414yes—
49C23×C4×C113C2312yes—
50C23×C4×C113C2311yescharacteristic
51C23×C4×C113C2312yes—
52C23×C4×C113C2311yescharacteristic
53C23×C4×C113C2311yescharacteristic
54C23×C4×C113C2311yescharacteristic
55C23×C4×C113C2312yes—
56C23×C4×C113C2312yes—
57C23×C4×C113C2311yescharacteristic
58C23×C4×C113C2311yescharacteristic
59C2×C4⋊C4×C113—24no—
60C2×C4⋊C4×C113—24no—
61C2×C4⋊C4×C113C2×C418yescomplemented
62C2×C22⋊C4×C113—24no—
63C2×C22⋊C4×C113—24no—
64C2×C22⋊C4×C113—24no—
65C2×C22⋊C4×C113—24no—
66C2×C22⋊C4×C113—24no—
67C2×C22⋊C4×C113C2×C414yes—
68C2×C22⋊C4×C113C2×C418yes—
69C2×C22⋊C4×C113C2×C418yes—
70C2×C22⋊C4×C113C2×C414yes—
71C2×C22⋊C4×C113C2×C418yes—
72C2×C42×C113—24no—
73C2×C42×C113—22no—
74C2×C42×C113—24no—
75C2×C42×C113—22no—
76C2×C42×C113—22no—
77C2×C42×C113—24no—
78C2×C42×C113—24no—
79C2×C42×C113—22no—
80C2×C42×C113—22no—
81C2×C42×C113—24no—
82C2×C42×C113—22no—
83C2×C42×C113—22no—
84C2×C42×C113—22no—
85C2×C42×C113—22no—
86C2×C42×C113—22no—
87C2×C42×C113—22no—
88C2×C42×C113—22no—
89C2×C42×C113—22no—
90C2×C42×C113—22no—
91C2×C42×C113C2×C414yes—
92C2×C42×C113C2×C414yes—
93C2×C42×C113C2×C418yescomplemented
94C2×C42×C113D414yes—
95C2×C42×C113D414yes—
96#95×C113—24no—
97#95×C113—24no—
98#95×C113—24no—
99#95×C113—24no—
100#95×C113—24no—
101#95×C113C2×C414yes—
102#95×C113C2×C414yes—
103#95×C113C2×C418yescomplemented
104#95×C113C2×C418yescomplemented
105C24×C113—21no—
106C24×C113—21no—
107C24×C113—22no—
108C24×C113—22no—
109C24×C113—22no—
110C24×C113—21no—
111C24×C113—21no—
112C24×C113—21no—
113C24×C113—21no—
114C24×C113C22×C414yes—
115C24×C113C22×C412yes—
116C24×C113C2411yescharacteristic
117C22×C4×C113—21no—
118C22×C4×C113—22no—
119C22×C4×C113—21no—
120C22×C4×C113—21no—
121C22×C4×C113—21no—
122C22×C4×C113—21no—
123C22×C4×C113—22no—
124C22×C4×C113—21no—
125C22×C4×C113—22no—
126C22×C4×C113—22no—
127C22×C4×C113—22no—
128C22×C4×C113—22no—
129C22×C4×C113—22no—
130C22×C4×C113—22no—
131C22×C4×C113—22no—
132C22×C4×C113—22no—
133C22×C4×C113—22no—
134C22×C4×C113—21no—
135C22×C4×C113—21no—
136C22×C4×C113—21no—
137C22×C4×C113—22no—
138C22×C4×C113—22no—
139C22×C4×C113—22no—
140C22×C4×C113—22no—
141C22×C4×C113—22no—
142C22×C4×C113—22no—
143C22×C4×C113—22no—
144C22×C4×C113—21no—
145C22×C4×C113—22no—
146C22×C4×C113—22no—
147C22×C4×C113—22no—
148C22×C4×C113—22no—
149C22×C4×C113—22no—
150C22×C4×C113—22no—
151C22×C4×C113—22no—
152C22×C4×C113—21no—
153C22×C4×C113—21no—
154C22×C4×C113—21no—
155C22×C4×C113—21no—
156C22×C4×C113—28no—
157C22×C4×C113—28no—
158C22×C4×C113—28no—
159C22×C4×C113—44no—
160C22×C4×C113—44no—
161C22×C4×C113—44no—
162C22×C4×C113—44no—
163C22×C4×C113C22×C412yes—
164C22×C4×C113C22×C412yes—
165C22×C4×C113C22×C414yes—
166C22×C4×C113C22×C414yes—
167C22×C4×C113C22×C412yes—
168C22×C4×C113C22×C412yes—
169C22×C4×C113C22×C414yes—
170C22×C4×C113C22×C414yes—
171C22×C4×C113C22×C412yes—
172C22×C4×C113C22×C414yes—
173C22×C4×C113C22×C414yes—
174C22×C4×C113C22×C412yes—
175C22×C4×C113C2×D414yes—
176C22×C4×C113C2×D414yes—
177C22×C4×C113C2×D412yes—
178C22×C4×C113C2×D412yes—
179C22×C4×C113#4114yes—
180C22×C4×C113#4114yes—
181C22×C4×C113#4114yes—
182C22×C4×C113#4112yes—
183C22×C4×C113#4112yes—
184C22×C4×C113#4112yes—
185C22×C4×C113#4112yes—
186C4⋊C4×C113—216no—
187C22⋊C4×C113—28no—
188C22⋊C4×C113—216no—
189C22⋊C4×C113—216no—
190C22⋊C4×C113C42116yescomplemented
191C42×C113—216no—
192C42×C113—28no—
193C42×C113—28no—
194C42×C113—216no—
195C42×C113—28no—
196C42×C113—28no—
197C42×C113—44no—
198C42×C113—44no—
199C23×C113—22no—
200C23×C113—22no—
201C23×C113—24no—
202C23×C113—24no—
203C23×C113—22no—
204C23×C113—22no—
205C23×C113—24no—
206C23×C113—24no—
207C23×C113—24no—
208C23×C113—24no—
209C23×C113—22no—
210C23×C113—22no—
211C23×C113—41no—
212C23×C113—41no—
213C23×C113—42no—
214C23×C113—41no—
215C23×C113—41no—
216C23×C113—42no—
217C23×C113—42no—
218C23×C113—42no—
219C23×C113—42no—
220C23×C113—42no—
221C23×C113C2×C4214yes—
222C23×C113C23×C411yescharacteristic
223C23×C113C23×C412yes—
224C23×C113C22×D411yescharacteristic
225C23×C113C22×D411yescharacteristic
226C23×C113C2×#4111yescharacteristic
227C23×C113C2×#4111yescharacteristic
228C23×C113C2×#4112yes—
229C23×C113C2×#4111yescharacteristic
230C23×C113C2×#4112yes—
231C23×C113C2×#4111yescharacteristic
232C23×C113C2×#4112yes—
233C2×C4×C113—22no—
234C2×C4×C113—22no—
235C2×C4×C113—24no—
236C2×C4×C113—22no—
237C2×C4×C113—24no—
238C2×C4×C113—24no—
239C2×C4×C113—24no—
240C2×C4×C113—24no—
241C2×C4×C113—22no—
242C2×C4×C113—22no—
243C2×C4×C113—22no—
244C2×C4×C113—24no—
245C2×C4×C113—24no—
246C2×C4×C113—24no—
247C2×C4×C113—24no—
248C2×C4×C113—24no—
249C2×C4×C113—24no—
250C2×C4×C113—24no—
251C2×C4×C113—24no—
252C2×C4×C113—24no—
253C2×C4×C113—24no—
254C2×C4×C113—24no—
255C2×C4×C113—24no—
256C2×C4×C113—24no—
257C2×C4×C113—22no—
258C2×C4×C113—22no—
259C2×C4×C113—22no—
260C2×C4×C113—24no—
261C2×C4×C113—24no—
262C2×C4×C113—24no—
263C2×C4×C113—22no—
264C2×C4×C113—22no—
265C2×C4×C113—22no—
266C2×C4×C113—24no—
267C2×C4×C113—24no—
268C2×C4×C113—24no—
269C2×C4×C113—42no—
270C2×C4×C113—41no—
271C2×C4×C113—41no—
272C2×C4×C113—42no—
273C2×C4×C113—42no—
274C2×C4×C113—41no—
275C2×C4×C113—41no—
276C2×C4×C113—42no—
277C2×C4×C113—42no—
278C2×C4×C113—42no—
279C2×C4×C113—42no—
280C2×C4×C113—42no—
281C2×C4×C113—42no—
282C2×C4×C113—42no—
283C2×C4×C113—416no—
284C2×C4×C113C2×C4214yes—
285C2×C4×C113C2×C4214yes—
286C2×C4×C113#11714yes—
287C2×C4×C113#11714yes—
288C2×C4×C113C4×D418yes—
289C2×C4×C113C4×D418yes—
290C2×C4×C113C4×D414yes—
291C2×C4×C113C4×D414yes—
292C2×C4×C113#12114yes—
293C2×C4×C113#12314yes—
294C2×C4×C113#12414yes—
295C2×C4×C113#12614yes—
296C22×C113—24no—
297C22×C113—24no—
298C22×C113—24no—
299C22×C113—44no—
300C22×C113—42no—
301C22×C113—42no—
302C22×C113—42no—
303C22×C113—42no—
304C22×C113—44no—
305C22×C113—44no—
306C22×C113—44no—
307C22×C113C22×C4211yescharacteristic
308C22×C113C2×#11711yescharacteristic
309C22×C113C2×#11711yescharacteristic
310C22×C113C2×C4×D411yescharacteristic
311C22×C113C2×C4×D411yescharacteristic
312C22×C113C2×C4×D412yes—
313C22×C113C2×C4×D412yes—
314C22×C113C4×#4112yes—
315C22×C113C4×#4112yes—
316C22×C113C4×#4112yes—
317C22×C113C4×#4112yes—
318C22×C113C4×#4111yescharacteristic
319C22×C113C4×#4111yescharacteristic
320C22×C113C2×#12111yescharacteristic
321C22×C113C2×#12311yescharacteristic
322C22×C113#52512yes—
323C22×C113C2×#12411yescharacteristic
324C22×C113C2×#12611yescharacteristic
325C22×C113#52912yes—
326C22×C113#52912yes—
327C22×C113#52912yes—
328C22×C113#52912yes—
329C22×C113#53212yes—
330C4×C113—24no—
331C4×C113—24no—
332C4×C113—24no—
333C4×C113—28no—
334C4×C113—28no—
335C4×C113—42no—
336C4×C113—42no—
337C4×C113—44no—
338C4×C113—44no—
339C4×C113#38818yesdirect product factor
340C4×#388C11311yesmaximal, characteristic, direct product factor, Sylow
341C2×C113—44no—
342C2×C113C4×#11711yescharacteristic
343C2×C113C42×D411yescharacteristic
344C2×C113C42×D411yescharacteristic
345C2×C113C2×#38811yescharacteristic
346C2×C113#229011yescharacteristic
347C2×C113#229311yescharacteristic
348C2×C113#229811yescharacteristic
349C2×C113C4×#12112yes—
350C2×C113C4×#12312yes—
351C2×C113C4×#12412yes—
352C2×C113C4×#12612yes—
353C2×#388C2×C11312yes—
354C2×C4×C4⋊C4C2×C11311yescharacteristic, complemented
355C2×C4×C22⋊C4C2×C11311yescharacteristic
356C2×C4×C22⋊C4C2×C11311yescharacteristic
357C2×C4×C22⋊C4C2×C11311yescharacteristic
358C2×C43C2×C11311yescharacteristic, complemented
359#1437C2×C11312yes—
360#1436C2×C11312yescomplemented
361#1434C2×C11312yescomplemented
362C4×#95C2×C11311yescharacteristic, complemented
363C4×#95C2×C11311yescharacteristic, complemented
364C113C4×#38811yescharacteristic, direct product factor, Sylow
365C24×C4C22×C11311yescharacteristic
366C22×C4⋊C4C22×C11312yes—
367C22×C22⋊C4C22×C11311yescharacteristic
368C22×C22⋊C4C22×C11312yes—
369C22×C22⋊C4C22×C11312yes—
370C22×C22⋊C4C22×C11311yescharacteristic
371C22×C42C22×C11311yescharacteristic
372C22×C42C22×C11311yescharacteristic
373C22×C42C22×C11312yes—
374C22×C42C22×C11311yescharacteristic
375C22×C42C22×C11311yescharacteristic
376C22×C42C22×C11312yes—
377C22×C42C22×C11311yescharacteristic
378C22×C42C22×C11311yescharacteristic
379#388C4×C113116yesdirect product factor
380C4×C4⋊C4—24no—
381C4×C22⋊C4—24no—
382C4×C22⋊C4—24no—
383C4×C22⋊C4C4×C11318yescomplemented
384C2×#95C22×C11312yes—
385C2×#95C22×C11312yes—
386C2×#95C22×C11312yes—
387C2×#95C22×C11312yes—
388C2×#95C22×C11312yes—
389C2×#95C22×C11311yescharacteristic
390C2×#95C22×C11311yescharacteristic
391C2×#95C22×C11312yes—
392C2×#95C22×C11312yes—
393C43—24no—
394C25C23×C11311yescharacteristic
395C23×C4—22no—
396C23×C4—22no—
397C23×C4—22no—
398C23×C4—22no—
399C23×C4—22no—
400C23×C4—22no—
401C23×C4C2×C4×C11314yes—
402C23×C4C23×C11312yes—
403C23×C4C23×C11311yescharacteristic
404C23×C4C23×C11312yes—
405C23×C4C23×C11311yescharacteristic
406C23×C4C23×C11311yescharacteristic
407C23×C4C23×C11311yescharacteristic
408C23×C4C23×C11312yes—
409C23×C4C23×C11312yes—
410C23×C4C23×C11311yescharacteristic
411C23×C4C23×C11311yescharacteristic
412C2×C4⋊C4—24no—
413C2×C4⋊C4—24no—
414C2×C4⋊C4C2×C4×C11318yescomplemented
415C2×C22⋊C4—24no—
416C2×C22⋊C4—24no—
417C2×C22⋊C4—24no—
418C2×C22⋊C4—24no—
419C2×C22⋊C4—24no—
420C2×C22⋊C4C2×C4×C11314yes—
421C2×C22⋊C4C2×C4×C11318yes—
422C2×C22⋊C4C2×C4×C11318yes—
423C2×C22⋊C4C2×C4×C11314yes—
424C2×C22⋊C4C2×C4×C11318yes—
425C2×C42—24no—
426C2×C42—22no—
427C2×C42—24no—
428C2×C42—22no—
429C2×C42—22no—
430C2×C42—24no—
431C2×C42—24no—
432C2×C42—22no—
433C2×C42—22no—
434C2×C42—24no—
435C2×C42—22no—
436C2×C42—22no—
437C2×C42—22no—
438C2×C42—22no—
439C2×C42—22no—
440C2×C42—22no—
441C2×C42—22no—
442C2×C42—22no—
443C2×C42—22no—
444C2×C42C2×C4×C11314yes—
445C2×C42C2×C4×C11314yes—
446C2×C42C2×C4×C11318yescomplemented
447C2×C42D4×C11314yes—
448C2×C42D4×C11314yes—
449#95—24no—
450#95—24no—
451#95—24no—
452#95—24no—
453#95—24no—
454#95C2×C4×C11314yes—
455#95C2×C4×C11314yes—
456#95C2×C4×C11318yescomplemented
457#95C2×C4×C11318yescomplemented
458C24—21no—
459C24—21no—
460C24—22no—
461C24—22no—
462C24—22no—
463C24—21no—
464C24—21no—
465C24—21no—
466C24—21no—
467C24C22×C4×C11314yes—
468C24C22×C4×C11312yes—
469C24C24×C11311yescharacteristic
470C22×C4—21no—
471C22×C4—22no—
472C22×C4—21no—
473C22×C4—21no—
474C22×C4—21no—
475C22×C4—21no—
476C22×C4—22no—
477C22×C4—21no—
478C22×C4—22no—
479C22×C4—22no—
480C22×C4—22no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—22no—
486C22×C4—22no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—22no—
493C22×C4—22no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—21no—
498C22×C4—22no—
499C22×C4—22no—
500C22×C4—22no—
501C22×C4—22no—
502C22×C4—22no—
503C22×C4—22no—
504C22×C4—22no—
505C22×C4—21no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—28no—
510C22×C4—28no—
511C22×C4—28no—
512C22×C4—44no—
513C22×C4—44no—
514C22×C4—44no—
515C22×C4—44no—
516C22×C4C22×C4×C11312yes—
517C22×C4C22×C4×C11312yes—
518C22×C4C22×C4×C11314yes—
519C22×C4C22×C4×C11314yes—
520C22×C4C22×C4×C11312yes—
521C22×C4C22×C4×C11312yes—
522C22×C4C22×C4×C11314yes—
523C22×C4C22×C4×C11314yes—
524C22×C4C22×C4×C11312yes—
525C22×C4C22×C4×C11314yes—
526C22×C4C22×C4×C11314yes—
527C22×C4C22×C4×C11312yes—
528C22×C4C2×D4×C11314yes—
529C22×C4C2×D4×C11314yes—
530C22×C4C2×D4×C11312yes—
531C22×C4C2×D4×C11312yes—
532C22×C4#41×C11314yes—
533C22×C4#41×C11314yes—
534C22×C4#41×C11314yes—
535C22×C4#41×C11312yes—
536C22×C4#41×C11312yes—
537C22×C4#41×C11312yes—
538C22×C4#41×C11312yes—
539C4⋊C4—216no—
540C22⋊C4—28no—
541C22⋊C4—216no—
542C22⋊C4—216no—
543C22⋊C4C42×C113116yescomplemented
544C42—216no—
545C42—28no—
546C42—28no—
547C42—216no—
548C42—28no—
549C42—28no—
550C42—44no—
551C42—44no—
552C23—22no—
553C23—22no—
554C23—24no—
555C23—24no—
556C23—22no—
557C23—22no—
558C23—24no—
559C23—24no—
560C23—22no—
561C23—22no—
562C23—24no—
563C23—24no—
564C23—41no—
565C23—41no—
566C23—42no—
567C23—41no—
568C23—41no—
569C23—42no—
570C23—42no—
571C23—42no—
572C23—42no—
573C23—42no—
574C23C2×C42×C11314yes—
575C23C23×C4×C11311yescharacteristic
576C23C23×C4×C11312yes—
577C23C22×D4×C11311yescharacteristic
578C23C22×D4×C11311yescharacteristic
579C23C2×#41×C11311yescharacteristic
580C23C2×#41×C11311yescharacteristic
581C23C2×#41×C11312yes—
582C23C2×#41×C11311yescharacteristic
583C23C2×#41×C11312yes—
584C23C2×#41×C11311yescharacteristic
585C23C2×#41×C11312yes—
586C2×C4—22no—
587C2×C4—24no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—24no—
591C2×C4—24no—
592C2×C4—22no—
593C2×C4—24no—
594C2×C4—24no—
595C2×C4—24no—
596C2×C4—22no—
597C2×C4—22no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—24no—
601C2×C4—24no—
602C2×C4—24no—
603C2×C4—24no—
604C2×C4—24no—
605C2×C4—24no—
606C2×C4—24no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—24no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—24no—
614C2×C4—24no—
615C2×C4—24no—
616C2×C4—22no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—24no—
620C2×C4—24no—
621C2×C4—24no—
622C2×C4—42no—
623C2×C4—41no—
624C2×C4—41no—
625C2×C4—42no—
626C2×C4—42no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—42no—
632C2×C4—42no—
633C2×C4—42no—
634C2×C4—42no—
635C2×C4—42no—
636C2×C4—416no—
637C2×C4C2×C42×C11314yes—
638C2×C4C2×C42×C11314yes—
639C2×C4#117×C11314yes—
640C2×C4#117×C11314yes—
641C2×C4C4×D4×C11318yes—
642C2×C4C4×D4×C11318yes—
643C2×C4C4×D4×C11314yes—
644C2×C4C4×D4×C11314yes—
645C2×C4#121×C11314yes—
646C2×C4#123×C11314yes—
647C2×C4#124×C11314yes—
648C2×C4#126×C11314yes—
649C22—24no—
650C22—24no—
651C22—24no—
652C22—42no—
653C22—42no—
654C22—42no—
655C22—42no—
656C22—44no—
657C22—44no—
658C22—44no—
659C22—44no—
660C22C22×C42×C11311yescharacteristic
661C22C2×#117×C11311yescharacteristic
662C22C2×#117×C11311yescharacteristic
663C22C2×C4×D4×C11311yescharacteristic
664C22C2×C4×D4×C11311yescharacteristic
665C22C2×C4×D4×C11312yes—
666C22C2×C4×D4×C11312yes—
667C22C4×#41×C11311yescharacteristic
668C22C4×#41×C11311yescharacteristic
669C22C4×#41×C11312yes—
670C22C4×#41×C11312yes—
671C22C4×#41×C11312yes—
672C22C4×#41×C11312yes—
673C22C2×#121×C11311yescharacteristic
674C22C2×#123×C11311yescharacteristic
675C22#525×C11312yes—
676C22C2×#124×C11311yescharacteristic
677C22C2×#126×C11311yescharacteristic
678C22#529×C11312yes—
679C22#529×C11312yes—
680C22#529×C11312yes—
681C22#529×C11312yes—
682C22#532×C11312yes—
683C4—24no—
684C4—28no—
685C4—28no—
686C4—24no—
687C4—24no—
688C4—42no—
689C4—42no—
690C4—44no—
691C4—44no—
692C4#388×C11318yesdirect product factor
693C2—44no—
694C2C4×#117×C11311yescharacteristic
695C2C42×D4×C11311yescharacteristic
696C2C42×D4×C11311yescharacteristic
697C2C2×#388×C11311yescharacteristic
698C2C113×#229011yescharacteristic
699C2C113×#229311yescharacteristic
700C2C113×#229811yescharacteristic
701C2C4×#121×C11312yes—
702C2C4×#123×C11312yes—
703C2C4×#124×C11312yes—
704C2C4×#126×C11312yes—
subgroupG/H
centerC23×C4×C113C23
commutatorC22C22×C42×C113
Frattini, cosocleC24C24×C113
socleC24×C113C24
prime radicalC25×C113C23
LCSG ▷ C22 ▷ C1
UCSC1 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×C4⋊C4×C113C2semidirect
6. C2×C43×C113C2semidirect
8. C113×#1436C2semidirect
9. C113×#1434C2semidirect
10. C4×#95×C113C2semidirect
11. C4×#95×C113C2semidirect
26. #388×C113C4direct (N × H)
30. C4×C22⋊C4×C113C4semidirect
61. C2×C4⋊C4×C113C2×C4semidirect
93. C2×C42×C113C2×C4semidirect
103. #95×C113C2×C4semidirect
104. #95×C113C2×C4semidirect
190. C22⋊C4×C113C42semidirect
339. C4×C113#388direct (N × H)
340. C4×#388C113direct (N × H)
354. C2×C4×C4⋊C4C2×C113semidirect
358. C2×C43C2×C113semidirect
360. #1436C2×C113semidirect
361. #1434C2×C113semidirect
362. C4×#95C2×C113semidirect
363. C4×#95C2×C113semidirect
364. C113C4×#388direct (N × H)
379. #388C4×C113direct (N × H)
383. C4×C22⋊C4C4×C113semidirect
414. C2×C4⋊C4C2×C4×C113semidirect
446. C2×C42C2×C4×C113semidirect
456. #95C2×C4×C113semidirect
457. #95C2×C4×C113semidirect
543. C22⋊C4C42×C113semidirect
692. C4#388×C113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#388×C1132
C2×C4×C4⋊C4×C1132
C2×C4×C22⋊C4×C1132
C2×C43×C1132
C113×#14372
C113×#14362
C113×#14342
C4×#95×C1132
C4×#388113