Finite Group Databasebeta

← C113×#17684 #43285704

Subgroups — C113×#17684 #43285704

Order 28928.

932 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3517C211yesmaximal, characteristic
2C113×#2970C211yesmaximal, characteristic, complemented
3C113×#2923C211yesmaximal, characteristic, complemented
4C113×#1536C212yesmaximal, complemented
5C113×#1535C212yesmaximal, complemented
6C113×#1532C212yesmaximal, complemented
7C113×#1530C211yesmaximal, characteristic, complemented
8C113×#1530C212yesmaximal, complemented
9C113×#1529C211yesmaximal, characteristic, complemented
10C113×#1525C211yesmaximal, characteristic, complemented
11C113×#1524C211yesmaximal, characteristic, complemented
12#557×C113C411yescharacteristic
13#553×C113—21no—
14#553×C113—22no—
15#550×C113—21no—
16#550×C113C411yescharacteristic
17#550×C113C412yes—
18#550×C113C411yescharacteristic
19#547×C113C411yescharacteristic
20#547×C113C412yes—
21#540×C113—21no—
22#540×C113—22no—
23#532×C113C2211yescharacteristic
24#532×C113C2212yes—
25#529×C113C2211yescharacteristic
26#529×C113C2212yes—
27#520×C113—21no—
28C4×#41×C113C2211yescharacteristic
29#446×C113—21no—
30#435×C113—22no—
31C8×D4×C113—21no—
32#433×C113—22no—
33#432×C113C2211yescharacteristic
34#432×C113C2212yes—
35#432×C113C2212yes—
36#432×C113C2212yes—
37#424×C113—21no—
38#408×C113—21no—
39C4×M16×C113C2211yescharacteristic
40C4×M16×C113C2211yescharacteristic
41C2×#97×C113C2211yescharacteristic
42C2×#97×C113C2212yes—
43#330×C113C2211yescharacteristic
44#330×C113C2211yescharacteristic
45#330×C113C2212yes—
46#329×C113C2211yescharacteristic
47#329×C113C2211yescharacteristic
48#329×C113C2212yes—
49#329×C113C2212yes—
50#329×C113C2212yes—
51#329×C113C2212yes—
52#329×C113C2212yes—
53C2×#41×C113—21no—
54C2×#41×C113C2×C412yes—
55C2×#41×C113C2×C412yes—
56C2×#41×C113C2×C412yes—
57C2×#41×C113D411yescharacteristic
58C2×M16×C113—21no—
59C2×M16×C113—21no—
60C22×C8×C113—21no—
61C22×C8×C113—22no—
62C4⋊Q8×C113C2×C411yescharacteristic
63C4⋊Q8×C113C2×C412yes—
64#127×C113—21no—
65#127×C113—22no—
66#127×C113C2×C411yescharacteristic
67#127×C113C2×C412yes—
68#126×C113—21no—
69#126×C113—22no—
70#125×C113—22no—
71#125×C113—21no—
72#125×C113C2311yescharacteristic
73#124×C113C2311yescharacteristic
74#124×C113C2312yes—
75#123×C113—22no—
76#123×C113—21no—
77#123×C113—22no—
78#123×C113—22no—
79#123×C113—22no—
80C22⋊Q8×C113C2×C411yescharacteristic
81C22⋊Q8×C113C2×C412yes—
82#121×C113—21no—
83#121×C113—22no—
84#121×C113—22no—
85#121×C113—21no—
86#121×C113—21no—
87#121×C113—22no—
88#121×C113—22no—
89#121×C113—21no—
90#121×C113—22no—
91#121×C113—22no—
92#121×C113—22no—
93#121×C113C2×C411yescharacteristic
94#121×C113C2×C412yes—
95C4×Q8×C113—21no—
96C4×Q8×C113C2×C411yescharacteristic
97C4×Q8×C113C2×C412yes—
98C4×Q8×C113C2×C411yescharacteristic
99C4×Q8×C113D411yescharacteristic
100C4×D4×C113—21no—
101C4×D4×C113—22no—
102C4×D4×C113—22no—
103C4×D4×C113—21no—
104C4×D4×C113—21no—
105C4×D4×C113—22no—
106C4×D4×C113—21no—
107C4×D4×C113—22no—
108C4×D4×C113C2×C411yescharacteristic
109C4×D4×C113C2×C412yes—
110C4×D4×C113C2×C411yescharacteristic
111C4×D4×C113C2×C412yes—
112C4×D4×C113D411yescharacteristic
113C4×D4×C113D412yes—
114#117×C113—21no—
115#117×C113—22no—
116#117×C113D411yescharacteristic
117#117×C113D412yes—
118C2×C4⋊C4×C113—22no—
119C2×C4⋊C4×C113—21no—
120C2×C42×C113C2311yescharacteristic
121C2×C42×C113C2312yes—
122C4⋊C8×C113—22no—
123C4⋊C8×C113—22no—
124C4⋊C8×C113—21no—
125C4⋊C8×C113—22no—
126C22⋊C8×C113—22no—
127C22⋊C8×C113—22no—
128C22⋊C8×C113—22no—
129C22⋊C8×C113—21no—
130#97×C113—21no—
131#97×C113—22no—
132#97×C113C2311yescharacteristic
133#97×C113C2311yescharacteristic
134#97×C113C2311yescharacteristic
135#97×C113C2312yes—
136#97×C113C2311yescharacteristic
137#97×C113C2312yes—
138C4×C8×C113—21no—
139C4×C8×C113—21no—
140#41×C113—42no—
141#41×C113—44no—
142#41×C113—82no—
143#41×C113—82no—
144#41×C113—82no—
145C2×Q8×C113C22⋊C411yescharacteristic
146C2×Q8×C113C22×C411yescharacteristic
147C2×Q8×C113C22×C412yes—
148C2×D4×C113—21no—
149C2×D4×C113—22no—
150C2×D4×C113—22no—
151C2×D4×C113—22no—
152C2×D4×C113—22no—
153C2×D4×C113—22no—
154C2×D4×C113—21no—
155C2×D4×C113—21no—
156C2×D4×C113—22no—
157C2×D4×C113C22⋊C411yescharacteristic
158C2×D4×C113C22⋊C412yes—
159C2×D4×C113C22×C411yescharacteristic
160C2×D4×C113C22×C412yes—
161C22×C4×C113—22no—
162C22×C4×C113—21no—
163C22×C4×C113—22no—
164C22×C4×C113—22no—
165C22×C4×C113—22no—
166C22×C4×C113C22×C411yescharacteristic
167C22×C4×C113C22×C412yes—
168C22×C4×C113C2×D411yescharacteristic
169C22×C4×C113C2×D412yes—
170C22×C4×C113C2×D412yes—
171C22×C4×C113C2×D411yescharacteristic
172M16×C113—42no—
173M16×C113—42no—
174C2×C8×C113—21no—
175C2×C8×C113—22no—
176C2×C8×C113—21no—
177C2×C8×C113—21no—
178C2×C8×C113—21no—
179C2×C8×C113—22no—
180C2×C8×C113—44no—
181C2×C8×C113—42no—
182C4⋊C4×C113—21no—
183C4⋊C4×C113—22no—
184C4⋊C4×C113—22no—
185C4⋊C4×C113—21no—
186C4⋊C4×C113—21no—
187C4⋊C4×C113—22no—
188C4⋊C4×C113—21no—
189C4⋊C4×C113—22no—
190C4⋊C4×C113—21no—
191C4⋊C4×C113—21no—
192C4⋊C4×C113C22⋊C412yes—
193C4⋊C4×C113C22⋊C411yescharacteristic
194C4⋊C4×C113C22⋊C412yes—
195C4⋊C4×C113C22⋊C411yescharacteristic
196C4⋊C4×C113C22×C411yescharacteristic
197C4⋊C4×C113C22×C411yescharacteristic
198C22⋊C4×C113—21no—
199C22⋊C4×C113—22no—
200C22⋊C4×C113—21no—
201C22⋊C4×C113—22no—
202C22⋊C4×C113—21no—
203C22⋊C4×C113—22no—
204C22⋊C4×C113—21no—
205C22⋊C4×C113—22no—
206C22⋊C4×C113—21no—
207C22⋊C4×C113—22no—
208C22⋊C4×C113C22⋊C412yes—
209C22⋊C4×C113C22⋊C412yes—
210C22⋊C4×C113C22⋊C412yes—
211C42×C113—22no—
212C42×C113—21no—
213C42×C113C22×C412yes—
214C42×C113C22×C411yescharacteristic
215C42×C113C2×D411yescharacteristic
216C42×C113C2×D411yescharacteristic
217C42×C113C2×D412yes—
218C42×C113C2×D412yes—
219C42×C113C2411yescharacteristic
220C23×C113—22no—
221C23×C113—21no—
222C23×C113C2×C22⋊C411yescharacteristic
223C23×C113C2×C22⋊C412yes—
224Q8×C113—22no—
225Q8×C113—41no—
226Q8×C113—42no—
227D4×C113—22no—
228D4×C113—42no—
229D4×C113—41no—
230D4×C113—42no—
231D4×C113—44no—
232D4×C113—42no—
233D4×C113—82no—
234D4×C113—81no—
235D4×C113—82no—
236D4×C113—81no—
237D4×C113—82no—
238D4×C113—82no—
239D4×C113—82no—
240C2×C4×C113—22no—
241C2×C4×C113—21no—
242C2×C4×C113—22no—
243C2×C4×C113—21no—
244C2×C4×C113—21no—
245C2×C4×C113—42no—
246C2×C4×C113—41no—
247C2×C4×C113—41no—
248C2×C4×C113—42no—
249C2×C4×C113—42no—
250C2×C4×C113—44no—
251C2×C4×C113—42no—
252C2×C4×C113—82no—
253C2×C4×C113—82no—
254C2×C4×C113—82no—
255C2×C4×C113C2×C22⋊C412yes—
256C2×C4×C113C2×C22⋊C411yescharacteristic
257C2×C4×C113C2×C22⋊C412yes—
258C2×C4×C113C2×C22⋊C411yescharacteristic
259C2×C4×C113C2×C22⋊C412yes—
260C2×C4×C113C2×C22⋊C411yescharacteristic
261C2×C4×C113C23×C411yescharacteristic
262C2×C4×C113C22×D411yescharacteristic
263C2×C4×C113C22×D411yescharacteristic
264C8×C113—22no—
265C8×C113—41no—
266C8×C113—41no—
267C8×C113—42no—
268C8×C113—42no—
269C8×C113—41no—
270C22×C113—21no—
271C22×C113—22no—
272C22×C113—21no—
273C22×C113—22no—
274C22×C113—22no—
275C22×C113—21no—
276C22×C113—42no—
277C22×C113—41no—
278C22×C113—42no—
279C22×C113—41no—
280C22×C113—42no—
281C22×C113—41no—
282C22×C113C22×C22⋊C411yescharacteristic
283C4×C113—21no—
284C4×C113—21no—
285C4×C113—22no—
286C4×C113—21no—
287C4×C113—22no—
288C4×C113—21no—
289C4×C113—22no—
290C4×C113—21no—
291C4×C113—42no—
292C4×C113—41no—
293C4×C113—41no—
294C4×C113—41no—
295C4×C113#42112yes—
296#17684C11311yesmaximal, characteristic, direct product factor, Sylow
297C2×C113—41no—
298C2×C113—42no—
299C2×C113—82no—
300C2×C113—81no—
301C2×C113#288811yescharacteristic
302C2×C113C2×#42111yescharacteristic
303C2×C113#290111yescharacteristic
304#3517C2×C11311yescharacteristic
305#2970C2×C11311yescharacteristic, complemented
306#2923C2×C11311yescharacteristic, complemented
307#1536C2×C11312yescomplemented
308#1535C2×C11312yescomplemented
309#1532C2×C11312yescomplemented
310#1530C2×C11312yescomplemented
311#1530C2×C11311yescharacteristic, complemented
312#1529C2×C11311yescharacteristic, complemented
313#1525C2×C11311yescharacteristic, complemented
314#1524C2×C11311yescharacteristic, complemented
315C113#1768411yescharacteristic, direct product factor, Sylow
316#557C4×C11311yescharacteristic
317#553—21no—
318#553—22no—
319#550—21no—
320#550C4×C11311yescharacteristic
321#550C4×C11312yes—
322#550C4×C11311yescharacteristic
323#547C4×C11311yescharacteristic
324#547C4×C11312yes—
325#540—21no—
326#540—22no—
327#532C22×C11312yes—
328#532C22×C11311yescharacteristic
329#529C22×C11311yescharacteristic
330#529C22×C11312yes—
331#520—21no—
332C4×#41C22×C11311yescharacteristic
333#446—21no—
334#435—22no—
335C8×D4—21no—
336#433—22no—
337#432C22×C11312yes—
338#432C22×C11312yes—
339#432C22×C11312yes—
340#432C22×C11311yescharacteristic
341#424—21no—
342#408—21no—
343C4×M16C22×C11311yescharacteristic
344C4×M16C22×C11311yescharacteristic
345C2×#97C22×C11311yescharacteristic
346C2×#97C22×C11312yes—
347#330C22×C11311yescharacteristic
348#330C22×C11311yescharacteristic
349#330C22×C11312yes—
350#329C22×C11311yescharacteristic
351#329C22×C11312yes—
352#329C22×C11312yes—
353#329C22×C11312yes—
354#329C22×C11311yescharacteristic
355#329C22×C11312yes—
356#329C22×C11312yes—
357C2×#41—21no—
358C2×#41C2×C4×C11312yes—
359C2×#41C2×C4×C11312yes—
360C2×#41C2×C4×C11312yes—
361C2×#41D4×C11311yescharacteristic
362C2×M16—21no—
363C2×M16—21no—
364C22×C8—21no—
365C22×C8—22no—
366C4⋊Q8C2×C4×C11312yes—
367C4⋊Q8C2×C4×C11311yescharacteristic
368#127—21no—
369#127—22no—
370#127C2×C4×C11312yes—
371#127C2×C4×C11311yescharacteristic
372#126—21no—
373#126—22no—
374#125—22no—
375#125—21no—
376#125C23×C11311yescharacteristic
377#124C23×C11311yescharacteristic
378#124C23×C11312yes—
379#123—22no—
380#123—21no—
381#123—22no—
382#123—22no—
383#123—22no—
384C22⋊Q8C2×C4×C11311yescharacteristic
385C22⋊Q8C2×C4×C11312yes—
386#121—21no—
387#121—22no—
388#121—22no—
389#121—21no—
390#121—21no—
391#121—22no—
392#121—22no—
393#121—21no—
394#121—22no—
395#121—22no—
396#121—22no—
397#121C2×C4×C11311yescharacteristic
398#121C2×C4×C11312yes—
399C4×Q8—21no—
400C4×Q8C2×C4×C11311yescharacteristic
401C4×Q8C2×C4×C11312yes—
402C4×Q8C2×C4×C11311yescharacteristic
403C4×Q8D4×C11311yescharacteristic
404C4×D4—21no—
405C4×D4—22no—
406C4×D4—22no—
407C4×D4—21no—
408C4×D4—21no—
409C4×D4—22no—
410C4×D4—21no—
411C4×D4—22no—
412C4×D4C2×C4×C11311yescharacteristic
413C4×D4C2×C4×C11312yes—
414C4×D4C2×C4×C11311yescharacteristic
415C4×D4C2×C4×C11312yes—
416C4×D4D4×C11311yescharacteristic
417C4×D4D4×C11312yes—
418#117—21no—
419#117—22no—
420#117D4×C11311yescharacteristic
421#117D4×C11312yes—
422C2×C4⋊C4—22no—
423C2×C4⋊C4—21no—
424C2×C42C23×C11311yescharacteristic
425C2×C42C23×C11312yes—
426C4⋊C8—22no—
427C4⋊C8—22no—
428C4⋊C8—21no—
429C4⋊C8—22no—
430C22⋊C8—22no—
431C22⋊C8—22no—
432C22⋊C8—22no—
433C22⋊C8—21no—
434#97—21no—
435#97—22no—
436#97C23×C11311yescharacteristic
437#97C23×C11311yescharacteristic
438#97C23×C11312yes—
439#97C23×C11311yescharacteristic
440#97C23×C11311yescharacteristic
441#97C23×C11312yes—
442C4×C8—21no—
443C4×C8—21no—
444#41—42no—
445#41—44no—
446#41—82no—
447#41—82no—
448#41—82no—
449C2×Q8C22⋊C4×C11311yescharacteristic
450C2×Q8C22×C4×C11311yescharacteristic
451C2×Q8C22×C4×C11312yes—
452C2×D4—21no—
453C2×D4—22no—
454C2×D4—22no—
455C2×D4—22no—
456C2×D4—22no—
457C2×D4—22no—
458C2×D4—21no—
459C2×D4—21no—
460C2×D4—22no—
461C2×D4C22⋊C4×C11311yescharacteristic
462C2×D4C22⋊C4×C11312yes—
463C2×D4C22×C4×C11311yescharacteristic
464C2×D4C22×C4×C11312yes—
465C22×C4—22no—
466C22×C4—21no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4C22×C4×C11311yescharacteristic
471C22×C4C22×C4×C11312yes—
472C22×C4C2×D4×C11311yescharacteristic
473C22×C4C2×D4×C11312yes—
474C22×C4C2×D4×C11312yes—
475C22×C4C2×D4×C11311yescharacteristic
476M16—42no—
477M16—42no—
478C2×C8—21no—
479C2×C8—22no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—22no—
484C2×C8—44no—
485C2×C8—42no—
486C4⋊C4—21no—
487C4⋊C4—22no—
488C4⋊C4—22no—
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—22no—
492C4⋊C4—21no—
493C4⋊C4—22no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4C22⋊C4×C11312yes—
497C4⋊C4C22⋊C4×C11311yescharacteristic
498C4⋊C4C22⋊C4×C11312yes—
499C4⋊C4C22⋊C4×C11311yescharacteristic
500C4⋊C4C22×C4×C11311yescharacteristic
501C4⋊C4C22×C4×C11311yescharacteristic
502C22⋊C4—21no—
503C22⋊C4—22no—
504C22⋊C4—21no—
505C22⋊C4—22no—
506C22⋊C4—21no—
507C22⋊C4—22no—
508C22⋊C4—21no—
509C22⋊C4—22no—
510C22⋊C4—21no—
511C22⋊C4—22no—
512C22⋊C4C22⋊C4×C11312yes—
513C22⋊C4C22⋊C4×C11312yes—
514C22⋊C4C22⋊C4×C11312yes—
515C42—22no—
516C42—21no—
517C42C22×C4×C11312yes—
518C42C22×C4×C11311yescharacteristic
519C42C2×D4×C11311yescharacteristic
520C42C2×D4×C11311yescharacteristic
521C42C2×D4×C11312yes—
522C42C2×D4×C11312yes—
523C42C24×C11311yescharacteristic
524C23—22no—
525C23—21no—
526C23C2×C22⋊C4×C11311yescharacteristic
527C23C2×C22⋊C4×C11312yes—
528Q8—22no—
529Q8—41no—
530Q8—42no—
531D4—22no—
532D4—42no—
533D4—41no—
534D4—42no—
535D4—44no—
536D4—42no—
537D4—82no—
538D4—81no—
539D4—82no—
540D4—82no—
541D4—82no—
542D4—82no—
543D4—81no—
544C2×C4—22no—
545C2×C4—21no—
546C2×C4—22no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—42no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—44no—
555C2×C4—42no—
556C2×C4—82no—
557C2×C4—82no—
558C2×C4—82no—
559C2×C4C2×C22⋊C4×C11312yes—
560C2×C4C2×C22⋊C4×C11311yescharacteristic
561C2×C4C2×C22⋊C4×C11312yes—
562C2×C4C2×C22⋊C4×C11311yescharacteristic
563C2×C4C2×C22⋊C4×C11312yes—
564C2×C4C2×C22⋊C4×C11311yescharacteristic
565C2×C4C23×C4×C11311yescharacteristic
566C2×C4C22×D4×C11311yescharacteristic
567C2×C4C22×D4×C11311yescharacteristic
568C8—22no—
569C8—41no—
570C8—41no—
571C8—42no—
572C8—42no—
573C8—41no—
574C22—21no—
575C22—22no—
576C22—21no—
577C22—22no—
578C22—22no—
579C22—21no—
580C22—42no—
581C22—41no—
582C22—42no—
583C22—41no—
584C22—42no—
585C22—41no—
586C22C22×C22⋊C4×C11311yescharacteristic
587C4—21no—
588C4—21no—
589C4—22no—
590C4—21no—
591C4—22no—
592C4—21no—
593C4—22no—
594C4—21no—
595C4—42no—
596C4—41no—
597C4—41no—
598C4—41no—
599C4#421×C11312yes—
600C2—41no—
601C2—42no—
602C2—82no—
603C2—81no—
604C2C113×#288811yescharacteristic
605C2C2×#421×C11311yescharacteristic
606C2C113×#290111yescharacteristic
subgroupG/H
center, socleC22×C113C22×C22⋊C4
commutatorC2×C4C23×C4×C113
Frattini, cosocleC42C24×C113
prime radicalC113×#3517C2
LCSG ▷ C2×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C4×#41×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#2970C2semidirect
3. C113×#2923C2semidirect
4. C113×#1536C2semidirect
5. C113×#1535C2semidirect
6. C113×#1532C2semidirect
7. C113×#1530C2semidirect
8. C113×#1530C2semidirect
9. C113×#1529C2semidirect
10. C113×#1525C2semidirect
11. C113×#1524C2semidirect
296. #17684C113direct (N × H)
305. #2970C2×C113semidirect
306. #2923C2×C113semidirect
307. #1536C2×C113semidirect
308. #1535C2×C113semidirect
309. #1532C2×C113semidirect
310. #1530C2×C113semidirect
311. #1530C2×C113semidirect
312. #1529C2×C113semidirect
313. #1525C2×C113semidirect
314. #1524C2×C113semidirect
315. C113#17684direct (N × H)

Maximal subgroups

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

subgroupindex
C113×#35172
C113×#29702
C113×#29232
C113×#15362
C113×#15352
C113×#15322
C113×#15302
C113×#15292
C113×#15252
C113×#15242
#17684113