Finite Group Databasebeta

← C103×#9921 #39915196

Subgroups — C103×#9921 #39915196

Order 26368.

672 conjugacy classes of subgroups.

The subgroup lattice has 480 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#481×C103C211yesmaximal, characteristic
2C103×#2618C211yesmaximal, characteristic
3C2×#400×C103C211yesmaximal, characteristic, complemented
4C103×#1824C211yesmaximal, characteristic, complemented
5C2×#327×C103C211yesmaximal, characteristic
6C2×#324×C103C211yesmaximal, characteristic, complemented
7C103×#1294C211yesmaximal, characteristic, complemented
8C2×#123×C103—21no—
9C2×#121×C103C2211yescharacteristic
10C22×C4⋊C4×C103C2211yescharacteristic
11C22×C4⋊C4×C103C2211yescharacteristic
12#481×C103—22no—
13#481×C103—22no—
14C2×#106×C103—21no—
15C2×#102×C103—21no—
16C2×C22⋊C8×C103C2211yescharacteristic
17C2×C22⋊C8×C103C2211yescharacteristic
18#400×C103—22no—
19#400×C103—22no—
20#398×C103—21no—
21#396×C103—22no—
22#394×C103—21no—
23#386×C103—21no—
24#380×C103C2211yescharacteristic
25C2×#95×C103—21no—
26C2×#95×C103—21no—
27C2×#95×C103C2211yescharacteristic
28#340×C103—22no—
29#327×C103—22no—
30#324×C103—22no—
31C22×D4×C103—21no—
32C22×D4×C103D411yescharacteristic
33C23×C4×C103—21no—
34C23×C4×C103—21no—
35C23×C4×C103D411yescharacteristic
36C23×C4×C103D411yescharacteristic
37C23×C4×C103C2311yescharacteristic
38C22×C8×C103—21no—
39C22×C8×C103—21no—
40#123×C103—42no—
41#123×C103—42no—
42#121×C103—21no—
43#121×C103—21no—
44#121×C103—21no—
45#121×C103—21no—
46C2×C4⋊C4×C103—21no—
47C2×C4⋊C4×C103—21no—
48C2×C4⋊C4×C103—21no—
49C2×C4⋊C4×C103—21no—
50C2×C4⋊C4×C103—22no—
51C2×C4⋊C4×C103—21no—
52C2×C4⋊C4×C103—21no—
53C2×C4⋊C4×C103—21no—
54C2×C4⋊C4×C103—21no—
55C2×C4⋊C4×C103—21no—
56C2×C4⋊C4×C103—21no—
57C2×C4⋊C4×C103—21no—
58C2×C4⋊C4×C103D411yescharacteristic
59C2×C4⋊C4×C103D412yes—
60C2×C4⋊C4×C103D412yes—
61C2×C22⋊C4×C103—22no—
62C2×C22⋊C4×C103—21no—
63C2×C22⋊C4×C103—21no—
64C2×C22⋊C4×C103—22no—
65#106×C103—24no—
66#102×C103—24no—
67C22⋊C8×C103—21no—
68C22⋊C8×C103—21no—
69C22⋊C8×C103—21no—
70C22⋊C8×C103D412yes—
71#95×C103—24no—
72#95×C103—24no—
73#95×C103—22no—
74#95×C103—21no—
75#95×C103—21no—
76#95×C103D412yes—
77C24×C103—21no—
78C24×C103C2×D411yescharacteristic
79C2×D4×C103—21no—
80C2×D4×C103—21no—
81C2×D4×C103—42no—
82C2×D4×C103—41no—
83C2×D4×C103—41no—
84C2×D4×C103—41no—
85C2×D4×C103—41no—
86C2×D4×C103—41no—
87C2×D4×C103—41no—
88C22×C4×C103—21no—
89C22×C4×C103—21no—
90C22×C4×C103—21no—
91C22×C4×C103—21no—
92C22×C4×C103—21no—
93C22×C4×C103—21no—
94C22×C4×C103—22no—
95C22×C4×C103—21no—
96C22×C4×C103—22no—
97C22×C4×C103—22no—
98C22×C4×C103—21no—
99C22×C4×C103—21no—
100C22×C4×C103—21no—
101C22×C4×C103—42no—
102C22×C4×C103—42no—
103C22×C4×C103—42no—
104C22×C4×C103—42no—
105C22×C4×C103—44no—
106C22×C4×C103—41no—
107C22×C4×C103—41no—
108C22×C4×C103—41no—
109C22×C4×C103—41no—
110C22×C4×C103SD1612yes—
111C22×C4×C103C2×D411yescharacteristic
112C22×C4×C103C2×D411yescharacteristic
113C22×C4×C103C2×D411yescharacteristic
114C22×C4×C103C2×D411yescharacteristic
115C22×C4×C103C2×D411yescharacteristic
116C22×C4×C103#4111yescharacteristic
117C2×C8×C103—22no—
118C2×C8×C103—42no—
119C2×C8×C103—42no—
120C2×C8×C103—41no—
121C4⋊C4×C103—22no—
122C4⋊C4×C103—21no—
123C4⋊C4×C103—22no—
124C4⋊C4×C103—21no—
125C4⋊C4×C103—42no—
126C4⋊C4×C103—44no—
127C4⋊C4×C103—41no—
128C4⋊C4×C103—41no—
129C4⋊C4×C103—41no—
130C4⋊C4×C103—41no—
131C4⋊C4×C103—41no—
132C4⋊C4×C103—41no—
133C22⋊C4×C103—44no—
134C22⋊C4×C103—41no—
135C22⋊C4×C103—41no—
136C22⋊C4×C103—41no—
137C22⋊C4×C103—41no—
138C22⋊C4×C103—82no—
139C23×C103—22no—
140C23×C103—22no—
141C23×C103—41no—
142C23×C103—41no—
143C23×C103—41no—
144C23×C103—42no—
145C23×C103—42no—
146C23×C103#12011yescharacteristic
147C23×C103#12011yescharacteristic
148C23×C103#12111yescharacteristic
149C23×C103C2×SD1611yescharacteristic
150C23×C103#13511yescharacteristic
151C23×C103AGL(1,ℤ/8)11yescharacteristic
152C23×C103#13711yescharacteristic
153D4×C103—42no—
154D4×C103—81no—
155D4×C103—81no—
156D4×C103—81no—
157D4×C103—81no—
158D4×C103—81no—
159C2×C4×C103—22no—
160C2×C4×C103—22no—
161C2×C4×C103—22no—
162C2×C4×C103—22no—
163C2×C4×C103—22no—
164C2×C4×C103—41no—
165C2×C4×C103—41no—
166C2×C4×C103—41no—
167C2×C4×C103—41no—
168C2×C4×C103—41no—
169C2×C4×C103—41no—
170C2×C4×C103—41no—
171C2×C4×C103—41no—
172C2×C4×C103—42no—
173C2×C4×C103—42no—
174C2×C4×C103—44no—
175C2×C4×C103—42no—
176C2×C4×C103—41no—
177C2×C4×C103—42no—
178C2×C4×C103—41no—
179C2×C4×C103—42no—
180C2×C4×C103—42no—
181C2×C4×C103—41no—
182C2×C4×C103—41no—
183C2×C4×C103—42no—
184C2×C4×C103—42no—
185C2×C4×C103—42no—
186C2×C4×C103—82no—
187C2×C4×C103—82no—
188C2×C4×C103—82no—
189C2×C4×C103—82no—
190C2×C4×C103—81no—
191C2×C4×C103#12011yescharacteristic
192C2×C4×C103#12111yescharacteristic
193C2×C4×C103#12111yescharacteristic
194C2×C4×C103#12711yescharacteristic
195C8×C103—42no—
196C8×C103—81no—
197C22×C103—22no—
198C22×C103—22no—
199C22×C103—22no—
200C22×C103—22no—
201C22×C103—21no—
202C22×C103—21no—
203C22×C103—21no—
204C22×C103—21no—
205C22×C103—82no—
206C22×C103—82no—
207C22×C103—81no—
208C22×C103—81no—
209C22×C103—81no—
210C22×C103#39211yescharacteristic
211C22×C103#44811yescharacteristic
212C22×C103#44911yescharacteristic
213C22×C103#45011yescharacteristic
214C22×C103#45211yescharacteristic
215C22×C103#45412yes—
216C22×C103#45812yes—
217C22×C103#46511yescharacteristic
218C22×C103#46811yescharacteristic
219C4×C103—21no—
220C4×C103—21no—
221C4×C103—21no—
222C4×C103—21no—
223C4×C103—42no—
224C4×C103—82no—
225C4×C103—82no—
226C4×C103—81no—
227C4×C103—82no—
228C4×C103—81no—
229#9921C10311yesmaximal, characteristic, direct product factor, Sylow
230C2×C103—21no—
231C2×C103—21no—
232C2×C103—21no—
233C2×C103—21no—
234C2×C103—161no—
235C2×C103#161512yes—
236C2×C103#161612yes—
237C2×C103#200011yescharacteristic
238C2×C103#200311yescharacteristic
239C2×C103#202211yescharacteristic
240C2×#481C2×C10311yescharacteristic
241#2618C2×C10311yescharacteristic
242C2×#400C2×C10311yescharacteristic, complemented
243#1824C2×C10311yescharacteristic, complemented
244C2×#327C2×C10311yescharacteristic
245C2×#324C2×C10311yescharacteristic, complemented
246#1294C2×C10311yescharacteristic, complemented
247C103#992111yescharacteristic, direct product factor, Sylow
248C2×#123—21no—
249C2×#121C22×C10311yescharacteristic
250C22×C4⋊C4C22×C10311yescharacteristic
251C22×C4⋊C4C22×C10311yescharacteristic
252#481—22no—
253#481—22no—
254C2×#106—21no—
255C2×#102—21no—
256C2×C22⋊C8C22×C10311yescharacteristic
257C2×C22⋊C8C22×C10311yescharacteristic
258#400—22no—
259#400—22no—
260#398—21no—
261#396—22no—
262#394—21no—
263#386—21no—
264#380C22×C10311yescharacteristic
265C2×#95—21no—
266C2×#95—21no—
267C2×#95C22×C10311yescharacteristic
268#340—22no—
269#327—22no—
270#324—22no—
271C22×D4—21no—
272C22×D4D4×C10311yescharacteristic
273C23×C4—21no—
274C23×C4—21no—
275C23×C4D4×C10311yescharacteristic
276C23×C4D4×C10311yescharacteristic
277C23×C4C23×C10311yescharacteristic
278C22×C8—21no—
279C22×C8—21no—
280#123—42no—
281#123—42no—
282#121—21no—
283#121—21no—
284#121—21no—
285#121—21no—
286C2×C4⋊C4—21no—
287C2×C4⋊C4—21no—
288C2×C4⋊C4—21no—
289C2×C4⋊C4—21no—
290C2×C4⋊C4—22no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—21no—
295C2×C4⋊C4—21no—
296C2×C4⋊C4—21no—
297C2×C4⋊C4—21no—
298C2×C4⋊C4D4×C10312yes—
299C2×C4⋊C4D4×C10311yescharacteristic
300C2×C4⋊C4D4×C10312yes—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—21no—
303C2×C22⋊C4—21no—
304C2×C22⋊C4—22no—
305#106—24no—
306#102—24no—
307C22⋊C8—21no—
308C22⋊C8—21no—
309C22⋊C8—21no—
310C22⋊C8D4×C10312yes—
311#95—24no—
312#95—24no—
313#95—22no—
314#95—21no—
315#95—21no—
316#95D4×C10312yes—
317C24—21no—
318C24C2×D4×C10311yescharacteristic
319C2×D4—21no—
320C2×D4—21no—
321C2×D4—42no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—41no—
327C2×D4—41no—
328C22×C4—21no—
329C22×C4—21no—
330C22×C4—21no—
331C22×C4—21no—
332C22×C4—21no—
333C22×C4—21no—
334C22×C4—22no—
335C22×C4—21no—
336C22×C4—22no—
337C22×C4—22no—
338C22×C4—21no—
339C22×C4—21no—
340C22×C4—21no—
341C22×C4—42no—
342C22×C4—42no—
343C22×C4—42no—
344C22×C4—42no—
345C22×C4—44no—
346C22×C4—41no—
347C22×C4—41no—
348C22×C4—41no—
349C22×C4—41no—
350C22×C4SD16×C10312yes—
351C22×C4C2×D4×C10311yescharacteristic
352C22×C4C2×D4×C10311yescharacteristic
353C22×C4C2×D4×C10311yescharacteristic
354C22×C4C2×D4×C10311yescharacteristic
355C22×C4C2×D4×C10311yescharacteristic
356C22×C4#41×C10311yescharacteristic
357C2×C8—22no—
358C2×C8—42no—
359C2×C8—42no—
360C2×C8—41no—
361C4⋊C4—22no—
362C4⋊C4—21no—
363C4⋊C4—22no—
364C4⋊C4—21no—
365C4⋊C4—42no—
366C4⋊C4—44no—
367C4⋊C4—41no—
368C4⋊C4—41no—
369C4⋊C4—41no—
370C4⋊C4—41no—
371C4⋊C4—41no—
372C4⋊C4—41no—
373C22⋊C4—44no—
374C22⋊C4—41no—
375C22⋊C4—41no—
376C22⋊C4—41no—
377C22⋊C4—41no—
378C22⋊C4—82no—
379C23—22no—
380C23—22no—
381C23—41no—
382C23—41no—
383C23—41no—
384C23—42no—
385C23—42no—
386C23#120×C10311yescharacteristic
387C23#120×C10311yescharacteristic
388C23#121×C10311yescharacteristic
389C23C2×SD16×C10311yescharacteristic
390C23#135×C10311yescharacteristic
391C23AGL(1,ℤ/8)×C10311yescharacteristic
392C23#137×C10311yescharacteristic
393D4—42no—
394D4—81no—
395D4—81no—
396D4—81no—
397D4—81no—
398D4—81no—
399C2×C4—22no—
400C2×C4—22no—
401C2×C4—22no—
402C2×C4—22no—
403C2×C4—22no—
404C2×C4—41no—
405C2×C4—41no—
406C2×C4—41no—
407C2×C4—41no—
408C2×C4—41no—
409C2×C4—41no—
410C2×C4—41no—
411C2×C4—41no—
412C2×C4—42no—
413C2×C4—42no—
414C2×C4—44no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—41no—
419C2×C4—42no—
420C2×C4—42no—
421C2×C4—41no—
422C2×C4—41no—
423C2×C4—42no—
424C2×C4—42no—
425C2×C4—42no—
426C2×C4—82no—
427C2×C4—82no—
428C2×C4—82no—
429C2×C4—82no—
430C2×C4—81no—
431C2×C4#120×C10311yescharacteristic
432C2×C4#121×C10311yescharacteristic
433C2×C4#121×C10311yescharacteristic
434C2×C4#127×C10311yescharacteristic
435C8—42no—
436C8—81no—
437C22—21no—
438C22—21no—
439C22—21no—
440C22—21no—
441C22—22no—
442C22—22no—
443C22—22no—
444C22—22no—
445C22—81no—
446C22—81no—
447C22—81no—
448C22—82no—
449C22—82no—
450C22#392×C10311yescharacteristic
451C22#448×C10311yescharacteristic
452C22#449×C10311yescharacteristic
453C22#450×C10311yescharacteristic
454C22#452×C10311yescharacteristic
455C22#454×C10312yes—
456C22#458×C10312yes—
457C22#465×C10311yescharacteristic
458C22#468×C10311yescharacteristic
459C4—21no—
460C4—21no—
461C4—21no—
462C4—21no—
463C4—42no—
464C4—82no—
465C4—81no—
466C4—82no—
467C4—81no—
468C4—82no—
469C2—21no—
470C2—21no—
471C2—21no—
472C2—21no—
473C2—161no—
474C2C103×#161512yes—
475C2C103×#161612yes—
476C2C103×#200011yescharacteristic
477C2C103×#200311yescharacteristic
478C2C103×#202211yescharacteristic
subgroupG/H
center, socleC23×C103#120
commutator, Frattini, cosocleC23×C4C23×C103
prime radicalC2×#121×C103C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C23×C103 ◁ C23×C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#400×C103C2semidirect
4. C103×#1824C2semidirect
6. C2×#324×C103C2semidirect
7. C103×#1294C2semidirect
229. #9921C103direct (N × H)
242. C2×#400C2×C103semidirect
243. #1824C2×C103semidirect
245. C2×#324C2×C103semidirect
246. #1294C2×C103semidirect
247. C103#9921direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#481×C1032
C103×#26182
C2×#400×C1032
C103×#18242
C2×#327×C1032
C2×#324×C1032
C103×#12942
#9921103