Finite Group Databasebeta

← C109×#24432 #42142426

Subgroups — C109×#24432 #42142426

Order 27904.

1922 conjugacy classes of subgroups.

The subgroup lattice has 996 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C109C211yesmaximal, characteristic
2C2×#465×C109C211yesmaximal, characteristic, complemented
3C2×#450×C109C211yesmaximal, characteristic, complemented
4C2×#450×C109C211yesmaximal, characteristic, complemented
5C22×#102×C109C211yesmaximal, characteristic, complemented
6C109×#2417C211yesmaximal, characteristic, complemented
7C109×#2041C211yesmaximal, characteristic, complemented
8C109×#2034C211yesmaximal, characteristic, complemented
9C109×#2014C211yesmaximal, characteristic, complemented
10C109×#2000C211yesmaximal, characteristic, complemented
11C109×#1877C211yesmaximal, characteristic, complemented
12C109×#1874C211yesmaximal, characteristic, complemented
13C109×#1869C211yesmaximal, characteristic, complemented
14C109×#1864C211yesmaximal, characteristic, complemented
15C109×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C109—21no—
17C23×D4×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C22×SD16×C109C2211yescharacteristic
20C22×SD16×C109C2211yescharacteristic, complemented
21C22×SD16×C109C2211yescharacteristic, complemented
22C23×C8×C109C2211yescharacteristic, complemented
23D42×C109—24no—
24D42×C109—24no—
25C2×#127×C109C2211yescharacteristic
26C2×C22⋊Q8×C109C2211yescharacteristic, complemented
27C2×C22⋊Q8×C109C2211yescharacteristic, complemented
28C2×#121×C109—21no—
29C2×#121×C109C2211yescharacteristic
30C2×#121×C109C2211yescharacteristic
31C2×#120×C109—21no—
32C2×#120×C109—21no—
33C2×C4×D4×C109C2211yescharacteristic
34C2×C4×D4×C109C2211yescharacteristic
35C22×C4⋊C4×C109C2211yescharacteristic, complemented
36#465×C109—24no—
37#450×C109—24no—
38#450×C109—24no—
39C2×#106×C109C2211yescharacteristic, complemented
40C2×#103×C109C2211yescharacteristic, complemented
41C2×#102×C109—24no—
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
45C2×#102×C109C2211yescharacteristic, complemented
46C2×#102×C109C2211yescharacteristic, complemented
47C2×#102×C109C2211yescharacteristic, complemented
48C2×#102×C109C2211yescharacteristic, complemented
49C2×#102×C109C2211yescharacteristic, complemented
50C2×#102×C109C2211yescharacteristic, complemented
51C2×C22⋊C8×C109C2211yescharacteristic, complemented
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—
66C25×C109—21no—
67C22×Q8×C109C2311yescharacteristic
68C22×D4×C109—22no—
69C22×D4×C109—22no—
70C22×D4×C109—28no—
71C22×D4×C109—21no—
72C22×D4×C109—21no—
73C22×D4×C109—22no—
74C22×D4×C109—22no—
75C22×D4×C109—22no—
76C22×D4×C109—22no—
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109—22no—
81C22×D4×C109—21no—
82C22×D4×C109—41no—
83C22×D4×C109—41no—
84C22×D4×C109—41no—
85C22×D4×C109—41no—
86C22×D4×C109—44no—
87C22×D4×C109—44no—
88C22×D4×C109D411yescharacteristic
89C22×D4×C109D414yes—
90C22×D4×C109C2311yescharacteristic
91C22×D4×C109C2311yescharacteristic
92C22×D4×C109C2311yescharacteristic
93C23×C4×C109—21no—
94C23×C4×C109—21no—
95C23×C4×C109C2311yescharacteristic
96C23×C4×C109C2311yescharacteristic
97C2×SD16×C109—22no—
98C2×SD16×C109—22no—
99C2×SD16×C109—22no—
100C2×SD16×C109—22no—
101C2×SD16×C109—22no—
102C2×SD16×C109—22no—
103C2×SD16×C109—41no—
104C2×SD16×C109—41no—
105C2×SD16×C109—41no—
106C22×C8×C109—22no—
107C22×C8×C109—22no—
108C22×C8×C109—41no—
109C22×C8×C109C2311yescharacteristic
110C22×C8×C109C2311yescharacteristic
111C22×C8×C109C2311yescharacteristic
112C22×C8×C109C2311yescharacteristic
113#127×C109—22no—
114#127×C109—22no—
115C22⋊Q8×C109—22no—
116C22⋊Q8×C109—22no—
117C22⋊Q8×C109—22no—
118C22⋊Q8×C109—41no—
119#121×C109—28no—
120#121×C109—22no—
121#121×C109—22no—
122#121×C109—22no—
123#121×C109D414yes—
124#120×C109—28no—
125#120×C109—28no—
126C4×D4×C109—22no—
127C4×D4×C109—22no—
128C4×D4×C109—22no—
129C4×D4×C109—22no—
130C2×C4⋊C4×C109—22no—
131C2×C4⋊C4×C109—21no—
132C2×C4⋊C4×C109—21no—
133C2×C4⋊C4×C109—21no—
134C2×C4⋊C4×C109—21no—
135C2×C4⋊C4×C109—41no—
136C2×C4⋊C4×C109D411yescharacteristic
137C2×C4⋊C4×C109C2311yescharacteristic
138C2×C4⋊C4×C109C2311yescharacteristic
139C2×C4⋊C4×C109C2311yescharacteristic
140C2×C4⋊C4×C109C2311yescharacteristic
141C2×C22⋊C4×C109—21no—
142C2×C22⋊C4×C109—21no—
143C2×C22⋊C4×C109—21no—
144C2×C22⋊C4×C109—21no—
145C2×C22⋊C4×C109—21no—
146C2×C22⋊C4×C109—21no—
147C2×C22⋊C4×C109D411yescharacteristic
148C2×C22⋊C4×C109D411yescharacteristic
149C2×C42×C109C2311yescharacteristic
150#106×C109—22no—
151#103×C109—22no—
152#102×C109—22no—
153#102×C109—22no—
154#102×C109—22no—
155#102×C109—22no—
156#102×C109—22no—
157#102×C109—22no—
158#102×C109—22no—
159#102×C109—41no—
160#102×C109D414yescomplemented
161C22⋊C8×C109—22no—
162C22⋊C8×C109—22no—
163C22⋊C8×C109—41no—
164#95×C109—21no—
165#95×C109—21no—
166#95×C109—21no—
167#95×C109—21no—
168C24×C109—21no—
169C24×C109—24no—
170C24×C109—21no—
171C24×C109—21no—
172C24×C109—24no—
173C24×C109—42no—
174C24×C109—42no—
175C24×C109—42no—
176C24×C109—42no—
177C24×C109—42no—
178C24×C109—42no—
179C24×C109—42no—
180C24×C109—42no—
181C24×C109—81no—
182C24×C109—81no—
183C24×C109—81no—
184C24×C109—81no—
185C24×C109C2×D411yescharacteristic
186C24×C109C2×D411yescharacteristic
187C2×Q8×C109—21no—
188C2×Q8×C109—21no—
189C2×Q8×C109—21no—
190C2×Q8×C109—21no—
191C2×Q8×C109—21no—
192C2×Q8×C109—21no—
193C2×D4×C109—22no—
194C2×D4×C109—22no—
195C2×D4×C109—28no—
196C2×D4×C109—24no—
197C2×D4×C109—24no—
198C2×D4×C109—24no—
199C2×D4×C109—24no—
200C2×D4×C109—24no—
201C2×D4×C109—24no—
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—21no—
209C2×D4×C109—21no—
210C2×D4×C109—21no—
211C2×D4×C109—21no—
212C2×D4×C109—21no—
213C2×D4×C109—21no—
214C2×D4×C109—21no—
215C2×D4×C109—44no—
216C2×D4×C109—44no—
217C2×D4×C109—44no—
218C2×D4×C109—42no—
219C2×D4×C109—42no—
220C2×D4×C109—42no—
221C2×D4×C109—42no—
222C2×D4×C109—42no—
223C2×D4×C109—44no—
224C2×D4×C109—44no—
225C2×D4×C109—432no—
226C2×D4×C109—44no—
227C2×D4×C109—42no—
228C2×D4×C109—42no—
229C2×D4×C109—42no—
230C2×D4×C109—42no—
231C2×D4×C109—44no—
232C2×D4×C109—42no—
233C2×D4×C109—81no—
234C2×D4×C109—81no—
235C2×D4×C109SD1614yescomplemented
236C2×D4×C109C2×D412yes—
237C2×D4×C109C2×D412yes—
238C2×D4×C109C2×D412yes—
239C2×D4×C109C2×D412yes—
240C2×D4×C109#4112yes—
241C22×C4×C109—21no—
242C22×C4×C109—21no—
243C22×C4×C109—21no—
244C22×C4×C109—21no—
245C22×C4×C109—24no—
246C22×C4×C109—21no—
247C22×C4×C109—21no—
248C22×C4×C109—21no—
249C22×C4×C109—21no—
250C22×C4×C109—21no—
251C22×C4×C109—21no—
252C22×C4×C109—21no—
253C22×C4×C109—21no—
254C22×C4×C109—21no—
255C22×C4×C109—21no—
256C22×C4×C109—21no—
257C22×C4×C109—42no—
258C22×C4×C109—42no—
259C22×C4×C109—42no—
260C22×C4×C109—42no—
261C22×C4×C109—81no—
262C22×C4×C109C2×D411yescharacteristic
263C22×C4×C109C2×D411yescharacteristic
264C22×C4×C109C2×D411yescharacteristic
265C22×C4×C109C2×D412yes—
266C22×C4×C109C2×D412yes—
267C22×C4×C109C2×D411yescharacteristic
268C22×C4×C109C2411yescharacteristic
269SD16×C109—44no—
270SD16×C109—44no—
271SD16×C109—44no—
272C2×C8×C109—21no—
273C2×C8×C109—21no—
274C2×C8×C109—21no—
275C2×C8×C109—21no—
276C2×C8×C109—21no—
277C2×C8×C109—21no—
278C2×C8×C109—21no—
279C2×C8×C109—21no—
280C2×C8×C109—21no—
281C2×C8×C109—21no—
282C2×C8×C109—21no—
283C2×C8×C109—44no—
284C2×C8×C109C2×D412yescomplemented
285C4⋊C4×C109—22no—
286C4⋊C4×C109—21no—
287C4⋊C4×C109—21no—
288C4⋊C4×C109—21no—
289C4⋊C4×C109—21no—
290C4⋊C4×C109—21no—
291C4⋊C4×C109—21no—
292C4⋊C4×C109—42no—
293C4⋊C4×C109—42no—
294C4⋊C4×C109—42no—
295C4⋊C4×C109—81no—
296C4⋊C4×C109C2×D412yes—
297C4⋊C4×C109C2×D412yescomplemented
298C22⋊C4×C109—24no—
299C22⋊C4×C109—24no—
300C22⋊C4×C109—22no—
301C22⋊C4×C109—24no—
302C22⋊C4×C109—22no—
303C22⋊C4×C109—42no—
304C22⋊C4×C109—42no—
305C22⋊C4×C109—81no—
306C42×C109—21no—
307C42×C109—21no—
308C23×C109—21no—
309C23×C109—21no—
310C23×C109—21no—
311C23×C109—21no—
312C23×C109—21no—
313C23×C109—22no—
314C23×C109—21no—
315C23×C109—22no—
316C23×C109—21no—
317C23×C109—22no—
318C23×C109—21no—
319C23×C109—21no—
320C23×C109—21no—
321C23×C109—22no—
322C23×C109—22no—
323C23×C109—48no—
324C23×C109—48no—
325C23×C109—48no—
326C23×C109—41no—
327C23×C109—41no—
328C23×C109—41no—
329C23×C109—41no—
330C23×C109—41no—
331C23×C109—41no—
332C23×C109—41no—
333C23×C109—41no—
334C23×C109—41no—
335C23×C109—41no—
336C23×C109—41no—
337C23×C109—41no—
338C23×C109—41no—
339C23×C109—41no—
340C23×C109—41no—
341C23×C109—41no—
342C23×C109—48no—
343C23×C109—84no—
344C23×C109—84no—
345C23×C109—84no—
346C23×C109—84no—
347C23×C109—84no—
348C23×C109—84no—
349C23×C109—84no—
350C23×C109—84no—
351C23×C109—84no—
352C23×C109—84no—
353C23×C109#12012yes—
354C23×C109C2×SD1612yes—
355C23×C109C2×SD1612yes—
356C23×C109AGL(1,ℤ/8)12yes—
357C23×C109C22×D411yescharacteristic
358Q8×C109—41no—
359Q8×C109—41no—
360Q8×C109—41no—
361Q8×C109—41no—
362D4×C109—28no—
363D4×C109—22no—
364D4×C109—22no—
365D4×C109—22no—
366D4×C109—22no—
367D4×C109—22no—
368D4×C109—22no—
369D4×C109—22no—
370D4×C109—48no—
371D4×C109—48no—
372D4×C109—48no—
373D4×C109—48no—
374D4×C109—48no—
375D4×C109—41no—
376D4×C109—41no—
377D4×C109—41no—
378D4×C109—41no—
379D4×C109—84no—
380D4×C109#12114yes—
381C2×C4×C109—21no—
382C2×C4×C109—21no—
383C2×C4×C109—21no—
384C2×C4×C109—21no—
385C2×C4×C109—22no—
386C2×C4×C109—22no—
387C2×C4×C109—22no—
388C2×C4×C109—22no—
389C2×C4×C109—21no—
390C2×C4×C109—21no—
391C2×C4×C109—22no—
392C2×C4×C109—22no—
393C2×C4×C109—21no—
394C2×C4×C109—21no—
395C2×C4×C109—21no—
396C2×C4×C109—21no—
397C2×C4×C109—48no—
398C2×C4×C109—41no—
399C2×C4×C109—41no—
400C2×C4×C109—41no—
401C2×C4×C109—41no—
402C2×C4×C109—41no—
403C2×C4×C109—41no—
404C2×C4×C109—41no—
405C2×C4×C109—41no—
406C2×C4×C109—41no—
407C2×C4×C109—41no—
408C2×C4×C109—41no—
409C2×C4×C109—41no—
410C2×C4×C109—41no—
411C2×C4×C109—41no—
412C2×C4×C109—41no—
413C2×C4×C109—41no—
414C2×C4×C109—41no—
415C2×C4×C109—84no—
416C2×C4×C109#12012yes—
417C2×C4×C109C2×SD1612yes—
418C2×C4×C109C22×D411yescharacteristic
419C2×C4×C109C22×D411yescharacteristic
420C2×C4×C109C22×D411yescharacteristic
421C2×C4×C109C2×#4111yescharacteristic
422C2×C4×C109H(5,𝔽2)11yescharacteristic
423C2×C4×C109H(5,𝔽2)11yescharacteristic
424C8×C109—22no—
425C8×C109—41no—
426C8×C109—41no—
427C8×C109—41no—
428C22×C109—22no—
429C22×C109—22no—
430C22×C109—22no—
431C22×C109—22no—
432C22×C109—22no—
433C22×C109—22no—
434C22×C109—24no—
435C22×C109—22no—
436C22×C109—22no—
437C22×C109—22no—
438C22×C109—41no—
439C22×C109—42no—
440C22×C109—41no—
441C22×C109—42no—
442C22×C109—41no—
443C22×C109—42no—
444C22×C109—42no—
445C22×C109—42no—
446C22×C109—41no—
447C22×C109—42no—
448C22×C109—42no—
449C22×C109—42no—
450C22×C109—42no—
451C22×C109—42no—
452C22×C109—42no—
453C22×C109—42no—
454C22×C109—816no—
455C22×C109—816no—
456C22×C109—81no—
457C22×C109—81no—
458C22×C109—81no—
459C22×C109—81no—
460C22×C109—81no—
461C22×C109—81no—
462C22×C109—81no—
463C22×C109—81no—
464C22×C109#45014yescomplemented
465C22×C109C2×#12011yescharacteristic
466C22×C109D4211yescharacteristic
467C22×C109#54611yescharacteristic
468C22×C109C22×SD1611yescharacteristic
469C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
470C22×C109#57611yescharacteristic
471C22×C109#57711yescharacteristic
472C4×C109—22no—
473C4×C109—22no—
474C4×C109—41no—
475C4×C109—42no—
476C4×C109—42no—
477C4×C109—41no—
478C4×C109—81no—
479C4×C109—81no—
480C4×C109—81no—
481C4×C109C2×#12111yescharacteristic
482C4×C109#53411yescharacteristic
483C4×C109D4211yescharacteristic
484C4×C109#54611yescharacteristic
485#24432C10911yesmaximal, characteristic, direct product factor, Sylow
486C2×C109—24no—
487C2×C109—42no—
488C2×C109—44no—
489C2×C109—82no—
490C2×C109—82no—
491C2×C109#241011yescharacteristic
492C2×C109C2×#45011yescharacteristic
493C2×C109#301211yescharacteristic
494C2×C109#326411yescharacteristic
495C2×C109D4×SD1611yescharacteristic
496C2×C109#329511yescharacteristic
497C2×C109#331011yescharacteristic
498C2×D42C2×C10911yescharacteristic
499C2×#465C2×C10911yescharacteristic, complemented
500C2×#450C2×C10911yescharacteristic, complemented
501C2×#450C2×C10911yescharacteristic, complemented
502C22×#102C2×C10911yescharacteristic, complemented
503#2417C2×C10911yescharacteristic, complemented
504#2041C2×C10911yescharacteristic, complemented
505#2034C2×C10911yescharacteristic, complemented
506#2014C2×C10911yescharacteristic, complemented
507#2000C2×C10911yescharacteristic, complemented
508#1877C2×C10911yescharacteristic, complemented
509#1874C2×C10911yescharacteristic, complemented
510#1869C2×C10911yescharacteristic, complemented
511#1864C2×C10911yescharacteristic, complemented
512#1786C2×C10911yescharacteristic, complemented
513C109#2443211yescharacteristic, direct product factor, Sylow
514C23×D4—21no—
515C23×D4C22×C10911yescharacteristic
516C23×D4C22×C10911yescharacteristic
517C22×SD16C22×C10911yescharacteristic
518C22×SD16C22×C10911yescharacteristic, complemented
519C22×SD16C22×C10911yescharacteristic, complemented
520C23×C8C22×C10911yescharacteristic, complemented
521D42—24no—
522D42—24no—
523C2×#127C22×C10911yescharacteristic
524C2×C22⋊Q8C22×C10911yescharacteristic, complemented
525C2×C22⋊Q8C22×C10911yescharacteristic, complemented
526C2×#121—21no—
527C2×#121C22×C10911yescharacteristic
528C2×#121C22×C10911yescharacteristic
529C2×#120—21no—
530C2×#120—21no—
531C2×C4×D4C22×C10911yescharacteristic
532C2×C4×D4C22×C10911yescharacteristic
533C22×C4⋊C4C22×C10911yescharacteristic, complemented
534#465—24no—
535#450—24no—
536#450—24no—
537C2×#106C22×C10911yescharacteristic, complemented
538C2×#103C22×C10911yescharacteristic, complemented
539C2×#102—24no—
540C2×#102C22×C10911yescharacteristic
541C2×#102C22×C10911yescharacteristic
542C2×#102C22×C10911yescharacteristic
543C2×#102C22×C10911yescharacteristic, complemented
544C2×#102C22×C10911yescharacteristic, complemented
545C2×#102C22×C10911yescharacteristic, complemented
546C2×#102C22×C10911yescharacteristic, complemented
547C2×#102C22×C10911yescharacteristic, complemented
548C2×#102C22×C10911yescharacteristic, complemented
549C2×C22⋊C8C22×C10911yescharacteristic, complemented
550C2×C22⋊C8C22×C10911yescharacteristic, complemented
551C2×C22⋊C8C22×C10911yescharacteristic, complemented
552#398—21no—
553#396—21no—
554#391C22×C10911yescharacteristic, complemented
555#389C22×C10911yescharacteristic, complemented
556#386—21no—
557#380—21no—
558#380C22×C10911yescharacteristic, complemented
559#340C22×C10911yescharacteristic, complemented
560#340C22×C10911yescharacteristic, complemented
561#336C22×C10911yescharacteristic, complemented
562#336C22×C10911yescharacteristic, complemented
563C25—21no—
564C25—21no—
565C22×Q8C23×C10911yescharacteristic
566C22×D4—22no—
567C22×D4—22no—
568C22×D4—28no—
569C22×D4—21no—
570C22×D4—21no—
571C22×D4—22no—
572C22×D4—22no—
573C22×D4—22no—
574C22×D4—22no—
575C22×D4—21no—
576C22×D4—21no—
577C22×D4—21no—
578C22×D4—22no—
579C22×D4—21no—
580C22×D4—41no—
581C22×D4—41no—
582C22×D4—41no—
583C22×D4—41no—
584C22×D4—44no—
585C22×D4—44no—
586C22×D4D4×C10911yescharacteristic
587C22×D4D4×C10914yes—
588C22×D4C23×C10911yescharacteristic
589C22×D4C23×C10911yescharacteristic
590C22×D4C23×C10911yescharacteristic
591C23×C4—21no—
592C23×C4—21no—
593C23×C4C23×C10911yescharacteristic
594C23×C4C23×C10911yescharacteristic
595C2×SD16—22no—
596C2×SD16—22no—
597C2×SD16—22no—
598C2×SD16—22no—
599C2×SD16—22no—
600C2×SD16—22no—
601C2×SD16—41no—
602C2×SD16—41no—
603C2×SD16—41no—
604C22×C8—22no—
605C22×C8—22no—
606C22×C8—41no—
607C22×C8C23×C10911yescharacteristic
608C22×C8C23×C10911yescharacteristic
609C22×C8C23×C10911yescharacteristic
610C22×C8C23×C10911yescharacteristic
611#127—22no—
612#127—22no—
613C22⋊Q8—22no—
614C22⋊Q8—22no—
615C22⋊Q8—22no—
616C22⋊Q8—41no—
617#121—28no—
618#121—22no—
619#121—22no—
620#121—22no—
621#121D4×C10914yes—
622#120—28no—
623#120—28no—
624C4×D4—22no—
625C4×D4—22no—
626C4×D4—22no—
627C4×D4—22no—
628C2×C4⋊C4—22no—
629C2×C4⋊C4—21no—
630C2×C4⋊C4—21no—
631C2×C4⋊C4—21no—
632C2×C4⋊C4—21no—
633C2×C4⋊C4—41no—
634C2×C4⋊C4D4×C10911yescharacteristic
635C2×C4⋊C4C23×C10911yescharacteristic
636C2×C4⋊C4C23×C10911yescharacteristic
637C2×C4⋊C4C23×C10911yescharacteristic
638C2×C4⋊C4C23×C10911yescharacteristic
639C2×C22⋊C4—21no—
640C2×C22⋊C4—21no—
641C2×C22⋊C4—21no—
642C2×C22⋊C4—21no—
643C2×C22⋊C4—21no—
644C2×C22⋊C4—21no—
645C2×C22⋊C4D4×C10911yescharacteristic
646C2×C22⋊C4D4×C10911yescharacteristic
647C2×C42C23×C10911yescharacteristic
648#106—22no—
649#103—22no—
650#102—22no—
651#102—22no—
652#102—22no—
653#102—22no—
654#102—22no—
655#102—22no—
656#102—22no—
657#102—41no—
658#102D4×C10914yescomplemented
659C22⋊C8—22no—
660C22⋊C8—22no—
661C22⋊C8—41no—
662#95—21no—
663#95—21no—
664#95—21no—
665#95—21no—
666C24—21no—
667C24—24no—
668C24—21no—
669C24—21no—
670C24—24no—
671C24—42no—
672C24—42no—
673C24—42no—
674C24—42no—
675C24—42no—
676C24—42no—
677C24—42no—
678C24—42no—
679C24—81no—
680C24—81no—
681C24—81no—
682C24—81no—
683C24C2×D4×C10911yescharacteristic
684C24C2×D4×C10911yescharacteristic
685C2×Q8—21no—
686C2×Q8—21no—
687C2×Q8—21no—
688C2×Q8—21no—
689C2×Q8—21no—
690C2×Q8—21no—
691C2×D4—22no—
692C2×D4—22no—
693C2×D4—28no—
694C2×D4—24no—
695C2×D4—24no—
696C2×D4—24no—
697C2×D4—24no—
698C2×D4—24no—
699C2×D4—24no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—21no—
711C2×D4—21no—
712C2×D4—21no—
713C2×D4—44no—
714C2×D4—44no—
715C2×D4—44no—
716C2×D4—42no—
717C2×D4—42no—
718C2×D4—42no—
719C2×D4—42no—
720C2×D4—42no—
721C2×D4—44no—
722C2×D4—44no—
723C2×D4—432no—
724C2×D4—44no—
725C2×D4—42no—
726C2×D4—42no—
727C2×D4—42no—
728C2×D4—42no—
729C2×D4—44no—
730C2×D4—42no—
731C2×D4—81no—
732C2×D4—81no—
733C2×D4SD16×C10914yescomplemented
734C2×D4C2×D4×C10912yes—
735C2×D4C2×D4×C10912yes—
736C2×D4C2×D4×C10912yes—
737C2×D4C2×D4×C10912yes—
738C2×D4#41×C10912yes—
739C22×C4—21no—
740C22×C4—21no—
741C22×C4—21no—
742C22×C4—21no—
743C22×C4—24no—
744C22×C4—21no—
745C22×C4—21no—
746C22×C4—21no—
747C22×C4—21no—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—21no—
752C22×C4—21no—
753C22×C4—21no—
754C22×C4—21no—
755C22×C4—42no—
756C22×C4—42no—
757C22×C4—42no—
758C22×C4—42no—
759C22×C4—81no—
760C22×C4C2×D4×C10911yescharacteristic
761C22×C4C2×D4×C10911yescharacteristic
762C22×C4C2×D4×C10911yescharacteristic
763C22×C4C2×D4×C10912yes—
764C22×C4C2×D4×C10912yes—
765C22×C4C2×D4×C10911yescharacteristic
766C22×C4C24×C10911yescharacteristic
767SD16—44no—
768SD16—44no—
769SD16—44no—
770C2×C8—21no—
771C2×C8—21no—
772C2×C8—21no—
773C2×C8—21no—
774C2×C8—21no—
775C2×C8—21no—
776C2×C8—21no—
777C2×C8—21no—
778C2×C8—21no—
779C2×C8—21no—
780C2×C8—21no—
781C2×C8—44no—
782C2×C8C2×D4×C10912yescomplemented
783C4⋊C4—22no—
784C4⋊C4—21no—
785C4⋊C4—21no—
786C4⋊C4—21no—
787C4⋊C4—21no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—42no—
791C4⋊C4—42no—
792C4⋊C4—42no—
793C4⋊C4—81no—
794C4⋊C4C2×D4×C10912yes—
795C4⋊C4C2×D4×C10912yescomplemented
796C22⋊C4—24no—
797C22⋊C4—24no—
798C22⋊C4—22no—
799C22⋊C4—24no—
800C22⋊C4—22no—
801C22⋊C4—42no—
802C22⋊C4—42no—
803C22⋊C4—81no—
804C42—21no—
805C42—21no—
806C23—21no—
807C23—21no—
808C23—21no—
809C23—21no—
810C23—21no—
811C23—22no—
812C23—21no—
813C23—22no—
814C23—21no—
815C23—22no—
816C23—21no—
817C23—21no—
818C23—21no—
819C23—22no—
820C23—22no—
821C23—48no—
822C23—48no—
823C23—48no—
824C23—41no—
825C23—41no—
826C23—41no—
827C23—41no—
828C23—41no—
829C23—41no—
830C23—41no—
831C23—41no—
832C23—41no—
833C23—41no—
834C23—41no—
835C23—41no—
836C23—41no—
837C23—41no—
838C23—41no—
839C23—41no—
840C23—48no—
841C23—84no—
842C23—84no—
843C23—84no—
844C23—84no—
845C23—84no—
846C23—84no—
847C23—84no—
848C23—84no—
849C23—84no—
850C23—84no—
851C23#120×C10912yes—
852C23C2×SD16×C10912yes—
853C23C2×SD16×C10912yes—
854C23AGL(1,ℤ/8)×C10912yes—
855C23C22×D4×C10911yescharacteristic
856Q8—41no—
857Q8—41no—
858Q8—41no—
859Q8—41no—
860D4—28no—
861D4—22no—
862D4—22no—
863D4—22no—
864D4—22no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—48no—
869D4—48no—
870D4—48no—
871D4—48no—
872D4—48no—
873D4—41no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—84no—
878D4#121×C10914yes—
879C2×C4—21no—
880C2×C4—21no—
881C2×C4—21no—
882C2×C4—21no—
883C2×C4—22no—
884C2×C4—22no—
885C2×C4—22no—
886C2×C4—22no—
887C2×C4—21no—
888C2×C4—21no—
889C2×C4—22no—
890C2×C4—22no—
891C2×C4—21no—
892C2×C4—21no—
893C2×C4—21no—
894C2×C4—21no—
895C2×C4—48no—
896C2×C4—41no—
897C2×C4—41no—
898C2×C4—41no—
899C2×C4—41no—
900C2×C4—41no—
901C2×C4—41no—
902C2×C4—41no—
903C2×C4—41no—
904C2×C4—41no—
905C2×C4—41no—
906C2×C4—41no—
907C2×C4—41no—
908C2×C4—41no—
909C2×C4—41no—
910C2×C4—41no—
911C2×C4—41no—
912C2×C4—41no—
913C2×C4—84no—
914C2×C4#120×C10912yes—
915C2×C4C2×SD16×C10912yes—
916C2×C4C22×D4×C10911yescharacteristic
917C2×C4C22×D4×C10911yescharacteristic
918C2×C4C22×D4×C10911yescharacteristic
919C2×C4C2×#41×C10911yescharacteristic
920C2×C4H(5,𝔽2)×C10911yescharacteristic
921C2×C4H(5,𝔽2)×C10911yescharacteristic
922C8—22no—
923C8—41no—
924C8—41no—
925C8—41no—
926C22—22no—
927C22—22no—
928C22—22no—
929C22—22no—
930C22—22no—
931C22—22no—
932C22—22no—
933C22—22no—
934C22—22no—
935C22—24no—
936C22—42no—
937C22—41no—
938C22—42no—
939C22—41no—
940C22—42no—
941C22—42no—
942C22—42no—
943C22—41no—
944C22—42no—
945C22—41no—
946C22—42no—
947C22—42no—
948C22—42no—
949C22—42no—
950C22—42no—
951C22—42no—
952C22—816no—
953C22—816no—
954C22—81no—
955C22—81no—
956C22—81no—
957C22—81no—
958C22—81no—
959C22—81no—
960C22—81no—
961C22—81no—
962C22#450×C10914yescomplemented
963C22C2×#120×C10911yescharacteristic
964C22D42×C10911yescharacteristic
965C22#546×C10911yescharacteristic
966C22C22×SD16×C10911yescharacteristic
967C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
968C22#576×C10911yescharacteristic
969C22#577×C10911yescharacteristic
970C4—22no—
971C4—22no—
972C4—42no—
973C4—42no—
974C4—41no—
975C4—41no—
976C4—81no—
977C4—81no—
978C4—81no—
979C4C2×#121×C10911yescharacteristic
980C4#534×C10911yescharacteristic
981C4D42×C10911yescharacteristic
982C4#546×C10911yescharacteristic
983C2—24no—
984C2—42no—
985C2—44no—
986C2—82no—
987C2—82no—
988C2C109×#241011yescharacteristic
989C2C2×#450×C10911yescharacteristic
990C2C109×#301211yescharacteristic
991C2C109×#326411yescharacteristic
992C2D4×SD16×C10911yescharacteristic
993C2C109×#329511yescharacteristic
994C2C109×#331011yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC2×D42×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×#465×C109C2semidirect
3. C2×#450×C109C2semidirect
4. C2×#450×C109C2semidirect
5. C22×#102×C109C2semidirect
6. C109×#2417C2semidirect
7. C109×#2041C2semidirect
8. C109×#2034C2semidirect
9. C109×#2014C2semidirect
10. C109×#2000C2semidirect
11. C109×#1877C2semidirect
12. C109×#1874C2semidirect
13. C109×#1869C2semidirect
14. C109×#1864C2semidirect
15. C109×#1786C2semidirect
20. C22×SD16×C109C22semidirect
21. C22×SD16×C109C22semidirect
22. C23×C8×C109C22semidirect
26. C2×C22⋊Q8×C109C22semidirect
27. C2×C22⋊Q8×C109C22semidirect
35. C22×C4⋊C4×C109C22semidirect
39. C2×#106×C109C22semidirect
40. C2×#103×C109C22semidirect
45. C2×#102×C109C22semidirect
46. C2×#102×C109C22semidirect
47. C2×#102×C109C22semidirect
48. C2×#102×C109C22semidirect
49. C2×#102×C109C22semidirect
50. C2×#102×C109C22semidirect
51. C2×C22⋊C8×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
160. #102×C109D4semidirect
235. C2×D4×C109SD16semidirect
284. C2×C8×C109C2×D4semidirect
297. C4⋊C4×C109C2×D4semidirect
464. C22×C109#450semidirect
485. #24432C109direct (N × H)
499. C2×#465C2×C109semidirect
500. C2×#450C2×C109semidirect
501. C2×#450C2×C109semidirect
502. C22×#102C2×C109semidirect
503. #2417C2×C109semidirect
504. #2041C2×C109semidirect
505. #2034C2×C109semidirect
506. #2014C2×C109semidirect
507. #2000C2×C109semidirect
508. #1877C2×C109semidirect
509. #1874C2×C109semidirect
510. #1869C2×C109semidirect
511. #1864C2×C109semidirect
512. #1786C2×C109semidirect
513. C109#24432direct (N × H)
518. C22×SD16C22×C109semidirect
519. C22×SD16C22×C109semidirect
520. C23×C8C22×C109semidirect
524. C2×C22⋊Q8C22×C109semidirect
525. C2×C22⋊Q8C22×C109semidirect
533. C22×C4⋊C4C22×C109semidirect
537. C2×#106C22×C109semidirect
538. C2×#103C22×C109semidirect
543. C2×#102C22×C109semidirect
544. C2×#102C22×C109semidirect
545. C2×#102C22×C109semidirect
546. C2×#102C22×C109semidirect
547. C2×#102C22×C109semidirect
548. C2×#102C22×C109semidirect
549. C2×C22⋊C8C22×C109semidirect
550. C2×C22⋊C8C22×C109semidirect
551. C2×C22⋊C8C22×C109semidirect
554. #391C22×C109semidirect
555. #389C22×C109semidirect
558. #380C22×C109semidirect
559. #340C22×C109semidirect
560. #340C22×C109semidirect
561. #336C22×C109semidirect
562. #336C22×C109semidirect
658. #102D4×C109semidirect
733. C2×D4SD16×C109semidirect
782. C2×C8C2×D4×C109semidirect
795. C4⋊C4C2×D4×C109semidirect
962. C22#450×C109semidirect

Maximal subgroups

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

subgroupindex
C2×D42×C1092
C2×#465×C1092
C2×#450×C1092
C22×#102×C1092
C109×#24172
C109×#20412
C109×#20342
C109×#20142
C109×#20002
C109×#18772
C109×#18742
C109×#18692
C109×#18642
C109×#17862
#24432109