Finite Group Databasebeta

← C103×#17921 #39923196

Subgroups — C103×#17921 #39923196

Order 26368.

598 conjugacy classes of subgroups.

The subgroup lattice has 564 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3107C211yesmaximal, characteristic
2C103×#2988C211yesmaximal, characteristic
3C103×#2985C211yesmaximal, characteristic, complemented
4C103×#1587C211yesmaximal, characteristic, complemented
5C103×#1585C211yesmaximal, characteristic, complemented
6C103×#1584C211yesmaximal, characteristic, complemented
7C103×#1582C211yesmaximal, characteristic, complemented
8C103×#1579C211yesmaximal, characteristic, complemented
9C103×SD16⋊C8C211yesmaximal, characteristic, complemented
10C8×Q16×C103C211yesmaximal, characteristic, complemented
11C8×SD16×C103C211yesmaximal, characteristic, complemented
12C103×#1573C211yesmaximal, characteristic, complemented
13C103×#1488C211yesmaximal, characteristic
14C103×#1481C211yesmaximal, characteristic, complemented
15C103×#1454C211yesmaximal, characteristic, complemented
16#533×C103C2211yescharacteristic
17C4×#41×C103C2211yescharacteristic
18#485×C103C411yescharacteristic
19#485×C103C411yescharacteristic
20#475×C103C411yescharacteristic
21#474×C103C411yescharacteristic
22#462×C103C411yescharacteristic
23#461×C103C411yescharacteristic
24#452×C103C411yescharacteristic
25#452×C103C411yescharacteristic
26#446×C103—21no—
27#446×C103—21no—
28#446×C103C2211yescharacteristic
29#446×C103C2211yescharacteristic
30C8×Q8×C103C2211yescharacteristic
31C8×Q8×C103C2211yescharacteristic
32C8×Q8×C103C2211yescharacteristic
33C8×Q8×C103C2211yescharacteristic
34C4×Q16×C103C2211yescharacteristic
35C4×Q16×C103C2211yescharacteristic
36C4×SD16×C103C2211yescharacteristic
37C4×SD16×C103C2211yescharacteristic
38C8×D4×C103—21no—
39C8×D4×C103—21no—
40C8×D4×C103C2211yescharacteristic
41C8×D4×C103C2211yescharacteristic
42#433×C103—21no—
43#433×C103—21no—
44#432×C103C2211yescharacteristic
45#431×C103—21no—
46#431×C103C2211yescharacteristic
47#431×C103C2211yescharacteristic
48#431×C103C2211yescharacteristic
49C2×C4⋊C8×C103—21no—
50C2×C4⋊C8×C103C2211yescharacteristic
51#335×C103C2211yescharacteristic
52#335×C103C2211yescharacteristic
53#334×C103C2211yescharacteristic
54#334×C103C2211yescharacteristic
55Q8⋊C8×C103C2211yescharacteristic
56Q8⋊C8×C103C2211yescharacteristic
57Q8⋊C8×C103C2211yescharacteristic
58Q8⋊C8×C103C2211yescharacteristic
59Q8⋊C8×C103C2211yescharacteristic
60Q8⋊C8×C103C2211yescharacteristic
61D4⋊C8×C103C2211yescharacteristic
62D4⋊C8×C103C2211yescharacteristic
63#322×C103C2211yescharacteristic
64#322×C103C2211yescharacteristic
65#322×C103C2211yescharacteristic
66C82×C103C2211yescharacteristic
67C2×#41×C103C2×C411yescharacteristic
68C2×Q16×C103C2×C411yescharacteristic
69C2×Q16×C103C2×C411yescharacteristic
70C2×SD16×C103C2×C411yescharacteristic
71C2×SD16×C103C2×C411yescharacteristic
72C22×C8×C103—21no—
73C22×C8×C103—21no—
74C22×C8×C103—21no—
75C4⋊Q8×C103C2×C411yescharacteristic
76C4⋊Q8×C103C2×C411yescharacteristic
77#125×C103—21no—
78C22⋊Q8×C103—21no—
79C22⋊Q8×C103C2×C411yescharacteristic
80C22⋊Q8×C103C2×C411yescharacteristic
81C4×Q8×C103—21no—
82C4×Q8×C103C2×C411yescharacteristic
83C4×Q8×C103C2311yescharacteristic
84C4×Q8×C103C2311yescharacteristic
85C4×Q8×C103C2311yescharacteristic
86C4×D4×C103—21no—
87C4×D4×C103—21no—
88C4×D4×C103C2×C411yescharacteristic
89C4×D4×C103C2311yescharacteristic
90#117×C103—21no—
91#117×C103—21no—
92#117×C103C2×C411yescharacteristic
93C2×C42×C103—21no—
94C2×C42×C103C2311yescharacteristic
95#107×C103C2×C411yescharacteristic
96#107×C103C2×C411yescharacteristic
97#106×C103C2×C411yescharacteristic
98#106×C103C2×C411yescharacteristic
99C4⋊C8×C103—21no—
100C4⋊C8×C103—21no—
101C4⋊C8×C103—21no—
102C4⋊C8×C103—21no—
103C4⋊C8×C103—21no—
104C4⋊C8×C103—21no—
105C4⋊C8×C103—21no—
106C4⋊C8×C103—21no—
107C4⋊C8×C103C2×C411yescharacteristic
108C4⋊C8×C103C2×C411yescharacteristic
109C4⋊C8×C103D411yescharacteristic
110C4⋊C8×C103D411yescharacteristic
111C4⋊C8×C103C2311yescharacteristic
112C4⋊C8×C103C2311yescharacteristic
113C4⋊C8×C103C2311yescharacteristic
114C4⋊C8×C103C2311yescharacteristic
115#103×C103C2×C411yescharacteristic
116#103×C103C2×C411yescharacteristic
117#103×C103C2×C411yescharacteristic
118#103×C103C2×C411yescharacteristic
119#103×C103C2×C411yescharacteristic
120#103×C103C2×C411yescharacteristic
121#102×C103C2×C411yescharacteristic
122#102×C103C2×C411yescharacteristic
123C22⋊C8×C103—21no—
124C22⋊C8×C103—21no—
125C22⋊C8×C103—21no—
126C22⋊C8×C103—21no—
127C22⋊C8×C103C2×C411yescharacteristic
128C22⋊C8×C103C2×C411yescharacteristic
129C22⋊C8×C103D411yescharacteristic
130C22⋊C8×C103D411yescharacteristic
131#97×C103—21no—
132#97×C103—21no—
133#97×C103—21no—
134C4×C8×C103—21no—
135C4×C8×C103—21no—
136C4×C8×C103—21no—
137C4×C8×C103—21no—
138C4×C8×C103C2311yescharacteristic
139C4×C8×C103C2311yescharacteristic
140C4×C8×C103C2311yescharacteristic
141C4×C8×C103C2311yescharacteristic
142C4×C8×C103C2311yescharacteristic
143C4×C8×C103C2311yescharacteristic
144#41×C103—22no—
145#41×C103—22no—
146C2×Q8×C103—21no—
147C2×Q8×C103C22×C411yescharacteristic
148C2×Q8×C103C22×C411yescharacteristic
149C2×Q8×C103C22×C411yescharacteristic
150C2×D4×C103—21no—
151C2×D4×C103C22×C411yescharacteristic
152C22×C4×C103—21no—
153C22×C4×C103—21no—
154C22×C4×C103—21no—
155C22×C4×C103C22×C411yescharacteristic
156C22×C4×C103C2×D411yescharacteristic
157C22×C4×C103#4111yescharacteristic
158Q16×C103—22no—
159Q16×C103—22no—
160SD16×C103—22no—
161SD16×C103—22no—
162C2×C8×C103—21no—
163C2×C8×C103—21no—
164C2×C8×C103—21no—
165C2×C8×C103—21no—
166C2×C8×C103—21no—
167C2×C8×C103—21no—
168C2×C8×C103—81no—
169C2×C8×C103—81no—
170C2×C8×C103—81no—
171C2×C8×C103C22×C411yescharacteristic
172C2×C8×C103C22×C411yescharacteristic
173C2×C8×C103C22×C411yescharacteristic
174C2×C8×C103C22×C411yescharacteristic
175C2×C8×C103C2×D411yescharacteristic
176C2×C8×C103C2×D411yescharacteristic
177C2×C8×C103C2×D411yescharacteristic
178C2×C8×C103C2×D411yescharacteristic
179C4⋊C4×C103—21no—
180C4⋊C4×C103—21no—
181C4⋊C4×C103—21no—
182C4⋊C4×C103—21no—
183C4⋊C4×C103—21no—
184C4⋊C4×C103—21no—
185C4⋊C4×C103—21no—
186C4⋊C4×C103—21no—
187C4⋊C4×C103—21no—
188C4⋊C4×C103C22×C411yescharacteristic
189C4⋊C4×C103C22×C411yescharacteristic
190C4⋊C4×C103C22×C411yescharacteristic
191C4⋊C4×C103C22×C411yescharacteristic
192C22⋊C4×C103—21no—
193C22⋊C4×C103—21no—
194C22⋊C4×C103—21no—
195C22⋊C4×C103—21no—
196C22⋊C4×C103—21no—
197C42×C103—21no—
198C42×C103—21no—
199C42×C103—21no—
200C42×C103—21no—
201C42×C103—21no—
202C42×C103C22×C411yescharacteristic
203C42×C103C2×D411yescharacteristic
204C42×C103#4111yescharacteristic
205C42×C103C2411yescharacteristic
206C23×C103—21no—
207C23×C103C4×D411yescharacteristic
208Q8×C103—21no—
209Q8×C103—21no—
210Q8×C103—21no—
211Q8×C103—21no—
212Q8×C103—21no—
213Q8×C103—81no—
214Q8×C103#13112yes—
215D4×C103—24no—
216D4×C103—21no—
217D4×C103#13112yes—
218C2×C4×C103—24no—
219C2×C4×C103—21no—
220C2×C4×C103—21no—
221C2×C4×C103—21no—
222C2×C4×C103—21no—
223C2×C4×C103—21no—
224C2×C4×C103—21no—
225C2×C4×C103—21no—
226C2×C4×C103—21no—
227C2×C4×C103—21no—
228C2×C4×C103—21no—
229C2×C4×C103—21no—
230C2×C4×C103—41no—
231C2×C4×C103—41no—
232C2×C4×C103—41no—
233C2×C4×C103—81no—
234C2×C4×C103C4×D411yescharacteristic
235C2×C4×C103C4×D411yescharacteristic
236C2×C4×C103C4×D411yescharacteristic
237C2×C4×C103C23×C411yescharacteristic
238C2×C4×C103C22×D411yescharacteristic
239C2×C4×C103C2×#4111yescharacteristic
240C8×C103—21no—
241C8×C103—21no—
242C8×C103—21no—
243C8×C103—21no—
244C8×C103—21no—
245C8×C103—21no—
246C8×C103—21no—
247C8×C103—21no—
248C8×C103—41no—
249C8×C103—41no—
250C8×C103—41no—
251C8×C103—41no—
252C8×C103—41no—
253C8×C103—41no—
254C22×C103—21no—
255C22×C103—22no—
256C22×C103—21no—
257C22×C103—21no—
258C22×C103—41no—
259C22×C103—41no—
260C22×C103C2×C4×D411yescharacteristic
261C4×C103—21no—
262C4×C103—22no—
263C4×C103—21no—
264C4×C103—21no—
265C4×C103—21no—
266C4×C103—41no—
267C4×C103—41no—
268C4×C103—41no—
269C4×C103—41no—
270C4×C103—41no—
271C4×C103—41no—
272C4×C103C2×#13111yescharacteristic
273C4×C103C2×#13111yescharacteristic
274C4×C103#57711yescharacteristic
275C4×C103#57811yescharacteristic
276#17921C10311yesmaximal, characteristic, direct product factor, Sylow
277C2×C103—41no—
278C2×C103—42no—
279C2×C103#292911yescharacteristic
280C2×C103#294711yescharacteristic
281C2×C103#295711yescharacteristic
282#3107C2×C10311yescharacteristic
283#2988C2×C10311yescharacteristic
284#2985C2×C10311yescharacteristic, complemented
285#1587C2×C10311yescharacteristic, complemented
286#1585C2×C10311yescharacteristic, complemented
287#1584C2×C10311yescharacteristic, complemented
288#1582C2×C10311yescharacteristic, complemented
289#1579C2×C10311yescharacteristic, complemented
290SD16⋊C8C2×C10311yescharacteristic, complemented
291C8×Q16C2×C10311yescharacteristic, complemented
292C8×SD16C2×C10311yescharacteristic, complemented
293#1573C2×C10311yescharacteristic, complemented
294#1488C2×C10311yescharacteristic
295#1481C2×C10311yescharacteristic, complemented
296#1454C2×C10311yescharacteristic, complemented
297C103#1792111yescharacteristic, direct product factor, Sylow
298#533C22×C10311yescharacteristic
299C4×#41C22×C10311yescharacteristic
300#485C4×C10311yescharacteristic
301#485C4×C10311yescharacteristic
302#475C4×C10311yescharacteristic
303#474C4×C10311yescharacteristic
304#462C4×C10311yescharacteristic
305#461C4×C10311yescharacteristic
306#452C4×C10311yescharacteristic
307#452C4×C10311yescharacteristic
308#446—21no—
309#446—21no—
310#446C22×C10311yescharacteristic
311#446C22×C10311yescharacteristic
312C8×Q8C22×C10311yescharacteristic
313C8×Q8C22×C10311yescharacteristic
314C8×Q8C22×C10311yescharacteristic
315C8×Q8C22×C10311yescharacteristic
316C4×Q16C22×C10311yescharacteristic
317C4×Q16C22×C10311yescharacteristic
318C4×SD16C22×C10311yescharacteristic
319C4×SD16C22×C10311yescharacteristic
320C8×D4—21no—
321C8×D4—21no—
322C8×D4C22×C10311yescharacteristic
323C8×D4C22×C10311yescharacteristic
324#433—21no—
325#433—21no—
326#432C22×C10311yescharacteristic
327#431—21no—
328#431C22×C10311yescharacteristic
329#431C22×C10311yescharacteristic
330#431C22×C10311yescharacteristic
331C2×C4⋊C8—21no—
332C2×C4⋊C8C22×C10311yescharacteristic
333#335C22×C10311yescharacteristic
334#335C22×C10311yescharacteristic
335#334C22×C10311yescharacteristic
336#334C22×C10311yescharacteristic
337Q8⋊C8C22×C10311yescharacteristic
338Q8⋊C8C22×C10311yescharacteristic
339Q8⋊C8C22×C10311yescharacteristic
340Q8⋊C8C22×C10311yescharacteristic
341Q8⋊C8C22×C10311yescharacteristic
342Q8⋊C8C22×C10311yescharacteristic
343D4⋊C8C22×C10311yescharacteristic
344D4⋊C8C22×C10311yescharacteristic
345#322C22×C10311yescharacteristic
346#322C22×C10311yescharacteristic
347#322C22×C10311yescharacteristic
348C82C22×C10311yescharacteristic
349C2×#41C2×C4×C10311yescharacteristic
350C2×Q16C2×C4×C10311yescharacteristic
351C2×Q16C2×C4×C10311yescharacteristic
352C2×SD16C2×C4×C10311yescharacteristic
353C2×SD16C2×C4×C10311yescharacteristic
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—21no—
357C4⋊Q8C2×C4×C10311yescharacteristic
358C4⋊Q8C2×C4×C10311yescharacteristic
359#125—21no—
360C22⋊Q8—21no—
361C22⋊Q8C2×C4×C10311yescharacteristic
362C22⋊Q8C2×C4×C10311yescharacteristic
363C4×Q8—21no—
364C4×Q8C2×C4×C10311yescharacteristic
365C4×Q8C23×C10311yescharacteristic
366C4×Q8C23×C10311yescharacteristic
367C4×Q8C23×C10311yescharacteristic
368C4×D4—21no—
369C4×D4—21no—
370C4×D4C2×C4×C10311yescharacteristic
371C4×D4C23×C10311yescharacteristic
372#117—21no—
373#117—21no—
374#117C2×C4×C10311yescharacteristic
375C2×C42—21no—
376C2×C42C23×C10311yescharacteristic
377#107C2×C4×C10311yescharacteristic
378#107C2×C4×C10311yescharacteristic
379#106C2×C4×C10311yescharacteristic
380#106C2×C4×C10311yescharacteristic
381C4⋊C8—21no—
382C4⋊C8—21no—
383C4⋊C8—21no—
384C4⋊C8—21no—
385C4⋊C8—21no—
386C4⋊C8—21no—
387C4⋊C8—21no—
388C4⋊C8—21no—
389C4⋊C8C2×C4×C10311yescharacteristic
390C4⋊C8C2×C4×C10311yescharacteristic
391C4⋊C8D4×C10311yescharacteristic
392C4⋊C8D4×C10311yescharacteristic
393C4⋊C8C23×C10311yescharacteristic
394C4⋊C8C23×C10311yescharacteristic
395C4⋊C8C23×C10311yescharacteristic
396C4⋊C8C23×C10311yescharacteristic
397#103C2×C4×C10311yescharacteristic
398#103C2×C4×C10311yescharacteristic
399#103C2×C4×C10311yescharacteristic
400#103C2×C4×C10311yescharacteristic
401#103C2×C4×C10311yescharacteristic
402#103C2×C4×C10311yescharacteristic
403#102C2×C4×C10311yescharacteristic
404#102C2×C4×C10311yescharacteristic
405C22⋊C8—21no—
406C22⋊C8—21no—
407C22⋊C8—21no—
408C22⋊C8—21no—
409C22⋊C8C2×C4×C10311yescharacteristic
410C22⋊C8C2×C4×C10311yescharacteristic
411C22⋊C8D4×C10311yescharacteristic
412C22⋊C8D4×C10311yescharacteristic
413#97—21no—
414#97—21no—
415#97—21no—
416C4×C8—21no—
417C4×C8—21no—
418C4×C8—21no—
419C4×C8—21no—
420C4×C8C23×C10311yescharacteristic
421C4×C8C23×C10311yescharacteristic
422C4×C8C23×C10311yescharacteristic
423C4×C8C23×C10311yescharacteristic
424C4×C8C23×C10311yescharacteristic
425C4×C8C23×C10311yescharacteristic
426#41—22no—
427#41—22no—
428C2×Q8—21no—
429C2×Q8C22×C4×C10311yescharacteristic
430C2×Q8C22×C4×C10311yescharacteristic
431C2×Q8C22×C4×C10311yescharacteristic
432C2×D4—21no—
433C2×D4C22×C4×C10311yescharacteristic
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4C22×C4×C10311yescharacteristic
438C22×C4C2×D4×C10311yescharacteristic
439C22×C4#41×C10311yescharacteristic
440Q16—22no—
441Q16—22no—
442SD16—22no—
443SD16—22no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—81no—
451C2×C8—81no—
452C2×C8—81no—
453C2×C8C22×C4×C10311yescharacteristic
454C2×C8C22×C4×C10311yescharacteristic
455C2×C8C22×C4×C10311yescharacteristic
456C2×C8C22×C4×C10311yescharacteristic
457C2×C8C2×D4×C10311yescharacteristic
458C2×C8C2×D4×C10311yescharacteristic
459C2×C8C2×D4×C10311yescharacteristic
460C2×C8C2×D4×C10311yescharacteristic
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4C22×C4×C10311yescharacteristic
471C4⋊C4C22×C4×C10311yescharacteristic
472C4⋊C4C22×C4×C10311yescharacteristic
473C4⋊C4C22×C4×C10311yescharacteristic
474C22⋊C4—21no—
475C22⋊C4—21no—
476C22⋊C4—21no—
477C22⋊C4—21no—
478C22⋊C4—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—21no—
483C42—21no—
484C42C22×C4×C10311yescharacteristic
485C42C2×D4×C10311yescharacteristic
486C42#41×C10311yescharacteristic
487C42C24×C10311yescharacteristic
488C23—21no—
489C23C4×D4×C10311yescharacteristic
490Q8—21no—
491Q8—21no—
492Q8—21no—
493Q8—21no—
494Q8—21no—
495Q8—81no—
496Q8#131×C10312yes—
497D4—24no—
498D4—21no—
499D4#131×C10312yes—
500C2×C4—24no—
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—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4—81no—
516C2×C4C4×D4×C10311yescharacteristic
517C2×C4C4×D4×C10311yescharacteristic
518C2×C4C4×D4×C10311yescharacteristic
519C2×C4C23×C4×C10311yescharacteristic
520C2×C4C22×D4×C10311yescharacteristic
521C2×C4C2×#41×C10311yescharacteristic
522C8—21no—
523C8—21no—
524C8—21no—
525C8—21no—
526C8—21no—
527C8—21no—
528C8—21no—
529C8—21no—
530C8—41no—
531C8—41no—
532C8—41no—
533C8—41no—
534C8—41no—
535C8—41no—
536C22—21no—
537C22—21no—
538C22—22no—
539C22—21no—
540C22—41no—
541C22—41no—
542C22C2×C4×D4×C10311yescharacteristic
543C4—21no—
544C4—21no—
545C4—21no—
546C4—22no—
547C4—21no—
548C4—41no—
549C4—41no—
550C4—41no—
551C4—41no—
552C4—41no—
553C4—41no—
554C4C2×#131×C10311yescharacteristic
555C4C2×#131×C10311yescharacteristic
556C4#577×C10311yescharacteristic
557C4#578×C10311yescharacteristic
558C2—41no—
559C2—42no—
560C2C103×#292911yescharacteristic
561C2C103×#294711yescharacteristic
562C2C103×#295711yescharacteristic
subgroupG/H
centerC2×C4×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC42C24×C103
socleC22×C103C2×C4×D4
prime radicalC2×#41×C103C2×C4
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ #431×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C103×#2985C2semidirect
4. C103×#1587C2semidirect
5. C103×#1585C2semidirect
6. C103×#1584C2semidirect
7. C103×#1582C2semidirect
8. C103×#1579C2semidirect
9. C103×SD16⋊C8C2semidirect
10. C8×Q16×C103C2semidirect
11. C8×SD16×C103C2semidirect
12. C103×#1573C2semidirect
14. C103×#1481C2semidirect
15. C103×#1454C2semidirect
276. #17921C103direct (N × H)
284. #2985C2×C103semidirect
285. #1587C2×C103semidirect
286. #1585C2×C103semidirect
287. #1584C2×C103semidirect
288. #1582C2×C103semidirect
289. #1579C2×C103semidirect
290. SD16⋊C8C2×C103semidirect
291. C8×Q16C2×C103semidirect
292. C8×SD16C2×C103semidirect
293. #1573C2×C103semidirect
295. #1481C2×C103semidirect
296. #1454C2×C103semidirect
297. C103#17921direct (N × H)

Maximal subgroups

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

subgroupindex
C103×#31072
C103×#29882
C103×#29852
C103×#15872
C103×#15852
C103×#15842
C103×#15822
C103×#15792
C103×SD16⋊C82
C8×Q16×C1032
C8×SD16×C1032
C103×#15732
C103×#14882
C103×#14812
C103×#14542
#17921103