Finite Group Databasebeta

← C113×#25136 #43293156

Subgroups — C113×#25136 #43293156

Order 28928.

1264 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#468×C113C211yesmaximal, characteristic, complemented
2C2×#450×C113C211yesmaximal, characteristic, complemented
3C2×#436×C113C211yesmaximal, characteristic, complemented
4C2×#418×C113C211yesmaximal, characteristic, complemented
5C113×#2415C211yesmaximal, characteristic, complemented
6C113×#2408C211yesmaximal, characteristic
7C113×#2067C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2034C211yesmaximal, characteristic, complemented
10C113×#2000C211yesmaximal, characteristic, complemented
11C113×#1968C211yesmaximal, characteristic, complemented
12C113×#1934C211yesmaximal, characteristic, complemented
13C113×#1895C211yesmaximal, characteristic, complemented
14C113×#1894C211yesmaximal, characteristic, complemented
15C113×#1854C211yesmaximal, characteristic, complemented
16C23×D4×C113C2211yescharacteristic
17C22×SD16×C113C2211yescharacteristic
18C22×SD16×C113C2211yescharacteristic
19C22×M16×C113C2211yescharacteristic
20C22×M16×C113C2211yescharacteristic, complemented
21C2×C22⋊Q8×C113C2211yescharacteristic
22C2×C22⋊Q8×C113C2211yescharacteristic, complemented
23C2×#121×C113C2211yescharacteristic
24C2×#121×C113C2211yescharacteristic
25C2×#120×C113—21no—
26C2×C4×D4×C113C2211yescharacteristic
27C2×#117×C113C2211yescharacteristic
28#468×C113—24no—
29#450×C113—24no—
30#436×C113—24no—
31C2×#107×C113C2211yescharacteristic, complemented
32C2×#106×C113C2211yescharacteristic, complemented
33C2×C4⋊C8×C113C2211yescharacteristic, complemented
34#418×C113—24no—
35C2×#103×C113C2211yescharacteristic, complemented
36C2×#103×C113C2211yescharacteristic, complemented
37C2×#102×C113C2211yescharacteristic
38C2×#102×C113C2211yescharacteristic
39C2×#102×C113C2211yescharacteristic
40C2×#102×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×C22⋊C8×C113C2211yescharacteristic
44C2×C22⋊C8×C113C2211yescharacteristic, complemented
45C2×C4×C8×C113C2211yescharacteristic, complemented
46#397×C113—21no—
47#394×C113—21no—
48#394×C113—21no—
49#392×C113—21no—
50#391×C113C2211yescharacteristic, complemented
51#390×C113C2211yescharacteristic
52#390×C113C2211yescharacteristic
53#389×C113—21no—
54#389×C113C2211yescharacteristic, complemented
55#388×C113—21no—
56#380×C113C2211yescharacteristic
57#380×C113C2211yescharacteristic, complemented
58#379×C113—21no—
59#340×C113C2211yescharacteristic, complemented
60#340×C113C2211yescharacteristic, complemented
61#340×C113C2211yescharacteristic, complemented
62#340×C113C2211yescharacteristic, complemented
63C25×C113—21no—
64C22×Q8×C113C2311yescharacteristic
65C22×D4×C113—22no—
66C22×D4×C113—22no—
67C22×D4×C113—21no—
68C22×D4×C113—21no—
69C22×D4×C113—22no—
70C22×D4×C113—21no—
71C22×D4×C113—22no—
72C22×D4×C113—41no—
73C22×D4×C113—41no—
74C22×D4×C113D411yescharacteristic
75C22×D4×C113C2311yescharacteristic
76C22×D4×C113C2311yescharacteristic
77C23×C4×C113C2311yescharacteristic
78C23×C4×C113C2311yescharacteristic
79C2×SD16×C113—22no—
80C2×SD16×C113—22no—
81C2×SD16×C113—22no—
82C2×SD16×C113—22no—
83C2×SD16×C113—41no—
84C2×SD16×C113—41no—
85C2×M16×C113—22no—
86C2×M16×C113—22no—
87C2×M16×C113—22no—
88C2×M16×C113—22no—
89C2×M16×C113—41no—
90C2×M16×C113—41no—
91C22×C8×C113C2311yescharacteristic
92C22×C8×C113C2311yescharacteristic
93C22×C8×C113C2311yescharacteristic
94C22×C8×C113C2311yescharacteristic
95C22⋊Q8×C113—22no—
96C22⋊Q8×C113—22no—
97C22⋊Q8×C113—22no—
98C22⋊Q8×C113—41no—
99#121×C113—22no—
100#121×C113—22no—
101#121×C113—41no—
102#121×C113—41no—
103#120×C113—44no—
104C4×D4×C113—22no—
105C4×D4×C113—22no—
106#117×C113—22no—
107#117×C113—41no—
108C2×C4⋊C4×C113—21no—
109C2×C4⋊C4×C113—21no—
110C2×C4⋊C4×C113—21no—
111C2×C4⋊C4×C113D411yescharacteristic
112C2×C4⋊C4×C113C2311yescharacteristic
113C2×C4⋊C4×C113C2311yescharacteristic
114C2×C4⋊C4×C113C2311yescharacteristic
115C2×C4⋊C4×C113C2311yescharacteristic
116C2×C4⋊C4×C113C2311yescharacteristic
117C2×C22⋊C4×C113—21no—
118C2×C22⋊C4×C113—21no—
119C2×C22⋊C4×C113—21no—
120C2×C22⋊C4×C113—21no—
121C2×C22⋊C4×C113—21no—
122C2×C22⋊C4×C113—21no—
123C2×C22⋊C4×C113—21no—
124C2×C22⋊C4×C113—21no—
125C2×C22⋊C4×C113—21no—
126C2×C22⋊C4×C113—21no—
127C2×C22⋊C4×C113—21no—
128C2×C22⋊C4×C113D411yescharacteristic
129C2×C22⋊C4×C113D411yescharacteristic
130C2×C42×C113—21no—
131C2×C42×C113C2311yescharacteristic
132#107×C113—22no—
133#106×C113—41no—
134C4⋊C8×C113—22no—
135#103×C113—22no—
136#103×C113—41no—
137#102×C113—22no—
138#102×C113—22no—
139#102×C113—22no—
140#102×C113—22no—
141#102×C113—22no—
142#102×C113D414yescomplemented
143C22⋊C8×C113—22no—
144C22⋊C8×C113D414yescomplemented
145C4×C8×C113—22no—
146#95×C113—21no—
147#95×C113—21no—
148#95×C113—21no—
149#95×C113—21no—
150#95×C113—21no—
151C24×C113—21no—
152C24×C113—21no—
153C24×C113—42no—
154C24×C113—42no—
155C24×C113—42no—
156C24×C113—42no—
157C24×C113—42no—
158C24×C113—81no—
159C24×C113—81no—
160C24×C113C2×D411yescharacteristic
161C24×C113C2×D411yescharacteristic
162C2×Q8×C113—21no—
163C2×Q8×C113—21no—
164C2×Q8×C113—21no—
165C2×Q8×C113—21no—
166C2×Q8×C113—21no—
167C2×Q8×C113—21no—
168C2×D4×C113—28no—
169C2×D4×C113—22no—
170C2×D4×C113—22no—
171C2×D4×C113—21no—
172C2×D4×C113—21no—
173C2×D4×C113—21no—
174C2×D4×C113—21no—
175C2×D4×C113—21no—
176C2×D4×C113—21no—
177C2×D4×C113—21no—
178C2×D4×C113—21no—
179C2×D4×C113—21no—
180C2×D4×C113—21no—
181C2×D4×C113—44no—
182C2×D4×C113—44no—
183C2×D4×C113—41no—
184C2×D4×C113—42no—
185C2×D4×C113—42no—
186C2×D4×C113—44no—
187C2×D4×C113—42no—
188C2×D4×C113—42no—
189C2×D4×C113—42no—
190C2×D4×C113—42no—
191C2×D4×C113—42no—
192C2×D4×C113—81no—
193C2×D4×C113—81no—
194C2×D4×C113C2×D412yes—
195C2×D4×C113#4112yes—
196C22×C4×C113—21no—
197C22×C4×C113—21no—
198C22×C4×C113—21no—
199C22×C4×C113—21no—
200C22×C4×C113—21no—
201C22×C4×C113—21no—
202C22×C4×C113—21no—
203C22×C4×C113—21no—
204C22×C4×C113—21no—
205C22×C4×C113—21no—
206C22×C4×C113—21no—
207C22×C4×C113—21no—
208C22×C4×C113—21no—
209C22×C4×C113—21no—
210C22×C4×C113—21no—
211C22×C4×C113—21no—
212C22×C4×C113C2×D411yescharacteristic
213C22×C4×C113C2×D411yescharacteristic
214C22×C4×C113C2×D411yescharacteristic
215C22×C4×C113C2×D412yes—
216C22×C4×C113C2×D411yescharacteristic
217C22×C4×C113#4112yes—
218C22×C4×C113C2411yescharacteristic
219SD16×C113—44no—
220SD16×C113—44no—
221M16×C113—44no—
222M16×C113—44no—
223C2×C8×C113—21no—
224C2×C8×C113—21no—
225C2×C8×C113—21no—
226C2×C8×C113—21no—
227C2×C8×C113—21no—
228C2×C8×C113—21no—
229C2×C8×C113—21no—
230C2×C8×C113—21no—
231C2×C8×C113—21no—
232C2×C8×C113C2×D412yes—
233C2×C8×C113C2×D412yes—
234C2×C8×C113C2×D412yes—
235C4⋊C4×C113—22no—
236C4⋊C4×C113—21no—
237C4⋊C4×C113—21no—
238C4⋊C4×C113—21no—
239C4⋊C4×C113—21no—
240C4⋊C4×C113—21no—
241C4⋊C4×C113—21no—
242C4⋊C4×C113—21no—
243C4⋊C4×C113—21no—
244C4⋊C4×C113—21no—
245C4⋊C4×C113—42no—
246C4⋊C4×C113—42no—
247C4⋊C4×C113—42no—
248C4⋊C4×C113C2×D412yes—
249C22⋊C4×C113—22no—
250C22⋊C4×C113—22no—
251C22⋊C4×C113—42no—
252C22⋊C4×C113—42no—
253C22⋊C4×C113—42no—
254C22⋊C4×C113—42no—
255C22⋊C4×C113—42no—
256C22⋊C4×C113—42no—
257C22⋊C4×C113—42no—
258C22⋊C4×C113—42no—
259C22⋊C4×C113—42no—
260C22⋊C4×C113—81no—
261C22⋊C4×C113—81no—
262C42×C113—21no—
263C42×C113—21no—
264C42×C113—42no—
265C23×C113—21no—
266C23×C113—21no—
267C23×C113—21no—
268C23×C113—21no—
269C23×C113—21no—
270C23×C113—21no—
271C23×C113—21no—
272C23×C113—21no—
273C23×C113—22no—
274C23×C113—22no—
275C23×C113—21no—
276C23×C113—21no—
277C23×C113—21no—
278C23×C113—21no—
279C23×C113—21no—
280C23×C113—48no—
281C23×C113—41no—
282C23×C113—41no—
283C23×C113—41no—
284C23×C113—41no—
285C23×C113—41no—
286C23×C113—41no—
287C23×C113—41no—
288C23×C113—41no—
289C23×C113—41no—
290C23×C113—41no—
291C23×C113—41no—
292C23×C113—41no—
293C23×C113—84no—
294C23×C113—84no—
295C23×C113—84no—
296C23×C113—84no—
297C23×C113—84no—
298C23×C113—84no—
299C23×C113#12112yes—
300C23×C113C22×D411yescharacteristic
301Q8×C113—41no—
302Q8×C113—41no—
303Q8×C113—41no—
304Q8×C113—41no—
305D4×C113—22no—
306D4×C113—22no—
307D4×C113—22no—
308D4×C113—22no—
309D4×C113—44no—
310D4×C113—48no—
311D4×C113—41no—
312D4×C113—41no—
313D4×C113—41no—
314D4×C113—41no—
315D4×C113—84no—
316D4×C113—84no—
317C2×C4×C113—21no—
318C2×C4×C113—21no—
319C2×C4×C113—21no—
320C2×C4×C113—21no—
321C2×C4×C113—22no—
322C2×C4×C113—22no—
323C2×C4×C113—22no—
324C2×C4×C113—22no—
325C2×C4×C113—21no—
326C2×C4×C113—21no—
327C2×C4×C113—22no—
328C2×C4×C113—21no—
329C2×C4×C113—21no—
330C2×C4×C113—21no—
331C2×C4×C113—21no—
332C2×C4×C113—41no—
333C2×C4×C113—41no—
334C2×C4×C113—41no—
335C2×C4×C113—41no—
336C2×C4×C113—41no—
337C2×C4×C113—41no—
338C2×C4×C113—41no—
339C2×C4×C113—41no—
340C2×C4×C113—41no—
341C2×C4×C113—41no—
342C2×C4×C113—41no—
343C2×C4×C113—41no—
344C2×C4×C113—41no—
345C2×C4×C113—41no—
346C2×C4×C113—41no—
347C2×C4×C113—41no—
348C2×C4×C113—41no—
349C2×C4×C113—41no—
350C2×C4×C113—41no—
351C2×C4×C113—41no—
352C2×C4×C113—41no—
353C2×C4×C113#12112yes—
354C2×C4×C113AGL(1,ℤ/8)12yes—
355C2×C4×C113C22×D411yescharacteristic
356C2×C4×C113C22×D411yescharacteristic
357C2×C4×C113C2×#4111yescharacteristic
358C2×C4×C113C2×#4111yescharacteristic
359C2×C4×C113H(5,𝔽2)11yescharacteristic
360C2×C4×C113H(5,𝔽2)11yescharacteristic
361C8×C113—22no—
362C8×C113—22no—
363C8×C113—22no—
364C8×C113—41no—
365C22×C113—22no—
366C22×C113—22no—
367C22×C113—22no—
368C22×C113—41no—
369C22×C113—41no—
370C22×C113—41no—
371C22×C113—41no—
372C22×C113—41no—
373C22×C113—42no—
374C22×C113—42no—
375C22×C113—41no—
376C22×C113—42no—
377C22×C113—41no—
378C22×C113—42no—
379C22×C113—41no—
380C22×C113—41no—
381C22×C113—41no—
382C22×C113—42no—
383C22×C113—41no—
384C22×C113—42no—
385C22×C113—816no—
386C22×C113—81no—
387C22×C113—81no—
388C22×C113—81no—
389C22×C113—81no—
390C22×C113—81no—
391C22×C113—81no—
392C22×C113—81no—
393C22×C113—81no—
394C22×C113C2×#12111yescharacteristic
395C22×C113D4211yescharacteristic
396C22×C113#54611yescharacteristic
397C22×C113C2×AGL(1,ℤ/8)11yescharacteristic
398C22×C113#57511yescharacteristic
399C22×C113#57711yescharacteristic
400C22×C113#57711yescharacteristic
401C4×C113—22no—
402C4×C113—22no—
403C4×C113—41no—
404C4×C113—42no—
405C4×C113—41no—
406C4×C113—81no—
407C4×C113—81no—
408C4×C113—81no—
409C4×C113—81no—
410C4×C113—81no—
411C4×C113#52511yescharacteristic
412C4×C113#53811yescharacteristic
413C4×C113D4211yescharacteristic
414C4×C113#54611yescharacteristic
415#25136C11311yesmaximal, characteristic, direct product factor, Sylow
416C2×C113—42no—
417C2×C113—81no—
418C2×C113—82no—
419C2×C113—82no—
420C2×C113#242411yescharacteristic
421C2×C113#305511yescharacteristic
422C2×C113#305711yescharacteristic
423C2×C113#327211yescharacteristic
424C2×C113#327511yescharacteristic
425C2×C113#332311yescharacteristic
426C2×C113#332411yescharacteristic
427C2×#468C2×C11311yescharacteristic, complemented
428C2×#450C2×C11311yescharacteristic, complemented
429C2×#436C2×C11311yescharacteristic, complemented
430C2×#418C2×C11311yescharacteristic, complemented
431#2415C2×C11311yescharacteristic, complemented
432#2408C2×C11311yescharacteristic
433#2067C2×C11311yescharacteristic, complemented
434#2055C2×C11311yescharacteristic, complemented
435#2034C2×C11311yescharacteristic, complemented
436#2000C2×C11311yescharacteristic, complemented
437#1968C2×C11311yescharacteristic, complemented
438#1934C2×C11311yescharacteristic, complemented
439#1895C2×C11311yescharacteristic, complemented
440#1894C2×C11311yescharacteristic, complemented
441#1854C2×C11311yescharacteristic, complemented
442C113#2513611yescharacteristic, direct product factor, Sylow
443C23×D4C22×C11311yescharacteristic
444C22×SD16C22×C11311yescharacteristic
445C22×SD16C22×C11311yescharacteristic
446C22×M16C22×C11311yescharacteristic
447C22×M16C22×C11311yescharacteristic, complemented
448C2×C22⋊Q8C22×C11311yescharacteristic
449C2×C22⋊Q8C22×C11311yescharacteristic, complemented
450C2×#121C22×C11311yescharacteristic
451C2×#121C22×C11311yescharacteristic
452C2×#120—21no—
453C2×C4×D4C22×C11311yescharacteristic
454C2×#117C22×C11311yescharacteristic
455#468—24no—
456#450—24no—
457#436—24no—
458C2×#107C22×C11311yescharacteristic, complemented
459C2×#106C22×C11311yescharacteristic, complemented
460C2×C4⋊C8C22×C11311yescharacteristic, complemented
461#418—24no—
462C2×#103C22×C11311yescharacteristic, complemented
463C2×#103C22×C11311yescharacteristic, complemented
464C2×#102C22×C11311yescharacteristic
465C2×#102C22×C11311yescharacteristic
466C2×#102C22×C11311yescharacteristic
467C2×#102C22×C11311yescharacteristic
468C2×#102C22×C11311yescharacteristic
469C2×#102C22×C11311yescharacteristic
470C2×C22⋊C8C22×C11311yescharacteristic
471C2×C22⋊C8C22×C11311yescharacteristic, complemented
472C2×C4×C8C22×C11311yescharacteristic, complemented
473#397—21no—
474#394—21no—
475#394—21no—
476#392—21no—
477#391C22×C11311yescharacteristic, complemented
478#390C22×C11311yescharacteristic
479#390C22×C11311yescharacteristic
480#389—21no—
481#389C22×C11311yescharacteristic, complemented
482#388—21no—
483#380C22×C11311yescharacteristic
484#380C22×C11311yescharacteristic, complemented
485#379—21no—
486#340C22×C11311yescharacteristic, complemented
487#340C22×C11311yescharacteristic, complemented
488#340C22×C11311yescharacteristic, complemented
489#340C22×C11311yescharacteristic, complemented
490C25—21no—
491C22×Q8C23×C11311yescharacteristic
492C22×D4—22no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—21no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—22no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4D4×C11311yescharacteristic
502C22×D4C23×C11311yescharacteristic
503C22×D4C23×C11311yescharacteristic
504C23×C4C23×C11311yescharacteristic
505C23×C4C23×C11311yescharacteristic
506C2×SD16—22no—
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—41no—
511C2×SD16—41no—
512C2×M16—22no—
513C2×M16—22no—
514C2×M16—22no—
515C2×M16—22no—
516C2×M16—41no—
517C2×M16—41no—
518C22×C8C23×C11311yescharacteristic
519C22×C8C23×C11311yescharacteristic
520C22×C8C23×C11311yescharacteristic
521C22×C8C23×C11311yescharacteristic
522C22⋊Q8—22no—
523C22⋊Q8—22no—
524C22⋊Q8—22no—
525C22⋊Q8—41no—
526#121—22no—
527#121—22no—
528#121—41no—
529#121—41no—
530#120—44no—
531C4×D4—22no—
532C4×D4—22no—
533#117—22no—
534#117—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4D4×C11311yescharacteristic
539C2×C4⋊C4C23×C11311yescharacteristic
540C2×C4⋊C4C23×C11311yescharacteristic
541C2×C4⋊C4C23×C11311yescharacteristic
542C2×C4⋊C4C23×C11311yescharacteristic
543C2×C4⋊C4C23×C11311yescharacteristic
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4D4×C11311yescharacteristic
556C2×C22⋊C4D4×C11311yescharacteristic
557C2×C42—21no—
558C2×C42C23×C11311yescharacteristic
559#107—22no—
560#106—41no—
561C4⋊C8—22no—
562#103—22no—
563#103—41no—
564#102—22no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102D4×C11314yescomplemented
570C22⋊C8—22no—
571C22⋊C8D4×C11314yescomplemented
572C4×C8—22no—
573#95—21no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578C24—21no—
579C24—21no—
580C24—42no—
581C24—42no—
582C24—42no—
583C24—42no—
584C24—42no—
585C24—81no—
586C24—81no—
587C24C2×D4×C11311yescharacteristic
588C24C2×D4×C11311yescharacteristic
589C2×Q8—21no—
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×D4—28no—
596C2×D4—22no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—44no—
609C2×D4—44no—
610C2×D4—41no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—44no—
614C2×D4—42no—
615C2×D4—42no—
616C2×D4—42no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4—81no—
621C2×D4C2×D4×C11312yes—
622C2×D4#41×C11312yes—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4C2×D4×C11311yescharacteristic
640C22×C4C2×D4×C11311yescharacteristic
641C22×C4C2×D4×C11311yescharacteristic
642C22×C4C2×D4×C11312yes—
643C22×C4C2×D4×C11311yescharacteristic
644C22×C4#41×C11312yes—
645C22×C4C24×C11311yescharacteristic
646SD16—44no—
647SD16—44no—
648M16—44no—
649M16—44no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8C2×D4×C11312yes—
660C2×C8C2×D4×C11312yes—
661C2×C8C2×D4×C11312yes—
662C4⋊C4—22no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—42no—
673C4⋊C4—42no—
674C4⋊C4—42no—
675C4⋊C4C2×D4×C11312yes—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—42no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—21no—
697C23—21no—
698C23—21no—
699C23—21no—
700C23—22no—
701C23—22no—
702C23—21no—
703C23—21no—
704C23—21no—
705C23—21no—
706C23—21no—
707C23—48no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—84no—
721C23—84no—
722C23—84no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23#121×C11312yes—
727C23C22×D4×C11311yescharacteristic
728Q8—41no—
729Q8—41no—
730Q8—41no—
731Q8—41no—
732D4—22no—
733D4—22no—
734D4—22no—
735D4—22no—
736D4—44no—
737D4—48no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—84no—
743D4—84no—
744C2×C4—21no—
745C2×C4—21no—
746C2×C4—21no—
747C2×C4—21no—
748C2×C4—22no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—41no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4#121×C11312yes—
781C2×C4AGL(1,ℤ/8)×C11312yes—
782C2×C4C22×D4×C11311yescharacteristic
783C2×C4C22×D4×C11311yescharacteristic
784C2×C4C2×#41×C11311yescharacteristic
785C2×C4C2×#41×C11311yescharacteristic
786C2×C4H(5,𝔽2)×C11311yescharacteristic
787C2×C4H(5,𝔽2)×C11311yescharacteristic
788C8—22no—
789C8—22no—
790C8—22no—
791C8—41no—
792C22—22no—
793C22—22no—
794C22—22no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—41no—
800C22—41no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—41no—
811C22—42no—
812C22—816no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22C2×#121×C11311yescharacteristic
822C22D42×C11311yescharacteristic
823C22#546×C11311yescharacteristic
824C22C2×AGL(1,ℤ/8)×C11311yescharacteristic
825C22#575×C11311yescharacteristic
826C22#577×C11311yescharacteristic
827C22#577×C11311yescharacteristic
828C4—22no—
829C4—22no—
830C4—41no—
831C4—41no—
832C4—42no—
833C4—81no—
834C4—81no—
835C4—81no—
836C4—81no—
837C4—81no—
838C4#525×C11311yescharacteristic
839C4#538×C11311yescharacteristic
840C4D42×C11311yescharacteristic
841C4#546×C11311yescharacteristic
842C2—42no—
843C2—81no—
844C2—82no—
845C2—82no—
846C2C113×#242411yescharacteristic
847C2C113×#305511yescharacteristic
848C2C113×#305711yescharacteristic
849C2C113×#327211yescharacteristic
850C2C113×#327511yescharacteristic
851C2C113×#332311yescharacteristic
852C2C113×#332411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
prime radicalC113×#2408C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C2×C4×D4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#468×C113C2semidirect
2. C2×#450×C113C2semidirect
3. C2×#436×C113C2semidirect
4. C2×#418×C113C2semidirect
5. C113×#2415C2semidirect
7. C113×#2067C2semidirect
8. C113×#2055C2semidirect
9. C113×#2034C2semidirect
10. C113×#2000C2semidirect
11. C113×#1968C2semidirect
12. C113×#1934C2semidirect
13. C113×#1895C2semidirect
14. C113×#1894C2semidirect
15. C113×#1854C2semidirect
20. C22×M16×C113C22semidirect
22. C2×C22⋊Q8×C113C22semidirect
31. C2×#107×C113C22semidirect
32. C2×#106×C113C22semidirect
33. C2×C4⋊C8×C113C22semidirect
35. C2×#103×C113C22semidirect
36. C2×#103×C113C22semidirect
44. C2×C22⋊C8×C113C22semidirect
45. C2×C4×C8×C113C22semidirect
50. #391×C113C22semidirect
54. #389×C113C22semidirect
57. #380×C113C22semidirect
59. #340×C113C22semidirect
60. #340×C113C22semidirect
61. #340×C113C22semidirect
62. #340×C113C22semidirect
142. #102×C113D4semidirect
144. C22⋊C8×C113D4semidirect
415. #25136C113direct (N × H)
427. C2×#468C2×C113semidirect
428. C2×#450C2×C113semidirect
429. C2×#436C2×C113semidirect
430. C2×#418C2×C113semidirect
431. #2415C2×C113semidirect
433. #2067C2×C113semidirect
434. #2055C2×C113semidirect
435. #2034C2×C113semidirect
436. #2000C2×C113semidirect
437. #1968C2×C113semidirect
438. #1934C2×C113semidirect
439. #1895C2×C113semidirect
440. #1894C2×C113semidirect
441. #1854C2×C113semidirect
442. C113#25136direct (N × H)
447. C22×M16C22×C113semidirect
449. C2×C22⋊Q8C22×C113semidirect
458. C2×#107C22×C113semidirect
459. C2×#106C22×C113semidirect
460. C2×C4⋊C8C22×C113semidirect
462. C2×#103C22×C113semidirect
463. C2×#103C22×C113semidirect
471. C2×C22⋊C8C22×C113semidirect
472. C2×C4×C8C22×C113semidirect
477. #391C22×C113semidirect
481. #389C22×C113semidirect
484. #380C22×C113semidirect
486. #340C22×C113semidirect
487. #340C22×C113semidirect
488. #340C22×C113semidirect
489. #340C22×C113semidirect
569. #102D4×C113semidirect
571. C22⋊C8D4×C113semidirect

Maximal subgroups

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

subgroupindex
C2×#468×C1132
C2×#450×C1132
C2×#436×C1132
C2×#418×C1132
C113×#24152
C113×#24082
C113×#20672
C113×#20552
C113×#20342
C113×#20002
C113×#19682
C113×#19342
C113×#18952
C113×#18942
C113×#18542
#25136113