Finite Group Databasebeta

← C109×#24426 #42142420

Subgroups — C109×#24426 #42142420

Order 27904.

1604 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C109C211yesmaximal, characteristic
2C2×#467×C109C211yesmaximal, characteristic, complemented
3C2×#452×C109C211yesmaximal, characteristic, complemented
4C2×#450×C109C211yesmaximal, characteristic, complemented
5C22×#102×C109C211yesmaximal, characteristic, complemented
6C109×#2417C211yesmaximal, characteristic, complemented
7C109×#2042C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#2015C211yesmaximal, characteristic, complemented
10C109×#2000C211yesmaximal, characteristic, complemented
11C109×#1877C211yesmaximal, characteristic, complemented
12C109×#1872C211yesmaximal, characteristic, complemented
13C109×#1869C211yesmaximal, characteristic, complemented
14C109×#1862C211yesmaximal, characteristic, complemented
15C109×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C23×D4×C109C2211yescharacteristic
18C22×Q16×C109C2211yescharacteristic, complemented
19C22×SD16×C109C2211yescharacteristic
20C22×SD16×C109C2211yescharacteristic
21C23×C8×C109C2211yescharacteristic
22#546×C109—24no—
23#546×C109—24no—
24C2×#124×C109C2211yescharacteristic
25C2×#123×C109—21no—
26C2×C22⋊Q8×C109C2211yescharacteristic
27C2×C22⋊Q8×C109C2211yescharacteristic
28C2×C22⋊Q8×C109C2211yescharacteristic, complemented
29C2×#121×C109—21no—
30C2×#121×C109C2211yescharacteristic
31C2×#120×C109—21no—
32C2×C4×D4×C109C2211yescharacteristic
33C2×C4×D4×C109C2211yescharacteristic
34C22×C4⋊C4×C109C2211yescharacteristic
35C22×C22⋊C4×C109—21no—
36#467×C109—24no—
37#452×C109—24no—
38#450×C109—24no—
39C2×#107×C109C2211yescharacteristic, complemented
40C2×#103×C109C2211yescharacteristic, complemented
41C2×#103×C109C2211yescharacteristic, complemented
42C2×#103×C109C2211yescharacteristic, complemented
43C2×#103×C109C2211yescharacteristic, complemented
44C2×#102×C109—24no—
45C2×#102×C109C2211yescharacteristic
46C2×#102×C109C2211yescharacteristic
47C2×#102×C109C2211yescharacteristic
48C2×#102×C109C2211yescharacteristic
49C2×#102×C109C2211yescharacteristic
50C2×#102×C109C2211yescharacteristic
51C2×C22⋊C8×C109C2211yescharacteristic
52C2×C22⋊C8×C109C2211yescharacteristic, complemented
53C2×C22⋊C8×C109C2211yescharacteristic, complemented
54#398×C109—21no—
55#396×C109—21no—
56#391×C109C2211yescharacteristic, complemented
57#389×C109C2211yescharacteristic, complemented
58#386×C109—21no—
59#380×C109—21no—
60#380×C109C2211yescharacteristic, complemented
61#340×C109C2211yescharacteristic, complemented
62#340×C109C2211yescharacteristic, complemented
63#336×C109C2211yescharacteristic, complemented
64#336×C109C2211yescharacteristic, complemented
65C25×C109—21no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—22no—
69C2×#41×C109—22no—
70C2×#41×C109—41no—
71C2×#41×C109—41no—
72C22×Q8×C109C2311yescharacteristic
73C22×Q8×C109C2311yescharacteristic
74C22×D4×C109—22no—
75C22×D4×C109—22no—
76C22×D4×C109—21no—
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—22no—
80C22×D4×C109—41no—
81C22×D4×C109—41no—
82C22×D4×C109D411yescharacteristic
83C22×D4×C109D414yes—
84C22×D4×C109C2311yescharacteristic
85C22×D4×C109C2311yescharacteristic
86C23×C4×C109—21no—
87C23×C4×C109—21no—
88C23×C4×C109—21no—
89C23×C4×C109C2311yescharacteristic
90C23×C4×C109C2311yescharacteristic
91C2×Q16×C109—22no—
92C2×Q16×C109—22no—
93C2×Q16×C109—41no—
94C2×SD16×C109—22no—
95C2×SD16×C109—22no—
96C2×SD16×C109—22no—
97C2×SD16×C109—22no—
98C2×SD16×C109—41no—
99C2×SD16×C109—41no—
100C22×C8×C109—22no—
101C22×C8×C109—22no—
102C22×C8×C109—41no—
103C22×C8×C109C2311yescharacteristic
104C22×C8×C109C2311yescharacteristic
105C22×C8×C109C2311yescharacteristic
106C22×C8×C109C2311yescharacteristic
107#124×C109—22no—
108#124×C109—22no—
109#123×C109—28no—
110C22⋊Q8×C109—22no—
111C22⋊Q8×C109—22no—
112C22⋊Q8×C109—22no—
113C22⋊Q8×C109—22no—
114C22⋊Q8×C109—41no—
115C22⋊Q8×C109D414yes—
116#121×C109—28no—
117#121×C109—22no—
118#121×C109—22no—
119#120×C109—28no—
120C4×D4×C109—22no—
121C4×D4×C109—22no—
122C4×D4×C109—22no—
123C4×D4×C109—22no—
124C2×C4⋊C4×C109—21no—
125C2×C4⋊C4×C109—22no—
126C2×C4⋊C4×C109—21no—
127C2×C4⋊C4×C109—21no—
128C2×C4⋊C4×C109—21no—
129C2×C4⋊C4×C109—21no—
130C2×C4⋊C4×C109—41no—
131C2×C4⋊C4×C109D411yescharacteristic
132C2×C4⋊C4×C109C2311yescharacteristic
133C2×C4⋊C4×C109C2311yescharacteristic
134C2×C4⋊C4×C109C2311yescharacteristic
135C2×C4⋊C4×C109C2311yescharacteristic
136C2×C22⋊C4×C109—28no—
137C2×C22⋊C4×C109—21no—
138C2×C22⋊C4×C109—21no—
139C2×C22⋊C4×C109—21no—
140C2×C22⋊C4×C109—21no—
141C2×C22⋊C4×C109—21no—
142C2×C22⋊C4×C109—21no—
143C2×C22⋊C4×C109—21no—
144C2×C22⋊C4×C109—21no—
145C2×C22⋊C4×C109D411yescharacteristic
146C2×C22⋊C4×C109D411yescharacteristic
147C2×C42×C109C2311yescharacteristic
148#107×C109—22no—
149#103×C109—22no—
150#103×C109—22no—
151#103×C109—22no—
152#103×C109—41no—
153#102×C109—22no—
154#102×C109—22no—
155#102×C109—22no—
156#102×C109—22no—
157#102×C109—22no—
158#102×C109D414yescomplemented
159C22⋊C8×C109—22no—
160C22⋊C8×C109—22no—
161C22⋊C8×C109—41no—
162#95×C109—21no—
163#95×C109—21no—
164#95×C109—21no—
165#95×C109—21no—
166C24×C109—21no—
167C24×C109—21no—
168C24×C109—24no—
169C24×C109—42no—
170C24×C109—42no—
171C24×C109—42no—
172C24×C109—42no—
173C24×C109—81no—
174C24×C109—81no—
175C24×C109C2×D411yescharacteristic
176C24×C109C2×D411yescharacteristic
177#41×C109—44no—
178#41×C109—44no—
179#41×C109—44no—
180#41×C109—44no—
181C2×Q8×C109—21no—
182C2×Q8×C109—21no—
183C2×Q8×C109—21no—
184C2×Q8×C109—21no—
185C2×Q8×C109—21no—
186C2×Q8×C109—21no—
187C2×Q8×C109—21no—
188C2×Q8×C109—21no—
189C2×Q8×C109—21no—
190C2×Q8×C109—21no—
191C2×Q8×C109—21no—
192C2×Q8×C109C2×D412yes—
193C2×D4×C109—28no—
194C2×D4×C109—24no—
195C2×D4×C109—22no—
196C2×D4×C109—22no—
197C2×D4×C109—22no—
198C2×D4×C109—24no—
199C2×D4×C109—24no—
200C2×D4×C109—21no—
201C2×D4×C109—21no—
202C2×D4×C109—21no—
203C2×D4×C109—21no—
204C2×D4×C109—21no—
205C2×D4×C109—21no—
206C2×D4×C109—21no—
207C2×D4×C109—21no—
208C2×D4×C109—44no—
209C2×D4×C109—44no—
210C2×D4×C109—44no—
211C2×D4×C109—42no—
212C2×D4×C109—42no—
213C2×D4×C109—42no—
214C2×D4×C109—42no—
215C2×D4×C109—81no—
216C2×D4×C109—81no—
217C2×D4×C109C2×D412yes—
218C2×D4×C109C2×D412yes—
219C2×D4×C109C2×D412yes—
220C2×D4×C109#4112yes—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—21no—
224C22×C4×C109—21no—
225C22×C4×C109—24no—
226C22×C4×C109—21no—
227C22×C4×C109—21no—
228C22×C4×C109—21no—
229C22×C4×C109—24no—
230C22×C4×C109—21no—
231C22×C4×C109—21no—
232C22×C4×C109—21no—
233C22×C4×C109—21no—
234C22×C4×C109—21no—
235C22×C4×C109—21no—
236C22×C4×C109—21no—
237C22×C4×C109—21no—
238C22×C4×C109—21no—
239C22×C4×C109—42no—
240C22×C4×C109—42no—
241C22×C4×C109—42no—
242C22×C4×C109—42no—
243C22×C4×C109—81no—
244C22×C4×C109—81no—
245C22×C4×C109—81no—
246C22×C4×C109C2×D411yescharacteristic
247C22×C4×C109C2×D411yescharacteristic
248C22×C4×C109C2×D411yescharacteristic
249C22×C4×C109C2×D411yescharacteristic
250C22×C4×C109C2×D412yes—
251C22×C4×C109C2×D412yes—
252C22×C4×C109C2411yescharacteristic
253Q16×C109—44no—
254SD16×C109—44no—
255SD16×C109—44no—
256C2×C8×C109—21no—
257C2×C8×C109—21no—
258C2×C8×C109—21no—
259C2×C8×C109—21no—
260C2×C8×C109—21no—
261C2×C8×C109—21no—
262C2×C8×C109—21no—
263C2×C8×C109—21no—
264C2×C8×C109—21no—
265C2×C8×C109—21no—
266C2×C8×C109—21no—
267C2×C8×C109—44no—
268C2×C8×C109C2×D412yes—
269C4⋊C4×C109—24no—
270C4⋊C4×C109—22no—
271C4⋊C4×C109—21no—
272C4⋊C4×C109—21no—
273C4⋊C4×C109—21no—
274C4⋊C4×C109—21no—
275C4⋊C4×C109—21no—
276C4⋊C4×C109—21no—
277C4⋊C4×C109—42no—
278C4⋊C4×C109—42no—
279C4⋊C4×C109—42no—
280C4⋊C4×C109—81no—
281C4⋊C4×C109C2×D412yes—
282C4⋊C4×C109C2×D412yes—
283C22⋊C4×C109—24no—
284C22⋊C4×C109—24no—
285C22⋊C4×C109—24no—
286C22⋊C4×C109—24no—
287C22⋊C4×C109—22no—
288C22⋊C4×C109—24no—
289C22⋊C4×C109—22no—
290C22⋊C4×C109—42no—
291C22⋊C4×C109—42no—
292C22⋊C4×C109—81no—
293C42×C109—21no—
294C42×C109—21no—
295C23×C109—21no—
296C23×C109—21no—
297C23×C109—21no—
298C23×C109—21no—
299C23×C109—22no—
300C23×C109—22no—
301C23×C109—22no—
302C23×C109—22no—
303C23×C109—21no—
304C23×C109—21no—
305C23×C109—21no—
306C23×C109—21no—
307C23×C109—21no—
308C23×C109—21no—
309C23×C109—21no—
310C23×C109—48no—
311C23×C109—41no—
312C23×C109—41no—
313C23×C109—41no—
314C23×C109—41no—
315C23×C109—41no—
316C23×C109—41no—
317C23×C109—41no—
318C23×C109—41no—
319C23×C109—41no—
320C23×C109—41no—
321C23×C109—48no—
322C23×C109—84no—
323C23×C109—84no—
324C23×C109—84no—
325C23×C109—84no—
326C23×C109—84no—
327C23×C109#12012yes—
328C23×C109#13512yes—
329C23×C109#13712yes—
330C23×C109C22×D411yescharacteristic
331Q8×C109—22no—
332Q8×C109—22no—
333Q8×C109—41no—
334Q8×C109—41no—
335Q8×C109—41no—
336Q8×C109—41no—
337Q8×C109—41no—
338Q8×C109—41no—
339D4×C109—22no—
340D4×C109—22no—
341D4×C109—22no—
342D4×C109—22no—
343D4×C109—22no—
344D4×C109—48no—
345D4×C109—48no—
346D4×C109—44no—
347D4×C109—41no—
348D4×C109—41no—
349D4×C109—84no—
350D4×C109#12114yes—
351C2×C4×C109—21no—
352C2×C4×C109—21no—
353C2×C4×C109—22no—
354C2×C4×C109—22no—
355C2×C4×C109—22no—
356C2×C4×C109—22no—
357C2×C4×C109—21no—
358C2×C4×C109—21no—
359C2×C4×C109—22no—
360C2×C4×C109—21no—
361C2×C4×C109—22no—
362C2×C4×C109—22no—
363C2×C4×C109—21no—
364C2×C4×C109—21no—
365C2×C4×C109—21no—
366C2×C4×C109—21no—
367C2×C4×C109—21no—
368C2×C4×C109—21no—
369C2×C4×C109—48no—
370C2×C4×C109—41no—
371C2×C4×C109—41no—
372C2×C4×C109—41no—
373C2×C4×C109—41no—
374C2×C4×C109—41no—
375C2×C4×C109—41no—
376C2×C4×C109—41no—
377C2×C4×C109—41no—
378C2×C4×C109—41no—
379C2×C4×C109—41no—
380C2×C4×C109—41no—
381C2×C4×C109—41no—
382C2×C4×C109—41no—
383C2×C4×C109—41no—
384C2×C4×C109—41no—
385C2×C4×C109—41no—
386C2×C4×C109—41no—
387C2×C4×C109—41no—
388C2×C4×C109—41no—
389C2×C4×C109—84no—
390C2×C4×C109—84no—
391C2×C4×C109#12012yes—
392C2×C4×C109C22×D411yescharacteristic
393C2×C4×C109C22×D411yescharacteristic
394C2×C4×C109C22×D411yescharacteristic
395C2×C4×C109C2×#4111yescharacteristic
396C2×C4×C109H(5,𝔽2)11yescharacteristic
397C2×C4×C109H(5,𝔽2)11yescharacteristic
398C8×C109—22no—
399C8×C109—41no—
400C8×C109—41no—
401C8×C109—41no—
402C22×C109—22no—
403C22×C109—22no—
404C22×C109—22no—
405C22×C109—22no—
406C22×C109—22no—
407C22×C109—22no—
408C22×C109—24no—
409C22×C109—42no—
410C22×C109—42no—
411C22×C109—42no—
412C22×C109—42no—
413C22×C109—42no—
414C22×C109—42no—
415C22×C109—41no—
416C22×C109—42no—
417C22×C109—41no—
418C22×C109—42no—
419C22×C109—41no—
420C22×C109—41no—
421C22×C109—42no—
422C22×C109—41no—
423C22×C109—41no—
424C22×C109—41no—
425C22×C109—816no—
426C22×C109—81no—
427C22×C109—81no—
428C22×C109—81no—
429C22×C109—81no—
430C22×C109#45214yescomplemented
431C22×C109C2×#12011yescharacteristic
432C22×C109D4211yescharacteristic
433C22×C109#54611yescharacteristic
434C22×C109C2×#13511yescharacteristic
435C22×C109C2×#13711yescharacteristic
436C22×C109#57611yescharacteristic
437C22×C109#57711yescharacteristic
438C4×C109—22no—
439C4×C109—41no—
440C4×C109—42no—
441C4×C109—41no—
442C4×C109—41no—
443C4×C109—42no—
444C4×C109—42no—
445C4×C109—81no—
446C4×C109—81no—
447C4×C109—81no—
448C4×C109C2×#12111yescharacteristic
449C4×C109#53411yescharacteristic
450C4×C109D4211yescharacteristic
451C4×C109#54611yescharacteristic
452#24426C10911yesmaximal, characteristic, direct product factor, Sylow
453C2×C109—24no—
454C2×C109—44no—
455C2×C109—81no—
456C2×C109—82no—
457C2×C109#241011yescharacteristic
458C2×C109C2×#45211yescharacteristic
459C2×C109#301211yescharacteristic
460C2×C109#326611yescharacteristic
461C2×C109#328011yescharacteristic
462C2×C109#329611yescharacteristic
463C2×C109#331411yescharacteristic
464C2×#546C2×C10911yescharacteristic
465C2×#467C2×C10911yescharacteristic, complemented
466C2×#452C2×C10911yescharacteristic, complemented
467C2×#450C2×C10911yescharacteristic, complemented
468C22×#102C2×C10911yescharacteristic, complemented
469#2417C2×C10911yescharacteristic, complemented
470#2042C2×C10911yescharacteristic, complemented
471#2033C2×C10911yescharacteristic, complemented
472#2015C2×C10911yescharacteristic, complemented
473#2000C2×C10911yescharacteristic, complemented
474#1877C2×C10911yescharacteristic, complemented
475#1872C2×C10911yescharacteristic, complemented
476#1869C2×C10911yescharacteristic, complemented
477#1862C2×C10911yescharacteristic, complemented
478#1788C2×C10911yescharacteristic, complemented
479C109#2442611yescharacteristic, direct product factor, Sylow
480C22×#41C22×C10911yescharacteristic
481C23×D4C22×C10911yescharacteristic
482C22×Q16C22×C10911yescharacteristic, complemented
483C22×SD16C22×C10911yescharacteristic
484C22×SD16C22×C10911yescharacteristic
485C23×C8C22×C10911yescharacteristic
486#546—24no—
487#546—24no—
488C2×#124C22×C10911yescharacteristic
489C2×#123—21no—
490C2×C22⋊Q8C22×C10911yescharacteristic
491C2×C22⋊Q8C22×C10911yescharacteristic
492C2×C22⋊Q8C22×C10911yescharacteristic, complemented
493C2×#121—21no—
494C2×#121C22×C10911yescharacteristic
495C2×#120—21no—
496C2×C4×D4C22×C10911yescharacteristic
497C2×C4×D4C22×C10911yescharacteristic
498C22×C4⋊C4C22×C10911yescharacteristic
499C22×C22⋊C4—21no—
500#467—24no—
501#452—24no—
502#450—24no—
503C2×#107C22×C10911yescharacteristic, complemented
504C2×#103C22×C10911yescharacteristic, complemented
505C2×#103C22×C10911yescharacteristic, complemented
506C2×#103C22×C10911yescharacteristic, complemented
507C2×#103C22×C10911yescharacteristic, complemented
508C2×#102—24no—
509C2×#102C22×C10911yescharacteristic
510C2×#102C22×C10911yescharacteristic
511C2×#102C22×C10911yescharacteristic
512C2×#102C22×C10911yescharacteristic
513C2×#102C22×C10911yescharacteristic
514C2×#102C22×C10911yescharacteristic
515C2×C22⋊C8C22×C10911yescharacteristic
516C2×C22⋊C8C22×C10911yescharacteristic, complemented
517C2×C22⋊C8C22×C10911yescharacteristic, complemented
518#398—21no—
519#396—21no—
520#391C22×C10911yescharacteristic, complemented
521#389C22×C10911yescharacteristic, complemented
522#386—21no—
523#380—21no—
524#380C22×C10911yescharacteristic, complemented
525#340C22×C10911yescharacteristic, complemented
526#340C22×C10911yescharacteristic, complemented
527#336C22×C10911yescharacteristic, complemented
528#336C22×C10911yescharacteristic, complemented
529C25—21no—
530C2×#41—22no—
531C2×#41—22no—
532C2×#41—22no—
533C2×#41—22no—
534C2×#41—41no—
535C2×#41—41no—
536C22×Q8C23×C10911yescharacteristic
537C22×Q8C23×C10911yescharacteristic
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—21no—
541C22×D4—21no—
542C22×D4—21no—
543C22×D4—22no—
544C22×D4—41no—
545C22×D4—41no—
546C22×D4D4×C10911yescharacteristic
547C22×D4D4×C10914yes—
548C22×D4C23×C10911yescharacteristic
549C22×D4C23×C10911yescharacteristic
550C23×C4—21no—
551C23×C4—21no—
552C23×C4—21no—
553C23×C4C23×C10911yescharacteristic
554C23×C4C23×C10911yescharacteristic
555C2×Q16—22no—
556C2×Q16—22no—
557C2×Q16—41no—
558C2×SD16—22no—
559C2×SD16—22no—
560C2×SD16—22no—
561C2×SD16—22no—
562C2×SD16—41no—
563C2×SD16—41no—
564C22×C8—22no—
565C22×C8—22no—
566C22×C8—41no—
567C22×C8C23×C10911yescharacteristic
568C22×C8C23×C10911yescharacteristic
569C22×C8C23×C10911yescharacteristic
570C22×C8C23×C10911yescharacteristic
571#124—22no—
572#124—22no—
573#123—28no—
574C22⋊Q8—22no—
575C22⋊Q8—22no—
576C22⋊Q8—22no—
577C22⋊Q8—22no—
578C22⋊Q8—41no—
579C22⋊Q8D4×C10914yes—
580#121—28no—
581#121—22no—
582#121—22no—
583#120—28no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—41no—
595C2×C4⋊C4D4×C10911yescharacteristic
596C2×C4⋊C4C23×C10911yescharacteristic
597C2×C4⋊C4C23×C10911yescharacteristic
598C2×C4⋊C4C23×C10911yescharacteristic
599C2×C4⋊C4C23×C10911yescharacteristic
600C2×C22⋊C4—28no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—21no—
609C2×C22⋊C4D4×C10911yescharacteristic
610C2×C22⋊C4D4×C10911yescharacteristic
611C2×C42C23×C10911yescharacteristic
612#107—22no—
613#103—22no—
614#103—22no—
615#103—22no—
616#103—41no—
617#102—22no—
618#102—22no—
619#102—22no—
620#102—22no—
621#102—22no—
622#102D4×C10914yescomplemented
623C22⋊C8—22no—
624C22⋊C8—22no—
625C22⋊C8—41no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630C24—21no—
631C24—21no—
632C24—24no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—81no—
638C24—81no—
639C24C2×D4×C10911yescharacteristic
640C24C2×D4×C10911yescharacteristic
641#41—44no—
642#41—44no—
643#41—44no—
644#41—44no—
645C2×Q8—21no—
646C2×Q8—21no—
647C2×Q8—21no—
648C2×Q8—21no—
649C2×Q8—21no—
650C2×Q8—21no—
651C2×Q8—21no—
652C2×Q8—21no—
653C2×Q8—21no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8C2×D4×C10912yes—
657C2×D4—28no—
658C2×D4—24no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—24no—
663C2×D4—24no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—44no—
673C2×D4—44no—
674C2×D4—44no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—42no—
678C2×D4—42no—
679C2×D4—81no—
680C2×D4—81no—
681C2×D4C2×D4×C10912yes—
682C2×D4C2×D4×C10912yes—
683C2×D4C2×D4×C10912yes—
684C2×D4#41×C10912yes—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—24no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—24no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—42no—
704C22×C4—42no—
705C22×C4—42no—
706C22×C4—42no—
707C22×C4—81no—
708C22×C4—81no—
709C22×C4—81no—
710C22×C4C2×D4×C10911yescharacteristic
711C22×C4C2×D4×C10911yescharacteristic
712C22×C4C2×D4×C10911yescharacteristic
713C22×C4C2×D4×C10911yescharacteristic
714C22×C4C2×D4×C10912yes—
715C22×C4C2×D4×C10912yes—
716C22×C4C24×C10911yescharacteristic
717Q16—44no—
718SD16—44no—
719SD16—44no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—21no—
723C2×C8—21no—
724C2×C8—21no—
725C2×C8—21no—
726C2×C8—21no—
727C2×C8—21no—
728C2×C8—21no—
729C2×C8—21no—
730C2×C8—21no—
731C2×C8—44no—
732C2×C8C2×D4×C10912yes—
733C4⋊C4—24no—
734C4⋊C4—22no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—42no—
742C4⋊C4—42no—
743C4⋊C4—42no—
744C4⋊C4—81no—
745C4⋊C4C2×D4×C10912yes—
746C4⋊C4C2×D4×C10912yes—
747C22⋊C4—24no—
748C22⋊C4—24no—
749C22⋊C4—24no—
750C22⋊C4—24no—
751C22⋊C4—22no—
752C22⋊C4—24no—
753C22⋊C4—22no—
754C22⋊C4—42no—
755C22⋊C4—42no—
756C22⋊C4—81no—
757C42—21no—
758C42—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—21no—
773C23—21no—
774C23—48no—
775C23—41no—
776C23—41no—
777C23—41no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—48no—
786C23—84no—
787C23—84no—
788C23—84no—
789C23—84no—
790C23—84no—
791C23#120×C10912yes—
792C23#135×C10912yes—
793C23#137×C10912yes—
794C23C22×D4×C10911yescharacteristic
795Q8—22no—
796Q8—22no—
797Q8—41no—
798Q8—41no—
799Q8—41no—
800Q8—41no—
801Q8—41no—
802Q8—41no—
803D4—22no—
804D4—22no—
805D4—22no—
806D4—22no—
807D4—22no—
808D4—48no—
809D4—48no—
810D4—44no—
811D4—41no—
812D4—41no—
813D4—84no—
814D4#121×C10914yes—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—21no—
825C2×C4—22no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—21no—
832C2×C4—21no—
833C2×C4—48no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—84no—
854C2×C4—84no—
855C2×C4#120×C10912yes—
856C2×C4C22×D4×C10911yescharacteristic
857C2×C4C22×D4×C10911yescharacteristic
858C2×C4C22×D4×C10911yescharacteristic
859C2×C4C2×#41×C10911yescharacteristic
860C2×C4H(5,𝔽2)×C10911yescharacteristic
861C2×C4H(5,𝔽2)×C10911yescharacteristic
862C8—22no—
863C8—41no—
864C8—41no—
865C8—41no—
866C22—22no—
867C22—22no—
868C22—22no—
869C22—22no—
870C22—22no—
871C22—22no—
872C22—24no—
873C22—42no—
874C22—42no—
875C22—42no—
876C22—42no—
877C22—42no—
878C22—42no—
879C22—41no—
880C22—42no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—816no—
890C22—81no—
891C22—81no—
892C22—81no—
893C22—81no—
894C22#452×C10914yescomplemented
895C22C2×#120×C10911yescharacteristic
896C22D42×C10911yescharacteristic
897C22#546×C10911yescharacteristic
898C22C2×#135×C10911yescharacteristic
899C22C2×#137×C10911yescharacteristic
900C22#576×C10911yescharacteristic
901C22#577×C10911yescharacteristic
902C4—22no—
903C4—41no—
904C4—41no—
905C4—42no—
906C4—42no—
907C4—41no—
908C4—42no—
909C4—81no—
910C4—81no—
911C4—81no—
912C4C2×#121×C10911yescharacteristic
913C4#534×C10911yescharacteristic
914C4D42×C10911yescharacteristic
915C4#546×C10911yescharacteristic
916C2—24no—
917C2—44no—
918C2—81no—
919C2—82no—
920C2C109×#241011yescharacteristic
921C2C2×#452×C10911yescharacteristic
922C2C109×#301211yescharacteristic
923C2C109×#326611yescharacteristic
924C2C109×#328011yescharacteristic
925C2C109×#329611yescharacteristic
926C2C109×#331411yescharacteristic
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×#467×C109C2semidirect
3. C2×#452×C109C2semidirect
4. C2×#450×C109C2semidirect
5. C22×#102×C109C2semidirect
6. C109×#2417C2semidirect
7. C109×#2042C2semidirect
8. C109×#2033C2semidirect
9. C109×#2015C2semidirect
10. C109×#2000C2semidirect
11. C109×#1877C2semidirect
12. C109×#1872C2semidirect
13. C109×#1869C2semidirect
14. C109×#1862C2semidirect
15. C109×#1788C2semidirect
18. C22×Q16×C109C22semidirect
28. C2×C22⋊Q8×C109C22semidirect
39. C2×#107×C109C22semidirect
40. C2×#103×C109C22semidirect
41. C2×#103×C109C22semidirect
42. C2×#103×C109C22semidirect
43. C2×#103×C109C22semidirect
52. C2×C22⋊C8×C109C22semidirect
53. C2×C22⋊C8×C109C22semidirect
56. #391×C109C22semidirect
57. #389×C109C22semidirect
60. #380×C109C22semidirect
61. #340×C109C22semidirect
62. #340×C109C22semidirect
63. #336×C109C22semidirect
64. #336×C109C22semidirect
158. #102×C109D4semidirect
430. C22×C109#452semidirect
452. #24426C109direct (N × H)
465. C2×#467C2×C109semidirect
466. C2×#452C2×C109semidirect
467. C2×#450C2×C109semidirect
468. C22×#102C2×C109semidirect
469. #2417C2×C109semidirect
470. #2042C2×C109semidirect
471. #2033C2×C109semidirect
472. #2015C2×C109semidirect
473. #2000C2×C109semidirect
474. #1877C2×C109semidirect
475. #1872C2×C109semidirect
476. #1869C2×C109semidirect
477. #1862C2×C109semidirect
478. #1788C2×C109semidirect
479. C109#24426direct (N × H)
482. C22×Q16C22×C109semidirect
492. C2×C22⋊Q8C22×C109semidirect
503. C2×#107C22×C109semidirect
504. C2×#103C22×C109semidirect
505. C2×#103C22×C109semidirect
506. C2×#103C22×C109semidirect
507. C2×#103C22×C109semidirect
516. C2×C22⋊C8C22×C109semidirect
517. C2×C22⋊C8C22×C109semidirect
520. #391C22×C109semidirect
521. #389C22×C109semidirect
524. #380C22×C109semidirect
525. #340C22×C109semidirect
526. #340C22×C109semidirect
527. #336C22×C109semidirect
528. #336C22×C109semidirect
622. #102D4×C109semidirect
894. C22#452×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×#467×C1092
C2×#452×C1092
C2×#450×C1092
C22×#102×C1092
C109×#24172
C109×#20422
C109×#20332
C109×#20152
C109×#20002
C109×#18772
C109×#18722
C109×#18692
C109×#18622
C109×#17882
#24426109