Finite Group Databasebeta

← C103×#25379 #39930654

Subgroups — C103×#25379 #39930654

Order 26368.

958 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#497×C103C211yesmaximal, characteristic
2C2×#464×C103C211yesmaximal, characteristic
3C2×#462×C103C211yesmaximal, characteristic, complemented
4C2×#462×C103C211yesmaximal, characteristic, complemented
5C103×#2545C211yesmaximal, characteristic
6C103×#2365C211yesmaximal, characteristic, complemented
7C103×#2056C211yesmaximal, characteristic, complemented
8C103×#2055C211yesmaximal, characteristic
9C103×#2016C211yesmaximal, characteristic, complemented
10C103×#2015C211yesmaximal, characteristic
11C103×#1983C211yesmaximal, characteristic
12C103×#1940C211yesmaximal, characteristic, complemented
13C103×#1880C211yesmaximal, characteristic
14C103×#1878C211yesmaximal, characteristic, complemented
15C103×#1763C211yesmaximal, characteristic, complemented
16C22×Q16×C103C2211yescharacteristic
17C22×Q16×C103C2211yescharacteristic
18C22×Q16×C103C2211yescharacteristic
19C22×Q16×C103C2211yescharacteristic
20C22×SD16×C103C2211yescharacteristic
21C22×SD16×C103C2211yescharacteristic
22C2×C4⋊Q8×C103C2211yescharacteristic
23C2×C4⋊Q8×C103C2211yescharacteristic
24C2×#124×C103C2211yescharacteristic
25C2×#124×C103C2211yescharacteristic
26C2×C4×Q8×C103C2211yescharacteristic
27C2×C4×Q8×C103C2211yescharacteristic
28C2×C4×Q8×C103C2211yescharacteristic
29#497×C103—24no—
30#464×C103—24no—
31#462×C103—24no—
32#462×C103—24no—
33C2×C4⋊C8×C103C2211yescharacteristic
34C2×C4⋊C8×C103C2211yescharacteristic
35C2×C4⋊C8×C103C2211yescharacteristic
36C2×#103×C103C2211yescharacteristic
37C2×#103×C103C2211yescharacteristic
38C2×#103×C103C2211yescharacteristic
39C2×#103×C103C2211yescharacteristic
40C2×#103×C103C2211yescharacteristic
41C2×#103×C103C2211yescharacteristic
42C2×#102×C103C2211yescharacteristic
43C2×#102×C103C2211yescharacteristic
44C2×#97×C103C2211yescharacteristic
45#396×C103—21no—
46#396×C103—21no—
47#391×C103C2211yescharacteristic
48#391×C103C2211yescharacteristic
49#391×C103C2211yescharacteristic
50#390×C103C2211yescharacteristic
51#389×C103—21no—
52#388×C103—21no—
53#388×C103—21no—
54#387×C103—21no—
55#387×C103—21no—
56C4×C4⋊C4×C103—21no—
57C4×C4⋊C4×C103C2211yescharacteristic
58C4×C4⋊C4×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#336×C103C2211yescharacteristic
62#336×C103C2211yescharacteristic
63C22×Q8×C103C2311yescharacteristic
64C22×Q8×C103C2311yescharacteristic
65C22×Q8×C103C2311yescharacteristic
66C22×Q8×C103C2311yescharacteristic
67C22×D4×C103C2311yescharacteristic
68C2×Q16×C103—22no—
69C2×Q16×C103—22no—
70C2×Q16×C103—22no—
71C2×Q16×C103—22no—
72C2×Q16×C103—22no—
73C2×Q16×C103—22no—
74C2×Q16×C103—22no—
75C2×Q16×C103—22no—
76C2×Q16×C103—41no—
77C2×Q16×C103—41no—
78C2×Q16×C103—41no—
79C2×Q16×C103—41no—
80C2×SD16×C103—22no—
81C2×SD16×C103—22no—
82C2×SD16×C103—22no—
83C2×SD16×C103—22no—
84C2×SD16×C103—41no—
85C2×SD16×C103—41no—
86C22×C8×C103C2311yescharacteristic
87C22×C8×C103C2311yescharacteristic
88C22×C8×C103C2311yescharacteristic
89C22×C8×C103C2311yescharacteristic
90C4⋊Q8×C103—22no—
91C4⋊Q8×C103—22no—
92C4⋊Q8×C103—41no—
93C4⋊Q8×C103D414yes—
94#124×C103—22no—
95#124×C103—22no—
96#124×C103—22no—
97#124×C103—41no—
98C4×Q8×C103—22no—
99C4×Q8×C103—22no—
100C4×Q8×C103—22no—
101C4×Q8×C103—22no—
102C4×Q8×C103—41no—
103C4×Q8×C103—41no—
104C2×C4⋊C4×C103—21no—
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×C103D411yescharacteristic
112C2×C4⋊C4×C103D411yescharacteristic
113C2×C4⋊C4×C103C2311yescharacteristic
114C2×C4⋊C4×C103C2311yescharacteristic
115C2×C4⋊C4×C103C2311yescharacteristic
116C2×C22⋊C4×C103—21no—
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×C42×C103—21no—
123C2×C42×C103—21no—
124C2×C42×C103—21no—
125C2×C42×C103—21no—
126C2×C42×C103C2311yescharacteristic
127C2×C42×C103C2311yescharacteristic
128C2×C42×C103C2311yescharacteristic
129C4⋊C8×C103—22no—
130C4⋊C8×C103—22no—
131C4⋊C8×C103—22no—
132#103×C103—22no—
133#103×C103—22no—
134#103×C103—22no—
135#103×C103—22no—
136#103×C103—41no—
137#103×C103D414yes—
138#102×C103—22no—
139#102×C103—41no—
140#97×C103—22no—
141#95×C103—21no—
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—
151C2×Q8×C103—21no—
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×C103—21no—
170C2×Q8×C103—21no—
171C2×Q8×C103—21no—
172C2×Q8×C103C2×D412yes—
173C2×Q8×C103C2×D412yes—
174C2×Q8×C103C2×D412yes—
175C2×D4×C103—21no—
176C2×D4×C103—21no—
177C2×D4×C103—21no—
178C2×D4×C103—21no—
179C2×D4×C103—21no—
180C2×D4×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×C103C2×D411yescharacteristic
189C22×C4×C103C2×D411yescharacteristic
190C22×C4×C103C2×D411yescharacteristic
191C22×C4×C103C2×D411yescharacteristic
192C22×C4×C103C2×D411yescharacteristic
193C22×C4×C103C2×D411yescharacteristic
194C22×C4×C103C2411yescharacteristic
195Q16×C103—44no—
196Q16×C103—44no—
197Q16×C103—44no—
198Q16×C103—44no—
199SD16×C103—44no—
200SD16×C103—44no—
201C2×C8×C103—21no—
202C2×C8×C103—21no—
203C2×C8×C103—21no—
204C2×C8×C103—21no—
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×C103C2×D412yes—
212C2×C8×C103#4112yes—
213C4⋊C4×C103—24no—
214C4⋊C4×C103—24no—
215C4⋊C4×C103—22no—
216C4⋊C4×C103—21no—
217C4⋊C4×C103—21no—
218C4⋊C4×C103—21no—
219C4⋊C4×C103—21no—
220C4⋊C4×C103—21no—
221C4⋊C4×C103—41no—
222C4⋊C4×C103—42no—
223C4⋊C4×C103—42no—
224C4⋊C4×C103—42no—
225C4⋊C4×C103—42no—
226C4⋊C4×C103—42no—
227C4⋊C4×C103C2×D412yes—
228C22⋊C4×C103—42no—
229C22⋊C4×C103—42no—
230C22⋊C4×C103—42no—
231C22⋊C4×C103—42no—
232C22⋊C4×C103—42no—
233C22⋊C4×C103—42no—
234C42×C103—21no—
235C42×C103—21no—
236C42×C103—21no—
237C42×C103—21no—
238C42×C103—42no—
239C42×C103—42no—
240C42×C103—42no—
241C42×C103—42no—
242C42×C103C2×D412yes—
243C42×C103#4112yes—
244C23×C103—41no—
245C23×C103—41no—
246C23×C103—41no—
247C23×C103—41no—
248C23×C103—41no—
249C23×C103—41no—
250C23×C103—41no—
251C23×C103C22×D411yescharacteristic
252Q8×C103—22no—
253Q8×C103—22no—
254Q8×C103—22no—
255Q8×C103—22no—
256Q8×C103—22no—
257Q8×C103—22no—
258Q8×C103—41no—
259Q8×C103—41no—
260Q8×C103—41no—
261Q8×C103—41no—
262Q8×C103—41no—
263Q8×C103—41no—
264Q8×C103—41no—
265Q8×C103—41no—
266Q8×C103—41no—
267Q8×C103—41no—
268D4×C103—41no—
269D4×C103—41no—
270D4×C103—41no—
271D4×C103—41no—
272C2×C4×C103—21no—
273C2×C4×C103—21no—
274C2×C4×C103—21no—
275C2×C4×C103—21no—
276C2×C4×C103—21no—
277C2×C4×C103—21no—
278C2×C4×C103—22no—
279C2×C4×C103—22no—
280C2×C4×C103—21no—
281C2×C4×C103—21no—
282C2×C4×C103—21no—
283C2×C4×C103—22no—
284C2×C4×C103—22no—
285C2×C4×C103—21no—
286C2×C4×C103—21no—
287C2×C4×C103—21no—
288C2×C4×C103—21no—
289C2×C4×C103—21no—
290C2×C4×C103—21no—
291C2×C4×C103—41no—
292C2×C4×C103—41no—
293C2×C4×C103—41no—
294C2×C4×C103—41no—
295C2×C4×C103—41no—
296C2×C4×C103—41no—
297C2×C4×C103—41no—
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#12112yes—
309C2×C4×C103#12112yes—
310C2×C4×C103#13712yes—
311C2×C4×C103C22×D411yescharacteristic
312C2×C4×C103C22×D411yescharacteristic
313C2×C4×C103C2×#4111yescharacteristic
314C2×C4×C103C2×#4111yescharacteristic
315C2×C4×C103H(5,𝔽2)11yescharacteristic
316C2×C4×C103H(5,𝔽2)11yescharacteristic
317C8×C103—22no—
318C8×C103—22no—
319C8×C103—41no—
320C8×C103—41no—
321C22×C103—81no—
322C22×C103—81no—
323C22×C103—81no—
324C22×C103—81no—
325C22×C103—81no—
326C22×C103—81no—
327C22×C103—81no—
328C22×C103C2×#12111yescharacteristic
329C22×C103D4211yescharacteristic
330C22×C103#55011yescharacteristic
331C22×C103C2×#13711yescharacteristic
332C22×C103#57511yescharacteristic
333C22×C103#57811yescharacteristic
334C22×C103#57811yescharacteristic
335C4×C103—22no—
336C4×C103—22no—
337C4×C103—22no—
338C4×C103—42no—
339C4×C103—42no—
340C4×C103—42no—
341C4×C103—41no—
342C4×C103—41no—
343C4×C103—42no—
344C4×C103—41no—
345C4×C103—81no—
346C4×C103—81no—
347C4×C103—81no—
348C4×C103#53211yescharacteristic
349C4×C103#54011yescharacteristic
350C4×C103D4211yescharacteristic
351C4×C103#54611yescharacteristic
352#25379C10311yesmaximal, characteristic, direct product factor, Sylow
353C2×C103—161no—
354C2×C103#242811yescharacteristic
355C2×C103#303711yescharacteristic
356C2×C103#304411yescharacteristic
357C2×C103#326911yescharacteristic
358C2×C103#327011yescharacteristic
359C2×C103#339811yescharacteristic
360C2×C103#340211yescharacteristic
361C2×#497C2×C10311yescharacteristic
362C2×#464C2×C10311yescharacteristic
363C2×#462C2×C10311yescharacteristic, complemented
364C2×#462C2×C10311yescharacteristic, complemented
365#2545C2×C10311yescharacteristic
366#2365C2×C10311yescharacteristic, complemented
367#2056C2×C10311yescharacteristic, complemented
368#2055C2×C10311yescharacteristic
369#2016C2×C10311yescharacteristic, complemented
370#2015C2×C10311yescharacteristic
371#1983C2×C10311yescharacteristic
372#1940C2×C10311yescharacteristic, complemented
373#1880C2×C10311yescharacteristic
374#1878C2×C10311yescharacteristic, complemented
375#1763C2×C10311yescharacteristic, complemented
376C103#2537911yescharacteristic, direct product factor, Sylow
377C22×Q16C22×C10311yescharacteristic
378C22×Q16C22×C10311yescharacteristic
379C22×Q16C22×C10311yescharacteristic
380C22×Q16C22×C10311yescharacteristic
381C22×SD16C22×C10311yescharacteristic
382C22×SD16C22×C10311yescharacteristic
383C2×C4⋊Q8C22×C10311yescharacteristic
384C2×C4⋊Q8C22×C10311yescharacteristic
385C2×#124C22×C10311yescharacteristic
386C2×#124C22×C10311yescharacteristic
387C2×C4×Q8C22×C10311yescharacteristic
388C2×C4×Q8C22×C10311yescharacteristic
389C2×C4×Q8C22×C10311yescharacteristic
390#497—24no—
391#464—24no—
392#462—24no—
393#462—24no—
394C2×C4⋊C8C22×C10311yescharacteristic
395C2×C4⋊C8C22×C10311yescharacteristic
396C2×C4⋊C8C22×C10311yescharacteristic
397C2×#103C22×C10311yescharacteristic
398C2×#103C22×C10311yescharacteristic
399C2×#103C22×C10311yescharacteristic
400C2×#103C22×C10311yescharacteristic
401C2×#103C22×C10311yescharacteristic
402C2×#103C22×C10311yescharacteristic
403C2×#102C22×C10311yescharacteristic
404C2×#102C22×C10311yescharacteristic
405C2×#97C22×C10311yescharacteristic
406#396—21no—
407#396—21no—
408#391C22×C10311yescharacteristic
409#391C22×C10311yescharacteristic
410#391C22×C10311yescharacteristic
411#390C22×C10311yescharacteristic
412#389—21no—
413#388—21no—
414#388—21no—
415#387—21no—
416#387—21no—
417C4×C4⋊C4—21no—
418C4×C4⋊C4C22×C10311yescharacteristic
419C4×C4⋊C4C22×C10311yescharacteristic
420#340C22×C10311yescharacteristic
421#340C22×C10311yescharacteristic
422#336C22×C10311yescharacteristic
423#336C22×C10311yescharacteristic
424C22×Q8C23×C10311yescharacteristic
425C22×Q8C23×C10311yescharacteristic
426C22×Q8C23×C10311yescharacteristic
427C22×Q8C23×C10311yescharacteristic
428C22×D4C23×C10311yescharacteristic
429C2×Q16—22no—
430C2×Q16—22no—
431C2×Q16—22no—
432C2×Q16—22no—
433C2×Q16—22no—
434C2×Q16—22no—
435C2×Q16—22no—
436C2×Q16—22no—
437C2×Q16—41no—
438C2×Q16—41no—
439C2×Q16—41no—
440C2×Q16—41no—
441C2×SD16—22no—
442C2×SD16—22no—
443C2×SD16—22no—
444C2×SD16—22no—
445C2×SD16—41no—
446C2×SD16—41no—
447C22×C8C23×C10311yescharacteristic
448C22×C8C23×C10311yescharacteristic
449C22×C8C23×C10311yescharacteristic
450C22×C8C23×C10311yescharacteristic
451C4⋊Q8—22no—
452C4⋊Q8—22no—
453C4⋊Q8—41no—
454C4⋊Q8D4×C10314yes—
455#124—22no—
456#124—22no—
457#124—22no—
458#124—41no—
459C4×Q8—22no—
460C4×Q8—22no—
461C4×Q8—22no—
462C4×Q8—22no—
463C4×Q8—41no—
464C4×Q8—41no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—21no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—21no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4D4×C10311yescharacteristic
473C2×C4⋊C4D4×C10311yescharacteristic
474C2×C4⋊C4C23×C10311yescharacteristic
475C2×C4⋊C4C23×C10311yescharacteristic
476C2×C4⋊C4C23×C10311yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C42—21no—
484C2×C42—21no—
485C2×C42—21no—
486C2×C42—21no—
487C2×C42C23×C10311yescharacteristic
488C2×C42C23×C10311yescharacteristic
489C2×C42C23×C10311yescharacteristic
490C4⋊C8—22no—
491C4⋊C8—22no—
492C4⋊C8—22no—
493#103—22no—
494#103—22no—
495#103—22no—
496#103—22no—
497#103—41no—
498#103D4×C10314yes—
499#102—22no—
500#102—41no—
501#97—22no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509#95D4×C10311yescharacteristic
510#95D4×C10311yescharacteristic
511C24—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×Q8—21no—
527C2×Q8—21no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8C2×D4×C10312yes—
534C2×Q8C2×D4×C10312yes—
535C2×Q8C2×D4×C10312yes—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4C2×D4×C10311yescharacteristic
550C22×C4C2×D4×C10311yescharacteristic
551C22×C4C2×D4×C10311yescharacteristic
552C22×C4C2×D4×C10311yescharacteristic
553C22×C4C2×D4×C10311yescharacteristic
554C22×C4C2×D4×C10311yescharacteristic
555C22×C4C24×C10311yescharacteristic
556Q16—44no—
557Q16—44no—
558Q16—44no—
559Q16—44no—
560SD16—44no—
561SD16—44no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—21no—
571C2×C8—21no—
572C2×C8C2×D4×C10312yes—
573C2×C8#41×C10312yes—
574C4⋊C4—24no—
575C4⋊C4—24no—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—41no—
583C4⋊C4—42no—
584C4⋊C4—42no—
585C4⋊C4—42no—
586C4⋊C4—42no—
587C4⋊C4—42no—
588C4⋊C4C2×D4×C10312yes—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—42no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—42no—
600C42—42no—
601C42—42no—
602C42—42no—
603C42C2×D4×C10312yes—
604C42#41×C10312yes—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23C22×D4×C10311yescharacteristic
613Q8—22no—
614Q8—22no—
615Q8—22no—
616Q8—22no—
617Q8—22no—
618Q8—22no—
619Q8—41no—
620Q8—41no—
621Q8—41no—
622Q8—41no—
623Q8—41no—
624Q8—41no—
625Q8—41no—
626Q8—41no—
627Q8—41no—
628Q8—41no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—41no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4#121×C10312yes—
670C2×C4#121×C10312yes—
671C2×C4#137×C10312yes—
672C2×C4C22×D4×C10311yescharacteristic
673C2×C4C22×D4×C10311yescharacteristic
674C2×C4C2×#41×C10311yescharacteristic
675C2×C4C2×#41×C10311yescharacteristic
676C2×C4H(5,𝔽2)×C10311yescharacteristic
677C2×C4H(5,𝔽2)×C10311yescharacteristic
678C8—22no—
679C8—22no—
680C8—41no—
681C8—41no—
682C22—81no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22C2×#121×C10311yescharacteristic
690C22D42×C10311yescharacteristic
691C22#550×C10311yescharacteristic
692C22C2×#137×C10311yescharacteristic
693C22#575×C10311yescharacteristic
694C22#578×C10311yescharacteristic
695C22#578×C10311yescharacteristic
696C4—22no—
697C4—22no—
698C4—22no—
699C4—41no—
700C4—41no—
701C4—42no—
702C4—41no—
703C4—42no—
704C4—42no—
705C4—42no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4#532×C10311yescharacteristic
710C4#540×C10311yescharacteristic
711C4D42×C10311yescharacteristic
712C4#546×C10311yescharacteristic
713C2—161no—
714C2C103×#242811yescharacteristic
715C2C103×#303711yescharacteristic
716C2C103×#304411yescharacteristic
717C2C103×#326911yescharacteristic
718C2C103×#327011yescharacteristic
719C2C103×#339811yescharacteristic
720C2C103×#340211yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutator, Frattini, cosocleC22×C4C24×C103
prime radicalC22×D4×C103C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C4×C4⋊C4×C103 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#462×C103C2semidirect
4. C2×#462×C103C2semidirect
6. C103×#2365C2semidirect
7. C103×#2056C2semidirect
9. C103×#2016C2semidirect
12. C103×#1940C2semidirect
14. C103×#1878C2semidirect
15. C103×#1763C2semidirect
352. #25379C103direct (N × H)
363. C2×#462C2×C103semidirect
364. C2×#462C2×C103semidirect
366. #2365C2×C103semidirect
367. #2056C2×C103semidirect
369. #2016C2×C103semidirect
372. #1940C2×C103semidirect
374. #1878C2×C103semidirect
375. #1763C2×C103semidirect
376. C103#25379direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#497×C1032
C2×#464×C1032
C2×#462×C1032
C103×#25452
C103×#23652
C103×#20562
C103×#20552
C103×#20162
C103×#20152
C103×#19832
C103×#19402
C103×#18802
C103×#18782
C103×#17632
#25379103