Finite Group Databasebeta

← C109×#25147 #42143141

Subgroups — C109×#25147 #42143141

Order 27904.

1022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#471×C109C211yesmaximal, characteristic, complemented
2C109×#3055C211yesmaximal, characteristic, complemented
3C109×#3005C211yesmaximal, characteristic, complemented
4C2×#449×C109C211yesmaximal, characteristic, complemented
5C109×#2933C211yesmaximal, characteristic, complemented
6C2×#413×C109C211yesmaximal, characteristic, complemented
7C109×#2063C211yesmaximal, characteristic, complemented
8C109×#2052C211yesmaximal, characteristic, complemented
9C109×#2046C211yesmaximal, characteristic, complemented
10C109×#2018C211yesmaximal, characteristic, complemented
11C109×#1978C211yesmaximal, characteristic, complemented
12C109×#1930C211yesmaximal, characteristic, complemented
13C109×#1907C211yesmaximal, characteristic, complemented
14C109×#1900C211yesmaximal, characteristic, complemented
15C109×#1855C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C2×#137×C109C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C109C2211yescharacteristic
20C22×SD16×C109C2211yescharacteristic
21C22×D8×C109C2211yescharacteristic
22C2×#131×C109C2211yescharacteristic
23C22×M16×C109C2211yescharacteristic
24C22×M16×C109C2211yescharacteristic
25#525×C109C2211yescharacteristic
26C2×#121×C109C2211yescharacteristic
27#471×C109—24no—
28#469×C109—21no—
29#468×C109—21no—
30#466×C109—21no—
31#465×C109—21no—
32#452×C109—21no—
33#452×C109—21no—
34#449×C109—21no—
35#449×C109—21no—
36#449×C109—21no—
37#449×C109—21no—
38#449×C109—21no—
39#449×C109—21no—
40#436×C109—21no—
41#435×C109—21no—
42#435×C109—21no—
43C8×D4×C109—21no—
44C2×#108×C109C2211yescharacteristic
45C2×#108×C109C2211yescharacteristic
46#428×C109C2211yescharacteristic
47#424×C109C2211yescharacteristic
48#419×C109C2211yescharacteristic
49#418×C109C2211yescharacteristic
50#418×C109C2211yescharacteristic
51#417×C109C2211yescharacteristic
52C2×#103×C109C2211yescharacteristic
53C2×#102×C109C2211yescharacteristic
54#413×C109—24no—
55C2×#101×C109C2211yescharacteristic
56C2×#101×C109C2211yescharacteristic
57C2×#100×C109C2211yescharacteristic
58C2×#100×C109C2211yescharacteristic
59C2×#100×C109C2211yescharacteristic
60C2×#100×C109C2211yescharacteristic
61#408×C109C2211yescharacteristic
62#407×C109C2211yescharacteristic
63C2×C22⋊C8×C109C2211yescharacteristic
64#405×C109C2211yescharacteristic
65#343×C109C2211yescharacteristic
66#343×C109C2211yescharacteristic
67#341×C109C2211yescharacteristic
68#341×C109C2211yescharacteristic
69C2×#41×C109—22no—
70C2×#41×C109—22no—
71C2×#41×C109—21no—
72C2×#41×C109—21no—
73C2×#41×C109—21no—
74C2×#41×C109—21no—
75C2×#41×C109—41no—
76C2×#41×C109—41no—
77C2×#41×C109C2311yescharacteristic
78C22×Q8×C109C2311yescharacteristic
79C22×D4×C109—21no—
80C22×D4×C109—21no—
81C22×D4×C109C2311yescharacteristic
82C22×D4×C109C2311yescharacteristic
83C23×C4×C109—21no—
84C23×C4×C109C2311yescharacteristic
85#137×C109—22no—
86#137×C109—41no—
87AGL(1,ℤ/8)×C109—22no—
88AGL(1,ℤ/8)×C109—22no—
89AGL(1,ℤ/8)×C109—41no—
90AGL(1,ℤ/8)×C109—41no—
91C2×Q16×C109—21no—
92C2×SD16×C109—22no—
93C2×SD16×C109—21no—
94C2×SD16×C109—21no—
95C2×SD16×C109—21no—
96C2×SD16×C109—21no—
97C2×SD16×C109—21no—
98C2×SD16×C109—41no—
99C2×D8×C109—21no—
100C2×D8×C109—21no—
101C2×D8×C109—22no—
102C2×D8×C109—21no—
103C2×D8×C109—21no—
104C2×D8×C109—41no—
105#131×C109—22no—
106#131×C109—41no—
107C2×M16×C109—21no—
108C2×M16×C109—21no—
109C2×M16×C109—21no—
110C2×M16×C109—22no—
111C2×M16×C109—22no—
112C2×M16×C109—41no—
113C2×M16×C109—41no—
114C2×M16×C109C2311yescharacteristic
115C2×M16×C109C2311yescharacteristic
116C2×M16×C109C2311yescharacteristic
117C2×M16×C109C2311yescharacteristic
118C2×M16×C109C2311yescharacteristic
119C2×M16×C109C2311yescharacteristic
120C22×C8×C109—21no—
121C22×C8×C109—21no—
122C22×C8×C109—21no—
123C22×C8×C109C2311yescharacteristic
124C22×C8×C109C2311yescharacteristic
125#123×C109—21no—
126C22⋊Q8×C109D411yescharacteristic
127C22⋊Q8×C109D411yescharacteristic
128#121×C109—21no—
129#121×C109—21no—
130#121×C109—21no—
131#121×C109—21no—
132#121×C109D411yescharacteristic
133#121×C109D411yescharacteristic
134#120×C109—21no—
135C4×D4×C109—21no—
136C4×D4×C109—21no—
137#117×C109C2311yescharacteristic
138C2×C4⋊C4×C109C2311yescharacteristic
139C2×C22⋊C4×C109—21no—
140#108×C109—22no—
141#108×C109—41no—
142#107×C109—21no—
143#106×C109—21no—
144C4⋊C8×C109—21no—
145C4⋊C8×C109—21no—
146#103×C109—21no—
147#103×C109—21no—
148#103×C109—21no—
149#103×C109—21no—
150#103×C109—21no—
151#102×C109—21no—
152#102×C109—21no—
153#102×C109—21no—
154#102×C109—21no—
155#102×C109—21no—
156#102×C109—21no—
157#102×C109—21no—
158#101×C109—22no—
159#101×C109D414yescomplemented
160#100×C109—22no—
161#100×C109—22no—
162#100×C109—22no—
163#100×C109—41no—
164C22⋊C8×C109—21no—
165C22⋊C8×C109—21no—
166C22⋊C8×C109—21no—
167C22⋊C8×C109—21no—
168C22⋊C8×C109D411yescharacteristic
169C22⋊C8×C109D411yescharacteristic
170C22⋊C8×C109D411yescharacteristic
171C22⋊C8×C109D411yescharacteristic
172#97×C109—21no—
173C4×C8×C109—21no—
174C24×C109—21no—
175C24×C109—21no—
176C24×C109#4111yescharacteristic
177#41×C109—21no—
178#41×C109—21no—
179#41×C109—21no—
180#41×C109—21no—
181#41×C109—42no—
182#41×C109—42no—
183#41×C109—42no—
184#41×C109—42no—
185#41×C109—42no—
186#41×C109—42no—
187#41×C109—42no—
188#41×C109—42no—
189C2×Q8×C109—21no—
190C2×Q8×C109—21no—
191C2×Q8×C109—21no—
192C2×Q8×C109—21no—
193C2×Q8×C109—21no—
194C2×Q8×C109C2×D412yes—
195C2×Q8×C109C2×D411yescharacteristic
196C2×D4×C109—24no—
197C2×D4×C109—21no—
198C2×D4×C109—21no—
199C2×D4×C109—21no—
200C2×D4×C109—21no—
201C2×D4×C109—21no—
202C2×D4×C109—21no—
203C2×D4×C109—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—42no—
212C2×D4×C109—41no—
213C2×D4×C109—41no—
214C2×D4×C109—41no—
215C2×D4×C109—41no—
216C2×D4×C109—82no—
217C2×D4×C109C2×D411yescharacteristic
218C2×D4×C109#4112yes—
219C22×C4×C109—21no—
220C22×C4×C109—21no—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—24no—
224C22×C4×C109—21no—
225C22×C4×C109—21no—
226C22×C4×C109—21no—
227C22×C4×C109—42no—
228C22×C4×C109—41no—
229C22×C4×C109—41no—
230C22×C4×C109C2×D411yescharacteristic
231C22×C4×C109C2×D411yescharacteristic
232C22×C4×C109C2×D411yescharacteristic
233C22×C4×C109C2×D411yescharacteristic
234C22×C4×C109#4111yescharacteristic
235C22×C4×C109C2411yescharacteristic
236Q16×C109—42no—
237SD16×C109—42no—
238SD16×C109—42no—
239SD16×C109—42no—
240SD16×C109—42no—
241SD16×C109—42no—
242D8×C109—42no—
243D8×C109—42no—
244D8×C109—42no—
245D8×C109—42no—
246M16×C109—21no—
247M16×C109—21no—
248M16×C109—21no—
249M16×C109—21no—
250M16×C109—21no—
251M16×C109—21no—
252M16×C109—21no—
253M16×C109—21no—
254M16×C109—21no—
255M16×C109—21no—
256M16×C109—42no—
257M16×C109—42no—
258M16×C109—42no—
259M16×C109C2×D412yes—
260M16×C109C2×D412yes—
261C2×C8×C109—21no—
262C2×C8×C109—21no—
263C2×C8×C109—21no—
264C2×C8×C109—21no—
265C2×C8×C109—21no—
266C2×C8×C109—21no—
267C2×C8×C109—21no—
268C2×C8×C109—21no—
269C2×C8×C109—21no—
270C2×C8×C109—21no—
271C2×C8×C109—42no—
272C2×C8×C109—42no—
273C2×C8×C109—42no—
274C2×C8×C109C2×D411yescharacteristic
275C2×C8×C109C2×D411yescharacteristic
276C2×C8×C109C2×D411yescharacteristic
277C2×C8×C109C2×D411yescharacteristic
278C4⋊C4×C109—21no—
279C4⋊C4×C109—21no—
280C4⋊C4×C109—21no—
281C4⋊C4×C109—21no—
282C4⋊C4×C109C2×D411yescharacteristic
283C4⋊C4×C109C2×D411yescharacteristic
284C22⋊C4×C109—21no—
285C22⋊C4×C109—21no—
286C22⋊C4×C109—21no—
287C22⋊C4×C109—21no—
288C22⋊C4×C109—21no—
289C22⋊C4×C109—41no—
290C22⋊C4×C109—41no—
291C42×C109—21no—
292C23×C109—21no—
293C23×C109—21no—
294C23×C109—21no—
295C23×C109—22no—
296C23×C109—41no—
297C23×C109—41no—
298C23×C109—41no—
299C23×C109—41no—
300C23×C109—41no—
301C23×C109—41no—
302C23×C109—41no—
303C23×C109—81no—
304C23×C109—81no—
305C23×C109—81no—
306C23×C109—81no—
307C23×C109#12111yescharacteristic
308C23×C109#12111yescharacteristic
309C23×C109C2×#4111yescharacteristic
310Q8×C109—21no—
311Q8×C109—22no—
312Q8×C109—22no—
313Q8×C109—21no—
314Q8×C109—41no—
315Q8×C109—41no—
316D4×C109—21no—
317D4×C109—22no—
318D4×C109—21no—
319D4×C109—22no—
320D4×C109—42no—
321D4×C109—44no—
322D4×C109—44no—
323D4×C109—41no—
324D4×C109—41no—
325D4×C109—41no—
326D4×C109—41no—
327D4×C109—41no—
328D4×C109—41no—
329D4×C109—41no—
330D4×C109—41no—
331D4×C109—81no—
332D4×C109—82no—
333D4×C109—82no—
334C2×C4×C109—21no—
335C2×C4×C109—21no—
336C2×C4×C109—21no—
337C2×C4×C109—21no—
338C2×C4×C109—21no—
339C2×C4×C109—21no—
340C2×C4×C109—21no—
341C2×C4×C109—21no—
342C2×C4×C109—21no—
343C2×C4×C109—21no—
344C2×C4×C109—21no—
345C2×C4×C109—21no—
346C2×C4×C109—21no—
347C2×C4×C109—22no—
348C2×C4×C109—44no—
349C2×C4×C109—44no—
350C2×C4×C109—41no—
351C2×C4×C109—41no—
352C2×C4×C109—41no—
353C2×C4×C109—41no—
354C2×C4×C109—41no—
355C2×C4×C109—81no—
356C2×C4×C109#12111yescharacteristic
357C2×C4×C109#12111yescharacteristic
358C2×C4×C109C22×D411yescharacteristic
359C2×C4×C109C22×D411yescharacteristic
360C2×C4×C109C22×D411yescharacteristic
361C2×C4×C109C2×#4111yescharacteristic
362C2×C4×C109H(5,𝔽2)11yescharacteristic
363C2×C4×C109H(5,𝔽2)11yescharacteristic
364C8×C109—21no—
365C8×C109—21no—
366C8×C109—22no—
367C8×C109—22no—
368C8×C109—21no—
369C8×C109—21no—
370C8×C109—41no—
371C8×C109—41no—
372C8×C109—41no—
373C8×C109—41no—
374C22×C109—21no—
375C22×C109—21no—
376C22×C109—21no—
377C22×C109—21no—
378C22×C109—21no—
379C22×C109—21no—
380C22×C109—21no—
381C22×C109—21no—
382C22×C109—42no—
383C22×C109—41no—
384C22×C109—41no—
385C22×C109—41no—
386C22×C109—81no—
387C22×C109—81no—
388C22×C109—82no—
389C22×C109—82no—
390C22×C109—81no—
391C22×C109—81no—
392C22×C109—81no—
393C22×C109—81no—
394C22×C109—81no—
395C22×C109—161no—
396C22×C109—161no—
397C22×C109C2×#12111yescharacteristic
398C22×C109#52511yescharacteristic
399C22×C109#53811yescharacteristic
400C4×C109—21no—
401C4×C109—21no—
402C4×C109—42no—
403C4×C109—41no—
404C4×C109—41no—
405C4×C109—41no—
406C4×C109—81no—
407C4×C109D4211yescharacteristic
408C4×C109D4211yescharacteristic
409C4×C109#54611yescharacteristic
410C4×C109#54611yescharacteristic
411#25147C10911yesmaximal, characteristic, direct product factor, Sylow
412C2×C109—21no—
413C2×C109—21no—
414C2×C109—41no—
415C2×C109—41no—
416C2×C109—81no—
417C2×C109—82no—
418C2×C109—161no—
419C2×C109#242411yescharacteristic
420C2×C109#306711yescharacteristic
421C2×C109#306811yescharacteristic
422C2×#471C2×C10911yescharacteristic, complemented
423#3055C2×C10911yescharacteristic, complemented
424#3005C2×C10911yescharacteristic, complemented
425C2×#449C2×C10911yescharacteristic, complemented
426#2933C2×C10911yescharacteristic, complemented
427C2×#413C2×C10911yescharacteristic, complemented
428#2063C2×C10911yescharacteristic, complemented
429#2052C2×C10911yescharacteristic, complemented
430#2046C2×C10911yescharacteristic, complemented
431#2018C2×C10911yescharacteristic, complemented
432#1978C2×C10911yescharacteristic, complemented
433#1930C2×C10911yescharacteristic, complemented
434#1907C2×C10911yescharacteristic, complemented
435#1900C2×C10911yescharacteristic, complemented
436#1855C2×C10911yescharacteristic, complemented
437C109#2514711yescharacteristic, direct product factor, Sylow
438C22×#41C22×C10911yescharacteristic
439C2×#137C22×C10911yescharacteristic
440C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
441C2×AGL(1,ℤ/8)C22×C10911yescharacteristic
442C22×SD16C22×C10911yescharacteristic
443C22×D8C22×C10911yescharacteristic
444C2×#131C22×C10911yescharacteristic
445C22×M16C22×C10911yescharacteristic
446C22×M16C22×C10911yescharacteristic
447#525C22×C10911yescharacteristic
448C2×#121C22×C10911yescharacteristic
449#471—24no—
450#469—21no—
451#468—21no—
452#466—21no—
453#465—21no—
454#452—21no—
455#452—21no—
456#449—21no—
457#449—21no—
458#449—21no—
459#449—21no—
460#449—21no—
461#449—21no—
462#436—21no—
463#435—21no—
464#435—21no—
465C8×D4—21no—
466C2×#108C22×C10911yescharacteristic
467C2×#108C22×C10911yescharacteristic
468#428C22×C10911yescharacteristic
469#424C22×C10911yescharacteristic
470#419C22×C10911yescharacteristic
471#418C22×C10911yescharacteristic
472#418C22×C10911yescharacteristic
473#417C22×C10911yescharacteristic
474C2×#103C22×C10911yescharacteristic
475C2×#102C22×C10911yescharacteristic
476#413—24no—
477C2×#101C22×C10911yescharacteristic
478C2×#101C22×C10911yescharacteristic
479C2×#100C22×C10911yescharacteristic
480C2×#100C22×C10911yescharacteristic
481C2×#100C22×C10911yescharacteristic
482C2×#100C22×C10911yescharacteristic
483#408C22×C10911yescharacteristic
484#407C22×C10911yescharacteristic
485C2×C22⋊C8C22×C10911yescharacteristic
486#405C22×C10911yescharacteristic
487#343C22×C10911yescharacteristic
488#343C22×C10911yescharacteristic
489#341C22×C10911yescharacteristic
490#341C22×C10911yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41C23×C10911yescharacteristic
500C22×Q8C23×C10911yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C23×C10911yescharacteristic
504C22×D4C23×C10911yescharacteristic
505C23×C4—21no—
506C23×C4C23×C10911yescharacteristic
507#137—22no—
508#137—41no—
509AGL(1,ℤ/8)—22no—
510AGL(1,ℤ/8)—22no—
511AGL(1,ℤ/8)—41no—
512AGL(1,ℤ/8)—41no—
513C2×Q16—21no—
514C2×SD16—22no—
515C2×SD16—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—41no—
521C2×D8—21no—
522C2×D8—21no—
523C2×D8—22no—
524C2×D8—21no—
525C2×D8—21no—
526C2×D8—41no—
527#131—22no—
528#131—41no—
529C2×M16—21no—
530C2×M16—21no—
531C2×M16—21no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16C23×C10911yescharacteristic
537C2×M16C23×C10911yescharacteristic
538C2×M16C23×C10911yescharacteristic
539C2×M16C23×C10911yescharacteristic
540C2×M16C23×C10911yescharacteristic
541C2×M16C23×C10911yescharacteristic
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8C23×C10911yescharacteristic
546C22×C8C23×C10911yescharacteristic
547#123—21no—
548C22⋊Q8D4×C10911yescharacteristic
549C22⋊Q8D4×C10911yescharacteristic
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121D4×C10911yescharacteristic
555#121D4×C10911yescharacteristic
556#120—21no—
557C4×D4—21no—
558C4×D4—21no—
559#117C23×C10911yescharacteristic
560C2×C4⋊C4C23×C10911yescharacteristic
561C2×C22⋊C4—21no—
562#108—22no—
563#108—41no—
564#107—21no—
565#106—21no—
566C4⋊C8—21no—
567C4⋊C8—21no—
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#103—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#101—22no—
581#101D4×C10914yescomplemented
582#100—22no—
583#100—22no—
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8D4×C10911yescharacteristic
591C22⋊C8D4×C10911yescharacteristic
592C22⋊C8D4×C10911yescharacteristic
593C22⋊C8D4×C10911yescharacteristic
594#97—21no—
595C4×C8—21no—
596C24—21no—
597C24—21no—
598C24#41×C10911yescharacteristic
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×D4×C10912yes—
617C2×Q8C2×D4×C10911yescharacteristic
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—42no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—82no—
639C2×D4C2×D4×C10911yescharacteristic
640C2×D4#41×C10912yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—42no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4C2×D4×C10911yescharacteristic
653C22×C4C2×D4×C10911yescharacteristic
654C22×C4C2×D4×C10911yescharacteristic
655C22×C4C2×D4×C10911yescharacteristic
656C22×C4#41×C10911yescharacteristic
657C22×C4C24×C10911yescharacteristic
658Q16—42no—
659SD16—42no—
660SD16—42no—
661SD16—42no—
662SD16—42no—
663SD16—42no—
664D8—42no—
665D8—42no—
666D8—42no—
667D8—42no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16—42no—
680M16—42no—
681M16C2×D4×C10912yes—
682M16C2×D4×C10912yes—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8C2×D4×C10911yescharacteristic
697C2×C8C2×D4×C10911yescharacteristic
698C2×C8C2×D4×C10911yescharacteristic
699C2×C8C2×D4×C10911yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4C2×D4×C10911yescharacteristic
705C4⋊C4C2×D4×C10911yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—41no—
712C22⋊C4—41no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23#121×C10911yescharacteristic
730C23#121×C10911yescharacteristic
731C23C2×#41×C10911yescharacteristic
732Q8—21no—
733Q8—22no—
734Q8—22no—
735Q8—21no—
736Q8—41no—
737Q8—41no—
738D4—21no—
739D4—22no—
740D4—21no—
741D4—22no—
742D4—44no—
743D4—44no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—82no—
755D4—82no—
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—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4#121×C10911yescharacteristic
779C2×C4#121×C10911yescharacteristic
780C2×C4C22×D4×C10911yescharacteristic
781C2×C4C22×D4×C10911yescharacteristic
782C2×C4C22×D4×C10911yescharacteristic
783C2×C4C2×#41×C10911yescharacteristic
784C2×C4H(5,𝔽2)×C10911yescharacteristic
785C2×C4H(5,𝔽2)×C10911yescharacteristic
786C8—21no—
787C8—21no—
788C8—22no—
789C8—22no—
790C8—21no—
791C8—21no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—161no—
818C22—161no—
819C22C2×#121×C10911yescharacteristic
820C22#525×C10911yescharacteristic
821C22#538×C10911yescharacteristic
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—81no—
829C4D42×C10911yescharacteristic
830C4D42×C10911yescharacteristic
831C4#546×C10911yescharacteristic
832C4#546×C10911yescharacteristic
833C2—21no—
834C2—21no—
835C2—41no—
836C2—41no—
837C2—81no—
838C2—82no—
839C2—161no—
840C2C109×#242411yescharacteristic
841C2C109×#306711yescharacteristic
842C2C109×#306811yescharacteristic
subgroupG/H
center, socleC22×C109C2×#121
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#471×C109C2semidirect
2. C109×#3055C2semidirect
3. C109×#3005C2semidirect
4. C2×#449×C109C2semidirect
5. C109×#2933C2semidirect
6. C2×#413×C109C2semidirect
7. C109×#2063C2semidirect
8. C109×#2052C2semidirect
9. C109×#2046C2semidirect
10. C109×#2018C2semidirect
11. C109×#1978C2semidirect
12. C109×#1930C2semidirect
13. C109×#1907C2semidirect
14. C109×#1900C2semidirect
15. C109×#1855C2semidirect
159. #101×C109D4semidirect
411. #25147C109direct (N × H)
422. C2×#471C2×C109semidirect
423. #3055C2×C109semidirect
424. #3005C2×C109semidirect
425. C2×#449C2×C109semidirect
426. #2933C2×C109semidirect
427. C2×#413C2×C109semidirect
428. #2063C2×C109semidirect
429. #2052C2×C109semidirect
430. #2046C2×C109semidirect
431. #2018C2×C109semidirect
432. #1978C2×C109semidirect
433. #1930C2×C109semidirect
434. #1907C2×C109semidirect
435. #1900C2×C109semidirect
436. #1855C2×C109semidirect
437. C109#25147direct (N × H)
581. #101D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#471×C1092
C109×#30552
C109×#30052
C2×#449×C1092
C109×#29332
C2×#413×C1092
C109×#20632
C109×#20522
C109×#20462
C109×#20182
C109×#19782
C109×#19302
C109×#19072
C109×#19002
C109×#18552
#25147109