Finite Group Databasebeta

← C103×#33832 #39939107

Subgroups — C103×#33832 #39939107

Order 26368.

686 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#510×C103C211yesmaximal, characteristic, complemented
2C22×SD32×C103C211yesmaximal, characteristic, complemented
3D4×Q16×C103C211yesmaximal, characteristic, complemented
4C103×#3280C211yesmaximal, characteristic
5C103×#2251C211yesmaximal, characteristic, complemented
6C103×#2220C211yesmaximal, characteristic, complemented
7C103×#2216C211yesmaximal, characteristic, complemented
8C103×#2211C211yesmaximal, characteristic, complemented
9C103×#2208C211yesmaximal, characteristic, complemented
10C103×#2189C211yesmaximal, characteristic, complemented
11C103×#2188C211yesmaximal, characteristic, complemented
12C103×#2187C211yesmaximal, characteristic, complemented
13C103×#2185C211yesmaximal, characteristic, complemented
14C103×#2175C211yesmaximal, characteristic, complemented
15C103×#2168C211yesmaximal, characteristic, complemented
16C2×#135×C103C2211yescharacteristic
17C22×Q16×C103C2211yescharacteristic
18C22×Q16×C103C2211yescharacteristic, complemented
19C22×D8×C103C2211yescharacteristic
20D4×Q8×C103—21no—
21#546×C103—21no—
22#510×C103—24no—
23C2×Q32×C103C2211yescharacteristic, complemented
24C2×Q32×C103C2211yescharacteristic, complemented
25C2×Q32×C103C2211yescharacteristic, complemented
26C2×SD32×C103—24no—
27C2×SD32×C103C2211yescharacteristic
28C2×SD32×C103C2211yescharacteristic
29C2×SD32×C103C2211yescharacteristic
30C2×SD32×C103C2211yescharacteristic
31C2×SD32×C103C2211yescharacteristic
32C2×SD32×C103C2211yescharacteristic
33C2×M32×C103C2211yescharacteristic, complemented
34C22×C16×C103C2211yescharacteristic
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#462×C103—21no—
43#451×C103—21no—
44#451×C103—21no—
45#450×C103—21no—
46#449×C103—21no—
47C4×Q16×C103C2211yescharacteristic, complemented
48C4×D8×C103C2211yescharacteristic
49C8×D4×C103C2211yescharacteristic
50#366×C103C2211yescharacteristic, complemented
51C4⋊C16×C103C2211yescharacteristic, complemented
52#358×C103C2211yescharacteristic, complemented
53#358×C103C2211yescharacteristic, complemented
54#358×C103C2211yescharacteristic, complemented
55#358×C103C2211yescharacteristic, complemented
56#357×C103C2211yescharacteristic
57#357×C103C2211yescharacteristic
58C22⋊C16×C103C2211yescharacteristic
59C22⋊C16×C103C2211yescharacteristic, complemented
60#346×C103C2211yescharacteristic, complemented
61C2×#41×C103—21no—
62C22×Q8×C103—21no—
63C22×Q8×C103—21no—
64C22×D4×C103—21no—
65#135×C103—22no—
66#135×C103—41no—
67C2×Q16×C103—22no—
68C2×Q16×C103—22no—
69C2×Q16×C103—21no—
70C2×Q16×C103—21no—
71C2×Q16×C103—21no—
72C2×Q16×C103—41no—
73C2×Q16×C103—41no—
74C2×Q16×C103C2311yescharacteristic
75C2×Q16×C103C2311yescharacteristic
76C2×Q16×C103C2311yescharacteristic
77C2×Q16×C103C2311yescharacteristic
78C2×SD16×C103—21no—
79C2×SD16×C103—21no—
80C2×D8×C103—22no—
81C2×D8×C103—21no—
82C2×D8×C103—41no—
83C2×D8×C103C2311yescharacteristic
84C2×D8×C103C2311yescharacteristic
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87C4⋊Q8×C103—21no—
88C4⋊Q8×C103—41no—
89#124×C103—21no—
90#123×C103—41no—
91C22⋊Q8×C103—21no—
92C22⋊Q8×C103—21no—
93C22⋊Q8×C103—21no—
94C22⋊Q8×C103—41no—
95C22⋊Q8×C103—41no—
96#121×C103—21no—
97#121×C103—41no—
98#120×C103—41no—
99C4×Q8×C103—21no—
100C4×D4×C103—21no—
101C4×D4×C103—41no—
102C4×D4×C103D411yescharacteristic
103C2×C22⋊C4×C103—41no—
104Q32×C103—22no—
105Q32×C103—22no—
106Q32×C103—41no—
107SD32×C103—22no—
108SD32×C103—22no—
109SD32×C103—22no—
110SD32×C103—22no—
111SD32×C103—41no—
112SD32×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#103×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—81no—
134C2×Q8×C103—21no—
135C2×Q8×C103—21no—
136C2×Q8×C103—21no—
137C2×Q8×C103—21no—
138C2×Q8×C103—42no—
139C2×Q8×C103—42no—
140C2×Q8×C103—41no—
141C2×Q8×C103—41no—
142C2×Q8×C103—81no—
143C2×Q8×C103—81no—
144C2×D4×C103—21no—
145C2×D4×C103—21no—
146C2×D4×C103—42no—
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×C103C2×D411yescharacteristic
157C22×C4×C103C2×D411yescharacteristic
158Q16×C103—21no—
159Q16×C103—21no—
160Q16×C103—21no—
161Q16×C103—21no—
162Q16×C103—21no—
163Q16×C103—21no—
164Q16×C103—21no—
165Q16×C103—42no—
166Q16×C103—42no—
167Q16×C103—81no—
168Q16×C103C2×D412yes—
169SD16×C103—42no—
170SD16×C103—81no—
171D8×C103—21no—
172D8×C103—21no—
173D8×C103—21no—
174D8×C103—42no—
175D8×C103C2×D412yes—
176C2×C8×C103—21no—
177C2×C8×C103—21no—
178C2×C8×C103—21no—
179C2×C8×C103—21no—
180C2×C8×C103C2×D411yescharacteristic
181C2×C8×C103C2×D411yescharacteristic
182C2×C8×C103C2×D411yescharacteristic
183C2×C8×C103C2411yescharacteristic
184C4⋊C4×C103—21no—
185C4⋊C4×C103—21no—
186C4⋊C4×C103—41no—
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×C103D811yescharacteristic
201C22⋊C4×C103D811yescharacteristic
202C42×C103—41no—
203C42×C103C2×D411yescharacteristic
204C16×C103—21no—
205C16×C103—21no—
206C16×C103—21no—
207C16×C103C2×D412yes—
208C23×C103—41no—
209C23×C103—41no—
210C23×C103—82no—
211C23×C103—82no—
212C23×C103—161no—
213C23×C103C2×D811yescharacteristic
214C23×C103C2×D811yescharacteristic
215Q8×C103—22no—
216Q8×C103—41no—
217Q8×C103—41no—
218Q8×C103—41no—
219Q8×C103—41no—
220Q8×C103—41no—
221Q8×C103—41no—
222Q8×C103—41no—
223Q8×C103—82no—
224Q8×C103—82no—
225D4×C103—22no—
226D4×C103—22no—
227D4×C103—41no—
228D4×C103—41no—
229D4×C103—41no—
230D4×C103—82no—
231D4×C103—82no—
232D4×C103—161no—
233C2×C4×C103—21no—
234C2×C4×C103—21no—
235C2×C4×C103—21no—
236C2×C4×C103—21no—
237C2×C4×C103—41no—
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—161no—
247C2×C4×C103C2×D811yescharacteristic
248C2×C4×C103C2×D811yescharacteristic
249C2×C4×C103C2×D811yescharacteristic
250C2×C4×C103C2×D811yescharacteristic
251C2×C4×C103C22×D411yescharacteristic
252C8×C103—21no—
253C8×C103—21no—
254C8×C103—21no—
255C8×C103C22×D411yescharacteristic
256C8×C103H(5,𝔽2)11yescharacteristic
257C22×C103—21no—
258C22×C103—21no—
259C22×C103—21no—
260C22×C103—21no—
261C22×C103—21no—
262C22×C103—42no—
263C22×C103—81no—
264C22×C103—81no—
265C22×C103—81no—
266C22×C103—81no—
267C22×C103—81no—
268C22×C103—164no—
269C22×C103#51012yescomplemented
270C22×C103C22×D811yescharacteristic
271C4×C103—21no—
272C4×C103—21no—
273C4×C103—21no—
274C4×C103—21no—
275C4×C103—42no—
276C4×C103—81no—
277C4×C103—81no—
278C4×C103—81no—
279C4×C103—81no—
280C4×C103—81no—
281C4×C103D4211yescharacteristic
282C4×C103#57611yescharacteristic
283#33832C10311yesmaximal, characteristic, direct product factor, Sylow
284C2×C103—22no—
285C2×C103—41no—
286C2×C103—82no—
287C2×C103—161no—
288C2×C103D4×D811yescharacteristic
289C2×C103C2×#51011yescharacteristic
290C2×C103#341611yescharacteristic
291C2×#510C2×C10311yescharacteristic, complemented
292C22×SD32C2×C10311yescharacteristic, complemented
293D4×Q16C2×C10311yescharacteristic, complemented
294#3280C2×C10311yescharacteristic
295#2251C2×C10311yescharacteristic, complemented
296#2220C2×C10311yescharacteristic, complemented
297#2216C2×C10311yescharacteristic, complemented
298#2211C2×C10311yescharacteristic, complemented
299#2208C2×C10311yescharacteristic, complemented
300#2189C2×C10311yescharacteristic, complemented
301#2188C2×C10311yescharacteristic, complemented
302#2187C2×C10311yescharacteristic, complemented
303#2185C2×C10311yescharacteristic, complemented
304#2175C2×C10311yescharacteristic, complemented
305#2168C2×C10311yescharacteristic, complemented
306C103#3383211yescharacteristic, direct product factor, Sylow
307C2×#135C22×C10311yescharacteristic
308C22×Q16C22×C10311yescharacteristic
309C22×Q16C22×C10311yescharacteristic, complemented
310C22×D8C22×C10311yescharacteristic
311D4×Q8—21no—
312#546—21no—
313#510—24no—
314C2×Q32C22×C10311yescharacteristic, complemented
315C2×Q32C22×C10311yescharacteristic, complemented
316C2×Q32C22×C10311yescharacteristic, complemented
317C2×SD32—24no—
318C2×SD32C22×C10311yescharacteristic
319C2×SD32C22×C10311yescharacteristic
320C2×SD32C22×C10311yescharacteristic
321C2×SD32C22×C10311yescharacteristic
322C2×SD32C22×C10311yescharacteristic
323C2×SD32C22×C10311yescharacteristic
324C2×M32C22×C10311yescharacteristic, complemented
325C22×C16C22×C10311yescharacteristic
326#495C22×C10311yescharacteristic
327#494C22×C10311yescharacteristic, complemented
328#467C22×C10311yescharacteristic
329#467C22×C10311yescharacteristic
330#467C22×C10311yescharacteristic, complemented
331#466C22×C10311yescharacteristic
332#463—21no—
333#462—21no—
334#451—21no—
335#451—21no—
336#450—21no—
337#449—21no—
338C4×Q16C22×C10311yescharacteristic, complemented
339C4×D8C22×C10311yescharacteristic
340C8×D4C22×C10311yescharacteristic
341#366C22×C10311yescharacteristic, complemented
342C4⋊C16C22×C10311yescharacteristic, complemented
343#358C22×C10311yescharacteristic, complemented
344#358C22×C10311yescharacteristic, complemented
345#358C22×C10311yescharacteristic, complemented
346#358C22×C10311yescharacteristic, complemented
347#357C22×C10311yescharacteristic
348#357C22×C10311yescharacteristic
349C22⋊C16C22×C10311yescharacteristic
350C22⋊C16C22×C10311yescharacteristic, complemented
351#346C22×C10311yescharacteristic, complemented
352C2×#41—21no—
353C22×Q8—21no—
354C22×Q8—21no—
355C22×D4—21no—
356#135—22no—
357#135—41no—
358C2×Q16—22no—
359C2×Q16—22no—
360C2×Q16—21no—
361C2×Q16—21no—
362C2×Q16—21no—
363C2×Q16—41no—
364C2×Q16—41no—
365C2×Q16C23×C10311yescharacteristic
366C2×Q16C23×C10311yescharacteristic
367C2×Q16C23×C10311yescharacteristic
368C2×Q16C23×C10311yescharacteristic
369C2×SD16—21no—
370C2×SD16—21no—
371C2×D8—22no—
372C2×D8—21no—
373C2×D8—41no—
374C2×D8C23×C10311yescharacteristic
375C2×D8C23×C10311yescharacteristic
376C22×C8C23×C10311yescharacteristic
377C22×C8C23×C10311yescharacteristic
378C4⋊Q8—21no—
379C4⋊Q8—41no—
380#124—21no—
381#123—41no—
382C22⋊Q8—21no—
383C22⋊Q8—21no—
384C22⋊Q8—21no—
385C22⋊Q8—41no—
386C22⋊Q8—41no—
387#121—21no—
388#121—41no—
389#120—41no—
390C4×Q8—21no—
391C4×D4—21no—
392C4×D4—41no—
393C4×D4D4×C10311yescharacteristic
394C2×C22⋊C4—41no—
395Q32—22no—
396Q32—22no—
397Q32—41no—
398SD32—22no—
399SD32—22no—
400SD32—22no—
401SD32—22no—
402SD32—41no—
403SD32D4×C10314yescomplemented
404M32—22no—
405C2×C16—22no—
406C2×C16C23×C10311yescharacteristic
407C2×C16C23×C10311yescharacteristic
408C2×C16C23×C10311yescharacteristic
409C2×C16C23×C10311yescharacteristic
410#107C23×C10311yescharacteristic
411#107C23×C10311yescharacteristic
412C4⋊C8D4×C10311yescharacteristic
413#103—21no—
414#103—21no—
415#103—21no—
416#103—21no—
417#102—21no—
418#102—21no—
419C22⋊C8D4×C10311yescharacteristic
420C22⋊C8D4×C10311yescharacteristic
421C4×C8C23×C10311yescharacteristic
422C24—41no—
423#41—42no—
424#41—81no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—42no—
430C2×Q8—42no—
431C2×Q8—41no—
432C2×Q8—41no—
433C2×Q8—81no—
434C2×Q8—81no—
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—42no—
438C2×D4—41no—
439C2×D4—41no—
440C2×D4—41no—
441C2×D4—81no—
442C2×D4D8×C10311yescharacteristic
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4C2×D4×C10311yescharacteristic
448C22×C4C2×D4×C10311yescharacteristic
449Q16—21no—
450Q16—21no—
451Q16—21no—
452Q16—21no—
453Q16—21no—
454Q16—21no—
455Q16—21no—
456Q16—42no—
457Q16—42no—
458Q16—81no—
459Q16C2×D4×C10312yes—
460SD16—42no—
461SD16—81no—
462D8—21no—
463D8—21no—
464D8—21no—
465D8—42no—
466D8C2×D4×C10312yes—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8C2×D4×C10311yescharacteristic
472C2×C8C2×D4×C10311yescharacteristic
473C2×C8C2×D4×C10311yescharacteristic
474C2×C8C24×C10311yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—41no—
478C4⋊C4—41no—
479C4⋊C4—41no—
480C4⋊C4—41no—
481C4⋊C4—41no—
482C4⋊C4—41no—
483C4⋊C4D8×C10311yescharacteristic
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C22⋊C4D8×C10311yescharacteristic
492C22⋊C4D8×C10311yescharacteristic
493C42—41no—
494C42C2×D4×C10311yescharacteristic
495C16—21no—
496C16—21no—
497C16—21no—
498C16C2×D4×C10312yes—
499C23—41no—
500C23—41no—
501C23—82no—
502C23—82no—
503C23—161no—
504C23C2×D8×C10311yescharacteristic
505C23C2×D8×C10311yescharacteristic
506Q8—22no—
507Q8—41no—
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512Q8—41no—
513Q8—41no—
514Q8—82no—
515Q8—82no—
516D4—22no—
517D4—22no—
518D4—41no—
519D4—41no—
520D4—41no—
521D4—82no—
522D4—82no—
523D4—161no—
524C2×C4—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—82no—
535C2×C4—82no—
536C2×C4—82no—
537C2×C4—161no—
538C2×C4C2×D8×C10311yescharacteristic
539C2×C4C2×D8×C10311yescharacteristic
540C2×C4C2×D8×C10311yescharacteristic
541C2×C4C2×D8×C10311yescharacteristic
542C2×C4C22×D4×C10311yescharacteristic
543C8—21no—
544C8—21no—
545C8—21no—
546C8C22×D4×C10311yescharacteristic
547C8H(5,𝔽2)×C10311yescharacteristic
548C22—21no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—42no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—164no—
560C22#510×C10312yescomplemented
561C22C22×D8×C10311yescharacteristic
562C4—21no—
563C4—21no—
564C4—21no—
565C4—21no—
566C4—42no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4D42×C10311yescharacteristic
573C4#576×C10311yescharacteristic
574C2—22no—
575C2—41no—
576C2—82no—
577C2—161no—
578C2D4×D8×C10311yescharacteristic
579C2C2×#510×C10311yescharacteristic
580C2C103×#341611yescharacteristic
subgroupG/H
center, socleC22×C103C22×D8
commutator, Frattini, cosocleC2×C8C24×C103
prime radicalC103×#3280C2
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×#510×C103C2semidirect
2. C22×SD32×C103C2semidirect
3. D4×Q16×C103C2semidirect
5. C103×#2251C2semidirect
6. C103×#2220C2semidirect
7. C103×#2216C2semidirect
8. C103×#2211C2semidirect
9. C103×#2208C2semidirect
10. C103×#2189C2semidirect
11. C103×#2188C2semidirect
12. C103×#2187C2semidirect
13. C103×#2185C2semidirect
14. C103×#2175C2semidirect
15. C103×#2168C2semidirect
18. C22×Q16×C103C22semidirect
23. C2×Q32×C103C22semidirect
24. C2×Q32×C103C22semidirect
25. C2×Q32×C103C22semidirect
33. C2×M32×C103C22semidirect
36. #494×C103C22semidirect
39. #467×C103C22semidirect
47. C4×Q16×C103C22semidirect
50. #366×C103C22semidirect
51. C4⋊C16×C103C22semidirect
52. #358×C103C22semidirect
53. #358×C103C22semidirect
54. #358×C103C22semidirect
55. #358×C103C22semidirect
59. C22⋊C16×C103C22semidirect
60. #346×C103C22semidirect
112. SD32×C103D4semidirect
269. C22×C103#510semidirect
283. #33832C103direct (N × H)
291. C2×#510C2×C103semidirect
292. C22×SD32C2×C103semidirect
293. D4×Q16C2×C103semidirect
295. #2251C2×C103semidirect
296. #2220C2×C103semidirect
297. #2216C2×C103semidirect
298. #2211C2×C103semidirect
299. #2208C2×C103semidirect
300. #2189C2×C103semidirect
301. #2188C2×C103semidirect
302. #2187C2×C103semidirect
303. #2185C2×C103semidirect
304. #2175C2×C103semidirect
305. #2168C2×C103semidirect
306. C103#33832direct (N × H)
309. C22×Q16C22×C103semidirect
314. C2×Q32C22×C103semidirect
315. C2×Q32C22×C103semidirect
316. C2×Q32C22×C103semidirect
324. C2×M32C22×C103semidirect
327. #494C22×C103semidirect
330. #467C22×C103semidirect
338. C4×Q16C22×C103semidirect
341. #366C22×C103semidirect
342. C4⋊C16C22×C103semidirect
343. #358C22×C103semidirect
344. #358C22×C103semidirect
345. #358C22×C103semidirect
346. #358C22×C103semidirect
350. C22⋊C16C22×C103semidirect
351. #346C22×C103semidirect
403. SD32D4×C103semidirect
560. C22#510×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#510×C1032
C22×SD32×C1032
D4×Q16×C1032
C103×#32802
C103×#22512
C103×#22202
C103×#22162
C103×#22112
C103×#22082
C103×#21892
C103×#21882
C103×#21872
C103×#21852
C103×#21752
C103×#21682
#33832103