Finite Group Databasebeta

← C103×#29400 #39934675

Subgroups — C103×#29400 #39934675

Order 26368.

672 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2331C211yesmaximal, characteristic, complemented
2C103×#2319C211yesmaximal, characteristic
3C103×#2085C211yesmaximal, characteristic, complemented
4C103×#2073C211yesmaximal, characteristic
5C103×#2058C211yesmaximal, characteristic, complemented
6C103×#2023C211yesmaximal, characteristic
7C103×#1926C211yesmaximal, characteristic
8C103×#1926C211yesmaximal, characteristic
9C103×#1920C211yesmaximal, characteristic, complemented
10C103×#1920C211yesmaximal, characteristic, complemented
11C103×#1919C211yesmaximal, characteristic, complemented
12C103×#1918C211yesmaximal, characteristic, complemented
13C103×#1864C211yesmaximal, characteristic
14C103×#1862C211yesmaximal, characteristic
15C103×#1840C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C103C2211yescharacteristic
17C2×C4×D4×C103C2211yescharacteristic
18C2×#107×C103C2211yescharacteristic
19C2×#106×C103C2211yescharacteristic
20C2×#106×C103C2211yescharacteristic
21C2×#106×C103C2211yescharacteristic
22C2×#102×C103C2211yescharacteristic
23C2×#102×C103C2211yescharacteristic
24C2×#102×C103C2211yescharacteristic
25C2×#102×C103C2211yescharacteristic
26#391×C103—21no—
27#391×C103—21no—
28#390×C103C2211yescharacteristic
29#390×C103C2211yescharacteristic
30#389×C103C2211yescharacteristic
31#389×C103C2211yescharacteristic
32#389×C103C2211yescharacteristic
33#389×C103C2211yescharacteristic
34#388×C103—21no—
35#388×C103—21no—
36#387×C103—21no—
37#387×C103—21no—
38#382×C103C2211yescharacteristic
39#381×C103—21no—
40#380×C103—21no—
41C4×C4⋊C4×C103C2211yescharacteristic
42C4×C4⋊C4×C103C2211yescharacteristic
43C4×C4⋊C4×C103C2211yescharacteristic
44#376×C103C2211yescharacteristic
45#340×C103C2211yescharacteristic
46#340×C103C2211yescharacteristic
47#340×C103C2211yescharacteristic
48#340×C103C2211yescharacteristic
49#340×C103C2211yescharacteristic
50#340×C103C2211yescharacteristic
51#340×C103C2211yescharacteristic
52#340×C103C2211yescharacteristic
53#336×C103C2211yescharacteristic
54#336×C103C2211yescharacteristic
55#336×C103C2211yescharacteristic
56#336×C103C2211yescharacteristic
57#336×C103C2211yescharacteristic
58#336×C103C2211yescharacteristic
59C22×Q8×C103—21no—
60C22×D4×C103C2311yescharacteristic
61C23×C4×C103—21no—
62C22×C8×C103C2311yescharacteristic
63C22×C8×C103C2311yescharacteristic
64C22×C8×C103C2311yescharacteristic
65C22×C8×C103C2311yescharacteristic
66C4⋊Q8×C103—22no—
67C4⋊Q8×C103—22no—
68C4×D4×C103—22no—
69C4×D4×C103—22no—
70C2×C4⋊C4×C103—21no—
71C2×C4⋊C4×C103—21no—
72C2×C4⋊C4×C103—21no—
73C2×C4⋊C4×C103—21no—
74C2×C4⋊C4×C103—21no—
75C2×C4⋊C4×C103C2311yescharacteristic
76C2×C4⋊C4×C103C2311yescharacteristic
77C2×C4⋊C4×C103C2311yescharacteristic
78C2×C4⋊C4×C103C2311yescharacteristic
79C2×C4⋊C4×C103C2311yescharacteristic
80C2×C4⋊C4×C103C2311yescharacteristic
81C2×C4⋊C4×C103C2311yescharacteristic
82C2×C22⋊C4×C103—21no—
83C2×C22⋊C4×C103—21no—
84C2×C22⋊C4×C103—21no—
85C2×C22⋊C4×C103—21no—
86C2×C22⋊C4×C103—21no—
87C2×C42×C103—21no—
88C2×C42×C103—21no—
89C2×C42×C103—21no—
90C2×C42×C103C2311yescharacteristic
91C2×C42×C103C2311yescharacteristic
92C2×C42×C103C2311yescharacteristic
93#107×C103—22no—
94#106×C103—22no—
95#106×C103—22no—
96#106×C103—22no—
97#102×C103—22no—
98#102×C103—22no—
99#102×C103—22no—
100#102×C103—22no—
101#95×C103—21no—
102#95×C103—21no—
103#95×C103—21no—
104#95×C103—21no—
105#95×C103—21no—
106#95×C103—21no—
107#95×C103—21no—
108#95×C103—21no—
109#95×C103—21no—
110#95×C103D411yescharacteristic
111#95×C103D411yescharacteristic
112#95×C103D411yescharacteristic
113#95×C103D411yescharacteristic
114C24×C103—21no—
115C2×Q8×C103—24no—
116C2×Q8×C103—81no—
117C2×Q8×C103—81no—
118C2×D4×C103—21no—
119C2×D4×C103—21no—
120C2×D4×C103—21no—
121C2×D4×C103—21no—
122C2×D4×C103—21no—
123C2×D4×C103#4112yes—
124C22×C4×C103—21no—
125C22×C4×C103—21no—
126C22×C4×C103—21no—
127C22×C4×C103—24no—
128C22×C4×C103—21no—
129C22×C4×C103—21no—
130C22×C4×C103—21no—
131C22×C4×C103—21no—
132C22×C4×C103—81no—
133C22×C4×C103—81no—
134C22×C4×C103C2×D411yescharacteristic
135C22×C4×C103C2×D411yescharacteristic
136C22×C4×C103C2×D411yescharacteristic
137C22×C4×C103C2×D411yescharacteristic
138C22×C4×C103C2×D411yescharacteristic
139C22×C4×C103C2×D411yescharacteristic
140C22×C4×C103C2411yescharacteristic
141C2×C8×C103—21no—
142C2×C8×C103—21no—
143C2×C8×C103—21no—
144C2×C8×C103—21no—
145C2×C8×C103—21no—
146C2×C8×C103—21no—
147C2×C8×C103—21no—
148C2×C8×C103—21no—
149C2×C8×C103—21no—
150C2×C8×C103—21no—
151C2×C8×C103—21no—
152C2×C8×C103—21no—
153C4⋊C4×C103—24no—
154C4⋊C4×C103—21no—
155C4⋊C4×C103—21no—
156C4⋊C4×C103—21no—
157C4⋊C4×C103—21no—
158C4⋊C4×C103—21no—
159C4⋊C4×C103—21no—
160C4⋊C4×C103—21no—
161C4⋊C4×C103—21no—
162C4⋊C4×C103—21no—
163C4⋊C4×C103—21no—
164C4⋊C4×C103—21no—
165C4⋊C4×C103—81no—
166C4⋊C4×C103—81no—
167C4⋊C4×C103—81no—
168C4⋊C4×C103—81no—
169C4⋊C4×C103#4112yes—
170C4⋊C4×C103#4112yes—
171C4⋊C4×C103#4112yes—
172C22⋊C4×C103—24no—
173C22⋊C4×C103—81no—
174C22⋊C4×C103—81no—
175C22⋊C4×C103—81no—
176C22⋊C4×C103—81no—
177C42×C103—21no—
178C42×C103—21no—
179C42×C103—21no—
180C42×C103—21no—
181C42×C103—21no—
182C42×C103—21no—
183C42×C103—81no—
184C42×C103—81no—
185C42×C103—81no—
186C23×C103—22no—
187C23×C103—41no—
188C23×C103—41no—
189C23×C103—41no—
190C23×C103—41no—
191C23×C103—41no—
192C23×C103—41no—
193C23×C103C22×D411yescharacteristic
194Q8×C103—84no—
195D4×C103—22no—
196D4×C103—22no—
197D4×C103—41no—
198D4×C103—41no—
199C2×C4×C103—21no—
200C2×C4×C103—21no—
201C2×C4×C103—21no—
202C2×C4×C103—21no—
203C2×C4×C103—22no—
204C2×C4×C103—22no—
205C2×C4×C103—22no—
206C2×C4×C103—21no—
207C2×C4×C103—21no—
208C2×C4×C103—21no—
209C2×C4×C103—21no—
210C2×C4×C103—21no—
211C2×C4×C103—21no—
212C2×C4×C103—21no—
213C2×C4×C103—21no—
214C2×C4×C103—21no—
215C2×C4×C103—21no—
216C2×C4×C103—21no—
217C2×C4×C103—21no—
218C2×C4×C103—21no—
219C2×C4×C103—21no—
220C2×C4×C103—41no—
221C2×C4×C103—41no—
222C2×C4×C103—41no—
223C2×C4×C103—41no—
224C2×C4×C103—41no—
225C2×C4×C103—41no—
226C2×C4×C103—41no—
227C2×C4×C103—41no—
228C2×C4×C103—41no—
229C2×C4×C103—41no—
230C2×C4×C103—41no—
231C2×C4×C103—41no—
232C2×C4×C103—41no—
233C2×C4×C103—41no—
234C2×C4×C103—41no—
235C2×C4×C103—41no—
236C2×C4×C103—41no—
237C2×C4×C103—41no—
238C2×C4×C103—84no—
239C2×C4×C103C2×#4111yescharacteristic
240C2×C4×C103C2×#4111yescharacteristic
241C2×C4×C103C2×#4111yescharacteristic
242C2×C4×C103C2×#4111yescharacteristic
243C2×C4×C1032−1+411yescharacteristic
244C2×C4×C1032−1+411yescharacteristic
245C8×C103—41no—
246C8×C103—41no—
247C8×C103—41no—
248C8×C103—41no—
249C22×C103—42no—
250C22×C103—42no—
251C22×C103—42no—
252C22×C103—81no—
253C22×C103—81no—
254C22×C103—81no—
255C22×C103—81no—
256C22×C103#52511yescharacteristic
257C22×C103#52511yescharacteristic
258C22×C103#53611yescharacteristic
259C22×C103#57611yescharacteristic
260C22×C103#57711yescharacteristic
261C22×C103#57711yescharacteristic
262C22×C103#57711yescharacteristic
263C4×C103—41no—
264C4×C103—41no—
265C4×C103—42no—
266C4×C103—42no—
267C4×C103—42no—
268C4×C103—41no—
269C4×C103—41no—
270C4×C103—41no—
271C4×C103—41no—
272C4×C103—81no—
273C4×C103—81no—
274C4×C103—81no—
275C4×C103—81no—
276C4×C103#55211yescharacteristic
277C4×C103#55211yescharacteristic
278C4×C103#55611yescharacteristic
279C4×C103#55611yescharacteristic
280#29400C10311yesmaximal, characteristic, direct product factor, Sylow
281C2×C103—82no—
282C2×C103#259911yescharacteristic
283C2×C103#311811yescharacteristic
284C2×C103#311811yescharacteristic
285C2×C103#312511yescharacteristic
286C2×C103#312611yescharacteristic
287C2×C103#324111yescharacteristic
288C2×C103#324411yescharacteristic
289#2331C2×C10311yescharacteristic, complemented
290#2319C2×C10311yescharacteristic
291#2085C2×C10311yescharacteristic, complemented
292#2073C2×C10311yescharacteristic
293#2058C2×C10311yescharacteristic, complemented
294#2023C2×C10311yescharacteristic
295#1926C2×C10311yescharacteristic
296#1926C2×C10311yescharacteristic
297#1920C2×C10311yescharacteristic, complemented
298#1920C2×C10311yescharacteristic, complemented
299#1919C2×C10311yescharacteristic, complemented
300#1918C2×C10311yescharacteristic, complemented
301#1864C2×C10311yescharacteristic
302#1862C2×C10311yescharacteristic
303#1840C2×C10311yescharacteristic, complemented
304C103#2940011yescharacteristic, direct product factor, Sylow
305C2×C4⋊Q8C22×C10311yescharacteristic
306C2×C4×D4C22×C10311yescharacteristic
307C2×#107C22×C10311yescharacteristic
308C2×#106C22×C10311yescharacteristic
309C2×#106C22×C10311yescharacteristic
310C2×#106C22×C10311yescharacteristic
311C2×#102C22×C10311yescharacteristic
312C2×#102C22×C10311yescharacteristic
313C2×#102C22×C10311yescharacteristic
314C2×#102C22×C10311yescharacteristic
315#391—21no—
316#391—21no—
317#390C22×C10311yescharacteristic
318#390C22×C10311yescharacteristic
319#389C22×C10311yescharacteristic
320#389C22×C10311yescharacteristic
321#389C22×C10311yescharacteristic
322#389C22×C10311yescharacteristic
323#388—21no—
324#388—21no—
325#387—21no—
326#387—21no—
327#382C22×C10311yescharacteristic
328#381—21no—
329#380—21no—
330C4×C4⋊C4C22×C10311yescharacteristic
331C4×C4⋊C4C22×C10311yescharacteristic
332C4×C4⋊C4C22×C10311yescharacteristic
333#376C22×C10311yescharacteristic
334#340C22×C10311yescharacteristic
335#340C22×C10311yescharacteristic
336#340C22×C10311yescharacteristic
337#340C22×C10311yescharacteristic
338#340C22×C10311yescharacteristic
339#340C22×C10311yescharacteristic
340#340C22×C10311yescharacteristic
341#340C22×C10311yescharacteristic
342#336C22×C10311yescharacteristic
343#336C22×C10311yescharacteristic
344#336C22×C10311yescharacteristic
345#336C22×C10311yescharacteristic
346#336C22×C10311yescharacteristic
347#336C22×C10311yescharacteristic
348C22×Q8—21no—
349C22×D4C23×C10311yescharacteristic
350C23×C4—21no—
351C22×C8C23×C10311yescharacteristic
352C22×C8C23×C10311yescharacteristic
353C22×C8C23×C10311yescharacteristic
354C22×C8C23×C10311yescharacteristic
355C4⋊Q8—22no—
356C4⋊Q8—22no—
357C4×D4—22no—
358C4×D4—22no—
359C2×C4⋊C4—21no—
360C2×C4⋊C4—21no—
361C2×C4⋊C4—21no—
362C2×C4⋊C4—21no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4C23×C10311yescharacteristic
365C2×C4⋊C4C23×C10311yescharacteristic
366C2×C4⋊C4C23×C10311yescharacteristic
367C2×C4⋊C4C23×C10311yescharacteristic
368C2×C4⋊C4C23×C10311yescharacteristic
369C2×C4⋊C4C23×C10311yescharacteristic
370C2×C4⋊C4C23×C10311yescharacteristic
371C2×C22⋊C4—21no—
372C2×C22⋊C4—21no—
373C2×C22⋊C4—21no—
374C2×C22⋊C4—21no—
375C2×C22⋊C4—21no—
376C2×C42—21no—
377C2×C42—21no—
378C2×C42—21no—
379C2×C42C23×C10311yescharacteristic
380C2×C42C23×C10311yescharacteristic
381C2×C42C23×C10311yescharacteristic
382#107—22no—
383#106—22no—
384#106—22no—
385#106—22no—
386#102—22no—
387#102—22no—
388#102—22no—
389#102—22no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95—21no—
396#95—21no—
397#95—21no—
398#95—21no—
399#95D4×C10311yescharacteristic
400#95D4×C10311yescharacteristic
401#95D4×C10311yescharacteristic
402#95D4×C10311yescharacteristic
403C24—21no—
404C2×Q8—24no—
405C2×Q8—81no—
406C2×Q8—81no—
407C2×D4—21no—
408C2×D4—21no—
409C2×D4—21no—
410C2×D4—21no—
411C2×D4—21no—
412C2×D4#41×C10312yes—
413C22×C4—21no—
414C22×C4—21no—
415C22×C4—21no—
416C22×C4—24no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—81no—
422C22×C4—81no—
423C22×C4C2×D4×C10311yescharacteristic
424C22×C4C2×D4×C10311yescharacteristic
425C22×C4C2×D4×C10311yescharacteristic
426C22×C4C2×D4×C10311yescharacteristic
427C22×C4C2×D4×C10311yescharacteristic
428C22×C4C2×D4×C10311yescharacteristic
429C22×C4C24×C10311yescharacteristic
430C2×C8—21no—
431C2×C8—21no—
432C2×C8—21no—
433C2×C8—21no—
434C2×C8—21no—
435C2×C8—21no—
436C2×C8—21no—
437C2×C8—21no—
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C4⋊C4—24no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—21no—
448C4⋊C4—21no—
449C4⋊C4—21no—
450C4⋊C4—21no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—81no—
455C4⋊C4—81no—
456C4⋊C4—81no—
457C4⋊C4—81no—
458C4⋊C4#41×C10312yes—
459C4⋊C4#41×C10312yes—
460C4⋊C4#41×C10312yes—
461C22⋊C4—24no—
462C22⋊C4—81no—
463C22⋊C4—81no—
464C22⋊C4—81no—
465C22⋊C4—81no—
466C42—21no—
467C42—21no—
468C42—21no—
469C42—21no—
470C42—21no—
471C42—21no—
472C42—81no—
473C42—81no—
474C42—81no—
475C23—22no—
476C23—41no—
477C23—41no—
478C23—41no—
479C23—41no—
480C23—41no—
481C23—41no—
482C23C22×D4×C10311yescharacteristic
483Q8—84no—
484D4—22no—
485D4—22no—
486D4—41no—
487D4—41no—
488C2×C4—21no—
489C2×C4—21no—
490C2×C4—21no—
491C2×C4—21no—
492C2×C4—22no—
493C2×C4—22no—
494C2×C4—22no—
495C2×C4—21no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—21no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—84no—
528C2×C4C2×#41×C10311yescharacteristic
529C2×C4C2×#41×C10311yescharacteristic
530C2×C4C2×#41×C10311yescharacteristic
531C2×C4C2×#41×C10311yescharacteristic
532C2×C42−1+4×C10311yescharacteristic
533C2×C42−1+4×C10311yescharacteristic
534C8—41no—
535C8—41no—
536C8—41no—
537C8—41no—
538C22—42no—
539C22—42no—
540C22—42no—
541C22—81no—
542C22—81no—
543C22—81no—
544C22—81no—
545C22#525×C10311yescharacteristic
546C22#525×C10311yescharacteristic
547C22#536×C10311yescharacteristic
548C22#576×C10311yescharacteristic
549C22#577×C10311yescharacteristic
550C22#577×C10311yescharacteristic
551C22#577×C10311yescharacteristic
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—42no—
557C4—42no—
558C4—42no—
559C4—41no—
560C4—41no—
561C4—81no—
562C4—81no—
563C4—81no—
564C4—81no—
565C4#552×C10311yescharacteristic
566C4#552×C10311yescharacteristic
567C4#556×C10311yescharacteristic
568C4#556×C10311yescharacteristic
569C2—82no—
570C2C103×#259911yescharacteristic
571C2C103×#311811yescharacteristic
572C2C103×#311811yescharacteristic
573C2C103×#312511yescharacteristic
574C2C103×#312611yescharacteristic
575C2C103×#324111yescharacteristic
576C2C103×#324411yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ #376×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#2331C2semidirect
3. C103×#2085C2semidirect
5. C103×#2058C2semidirect
9. C103×#1920C2semidirect
10. C103×#1920C2semidirect
11. C103×#1919C2semidirect
12. C103×#1918C2semidirect
15. C103×#1840C2semidirect
280. #29400C103direct (N × H)
289. #2331C2×C103semidirect
291. #2085C2×C103semidirect
293. #2058C2×C103semidirect
297. #1920C2×C103semidirect
298. #1920C2×C103semidirect
299. #1919C2×C103semidirect
300. #1918C2×C103semidirect
303. #1840C2×C103semidirect
304. C103#29400direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#23312
C103×#23192
C103×#20852
C103×#20732
C103×#20582
C103×#20232
C103×#19262
C103×#19202
C103×#19192
C103×#19182
C103×#18642
C103×#18622
C103×#18402
#29400103