Finite Group Databasebeta

← C103×#33833 #39939108

Subgroups — C103×#33833 #39939108

Order 26368.

692 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#509×C103C211yesmaximal, characteristic, complemented
2C2×#508×C103C211yesmaximal, characteristic, complemented
3C103×#3283C211yesmaximal, characteristic, complemented
4C103×#3280C211yesmaximal, characteristic, complemented
5C103×#2251C211yesmaximal, characteristic, complemented
6C103×#2219C211yesmaximal, characteristic, complemented
7C103×#2217C211yesmaximal, characteristic, complemented
8C103×#2210C211yesmaximal, characteristic, complemented
9C103×#2208C211yesmaximal, characteristic, complemented
10C103×#2189C211yesmaximal, characteristic, complemented
11C103×#2189C211yesmaximal, characteristic, complemented
12C103×#2187C211yesmaximal, characteristic, complemented
13C103×#2186C211yesmaximal, characteristic, complemented
14C103×#2177C211yesmaximal, characteristic, complemented
15C103×#2168C211yesmaximal, characteristic, complemented
16C2×#135×C103C2211yescharacteristic
17C2×#135×C103C2211yescharacteristic
18C2×#135×C103C2211yescharacteristic, complemented
19C22×D8×C103C2211yescharacteristic
20#547×C103—21no—
21#546×C103—21no—
22#509×C103—24no—
23#508×C103—24no—
24C2×Q32×C103C2211yescharacteristic, complemented
25C2×Q32×C103C2211yescharacteristic, complemented
26C2×SD32×C103C2211yescharacteristic
27C2×SD32×C103C2211yescharacteristic
28C2×SD32×C103C2211yescharacteristic
29C2×SD32×C103C2211yescharacteristic
30C2×SD32×C103C2211yescharacteristic, complemented
31C2×D16×C103C2211yescharacteristic
32C2×D16×C103C2211yescharacteristic
33C2×M32×C103C2211yescharacteristic
34C22×C16×C103C2211yescharacteristic, complemented
35#495×C103C2211yescharacteristic
36#494×C103C2211yescharacteristic, complemented
37#467×C103C2211yescharacteristic
38#467×C103C2211yescharacteristic
39#467×C103C2211yescharacteristic, complemented
40#466×C103C2211yescharacteristic
41#463×C103—21no—
42#461×C103—21no—
43#452×C103—21no—
44#452×C103—21no—
45#450×C103—21no—
46#449×C103—21no—
47C4×D8×C103C2211yescharacteristic
48C4×D8×C103C2211yescharacteristic, complemented
49C8×D4×C103C2211yescharacteristic
50#367×C103C2211yescharacteristic, complemented
51C4⋊C16×C103C2211yescharacteristic, complemented
52#358×C103C2211yescharacteristic, complemented
53#358×C103C2211yescharacteristic, complemented
54#358×C103C2211yescharacteristic, complemented
55#357×C103C2211yescharacteristic
56#357×C103C2211yescharacteristic
57#357×C103C2211yescharacteristic, complemented
58C22⋊C16×C103C2211yescharacteristic
59C22⋊C16×C103C2211yescharacteristic, complemented
60#346×C103C2211yescharacteristic, complemented
61C2×#41×C103—21no—
62C2×#41×C103—21no—
63C2×#41×C103—21no—
64C22×D4×C103—21no—
65#135×C103—22no—
66#135×C103—22no—
67#135×C103—22no—
68#135×C103—41no—
69#135×C103—41no—
70#135×C103—41no—
71C2×Q16×C103—21no—
72C2×Q16×C103C2311yescharacteristic
73C2×Q16×C103C2311yescharacteristic
74C2×Q16×C103C2311yescharacteristic
75C2×SD16×C103—21no—
76C2×SD16×C103—21no—
77C2×SD16×C103—21no—
78C2×SD16×C103—21no—
79C2×D8×C103—22no—
80C2×D8×C103—21no—
81C2×D8×C103—41no—
82C2×D8×C103C2311yescharacteristic
83C2×D8×C103C2311yescharacteristic
84C2×D8×C103C2311yescharacteristic
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87C4⋊Q8×C103—21no—
88#124×C103—21no—
89#123×C103—41no—
90#123×C103—41no—
91#123×C103—41no—
92C22⋊Q8×C103—21no—
93C22⋊Q8×C103—21no—
94C22⋊Q8×C103—21no—
95#121×C103—21no—
96#121×C103—41no—
97#121×C103—41no—
98#120×C103—41no—
99C4×D4×C103—21no—
100C4×D4×C103—21no—
101C4×D4×C103D411yescharacteristic
102C2×C4⋊C4×C103—41no—
103C2×C22⋊C4×C103—41no—
104Q32×C103—22no—
105Q32×C103—41no—
106SD32×C103—22no—
107SD32×C103—22no—
108SD32×C103—22no—
109SD32×C103—22no—
110SD32×C103—41no—
111D16×C103—22no—
112D16×C103D414yescomplemented
113M32×C103—22no—
114C2×C16×C103—22no—
115C2×C16×C103C2311yescharacteristic
116C2×C16×C103C2311yescharacteristic
117C2×C16×C103C2311yescharacteristic
118C2×C16×C103C2311yescharacteristic
119#107×C103C2311yescharacteristic
120#107×C103C2311yescharacteristic
121C4⋊C8×C103D411yescharacteristic
122#103×C103—21no—
123#103×C103—21no—
124#103×C103—21no—
125#102×C103—21no—
126#102×C103—21no—
127#102×C103—21no—
128C22⋊C8×C103D411yescharacteristic
129C22⋊C8×C103D411yescharacteristic
130C4×C8×C103C2311yescharacteristic
131C24×C103—41no—
132#41×C103—42no—
133#41×C103—42no—
134#41×C103—42no—
135#41×C103—81no—
136#41×C103—81no—
137#41×C103—81no—
138C2×Q8×C103—21no—
139C2×Q8×C103—21no—
140C2×Q8×C103—21no—
141C2×D4×C103—21no—
142C2×D4×C103—21no—
143C2×D4×C103—21no—
144C2×D4×C103—42no—
145C2×D4×C103—41no—
146C2×D4×C103—41no—
147C2×D4×C103—41no—
148C2×D4×C103—41no—
149C2×D4×C103—41no—
150C2×D4×C103—81no—
151C2×D4×C103D811yescharacteristic
152C22×C4×C103—41no—
153C22×C4×C103—41no—
154C22×C4×C103—41no—
155C22×C4×C103—41no—
156C22×C4×C103—41no—
157C22×C4×C103C2×D411yescharacteristic
158C22×C4×C103C2×D411yescharacteristic
159Q16×C103—21no—
160Q16×C103—21no—
161Q16×C103—21no—
162Q16×C103—21no—
163Q16×C103—21no—
164Q16×C103—21no—
165Q16×C103—81no—
166SD16×C103—42no—
167SD16×C103—42no—
168SD16×C103—42no—
169SD16×C103—81no—
170D8×C103—21no—
171D8×C103—21no—
172D8×C103—21no—
173D8×C103—21no—
174D8×C103—42no—
175D8×C103C2×D412yes—
176D8×C103C2×D412yes—
177C2×C8×C103—21no—
178C2×C8×C103—21no—
179C2×C8×C103—21no—
180C2×C8×C103—21no—
181C2×C8×C103C2×D411yescharacteristic
182C2×C8×C103C2×D411yescharacteristic
183C2×C8×C103C2×D411yescharacteristic
184C2×C8×C103C2411yescharacteristic
185C4⋊C4×C103—21no—
186C4⋊C4×C103—21no—
187C4⋊C4×C103—41no—
188C4⋊C4×C103—41no—
189C4⋊C4×C103—41no—
190C4⋊C4×C103—41no—
191C4⋊C4×C103—41no—
192C4⋊C4×C103D811yescharacteristic
193C22⋊C4×C103—41no—
194C22⋊C4×C103—41no—
195C22⋊C4×C103—41no—
196C22⋊C4×C103—41no—
197C22⋊C4×C103—41no—
198C22⋊C4×C103—41no—
199C22⋊C4×C103—41no—
200C22⋊C4×C103—41no—
201C22⋊C4×C103D811yescharacteristic
202C22⋊C4×C103D811yescharacteristic
203C42×C103C2×D411yescharacteristic
204C16×C103—21no—
205C16×C103—21no—
206C16×C103—21no—
207C16×C103C2×D412yes—
208C23×C103—41no—
209C23×C103—41no—
210C23×C103—41no—
211C23×C103—82no—
212C23×C103—82no—
213C23×C103—161no—
214C23×C103C2×D811yescharacteristic
215C23×C103C2×D811yescharacteristic
216Q8×C103—41no—
217Q8×C103—41no—
218Q8×C103—41no—
219Q8×C103—41no—
220Q8×C103—41no—
221Q8×C103—41no—
222D4×C103—22no—
223D4×C103—22no—
224D4×C103—41no—
225D4×C103—41no—
226D4×C103—41no—
227D4×C103—41no—
228D4×C103—41no—
229D4×C103—82no—
230D4×C103—82no—
231D4×C103—82no—
232D4×C103—82no—
233D4×C103—161no—
234C2×C4×C103—21no—
235C2×C4×C103—21no—
236C2×C4×C103—21no—
237C2×C4×C103—21no—
238C2×C4×C103—41no—
239C2×C4×C103—41no—
240C2×C4×C103—41no—
241C2×C4×C103—41no—
242C2×C4×C103—41no—
243C2×C4×C103—82no—
244C2×C4×C103—82no—
245C2×C4×C103—82no—
246C2×C4×C103—82no—
247C2×C4×C103—161no—
248C2×C4×C103C2×D811yescharacteristic
249C2×C4×C103C2×D811yescharacteristic
250C2×C4×C103C2×D811yescharacteristic
251C2×C4×C103C2×D811yescharacteristic
252C2×C4×C103C22×D411yescharacteristic
253C8×C103—21no—
254C8×C103—21no—
255C8×C103—21no—
256C8×C103C22×D411yescharacteristic
257C8×C103H(5,𝔽2)11yescharacteristic
258C22×C103—21no—
259C22×C103—21no—
260C22×C103—21no—
261C22×C103—21no—
262C22×C103—21no—
263C22×C103—21no—
264C22×C103—42no—
265C22×C103—42no—
266C22×C103—81no—
267C22×C103—81no—
268C22×C103—81no—
269C22×C103—81no—
270C22×C103—81no—
271C22×C103—81no—
272C22×C103—81no—
273C22×C103—164no—
274C22×C103C22×D811yescharacteristic
275C4×C103—21no—
276C4×C103—21no—
277C4×C103—21no—
278C4×C103—21no—
279C4×C103—81no—
280C4×C103—81no—
281C4×C103—81no—
282C4×C103—81no—
283C4×C103—81no—
284C4×C103D4211yescharacteristic
285C4×C103#57611yescharacteristic
286#33833C10311yesmaximal, characteristic, direct product factor, Sylow
287C2×C103—41no—
288C2×C103—41no—
289C2×C103—82no—
290C2×C103—82no—
291C2×C103—161no—
292C2×C103D4×D811yescharacteristic
293C2×C103#341411yescharacteristic
294C2×C103#341611yescharacteristic
295C2×#509C2×C10311yescharacteristic, complemented
296C2×#508C2×C10311yescharacteristic, complemented
297#3283C2×C10311yescharacteristic, complemented
298#3280C2×C10311yescharacteristic, complemented
299#2251C2×C10311yescharacteristic, complemented
300#2219C2×C10311yescharacteristic, complemented
301#2217C2×C10311yescharacteristic, complemented
302#2210C2×C10311yescharacteristic, complemented
303#2208C2×C10311yescharacteristic, complemented
304#2189C2×C10311yescharacteristic, complemented
305#2189C2×C10311yescharacteristic, complemented
306#2187C2×C10311yescharacteristic, complemented
307#2186C2×C10311yescharacteristic, complemented
308#2177C2×C10311yescharacteristic, complemented
309#2168C2×C10311yescharacteristic, complemented
310C103#3383311yescharacteristic, direct product factor, Sylow
311C2×#135C22×C10311yescharacteristic
312C2×#135C22×C10311yescharacteristic
313C2×#135C22×C10311yescharacteristic, complemented
314C22×D8C22×C10311yescharacteristic
315#547—21no—
316#546—21no—
317#509—24no—
318#508—24no—
319C2×Q32C22×C10311yescharacteristic, complemented
320C2×Q32C22×C10311yescharacteristic, complemented
321C2×SD32C22×C10311yescharacteristic
322C2×SD32C22×C10311yescharacteristic
323C2×SD32C22×C10311yescharacteristic
324C2×SD32C22×C10311yescharacteristic
325C2×SD32C22×C10311yescharacteristic, complemented
326C2×D16C22×C10311yescharacteristic
327C2×D16C22×C10311yescharacteristic
328C2×M32C22×C10311yescharacteristic
329C22×C16C22×C10311yescharacteristic, complemented
330#495C22×C10311yescharacteristic
331#494C22×C10311yescharacteristic, complemented
332#467C22×C10311yescharacteristic
333#467C22×C10311yescharacteristic
334#467C22×C10311yescharacteristic, complemented
335#466C22×C10311yescharacteristic
336#463—21no—
337#461—21no—
338#452—21no—
339#452—21no—
340#450—21no—
341#449—21no—
342C4×D8C22×C10311yescharacteristic
343C4×D8C22×C10311yescharacteristic, complemented
344C8×D4C22×C10311yescharacteristic
345#367C22×C10311yescharacteristic, complemented
346C4⋊C16C22×C10311yescharacteristic, complemented
347#358C22×C10311yescharacteristic, complemented
348#358C22×C10311yescharacteristic, complemented
349#358C22×C10311yescharacteristic, complemented
350#357C22×C10311yescharacteristic
351#357C22×C10311yescharacteristic
352#357C22×C10311yescharacteristic, complemented
353C22⋊C16C22×C10311yescharacteristic
354C22⋊C16C22×C10311yescharacteristic, complemented
355#346C22×C10311yescharacteristic, complemented
356C2×#41—21no—
357C2×#41—21no—
358C2×#41—21no—
359C22×D4—21no—
360#135—22no—
361#135—22no—
362#135—22no—
363#135—41no—
364#135—41no—
365#135—41no—
366C2×Q16—21no—
367C2×Q16C23×C10311yescharacteristic
368C2×Q16C23×C10311yescharacteristic
369C2×Q16C23×C10311yescharacteristic
370C2×SD16—21no—
371C2×SD16—21no—
372C2×SD16—21no—
373C2×SD16—21no—
374C2×D8—22no—
375C2×D8—21no—
376C2×D8—41no—
377C2×D8C23×C10311yescharacteristic
378C2×D8C23×C10311yescharacteristic
379C2×D8C23×C10311yescharacteristic
380C22×C8C23×C10311yescharacteristic
381C22×C8C23×C10311yescharacteristic
382C4⋊Q8—21no—
383#124—21no—
384#123—41no—
385#123—41no—
386#123—41no—
387C22⋊Q8—21no—
388C22⋊Q8—21no—
389C22⋊Q8—21no—
390#121—21no—
391#121—41no—
392#121—41no—
393#120—41no—
394C4×D4—21no—
395C4×D4—21no—
396C4×D4D4×C10311yescharacteristic
397C2×C4⋊C4—41no—
398C2×C22⋊C4—41no—
399Q32—22no—
400Q32—41no—
401SD32—22no—
402SD32—22no—
403SD32—22no—
404SD32—22no—
405SD32—41no—
406D16—22no—
407D16D4×C10314yescomplemented
408M32—22no—
409C2×C16—22no—
410C2×C16C23×C10311yescharacteristic
411C2×C16C23×C10311yescharacteristic
412C2×C16C23×C10311yescharacteristic
413C2×C16C23×C10311yescharacteristic
414#107C23×C10311yescharacteristic
415#107C23×C10311yescharacteristic
416C4⋊C8D4×C10311yescharacteristic
417#103—21no—
418#103—21no—
419#103—21no—
420#102—21no—
421#102—21no—
422#102—21no—
423C22⋊C8D4×C10311yescharacteristic
424C22⋊C8D4×C10311yescharacteristic
425C4×C8C23×C10311yescharacteristic
426C24—41no—
427#41—42no—
428#41—42no—
429#41—42no—
430#41—81no—
431#41—81no—
432#41—81no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—42no—
440C2×D4—41no—
441C2×D4—41no—
442C2×D4—41no—
443C2×D4—41no—
444C2×D4—41no—
445C2×D4—81no—
446C2×D4D8×C10311yescharacteristic
447C22×C4—41no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—41no—
452C22×C4C2×D4×C10311yescharacteristic
453C22×C4C2×D4×C10311yescharacteristic
454Q16—21no—
455Q16—21no—
456Q16—21no—
457Q16—21no—
458Q16—21no—
459Q16—21no—
460Q16—81no—
461SD16—42no—
462SD16—42no—
463SD16—42no—
464SD16—81no—
465D8—21no—
466D8—21no—
467D8—21no—
468D8—21no—
469D8—42no—
470D8C2×D4×C10312yes—
471D8C2×D4×C10312yes—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8C2×D4×C10311yescharacteristic
477C2×C8C2×D4×C10311yescharacteristic
478C2×C8C2×D4×C10311yescharacteristic
479C2×C8C24×C10311yescharacteristic
480C4⋊C4—21no—
481C4⋊C4—21no—
482C4⋊C4—41no—
483C4⋊C4—41no—
484C4⋊C4—41no—
485C4⋊C4—41no—
486C4⋊C4—41no—
487C4⋊C4D8×C10311yescharacteristic
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4—41no—
492C22⋊C4—41no—
493C22⋊C4—41no—
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4D8×C10311yescharacteristic
497C22⋊C4D8×C10311yescharacteristic
498C42C2×D4×C10311yescharacteristic
499C16—21no—
500C16—21no—
501C16—21no—
502C16C2×D4×C10312yes—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—82no—
507C23—82no—
508C23—161no—
509C23C2×D8×C10311yescharacteristic
510C23C2×D8×C10311yescharacteristic
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—41no—
515Q8—41no—
516Q8—41no—
517D4—22no—
518D4—22no—
519D4—41no—
520D4—41no—
521D4—41no—
522D4—41no—
523D4—41no—
524D4—82no—
525D4—82no—
526D4—82no—
527D4—82no—
528D4—161no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—82no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—82no—
542C2×C4—161no—
543C2×C4C2×D8×C10311yescharacteristic
544C2×C4C2×D8×C10311yescharacteristic
545C2×C4C2×D8×C10311yescharacteristic
546C2×C4C2×D8×C10311yescharacteristic
547C2×C4C22×D4×C10311yescharacteristic
548C8—21no—
549C8—21no—
550C8—21no—
551C8C22×D4×C10311yescharacteristic
552C8H(5,𝔽2)×C10311yescharacteristic
553C22—21no—
554C22—21no—
555C22—21no—
556C22—21no—
557C22—21no—
558C22—21no—
559C22—42no—
560C22—42no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22—81no—
567C22—81no—
568C22—164no—
569C22C22×D8×C10311yescharacteristic
570C4—21no—
571C4—21no—
572C4—21no—
573C4—21no—
574C4—81no—
575C4—81no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4D42×C10311yescharacteristic
580C4#576×C10311yescharacteristic
581C2—41no—
582C2—41no—
583C2—82no—
584C2—82no—
585C2—161no—
586C2D4×D8×C10311yescharacteristic
587C2C103×#341411yescharacteristic
588C2C103×#341611yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C103 ◁ C4×D4×C103 ◁ C8×D4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#509×C103C2semidirect
2. C2×#508×C103C2semidirect
3. C103×#3283C2semidirect
4. C103×#3280C2semidirect
5. C103×#2251C2semidirect
6. C103×#2219C2semidirect
7. C103×#2217C2semidirect
8. C103×#2210C2semidirect
9. C103×#2208C2semidirect
10. C103×#2189C2semidirect
11. C103×#2189C2semidirect
12. C103×#2187C2semidirect
13. C103×#2186C2semidirect
14. C103×#2177C2semidirect
15. C103×#2168C2semidirect
18. C2×#135×C103C22semidirect
24. C2×Q32×C103C22semidirect
25. C2×Q32×C103C22semidirect
30. C2×SD32×C103C22semidirect
34. C22×C16×C103C22semidirect
36. #494×C103C22semidirect
39. #467×C103C22semidirect
48. C4×D8×C103C22semidirect
50. #367×C103C22semidirect
51. C4⋊C16×C103C22semidirect
52. #358×C103C22semidirect
53. #358×C103C22semidirect
54. #358×C103C22semidirect
57. #357×C103C22semidirect
59. C22⋊C16×C103C22semidirect
60. #346×C103C22semidirect
112. D16×C103D4semidirect
286. #33833C103direct (N × H)
295. C2×#509C2×C103semidirect
296. C2×#508C2×C103semidirect
297. #3283C2×C103semidirect
298. #3280C2×C103semidirect
299. #2251C2×C103semidirect
300. #2219C2×C103semidirect
301. #2217C2×C103semidirect
302. #2210C2×C103semidirect
303. #2208C2×C103semidirect
304. #2189C2×C103semidirect
305. #2189C2×C103semidirect
306. #2187C2×C103semidirect
307. #2186C2×C103semidirect
308. #2177C2×C103semidirect
309. #2168C2×C103semidirect
310. C103#33833direct (N × H)
313. C2×#135C22×C103semidirect
319. C2×Q32C22×C103semidirect
320. C2×Q32C22×C103semidirect
325. C2×SD32C22×C103semidirect
329. C22×C16C22×C103semidirect
331. #494C22×C103semidirect
334. #467C22×C103semidirect
343. C4×D8C22×C103semidirect
345. #367C22×C103semidirect
346. C4⋊C16C22×C103semidirect
347. #358C22×C103semidirect
348. #358C22×C103semidirect
349. #358C22×C103semidirect
352. #357C22×C103semidirect
354. C22⋊C16C22×C103semidirect
355. #346C22×C103semidirect
407. D16D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#509×C1032
C2×#508×C1032
C103×#32832
C103×#32802
C103×#22512
C103×#22192
C103×#22172
C103×#22102
C103×#22082
C103×#21892
C103×#21872
C103×#21862
C103×#21772
C103×#21682
#33833103