Finite Group Databasebeta

← C109×#22423 #42140417

Subgroups — C109×#22423 #42140417

Order 27904.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C109C211yesmaximal, characteristic
2C2×#435×C109C211yesmaximal, characteristic, complemented
3C2×#418×C109C211yesmaximal, characteristic, complemented
4C22×#102×C109C211yesmaximal, characteristic, complemented
5C109×#2352C211yesmaximal, characteristic, complemented
6C109×#1982C211yesmaximal, characteristic, complemented
7C109×#1961C211yesmaximal, characteristic, complemented
8C109×#1895C211yesmaximal, characteristic, complemented
9C109×#1893C211yesmaximal, characteristic, complemented
10C109×#1875C211yesmaximal, characteristic, complemented
11C109×#1874C211yesmaximal, characteristic, complemented
12C109×#1804C211yesmaximal, characteristic, complemented
13C109×#1786C211yesmaximal, characteristic, complemented
14C109×#1786C211yesmaximal, characteristic, complemented
15C109×#1762C211yesmaximal, characteristic, complemented
16C23×D4×C109—21no—
17C23×D4×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C22×M16×C109C2211yescharacteristic, complemented
20C23×C8×C109C2211yescharacteristic, complemented
21D42×C109—24no—
22D42×C109C418yescomplemented
23C2×#127×C109C2211yescharacteristic
24C2×#121×C109—21no—
25C2×#121×C109C2211yescharacteristic
26C2×#121×C109C2211yescharacteristic
27C2×#120×C109—21no—
28C2×#120×C109—21no—
29C2×C4×D4×C109C2211yescharacteristic
30C2×C4×D4×C109C2211yescharacteristic
31C2×#117×C109C2211yescharacteristic, complemented
32C22×C4⋊C4×C109C2211yescharacteristic, complemented
33#435×C109—24no—
34C2×C4⋊C8×C109C2211yescharacteristic, complemented
35#418×C109—24no—
36C2×#102×C109—24no—
37C2×#102×C109C2211yescharacteristic
38C2×#102×C109C2211yescharacteristic
39C2×#102×C109C2211yescharacteristic
40C2×#102×C109C2211yescharacteristic
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×#102×C109C2211yescharacteristic, complemented
48C2×#102×C109C2211yescharacteristic, complemented
49C2×C22⋊C8×C109C2211yescharacteristic, complemented
50C2×C22⋊C8×C109C2211yescharacteristic, complemented
51C2×#97×C109C2211yescharacteristic, complemented
52#388×C109—21no—
53#387×C109—21no—
54#386×C109—21no—
55#382×C109C2211yescharacteristic, complemented
56#380×C109C2211yescharacteristic, complemented
57#380×C109C2211yescharacteristic, complemented
58C4×C4⋊C4×C109C2211yescharacteristic, complemented
59C4×C22⋊C4×C109—21no—
60#340×C109C2211yescharacteristic, complemented
61#340×C109C2211yescharacteristic, complemented
62#340×C109C2211yescharacteristic, complemented
63#340×C109C2211yescharacteristic, complemented
64C25×C109—21no—
65C25×C109—21no—
66C22×D4×C109—22no—
67C22×D4×C109—22no—
68C22×D4×C109—22no—
69C22×D4×C109—22no—
70C22×D4×C109—21no—
71C22×D4×C109—21no—
72C22×D4×C109—28no—
73C22×D4×C109—21no—
74C22×D4×C109—21no—
75C22×D4×C109—21no—
76C22×D4×C109—22no—
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×C109C2×C414yes—
86C22×D4×C109C2×C414yescomplemented
87C22×D4×C109D411yescharacteristic
88C22×D4×C109C2311yescharacteristic
89C22×D4×C109C2311yescharacteristic
90C22×D4×C109C2311yescharacteristic
91C23×C4×C109—21no—
92C23×C4×C109—21no—
93C23×C4×C109C2311yescharacteristic
94C23×C4×C109C2311yescharacteristic
95C2×M16×C109—22no—
96C2×M16×C109—22no—
97C2×M16×C109—41no—
98C22×C8×C109—22no—
99C22×C8×C109—22no—
100C22×C8×C109—41no—
101C22×C8×C109C2311yescharacteristic
102C22×C8×C109C2311yescharacteristic
103C22×C8×C109C2311yescharacteristic
104C22×C8×C109C2311yescharacteristic
105#127×C109—22no—
106#127×C109C2×C414yescomplemented
107#121×C109—22no—
108#121×C109—22no—
109#121×C109—28no—
110#121×C109C2×C414yes—
111#121×C109C2×C414yescomplemented
112#120×C109—28no—
113#120×C109—28no—
114C4×D4×C109—22no—
115C4×D4×C109C2×C414yes—
116C4×D4×C109C2×C414yescomplemented
117C4×D4×C109D414yes—
118#117×C109—22no—
119#117×C109—41no—
120C2×C4⋊C4×C109—22no—
121C2×C4⋊C4×C109—21no—
122C2×C4⋊C4×C109—41no—
123C2×C4⋊C4×C109D411yescharacteristic
124C2×C4⋊C4×C109C2311yescharacteristic
125C2×C4⋊C4×C109C2311yescharacteristic
126C2×C4⋊C4×C109C2311yescharacteristic
127C2×C4⋊C4×C109C2311yescharacteristic
128C2×C4⋊C4×C109C2311yescharacteristic
129C2×C22⋊C4×C109—21no—
130C2×C22⋊C4×C109—21no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109—21no—
134C2×C22⋊C4×C109—21no—
135C2×C22⋊C4×C109D411yescharacteristic
136C2×C22⋊C4×C109D411yescharacteristic
137C2×C42×C109—21no—
138C2×C42×C109—21no—
139C2×C42×C109C2311yescharacteristic
140C4⋊C8×C109—22no—
141#102×C109—22no—
142#102×C109—22no—
143#102×C109—22no—
144#102×C109—22no—
145#102×C109—22no—
146#102×C109—22no—
147#102×C109—22no—
148#102×C109—41no—
149#102×C109—41no—
150#102×C109—41no—
151#102×C109—41no—
152#102×C109D414yescomplemented
153C22⋊C8×C109—22no—
154C22⋊C8×C109—22no—
155#97×C109—22no—
156#95×C109—21no—
157#95×C109—21no—
158#95×C109—21no—
159#95×C109—21no—
160#95×C109—21no—
161C24×C109—21no—
162C24×C109—21no—
163C24×C109—21no—
164C24×C109—24no—
165C24×C109—24no—
166C24×C109—42no—
167C24×C109—42no—
168C24×C109—42no—
169C24×C109—42no—
170C24×C109—42no—
171C24×C109—42no—
172C24×C109—42no—
173C24×C109—42no—
174C24×C109—81no—
175C24×C109—81no—
176C24×C109—81no—
177C24×C109—81no—
178C24×C109C2×D411yescharacteristic
179C24×C109C2×D411yescharacteristic
180C2×D4×C109—22no—
181C2×D4×C109—22no—
182C2×D4×C109—28no—
183C2×D4×C109—28no—
184C2×D4×C109—24no—
185C2×D4×C109—24no—
186C2×D4×C109—24no—
187C2×D4×C109—24no—
188C2×D4×C109—24no—
189C2×D4×C109—24no—
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—21no—
199C2×D4×C109—21no—
200C2×D4×C109—21no—
201C2×D4×C109—21no—
202C2×D4×C109—21no—
203C2×D4×C109—44no—
204C2×D4×C109—44no—
205C2×D4×C109—44no—
206C2×D4×C109—44no—
207C2×D4×C109—44no—
208C2×D4×C109—44no—
209C2×D4×C109—42no—
210C2×D4×C109—42no—
211C2×D4×C109—42no—
212C2×D4×C109—42no—
213C2×D4×C109—42no—
214C2×D4×C109—42no—
215C2×D4×C109—432no—
216C2×D4×C109—42no—
217C2×D4×C109—42no—
218C2×D4×C109—42no—
219C2×D4×C109—42no—
220C2×D4×C109—81no—
221C2×D4×C109—81no—
222C2×D4×C109C22⋊C414yes—
223C2×D4×C109C22×C412yes—
224C2×D4×C109C22×C412yes—
225C2×D4×C109C22×C412yes—
226C2×D4×C109C2×D412yes—
227C2×D4×C109#4112yes—
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—24no—
239C22×C4×C109—21no—
240C22×C4×C109—21no—
241C22×C4×C109—21no—
242C22×C4×C109—42no—
243C22×C4×C109—42no—
244C22×C4×C109—42no—
245C22×C4×C109—42no—
246C22×C4×C109—81no—
247C22×C4×C109C22×C412yes—
248C22×C4×C109C22×C412yes—
249C22×C4×C109C2×D411yescharacteristic
250C22×C4×C109C2×D411yescharacteristic
251C22×C4×C109C2×D411yescharacteristic
252C22×C4×C109C2×D411yescharacteristic
253C22×C4×C109C2×D412yes—
254C22×C4×C109C2×D412yes—
255C22×C4×C109C2411yescharacteristic
256M16×C109—44no—
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—21no—
268C2×C8×C109—44no—
269C2×C8×C109C2×D412yescomplemented
270C4⋊C4×C109—21no—
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—21no—
278C4⋊C4×C109—42no—
279C4⋊C4×C109C22⋊C414yes—
280C4⋊C4×C109C22×C412yes—
281C4⋊C4×C109C2×D412yescomplemented
282C22⋊C4×C109—24no—
283C22⋊C4×C109—24no—
284C22⋊C4×C109—24no—
285C22⋊C4×C109—42no—
286C22⋊C4×C109—42no—
287C22⋊C4×C109—81no—
288C22⋊C4×C109C22⋊C414yes—
289C22⋊C4×C109C22⋊C414yes—
290C42×C109—42no—
291C42×C109—81no—
292C42×C109C22×C412yes—
293C42×C109C2×D412yes—
294C23×C109—21no—
295C23×C109—21no—
296C23×C109—21no—
297C23×C109—21no—
298C23×C109—22no—
299C23×C109—21no—
300C23×C109—22no—
301C23×C109—21no—
302C23×C109—22no—
303C23×C109—21no—
304C23×C109—21no—
305C23×C109—21no—
306C23×C109—21no—
307C23×C109—22no—
308C23×C109—22no—
309C23×C109—48no—
310C23×C109—48no—
311C23×C109—48no—
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—41no—
324C23×C109—41no—
325C23×C109—41no—
326C23×C109—41no—
327C23×C109—41no—
328C23×C109—48no—
329C23×C109—84no—
330C23×C109—84no—
331C23×C109—84no—
332C23×C109—84no—
333C23×C109—84no—
334C23×C109—84no—
335C23×C109—84no—
336C23×C109—84no—
337C23×C109—84no—
338C23×C109—84no—
339C23×C109C2×C22⋊C412yes—
340C23×C109C2×C22⋊C412yes—
341C23×C109AGL(1,ℤ/8)12yes—
342C23×C109AGL(1,ℤ/8)12yes—
343C23×C109C22×D411yescharacteristic
344D4×C109—28no—
345D4×C109—22no—
346D4×C109—22no—
347D4×C109—22no—
348D4×C109—22no—
349D4×C109—22no—
350D4×C109—22no—
351D4×C109—22no—
352D4×C109—48no—
353D4×C109—48no—
354D4×C109—48no—
355D4×C109—48no—
356D4×C109—48no—
357D4×C109—41no—
358D4×C109—41no—
359D4×C109—41no—
360D4×C109—41no—
361D4×C109—84no—
362D4×C109C4×D414yes—
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—21no—
370C2×C4×C109—21no—
371C2×C4×C109—22no—
372C2×C4×C109—22no—
373C2×C4×C109—22no—
374C2×C4×C109—22no—
375C2×C4×C109—22no—
376C2×C4×C109—22no—
377C2×C4×C109—22no—
378C2×C4×C109—22no—
379C2×C4×C109—22no—
380C2×C4×C109—22no—
381C2×C4×C109—48no—
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—41no—
390C2×C4×C109—41no—
391C2×C4×C109—41no—
392C2×C4×C109—41no—
393C2×C4×C109—41no—
394C2×C4×C109—41no—
395C2×C4×C109—84no—
396C2×C4×C109C2×C22⋊C412yes—
397C2×C4×C109C2×C22⋊C412yes—
398C2×C4×C109C2×C22⋊C412yes—
399C2×C4×C109C2×C22⋊C412yes—
400C2×C4×C109C23×C411yescharacteristic
401C2×C4×C109C22×D411yescharacteristic
402C2×C4×C109C22×D411yescharacteristic
403C2×C4×C109C2×#4111yescharacteristic
404C2×C4×C109H(5,𝔽2)11yescharacteristic
405C2×C4×C109H(5,𝔽2)11yescharacteristic
406C8×C109—22no—
407C8×C109—41no—
408C8×C109—41no—
409C8×C109—41no—
410C22×C109—22no—
411C22×C109—22no—
412C22×C109—22no—
413C22×C109—22no—
414C22×C109—22no—
415C22×C109—22no—
416C22×C109—22no—
417C22×C109—24no—
418C22×C109—22no—
419C22×C109—22no—
420C22×C109—42no—
421C22×C109—42no—
422C22×C109—41no—
423C22×C109—42no—
424C22×C109—41no—
425C22×C109—42no—
426C22×C109—41no—
427C22×C109—42no—
428C22×C109—41no—
429C22×C109—42no—
430C22×C109—42no—
431C22×C109—42no—
432C22×C109—42no—
433C22×C109—42no—
434C22×C109—42no—
435C22×C109—42no—
436C22×C109—816no—
437C22×C109—816no—
438C22×C109—81no—
439C22×C109—81no—
440C22×C109—81no—
441C22×C109—81no—
442C22×C109—81no—
443C22×C109—81no—
444C22×C109—81no—
445C22×C109—81no—
446C22×C109#41814yescomplemented
447C22×C109C22×C22⋊C411yescharacteristic
448C22×C109D4211yescharacteristic
449C22×C109#54611yescharacteristic
450C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
451C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
452C22×C109#57611yescharacteristic
453C22×C109#57711yescharacteristic
454C4×C109—22no—
455C4×C109—22no—
456C4×C109—22no—
457C4×C109—22no—
458C4×C109—42no—
459C4×C109—42no—
460C4×C109—81no—
461C4×C109—81no—
462C4×C109—81no—
463C4×C109C2×C4×D411yescharacteristic
464C4×C109#51811yescharacteristic
465C4×C109D4211yescharacteristic
466C4×C109#54611yescharacteristic
467#22423C10911yesmaximal, characteristic, direct product factor, Sylow
468C2×C109—24no—
469C2×C109—42no—
470C2×C109—44no—
471C2×C109—82no—
472C2×C109—82no—
473C2×C109D4×C22⋊C411yescharacteristic
474C2×C109C2×#41811yescharacteristic
475C2×C109#289711yescharacteristic
476C2×C109#326411yescharacteristic
477C2×C109#326511yescharacteristic
478C2×C109#331011yescharacteristic
479C2×C109#331811yescharacteristic
480C2×D42C2×C10911yescharacteristic
481C2×#435C2×C10911yescharacteristic, complemented
482C2×#418C2×C10911yescharacteristic, complemented
483C22×#102C2×C10911yescharacteristic, complemented
484#2352C2×C10911yescharacteristic, complemented
485#1982C2×C10911yescharacteristic, complemented
486#1961C2×C10911yescharacteristic, complemented
487#1895C2×C10911yescharacteristic, complemented
488#1893C2×C10911yescharacteristic, complemented
489#1875C2×C10911yescharacteristic, complemented
490#1874C2×C10911yescharacteristic, complemented
491#1804C2×C10911yescharacteristic, complemented
492#1786C2×C10911yescharacteristic, complemented
493#1786C2×C10911yescharacteristic, complemented
494#1762C2×C10911yescharacteristic, complemented
495C109#2242311yescharacteristic, direct product factor, Sylow
496C23×D4—21no—
497C23×D4C22×C10911yescharacteristic
498C23×D4C22×C10911yescharacteristic
499C22×M16C22×C10911yescharacteristic, complemented
500C23×C8C22×C10911yescharacteristic, complemented
501D42—24no—
502D42C4×C10918yescomplemented
503C2×#127C22×C10911yescharacteristic
504C2×#121—21no—
505C2×#121C22×C10911yescharacteristic
506C2×#121C22×C10911yescharacteristic
507C2×#120—21no—
508C2×#120—21no—
509C2×C4×D4C22×C10911yescharacteristic
510C2×C4×D4C22×C10911yescharacteristic
511C2×#117C22×C10911yescharacteristic, complemented
512C22×C4⋊C4C22×C10911yescharacteristic, complemented
513#435—24no—
514C2×C4⋊C8C22×C10911yescharacteristic, complemented
515#418—24no—
516C2×#102—24no—
517C2×#102C22×C10911yescharacteristic
518C2×#102C22×C10911yescharacteristic
519C2×#102C22×C10911yescharacteristic
520C2×#102C22×C10911yescharacteristic
521C2×#102C22×C10911yescharacteristic, complemented
522C2×#102C22×C10911yescharacteristic, complemented
523C2×#102C22×C10911yescharacteristic, complemented
524C2×#102C22×C10911yescharacteristic, complemented
525C2×#102C22×C10911yescharacteristic, complemented
526C2×#102C22×C10911yescharacteristic, complemented
527C2×#102C22×C10911yescharacteristic, complemented
528C2×#102C22×C10911yescharacteristic, complemented
529C2×C22⋊C8C22×C10911yescharacteristic, complemented
530C2×C22⋊C8C22×C10911yescharacteristic, complemented
531C2×#97C22×C10911yescharacteristic, complemented
532#388—21no—
533#387—21no—
534#386—21no—
535#382C22×C10911yescharacteristic, complemented
536#380C22×C10911yescharacteristic, complemented
537#380C22×C10911yescharacteristic, complemented
538C4×C4⋊C4C22×C10911yescharacteristic, complemented
539C4×C22⋊C4—21no—
540#340C22×C10911yescharacteristic, complemented
541#340C22×C10911yescharacteristic, complemented
542#340C22×C10911yescharacteristic, complemented
543#340C22×C10911yescharacteristic, complemented
544C25—21no—
545C25—21no—
546C22×D4—22no—
547C22×D4—22no—
548C22×D4—22no—
549C22×D4—22no—
550C22×D4—21no—
551C22×D4—21no—
552C22×D4—28no—
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—21no—
559C22×D4—41no—
560C22×D4—41no—
561C22×D4—41no—
562C22×D4—41no—
563C22×D4—44no—
564C22×D4—44no—
565C22×D4C2×C4×C10914yes—
566C22×D4C2×C4×C10914yescomplemented
567C22×D4D4×C10911yescharacteristic
568C22×D4C23×C10911yescharacteristic
569C22×D4C23×C10911yescharacteristic
570C22×D4C23×C10911yescharacteristic
571C23×C4—21no—
572C23×C4—21no—
573C23×C4C23×C10911yescharacteristic
574C23×C4C23×C10911yescharacteristic
575C2×M16—22no—
576C2×M16—22no—
577C2×M16—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C10911yescharacteristic
582C22×C8C23×C10911yescharacteristic
583C22×C8C23×C10911yescharacteristic
584C22×C8C23×C10911yescharacteristic
585#127—22no—
586#127C2×C4×C10914yescomplemented
587#121—22no—
588#121—22no—
589#121—28no—
590#121C2×C4×C10914yes—
591#121C2×C4×C10914yescomplemented
592#120—28no—
593#120—28no—
594C4×D4—22no—
595C4×D4C2×C4×C10914yes—
596C4×D4C2×C4×C10914yescomplemented
597C4×D4D4×C10914yes—
598#117—22no—
599#117—41no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—21no—
602C2×C4⋊C4—41no—
603C2×C4⋊C4D4×C10911yescharacteristic
604C2×C4⋊C4C23×C10911yescharacteristic
605C2×C4⋊C4C23×C10911yescharacteristic
606C2×C4⋊C4C23×C10911yescharacteristic
607C2×C4⋊C4C23×C10911yescharacteristic
608C2×C4⋊C4C23×C10911yescharacteristic
609C2×C22⋊C4—21no—
610C2×C22⋊C4—21no—
611C2×C22⋊C4—21no—
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4D4×C10911yescharacteristic
616C2×C22⋊C4D4×C10911yescharacteristic
617C2×C42—21no—
618C2×C42—21no—
619C2×C42C23×C10911yescharacteristic
620C4⋊C8—22no—
621#102—22no—
622#102—22no—
623#102—22no—
624#102—22no—
625#102—22no—
626#102—22no—
627#102—22no—
628#102—41no—
629#102—41no—
630#102—41no—
631#102—41no—
632#102D4×C10914yescomplemented
633C22⋊C8—22no—
634C22⋊C8—22no—
635#97—22no—
636#95—21no—
637#95—21no—
638#95—21no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—24no—
645C24—24no—
646C24—42no—
647C24—42no—
648C24—42no—
649C24—42no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24—81no—
657C24—81no—
658C24C2×D4×C10911yescharacteristic
659C24C2×D4×C10911yescharacteristic
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—24no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—44no—
686C2×D4—44no—
687C2×D4—44no—
688C2×D4—44no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—432no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4C22⋊C4×C10914yes—
703C2×D4C22×C4×C10912yes—
704C2×D4C22×C4×C10912yes—
705C2×D4C22×C4×C10912yes—
706C2×D4C2×D4×C10912yes—
707C2×D4#41×C10912yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4—81no—
727C22×C4C22×C4×C10912yes—
728C22×C4C22×C4×C10912yes—
729C22×C4C2×D4×C10911yescharacteristic
730C22×C4C2×D4×C10911yescharacteristic
731C22×C4C2×D4×C10911yescharacteristic
732C22×C4C2×D4×C10911yescharacteristic
733C22×C4C2×D4×C10912yes—
734C22×C4C2×D4×C10912yes—
735C22×C4C24×C10911yescharacteristic
736M16—44no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—44no—
749C2×C8C2×D4×C10912yescomplemented
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—42no—
759C4⋊C4C22⋊C4×C10914yes—
760C4⋊C4C22×C4×C10912yes—
761C4⋊C4C2×D4×C10912yescomplemented
762C22⋊C4—24no—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—81no—
768C22⋊C4C22⋊C4×C10914yes—
769C22⋊C4C22⋊C4×C10914yes—
770C42—42no—
771C42—81no—
772C42C22×C4×C10912yes—
773C42C2×D4×C10912yes—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—22no—
788C23—22no—
789C23—48no—
790C23—48no—
791C23—48no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—48no—
809C23—84no—
810C23—84no—
811C23—84no—
812C23—84no—
813C23—84no—
814C23—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23C2×C22⋊C4×C10912yes—
820C23C2×C22⋊C4×C10912yes—
821C23AGL(1,ℤ/8)×C10912yes—
822C23AGL(1,ℤ/8)×C10912yes—
823C23C22×D4×C10911yescharacteristic
824D4—28no—
825D4—22no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—22no—
832D4—48no—
833D4—48no—
834D4—48no—
835D4—48no—
836D4—48no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—41no—
841D4—84no—
842D4C4×D4×C10914yes—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—21no—
847C2×C4—21no—
848C2×C4—21no—
849C2×C4—21no—
850C2×C4—21no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—48no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—84no—
876C2×C4C2×C22⋊C4×C10912yes—
877C2×C4C2×C22⋊C4×C10912yes—
878C2×C4C2×C22⋊C4×C10912yes—
879C2×C4C2×C22⋊C4×C10912yes—
880C2×C4C23×C4×C10911yescharacteristic
881C2×C4C22×D4×C10911yescharacteristic
882C2×C4C22×D4×C10911yescharacteristic
883C2×C4C2×#41×C10911yescharacteristic
884C2×C4H(5,𝔽2)×C10911yescharacteristic
885C2×C4H(5,𝔽2)×C10911yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—22no—
899C22—22no—
900C22—41no—
901C22—42no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—42no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—816no—
917C22—816no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22#418×C10914yescomplemented
927C22C22×C22⋊C4×C10911yescharacteristic
928C22D42×C10911yescharacteristic
929C22#546×C10911yescharacteristic
930C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
931C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
932C22#576×C10911yescharacteristic
933C22#577×C10911yescharacteristic
934C4—22no—
935C4—22no—
936C4—22no—
937C4—22no—
938C4—42no—
939C4—42no—
940C4—81no—
941C4—81no—
942C4—81no—
943C4C2×C4×D4×C10911yescharacteristic
944C4#518×C10911yescharacteristic
945C4D42×C10911yescharacteristic
946C4#546×C10911yescharacteristic
947C2—24no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—82no—
952C2D4×C22⋊C4×C10911yescharacteristic
953C2C2×#418×C10911yescharacteristic
954C2C109×#289711yescharacteristic
955C2C109×#326411yescharacteristic
956C2C109×#326511yescharacteristic
957C2C109×#331011yescharacteristic
958C2C109×#331811yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutatorC2×C4C23×C4×C109
Frattini, cosocleC22×C4C24×C109
prime radicalC2×D42×C109C2
LCSG ▷ C2×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×#435×C109C2semidirect
3. C2×#418×C109C2semidirect
4. C22×#102×C109C2semidirect
5. C109×#2352C2semidirect
6. C109×#1982C2semidirect
7. C109×#1961C2semidirect
8. C109×#1895C2semidirect
9. C109×#1893C2semidirect
10. C109×#1875C2semidirect
11. C109×#1874C2semidirect
12. C109×#1804C2semidirect
13. C109×#1786C2semidirect
14. C109×#1786C2semidirect
15. C109×#1762C2semidirect
19. C22×M16×C109C22semidirect
20. C23×C8×C109C22semidirect
22. D42×C109C4semidirect
31. C2×#117×C109C22semidirect
32. C22×C4⋊C4×C109C22semidirect
34. C2×C4⋊C8×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×#102×C109C22semidirect
48. C2×#102×C109C22semidirect
49. C2×C22⋊C8×C109C22semidirect
50. C2×C22⋊C8×C109C22semidirect
51. C2×#97×C109C22semidirect
55. #382×C109C22semidirect
56. #380×C109C22semidirect
57. #380×C109C22semidirect
58. C4×C4⋊C4×C109C22semidirect
60. #340×C109C22semidirect
61. #340×C109C22semidirect
62. #340×C109C22semidirect
63. #340×C109C22semidirect
86. C22×D4×C109C2×C4semidirect
106. #127×C109C2×C4semidirect
111. #121×C109C2×C4semidirect
116. C4×D4×C109C2×C4semidirect
152. #102×C109D4semidirect
269. C2×C8×C109C2×D4semidirect
281. C4⋊C4×C109C2×D4semidirect
446. C22×C109#418semidirect
467. #22423C109direct (N × H)
481. C2×#435C2×C109semidirect
482. C2×#418C2×C109semidirect
483. C22×#102C2×C109semidirect
484. #2352C2×C109semidirect
485. #1982C2×C109semidirect
486. #1961C2×C109semidirect
487. #1895C2×C109semidirect
488. #1893C2×C109semidirect
489. #1875C2×C109semidirect
490. #1874C2×C109semidirect
491. #1804C2×C109semidirect
492. #1786C2×C109semidirect
493. #1786C2×C109semidirect
494. #1762C2×C109semidirect
495. C109#22423direct (N × H)
499. C22×M16C22×C109semidirect
500. C23×C8C22×C109semidirect
502. D42C4×C109semidirect
511. C2×#117C22×C109semidirect
512. C22×C4⋊C4C22×C109semidirect
514. C2×C4⋊C8C22×C109semidirect
521. C2×#102C22×C109semidirect
522. C2×#102C22×C109semidirect
523. C2×#102C22×C109semidirect
524. C2×#102C22×C109semidirect
525. C2×#102C22×C109semidirect
526. C2×#102C22×C109semidirect
527. C2×#102C22×C109semidirect
528. C2×#102C22×C109semidirect
529. C2×C22⋊C8C22×C109semidirect
530. C2×C22⋊C8C22×C109semidirect
531. C2×#97C22×C109semidirect
535. #382C22×C109semidirect
536. #380C22×C109semidirect
537. #380C22×C109semidirect
538. C4×C4⋊C4C22×C109semidirect
540. #340C22×C109semidirect
541. #340C22×C109semidirect
542. #340C22×C109semidirect
543. #340C22×C109semidirect
566. C22×D4C2×C4×C109semidirect
586. #127C2×C4×C109semidirect
591. #121C2×C4×C109semidirect
596. C4×D4C2×C4×C109semidirect
632. #102D4×C109semidirect
749. C2×C8C2×D4×C109semidirect
761. C4⋊C4C2×D4×C109semidirect
926. C22#418×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×#435×C1092
C2×#418×C1092
C22×#102×C1092
C109×#23522
C109×#19822
C109×#19612
C109×#18952
C109×#18932
C109×#18752
C109×#18742
C109×#18042
C109×#17862
C109×#17622
#22423109