Finite Group Databasebeta

← C113×#18434 #43286454

Subgroups — C113×#18434 #43286454

Order 28928.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C113×#3560C211yesmaximal, characteristic, complemented
2C113×#3213C211yesmaximal, characteristic, complemented
3C113×#3211C211yesmaximal, characteristic, complemented
4C113×#2662C211yesmaximal, characteristic, complemented
5C113×#1606C211yesmaximal, characteristic, complemented
6C113×#1604C211yesmaximal, characteristic, complemented
7C113×#1603C211yesmaximal, characteristic, complemented
8C113×#1601C211yesmaximal, characteristic, complemented
9C113×#1600C211yesmaximal, characteristic, complemented
10C113×#1598C211yesmaximal, characteristic, complemented
11C113×#1597C211yesmaximal, characteristic, complemented
12C113×#1595C211yesmaximal, characteristic, complemented
13C113×#1509C211yesmaximal, characteristic, complemented
14C113×#1502C211yesmaximal, characteristic, complemented
15C113×#1473C211yesmaximal, characteristic, complemented
16#563×C113—21no—
17#560×C113—21no—
18#553×C113—21no—
19#553×C113—21no—
20#551×C113—21no—
21#547×C113—21no—
22#546×C113—21no—
23#546×C113—21no—
24#542×C113—21no—
25#539×C113—21no—
26#539×C113C2211yescharacteristic
27#538×C113—21no—
28#538×C113—21no—
29#538×C113C2211yescharacteristic
30#537×C113C2211yescharacteristic
31#534×C113C2211yescharacteristic
32#532×C113C2211yescharacteristic
33#529×C113C2211yescharacteristic
34C2×#126×C113C2211yescharacteristic
35C2×#124×C113C2211yescharacteristic, complemented
36#496×C113—21no—
37#495×C113—21no—
38#489×C113—21no—
39#488×C113—21no—
40#464×C113—21no—
41#463×C113—21no—
42#463×C113—21no—
43#463×C113—21no—
44#451×C113C2211yescharacteristic, complemented
45#450×C113C2211yescharacteristic, complemented
46#448×C113C2211yescharacteristic
47#448×C113C2211yescharacteristic
48#448×C113C2211yescharacteristic, complemented
49#447×C113C2211yescharacteristic
50#447×C113C2211yescharacteristic
51#447×C113C2211yescharacteristic, complemented
52#432×C113C2211yescharacteristic, complemented
53#431×C113C2211yescharacteristic, complemented
54#396×C113—21no—
55#395×C113C2211yescharacteristic, complemented
56#394×C113—21no—
57#394×C113C2211yescharacteristic, complemented
58#393×C113C2211yescharacteristic
59#392×C113C2211yescharacteristic
60#390×C113—21no—
61#388×C113—21no—
62C4×C4⋊C4×C113C2211yescharacteristic, complemented
63#328×C113C2211yescharacteristic, complemented
64#328×C113C2211yescharacteristic, complemented
65#327×C113C2211yescharacteristic
66#327×C113C2211yescharacteristic
67#327×C113C2211yescharacteristic
68#327×C113C2211yescharacteristic
69#327×C113C2211yescharacteristic, complemented
70#327×C113C2211yescharacteristic, complemented
71#324×C113C2211yescharacteristic, complemented
72#324×C113C2211yescharacteristic, complemented
73#323×C113C2211yescharacteristic
74#323×C113C2211yescharacteristic
75C2×#41×C113—21no—
76C2×#41×C113—21no—
77C22×Q8×C113C2311yescharacteristic
78C22×D4×C113—21no—
79C22×D4×C113—21no—
80C22×D4×C113C2311yescharacteristic
81C2×Q16×C113—21no—
82C2×SD16×C113—21no—
83C2×SD16×C113—21no—
84C2×SD16×C113—21no—
85C2×SD16×C113—21no—
86C2×D8×C113—21no—
87C2×D8×C113—21no—
88C2×D8×C113—21no—
89C4⋊Q8×C113—21no—
90C4⋊Q8×C113D411yescharacteristic, complemented
91#127×C113D411yescharacteristic, complemented
92#126×C113—21no—
93#126×C113—21no—
94#126×C113—21no—
95#126×C113—21no—
96#126×C113—21no—
97#126×C113—21no—
98#126×C113—21no—
99#126×C113—21no—
100#126×C113—21no—
101#125×C113—21no—
102#125×C113—21no—
103#125×C113D411yescharacteristic, complemented
104#124×C113—21no—
105#124×C113—21no—
106#124×C113—21no—
107#124×C113—21no—
108#124×C113—21no—
109#124×C113—21no—
110#124×C113—21no—
111#124×C113—21no—
112#124×C113D411yescharacteristic, complemented
113#123×C113—21no—
114#123×C113—21no—
115#123×C113—21no—
116#123×C113—21no—
117#123×C113—21no—
118#123×C113—21no—
119#123×C113—21no—
120#123×C113—21no—
121#123×C113—21no—
122#123×C113—21no—
123#123×C113—21no—
124#123×C113—21no—
125C22⋊Q8×C113—21no—
126C22⋊Q8×C113—21no—
127C22⋊Q8×C113—21no—
128C22⋊Q8×C113—21no—
129C22⋊Q8×C113—21no—
130C22⋊Q8×C113—21no—
131C22⋊Q8×C113—21no—
132C22⋊Q8×C113C2311yescharacteristic
133#121×C113—21no—
134#121×C113—21no—
135#121×C113—21no—
136#121×C113—21no—
137#121×C113—21no—
138#121×C113—21no—
139#121×C113—21no—
140#121×C113—21no—
141#121×C113—21no—
142#121×C113—21no—
143#121×C113—21no—
144#121×C113—21no—
145#121×C113C2311yescharacteristic
146#121×C113C2311yescharacteristic
147#121×C113C2311yescharacteristic
148#120×C113—21no—
149#120×C113—21no—
150#120×C113—21no—
151#120×C113—21no—
152#120×C113—21no—
153C4×Q8×C113D411yescharacteristic, complemented
154C4×D4×C113—21no—
155C4×D4×C113—21no—
156C4×D4×C113—21no—
157C4×D4×C113—21no—
158C4×D4×C113—21no—
159C4×D4×C113—21no—
160C4×D4×C113—21no—
161C4×D4×C113—21no—
162C4×D4×C113D411yescharacteristic, complemented
163C4×D4×C113D411yescharacteristic, complemented
164C4×D4×C113D411yescharacteristic, complemented
165#117×C113—21no—
166#117×C113—21no—
167C2×C4⋊C4×C113—21no—
168C2×C4⋊C4×C113—21no—
169C2×C4⋊C4×C113—21no—
170C2×C4⋊C4×C113D411yescharacteristic
171C2×C4⋊C4×C113D411yescharacteristic
172C2×C4⋊C4×C113C2311yescharacteristic
173C2×C22⋊C4×C113—21no—
174C2×C22⋊C4×C113—21no—
175C2×C22⋊C4×C113—21no—
176C2×C22⋊C4×C113—21no—
177C2×C22⋊C4×C113—21no—
178C2×C22⋊C4×C113—21no—
179C2×C22⋊C4×C113—21no—
180C2×C22⋊C4×C113—21no—
181C2×C22⋊C4×C113D411yescharacteristic
182C2×C22⋊C4×C113D411yescharacteristic
183C2×C22⋊C4×C113C2311yescharacteristic
184C2×C42×C113—21no—
185C2×C42×C113C2311yescharacteristic
186C4⋊C8×C113—21no—
187C4⋊C8×C113—21no—
188#103×C113—21no—
189#103×C113—21no—
190#103×C113—21no—
191#103×C113—21no—
192#102×C113—21no—
193#102×C113—21no—
194#102×C113—21no—
195#102×C113—21no—
196C22⋊C8×C113C2311yescharacteristic
197C22⋊C8×C113C2311yescharacteristic
198C22⋊C8×C113C2311yescharacteristic
199C22⋊C8×C113C2311yescharacteristic
200#97×C113—21no—
201C4×C8×C113—21no—
202#95×C113—21no—
203#95×C113—21no—
204#95×C113C2311yescharacteristic
205#95×C113C2311yescharacteristic
206C24×C113—21no—
207C24×C113—21no—
208C24×C113C2×D411yescharacteristic
209#41×C113—81no—
210#41×C113—81no—
211#41×C113—81no—
212#41×C113—81no—
213C2×Q8×C113—21no—
214C2×Q8×C113—21no—
215C2×Q8×C113—21no—
216C2×Q8×C113—21no—
217C2×Q8×C113—81no—
218C2×Q8×C113C2×D411yescharacteristic
219C2×D4×C113—21no—
220C2×D4×C113—21no—
221C2×D4×C113—21no—
222C2×D4×C113—21no—
223C2×D4×C113—21no—
224C2×D4×C113—21no—
225C2×D4×C113—21no—
226C2×D4×C113—21no—
227C2×D4×C113—21no—
228C2×D4×C113—21no—
229C2×D4×C113—21no—
230C2×D4×C113—21no—
231C2×D4×C113—21no—
232C2×D4×C113—21no—
233C2×D4×C113—42no—
234C2×D4×C113—81no—
235C2×D4×C113—81no—
236C2×D4×C113—81no—
237C2×D4×C113—81no—
238C2×D4×C113—81no—
239C2×D4×C113C2×D411yescharacteristic
240C2×D4×C113C2×D411yescharacteristic
241C2×D4×C113C2×D411yescharacteristic
242C22×C4×C113—21no—
243C22×C4×C113—21no—
244C22×C4×C113—21no—
245C22×C4×C113—21no—
246C22×C4×C113—21no—
247C22×C4×C113—21no—
248C22×C4×C113—21no—
249C22×C4×C113—21no—
250C22×C4×C113—21no—
251C22×C4×C113—21no—
252C22×C4×C113—21no—
253C22×C4×C113C2×D411yescharacteristic
254C22×C4×C113C2×D411yescharacteristic
255C22×C4×C113C2×D411yescharacteristic
256C22×C4×C113C2×D411yescharacteristic
257C22×C4×C113C2×D411yescharacteristic
258C22×C4×C113C2411yescharacteristic
259Q16×C113—81no—
260SD16×C113—81no—
261SD16×C113—81no—
262SD16×C113—81no—
263SD16×C113—81no—
264D8×C113—81no—
265D8×C113—81no—
266D8×C113—81no—
267C2×C8×C113—21no—
268C2×C8×C113—21no—
269C2×C8×C113—21no—
270C2×C8×C113—21no—
271C4⋊C4×C113—21no—
272C4⋊C4×C113—21no—
273C4⋊C4×C113—21no—
274C4⋊C4×C113—21no—
275C4⋊C4×C113—21no—
276C4⋊C4×C113—21no—
277C4⋊C4×C113—21no—
278C4⋊C4×C113—21no—
279C4⋊C4×C113—21no—
280C4⋊C4×C113—21no—
281C4⋊C4×C113—21no—
282C4⋊C4×C113—21no—
283C4⋊C4×C113—21no—
284C4⋊C4×C113—21no—
285C4⋊C4×C113—21no—
286C4⋊C4×C113—21no—
287C4⋊C4×C113—21no—
288C4⋊C4×C113—42no—
289C4⋊C4×C113—81no—
290C4⋊C4×C113C2×D411yescharacteristic
291C4⋊C4×C113C2×D411yescharacteristic
292C4⋊C4×C113C2×D411yescharacteristic
293C4⋊C4×C113C2×D411yescharacteristic
294C22⋊C4×C113—21no—
295C22⋊C4×C113—21no—
296C22⋊C4×C113—21no—
297C22⋊C4×C113—21no—
298C22⋊C4×C113—21no—
299C22⋊C4×C113—21no—
300C22⋊C4×C113—21no—
301C22⋊C4×C113—21no—
302C22⋊C4×C113—21no—
303C22⋊C4×C113—21no—
304C22⋊C4×C113—21no—
305C22⋊C4×C113—21no—
306C22⋊C4×C113—21no—
307C22⋊C4×C113—21no—
308C22⋊C4×C113—21no—
309C22⋊C4×C113—21no—
310C22⋊C4×C113—21no—
311C22⋊C4×C113—21no—
312C22⋊C4×C113—21no—
313C22⋊C4×C113—21no—
314C22⋊C4×C113—21no—
315C22⋊C4×C113—21no—
316C22⋊C4×C113—21no—
317C22⋊C4×C113—21no—
318C22⋊C4×C113—21no—
319C22⋊C4×C113—42no—
320C22⋊C4×C113—41no—
321C22⋊C4×C113—41no—
322C22⋊C4×C113—41no—
323C22⋊C4×C113—41no—
324C22⋊C4×C113—81no—
325C22⋊C4×C113—81no—
326C22⋊C4×C113—81no—
327C42×C113—21no—
328C42×C113—21no—
329C42×C113—21no—
330C42×C113—81no—
331C42×C113C2×D411yescharacteristic
332C42×C113C2×D411yescharacteristic
333C42×C113C2×D411yescharacteristic
334C42×C113C2×D411yescharacteristic
335C23×C113—21no—
336C23×C113—21no—
337C23×C113—21no—
338C23×C113—21no—
339C23×C113—21no—
340C23×C113—21no—
341C23×C113—41no—
342C23×C113—41no—
343C23×C113—41no—
344C23×C113—41no—
345C23×C113—41no—
346C23×C113—41no—
347C23×C113—41no—
348C23×C113—41no—
349C23×C113—41no—
350C23×C113—81no—
351C23×C113—81no—
352C23×C113—81no—
353C23×C113C22×D411yescharacteristic
354Q8×C113—41no—
355Q8×C113—41no—
356Q8×C113—41no—
357Q8×C113—41no—
358Q8×C113—41no—
359Q8×C113—81no—
360Q8×C113—81no—
361D4×C113—41no—
362D4×C113—41no—
363D4×C113—41no—
364D4×C113—41no—
365D4×C113—41no—
366D4×C113—41no—
367D4×C113—41no—
368D4×C113—41no—
369D4×C113—41no—
370D4×C113—41no—
371D4×C113—41no—
372D4×C113—41no—
373D4×C113—41no—
374D4×C113—81no—
375D4×C113—81no—
376D4×C113—81no—
377D4×C113—81no—
378D4×C113—81no—
379D4×C113—81no—
380D4×C113—81no—
381D4×C113—81no—
382D4×C113—81no—
383D4×C113—84no—
384C2×C4×C113—21no—
385C2×C4×C113—21no—
386C2×C4×C113—22no—
387C2×C4×C113—21no—
388C2×C4×C113—21no—
389C2×C4×C113—21no—
390C2×C4×C113—21no—
391C2×C4×C113—21no—
392C2×C4×C113—21no—
393C2×C4×C113—21no—
394C2×C4×C113—21no—
395C2×C4×C113—21no—
396C2×C4×C113—21no—
397C2×C4×C113—41no—
398C2×C4×C113—41no—
399C2×C4×C113—41no—
400C2×C4×C113—41no—
401C2×C4×C113—41no—
402C2×C4×C113—41no—
403C2×C4×C113—41no—
404C2×C4×C113—41no—
405C2×C4×C113—41no—
406C2×C4×C113—41no—
407C2×C4×C113—41no—
408C2×C4×C113—41no—
409C2×C4×C113—81no—
410C2×C4×C113—81no—
411C2×C4×C113—81no—
412C2×C4×C113—81no—
413C2×C4×C113—81no—
414C2×C4×C113—81no—
415C2×C4×C113—81no—
416C2×C4×C113—81no—
417C2×C4×C113#12011yescharacteristic
418C2×C4×C113#12011yescharacteristic
419C2×C4×C113#12011yescharacteristic
420C2×C4×C113#12011yescharacteristic
421C2×C4×C113C22×D411yescharacteristic
422C2×C4×C113C22×D411yescharacteristic
423C8×C113—41no—
424C8×C113—41no—
425C8×C113—41no—
426C8×C113—41no—
427C22×C113—21no—
428C22×C113—21no—
429C22×C113—41no—
430C22×C113—41no—
431C22×C113—41no—
432C22×C113—41no—
433C22×C113—41no—
434C22×C113—41no—
435C22×C113—41no—
436C22×C113—41no—
437C22×C113—41no—
438C22×C113—41no—
439C22×C113—41no—
440C22×C113—41no—
441C22×C113—81no—
442C22×C113—81no—
443C22×C113—81no—
444C22×C113—81no—
445C22×C113—81no—
446C22×C113—81no—
447C22×C113—81no—
448C22×C113—81no—
449C22×C113—81no—
450C22×C113—162no—
451C22×C113C2×#12011yescharacteristic
452C22×C113#57611yescharacteristic
453C22×C113#57711yescharacteristic
454C4×C113—21no—
455C4×C113—21no—
456C4×C113—21no—
457C4×C113—21no—
458C4×C113—21no—
459C4×C113—21no—
460C4×C113—42no—
461C4×C113—41no—
462C4×C113—41no—
463C4×C113—41no—
464C4×C113—41no—
465C4×C113—41no—
466C4×C113—41no—
467C4×C113—41no—
468C4×C113—41no—
469C4×C113—81no—
470C4×C113—81no—
471#18434C11311yesmaximal, characteristic, direct product factor, Sylow
472C2×C113—21no—
473C2×C113—21no—
474C2×C113—81no—
475C2×C113—81no—
476C2×C113—81no—
477C2×C113—81no—
478C2×C113—161no—
479C2×C113#301211yescharacteristic
480C2×C113#301811yescharacteristic
481C2×C113#302711yescharacteristic
482#3560C2×C11311yescharacteristic, complemented
483#3213C2×C11311yescharacteristic, complemented
484#3211C2×C11311yescharacteristic, complemented
485#2662C2×C11311yescharacteristic, complemented
486#1606C2×C11311yescharacteristic, complemented
487#1604C2×C11311yescharacteristic, complemented
488#1603C2×C11311yescharacteristic, complemented
489#1601C2×C11311yescharacteristic, complemented
490#1600C2×C11311yescharacteristic, complemented
491#1598C2×C11311yescharacteristic, complemented
492#1597C2×C11311yescharacteristic, complemented
493#1595C2×C11311yescharacteristic, complemented
494#1509C2×C11311yescharacteristic, complemented
495#1502C2×C11311yescharacteristic, complemented
496#1473C2×C11311yescharacteristic, complemented
497C113#1843411yescharacteristic, direct product factor, Sylow
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C11311yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C11311yescharacteristic
512#537C22×C11311yescharacteristic
513#534C22×C11311yescharacteristic
514#532C22×C11311yescharacteristic
515#529C22×C11311yescharacteristic
516C2×#126C22×C11311yescharacteristic
517C2×#124C22×C11311yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C11311yescharacteristic, complemented
527#450C22×C11311yescharacteristic, complemented
528#448C22×C11311yescharacteristic
529#448C22×C11311yescharacteristic
530#448C22×C11311yescharacteristic, complemented
531#447C22×C11311yescharacteristic
532#447C22×C11311yescharacteristic
533#447C22×C11311yescharacteristic, complemented
534#432C22×C11311yescharacteristic, complemented
535#431C22×C11311yescharacteristic, complemented
536#396—21no—
537#395C22×C11311yescharacteristic, complemented
538#394—21no—
539#394C22×C11311yescharacteristic, complemented
540#393C22×C11311yescharacteristic
541#392C22×C11311yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C11311yescharacteristic, complemented
545#328C22×C11311yescharacteristic, complemented
546#328C22×C11311yescharacteristic, complemented
547#327C22×C11311yescharacteristic
548#327C22×C11311yescharacteristic
549#327C22×C11311yescharacteristic
550#327C22×C11311yescharacteristic
551#327C22×C11311yescharacteristic, complemented
552#327C22×C11311yescharacteristic, complemented
553#324C22×C11311yescharacteristic, complemented
554#324C22×C11311yescharacteristic, complemented
555#323C22×C11311yescharacteristic
556#323C22×C11311yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C11311yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C11311yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C11311yescharacteristic, complemented
573#127D4×C11311yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C11311yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C11311yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C11311yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C11311yescharacteristic
628#121C23×C11311yescharacteristic
629#121C23×C11311yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C11311yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C11311yescharacteristic, complemented
645C4×D4D4×C11311yescharacteristic, complemented
646C4×D4D4×C11311yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C11311yescharacteristic
653C2×C4⋊C4D4×C11311yescharacteristic
654C2×C4⋊C4C23×C11311yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C11311yescharacteristic
664C2×C22⋊C4D4×C11311yescharacteristic
665C2×C22⋊C4C23×C11311yescharacteristic
666C2×C42—21no—
667C2×C42C23×C11311yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C11311yescharacteristic
679C22⋊C8C23×C11311yescharacteristic
680C22⋊C8C23×C11311yescharacteristic
681C22⋊C8C23×C11311yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C11311yescharacteristic
687#95C23×C11311yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C11311yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C11311yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C11311yescharacteristic
722C2×D4C2×D4×C11311yescharacteristic
723C2×D4C2×D4×C11311yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C11311yescharacteristic
736C22×C4C2×D4×C11311yescharacteristic
737C22×C4C2×D4×C11311yescharacteristic
738C22×C4C2×D4×C11311yescharacteristic
739C22×C4C2×D4×C11311yescharacteristic
740C22×C4C24×C11311yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C11311yescharacteristic
773C4⋊C4C2×D4×C11311yescharacteristic
774C4⋊C4C2×D4×C11311yescharacteristic
775C4⋊C4C2×D4×C11311yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C11311yescharacteristic
814C42C2×D4×C11311yescharacteristic
815C42C2×D4×C11311yescharacteristic
816C42C2×D4×C11311yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C11311yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C11311yescharacteristic
900C2×C4#120×C11311yescharacteristic
901C2×C4#120×C11311yescharacteristic
902C2×C4#120×C11311yescharacteristic
903C2×C4C22×D4×C11311yescharacteristic
904C2×C4C22×D4×C11311yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C11311yescharacteristic
934C22#576×C11311yescharacteristic
935C22#577×C11311yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C113×#301211yescharacteristic
961C2C113×#301811yescharacteristic
962C2C113×#302711yescharacteristic
subgroupG/H
center, socleC22×C113C2×#120
commutator, Frattini, cosocleC22×C4C24×C113
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C113 ◁ C2×C42×C113 ◁ G

Complements

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

NH ≅ G/Ntype
1. C113×#3560C2semidirect
2. C113×#3213C2semidirect
3. C113×#3211C2semidirect
4. C113×#2662C2semidirect
5. C113×#1606C2semidirect
6. C113×#1604C2semidirect
7. C113×#1603C2semidirect
8. C113×#1601C2semidirect
9. C113×#1600C2semidirect
10. C113×#1598C2semidirect
11. C113×#1597C2semidirect
12. C113×#1595C2semidirect
13. C113×#1509C2semidirect
14. C113×#1502C2semidirect
15. C113×#1473C2semidirect
35. C2×#124×C113C22semidirect
44. #451×C113C22semidirect
45. #450×C113C22semidirect
48. #448×C113C22semidirect
51. #447×C113C22semidirect
52. #432×C113C22semidirect
53. #431×C113C22semidirect
55. #395×C113C22semidirect
57. #394×C113C22semidirect
62. C4×C4⋊C4×C113C22semidirect
63. #328×C113C22semidirect
64. #328×C113C22semidirect
69. #327×C113C22semidirect
70. #327×C113C22semidirect
71. #324×C113C22semidirect
72. #324×C113C22semidirect
90. C4⋊Q8×C113D4semidirect
91. #127×C113D4semidirect
103. #125×C113D4semidirect
112. #124×C113D4semidirect
153. C4×Q8×C113D4semidirect
162. C4×D4×C113D4semidirect
163. C4×D4×C113D4semidirect
164. C4×D4×C113D4semidirect
471. #18434C113direct (N × H)
482. #3560C2×C113semidirect
483. #3213C2×C113semidirect
484. #3211C2×C113semidirect
485. #2662C2×C113semidirect
486. #1606C2×C113semidirect
487. #1604C2×C113semidirect
488. #1603C2×C113semidirect
489. #1601C2×C113semidirect
490. #1600C2×C113semidirect
491. #1598C2×C113semidirect
492. #1597C2×C113semidirect
493. #1595C2×C113semidirect
494. #1509C2×C113semidirect
495. #1502C2×C113semidirect
496. #1473C2×C113semidirect
497. C113#18434direct (N × H)
517. C2×#124C22×C113semidirect
526. #451C22×C113semidirect
527. #450C22×C113semidirect
530. #448C22×C113semidirect
533. #447C22×C113semidirect
534. #432C22×C113semidirect
535. #431C22×C113semidirect
537. #395C22×C113semidirect
539. #394C22×C113semidirect
544. C4×C4⋊C4C22×C113semidirect
545. #328C22×C113semidirect
546. #328C22×C113semidirect
551. #327C22×C113semidirect
552. #327C22×C113semidirect
553. #324C22×C113semidirect
554. #324C22×C113semidirect
572. C4⋊Q8D4×C113semidirect
573. #127D4×C113semidirect
585. #125D4×C113semidirect
594. #124D4×C113semidirect
635. C4×Q8D4×C113semidirect
644. C4×D4D4×C113semidirect
645. C4×D4D4×C113semidirect
646. C4×D4D4×C113semidirect

Maximal subgroups

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

subgroupindex
C113×#35602
C113×#32132
C113×#32112
C113×#26622
C113×#16062
C113×#16042
C113×#16032
C113×#16012
C113×#16002
C113×#15982
C113×#15972
C113×#15952
C113×#15092
C113×#15022
C113×#14732
#18434113