Finite Group Databasebeta

← C103×#21772 #39927047

Subgroups — C103×#21772 #39927047

Order 26368.

1390 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#537×C103C211yesmaximal, characteristic
2C2×#408×C103C211yesmaximal, characteristic, complemented
3C103×#2311C211yesmaximal, characteristic, complemented
4C103×#1895C211yesmaximal, characteristic, complemented
5C103×#1894C211yesmaximal, characteristic, complemented
6C103×#1893C211yesmaximal, characteristic, complemented
7C103×#1892C211yesmaximal, characteristic, complemented
8C103×#1875C211yesmaximal, characteristic, complemented
9C103×#1874C211yesmaximal, characteristic, complemented
10C103×#1873C211yesmaximal, characteristic, complemented
11C103×#1872C211yesmaximal, characteristic, complemented
12C103×#1824C211yesmaximal, characteristic, complemented
13C103×#1823C211yesmaximal, characteristic, complemented
14C103×#1788C211yesmaximal, characteristic, complemented
15C103×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C103C2211yescharacteristic
17C22×#41×C103C2211yescharacteristic
18C22×M16×C103C2211yescharacteristic
19C23×C8×C103C2211yescharacteristic
20#537×C103—24no—
21#537×C103C418yescomplemented
22C2×C22⋊Q8×C103—21no—
23C2×C22⋊Q8×C103C2211yescharacteristic
24C2×C22⋊Q8×C103C2211yescharacteristic
25C2×#121×C103—21no—
26C2×#121×C103—21no—
27C2×#121×C103—21no—
28C2×#121×C103C2211yescharacteristic
29C2×#121×C103C2211yescharacteristic
30C2×#117×C103C2211yescharacteristic
31C22×C4⋊C4×C103C2211yescharacteristic
32C22×C4⋊C4×C103C2211yescharacteristic
33C2×#103×C103C2211yescharacteristic
34C2×#103×C103C2211yescharacteristic
35C2×#103×C103C2211yescharacteristic
36C2×#103×C103C2211yescharacteristic
37C2×#102×C103C2211yescharacteristic
38C2×#102×C103C2211yescharacteristic
39C2×#102×C103C2211yescharacteristic
40C2×#102×C103C2211yescharacteristic
41#408×C103—24no—
42C2×C22⋊C8×C103C2211yescharacteristic
43C2×C22⋊C8×C103C2211yescharacteristic
44C2×C22⋊C8×C103C2211yescharacteristic
45C2×C22⋊C8×C103C2211yescharacteristic
46#391×C103—21no—
47#390×C103—21no—
48#386×C103—21no—
49#386×C103—21no—
50#380×C103C2211yescharacteristic
51#380×C103C2211yescharacteristic
52#380×C103C2211yescharacteristic
53#380×C103C2211yescharacteristic
54#340×C103C2211yescharacteristic
55#340×C103C2211yescharacteristic
56#340×C103C2211yescharacteristic
57#340×C103C2211yescharacteristic
58#340×C103C2211yescharacteristic
59#340×C103C2211yescharacteristic
60#340×C103C2211yescharacteristic
61#340×C103C2211yescharacteristic
62C2×#41×C103—22no—
63C2×#41×C103—41no—
64C2×#41×C103—41no—
65C2×#41×C103—41no—
66C2×#41×C103—41no—
67C2×#41×C103—41no—
68C2×#41×C103—41no—
69C2×#41×C103—41no—
70C2×#41×C103—41no—
71C2×#41×C103C2×C414yes—
72C2×#41×C103C2×C414yescomplemented
73C2×#41×C103D414yes—
74C22×Q8×C103D411yescharacteristic
75C22×Q8×C103C2311yescharacteristic
76C22×D4×C103—21no—
77C22×D4×C103—21no—
78C22×D4×C103—21no—
79C22×D4×C103D411yescharacteristic
80C22×D4×C103D411yescharacteristic
81C22×D4×C103D411yescharacteristic
82C22×D4×C103C2311yescharacteristic
83C23×C4×C103—21no—
84C23×C4×C103—21no—
85C23×C4×C103—21no—
86C23×C4×C103C2311yescharacteristic
87C23×C4×C103C2311yescharacteristic
88C23×C4×C103C2311yescharacteristic
89C2×M16×C103—22no—
90C2×M16×C103—41no—
91C2×M16×C103—41no—
92C22×C8×C103—22no—
93C22×C8×C103—41no—
94C22×C8×C103—41no—
95C22×C8×C103C2311yescharacteristic
96C22×C8×C103C2311yescharacteristic
97C22×C8×C103C2311yescharacteristic
98C22×C8×C103C2311yescharacteristic
99C22⋊Q8×C103—28no—
100C22⋊Q8×C103—22no—
101C22⋊Q8×C103—22no—
102C22⋊Q8×C103C2×C414yes—
103C22⋊Q8×C103C2×C414yescomplemented
104#121×C103—28no—
105#121×C103—28no—
106#121×C103—28no—
107#121×C103—22no—
108#121×C103—22no—
109#121×C103C2×C414yes—
110#121×C103C2×C414yescomplemented
111#117×C103—41no—
112#117×C103—41no—
113C2×C4⋊C4×C103—21no—
114C2×C4⋊C4×C103—22no—
115C2×C4⋊C4×C103—21no—
116C2×C4⋊C4×C103—21no—
117C2×C4⋊C4×C103—21no—
118C2×C4⋊C4×C103—41no—
119C2×C4⋊C4×C103—41no—
120C2×C4⋊C4×C103C2×C414yescomplemented
121C2×C4⋊C4×C103C2311yescharacteristic
122C2×C4⋊C4×C103C2311yescharacteristic
123C2×C4⋊C4×C103C2311yescharacteristic
124C2×C4⋊C4×C103C2311yescharacteristic
125C2×C4⋊C4×C103C2311yescharacteristic
126C2×C4⋊C4×C103C2311yescharacteristic
127C2×C22⋊C4×C103—21no—
128C2×C22⋊C4×C103—21no—
129C2×C22⋊C4×C103—21no—
130C2×C22⋊C4×C103—21no—
131C2×C22⋊C4×C103—21no—
132C2×C22⋊C4×C103—21no—
133C2×C22⋊C4×C103—21no—
134C2×C22⋊C4×C103—21no—
135C2×C22⋊C4×C103—21no—
136C2×C42×C103—21no—
137#103×C103—41no—
138#103×C103—41no—
139#103×C103—41no—
140#103×C103—41no—
141#102×C103—41no—
142#102×C103—41no—
143#102×C103—41no—
144#102×C103—41no—
145C22⋊C8×C103—22no—
146C22⋊C8×C103—22no—
147C22⋊C8×C103—22no—
148C22⋊C8×C103—22no—
149#95×C103—21no—
150#95×C103—21no—
151#95×C103—21no—
152#95×C103—21no—
153C24×C103—21no—
154C24×C103C2×D411yescharacteristic
155C24×C103C2×D411yescharacteristic
156C24×C103C2×D411yescharacteristic
157#41×C103—44no—
158#41×C103—44no—
159#41×C103—44no—
160#41×C103—44no—
161#41×C103—44no—
162#41×C103—44no—
163#41×C103—44no—
164#41×C103—44no—
165C2×Q8×C103—21no—
166C2×Q8×C103—21no—
167C2×Q8×C103—21no—
168C2×Q8×C103—21no—
169C2×Q8×C103—21no—
170C2×Q8×C103—41no—
171C2×Q8×C103—41no—
172C2×Q8×C103C22⋊C414yes—
173C2×Q8×C103C22×C412yes—
174C2×D4×C103—24no—
175C2×D4×C103—24no—
176C2×D4×C103—24no—
177C2×D4×C103—21no—
178C2×D4×C103—21no—
179C2×D4×C103—21no—
180C2×D4×C103—21no—
181C2×D4×C103—21no—
182C2×D4×C103—41no—
183C2×D4×C103—41no—
184C2×D4×C103—41no—
185C2×D4×C103—41no—
186C2×D4×C103—41no—
187C2×D4×C103—41no—
188C2×D4×C103—42no—
189C2×D4×C103—42no—
190C2×D4×C103—81no—
191C2×D4×C103—81no—
192C2×D4×C103—81no—
193C2×D4×C103—81no—
194C2×D4×C103C22⋊C414yes—
195C2×D4×C103C22⋊C414yes—
196C2×D4×C103C22⋊C414yes—
197C2×D4×C103C22×C412yes—
198C22×C4×C103—21no—
199C22×C4×C103—21no—
200C22×C4×C103—21no—
201C22×C4×C103—21no—
202C22×C4×C103—21no—
203C22×C4×C103—21no—
204C22×C4×C103—21no—
205C22×C4×C103—21no—
206C22×C4×C103—21no—
207C22×C4×C103—21no—
208C22×C4×C103—21no—
209C22×C4×C103—21no—
210C22×C4×C103—21no—
211C22×C4×C103—21no—
212C22×C4×C103—21no—
213C22×C4×C103—24no—
214C22×C4×C103—24no—
215C22×C4×C103—21no—
216C22×C4×C103—21no—
217C22×C4×C103—21no—
218C22×C4×C103—21no—
219C22×C4×C103—42no—
220C22×C4×C103—42no—
221C22×C4×C103—42no—
222C22×C4×C103—81no—
223C22×C4×C103—81no—
224C22×C4×C103—81no—
225C22×C4×C103—81no—
226C22×C4×C103C22×C412yes—
227C22×C4×C103C22×C412yes—
228C22×C4×C103C22×C412yes—
229C22×C4×C103C2×D411yescharacteristic
230C22×C4×C103C2×D411yescharacteristic
231C22×C4×C103C2×D411yescharacteristic
232C22×C4×C103C2×D412yes—
233C22×C4×C103C2×D412yes—
234C22×C4×C103C2×D412yes—
235C22×C4×C103C2411yescharacteristic
236M16×C103—44no—
237C2×C8×C103—21no—
238C2×C8×C103—21no—
239C2×C8×C103—21no—
240C2×C8×C103—21no—
241C2×C8×C103—21no—
242C2×C8×C103—21no—
243C2×C8×C103—21no—
244C2×C8×C103—21no—
245C2×C8×C103—21no—
246C2×C8×C103—21no—
247C2×C8×C103—21no—
248C2×C8×C103—21no—
249C2×C8×C103—44no—
250C4⋊C4×C103—24no—
251C4⋊C4×C103—24no—
252C4⋊C4×C103—24no—
253C4⋊C4×C103—21no—
254C4⋊C4×C103—21no—
255C4⋊C4×C103—21no—
256C4⋊C4×C103—21no—
257C4⋊C4×C103—21no—
258C4⋊C4×C103—21no—
259C4⋊C4×C103—21no—
260C4⋊C4×C103—21no—
261C4⋊C4×C103—21no—
262C4⋊C4×C103—21no—
263C4⋊C4×C103—42no—
264C4⋊C4×C103C22×C412yes—
265C4⋊C4×C103C22×C412yes—
266C22⋊C4×C103—24no—
267C22⋊C4×C103—24no—
268C22⋊C4×C103—24no—
269C22⋊C4×C103—24no—
270C22⋊C4×C103—42no—
271C22⋊C4×C103—81no—
272C22⋊C4×C103—81no—
273C22⋊C4×C103—81no—
274C22⋊C4×C103—81no—
275C42×C103—42no—
276C23×C103—21no—
277C23×C103—21no—
278C23×C103—21no—
279C23×C103—21no—
280C23×C103—21no—
281C23×C103—21no—
282C23×C103—21no—
283C23×C103—21no—
284C23×C103—21no—
285C23×C103—21no—
286C23×C103—21no—
287C23×C103—21no—
288C23×C103—21no—
289C23×C103—21no—
290C23×C103—21no—
291C23×C103—21no—
292C23×C103—21no—
293C23×C103—21no—
294C23×C103—22no—
295C23×C103—41no—
296C23×C103—41no—
297C23×C103—41no—
298C23×C103—41no—
299C23×C103—41no—
300C23×C103—41no—
301C23×C103C2×C22⋊C412yes—
302C23×C103C2×C22⋊C412yes—
303C23×C103C2×C22⋊C412yes—
304C23×C103C22×D411yescharacteristic
305Q8×C103—22no—
306Q8×C103—22no—
307Q8×C103—44no—
308Q8×C103—41no—
309Q8×C103—41no—
310D4×C103—22no—
311D4×C103—22no—
312D4×C103—44no—
313D4×C103—44no—
314D4×C103—44no—
315D4×C103—48no—
316D4×C103—41no—
317D4×C103—41no—
318D4×C103—84no—
319D4×C103—84no—
320C2×C4×C103—21no—
321C2×C4×C103—21no—
322C2×C4×C103—21no—
323C2×C4×C103—21no—
324C2×C4×C103—21no—
325C2×C4×C103—21no—
326C2×C4×C103—22no—
327C2×C4×C103—22no—
328C2×C4×C103—22no—
329C2×C4×C103—22no—
330C2×C4×C103—22no—
331C2×C4×C103—22no—
332C2×C4×C103—22no—
333C2×C4×C103—22no—
334C2×C4×C103—22no—
335C2×C4×C103—22no—
336C2×C4×C103—22no—
337C2×C4×C103—22no—
338C2×C4×C103—22no—
339C2×C4×C103—22no—
340C2×C4×C103—22no—
341C2×C4×C103—48no—
342C2×C4×C103—41no—
343C2×C4×C103—41no—
344C2×C4×C103—41no—
345C2×C4×C103—41no—
346C2×C4×C103—41no—
347C2×C4×C103—41no—
348C2×C4×C103—41no—
349C2×C4×C103—41no—
350C2×C4×C103—41no—
351C2×C4×C103—41no—
352C2×C4×C103—41no—
353C2×C4×C103—41no—
354C2×C4×C103—41no—
355C2×C4×C103—41no—
356C2×C4×C103—41no—
357C2×C4×C103—41no—
358C2×C4×C103—41no—
359C2×C4×C103—41no—
360C2×C4×C103—84no—
361C2×C4×C103—84no—
362C2×C4×C103C2×C22⋊C412yes—
363C2×C4×C103C2×C22⋊C412yes—
364C2×C4×C103C2×C22⋊C412yes—
365C2×C4×C103C23×C411yescharacteristic
366C2×C4×C103C22×D411yescharacteristic
367C2×C4×C103H(5,𝔽2)11yescharacteristic
368C2×C4×C103H(5,𝔽2)11yescharacteristic
369C2×C4×C103H(5,𝔽2)11yescharacteristic
370C2×C4×C103H(5,𝔽2)11yescharacteristic
371C8×C103—41no—
372C8×C103—41no—
373C8×C103—41no—
374C8×C103—41no—
375C22×C103—22no—
376C22×C103—22no—
377C22×C103—22no—
378C22×C103—22no—
379C22×C103—22no—
380C22×C103—22no—
381C22×C103—22no—
382C22×C103—22no—
383C22×C103—22no—
384C22×C103—41no—
385C22×C103—41no—
386C22×C103—41no—
387C22×C103—41no—
388C22×C103—41no—
389C22×C103—41no—
390C22×C103—41no—
391C22×C103—41no—
392C22×C103—41no—
393C22×C103—41no—
394C22×C103—41no—
395C22×C103—41no—
396C22×C103—42no—
397C22×C103—42no—
398C22×C103—42no—
399C22×C103—81no—
400C22×C103—81no—
401C22×C103—81no—
402C22×C103—81no—
403C22×C103C22×C22⋊C411yescharacteristic
404C22×C103#53411yescharacteristic
405C22×C103#53411yescharacteristic
406C22×C103#57611yescharacteristic
407C22×C103#57711yescharacteristic
408C22×C103#57711yescharacteristic
409C22×C103#57811yescharacteristic
410C4×C103—22no—
411C4×C103—22no—
412C4×C103—22no—
413C4×C103—42no—
414C4×C103—42no—
415C4×C103—42no—
416C4×C103—81no—
417C4×C103—81no—
418C4×C103—81no—
419C4×C103—81no—
420C4×C103#51811yescharacteristic
421C4×C103#51811yescharacteristic
422C4×C103#53411yescharacteristic
423C4×C103#53411yescharacteristic
424#21772C10311yesmaximal, characteristic, direct product factor, Sylow
425C2×C103—42no—
426C2×C103—42no—
427C2×C103—42no—
428C2×C103—82no—
429C2×C103#230811yescharacteristic
430C2×C103#289711yescharacteristic
431C2×C103#289811yescharacteristic
432C2×C103#319811yescharacteristic
433C2×C103#320111yescharacteristic
434C2×C103#320311yescharacteristic
435C2×C103#320411yescharacteristic
436C2×#537C2×C10311yescharacteristic
437C2×#408C2×C10311yescharacteristic, complemented
438#2311C2×C10311yescharacteristic, complemented
439#1895C2×C10311yescharacteristic, complemented
440#1894C2×C10311yescharacteristic, complemented
441#1893C2×C10311yescharacteristic, complemented
442#1892C2×C10311yescharacteristic, complemented
443#1875C2×C10311yescharacteristic, complemented
444#1874C2×C10311yescharacteristic, complemented
445#1873C2×C10311yescharacteristic, complemented
446#1872C2×C10311yescharacteristic, complemented
447#1824C2×C10311yescharacteristic, complemented
448#1823C2×C10311yescharacteristic, complemented
449#1788C2×C10311yescharacteristic, complemented
450#1788C2×C10311yescharacteristic, complemented
451C103#2177211yescharacteristic, direct product factor, Sylow
452C22×#41C22×C10311yescharacteristic
453C22×#41C22×C10311yescharacteristic
454C22×M16C22×C10311yescharacteristic
455C23×C8C22×C10311yescharacteristic
456#537—24no—
457#537C4×C10318yescomplemented
458C2×C22⋊Q8—21no—
459C2×C22⋊Q8C22×C10311yescharacteristic
460C2×C22⋊Q8C22×C10311yescharacteristic
461C2×#121—21no—
462C2×#121—21no—
463C2×#121—21no—
464C2×#121C22×C10311yescharacteristic
465C2×#121C22×C10311yescharacteristic
466C2×#117C22×C10311yescharacteristic
467C22×C4⋊C4C22×C10311yescharacteristic
468C22×C4⋊C4C22×C10311yescharacteristic
469C2×#103C22×C10311yescharacteristic
470C2×#103C22×C10311yescharacteristic
471C2×#103C22×C10311yescharacteristic
472C2×#103C22×C10311yescharacteristic
473C2×#102C22×C10311yescharacteristic
474C2×#102C22×C10311yescharacteristic
475C2×#102C22×C10311yescharacteristic
476C2×#102C22×C10311yescharacteristic
477#408—24no—
478C2×C22⋊C8C22×C10311yescharacteristic
479C2×C22⋊C8C22×C10311yescharacteristic
480C2×C22⋊C8C22×C10311yescharacteristic
481C2×C22⋊C8C22×C10311yescharacteristic
482#391—21no—
483#390—21no—
484#386—21no—
485#386—21no—
486#380C22×C10311yescharacteristic
487#380C22×C10311yescharacteristic
488#380C22×C10311yescharacteristic
489#380C22×C10311yescharacteristic
490#340C22×C10311yescharacteristic
491#340C22×C10311yescharacteristic
492#340C22×C10311yescharacteristic
493#340C22×C10311yescharacteristic
494#340C22×C10311yescharacteristic
495#340C22×C10311yescharacteristic
496#340C22×C10311yescharacteristic
497#340C22×C10311yescharacteristic
498C2×#41—22no—
499C2×#41—41no—
500C2×#41—41no—
501C2×#41—41no—
502C2×#41—41no—
503C2×#41—41no—
504C2×#41—41no—
505C2×#41—41no—
506C2×#41—41no—
507C2×#41C2×C4×C10314yes—
508C2×#41C2×C4×C10314yescomplemented
509C2×#41D4×C10314yes—
510C22×Q8D4×C10311yescharacteristic
511C22×Q8C23×C10311yescharacteristic
512C22×D4—21no—
513C22×D4—21no—
514C22×D4—21no—
515C22×D4D4×C10311yescharacteristic
516C22×D4D4×C10311yescharacteristic
517C22×D4D4×C10311yescharacteristic
518C22×D4C23×C10311yescharacteristic
519C23×C4—21no—
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C10311yescharacteristic
523C23×C4C23×C10311yescharacteristic
524C23×C4C23×C10311yescharacteristic
525C2×M16—22no—
526C2×M16—41no—
527C2×M16—41no—
528C22×C8—22no—
529C22×C8—41no—
530C22×C8—41no—
531C22×C8C23×C10311yescharacteristic
532C22×C8C23×C10311yescharacteristic
533C22×C8C23×C10311yescharacteristic
534C22×C8C23×C10311yescharacteristic
535C22⋊Q8—28no—
536C22⋊Q8—22no—
537C22⋊Q8—22no—
538C22⋊Q8C2×C4×C10314yes—
539C22⋊Q8C2×C4×C10314yescomplemented
540#121—28no—
541#121—28no—
542#121—28no—
543#121—22no—
544#121—22no—
545#121C2×C4×C10314yes—
546#121C2×C4×C10314yescomplemented
547#117—41no—
548#117—41no—
549C2×C4⋊C4—21no—
550C2×C4⋊C4—22no—
551C2×C4⋊C4—21no—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—21no—
554C2×C4⋊C4—41no—
555C2×C4⋊C4—41no—
556C2×C4⋊C4C2×C4×C10314yescomplemented
557C2×C4⋊C4C23×C10311yescharacteristic
558C2×C4⋊C4C23×C10311yescharacteristic
559C2×C4⋊C4C23×C10311yescharacteristic
560C2×C4⋊C4C23×C10311yescharacteristic
561C2×C4⋊C4C23×C10311yescharacteristic
562C2×C4⋊C4C23×C10311yescharacteristic
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4—21no—
566C2×C22⋊C4—21no—
567C2×C22⋊C4—21no—
568C2×C22⋊C4—21no—
569C2×C22⋊C4—21no—
570C2×C22⋊C4—21no—
571C2×C22⋊C4—21no—
572C2×C42—21no—
573#103—41no—
574#103—41no—
575#103—41no—
576#103—41no—
577#102—41no—
578#102—41no—
579#102—41no—
580#102—41no—
581C22⋊C8—22no—
582C22⋊C8—22no—
583C22⋊C8—22no—
584C22⋊C8—22no—
585#95—21no—
586#95—21no—
587#95—21no—
588#95—21no—
589C24—21no—
590C24C2×D4×C10311yescharacteristic
591C24C2×D4×C10311yescharacteristic
592C24C2×D4×C10311yescharacteristic
593#41—44no—
594#41—44no—
595#41—44no—
596#41—44no—
597#41—44no—
598#41—44no—
599#41—44no—
600#41—44no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—41no—
607C2×Q8—41no—
608C2×Q8C22⋊C4×C10314yes—
609C2×Q8C22×C4×C10312yes—
610C2×D4—24no—
611C2×D4—24no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—41no—
619C2×D4—41no—
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—42no—
625C2×D4—42no—
626C2×D4—81no—
627C2×D4—81no—
628C2×D4—81no—
629C2×D4—81no—
630C2×D4C22⋊C4×C10314yes—
631C2×D4C22⋊C4×C10314yes—
632C2×D4C22⋊C4×C10314yes—
633C2×D4C22×C4×C10312yes—
634C22×C4—21no—
635C22×C4—21no—
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—24no—
650C22×C4—24no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—42no—
656C22×C4—42no—
657C22×C4—42no—
658C22×C4—81no—
659C22×C4—81no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C22×C4×C10312yes—
663C22×C4C22×C4×C10312yes—
664C22×C4C22×C4×C10312yes—
665C22×C4C2×D4×C10311yescharacteristic
666C22×C4C2×D4×C10311yescharacteristic
667C22×C4C2×D4×C10311yescharacteristic
668C22×C4C2×D4×C10312yes—
669C22×C4C2×D4×C10312yes—
670C22×C4C2×D4×C10312yes—
671C22×C4C24×C10311yescharacteristic
672M16—44no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—21no—
681C2×C8—21no—
682C2×C8—21no—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—44no—
686C4⋊C4—24no—
687C4⋊C4—24no—
688C4⋊C4—24no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—42no—
700C4⋊C4C22×C4×C10312yes—
701C4⋊C4C22×C4×C10312yes—
702C22⋊C4—24no—
703C22⋊C4—24no—
704C22⋊C4—24no—
705C22⋊C4—24no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—81no—
709C22⋊C4—81no—
710C22⋊C4—81no—
711C42—42no—
712C23—21no—
713C23—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—21no—
730C23—22no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23C2×C22⋊C4×C10312yes—
738C23C2×C22⋊C4×C10312yes—
739C23C2×C22⋊C4×C10312yes—
740C23C22×D4×C10311yescharacteristic
741Q8—22no—
742Q8—22no—
743Q8—44no—
744Q8—41no—
745Q8—41no—
746D4—22no—
747D4—22no—
748D4—44no—
749D4—44no—
750D4—44no—
751D4—48no—
752D4—41no—
753D4—41no—
754D4—84no—
755D4—84no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—22no—
763C2×C4—22no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—22no—
777C2×C4—48no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—84no—
797C2×C4—84no—
798C2×C4C2×C22⋊C4×C10312yes—
799C2×C4C2×C22⋊C4×C10312yes—
800C2×C4C2×C22⋊C4×C10312yes—
801C2×C4C23×C4×C10311yescharacteristic
802C2×C4C22×D4×C10311yescharacteristic
803C2×C4H(5,𝔽2)×C10311yescharacteristic
804C2×C4H(5,𝔽2)×C10311yescharacteristic
805C2×C4H(5,𝔽2)×C10311yescharacteristic
806C2×C4H(5,𝔽2)×C10311yescharacteristic
807C8—41no—
808C8—41no—
809C8—41no—
810C8—41no—
811C22—22no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—22no—
817C22—22no—
818C22—22no—
819C22—22no—
820C22—41no—
821C22—41no—
822C22—41no—
823C22—41no—
824C22—41no—
825C22—41no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—42no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22C22×C22⋊C4×C10311yescharacteristic
840C22#534×C10311yescharacteristic
841C22#534×C10311yescharacteristic
842C22#576×C10311yescharacteristic
843C22#577×C10311yescharacteristic
844C22#577×C10311yescharacteristic
845C22#578×C10311yescharacteristic
846C4—22no—
847C4—22no—
848C4—22no—
849C4—42no—
850C4—42no—
851C4—42no—
852C4—81no—
853C4—81no—
854C4—81no—
855C4—81no—
856C4#518×C10311yescharacteristic
857C4#518×C10311yescharacteristic
858C4#534×C10311yescharacteristic
859C4#534×C10311yescharacteristic
860C2—42no—
861C2—42no—
862C2—42no—
863C2—82no—
864C2C103×#230811yescharacteristic
865C2C103×#289711yescharacteristic
866C2C103×#289811yescharacteristic
867C2C103×#319811yescharacteristic
868C2C103×#320111yescharacteristic
869C2C103×#320311yescharacteristic
870C2C103×#320411yescharacteristic
subgroupG/H
center, socleC23×C103C22×D4
commutatorC2×C4C23×C4×C103
Frattini, cosocleC22×C4C24×C103
prime radicalC2×#537×C103C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C103 ◁ C22×#41×C103 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#408×C103C2semidirect
3. C103×#2311C2semidirect
4. C103×#1895C2semidirect
5. C103×#1894C2semidirect
6. C103×#1893C2semidirect
7. C103×#1892C2semidirect
8. C103×#1875C2semidirect
9. C103×#1874C2semidirect
10. C103×#1873C2semidirect
11. C103×#1872C2semidirect
12. C103×#1824C2semidirect
13. C103×#1823C2semidirect
14. C103×#1788C2semidirect
15. C103×#1788C2semidirect
21. #537×C103C4semidirect
72. C2×#41×C103C2×C4semidirect
103. C22⋊Q8×C103C2×C4semidirect
110. #121×C103C2×C4semidirect
120. C2×C4⋊C4×C103C2×C4semidirect
424. #21772C103direct (N × H)
437. C2×#408C2×C103semidirect
438. #2311C2×C103semidirect
439. #1895C2×C103semidirect
440. #1894C2×C103semidirect
441. #1893C2×C103semidirect
442. #1892C2×C103semidirect
443. #1875C2×C103semidirect
444. #1874C2×C103semidirect
445. #1873C2×C103semidirect
446. #1872C2×C103semidirect
447. #1824C2×C103semidirect
448. #1823C2×C103semidirect
449. #1788C2×C103semidirect
450. #1788C2×C103semidirect
451. C103#21772direct (N × H)
457. #537C4×C103semidirect
508. C2×#41C2×C4×C103semidirect
539. C22⋊Q8C2×C4×C103semidirect
546. #121C2×C4×C103semidirect
556. C2×C4⋊C4C2×C4×C103semidirect

Maximal subgroups

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

subgroupindex
C2×#537×C1032
C2×#408×C1032
C103×#23112
C103×#18952
C103×#18942
C103×#18932
C103×#18922
C103×#18752
C103×#18742
C103×#18732
C103×#18722
C103×#18242
C103×#18232
C103×#17882
#21772103