Finite Group Databasebeta

← C103×#9938 #39915213

Subgroups — C103×#9938 #39915213

Order 26368.

1008 conjugacy classes of subgroups; only the 102 normal subgroups are shown.

normal subgroups only

This group has 1008 conjugacy classes of subgroups — too many to draw. Only its 102 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3006C211yesmaximal, characteristic, complemented
2C103×#2539C211yesmaximal, characteristic, complemented
3C103×#2404C211yesmaximal, characteristic, complemented
4C103×#1789C211yesmaximal, characteristic, complemented
5C103×#1510C211yesmaximal, characteristic, complemented
6C103×#1462C211yesmaximal, characteristic, complemented
7C103×#1284C211yesmaximal, characteristic, complemented
8C22×#41×C103C2211yescharacteristic
9C2×AGL(1,ℤ/8)×C103—21no—
10C2×#123×C103—21no—
11C2×#121×C103C2211yescharacteristic
12C2×#120×C103—21no—
13C2×#120×C103—21no—
14C22×C22⋊C4×C103C2211yescharacteristic
15#449×C103—22no—
16#448×C103—21no—
17#447×C103—21no—
18C2×#104×C103—22no—
19#417×C103—21no—
20#407×C103C2211yescharacteristic
21#407×C103C2211yescharacteristic
22#399×C103—21no—
23#393×C103—21no—
24#392×C103—21no—
25#392×C103—21no—
26#390×C103—22no—
27#386×C103—21no—
28#386×C103—22no—
29#381×C103C2211yescharacteristic
30C4×C22⋊C4×C103C2211yescharacteristic
31#327×C103—22no—
32#323×C103—22no—
33C25×C103D411yescharacteristic
34C2×#41×C103—21no—
35C2×#41×C103—21no—
36C2×#41×C103—21no—
37C2×#41×C103—21no—
38C2×#41×C103—44no—
39C22×Q8×C103D411yescharacteristic, complemented
40C22×D4×C103—21no—
41C22×D4×C103—21no—
42C22×D4×C103—22no—
43C22×D4×C103—22no—
44C22×D4×C103D411yescharacteristic, complemented
45C22×D4×C103D411yescharacteristic, complemented
46C23×C4×C103—21no—
47C23×C4×C103D411yescharacteristic
48C23×C4×C103C2311yescharacteristic
49AGL(1,ℤ/8)×C103—44no—
50C2×SD16×C103—22no—
51C2×D8×C103—22no—
52C2×M16×C103—21no—
53C2×M16×C103—21no—
54#123×C103—44no—
55#121×C103—21no—
56#121×C103—21no—
57#121×C103—21no—
58#121×C103—21no—
59#120×C103—44no—
60#120×C103—44no—
61C2×C4⋊C4×C103—22no—
62C2×C4⋊C4×C103D411yescharacteristic, complemented
63C2×C22⋊C4×C103—21no—
64C2×C22⋊C4×C103—22no—
65C2×C22⋊C4×C103—22no—
66C2×C22⋊C4×C103—22no—
67C2×C22⋊C4×C103—21no—
68C2×C22⋊C4×C103—21no—
69C2×C22⋊C4×C103—21no—
70C2×C22⋊C4×C103—21no—
71C2×C22⋊C4×C103—21no—
72C2×C22⋊C4×C103—21no—
73C2×C22⋊C4×C103—21no—
74C2×C22⋊C4×C103—21no—
75C2×C22⋊C4×C103—22no—
76C2×C42×C103D412yescomplemented
77#104×C103—44no—
78#103×C103—22no—
79#102×C103—22no—
80C22⋊C8×C103—21no—
81C22⋊C8×C103—21no—
82C22⋊C8×C103—21no—
83C22⋊C8×C103D412yescomplemented
84#95×C103—22no—
85#95×C103—21no—
86#95×C103—21no—
87#95×C103D412yescomplemented
88C24×C103—21no—
89C24×C103—21no—
90C24×C103—21no—
91C24×C103—21no—
92C24×C103—21no—
93C24×C103—42no—
94C24×C103—42no—
95C24×C103—42no—
96C24×C103C2×D411yescharacteristic
97#41×C103—24no—
98#41×C103—24no—
99#41×C103—42no—
100#41×C103—42no—
101#41×C103—42no—
102#41×C103—42no—
103#41×C103—42no—
104#41×C103—42no—
105C2×Q8×C103—21no—
106C2×Q8×C103—21no—
107C2×Q8×C103—42no—
108C2×D4×C103—24no—
109C2×D4×C103—21no—
110C2×D4×C103—21no—
111C2×D4×C103—21no—
112C2×D4×C103—21no—
113C2×D4×C103—42no—
114C2×D4×C103—44no—
115C2×D4×C103—42no—
116C2×D4×C103—42no—
117C2×D4×C103—41no—
118C2×D4×C103—41no—
119C2×D4×C103—42no—
120C2×D4×C103—44no—
121C2×D4×C103—42no—
122C2×D4×C103—44no—
123C2×D4×C103—44no—
124C2×D4×C103—41no—
125C2×D4×C103—41no—
126C2×D4×C103—82no—
127C2×D4×C103—82no—
128C22×C4×C103—21no—
129C22×C4×C103—22no—
130C22×C4×C103—22no—
131C22×C4×C103—21no—
132C22×C4×C103—21no—
133C22×C4×C103—21no—
134C22×C4×C103—21no—
135C22×C4×C103—42no—
136C22×C4×C103—42no—
137C22×C4×C103—42no—
138C22×C4×C103—41no—
139C22×C4×C103—41no—
140C22×C4×C103—42no—
141C22×C4×C103C2×D411yescharacteristic
142C22×C4×C103C2×D411yescharacteristic
143C22×C4×C103C2×D411yescharacteristic
144C22×C4×C103C2×D411yescharacteristic
145C22×C4×C103C2×D411yescharacteristic
146C22×C4×C103#4111yescharacteristic
147SD16×C103—44no—
148D8×C103—44no—
149M16×C103—42no—
150M16×C103—42no—
151C2×C8×C103—22no—
152C2×C8×C103—41no—
153C4⋊C4×C103—21no—
154C4⋊C4×C103—21no—
155C4⋊C4×C103—44no—
156C22⋊C4×C103—24no—
157C22⋊C4×C103—44no—
158C22⋊C4×C103—44no—
159C22⋊C4×C103—44no—
160C22⋊C4×C103—42no—
161C22⋊C4×C103—41no—
162C22⋊C4×C103—41no—
163C22⋊C4×C103—41no—
164C22⋊C4×C103—41no—
165C22⋊C4×C103—41no—
166C22⋊C4×C103—41no—
167C22⋊C4×C103—82no—
168C42×C103—42no—
169C23×C103—22no—
170C23×C103—22no—
171C23×C103—22no—
172C23×C103—22no—
173C23×C103—22no—
174C23×C103—22no—
175C23×C103—41no—
176C23×C103—42no—
177C23×C103—42no—
178C23×C103—41no—
179C23×C103—42no—
180C23×C103—41no—
181C23×C103—41no—
182C23×C103—41no—
183C23×C103—41no—
184C23×C103—41no—
185C23×C103—42no—
186C23×C103—41no—
187C23×C103—41no—
188C23×C103—42no—
189C23×C103—42no—
190C23×C103—42no—
191C23×C103—41no—
192C23×C103—42no—
193C23×C103—81no—
194C23×C103—81no—
195C23×C103—88no—
196C23×C103#12011yescharacteristic
197C23×C103#12011yescharacteristic
198C23×C103#12111yescharacteristic
199Q8×C103—22no—
200Q8×C103—22no—
201Q8×C103—41no—
202Q8×C103—41no—
203D4×C103—22no—
204D4×C103—22no—
205D4×C103—41no—
206D4×C103—41no—
207D4×C103—42no—
208D4×C103—44no—
209D4×C103—44no—
210D4×C103—81no—
211D4×C103—88no—
212D4×C103—82no—
213D4×C103—88no—
214D4×C103—82no—
215C2×C4×C103—22no—
216C2×C4×C103—22no—
217C2×C4×C103—24no—
218C2×C4×C103—22no—
219C2×C4×C103—41no—
220C2×C4×C103—41no—
221C2×C4×C103—41no—
222C2×C4×C103—41no—
223C2×C4×C103—44no—
224C2×C4×C103—44no—
225C2×C4×C103—41no—
226C2×C4×C103—42no—
227C2×C4×C103—41no—
228C2×C4×C103—42no—
229C2×C4×C103—42no—
230C2×C4×C103—41no—
231C2×C4×C103—42no—
232C2×C4×C103—41no—
233C2×C4×C103—42no—
234C2×C4×C103—41no—
235C2×C4×C103—41no—
236C2×C4×C103—42no—
237C2×C4×C103—42no—
238C2×C4×C103—81no—
239C2×C4×C103#12011yescharacteristic
240C2×C4×C103#12111yescharacteristic
241C2×C4×C103#12111yescharacteristic
242C2×C4×C103#12711yescharacteristic
243C8×C103—42no—
244C8×C103—81no—
245C22×C103—21no—
246C22×C103—21no—
247C22×C103—21no—
248C22×C103—21no—
249C22×C103—21no—
250C22×C103—21no—
251C22×C103—21no—
252C22×C103—44no—
253C22×C103—44no—
254C22×C103—44no—
255C22×C103—44no—
256C22×C103—42no—
257C22×C103—42no—
258C22×C103—82no—
259C22×C103—82no—
260C22×C103—82no—
261C22×C103—82no—
262C22×C103—82no—
263C22×C103—82no—
264C22×C103—82no—
265C22×C103—81no—
266C22×C103—81no—
267C22×C103—81no—
268C22×C103—81no—
269C22×C103—81no—
270C22×C103—81no—
271C22×C103—81no—
272C22×C103#39211yescharacteristic
273C22×C103#45312yes—
274C22×C103B(4,𝔽2)12yes—
275C4×C103—21no—
276C4×C103—21no—
277C4×C103—21no—
278C4×C103—21no—
279C4×C103—44no—
280C4×C103—42no—
281C4×C103—82no—
282C4×C103—81no—
283C4×C103—81no—
284#9938C10311yesmaximal, characteristic, direct product factor, Sylow
285C2×C103—22no—
286C2×C103—22no—
287C2×C103—41no—
288C2×C103—82no—
289C2×C103—82no—
290C2×C103—161no—
291C2×C103#200211yescharacteristic
292C2×C103#201011yescharacteristic
293C2×C103#202111yescharacteristic
294#3006C2×C10311yescharacteristic, complemented
295#2539C2×C10311yescharacteristic, complemented
296#2404C2×C10311yescharacteristic, complemented
297#1789C2×C10311yescharacteristic, complemented
298#1510C2×C10311yescharacteristic, complemented
299#1462C2×C10311yescharacteristic, complemented
300#1284C2×C10311yescharacteristic, complemented
301C103#993811yescharacteristic, direct product factor, Sylow
302C22×#41C22×C10311yescharacteristic
303C2×AGL(1,ℤ/8)—21no—
304C2×#123—21no—
305C2×#121C22×C10311yescharacteristic
306C2×#120—21no—
307C2×#120—21no—
308C22×C22⋊C4C22×C10311yescharacteristic
309#449—22no—
310#448—21no—
311#447—21no—
312C2×#104—22no—
313#417—21no—
314#407C22×C10311yescharacteristic
315#407C22×C10311yescharacteristic
316#399—21no—
317#393—21no—
318#392—21no—
319#392—21no—
320#390—22no—
321#386—21no—
322#386—22no—
323#381C22×C10311yescharacteristic
324C4×C22⋊C4C22×C10311yescharacteristic
325#327—22no—
326#323—22no—
327C25D4×C10311yescharacteristic
328C2×#41—21no—
329C2×#41—21no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—44no—
333C22×Q8D4×C10311yescharacteristic, complemented
334C22×D4—21no—
335C22×D4—21no—
336C22×D4—22no—
337C22×D4—22no—
338C22×D4D4×C10311yescharacteristic, complemented
339C22×D4D4×C10311yescharacteristic, complemented
340C23×C4—21no—
341C23×C4D4×C10311yescharacteristic
342C23×C4C23×C10311yescharacteristic
343AGL(1,ℤ/8)—44no—
344C2×SD16—22no—
345C2×D8—22no—
346C2×M16—21no—
347C2×M16—21no—
348#123—44no—
349#121—21no—
350#121—21no—
351#121—21no—
352#121—21no—
353#120—44no—
354#120—44no—
355C2×C4⋊C4—22no—
356C2×C4⋊C4D4×C10311yescharacteristic, complemented
357C2×C22⋊C4—21no—
358C2×C22⋊C4—22no—
359C2×C22⋊C4—22no—
360C2×C22⋊C4—22no—
361C2×C22⋊C4—21no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4—21no—
369C2×C22⋊C4—22no—
370C2×C42D4×C10312yescomplemented
371#104—44no—
372#103—22no—
373#102—22no—
374C22⋊C8—21no—
375C22⋊C8—21no—
376C22⋊C8—21no—
377C22⋊C8D4×C10312yescomplemented
378#95—22no—
379#95—21no—
380#95—21no—
381#95D4×C10312yescomplemented
382C24—21no—
383C24—21no—
384C24—21no—
385C24—21no—
386C24—21no—
387C24—42no—
388C24—42no—
389C24—42no—
390C24C2×D4×C10311yescharacteristic
391#41—24no—
392#41—24no—
393#41—42no—
394#41—42no—
395#41—42no—
396#41—42no—
397#41—42no—
398#41—42no—
399C2×Q8—21no—
400C2×Q8—21no—
401C2×Q8—42no—
402C2×D4—24no—
403C2×D4—21no—
404C2×D4—21no—
405C2×D4—21no—
406C2×D4—21no—
407C2×D4—42no—
408C2×D4—44no—
409C2×D4—42no—
410C2×D4—42no—
411C2×D4—41no—
412C2×D4—41no—
413C2×D4—42no—
414C2×D4—44no—
415C2×D4—42no—
416C2×D4—44no—
417C2×D4—44no—
418C2×D4—41no—
419C2×D4—41no—
420C2×D4—82no—
421C2×D4—82no—
422C22×C4—21no—
423C22×C4—22no—
424C22×C4—22no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—21no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—42no—
432C22×C4—41no—
433C22×C4—41no—
434C22×C4—42no—
435C22×C4C2×D4×C10311yescharacteristic
436C22×C4C2×D4×C10311yescharacteristic
437C22×C4C2×D4×C10311yescharacteristic
438C22×C4C2×D4×C10311yescharacteristic
439C22×C4C2×D4×C10311yescharacteristic
440C22×C4#41×C10311yescharacteristic
441SD16—44no—
442D8—44no—
443M16—42no—
444M16—42no—
445C2×C8—22no—
446C2×C8—41no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—44no—
450C22⋊C4—24no—
451C22⋊C4—44no—
452C22⋊C4—44no—
453C22⋊C4—44no—
454C22⋊C4—42no—
455C22⋊C4—41no—
456C22⋊C4—41no—
457C22⋊C4—41no—
458C22⋊C4—41no—
459C22⋊C4—41no—
460C22⋊C4—41no—
461C22⋊C4—82no—
462C42—42no—
463C23—22no—
464C23—22no—
465C23—22no—
466C23—22no—
467C23—22no—
468C23—22no—
469C23—41no—
470C23—42no—
471C23—42no—
472C23—41no—
473C23—42no—
474C23—41no—
475C23—41no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—42no—
480C23—41no—
481C23—41no—
482C23—42no—
483C23—42no—
484C23—42no—
485C23—41no—
486C23—42no—
487C23—81no—
488C23—81no—
489C23—88no—
490C23#120×C10311yescharacteristic
491C23#120×C10311yescharacteristic
492C23#121×C10311yescharacteristic
493Q8—22no—
494Q8—22no—
495Q8—41no—
496Q8—41no—
497D4—22no—
498D4—22no—
499D4—41no—
500D4—41no—
501D4—42no—
502D4—44no—
503D4—44no—
504D4—81no—
505D4—88no—
506D4—82no—
507D4—88no—
508D4—82no—
509C2×C4—22no—
510C2×C4—22no—
511C2×C4—24no—
512C2×C4—22no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—44no—
518C2×C4—44no—
519C2×C4—41no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—42no—
524C2×C4—41no—
525C2×C4—42no—
526C2×C4—41no—
527C2×C4—42no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—81no—
533C2×C4#120×C10311yescharacteristic
534C2×C4#121×C10311yescharacteristic
535C2×C4#121×C10311yescharacteristic
536C2×C4#127×C10311yescharacteristic
537C8—42no—
538C8—81no—
539C22—21no—
540C22—21no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—21no—
545C22—21no—
546C22—44no—
547C22—44no—
548C22—44no—
549C22—44no—
550C22—42no—
551C22—42no—
552C22—82no—
553C22—82no—
554C22—82no—
555C22—82no—
556C22—82no—
557C22—82no—
558C22—82no—
559C22—81no—
560C22—81no—
561C22—81no—
562C22—81no—
563C22—81no—
564C22—81no—
565C22—81no—
566C22#392×C10311yescharacteristic
567C22#453×C10312yes—
568C22B(4,𝔽2)×C10312yes—
569C4—21no—
570C4—21no—
571C4—21no—
572C4—21no—
573C4—44no—
574C4—42no—
575C4—82no—
576C4—81no—
577C4—81no—
578C2—22no—
579C2—22no—
580C2—41no—
581C2—82no—
582C2—82no—
583C2—161no—
584C2C103×#200211yescharacteristic
585C2C103×#201011yescharacteristic
586C2C103×#202111yescharacteristic
subgroupG/H
center, socleC22×C103#392
commutator, Frattini, cosocleC23×C4C23×C103
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3006C2semidirect
2. C103×#2539C2semidirect
3. C103×#2404C2semidirect
4. C103×#1789C2semidirect
5. C103×#1510C2semidirect
6. C103×#1462C2semidirect
7. C103×#1284C2semidirect
39. C22×Q8×C103D4semidirect
44. C22×D4×C103D4semidirect
45. C22×D4×C103D4semidirect
62. C2×C4⋊C4×C103D4semidirect
76. C2×C42×C103D4semidirect
83. C22⋊C8×C103D4semidirect
87. #95×C103D4semidirect
284. #9938C103direct (N × H)
294. #3006C2×C103semidirect
295. #2539C2×C103semidirect
296. #2404C2×C103semidirect
297. #1789C2×C103semidirect
298. #1510C2×C103semidirect
299. #1462C2×C103semidirect
300. #1284C2×C103semidirect
301. C103#9938direct (N × H)
333. C22×Q8D4×C103semidirect
338. C22×D4D4×C103semidirect
339. C22×D4D4×C103semidirect
356. C2×C4⋊C4D4×C103semidirect
370. C2×C42D4×C103semidirect
377. C22⋊C8D4×C103semidirect
381. #95D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#30062
C103×#25392
C103×#24042
C103×#17892
C103×#15102
C103×#14622
C103×#12842
#9938103