Finite Group Databasebeta

← C109×#24440 #42142434

Subgroups — C109×#24440 #42142434

Order 27904.

1938 conjugacy classes of subgroups.

The subgroup lattice has 1028 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C109C211yesmaximal, characteristic, complemented
2C2×#469×C109C211yesmaximal, characteristic, complemented
3C2×#447×C109C211yesmaximal, characteristic, complemented
4C2×#447×C109C211yesmaximal, characteristic, complemented
5C2×#418×C109C211yesmaximal, characteristic, complemented
6C109×#2414C211yesmaximal, characteristic, complemented
7C109×#2041C211yesmaximal, characteristic, complemented
8C109×#2034C211yesmaximal, characteristic, complemented
9C109×#2011C211yesmaximal, characteristic, complemented
10C109×#1999C211yesmaximal, characteristic, complemented
11C109×#1879C211yesmaximal, characteristic, complemented
12C109×#1875C211yesmaximal, characteristic, complemented
13C109×#1870C211yesmaximal, characteristic, complemented
14C109×#1864C211yesmaximal, characteristic, complemented
15C109×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C109—21no—
17C23×D4×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C22×D8×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic, complemented
21C22×D8×C109C2211yescharacteristic, complemented
22C22×M16×C109C2211yescharacteristic, complemented
23D42×C109—24no—
24D42×C109—24no—
25C2×#127×C109C2211yescharacteristic
26C2×#121×C109—21no—
27C2×#121×C109C2211yescharacteristic
28C2×#121×C109C2211yescharacteristic
29C2×#121×C109C2211yescharacteristic, complemented
30C2×#121×C109C2211yescharacteristic, complemented
31C2×#120×C109—21no—
32C2×#120×C109—21no—
33C2×C4×D4×C109C2211yescharacteristic
34C2×C4×D4×C109C2211yescharacteristic
35C2×#117×C109C2211yescharacteristic, complemented
36#469×C109—24no—
37#447×C109—24no—
38#447×C109—24no—
39C2×#106×C109C2211yescharacteristic, complemented
40#418×C109—24no—
41C2×#102×C109C2211yescharacteristic
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic, complemented
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#394×C109—21no—
55#392×C109—21no—
56#390×C109—21no—
57#390×C109C2211yescharacteristic, complemented
58#389×C109C2211yescharacteristic, complemented
59#388×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×D4×C109—22no—
68C22×D4×C109—22no—
69C22×D4×C109—28no—
70C22×D4×C109—21no—
71C22×D4×C109—21no—
72C22×D4×C109—22no—
73C22×D4×C109—22no—
74C22×D4×C109—22no—
75C22×D4×C109—22no—
76C22×D4×C109—21no—
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109—21no—
81C22×D4×C109—22no—
82C22×D4×C109—21no—
83C22×D4×C109—41no—
84C22×D4×C109—41no—
85C22×D4×C109—41no—
86C22×D4×C109—41no—
87C22×D4×C109—44no—
88C22×D4×C109—44no—
89C22×D4×C109D411yescharacteristic
90C22×D4×C109D414yescomplemented
91C22×D4×C109C2311yescharacteristic
92C22×D4×C109C2311yescharacteristic
93C22×D4×C109C2311yescharacteristic
94C22×D4×C109C2311yescharacteristic
95C23×C4×C109—21no—
96C23×C4×C109C2311yescharacteristic
97C23×C4×C109C2311yescharacteristic
98C2×D8×C109—22no—
99C2×D8×C109—22no—
100C2×D8×C109—22no—
101C2×D8×C109—22no—
102C2×D8×C109—22no—
103C2×D8×C109—22no—
104C2×D8×C109—41no—
105C2×D8×C109—41no—
106C2×D8×C109—41no—
107C2×M16×C109—22no—
108C2×M16×C109—22no—
109C2×M16×C109—41no—
110C22×C8×C109C2311yescharacteristic
111C22×C8×C109C2311yescharacteristic
112C22×C8×C109C2311yescharacteristic
113C22×C8×C109C2311yescharacteristic
114#127×C109—22no—
115#127×C109—22no—
116#121×C109—28no—
117#121×C109—22no—
118#121×C109—22no—
119#121×C109—22no—
120#121×C109—22no—
121#121×C109—22no—
122#121×C109—22no—
123#121×C109—41no—
124#121×C109D414yescomplemented
125#120×C109—28no—
126#120×C109—28no—
127C4×D4×C109—22no—
128C4×D4×C109—22no—
129C4×D4×C109—22no—
130C4×D4×C109—22no—
131#117×C109—22no—
132#117×C109—41no—
133C2×C4⋊C4×C109—21no—
134C2×C4⋊C4×C109D411yescharacteristic
135C2×C4⋊C4×C109C2311yescharacteristic
136C2×C4⋊C4×C109C2311yescharacteristic
137C2×C4⋊C4×C109C2311yescharacteristic
138C2×C4⋊C4×C109C2311yescharacteristic
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×C109—21no—
146C2×C22⋊C4×C109—21no—
147C2×C22⋊C4×C109—21no—
148C2×C22⋊C4×C109D411yescharacteristic
149C2×C22⋊C4×C109D411yescharacteristic
150C2×C42×C109—21no—
151C2×C42×C109C2311yescharacteristic
152#106×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—22no—
160#102×C109—22no—
161#102×C109—41no—
162#102×C109D414yescomplemented
163C22⋊C8×C109—22no—
164C22⋊C8×C109—22no—
165C22⋊C8×C109—41no—
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—21no—
174C24×C109—42no—
175C24×C109—42no—
176C24×C109—42no—
177C24×C109—42no—
178C24×C109—42no—
179C24×C109—42no—
180C24×C109—42no—
181C24×C109—42no—
182C24×C109—81no—
183C24×C109—81no—
184C24×C109—81no—
185C24×C109—81no—
186C24×C109C2×D411yescharacteristic
187C24×C109C2×D411yescharacteristic
188C2×D4×C109—22no—
189C2×D4×C109—22no—
190C2×D4×C109—28no—
191C2×D4×C109—24no—
192C2×D4×C109—24no—
193C2×D4×C109—24no—
194C2×D4×C109—24no—
195C2×D4×C109—24no—
196C2×D4×C109—24no—
197C2×D4×C109—22no—
198C2×D4×C109—21no—
199C2×D4×C109—21no—
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—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—21no—
216C2×D4×C109—21no—
217C2×D4×C109—44no—
218C2×D4×C109—44no—
219C2×D4×C109—44no—
220C2×D4×C109—42no—
221C2×D4×C109—42no—
222C2×D4×C109—42no—
223C2×D4×C109—42no—
224C2×D4×C109—42no—
225C2×D4×C109—42no—
226C2×D4×C109—44no—
227C2×D4×C109—44no—
228C2×D4×C109—432no—
229C2×D4×C109—44no—
230C2×D4×C109—42no—
231C2×D4×C109—42no—
232C2×D4×C109—42no—
233C2×D4×C109—42no—
234C2×D4×C109—44no—
235C2×D4×C109—42no—
236C2×D4×C109—42no—
237C2×D4×C109—42no—
238C2×D4×C109—81no—
239C2×D4×C109—81no—
240C2×D4×C109—81no—
241C2×D4×C109—81no—
242C2×D4×C109—81no—
243C2×D4×C109C2×D412yes—
244C2×D4×C109C2×D412yes—
245C2×D4×C109C2×D412yes—
246C2×D4×C109C2×D412yes—
247C2×D4×C109#4112yes—
248C22×C4×C109—21no—
249C22×C4×C109—21no—
250C22×C4×C109—21no—
251C22×C4×C109—21no—
252C22×C4×C109—24no—
253C22×C4×C109—21no—
254C22×C4×C109—21no—
255C22×C4×C109—21no—
256C22×C4×C109—21no—
257C22×C4×C109—21no—
258C22×C4×C109—21no—
259C22×C4×C109—21no—
260C22×C4×C109—21no—
261C22×C4×C109—21no—
262C22×C4×C109—21no—
263C22×C4×C109—42no—
264C22×C4×C109—42no—
265C22×C4×C109C2×D411yescharacteristic
266C22×C4×C109C2×D411yescharacteristic
267C22×C4×C109C2×D411yescharacteristic
268C22×C4×C109C2×D412yes—
269C22×C4×C109C2×D412yes—
270C22×C4×C109C2×D411yescharacteristic
271C22×C4×C109C2411yescharacteristic
272D8×C109—44no—
273D8×C109—44no—
274D8×C109—44no—
275M16×C109—44no—
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—21no—
284C2×C8×C109—21no—
285C2×C8×C109—21no—
286C2×C8×C109—21no—
287C2×C8×C109C2×D412yescomplemented
288C4⋊C4×C109—22no—
289C4⋊C4×C109—21no—
290C4⋊C4×C109—21no—
291C4⋊C4×C109—21no—
292C4⋊C4×C109—21no—
293C4⋊C4×C109—21no—
294C4⋊C4×C109—21no—
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—42no—
306C22⋊C4×C109—42no—
307C22⋊C4×C109—81no—
308C22⋊C4×C109—81no—
309C42×C109—21no—
310C42×C109—21no—
311C42×C109—42no—
312C23×C109—21no—
313C23×C109—22no—
314C23×C109—21no—
315C23×C109—21no—
316C23×C109—22no—
317C23×C109—21no—
318C23×C109—21no—
319C23×C109—22no—
320C23×C109—21no—
321C23×C109—21no—
322C23×C109—21no—
323C23×C109—21no—
324C23×C109—21no—
325C23×C109—21no—
326C23×C109—21no—
327C23×C109—22no—
328C23×C109—22no—
329C23×C109—48no—
330C23×C109—48no—
331C23×C109—48no—
332C23×C109—48no—
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—41no—
343C23×C109—41no—
344C23×C109—41no—
345C23×C109—41no—
346C23×C109—41no—
347C23×C109—41no—
348C23×C109—41no—
349C23×C109—41no—
350C23×C109—41no—
351C23×C109—41no—
352C23×C109—41no—
353C23×C109—41no—
354C23×C109—41no—
355C23×C109—41no—
356C23×C109—84no—
357C23×C109—84no—
358C23×C109—84no—
359C23×C109—84no—
360C23×C109—84no—
361C23×C109—84no—
362C23×C109—84no—
363C23×C109—84no—
364C23×C109—84no—
365C23×C109—84no—
366C23×C109#12012yes—
367C23×C109AGL(1,ℤ/8)12yes—
368C23×C109C22×D411yescharacteristic
369D4×C109—28no—
370D4×C109—22no—
371D4×C109—22no—
372D4×C109—22no—
373D4×C109—22no—
374D4×C109—22no—
375D4×C109—22no—
376D4×C109—22no—
377D4×C109—48no—
378D4×C109—48no—
379D4×C109—48no—
380D4×C109—48no—
381D4×C109—48no—
382D4×C109—41no—
383D4×C109—41no—
384D4×C109—41no—
385D4×C109—41no—
386D4×C109—41no—
387D4×C109—41no—
388D4×C109—41no—
389D4×C109—41no—
390D4×C109—84no—
391D4×C109—84no—
392D4×C109—84no—
393D4×C109#12114yes—
394C2×C4×C109—21no—
395C2×C4×C109—21no—
396C2×C4×C109—21no—
397C2×C4×C109—21no—
398C2×C4×C109—22no—
399C2×C4×C109—22no—
400C2×C4×C109—22no—
401C2×C4×C109—22no—
402C2×C4×C109—21no—
403C2×C4×C109—21no—
404C2×C4×C109—22no—
405C2×C4×C109—22no—
406C2×C4×C109—21no—
407C2×C4×C109—21no—
408C2×C4×C109—21no—
409C2×C4×C109—21no—
410C2×C4×C109—48no—
411C2×C4×C109—41no—
412C2×C4×C109—41no—
413C2×C4×C109—41no—
414C2×C4×C109—41no—
415C2×C4×C109—41no—
416C2×C4×C109—41no—
417C2×C4×C109—41no—
418C2×C4×C109—41no—
419C2×C4×C109—41no—
420C2×C4×C109—41no—
421C2×C4×C109—41no—
422C2×C4×C109—41no—
423C2×C4×C109—41no—
424C2×C4×C109—41no—
425C2×C4×C109#12012yes—
426C2×C4×C109AGL(1,ℤ/8)12yes—
427C2×C4×C109C22×D411yescharacteristic
428C2×C4×C109C22×D411yescharacteristic
429C2×C4×C109C22×D411yescharacteristic
430C2×C4×C109C2×#4111yescharacteristic
431C2×C4×C109H(5,𝔽2)11yescharacteristic
432C2×C4×C109H(5,𝔽2)11yescharacteristic
433C8×C109—22no—
434C8×C109—41no—
435C8×C109—41no—
436C8×C109—41no—
437C22×C109—22no—
438C22×C109—24no—
439C22×C109—22no—
440C22×C109—22no—
441C22×C109—22no—
442C22×C109—22no—
443C22×C109—22no—
444C22×C109—41no—
445C22×C109—42no—
446C22×C109—41no—
447C22×C109—42no—
448C22×C109—41no—
449C22×C109—42no—
450C22×C109—41no—
451C22×C109—41no—
452C22×C109—42no—
453C22×C109—41no—
454C22×C109—42no—
455C22×C109—41no—
456C22×C109—41no—
457C22×C109—42no—
458C22×C109—42no—
459C22×C109—42no—
460C22×C109—42no—
461C22×C109—42no—
462C22×C109—42no—
463C22×C109—42no—
464C22×C109—816no—
465C22×C109—816no—
466C22×C109—81no—
467C22×C109—81no—
468C22×C109—81no—
469C22×C109—81no—
470C22×C109—81no—
471C22×C109—81no—
472C22×C109—81no—
473C22×C109—81no—
474C22×C109—81no—
475C22×C109—81no—
476C22×C109—81no—
477C22×C109—81no—
478C22×C109—81no—
479C22×C109—81no—
480C22×C109—81no—
481C22×C109C2×#12011yescharacteristic
482C22×C109D4211yescharacteristic
483C22×C109#54611yescharacteristic
484C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
485C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
486C22×C109#57611yescharacteristic
487C22×C109#57611yescharacteristic
488C4×C109—22no—
489C4×C109—22no—
490C4×C109—41no—
491C4×C109—42no—
492C4×C109—41no—
493C4×C109—42no—
494C4×C109—81no—
495C4×C109—81no—
496C4×C109C2×#12111yescharacteristic
497C4×C109#53411yescharacteristic
498C4×C109D4211yescharacteristic
499C4×C109#54611yescharacteristic
500#24440C10911yesmaximal, characteristic, direct product factor, Sylow
501C2×C109—42no—
502C2×C109—42no—
503C2×C109—44no—
504C2×C109—82no—
505C2×C109—82no—
506C2×C109—161no—
507C2×C109#241011yescharacteristic
508C2×C109#300311yescharacteristic
509C2×C109#300811yescharacteristic
510C2×C109#326411yescharacteristic
511C2×C109#327411yescharacteristic
512C2×C109#331811yescharacteristic
513C2×C109#332511yescharacteristic
514C2×D42C2×C10911yescharacteristic, complemented
515C2×#469C2×C10911yescharacteristic, complemented
516C2×#447C2×C10911yescharacteristic, complemented
517C2×#447C2×C10911yescharacteristic, complemented
518C2×#418C2×C10911yescharacteristic, complemented
519#2414C2×C10911yescharacteristic, complemented
520#2041C2×C10911yescharacteristic, complemented
521#2034C2×C10911yescharacteristic, complemented
522#2011C2×C10911yescharacteristic, complemented
523#1999C2×C10911yescharacteristic, complemented
524#1879C2×C10911yescharacteristic, complemented
525#1875C2×C10911yescharacteristic, complemented
526#1870C2×C10911yescharacteristic, complemented
527#1864C2×C10911yescharacteristic, complemented
528#1786C2×C10911yescharacteristic, complemented
529C109#2444011yescharacteristic, direct product factor, Sylow
530C23×D4—21no—
531C23×D4C22×C10911yescharacteristic
532C23×D4C22×C10911yescharacteristic
533C22×D8C22×C10911yescharacteristic
534C22×D8C22×C10911yescharacteristic, complemented
535C22×D8C22×C10911yescharacteristic, complemented
536C22×M16C22×C10911yescharacteristic, complemented
537D42—24no—
538D42—24no—
539C2×#127C22×C10911yescharacteristic
540C2×#121—21no—
541C2×#121C22×C10911yescharacteristic
542C2×#121C22×C10911yescharacteristic
543C2×#121C22×C10911yescharacteristic, complemented
544C2×#121C22×C10911yescharacteristic, complemented
545C2×#120—21no—
546C2×#120—21no—
547C2×C4×D4C22×C10911yescharacteristic
548C2×C4×D4C22×C10911yescharacteristic
549C2×#117C22×C10911yescharacteristic, complemented
550#469—24no—
551#447—24no—
552#447—24no—
553C2×#106C22×C10911yescharacteristic, complemented
554#418—24no—
555C2×#102C22×C10911yescharacteristic
556C2×#102C22×C10911yescharacteristic
557C2×#102C22×C10911yescharacteristic
558C2×#102C22×C10911yescharacteristic, complemented
559C2×#102C22×C10911yescharacteristic, complemented
560C2×#102C22×C10911yescharacteristic, complemented
561C2×#102C22×C10911yescharacteristic, complemented
562C2×#102C22×C10911yescharacteristic, complemented
563C2×#102C22×C10911yescharacteristic, complemented
564C2×#102C22×C10911yescharacteristic, complemented
565C2×C22⋊C8C22×C10911yescharacteristic, complemented
566C2×C22⋊C8C22×C10911yescharacteristic, complemented
567C2×C22⋊C8C22×C10911yescharacteristic, complemented
568#394—21no—
569#392—21no—
570#390—21no—
571#390C22×C10911yescharacteristic, complemented
572#389C22×C10911yescharacteristic, complemented
573#388—21no—
574#380C22×C10911yescharacteristic, complemented
575#340C22×C10911yescharacteristic, complemented
576#340C22×C10911yescharacteristic, complemented
577#336C22×C10911yescharacteristic, complemented
578#336C22×C10911yescharacteristic, complemented
579C25—21no—
580C25—21no—
581C22×D4—22no—
582C22×D4—22no—
583C22×D4—28no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—22no—
587C22×D4—22no—
588C22×D4—22no—
589C22×D4—22no—
590C22×D4—21no—
591C22×D4—21no—
592C22×D4—21no—
593C22×D4—21no—
594C22×D4—21no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—41no—
598C22×D4—41no—
599C22×D4—41no—
600C22×D4—41no—
601C22×D4—44no—
602C22×D4—44no—
603C22×D4D4×C10911yescharacteristic
604C22×D4D4×C10914yescomplemented
605C22×D4C23×C10911yescharacteristic
606C22×D4C23×C10911yescharacteristic
607C22×D4C23×C10911yescharacteristic
608C22×D4C23×C10911yescharacteristic
609C23×C4—21no—
610C23×C4C23×C10911yescharacteristic
611C23×C4C23×C10911yescharacteristic
612C2×D8—22no—
613C2×D8—22no—
614C2×D8—22no—
615C2×D8—22no—
616C2×D8—22no—
617C2×D8—22no—
618C2×D8—41no—
619C2×D8—41no—
620C2×D8—41no—
621C2×M16—22no—
622C2×M16—22no—
623C2×M16—41no—
624C22×C8C23×C10911yescharacteristic
625C22×C8C23×C10911yescharacteristic
626C22×C8C23×C10911yescharacteristic
627C22×C8C23×C10911yescharacteristic
628#127—22no—
629#127—22no—
630#121—28no—
631#121—22no—
632#121—22no—
633#121—22no—
634#121—22no—
635#121—22no—
636#121—22no—
637#121—41no—
638#121D4×C10914yescomplemented
639#120—28no—
640#120—28no—
641C4×D4—22no—
642C4×D4—22no—
643C4×D4—22no—
644C4×D4—22no—
645#117—22no—
646#117—41no—
647C2×C4⋊C4—21no—
648C2×C4⋊C4D4×C10911yescharacteristic
649C2×C4⋊C4C23×C10911yescharacteristic
650C2×C4⋊C4C23×C10911yescharacteristic
651C2×C4⋊C4C23×C10911yescharacteristic
652C2×C4⋊C4C23×C10911yescharacteristic
653C2×C22⋊C4—21no—
654C2×C22⋊C4—21no—
655C2×C22⋊C4—21no—
656C2×C22⋊C4—21no—
657C2×C22⋊C4—21no—
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4D4×C10911yescharacteristic
663C2×C22⋊C4D4×C10911yescharacteristic
664C2×C42—21no—
665C2×C42C23×C10911yescharacteristic
666#106—22no—
667#102—22no—
668#102—22no—
669#102—22no—
670#102—22no—
671#102—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—41no—
676#102D4×C10914yescomplemented
677C22⋊C8—22no—
678C22⋊C8—22no—
679C22⋊C8—41no—
680#95—21no—
681#95—21no—
682C24—21no—
683C24—24no—
684C24—21no—
685C24—21no—
686C24—24no—
687C24—21no—
688C24—42no—
689C24—42no—
690C24—42no—
691C24—42no—
692C24—42no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—81no—
697C24—81no—
698C24—81no—
699C24—81no—
700C24C2×D4×C10911yescharacteristic
701C24C2×D4×C10911yescharacteristic
702C2×D4—22no—
703C2×D4—22no—
704C2×D4—28no—
705C2×D4—24no—
706C2×D4—24no—
707C2×D4—24no—
708C2×D4—24no—
709C2×D4—24no—
710C2×D4—24no—
711C2×D4—22no—
712C2×D4—21no—
713C2×D4—21no—
714C2×D4—21no—
715C2×D4—21no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—44no—
732C2×D4—44no—
733C2×D4—44no—
734C2×D4—42no—
735C2×D4—42no—
736C2×D4—42no—
737C2×D4—42no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—44no—
741C2×D4—44no—
742C2×D4—432no—
743C2×D4—44no—
744C2×D4—42no—
745C2×D4—42no—
746C2×D4—42no—
747C2×D4—42no—
748C2×D4—44no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—81no—
755C2×D4—81no—
756C2×D4—81no—
757C2×D4C2×D4×C10912yes—
758C2×D4C2×D4×C10912yes—
759C2×D4C2×D4×C10912yes—
760C2×D4C2×D4×C10912yes—
761C2×D4#41×C10912yes—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—24no—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—42no—
778C22×C4—42no—
779C22×C4C2×D4×C10911yescharacteristic
780C22×C4C2×D4×C10911yescharacteristic
781C22×C4C2×D4×C10911yescharacteristic
782C22×C4C2×D4×C10912yes—
783C22×C4C2×D4×C10912yes—
784C22×C4C2×D4×C10911yescharacteristic
785C22×C4C24×C10911yescharacteristic
786D8—44no—
787D8—44no—
788D8—44no—
789M16—44no—
790C2×C8—21no—
791C2×C8—21no—
792C2×C8—21no—
793C2×C8—21no—
794C2×C8—21no—
795C2×C8—21no—
796C2×C8—21no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8C2×D4×C10912yescomplemented
802C4⋊C4—22no—
803C4⋊C4—21no—
804C4⋊C4—21no—
805C4⋊C4—21no—
806C4⋊C4—21no—
807C4⋊C4—21no—
808C4⋊C4—21no—
809C4⋊C4—81no—
810C4⋊C4C2×D4×C10912yes—
811C4⋊C4C2×D4×C10912yescomplemented
812C22⋊C4—24no—
813C22⋊C4—24no—
814C22⋊C4—22no—
815C22⋊C4—24no—
816C22⋊C4—22no—
817C22⋊C4—42no—
818C22⋊C4—42no—
819C22⋊C4—42no—
820C22⋊C4—42no—
821C22⋊C4—81no—
822C22⋊C4—81no—
823C42—21no—
824C42—21no—
825C42—42no—
826C23—21no—
827C23—22no—
828C23—21no—
829C23—21no—
830C23—22no—
831C23—21no—
832C23—21no—
833C23—22no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—21no—
839C23—21no—
840C23—21no—
841C23—22no—
842C23—22no—
843C23—48no—
844C23—48no—
845C23—48no—
846C23—48no—
847C23—41no—
848C23—41no—
849C23—41no—
850C23—41no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—41no—
868C23—41no—
869C23—41no—
870C23—84no—
871C23—84no—
872C23—84no—
873C23—84no—
874C23—84no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23#120×C10912yes—
881C23AGL(1,ℤ/8)×C10912yes—
882C23C22×D4×C10911yescharacteristic
883D4—28no—
884D4—22no—
885D4—22no—
886D4—22no—
887D4—22no—
888D4—22no—
889D4—22no—
890D4—22no—
891D4—48no—
892D4—48no—
893D4—48no—
894D4—48no—
895D4—48no—
896D4—41no—
897D4—41no—
898D4—41no—
899D4—41no—
900D4—41no—
901D4—41no—
902D4—41no—
903D4—41no—
904D4—84no—
905D4—84no—
906D4—84no—
907D4#121×C10914yes—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—22no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—22no—
919C2×C4—22no—
920C2×C4—21no—
921C2×C4—21no—
922C2×C4—21no—
923C2×C4—21no—
924C2×C4—48no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—41no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4#120×C10912yes—
940C2×C4AGL(1,ℤ/8)×C10912yes—
941C2×C4C22×D4×C10911yescharacteristic
942C2×C4C22×D4×C10911yescharacteristic
943C2×C4C22×D4×C10911yescharacteristic
944C2×C4C2×#41×C10911yescharacteristic
945C2×C4H(5,𝔽2)×C10911yescharacteristic
946C2×C4H(5,𝔽2)×C10911yescharacteristic
947C8—22no—
948C8—41no—
949C8—41no—
950C8—41no—
951C22—22no—
952C22—22no—
953C22—22no—
954C22—22no—
955C22—22no—
956C22—22no—
957C22—24no—
958C22—42no—
959C22—41no—
960C22—42no—
961C22—41no—
962C22—42no—
963C22—41no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—42no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—41no—
972C22—42no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—42no—
977C22—42no—
978C22—816no—
979C22—816no—
980C22—81no—
981C22—81no—
982C22—81no—
983C22—81no—
984C22—81no—
985C22—81no—
986C22—81no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22C2×#120×C10911yescharacteristic
996C22D42×C10911yescharacteristic
997C22#546×C10911yescharacteristic
998C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
999C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
1000C22#576×C10911yescharacteristic
1001C22#576×C10911yescharacteristic
1002C4—22no—
1003C4—22no—
1004C4—42no—
1005C4—41no—
1006C4—42no—
1007C4—41no—
1008C4—81no—
1009C4—81no—
1010C4C2×#121×C10911yescharacteristic
1011C4#534×C10911yescharacteristic
1012C4D42×C10911yescharacteristic
1013C4#546×C10911yescharacteristic
1014C2—42no—
1015C2—42no—
1016C2—44no—
1017C2—82no—
1018C2—82no—
1019C2—161no—
1020C2C109×#241011yescharacteristic
1021C2C109×#300311yescharacteristic
1022C2C109×#300811yescharacteristic
1023C2C109×#326411yescharacteristic
1024C2C109×#327411yescharacteristic
1025C2C109×#331811yescharacteristic
1026C2C109×#332511yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
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
1. C2×D42×C109C2semidirect
2. C2×#469×C109C2semidirect
3. C2×#447×C109C2semidirect
4. C2×#447×C109C2semidirect
5. C2×#418×C109C2semidirect
6. C109×#2414C2semidirect
7. C109×#2041C2semidirect
8. C109×#2034C2semidirect
9. C109×#2011C2semidirect
10. C109×#1999C2semidirect
11. C109×#1879C2semidirect
12. C109×#1875C2semidirect
13. C109×#1870C2semidirect
14. C109×#1864C2semidirect
15. C109×#1786C2semidirect
20. C22×D8×C109C22semidirect
21. C22×D8×C109C22semidirect
22. C22×M16×C109C22semidirect
29. C2×#121×C109C22semidirect
30. C2×#121×C109C22semidirect
35. C2×#117×C109C22semidirect
39. C2×#106×C109C22semidirect
44. C2×#102×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
57. #390×C109C22semidirect
58. #389×C109C22semidirect
60. #380×C109C22semidirect
61. #340×C109C22semidirect
62. #340×C109C22semidirect
63. #336×C109C22semidirect
64. #336×C109C22semidirect
90. C22×D4×C109D4semidirect
124. #121×C109D4semidirect
162. #102×C109D4semidirect
287. C2×C8×C109C2×D4semidirect
297. C4⋊C4×C109C2×D4semidirect
500. #24440C109direct (N × H)
514. C2×D42C2×C109semidirect
515. C2×#469C2×C109semidirect
516. C2×#447C2×C109semidirect
517. C2×#447C2×C109semidirect
518. C2×#418C2×C109semidirect
519. #2414C2×C109semidirect
520. #2041C2×C109semidirect
521. #2034C2×C109semidirect
522. #2011C2×C109semidirect
523. #1999C2×C109semidirect
524. #1879C2×C109semidirect
525. #1875C2×C109semidirect
526. #1870C2×C109semidirect
527. #1864C2×C109semidirect
528. #1786C2×C109semidirect
529. C109#24440direct (N × H)
534. C22×D8C22×C109semidirect
535. C22×D8C22×C109semidirect
536. C22×M16C22×C109semidirect
543. C2×#121C22×C109semidirect
544. C2×#121C22×C109semidirect
549. C2×#117C22×C109semidirect
553. C2×#106C22×C109semidirect
558. C2×#102C22×C109semidirect
559. C2×#102C22×C109semidirect
560. C2×#102C22×C109semidirect
561. C2×#102C22×C109semidirect
562. C2×#102C22×C109semidirect
563. C2×#102C22×C109semidirect
564. C2×#102C22×C109semidirect
565. C2×C22⋊C8C22×C109semidirect
566. C2×C22⋊C8C22×C109semidirect
567. C2×C22⋊C8C22×C109semidirect
571. #390C22×C109semidirect
572. #389C22×C109semidirect
574. #380C22×C109semidirect
575. #340C22×C109semidirect
576. #340C22×C109semidirect
577. #336C22×C109semidirect
578. #336C22×C109semidirect
604. C22×D4D4×C109semidirect
638. #121D4×C109semidirect
676. #102D4×C109semidirect
801. C2×C8C2×D4×C109semidirect
811. C4⋊C4C2×D4×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×#469×C1092
C2×#447×C1092
C2×#418×C1092
C109×#24142
C109×#20412
C109×#20342
C109×#20112
C109×#19992
C109×#18792
C109×#18752
C109×#18702
C109×#18642
C109×#17862
#24440109