Finite Group Databasebeta

← C103×#24565 #39929840

Subgroups — C103×#24565 #39929840

Order 26368.

1040 conjugacy classes of subgroups.

The subgroup lattice has 800 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C103C211yesmaximal, characteristic, complemented
2C2×#408×C103C211yesmaximal, characteristic, complemented
3C103×#2615C211yesmaximal, characteristic
4C103×#2311C211yesmaximal, characteristic, complemented
5C103×#2077C211yesmaximal, characteristic, complemented
6C103×#2076C211yesmaximal, characteristic, complemented
7C103×#2033C211yesmaximal, characteristic, complemented
8C103×#2033C211yesmaximal, characteristic, complemented
9C103×#1895C211yesmaximal, characteristic, complemented
10C103×#1893C211yesmaximal, characteristic, complemented
11C103×#1874C211yesmaximal, characteristic, complemented
12C103×#1852C211yesmaximal, characteristic, complemented
13C103×#1825C211yesmaximal, characteristic, complemented
14C103×#1809C211yesmaximal, characteristic, complemented
15C103×#1808C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×M16×C103C2211yescharacteristic
18C23×C8×C103C2211yescharacteristic
19C2×#121×C103C2211yescharacteristic
20C2×#121×C103C2211yescharacteristic
21C2×#121×C103C2211yescharacteristic
22C2×#117×C103C2211yescharacteristic
23C22×C4⋊C4×C103C2211yescharacteristic
24#482×C103—24no—
25C2×#107×C103C2211yescharacteristic
26C2×#107×C103C2211yescharacteristic
27C2×#107×C103C2211yescharacteristic
28C2×#106×C103C2211yescharacteristic
29C2×#102×C103C2211yescharacteristic
30C2×#102×C103C2211yescharacteristic
31C2×#102×C103C2211yescharacteristic
32C2×#102×C103C2211yescharacteristic
33#408×C103—24no—
34C2×C22⋊C8×C103C2211yescharacteristic
35C2×C22⋊C8×C103C2211yescharacteristic
36C2×C22⋊C8×C103C2211yescharacteristic
37C2×C22⋊C8×C103C2211yescharacteristic
38#393×C103—21no—
39#392×C103—21no—
40#392×C103—21no—
41#392×C103—21no—
42#391×C103—21no—
43#390×C103—21no—
44#386×C103—21no—
45#386×C103—21no—
46#380×C103C2211yescharacteristic
47#380×C103C2211yescharacteristic
48#380×C103C2211yescharacteristic
49#380×C103C2211yescharacteristic
50#380×C103C2211yescharacteristic
51#380×C103C2211yescharacteristic
52#380×C103C2211yescharacteristic
53#340×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61C2×#41×C103—22no—
62C2×#41×C103—22no—
63C2×#41×C103—22no—
64C2×#41×C103—22no—
65C2×#41×C103—41no—
66C2×#41×C103—41no—
67C22×Q8×C103D411yescharacteristic
68C22×D4×C103—21no—
69C22×D4×C103—21no—
70C22×D4×C103—21no—
71C22×D4×C103D411yescharacteristic
72C22×D4×C103D411yescharacteristic
73C22×D4×C103D411yescharacteristic
74C22×D4×C103C2311yescharacteristic
75C23×C4×C103—21no—
76C23×C4×C103C2311yescharacteristic
77C23×C4×C103C2311yescharacteristic
78C23×C4×C103C2311yescharacteristic
79C2×M16×C103—22no—
80C2×M16×C103—22no—
81C2×M16×C103—41no—
82C22×C8×C103—22no—
83C22×C8×C103—22no—
84C22×C8×C103—41no—
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89#121×C103—22no—
90#121×C103—22no—
91#121×C103—22no—
92#121×C103—22no—
93#121×C103—41no—
94#121×C103—41no—
95#117×C103—22no—
96#117×C103—22no—
97C2×C4⋊C4×C103—21no—
98C2×C4⋊C4×C103—41no—
99C2×C4⋊C4×C103—41no—
100C2×C4⋊C4×C103C2311yescharacteristic
101C2×C4⋊C4×C103C2311yescharacteristic
102C2×C4⋊C4×C103C2311yescharacteristic
103C2×C4⋊C4×C103C2311yescharacteristic
104C2×C4⋊C4×C103C2311yescharacteristic
105C2×C4⋊C4×C103C2311yescharacteristic
106C2×C4⋊C4×C103C2311yescharacteristic
107C2×C22⋊C4×C103—21no—
108C2×C22⋊C4×C103—21no—
109C2×C22⋊C4×C103—21no—
110C2×C22⋊C4×C103—21no—
111C2×C22⋊C4×C103—21no—
112C2×C22⋊C4×C103—21no—
113C2×C22⋊C4×C103—21no—
114C2×C22⋊C4×C103—21no—
115C2×C22⋊C4×C103—21no—
116C2×C22⋊C4×C103—21no—
117C2×C22⋊C4×C103—21no—
118C2×C42×C103—21no—
119#107×C103—22no—
120#107×C103—41no—
121#107×C103—41no—
122#106×C103—22no—
123#102×C103—22no—
124#102×C103—22no—
125#102×C103—41no—
126#102×C103—41no—
127C22⋊C8×C103—22no—
128C22⋊C8×C103—22no—
129C22⋊C8×C103—22no—
130C22⋊C8×C103D414yescomplemented
131#95×C103—21no—
132#95×C103—21no—
133#95×C103—21no—
134#95×C103—21no—
135#95×C103—21no—
136#95×C103—21no—
137#95×C103—21no—
138C24×C103—21no—
139C24×C103C2×D411yescharacteristic
140C24×C103C2×D411yescharacteristic
141C24×C103C2×D411yescharacteristic
142#41×C103—44no—
143#41×C103—44no—
144#41×C103—44no—
145#41×C103—44no—
146C2×Q8×C103—22no—
147C2×Q8×C103—22no—
148C2×Q8×C103—41no—
149C2×D4×C103—22no—
150C2×D4×C103—22no—
151C2×D4×C103—22no—
152C2×D4×C103—22no—
153C2×D4×C103—22no—
154C2×D4×C103—22no—
155C2×D4×C103—21no—
156C2×D4×C103—21no—
157C2×D4×C103—21no—
158C2×D4×C103—21no—
159C2×D4×C103—21no—
160C2×D4×C103—21no—
161C2×D4×C103—41no—
162C2×D4×C103—41no—
163C2×D4×C103—41no—
164C2×D4×C103—42no—
165C2×D4×C103—42no—
166C2×D4×C103—42no—
167C2×D4×C103—81no—
168C2×D4×C103—81no—
169C2×D4×C103—81no—
170C2×D4×C103—81no—
171C2×D4×C103—81no—
172C2×D4×C103—81no—
173C22×C4×C103—21no—
174C22×C4×C103—21no—
175C22×C4×C103—21no—
176C22×C4×C103—21no—
177C22×C4×C103—21no—
178C22×C4×C103—21no—
179C22×C4×C103—21no—
180C22×C4×C103—21no—
181C22×C4×C103—21no—
182C22×C4×C103—21no—
183C22×C4×C103—21no—
184C22×C4×C103—21no—
185C22×C4×C103—21no—
186C22×C4×C103—21no—
187C22×C4×C103—21no—
188C22×C4×C103—21no—
189C22×C4×C103—21no—
190C22×C4×C103—21no—
191C22×C4×C103—21no—
192C22×C4×C103—21no—
193C22×C4×C103—21no—
194C22×C4×C103—42no—
195C22×C4×C103—81no—
196C22×C4×C103—81no—
197C22×C4×C103C2×D411yescharacteristic
198C22×C4×C103C2×D411yescharacteristic
199C22×C4×C103C2×D412yes—
200C22×C4×C103C2×D411yescharacteristic
201C22×C4×C103#4112yes—
202C22×C4×C103#4112yes—
203C22×C4×C103#4112yes—
204C22×C4×C103C2411yescharacteristic
205M16×C103—44no—
206C2×C8×C103—21no—
207C2×C8×C103—21no—
208C2×C8×C103—21no—
209C2×C8×C103—21no—
210C2×C8×C103—21no—
211C2×C8×C103—21no—
212C2×C8×C103—21no—
213C2×C8×C103—21no—
214C2×C8×C103—21no—
215C2×C8×C103—21no—
216C2×C8×C103—44no—
217C2×C8×C103C2×D412yes—
218C2×C8×C103C2×D412yes—
219C4⋊C4×C103—21no—
220C4⋊C4×C103—21no—
221C4⋊C4×C103—21no—
222C4⋊C4×C103—21no—
223C4⋊C4×C103—21no—
224C4⋊C4×C103—21no—
225C4⋊C4×C103—21no—
226C4⋊C4×C103—21no—
227C4⋊C4×C103—21no—
228C4⋊C4×C103—21no—
229C4⋊C4×C103—21no—
230C4⋊C4×C103—21no—
231C4⋊C4×C103—21no—
232C4⋊C4×C103—21no—
233C4⋊C4×C103—42no—
234C22⋊C4×C103—42no—
235C22⋊C4×C103—42no—
236C22⋊C4×C103—42no—
237C22⋊C4×C103—42no—
238C22⋊C4×C103—81no—
239C22⋊C4×C103—81no—
240C22⋊C4×C103—81no—
241C22⋊C4×C103—81no—
242C22⋊C4×C103—81no—
243C22⋊C4×C103—81no—
244C22⋊C4×C103—81no—
245C42×C103—42no—
246C23×C103—21no—
247C23×C103—21no—
248C23×C103—21no—
249C23×C103—21no—
250C23×C103—21no—
251C23×C103—21no—
252C23×C103—21no—
253C23×C103—21no—
254C23×C103—21no—
255C23×C103—21no—
256C23×C103—21no—
257C23×C103—21no—
258C23×C103—21no—
259C23×C103—21no—
260C23×C103—21no—
261C23×C103—21no—
262C23×C103—21no—
263C23×C103—21no—
264C23×C103—21no—
265C23×C103—41no—
266C23×C103—41no—
267C23×C103—41no—
268C23×C103—41no—
269C23×C103—41no—
270C23×C103—41no—
271C23×C103—41no—
272C23×C103#12112yes—
273C23×C103#12312yes—
274C23×C103C22×D411yescharacteristic
275Q8×C103—44no—
276D4×C103—44no—
277D4×C103—44no—
278D4×C103—44no—
279D4×C103—41no—
280D4×C103—41no—
281D4×C103—41no—
282D4×C103—41no—
283D4×C103—84no—
284D4×C103—84no—
285D4×C103—84no—
286C2×C4×C103—21no—
287C2×C4×C103—21no—
288C2×C4×C103—21no—
289C2×C4×C103—21no—
290C2×C4×C103—22no—
291C2×C4×C103—22no—
292C2×C4×C103—22no—
293C2×C4×C103—22no—
294C2×C4×C103—22no—
295C2×C4×C103—22no—
296C2×C4×C103—22no—
297C2×C4×C103—22no—
298C2×C4×C103—21no—
299C2×C4×C103—21no—
300C2×C4×C103—21no—
301C2×C4×C103—41no—
302C2×C4×C103—41no—
303C2×C4×C103—41no—
304C2×C4×C103—41no—
305C2×C4×C103—41no—
306C2×C4×C103—41no—
307C2×C4×C103—41no—
308C2×C4×C103—41no—
309C2×C4×C103—41no—
310C2×C4×C103—41no—
311C2×C4×C103—41no—
312C2×C4×C103—41no—
313C2×C4×C103—41no—
314C2×C4×C103—41no—
315C2×C4×C103—41no—
316C2×C4×C103—41no—
317C2×C4×C103—41no—
318C2×C4×C103—41no—
319C2×C4×C103—41no—
320C2×C4×C103—41no—
321C2×C4×C103—41no—
322C2×C4×C103—41no—
323C2×C4×C103—41no—
324C2×C4×C103—41no—
325C2×C4×C103—41no—
326C2×C4×C103—84no—
327C2×C4×C103#12112yes—
328C2×C4×C103#12312yes—
329C2×C4×C103C22×D411yescharacteristic
330C2×C4×C103C2×#4111yescharacteristic
331C2×C4×C103C2×#4111yescharacteristic
332C2×C4×C103C2×#4111yescharacteristic
333C2×C4×C103H(5,𝔽2)11yescharacteristic
334C2×C4×C103H(5,𝔽2)11yescharacteristic
335C8×C103—22no—
336C8×C103—22no—
337C8×C103—41no—
338C8×C103—41no—
339C22×C103—22no—
340C22×C103—22no—
341C22×C103—22no—
342C22×C103—22no—
343C22×C103—22no—
344C22×C103—22no—
345C22×C103—41no—
346C22×C103—41no—
347C22×C103—41no—
348C22×C103—41no—
349C22×C103—41no—
350C22×C103—41no—
351C22×C103—41no—
352C22×C103—41no—
353C22×C103—41no—
354C22×C103—41no—
355C22×C103—41no—
356C22×C103—41no—
357C22×C103—41no—
358C22×C103—41no—
359C22×C103—41no—
360C22×C103—81no—
361C22×C103—81no—
362C22×C103—81no—
363C22×C103—81no—
364C22×C103—81no—
365C22×C103—81no—
366C22×C103—81no—
367C22×C103C2×#12111yescharacteristic
368C22×C103C2×#12311yescharacteristic
369C22×C103#53411yescharacteristic
370C22×C103#57611yescharacteristic
371C22×C103#57611yescharacteristic
372C22×C103#57711yescharacteristic
373C22×C103#57811yescharacteristic
374C4×C103—22no—
375C4×C103—22no—
376C4×C103—41no—
377C4×C103—81no—
378C4×C103—81no—
379C4×C103—81no—
380C4×C103—81no—
381C4×C103—81no—
382C4×C103—81no—
383C4×C103—81no—
384C4×C103#54611yescharacteristic
385C4×C103#54611yescharacteristic
386C4×C103#55111yescharacteristic
387C4×C103#55111yescharacteristic
388#24565C10311yesmaximal, characteristic, direct product factor, Sylow
389C2×C103—42no—
390C2×C103—42no—
391C2×C103—81no—
392C2×C103—161no—
393C2×C103#241211yescharacteristic
394C2×C103#306111yescharacteristic
395C2×C103#306211yescharacteristic
396C2×C103#309611yescharacteristic
397C2×C103#309811yescharacteristic
398C2×C103#319911yescharacteristic
399C2×C103#320111yescharacteristic
400C2×#482C2×C10311yescharacteristic, complemented
401C2×#408C2×C10311yescharacteristic, complemented
402#2615C2×C10311yescharacteristic
403#2311C2×C10311yescharacteristic, complemented
404#2077C2×C10311yescharacteristic, complemented
405#2076C2×C10311yescharacteristic, complemented
406#2033C2×C10311yescharacteristic, complemented
407#2033C2×C10311yescharacteristic, complemented
408#1895C2×C10311yescharacteristic, complemented
409#1893C2×C10311yescharacteristic, complemented
410#1874C2×C10311yescharacteristic, complemented
411#1852C2×C10311yescharacteristic, complemented
412#1825C2×C10311yescharacteristic, complemented
413#1809C2×C10311yescharacteristic, complemented
414#1808C2×C10311yescharacteristic, complemented
415C103#2456511yescharacteristic, direct product factor, Sylow
416C22×#41C22×C10311yescharacteristic
417C22×M16C22×C10311yescharacteristic
418C23×C8C22×C10311yescharacteristic
419C2×#121C22×C10311yescharacteristic
420C2×#121C22×C10311yescharacteristic
421C2×#121C22×C10311yescharacteristic
422C2×#117C22×C10311yescharacteristic
423C22×C4⋊C4C22×C10311yescharacteristic
424#482—24no—
425C2×#107C22×C10311yescharacteristic
426C2×#107C22×C10311yescharacteristic
427C2×#107C22×C10311yescharacteristic
428C2×#106C22×C10311yescharacteristic
429C2×#102C22×C10311yescharacteristic
430C2×#102C22×C10311yescharacteristic
431C2×#102C22×C10311yescharacteristic
432C2×#102C22×C10311yescharacteristic
433#408—24no—
434C2×C22⋊C8C22×C10311yescharacteristic
435C2×C22⋊C8C22×C10311yescharacteristic
436C2×C22⋊C8C22×C10311yescharacteristic
437C2×C22⋊C8C22×C10311yescharacteristic
438#393—21no—
439#392—21no—
440#392—21no—
441#392—21no—
442#391—21no—
443#390—21no—
444#386—21no—
445#386—21no—
446#380C22×C10311yescharacteristic
447#380C22×C10311yescharacteristic
448#380C22×C10311yescharacteristic
449#380C22×C10311yescharacteristic
450#380C22×C10311yescharacteristic
451#380C22×C10311yescharacteristic
452#380C22×C10311yescharacteristic
453#340C22×C10311yescharacteristic
454#340C22×C10311yescharacteristic
455#340C22×C10311yescharacteristic
456#340C22×C10311yescharacteristic
457#340C22×C10311yescharacteristic
458#340C22×C10311yescharacteristic
459#340C22×C10311yescharacteristic
460#340C22×C10311yescharacteristic
461C2×#41—22no—
462C2×#41—22no—
463C2×#41—22no—
464C2×#41—22no—
465C2×#41—41no—
466C2×#41—41no—
467C22×Q8D4×C10311yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4D4×C10311yescharacteristic
472C22×D4D4×C10311yescharacteristic
473C22×D4D4×C10311yescharacteristic
474C22×D4C23×C10311yescharacteristic
475C23×C4—21no—
476C23×C4C23×C10311yescharacteristic
477C23×C4C23×C10311yescharacteristic
478C23×C4C23×C10311yescharacteristic
479C2×M16—22no—
480C2×M16—22no—
481C2×M16—41no—
482C22×C8—22no—
483C22×C8—22no—
484C22×C8—41no—
485C22×C8C23×C10311yescharacteristic
486C22×C8C23×C10311yescharacteristic
487C22×C8C23×C10311yescharacteristic
488C22×C8C23×C10311yescharacteristic
489#121—22no—
490#121—22no—
491#121—22no—
492#121—22no—
493#121—41no—
494#121—41no—
495#117—22no—
496#117—22no—
497C2×C4⋊C4—21no—
498C2×C4⋊C4—41no—
499C2×C4⋊C4—41no—
500C2×C4⋊C4C23×C10311yescharacteristic
501C2×C4⋊C4C23×C10311yescharacteristic
502C2×C4⋊C4C23×C10311yescharacteristic
503C2×C4⋊C4C23×C10311yescharacteristic
504C2×C4⋊C4C23×C10311yescharacteristic
505C2×C4⋊C4C23×C10311yescharacteristic
506C2×C4⋊C4C23×C10311yescharacteristic
507C2×C22⋊C4—21no—
508C2×C22⋊C4—21no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—21no—
512C2×C22⋊C4—21no—
513C2×C22⋊C4—21no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4—21no—
516C2×C22⋊C4—21no—
517C2×C22⋊C4—21no—
518C2×C42—21no—
519#107—22no—
520#107—41no—
521#107—41no—
522#106—22no—
523#102—22no—
524#102—22no—
525#102—41no—
526#102—41no—
527C22⋊C8—22no—
528C22⋊C8—22no—
529C22⋊C8—22no—
530C22⋊C8D4×C10314yescomplemented
531#95—21no—
532#95—21no—
533#95—21no—
534#95—21no—
535#95—21no—
536#95—21no—
537#95—21no—
538C24—21no—
539C24C2×D4×C10311yescharacteristic
540C24C2×D4×C10311yescharacteristic
541C24C2×D4×C10311yescharacteristic
542#41—44no—
543#41—44no—
544#41—44no—
545#41—44no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—41no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—41no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—81no—
570C2×D4—81no—
571C2×D4—81no—
572C2×D4—81no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—21no—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—42no—
595C22×C4—81no—
596C22×C4—81no—
597C22×C4C2×D4×C10311yescharacteristic
598C22×C4C2×D4×C10311yescharacteristic
599C22×C4C2×D4×C10312yes—
600C22×C4C2×D4×C10311yescharacteristic
601C22×C4#41×C10312yes—
602C22×C4#41×C10312yes—
603C22×C4#41×C10312yes—
604C22×C4C24×C10311yescharacteristic
605M16—44no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—21no—
615C2×C8—21no—
616C2×C8—44no—
617C2×C8C2×D4×C10312yes—
618C2×C8C2×D4×C10312yes—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—21no—
632C4⋊C4—21no—
633C4⋊C4—42no—
634C22⋊C4—42no—
635C22⋊C4—42no—
636C22⋊C4—42no—
637C22⋊C4—42no—
638C22⋊C4—81no—
639C22⋊C4—81no—
640C22⋊C4—81no—
641C22⋊C4—81no—
642C22⋊C4—81no—
643C22⋊C4—81no—
644C22⋊C4—81no—
645C42—42no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—21no—
651C23—21no—
652C23—21no—
653C23—21no—
654C23—21no—
655C23—21no—
656C23—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—21no—
661C23—21no—
662C23—21no—
663C23—21no—
664C23—21no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23#121×C10312yes—
673C23#123×C10312yes—
674C23C22×D4×C10311yescharacteristic
675Q8—44no—
676D4—44no—
677D4—44no—
678D4—44no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—84no—
684D4—84no—
685D4—84no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—21no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—41no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—41no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—84no—
727C2×C4#121×C10312yes—
728C2×C4#123×C10312yes—
729C2×C4C22×D4×C10311yescharacteristic
730C2×C4C2×#41×C10311yescharacteristic
731C2×C4C2×#41×C10311yescharacteristic
732C2×C4C2×#41×C10311yescharacteristic
733C2×C4H(5,𝔽2)×C10311yescharacteristic
734C2×C4H(5,𝔽2)×C10311yescharacteristic
735C8—22no—
736C8—22no—
737C8—41no—
738C8—41no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—22no—
745C22—41no—
746C22—41no—
747C22—41no—
748C22—41no—
749C22—41no—
750C22—41no—
751C22—41no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—81no—
761C22—81no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—81no—
766C22—81no—
767C22C2×#121×C10311yescharacteristic
768C22C2×#123×C10311yescharacteristic
769C22#534×C10311yescharacteristic
770C22#576×C10311yescharacteristic
771C22#576×C10311yescharacteristic
772C22#577×C10311yescharacteristic
773C22#578×C10311yescharacteristic
774C4—22no—
775C4—22no—
776C4—41no—
777C4—81no—
778C4—81no—
779C4—81no—
780C4—81no—
781C4—81no—
782C4—81no—
783C4—81no—
784C4#546×C10311yescharacteristic
785C4#546×C10311yescharacteristic
786C4#551×C10311yescharacteristic
787C4#551×C10311yescharacteristic
788C2—42no—
789C2—42no—
790C2—81no—
791C2—161no—
792C2C103×#241211yescharacteristic
793C2C103×#306111yescharacteristic
794C2C103×#306211yescharacteristic
795C2C103×#309611yescharacteristic
796C2C103×#309811yescharacteristic
797C2C103×#319911yescharacteristic
798C2C103×#320111yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC103×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C22×#41×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#482×C103C2semidirect
2. C2×#408×C103C2semidirect
4. C103×#2311C2semidirect
5. C103×#2077C2semidirect
6. C103×#2076C2semidirect
7. C103×#2033C2semidirect
8. C103×#2033C2semidirect
9. C103×#1895C2semidirect
10. C103×#1893C2semidirect
11. C103×#1874C2semidirect
12. C103×#1852C2semidirect
13. C103×#1825C2semidirect
14. C103×#1809C2semidirect
15. C103×#1808C2semidirect
130. C22⋊C8×C103D4semidirect
388. #24565C103direct (N × H)
400. C2×#482C2×C103semidirect
401. C2×#408C2×C103semidirect
403. #2311C2×C103semidirect
404. #2077C2×C103semidirect
405. #2076C2×C103semidirect
406. #2033C2×C103semidirect
407. #2033C2×C103semidirect
408. #1895C2×C103semidirect
409. #1893C2×C103semidirect
410. #1874C2×C103semidirect
411. #1852C2×C103semidirect
412. #1825C2×C103semidirect
413. #1809C2×C103semidirect
414. #1808C2×C103semidirect
415. C103#24565direct (N × H)
530. C22⋊C8D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C1032
C2×#408×C1032
C103×#26152
C103×#23112
C103×#20772
C103×#20762
C103×#20332
C103×#18952
C103×#18932
C103×#18742
C103×#18522
C103×#18252
C103×#18092
C103×#18082
#24565103