Finite Group Databasebeta

← C103×#33834 #39939109

Subgroups — C103×#33834 #39939109

Order 26368.

702 conjugacy classes of subgroups.

The subgroup lattice has 602 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×#3287C211yesmaximal, characteristic, complemented
4C103×#3280C211yesmaximal, characteristic, complemented
5C103×#2250C211yesmaximal, characteristic, complemented
6C103×#2220C211yesmaximal, characteristic, complemented
7C103×#2215C211yesmaximal, characteristic, complemented
8C103×#2211C211yesmaximal, characteristic, complemented
9C103×#2206C211yesmaximal, characteristic, complemented
10C103×#2189C211yesmaximal, characteristic, complemented
11C103×#2186C211yesmaximal, characteristic, complemented
12C103×#2186C211yesmaximal, characteristic, complemented
13C103×#2184C211yesmaximal, characteristic, complemented
14C103×#2175C211yesmaximal, characteristic, complemented
15C103×#2168C211yesmaximal, characteristic, complemented
16C2×#135×C103C2211yescharacteristic
17C2×#135×C103C2211yescharacteristic
18C2×#135×C103C2211yescharacteristic, complemented
19C22×D8×C103C2211yescharacteristic
20#550×C103—21no—
21#546×C103—21no—
22#509×C103—24no—
23#508×C103—24no—
24C2×Q32×C103C2211yescharacteristic, complemented
25C2×SD32×C103C2211yescharacteristic
26C2×SD32×C103C2211yescharacteristic
27C2×SD32×C103C2211yescharacteristic, complemented
28C2×SD32×C103C2211yescharacteristic, complemented
29C2×D16×C103C2211yescharacteristic
30C2×D16×C103C2211yescharacteristic
31C2×D16×C103C2211yescharacteristic
32C2×D16×C103C2211yescharacteristic
33C2×M32×C103C2211yescharacteristic
34C22×C16×C103C2211yescharacteristic, complemented
35#495×C103C2211yescharacteristic
36#493×C103C2211yescharacteristic, complemented
37#467×C103C2211yescharacteristic
38#466×C103C2211yescharacteristic
39#466×C103C2211yescharacteristic
40#466×C103C2211yescharacteristic, complemented
41#463×C103—21no—
42#460×C103—21no—
43#450×C103—21no—
44#449×C103—21no—
45#449×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#357×C103C2211yescharacteristic
55#357×C103C2211yescharacteristic
56#357×C103C2211yescharacteristic, complemented
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×C103C2311yescharacteristic
72C2×Q16×C103C2311yescharacteristic
73C2×SD16×C103—21no—
74C2×SD16×C103—21no—
75C2×SD16×C103—21no—
76C2×SD16×C103—21no—
77C2×D8×C103—22no—
78C2×D8×C103—21no—
79C2×D8×C103—21no—
80C2×D8×C103—41no—
81C2×D8×C103C2311yescharacteristic
82C2×D8×C103C2311yescharacteristic
83C2×D8×C103C2311yescharacteristic
84C2×D8×C103C2311yescharacteristic
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87#127×C103—21no—
88#127×C103—41no—
89#124×C103—21no—
90#123×C103—41no—
91C22⋊Q8×C103—21no—
92#121×C103—21no—
93#121×C103—21no—
94#121×C103—21no—
95#121×C103—41no—
96#121×C103—41no—
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—
105SD32×C103—22no—
106SD32×C103—22no—
107SD32×C103—41no—
108SD32×C103D414yescomplemented
109D16×C103—22no—
110D16×C103—22no—
111D16×C103—22no—
112D16×C103—41no—
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#102×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×D4×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—41no—
151C2×D4×C103—41no—
152C2×D4×C103—41no—
153C2×D4×C103—41no—
154C2×D4×C103—81no—
155C2×D4×C103D811yescharacteristic
156C22×C4×C103—41no—
157C22×C4×C103—41no—
158C22×C4×C103—41no—
159C22×C4×C103—41no—
160C22×C4×C103C2×D411yescharacteristic
161C22×C4×C103C2×D411yescharacteristic
162Q16×C103—21no—
163Q16×C103—21no—
164Q16×C103—21no—
165Q16×C103C2×D412yes—
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—21no—
175D8×C103—21no—
176D8×C103—21no—
177D8×C103—42no—
178D8×C103—81no—
179D8×C103C2×D412yes—
180C2×C8×C103—21no—
181C2×C8×C103—21no—
182C2×C8×C103—21no—
183C2×C8×C103—21no—
184C2×C8×C103C2×D411yescharacteristic
185C2×C8×C103C2×D411yescharacteristic
186C2×C8×C103C2×D411yescharacteristic
187C2×C8×C103C2411yescharacteristic
188C4⋊C4×C103—21no—
189C4⋊C4×C103—21no—
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—41no—
211C23×C103—41no—
212C23×C103—82no—
213C23×C103—82no—
214C23×C103—161no—
215C23×C103C2×D811yescharacteristic
216C23×C103C2×D811yescharacteristic
217Q8×C103—22no—
218Q8×C103—41no—
219Q8×C103—41no—
220Q8×C103—41no—
221D4×C103—22no—
222D4×C103—41no—
223D4×C103—41no—
224D4×C103—41no—
225D4×C103—41no—
226D4×C103—41no—
227D4×C103—41no—
228D4×C103—41no—
229D4×C103—41no—
230D4×C103—82no—
231D4×C103—82no—
232D4×C103—82no—
233D4×C103—82no—
234D4×C103—82no—
235D4×C103—161no—
236D4×C103—161no—
237D4×C103—161no—
238D4×C103—161no—
239C2×C4×C103—21no—
240C2×C4×C103—21no—
241C2×C4×C103—21no—
242C2×C4×C103—21no—
243C2×C4×C103—41no—
244C2×C4×C103—41no—
245C2×C4×C103—41no—
246C2×C4×C103—41no—
247C2×C4×C103—82no—
248C2×C4×C103—82no—
249C2×C4×C103—82no—
250C2×C4×C103—161no—
251C2×C4×C103C2×D811yescharacteristic
252C2×C4×C103C2×D811yescharacteristic
253C2×C4×C103C2×D811yescharacteristic
254C2×C4×C103C2×D811yescharacteristic
255C2×C4×C103C22×D411yescharacteristic
256C8×C103—21no—
257C8×C103—21no—
258C8×C103—21no—
259C8×C103C22×D411yescharacteristic
260C8×C103H(5,𝔽2)11yescharacteristic
261C22×C103—21no—
262C22×C103—21no—
263C22×C103—21no—
264C22×C103—21no—
265C22×C103—21no—
266C22×C103—21no—
267C22×C103—42no—
268C22×C103—81no—
269C22×C103—81no—
270C22×C103—81no—
271C22×C103—81no—
272C22×C103—81no—
273C22×C103—81no—
274C22×C103—81no—
275C22×C103—81no—
276C22×C103—81no—
277C22×C103—81no—
278C22×C103—81no—
279C22×C103—164no—
280C22×C103C22×D811yescharacteristic
281C4×C103—21no—
282C4×C103—21no—
283C4×C103—21no—
284C4×C103—21no—
285C4×C103—42no—
286C4×C103—81no—
287C4×C103—81no—
288C4×C103—81no—
289C4×C103D4211yescharacteristic
290C4×C103#57611yescharacteristic
291#33834C10311yesmaximal, characteristic, direct product factor, Sylow
292C2×C103—41no—
293C2×C103—41no—
294C2×C103—82no—
295C2×C103—161no—
296C2×C103—161no—
297C2×C103—161no—
298C2×C103D4×D811yescharacteristic
299C2×C103#341411yescharacteristic
300C2×C103#341511yescharacteristic
301C2×#509C2×C10311yescharacteristic, complemented
302C2×#508C2×C10311yescharacteristic, complemented
303#3287C2×C10311yescharacteristic, complemented
304#3280C2×C10311yescharacteristic, complemented
305#2250C2×C10311yescharacteristic, complemented
306#2220C2×C10311yescharacteristic, complemented
307#2215C2×C10311yescharacteristic, complemented
308#2211C2×C10311yescharacteristic, complemented
309#2206C2×C10311yescharacteristic, complemented
310#2189C2×C10311yescharacteristic, complemented
311#2186C2×C10311yescharacteristic, complemented
312#2186C2×C10311yescharacteristic, complemented
313#2184C2×C10311yescharacteristic, complemented
314#2175C2×C10311yescharacteristic, complemented
315#2168C2×C10311yescharacteristic, complemented
316C103#3383411yescharacteristic, direct product factor, Sylow
317C2×#135C22×C10311yescharacteristic
318C2×#135C22×C10311yescharacteristic
319C2×#135C22×C10311yescharacteristic, complemented
320C22×D8C22×C10311yescharacteristic
321#550—21no—
322#546—21no—
323#509—24no—
324#508—24no—
325C2×Q32C22×C10311yescharacteristic, complemented
326C2×SD32C22×C10311yescharacteristic
327C2×SD32C22×C10311yescharacteristic
328C2×SD32C22×C10311yescharacteristic, complemented
329C2×SD32C22×C10311yescharacteristic, complemented
330C2×D16C22×C10311yescharacteristic
331C2×D16C22×C10311yescharacteristic
332C2×D16C22×C10311yescharacteristic
333C2×D16C22×C10311yescharacteristic
334C2×M32C22×C10311yescharacteristic
335C22×C16C22×C10311yescharacteristic, complemented
336#495C22×C10311yescharacteristic
337#493C22×C10311yescharacteristic, complemented
338#467C22×C10311yescharacteristic
339#466C22×C10311yescharacteristic
340#466C22×C10311yescharacteristic
341#466C22×C10311yescharacteristic, complemented
342#463—21no—
343#460—21no—
344#450—21no—
345#449—21no—
346#449—21no—
347#449—21no—
348C4×Q16C22×C10311yescharacteristic, complemented
349C4×D8C22×C10311yescharacteristic
350C8×D4C22×C10311yescharacteristic
351#366C22×C10311yescharacteristic, complemented
352C4⋊C16C22×C10311yescharacteristic, complemented
353#358C22×C10311yescharacteristic, complemented
354#358C22×C10311yescharacteristic, complemented
355#357C22×C10311yescharacteristic
356#357C22×C10311yescharacteristic
357#357C22×C10311yescharacteristic, complemented
358#357C22×C10311yescharacteristic, complemented
359C22⋊C16C22×C10311yescharacteristic
360C22⋊C16C22×C10311yescharacteristic, complemented
361#346C22×C10311yescharacteristic, complemented
362C2×#41—21no—
363C2×#41—21no—
364C2×#41—21no—
365C22×D4—21no—
366#135—22no—
367#135—22no—
368#135—22no—
369#135—41no—
370#135—41no—
371#135—41no—
372C2×Q16C23×C10311yescharacteristic
373C2×Q16C23×C10311yescharacteristic
374C2×SD16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×D8—22no—
379C2×D8—21no—
380C2×D8—21no—
381C2×D8—41no—
382C2×D8C23×C10311yescharacteristic
383C2×D8C23×C10311yescharacteristic
384C2×D8C23×C10311yescharacteristic
385C2×D8C23×C10311yescharacteristic
386C22×C8C23×C10311yescharacteristic
387C22×C8C23×C10311yescharacteristic
388#127—21no—
389#127—41no—
390#124—21no—
391#123—41no—
392C22⋊Q8—21no—
393#121—21no—
394#121—21no—
395#121—21no—
396#121—41no—
397#121—41no—
398#121—41no—
399#120—41no—
400C4×Q8—21no—
401C4×D4—21no—
402C4×D4—41no—
403C4×D4D4×C10311yescharacteristic
404C2×C22⋊C4—41no—
405Q32—22no—
406SD32—22no—
407SD32—22no—
408SD32—41no—
409SD32D4×C10314yescomplemented
410D16—22no—
411D16—22no—
412D16—22no—
413D16—41no—
414M32—22no—
415C2×C16—22no—
416C2×C16C23×C10311yescharacteristic
417C2×C16C23×C10311yescharacteristic
418C2×C16C23×C10311yescharacteristic
419C2×C16C23×C10311yescharacteristic
420#107C23×C10311yescharacteristic
421#107C23×C10311yescharacteristic
422C4⋊C8D4×C10311yescharacteristic
423#103—21no—
424#103—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429C22⋊C8D4×C10311yescharacteristic
430C22⋊C8D4×C10311yescharacteristic
431C4×C8C23×C10311yescharacteristic
432C24—41no—
433#41—42no—
434#41—42no—
435#41—42no—
436#41—81no—
437#41—81no—
438#41—81no—
439C2×Q8—21no—
440C2×Q8—21no—
441C2×D4—21no—
442C2×D4—21no—
443C2×D4—21no—
444C2×D4—21no—
445C2×D4—42no—
446C2×D4—41no—
447C2×D4—41no—
448C2×D4—41no—
449C2×D4—41no—
450C2×D4—41no—
451C2×D4—41no—
452C2×D4—41no—
453C2×D4—41no—
454C2×D4—41no—
455C2×D4—81no—
456C2×D4D8×C10311yescharacteristic
457C22×C4—41no—
458C22×C4—41no—
459C22×C4—41no—
460C22×C4—41no—
461C22×C4C2×D4×C10311yescharacteristic
462C22×C4C2×D4×C10311yescharacteristic
463Q16—21no—
464Q16—21no—
465Q16—21no—
466Q16C2×D4×C10312yes—
467SD16—42no—
468SD16—42no—
469SD16—42no—
470SD16—81no—
471D8—21no—
472D8—21no—
473D8—21no—
474D8—21no—
475D8—21no—
476D8—21no—
477D8—21no—
478D8—42no—
479D8—81no—
480D8C2×D4×C10312yes—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8C2×D4×C10311yescharacteristic
486C2×C8C2×D4×C10311yescharacteristic
487C2×C8C2×D4×C10311yescharacteristic
488C2×C8C24×C10311yescharacteristic
489C4⋊C4—21no—
490C4⋊C4—21no—
491C4⋊C4—41no—
492C4⋊C4—41no—
493C4⋊C4D8×C10311yescharacteristic
494C22⋊C4—41no—
495C22⋊C4—41no—
496C22⋊C4—41no—
497C22⋊C4—41no—
498C22⋊C4—41no—
499C22⋊C4—41no—
500C22⋊C4—41no—
501C22⋊C4D8×C10311yescharacteristic
502C22⋊C4D8×C10311yescharacteristic
503C42—41no—
504C42C2×D4×C10311yescharacteristic
505C16—21no—
506C16—21no—
507C16—21no—
508C16C2×D4×C10312yes—
509C23—41no—
510C23—41no—
511C23—41no—
512C23—41no—
513C23—82no—
514C23—82no—
515C23—161no—
516C23C2×D8×C10311yescharacteristic
517C23C2×D8×C10311yescharacteristic
518Q8—22no—
519Q8—41no—
520Q8—41no—
521Q8—41no—
522D4—22no—
523D4—41no—
524D4—41no—
525D4—41no—
526D4—41no—
527D4—41no—
528D4—41no—
529D4—41no—
530D4—41no—
531D4—82no—
532D4—82no—
533D4—82no—
534D4—82no—
535D4—82no—
536D4—161no—
537D4—161no—
538D4—161no—
539D4—161no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—82no—
549C2×C4—82no—
550C2×C4—82no—
551C2×C4—161no—
552C2×C4C2×D8×C10311yescharacteristic
553C2×C4C2×D8×C10311yescharacteristic
554C2×C4C2×D8×C10311yescharacteristic
555C2×C4C2×D8×C10311yescharacteristic
556C2×C4C22×D4×C10311yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8C22×D4×C10311yescharacteristic
561C8H(5,𝔽2)×C10311yescharacteristic
562C22—21no—
563C22—21no—
564C22—21no—
565C22—21no—
566C22—21no—
567C22—21no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22—81no—
574C22—81no—
575C22—81no—
576C22—81no—
577C22—81no—
578C22—81no—
579C22—81no—
580C22—164no—
581C22C22×D8×C10311yescharacteristic
582C4—21no—
583C4—21no—
584C4—21no—
585C4—21no—
586C4—42no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4D42×C10311yescharacteristic
591C4#576×C10311yescharacteristic
592C2—41no—
593C2—41no—
594C2—82no—
595C2—161no—
596C2—161no—
597C2—161no—
598C2D4×D8×C10311yescharacteristic
599C2C103×#341411yescharacteristic
600C2C103×#341511yescharacteristic
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×#3287C2semidirect
4. C103×#3280C2semidirect
5. C103×#2250C2semidirect
6. C103×#2220C2semidirect
7. C103×#2215C2semidirect
8. C103×#2211C2semidirect
9. C103×#2206C2semidirect
10. C103×#2189C2semidirect
11. C103×#2186C2semidirect
12. C103×#2186C2semidirect
13. C103×#2184C2semidirect
14. C103×#2175C2semidirect
15. C103×#2168C2semidirect
18. C2×#135×C103C22semidirect
24. C2×Q32×C103C22semidirect
27. C2×SD32×C103C22semidirect
28. C2×SD32×C103C22semidirect
34. C22×C16×C103C22semidirect
36. #493×C103C22semidirect
40. #466×C103C22semidirect
47. C4×Q16×C103C22semidirect
50. #366×C103C22semidirect
51. C4⋊C16×C103C22semidirect
52. #358×C103C22semidirect
53. #358×C103C22semidirect
56. #357×C103C22semidirect
57. #357×C103C22semidirect
59. C22⋊C16×C103C22semidirect
60. #346×C103C22semidirect
108. SD32×C103D4semidirect
291. #33834C103direct (N × H)
301. C2×#509C2×C103semidirect
302. C2×#508C2×C103semidirect
303. #3287C2×C103semidirect
304. #3280C2×C103semidirect
305. #2250C2×C103semidirect
306. #2220C2×C103semidirect
307. #2215C2×C103semidirect
308. #2211C2×C103semidirect
309. #2206C2×C103semidirect
310. #2189C2×C103semidirect
311. #2186C2×C103semidirect
312. #2186C2×C103semidirect
313. #2184C2×C103semidirect
314. #2175C2×C103semidirect
315. #2168C2×C103semidirect
316. C103#33834direct (N × H)
319. C2×#135C22×C103semidirect
325. C2×Q32C22×C103semidirect
328. C2×SD32C22×C103semidirect
329. C2×SD32C22×C103semidirect
335. C22×C16C22×C103semidirect
337. #493C22×C103semidirect
341. #466C22×C103semidirect
348. C4×Q16C22×C103semidirect
351. #366C22×C103semidirect
352. C4⋊C16C22×C103semidirect
353. #358C22×C103semidirect
354. #358C22×C103semidirect
357. #357C22×C103semidirect
358. #357C22×C103semidirect
360. C22⋊C16C22×C103semidirect
361. #346C22×C103semidirect
409. SD32D4×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×#32872
C103×#32802
C103×#22502
C103×#22202
C103×#22152
C103×#22112
C103×#22062
C103×#21892
C103×#21862
C103×#21842
C103×#21752
C103×#21682
#33834103