Finite Group Databasebeta

← C109×#24050 #42142044

Subgroups — C109×#24050 #42142044

Order 27904.

1450 conjugacy classes of subgroups.

The subgroup lattice has 874 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C109C211yesmaximal, characteristic
2C2×#485×C109C211yesmaximal, characteristic, complemented
3C2×#418×C109C211yesmaximal, characteristic, complemented
4C109×#2485C211yesmaximal, characteristic, complemented
5C109×#2042C211yesmaximal, characteristic, complemented
6C109×#2042C211yesmaximal, characteristic, complemented
7C109×#2034C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#1894C211yesmaximal, characteristic, complemented
10C109×#1870C211yesmaximal, characteristic, complemented
11C109×#1864C211yesmaximal, characteristic, complemented
12C109×#1862C211yesmaximal, characteristic, complemented
13C109×#1788C211yesmaximal, characteristic, complemented
14C109×#1788C211yesmaximal, characteristic, complemented
15C109×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C23×D4×C109C2211yescharacteristic
18C22×M16×C109C2211yescharacteristic
19#546×C109—24no—
20#546×C109—24no—
21C2×#124×C109C2211yescharacteristic
22C2×#123×C109—21no—
23C2×C22⋊Q8×C109C2211yescharacteristic
24C2×#121×C109—21no—
25C2×#121×C109C2211yescharacteristic
26C2×#120×C109—21no—
27C2×C4×D4×C109C2211yescharacteristic
28C2×C4×D4×C109C2211yescharacteristic
29C2×#117×C109C2211yescharacteristic
30C22×C22⋊C4×C109—21no—
31#485×C109—24no—
32C2×#107×C109C2211yescharacteristic, complemented
33C2×#106×C109C2211yescharacteristic, complemented
34#418×C109—24no—
35C2×#103×C109C2211yescharacteristic, complemented
36C2×#103×C109C2211yescharacteristic, complemented
37C2×#103×C109C2211yescharacteristic, complemented
38C2×#103×C109C2211yescharacteristic, complemented
39C2×#102×C109C2211yescharacteristic
40C2×#102×C109C2211yescharacteristic
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
45C2×#102×C109C2211yescharacteristic
46C2×#102×C109C2211yescharacteristic
47C2×C22⋊C8×C109C2211yescharacteristic
48C2×C22⋊C8×C109C2211yescharacteristic, complemented
49C2×C22⋊C8×C109C2211yescharacteristic, complemented
50#397×C109—21no—
51#394×C109—21no—
52#389×C109C2211yescharacteristic, complemented
53#389×C109C2211yescharacteristic, complemented
54#388×C109—21no—
55#387×C109—21no—
56#380×C109C2211yescharacteristic
57#380×C109C2211yescharacteristic, complemented
58#380×C109C2211yescharacteristic, complemented
59#340×C109C2211yescharacteristic, complemented
60#340×C109C2211yescharacteristic, complemented
61#336×C109C2211yescharacteristic, complemented
62#336×C109C2211yescharacteristic, complemented
63C25×C109—21no—
64C2×#41×C109—22no—
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—41no—
69C2×#41×C109—41no—
70C22×Q8×C109C2311yescharacteristic
71C22×D4×C109—22no—
72C22×D4×C109—22no—
73C22×D4×C109—21no—
74C22×D4×C109—21no—
75C22×D4×C109—21no—
76C22×D4×C109—22no—
77C22×D4×C109—41no—
78C22×D4×C109—41no—
79C22×D4×C109D414yes—
80C22×D4×C109D411yescharacteristic
81C22×D4×C109C2311yescharacteristic
82C22×D4×C109C2311yescharacteristic
83C23×C4×C109—21no—
84C23×C4×C109—21no—
85C23×C4×C109C2311yescharacteristic
86C23×C4×C109C2311yescharacteristic
87C2×M16×C109—22no—
88C2×M16×C109—41no—
89C2×M16×C109—41no—
90C22×C8×C109C2311yescharacteristic
91C22×C8×C109C2311yescharacteristic
92C22×C8×C109C2311yescharacteristic
93C22×C8×C109C2311yescharacteristic
94#124×C109—22no—
95#124×C109—22no—
96#123×C109—28no—
97C22⋊Q8×C109—22no—
98C22⋊Q8×C109D414yes—
99#121×C109—28no—
100#121×C109—22no—
101#121×C109—22no—
102#120×C109—28no—
103C4×D4×C109—22no—
104C4×D4×C109—22no—
105C4×D4×C109—22no—
106C4×D4×C109—22no—
107#117×C109—22no—
108#117×C109—22no—
109C2×C4⋊C4×C109—21no—
110C2×C4⋊C4×C109—21no—
111C2×C4⋊C4×C109—21no—
112C2×C4⋊C4×C109D411yescharacteristic
113C2×C4⋊C4×C109C2311yescharacteristic
114C2×C4⋊C4×C109C2311yescharacteristic
115C2×C4⋊C4×C109C2311yescharacteristic
116C2×C4⋊C4×C109C2311yescharacteristic
117C2×C4⋊C4×C109C2311yescharacteristic
118C2×C22⋊C4×C109—28no—
119C2×C22⋊C4×C109—21no—
120C2×C22⋊C4×C109—21no—
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—21no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—21no—
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109—21no—
128C2×C22⋊C4×C109D411yescharacteristic
129C2×C22⋊C4×C109D411yescharacteristic
130C2×C42×C109—21no—
131C2×C42×C109C2311yescharacteristic
132#107×C109—22no—
133#106×C109—22no—
134#103×C109—22no—
135#103×C109—22no—
136#103×C109—41no—
137#103×C109—41no—
138#102×C109—22no—
139#102×C109—22no—
140#102×C109—22no—
141#102×C109—22no—
142#102×C109—22no—
143#102×C109—22no—
144#102×C109—41no—
145#102×C109—41no—
146C22⋊C8×C109—22no—
147C22⋊C8×C109—41no—
148C22⋊C8×C109—41no—
149#95×C109—21no—
150#95×C109—21no—
151#95×C109—21no—
152#95×C109—21no—
153#95×C109—21no—
154C24×C109—21no—
155C24×C109—21no—
156C24×C109—24no—
157C24×C109—42no—
158C24×C109—42no—
159C24×C109—42no—
160C24×C109—42no—
161C24×C109—81no—
162C24×C109—81no—
163C24×C109C2×D411yescharacteristic
164C24×C109C2×D411yescharacteristic
165#41×C109—44no—
166#41×C109—44no—
167#41×C109—44no—
168#41×C109—44no—
169C2×Q8×C109—21no—
170C2×Q8×C109—21no—
171C2×Q8×C109—21no—
172C2×Q8×C109—21no—
173C2×Q8×C109—21no—
174C2×Q8×C109C2×D412yes—
175C2×D4×C109—28no—
176C2×D4×C109—24no—
177C2×D4×C109—22no—
178C2×D4×C109—24no—
179C2×D4×C109—24no—
180C2×D4×C109—21no—
181C2×D4×C109—21no—
182C2×D4×C109—21no—
183C2×D4×C109—21no—
184C2×D4×C109—21no—
185C2×D4×C109—21no—
186C2×D4×C109—21no—
187C2×D4×C109—21no—
188C2×D4×C109—44no—
189C2×D4×C109—44no—
190C2×D4×C109—44no—
191C2×D4×C109—41no—
192C2×D4×C109—41no—
193C2×D4×C109—42no—
194C2×D4×C109—42no—
195C2×D4×C109—42no—
196C2×D4×C109—42no—
197C2×D4×C109—81no—
198C2×D4×C109—81no—
199C2×D4×C109C2×D412yes—
200C2×D4×C109C2×D412yes—
201C2×D4×C109#4112yes—
202C2×D4×C109#4112yes—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—21no—
206C22×C4×C109—21no—
207C22×C4×C109—24no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—24no—
211C22×C4×C109—21no—
212C22×C4×C109—21no—
213C22×C4×C109—21no—
214C22×C4×C109—21no—
215C22×C4×C109—21no—
216C22×C4×C109—21no—
217C22×C4×C109—21no—
218C22×C4×C109—21no—
219C22×C4×C109—21no—
220C22×C4×C109—21no—
221C22×C4×C109—42no—
222C22×C4×C109—42no—
223C22×C4×C109—81no—
224C22×C4×C109—81no—
225C22×C4×C109C2×D411yescharacteristic
226C22×C4×C109C2×D411yescharacteristic
227C22×C4×C109C2×D411yescharacteristic
228C22×C4×C109C2×D411yescharacteristic
229C22×C4×C109C2×D412yes—
230C22×C4×C109C2×D412yes—
231C22×C4×C109C2411yescharacteristic
232M16×C109—44no—
233C2×C8×C109—21no—
234C2×C8×C109—21no—
235C2×C8×C109—21no—
236C2×C8×C109—21no—
237C2×C8×C109—21no—
238C2×C8×C109—21no—
239C2×C8×C109—21no—
240C2×C8×C109—21no—
241C2×C8×C109—21no—
242C2×C8×C109—21no—
243C2×C8×C109—21no—
244C2×C8×C109—21no—
245C4⋊C4×C109—24no—
246C4⋊C4×C109—22no—
247C4⋊C4×C109—21no—
248C4⋊C4×C109—21no—
249C4⋊C4×C109—21no—
250C4⋊C4×C109—21no—
251C4⋊C4×C109—21no—
252C4⋊C4×C109—21no—
253C4⋊C4×C109—21no—
254C4⋊C4×C109—21no—
255C4⋊C4×C109—21no—
256C4⋊C4×C109—42no—
257C4⋊C4×C109—81no—
258C4⋊C4×C109C2×D412yes—
259C22⋊C4×C109—24no—
260C22⋊C4×C109—24no—
261C22⋊C4×C109—24no—
262C22⋊C4×C109—24no—
263C22⋊C4×C109—22no—
264C22⋊C4×C109—24no—
265C22⋊C4×C109—22no—
266C22⋊C4×C109—42no—
267C22⋊C4×C109—42no—
268C22⋊C4×C109—81no—
269C22⋊C4×C109—81no—
270C42×C109—21no—
271C42×C109—21no—
272C42×C109—42no—
273C23×C109—22no—
274C23×C109—21no—
275C23×C109—21no—
276C23×C109—22no—
277C23×C109—22no—
278C23×C109—21no—
279C23×C109—21no—
280C23×C109—21no—
281C23×C109—21no—
282C23×C109—22no—
283C23×C109—21no—
284C23×C109—21no—
285C23×C109—21no—
286C23×C109—21no—
287C23×C109—21no—
288C23×C109—21no—
289C23×C109—21no—
290C23×C109—48no—
291C23×C109—48no—
292C23×C109—41no—
293C23×C109—41no—
294C23×C109—41no—
295C23×C109—41no—
296C23×C109—41no—
297C23×C109—41no—
298C23×C109—41no—
299C23×C109—41no—
300C23×C109—41no—
301C23×C109—41no—
302C23×C109—84no—
303C23×C109—84no—
304C23×C109—84no—
305C23×C109—84no—
306C23×C109—84no—
307C23×C109#12012yes—
308C23×C109C22×D411yescharacteristic
309Q8×C109—22no—
310Q8×C109—22no—
311Q8×C109—41no—
312Q8×C109—41no—
313D4×C109—22no—
314D4×C109—22no—
315D4×C109—22no—
316D4×C109—22no—
317D4×C109—22no—
318D4×C109—48no—
319D4×C109—44no—
320D4×C109—48no—
321D4×C109—41no—
322D4×C109—41no—
323D4×C109—84no—
324D4×C109#12314yes—
325C2×C4×C109—21no—
326C2×C4×C109—21no—
327C2×C4×C109—22no—
328C2×C4×C109—22no—
329C2×C4×C109—22no—
330C2×C4×C109—22no—
331C2×C4×C109—21no—
332C2×C4×C109—21no—
333C2×C4×C109—22no—
334C2×C4×C109—21no—
335C2×C4×C109—22no—
336C2×C4×C109—21no—
337C2×C4×C109—21no—
338C2×C4×C109—21no—
339C2×C4×C109—21no—
340C2×C4×C109—21no—
341C2×C4×C109—21no—
342C2×C4×C109—48no—
343C2×C4×C109—41no—
344C2×C4×C109—41no—
345C2×C4×C109—41no—
346C2×C4×C109—41no—
347C2×C4×C109—41no—
348C2×C4×C109—41no—
349C2×C4×C109—41no—
350C2×C4×C109—41no—
351C2×C4×C109—41no—
352C2×C4×C109—41no—
353C2×C4×C109—41no—
354C2×C4×C109—41no—
355C2×C4×C109—41no—
356C2×C4×C109—41no—
357C2×C4×C109—41no—
358C2×C4×C109—41no—
359C2×C4×C109—41no—
360C2×C4×C109—41no—
361C2×C4×C109—41no—
362C2×C4×C109—41no—
363C2×C4×C109—84no—
364C2×C4×C109#12012yes—
365C2×C4×C109C22×D411yescharacteristic
366C2×C4×C109C22×D411yescharacteristic
367C2×C4×C109C2×#4111yescharacteristic
368C2×C4×C109C2×#4111yescharacteristic
369C2×C4×C109H(5,𝔽2)11yescharacteristic
370C2×C4×C109H(5,𝔽2)11yescharacteristic
371C8×C109—41no—
372C8×C109—41no—
373C8×C109—41no—
374C8×C109—41no—
375C22×C109—22no—
376C22×C109—24no—
377C22×C109—22no—
378C22×C109—22no—
379C22×C109—42no—
380C22×C109—42no—
381C22×C109—41no—
382C22×C109—42no—
383C22×C109—41no—
384C22×C109—42no—
385C22×C109—41no—
386C22×C109—42no—
387C22×C109—41no—
388C22×C109—42no—
389C22×C109—41no—
390C22×C109—42no—
391C22×C109—41no—
392C22×C109—42no—
393C22×C109—41no—
394C22×C109—42no—
395C22×C109—41no—
396C22×C109—41no—
397C22×C109—41no—
398C22×C109—41no—
399C22×C109—816no—
400C22×C109—81no—
401C22×C109—81no—
402C22×C109—81no—
403C22×C109—81no—
404C22×C109C2×#12011yescharacteristic
405C22×C109#54611yescharacteristic
406C22×C109#54611yescharacteristic
407C22×C109#57511yescharacteristic
408C22×C109#57511yescharacteristic
409C22×C109#57611yescharacteristic
410C22×C109#57711yescharacteristic
411C4×C109—22no—
412C4×C109—41no—
413C4×C109—42no—
414C4×C109—41no—
415C4×C109—41no—
416C4×C109—42no—
417C4×C109—81no—
418C4×C109—81no—
419C4×C109—81no—
420C4×C109—81no—
421C4×C109C2×#12311yescharacteristic
422C4×C109#53411yescharacteristic
423C4×C109#54611yescharacteristic
424C4×C109#54611yescharacteristic
425#24050C10911yesmaximal, characteristic, direct product factor, Sylow
426C2×C109—42no—
427C2×C109—44no—
428C2×C109—81no—
429C2×C109—82no—
430C2×C109#240511yescharacteristic
431C2×C109#300511yescharacteristic
432C2×C109#301211yescharacteristic
433C2×C109#331111yescharacteristic
434C2×C109#331911yescharacteristic
435C2×C109#332211yescharacteristic
436C2×C109#332311yescharacteristic
437C2×#546C2×C10911yescharacteristic
438C2×#485C2×C10911yescharacteristic, complemented
439C2×#418C2×C10911yescharacteristic, complemented
440#2485C2×C10911yescharacteristic, complemented
441#2042C2×C10911yescharacteristic, complemented
442#2042C2×C10911yescharacteristic, complemented
443#2034C2×C10911yescharacteristic, complemented
444#2033C2×C10911yescharacteristic, complemented
445#1894C2×C10911yescharacteristic, complemented
446#1870C2×C10911yescharacteristic, complemented
447#1864C2×C10911yescharacteristic, complemented
448#1862C2×C10911yescharacteristic, complemented
449#1788C2×C10911yescharacteristic, complemented
450#1788C2×C10911yescharacteristic, complemented
451#1786C2×C10911yescharacteristic, complemented
452C109#2405011yescharacteristic, direct product factor, Sylow
453C22×#41C22×C10911yescharacteristic
454C23×D4C22×C10911yescharacteristic
455C22×M16C22×C10911yescharacteristic
456#546—24no—
457#546—24no—
458C2×#124C22×C10911yescharacteristic
459C2×#123—21no—
460C2×C22⋊Q8C22×C10911yescharacteristic
461C2×#121—21no—
462C2×#121C22×C10911yescharacteristic
463C2×#120—21no—
464C2×C4×D4C22×C10911yescharacteristic
465C2×C4×D4C22×C10911yescharacteristic
466C2×#117C22×C10911yescharacteristic
467C22×C22⋊C4—21no—
468#485—24no—
469C2×#107C22×C10911yescharacteristic, complemented
470C2×#106C22×C10911yescharacteristic, complemented
471#418—24no—
472C2×#103C22×C10911yescharacteristic, complemented
473C2×#103C22×C10911yescharacteristic, complemented
474C2×#103C22×C10911yescharacteristic, complemented
475C2×#103C22×C10911yescharacteristic, complemented
476C2×#102C22×C10911yescharacteristic
477C2×#102C22×C10911yescharacteristic
478C2×#102C22×C10911yescharacteristic
479C2×#102C22×C10911yescharacteristic
480C2×#102C22×C10911yescharacteristic
481C2×#102C22×C10911yescharacteristic
482C2×#102C22×C10911yescharacteristic
483C2×#102C22×C10911yescharacteristic
484C2×C22⋊C8C22×C10911yescharacteristic
485C2×C22⋊C8C22×C10911yescharacteristic, complemented
486C2×C22⋊C8C22×C10911yescharacteristic, complemented
487#397—21no—
488#394—21no—
489#389C22×C10911yescharacteristic, complemented
490#389C22×C10911yescharacteristic, complemented
491#388—21no—
492#387—21no—
493#380C22×C10911yescharacteristic
494#380C22×C10911yescharacteristic, complemented
495#380C22×C10911yescharacteristic, complemented
496#340C22×C10911yescharacteristic, complemented
497#340C22×C10911yescharacteristic, complemented
498#336C22×C10911yescharacteristic, complemented
499#336C22×C10911yescharacteristic, complemented
500C25—21no—
501C2×#41—22no—
502C2×#41—22no—
503C2×#41—22no—
504C2×#41—22no—
505C2×#41—41no—
506C2×#41—41no—
507C22×Q8C23×C10911yescharacteristic
508C22×D4—22no—
509C22×D4—22no—
510C22×D4—21no—
511C22×D4—21no—
512C22×D4—21no—
513C22×D4—22no—
514C22×D4—41no—
515C22×D4—41no—
516C22×D4D4×C10914yes—
517C22×D4D4×C10911yescharacteristic
518C22×D4C23×C10911yescharacteristic
519C22×D4C23×C10911yescharacteristic
520C23×C4—21no—
521C23×C4—21no—
522C23×C4C23×C10911yescharacteristic
523C23×C4C23×C10911yescharacteristic
524C2×M16—22no—
525C2×M16—41no—
526C2×M16—41no—
527C22×C8C23×C10911yescharacteristic
528C22×C8C23×C10911yescharacteristic
529C22×C8C23×C10911yescharacteristic
530C22×C8C23×C10911yescharacteristic
531#124—22no—
532#124—22no—
533#123—28no—
534C22⋊Q8—22no—
535C22⋊Q8D4×C10914yes—
536#121—28no—
537#121—22no—
538#121—22no—
539#120—28no—
540C4×D4—22no—
541C4×D4—22no—
542C4×D4—22no—
543C4×D4—22no—
544#117—22no—
545#117—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C4⋊C4—21no—
549C2×C4⋊C4D4×C10911yescharacteristic
550C2×C4⋊C4C23×C10911yescharacteristic
551C2×C4⋊C4C23×C10911yescharacteristic
552C2×C4⋊C4C23×C10911yescharacteristic
553C2×C4⋊C4C23×C10911yescharacteristic
554C2×C4⋊C4C23×C10911yescharacteristic
555C2×C22⋊C4—28no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—21no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—21no—
564C2×C22⋊C4—21no—
565C2×C22⋊C4D4×C10911yescharacteristic
566C2×C22⋊C4D4×C10911yescharacteristic
567C2×C42—21no—
568C2×C42C23×C10911yescharacteristic
569#107—22no—
570#106—22no—
571#103—22no—
572#103—22no—
573#103—41no—
574#103—41no—
575#102—22no—
576#102—22no—
577#102—22no—
578#102—22no—
579#102—22no—
580#102—22no—
581#102—41no—
582#102—41no—
583C22⋊C8—22no—
584C22⋊C8—41no—
585C22⋊C8—41no—
586#95—21no—
587#95—21no—
588#95—21no—
589#95—21no—
590#95—21no—
591C24—21no—
592C24—21no—
593C24—24no—
594C24—42no—
595C24—42no—
596C24—42no—
597C24—42no—
598C24—81no—
599C24—81no—
600C24C2×D4×C10911yescharacteristic
601C24C2×D4×C10911yescharacteristic
602#41—44no—
603#41—44no—
604#41—44no—
605#41—44no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—21no—
609C2×Q8—21no—
610C2×Q8—21no—
611C2×Q8C2×D4×C10912yes—
612C2×D4—28no—
613C2×D4—24no—
614C2×D4—22no—
615C2×D4—24no—
616C2×D4—24no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—44no—
626C2×D4—44no—
627C2×D4—44no—
628C2×D4—41no—
629C2×D4—41no—
630C2×D4—42no—
631C2×D4—42no—
632C2×D4—42no—
633C2×D4—42no—
634C2×D4—81no—
635C2×D4—81no—
636C2×D4C2×D4×C10912yes—
637C2×D4C2×D4×C10912yes—
638C2×D4#41×C10912yes—
639C2×D4#41×C10912yes—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—24no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—24no—
648C22×C4—21no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—42no—
659C22×C4—42no—
660C22×C4—81no—
661C22×C4—81no—
662C22×C4C2×D4×C10911yescharacteristic
663C22×C4C2×D4×C10911yescharacteristic
664C22×C4C2×D4×C10911yescharacteristic
665C22×C4C2×D4×C10911yescharacteristic
666C22×C4C2×D4×C10912yes—
667C22×C4C2×D4×C10912yes—
668C22×C4C24×C10911yescharacteristic
669M16—44no—
670C2×C8—21no—
671C2×C8—21no—
672C2×C8—21no—
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—
682C4⋊C4—24no—
683C4⋊C4—22no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—42no—
694C4⋊C4—81no—
695C4⋊C4C2×D4×C10912yes—
696C22⋊C4—24no—
697C22⋊C4—24no—
698C22⋊C4—24no—
699C22⋊C4—24no—
700C22⋊C4—22no—
701C22⋊C4—24no—
702C22⋊C4—22no—
703C22⋊C4—42no—
704C22⋊C4—42no—
705C22⋊C4—81no—
706C22⋊C4—81no—
707C42—21no—
708C42—21no—
709C42—42no—
710C23—22no—
711C23—21no—
712C23—21no—
713C23—22no—
714C23—22no—
715C23—21no—
716C23—21no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—48no—
728C23—48no—
729C23—41no—
730C23—41no—
731C23—41no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—41no—
736C23—41no—
737C23—41no—
738C23—41no—
739C23—84no—
740C23—84no—
741C23—84no—
742C23—84no—
743C23—84no—
744C23#120×C10912yes—
745C23C22×D4×C10911yescharacteristic
746Q8—22no—
747Q8—22no—
748Q8—41no—
749Q8—41no—
750D4—22no—
751D4—22no—
752D4—22no—
753D4—22no—
754D4—22no—
755D4—48no—
756D4—48no—
757D4—44no—
758D4—41no—
759D4—41no—
760D4—84no—
761D4#123×C10914yes—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—22no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—48no—
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—41no—
797C2×C4—41no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—84no—
801C2×C4#120×C10912yes—
802C2×C4C22×D4×C10911yescharacteristic
803C2×C4C22×D4×C10911yescharacteristic
804C2×C4C2×#41×C10911yescharacteristic
805C2×C4C2×#41×C10911yescharacteristic
806C2×C4H(5,𝔽2)×C10911yescharacteristic
807C2×C4H(5,𝔽2)×C10911yescharacteristic
808C8—41no—
809C8—41no—
810C8—41no—
811C8—41no—
812C22—22no—
813C22—22no—
814C22—22no—
815C22—24no—
816C22—42no—
817C22—42no—
818C22—41no—
819C22—42no—
820C22—41no—
821C22—42no—
822C22—41no—
823C22—42no—
824C22—41no—
825C22—42no—
826C22—41no—
827C22—42no—
828C22—41no—
829C22—42no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—41no—
834C22—41no—
835C22—42no—
836C22—816no—
837C22—81no—
838C22—81no—
839C22—81no—
840C22—81no—
841C22C2×#120×C10911yescharacteristic
842C22#546×C10911yescharacteristic
843C22#546×C10911yescharacteristic
844C22#575×C10911yescharacteristic
845C22#575×C10911yescharacteristic
846C22#576×C10911yescharacteristic
847C22#577×C10911yescharacteristic
848C4—22no—
849C4—41no—
850C4—41no—
851C4—42no—
852C4—41no—
853C4—42no—
854C4—81no—
855C4—81no—
856C4—81no—
857C4—81no—
858C4C2×#123×C10911yescharacteristic
859C4#534×C10911yescharacteristic
860C4#546×C10911yescharacteristic
861C4#546×C10911yescharacteristic
862C2—42no—
863C2—44no—
864C2—81no—
865C2—82no—
866C2C109×#240511yescharacteristic
867C2C109×#300511yescharacteristic
868C2C109×#301211yescharacteristic
869C2C109×#331111yescharacteristic
870C2C109×#331911yescharacteristic
871C2C109×#332211yescharacteristic
872C2C109×#332311yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC2×#546×C109C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#485×C109C2semidirect
3. C2×#418×C109C2semidirect
4. C109×#2485C2semidirect
5. C109×#2042C2semidirect
6. C109×#2042C2semidirect
7. C109×#2034C2semidirect
8. C109×#2033C2semidirect
9. C109×#1894C2semidirect
10. C109×#1870C2semidirect
11. C109×#1864C2semidirect
12. C109×#1862C2semidirect
13. C109×#1788C2semidirect
14. C109×#1788C2semidirect
15. C109×#1786C2semidirect
32. C2×#107×C109C22semidirect
33. C2×#106×C109C22semidirect
35. C2×#103×C109C22semidirect
36. C2×#103×C109C22semidirect
37. C2×#103×C109C22semidirect
38. C2×#103×C109C22semidirect
48. C2×C22⋊C8×C109C22semidirect
49. C2×C22⋊C8×C109C22semidirect
52. #389×C109C22semidirect
53. #389×C109C22semidirect
57. #380×C109C22semidirect
58. #380×C109C22semidirect
59. #340×C109C22semidirect
60. #340×C109C22semidirect
61. #336×C109C22semidirect
62. #336×C109C22semidirect
425. #24050C109direct (N × H)
438. C2×#485C2×C109semidirect
439. C2×#418C2×C109semidirect
440. #2485C2×C109semidirect
441. #2042C2×C109semidirect
442. #2042C2×C109semidirect
443. #2034C2×C109semidirect
444. #2033C2×C109semidirect
445. #1894C2×C109semidirect
446. #1870C2×C109semidirect
447. #1864C2×C109semidirect
448. #1862C2×C109semidirect
449. #1788C2×C109semidirect
450. #1788C2×C109semidirect
451. #1786C2×C109semidirect
452. C109#24050direct (N × H)
469. C2×#107C22×C109semidirect
470. C2×#106C22×C109semidirect
472. C2×#103C22×C109semidirect
473. C2×#103C22×C109semidirect
474. C2×#103C22×C109semidirect
475. C2×#103C22×C109semidirect
485. C2×C22⋊C8C22×C109semidirect
486. C2×C22⋊C8C22×C109semidirect
489. #389C22×C109semidirect
490. #389C22×C109semidirect
494. #380C22×C109semidirect
495. #380C22×C109semidirect
496. #340C22×C109semidirect
497. #340C22×C109semidirect
498. #336C22×C109semidirect
499. #336C22×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1092
C2×#485×C1092
C2×#418×C1092
C109×#24852
C109×#20422
C109×#20342
C109×#20332
C109×#18942
C109×#18702
C109×#18642
C109×#18622
C109×#17882
C109×#17862
#24050109