Finite Group Databasebeta

← C113×#24362 #43292382

Subgroups — C113×#24362 #43292382

Order 28928.

1484 conjugacy classes of subgroups.

The subgroup lattice has 898 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#135×C113C211yesmaximal, characteristic, complemented
2C2×#464×C113C211yesmaximal, characteristic, complemented
3C2×#460×C113C211yesmaximal, characteristic, complemented
4C2×#449×C113C211yesmaximal, characteristic, complemented
5C113×#2431C211yesmaximal, characteristic, complemented
6C113×#2341C211yesmaximal, characteristic, complemented
7C113×#2055C211yesmaximal, characteristic, complemented
8C113×#2054C211yesmaximal, characteristic, complemented
9C113×#2012C211yesmaximal, characteristic, complemented
10C113×#2011C211yesmaximal, characteristic, complemented
11C113×#1893C211yesmaximal, characteristic, complemented
12C113×#1880C211yesmaximal, characteristic, complemented
13C113×#1878C211yesmaximal, 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×Q8×C113C2211yescharacteristic
32C2×C4×Q8×C113C2211yescharacteristic
33#464×C113—24no—
34#460×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#390×C113—21no—
51#390×C113—21no—
52#390×C113C2211yescharacteristic
53#390×C113C2211yescharacteristic
54#390×C113C2211yescharacteristic
55#386×C113—21no—
56#386×C113—21no—
57#380×C113—21no—
58#380×C113C2211yescharacteristic
59C4×C22⋊C4×C113—21no—
60C4×C22⋊C4×C113C2211yescharacteristic
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×C113C2311yescharacteristic
90#135×C113—232no—
91C2×Q16×C113—22no—
92C2×Q16×C113—22no—
93C2×Q16×C113D414yescomplemented
94C2×SD16×C113—22no—
95C2×SD16×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×C113D414yescomplemented
103C2×D8×C113—22no—
104C2×D8×C113—22no—
105C2×D8×C113—22no—
106C2×D8×C113—22no—
107C2×D8×C113—41no—
108C2×D8×C113—41no—
109C22×C8×C113—22no—
110C22×C8×C113—22no—
111C22×C8×C113—22no—
112C22×C8×C113C2311yescharacteristic
113C22×C8×C113C2311yescharacteristic
114C22×C8×C113C2311yescharacteristic
115C22×C8×C113C2311yescharacteristic
116#127×C113—22no—
117#127×C113—41no—
118#124×C113—22no—
119#124×C113—41no—
120#121×C113—22no—
121#121×C113—22no—
122C4×Q8×C113—22no—
123C4×Q8×C113—22no—
124C4×Q8×C113—41no—
125C4×Q8×C113—41no—
126C2×C4⋊C4×C113—21no—
127C2×C4⋊C4×C113—21no—
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×C113—21no—
140C2×C22⋊C4×C113—21no—
141C2×C22⋊C4×C113D411yescharacteristic
142C2×C22⋊C4×C113D411yescharacteristic
143C2×C42×C113—21no—
144C2×C42×C113—21no—
145C2×C42×C113C2311yescharacteristic
146C2×C42×C113C2311yescharacteristic
147C4⋊C8×C113—22no—
148C4⋊C8×C113—22no—
149#103×C113—22no—
150#103×C113—22no—
151#103×C113—41no—
152#102×C113—22no—
153#102×C113—22no—
154#102×C113—22no—
155#102×C113—22no—
156#102×C113—41no—
157C22⋊C8×C113—22no—
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×C113C2×D412yes—
184C2×Q8×C113C2×D412yes—
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—21no—
203C2×D4×C113—21no—
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—42no—
213C2×D4×C113—42no—
214C2×D4×C113—81no—
215C2×D4×C113—81no—
216C2×D4×C113—81no—
217C2×D4×C113—81no—
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×C113C2×D411yescharacteristic
236C22×C4×C113C2×D411yescharacteristic
237C22×C4×C113C2×D411yescharacteristic
238C22×C4×C113C2×D411yescharacteristic
239C22×C4×C113C2×D412yes—
240C22×C4×C113C2×D411yescharacteristic
241C22×C4×C113#4112yes—
242C22×C4×C113C2411yescharacteristic
243Q16×C113—28no—
244SD16×C113—28no—
245SD16×C113—28no—
246SD16×C113—44no—
247D8×C113—28no—
248D8×C113—44no—
249C2×C8×C113—28no—
250C2×C8×C113—21no—
251C2×C8×C113—21no—
252C2×C8×C113—21no—
253C2×C8×C113—21no—
254C2×C8×C113—21no—
255C2×C8×C113—21no—
256C2×C8×C113—21no—
257C2×C8×C113—21no—
258C2×C8×C113—21no—
259C2×C8×C113—21no—
260C2×C8×C113C2×D412yes—
261C2×C8×C113C2×D412yes—
262C4⋊C4×C113—21no—
263C4⋊C4×C113—21no—
264C4⋊C4×C113—21no—
265C4⋊C4×C113—21no—
266C4⋊C4×C113—21no—
267C4⋊C4×C113—21no—
268C4⋊C4×C113—42no—
269C4⋊C4×C113—42no—
270C22⋊C4×C113—22no—
271C22⋊C4×C113—41no—
272C22⋊C4×C113—42no—
273C22⋊C4×C113—42no—
274C22⋊C4×C113—42no—
275C22⋊C4×C113—42no—
276C22⋊C4×C113—42no—
277C22⋊C4×C113—81no—
278C22⋊C4×C113—81no—
279C22⋊C4×C113—81no—
280C22⋊C4×C113—81no—
281C22⋊C4×C113—81no—
282C42×C113—21no—
283C42×C113—21no—
284C42×C113—21no—
285C42×C113—21no—
286C42×C113—42no—
287C42×C113—42no—
288C23×C113—21no—
289C23×C113—21no—
290C23×C113—21no—
291C23×C113—21no—
292C23×C113—21no—
293C23×C113—21no—
294C23×C113—22no—
295C23×C113—22no—
296C23×C113—41no—
297C23×C113—41no—
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—22no—
322Q8×C113—41no—
323Q8×C113—41no—
324Q8×C113#12014yes—
325D4×C113—22no—
326D4×C113—22no—
327D4×C113—22no—
328D4×C113—22no—
329D4×C113—48no—
330D4×C113—48no—
331D4×C113—41no—
332D4×C113—41no—
333D4×C113—41no—
334D4×C113—41no—
335D4×C113—41no—
336D4×C113—41no—
337D4×C113—41no—
338D4×C113—41no—
339D4×C113—84no—
340D4×C113—84no—
341D4×C113—84no—
342C2×C4×C113—22no—
343C2×C4×C113—21no—
344C2×C4×C113—22no—
345C2×C4×C113—22no—
346C2×C4×C113—21no—
347C2×C4×C113—21no—
348C2×C4×C113—21no—
349C2×C4×C113—22no—
350C2×C4×C113—22no—
351C2×C4×C113—22no—
352C2×C4×C113—22no—
353C2×C4×C113—21no—
354C2×C4×C113—21no—
355C2×C4×C113—21no—
356C2×C4×C113—22no—
357C2×C4×C113—21no—
358C2×C4×C113—21no—
359C2×C4×C113—21no—
360C2×C4×C113—21no—
361C2×C4×C113—21no—
362C2×C4×C113—21no—
363C2×C4×C113—48no—
364C2×C4×C113—48no—
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#12112yes—
377C2×C4×C113#13512yescomplemented
378C2×C4×C113C22×D411yescharacteristic
379C2×C4×C113C22×D411yescharacteristic
380C2×C4×C113C22×D411yescharacteristic
381C2×C4×C113C2×#4111yescharacteristic
382C2×C4×C113H(5,𝔽2)11yescharacteristic
383C2×C4×C113H(5,𝔽2)11yescharacteristic
384C8×C113—22no—
385C8×C113—22no—
386C8×C113—41no—
387C8×C113—41no—
388C22×C113—22no—
389C22×C113—22no—
390C22×C113—22no—
391C22×C113—41no—
392C22×C113—41no—
393C22×C113—41no—
394C22×C113—41no—
395C22×C113—42no—
396C22×C113—42no—
397C22×C113—42no—
398C22×C113—42no—
399C22×C113—42no—
400C22×C113—42no—
401C22×C113—81no—
402C22×C113—81no—
403C22×C113—81no—
404C22×C113—81no—
405C22×C113—81no—
406C22×C113—81no—
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×C113C2×#12111yescharacteristic
417C22×C113D4211yescharacteristic
418C22×C113D4211yescharacteristic
419C22×C113C2×#13511yescharacteristic
420C22×C113#57511yescharacteristic
421C22×C113#57611yescharacteristic
422C22×C113#57711yescharacteristic
423C4×C113—22no—
424C4×C113—24no—
425C4×C113—22no—
426C4×C113—42no—
427C4×C113—41no—
428C4×C113—41no—
429C4×C113—41no—
430C4×C113—81no—
431C4×C113—81no—
432C4×C113—81no—
433C4×C113C2×#12011yescharacteristic
434C4×C113#53411yescharacteristic
435C4×C113#54611yescharacteristic
436C4×C113#54611yescharacteristic
437#24362C11311yesmaximal, characteristic, direct product factor, Sylow
438C2×C113—42no—
439C2×C113—82no—
440C2×C113—82no—
441C2×C113—161no—
442C2×C113#241011yescharacteristic
443C2×C113#303511yescharacteristic
444C2×C113#304511yescharacteristic
445C2×C113#326811yescharacteristic
446C2×C113#327111yescharacteristic
447C2×C113#328211yescharacteristic
448C2×C113#328711yescharacteristic
449C22×#135C2×C11311yescharacteristic, complemented
450C2×#464C2×C11311yescharacteristic, complemented
451C2×#460C2×C11311yescharacteristic, complemented
452C2×#449C2×C11311yescharacteristic, complemented
453#2431C2×C11311yescharacteristic, complemented
454#2341C2×C11311yescharacteristic, complemented
455#2055C2×C11311yescharacteristic, complemented
456#2054C2×C11311yescharacteristic, complemented
457#2012C2×C11311yescharacteristic, complemented
458#2011C2×C11311yescharacteristic, complemented
459#1893C2×C11311yescharacteristic, complemented
460#1880C2×C11311yescharacteristic, complemented
461#1878C2×C11311yescharacteristic, complemented
462#1850C2×C11311yescharacteristic, complemented
463#1788C2×C11311yescharacteristic, complemented
464C113#2436211yescharacteristic, direct product factor, Sylow
465C22×#41C22×C11311yescharacteristic
466C22×#41C22×C11311yescharacteristic
467C2×#135—24no—
468C2×#135—24no—
469C2×#135—24no—
470C22×Q16C22×C11311yescharacteristic
471C22×SD16C22×C11311yescharacteristic
472C22×SD16C22×C11311yescharacteristic
473C22×SD16C22×C11311yescharacteristic
474C22×D8C22×C11311yescharacteristic
475C22×D8C22×C11311yescharacteristic
476C23×C8C22×C11311yescharacteristic
477C2×#127C22×C11311yescharacteristic
478C2×#124C22×C11311yescharacteristic
479C2×#121C22×C11311yescharacteristic
480C2×C4×Q8C22×C11311yescharacteristic
481C2×C4×Q8C22×C11311yescharacteristic
482#464—24no—
483#460—24no—
484#449—24no—
485C2×C4⋊C8C22×C11311yescharacteristic
486C2×C4⋊C8C22×C11311yescharacteristic
487C2×#103C22×C11311yescharacteristic
488C2×#103C22×C11311yescharacteristic
489C2×#103C22×C11311yescharacteristic
490C2×#102C22×C11311yescharacteristic
491C2×#102C22×C11311yescharacteristic
492C2×#102C22×C11311yescharacteristic
493C2×#102C22×C11311yescharacteristic
494C2×#102C22×C11311yescharacteristic
495C2×C22⋊C8C22×C11311yescharacteristic
496#392—21no—
497#392—21no—
498#391C22×C11311yescharacteristic
499#390—21no—
500#390—21no—
501#390C22×C11311yescharacteristic
502#390C22×C11311yescharacteristic
503#390C22×C11311yescharacteristic
504#386—21no—
505#386—21no—
506#380—21no—
507#380C22×C11311yescharacteristic
508C4×C22⋊C4—21no—
509C4×C22⋊C4C22×C11311yescharacteristic
510#340C22×C11311yescharacteristic
511#340C22×C11311yescharacteristic
512#336C22×C11311yescharacteristic
513#336C22×C11311yescharacteristic
514C2×#41—22no—
515C2×#41—22no—
516C2×#41—22no—
517C2×#41—22no—
518C2×#41—22no—
519C2×#41—22no—
520C2×#41—22no—
521C2×#41—41no—
522C2×#41—41no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41D4×C11314yescomplemented
526C22×Q8C23×C11311yescharacteristic
527C22×Q8C23×C11311yescharacteristic
528C22×D4—21no—
529C22×D4—21no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4C23×C11311yescharacteristic
534C22×D4C23×C11311yescharacteristic
535C22×D4C23×C11311yescharacteristic
536C23×C4—21no—
537C23×C4—21no—
538C23×C4C23×C11311yescharacteristic
539#135—232no—
540C2×Q16—22no—
541C2×Q16—22no—
542C2×Q16D4×C11314yescomplemented
543C2×SD16—22no—
544C2×SD16—22no—
545C2×SD16—22no—
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16D4×C11314yescomplemented
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C2×D8—22no—
556C2×D8—41no—
557C2×D8—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—22no—
561C22×C8C23×C11311yescharacteristic
562C22×C8C23×C11311yescharacteristic
563C22×C8C23×C11311yescharacteristic
564C22×C8C23×C11311yescharacteristic
565#127—22no—
566#127—41no—
567#124—22no—
568#124—41no—
569#121—22no—
570#121—22no—
571C4×Q8—22no—
572C4×Q8—22no—
573C4×Q8—41no—
574C4×Q8—41no—
575C2×C4⋊C4—21no—
576C2×C4⋊C4—21no—
577C2×C4⋊C4C23×C11311yescharacteristic
578C2×C4⋊C4C23×C11311yescharacteristic
579C2×C4⋊C4C23×C11311yescharacteristic
580C2×C22⋊C4—21no—
581C2×C22⋊C4—21no—
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×C42—21no—
593C2×C42—21no—
594C2×C42C23×C11311yescharacteristic
595C2×C42C23×C11311yescharacteristic
596C4⋊C8—22no—
597C4⋊C8—22no—
598#103—22no—
599#103—22no—
600#103—41no—
601#102—22no—
602#102—22no—
603#102—22no—
604#102—22no—
605#102—41no—
606C22⋊C8—22no—
607#95—21no—
608#95—21no—
609#95—21no—
610#95D4×C11311yescharacteristic
611#95D4×C11311yescharacteristic
612C24—21no—
613C24—21no—
614C24—21no—
615C24C2×D4×C11311yescharacteristic
616#41—28no—
617#41—28no—
618#41—44no—
619#41—44no—
620#41—44no—
621#41—44no—
622#41—44no—
623#41—44no—
624C2×Q8—21no—
625C2×Q8—21no—
626C2×Q8—21no—
627C2×Q8—21no—
628C2×Q8—21no—
629C2×Q8—21no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8C2×D4×C11312yes—
633C2×Q8C2×D4×C11312yes—
634C2×Q8C2×D4×C11312yes—
635C2×Q8C2×D4×C11312yes—
636C2×D4—24no—
637C2×D4—21no—
638C2×D4—21no—
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—
669C22×C4—21no—
670C22×C4—21no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—24no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—42no—
680C22×C4—42no—
681C22×C4—42no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4C2×D4×C11311yescharacteristic
685C22×C4C2×D4×C11311yescharacteristic
686C22×C4C2×D4×C11311yescharacteristic
687C22×C4C2×D4×C11311yescharacteristic
688C22×C4C2×D4×C11312yes—
689C22×C4C2×D4×C11311yescharacteristic
690C22×C4#41×C11312yes—
691C22×C4C24×C11311yescharacteristic
692Q16—28no—
693SD16—28no—
694SD16—28no—
695SD16—44no—
696D8—28no—
697D8—44no—
698C2×C8—28no—
699C2×C8—21no—
700C2×C8—21no—
701C2×C8—21no—
702C2×C8—21no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8C2×D4×C11312yes—
710C2×C8C2×D4×C11312yes—
711C4⋊C4—21no—
712C4⋊C4—21no—
713C4⋊C4—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—42no—
718C4⋊C4—42no—
719C22⋊C4—22no—
720C22⋊C4—41no—
721C22⋊C4—42no—
722C22⋊C4—42no—
723C22⋊C4—42no—
724C22⋊C4—42no—
725C22⋊C4—42no—
726C22⋊C4—81no—
727C22⋊C4—81no—
728C22⋊C4—81no—
729C22⋊C4—81no—
730C22⋊C4—81no—
731C42—21no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—42no—
736C42—42no—
737C23—21no—
738C23—21no—
739C23—21no—
740C23—21no—
741C23—21no—
742C23—21no—
743C23—22no—
744C23—22no—
745C23—41no—
746C23—41no—
747C23—41no—
748C23—41no—
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#121×C11312yes—
765C23C22×D4×C11311yescharacteristic
766Q8—22no—
767Q8—22no—
768Q8—22no—
769Q8—22no—
770Q8—22no—
771Q8—41no—
772Q8—41no—
773Q8#120×C11314yes—
774D4—22no—
775D4—22no—
776D4—22no—
777D4—22no—
778D4—48no—
779D4—48no—
780D4—41no—
781D4—41no—
782D4—41no—
783D4—41no—
784D4—41no—
785D4—41no—
786D4—41no—
787D4—41no—
788D4—84no—
789D4—84no—
790D4—84no—
791C2×C4—22no—
792C2×C4—21no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—21no—
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#121×C11312yes—
826C2×C4#135×C11312yescomplemented
827C2×C4C22×D4×C11311yescharacteristic
828C2×C4C22×D4×C11311yescharacteristic
829C2×C4C22×D4×C11311yescharacteristic
830C2×C4C2×#41×C11311yescharacteristic
831C2×C4H(5,𝔽2)×C11311yescharacteristic
832C2×C4H(5,𝔽2)×C11311yescharacteristic
833C8—22no—
834C8—22no—
835C8—41no—
836C8—41no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—42no—
845C22—42no—
846C22—42no—
847C22—42no—
848C22—42no—
849C22—42no—
850C22—81no—
851C22—81no—
852C22—81no—
853C22—81no—
854C22—81no—
855C22—81no—
856C22—81no—
857C22—81no—
858C22—81no—
859C22—81no—
860C22—81no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—81no—
865C22C2×#121×C11311yescharacteristic
866C22D42×C11311yescharacteristic
867C22D42×C11311yescharacteristic
868C22C2×#135×C11311yescharacteristic
869C22#575×C11311yescharacteristic
870C22#576×C11311yescharacteristic
871C22#577×C11311yescharacteristic
872C4—22no—
873C4—24no—
874C4—22no—
875C4—42no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C4—81no—
881C4—81no—
882C4C2×#120×C11311yescharacteristic
883C4#534×C11311yescharacteristic
884C4#546×C11311yescharacteristic
885C4#546×C11311yescharacteristic
886C2—42no—
887C2—82no—
888C2—82no—
889C2—161no—
890C2C113×#241011yescharacteristic
891C2C113×#303511yescharacteristic
892C2C113×#304511yescharacteristic
893C2C113×#326811yescharacteristic
894C2C113×#327111yescharacteristic
895C2C113×#328211yescharacteristic
896C2C113×#328711yescharacteristic
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×#464×C113C2semidirect
3. C2×#460×C113C2semidirect
4. C2×#449×C113C2semidirect
5. C113×#2431C2semidirect
6. C113×#2341C2semidirect
7. C113×#2055C2semidirect
8. C113×#2054C2semidirect
9. C113×#2012C2semidirect
10. C113×#2011C2semidirect
11. C113×#1893C2semidirect
12. C113×#1880C2semidirect
13. C113×#1878C2semidirect
14. C113×#1850C2semidirect
15. C113×#1788C2semidirect
76. C2×#41×C113D4semidirect
93. C2×Q16×C113D4semidirect
102. C2×SD16×C113D4semidirect
377. C2×C4×C113#135semidirect
437. #24362C113direct (N × H)
449. C22×#135C2×C113semidirect
450. C2×#464C2×C113semidirect
451. C2×#460C2×C113semidirect
452. C2×#449C2×C113semidirect
453. #2431C2×C113semidirect
454. #2341C2×C113semidirect
455. #2055C2×C113semidirect
456. #2054C2×C113semidirect
457. #2012C2×C113semidirect
458. #2011C2×C113semidirect
459. #1893C2×C113semidirect
460. #1880C2×C113semidirect
461. #1878C2×C113semidirect
462. #1850C2×C113semidirect
463. #1788C2×C113semidirect
464. C113#24362direct (N × H)
525. C2×#41D4×C113semidirect
542. C2×Q16D4×C113semidirect
551. C2×SD16D4×C113semidirect
826. 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×#464×C1132
C2×#460×C1132
C2×#449×C1132
C113×#24312
C113×#23412
C113×#20552
C113×#20542
C113×#20122
C113×#20112
C113×#18932
C113×#18802
C113×#18782
C113×#18502
C113×#17882
#24362113