Finite Group Databasebeta

← C109×#24044 #42142038

Subgroups — C109×#24044 #42142038

Order 27904.

1768 conjugacy classes of subgroups.

The subgroup lattice has 942 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C109C211yesmaximal, characteristic
2C2×#482×C109C211yesmaximal, characteristic, complemented
3C2×#418×C109C211yesmaximal, characteristic, complemented
4C109×#2485C211yesmaximal, characteristic, complemented
5C109×#2041C211yesmaximal, characteristic, complemented
6C109×#2041C211yesmaximal, characteristic, complemented
7C109×#2034C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#1895C211yesmaximal, characteristic, complemented
10C109×#1870C211yesmaximal, characteristic, complemented
11C109×#1864C211yesmaximal, characteristic, complemented
12C109×#1862C211yesmaximal, characteristic, complemented
13C109×#1786C211yesmaximal, characteristic, complemented
14C109×#1786C211yesmaximal, characteristic, complemented
15C109×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C109—21no—
17C23×D4×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C22×M16×C109C2211yescharacteristic, complemented
20D42×C109—24no—
21D42×C109—24no—
22C2×#127×C109C2211yescharacteristic
23C2×#121×C109—21no—
24C2×#121×C109C2211yescharacteristic
25C2×#121×C109C2211yescharacteristic
26C2×#120×C109—21no—
27C2×#120×C109—21no—
28C2×C4×D4×C109C2211yescharacteristic
29C2×C4×D4×C109C2211yescharacteristic
30C2×#117×C109C2211yescharacteristic, complemented
31#482×C109—24no—
32C2×#107×C109C2211yescharacteristic, complemented
33C2×#106×C109C2211yescharacteristic, complemented
34#418×C109—24no—
35C2×#102×C109C2211yescharacteristic
36C2×#102×C109C2211yescharacteristic
37C2×#102×C109C2211yescharacteristic
38C2×#102×C109C2211yescharacteristic
39C2×#102×C109C2211yescharacteristic, complemented
40C2×#102×C109C2211yescharacteristic, complemented
41C2×#102×C109C2211yescharacteristic, complemented
42C2×#102×C109C2211yescharacteristic, complemented
43C2×#102×C109C2211yescharacteristic, complemented
44C2×#102×C109C2211yescharacteristic, complemented
45C2×#102×C109C2211yescharacteristic, complemented
46C2×#102×C109C2211yescharacteristic, complemented
47C2×C22⋊C8×C109C2211yescharacteristic, complemented
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, complemented
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—
64C25×C109—21no—
65C22×D4×C109—22no—
66C22×D4×C109—22no—
67C22×D4×C109—28no—
68C22×D4×C109—21no—
69C22×D4×C109—21no—
70C22×D4×C109—22no—
71C22×D4×C109—22no—
72C22×D4×C109—22no—
73C22×D4×C109—22no—
74C22×D4×C109—21no—
75C22×D4×C109—21no—
76C22×D4×C109—21no—
77C22×D4×C109—22no—
78C22×D4×C109—21no—
79C22×D4×C109—41no—
80C22×D4×C109—41no—
81C22×D4×C109—41no—
82C22×D4×C109—41no—
83C22×D4×C109—44no—
84C22×D4×C109—44no—
85C22×D4×C109D411yescharacteristic
86C22×D4×C109D414yes—
87C22×D4×C109C2311yescharacteristic
88C22×D4×C109C2311yescharacteristic
89C22×D4×C109C2311yescharacteristic
90C23×C4×C109—21no—
91C23×C4×C109C2311yescharacteristic
92C23×C4×C109C2311yescharacteristic
93C2×M16×C109—22no—
94C2×M16×C109—41no—
95C2×M16×C109—41no—
96C22×C8×C109C2311yescharacteristic
97C22×C8×C109C2311yescharacteristic
98C22×C8×C109C2311yescharacteristic
99C22×C8×C109C2311yescharacteristic
100#127×C109—22no—
101#127×C109—22no—
102#121×C109—28no—
103#121×C109—22no—
104#121×C109—22no—
105#121×C109—22no—
106#121×C109D414yes—
107#120×C109—28no—
108#120×C109—28no—
109C4×D4×C109—22no—
110C4×D4×C109—22no—
111C4×D4×C109—22no—
112C4×D4×C109—22no—
113#117×C109—22no—
114#117×C109—22no—
115C2×C4⋊C4×C109—21no—
116C2×C4⋊C4×C109—21no—
117C2×C4⋊C4×C109D411yescharacteristic
118C2×C4⋊C4×C109C2311yescharacteristic
119C2×C4⋊C4×C109C2311yescharacteristic
120C2×C4⋊C4×C109C2311yescharacteristic
121C2×C4⋊C4×C109C2311yescharacteristic
122C2×C4⋊C4×C109C2311yescharacteristic
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×C109—21no—
129C2×C22⋊C4×C109—21no—
130C2×C22⋊C4×C109D411yescharacteristic
131C2×C22⋊C4×C109D411yescharacteristic
132C2×C42×C109—21no—
133C2×C42×C109C2311yescharacteristic
134#107×C109—22no—
135#106×C109—22no—
136#102×C109—22no—
137#102×C109—22no—
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—
146#102×C109—41no—
147#102×C109—41no—
148C22⋊C8×C109—22no—
149C22⋊C8×C109—41no—
150C22⋊C8×C109—41no—
151#95×C109—21no—
152#95×C109—21no—
153#95×C109—21no—
154#95×C109—21no—
155#95×C109—21no—
156C24×C109—21no—
157C24×C109—24no—
158C24×C109—21no—
159C24×C109—21no—
160C24×C109—24no—
161C24×C109—42no—
162C24×C109—42no—
163C24×C109—42no—
164C24×C109—42no—
165C24×C109—42no—
166C24×C109—42no—
167C24×C109—42no—
168C24×C109—42no—
169C24×C109—81no—
170C24×C109—81no—
171C24×C109—81no—
172C24×C109—81no—
173C24×C109C2×D411yescharacteristic
174C24×C109C2×D411yescharacteristic
175C2×D4×C109—22no—
176C2×D4×C109—22no—
177C2×D4×C109—28no—
178C2×D4×C109—24no—
179C2×D4×C109—24no—
180C2×D4×C109—24no—
181C2×D4×C109—24no—
182C2×D4×C109—24no—
183C2×D4×C109—24no—
184C2×D4×C109—22no—
185C2×D4×C109—21no—
186C2×D4×C109—21no—
187C2×D4×C109—21no—
188C2×D4×C109—21no—
189C2×D4×C109—21no—
190C2×D4×C109—21no—
191C2×D4×C109—21no—
192C2×D4×C109—21no—
193C2×D4×C109—21no—
194C2×D4×C109—21no—
195C2×D4×C109—21no—
196C2×D4×C109—21no—
197C2×D4×C109—21no—
198C2×D4×C109—44no—
199C2×D4×C109—44no—
200C2×D4×C109—44no—
201C2×D4×C109—42no—
202C2×D4×C109—42no—
203C2×D4×C109—42no—
204C2×D4×C109—42no—
205C2×D4×C109—42no—
206C2×D4×C109—44no—
207C2×D4×C109—44no—
208C2×D4×C109—432no—
209C2×D4×C109—44no—
210C2×D4×C109—42no—
211C2×D4×C109—42no—
212C2×D4×C109—42no—
213C2×D4×C109—42no—
214C2×D4×C109—44no—
215C2×D4×C109—42no—
216C2×D4×C109—81no—
217C2×D4×C109—81no—
218C2×D4×C109C2×D412yes—
219C2×D4×C109C2×D412yes—
220C2×D4×C109C2×D412yes—
221C2×D4×C109#4112yes—
222C2×D4×C109#4112yes—
223C22×C4×C109—21no—
224C22×C4×C109—21no—
225C22×C4×C109—21no—
226C22×C4×C109—21no—
227C22×C4×C109—24no—
228C22×C4×C109—21no—
229C22×C4×C109—21no—
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×C109C2×D411yescharacteristic
242C22×C4×C109C2×D411yescharacteristic
243C22×C4×C109C2×D411yescharacteristic
244C22×C4×C109C2×D412yes—
245C22×C4×C109C2×D412yes—
246C22×C4×C109C2×D411yescharacteristic
247C22×C4×C109C2411yescharacteristic
248M16×C109—44no—
249C2×C8×C109—21no—
250C2×C8×C109—21no—
251C2×C8×C109—21no—
252C2×C8×C109—21no—
253C2×C8×C109—21no—
254C2×C8×C109—21no—
255C2×C8×C109—21no—
256C2×C8×C109—21no—
257C2×C8×C109—21no—
258C2×C8×C109—21no—
259C2×C8×C109—21no—
260C2×C8×C109—21no—
261C4⋊C4×C109—22no—
262C4⋊C4×C109—21no—
263C4⋊C4×C109—21no—
264C4⋊C4×C109—21no—
265C4⋊C4×C109—21no—
266C4⋊C4×C109—21no—
267C4⋊C4×C109—21no—
268C4⋊C4×C109—21no—
269C4⋊C4×C109—21no—
270C4⋊C4×C109—21no—
271C4⋊C4×C109—42no—
272C4⋊C4×C109—81no—
273C4⋊C4×C109C2×D412yes—
274C22⋊C4×C109—24no—
275C22⋊C4×C109—24no—
276C22⋊C4×C109—22no—
277C22⋊C4×C109—24no—
278C22⋊C4×C109—22no—
279C22⋊C4×C109—42no—
280C22⋊C4×C109—42no—
281C22⋊C4×C109—81no—
282C22⋊C4×C109—81no—
283C42×C109—21no—
284C42×C109—21no—
285C42×C109—42no—
286C23×C109—21no—
287C23×C109—22no—
288C23×C109—21no—
289C23×C109—21no—
290C23×C109—21no—
291C23×C109—21no—
292C23×C109—22no—
293C23×C109—22no—
294C23×C109—21no—
295C23×C109—21no—
296C23×C109—21no—
297C23×C109—21no—
298C23×C109—21no—
299C23×C109—21no—
300C23×C109—21no—
301C23×C109—22no—
302C23×C109—22no—
303C23×C109—48no—
304C23×C109—48no—
305C23×C109—48no—
306C23×C109—48no—
307C23×C109—41no—
308C23×C109—41no—
309C23×C109—41no—
310C23×C109—41no—
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—41no—
322C23×C109—41no—
323C23×C109—84no—
324C23×C109—84no—
325C23×C109—84no—
326C23×C109—84no—
327C23×C109—84no—
328C23×C109—84no—
329C23×C109—84no—
330C23×C109—84no—
331C23×C109—84no—
332C23×C109—84no—
333C23×C109#12012yes—
334C23×C109AGL(1,ℤ/8)12yes—
335C23×C109C22×D411yescharacteristic
336D4×C109—28no—
337D4×C109—22no—
338D4×C109—22no—
339D4×C109—22no—
340D4×C109—22no—
341D4×C109—22no—
342D4×C109—22no—
343D4×C109—22no—
344D4×C109—48no—
345D4×C109—48no—
346D4×C109—48no—
347D4×C109—48no—
348D4×C109—48no—
349D4×C109—41no—
350D4×C109—41no—
351D4×C109—41no—
352D4×C109—41no—
353D4×C109—84no—
354D4×C109#12314yes—
355C2×C4×C109—21no—
356C2×C4×C109—21no—
357C2×C4×C109—21no—
358C2×C4×C109—21no—
359C2×C4×C109—22no—
360C2×C4×C109—22no—
361C2×C4×C109—22no—
362C2×C4×C109—22no—
363C2×C4×C109—21no—
364C2×C4×C109—21no—
365C2×C4×C109—22no—
366C2×C4×C109—21no—
367C2×C4×C109—21no—
368C2×C4×C109—21no—
369C2×C4×C109—21no—
370C2×C4×C109—48no—
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#12012yes—
390C2×C4×C109AGL(1,ℤ/8)12yes—
391C2×C4×C109C22×D411yescharacteristic
392C2×C4×C109C22×D411yescharacteristic
393C2×C4×C109C2×#4111yescharacteristic
394C2×C4×C109C2×#4111yescharacteristic
395C2×C4×C109H(5,𝔽2)11yescharacteristic
396C2×C4×C109H(5,𝔽2)11yescharacteristic
397C8×C109—41no—
398C8×C109—41no—
399C8×C109—41no—
400C8×C109—41no—
401C22×C109—22no—
402C22×C109—24no—
403C22×C109—22no—
404C22×C109—22no—
405C22×C109—22no—
406C22×C109—22no—
407C22×C109—22no—
408C22×C109—41no—
409C22×C109—42no—
410C22×C109—41no—
411C22×C109—42no—
412C22×C109—41no—
413C22×C109—42no—
414C22×C109—41no—
415C22×C109—42no—
416C22×C109—41no—
417C22×C109—41no—
418C22×C109—42no—
419C22×C109—41no—
420C22×C109—41no—
421C22×C109—42no—
422C22×C109—42no—
423C22×C109—42no—
424C22×C109—42no—
425C22×C109—42no—
426C22×C109—42no—
427C22×C109—42no—
428C22×C109—816no—
429C22×C109—816no—
430C22×C109—81no—
431C22×C109—81no—
432C22×C109—81no—
433C22×C109—81no—
434C22×C109—81no—
435C22×C109—81no—
436C22×C109—81no—
437C22×C109—81no—
438C22×C109C2×#12011yescharacteristic
439C22×C109#54611yescharacteristic
440C22×C109#54611yescharacteristic
441C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
443C22×C109#57611yescharacteristic
444C22×C109#57711yescharacteristic
445C4×C109—22no—
446C4×C109—22no—
447C4×C109—41no—
448C4×C109—42no—
449C4×C109—41no—
450C4×C109—81no—
451C4×C109—81no—
452C4×C109—81no—
453C4×C109—81no—
454C4×C109C2×#12311yescharacteristic
455C4×C109#53411yescharacteristic
456C4×C109#54611yescharacteristic
457C4×C109#54611yescharacteristic
458#24044C10911yesmaximal, characteristic, direct product factor, Sylow
459C2×C109—42no—
460C2×C109—42no—
461C2×C109—44no—
462C2×C109—82no—
463C2×C109—82no—
464C2×C109#240511yescharacteristic
465C2×C109#300311yescharacteristic
466C2×C109#301211yescharacteristic
467C2×C109#331011yescharacteristic
468C2×C109#331811yescharacteristic
469C2×C109#332411yescharacteristic
470C2×C109#332511yescharacteristic
471C2×D42C2×C10911yescharacteristic
472C2×#482C2×C10911yescharacteristic, complemented
473C2×#418C2×C10911yescharacteristic, complemented
474#2485C2×C10911yescharacteristic, complemented
475#2041C2×C10911yescharacteristic, complemented
476#2041C2×C10911yescharacteristic, complemented
477#2034C2×C10911yescharacteristic, complemented
478#2033C2×C10911yescharacteristic, complemented
479#1895C2×C10911yescharacteristic, complemented
480#1870C2×C10911yescharacteristic, complemented
481#1864C2×C10911yescharacteristic, complemented
482#1862C2×C10911yescharacteristic, complemented
483#1786C2×C10911yescharacteristic, complemented
484#1786C2×C10911yescharacteristic, complemented
485#1786C2×C10911yescharacteristic, complemented
486C109#2404411yescharacteristic, direct product factor, Sylow
487C23×D4—21no—
488C23×D4C22×C10911yescharacteristic
489C23×D4C22×C10911yescharacteristic
490C22×M16C22×C10911yescharacteristic, complemented
491D42—24no—
492D42—24no—
493C2×#127C22×C10911yescharacteristic
494C2×#121—21no—
495C2×#121C22×C10911yescharacteristic
496C2×#121C22×C10911yescharacteristic
497C2×#120—21no—
498C2×#120—21no—
499C2×C4×D4C22×C10911yescharacteristic
500C2×C4×D4C22×C10911yescharacteristic
501C2×#117C22×C10911yescharacteristic, complemented
502#482—24no—
503C2×#107C22×C10911yescharacteristic, complemented
504C2×#106C22×C10911yescharacteristic, complemented
505#418—24no—
506C2×#102C22×C10911yescharacteristic
507C2×#102C22×C10911yescharacteristic
508C2×#102C22×C10911yescharacteristic
509C2×#102C22×C10911yescharacteristic
510C2×#102C22×C10911yescharacteristic, complemented
511C2×#102C22×C10911yescharacteristic, complemented
512C2×#102C22×C10911yescharacteristic, complemented
513C2×#102C22×C10911yescharacteristic, complemented
514C2×#102C22×C10911yescharacteristic, complemented
515C2×#102C22×C10911yescharacteristic, complemented
516C2×#102C22×C10911yescharacteristic, complemented
517C2×#102C22×C10911yescharacteristic, complemented
518C2×C22⋊C8C22×C10911yescharacteristic, complemented
519C2×C22⋊C8C22×C10911yescharacteristic, complemented
520C2×C22⋊C8C22×C10911yescharacteristic, complemented
521#397—21no—
522#394—21no—
523#389C22×C10911yescharacteristic, complemented
524#389C22×C10911yescharacteristic, complemented
525#388—21no—
526#387—21no—
527#380C22×C10911yescharacteristic, complemented
528#380C22×C10911yescharacteristic, complemented
529#380C22×C10911yescharacteristic, complemented
530#340C22×C10911yescharacteristic, complemented
531#340C22×C10911yescharacteristic, complemented
532#336C22×C10911yescharacteristic, complemented
533#336C22×C10911yescharacteristic, complemented
534C25—21no—
535C25—21no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—28no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—22no—
545C22×D4—21no—
546C22×D4—21no—
547C22×D4—21no—
548C22×D4—22no—
549C22×D4—21no—
550C22×D4—41no—
551C22×D4—41no—
552C22×D4—41no—
553C22×D4—41no—
554C22×D4—44no—
555C22×D4—44no—
556C22×D4D4×C10911yescharacteristic
557C22×D4D4×C10914yes—
558C22×D4C23×C10911yescharacteristic
559C22×D4C23×C10911yescharacteristic
560C22×D4C23×C10911yescharacteristic
561C23×C4—21no—
562C23×C4C23×C10911yescharacteristic
563C23×C4C23×C10911yescharacteristic
564C2×M16—22no—
565C2×M16—41no—
566C2×M16—41no—
567C22×C8C23×C10911yescharacteristic
568C22×C8C23×C10911yescharacteristic
569C22×C8C23×C10911yescharacteristic
570C22×C8C23×C10911yescharacteristic
571#127—22no—
572#127—22no—
573#121—28no—
574#121—22no—
575#121—22no—
576#121—22no—
577#121D4×C10914yes—
578#120—28no—
579#120—28no—
580C4×D4—22no—
581C4×D4—22no—
582C4×D4—22no—
583C4×D4—22no—
584#117—22no—
585#117—22no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4D4×C10911yescharacteristic
589C2×C4⋊C4C23×C10911yescharacteristic
590C2×C4⋊C4C23×C10911yescharacteristic
591C2×C4⋊C4C23×C10911yescharacteristic
592C2×C4⋊C4C23×C10911yescharacteristic
593C2×C4⋊C4C23×C10911yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4D4×C10911yescharacteristic
602C2×C22⋊C4D4×C10911yescharacteristic
603C2×C42—21no—
604C2×C42C23×C10911yescharacteristic
605#107—22no—
606#106—22no—
607#102—22no—
608#102—22no—
609#102—22no—
610#102—22no—
611#102—22no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102—41no—
616#102—41no—
617#102—41no—
618#102—41no—
619C22⋊C8—22no—
620C22⋊C8—41no—
621C22⋊C8—41no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—21no—
626#95—21no—
627C24—21no—
628C24—24no—
629C24—21no—
630C24—21no—
631C24—24no—
632C24—42no—
633C24—42no—
634C24—42no—
635C24—42no—
636C24—42no—
637C24—42no—
638C24—42no—
639C24—42no—
640C24—81no—
641C24—81no—
642C24—81no—
643C24—81no—
644C24C2×D4×C10911yescharacteristic
645C24C2×D4×C10911yescharacteristic
646C2×D4—22no—
647C2×D4—22no—
648C2×D4—28no—
649C2×D4—24no—
650C2×D4—24no—
651C2×D4—24no—
652C2×D4—24no—
653C2×D4—24no—
654C2×D4—24no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—42no—
673C2×D4—42no—
674C2×D4—42no—
675C2×D4—42no—
676C2×D4—42no—
677C2×D4—44no—
678C2×D4—44no—
679C2×D4—432no—
680C2×D4—44no—
681C2×D4—42no—
682C2×D4—42no—
683C2×D4—42no—
684C2×D4—42no—
685C2×D4—44no—
686C2×D4—42no—
687C2×D4—81no—
688C2×D4—81no—
689C2×D4C2×D4×C10912yes—
690C2×D4C2×D4×C10912yes—
691C2×D4C2×D4×C10912yes—
692C2×D4#41×C10912yes—
693C2×D4#41×C10912yes—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—24no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—42no—
711C22×C4—42no—
712C22×C4C2×D4×C10911yescharacteristic
713C22×C4C2×D4×C10911yescharacteristic
714C22×C4C2×D4×C10911yescharacteristic
715C22×C4C2×D4×C10912yes—
716C22×C4C2×D4×C10912yes—
717C22×C4C2×D4×C10911yescharacteristic
718C22×C4C24×C10911yescharacteristic
719M16—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—21no—
732C4⋊C4—22no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4—21no—
738C4⋊C4—21no—
739C4⋊C4—21no—
740C4⋊C4—21no—
741C4⋊C4—21no—
742C4⋊C4—42no—
743C4⋊C4—81no—
744C4⋊C4C2×D4×C10912yes—
745C22⋊C4—24no—
746C22⋊C4—24no—
747C22⋊C4—22no—
748C22⋊C4—24no—
749C22⋊C4—22no—
750C22⋊C4—42no—
751C22⋊C4—42no—
752C22⋊C4—81no—
753C22⋊C4—81no—
754C42—21no—
755C42—21no—
756C42—42no—
757C23—21no—
758C23—22no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—22no—
764C23—22no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—21no—
772C23—22no—
773C23—22no—
774C23—48no—
775C23—48no—
776C23—48no—
777C23—48no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—84no—
795C23—84no—
796C23—84no—
797C23—84no—
798C23—84no—
799C23—84no—
800C23—84no—
801C23—84no—
802C23—84no—
803C23—84no—
804C23#120×C10912yes—
805C23AGL(1,ℤ/8)×C10912yes—
806C23C22×D4×C10911yescharacteristic
807D4—28no—
808D4—22no—
809D4—22no—
810D4—22no—
811D4—22no—
812D4—22no—
813D4—22no—
814D4—22no—
815D4—48no—
816D4—48no—
817D4—48no—
818D4—48no—
819D4—48no—
820D4—41no—
821D4—41no—
822D4—41no—
823D4—41no—
824D4—84no—
825D4#123×C10914yes—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—22no—
831C2×C4—22no—
832C2×C4—22no—
833C2×C4—22no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—48no—
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—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4#120×C10912yes—
861C2×C4AGL(1,ℤ/8)×C10912yes—
862C2×C4C22×D4×C10911yescharacteristic
863C2×C4C22×D4×C10911yescharacteristic
864C2×C4C2×#41×C10911yescharacteristic
865C2×C4C2×#41×C10911yescharacteristic
866C2×C4H(5,𝔽2)×C10911yescharacteristic
867C2×C4H(5,𝔽2)×C10911yescharacteristic
868C8—41no—
869C8—41no—
870C8—41no—
871C8—41no—
872C22—22no—
873C22—22no—
874C22—22no—
875C22—22no—
876C22—22no—
877C22—22no—
878C22—24no—
879C22—42no—
880C22—41no—
881C22—42no—
882C22—41no—
883C22—42no—
884C22—41no—
885C22—42no—
886C22—41no—
887C22—41no—
888C22—42no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—816no—
900C22—816no—
901C22—81no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22C2×#120×C10911yescharacteristic
910C22#546×C10911yescharacteristic
911C22#546×C10911yescharacteristic
912C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
913C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
914C22#576×C10911yescharacteristic
915C22#577×C10911yescharacteristic
916C4—22no—
917C4—22no—
918C4—42no—
919C4—41no—
920C4—41no—
921C4—81no—
922C4—81no—
923C4—81no—
924C4—81no—
925C4C2×#123×C10911yescharacteristic
926C4#534×C10911yescharacteristic
927C4#546×C10911yescharacteristic
928C4#546×C10911yescharacteristic
929C2—42no—
930C2—42no—
931C2—44no—
932C2—82no—
933C2—82no—
934C2C109×#240511yescharacteristic
935C2C109×#300311yescharacteristic
936C2C109×#301211yescharacteristic
937C2C109×#331011yescharacteristic
938C2C109×#331811yescharacteristic
939C2C109×#332411yescharacteristic
940C2C109×#332511yescharacteristic
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×#482×C109C2semidirect
3. C2×#418×C109C2semidirect
4. C109×#2485C2semidirect
5. C109×#2041C2semidirect
6. C109×#2041C2semidirect
7. C109×#2034C2semidirect
8. C109×#2033C2semidirect
9. C109×#1895C2semidirect
10. C109×#1870C2semidirect
11. C109×#1864C2semidirect
12. C109×#1862C2semidirect
13. C109×#1786C2semidirect
14. C109×#1786C2semidirect
15. C109×#1786C2semidirect
19. C22×M16×C109C22semidirect
30. C2×#117×C109C22semidirect
32. C2×#107×C109C22semidirect
33. C2×#106×C109C22semidirect
39. C2×#102×C109C22semidirect
40. C2×#102×C109C22semidirect
41. C2×#102×C109C22semidirect
42. C2×#102×C109C22semidirect
43. C2×#102×C109C22semidirect
44. C2×#102×C109C22semidirect
45. C2×#102×C109C22semidirect
46. C2×#102×C109C22semidirect
47. C2×C22⋊C8×C109C22semidirect
48. C2×C22⋊C8×C109C22semidirect
49. C2×C22⋊C8×C109C22semidirect
52. #389×C109C22semidirect
53. #389×C109C22semidirect
56. #380×C109C22semidirect
57. #380×C109C22semidirect
58. #380×C109C22semidirect
59. #340×C109C22semidirect
60. #340×C109C22semidirect
61. #336×C109C22semidirect
62. #336×C109C22semidirect
458. #24044C109direct (N × H)
472. C2×#482C2×C109semidirect
473. C2×#418C2×C109semidirect
474. #2485C2×C109semidirect
475. #2041C2×C109semidirect
476. #2041C2×C109semidirect
477. #2034C2×C109semidirect
478. #2033C2×C109semidirect
479. #1895C2×C109semidirect
480. #1870C2×C109semidirect
481. #1864C2×C109semidirect
482. #1862C2×C109semidirect
483. #1786C2×C109semidirect
484. #1786C2×C109semidirect
485. #1786C2×C109semidirect
486. C109#24044direct (N × H)
490. C22×M16C22×C109semidirect
501. C2×#117C22×C109semidirect
503. C2×#107C22×C109semidirect
504. C2×#106C22×C109semidirect
510. C2×#102C22×C109semidirect
511. C2×#102C22×C109semidirect
512. C2×#102C22×C109semidirect
513. C2×#102C22×C109semidirect
514. C2×#102C22×C109semidirect
515. C2×#102C22×C109semidirect
516. C2×#102C22×C109semidirect
517. C2×#102C22×C109semidirect
518. C2×C22⋊C8C22×C109semidirect
519. C2×C22⋊C8C22×C109semidirect
520. C2×C22⋊C8C22×C109semidirect
523. #389C22×C109semidirect
524. #389C22×C109semidirect
527. #380C22×C109semidirect
528. #380C22×C109semidirect
529. #380C22×C109semidirect
530. #340C22×C109semidirect
531. #340C22×C109semidirect
532. #336C22×C109semidirect
533. #336C22×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×#482×C1092
C2×#418×C1092
C109×#24852
C109×#20412
C109×#20342
C109×#20332
C109×#18952
C109×#18702
C109×#18642
C109×#18622
C109×#17862
#24044109