Finite Group Databasebeta

← C113×#24364 #43292384

Subgroups — C113×#24364 #43292384

Order 28928.

1512 conjugacy classes of subgroups.

The subgroup lattice has 902 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C113C211yesmaximal, characteristic, complemented
2C2×#463×C113C211yesmaximal, characteristic, complemented
3C2×#459×C113C211yesmaximal, characteristic, complemented
4C2×#449×C113C211yesmaximal, characteristic, complemented
5C113×#2431C211yesmaximal, characteristic, complemented
6C113×#2339C211yesmaximal, characteristic, complemented
7C113×#2056C211yesmaximal, characteristic, complemented
8C113×#2055C211yesmaximal, characteristic, complemented
9C113×#2015C211yesmaximal, characteristic, complemented
10C113×#2014C211yesmaximal, characteristic, complemented
11C113×#1893C211yesmaximal, characteristic, complemented
12C113×#1879C211yesmaximal, characteristic, complemented
13C113×#1877C211yesmaximal, characteristic, complemented
14C113×#1850C211yesmaximal, characteristic, complemented
15C113×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C113C2211yescharacteristic
17C22×#41×C113C2211yescharacteristic
18C2×#135×C113—24no—
19C2×#135×C113—24no—
20C2×#135×C113—24no—
21C22×Q16×C113C2211yescharacteristic
22C22×SD16×C113C2211yescharacteristic
23C22×SD16×C113C2211yescharacteristic
24C22×SD16×C113C2211yescharacteristic
25C22×D8×C113C2211yescharacteristic
26C22×D8×C113C2211yescharacteristic
27C23×C8×C113C2211yescharacteristic
28C2×#127×C113C2211yescharacteristic
29C2×#124×C113C2211yescharacteristic
30C2×#121×C113C2211yescharacteristic
31C2×C4×D4×C113C2211yescharacteristic
32C2×C4×D4×C113C2211yescharacteristic
33#463×C113—24no—
34#459×C113—24no—
35#449×C113—24no—
36C2×C4⋊C8×C113C2211yescharacteristic
37C2×C4⋊C8×C113C2211yescharacteristic
38C2×#103×C113C2211yescharacteristic
39C2×#103×C113C2211yescharacteristic
40C2×#103×C113C2211yescharacteristic
41C2×#102×C113C2211yescharacteristic
42C2×#102×C113C2211yescharacteristic
43C2×#102×C113C2211yescharacteristic
44C2×#102×C113C2211yescharacteristic
45C2×#102×C113C2211yescharacteristic
46C2×C22⋊C8×C113C2211yescharacteristic
47#392×C113—21no—
48#392×C113—21no—
49#391×C113C2211yescharacteristic
50#391×C113C2211yescharacteristic
51#391×C113C2211yescharacteristic
52#390×C113C2211yescharacteristic
53#386×C113—21no—
54#386×C113—21no—
55#386×C113—21no—
56#386×C113—21no—
57#381×C113—21no—
58#380×C113C2211yescharacteristic
59C4×C22⋊C4×C113C2211yescharacteristic
60C2×#95×C113—21no—
61#340×C113C2211yescharacteristic
62#340×C113C2211yescharacteristic
63#336×C113C2211yescharacteristic
64#336×C113C2211yescharacteristic
65C2×#41×C113—22no—
66C2×#41×C113—22no—
67C2×#41×C113—22no—
68C2×#41×C113—22no—
69C2×#41×C113—22no—
70C2×#41×C113—22no—
71C2×#41×C113—22no—
72C2×#41×C113—41no—
73C2×#41×C113—41no—
74C2×#41×C113—41no—
75C2×#41×C113—41no—
76C2×#41×C113D414yescomplemented
77C22×Q8×C113C2311yescharacteristic
78C22×Q8×C113C2311yescharacteristic
79C22×D4×C113—21no—
80C22×D4×C113—21no—
81C22×D4×C113—21no—
82C22×D4×C113—21no—
83C22×D4×C113—21no—
84C22×D4×C113C2311yescharacteristic
85C22×D4×C113C2311yescharacteristic
86C22×D4×C113C2311yescharacteristic
87C23×C4×C113—21no—
88C23×C4×C113—21no—
89C23×C4×C113—21no—
90C23×C4×C113—21no—
91C23×C4×C113C2311yescharacteristic
92#135×C113—232no—
93C2×Q16×C113—22no—
94C2×Q16×C113—22no—
95C2×Q16×C113—22no—
96C2×SD16×C113—22no—
97C2×SD16×C113—22no—
98C2×SD16×C113—22no—
99C2×SD16×C113—22no—
100C2×SD16×C113—22no—
101C2×SD16×C113—22no—
102C2×SD16×C113—41no—
103C2×SD16×C113—41no—
104C2×SD16×C113D414yescomplemented
105C2×D8×C113—22no—
106C2×D8×C113—22no—
107C2×D8×C113—22no—
108C2×D8×C113—22no—
109C2×D8×C113—22no—
110C2×D8×C113D414yescomplemented
111C22×C8×C113—22no—
112C22×C8×C113—22no—
113C22×C8×C113—22no—
114C22×C8×C113C2311yescharacteristic
115C22×C8×C113C2311yescharacteristic
116C22×C8×C113C2311yescharacteristic
117C22×C8×C113C2311yescharacteristic
118#127×C113—22no—
119#127×C113—41no—
120#124×C113—22no—
121#124×C113—41no—
122#121×C113—22no—
123#121×C113—22no—
124C4×D4×C113—22no—
125C4×D4×C113—22no—
126C4×D4×C113—41no—
127C4×D4×C113—41no—
128C2×C4⋊C4×C113C2311yescharacteristic
129C2×C4⋊C4×C113C2311yescharacteristic
130C2×C4⋊C4×C113C2311yescharacteristic
131C2×C22⋊C4×C113—21no—
132C2×C22⋊C4×C113—21no—
133C2×C22⋊C4×C113—21no—
134C2×C22⋊C4×C113—21no—
135C2×C22⋊C4×C113—21no—
136C2×C22⋊C4×C113—21no—
137C2×C22⋊C4×C113—21no—
138C2×C22⋊C4×C113—21no—
139C2×C22⋊C4×C113D411yescharacteristic
140C2×C22⋊C4×C113D411yescharacteristic
141C2×C42×C113C2311yescharacteristic
142C2×C42×C113C2311yescharacteristic
143C4⋊C8×C113—22no—
144C4⋊C8×C113—22no—
145#103×C113—22no—
146#103×C113—22no—
147#103×C113—41no—
148#102×C113—22no—
149#102×C113—22no—
150#102×C113—22no—
151#102×C113—22no—
152#102×C113—41no—
153C22⋊C8×C113—22no—
154#95×C113—21no—
155#95×C113—21no—
156#95×C113—21no—
157#95×C113—21no—
158#95×C113—21no—
159#95×C113—21no—
160#95×C113—21no—
161#95×C113D411yescharacteristic
162#95×C113D411yescharacteristic
163C24×C113—21no—
164C24×C113—21no—
165C24×C113—21no—
166C24×C113C2×D411yescharacteristic
167#41×C113—28no—
168#41×C113—28no—
169#41×C113—44no—
170#41×C113—44no—
171#41×C113—44no—
172#41×C113—44no—
173#41×C113—44no—
174#41×C113—44no—
175C2×Q8×C113—21no—
176C2×Q8×C113—21no—
177C2×Q8×C113—21no—
178C2×Q8×C113—21no—
179C2×Q8×C113—21no—
180C2×Q8×C113—21no—
181C2×Q8×C113—21no—
182C2×Q8×C113—21no—
183C2×Q8×C113—21no—
184C2×Q8×C113—21no—
185C2×Q8×C113C2×D412yes—
186C2×Q8×C113C2×D412yes—
187C2×D4×C113—24no—
188C2×D4×C113—21no—
189C2×D4×C113—21no—
190C2×D4×C113—21no—
191C2×D4×C113—21no—
192C2×D4×C113—21no—
193C2×D4×C113—21no—
194C2×D4×C113—21no—
195C2×D4×C113—21no—
196C2×D4×C113—21no—
197C2×D4×C113—21no—
198C2×D4×C113—21no—
199C2×D4×C113—21no—
200C2×D4×C113—21no—
201C2×D4×C113—21no—
202C2×D4×C113—42no—
203C2×D4×C113—42no—
204C2×D4×C113—42no—
205C2×D4×C113—42no—
206C2×D4×C113—42no—
207C2×D4×C113—42no—
208C2×D4×C113—42no—
209C2×D4×C113—42no—
210C2×D4×C113—42no—
211C2×D4×C113—42no—
212C2×D4×C113—81no—
213C2×D4×C113—81no—
214C2×D4×C113—81no—
215C2×D4×C113—81no—
216C2×D4×C113C2×D412yes—
217C2×D4×C113C2×D412yes—
218C2×D4×C113C2×D412yes—
219C2×D4×C113C2×D412yes—
220C22×C4×C113—21no—
221C22×C4×C113—21no—
222C22×C4×C113—21no—
223C22×C4×C113—21no—
224C22×C4×C113—21no—
225C22×C4×C113—21no—
226C22×C4×C113—24no—
227C22×C4×C113—21no—
228C22×C4×C113—21no—
229C22×C4×C113—21no—
230C22×C4×C113—42no—
231C22×C4×C113—42no—
232C22×C4×C113—42no—
233C22×C4×C113—42no—
234C22×C4×C113—42no—
235C22×C4×C113—42no—
236C22×C4×C113—42no—
237C22×C4×C113—42no—
238C22×C4×C113—42no—
239C22×C4×C113—81no—
240C22×C4×C113—81no—
241C22×C4×C113C2×D411yescharacteristic
242C22×C4×C113C2×D411yescharacteristic
243C22×C4×C113C2×D411yescharacteristic
244C22×C4×C113C2×D411yescharacteristic
245C22×C4×C113C2×D412yes—
246C22×C4×C113C2×D411yescharacteristic
247C22×C4×C113#4112yes—
248C22×C4×C113C2411yescharacteristic
249Q16×C113—28no—
250SD16×C113—28no—
251SD16×C113—28no—
252SD16×C113—44no—
253D8×C113—28no—
254D8×C113—44no—
255C2×C8×C113—28no—
256C2×C8×C113—21no—
257C2×C8×C113—21no—
258C2×C8×C113—21no—
259C2×C8×C113—21no—
260C2×C8×C113—21no—
261C2×C8×C113—21no—
262C2×C8×C113—21no—
263C2×C8×C113—21no—
264C2×C8×C113—21no—
265C2×C8×C113—21no—
266C2×C8×C113C2×D412yes—
267C2×C8×C113C2×D412yes—
268C4⋊C4×C113—21no—
269C4⋊C4×C113—21no—
270C4⋊C4×C113—21no—
271C4⋊C4×C113—21no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C22⋊C4×C113—22no—
275C22⋊C4×C113—41no—
276C22⋊C4×C113—42no—
277C22⋊C4×C113—42no—
278C22⋊C4×C113—42no—
279C22⋊C4×C113—42no—
280C22⋊C4×C113—42no—
281C22⋊C4×C113—81no—
282C22⋊C4×C113—81no—
283C22⋊C4×C113—81no—
284C42×C113—21no—
285C42×C113—21no—
286C42×C113—21no—
287C42×C113—21no—
288C23×C113—22no—
289C23×C113—22no—
290C23×C113—22no—
291C23×C113—21no—
292C23×C113—21no—
293C23×C113—21no—
294C23×C113—21no—
295C23×C113—21no—
296C23×C113—21no—
297C23×C113—22no—
298C23×C113—41no—
299C23×C113—41no—
300C23×C113—41no—
301C23×C113—41no—
302C23×C113—41no—
303C23×C113—41no—
304C23×C113—41no—
305C23×C113—41no—
306C23×C113—41no—
307C23×C113—41no—
308C23×C113—41no—
309C23×C113—41no—
310C23×C113—41no—
311C23×C113—41no—
312C23×C113—41no—
313C23×C113—41no—
314C23×C113—41no—
315C23×C113#12112yes—
316C23×C113C22×D411yescharacteristic
317Q8×C113—22no—
318Q8×C113—22no—
319Q8×C113—22no—
320Q8×C113—22no—
321Q8×C113—41no—
322Q8×C113—41no—
323Q8×C113—41no—
324Q8×C113—41no—
325D4×C113—22no—
326D4×C113—22no—
327D4×C113—22no—
328D4×C113—22no—
329D4×C113—22no—
330D4×C113—48no—
331D4×C113—48no—
332D4×C113—41no—
333D4×C113—41no—
334D4×C113—41no—
335D4×C113—41no—
336D4×C113—41no—
337D4×C113—41no—
338D4×C113—84no—
339D4×C113—84no—
340D4×C113—84no—
341D4×C113#12014yes—
342C2×C4×C113—21no—
343C2×C4×C113—21no—
344C2×C4×C113—21no—
345C2×C4×C113—21no—
346C2×C4×C113—22no—
347C2×C4×C113—22no—
348C2×C4×C113—22no—
349C2×C4×C113—22no—
350C2×C4×C113—22no—
351C2×C4×C113—21no—
352C2×C4×C113—21no—
353C2×C4×C113—21no—
354C2×C4×C113—22no—
355C2×C4×C113—21no—
356C2×C4×C113—21no—
357C2×C4×C113—21no—
358C2×C4×C113—21no—
359C2×C4×C113—21no—
360C2×C4×C113—21no—
361C2×C4×C113—48no—
362C2×C4×C113—48no—
363C2×C4×C113—41no—
364C2×C4×C113—41no—
365C2×C4×C113—41no—
366C2×C4×C113—41no—
367C2×C4×C113—41no—
368C2×C4×C113—41no—
369C2×C4×C113—41no—
370C2×C4×C113—41no—
371C2×C4×C113—41no—
372C2×C4×C113—41no—
373C2×C4×C113—41no—
374C2×C4×C113—41no—
375C2×C4×C113—41no—
376C2×C4×C113—84no—
377C2×C4×C113—84no—
378C2×C4×C113#12112yes—
379C2×C4×C113#13512yescomplemented
380C2×C4×C113C22×D411yescharacteristic
381C2×C4×C113C22×D411yescharacteristic
382C2×C4×C113C22×D411yescharacteristic
383C2×C4×C113C2×#4111yescharacteristic
384C2×C4×C113H(5,𝔽2)11yescharacteristic
385C2×C4×C113H(5,𝔽2)11yescharacteristic
386C8×C113—22no—
387C8×C113—22no—
388C8×C113—41no—
389C8×C113—41no—
390C22×C113—22no—
391C22×C113—24no—
392C22×C113—22no—
393C22×C113—22no—
394C22×C113—41no—
395C22×C113—42no—
396C22×C113—42no—
397C22×C113—41no—
398C22×C113—42no—
399C22×C113—41no—
400C22×C113—41no—
401C22×C113—42no—
402C22×C113—42no—
403C22×C113—42no—
404C22×C113—42no—
405C22×C113—42no—
406C22×C113—42no—
407C22×C113—81no—
408C22×C113—81no—
409C22×C113—81no—
410C22×C113—81no—
411C22×C113—81no—
412C22×C113—81no—
413C22×C113—81no—
414C22×C113—81no—
415C22×C113—81no—
416C22×C113—81no—
417C22×C113—81no—
418C22×C113C2×#12111yescharacteristic
419C22×C113D4211yescharacteristic
420C22×C113D4211yescharacteristic
421C22×C113C2×#13511yescharacteristic
422C22×C113#57511yescharacteristic
423C22×C113#57611yescharacteristic
424C22×C113#57711yescharacteristic
425C4×C113—22no—
426C4×C113—22no—
427C4×C113—42no—
428C4×C113—42no—
429C4×C113—41no—
430C4×C113—41no—
431C4×C113—41no—
432C4×C113—81no—
433C4×C113—81no—
434C4×C113—81no—
435C4×C113C2×#12011yescharacteristic
436C4×C113#53411yescharacteristic
437C4×C113#54611yescharacteristic
438C4×C113#54611yescharacteristic
439#24364C11311yesmaximal, characteristic, direct product factor, Sylow
440C2×C113—42no—
441C2×C113—44no—
442C2×C113—82no—
443C2×C113—161no—
444C2×C113#241011yescharacteristic
445C2×C113#303511yescharacteristic
446C2×C113#304511yescharacteristic
447C2×C113#326711yescharacteristic
448C2×C113#326811yescharacteristic
449C2×C113#328011yescharacteristic
450C2×C113#328411yescharacteristic
451C22×#135C2×C11311yescharacteristic, complemented
452C2×#463C2×C11311yescharacteristic, complemented
453C2×#459C2×C11311yescharacteristic, complemented
454C2×#449C2×C11311yescharacteristic, complemented
455#2431C2×C11311yescharacteristic, complemented
456#2339C2×C11311yescharacteristic, complemented
457#2056C2×C11311yescharacteristic, complemented
458#2055C2×C11311yescharacteristic, complemented
459#2015C2×C11311yescharacteristic, complemented
460#2014C2×C11311yescharacteristic, complemented
461#1893C2×C11311yescharacteristic, complemented
462#1879C2×C11311yescharacteristic, complemented
463#1877C2×C11311yescharacteristic, complemented
464#1850C2×C11311yescharacteristic, complemented
465#1788C2×C11311yescharacteristic, complemented
466C113#2436411yescharacteristic, direct product factor, Sylow
467C22×#41C22×C11311yescharacteristic
468C22×#41C22×C11311yescharacteristic
469C2×#135—24no—
470C2×#135—24no—
471C2×#135—24no—
472C22×Q16C22×C11311yescharacteristic
473C22×SD16C22×C11311yescharacteristic
474C22×SD16C22×C11311yescharacteristic
475C22×SD16C22×C11311yescharacteristic
476C22×D8C22×C11311yescharacteristic
477C22×D8C22×C11311yescharacteristic
478C23×C8C22×C11311yescharacteristic
479C2×#127C22×C11311yescharacteristic
480C2×#124C22×C11311yescharacteristic
481C2×#121C22×C11311yescharacteristic
482C2×C4×D4C22×C11311yescharacteristic
483C2×C4×D4C22×C11311yescharacteristic
484#463—24no—
485#459—24no—
486#449—24no—
487C2×C4⋊C8C22×C11311yescharacteristic
488C2×C4⋊C8C22×C11311yescharacteristic
489C2×#103C22×C11311yescharacteristic
490C2×#103C22×C11311yescharacteristic
491C2×#103C22×C11311yescharacteristic
492C2×#102C22×C11311yescharacteristic
493C2×#102C22×C11311yescharacteristic
494C2×#102C22×C11311yescharacteristic
495C2×#102C22×C11311yescharacteristic
496C2×#102C22×C11311yescharacteristic
497C2×C22⋊C8C22×C11311yescharacteristic
498#392—21no—
499#392—21no—
500#391C22×C11311yescharacteristic
501#391C22×C11311yescharacteristic
502#391C22×C11311yescharacteristic
503#390C22×C11311yescharacteristic
504#386—21no—
505#386—21no—
506#386—21no—
507#386—21no—
508#381—21no—
509#380C22×C11311yescharacteristic
510C4×C22⋊C4C22×C11311yescharacteristic
511C2×#95—21no—
512#340C22×C11311yescharacteristic
513#340C22×C11311yescharacteristic
514#336C22×C11311yescharacteristic
515#336C22×C11311yescharacteristic
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41—41no—
526C2×#41—41no—
527C2×#41D4×C11314yescomplemented
528C22×Q8C23×C11311yescharacteristic
529C22×Q8C23×C11311yescharacteristic
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4C23×C11311yescharacteristic
536C22×D4C23×C11311yescharacteristic
537C22×D4C23×C11311yescharacteristic
538C23×C4—21no—
539C23×C4—21no—
540C23×C4—21no—
541C23×C4—21no—
542C23×C4C23×C11311yescharacteristic
543#135—232no—
544C2×Q16—22no—
545C2×Q16—22no—
546C2×Q16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×SD16D4×C11314yescomplemented
556C2×D8—22no—
557C2×D8—22no—
558C2×D8—22no—
559C2×D8—22no—
560C2×D8—22no—
561C2×D8D4×C11314yescomplemented
562C22×C8—22no—
563C22×C8—22no—
564C22×C8—22no—
565C22×C8C23×C11311yescharacteristic
566C22×C8C23×C11311yescharacteristic
567C22×C8C23×C11311yescharacteristic
568C22×C8C23×C11311yescharacteristic
569#127—22no—
570#127—41no—
571#124—22no—
572#124—41no—
573#121—22no—
574#121—22no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—41no—
578C4×D4—41no—
579C2×C4⋊C4C23×C11311yescharacteristic
580C2×C4⋊C4C23×C11311yescharacteristic
581C2×C4⋊C4C23×C11311yescharacteristic
582C2×C22⋊C4—21no—
583C2×C22⋊C4—21no—
584C2×C22⋊C4—21no—
585C2×C22⋊C4—21no—
586C2×C22⋊C4—21no—
587C2×C22⋊C4—21no—
588C2×C22⋊C4—21no—
589C2×C22⋊C4—21no—
590C2×C22⋊C4D4×C11311yescharacteristic
591C2×C22⋊C4D4×C11311yescharacteristic
592C2×C42C23×C11311yescharacteristic
593C2×C42C23×C11311yescharacteristic
594C4⋊C8—22no—
595C4⋊C8—22no—
596#103—22no—
597#103—22no—
598#103—41no—
599#102—22no—
600#102—22no—
601#102—22no—
602#102—22no—
603#102—41no—
604C22⋊C8—22no—
605#95—21no—
606#95—21no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95—21no—
611#95—21no—
612#95D4×C11311yescharacteristic
613#95D4×C11311yescharacteristic
614C24—21no—
615C24—21no—
616C24—21no—
617C24C2×D4×C11311yescharacteristic
618#41—28no—
619#41—28no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624#41—44no—
625#41—44no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8C2×D4×C11312yes—
637C2×Q8C2×D4×C11312yes—
638C2×D4—24no—
639C2×D4—21no—
640C2×D4—21no—
641C2×D4—21no—
642C2×D4—21no—
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4—21no—
647C2×D4—21no—
648C2×D4—21no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—42no—
654C2×D4—42no—
655C2×D4—42no—
656C2×D4—42no—
657C2×D4—42no—
658C2×D4—42no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—81no—
664C2×D4—81no—
665C2×D4—81no—
666C2×D4—81no—
667C2×D4C2×D4×C11312yes—
668C2×D4C2×D4×C11312yes—
669C2×D4C2×D4×C11312yes—
670C2×D4C2×D4×C11312yes—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—81no—
691C22×C4—81no—
692C22×C4C2×D4×C11311yescharacteristic
693C22×C4C2×D4×C11311yescharacteristic
694C22×C4C2×D4×C11311yescharacteristic
695C22×C4C2×D4×C11311yescharacteristic
696C22×C4C2×D4×C11312yes—
697C22×C4C2×D4×C11311yescharacteristic
698C22×C4#41×C11312yes—
699C22×C4C24×C11311yescharacteristic
700Q16—28no—
701SD16—28no—
702SD16—28no—
703SD16—44no—
704D8—28no—
705D8—44no—
706C2×C8—28no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8C2×D4×C11312yes—
718C2×C8C2×D4×C11312yes—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C22⋊C4—22no—
726C22⋊C4—41no—
727C22⋊C4—42no—
728C22⋊C4—42no—
729C22⋊C4—42no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C22⋊C4—81no—
733C22⋊C4—81no—
734C22⋊C4—81no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—21no—
743C23—21no—
744C23—21no—
745C23—21no—
746C23—21no—
747C23—21no—
748C23—22no—
749C23—41no—
750C23—41no—
751C23—41no—
752C23—41no—
753C23—41no—
754C23—41no—
755C23—41no—
756C23—41no—
757C23—41no—
758C23—41no—
759C23—41no—
760C23—41no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23#121×C11312yes—
767C23C22×D4×C11311yescharacteristic
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—22no—
772Q8—41no—
773Q8—41no—
774Q8—41no—
775Q8—41no—
776D4—22no—
777D4—22no—
778D4—22no—
779D4—22no—
780D4—22no—
781D4—48no—
782D4—48no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—41no—
789D4—84no—
790D4—84no—
791D4—84no—
792D4#120×C11314yes—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—21no—
811C2×C4—21no—
812C2×C4—48no—
813C2×C4—48no—
814C2×C4—41no—
815C2×C4—41no—
816C2×C4—41no—
817C2×C4—41no—
818C2×C4—41no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—84no—
828C2×C4—84no—
829C2×C4#121×C11312yes—
830C2×C4#135×C11312yescomplemented
831C2×C4C22×D4×C11311yescharacteristic
832C2×C4C22×D4×C11311yescharacteristic
833C2×C4C22×D4×C11311yescharacteristic
834C2×C4C2×#41×C11311yescharacteristic
835C2×C4H(5,𝔽2)×C11311yescharacteristic
836C2×C4H(5,𝔽2)×C11311yescharacteristic
837C8—22no—
838C8—22no—
839C8—41no—
840C8—41no—
841C22—22no—
842C22—22no—
843C22—24no—
844C22—22no—
845C22—42no—
846C22—41no—
847C22—42no—
848C22—42no—
849C22—41no—
850C22—42no—
851C22—41no—
852C22—41no—
853C22—42no—
854C22—42no—
855C22—42no—
856C22—42no—
857C22—42no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22—81no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22C2×#121×C11311yescharacteristic
870C22D42×C11311yescharacteristic
871C22D42×C11311yescharacteristic
872C22C2×#135×C11311yescharacteristic
873C22#575×C11311yescharacteristic
874C22#576×C11311yescharacteristic
875C22#577×C11311yescharacteristic
876C4—22no—
877C4—22no—
878C4—42no—
879C4—42no—
880C4—41no—
881C4—41no—
882C4—41no—
883C4—81no—
884C4—81no—
885C4—81no—
886C4C2×#120×C11311yescharacteristic
887C4#534×C11311yescharacteristic
888C4#546×C11311yescharacteristic
889C4#546×C11311yescharacteristic
890C2—42no—
891C2—44no—
892C2—82no—
893C2—161no—
894C2C113×#241011yescharacteristic
895C2C113×#303511yescharacteristic
896C2C113×#304511yescharacteristic
897C2C113×#326711yescharacteristic
898C2C113×#326811yescharacteristic
899C2C113×#328011yescharacteristic
900C2C113×#328411yescharacteristic
subgroupG/H
center, socleC23×C113C22×D4
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C113 ◁ C4×C22⋊C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C22×#135×C113C2semidirect
2. C2×#463×C113C2semidirect
3. C2×#459×C113C2semidirect
4. C2×#449×C113C2semidirect
5. C113×#2431C2semidirect
6. C113×#2339C2semidirect
7. C113×#2056C2semidirect
8. C113×#2055C2semidirect
9. C113×#2015C2semidirect
10. C113×#2014C2semidirect
11. C113×#1893C2semidirect
12. C113×#1879C2semidirect
13. C113×#1877C2semidirect
14. C113×#1850C2semidirect
15. C113×#1788C2semidirect
76. C2×#41×C113D4semidirect
104. C2×SD16×C113D4semidirect
110. C2×D8×C113D4semidirect
379. C2×C4×C113#135semidirect
439. #24364C113direct (N × H)
451. C22×#135C2×C113semidirect
452. C2×#463C2×C113semidirect
453. C2×#459C2×C113semidirect
454. C2×#449C2×C113semidirect
455. #2431C2×C113semidirect
456. #2339C2×C113semidirect
457. #2056C2×C113semidirect
458. #2055C2×C113semidirect
459. #2015C2×C113semidirect
460. #2014C2×C113semidirect
461. #1893C2×C113semidirect
462. #1879C2×C113semidirect
463. #1877C2×C113semidirect
464. #1850C2×C113semidirect
465. #1788C2×C113semidirect
466. C113#24364direct (N × H)
527. C2×#41D4×C113semidirect
555. C2×SD16D4×C113semidirect
561. C2×D8D4×C113semidirect
830. C2×C4#135×C113semidirect

Maximal subgroups

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

subgroupindex
C22×#135×C1132
C2×#463×C1132
C2×#459×C1132
C2×#449×C1132
C113×#24312
C113×#23392
C113×#20562
C113×#20552
C113×#20152
C113×#20142
C113×#18932
C113×#18792
C113×#18772
C113×#18502
C113×#17882
#24364113