Finite Group Databasebeta

← C103×#22588 #39927863

Subgroups — C103×#22588 #39927863

Order 26368.

888 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#2924C211yesmaximal, characteristic, complemented
2C103×#2896C211yesmaximal, characteristic
3C103×#2880C211yesmaximal, characteristic
4C103×#1938C211yesmaximal, characteristic, complemented
5C103×#1937C211yesmaximal, characteristic, complemented
6C103×#1929C211yesmaximal, characteristic, complemented
7C103×#1929C211yesmaximal, characteristic, complemented
8C103×#1866C211yesmaximal, characteristic, complemented
9C103×#1866C211yesmaximal, characteristic, complemented
10C103×#1826C211yesmaximal, characteristic, complemented
11C103×#1811C211yesmaximal, characteristic, complemented
12C103×#1789C211yesmaximal, characteristic
13C103×#1765C211yesmaximal, characteristic, complemented
14C103×#1764C211yesmaximal, characteristic, complemented
15C103×#1753C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C2×#131×C103C2211yescharacteristic
18C2×#131×C103C2211yescharacteristic
19C22×M16×C103C2211yescharacteristic
20C2×#117×C103C2211yescharacteristic
21#433×C103—21no—
22#433×C103—21no—
23#432×C103—21no—
24#431×C103—21no—
25C2×#108×C103C2211yescharacteristic, complemented
26C2×#108×C103C2211yescharacteristic, complemented
27#424×C103C2211yescharacteristic, complemented
28#424×C103C2211yescharacteristic, complemented
29C2×#104×C103C2211yescharacteristic
30C2×#104×C103C2211yescharacteristic
31C2×#104×C103C2211yescharacteristic
32C2×#104×C103C2211yescharacteristic
33#419×C103C411yescharacteristic, complemented
34#419×C103C411yescharacteristic, complemented
35#418×C103C411yescharacteristic, complemented
36#418×C103C411yescharacteristic, complemented
37#417×C103C411yescharacteristic, complemented
38#417×C103C411yescharacteristic, complemented
39#417×C103C411yescharacteristic, complemented
40#417×C103C411yescharacteristic, complemented
41#416×C103C2211yescharacteristic
42#416×C103C2211yescharacteristic
43#416×C103C2211yescharacteristic
44#416×C103C2211yescharacteristic
45#408×C103—21no—
46#408×C103—21no—
47#408×C103C2211yescharacteristic
48#408×C103C2211yescharacteristic
49#407×C103—21no—
50#407×C103C2211yescharacteristic
51#407×C103C2211yescharacteristic
52C2×C22⋊C8×C103—21no—
53C2×C22⋊C8×C103C2211yescharacteristic
54#405×C103C2211yescharacteristic, complemented
55#405×C103C2211yescharacteristic, complemented
56C2×#97×C103C2211yescharacteristic, complemented
57C2×C4×C8×C103C2211yescharacteristic, complemented
58C4×C22⋊C4×C103C2211yescharacteristic
59#341×C103C2211yescharacteristic, complemented
60#341×C103C2211yescharacteristic, complemented
61#339×C103C2211yescharacteristic, complemented
62#339×C103C2211yescharacteristic, complemented
63#339×C103C2211yescharacteristic, complemented
64#339×C103C2211yescharacteristic, complemented
65#336×C103C2211yescharacteristic, complemented
66#336×C103C2211yescharacteristic, complemented
67C2×#41×C103—21no—
68C2×#41×C103—21no—
69C2×#41×C103—22no—
70C2×#41×C103—22no—
71C2×#41×C103—41no—
72C2×#41×C103—41no—
73C2×#41×C103C2×C411yescharacteristic
74C2×#41×C103C2×C411yescharacteristic
75C2×#41×C103C2311yescharacteristic
76C2×#41×C103C2311yescharacteristic
77C22×Q8×C103C2×C411yescharacteristic
78C22×D4×C103—21no—
79C22×D4×C103C2×C411yescharacteristic
80C23×C4×C103—21no—
81C23×C4×C103C2311yescharacteristic
82#131×C103—22no—
83#131×C103—22no—
84#131×C103—41no—
85#131×C103—41no—
86C2×M16×C103—21no—
87C2×M16×C103—21no—
88C2×M16×C103—41no—
89C2×M16×C103—41no—
90C2×M16×C103C2×C411yescharacteristic
91C2×M16×C103C2×C411yescharacteristic
92C2×M16×C103C2×C411yescharacteristic
93C2×M16×C103C2×C411yescharacteristic
94C2×M16×C103C2311yescharacteristic
95C2×M16×C103C2311yescharacteristic
96C2×M16×C103C2311yescharacteristic
97C2×M16×C103C2311yescharacteristic
98C22×C8×C103—21no—
99C22×C8×C103—21no—
100C22×C8×C103C2311yescharacteristic
101C22×C8×C103C2311yescharacteristic
102C22×C8×C103C2311yescharacteristic
103C22×C8×C103C2311yescharacteristic
104#117×C103—21no—
105#117×C103—21no—
106#117×C103C2×C411yescharacteristic
107#117×C103C2×C411yescharacteristic
108#117×C103C2311yescharacteristic
109#117×C103C2311yescharacteristic
110C2×C4⋊C4×C103C2×C411yescharacteristic
111C2×C4⋊C4×C103C2×C411yescharacteristic
112C2×C22⋊C4×C103—21no—
113C2×C22⋊C4×C103—21no—
114C2×C42×C103—21no—
115C2×C42×C103C2311yescharacteristic
116C2×C42×C103C2311yescharacteristic
117#108×C103—41no—
118#108×C103—41no—
119C4⋊C8×C103—21no—
120C4⋊C8×C103—21no—
121C4⋊C8×C103—21no—
122C4⋊C8×C103—21no—
123#104×C103—22no—
124#104×C103—22no—
125#104×C103—41no—
126#104×C103—41no—
127#103×C103C2×C411yescharacteristic
128#103×C103C2×C411yescharacteristic
129#103×C103C2×C411yescharacteristic
130#103×C103C2×C411yescharacteristic
131#103×C103C2×C411yescharacteristic
132#103×C103C2×C411yescharacteristic
133#103×C103C2×C411yescharacteristic
134#103×C103C2×C411yescharacteristic
135#102×C103C2×C411yescharacteristic
136#102×C103C2×C411yescharacteristic
137#102×C103C2×C411yescharacteristic
138#102×C103C2×C411yescharacteristic
139#102×C103C2×C411yescharacteristic
140#102×C103C2×C411yescharacteristic
141#102×C103C2×C411yescharacteristic
142#102×C103C2×C411yescharacteristic
143C22⋊C8×C103—21no—
144C22⋊C8×C103—21no—
145C22⋊C8×C103—21no—
146C22⋊C8×C103—21no—
147C22⋊C8×C103—21no—
148C22⋊C8×C103—21no—
149C22⋊C8×C103—21no—
150C22⋊C8×C103—21no—
151C22⋊C8×C103D411yescharacteristic
152C22⋊C8×C103D411yescharacteristic
153C22⋊C8×C103D411yescharacteristic
154C22⋊C8×C103D411yescharacteristic
155#97×C103—21no—
156#97×C103—21no—
157#97×C103—41no—
158C4×C8×C103—21no—
159C4×C8×C103—21no—
160C4×C8×C103—41no—
161#95×C103—21no—
162C24×C103—21no—
163C24×C103#4111yescharacteristic
164#41×C103—21no—
165#41×C103—21no—
166#41×C103—22no—
167#41×C103—22no—
168#41×C103—21no—
169#41×C103—21no—
170#41×C103—21no—
171#41×C103—21no—
172#41×C103—42no—
173#41×C103—42no—
174#41×C103—41no—
175#41×C103—41no—
176#41×C103—42no—
177#41×C103—42no—
178#41×C103#4112yes—
179#41×C103#4112yes—
180C2×Q8×C103—21no—
181C2×Q8×C103—22no—
182C2×Q8×C103—41no—
183C2×Q8×C103C22×C411yescharacteristic
184C2×Q8×C103C22×C411yescharacteristic
185C2×D4×C103—21no—
186C2×D4×C103—22no—
187C2×D4×C103—21no—
188C2×D4×C103—21no—
189C2×D4×C103—21no—
190C2×D4×C103—21no—
191C2×D4×C103—41no—
192C2×D4×C103—42no—
193C2×D4×C103—42no—
194C2×D4×C103C22×C411yescharacteristic
195C2×D4×C103C22×C411yescharacteristic
196C22×C4×C103—21no—
197C22×C4×C103—21no—
198C22×C4×C103—21no—
199C22×C4×C103—21no—
200C22×C4×C103—21no—
201C22×C4×C103—21no—
202C22×C4×C103—21no—
203C22×C4×C103—21no—
204C22×C4×C103—21no—
205C22×C4×C103—21no—
206C22×C4×C103—21no—
207C22×C4×C103—21no—
208C22×C4×C103—21no—
209C22×C4×C103—42no—
210C22×C4×C103—42no—
211C22×C4×C103C22×C411yescharacteristic
212C22×C4×C103C22×C411yescharacteristic
213C22×C4×C103C2×D411yescharacteristic
214C22×C4×C103C2×D411yescharacteristic
215C22×C4×C103#4111yescharacteristic
216C22×C4×C103C2411yescharacteristic
217M16×C103—21no—
218M16×C103—21no—
219M16×C103—21no—
220M16×C103—21no—
221M16×C103—21no—
222M16×C103—21no—
223M16×C103—21no—
224M16×C103—21no—
225M16×C103—41no—
226M16×C103—41no—
227M16×C103—41no—
228M16×C103—41no—
229M16×C103—42no—
230M16×C103—42no—
231C2×C8×C103—21no—
232C2×C8×C103—21no—
233C2×C8×C103—21no—
234C2×C8×C103—21no—
235C2×C8×C103—21no—
236C2×C8×C103—21no—
237C2×C8×C103—21no—
238C2×C8×C103—21no—
239C2×C8×C103—21no—
240C2×C8×C103—21no—
241C2×C8×C103—21no—
242C2×C8×C103—21no—
243C2×C8×C103—42no—
244C2×C8×C103—42no—
245C2×C8×C103C22×C411yescharacteristic
246C2×C8×C103C22×C411yescharacteristic
247C2×C8×C103C22×C411yescharacteristic
248C2×C8×C103C22×C411yescharacteristic
249C2×C8×C103C2×D411yescharacteristic
250C2×C8×C103C2×D411yescharacteristic
251C2×C8×C103C2×D411yescharacteristic
252C2×C8×C103C2×D411yescharacteristic
253C4⋊C4×C103—21no—
254C4⋊C4×C103—21no—
255C4⋊C4×C103C22×C411yescharacteristic
256C4⋊C4×C103C22×C411yescharacteristic
257C4⋊C4×C103C22×C411yescharacteristic
258C4⋊C4×C103C22×C411yescharacteristic
259C22⋊C4×C103—21no—
260C22⋊C4×C103—21no—
261C22⋊C4×C103—21no—
262C22⋊C4×C103—21no—
263C22⋊C4×C103—42no—
264C42×C103—21no—
265C42×C103—21no—
266C42×C103—21no—
267C42×C103—21no—
268C42×C103—21no—
269C42×C103—21no—
270C42×C103—21no—
271C42×C103—21no—
272C23×C103—21no—
273C23×C103—21no—
274C23×C103—21no—
275C23×C103—21no—
276C23×C103—41no—
277C23×C103—41no—
278C23×C103—42no—
279C23×C103—42no—
280C23×C103—81no—
281C23×C103C4×D411yescharacteristic
282C23×C103C4×D411yescharacteristic
283C23×C103C2×#4111yescharacteristic
284Q8×C103—21no—
285Q8×C103—21no—
286Q8×C103—21no—
287Q8×C103—42no—
288Q8×C103#11712yes—
289D4×C103—22no—
290D4×C103—22no—
291D4×C103—21no—
292D4×C103—21no—
293D4×C103—21no—
294D4×C103—42no—
295D4×C103—42no—
296D4×C103—42no—
297D4×C103—41no—
298D4×C103—41no—
299D4×C103#11712yes—
300C2×C4×C103—21no—
301C2×C4×C103—21no—
302C2×C4×C103—21no—
303C2×C4×C103—21no—
304C2×C4×C103—21no—
305C2×C4×C103—21no—
306C2×C4×C103—21no—
307C2×C4×C103—22no—
308C2×C4×C103—22no—
309C2×C4×C103—21no—
310C2×C4×C103—21no—
311C2×C4×C103—21no—
312C2×C4×C103—21no—
313C2×C4×C103—22no—
314C2×C4×C103—21no—
315C2×C4×C103—21no—
316C2×C4×C103—21no—
317C2×C4×C103—21no—
318C2×C4×C103—21no—
319C2×C4×C103—42no—
320C2×C4×C103—42no—
321C2×C4×C103—42no—
322C2×C4×C103—41no—
323C2×C4×C103—42no—
324C2×C4×C103—41no—
325C2×C4×C103—41no—
326C2×C4×C103—41no—
327C2×C4×C103—41no—
328C2×C4×C103—41no—
329C2×C4×C103—41no—
330C2×C4×C103—81no—
331C2×C4×C103C4×D411yescharacteristic
332C2×C4×C103C4×D411yescharacteristic
333C2×C4×C103C23×C411yescharacteristic
334C2×C4×C103C22×D411yescharacteristic
335C2×C4×C103C2×#4111yescharacteristic
336C2×C4×C103C2×#4111yescharacteristic
337C2×C4×C103H(5,𝔽2)11yescharacteristic
338C2×C4×C103H(5,𝔽2)11yescharacteristic
339C8×C103—21no—
340C8×C103—21no—
341C8×C103—21no—
342C8×C103—21no—
343C8×C103—21no—
344C8×C103—21no—
345C8×C103—21no—
346C8×C103—21no—
347C8×C103—41no—
348C8×C103—41no—
349C8×C103—41no—
350C8×C103—41no—
351C22×C103—21no—
352C22×C103—21no—
353C22×C103—21no—
354C22×C103—21no—
355C22×C103—22no—
356C22×C103—21no—
357C22×C103—21no—
358C22×C103—21no—
359C22×C103—21no—
360C22×C103—41no—
361C22×C103—41no—
362C22×C103—41no—
363C22×C103—41no—
364C22×C103—41no—
365C22×C103—81no—
366C22×C103—81no—
367C22×C103—84no—
368C22×C103C2×C4×D411yescharacteristic
369C22×C103#55111yescharacteristic
370C22×C103#55111yescharacteristic
371C4×C103—21no—
372C4×C103—21no—
373C4×C103—22no—
374C4×C103—42no—
375C4×C103—41no—
376C4×C103—41no—
377C4×C103—41no—
378C4×C103—41no—
379C4×C103—41no—
380C4×C103—81no—
381C4×C103C2×#11711yescharacteristic
382C4×C103#51811yescharacteristic
383C4×C103#54611yescharacteristic
384C4×C103#54611yescharacteristic
385#22588C10311yesmaximal, characteristic, direct product factor, Sylow
386C2×C103—21no—
387C2×C103—21no—
388C2×C103—41no—
389C2×C103—41no—
390C2×C103—42no—
391C2×C103—81no—
392C2×C103#234211yescharacteristic
393C2×C103#295511yescharacteristic
394C2×C103#295611yescharacteristic
395#2924C2×C10311yescharacteristic, complemented
396#2896C2×C10311yescharacteristic
397#2880C2×C10311yescharacteristic
398#1938C2×C10311yescharacteristic, complemented
399#1937C2×C10311yescharacteristic, complemented
400#1929C2×C10311yescharacteristic, complemented
401#1929C2×C10311yescharacteristic, complemented
402#1866C2×C10311yescharacteristic, complemented
403#1866C2×C10311yescharacteristic, complemented
404#1826C2×C10311yescharacteristic, complemented
405#1811C2×C10311yescharacteristic, complemented
406#1789C2×C10311yescharacteristic
407#1765C2×C10311yescharacteristic, complemented
408#1764C2×C10311yescharacteristic, complemented
409#1753C2×C10311yescharacteristic, complemented
410C103#2258811yescharacteristic, direct product factor, Sylow
411C22×#41C22×C10311yescharacteristic
412C2×#131C22×C10311yescharacteristic
413C2×#131C22×C10311yescharacteristic
414C22×M16C22×C10311yescharacteristic
415C2×#117C22×C10311yescharacteristic
416#433—21no—
417#433—21no—
418#432—21no—
419#431—21no—
420C2×#108C22×C10311yescharacteristic, complemented
421C2×#108C22×C10311yescharacteristic, complemented
422#424C22×C10311yescharacteristic, complemented
423#424C22×C10311yescharacteristic, complemented
424C2×#104C22×C10311yescharacteristic
425C2×#104C22×C10311yescharacteristic
426C2×#104C22×C10311yescharacteristic
427C2×#104C22×C10311yescharacteristic
428#419C4×C10311yescharacteristic, complemented
429#419C4×C10311yescharacteristic, complemented
430#418C4×C10311yescharacteristic, complemented
431#418C4×C10311yescharacteristic, complemented
432#417C4×C10311yescharacteristic, complemented
433#417C4×C10311yescharacteristic, complemented
434#417C4×C10311yescharacteristic, complemented
435#417C4×C10311yescharacteristic, complemented
436#416C22×C10311yescharacteristic
437#416C22×C10311yescharacteristic
438#416C22×C10311yescharacteristic
439#416C22×C10311yescharacteristic
440#408—21no—
441#408—21no—
442#408C22×C10311yescharacteristic
443#408C22×C10311yescharacteristic
444#407—21no—
445#407C22×C10311yescharacteristic
446#407C22×C10311yescharacteristic
447C2×C22⋊C8—21no—
448C2×C22⋊C8C22×C10311yescharacteristic
449#405C22×C10311yescharacteristic, complemented
450#405C22×C10311yescharacteristic, complemented
451C2×#97C22×C10311yescharacteristic, complemented
452C2×C4×C8C22×C10311yescharacteristic, complemented
453C4×C22⋊C4C22×C10311yescharacteristic
454#341C22×C10311yescharacteristic, complemented
455#341C22×C10311yescharacteristic, complemented
456#339C22×C10311yescharacteristic, complemented
457#339C22×C10311yescharacteristic, complemented
458#339C22×C10311yescharacteristic, complemented
459#339C22×C10311yescharacteristic, complemented
460#336C22×C10311yescharacteristic, complemented
461#336C22×C10311yescharacteristic, complemented
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—22no—
465C2×#41—22no—
466C2×#41—41no—
467C2×#41—41no—
468C2×#41C2×C4×C10311yescharacteristic
469C2×#41C2×C4×C10311yescharacteristic
470C2×#41C23×C10311yescharacteristic
471C2×#41C23×C10311yescharacteristic
472C22×Q8C2×C4×C10311yescharacteristic
473C22×D4—21no—
474C22×D4C2×C4×C10311yescharacteristic
475C23×C4—21no—
476C23×C4C23×C10311yescharacteristic
477#131—22no—
478#131—22no—
479#131—41no—
480#131—41no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—41no—
484C2×M16—41no—
485C2×M16C2×C4×C10311yescharacteristic
486C2×M16C2×C4×C10311yescharacteristic
487C2×M16C2×C4×C10311yescharacteristic
488C2×M16C2×C4×C10311yescharacteristic
489C2×M16C23×C10311yescharacteristic
490C2×M16C23×C10311yescharacteristic
491C2×M16C23×C10311yescharacteristic
492C2×M16C23×C10311yescharacteristic
493C22×C8—21no—
494C22×C8—21no—
495C22×C8C23×C10311yescharacteristic
496C22×C8C23×C10311yescharacteristic
497C22×C8C23×C10311yescharacteristic
498C22×C8C23×C10311yescharacteristic
499#117—21no—
500#117—21no—
501#117C2×C4×C10311yescharacteristic
502#117C2×C4×C10311yescharacteristic
503#117C23×C10311yescharacteristic
504#117C23×C10311yescharacteristic
505C2×C4⋊C4C2×C4×C10311yescharacteristic
506C2×C4⋊C4C2×C4×C10311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C42—21no—
510C2×C42C23×C10311yescharacteristic
511C2×C42C23×C10311yescharacteristic
512#108—41no—
513#108—41no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518#104—22no—
519#104—22no—
520#104—41no—
521#104—41no—
522#103C2×C4×C10311yescharacteristic
523#103C2×C4×C10311yescharacteristic
524#103C2×C4×C10311yescharacteristic
525#103C2×C4×C10311yescharacteristic
526#103C2×C4×C10311yescharacteristic
527#103C2×C4×C10311yescharacteristic
528#103C2×C4×C10311yescharacteristic
529#103C2×C4×C10311yescharacteristic
530#102C2×C4×C10311yescharacteristic
531#102C2×C4×C10311yescharacteristic
532#102C2×C4×C10311yescharacteristic
533#102C2×C4×C10311yescharacteristic
534#102C2×C4×C10311yescharacteristic
535#102C2×C4×C10311yescharacteristic
536#102C2×C4×C10311yescharacteristic
537#102C2×C4×C10311yescharacteristic
538C22⋊C8—21no—
539C22⋊C8—21no—
540C22⋊C8—21no—
541C22⋊C8—21no—
542C22⋊C8—21no—
543C22⋊C8—21no—
544C22⋊C8—21no—
545C22⋊C8—21no—
546C22⋊C8D4×C10311yescharacteristic
547C22⋊C8D4×C10311yescharacteristic
548C22⋊C8D4×C10311yescharacteristic
549C22⋊C8D4×C10311yescharacteristic
550#97—21no—
551#97—21no—
552#97—41no—
553C4×C8—21no—
554C4×C8—21no—
555C4×C8—41no—
556#95—21no—
557C24—21no—
558C24#41×C10311yescharacteristic
559#41—21no—
560#41—21no—
561#41—22no—
562#41—22no—
563#41—21no—
564#41—21no—
565#41—21no—
566#41—21no—
567#41—42no—
568#41—42no—
569#41—41no—
570#41—41no—
571#41—42no—
572#41—42no—
573#41#41×C10312yes—
574#41#41×C10312yes—
575C2×Q8—21no—
576C2×Q8—22no—
577C2×Q8—41no—
578C2×Q8C22×C4×C10311yescharacteristic
579C2×Q8C22×C4×C10311yescharacteristic
580C2×D4—21no—
581C2×D4—22no—
582C2×D4—21no—
583C2×D4—21no—
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—41no—
587C2×D4—42no—
588C2×D4—42no—
589C2×D4C22×C4×C10311yescharacteristic
590C2×D4C22×C4×C10311yescharacteristic
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—21no—
600C22×C4—21no—
601C22×C4—21no—
602C22×C4—21no—
603C22×C4—21no—
604C22×C4—42no—
605C22×C4—42no—
606C22×C4C22×C4×C10311yescharacteristic
607C22×C4C22×C4×C10311yescharacteristic
608C22×C4C2×D4×C10311yescharacteristic
609C22×C4C2×D4×C10311yescharacteristic
610C22×C4#41×C10311yescharacteristic
611C22×C4C24×C10311yescharacteristic
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—41no—
621M16—41no—
622M16—41no—
623M16—41no—
624M16—42no—
625M16—42no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—21no—
629C2×C8—21no—
630C2×C8—21no—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8C22×C4×C10311yescharacteristic
641C2×C8C22×C4×C10311yescharacteristic
642C2×C8C22×C4×C10311yescharacteristic
643C2×C8C22×C4×C10311yescharacteristic
644C2×C8C2×D4×C10311yescharacteristic
645C2×C8C2×D4×C10311yescharacteristic
646C2×C8C2×D4×C10311yescharacteristic
647C2×C8C2×D4×C10311yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4C22×C4×C10311yescharacteristic
651C4⋊C4C22×C4×C10311yescharacteristic
652C4⋊C4C22×C4×C10311yescharacteristic
653C4⋊C4C22×C4×C10311yescharacteristic
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—42no—
659C42—21no—
660C42—21no—
661C42—21no—
662C42—21no—
663C42—21no—
664C42—21no—
665C42—21no—
666C42—21no—
667C23—21no—
668C23—21no—
669C23—21no—
670C23—21no—
671C23—41no—
672C23—41no—
673C23—42no—
674C23—42no—
675C23—81no—
676C23C4×D4×C10311yescharacteristic
677C23C4×D4×C10311yescharacteristic
678C23C2×#41×C10311yescharacteristic
679Q8—21no—
680Q8—21no—
681Q8—21no—
682Q8—42no—
683Q8#117×C10312yes—
684D4—22no—
685D4—22no—
686D4—21no—
687D4—21no—
688D4—21no—
689D4—42no—
690D4—42no—
691D4—42no—
692D4—41no—
693D4—41no—
694D4#117×C10312yes—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—21no—
702C2×C4—22no—
703C2×C4—22no—
704C2×C4—21no—
705C2×C4—21no—
706C2×C4—21no—
707C2×C4—21no—
708C2×C4—22no—
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—41no—
718C2×C4—42no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—81no—
726C2×C4C4×D4×C10311yescharacteristic
727C2×C4C4×D4×C10311yescharacteristic
728C2×C4C23×C4×C10311yescharacteristic
729C2×C4C22×D4×C10311yescharacteristic
730C2×C4C2×#41×C10311yescharacteristic
731C2×C4C2×#41×C10311yescharacteristic
732C2×C4H(5,𝔽2)×C10311yescharacteristic
733C2×C4H(5,𝔽2)×C10311yescharacteristic
734C8—21no—
735C8—21no—
736C8—21no—
737C8—21no—
738C8—21no—
739C8—21no—
740C8—21no—
741C8—21no—
742C8—41no—
743C8—41no—
744C8—41no—
745C8—41no—
746C22—21no—
747C22—21no—
748C22—21no—
749C22—21no—
750C22—21no—
751C22—21no—
752C22—21no—
753C22—21no—
754C22—22no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—84no—
763C22C2×C4×D4×C10311yescharacteristic
764C22#551×C10311yescharacteristic
765C22#551×C10311yescharacteristic
766C4—21no—
767C4—21no—
768C4—22no—
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4C2×#117×C10311yescharacteristic
777C4#518×C10311yescharacteristic
778C4#546×C10311yescharacteristic
779C4#546×C10311yescharacteristic
780C2—21no—
781C2—21no—
782C2—41no—
783C2—41no—
784C2—42no—
785C2—81no—
786C2C103×#234211yescharacteristic
787C2C103×#295511yescharacteristic
788C2C103×#295611yescharacteristic
subgroupG/H
centerC2×C4×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
socleC22×C103C2×C4×D4
prime radicalC22×#41×C103C22
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C103 ◁ C2×C22⋊C8×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#2924C2semidirect
4. C103×#1938C2semidirect
5. C103×#1937C2semidirect
6. C103×#1929C2semidirect
7. C103×#1929C2semidirect
8. C103×#1866C2semidirect
9. C103×#1866C2semidirect
10. C103×#1826C2semidirect
11. C103×#1811C2semidirect
13. C103×#1765C2semidirect
14. C103×#1764C2semidirect
15. C103×#1753C2semidirect
25. C2×#108×C103C22semidirect
26. C2×#108×C103C22semidirect
27. #424×C103C22semidirect
28. #424×C103C22semidirect
33. #419×C103C4semidirect
34. #419×C103C4semidirect
35. #418×C103C4semidirect
36. #418×C103C4semidirect
37. #417×C103C4semidirect
38. #417×C103C4semidirect
39. #417×C103C4semidirect
40. #417×C103C4semidirect
54. #405×C103C22semidirect
55. #405×C103C22semidirect
56. C2×#97×C103C22semidirect
57. C2×C4×C8×C103C22semidirect
59. #341×C103C22semidirect
60. #341×C103C22semidirect
61. #339×C103C22semidirect
62. #339×C103C22semidirect
63. #339×C103C22semidirect
64. #339×C103C22semidirect
65. #336×C103C22semidirect
66. #336×C103C22semidirect
385. #22588C103direct (N × H)
395. #2924C2×C103semidirect
398. #1938C2×C103semidirect
399. #1937C2×C103semidirect
400. #1929C2×C103semidirect
401. #1929C2×C103semidirect
402. #1866C2×C103semidirect
403. #1866C2×C103semidirect
404. #1826C2×C103semidirect
405. #1811C2×C103semidirect
407. #1765C2×C103semidirect
408. #1764C2×C103semidirect
409. #1753C2×C103semidirect
410. C103#22588direct (N × H)
420. C2×#108C22×C103semidirect
421. C2×#108C22×C103semidirect
422. #424C22×C103semidirect
423. #424C22×C103semidirect
428. #419C4×C103semidirect
429. #419C4×C103semidirect
430. #418C4×C103semidirect
431. #418C4×C103semidirect
432. #417C4×C103semidirect
433. #417C4×C103semidirect
434. #417C4×C103semidirect
435. #417C4×C103semidirect
449. #405C22×C103semidirect
450. #405C22×C103semidirect
451. C2×#97C22×C103semidirect
452. C2×C4×C8C22×C103semidirect
454. #341C22×C103semidirect
455. #341C22×C103semidirect
456. #339C22×C103semidirect
457. #339C22×C103semidirect
458. #339C22×C103semidirect
459. #339C22×C103semidirect
460. #336C22×C103semidirect
461. #336C22×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#29242
C103×#28962
C103×#28802
C103×#19382
C103×#19372
C103×#19292
C103×#18662
C103×#18262
C103×#18112
C103×#17892
C103×#17652
C103×#17642
C103×#17532
#22588103