Finite Group Databasebeta

← C109×#18414 #42136408

Subgroups — C109×#18414 #42136408

Order 27904.

1042 conjugacy classes of subgroups.

The subgroup lattice has 1010 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3534C211yesmaximal, characteristic, complemented
2C109×#3194C211yesmaximal, characteristic, complemented
3C109×#3186C211yesmaximal, characteristic, complemented
4C109×#2661C211yesmaximal, characteristic, complemented
5C109×#1612C211yesmaximal, characteristic, complemented
6C109×#1610C211yesmaximal, characteristic, complemented
7C109×#1609C211yesmaximal, characteristic, complemented
8C109×#1607C211yesmaximal, characteristic, complemented
9C109×#1600C211yesmaximal, characteristic, complemented
10C109×#1598C211yesmaximal, characteristic, complemented
11C109×#1597C211yesmaximal, characteristic, complemented
12C109×#1595C211yesmaximal, characteristic, complemented
13C109×#1507C211yesmaximal, characteristic, complemented
14C109×#1501C211yesmaximal, characteristic, complemented
15C109×#1468C211yesmaximal, characteristic, complemented
16#562×C109—21no—
17#560×C109—21no—
18#553×C109—21no—
19#551×C109—21no—
20#546×C109—21no—
21#546×C109—21no—
22#546×C109—21no—
23D42×C109—21no—
24#540×C109—21no—
25#539×C109—21no—
26#539×C109C2211yescharacteristic
27#538×C109—21no—
28#538×C109C2211yescharacteristic
29#537×C109C2211yescharacteristic
30#534×C109—21no—
31#534×C109C2211yescharacteristic
32#525×C109C2211yescharacteristic
33C2×#123×C109C2211yescharacteristic
34C2×#121×C109C2211yescharacteristic
35C2×#121×C109C2211yescharacteristic, complemented
36#483×C109C2211yescharacteristic, complemented
37#482×C109—21no—
38#480×C109—21no—
39#480×C109C2211yescharacteristic
40#480×C109C2211yescharacteristic, complemented
41#480×C109C2211yescharacteristic, complemented
42#469×C109—21no—
43#468×C109—21no—
44#466×C109—21no—
45#466×C109—21no—
46#450×C109C2211yescharacteristic, complemented
47#449×C109—21no—
48#447×C109—21no—
49#447×C109C2211yescharacteristic
50#447×C109C2211yescharacteristic, complemented
51#447×C109C2211yescharacteristic, complemented
52#407×C109C2211yescharacteristic, complemented
53C2×C22⋊C8×C109C2211yescharacteristic, complemented
54#398×C109C2211yescharacteristic, complemented
55#397×C109C2211yescharacteristic, complemented
56#394×C109—21no—
57#394×C109C2211yescharacteristic, complemented
58#392×C109—21no—
59#392×C109C2211yescharacteristic, complemented
60#390×C109—21no—
61#388×C109—21no—
62C4×C22⋊C4×C109C2211yescharacteristic, complemented
63#328×C109C2211yescharacteristic, complemented
64#328×C109C2211yescharacteristic, complemented
65#327×C109C2211yescharacteristic
66#327×C109C2211yescharacteristic
67#327×C109C2211yescharacteristic, complemented
68#327×C109C2211yescharacteristic, complemented
69#327×C109C2211yescharacteristic, complemented
70#327×C109C2211yescharacteristic, complemented
71#324×C109C2211yescharacteristic, complemented
72#324×C109C2211yescharacteristic, complemented
73#323×C109C2211yescharacteristic, complemented
74#323×C109C2211yescharacteristic, complemented
75C2×#41×C109—21no—
76C2×#41×C109D411yescharacteristic, complemented
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109—21no—
81C22×D4×C109—21no—
82C22×D4×C109D411yescharacteristic
83C22×D4×C109D411yescharacteristic, complemented
84C22×D4×C109C2311yescharacteristic
85C23×C4×C109C2311yescharacteristic
86C2×SD16×C109—21no—
87C2×D8×C109—21no—
88C2×D8×C109—21no—
89C2×D8×C109—21no—
90C2×M16×C109—21no—
91C22×C8×C109—21no—
92#127×C109—21no—
93#126×C109—21no—
94#126×C109—21no—
95#126×C109—21no—
96#126×C109—21no—
97#125×C109—21no—
98#125×C109—21no—
99#124×C109—21no—
100#124×C109—21no—
101#124×C109—21no—
102#123×C109—21no—
103#123×C109—21no—
104#123×C109—21no—
105#123×C109—21no—
106#123×C109—21no—
107#123×C109—21no—
108#123×C109—21no—
109#123×C109—21no—
110#123×C109—21no—
111#123×C109—21no—
112#123×C109—21no—
113#123×C109—21no—
114#123×C109—21no—
115#123×C109—21no—
116C22⋊Q8×C109—21no—
117C22⋊Q8×C109—21no—
118C22⋊Q8×C109—21no—
119C22⋊Q8×C109—21no—
120C22⋊Q8×C109—21no—
121C22⋊Q8×C109D411yescharacteristic, complemented
122C22⋊Q8×C109C2311yescharacteristic
123#121×C109—21no—
124#121×C109—21no—
125#121×C109—21no—
126#121×C109—21no—
127#121×C109—21no—
128#121×C109—21no—
129#121×C109—21no—
130#121×C109—21no—
131#121×C109—21no—
132#121×C109—21no—
133#121×C109—21no—
134#121×C109—21no—
135#121×C109—21no—
136#121×C109—21no—
137#121×C109—21no—
138#121×C109—21no—
139#121×C109—21no—
140#121×C109—21no—
141#121×C109—21no—
142#121×C109D411yescharacteristic, complemented
143#121×C109D411yescharacteristic, complemented
144#121×C109D411yescharacteristic, complemented
145#121×C109C2311yescharacteristic
146#121×C109C2311yescharacteristic
147#121×C109C2311yescharacteristic
148#120×C109—21no—
149#120×C109—21no—
150#120×C109—21no—
151#120×C109—21no—
152#120×C109—21no—
153#120×C109—21no—
154#120×C109—21no—
155#120×C109—21no—
156C4×D4×C109—21no—
157C4×D4×C109—21no—
158C4×D4×C109—21no—
159C4×D4×C109—21no—
160C4×D4×C109—21no—
161C4×D4×C109—21no—
162C4×D4×C109—21no—
163C4×D4×C109—21no—
164#117×C109—21no—
165#117×C109D411yescharacteristic, complemented
166C2×C4⋊C4×C109—21no—
167C2×C4⋊C4×C109D411yescharacteristic
168C2×C4⋊C4×C109D411yescharacteristic, complemented
169C2×C4⋊C4×C109C2311yescharacteristic
170C2×C4⋊C4×C109C2311yescharacteristic
171C2×C22⋊C4×C109—21no—
172C2×C22⋊C4×C109—21no—
173C2×C22⋊C4×C109—21no—
174C2×C22⋊C4×C109—21no—
175C2×C22⋊C4×C109—21no—
176C2×C22⋊C4×C109—21no—
177C2×C22⋊C4×C109—21no—
178C2×C22⋊C4×C109—21no—
179C2×C22⋊C4×C109—21no—
180C2×C22⋊C4×C109D411yescharacteristic
181C2×C22⋊C4×C109D411yescharacteristic
182C2×C22⋊C4×C109C2311yescharacteristic
183C2×C42×C109—21no—
184#107×C109—21no—
185#107×C109—21no—
186#107×C109—21no—
187#106×C109—21no—
188#103×C109—21no—
189#102×C109—21no—
190#102×C109—21no—
191#102×C109—21no—
192#102×C109—21no—
193#102×C109—21no—
194#102×C109—21no—
195#102×C109—21no—
196C22⋊C8×C109—21no—
197C22⋊C8×C109—21no—
198C22⋊C8×C109C2311yescharacteristic
199C22⋊C8×C109C2311yescharacteristic
200C22⋊C8×C109C2311yescharacteristic
201C22⋊C8×C109C2311yescharacteristic
202#95×C109—21no—
203#95×C109—21no—
204#95×C109C2311yescharacteristic
205#95×C109C2311yescharacteristic
206C24×C109—21no—
207C24×C109—21no—
208C24×C109—21no—
209C24×C109C2×D411yescharacteristic
210C24×C109C2×D411yescharacteristic
211#41×C109—81no—
212#41×C109—81no—
213#41×C109—81no—
214C2×Q8×C109—21no—
215C2×Q8×C109C2×D411yescharacteristic
216C2×D4×C109—21no—
217C2×D4×C109—21no—
218C2×D4×C109—21no—
219C2×D4×C109—21no—
220C2×D4×C109—21no—
221C2×D4×C109—21no—
222C2×D4×C109—21no—
223C2×D4×C109—21no—
224C2×D4×C109—21no—
225C2×D4×C109—21no—
226C2×D4×C109—21no—
227C2×D4×C109—21no—
228C2×D4×C109—21no—
229C2×D4×C109—21no—
230C2×D4×C109—21no—
231C2×D4×C109—21no—
232C2×D4×C109—21no—
233C2×D4×C109—21no—
234C2×D4×C109—21no—
235C2×D4×C109—42no—
236C2×D4×C109—41no—
237C2×D4×C109—41no—
238C2×D4×C109—81no—
239C2×D4×C109—81no—
240C2×D4×C109—81no—
241C2×D4×C109—81no—
242C2×D4×C109—81no—
243C2×D4×C109—81no—
244C2×D4×C109—81no—
245C2×D4×C109—81no—
246C2×D4×C109—81no—
247C2×D4×C109—81no—
248C2×D4×C109—81no—
249C2×D4×C109—82no—
250C2×D4×C109C2×D411yescharacteristic
251C2×D4×C109C2×D411yescharacteristic
252C2×D4×C109C2×D411yescharacteristic
253C22×C4×C109—21no—
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—81no—
264C22×C4×C109C2×D411yescharacteristic
265C22×C4×C109C2×D411yescharacteristic
266C22×C4×C109C2×D411yescharacteristic
267C22×C4×C109C2×D411yescharacteristic
268C22×C4×C109C2×D411yescharacteristic
269C22×C4×C109C2×D411yescharacteristic
270C22×C4×C109C2×D411yescharacteristic
271C22×C4×C109C2×D411yescharacteristic
272C22×C4×C109C2411yescharacteristic
273SD16×C109—81no—
274D8×C109—81no—
275D8×C109—81no—
276D8×C109—81no—
277M16×C109—81no—
278C2×C8×C109—21no—
279C2×C8×C109—21no—
280C2×C8×C109—21no—
281C2×C8×C109—21no—
282C2×C8×C109—81no—
283C4⋊C4×C109—21no—
284C4⋊C4×C109—21no—
285C4⋊C4×C109—21no—
286C4⋊C4×C109—21no—
287C4⋊C4×C109—21no—
288C4⋊C4×C109—21no—
289C4⋊C4×C109—21no—
290C4⋊C4×C109—21no—
291C4⋊C4×C109—21no—
292C4⋊C4×C109—21no—
293C4⋊C4×C109—21no—
294C4⋊C4×C109—21no—
295C4⋊C4×C109—21no—
296C4⋊C4×C109—21no—
297C4⋊C4×C109—21no—
298C4⋊C4×C109—81no—
299C4⋊C4×C109C2×D411yescharacteristic
300C4⋊C4×C109C2×D411yescharacteristic
301C4⋊C4×C109C2×D411yescharacteristic
302C4⋊C4×C109C2×D411yescharacteristic
303C22⋊C4×C109—21no—
304C22⋊C4×C109—21no—
305C22⋊C4×C109—21no—
306C22⋊C4×C109—21no—
307C22⋊C4×C109—21no—
308C22⋊C4×C109—21no—
309C22⋊C4×C109—21no—
310C22⋊C4×C109—21no—
311C22⋊C4×C109—21no—
312C22⋊C4×C109—21no—
313C22⋊C4×C109—21no—
314C22⋊C4×C109—21no—
315C22⋊C4×C109—21no—
316C22⋊C4×C109—21no—
317C22⋊C4×C109—21no—
318C22⋊C4×C109—21no—
319C22⋊C4×C109—21no—
320C22⋊C4×C109—21no—
321C22⋊C4×C109—21no—
322C22⋊C4×C109—21no—
323C22⋊C4×C109—21no—
324C22⋊C4×C109—21no—
325C22⋊C4×C109—21no—
326C22⋊C4×C109—21no—
327C22⋊C4×C109—21no—
328C22⋊C4×C109—42no—
329C22⋊C4×C109—42no—
330C22⋊C4×C109—41no—
331C22⋊C4×C109—41no—
332C22⋊C4×C109—81no—
333C22⋊C4×C109—81no—
334C22⋊C4×C109—81no—
335C42×C109—21no—
336C42×C109—21no—
337C42×C109—21no—
338C42×C109—81no—
339C23×C109—21no—
340C23×C109—21no—
341C23×C109—21no—
342C23×C109—21no—
343C23×C109—21no—
344C23×C109—21no—
345C23×C109—21no—
346C23×C109—21no—
347C23×C109—41no—
348C23×C109—41no—
349C23×C109—42no—
350C23×C109—41no—
351C23×C109—41no—
352C23×C109—41no—
353C23×C109—41no—
354C23×C109—41no—
355C23×C109—41no—
356C23×C109—41no—
357C23×C109—41no—
358C23×C109—41no—
359C23×C109—81no—
360C23×C109—81no—
361C23×C109—81no—
362C23×C109—81no—
363C23×C109—81no—
364C23×C109#12011yescharacteristic
365C23×C109#12011yescharacteristic
366C23×C109C22×D411yescharacteristic
367Q8×C109—41no—
368Q8×C109—81no—
369D4×C109—41no—
370D4×C109—41no—
371D4×C109—41no—
372D4×C109—41no—
373D4×C109—41no—
374D4×C109—41no—
375D4×C109—41no—
376D4×C109—42no—
377D4×C109—42no—
378D4×C109—41no—
379D4×C109—41no—
380D4×C109—41no—
381D4×C109—41no—
382D4×C109—41no—
383D4×C109—41no—
384D4×C109—81no—
385D4×C109—81no—
386D4×C109—81no—
387D4×C109—81no—
388D4×C109—81no—
389D4×C109—81no—
390D4×C109—81no—
391D4×C109—81no—
392D4×C109—81no—
393D4×C109—81no—
394D4×C109—81no—
395D4×C109—81no—
396D4×C109—84no—
397D4×C109—82no—
398D4×C109—82no—
399C2×C4×C109—22no—
400C2×C4×C109—21no—
401C2×C4×C109—21no—
402C2×C4×C109—21no—
403C2×C4×C109—21no—
404C2×C4×C109—21no—
405C2×C4×C109—21no—
406C2×C4×C109—21no—
407C2×C4×C109—21no—
408C2×C4×C109—21no—
409C2×C4×C109—21no—
410C2×C4×C109—41no—
411C2×C4×C109—41no—
412C2×C4×C109—41no—
413C2×C4×C109—41no—
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—81no—
427C2×C4×C109—81no—
428C2×C4×C109—81no—
429C2×C4×C109—81no—
430C2×C4×C109—81no—
431C2×C4×C109—81no—
432C2×C4×C109—81no—
433C2×C4×C109#12011yescharacteristic
434C2×C4×C109#12011yescharacteristic
435C2×C4×C109C22×D411yescharacteristic
436C2×C4×C109C22×D411yescharacteristic
437C8×C109—41no—
438C8×C109—41no—
439C8×C109—41no—
440C8×C109—41no—
441C22×C109—21no—
442C22×C109—21no—
443C22×C109—21no—
444C22×C109—21no—
445C22×C109—21no—
446C22×C109—21no—
447C22×C109—21no—
448C22×C109—21no—
449C22×C109—41no—
450C22×C109—41no—
451C22×C109—41no—
452C22×C109—41no—
453C22×C109—41no—
454C22×C109—41no—
455C22×C109—41no—
456C22×C109—41no—
457C22×C109—41no—
458C22×C109—41no—
459C22×C109—41no—
460C22×C109—41no—
461C22×C109—81no—
462C22×C109—81no—
463C22×C109—81no—
464C22×C109—81no—
465C22×C109—81no—
466C22×C109—81no—
467C22×C109—81no—
468C22×C109—81no—
469C22×C109—81no—
470C22×C109—81no—
471C22×C109—81no—
472C22×C109—162no—
473C22×C109—162no—
474C22×C109C2×#12011yescharacteristic
475C22×C109#57611yescharacteristic
476C22×C109#57611yescharacteristic
477C4×C109—21no—
478C4×C109—21no—
479C4×C109—21no—
480C4×C109—21no—
481C4×C109—42no—
482C4×C109—41no—
483C4×C109—41no—
484C4×C109—41no—
485C4×C109—41no—
486C4×C109—41no—
487C4×C109—41no—
488C4×C109—41no—
489C4×C109—41no—
490C4×C109—81no—
491C4×C109—81no—
492#18414C10911yesmaximal, characteristic, direct product factor, Sylow
493C2×C109—21no—
494C2×C109—21no—
495C2×C109—41no—
496C2×C109—41no—
497C2×C109—81no—
498C2×C109—81no—
499C2×C109—81no—
500C2×C109—81no—
501C2×C109—161no—
502C2×C109#300811yescharacteristic
503C2×C109#301811yescharacteristic
504C2×C109#302611yescharacteristic
505#3534C2×C10911yescharacteristic, complemented
506#3194C2×C10911yescharacteristic, complemented
507#3186C2×C10911yescharacteristic, complemented
508#2661C2×C10911yescharacteristic, complemented
509#1612C2×C10911yescharacteristic, complemented
510#1610C2×C10911yescharacteristic, complemented
511#1609C2×C10911yescharacteristic, complemented
512#1607C2×C10911yescharacteristic, complemented
513#1600C2×C10911yescharacteristic, complemented
514#1598C2×C10911yescharacteristic, complemented
515#1597C2×C10911yescharacteristic, complemented
516#1595C2×C10911yescharacteristic, complemented
517#1507C2×C10911yescharacteristic, complemented
518#1501C2×C10911yescharacteristic, complemented
519#1468C2×C10911yescharacteristic, complemented
520C109#1841411yescharacteristic, direct product factor, Sylow
521#562—21no—
522#560—21no—
523#553—21no—
524#551—21no—
525#546—21no—
526#546—21no—
527#546—21no—
528D42—21no—
529#540—21no—
530#539—21no—
531#539C22×C10911yescharacteristic
532#538—21no—
533#538C22×C10911yescharacteristic
534#537C22×C10911yescharacteristic
535#534—21no—
536#534C22×C10911yescharacteristic
537#525C22×C10911yescharacteristic
538C2×#123C22×C10911yescharacteristic
539C2×#121C22×C10911yescharacteristic
540C2×#121C22×C10911yescharacteristic, complemented
541#483C22×C10911yescharacteristic, complemented
542#482—21no—
543#480—21no—
544#480C22×C10911yescharacteristic
545#480C22×C10911yescharacteristic, complemented
546#480C22×C10911yescharacteristic, complemented
547#469—21no—
548#468—21no—
549#466—21no—
550#466—21no—
551#450C22×C10911yescharacteristic, complemented
552#449—21no—
553#447—21no—
554#447C22×C10911yescharacteristic
555#447C22×C10911yescharacteristic, complemented
556#447C22×C10911yescharacteristic, complemented
557#407C22×C10911yescharacteristic, complemented
558C2×C22⋊C8C22×C10911yescharacteristic, complemented
559#398C22×C10911yescharacteristic, complemented
560#397C22×C10911yescharacteristic, complemented
561#394—21no—
562#394C22×C10911yescharacteristic, complemented
563#392—21no—
564#392C22×C10911yescharacteristic, complemented
565#390—21no—
566#388—21no—
567C4×C22⋊C4C22×C10911yescharacteristic, complemented
568#328C22×C10911yescharacteristic, complemented
569#328C22×C10911yescharacteristic, complemented
570#327C22×C10911yescharacteristic
571#327C22×C10911yescharacteristic
572#327C22×C10911yescharacteristic, complemented
573#327C22×C10911yescharacteristic, complemented
574#327C22×C10911yescharacteristic, complemented
575#327C22×C10911yescharacteristic, complemented
576#324C22×C10911yescharacteristic, complemented
577#324C22×C10911yescharacteristic, complemented
578#323C22×C10911yescharacteristic, complemented
579#323C22×C10911yescharacteristic, complemented
580C2×#41—21no—
581C2×#41D4×C10911yescharacteristic, complemented
582C22×D4—21no—
583C22×D4—21no—
584C22×D4—21no—
585C22×D4—21no—
586C22×D4—21no—
587C22×D4D4×C10911yescharacteristic
588C22×D4D4×C10911yescharacteristic, complemented
589C22×D4C23×C10911yescharacteristic
590C23×C4C23×C10911yescharacteristic
591C2×SD16—21no—
592C2×D8—21no—
593C2×D8—21no—
594C2×D8—21no—
595C2×M16—21no—
596C22×C8—21no—
597#127—21no—
598#126—21no—
599#126—21no—
600#126—21no—
601#126—21no—
602#125—21no—
603#125—21no—
604#124—21no—
605#124—21no—
606#124—21no—
607#123—21no—
608#123—21no—
609#123—21no—
610#123—21no—
611#123—21no—
612#123—21no—
613#123—21no—
614#123—21no—
615#123—21no—
616#123—21no—
617#123—21no—
618#123—21no—
619#123—21no—
620#123—21no—
621C22⋊Q8—21no—
622C22⋊Q8—21no—
623C22⋊Q8—21no—
624C22⋊Q8—21no—
625C22⋊Q8—21no—
626C22⋊Q8D4×C10911yescharacteristic, complemented
627C22⋊Q8C23×C10911yescharacteristic
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—21no—
634#121—21no—
635#121—21no—
636#121—21no—
637#121—21no—
638#121—21no—
639#121—21no—
640#121—21no—
641#121—21no—
642#121—21no—
643#121—21no—
644#121—21no—
645#121—21no—
646#121—21no—
647#121D4×C10911yescharacteristic, complemented
648#121D4×C10911yescharacteristic, complemented
649#121D4×C10911yescharacteristic, complemented
650#121C23×C10911yescharacteristic
651#121C23×C10911yescharacteristic
652#121C23×C10911yescharacteristic
653#120—21no—
654#120—21no—
655#120—21no—
656#120—21no—
657#120—21no—
658#120—21no—
659#120—21no—
660#120—21no—
661C4×D4—21no—
662C4×D4—21no—
663C4×D4—21no—
664C4×D4—21no—
665C4×D4—21no—
666C4×D4—21no—
667C4×D4—21no—
668C4×D4—21no—
669#117—21no—
670#117D4×C10911yescharacteristic, complemented
671C2×C4⋊C4—21no—
672C2×C4⋊C4D4×C10911yescharacteristic
673C2×C4⋊C4D4×C10911yescharacteristic, complemented
674C2×C4⋊C4C23×C10911yescharacteristic
675C2×C4⋊C4C23×C10911yescharacteristic
676C2×C22⋊C4—21no—
677C2×C22⋊C4—21no—
678C2×C22⋊C4—21no—
679C2×C22⋊C4—21no—
680C2×C22⋊C4—21no—
681C2×C22⋊C4—21no—
682C2×C22⋊C4—21no—
683C2×C22⋊C4—21no—
684C2×C22⋊C4—21no—
685C2×C22⋊C4D4×C10911yescharacteristic
686C2×C22⋊C4D4×C10911yescharacteristic
687C2×C22⋊C4C23×C10911yescharacteristic
688C2×C42—21no—
689#107—21no—
690#107—21no—
691#107—21no—
692#106—21no—
693#103—21no—
694#102—21no—
695#102—21no—
696#102—21no—
697#102—21no—
698#102—21no—
699#102—21no—
700#102—21no—
701C22⋊C8—21no—
702C22⋊C8—21no—
703C22⋊C8C23×C10911yescharacteristic
704C22⋊C8C23×C10911yescharacteristic
705C22⋊C8C23×C10911yescharacteristic
706C22⋊C8C23×C10911yescharacteristic
707#95—21no—
708#95—21no—
709#95C23×C10911yescharacteristic
710#95C23×C10911yescharacteristic
711C24—21no—
712C24—21no—
713C24—21no—
714C24C2×D4×C10911yescharacteristic
715C24C2×D4×C10911yescharacteristic
716#41—81no—
717#41—81no—
718#41—81no—
719C2×Q8—21no—
720C2×Q8C2×D4×C10911yescharacteristic
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—21no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—21no—
739C2×D4—21no—
740C2×D4—42no—
741C2×D4—41no—
742C2×D4—41no—
743C2×D4—81no—
744C2×D4—81no—
745C2×D4—81no—
746C2×D4—81no—
747C2×D4—81no—
748C2×D4—81no—
749C2×D4—81no—
750C2×D4—81no—
751C2×D4—81no—
752C2×D4—81no—
753C2×D4—81no—
754C2×D4—82no—
755C2×D4C2×D4×C10911yescharacteristic
756C2×D4C2×D4×C10911yescharacteristic
757C2×D4C2×D4×C10911yescharacteristic
758C22×C4—21no—
759C22×C4—21no—
760C22×C4—21no—
761C22×C4—21no—
762C22×C4—21no—
763C22×C4—21no—
764C22×C4—21no—
765C22×C4—21no—
766C22×C4—21no—
767C22×C4—21no—
768C22×C4—81no—
769C22×C4C2×D4×C10911yescharacteristic
770C22×C4C2×D4×C10911yescharacteristic
771C22×C4C2×D4×C10911yescharacteristic
772C22×C4C2×D4×C10911yescharacteristic
773C22×C4C2×D4×C10911yescharacteristic
774C22×C4C2×D4×C10911yescharacteristic
775C22×C4C2×D4×C10911yescharacteristic
776C22×C4C2×D4×C10911yescharacteristic
777C22×C4C24×C10911yescharacteristic
778SD16—81no—
779D8—81no—
780D8—81no—
781D8—81no—
782M16—81no—
783C2×C8—21no—
784C2×C8—21no—
785C2×C8—21no—
786C2×C8—21no—
787C2×C8—81no—
788C4⋊C4—21no—
789C4⋊C4—21no—
790C4⋊C4—21no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—21no—
794C4⋊C4—21no—
795C4⋊C4—21no—
796C4⋊C4—21no—
797C4⋊C4—21no—
798C4⋊C4—21no—
799C4⋊C4—21no—
800C4⋊C4—21no—
801C4⋊C4—21no—
802C4⋊C4—21no—
803C4⋊C4—81no—
804C4⋊C4C2×D4×C10911yescharacteristic
805C4⋊C4C2×D4×C10911yescharacteristic
806C4⋊C4C2×D4×C10911yescharacteristic
807C4⋊C4C2×D4×C10911yescharacteristic
808C22⋊C4—21no—
809C22⋊C4—21no—
810C22⋊C4—21no—
811C22⋊C4—21no—
812C22⋊C4—21no—
813C22⋊C4—21no—
814C22⋊C4—21no—
815C22⋊C4—21no—
816C22⋊C4—21no—
817C22⋊C4—21no—
818C22⋊C4—21no—
819C22⋊C4—21no—
820C22⋊C4—21no—
821C22⋊C4—21no—
822C22⋊C4—21no—
823C22⋊C4—21no—
824C22⋊C4—21no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—21no—
830C22⋊C4—21no—
831C22⋊C4—21no—
832C22⋊C4—21no—
833C22⋊C4—42no—
834C22⋊C4—42no—
835C22⋊C4—41no—
836C22⋊C4—41no—
837C22⋊C4—81no—
838C22⋊C4—81no—
839C22⋊C4—81no—
840C42—21no—
841C42—21no—
842C42—21no—
843C42—81no—
844C23—21no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—21no—
849C23—21no—
850C23—21no—
851C23—21no—
852C23—41no—
853C23—41no—
854C23—42no—
855C23—41no—
856C23—41no—
857C23—41no—
858C23—41no—
859C23—41no—
860C23—41no—
861C23—41no—
862C23—41no—
863C23—41no—
864C23—81no—
865C23—81no—
866C23—81no—
867C23—81no—
868C23—81no—
869C23#120×C10911yescharacteristic
870C23#120×C10911yescharacteristic
871C23C22×D4×C10911yescharacteristic
872Q8—41no—
873Q8—81no—
874D4—41no—
875D4—41no—
876D4—41no—
877D4—41no—
878D4—41no—
879D4—41no—
880D4—41no—
881D4—42no—
882D4—42no—
883D4—41no—
884D4—41no—
885D4—41no—
886D4—41no—
887D4—41no—
888D4—41no—
889D4—81no—
890D4—81no—
891D4—81no—
892D4—81no—
893D4—81no—
894D4—81no—
895D4—81no—
896D4—81no—
897D4—81no—
898D4—81no—
899D4—81no—
900D4—81no—
901D4—84no—
902D4—82no—
903D4—82no—
904C2×C4—22no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—21no—
913C2×C4—21no—
914C2×C4—21no—
915C2×C4—41no—
916C2×C4—41no—
917C2×C4—41no—
918C2×C4—41no—
919C2×C4—41no—
920C2×C4—41no—
921C2×C4—41no—
922C2×C4—41no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—41no—
928C2×C4—41no—
929C2×C4—41no—
930C2×C4—41no—
931C2×C4—81no—
932C2×C4—81no—
933C2×C4—81no—
934C2×C4—81no—
935C2×C4—81no—
936C2×C4—81no—
937C2×C4—81no—
938C2×C4#120×C10911yescharacteristic
939C2×C4#120×C10911yescharacteristic
940C2×C4C22×D4×C10911yescharacteristic
941C2×C4C22×D4×C10911yescharacteristic
942C8—41no—
943C8—41no—
944C8—41no—
945C8—41no—
946C22—21no—
947C22—21no—
948C22—21no—
949C22—21no—
950C22—21no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—41no—
955C22—41no—
956C22—41no—
957C22—41no—
958C22—41no—
959C22—41no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—41no—
964C22—41no—
965C22—41no—
966C22—81no—
967C22—81no—
968C22—81no—
969C22—81no—
970C22—81no—
971C22—81no—
972C22—81no—
973C22—81no—
974C22—81no—
975C22—81no—
976C22—81no—
977C22—162no—
978C22—162no—
979C22C2×#120×C10911yescharacteristic
980C22#576×C10911yescharacteristic
981C22#576×C10911yescharacteristic
982C4—21no—
983C4—21no—
984C4—21no—
985C4—21no—
986C4—42no—
987C4—41no—
988C4—41no—
989C4—41no—
990C4—41no—
991C4—41no—
992C4—41no—
993C4—41no—
994C4—41no—
995C4—81no—
996C4—81no—
997C2—21no—
998C2—21no—
999C2—41no—
1000C2—41no—
1001C2—81no—
1002C2—81no—
1003C2—81no—
1004C2—81no—
1005C2—161no—
1006C2C109×#300811yescharacteristic
1007C2C109×#301811yescharacteristic
1008C2C109×#302611yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3534C2semidirect
2. C109×#3194C2semidirect
3. C109×#3186C2semidirect
4. C109×#2661C2semidirect
5. C109×#1612C2semidirect
6. C109×#1610C2semidirect
7. C109×#1609C2semidirect
8. C109×#1607C2semidirect
9. C109×#1600C2semidirect
10. C109×#1598C2semidirect
11. C109×#1597C2semidirect
12. C109×#1595C2semidirect
13. C109×#1507C2semidirect
14. C109×#1501C2semidirect
15. C109×#1468C2semidirect
35. C2×#121×C109C22semidirect
36. #483×C109C22semidirect
40. #480×C109C22semidirect
41. #480×C109C22semidirect
46. #450×C109C22semidirect
50. #447×C109C22semidirect
51. #447×C109C22semidirect
52. #407×C109C22semidirect
53. C2×C22⋊C8×C109C22semidirect
54. #398×C109C22semidirect
55. #397×C109C22semidirect
57. #394×C109C22semidirect
59. #392×C109C22semidirect
62. C4×C22⋊C4×C109C22semidirect
63. #328×C109C22semidirect
64. #328×C109C22semidirect
67. #327×C109C22semidirect
68. #327×C109C22semidirect
69. #327×C109C22semidirect
70. #327×C109C22semidirect
71. #324×C109C22semidirect
72. #324×C109C22semidirect
73. #323×C109C22semidirect
74. #323×C109C22semidirect
76. C2×#41×C109D4semidirect
83. C22×D4×C109D4semidirect
121. C22⋊Q8×C109D4semidirect
142. #121×C109D4semidirect
143. #121×C109D4semidirect
144. #121×C109D4semidirect
165. #117×C109D4semidirect
168. C2×C4⋊C4×C109D4semidirect
492. #18414C109direct (N × H)
505. #3534C2×C109semidirect
506. #3194C2×C109semidirect
507. #3186C2×C109semidirect
508. #2661C2×C109semidirect
509. #1612C2×C109semidirect
510. #1610C2×C109semidirect
511. #1609C2×C109semidirect
512. #1607C2×C109semidirect
513. #1600C2×C109semidirect
514. #1598C2×C109semidirect
515. #1597C2×C109semidirect
516. #1595C2×C109semidirect
517. #1507C2×C109semidirect
518. #1501C2×C109semidirect
519. #1468C2×C109semidirect
520. C109#18414direct (N × H)
540. C2×#121C22×C109semidirect
541. #483C22×C109semidirect
545. #480C22×C109semidirect
546. #480C22×C109semidirect
551. #450C22×C109semidirect
555. #447C22×C109semidirect
556. #447C22×C109semidirect
557. #407C22×C109semidirect
558. C2×C22⋊C8C22×C109semidirect
559. #398C22×C109semidirect
560. #397C22×C109semidirect
562. #394C22×C109semidirect
564. #392C22×C109semidirect
567. C4×C22⋊C4C22×C109semidirect
568. #328C22×C109semidirect
569. #328C22×C109semidirect
572. #327C22×C109semidirect
573. #327C22×C109semidirect
574. #327C22×C109semidirect
575. #327C22×C109semidirect
576. #324C22×C109semidirect
577. #324C22×C109semidirect
578. #323C22×C109semidirect
579. #323C22×C109semidirect
581. C2×#41D4×C109semidirect
588. C22×D4D4×C109semidirect
626. C22⋊Q8D4×C109semidirect
647. #121D4×C109semidirect
648. #121D4×C109semidirect
649. #121D4×C109semidirect
670. #117D4×C109semidirect
673. C2×C4⋊C4D4×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35342
C109×#31942
C109×#31862
C109×#26612
C109×#16122
C109×#16102
C109×#16092
C109×#16072
C109×#16002
C109×#15982
C109×#15972
C109×#15952
C109×#15072
C109×#15012
C109×#14682
#18414109