Finite Group Databasebeta

← C113×#10394 #43278414

Subgroups — C113×#10394 #43278414

Order 28928.

772 conjugacy classes of subgroups.

The subgroup lattice has 642 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#2617C211yesmaximal, characteristic
2C113×#1874C211yesmaximal, characteristic, complemented
3C113×#1852C211yesmaximal, characteristic, complemented
4C2×#327×C113C211yesmaximal, characteristic, complemented
5C2×#323×C113C211yesmaximal, characteristic, complemented
6C113×#1439C211yesmaximal, characteristic, complemented
7C113×#1294C211yesmaximal, characteristic, complemented
8C2×#121×C113C2211yescharacteristic
9C2×#120×C113—21no—
10C22×C4⋊C4×C113C2211yescharacteristic
11C22×C22⋊C4×C113—21no—
12C22×C22⋊C4×C113C2211yescharacteristic
13C2×#107×C113—21no—
14C2×#102×C113—21no—
15C2×C22⋊C8×C113C2211yescharacteristic
16C2×C22⋊C8×C113C2211yescharacteristic
17#397×C113—21no—
18#394×C113—21no—
19#394×C113—21no—
20#392×C113—21no—
21#386×C113—21no—
22#380×C113C2211yescharacteristic
23C2×#95×C113—21no—
24C2×#95×C113C2211yescharacteristic
25#340×C113—21no—
26#340×C113—21no—
27#327×C113—22no—
28#323×C113—22no—
29C25×C113D411yescharacteristic
30C22×D4×C113—21no—
31C22×D4×C113—21no—
32C22×D4×C113—21no—
33C22×D4×C113D411yescharacteristic
34C23×C4×C113—21no—
35C23×C4×C113—21no—
36C23×C4×C113D411yescharacteristic
37C23×C4×C113C2311yescharacteristic
38C22×C8×C113—21no—
39C22×C8×C113—21no—
40#121×C113—21no—
41#121×C113—21no—
42#121×C113—21no—
43#121×C113—21no—
44#120×C113—42no—
45#120×C113—42no—
46C2×C4⋊C4×C113—21no—
47C2×C4⋊C4×C113—21no—
48C2×C4⋊C4×C113—42no—
49C2×C4⋊C4×C113D411yescharacteristic
50C2×C4⋊C4×C113D411yescharacteristic
51C2×C4⋊C4×C113D411yescharacteristic
52C2×C22⋊C4×C113—21no—
53C2×C22⋊C4×C113—21no—
54C2×C22⋊C4×C113—21no—
55C2×C22⋊C4×C113—21no—
56C2×C22⋊C4×C113—21no—
57C2×C22⋊C4×C113—21no—
58C2×C22⋊C4×C113—21no—
59C2×C22⋊C4×C113—21no—
60C2×C22⋊C4×C113—21no—
61C2×C22⋊C4×C113—21no—
62C2×C22⋊C4×C113—21no—
63C2×C22⋊C4×C113—21no—
64C2×C22⋊C4×C113—42no—
65C2×C22⋊C4×C113—42no—
66C2×C22⋊C4×C113—42no—
67#107×C113—42no—
68#102×C113—42no—
69C22⋊C8×C113—21no—
70C22⋊C8×C113—21no—
71C22⋊C8×C113—21no—
72C22⋊C8×C113D412yescomplemented
73#95×C113—21no—
74#95×C113—21no—
75#95×C113—21no—
76#95×C113—21no—
77#95×C113—21no—
78#95×C113—42no—
79C24×C113—21no—
80C24×C113—21no—
81C24×C113—21no—
82C24×C113—21no—
83C24×C113—21no—
84C24×C113—21no—
85C24×C113—21no—
86C24×C113—41no—
87C24×C113—41no—
88C24×C113—41no—
89C24×C113—41no—
90C24×C113D812yes—
91C24×C113C2×D411yescharacteristic
92C2×D4×C113—21no—
93C2×D4×C113—21no—
94C2×D4×C113—41no—
95C2×D4×C113—41no—
96C2×D4×C113—42no—
97C2×D4×C113—42no—
98C2×D4×C113—41no—
99C2×D4×C113—41no—
100C2×D4×C113—41no—
101C2×D4×C113—41no—
102C2×D4×C113—41no—
103C2×D4×C113—41no—
104C2×D4×C113—81no—
105C2×D4×C113—81no—
106C2×D4×C113—81no—
107C2×D4×C113—81no—
108C22×C4×C113—22no—
109C22×C4×C113—22no—
110C22×C4×C113—21no—
111C22×C4×C113—21no—
112C22×C4×C113—21no—
113C22×C4×C113—21no—
114C22×C4×C113—21no—
115C22×C4×C113—21no—
116C22×C4×C113—41no—
117C22×C4×C113—41no—
118C22×C4×C113—41no—
119C22×C4×C113—41no—
120C22×C4×C113—41no—
121C22×C4×C113—41no—
122C22×C4×C113—41no—
123C22×C4×C113—41no—
124C22×C4×C113—41no—
125C22×C4×C113—41no—
126C22×C4×C113—41no—
127C22×C4×C113—41no—
128C22×C4×C113—41no—
129C22×C4×C113—41no—
130C22×C4×C113—41no—
131C22×C4×C113—41no—
132C22×C4×C113C2×D411yescharacteristic
133C22×C4×C113C2×D411yescharacteristic
134C22×C4×C113C2×D411yescharacteristic
135C22×C4×C113#4111yescharacteristic
136C22×C4×C113#4111yescharacteristic
137C22×C4×C113#4111yescharacteristic
138C2×C8×C113—22no—
139C2×C8×C113—41no—
140C2×C8×C113—41no—
141C2×C8×C113—41no—
142C2×C8×C113—41no—
143C2×C8×C113—41no—
144C4⋊C4×C113—22no—
145C4⋊C4×C113—22no—
146C4⋊C4×C113—21no—
147C4⋊C4×C113—21no—
148C4⋊C4×C113—41no—
149C4⋊C4×C113—41no—
150C4⋊C4×C113—41no—
151C4⋊C4×C113—41no—
152C22⋊C4×C113—42no—
153C22⋊C4×C113—42no—
154C22⋊C4×C113—48no—
155C22⋊C4×C113—41no—
156C22⋊C4×C113—41no—
157C22⋊C4×C113—41no—
158C22⋊C4×C113—41no—
159C22⋊C4×C113—41no—
160C22⋊C4×C113—41no—
161C22⋊C4×C113—41no—
162C22⋊C4×C113—41no—
163C22⋊C4×C113—81no—
164C22⋊C4×C113—81no—
165C23×C113—21no—
166C23×C113—21no—
167C23×C113—21no—
168C23×C113—21no—
169C23×C113—22no—
170C23×C113—22no—
171C23×C113—22no—
172C23×C113—42no—
173C23×C113—42no—
174C23×C113—42no—
175C23×C113—42no—
176C23×C113—42no—
177C23×C113—42no—
178C23×C113—41no—
179C23×C113—41no—
180C23×C113—41no—
181C23×C113—41no—
182C23×C113—41no—
183C23×C113—41no—
184C23×C113—41no—
185C23×C113—41no—
186C23×C113—41no—
187C23×C113—41no—
188C23×C113—41no—
189C23×C113—41no—
190C23×C113—41no—
191C23×C113—41no—
192C23×C113—41no—
193C23×C113—81no—
194C23×C113—81no—
195C23×C113—81no—
196C23×C113—81no—
197C23×C113—81no—
198C23×C113—81no—
199C23×C113#12011yescharacteristic
200C23×C113#12111yescharacteristic
201C23×C113#12311yescharacteristic
202C23×C113C2×D811yescharacteristic
203C23×C113#13511yescharacteristic
204C23×C113AGL(1,ℤ/8)11yescharacteristic
205C23×C113#13711yescharacteristic
206D4×C113—42no—
207D4×C113—81no—
208D4×C113—84no—
209D4×C113—84no—
210D4×C113—81no—
211D4×C113—81no—
212D4×C113—81no—
213D4×C113—81no—
214C2×C4×C113—21no—
215C2×C4×C113—21no—
216C2×C4×C113—21no—
217C2×C4×C113—21no—
218C2×C4×C113—41no—
219C2×C4×C113—41no—
220C2×C4×C113—41no—
221C2×C4×C113—41no—
222C2×C4×C113—42no—
223C2×C4×C113—42no—
224C2×C4×C113—42no—
225C2×C4×C113—42no—
226C2×C4×C113—42no—
227C2×C4×C113—42no—
228C2×C4×C113—41no—
229C2×C4×C113—41no—
230C2×C4×C113—41no—
231C2×C4×C113—41no—
232C2×C4×C113—41no—
233C2×C4×C113—41no—
234C2×C4×C113—41no—
235C2×C4×C113—41no—
236C2×C4×C113—41no—
237C2×C4×C113—41no—
238C2×C4×C113—42no—
239C2×C4×C113—41no—
240C2×C4×C113—41no—
241C2×C4×C113—81no—
242C2×C4×C113—81no—
243C2×C4×C113—81no—
244C2×C4×C113—81no—
245C2×C4×C113—81no—
246C2×C4×C113—81no—
247C2×C4×C113—81no—
248C2×C4×C113—81no—
249C2×C4×C113—81no—
250C2×C4×C113#12111yescharacteristic
251C2×C4×C113#12111yescharacteristic
252C2×C4×C113#12311yescharacteristic
253C2×C4×C113#12411yescharacteristic
254C8×C113—42no—
255C8×C113—81no—
256C22×C113—21no—
257C22×C113—21no—
258C22×C113—21no—
259C22×C113—21no—
260C22×C113—21no—
261C22×C113—21no—
262C22×C113—21no—
263C22×C113—21no—
264C22×C113—21no—
265C22×C113—21no—
266C22×C113—21no—
267C22×C113—21no—
268C22×C113—44no—
269C22×C113—42no—
270C22×C113—42no—
271C22×C113—42no—
272C22×C113—82no—
273C22×C113—82no—
274C22×C113—82no—
275C22×C113—81no—
276C22×C113—81no—
277C22×C113—81no—
278C22×C113—81no—
279C22×C113—81no—
280C22×C113—81no—
281C22×C113—81no—
282C22×C113—81no—
283C22×C113—81no—
284C22×C113—81no—
285C22×C113—81no—
286C22×C113#39411yescharacteristic
287C22×C113#44711yescharacteristic
288C22×C113#45211yescharacteristic
289C22×C113#45311yescharacteristic
290C22×C113#45511yescharacteristic
291C22×C113B(4,𝔽2)11yescharacteristic
292C22×C113#45811yescharacteristic
293C22×C113#46611yescharacteristic
294C22×C113#46811yescharacteristic
295C22×C113#48011yescharacteristic
296C22×C113#48211yescharacteristic
297C4×C113—21no—
298C4×C113—21no—
299C4×C113—21no—
300C4×C113—21no—
301C4×C113—82no—
302C4×C113—82no—
303C4×C113—81no—
304C4×C113—81no—
305C4×C113—81no—
306C4×C113—81no—
307#10394C11311yesmaximal, characteristic, direct product factor, Sylow
308C2×C113—21no—
309C2×C113—21no—
310C2×C113—21no—
311C2×C113—21no—
312C2×C113—82no—
313C2×C113—161no—
314C2×C113#159511yescharacteristic
315C2×C113#160611yescharacteristic
316C2×C113#160711yescharacteristic
317C2×C113#161811yescharacteristic
318C2×C113#203311yescharacteristic
319C2×C113#203711yescharacteristic
320C2×C113#204411yescharacteristic
321#2617C2×C11311yescharacteristic
322#1874C2×C11311yescharacteristic, complemented
323#1852C2×C11311yescharacteristic, complemented
324C2×#327C2×C11311yescharacteristic, complemented
325C2×#323C2×C11311yescharacteristic, complemented
326#1439C2×C11311yescharacteristic, complemented
327#1294C2×C11311yescharacteristic, complemented
328C113#1039411yescharacteristic, direct product factor, Sylow
329C2×#121C22×C11311yescharacteristic
330C2×#120—21no—
331C22×C4⋊C4C22×C11311yescharacteristic
332C22×C22⋊C4—21no—
333C22×C22⋊C4C22×C11311yescharacteristic
334C2×#107—21no—
335C2×#102—21no—
336C2×C22⋊C8C22×C11311yescharacteristic
337C2×C22⋊C8C22×C11311yescharacteristic
338#397—21no—
339#394—21no—
340#394—21no—
341#392—21no—
342#386—21no—
343#380C22×C11311yescharacteristic
344C2×#95—21no—
345C2×#95C22×C11311yescharacteristic
346#340—21no—
347#340—21no—
348#327—22no—
349#323—22no—
350C25D4×C11311yescharacteristic
351C22×D4—21no—
352C22×D4—21no—
353C22×D4—21no—
354C22×D4D4×C11311yescharacteristic
355C23×C4—21no—
356C23×C4—21no—
357C23×C4D4×C11311yescharacteristic
358C23×C4C23×C11311yescharacteristic
359C22×C8—21no—
360C22×C8—21no—
361#121—21no—
362#121—21no—
363#121—21no—
364#121—21no—
365#120—42no—
366#120—42no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—42no—
370C2×C4⋊C4D4×C11311yescharacteristic
371C2×C4⋊C4D4×C11311yescharacteristic
372C2×C4⋊C4D4×C11311yescharacteristic
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C22⋊C4—21no—
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C22⋊C4—42no—
386C2×C22⋊C4—42no—
387C2×C22⋊C4—42no—
388#107—42no—
389#102—42no—
390C22⋊C8—21no—
391C22⋊C8—21no—
392C22⋊C8—21no—
393C22⋊C8D4×C11312yescomplemented
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95—42no—
400C24—21no—
401C24—21no—
402C24—21no—
403C24—21no—
404C24—21no—
405C24—21no—
406C24—21no—
407C24—41no—
408C24—41no—
409C24—41no—
410C24—41no—
411C24D8×C11312yes—
412C24C2×D4×C11311yescharacteristic
413C2×D4—21no—
414C2×D4—21no—
415C2×D4—41no—
416C2×D4—41no—
417C2×D4—42no—
418C2×D4—42no—
419C2×D4—41no—
420C2×D4—41no—
421C2×D4—41no—
422C2×D4—41no—
423C2×D4—41no—
424C2×D4—41no—
425C2×D4—81no—
426C2×D4—81no—
427C2×D4—81no—
428C2×D4—81no—
429C22×C4—22no—
430C22×C4—22no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4—41no—
453C22×C4C2×D4×C11311yescharacteristic
454C22×C4C2×D4×C11311yescharacteristic
455C22×C4C2×D4×C11311yescharacteristic
456C22×C4#41×C11311yescharacteristic
457C22×C4#41×C11311yescharacteristic
458C22×C4#41×C11311yescharacteristic
459C2×C8—22no—
460C2×C8—41no—
461C2×C8—41no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C4⋊C4—22no—
466C4⋊C4—22no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—41no—
470C4⋊C4—41no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C22⋊C4—42no—
474C22⋊C4—42no—
475C22⋊C4—48no—
476C22⋊C4—41no—
477C22⋊C4—41no—
478C22⋊C4—41no—
479C22⋊C4—41no—
480C22⋊C4—41no—
481C22⋊C4—41no—
482C22⋊C4—41no—
483C22⋊C4—41no—
484C22⋊C4—81no—
485C22⋊C4—81no—
486C23—21no—
487C23—21no—
488C23—21no—
489C23—21no—
490C23—22no—
491C23—22no—
492C23—22no—
493C23—42no—
494C23—42no—
495C23—42no—
496C23—42no—
497C23—42no—
498C23—42no—
499C23—41no—
500C23—41no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23—41no—
508C23—41no—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—41no—
514C23—81no—
515C23—81no—
516C23—81no—
517C23—81no—
518C23—81no—
519C23—81no—
520C23#120×C11311yescharacteristic
521C23#121×C11311yescharacteristic
522C23#123×C11311yescharacteristic
523C23C2×D8×C11311yescharacteristic
524C23#135×C11311yescharacteristic
525C23AGL(1,ℤ/8)×C11311yescharacteristic
526C23#137×C11311yescharacteristic
527D4—42no—
528D4—81no—
529D4—84no—
530D4—84no—
531D4—81no—
532D4—81no—
533D4—81no—
534D4—81no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—42no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4—41no—
558C2×C4—41no—
559C2×C4—42no—
560C2×C4—41no—
561C2×C4—41no—
562C2×C4—81no—
563C2×C4—81no—
564C2×C4—81no—
565C2×C4—81no—
566C2×C4—81no—
567C2×C4—81no—
568C2×C4—81no—
569C2×C4—81no—
570C2×C4—81no—
571C2×C4#121×C11311yescharacteristic
572C2×C4#121×C11311yescharacteristic
573C2×C4#123×C11311yescharacteristic
574C2×C4#124×C11311yescharacteristic
575C8—42no—
576C8—81no—
577C22—21no—
578C22—21no—
579C22—21no—
580C22—21no—
581C22—21no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—44no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—82no—
594C22—82no—
595C22—82no—
596C22—81no—
597C22—81no—
598C22—81no—
599C22—81no—
600C22—81no—
601C22—81no—
602C22—81no—
603C22—81no—
604C22—81no—
605C22—81no—
606C22—81no—
607C22#394×C11311yescharacteristic
608C22#447×C11311yescharacteristic
609C22#452×C11311yescharacteristic
610C22#453×C11311yescharacteristic
611C22#455×C11311yescharacteristic
612C22B(4,𝔽2)×C11311yescharacteristic
613C22#458×C11311yescharacteristic
614C22#466×C11311yescharacteristic
615C22#468×C11311yescharacteristic
616C22#480×C11311yescharacteristic
617C22#482×C11311yescharacteristic
618C4—21no—
619C4—21no—
620C4—21no—
621C4—21no—
622C4—82no—
623C4—81no—
624C4—81no—
625C4—82no—
626C4—81no—
627C4—81no—
628C2—21no—
629C2—21no—
630C2—21no—
631C2—21no—
632C2—82no—
633C2—161no—
634C2C113×#159511yescharacteristic
635C2C113×#160611yescharacteristic
636C2C113×#160711yescharacteristic
637C2C113×#161811yescharacteristic
638C2C113×#203311yescharacteristic
639C2C113×#203711yescharacteristic
640C2C113×#204411yescharacteristic
subgroupG/H
center, socleC23×C113#120
commutator, Frattini, cosocleC23×C4C23×C113
prime radicalC113×#2617C2
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C113 ◁ C23×C4×C113 ◁ G

Complements

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

NH ≅ G/Ntype
2. C113×#1874C2semidirect
3. C113×#1852C2semidirect
4. C2×#327×C113C2semidirect
5. C2×#323×C113C2semidirect
6. C113×#1439C2semidirect
7. C113×#1294C2semidirect
72. C22⋊C8×C113D4semidirect
307. #10394C113direct (N × H)
322. #1874C2×C113semidirect
323. #1852C2×C113semidirect
324. C2×#327C2×C113semidirect
325. C2×#323C2×C113semidirect
326. #1439C2×C113semidirect
327. #1294C2×C113semidirect
328. C113#10394direct (N × H)
393. C22⋊C8D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#26172
C113×#18742
C113×#18522
C2×#327×C1132
C2×#323×C1132
C113×#14392
C113×#12942
#10394113