Finite Group Databasebeta

← C109×#25164 #42143158

Subgroups — C109×#25164 #42143158

Order 27904.

1296 conjugacy classes of subgroups.

The subgroup lattice has 856 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#463×C109C211yesmaximal, characteristic, complemented
2C2×#450×C109C211yesmaximal, characteristic, complemented
3C2×#447×C109C211yesmaximal, characteristic
4C2×#440×C109C211yesmaximal, characteristic, complemented
5C109×#2426C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C109C211yesmaximal, characteristic, complemented
7C109×#2067C211yesmaximal, characteristic, complemented
8C109×#2035C211yesmaximal, characteristic, complemented
9C109×#2033C211yesmaximal, characteristic, complemented
10C109×#2012C211yesmaximal, characteristic, complemented
11C109×#1972C211yesmaximal, characteristic, complemented
12C109×#1924C211yesmaximal, characteristic, complemented
13C109×#1880C211yesmaximal, characteristic, complemented
14C109×#1879C211yesmaximal, characteristic, complemented
15C109×#1864C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C22×SD16×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C22×D8×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic
21C2×#124×C109C2211yescharacteristic, complemented
22C2×C22⋊Q8×C109C2211yescharacteristic
23C2×#121×C109C2211yescharacteristic
24C2×C4×Q8×C109C2211yescharacteristic, complemented
25C2×C4×D4×C109C2211yescharacteristic
26C2×C4×D4×C109C2211yescharacteristic
27C22×C22⋊C4×C109—21no—
28#463×C109—24no—
29#450×C109—24no—
30#447×C109—24no—
31#440×C109—24no—
32C2×#107×C109C2211yescharacteristic, complemented
33C2×#106×C109C2211yescharacteristic, complemented
34C2×C4⋊C8×C109C2211yescharacteristic, complemented
35C2×#103×C109C2211yescharacteristic, complemented
36C2×#103×C109C2211yescharacteristic, complemented
37C2×#102×C109C2211yescharacteristic
38C2×#102×C109C2211yescharacteristic
39C2×#102×C109C2211yescharacteristic
40C2×#102×C109C2211yescharacteristic
41C2×#102×C109C2211yescharacteristic, complemented
42C2×#102×C109C2211yescharacteristic, complemented
43C2×C22⋊C8×C109C2211yescharacteristic
44C2×C22⋊C8×C109C2211yescharacteristic
45C2×#97×C109C2211yescharacteristic, complemented
46#396×C109—21no—
47#394×C109—21no—
48#390×C109—21no—
49#390×C109C2211yescharacteristic
50#390×C109C2211yescharacteristic
51#390×C109C2211yescharacteristic, complemented
52#389×C109C2211yescharacteristic, complemented
53#388×C109—21no—
54#386×C109—21no—
55#386×C109—21no—
56#380×C109C2211yescharacteristic
57#379×C109—21no—
58C4×C22⋊C4×C109C2211yescharacteristic
59#340×C109C2211yescharacteristic, complemented
60#340×C109C2211yescharacteristic, complemented
61#336×C109C2211yescharacteristic, complemented
62#336×C109C2211yescharacteristic, complemented
63C25×C109—21no—
64C22×Q8×C109C2311yescharacteristic
65C22×D4×C109—22no—
66C22×D4×C109—22no—
67C22×D4×C109—22no—
68C22×D4×C109—22no—
69C22×D4×C109—21no—
70C22×D4×C109—21no—
71C22×D4×C109—41no—
72C22×D4×C109—41no—
73C22×D4×C109C2311yescharacteristic
74C22×D4×C109C2311yescharacteristic
75C22×D4×C109C2311yescharacteristic
76C23×C4×C109—21no—
77C23×C4×C109—21no—
78C23×C4×C109C2311yescharacteristic
79C2×SD16×C109—22no—
80C2×SD16×C109—22no—
81C2×SD16×C109—22no—
82C2×SD16×C109—22no—
83C2×SD16×C109—41no—
84C2×SD16×C109D414yescomplemented
85C2×D8×C109—22no—
86C2×D8×C109—22no—
87C2×D8×C109—22no—
88C2×D8×C109—22no—
89C2×D8×C109—22no—
90C2×D8×C109—41no—
91C22×C8×C109C2311yescharacteristic
92C22×C8×C109C2311yescharacteristic
93C22×C8×C109C2311yescharacteristic
94C22×C8×C109C2311yescharacteristic
95#124×C109—22no—
96#124×C109—41no—
97C22⋊Q8×C109—22no—
98C22⋊Q8×C109—41no—
99#121×C109—22no—
100#121×C109—41no—
101C4×Q8×C109—22no—
102C4×Q8×C109—41no—
103C4×D4×C109—22no—
104C4×D4×C109—22no—
105C4×D4×C109—41no—
106C4×D4×C109—41no—
107C2×C4⋊C4×C109—21no—
108C2×C4⋊C4×C109—21no—
109C2×C4⋊C4×C109—21no—
110C2×C4⋊C4×C109C2311yescharacteristic
111C2×C4⋊C4×C109C2311yescharacteristic
112C2×C4⋊C4×C109C2311yescharacteristic
113C2×C4⋊C4×C109C2311yescharacteristic
114C2×C22⋊C4×C109—21no—
115C2×C22⋊C4×C109—21no—
116C2×C22⋊C4×C109—21no—
117C2×C22⋊C4×C109—21no—
118C2×C22⋊C4×C109—21no—
119C2×C22⋊C4×C109—21no—
120C2×C22⋊C4×C109—21no—
121C2×C22⋊C4×C109—21no—
122C2×C22⋊C4×C109—21no—
123C2×C22⋊C4×C109—21no—
124C2×C22⋊C4×C109—21no—
125C2×C22⋊C4×C109—21no—
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109—44no—
128C2×C22⋊C4×C109D411yescharacteristic
129C2×C22⋊C4×C109D411yescharacteristic
130C2×C42×C109—21no—
131C2×C42×C109C2311yescharacteristic
132C2×C42×C109C2311yescharacteristic
133#107×C109—22no—
134#106×C109—41no—
135C4⋊C8×C109—22no—
136#103×C109—22no—
137#103×C109—22no—
138#102×C109—22no—
139#102×C109—22no—
140#102×C109—22no—
141#102×C109—22no—
142#102×C109—41no—
143#102×C109D414yes—
144C22⋊C8×C109—22no—
145C22⋊C8×C109—22no—
146#97×C109—22no—
147#95×C109—21no—
148#95×C109—21no—
149#95×C109D411yescharacteristic
150#95×C109D411yescharacteristic
151C24×C109—21no—
152C24×C109—24no—
153C24×C109—21no—
154C24×C109—21no—
155C24×C109—42no—
156C24×C109—42no—
157C24×C109—42no—
158C24×C109—42no—
159C24×C109—81no—
160C24×C109—81no—
161C24×C109C2×D411yescharacteristic
162C2×Q8×C109—21no—
163C2×Q8×C109—21no—
164C2×Q8×C109—21no—
165C2×Q8×C109—21no—
166C2×Q8×C109—21no—
167C2×Q8×C109C2×D412yes—
168C2×D4×C109—24no—
169C2×D4×C109—21no—
170C2×D4×C109—21no—
171C2×D4×C109—21no—
172C2×D4×C109—21no—
173C2×D4×C109—21no—
174C2×D4×C109—21no—
175C2×D4×C109—21no—
176C2×D4×C109—21no—
177C2×D4×C109—21no—
178C2×D4×C109—21no—
179C2×D4×C109—21no—
180C2×D4×C109—21no—
181C2×D4×C109—21no—
182C2×D4×C109—21no—
183C2×D4×C109—42no—
184C2×D4×C109—42no—
185C2×D4×C109—42no—
186C2×D4×C109—44no—
187C2×D4×C109—44no—
188C2×D4×C109—44no—
189C2×D4×C109—44no—
190C2×D4×C109—42no—
191C2×D4×C109—81no—
192C2×D4×C109C2×D412yes—
193C2×D4×C109C2×D412yes—
194C2×D4×C109#4112yes—
195C2×D4×C109#4112yes—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109—21no—
199C22×C4×C109—21no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—21no—
206C22×C4×C109—21no—
207C22×C4×C109—42no—
208C22×C4×C109—42no—
209C22×C4×C109—42no—
210C22×C4×C109—42no—
211C22×C4×C109—81no—
212C22×C4×C109—81no—
213C22×C4×C109C2×D411yescharacteristic
214C22×C4×C109C2×D411yescharacteristic
215C22×C4×C109C2×D411yescharacteristic
216C22×C4×C109C2×D411yescharacteristic
217C22×C4×C109C2×D411yescharacteristic
218C22×C4×C109C2411yescharacteristic
219SD16×C109—28no—
220SD16×C109—44no—
221D8×C109—44no—
222D8×C109—44no—
223C2×C8×C109—21no—
224C2×C8×C109—21no—
225C2×C8×C109—21no—
226C2×C8×C109—21no—
227C2×C8×C109—21no—
228C2×C8×C109—21no—
229C2×C8×C109—21no—
230C2×C8×C109—21no—
231C2×C8×C109—21no—
232C2×C8×C109—21no—
233C2×C8×C109C2×D412yes—
234C2×C8×C109C2×D412yes—
235C4⋊C4×C109—21no—
236C4⋊C4×C109—21no—
237C4⋊C4×C109—21no—
238C4⋊C4×C109—21no—
239C4⋊C4×C109—21no—
240C4⋊C4×C109—21no—
241C4⋊C4×C109—21no—
242C4⋊C4×C109—42no—
243C4⋊C4×C109—42no—
244C4⋊C4×C109—81no—
245C4⋊C4×C109C2×D412yes—
246C22⋊C4×C109—22no—
247C22⋊C4×C109—41no—
248C22⋊C4×C109—42no—
249C22⋊C4×C109—42no—
250C22⋊C4×C109—42no—
251C22⋊C4×C109—42no—
252C22⋊C4×C109—42no—
253C22⋊C4×C109—42no—
254C22⋊C4×C109—42no—
255C22⋊C4×C109—42no—
256C22⋊C4×C109—42no—
257C22⋊C4×C109—42no—
258C22⋊C4×C109—81no—
259C22⋊C4×C109—81no—
260C22⋊C4×C109—81no—
261C42×C109—21no—
262C42×C109—21no—
263C42×C109—21no—
264C42×C109—21no—
265C42×C109—42no—
266C23×C109—21no—
267C23×C109—22no—
268C23×C109—21no—
269C23×C109—22no—
270C23×C109—22no—
271C23×C109—21no—
272C23×C109—21no—
273C23×C109—21no—
274C23×C109—21no—
275C23×C109—22no—
276C23×C109—48no—
277C23×C109—48no—
278C23×C109—41no—
279C23×C109—41no—
280C23×C109—41no—
281C23×C109—41no—
282C23×C109—41no—
283C23×C109—41no—
284C23×C109—41no—
285C23×C109—41no—
286C23×C109—41no—
287C23×C109—41no—
288C23×C109—41no—
289C23×C109—41no—
290C23×C109—41no—
291C23×C109—41no—
292C23×C109—41no—
293C23×C109—41no—
294C23×C109—41no—
295C23×C109—84no—
296C23×C109—84no—
297C23×C109—84no—
298C23×C109—84no—
299C23×C109—84no—
300C23×C109AGL(1,ℤ/8)12yes—
301C23×C109C22×D411yescharacteristic
302Q8×C109—22no—
303Q8×C109—22no—
304Q8×C109—41no—
305Q8×C109—41no—
306D4×C109—22no—
307D4×C109—22no—
308D4×C109—22no—
309D4×C109—22no—
310D4×C109—22no—
311D4×C109—48no—
312D4×C109—41no—
313D4×C109—41no—
314D4×C109—41no—
315D4×C109—41no—
316D4×C109—41no—
317D4×C109—41no—
318D4×C109—84no—
319D4×C109#12114yes—
320C2×C4×C109—21no—
321C2×C4×C109—21no—
322C2×C4×C109—21no—
323C2×C4×C109—21no—
324C2×C4×C109—21no—
325C2×C4×C109—22no—
326C2×C4×C109—22no—
327C2×C4×C109—21no—
328C2×C4×C109—21no—
329C2×C4×C109—21no—
330C2×C4×C109—21no—
331C2×C4×C109—21no—
332C2×C4×C109—21no—
333C2×C4×C109—21no—
334C2×C4×C109—21no—
335C2×C4×C109—21no—
336C2×C4×C109—21no—
337C2×C4×C109—41no—
338C2×C4×C109—41no—
339C2×C4×C109—41no—
340C2×C4×C109—41no—
341C2×C4×C109—41no—
342C2×C4×C109—41no—
343C2×C4×C109—41no—
344C2×C4×C109—41no—
345C2×C4×C109—41no—
346C2×C4×C109—41no—
347C2×C4×C109—41no—
348C2×C4×C109—41no—
349C2×C4×C109—41no—
350C2×C4×C109—41no—
351C2×C4×C109—41no—
352C2×C4×C109—41no—
353C2×C4×C109—41no—
354C2×C4×C109—84no—
355C2×C4×C109—84no—
356C2×C4×C109C22×D411yescharacteristic
357C2×C4×C109C22×D411yescharacteristic
358C2×C4×C109C2×#4111yescharacteristic
359C2×C4×C109C2×#4111yescharacteristic
360C2×C4×C109H(5,𝔽2)11yescharacteristic
361C2×C4×C109H(5,𝔽2)11yescharacteristic
362C8×C109—22no—
363C8×C109—22no—
364C8×C109—41no—
365C8×C109—41no—
366C22×C109—22no—
367C22×C109—24no—
368C22×C109—22no—
369C22×C109—22no—
370C22×C109—42no—
371C22×C109—41no—
372C22×C109—42no—
373C22×C109—41no—
374C22×C109—42no—
375C22×C109—42no—
376C22×C109—41no—
377C22×C109—42no—
378C22×C109—41no—
379C22×C109—42no—
380C22×C109—42no—
381C22×C109—42no—
382C22×C109—42no—
383C22×C109—816no—
384C22×C109—81no—
385C22×C109—81no—
386C22×C109—81no—
387C22×C109—81no—
388C22×C109—81no—
389C22×C109—81no—
390C22×C109—81no—
391C22×C109—81no—
392C22×C109—81no—
393C22×C109—81no—
394C22×C109—81no—
395C22×C109#52511yescharacteristic
396C22×C109D4211yescharacteristic
397C22×C109D4211yescharacteristic
398C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
399C22×C109#57511yescharacteristic
400C22×C109#57611yescharacteristic
401C22×C109#57711yescharacteristic
402C4×C109—41no—
403C4×C109—42no—
404C4×C109—41no—
405C4×C109—42no—
406C4×C109—41no—
407C4×C109—41no—
408C4×C109—41no—
409C4×C109—81no—
410C4×C109—81no—
411C4×C109—81no—
412C4×C109C2×#12111yescharacteristic
413C4×C109#53811yescharacteristic
414C4×C109#54611yescharacteristic
415C4×C109#54611yescharacteristic
416#25164C10911yesmaximal, characteristic, direct product factor, Sylow
417C2×C109—42no—
418C2×C109—44no—
419C2×C109—82no—
420C2×C109—161no—
421C2×C109#242411yescharacteristic
422C2×C109#311411yescharacteristic
423C2×C109#311811yescharacteristic
424C2×C109#326411yescharacteristic
425C2×C109#326511yescharacteristic
426C2×C109#326811yescharacteristic
427C2×C109#327511yescharacteristic
428C2×#463C2×C10911yescharacteristic, complemented
429C2×#450C2×C10911yescharacteristic, complemented
430C2×#447C2×C10911yescharacteristic
431C2×#440C2×C10911yescharacteristic, complemented
432#2426C2×C10911yescharacteristic, complemented
433D4×C22⋊C4C2×C10911yescharacteristic, complemented
434#2067C2×C10911yescharacteristic, complemented
435#2035C2×C10911yescharacteristic, complemented
436#2033C2×C10911yescharacteristic, complemented
437#2012C2×C10911yescharacteristic, complemented
438#1972C2×C10911yescharacteristic, complemented
439#1924C2×C10911yescharacteristic, complemented
440#1880C2×C10911yescharacteristic, complemented
441#1879C2×C10911yescharacteristic, complemented
442#1864C2×C10911yescharacteristic, complemented
443C109#2516411yescharacteristic, direct product factor, Sylow
444C23×D4C22×C10911yescharacteristic
445C22×SD16C22×C10911yescharacteristic
446C22×SD16C22×C10911yescharacteristic
447C22×D8C22×C10911yescharacteristic
448C22×D8C22×C10911yescharacteristic
449C2×#124C22×C10911yescharacteristic, complemented
450C2×C22⋊Q8C22×C10911yescharacteristic
451C2×#121C22×C10911yescharacteristic
452C2×C4×Q8C22×C10911yescharacteristic, complemented
453C2×C4×D4C22×C10911yescharacteristic
454C2×C4×D4C22×C10911yescharacteristic
455C22×C22⋊C4—21no—
456#463—24no—
457#450—24no—
458#447—24no—
459#440—24no—
460C2×#107C22×C10911yescharacteristic, complemented
461C2×#106C22×C10911yescharacteristic, complemented
462C2×C4⋊C8C22×C10911yescharacteristic, complemented
463C2×#103C22×C10911yescharacteristic, complemented
464C2×#103C22×C10911yescharacteristic, complemented
465C2×#102C22×C10911yescharacteristic
466C2×#102C22×C10911yescharacteristic
467C2×#102C22×C10911yescharacteristic
468C2×#102C22×C10911yescharacteristic
469C2×#102C22×C10911yescharacteristic, complemented
470C2×#102C22×C10911yescharacteristic, complemented
471C2×C22⋊C8C22×C10911yescharacteristic
472C2×C22⋊C8C22×C10911yescharacteristic
473C2×#97C22×C10911yescharacteristic, complemented
474#396—21no—
475#394—21no—
476#390—21no—
477#390C22×C10911yescharacteristic
478#390C22×C10911yescharacteristic
479#390C22×C10911yescharacteristic, complemented
480#389C22×C10911yescharacteristic, complemented
481#388—21no—
482#386—21no—
483#386—21no—
484#380C22×C10911yescharacteristic
485#379—21no—
486C4×C22⋊C4C22×C10911yescharacteristic
487#340C22×C10911yescharacteristic, complemented
488#340C22×C10911yescharacteristic, complemented
489#336C22×C10911yescharacteristic, complemented
490#336C22×C10911yescharacteristic, complemented
491C25—21no—
492C22×Q8C23×C10911yescharacteristic
493C22×D4—22no—
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—21no—
498C22×D4—21no—
499C22×D4—41no—
500C22×D4—41no—
501C22×D4C23×C10911yescharacteristic
502C22×D4C23×C10911yescharacteristic
503C22×D4C23×C10911yescharacteristic
504C23×C4—21no—
505C23×C4—21no—
506C23×C4C23×C10911yescharacteristic
507C2×SD16—22no—
508C2×SD16—22no—
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—41no—
512C2×SD16D4×C10914yescomplemented
513C2×D8—22no—
514C2×D8—22no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—41no—
519C22×C8C23×C10911yescharacteristic
520C22×C8C23×C10911yescharacteristic
521C22×C8C23×C10911yescharacteristic
522C22×C8C23×C10911yescharacteristic
523#124—22no—
524#124—41no—
525C22⋊Q8—22no—
526C22⋊Q8—41no—
527#121—22no—
528#121—41no—
529C4×Q8—22no—
530C4×Q8—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—41no—
534C4×D4—41no—
535C2×C4⋊C4—21no—
536C2×C4⋊C4—21no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4C23×C10911yescharacteristic
539C2×C4⋊C4C23×C10911yescharacteristic
540C2×C4⋊C4C23×C10911yescharacteristic
541C2×C4⋊C4C23×C10911yescharacteristic
542C2×C22⋊C4—21no—
543C2×C22⋊C4—21no—
544C2×C22⋊C4—21no—
545C2×C22⋊C4—21no—
546C2×C22⋊C4—21no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—44no—
556C2×C22⋊C4D4×C10911yescharacteristic
557C2×C22⋊C4D4×C10911yescharacteristic
558C2×C42—21no—
559C2×C42C23×C10911yescharacteristic
560C2×C42C23×C10911yescharacteristic
561#107—22no—
562#106—41no—
563C4⋊C8—22no—
564#103—22no—
565#103—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102—41no—
571#102D4×C10914yes—
572C22⋊C8—22no—
573C22⋊C8—22no—
574#97—22no—
575#95—21no—
576#95—21no—
577#95D4×C10911yescharacteristic
578#95D4×C10911yescharacteristic
579C24—21no—
580C24—24no—
581C24—21no—
582C24—21no—
583C24—42no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—81no—
588C24—81no—
589C24C2×D4×C10911yescharacteristic
590C2×Q8—21no—
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8C2×D4×C10912yes—
596C2×D4—24no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—21no—
605C2×D4—21no—
606C2×D4—21no—
607C2×D4—21no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—21no—
611C2×D4—42no—
612C2×D4—42no—
613C2×D4—42no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C10912yes—
621C2×D4C2×D4×C10912yes—
622C2×D4#41×C10912yes—
623C2×D4#41×C10912yes—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—21no—
635C22×C4—42no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—81no—
640C22×C4—81no—
641C22×C4C2×D4×C10911yescharacteristic
642C22×C4C2×D4×C10911yescharacteristic
643C22×C4C2×D4×C10911yescharacteristic
644C22×C4C2×D4×C10911yescharacteristic
645C22×C4C2×D4×C10911yescharacteristic
646C22×C4C24×C10911yescharacteristic
647SD16—28no—
648SD16—44no—
649D8—44no—
650D8—44no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8C2×D4×C10912yes—
662C2×C8C2×D4×C10912yes—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—42no—
671C4⋊C4—42no—
672C4⋊C4—81no—
673C4⋊C4C2×D4×C10912yes—
674C22⋊C4—22no—
675C22⋊C4—41no—
676C22⋊C4—42no—
677C22⋊C4—42no—
678C22⋊C4—42no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—81no—
687C22⋊C4—81no—
688C22⋊C4—81no—
689C42—21no—
690C42—21no—
691C42—21no—
692C42—21no—
693C42—42no—
694C23—21no—
695C23—22no—
696C23—21no—
697C23—22no—
698C23—22no—
699C23—21no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—22no—
704C23—48no—
705C23—48no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—41no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—84no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23AGL(1,ℤ/8)×C10912yes—
729C23C22×D4×C10911yescharacteristic
730Q8—22no—
731Q8—22no—
732Q8—41no—
733Q8—41no—
734D4—22no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—48no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—84no—
747D4#121×C10914yes—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—22no—
754C2×C4—22no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—84no—
783C2×C4—84no—
784C2×C4C22×D4×C10911yescharacteristic
785C2×C4C22×D4×C10911yescharacteristic
786C2×C4C2×#41×C10911yescharacteristic
787C2×C4C2×#41×C10911yescharacteristic
788C2×C4H(5,𝔽2)×C10911yescharacteristic
789C2×C4H(5,𝔽2)×C10911yescharacteristic
790C8—22no—
791C8—22no—
792C8—41no—
793C8—41no—
794C22—22no—
795C22—22no—
796C22—22no—
797C22—24no—
798C22—42no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—42no—
804C22—42no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—42no—
810C22—42no—
811C22—816no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22#525×C10911yescharacteristic
824C22D42×C10911yescharacteristic
825C22D42×C10911yescharacteristic
826C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
827C22#575×C10911yescharacteristic
828C22#576×C10911yescharacteristic
829C22#577×C10911yescharacteristic
830C4—41no—
831C4—42no—
832C4—41no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—42no—
837C4—81no—
838C4—81no—
839C4—81no—
840C4C2×#121×C10911yescharacteristic
841C4#538×C10911yescharacteristic
842C4#546×C10911yescharacteristic
843C4#546×C10911yescharacteristic
844C2—42no—
845C2—44no—
846C2—82no—
847C2—161no—
848C2C109×#242411yescharacteristic
849C2C109×#311411yescharacteristic
850C2C109×#311811yescharacteristic
851C2C109×#326411yescharacteristic
852C2C109×#326511yescharacteristic
853C2C109×#326811yescharacteristic
854C2C109×#327511yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC2×#447×C109C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C4×C22⋊C4×C109 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#463×C109C2semidirect
2. C2×#450×C109C2semidirect
4. C2×#440×C109C2semidirect
5. C109×#2426C2semidirect
6. D4×C22⋊C4×C109C2semidirect
7. C109×#2067C2semidirect
8. C109×#2035C2semidirect
9. C109×#2033C2semidirect
10. C109×#2012C2semidirect
11. C109×#1972C2semidirect
12. C109×#1924C2semidirect
13. C109×#1880C2semidirect
14. C109×#1879C2semidirect
15. C109×#1864C2semidirect
21. C2×#124×C109C22semidirect
24. C2×C4×Q8×C109C22semidirect
32. C2×#107×C109C22semidirect
33. C2×#106×C109C22semidirect
34. C2×C4⋊C8×C109C22semidirect
35. C2×#103×C109C22semidirect
36. C2×#103×C109C22semidirect
41. C2×#102×C109C22semidirect
42. C2×#102×C109C22semidirect
45. C2×#97×C109C22semidirect
51. #390×C109C22semidirect
52. #389×C109C22semidirect
59. #340×C109C22semidirect
60. #340×C109C22semidirect
61. #336×C109C22semidirect
62. #336×C109C22semidirect
84. C2×SD16×C109D4semidirect
416. #25164C109direct (N × H)
428. C2×#463C2×C109semidirect
429. C2×#450C2×C109semidirect
431. C2×#440C2×C109semidirect
432. #2426C2×C109semidirect
433. D4×C22⋊C4C2×C109semidirect
434. #2067C2×C109semidirect
435. #2035C2×C109semidirect
436. #2033C2×C109semidirect
437. #2012C2×C109semidirect
438. #1972C2×C109semidirect
439. #1924C2×C109semidirect
440. #1880C2×C109semidirect
441. #1879C2×C109semidirect
442. #1864C2×C109semidirect
443. C109#25164direct (N × H)
449. C2×#124C22×C109semidirect
452. C2×C4×Q8C22×C109semidirect
460. C2×#107C22×C109semidirect
461. C2×#106C22×C109semidirect
462. C2×C4⋊C8C22×C109semidirect
463. C2×#103C22×C109semidirect
464. C2×#103C22×C109semidirect
469. C2×#102C22×C109semidirect
470. C2×#102C22×C109semidirect
473. C2×#97C22×C109semidirect
479. #390C22×C109semidirect
480. #389C22×C109semidirect
487. #340C22×C109semidirect
488. #340C22×C109semidirect
489. #336C22×C109semidirect
490. #336C22×C109semidirect
512. C2×SD16D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C1092
C2×#450×C1092
C2×#447×C1092
C2×#440×C1092
C109×#24262
D4×C22⋊C4×C1092
C109×#20672
C109×#20352
C109×#20332
C109×#20122
C109×#19722
C109×#19242
C109×#18802
C109×#18792
C109×#18642
#25164109