Finite Group Databasebeta

← C103×#18252 #39923527

Subgroups — C103×#18252 #39923527

Order 26368.

1260 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3534C211yesmaximal, characteristic, complemented
2C103×#3006C211yesmaximal, characteristic, complemented
3C103×#3002C211yesmaximal, characteristic, complemented
4C103×#2430C211yesmaximal, characteristic, complemented
5C103×#1606C211yesmaximal, characteristic, complemented
6C103×#1604C211yesmaximal, characteristic, complemented
7C103×#1603C211yesmaximal, characteristic, complemented
8C103×#1601C211yesmaximal, characteristic, complemented
9C103×#1600C211yesmaximal, characteristic, complemented
10C103×#1598C211yesmaximal, characteristic, complemented
11C103×#1597C211yesmaximal, characteristic, complemented
12C103×#1595C211yesmaximal, characteristic, complemented
13C103×#1504C211yesmaximal, characteristic, complemented
14C2×#327×C103C211yesmaximal, characteristic, complemented
15C103×#1468C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic, complemented
17C2×AGL(1,ℤ/8)×C103—21no—
18C2×#135×C103—21no—
19#562×C103—21no—
20#560×C103—21no—
21#553×C103—21no—
22#551×C103—21no—
23#546×C103—21no—
24#546×C103—21no—
25#546×C103—21no—
26D42×C103—21no—
27#540×C103—21no—
28#539×C103—21no—
29#539×C103C2211yescharacteristic
30#538×C103—21no—
31#538×C103C2211yescharacteristic
32#537×C103C2211yescharacteristic
33#534×C103—21no—
34#534×C103C2211yescharacteristic
35#525×C103C2211yescharacteristic
36C2×#123×C103C2211yescharacteristic
37C2×#121×C103—21no—
38C2×#121×C103C2211yescharacteristic
39#452×C103—21no—
40#451×C103C2211yescharacteristic, complemented
41#450×C103C2211yescharacteristic, complemented
42#449×C103—21no—
43#449×C103—21no—
44#449×C103—21no—
45#448×C103C2211yescharacteristic
46#448×C103C2211yescharacteristic, complemented
47#448×C103C2211yescharacteristic, complemented
48#447×C103C2211yescharacteristic
49#447×C103C2211yescharacteristic, complemented
50#447×C103C2211yescharacteristic, complemented
51#417×C103—21no—
52#416×C103—21no—
53#407×C103C2211yescharacteristic, complemented
54C2×C22⋊C8×C103C2211yescharacteristic, complemented
55#395×C103C2211yescharacteristic, complemented
56#394×C103C2211yescharacteristic, complemented
57#393×C103C2211yescharacteristic, complemented
58#392×C103C2211yescharacteristic, complemented
59#386×C103—21no—
60#386×C103—21no—
61#385×C103—21no—
62C2×#95×C103C2211yescharacteristic, complemented
63#328×C103C2211yescharacteristic, complemented
64#328×C103C2211yescharacteristic, complemented
65#327×C103C2211yescharacteristic
66#327×C103C2211yescharacteristic
67#327×C103C2211yescharacteristic, complemented
68#327×C103C2211yescharacteristic, complemented
69#327×C103C2211yescharacteristic, complemented
70#327×C103C2211yescharacteristic, complemented
71#324×C103C2211yescharacteristic, complemented
72#324×C103C2211yescharacteristic, complemented
73#323×C103C2211yescharacteristic, complemented
74#323×C103C2211yescharacteristic, complemented
75C2×#41×C103—21no—
76C2×#41×C103—21no—
77C2×#41×C103—21no—
78C2×#41×C103—21no—
79C2×#41×C103—21no—
80C2×#41×C103—44no—
81C2×#41×C103D411yescharacteristic, complemented
82C22×Q8×C103C2311yescharacteristic
83C22×D4×C103—21no—
84C22×D4×C103—21no—
85C22×D4×C103—21no—
86C22×D4×C103—21no—
87C22×D4×C103—21no—
88C22×D4×C103D411yescharacteristic
89C22×D4×C103D411yescharacteristic, complemented
90C22×D4×C103C2311yescharacteristic
91C23×C4×C103—21no—
92C23×C4×C103—21no—
93C23×C4×C103C2311yescharacteristic
94AGL(1,ℤ/8)×C103—44no—
95#135×C103—44no—
96C2×Q16×C103—21no—
97C2×SD16×C103—21no—
98C2×SD16×C103—21no—
99C2×SD16×C103—21no—
100C2×SD16×C103—21no—
101C2×D8×C103—21no—
102C2×D8×C103—21no—
103C2×D8×C103—21no—
104C2×M16×C103—21no—
105C22×C8×C103—21no—
106#127×C103—21no—
107#126×C103—21no—
108#126×C103—21no—
109#126×C103—21no—
110#126×C103—21no—
111#125×C103—21no—
112#125×C103—21no—
113#124×C103—21no—
114#124×C103—21no—
115#124×C103—21no—
116#123×C103—21no—
117#123×C103—21no—
118#123×C103—21no—
119#123×C103—21no—
120#123×C103—21no—
121#123×C103—21no—
122#123×C103—21no—
123#123×C103—21no—
124#123×C103—21no—
125#123×C103—21no—
126#123×C103—21no—
127#123×C103—21no—
128#123×C103—21no—
129#123×C103—21no—
130C22⋊Q8×C103—21no—
131C22⋊Q8×C103—21no—
132C22⋊Q8×C103—21no—
133C22⋊Q8×C103—21no—
134C22⋊Q8×C103—21no—
135C22⋊Q8×C103D411yescharacteristic, complemented
136C22⋊Q8×C103C2311yescharacteristic
137#121×C103—21no—
138#121×C103—21no—
139#121×C103—21no—
140#121×C103—21no—
141#121×C103—21no—
142#121×C103—21no—
143#121×C103—21no—
144#121×C103—21no—
145#121×C103—21no—
146#121×C103—21no—
147#121×C103—21no—
148#121×C103—21no—
149#121×C103—21no—
150#121×C103—21no—
151#121×C103—21no—
152#121×C103—44no—
153#121×C103D411yescharacteristic, complemented
154#121×C103D411yescharacteristic, complemented
155#121×C103D411yescharacteristic, complemented
156#121×C103C2311yescharacteristic
157#121×C103C2311yescharacteristic
158#121×C103C2311yescharacteristic
159#120×C103—21no—
160#120×C103—21no—
161#120×C103—21no—
162#120×C103—21no—
163#120×C103—21no—
164#120×C103—21no—
165#120×C103—21no—
166#120×C103—21no—
167C4×D4×C103—21no—
168C4×D4×C103—21no—
169C4×D4×C103—21no—
170C4×D4×C103—21no—
171C4×D4×C103—21no—
172C4×D4×C103—21no—
173C4×D4×C103—21no—
174C4×D4×C103—21no—
175#117×C103—21no—
176#117×C103D411yescharacteristic, complemented
177C2×C4⋊C4×C103—21no—
178C2×C4⋊C4×C103D411yescharacteristic
179C2×C4⋊C4×C103D411yescharacteristic, complemented
180C2×C4⋊C4×C103C2311yescharacteristic
181C2×C22⋊C4×C103—21no—
182C2×C22⋊C4×C103—21no—
183C2×C22⋊C4×C103—21no—
184C2×C22⋊C4×C103—21no—
185C2×C22⋊C4×C103—21no—
186C2×C22⋊C4×C103—21no—
187C2×C22⋊C4×C103—21no—
188C2×C22⋊C4×C103D411yescharacteristic
189C2×C22⋊C4×C103D411yescharacteristic
190C2×C22⋊C4×C103C2311yescharacteristic
191#103×C103—21no—
192#103×C103—21no—
193#103×C103—21no—
194#103×C103—21no—
195#102×C103—21no—
196#102×C103—21no—
197#102×C103—21no—
198#102×C103—21no—
199C22⋊C8×C103—21no—
200C22⋊C8×C103—21no—
201C22⋊C8×C103C2311yescharacteristic
202C22⋊C8×C103C2311yescharacteristic
203C22⋊C8×C103C2311yescharacteristic
204C22⋊C8×C103C2311yescharacteristic
205#95×C103—21no—
206#95×C103—21no—
207#95×C103—21no—
208#95×C103C2311yescharacteristic
209#95×C103C2311yescharacteristic
210C24×C103—21no—
211C24×C103—21no—
212C24×C103—21no—
213C24×C103C2×D411yescharacteristic
214C24×C103C2×D411yescharacteristic
215#41×C103—24no—
216#41×C103—24no—
217#41×C103—42no—
218#41×C103—42no—
219#41×C103—42no—
220#41×C103—42no—
221#41×C103—42no—
222#41×C103—42no—
223#41×C103—42no—
224#41×C103—81no—
225#41×C103—81no—
226C2×Q8×C103—21no—
227C2×Q8×C103—21no—
228C2×Q8×C103—21no—
229C2×Q8×C103—42no—
230C2×Q8×C103C2×D411yescharacteristic
231C2×D4×C103—24no—
232C2×D4×C103—21no—
233C2×D4×C103—21no—
234C2×D4×C103—21no—
235C2×D4×C103—21no—
236C2×D4×C103—21no—
237C2×D4×C103—21no—
238C2×D4×C103—21no—
239C2×D4×C103—21no—
240C2×D4×C103—21no—
241C2×D4×C103—21no—
242C2×D4×C103—21no—
243C2×D4×C103—21no—
244C2×D4×C103—21no—
245C2×D4×C103—21no—
246C2×D4×C103—21no—
247C2×D4×C103—21no—
248C2×D4×C103—21no—
249C2×D4×C103—21no—
250C2×D4×C103—21no—
251C2×D4×C103—42no—
252C2×D4×C103—42no—
253C2×D4×C103—42no—
254C2×D4×C103—42no—
255C2×D4×C103—41no—
256C2×D4×C103—41no—
257C2×D4×C103—42no—
258C2×D4×C103—42no—
259C2×D4×C103—81no—
260C2×D4×C103—81no—
261C2×D4×C103—81no—
262C2×D4×C103—81no—
263C2×D4×C103—81no—
264C2×D4×C103—82no—
265C2×D4×C103C2×D411yescharacteristic
266C2×D4×C103C2×D411yescharacteristic
267C2×D4×C103C2×D411yescharacteristic
268C22×C4×C103—21no—
269C22×C4×C103—21no—
270C22×C4×C103—21no—
271C22×C4×C103—21no—
272C22×C4×C103—21no—
273C22×C4×C103—21no—
274C22×C4×C103—21no—
275C22×C4×C103—21no—
276C22×C4×C103—21no—
277C22×C4×C103—21no—
278C22×C4×C103—42no—
279C22×C4×C103—42no—
280C22×C4×C103—42no—
281C22×C4×C103—42no—
282C22×C4×C103—41no—
283C22×C4×C103—41no—
284C22×C4×C103—42no—
285C22×C4×C103—81no—
286C22×C4×C103C2×D411yescharacteristic
287C22×C4×C103C2×D411yescharacteristic
288C22×C4×C103C2×D411yescharacteristic
289C22×C4×C103C2×D411yescharacteristic
290C22×C4×C103C2×D411yescharacteristic
291C22×C4×C103C2×D411yescharacteristic
292C22×C4×C103C2×D411yescharacteristic
293C22×C4×C103C2×D411yescharacteristic
294C22×C4×C103C2411yescharacteristic
295Q16×C103—42no—
296SD16×C103—42no—
297SD16×C103—42no—
298SD16×C103—42no—
299SD16×C103—42no—
300D8×C103—42no—
301D8×C103—42no—
302D8×C103—42no—
303M16×C103—42no—
304C2×C8×C103—21no—
305C2×C8×C103—21no—
306C2×C8×C103—21no—
307C2×C8×C103—21no—
308C2×C8×C103—42no—
309C4⋊C4×C103—21no—
310C4⋊C4×C103—21no—
311C4⋊C4×C103—21no—
312C4⋊C4×C103—21no—
313C4⋊C4×C103—21no—
314C4⋊C4×C103—21no—
315C4⋊C4×C103—21no—
316C4⋊C4×C103—21no—
317C4⋊C4×C103—21no—
318C4⋊C4×C103—21no—
319C4⋊C4×C103—21no—
320C4⋊C4×C103—21no—
321C4⋊C4×C103—21no—
322C4⋊C4×C103—42no—
323C4⋊C4×C103C2×D411yescharacteristic
324C4⋊C4×C103C2×D411yescharacteristic
325C4⋊C4×C103C2×D411yescharacteristic
326C4⋊C4×C103C2×D411yescharacteristic
327C22⋊C4×C103—21no—
328C22⋊C4×C103—21no—
329C22⋊C4×C103—21no—
330C22⋊C4×C103—21no—
331C22⋊C4×C103—21no—
332C22⋊C4×C103—21no—
333C22⋊C4×C103—21no—
334C22⋊C4×C103—21no—
335C22⋊C4×C103—21no—
336C22⋊C4×C103—21no—
337C22⋊C4×C103—21no—
338C22⋊C4×C103—21no—
339C22⋊C4×C103—21no—
340C22⋊C4×C103—21no—
341C22⋊C4×C103—21no—
342C22⋊C4×C103—21no—
343C22⋊C4×C103—21no—
344C22⋊C4×C103—21no—
345C22⋊C4×C103—21no—
346C22⋊C4×C103—21no—
347C22⋊C4×C103—21no—
348C22⋊C4×C103—21no—
349C22⋊C4×C103—21no—
350C22⋊C4×C103—21no—
351C22⋊C4×C103—21no—
352C22⋊C4×C103—42no—
353C22⋊C4×C103—42no—
354C22⋊C4×C103—42no—
355C22⋊C4×C103—81no—
356C42×C103—21no—
357C42×C103—21no—
358C42×C103—21no—
359C23×C103—21no—
360C23×C103—21no—
361C23×C103—22no—
362C23×C103—22no—
363C23×C103—21no—
364C23×C103—21no—
365C23×C103—21no—
366C23×C103—21no—
367C23×C103—21no—
368C23×C103—21no—
369C23×C103—41no—
370C23×C103—41no—
371C23×C103—41no—
372C23×C103—41no—
373C23×C103—41no—
374C23×C103—41no—
375C23×C103—41no—
376C23×C103—41no—
377C23×C103—41no—
378C23×C103—42no—
379C23×C103—81no—
380C23×C103—81no—
381C23×C103—81no—
382C23×C103—81no—
383C23×C103—81no—
384C23×C103#12011yescharacteristic
385C23×C103#12011yescharacteristic
386C23×C103C22×D411yescharacteristic
387Q8×C103—22no—
388Q8×C103—22no—
389Q8×C103—41no—
390Q8×C103—41no—
391Q8×C103—41no—
392Q8×C103—81no—
393D4×C103—22no—
394D4×C103—22no—
395D4×C103—41no—
396D4×C103—41no—
397D4×C103—41no—
398D4×C103—41no—
399D4×C103—41no—
400D4×C103—44no—
401D4×C103—41no—
402D4×C103—41no—
403D4×C103—41no—
404D4×C103—41no—
405D4×C103—41no—
406D4×C103—41no—
407D4×C103—44no—
408D4×C103—42no—
409D4×C103—42no—
410D4×C103—81no—
411D4×C103—81no—
412D4×C103—81no—
413D4×C103—81no—
414D4×C103—81no—
415D4×C103—81no—
416D4×C103—81no—
417D4×C103—81no—
418D4×C103—81no—
419D4×C103—81no—
420D4×C103—81no—
421D4×C103—81no—
422D4×C103—84no—
423C2×C4×C103—22no—
424C2×C4×C103—22no—
425C2×C4×C103—22no—
426C2×C4×C103—22no—
427C2×C4×C103—21no—
428C2×C4×C103—21no—
429C2×C4×C103—21no—
430C2×C4×C103—21no—
431C2×C4×C103—21no—
432C2×C4×C103—21no—
433C2×C4×C103—21no—
434C2×C4×C103—21no—
435C2×C4×C103—21no—
436C2×C4×C103—21no—
437C2×C4×C103—41no—
438C2×C4×C103—41no—
439C2×C4×C103—41no—
440C2×C4×C103—41no—
441C2×C4×C103—44no—
442C2×C4×C103—44no—
443C2×C4×C103—41no—
444C2×C4×C103—41no—
445C2×C4×C103—41no—
446C2×C4×C103—41no—
447C2×C4×C103—41no—
448C2×C4×C103—41no—
449C2×C4×C103—41no—
450C2×C4×C103—41no—
451C2×C4×C103—41no—
452C2×C4×C103—81no—
453C2×C4×C103—81no—
454C2×C4×C103—81no—
455C2×C4×C103—81no—
456C2×C4×C103—81no—
457C2×C4×C103—81no—
458C2×C4×C103—81no—
459C2×C4×C103—84no—
460C2×C4×C103#12011yescharacteristic
461C2×C4×C103#12011yescharacteristic
462C2×C4×C103C22×D411yescharacteristic
463C2×C4×C103C22×D411yescharacteristic
464C8×C103—41no—
465C8×C103—41no—
466C8×C103—41no—
467C8×C103—41no—
468C22×C103—21no—
469C22×C103—21no—
470C22×C103—21no—
471C22×C103—21no—
472C22×C103—21no—
473C22×C103—21no—
474C22×C103—21no—
475C22×C103—42no—
476C22×C103—42no—
477C22×C103—42no—
478C22×C103—42no—
479C22×C103—41no—
480C22×C103—41no—
481C22×C103—41no—
482C22×C103—41no—
483C22×C103—41no—
484C22×C103—41no—
485C22×C103—41no—
486C22×C103—41no—
487C22×C103—42no—
488C22×C103—41no—
489C22×C103—41no—
490C22×C103—41no—
491C22×C103—41no—
492C22×C103—81no—
493C22×C103—81no—
494C22×C103—81no—
495C22×C103—81no—
496C22×C103—81no—
497C22×C103—81no—
498C22×C103—162no—
499C22×C103—162no—
500C22×C103B(4,𝔽2)12yes—
501C22×C103C2×#12011yescharacteristic
502C22×C103#57611yescharacteristic
503C22×C103#57711yescharacteristic
504C4×C103—21no—
505C4×C103—21no—
506C4×C103—21no—
507C4×C103—21no—
508C4×C103—42no—
509C4×C103—41no—
510C4×C103—41no—
511C4×C103—41no—
512C4×C103—41no—
513C4×C103—41no—
514C4×C103—41no—
515C4×C103—42no—
516C4×C103—41no—
517C4×C103—41no—
518C4×C103—81no—
519#18252C10311yesmaximal, characteristic, direct product factor, Sylow
520C2×C103—21no—
521C2×C103—21no—
522C2×C103—22no—
523C2×C103—41no—
524C2×C103—82no—
525C2×C103—81no—
526C2×C103—81no—
527C2×C103—81no—
528C2×C103—81no—
529C2×C103#301211yescharacteristic
530C2×C103#301811yescharacteristic
531C2×C103C2×B(4,𝔽2)11yescharacteristic
532#3534C2×C10311yescharacteristic, complemented
533#3006C2×C10311yescharacteristic, complemented
534#3002C2×C10311yescharacteristic, complemented
535#2430C2×C10311yescharacteristic, complemented
536#1606C2×C10311yescharacteristic, complemented
537#1604C2×C10311yescharacteristic, complemented
538#1603C2×C10311yescharacteristic, complemented
539#1601C2×C10311yescharacteristic, complemented
540#1600C2×C10311yescharacteristic, complemented
541#1598C2×C10311yescharacteristic, complemented
542#1597C2×C10311yescharacteristic, complemented
543#1595C2×C10311yescharacteristic, complemented
544#1504C2×C10311yescharacteristic, complemented
545C2×#327C2×C10311yescharacteristic, complemented
546#1468C2×C10311yescharacteristic, complemented
547C103#1825211yescharacteristic, direct product factor, Sylow
548C22×#41C22×C10311yescharacteristic, complemented
549C2×AGL(1,ℤ/8)—21no—
550C2×#135—21no—
551#562—21no—
552#560—21no—
553#553—21no—
554#551—21no—
555#546—21no—
556#546—21no—
557#546—21no—
558D42—21no—
559#540—21no—
560#539—21no—
561#539C22×C10311yescharacteristic
562#538—21no—
563#538C22×C10311yescharacteristic
564#537C22×C10311yescharacteristic
565#534—21no—
566#534C22×C10311yescharacteristic
567#525C22×C10311yescharacteristic
568C2×#123C22×C10311yescharacteristic
569C2×#121—21no—
570C2×#121C22×C10311yescharacteristic
571#452—21no—
572#451C22×C10311yescharacteristic, complemented
573#450C22×C10311yescharacteristic, complemented
574#449—21no—
575#449—21no—
576#449—21no—
577#448C22×C10311yescharacteristic
578#448C22×C10311yescharacteristic, complemented
579#448C22×C10311yescharacteristic, complemented
580#447C22×C10311yescharacteristic
581#447C22×C10311yescharacteristic, complemented
582#447C22×C10311yescharacteristic, complemented
583#417—21no—
584#416—21no—
585#407C22×C10311yescharacteristic, complemented
586C2×C22⋊C8C22×C10311yescharacteristic, complemented
587#395C22×C10311yescharacteristic, complemented
588#394C22×C10311yescharacteristic, complemented
589#393C22×C10311yescharacteristic, complemented
590#392C22×C10311yescharacteristic, complemented
591#386—21no—
592#386—21no—
593#385—21no—
594C2×#95C22×C10311yescharacteristic, complemented
595#328C22×C10311yescharacteristic, complemented
596#328C22×C10311yescharacteristic, complemented
597#327C22×C10311yescharacteristic
598#327C22×C10311yescharacteristic
599#327C22×C10311yescharacteristic, complemented
600#327C22×C10311yescharacteristic, complemented
601#327C22×C10311yescharacteristic, complemented
602#327C22×C10311yescharacteristic, complemented
603#324C22×C10311yescharacteristic, complemented
604#324C22×C10311yescharacteristic, complemented
605#323C22×C10311yescharacteristic, complemented
606#323C22×C10311yescharacteristic, complemented
607C2×#41—21no—
608C2×#41—21no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—44no—
613C2×#41D4×C10311yescharacteristic, complemented
614C22×Q8C23×C10311yescharacteristic
615C22×D4—21no—
616C22×D4—21no—
617C22×D4—21no—
618C22×D4—21no—
619C22×D4—21no—
620C22×D4D4×C10311yescharacteristic
621C22×D4D4×C10311yescharacteristic, complemented
622C22×D4C23×C10311yescharacteristic
623C23×C4—21no—
624C23×C4—21no—
625C23×C4C23×C10311yescharacteristic
626AGL(1,ℤ/8)—44no—
627#135—44no—
628C2×Q16—21no—
629C2×SD16—21no—
630C2×SD16—21no—
631C2×SD16—21no—
632C2×SD16—21no—
633C2×D8—21no—
634C2×D8—21no—
635C2×D8—21no—
636C2×M16—21no—
637C22×C8—21no—
638#127—21no—
639#126—21no—
640#126—21no—
641#126—21no—
642#126—21no—
643#125—21no—
644#125—21no—
645#124—21no—
646#124—21no—
647#124—21no—
648#123—21no—
649#123—21no—
650#123—21no—
651#123—21no—
652#123—21no—
653#123—21no—
654#123—21no—
655#123—21no—
656#123—21no—
657#123—21no—
658#123—21no—
659#123—21no—
660#123—21no—
661#123—21no—
662C22⋊Q8—21no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8D4×C10311yescharacteristic, complemented
668C22⋊Q8C23×C10311yescharacteristic
669#121—21no—
670#121—21no—
671#121—21no—
672#121—21no—
673#121—21no—
674#121—21no—
675#121—21no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—44no—
685#121D4×C10311yescharacteristic, complemented
686#121D4×C10311yescharacteristic, complemented
687#121D4×C10311yescharacteristic, complemented
688#121C23×C10311yescharacteristic
689#121C23×C10311yescharacteristic
690#121C23×C10311yescharacteristic
691#120—21no—
692#120—21no—
693#120—21no—
694#120—21no—
695#120—21no—
696#120—21no—
697#120—21no—
698#120—21no—
699C4×D4—21no—
700C4×D4—21no—
701C4×D4—21no—
702C4×D4—21no—
703C4×D4—21no—
704C4×D4—21no—
705C4×D4—21no—
706C4×D4—21no—
707#117—21no—
708#117D4×C10311yescharacteristic, complemented
709C2×C4⋊C4—21no—
710C2×C4⋊C4D4×C10311yescharacteristic
711C2×C4⋊C4D4×C10311yescharacteristic, complemented
712C2×C4⋊C4C23×C10311yescharacteristic
713C2×C22⋊C4—21no—
714C2×C22⋊C4—21no—
715C2×C22⋊C4—21no—
716C2×C22⋊C4—21no—
717C2×C22⋊C4—21no—
718C2×C22⋊C4—21no—
719C2×C22⋊C4—21no—
720C2×C22⋊C4D4×C10311yescharacteristic
721C2×C22⋊C4D4×C10311yescharacteristic
722C2×C22⋊C4C23×C10311yescharacteristic
723#103—21no—
724#103—21no—
725#103—21no—
726#103—21no—
727#102—21no—
728#102—21no—
729#102—21no—
730#102—21no—
731C22⋊C8—21no—
732C22⋊C8—21no—
733C22⋊C8C23×C10311yescharacteristic
734C22⋊C8C23×C10311yescharacteristic
735C22⋊C8C23×C10311yescharacteristic
736C22⋊C8C23×C10311yescharacteristic
737#95—21no—
738#95—21no—
739#95—21no—
740#95C23×C10311yescharacteristic
741#95C23×C10311yescharacteristic
742C24—21no—
743C24—21no—
744C24—21no—
745C24C2×D4×C10311yescharacteristic
746C24C2×D4×C10311yescharacteristic
747#41—24no—
748#41—24no—
749#41—42no—
750#41—42no—
751#41—42no—
752#41—42no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—81no—
757#41—81no—
758C2×Q8—21no—
759C2×Q8—21no—
760C2×Q8—21no—
761C2×Q8—42no—
762C2×Q8C2×D4×C10311yescharacteristic
763C2×D4—24no—
764C2×D4—21no—
765C2×D4—21no—
766C2×D4—21no—
767C2×D4—21no—
768C2×D4—21no—
769C2×D4—21no—
770C2×D4—21no—
771C2×D4—21no—
772C2×D4—21no—
773C2×D4—21no—
774C2×D4—21no—
775C2×D4—21no—
776C2×D4—21no—
777C2×D4—21no—
778C2×D4—21no—
779C2×D4—21no—
780C2×D4—21no—
781C2×D4—21no—
782C2×D4—21no—
783C2×D4—42no—
784C2×D4—42no—
785C2×D4—42no—
786C2×D4—42no—
787C2×D4—41no—
788C2×D4—41no—
789C2×D4—42no—
790C2×D4—42no—
791C2×D4—81no—
792C2×D4—81no—
793C2×D4—81no—
794C2×D4—81no—
795C2×D4—81no—
796C2×D4—82no—
797C2×D4C2×D4×C10311yescharacteristic
798C2×D4C2×D4×C10311yescharacteristic
799C2×D4C2×D4×C10311yescharacteristic
800C22×C4—21no—
801C22×C4—21no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—42no—
811C22×C4—42no—
812C22×C4—42no—
813C22×C4—42no—
814C22×C4—41no—
815C22×C4—41no—
816C22×C4—42no—
817C22×C4—81no—
818C22×C4C2×D4×C10311yescharacteristic
819C22×C4C2×D4×C10311yescharacteristic
820C22×C4C2×D4×C10311yescharacteristic
821C22×C4C2×D4×C10311yescharacteristic
822C22×C4C2×D4×C10311yescharacteristic
823C22×C4C2×D4×C10311yescharacteristic
824C22×C4C2×D4×C10311yescharacteristic
825C22×C4C2×D4×C10311yescharacteristic
826C22×C4C24×C10311yescharacteristic
827Q16—42no—
828SD16—42no—
829SD16—42no—
830SD16—42no—
831SD16—42no—
832D8—42no—
833D8—42no—
834D8—42no—
835M16—42no—
836C2×C8—21no—
837C2×C8—21no—
838C2×C8—21no—
839C2×C8—21no—
840C2×C8—42no—
841C4⋊C4—21no—
842C4⋊C4—21no—
843C4⋊C4—21no—
844C4⋊C4—21no—
845C4⋊C4—21no—
846C4⋊C4—21no—
847C4⋊C4—21no—
848C4⋊C4—21no—
849C4⋊C4—21no—
850C4⋊C4—21no—
851C4⋊C4—21no—
852C4⋊C4—21no—
853C4⋊C4—21no—
854C4⋊C4—42no—
855C4⋊C4C2×D4×C10311yescharacteristic
856C4⋊C4C2×D4×C10311yescharacteristic
857C4⋊C4C2×D4×C10311yescharacteristic
858C4⋊C4C2×D4×C10311yescharacteristic
859C22⋊C4—21no—
860C22⋊C4—21no—
861C22⋊C4—21no—
862C22⋊C4—21no—
863C22⋊C4—21no—
864C22⋊C4—21no—
865C22⋊C4—21no—
866C22⋊C4—21no—
867C22⋊C4—21no—
868C22⋊C4—21no—
869C22⋊C4—21no—
870C22⋊C4—21no—
871C22⋊C4—21no—
872C22⋊C4—21no—
873C22⋊C4—21no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—21no—
877C22⋊C4—21no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—42no—
885C22⋊C4—42no—
886C22⋊C4—42no—
887C22⋊C4—81no—
888C42—21no—
889C42—21no—
890C42—21no—
891C23—22no—
892C23—21no—
893C23—21no—
894C23—22no—
895C23—21no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—21no—
900C23—21no—
901C23—41no—
902C23—41no—
903C23—41no—
904C23—41no—
905C23—41no—
906C23—41no—
907C23—41no—
908C23—41no—
909C23—41no—
910C23—42no—
911C23—81no—
912C23—81no—
913C23—81no—
914C23—81no—
915C23—81no—
916C23#120×C10311yescharacteristic
917C23#120×C10311yescharacteristic
918C23C22×D4×C10311yescharacteristic
919Q8—22no—
920Q8—22no—
921Q8—41no—
922Q8—41no—
923Q8—41no—
924Q8—81no—
925D4—22no—
926D4—22no—
927D4—41no—
928D4—41no—
929D4—41no—
930D4—41no—
931D4—41no—
932D4—44no—
933D4—44no—
934D4—42no—
935D4—42no—
936D4—41no—
937D4—41no—
938D4—41no—
939D4—41no—
940D4—41no—
941D4—41no—
942D4—81no—
943D4—81no—
944D4—81no—
945D4—81no—
946D4—81no—
947D4—81no—
948D4—81no—
949D4—81no—
950D4—81no—
951D4—81no—
952D4—81no—
953D4—81no—
954D4—84no—
955C2×C4—22no—
956C2×C4—22no—
957C2×C4—22no—
958C2×C4—22no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—21no—
969C2×C4—41no—
970C2×C4—41no—
971C2×C4—41no—
972C2×C4—41no—
973C2×C4—44no—
974C2×C4—44no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—41no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—81no—
985C2×C4—81no—
986C2×C4—81no—
987C2×C4—81no—
988C2×C4—81no—
989C2×C4—81no—
990C2×C4—81no—
991C2×C4—84no—
992C2×C4#120×C10311yescharacteristic
993C2×C4#120×C10311yescharacteristic
994C2×C4C22×D4×C10311yescharacteristic
995C2×C4C22×D4×C10311yescharacteristic
996C8—41no—
997C8—41no—
998C8—41no—
999C8—41no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—42no—
1008C22—42no—
1009C22—42no—
1010C22—42no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—41no—
1019C22—42no—
1020C22—41no—
1021C22—41no—
1022C22—41no—
1023C22—41no—
1024C22—81no—
1025C22—81no—
1026C22—81no—
1027C22—81no—
1028C22—81no—
1029C22—81no—
1030C22—162no—
1031C22—162no—
1032C22B(4,𝔽2)×C10312yes—
1033C22C2×#120×C10311yescharacteristic
1034C22#576×C10311yescharacteristic
1035C22#577×C10311yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—21no—
1039C4—21no—
1040C4—42no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—42no—
1048C4—41no—
1049C4—41no—
1050C4—81no—
1051C2—21no—
1052C2—21no—
1053C2—22no—
1054C2—41no—
1055C2—82no—
1056C2—81no—
1057C2—81no—
1058C2—81no—
1059C2—81no—
1060C2C103×#301211yescharacteristic
1061C2C103×#301811yescharacteristic
1062C2C2×B(4,𝔽2)×C10311yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×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×#3534C2semidirect
2. C103×#3006C2semidirect
3. C103×#3002C2semidirect
4. C103×#2430C2semidirect
5. C103×#1606C2semidirect
6. C103×#1604C2semidirect
7. C103×#1603C2semidirect
8. C103×#1601C2semidirect
9. C103×#1600C2semidirect
10. C103×#1598C2semidirect
11. C103×#1597C2semidirect
12. C103×#1595C2semidirect
13. C103×#1504C2semidirect
14. C2×#327×C103C2semidirect
15. C103×#1468C2semidirect
16. C22×#41×C103C22semidirect
40. #451×C103C22semidirect
41. #450×C103C22semidirect
46. #448×C103C22semidirect
47. #448×C103C22semidirect
49. #447×C103C22semidirect
50. #447×C103C22semidirect
53. #407×C103C22semidirect
54. C2×C22⋊C8×C103C22semidirect
55. #395×C103C22semidirect
56. #394×C103C22semidirect
57. #393×C103C22semidirect
58. #392×C103C22semidirect
62. C2×#95×C103C22semidirect
63. #328×C103C22semidirect
64. #328×C103C22semidirect
67. #327×C103C22semidirect
68. #327×C103C22semidirect
69. #327×C103C22semidirect
70. #327×C103C22semidirect
71. #324×C103C22semidirect
72. #324×C103C22semidirect
73. #323×C103C22semidirect
74. #323×C103C22semidirect
81. C2×#41×C103D4semidirect
89. C22×D4×C103D4semidirect
135. C22⋊Q8×C103D4semidirect
153. #121×C103D4semidirect
154. #121×C103D4semidirect
155. #121×C103D4semidirect
176. #117×C103D4semidirect
179. C2×C4⋊C4×C103D4semidirect
519. #18252C103direct (N × H)
532. #3534C2×C103semidirect
533. #3006C2×C103semidirect
534. #3002C2×C103semidirect
535. #2430C2×C103semidirect
536. #1606C2×C103semidirect
537. #1604C2×C103semidirect
538. #1603C2×C103semidirect
539. #1601C2×C103semidirect
540. #1600C2×C103semidirect
541. #1598C2×C103semidirect
542. #1597C2×C103semidirect
543. #1595C2×C103semidirect
544. #1504C2×C103semidirect
545. C2×#327C2×C103semidirect
546. #1468C2×C103semidirect
547. C103#18252direct (N × H)
548. C22×#41C22×C103semidirect
572. #451C22×C103semidirect
573. #450C22×C103semidirect
578. #448C22×C103semidirect
579. #448C22×C103semidirect
581. #447C22×C103semidirect
582. #447C22×C103semidirect
585. #407C22×C103semidirect
586. C2×C22⋊C8C22×C103semidirect
587. #395C22×C103semidirect
588. #394C22×C103semidirect
589. #393C22×C103semidirect
590. #392C22×C103semidirect
594. C2×#95C22×C103semidirect
595. #328C22×C103semidirect
596. #328C22×C103semidirect
599. #327C22×C103semidirect
600. #327C22×C103semidirect
601. #327C22×C103semidirect
602. #327C22×C103semidirect
603. #324C22×C103semidirect
604. #324C22×C103semidirect
605. #323C22×C103semidirect
606. #323C22×C103semidirect
613. C2×#41D4×C103semidirect
621. C22×D4D4×C103semidirect
667. C22⋊Q8D4×C103semidirect
685. #121D4×C103semidirect
686. #121D4×C103semidirect
687. #121D4×C103semidirect
708. #117D4×C103semidirect
711. C2×C4⋊C4D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35342
C103×#30062
C103×#30022
C103×#24302
C103×#16062
C103×#16042
C103×#16032
C103×#16012
C103×#16002
C103×#15982
C103×#15972
C103×#15952
C103×#15042
C2×#327×C1032
C103×#14682
#18252103