Finite Group Databasebeta

← C109×#24424 #42142418

Subgroups — C109×#24424 #42142418

Order 27904.

1992 conjugacy classes of subgroups.

The subgroup lattice has 1036 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D42×C109C211yesmaximal, characteristic, complemented
2C2×#466×C109C211yesmaximal, characteristic, complemented
3C2×#447×C109C211yesmaximal, characteristic, complemented
4C2×#447×C109C211yesmaximal, characteristic, complemented
5C22×#102×C109C211yesmaximal, characteristic, complemented
6C109×#2416C211yesmaximal, characteristic, complemented
7C109×#2041C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#2011C211yesmaximal, characteristic, complemented
10C109×#1999C211yesmaximal, characteristic, complemented
11C109×#1879C211yesmaximal, characteristic, complemented
12C109×#1874C211yesmaximal, characteristic, complemented
13C109×#1869C211yesmaximal, characteristic, complemented
14C109×#1862C211yesmaximal, characteristic, complemented
15C109×#1786C211yesmaximal, characteristic, complemented
16C23×D4×C109—21no—
17C23×D4×C109C2211yescharacteristic
18C23×D4×C109C2211yescharacteristic
19C22×D8×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic, complemented
21C22×D8×C109C2211yescharacteristic, complemented
22C23×C8×C109C2211yescharacteristic, complemented
23D42×C109—24no—
24D42×C109—24no—
25C2×#127×C109C2211yescharacteristic
26C2×#121×C109—21no—
27C2×#121×C109—21no—
28C2×#121×C109C2211yescharacteristic
29C2×#121×C109C2211yescharacteristic
30C2×#121×C109C2211yescharacteristic, complemented
31C2×#121×C109C2211yescharacteristic, complemented
32C2×#120×C109—21no—
33C2×#120×C109—21no—
34C2×C4×D4×C109C2211yescharacteristic
35C2×C4×D4×C109C2211yescharacteristic
36C22×C4⋊C4×C109C2211yescharacteristic, complemented
37#466×C109—24no—
38#447×C109—24no—
39#447×C109—24no—
40C2×#107×C109C2211yescharacteristic, complemented
41C2×#102×C109—24no—
42C2×#102×C109C2211yescharacteristic
43C2×#102×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
45C2×#102×C109C2211yescharacteristic, complemented
46C2×#102×C109C2211yescharacteristic, complemented
47C2×#102×C109C2211yescharacteristic, complemented
48C2×#102×C109C2211yescharacteristic, complemented
49C2×#102×C109C2211yescharacteristic, complemented
50C2×#102×C109C2211yescharacteristic, complemented
51C2×#102×C109C2211yescharacteristic, complemented
52C2×C22⋊C8×C109C2211yescharacteristic, complemented
53C2×C22⋊C8×C109C2211yescharacteristic, complemented
54C2×C22⋊C8×C109C2211yescharacteristic, complemented
55#396×C109—21no—
56#394×C109—21no—
57#390×C109C2211yescharacteristic, complemented
58#389×C109C2211yescharacteristic, complemented
59#386×C109—21no—
60#380×C109C2211yescharacteristic, complemented
61#340×C109C2211yescharacteristic, complemented
62#340×C109C2211yescharacteristic, complemented
63#336×C109C2211yescharacteristic, complemented
64#336×C109C2211yescharacteristic, complemented
65C25×C109—21no—
66C25×C109—21no—
67C22×D4×C109—22no—
68C22×D4×C109—22no—
69C22×D4×C109—28no—
70C22×D4×C109—21no—
71C22×D4×C109—21no—
72C22×D4×C109—22no—
73C22×D4×C109—22no—
74C22×D4×C109—22no—
75C22×D4×C109—22no—
76C22×D4×C109—21no—
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109—21no—
81C22×D4×C109—22no—
82C22×D4×C109—21no—
83C22×D4×C109—41no—
84C22×D4×C109—41no—
85C22×D4×C109—41no—
86C22×D4×C109—41no—
87C22×D4×C109—44no—
88C22×D4×C109—44no—
89C22×D4×C109D411yescharacteristic
90C22×D4×C109D414yescomplemented
91C22×D4×C109C2311yescharacteristic
92C22×D4×C109C2311yescharacteristic
93C22×D4×C109C2311yescharacteristic
94C22×D4×C109C2311yescharacteristic
95C23×C4×C109—21no—
96C23×C4×C109—21no—
97C23×C4×C109C2311yescharacteristic
98C23×C4×C109C2311yescharacteristic
99C2×D8×C109—22no—
100C2×D8×C109—22no—
101C2×D8×C109—22no—
102C2×D8×C109—22no—
103C2×D8×C109—22no—
104C2×D8×C109—22no—
105C2×D8×C109—41no—
106C2×D8×C109—41no—
107C2×D8×C109—41no—
108C22×C8×C109—22no—
109C22×C8×C109—22no—
110C22×C8×C109—41no—
111C22×C8×C109C2311yescharacteristic
112C22×C8×C109C2311yescharacteristic
113C22×C8×C109C2311yescharacteristic
114C22×C8×C109C2311yescharacteristic
115#127×C109—22no—
116#127×C109—22no—
117#121×C109—28no—
118#121×C109—22no—
119#121×C109—22no—
120#121×C109—22no—
121#121×C109—22no—
122#121×C109—22no—
123#121×C109—22no—
124#121×C109—41no—
125#121×C109—44no—
126#121×C109D414yescomplemented
127#120×C109—28no—
128#120×C109—28no—
129C4×D4×C109—22no—
130C4×D4×C109—22no—
131C4×D4×C109—22no—
132C4×D4×C109—22no—
133C2×C4⋊C4×C109—22no—
134C2×C4⋊C4×C109—21no—
135C2×C4⋊C4×C109—21no—
136C2×C4⋊C4×C109—41no—
137C2×C4⋊C4×C109D411yescharacteristic
138C2×C4⋊C4×C109C2311yescharacteristic
139C2×C4⋊C4×C109C2311yescharacteristic
140C2×C4⋊C4×C109C2311yescharacteristic
141C2×C4⋊C4×C109C2311yescharacteristic
142C2×C22⋊C4×C109—21no—
143C2×C22⋊C4×C109—21no—
144C2×C22⋊C4×C109—21no—
145C2×C22⋊C4×C109—21no—
146C2×C22⋊C4×C109—21no—
147C2×C22⋊C4×C109—21no—
148C2×C22⋊C4×C109—21no—
149C2×C22⋊C4×C109—21no—
150C2×C22⋊C4×C109D411yescharacteristic
151C2×C22⋊C4×C109D411yescharacteristic
152C2×C42×C109C2311yescharacteristic
153#107×C109—22no—
154#102×C109—22no—
155#102×C109—22no—
156#102×C109—22no—
157#102×C109—22no—
158#102×C109—22no—
159#102×C109—22no—
160#102×C109—22no—
161#102×C109—22no—
162#102×C109—41no—
163#102×C109D414yescomplemented
164C22⋊C8×C109—22no—
165C22⋊C8×C109—22no—
166C22⋊C8×C109—41no—
167#95×C109—21no—
168#95×C109—21no—
169C24×C109—21no—
170C24×C109—24no—
171C24×C109—21no—
172C24×C109—21no—
173C24×C109—24no—
174C24×C109—21no—
175C24×C109—42no—
176C24×C109—42no—
177C24×C109—42no—
178C24×C109—42no—
179C24×C109—42no—
180C24×C109—42no—
181C24×C109—42no—
182C24×C109—42no—
183C24×C109—81no—
184C24×C109—81no—
185C24×C109—81no—
186C24×C109—81no—
187C24×C109C2×D411yescharacteristic
188C24×C109C2×D411yescharacteristic
189C2×D4×C109—22no—
190C2×D4×C109—22no—
191C2×D4×C109—28no—
192C2×D4×C109—24no—
193C2×D4×C109—24no—
194C2×D4×C109—24no—
195C2×D4×C109—24no—
196C2×D4×C109—24no—
197C2×D4×C109—24no—
198C2×D4×C109—21no—
199C2×D4×C109—21no—
200C2×D4×C109—21no—
201C2×D4×C109—21no—
202C2×D4×C109—21no—
203C2×D4×C109—21no—
204C2×D4×C109—21no—
205C2×D4×C109—21no—
206C2×D4×C109—21no—
207C2×D4×C109—21no—
208C2×D4×C109—21no—
209C2×D4×C109—21no—
210C2×D4×C109—21no—
211C2×D4×C109—21no—
212C2×D4×C109—21no—
213C2×D4×C109—21no—
214C2×D4×C109—21no—
215C2×D4×C109—21no—
216C2×D4×C109—21no—
217C2×D4×C109—44no—
218C2×D4×C109—44no—
219C2×D4×C109—44no—
220C2×D4×C109—42no—
221C2×D4×C109—42no—
222C2×D4×C109—42no—
223C2×D4×C109—42no—
224C2×D4×C109—42no—
225C2×D4×C109—42no—
226C2×D4×C109—44no—
227C2×D4×C109—44no—
228C2×D4×C109—432no—
229C2×D4×C109—44no—
230C2×D4×C109—42no—
231C2×D4×C109—42no—
232C2×D4×C109—42no—
233C2×D4×C109—42no—
234C2×D4×C109—44no—
235C2×D4×C109—42no—
236C2×D4×C109—42no—
237C2×D4×C109—42no—
238C2×D4×C109—42no—
239C2×D4×C109—42no—
240C2×D4×C109—81no—
241C2×D4×C109—81no—
242C2×D4×C109—81no—
243C2×D4×C109D814yescomplemented
244C2×D4×C109C2×D412yes—
245C2×D4×C109C2×D412yes—
246C2×D4×C109C2×D412yes—
247C2×D4×C109C2×D412yes—
248C2×D4×C109#4112yes—
249C22×C4×C109—21no—
250C22×C4×C109—21no—
251C22×C4×C109—21no—
252C22×C4×C109—21no—
253C22×C4×C109—24no—
254C22×C4×C109—21no—
255C22×C4×C109—21no—
256C22×C4×C109—21no—
257C22×C4×C109—21no—
258C22×C4×C109—21no—
259C22×C4×C109—21no—
260C22×C4×C109—21no—
261C22×C4×C109—21no—
262C22×C4×C109—21no—
263C22×C4×C109—21no—
264C22×C4×C109—42no—
265C22×C4×C109—42no—
266C22×C4×C109—42no—
267C22×C4×C109—42no—
268C22×C4×C109—81no—
269C22×C4×C109C2×D411yescharacteristic
270C22×C4×C109C2×D411yescharacteristic
271C22×C4×C109C2×D411yescharacteristic
272C22×C4×C109C2×D412yes—
273C22×C4×C109C2×D412yes—
274C22×C4×C109C2×D411yescharacteristic
275C22×C4×C109C2411yescharacteristic
276D8×C109—44no—
277D8×C109—44no—
278D8×C109—44no—
279C2×C8×C109—21no—
280C2×C8×C109—21no—
281C2×C8×C109—21no—
282C2×C8×C109—21no—
283C2×C8×C109—21no—
284C2×C8×C109—21no—
285C2×C8×C109—21no—
286C2×C8×C109—21no—
287C2×C8×C109—21no—
288C2×C8×C109—21no—
289C2×C8×C109—21no—
290C2×C8×C109—44no—
291C2×C8×C109C2×D412yescomplemented
292C4⋊C4×C109—22no—
293C4⋊C4×C109—21no—
294C4⋊C4×C109—21no—
295C4⋊C4×C109—21no—
296C4⋊C4×C109—21no—
297C4⋊C4×C109—21no—
298C4⋊C4×C109—21no—
299C4⋊C4×C109—42no—
300C4⋊C4×C109—42no—
301C4⋊C4×C109C2×D412yes—
302C4⋊C4×C109C2×D412yescomplemented
303C22⋊C4×C109—24no—
304C22⋊C4×C109—24no—
305C22⋊C4×C109—22no—
306C22⋊C4×C109—24no—
307C22⋊C4×C109—22no—
308C22⋊C4×C109—42no—
309C22⋊C4×C109—42no—
310C22⋊C4×C109—42no—
311C22⋊C4×C109—42no—
312C22⋊C4×C109—81no—
313C42×C109—21no—
314C42×C109—21no—
315C23×C109—21no—
316C23×C109—21no—
317C23×C109—21no—
318C23×C109—21no—
319C23×C109—21no—
320C23×C109—22no—
321C23×C109—21no—
322C23×C109—22no—
323C23×C109—21no—
324C23×C109—22no—
325C23×C109—21no—
326C23×C109—21no—
327C23×C109—21no—
328C23×C109—22no—
329C23×C109—22no—
330C23×C109—48no—
331C23×C109—48no—
332C23×C109—48no—
333C23×C109—41no—
334C23×C109—41no—
335C23×C109—41no—
336C23×C109—41no—
337C23×C109—41no—
338C23×C109—41no—
339C23×C109—41no—
340C23×C109—41no—
341C23×C109—41no—
342C23×C109—41no—
343C23×C109—41no—
344C23×C109—41no—
345C23×C109—41no—
346C23×C109—41no—
347C23×C109—41no—
348C23×C109—41no—
349C23×C109—48no—
350C23×C109—41no—
351C23×C109—41no—
352C23×C109—41no—
353C23×C109—41no—
354C23×C109—41no—
355C23×C109—41no—
356C23×C109—41no—
357C23×C109—84no—
358C23×C109—84no—
359C23×C109—84no—
360C23×C109—84no—
361C23×C109—84no—
362C23×C109—84no—
363C23×C109—84no—
364C23×C109—84no—
365C23×C109—84no—
366C23×C109—84no—
367C23×C109#12012yes—
368C23×C109C2×D812yes—
369C23×C109C2×D812yes—
370C23×C109AGL(1,ℤ/8)12yes—
371C23×C109C22×D411yescharacteristic
372D4×C109—28no—
373D4×C109—22no—
374D4×C109—22no—
375D4×C109—22no—
376D4×C109—22no—
377D4×C109—22no—
378D4×C109—22no—
379D4×C109—22no—
380D4×C109—48no—
381D4×C109—48no—
382D4×C109—48no—
383D4×C109—48no—
384D4×C109—48no—
385D4×C109—41no—
386D4×C109—41no—
387D4×C109—41no—
388D4×C109—41no—
389D4×C109—41no—
390D4×C109—41no—
391D4×C109—41no—
392D4×C109—41no—
393D4×C109—84no—
394D4×C109—84no—
395D4×C109—84no—
396D4×C109#12114yescomplemented
397C2×C4×C109—21no—
398C2×C4×C109—21no—
399C2×C4×C109—21no—
400C2×C4×C109—21no—
401C2×C4×C109—22no—
402C2×C4×C109—22no—
403C2×C4×C109—22no—
404C2×C4×C109—22no—
405C2×C4×C109—21no—
406C2×C4×C109—21no—
407C2×C4×C109—22no—
408C2×C4×C109—21no—
409C2×C4×C109—22no—
410C2×C4×C109—21no—
411C2×C4×C109—21no—
412C2×C4×C109—21no—
413C2×C4×C109—48no—
414C2×C4×C109—41no—
415C2×C4×C109—41no—
416C2×C4×C109—41no—
417C2×C4×C109—41no—
418C2×C4×C109—41no—
419C2×C4×C109—41no—
420C2×C4×C109—41no—
421C2×C4×C109—41no—
422C2×C4×C109—41no—
423C2×C4×C109—41no—
424C2×C4×C109—41no—
425C2×C4×C109—41no—
426C2×C4×C109—41no—
427C2×C4×C109—41no—
428C2×C4×C109—84no—
429C2×C4×C109#12012yes—
430C2×C4×C109C2×D812yes—
431C2×C4×C109C22×D411yescharacteristic
432C2×C4×C109C22×D411yescharacteristic
433C2×C4×C109C22×D411yescharacteristic
434C2×C4×C109C2×#4111yescharacteristic
435C2×C4×C109H(5,𝔽2)11yescharacteristic
436C2×C4×C109H(5,𝔽2)11yescharacteristic
437C8×C109—22no—
438C8×C109—41no—
439C8×C109—41no—
440C8×C109—41no—
441C22×C109—22no—
442C22×C109—22no—
443C22×C109—22no—
444C22×C109—22no—
445C22×C109—22no—
446C22×C109—22no—
447C22×C109—24no—
448C22×C109—22no—
449C22×C109—22no—
450C22×C109—22no—
451C22×C109—41no—
452C22×C109—42no—
453C22×C109—41no—
454C22×C109—42no—
455C22×C109—41no—
456C22×C109—42no—
457C22×C109—42no—
458C22×C109—42no—
459C22×C109—41no—
460C22×C109—42no—
461C22×C109—42no—
462C22×C109—42no—
463C22×C109—42no—
464C22×C109—42no—
465C22×C109—42no—
466C22×C109—42no—
467C22×C109—816no—
468C22×C109—816no—
469C22×C109—81no—
470C22×C109—81no—
471C22×C109—81no—
472C22×C109—81no—
473C22×C109—81no—
474C22×C109—81no—
475C22×C109—81no—
476C22×C109—81no—
477C22×C109—81no—
478C22×C109—81no—
479C22×C109—81no—
480C22×C109—81no—
481C22×C109—81no—
482C22×C109—81no—
483C22×C109—81no—
484C22×C109#44714yescomplemented
485C22×C109C2×#12011yescharacteristic
486C22×C109D4211yescharacteristic
487C22×C109#54611yescharacteristic
488C22×C109C22×D811yescharacteristic
489C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
490C22×C109#57611yescharacteristic
491C22×C109#57711yescharacteristic
492C4×C109—22no—
493C4×C109—22no—
494C4×C109—41no—
495C4×C109—42no—
496C4×C109—41no—
497C4×C109—42no—
498C4×C109—81no—
499C4×C109—81no—
500C4×C109C2×#12111yescharacteristic
501C4×C109#53411yescharacteristic
502C4×C109D4211yescharacteristic
503C4×C109#54611yescharacteristic
504#24424C10911yesmaximal, characteristic, direct product factor, Sylow
505C2×C109—24no—
506C2×C109—42no—
507C2×C109—44no—
508C2×C109—82no—
509C2×C109—82no—
510C2×C109—161no—
511C2×C109#241011yescharacteristic
512C2×C109C2×#44711yescharacteristic
513C2×C109#301211yescharacteristic
514C2×C109#326511yescharacteristic
515C2×C109D4×D811yescharacteristic
516C2×C109#329411yescharacteristic
517C2×C109#331811yescharacteristic
518C2×D42C2×C10911yescharacteristic, complemented
519C2×#466C2×C10911yescharacteristic, complemented
520C2×#447C2×C10911yescharacteristic, complemented
521C2×#447C2×C10911yescharacteristic, complemented
522C22×#102C2×C10911yescharacteristic, complemented
523#2416C2×C10911yescharacteristic, complemented
524#2041C2×C10911yescharacteristic, complemented
525#2033C2×C10911yescharacteristic, complemented
526#2011C2×C10911yescharacteristic, complemented
527#1999C2×C10911yescharacteristic, complemented
528#1879C2×C10911yescharacteristic, complemented
529#1874C2×C10911yescharacteristic, complemented
530#1869C2×C10911yescharacteristic, complemented
531#1862C2×C10911yescharacteristic, complemented
532#1786C2×C10911yescharacteristic, complemented
533C109#2442411yescharacteristic, direct product factor, Sylow
534C23×D4—21no—
535C23×D4C22×C10911yescharacteristic
536C23×D4C22×C10911yescharacteristic
537C22×D8C22×C10911yescharacteristic
538C22×D8C22×C10911yescharacteristic, complemented
539C22×D8C22×C10911yescharacteristic, complemented
540C23×C8C22×C10911yescharacteristic, complemented
541D42—24no—
542D42—24no—
543C2×#127C22×C10911yescharacteristic
544C2×#121—21no—
545C2×#121—21no—
546C2×#121C22×C10911yescharacteristic
547C2×#121C22×C10911yescharacteristic
548C2×#121C22×C10911yescharacteristic, complemented
549C2×#121C22×C10911yescharacteristic, complemented
550C2×#120—21no—
551C2×#120—21no—
552C2×C4×D4C22×C10911yescharacteristic
553C2×C4×D4C22×C10911yescharacteristic
554C22×C4⋊C4C22×C10911yescharacteristic, complemented
555#466—24no—
556#447—24no—
557#447—24no—
558C2×#107C22×C10911yescharacteristic, complemented
559C2×#102—24no—
560C2×#102C22×C10911yescharacteristic
561C2×#102C22×C10911yescharacteristic
562C2×#102C22×C10911yescharacteristic
563C2×#102C22×C10911yescharacteristic, complemented
564C2×#102C22×C10911yescharacteristic, complemented
565C2×#102C22×C10911yescharacteristic, complemented
566C2×#102C22×C10911yescharacteristic, complemented
567C2×#102C22×C10911yescharacteristic, complemented
568C2×#102C22×C10911yescharacteristic, complemented
569C2×#102C22×C10911yescharacteristic, complemented
570C2×C22⋊C8C22×C10911yescharacteristic, complemented
571C2×C22⋊C8C22×C10911yescharacteristic, complemented
572C2×C22⋊C8C22×C10911yescharacteristic, complemented
573#396—21no—
574#394—21no—
575#390C22×C10911yescharacteristic, complemented
576#389C22×C10911yescharacteristic, complemented
577#386—21no—
578#380C22×C10911yescharacteristic, complemented
579#340C22×C10911yescharacteristic, complemented
580#340C22×C10911yescharacteristic, complemented
581#336C22×C10911yescharacteristic, complemented
582#336C22×C10911yescharacteristic, complemented
583C25—21no—
584C25—21no—
585C22×D4—22no—
586C22×D4—22no—
587C22×D4—28no—
588C22×D4—21no—
589C22×D4—21no—
590C22×D4—22no—
591C22×D4—22no—
592C22×D4—22no—
593C22×D4—22no—
594C22×D4—21no—
595C22×D4—21no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4—21no—
599C22×D4—22no—
600C22×D4—21no—
601C22×D4—41no—
602C22×D4—41no—
603C22×D4—41no—
604C22×D4—41no—
605C22×D4—44no—
606C22×D4—44no—
607C22×D4D4×C10911yescharacteristic
608C22×D4D4×C10914yescomplemented
609C22×D4C23×C10911yescharacteristic
610C22×D4C23×C10911yescharacteristic
611C22×D4C23×C10911yescharacteristic
612C22×D4C23×C10911yescharacteristic
613C23×C4—21no—
614C23×C4—21no—
615C23×C4C23×C10911yescharacteristic
616C23×C4C23×C10911yescharacteristic
617C2×D8—22no—
618C2×D8—22no—
619C2×D8—22no—
620C2×D8—22no—
621C2×D8—22no—
622C2×D8—22no—
623C2×D8—41no—
624C2×D8—41no—
625C2×D8—41no—
626C22×C8—22no—
627C22×C8—22no—
628C22×C8—41no—
629C22×C8C23×C10911yescharacteristic
630C22×C8C23×C10911yescharacteristic
631C22×C8C23×C10911yescharacteristic
632C22×C8C23×C10911yescharacteristic
633#127—22no—
634#127—22no—
635#121—28no—
636#121—22no—
637#121—22no—
638#121—22no—
639#121—22no—
640#121—22no—
641#121—22no—
642#121—41no—
643#121—44no—
644#121D4×C10914yescomplemented
645#120—28no—
646#120—28no—
647C4×D4—22no—
648C4×D4—22no—
649C4×D4—22no—
650C4×D4—22no—
651C2×C4⋊C4—22no—
652C2×C4⋊C4—21no—
653C2×C4⋊C4—21no—
654C2×C4⋊C4—41no—
655C2×C4⋊C4D4×C10911yescharacteristic
656C2×C4⋊C4C23×C10911yescharacteristic
657C2×C4⋊C4C23×C10911yescharacteristic
658C2×C4⋊C4C23×C10911yescharacteristic
659C2×C4⋊C4C23×C10911yescharacteristic
660C2×C22⋊C4—21no—
661C2×C22⋊C4—21no—
662C2×C22⋊C4—21no—
663C2×C22⋊C4—21no—
664C2×C22⋊C4—21no—
665C2×C22⋊C4—21no—
666C2×C22⋊C4—21no—
667C2×C22⋊C4—21no—
668C2×C22⋊C4D4×C10911yescharacteristic
669C2×C22⋊C4D4×C10911yescharacteristic
670C2×C42C23×C10911yescharacteristic
671#107—22no—
672#102—22no—
673#102—22no—
674#102—22no—
675#102—22no—
676#102—22no—
677#102—22no—
678#102—22no—
679#102—22no—
680#102—41no—
681#102D4×C10914yescomplemented
682C22⋊C8—22no—
683C22⋊C8—22no—
684C22⋊C8—41no—
685#95—21no—
686#95—21no—
687C24—21no—
688C24—24no—
689C24—21no—
690C24—21no—
691C24—24no—
692C24—21no—
693C24—42no—
694C24—42no—
695C24—42no—
696C24—42no—
697C24—42no—
698C24—42no—
699C24—42no—
700C24—42no—
701C24—81no—
702C24—81no—
703C24—81no—
704C24—81no—
705C24C2×D4×C10911yescharacteristic
706C24C2×D4×C10911yescharacteristic
707C2×D4—22no—
708C2×D4—22no—
709C2×D4—28no—
710C2×D4—24no—
711C2×D4—24no—
712C2×D4—24no—
713C2×D4—24no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—21no—
717C2×D4—21no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—21no—
721C2×D4—21no—
722C2×D4—21no—
723C2×D4—21no—
724C2×D4—21no—
725C2×D4—21no—
726C2×D4—21no—
727C2×D4—21no—
728C2×D4—21no—
729C2×D4—21no—
730C2×D4—21no—
731C2×D4—21no—
732C2×D4—21no—
733C2×D4—21no—
734C2×D4—21no—
735C2×D4—44no—
736C2×D4—44no—
737C2×D4—44no—
738C2×D4—42no—
739C2×D4—42no—
740C2×D4—42no—
741C2×D4—42no—
742C2×D4—42no—
743C2×D4—42no—
744C2×D4—44no—
745C2×D4—44no—
746C2×D4—432no—
747C2×D4—44no—
748C2×D4—42no—
749C2×D4—42no—
750C2×D4—42no—
751C2×D4—42no—
752C2×D4—44no—
753C2×D4—42no—
754C2×D4—42no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—81no—
759C2×D4—81no—
760C2×D4—81no—
761C2×D4D8×C10914yescomplemented
762C2×D4C2×D4×C10912yes—
763C2×D4C2×D4×C10912yes—
764C2×D4C2×D4×C10912yes—
765C2×D4C2×D4×C10912yes—
766C2×D4#41×C10912yes—
767C22×C4—21no—
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—24no—
772C22×C4—21no—
773C22×C4—21no—
774C22×C4—21no—
775C22×C4—21no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—21no—
781C22×C4—21no—
782C22×C4—42no—
783C22×C4—42no—
784C22×C4—42no—
785C22×C4—42no—
786C22×C4—81no—
787C22×C4C2×D4×C10911yescharacteristic
788C22×C4C2×D4×C10911yescharacteristic
789C22×C4C2×D4×C10911yescharacteristic
790C22×C4C2×D4×C10912yes—
791C22×C4C2×D4×C10912yes—
792C22×C4C2×D4×C10911yescharacteristic
793C22×C4C24×C10911yescharacteristic
794D8—44no—
795D8—44no—
796D8—44no—
797C2×C8—21no—
798C2×C8—21no—
799C2×C8—21no—
800C2×C8—21no—
801C2×C8—21no—
802C2×C8—21no—
803C2×C8—21no—
804C2×C8—21no—
805C2×C8—21no—
806C2×C8—21no—
807C2×C8—21no—
808C2×C8—44no—
809C2×C8C2×D4×C10912yescomplemented
810C4⋊C4—22no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—21no—
814C4⋊C4—21no—
815C4⋊C4—21no—
816C4⋊C4—21no—
817C4⋊C4—42no—
818C4⋊C4—42no—
819C4⋊C4C2×D4×C10912yes—
820C4⋊C4C2×D4×C10912yescomplemented
821C22⋊C4—24no—
822C22⋊C4—24no—
823C22⋊C4—22no—
824C22⋊C4—24no—
825C22⋊C4—22no—
826C22⋊C4—42no—
827C22⋊C4—42no—
828C22⋊C4—42no—
829C22⋊C4—42no—
830C22⋊C4—81no—
831C42—21no—
832C42—21no—
833C23—21no—
834C23—21no—
835C23—21no—
836C23—21no—
837C23—21no—
838C23—22no—
839C23—21no—
840C23—22no—
841C23—21no—
842C23—22no—
843C23—21no—
844C23—21no—
845C23—21no—
846C23—22no—
847C23—22no—
848C23—48no—
849C23—48no—
850C23—48no—
851C23—41no—
852C23—41no—
853C23—41no—
854C23—41no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—41no—
865C23—41no—
866C23—41no—
867C23—48no—
868C23—41no—
869C23—41no—
870C23—41no—
871C23—41no—
872C23—41no—
873C23—41no—
874C23—41no—
875C23—84no—
876C23—84no—
877C23—84no—
878C23—84no—
879C23—84no—
880C23—84no—
881C23—84no—
882C23—84no—
883C23—84no—
884C23—84no—
885C23#120×C10912yes—
886C23C2×D8×C10912yes—
887C23C2×D8×C10912yes—
888C23AGL(1,ℤ/8)×C10912yes—
889C23C22×D4×C10911yescharacteristic
890D4—28no—
891D4—22no—
892D4—22no—
893D4—22no—
894D4—22no—
895D4—22no—
896D4—22no—
897D4—22no—
898D4—48no—
899D4—48no—
900D4—48no—
901D4—48no—
902D4—48no—
903D4—41no—
904D4—41no—
905D4—41no—
906D4—41no—
907D4—41no—
908D4—41no—
909D4—41no—
910D4—41no—
911D4—84no—
912D4—84no—
913D4—84no—
914D4#121×C10914yescomplemented
915C2×C4—21no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—22no—
920C2×C4—22no—
921C2×C4—22no—
922C2×C4—22no—
923C2×C4—21no—
924C2×C4—21no—
925C2×C4—22no—
926C2×C4—21no—
927C2×C4—22no—
928C2×C4—21no—
929C2×C4—21no—
930C2×C4—21no—
931C2×C4—48no—
932C2×C4—41no—
933C2×C4—41no—
934C2×C4—41no—
935C2×C4—41no—
936C2×C4—41no—
937C2×C4—41no—
938C2×C4—41no—
939C2×C4—41no—
940C2×C4—41no—
941C2×C4—41no—
942C2×C4—41no—
943C2×C4—41no—
944C2×C4—41no—
945C2×C4—41no—
946C2×C4—84no—
947C2×C4#120×C10912yes—
948C2×C4C2×D8×C10912yes—
949C2×C4C22×D4×C10911yescharacteristic
950C2×C4C22×D4×C10911yescharacteristic
951C2×C4C22×D4×C10911yescharacteristic
952C2×C4C2×#41×C10911yescharacteristic
953C2×C4H(5,𝔽2)×C10911yescharacteristic
954C2×C4H(5,𝔽2)×C10911yescharacteristic
955C8—22no—
956C8—41no—
957C8—41no—
958C8—41no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—22no—
963C22—22no—
964C22—22no—
965C22—22no—
966C22—22no—
967C22—22no—
968C22—24no—
969C22—42no—
970C22—41no—
971C22—42no—
972C22—41no—
973C22—42no—
974C22—42no—
975C22—42no—
976C22—41no—
977C22—42no—
978C22—41no—
979C22—42no—
980C22—42no—
981C22—42no—
982C22—42no—
983C22—42no—
984C22—42no—
985C22—816no—
986C22—816no—
987C22—81no—
988C22—81no—
989C22—81no—
990C22—81no—
991C22—81no—
992C22—81no—
993C22—81no—
994C22—81no—
995C22—81no—
996C22—81no—
997C22—81no—
998C22—81no—
999C22—81no—
1000C22—81no—
1001C22—81no—
1002C22#447×C10914yescomplemented
1003C22C2×#120×C10911yescharacteristic
1004C22D42×C10911yescharacteristic
1005C22#546×C10911yescharacteristic
1006C22C22×D8×C10911yescharacteristic
1007C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
1008C22#576×C10911yescharacteristic
1009C22#577×C10911yescharacteristic
1010C4—22no—
1011C4—22no—
1012C4—42no—
1013C4—41no—
1014C4—42no—
1015C4—41no—
1016C4—81no—
1017C4—81no—
1018C4C2×#121×C10911yescharacteristic
1019C4#534×C10911yescharacteristic
1020C4D42×C10911yescharacteristic
1021C4#546×C10911yescharacteristic
1022C2—24no—
1023C2—42no—
1024C2—44no—
1025C2—82no—
1026C2—82no—
1027C2—161no—
1028C2C109×#241011yescharacteristic
1029C2C2×#447×C10911yescharacteristic
1030C2C109×#301211yescharacteristic
1031C2C109×#326511yescharacteristic
1032C2D4×D8×C10911yescharacteristic
1033C2C109×#329411yescharacteristic
1034C2C109×#331811yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×D42×C109C2semidirect
2. C2×#466×C109C2semidirect
3. C2×#447×C109C2semidirect
4. C2×#447×C109C2semidirect
5. C22×#102×C109C2semidirect
6. C109×#2416C2semidirect
7. C109×#2041C2semidirect
8. C109×#2033C2semidirect
9. C109×#2011C2semidirect
10. C109×#1999C2semidirect
11. C109×#1879C2semidirect
12. C109×#1874C2semidirect
13. C109×#1869C2semidirect
14. C109×#1862C2semidirect
15. C109×#1786C2semidirect
20. C22×D8×C109C22semidirect
21. C22×D8×C109C22semidirect
22. C23×C8×C109C22semidirect
30. C2×#121×C109C22semidirect
31. C2×#121×C109C22semidirect
36. C22×C4⋊C4×C109C22semidirect
40. C2×#107×C109C22semidirect
45. C2×#102×C109C22semidirect
46. C2×#102×C109C22semidirect
47. C2×#102×C109C22semidirect
48. C2×#102×C109C22semidirect
49. C2×#102×C109C22semidirect
50. C2×#102×C109C22semidirect
51. C2×#102×C109C22semidirect
52. C2×C22⋊C8×C109C22semidirect
53. C2×C22⋊C8×C109C22semidirect
54. C2×C22⋊C8×C109C22semidirect
57. #390×C109C22semidirect
58. #389×C109C22semidirect
60. #380×C109C22semidirect
61. #340×C109C22semidirect
62. #340×C109C22semidirect
63. #336×C109C22semidirect
64. #336×C109C22semidirect
90. C22×D4×C109D4semidirect
126. #121×C109D4semidirect
163. #102×C109D4semidirect
243. C2×D4×C109D8semidirect
291. C2×C8×C109C2×D4semidirect
302. C4⋊C4×C109C2×D4semidirect
396. D4×C109#121semidirect
484. C22×C109#447semidirect
504. #24424C109direct (N × H)
518. C2×D42C2×C109semidirect
519. C2×#466C2×C109semidirect
520. C2×#447C2×C109semidirect
521. C2×#447C2×C109semidirect
522. C22×#102C2×C109semidirect
523. #2416C2×C109semidirect
524. #2041C2×C109semidirect
525. #2033C2×C109semidirect
526. #2011C2×C109semidirect
527. #1999C2×C109semidirect
528. #1879C2×C109semidirect
529. #1874C2×C109semidirect
530. #1869C2×C109semidirect
531. #1862C2×C109semidirect
532. #1786C2×C109semidirect
533. C109#24424direct (N × H)
538. C22×D8C22×C109semidirect
539. C22×D8C22×C109semidirect
540. C23×C8C22×C109semidirect
548. C2×#121C22×C109semidirect
549. C2×#121C22×C109semidirect
554. C22×C4⋊C4C22×C109semidirect
558. C2×#107C22×C109semidirect
563. C2×#102C22×C109semidirect
564. C2×#102C22×C109semidirect
565. C2×#102C22×C109semidirect
566. C2×#102C22×C109semidirect
567. C2×#102C22×C109semidirect
568. C2×#102C22×C109semidirect
569. C2×#102C22×C109semidirect
570. C2×C22⋊C8C22×C109semidirect
571. C2×C22⋊C8C22×C109semidirect
572. C2×C22⋊C8C22×C109semidirect
575. #390C22×C109semidirect
576. #389C22×C109semidirect
578. #380C22×C109semidirect
579. #340C22×C109semidirect
580. #340C22×C109semidirect
581. #336C22×C109semidirect
582. #336C22×C109semidirect
608. C22×D4D4×C109semidirect
644. #121D4×C109semidirect
681. #102D4×C109semidirect
761. C2×D4D8×C109semidirect
809. C2×C8C2×D4×C109semidirect
820. C4⋊C4C2×D4×C109semidirect
914. D4#121×C109semidirect
1002. C22#447×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×#466×C1092
C2×#447×C1092
C22×#102×C1092
C109×#24162
C109×#20412
C109×#20332
C109×#20112
C109×#19992
C109×#18792
C109×#18742
C109×#18692
C109×#18622
C109×#17862
#24424109