Finite Group Databasebeta

← C103×#18434 #39923709

Subgroups — C103×#18434 #39923709

Order 26368.

982 conjugacy classes of subgroups.

The subgroup lattice has 964 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C103×#3560C211yesmaximal, characteristic, complemented
2C103×#3213C211yesmaximal, characteristic, complemented
3C103×#3211C211yesmaximal, characteristic, complemented
4C103×#2662C211yesmaximal, 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×#1509C211yesmaximal, characteristic, complemented
14C103×#1502C211yesmaximal, characteristic, complemented
15C103×#1473C211yesmaximal, characteristic, complemented
16#563×C103—21no—
17#560×C103—21no—
18#553×C103—21no—
19#553×C103—21no—
20#551×C103—21no—
21#547×C103—21no—
22#546×C103—21no—
23#546×C103—21no—
24#542×C103—21no—
25#539×C103—21no—
26#539×C103C2211yescharacteristic
27#538×C103—21no—
28#538×C103—21no—
29#538×C103C2211yescharacteristic
30#537×C103C2211yescharacteristic
31#534×C103C2211yescharacteristic
32#532×C103C2211yescharacteristic
33#529×C103C2211yescharacteristic
34C2×#126×C103C2211yescharacteristic
35C2×#124×C103C2211yescharacteristic, complemented
36#496×C103—21no—
37#495×C103—21no—
38#489×C103—21no—
39#488×C103—21no—
40#464×C103—21no—
41#463×C103—21no—
42#463×C103—21no—
43#463×C103—21no—
44#451×C103C2211yescharacteristic, complemented
45#450×C103C2211yescharacteristic, complemented
46#448×C103C2211yescharacteristic
47#448×C103C2211yescharacteristic
48#448×C103C2211yescharacteristic, complemented
49#447×C103C2211yescharacteristic
50#447×C103C2211yescharacteristic
51#447×C103C2211yescharacteristic, complemented
52#432×C103C2211yescharacteristic, complemented
53#431×C103C2211yescharacteristic, complemented
54#396×C103—21no—
55#395×C103C2211yescharacteristic, complemented
56#394×C103—21no—
57#394×C103C2211yescharacteristic, complemented
58#393×C103C2211yescharacteristic
59#392×C103C2211yescharacteristic
60#390×C103—21no—
61#388×C103—21no—
62C4×C4⋊C4×C103C2211yescharacteristic, complemented
63#328×C103C2211yescharacteristic, complemented
64#328×C103C2211yescharacteristic, complemented
65#327×C103C2211yescharacteristic
66#327×C103C2211yescharacteristic
67#327×C103C2211yescharacteristic
68#327×C103C2211yescharacteristic
69#327×C103C2211yescharacteristic, complemented
70#327×C103C2211yescharacteristic, complemented
71#324×C103C2211yescharacteristic, complemented
72#324×C103C2211yescharacteristic, complemented
73#323×C103C2211yescharacteristic
74#323×C103C2211yescharacteristic
75C2×#41×C103—21no—
76C2×#41×C103—21no—
77C22×Q8×C103C2311yescharacteristic
78C22×D4×C103—21no—
79C22×D4×C103—21no—
80C22×D4×C103C2311yescharacteristic
81C2×Q16×C103—21no—
82C2×SD16×C103—21no—
83C2×SD16×C103—21no—
84C2×SD16×C103—21no—
85C2×SD16×C103—21no—
86C2×D8×C103—21no—
87C2×D8×C103—21no—
88C2×D8×C103—21no—
89C4⋊Q8×C103—21no—
90C4⋊Q8×C103D411yescharacteristic, complemented
91#127×C103D411yescharacteristic, complemented
92#126×C103—21no—
93#126×C103—21no—
94#126×C103—21no—
95#126×C103—21no—
96#126×C103—21no—
97#126×C103—21no—
98#126×C103—21no—
99#126×C103—21no—
100#126×C103—21no—
101#125×C103—21no—
102#125×C103—21no—
103#125×C103D411yescharacteristic, complemented
104#124×C103—21no—
105#124×C103—21no—
106#124×C103—21no—
107#124×C103—21no—
108#124×C103—21no—
109#124×C103—21no—
110#124×C103—21no—
111#124×C103—21no—
112#124×C103D411yescharacteristic, complemented
113#123×C103—21no—
114#123×C103—21no—
115#123×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—
125C22⋊Q8×C103—21no—
126C22⋊Q8×C103—21no—
127C22⋊Q8×C103—21no—
128C22⋊Q8×C103—21no—
129C22⋊Q8×C103—21no—
130C22⋊Q8×C103—21no—
131C22⋊Q8×C103—21no—
132C22⋊Q8×C103C2311yescharacteristic
133#121×C103—21no—
134#121×C103—21no—
135#121×C103—21no—
136#121×C103—21no—
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×C103C2311yescharacteristic
146#121×C103C2311yescharacteristic
147#121×C103C2311yescharacteristic
148#120×C103—21no—
149#120×C103—21no—
150#120×C103—21no—
151#120×C103—21no—
152#120×C103—21no—
153C4×Q8×C103D411yescharacteristic, complemented
154C4×D4×C103—21no—
155C4×D4×C103—21no—
156C4×D4×C103—21no—
157C4×D4×C103—21no—
158C4×D4×C103—21no—
159C4×D4×C103—21no—
160C4×D4×C103—21no—
161C4×D4×C103—21no—
162C4×D4×C103D411yescharacteristic, complemented
163C4×D4×C103D411yescharacteristic, complemented
164C4×D4×C103D411yescharacteristic, complemented
165#117×C103—21no—
166#117×C103—21no—
167C2×C4⋊C4×C103—21no—
168C2×C4⋊C4×C103—21no—
169C2×C4⋊C4×C103—21no—
170C2×C4⋊C4×C103D411yescharacteristic
171C2×C4⋊C4×C103D411yescharacteristic
172C2×C4⋊C4×C103C2311yescharacteristic
173C2×C22⋊C4×C103—21no—
174C2×C22⋊C4×C103—21no—
175C2×C22⋊C4×C103—21no—
176C2×C22⋊C4×C103—21no—
177C2×C22⋊C4×C103—21no—
178C2×C22⋊C4×C103—21no—
179C2×C22⋊C4×C103—21no—
180C2×C22⋊C4×C103—21no—
181C2×C22⋊C4×C103D411yescharacteristic
182C2×C22⋊C4×C103D411yescharacteristic
183C2×C22⋊C4×C103C2311yescharacteristic
184C2×C42×C103—21no—
185C2×C42×C103C2311yescharacteristic
186C4⋊C8×C103—21no—
187C4⋊C8×C103—21no—
188#103×C103—21no—
189#103×C103—21no—
190#103×C103—21no—
191#103×C103—21no—
192#102×C103—21no—
193#102×C103—21no—
194#102×C103—21no—
195#102×C103—21no—
196C22⋊C8×C103C2311yescharacteristic
197C22⋊C8×C103C2311yescharacteristic
198C22⋊C8×C103C2311yescharacteristic
199C22⋊C8×C103C2311yescharacteristic
200#97×C103—21no—
201C4×C8×C103—21no—
202#95×C103—21no—
203#95×C103—21no—
204#95×C103C2311yescharacteristic
205#95×C103C2311yescharacteristic
206C24×C103—21no—
207C24×C103—21no—
208C24×C103C2×D411yescharacteristic
209#41×C103—81no—
210#41×C103—81no—
211#41×C103—81no—
212#41×C103—81no—
213C2×Q8×C103—21no—
214C2×Q8×C103—21no—
215C2×Q8×C103—21no—
216C2×Q8×C103—21no—
217C2×Q8×C103—81no—
218C2×Q8×C103C2×D411yescharacteristic
219C2×D4×C103—21no—
220C2×D4×C103—21no—
221C2×D4×C103—21no—
222C2×D4×C103—21no—
223C2×D4×C103—21no—
224C2×D4×C103—21no—
225C2×D4×C103—21no—
226C2×D4×C103—21no—
227C2×D4×C103—21no—
228C2×D4×C103—21no—
229C2×D4×C103—21no—
230C2×D4×C103—21no—
231C2×D4×C103—21no—
232C2×D4×C103—21no—
233C2×D4×C103—42no—
234C2×D4×C103—81no—
235C2×D4×C103—81no—
236C2×D4×C103—81no—
237C2×D4×C103—81no—
238C2×D4×C103—81no—
239C2×D4×C103C2×D411yescharacteristic
240C2×D4×C103C2×D411yescharacteristic
241C2×D4×C103C2×D411yescharacteristic
242C22×C4×C103—21no—
243C22×C4×C103—21no—
244C22×C4×C103—21no—
245C22×C4×C103—21no—
246C22×C4×C103—21no—
247C22×C4×C103—21no—
248C22×C4×C103—21no—
249C22×C4×C103—21no—
250C22×C4×C103—21no—
251C22×C4×C103—21no—
252C22×C4×C103—21no—
253C22×C4×C103C2×D411yescharacteristic
254C22×C4×C103C2×D411yescharacteristic
255C22×C4×C103C2×D411yescharacteristic
256C22×C4×C103C2×D411yescharacteristic
257C22×C4×C103C2×D411yescharacteristic
258C22×C4×C103C2411yescharacteristic
259Q16×C103—81no—
260SD16×C103—81no—
261SD16×C103—81no—
262SD16×C103—81no—
263SD16×C103—81no—
264D8×C103—81no—
265D8×C103—81no—
266D8×C103—81no—
267C2×C8×C103—21no—
268C2×C8×C103—21no—
269C2×C8×C103—21no—
270C2×C8×C103—21no—
271C4⋊C4×C103—21no—
272C4⋊C4×C103—21no—
273C4⋊C4×C103—21no—
274C4⋊C4×C103—21no—
275C4⋊C4×C103—21no—
276C4⋊C4×C103—21no—
277C4⋊C4×C103—21no—
278C4⋊C4×C103—21no—
279C4⋊C4×C103—21no—
280C4⋊C4×C103—21no—
281C4⋊C4×C103—21no—
282C4⋊C4×C103—21no—
283C4⋊C4×C103—21no—
284C4⋊C4×C103—21no—
285C4⋊C4×C103—21no—
286C4⋊C4×C103—21no—
287C4⋊C4×C103—21no—
288C4⋊C4×C103—42no—
289C4⋊C4×C103—81no—
290C4⋊C4×C103C2×D411yescharacteristic
291C4⋊C4×C103C2×D411yescharacteristic
292C4⋊C4×C103C2×D411yescharacteristic
293C4⋊C4×C103C2×D411yescharacteristic
294C22⋊C4×C103—21no—
295C22⋊C4×C103—21no—
296C22⋊C4×C103—21no—
297C22⋊C4×C103—21no—
298C22⋊C4×C103—21no—
299C22⋊C4×C103—21no—
300C22⋊C4×C103—21no—
301C22⋊C4×C103—21no—
302C22⋊C4×C103—21no—
303C22⋊C4×C103—21no—
304C22⋊C4×C103—21no—
305C22⋊C4×C103—21no—
306C22⋊C4×C103—21no—
307C22⋊C4×C103—21no—
308C22⋊C4×C103—21no—
309C22⋊C4×C103—21no—
310C22⋊C4×C103—21no—
311C22⋊C4×C103—21no—
312C22⋊C4×C103—21no—
313C22⋊C4×C103—21no—
314C22⋊C4×C103—21no—
315C22⋊C4×C103—21no—
316C22⋊C4×C103—21no—
317C22⋊C4×C103—21no—
318C22⋊C4×C103—21no—
319C22⋊C4×C103—42no—
320C22⋊C4×C103—41no—
321C22⋊C4×C103—41no—
322C22⋊C4×C103—41no—
323C22⋊C4×C103—41no—
324C22⋊C4×C103—81no—
325C22⋊C4×C103—81no—
326C22⋊C4×C103—81no—
327C42×C103—21no—
328C42×C103—21no—
329C42×C103—21no—
330C42×C103—81no—
331C42×C103C2×D411yescharacteristic
332C42×C103C2×D411yescharacteristic
333C42×C103C2×D411yescharacteristic
334C42×C103C2×D411yescharacteristic
335C23×C103—21no—
336C23×C103—21no—
337C23×C103—21no—
338C23×C103—21no—
339C23×C103—21no—
340C23×C103—21no—
341C23×C103—41no—
342C23×C103—41no—
343C23×C103—41no—
344C23×C103—41no—
345C23×C103—41no—
346C23×C103—41no—
347C23×C103—41no—
348C23×C103—41no—
349C23×C103—41no—
350C23×C103—81no—
351C23×C103—81no—
352C23×C103—81no—
353C23×C103C22×D411yescharacteristic
354Q8×C103—41no—
355Q8×C103—41no—
356Q8×C103—41no—
357Q8×C103—41no—
358Q8×C103—41no—
359Q8×C103—81no—
360Q8×C103—81no—
361D4×C103—41no—
362D4×C103—41no—
363D4×C103—41no—
364D4×C103—41no—
365D4×C103—41no—
366D4×C103—41no—
367D4×C103—41no—
368D4×C103—41no—
369D4×C103—41no—
370D4×C103—41no—
371D4×C103—41no—
372D4×C103—41no—
373D4×C103—41no—
374D4×C103—81no—
375D4×C103—81no—
376D4×C103—81no—
377D4×C103—81no—
378D4×C103—81no—
379D4×C103—81no—
380D4×C103—81no—
381D4×C103—81no—
382D4×C103—81no—
383D4×C103—84no—
384C2×C4×C103—21no—
385C2×C4×C103—21no—
386C2×C4×C103—22no—
387C2×C4×C103—21no—
388C2×C4×C103—21no—
389C2×C4×C103—21no—
390C2×C4×C103—21no—
391C2×C4×C103—21no—
392C2×C4×C103—21no—
393C2×C4×C103—21no—
394C2×C4×C103—21no—
395C2×C4×C103—21no—
396C2×C4×C103—21no—
397C2×C4×C103—41no—
398C2×C4×C103—41no—
399C2×C4×C103—41no—
400C2×C4×C103—41no—
401C2×C4×C103—41no—
402C2×C4×C103—41no—
403C2×C4×C103—41no—
404C2×C4×C103—41no—
405C2×C4×C103—41no—
406C2×C4×C103—41no—
407C2×C4×C103—41no—
408C2×C4×C103—41no—
409C2×C4×C103—81no—
410C2×C4×C103—81no—
411C2×C4×C103—81no—
412C2×C4×C103—81no—
413C2×C4×C103—81no—
414C2×C4×C103—81no—
415C2×C4×C103—81no—
416C2×C4×C103—81no—
417C2×C4×C103#12011yescharacteristic
418C2×C4×C103#12011yescharacteristic
419C2×C4×C103#12011yescharacteristic
420C2×C4×C103#12011yescharacteristic
421C2×C4×C103C22×D411yescharacteristic
422C2×C4×C103C22×D411yescharacteristic
423C8×C103—41no—
424C8×C103—41no—
425C8×C103—41no—
426C8×C103—41no—
427C22×C103—21no—
428C22×C103—21no—
429C22×C103—41no—
430C22×C103—41no—
431C22×C103—41no—
432C22×C103—41no—
433C22×C103—41no—
434C22×C103—41no—
435C22×C103—41no—
436C22×C103—41no—
437C22×C103—41no—
438C22×C103—41no—
439C22×C103—41no—
440C22×C103—41no—
441C22×C103—81no—
442C22×C103—81no—
443C22×C103—81no—
444C22×C103—81no—
445C22×C103—81no—
446C22×C103—81no—
447C22×C103—81no—
448C22×C103—81no—
449C22×C103—81no—
450C22×C103—162no—
451C22×C103C2×#12011yescharacteristic
452C22×C103#57611yescharacteristic
453C22×C103#57711yescharacteristic
454C4×C103—21no—
455C4×C103—21no—
456C4×C103—21no—
457C4×C103—21no—
458C4×C103—21no—
459C4×C103—21no—
460C4×C103—42no—
461C4×C103—41no—
462C4×C103—41no—
463C4×C103—41no—
464C4×C103—41no—
465C4×C103—41no—
466C4×C103—41no—
467C4×C103—41no—
468C4×C103—41no—
469C4×C103—81no—
470C4×C103—81no—
471#18434C10311yesmaximal, characteristic, direct product factor, Sylow
472C2×C103—21no—
473C2×C103—21no—
474C2×C103—81no—
475C2×C103—81no—
476C2×C103—81no—
477C2×C103—81no—
478C2×C103—161no—
479C2×C103#301211yescharacteristic
480C2×C103#301811yescharacteristic
481C2×C103#302711yescharacteristic
482#3560C2×C10311yescharacteristic, complemented
483#3213C2×C10311yescharacteristic, complemented
484#3211C2×C10311yescharacteristic, complemented
485#2662C2×C10311yescharacteristic, complemented
486#1606C2×C10311yescharacteristic, complemented
487#1604C2×C10311yescharacteristic, complemented
488#1603C2×C10311yescharacteristic, complemented
489#1601C2×C10311yescharacteristic, complemented
490#1600C2×C10311yescharacteristic, complemented
491#1598C2×C10311yescharacteristic, complemented
492#1597C2×C10311yescharacteristic, complemented
493#1595C2×C10311yescharacteristic, complemented
494#1509C2×C10311yescharacteristic, complemented
495#1502C2×C10311yescharacteristic, complemented
496#1473C2×C10311yescharacteristic, complemented
497C103#1843411yescharacteristic, direct product factor, Sylow
498#563—21no—
499#560—21no—
500#553—21no—
501#553—21no—
502#551—21no—
503#547—21no—
504#546—21no—
505#546—21no—
506#542—21no—
507#539—21no—
508#539C22×C10311yescharacteristic
509#538—21no—
510#538—21no—
511#538C22×C10311yescharacteristic
512#537C22×C10311yescharacteristic
513#534C22×C10311yescharacteristic
514#532C22×C10311yescharacteristic
515#529C22×C10311yescharacteristic
516C2×#126C22×C10311yescharacteristic
517C2×#124C22×C10311yescharacteristic, complemented
518#496—21no—
519#495—21no—
520#489—21no—
521#488—21no—
522#464—21no—
523#463—21no—
524#463—21no—
525#463—21no—
526#451C22×C10311yescharacteristic, complemented
527#450C22×C10311yescharacteristic, complemented
528#448C22×C10311yescharacteristic
529#448C22×C10311yescharacteristic
530#448C22×C10311yescharacteristic, complemented
531#447C22×C10311yescharacteristic
532#447C22×C10311yescharacteristic
533#447C22×C10311yescharacteristic, complemented
534#432C22×C10311yescharacteristic, complemented
535#431C22×C10311yescharacteristic, complemented
536#396—21no—
537#395C22×C10311yescharacteristic, complemented
538#394—21no—
539#394C22×C10311yescharacteristic, complemented
540#393C22×C10311yescharacteristic
541#392C22×C10311yescharacteristic
542#390—21no—
543#388—21no—
544C4×C4⋊C4C22×C10311yescharacteristic, complemented
545#328C22×C10311yescharacteristic, complemented
546#328C22×C10311yescharacteristic, complemented
547#327C22×C10311yescharacteristic
548#327C22×C10311yescharacteristic
549#327C22×C10311yescharacteristic
550#327C22×C10311yescharacteristic
551#327C22×C10311yescharacteristic, complemented
552#327C22×C10311yescharacteristic, complemented
553#324C22×C10311yescharacteristic, complemented
554#324C22×C10311yescharacteristic, complemented
555#323C22×C10311yescharacteristic
556#323C22×C10311yescharacteristic
557C2×#41—21no—
558C2×#41—21no—
559C22×Q8C23×C10311yescharacteristic
560C22×D4—21no—
561C22×D4—21no—
562C22×D4C23×C10311yescharacteristic
563C2×Q16—21no—
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—21no—
567C2×SD16—21no—
568C2×D8—21no—
569C2×D8—21no—
570C2×D8—21no—
571C4⋊Q8—21no—
572C4⋊Q8D4×C10311yescharacteristic, complemented
573#127D4×C10311yescharacteristic, complemented
574#126—21no—
575#126—21no—
576#126—21no—
577#126—21no—
578#126—21no—
579#126—21no—
580#126—21no—
581#126—21no—
582#126—21no—
583#125—21no—
584#125—21no—
585#125D4×C10311yescharacteristic, complemented
586#124—21no—
587#124—21no—
588#124—21no—
589#124—21no—
590#124—21no—
591#124—21no—
592#124—21no—
593#124—21no—
594#124D4×C10311yescharacteristic, complemented
595#123—21no—
596#123—21no—
597#123—21no—
598#123—21no—
599#123—21no—
600#123—21no—
601#123—21no—
602#123—21no—
603#123—21no—
604#123—21no—
605#123—21no—
606#123—21no—
607C22⋊Q8—21no—
608C22⋊Q8—21no—
609C22⋊Q8—21no—
610C22⋊Q8—21no—
611C22⋊Q8—21no—
612C22⋊Q8—21no—
613C22⋊Q8—21no—
614C22⋊Q8C23×C10311yescharacteristic
615#121—21no—
616#121—21no—
617#121—21no—
618#121—21no—
619#121—21no—
620#121—21no—
621#121—21no—
622#121—21no—
623#121—21no—
624#121—21no—
625#121—21no—
626#121—21no—
627#121C23×C10311yescharacteristic
628#121C23×C10311yescharacteristic
629#121C23×C10311yescharacteristic
630#120—21no—
631#120—21no—
632#120—21no—
633#120—21no—
634#120—21no—
635C4×Q8D4×C10311yescharacteristic, complemented
636C4×D4—21no—
637C4×D4—21no—
638C4×D4—21no—
639C4×D4—21no—
640C4×D4—21no—
641C4×D4—21no—
642C4×D4—21no—
643C4×D4—21no—
644C4×D4D4×C10311yescharacteristic, complemented
645C4×D4D4×C10311yescharacteristic, complemented
646C4×D4D4×C10311yescharacteristic, complemented
647#117—21no—
648#117—21no—
649C2×C4⋊C4—21no—
650C2×C4⋊C4—21no—
651C2×C4⋊C4—21no—
652C2×C4⋊C4D4×C10311yescharacteristic
653C2×C4⋊C4D4×C10311yescharacteristic
654C2×C4⋊C4C23×C10311yescharacteristic
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4D4×C10311yescharacteristic
664C2×C22⋊C4D4×C10311yescharacteristic
665C2×C22⋊C4C23×C10311yescharacteristic
666C2×C42—21no—
667C2×C42C23×C10311yescharacteristic
668C4⋊C8—21no—
669C4⋊C8—21no—
670#103—21no—
671#103—21no—
672#103—21no—
673#103—21no—
674#102—21no—
675#102—21no—
676#102—21no—
677#102—21no—
678C22⋊C8C23×C10311yescharacteristic
679C22⋊C8C23×C10311yescharacteristic
680C22⋊C8C23×C10311yescharacteristic
681C22⋊C8C23×C10311yescharacteristic
682#97—21no—
683C4×C8—21no—
684#95—21no—
685#95—21no—
686#95C23×C10311yescharacteristic
687#95C23×C10311yescharacteristic
688C24—21no—
689C24—21no—
690C24C2×D4×C10311yescharacteristic
691#41—81no—
692#41—81no—
693#41—81no—
694#41—81no—
695C2×Q8—21no—
696C2×Q8—21no—
697C2×Q8—21no—
698C2×Q8—21no—
699C2×Q8—81no—
700C2×Q8C2×D4×C10311yescharacteristic
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—42no—
716C2×D4—81no—
717C2×D4—81no—
718C2×D4—81no—
719C2×D4—81no—
720C2×D4—81no—
721C2×D4C2×D4×C10311yescharacteristic
722C2×D4C2×D4×C10311yescharacteristic
723C2×D4C2×D4×C10311yescharacteristic
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—21no—
728C22×C4—21no—
729C22×C4—21no—
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4C2×D4×C10311yescharacteristic
736C22×C4C2×D4×C10311yescharacteristic
737C22×C4C2×D4×C10311yescharacteristic
738C22×C4C2×D4×C10311yescharacteristic
739C22×C4C2×D4×C10311yescharacteristic
740C22×C4C24×C10311yescharacteristic
741Q16—81no—
742SD16—81no—
743SD16—81no—
744SD16—81no—
745SD16—81no—
746D8—81no—
747D8—81no—
748D8—81no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—21no—
768C4⋊C4—21no—
769C4⋊C4—21no—
770C4⋊C4—42no—
771C4⋊C4—81no—
772C4⋊C4C2×D4×C10311yescharacteristic
773C4⋊C4C2×D4×C10311yescharacteristic
774C4⋊C4C2×D4×C10311yescharacteristic
775C4⋊C4C2×D4×C10311yescharacteristic
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—42no—
802C22⋊C4—41no—
803C22⋊C4—41no—
804C22⋊C4—41no—
805C22⋊C4—41no—
806C22⋊C4—81no—
807C22⋊C4—81no—
808C22⋊C4—81no—
809C42—21no—
810C42—21no—
811C42—21no—
812C42—81no—
813C42C2×D4×C10311yescharacteristic
814C42C2×D4×C10311yescharacteristic
815C42C2×D4×C10311yescharacteristic
816C42C2×D4×C10311yescharacteristic
817C23—21no—
818C23—21no—
819C23—21no—
820C23—21no—
821C23—21no—
822C23—21no—
823C23—41no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—81no—
833C23—81no—
834C23—81no—
835C23C22×D4×C10311yescharacteristic
836Q8—41no—
837Q8—41no—
838Q8—41no—
839Q8—41no—
840Q8—41no—
841Q8—81no—
842Q8—81no—
843D4—41no—
844D4—41no—
845D4—41no—
846D4—41no—
847D4—41no—
848D4—41no—
849D4—41no—
850D4—41no—
851D4—41no—
852D4—41no—
853D4—41no—
854D4—41no—
855D4—41no—
856D4—81no—
857D4—81no—
858D4—81no—
859D4—81no—
860D4—81no—
861D4—81no—
862D4—81no—
863D4—81no—
864D4—81no—
865D4—84no—
866C2×C4—21no—
867C2×C4—21no—
868C2×C4—22no—
869C2×C4—21no—
870C2×C4—21no—
871C2×C4—21no—
872C2×C4—21no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—21no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—41no—
887C2×C4—41no—
888C2×C4—41no—
889C2×C4—41no—
890C2×C4—41no—
891C2×C4—81no—
892C2×C4—81no—
893C2×C4—81no—
894C2×C4—81no—
895C2×C4—81no—
896C2×C4—81no—
897C2×C4—81no—
898C2×C4—81no—
899C2×C4#120×C10311yescharacteristic
900C2×C4#120×C10311yescharacteristic
901C2×C4#120×C10311yescharacteristic
902C2×C4#120×C10311yescharacteristic
903C2×C4C22×D4×C10311yescharacteristic
904C2×C4C22×D4×C10311yescharacteristic
905C8—41no—
906C8—41no—
907C8—41no—
908C8—41no—
909C22—21no—
910C22—21no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—41no—
921C22—41no—
922C22—41no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22—81no—
928C22—81no—
929C22—81no—
930C22—81no—
931C22—81no—
932C22—162no—
933C22C2×#120×C10311yescharacteristic
934C22#576×C10311yescharacteristic
935C22#577×C10311yescharacteristic
936C4—21no—
937C4—21no—
938C4—21no—
939C4—21no—
940C4—21no—
941C4—21no—
942C4—42no—
943C4—41no—
944C4—41no—
945C4—41no—
946C4—41no—
947C4—41no—
948C4—41no—
949C4—41no—
950C4—41no—
951C4—81no—
952C4—81no—
953C2—21no—
954C2—21no—
955C2—81no—
956C2—81no—
957C2—81no—
958C2—81no—
959C2—161no—
960C2C103×#301211yescharacteristic
961C2C103×#301811yescharacteristic
962C2C103×#302711yescharacteristic
subgroupG/H
center, socleC22×C103C2×#120
commutator, Frattini, cosocleC22×C4C24×C103
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C103 ◁ C2×C42×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C103×#3560C2semidirect
2. C103×#3213C2semidirect
3. C103×#3211C2semidirect
4. C103×#2662C2semidirect
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×#1509C2semidirect
14. C103×#1502C2semidirect
15. C103×#1473C2semidirect
35. C2×#124×C103C22semidirect
44. #451×C103C22semidirect
45. #450×C103C22semidirect
48. #448×C103C22semidirect
51. #447×C103C22semidirect
52. #432×C103C22semidirect
53. #431×C103C22semidirect
55. #395×C103C22semidirect
57. #394×C103C22semidirect
62. C4×C4⋊C4×C103C22semidirect
63. #328×C103C22semidirect
64. #328×C103C22semidirect
69. #327×C103C22semidirect
70. #327×C103C22semidirect
71. #324×C103C22semidirect
72. #324×C103C22semidirect
90. C4⋊Q8×C103D4semidirect
91. #127×C103D4semidirect
103. #125×C103D4semidirect
112. #124×C103D4semidirect
153. C4×Q8×C103D4semidirect
162. C4×D4×C103D4semidirect
163. C4×D4×C103D4semidirect
164. C4×D4×C103D4semidirect
471. #18434C103direct (N × H)
482. #3560C2×C103semidirect
483. #3213C2×C103semidirect
484. #3211C2×C103semidirect
485. #2662C2×C103semidirect
486. #1606C2×C103semidirect
487. #1604C2×C103semidirect
488. #1603C2×C103semidirect
489. #1601C2×C103semidirect
490. #1600C2×C103semidirect
491. #1598C2×C103semidirect
492. #1597C2×C103semidirect
493. #1595C2×C103semidirect
494. #1509C2×C103semidirect
495. #1502C2×C103semidirect
496. #1473C2×C103semidirect
497. C103#18434direct (N × H)
517. C2×#124C22×C103semidirect
526. #451C22×C103semidirect
527. #450C22×C103semidirect
530. #448C22×C103semidirect
533. #447C22×C103semidirect
534. #432C22×C103semidirect
535. #431C22×C103semidirect
537. #395C22×C103semidirect
539. #394C22×C103semidirect
544. C4×C4⋊C4C22×C103semidirect
545. #328C22×C103semidirect
546. #328C22×C103semidirect
551. #327C22×C103semidirect
552. #327C22×C103semidirect
553. #324C22×C103semidirect
554. #324C22×C103semidirect
572. C4⋊Q8D4×C103semidirect
573. #127D4×C103semidirect
585. #125D4×C103semidirect
594. #124D4×C103semidirect
635. C4×Q8D4×C103semidirect
644. C4×D4D4×C103semidirect
645. C4×D4D4×C103semidirect
646. C4×D4D4×C103semidirect

Maximal subgroups

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

subgroupindex
C103×#35602
C103×#32132
C103×#32112
C103×#26622
C103×#16062
C103×#16042
C103×#16032
C103×#16012
C103×#16002
C103×#15982
C103×#15972
C103×#15952
C103×#15092
C103×#15022
C103×#14732
#18434103