Finite Group Databasebeta

← C103×#25423 #39930698

Subgroups — C103×#25423 #39930698

Order 26368.

1006 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#497×C103C211yesmaximal, characteristic, complemented
2C2×#467×C103C211yesmaximal, characteristic, complemented
3C2×#465×C103C211yesmaximal, characteristic
4C2×#440×C103C211yesmaximal, characteristic, complemented
5C103×#2429C211yesmaximal, characteristic, complemented
6C103×#2427C211yesmaximal, characteristic
7C103×#2043C211yesmaximal, characteristic, complemented
8C103×#2042C211yesmaximal, characteristic, complemented
9C103×#2001C211yesmaximal, characteristic, complemented
10C103×#2000C211yesmaximal, characteristic
11C103×#1971C211yesmaximal, characteristic, complemented
12C103×#1943C211yesmaximal, characteristic, complemented
13C103×#1878C211yesmaximal, characteristic, complemented
14C103×#1877C211yesmaximal, characteristic, complemented
15C103×#1752C211yesmaximal, characteristic, complemented
16C22×Q16×C103C2211yescharacteristic
17C22×Q16×C103C2211yescharacteristic
18C22×SD16×C103C2211yescharacteristic
19C22×SD16×C103C2211yescharacteristic
20C23×C8×C103C2211yescharacteristic
21C2×C4⋊Q8×C103C2211yescharacteristic
22C2×#124×C103C2211yescharacteristic
23C2×C22⋊Q8×C103C2211yescharacteristic
24C2×C22⋊Q8×C103C2211yescharacteristic
25C2×C22⋊Q8×C103C2211yescharacteristic
26C2×#121×C103C2211yescharacteristic
27C2×C4×Q8×C103C2211yescharacteristic
28C2×C4×D4×C103C2211yescharacteristic
29#497×C103—24no—
30#467×C103—24no—
31#465×C103—24no—
32#440×C103—24no—
33C2×#107×C103C2211yescharacteristic
34C2×#106×C103C2211yescharacteristic
35C2×#103×C103C2211yescharacteristic
36C2×#103×C103C2211yescharacteristic
37C2×#103×C103C2211yescharacteristic
38C2×#103×C103C2211yescharacteristic
39C2×#103×C103C2211yescharacteristic
40C2×#103×C103C2211yescharacteristic
41C2×#102×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×C22⋊C8×C103C2211yescharacteristic
44C2×#97×C103C2211yescharacteristic
45C2×#97×C103C2211yescharacteristic
46#398×C103—21no—
47#397×C103—21no—
48#396×C103—21no—
49#394×C103—21no—
50#391×C103C2211yescharacteristic
51#391×C103C2211yescharacteristic
52#389×C103—21no—
53#389×C103C2211yescharacteristic
54#389×C103C2211yescharacteristic
55#388×C103—21no—
56#386×C103—21no—
57#380×C103—21no—
58C4×C22⋊C4×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#336×C103C2211yescharacteristic
62#336×C103C2211yescharacteristic
63C22×Q8×C103C2311yescharacteristic
64C22×Q8×C103C2311yescharacteristic
65C22×Q8×C103C2311yescharacteristic
66C22×D4×C103—21no—
67C22×D4×C103C2311yescharacteristic
68C23×C4×C103—21no—
69C23×C4×C103C2311yescharacteristic
70C2×Q16×C103—22no—
71C2×Q16×C103—22no—
72C2×Q16×C103—22no—
73C2×Q16×C103—22no—
74C2×Q16×C103—22no—
75C2×Q16×C103—41no—
76C2×SD16×C103—22no—
77C2×SD16×C103—22no—
78C2×SD16×C103—22no—
79C2×SD16×C103—22no—
80C2×SD16×C103—41no—
81C2×SD16×C103D414yes—
82C22×C8×C103—22no—
83C22×C8×C103—22no—
84C22×C8×C103—22no—
85C22×C8×C103C2311yescharacteristic
86C22×C8×C103C2311yescharacteristic
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89C4⋊Q8×C103—22no—
90C4⋊Q8×C103—41no—
91#124×C103—22no—
92#124×C103—41no—
93C22⋊Q8×C103—22no—
94C22⋊Q8×C103—22no—
95C22⋊Q8×C103—22no—
96C22⋊Q8×C103—41no—
97C22⋊Q8×C103—41no—
98C22⋊Q8×C103—41no—
99#121×C103—22no—
100#121×C103—41no—
101C4×Q8×C103—22no—
102C4×Q8×C103—41no—
103C4×D4×C103—22no—
104C4×D4×C103—41no—
105C2×C4⋊C4×C103—21no—
106C2×C4⋊C4×C103—21no—
107C2×C4⋊C4×C103—21no—
108C2×C4⋊C4×C103—21no—
109C2×C4⋊C4×C103—21no—
110C2×C4⋊C4×C103—21no—
111C2×C4⋊C4×C103—21no—
112C2×C4⋊C4×C103—21no—
113C2×C4⋊C4×C103C2311yescharacteristic
114C2×C4⋊C4×C103C2311yescharacteristic
115C2×C4⋊C4×C103C2311yescharacteristic
116C2×C4⋊C4×C103C2311yescharacteristic
117C2×C22⋊C4×C103—21no—
118C2×C22⋊C4×C103—21no—
119C2×C22⋊C4×C103—21no—
120C2×C22⋊C4×C103—21no—
121C2×C22⋊C4×C103—21no—
122C2×C22⋊C4×C103—21no—
123C2×C22⋊C4×C103—21no—
124C2×C22⋊C4×C103D411yescharacteristic
125C2×C22⋊C4×C103D411yescharacteristic
126C2×C42×C103—21no—
127C2×C42×C103C2311yescharacteristic
128C2×C42×C103C2311yescharacteristic
129#107×C103D414yescomplemented
130#106×C103—22no—
131#103×C103—22no—
132#103×C103—22no—
133#103×C103—22no—
134#103×C103—22no—
135#103×C103—41no—
136#103×C103—41no—
137#102×C103—22no—
138#102×C103—22no—
139C22⋊C8×C103—22no—
140#97×C103—22no—
141#97×C103—22no—
142#95×C103—21no—
143#95×C103—21no—
144#95×C103—21no—
145#95×C103—21no—
146#95×C103—21no—
147#95×C103—21no—
148#95×C103D411yescharacteristic
149#95×C103D411yescharacteristic
150C24×C103—21no—
151C24×C103C2×D411yescharacteristic
152C2×Q8×C103—21no—
153C2×Q8×C103—21no—
154C2×Q8×C103—21no—
155C2×Q8×C103—21no—
156C2×Q8×C103—21no—
157C2×Q8×C103—21no—
158C2×Q8×C103—21no—
159C2×Q8×C103—21no—
160C2×Q8×C103—21no—
161C2×Q8×C103—21no—
162C2×Q8×C103—21no—
163C2×Q8×C103—21no—
164C2×Q8×C103—21no—
165C2×Q8×C103—21no—
166C2×Q8×C103—21no—
167C2×Q8×C103—21no—
168C2×Q8×C103—21no—
169C2×Q8×C103C2×D412yes—
170C2×D4×C103—21no—
171C2×D4×C103—21no—
172C2×D4×C103—21no—
173C2×D4×C103—21no—
174C2×D4×C103—21no—
175C2×D4×C103—42no—
176C2×D4×C103—42no—
177C2×D4×C103—81no—
178C2×D4×C103C2×D412yes—
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—42no—
193C22×C4×C103—42no—
194C22×C4×C103—81no—
195C22×C4×C103C2×D411yescharacteristic
196C22×C4×C103C2×D411yescharacteristic
197C22×C4×C103C2×D411yescharacteristic
198C22×C4×C103C2×D411yescharacteristic
199C22×C4×C103C2×D411yescharacteristic
200C22×C4×C103C2411yescharacteristic
201Q16×C103—44no—
202Q16×C103—44no—
203SD16×C103—28no—
204SD16×C103—44no—
205C2×C8×C103—21no—
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—44no—
214C2×C8×C103C2×D412yes—
215C2×C8×C103C2×D412yes—
216C2×C8×C103#4112yes—
217C2×C8×C103#4112yes—
218C4⋊C4×C103—21no—
219C4⋊C4×C103—21no—
220C4⋊C4×C103—21no—
221C4⋊C4×C103—21no—
222C4⋊C4×C103—21no—
223C4⋊C4×C103—21no—
224C4⋊C4×C103—42no—
225C4⋊C4×C103—42no—
226C4⋊C4×C103—42no—
227C4⋊C4×C103—42no—
228C4⋊C4×C103—42no—
229C4⋊C4×C103—42no—
230C4⋊C4×C103—42no—
231C4⋊C4×C103—81no—
232C4⋊C4×C103C2×D412yes—
233C4⋊C4×C103C2×D412yes—
234C22⋊C4×C103—22no—
235C22⋊C4×C103—41no—
236C22⋊C4×C103—42no—
237C22⋊C4×C103—42no—
238C22⋊C4×C103—42no—
239C22⋊C4×C103—42no—
240C22⋊C4×C103—42no—
241C22⋊C4×C103—42no—
242C22⋊C4×C103—42no—
243C42×C103—21no—
244C42×C103—21no—
245C42×C103—21no—
246C42×C103—21no—
247C42×C103—42no—
248C23×C103—21no—
249C23×C103—21no—
250C23×C103—21no—
251C23×C103—21no—
252C23×C103—21no—
253C23×C103—21no—
254C23×C103—22no—
255C23×C103—41no—
256C23×C103—41no—
257C23×C103—41no—
258C23×C103—41no—
259C23×C103—41no—
260C23×C103—41no—
261C23×C103#13712yes—
262C23×C103C22×D411yescharacteristic
263Q8×C103—22no—
264Q8×C103—22no—
265Q8×C103—41no—
266Q8×C103—41no—
267Q8×C103—41no—
268Q8×C103—41no—
269Q8×C103—41no—
270Q8×C103—41no—
271Q8×C103—41no—
272Q8×C103—41no—
273Q8×C103—41no—
274Q8×C103—41no—
275D4×C103—22no—
276D4×C103—22no—
277D4×C103—41no—
278D4×C103—41no—
279D4×C103—84no—
280C2×C4×C103—21no—
281C2×C4×C103—21no—
282C2×C4×C103—21no—
283C2×C4×C103—21no—
284C2×C4×C103—21no—
285C2×C4×C103—22no—
286C2×C4×C103—22no—
287C2×C4×C103—21no—
288C2×C4×C103—22no—
289C2×C4×C103—21no—
290C2×C4×C103—21no—
291C2×C4×C103—21no—
292C2×C4×C103—21no—
293C2×C4×C103—21no—
294C2×C4×C103—21no—
295C2×C4×C103—21no—
296C2×C4×C103—21no—
297C2×C4×C103—21no—
298C2×C4×C103—41no—
299C2×C4×C103—41no—
300C2×C4×C103—41no—
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—84no—
321C2×C4×C103C22×D411yescharacteristic
322C2×C4×C103C22×D411yescharacteristic
323C2×C4×C103C2×#4111yescharacteristic
324C2×C4×C103C2×#4111yescharacteristic
325C2×C4×C103H(5,𝔽2)11yescharacteristic
326C2×C4×C103H(5,𝔽2)11yescharacteristic
327C8×C103—22no—
328C8×C103—41no—
329C8×C103—41no—
330C8×C103#12114yes—
331C22×C103—22no—
332C22×C103—22no—
333C22×C103—22no—
334C22×C103—41no—
335C22×C103—41no—
336C22×C103—41no—
337C22×C103—41no—
338C22×C103—42no—
339C22×C103—42no—
340C22×C103—42no—
341C22×C103—81no—
342C22×C103—81no—
343C22×C103—81no—
344C22×C103—81no—
345C22×C103#53211yescharacteristic
346C22×C103D4211yescharacteristic
347C22×C103D4211yescharacteristic
348C22×C103C2×#13711yescharacteristic
349C22×C103#57511yescharacteristic
350C22×C103#57711yescharacteristic
351C22×C103#57811yescharacteristic
352C4×C103—41no—
353C4×C103—42no—
354C4×C103—41no—
355C4×C103—41no—
356C4×C103—42no—
357C4×C103—42no—
358C4×C103—41no—
359C4×C103—41no—
360C4×C103—81no—
361C4×C103—81no—
362C4×C103—81no—
363C4×C103—81no—
364C4×C103C2×#12111yescharacteristic
365C4×C103#54011yescharacteristic
366C4×C103#54611yescharacteristic
367C4×C103#55011yescharacteristic
368#25423C10311yesmaximal, characteristic, direct product factor, Sylow
369C2×C103—42no—
370C2×C103—82no—
371C2×C103#242811yescharacteristic
372C2×C103#317811yescharacteristic
373C2×C103#318111yescharacteristic
374C2×C103#326611yescharacteristic
375C2×C103#326711yescharacteristic
376C2×C103#326911yescharacteristic
377C2×C103#327011yescharacteristic
378C2×#497C2×C10311yescharacteristic, complemented
379C2×#467C2×C10311yescharacteristic, complemented
380C2×#465C2×C10311yescharacteristic
381C2×#440C2×C10311yescharacteristic, complemented
382#2429C2×C10311yescharacteristic, complemented
383#2427C2×C10311yescharacteristic
384#2043C2×C10311yescharacteristic, complemented
385#2042C2×C10311yescharacteristic, complemented
386#2001C2×C10311yescharacteristic, complemented
387#2000C2×C10311yescharacteristic
388#1971C2×C10311yescharacteristic, complemented
389#1943C2×C10311yescharacteristic, complemented
390#1878C2×C10311yescharacteristic, complemented
391#1877C2×C10311yescharacteristic, complemented
392#1752C2×C10311yescharacteristic, complemented
393C103#2542311yescharacteristic, direct product factor, Sylow
394C22×Q16C22×C10311yescharacteristic
395C22×Q16C22×C10311yescharacteristic
396C22×SD16C22×C10311yescharacteristic
397C22×SD16C22×C10311yescharacteristic
398C23×C8C22×C10311yescharacteristic
399C2×C4⋊Q8C22×C10311yescharacteristic
400C2×#124C22×C10311yescharacteristic
401C2×C22⋊Q8C22×C10311yescharacteristic
402C2×C22⋊Q8C22×C10311yescharacteristic
403C2×C22⋊Q8C22×C10311yescharacteristic
404C2×#121C22×C10311yescharacteristic
405C2×C4×Q8C22×C10311yescharacteristic
406C2×C4×D4C22×C10311yescharacteristic
407#497—24no—
408#467—24no—
409#465—24no—
410#440—24no—
411C2×#107C22×C10311yescharacteristic
412C2×#106C22×C10311yescharacteristic
413C2×#103C22×C10311yescharacteristic
414C2×#103C22×C10311yescharacteristic
415C2×#103C22×C10311yescharacteristic
416C2×#103C22×C10311yescharacteristic
417C2×#103C22×C10311yescharacteristic
418C2×#103C22×C10311yescharacteristic
419C2×#102C22×C10311yescharacteristic
420C2×#102C22×C10311yescharacteristic
421C2×C22⋊C8C22×C10311yescharacteristic
422C2×#97C22×C10311yescharacteristic
423C2×#97C22×C10311yescharacteristic
424#398—21no—
425#397—21no—
426#396—21no—
427#394—21no—
428#391C22×C10311yescharacteristic
429#391C22×C10311yescharacteristic
430#389—21no—
431#389C22×C10311yescharacteristic
432#389C22×C10311yescharacteristic
433#388—21no—
434#386—21no—
435#380—21no—
436C4×C22⋊C4C22×C10311yescharacteristic
437#340C22×C10311yescharacteristic
438#340C22×C10311yescharacteristic
439#336C22×C10311yescharacteristic
440#336C22×C10311yescharacteristic
441C22×Q8C23×C10311yescharacteristic
442C22×Q8C23×C10311yescharacteristic
443C22×Q8C23×C10311yescharacteristic
444C22×D4—21no—
445C22×D4C23×C10311yescharacteristic
446C23×C4—21no—
447C23×C4C23×C10311yescharacteristic
448C2×Q16—22no—
449C2×Q16—22no—
450C2×Q16—22no—
451C2×Q16—22no—
452C2×Q16—22no—
453C2×Q16—41no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16—22no—
458C2×SD16—41no—
459C2×SD16D4×C10314yes—
460C22×C8—22no—
461C22×C8—22no—
462C22×C8—22no—
463C22×C8C23×C10311yescharacteristic
464C22×C8C23×C10311yescharacteristic
465C22×C8C23×C10311yescharacteristic
466C22×C8C23×C10311yescharacteristic
467C4⋊Q8—22no—
468C4⋊Q8—41no—
469#124—22no—
470#124—41no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—41no—
475C22⋊Q8—41no—
476C22⋊Q8—41no—
477#121—22no—
478#121—41no—
479C4×Q8—22no—
480C4×Q8—41no—
481C4×D4—22no—
482C4×D4—41no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—21no—
489C2×C4⋊C4—21no—
490C2×C4⋊C4—21no—
491C2×C4⋊C4C23×C10311yescharacteristic
492C2×C4⋊C4C23×C10311yescharacteristic
493C2×C4⋊C4C23×C10311yescharacteristic
494C2×C4⋊C4C23×C10311yescharacteristic
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C22⋊C4D4×C10311yescharacteristic
503C2×C22⋊C4D4×C10311yescharacteristic
504C2×C42—21no—
505C2×C42C23×C10311yescharacteristic
506C2×C42C23×C10311yescharacteristic
507#107D4×C10314yescomplemented
508#106—22no—
509#103—22no—
510#103—22no—
511#103—22no—
512#103—22no—
513#103—41no—
514#103—41no—
515#102—22no—
516#102—22no—
517C22⋊C8—22no—
518#97—22no—
519#97—22no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95D4×C10311yescharacteristic
527#95D4×C10311yescharacteristic
528C24—21no—
529C24C2×D4×C10311yescharacteristic
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8C2×D4×C10312yes—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—81no—
556C2×D4C2×D4×C10312yes—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—42no—
571C22×C4—42no—
572C22×C4—81no—
573C22×C4C2×D4×C10311yescharacteristic
574C22×C4C2×D4×C10311yescharacteristic
575C22×C4C2×D4×C10311yescharacteristic
576C22×C4C2×D4×C10311yescharacteristic
577C22×C4C2×D4×C10311yescharacteristic
578C22×C4C24×C10311yescharacteristic
579Q16—44no—
580Q16—44no—
581SD16—28no—
582SD16—44no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8—21no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—44no—
592C2×C8C2×D4×C10312yes—
593C2×C8C2×D4×C10312yes—
594C2×C8#41×C10312yes—
595C2×C8#41×C10312yes—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—42no—
604C4⋊C4—42no—
605C4⋊C4—42no—
606C4⋊C4—42no—
607C4⋊C4—42no—
608C4⋊C4—42no—
609C4⋊C4—81no—
610C4⋊C4C2×D4×C10312yes—
611C4⋊C4C2×D4×C10312yes—
612C22⋊C4—22no—
613C22⋊C4—41no—
614C22⋊C4—42no—
615C22⋊C4—42no—
616C22⋊C4—42no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C42—21no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—42no—
626C23—21no—
627C23—21no—
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23#137×C10312yes—
640C23C22×D4×C10311yescharacteristic
641Q8—22no—
642Q8—22no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653D4—22no—
654D4—22no—
655D4—41no—
656D4—41no—
657D4—84no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—21no—
666C2×C4—22no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—84no—
699C2×C4C22×D4×C10311yescharacteristic
700C2×C4C22×D4×C10311yescharacteristic
701C2×C4C2×#41×C10311yescharacteristic
702C2×C4C2×#41×C10311yescharacteristic
703C2×C4H(5,𝔽2)×C10311yescharacteristic
704C2×C4H(5,𝔽2)×C10311yescharacteristic
705C8—22no—
706C8—41no—
707C8—41no—
708C8#121×C10314yes—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22#532×C10311yescharacteristic
724C22D42×C10311yescharacteristic
725C22D42×C10311yescharacteristic
726C22C2×#137×C10311yescharacteristic
727C22#575×C10311yescharacteristic
728C22#577×C10311yescharacteristic
729C22#578×C10311yescharacteristic
730C4—41no—
731C4—41no—
732C4—42no—
733C4—42no—
734C4—41no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4—81no—
742C4C2×#121×C10311yescharacteristic
743C4#540×C10311yescharacteristic
744C4#546×C10311yescharacteristic
745C4#550×C10311yescharacteristic
746C2—42no—
747C2—82no—
748C2C103×#242811yescharacteristic
749C2C103×#317811yescharacteristic
750C2C103×#318111yescharacteristic
751C2C103×#326611yescharacteristic
752C2C103×#326711yescharacteristic
753C2C103×#326911yescharacteristic
754C2C103×#327011yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC2×#121×C103C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C22⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#497×C103C2semidirect
2. C2×#467×C103C2semidirect
4. C2×#440×C103C2semidirect
5. C103×#2429C2semidirect
7. C103×#2043C2semidirect
8. C103×#2042C2semidirect
9. C103×#2001C2semidirect
11. C103×#1971C2semidirect
12. C103×#1943C2semidirect
13. C103×#1878C2semidirect
14. C103×#1877C2semidirect
15. C103×#1752C2semidirect
129. #107×C103D4semidirect
368. #25423C103direct (N × H)
378. C2×#497C2×C103semidirect
379. C2×#467C2×C103semidirect
381. C2×#440C2×C103semidirect
382. #2429C2×C103semidirect
384. #2043C2×C103semidirect
385. #2042C2×C103semidirect
386. #2001C2×C103semidirect
388. #1971C2×C103semidirect
389. #1943C2×C103semidirect
390. #1878C2×C103semidirect
391. #1877C2×C103semidirect
392. #1752C2×C103semidirect
393. C103#25423direct (N × H)
507. #107D4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#497×C1032
C2×#467×C1032
C2×#465×C1032
C2×#440×C1032
C103×#24292
C103×#24272
C103×#20432
C103×#20422
C103×#20012
C103×#20002
C103×#19712
C103×#19432
C103×#18782
C103×#18772
C103×#17522
#25423103