Finite Group Databasebeta

← C109×#25160 #42143154

Subgroups — C109×#25160 #42143154

Order 27904.

1316 conjugacy classes of subgroups.

The subgroup lattice has 858 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×C4×D8×C109C211yesmaximal, characteristic, complemented
5C109×#2427C211yesmaximal, characteristic, complemented
6D4×C22⋊C4×C109C211yesmaximal, characteristic, complemented
7C109×#2067C211yesmaximal, characteristic, complemented
8C109×#2036C211yesmaximal, characteristic, complemented
9C109×#2034C211yesmaximal, characteristic, complemented
10C109×#2012C211yesmaximal, characteristic, complemented
11C109×#1968C211yesmaximal, characteristic, complemented
12C109×#1923C211yesmaximal, characteristic, complemented
13C109×#1879C211yesmaximal, characteristic, complemented
14C109×#1877C211yesmaximal, 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×D4×C109C2211yescharacteristic
25C2×C4×D4×C109C2211yescharacteristic
26C2×C4×D4×C109C2211yescharacteristic, complemented
27C22×C22⋊C4×C109—21no—
28#463×C109—24no—
29#450×C109—24no—
30#447×C109—24no—
31C4×D8×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×C4×C8×C109C2211yescharacteristic, complemented
46#397×C109—21no—
47#394×C109—21no—
48#391×C109C2211yescharacteristic, complemented
49#390×C109C2211yescharacteristic
50#390×C109C2211yescharacteristic
51#389×C109C2211yescharacteristic, complemented
52#386×C109—21no—
53#386×C109—21no—
54#386×C109—21no—
55#380×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×C109—21no—
79C23×C4×C109C2311yescharacteristic
80C2×SD16×C109—22no—
81C2×SD16×C109—22no—
82C2×SD16×C109—22no—
83C2×SD16×C109—22no—
84C2×SD16×C109—22no—
85C2×SD16×C109—41no—
86C2×D8×C109—22no—
87C2×D8×C109—22no—
88C2×D8×C109—22no—
89C2×D8×C109—22no—
90C2×D8×C109—41no—
91C2×D8×C109D414yes—
92C22×C8×C109C2311yescharacteristic
93C22×C8×C109C2311yescharacteristic
94C22×C8×C109C2311yescharacteristic
95C22×C8×C109C2311yescharacteristic
96#124×C109—22no—
97#124×C109—41no—
98C22⋊Q8×C109—22no—
99C22⋊Q8×C109—41no—
100#121×C109—22no—
101#121×C109—41no—
102C4×D4×C109—22no—
103C4×D4×C109—22no—
104C4×D4×C109—22no—
105C4×D4×C109—41no—
106C4×D4×C109—41no—
107C4×D4×C109—41no—
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—44no—
127C2×C22⋊C4×C109D411yescharacteristic
128C2×C22⋊C4×C109D411yescharacteristic
129C2×C42×C109C2311yescharacteristic
130C2×C42×C109C2311yescharacteristic
131#107×C109—22no—
132#106×C109—41no—
133C4⋊C8×C109—22no—
134#103×C109—22no—
135#103×C109—41no—
136#102×C109—22no—
137#102×C109—22no—
138#102×C109—22no—
139#102×C109—22no—
140#102×C109—22no—
141#102×C109D414yescomplemented
142C22⋊C8×C109—22no—
143C22⋊C8×C109—22no—
144C4×C8×C109—22no—
145#95×C109—21no—
146#95×C109—21no—
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×C109—21no—
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—42no—
183C2×D4×C109—42no—
184C2×D4×C109—44no—
185C2×D4×C109—44no—
186C2×D4×C109—44no—
187C2×D4×C109—44no—
188C2×D4×C109—42no—
189C2×D4×C109—42no—
190C2×D4×C109—81no—
191C2×D4×C109C2×D412yes—
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—42no—
212C22×C4×C109—42no—
213C22×C4×C109—81no—
214C22×C4×C109—81no—
215C22×C4×C109—81no—
216C22×C4×C109C2×D411yescharacteristic
217C22×C4×C109C2×D411yescharacteristic
218C22×C4×C109C2×D411yescharacteristic
219C22×C4×C109C2×D411yescharacteristic
220C22×C4×C109C2×D411yescharacteristic
221C22×C4×C109C2411yescharacteristic
222SD16×C109—44no—
223SD16×C109—44no—
224D8×C109—28no—
225D8×C109—44no—
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×C109—21no—
234C2×C8×C109—21no—
235C2×C8×C109—21no—
236C2×C8×C109C2×D412yes—
237C2×C8×C109C2×D412yes—
238C4⋊C4×C109—21no—
239C4⋊C4×C109—21no—
240C4⋊C4×C109—21no—
241C4⋊C4×C109—21no—
242C4⋊C4×C109—21no—
243C4⋊C4×C109—21no—
244C4⋊C4×C109—21no—
245C4⋊C4×C109—42no—
246C4⋊C4×C109—81no—
247C4⋊C4×C109C2×D412yes—
248C22⋊C4×C109—22no—
249C22⋊C4×C109—22no—
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—42no—
259C22⋊C4×C109—42no—
260C22⋊C4×C109—81no—
261C22⋊C4×C109—81no—
262C42×C109—21no—
263C42×C109—21no—
264C42×C109—21no—
265C42×C109—21no—
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—22no—
277C23×C109—48no—
278C23×C109—48no—
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×C109#13512yes—
301C23×C109C22×D411yescharacteristic
302Q8×C109—41no—
303Q8×C109—41no—
304Q8×C109—41no—
305Q8×C109—41no—
306D4×C109—22no—
307D4×C109—22no—
308D4×C109—22no—
309D4×C109—22no—
310D4×C109—22no—
311D4×C109—22no—
312D4×C109—22no—
313D4×C109—48no—
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—21no—
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—41no—
336C2×C4×C109—41no—
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—84no—
354C2×C4×C109—84no—
355C2×C4×C109—84no—
356C2×C4×C109AGL(1,ℤ/8)12yes—
357C2×C4×C109C22×D411yescharacteristic
358C2×C4×C109C22×D411yescharacteristic
359C2×C4×C109C2×#4111yescharacteristic
360C2×C4×C109C2×#4111yescharacteristic
361C2×C4×C109H(5,𝔽2)11yescharacteristic
362C2×C4×C109H(5,𝔽2)11yescharacteristic
363C8×C109—22no—
364C8×C109—22no—
365C8×C109—41no—
366C8×C109—41no—
367C22×C109—22no—
368C22×C109—24no—
369C22×C109—22no—
370C22×C109—22no—
371C22×C109—42no—
372C22×C109—41no—
373C22×C109—42no—
374C22×C109—41no—
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—42no—
384C22×C109—42no—
385C22×C109—42no—
386C22×C109—42no—
387C22×C109—816no—
388C22×C109—81no—
389C22×C109—81no—
390C22×C109—81no—
391C22×C109—81no—
392C22×C109—81no—
393C22×C109—81no—
394C22×C109—81no—
395C22×C109—81no—
396C22×C109#52511yescharacteristic
397C22×C109D4211yescharacteristic
398C22×C109D4211yescharacteristic
399C22×C109C2×#13511yescharacteristic
400C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
401C22×C109#57611yescharacteristic
402C22×C109#57711yescharacteristic
403C4×C109—22no—
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×C109—81no—
413C4×C109C2×#12111yescharacteristic
414C4×C109#53811yescharacteristic
415C4×C109#54611yescharacteristic
416C4×C109#54611yescharacteristic
417#25160C10911yesmaximal, characteristic, direct product factor, Sylow
418C2×C109—42no—
419C2×C109—44no—
420C2×C109—82no—
421C2×C109—82no—
422C2×C109#242411yescharacteristic
423C2×C109#310511yescharacteristic
424C2×C109#311811yescharacteristic
425C2×C109#326411yescharacteristic
426C2×C109#327211yescharacteristic
427C2×C109#328011yescharacteristic
428C2×C109#328211yescharacteristic
429C2×#463C2×C10911yescharacteristic, complemented
430C2×#450C2×C10911yescharacteristic, complemented
431C2×#447C2×C10911yescharacteristic
432C2×C4×D8C2×C10911yescharacteristic, complemented
433#2427C2×C10911yescharacteristic, complemented
434D4×C22⋊C4C2×C10911yescharacteristic, complemented
435#2067C2×C10911yescharacteristic, complemented
436#2036C2×C10911yescharacteristic, complemented
437#2034C2×C10911yescharacteristic, complemented
438#2012C2×C10911yescharacteristic, complemented
439#1968C2×C10911yescharacteristic, complemented
440#1923C2×C10911yescharacteristic, complemented
441#1879C2×C10911yescharacteristic, complemented
442#1877C2×C10911yescharacteristic, complemented
443#1864C2×C10911yescharacteristic, complemented
444C109#2516011yescharacteristic, direct product factor, Sylow
445C23×D4C22×C10911yescharacteristic
446C22×SD16C22×C10911yescharacteristic
447C22×SD16C22×C10911yescharacteristic
448C22×D8C22×C10911yescharacteristic
449C22×D8C22×C10911yescharacteristic
450C2×#124C22×C10911yescharacteristic, complemented
451C2×C22⋊Q8C22×C10911yescharacteristic
452C2×#121C22×C10911yescharacteristic
453C2×C4×D4C22×C10911yescharacteristic
454C2×C4×D4C22×C10911yescharacteristic
455C2×C4×D4C22×C10911yescharacteristic, complemented
456C22×C22⋊C4—21no—
457#463—24no—
458#450—24no—
459#447—24no—
460C4×D8—24no—
461C2×#107C22×C10911yescharacteristic, complemented
462C2×#106C22×C10911yescharacteristic, complemented
463C2×C4⋊C8C22×C10911yescharacteristic, complemented
464C2×#103C22×C10911yescharacteristic, complemented
465C2×#103C22×C10911yescharacteristic, complemented
466C2×#102C22×C10911yescharacteristic
467C2×#102C22×C10911yescharacteristic
468C2×#102C22×C10911yescharacteristic
469C2×#102C22×C10911yescharacteristic
470C2×#102C22×C10911yescharacteristic, complemented
471C2×#102C22×C10911yescharacteristic, complemented
472C2×C22⋊C8C22×C10911yescharacteristic
473C2×C22⋊C8C22×C10911yescharacteristic
474C2×C4×C8C22×C10911yescharacteristic, complemented
475#397—21no—
476#394—21no—
477#391C22×C10911yescharacteristic, complemented
478#390C22×C10911yescharacteristic
479#390C22×C10911yescharacteristic
480#389C22×C10911yescharacteristic, complemented
481#386—21no—
482#386—21no—
483#386—21no—
484#380—21no—
485#380C22×C10911yescharacteristic
486#379—21no—
487C4×C22⋊C4C22×C10911yescharacteristic
488#340C22×C10911yescharacteristic, complemented
489#340C22×C10911yescharacteristic, complemented
490#336C22×C10911yescharacteristic, complemented
491#336C22×C10911yescharacteristic, complemented
492C25—21no—
493C22×Q8C23×C10911yescharacteristic
494C22×D4—22no—
495C22×D4—22no—
496C22×D4—22no—
497C22×D4—22no—
498C22×D4—21no—
499C22×D4—21no—
500C22×D4—41no—
501C22×D4—41no—
502C22×D4C23×C10911yescharacteristic
503C22×D4C23×C10911yescharacteristic
504C22×D4C23×C10911yescharacteristic
505C23×C4—21no—
506C23×C4—21no—
507C23×C4—21no—
508C23×C4C23×C10911yescharacteristic
509C2×SD16—22no—
510C2×SD16—22no—
511C2×SD16—22no—
512C2×SD16—22no—
513C2×SD16—22no—
514C2×SD16—41no—
515C2×D8—22no—
516C2×D8—22no—
517C2×D8—22no—
518C2×D8—22no—
519C2×D8—41no—
520C2×D8D4×C10914yes—
521C22×C8C23×C10911yescharacteristic
522C22×C8C23×C10911yescharacteristic
523C22×C8C23×C10911yescharacteristic
524C22×C8C23×C10911yescharacteristic
525#124—22no—
526#124—41no—
527C22⋊Q8—22no—
528C22⋊Q8—41no—
529#121—22no—
530#121—41no—
531C4×D4—22no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—41no—
535C4×D4—41no—
536C4×D4—41no—
537C2×C4⋊C4—21no—
538C2×C4⋊C4—21no—
539C2×C4⋊C4C23×C10911yescharacteristic
540C2×C4⋊C4C23×C10911yescharacteristic
541C2×C4⋊C4C23×C10911yescharacteristic
542C2×C4⋊C4C23×C10911yescharacteristic
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×C42C23×C10911yescharacteristic
559C2×C42C23×C10911yescharacteristic
560#107—22no—
561#106—41no—
562C4⋊C8—22no—
563#103—22no—
564#103—41no—
565#102—22no—
566#102—22no—
567#102—22no—
568#102—22no—
569#102—22no—
570#102D4×C10914yescomplemented
571C22⋊C8—22no—
572C22⋊C8—22no—
573C4×C8—22no—
574#95—21no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95D4×C10911yescharacteristic
579#95D4×C10911yescharacteristic
580C24—21no—
581C24—24no—
582C24—21no—
583C24—21no—
584C24—42no—
585C24—42no—
586C24—42no—
587C24—42no—
588C24—81no—
589C24—81no—
590C24C2×D4×C10911yescharacteristic
591C2×Q8—21no—
592C2×Q8—21no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×D4—24no—
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—44no—
614C2×D4—44no—
615C2×D4—44no—
616C2×D4—44no—
617C2×D4—42no—
618C2×D4—42no—
619C2×D4—81no—
620C2×D4C2×D4×C10912yes—
621C2×D4C2×D4×C10912yes—
622C2×D4C2×D4×C10912yes—
623C2×D4#41×C10912yes—
624C2×D4#41×C10912yes—
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—21no—
636C22×C4—42no—
637C22×C4—42no—
638C22×C4—42no—
639C22×C4—42no—
640C22×C4—42no—
641C22×C4—42no—
642C22×C4—81no—
643C22×C4—81no—
644C22×C4—81no—
645C22×C4C2×D4×C10911yescharacteristic
646C22×C4C2×D4×C10911yescharacteristic
647C22×C4C2×D4×C10911yescharacteristic
648C22×C4C2×D4×C10911yescharacteristic
649C22×C4C2×D4×C10911yescharacteristic
650C22×C4C24×C10911yescharacteristic
651SD16—44no—
652SD16—44no—
653D8—28no—
654D8—44no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8C2×D4×C10912yes—
666C2×C8C2×D4×C10912yes—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—42no—
675C4⋊C4—81no—
676C4⋊C4C2×D4×C10912yes—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—42no—
680C22⋊C4—42no—
681C22⋊C4—42no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—42no—
685C22⋊C4—42no—
686C22⋊C4—42no—
687C22⋊C4—42no—
688C22⋊C4—42no—
689C22⋊C4—81no—
690C22⋊C4—81no—
691C42—21no—
692C42—21no—
693C42—21no—
694C42—21no—
695C23—21no—
696C23—22no—
697C23—21no—
698C23—22no—
699C23—22no—
700C23—21no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—48no—
707C23—48no—
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—41no—
724C23—84no—
725C23—84no—
726C23—84no—
727C23—84no—
728C23—84no—
729C23#135×C10912yes—
730C23C22×D4×C10911yescharacteristic
731Q8—41no—
732Q8—41no—
733Q8—41no—
734Q8—41no—
735D4—22no—
736D4—22no—
737D4—22no—
738D4—22no—
739D4—22no—
740D4—22no—
741D4—22no—
742D4—48no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—84no—
748D4#121×C10914yes—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—22no—
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—41no—
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×C4—84no—
785C2×C4AGL(1,ℤ/8)×C10912yes—
786C2×C4C22×D4×C10911yescharacteristic
787C2×C4C22×D4×C10911yescharacteristic
788C2×C4C2×#41×C10911yescharacteristic
789C2×C4C2×#41×C10911yescharacteristic
790C2×C4H(5,𝔽2)×C10911yescharacteristic
791C2×C4H(5,𝔽2)×C10911yescharacteristic
792C8—22no—
793C8—22no—
794C8—41no—
795C8—41no—
796C22—22no—
797C22—22no—
798C22—22no—
799C22—24no—
800C22—42no—
801C22—41no—
802C22—42no—
803C22—41no—
804C22—42no—
805C22—42no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—41no—
810C22—42no—
811C22—42no—
812C22—42no—
813C22—42no—
814C22—42no—
815C22—42no—
816C22—816no—
817C22—81no—
818C22—81no—
819C22—81no—
820C22—81no—
821C22—81no—
822C22—81no—
823C22—81no—
824C22—81no—
825C22#525×C10911yescharacteristic
826C22D42×C10911yescharacteristic
827C22D42×C10911yescharacteristic
828C22C2×#135×C10911yescharacteristic
829C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
830C22#576×C10911yescharacteristic
831C22#577×C10911yescharacteristic
832C4—22no—
833C4—42no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—81no—
839C4—81no—
840C4—81no—
841C4—81no—
842C4C2×#121×C10911yescharacteristic
843C4#538×C10911yescharacteristic
844C4#546×C10911yescharacteristic
845C4#546×C10911yescharacteristic
846C2—42no—
847C2—44no—
848C2—82no—
849C2—82no—
850C2C109×#242411yescharacteristic
851C2C109×#310511yescharacteristic
852C2C109×#311811yescharacteristic
853C2C109×#326411yescharacteristic
854C2C109×#327211yescharacteristic
855C2C109×#328011yescharacteristic
856C2C109×#328211yescharacteristic
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×C4×D8×C109C2semidirect
5. C109×#2427C2semidirect
6. D4×C22⋊C4×C109C2semidirect
7. C109×#2067C2semidirect
8. C109×#2036C2semidirect
9. C109×#2034C2semidirect
10. C109×#2012C2semidirect
11. C109×#1968C2semidirect
12. C109×#1923C2semidirect
13. C109×#1879C2semidirect
14. C109×#1877C2semidirect
15. C109×#1864C2semidirect
21. C2×#124×C109C22semidirect
26. C2×C4×D4×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×C4×C8×C109C22semidirect
48. #391×C109C22semidirect
51. #389×C109C22semidirect
59. #340×C109C22semidirect
60. #340×C109C22semidirect
61. #336×C109C22semidirect
62. #336×C109C22semidirect
141. #102×C109D4semidirect
417. #25160C109direct (N × H)
429. C2×#463C2×C109semidirect
430. C2×#450C2×C109semidirect
432. C2×C4×D8C2×C109semidirect
433. #2427C2×C109semidirect
434. D4×C22⋊C4C2×C109semidirect
435. #2067C2×C109semidirect
436. #2036C2×C109semidirect
437. #2034C2×C109semidirect
438. #2012C2×C109semidirect
439. #1968C2×C109semidirect
440. #1923C2×C109semidirect
441. #1879C2×C109semidirect
442. #1877C2×C109semidirect
443. #1864C2×C109semidirect
444. C109#25160direct (N × H)
450. C2×#124C22×C109semidirect
455. C2×C4×D4C22×C109semidirect
461. C2×#107C22×C109semidirect
462. C2×#106C22×C109semidirect
463. C2×C4⋊C8C22×C109semidirect
464. C2×#103C22×C109semidirect
465. C2×#103C22×C109semidirect
470. C2×#102C22×C109semidirect
471. C2×#102C22×C109semidirect
474. C2×C4×C8C22×C109semidirect
477. #391C22×C109semidirect
480. #389C22×C109semidirect
488. #340C22×C109semidirect
489. #340C22×C109semidirect
490. #336C22×C109semidirect
491. #336C22×C109semidirect
570. #102D4×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×C4×D8×C1092
C109×#24272
D4×C22⋊C4×C1092
C109×#20672
C109×#20362
C109×#20342
C109×#20122
C109×#19682
C109×#19232
C109×#18792
C109×#18772
C109×#18642
#25160109