Finite Group Databasebeta

← C109×#19010 #42137004

Subgroups — C109×#19010 #42137004

Order 27904.

920 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3529C211yesmaximal, characteristic, complemented
2C109×#3219C211yesmaximal, characteristic, complemented
3C109×#3214C211yesmaximal, characteristic, complemented
4C109×#3180C211yesmaximal, characteristic, complemented
5C109×#1664C211yesmaximal, characteristic, complemented
6C109×#1662C211yesmaximal, characteristic, complemented
7C109×#1661C211yesmaximal, characteristic, complemented
8C109×#1659C211yesmaximal, characteristic, complemented
9C109×#1657C211yesmaximal, characteristic, complemented
10C109×#1656C211yesmaximal, characteristic, complemented
11C109×#1656C211yesmaximal, characteristic, complemented
12C109×#1655C211yesmaximal, characteristic, complemented
13C109×#1535C211yesmaximal, characteristic, complemented
14C109×#1532C211yesmaximal, characteristic, complemented
15C109×#1530C211yesmaximal, characteristic, complemented
16#563×C109—21no—
17#563×C109C2211yescharacteristic
18#562×C109—21no—
19#562×C109—21no—
20#562×C109C2211yescharacteristic
21#562×C109C2211yescharacteristic
22H(3,𝔽4)×C109C2211yescharacteristic
23#560×C109—21no—
24#560×C109—21no—
25#560×C109—21no—
26#532×C109—21no—
27#532×C109C2211yescharacteristic
28#532×C109C2211yescharacteristic, complemented
29#529×C109—21no—
30#529×C109—21no—
31#529×C109C2211yescharacteristic
32#529×C109C2211yescharacteristic
33#525×C109—21no—
34#525×C109—21no—
35#525×C109—21no—
36#501×C109C2211yescharacteristic, complemented
37#497×C109C2211yescharacteristic
38#496×C109C2211yescharacteristic
39#496×C109C2211yescharacteristic
40#496×C109C2211yescharacteristic
41#496×C109C2211yescharacteristic, complemented
42#491×C109C2211yescharacteristic, complemented
43#490×C109C2211yescharacteristic, complemented
44#490×C109C2211yescharacteristic, complemented
45#489×C109C2211yescharacteristic
46#489×C109C2211yescharacteristic
47#489×C109C2211yescharacteristic, complemented
48#466×C109—21no—
49#465×C109—21no—
50#464×C109—21no—
51#463×C109—21no—
52#461×C109—21no—
53#459×C109—21no—
54#452×C109—21no—
55#449×C109—21no—
56#449×C109—21no—
57#449×C109—21no—
58#442×C109—21no—
59#440×C109—21no—
60#432×C109C2211yescharacteristic, complemented
61#432×C109C2211yescharacteristic, complemented
62C2×#97×C109C2211yescharacteristic, complemented
63#330×C109C2211yescharacteristic, complemented
64#330×C109C2211yescharacteristic, complemented
65#330×C109C2211yescharacteristic, complemented
66#330×C109C2211yescharacteristic, complemented
67#329×C109C2211yescharacteristic
68#329×C109C2211yescharacteristic
69#329×C109C2211yescharacteristic
70#329×C109C2211yescharacteristic
71#329×C109C2211yescharacteristic
72#329×C109C2211yescharacteristic
73#329×C109C2211yescharacteristic, complemented
74#329×C109C2211yescharacteristic, complemented
75C2×#41×C109—21no—
76C2×#41×C109—21no—
77C2×#41×C109D411yescharacteristic
78C2×#41×C109D411yescharacteristic
79C23×C4×C109—21no—
80C2×Q16×C109—21no—
81C2×SD16×C109—21no—
82C2×SD16×C109—21no—
83C2×SD16×C109—21no—
84C2×SD16×C109—21no—
85C2×SD16×C109—21no—
86C2×D8×C109—21no—
87C2×D8×C109—21no—
88C2×D8×C109—21no—
89C2×D8×C109—21no—
90C22×C8×C109—21no—
91C4⋊Q8×C109—21no—
92C4⋊Q8×C109D411yescharacteristic
93C4⋊Q8×C109C2311yescharacteristic
94#127×C109—21no—
95#127×C109D411yescharacteristic
96#127×C109C2311yescharacteristic
97#126×C109—21no—
98#126×C109—21no—
99#126×C109—21no—
100#126×C109—21no—
101#126×C109—21no—
102#126×C109—21no—
103#125×C109—21no—
104#125×C109—21no—
105#125×C109C2311yescharacteristic
106#125×C109C2311yescharacteristic
107#124×C109—21no—
108#124×C109—21no—
109#124×C109—21no—
110#124×C109—21no—
111#124×C109—21no—
112#124×C109C2311yescharacteristic
113#124×C109C2311yescharacteristic
114#124×C109C2311yescharacteristic
115#124×C109C2311yescharacteristic
116#123×C109—21no—
117#123×C109—21no—
118#123×C109—21no—
119#123×C109—21no—
120#123×C109—21no—
121#123×C109—21no—
122#123×C109—21no—
123#123×C109—21no—
124#123×C109—21no—
125#123×C109—21no—
126#123×C109—21no—
127#123×C109—21no—
128C22⋊Q8×C109—21no—
129C22⋊Q8×C109—21no—
130C22⋊Q8×C109—21no—
131C22⋊Q8×C109—21no—
132C22⋊Q8×C109—21no—
133C22⋊Q8×C109—21no—
134C22⋊Q8×C109—21no—
135C22⋊Q8×C109—21no—
136C22⋊Q8×C109D411yescharacteristic
137C22⋊Q8×C109D411yescharacteristic
138#121×C109—21no—
139#121×C109—21no—
140#121×C109—21no—
141#121×C109—21no—
142#121×C109—21no—
143#121×C109—21no—
144#121×C109—21no—
145#121×C109—21no—
146#121×C109—21no—
147#121×C109—21no—
148#121×C109—21no—
149#121×C109—21no—
150#121×C109—21no—
151#121×C109—21no—
152#121×C109—21no—
153#121×C109—21no—
154#121×C109D411yescharacteristic
155#121×C109D411yescharacteristic
156#120×C109—21no—
157#120×C109—21no—
158#120×C109—21no—
159#120×C109—21no—
160#120×C109—21no—
161#120×C109—21no—
162C4×Q8×C109D411yescharacteristic
163C4×Q8×C109D411yescharacteristic
164C4×D4×C109—21no—
165C4×D4×C109—21no—
166C4×D4×C109—21no—
167C4×D4×C109—21no—
168C4×D4×C109—21no—
169C4×D4×C109—21no—
170C4×D4×C109—21no—
171C4×D4×C109—21no—
172C4×D4×C109—21no—
173C4×D4×C109—21no—
174C4×D4×C109D411yescharacteristic
175C4×D4×C109D411yescharacteristic
176#117×C109—21no—
177#117×C109—21no—
178#117×C109—21no—
179C2×C42×C109—21no—
180C2×C42×C109C2311yescharacteristic
181#107×C109—21no—
182#106×C109—21no—
183C4⋊C8×C109—21no—
184C4⋊C8×C109—21no—
185#103×C109—21no—
186#103×C109—21no—
187#103×C109—21no—
188#103×C109—21no—
189#103×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—
196#102×C109—21no—
197C22⋊C8×C109—21no—
198C22⋊C8×C109—21no—
199#97×C109—21no—
200#97×C109C2311yescharacteristic
201#97×C109C2311yescharacteristic
202#97×C109C2311yescharacteristic
203#97×C109C2311yescharacteristic
204#97×C109C2311yescharacteristic
205#97×C109C2311yescharacteristic
206C24×C109—21no—
207#41×C109—81no—
208#41×C109—81no—
209#41×C109—82no—
210#41×C109—81no—
211#41×C109—81no—
212C2×Q8×C109—21no—
213C2×Q8×C109—21no—
214C2×Q8×C109C2×D411yescharacteristic
215C2×Q8×C109C2×D411yescharacteristic
216C2×Q8×C109C2×D411yescharacteristic
217C2×Q8×C109C2×D411yescharacteristic
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—41no—
235C2×D4×C109C2×D411yescharacteristic
236C2×D4×C109C2×D411yescharacteristic
237C2×D4×C109C2×D411yescharacteristic
238C2×D4×C109C2×D411yescharacteristic
239C22×C4×C109—21no—
240C22×C4×C109—21no—
241C22×C4×C109—21no—
242C22×C4×C109—21no—
243C22×C4×C109—21no—
244C22×C4×C109—21no—
245C22×C4×C109—21no—
246C22×C4×C109—21no—
247C22×C4×C109—21no—
248C22×C4×C109—41no—
249C22×C4×C109—82no—
250C22×C4×C109C2×D411yescharacteristic
251C22×C4×C109C2×D411yescharacteristic
252C22×C4×C109C2×D411yescharacteristic
253Q16×C109—81no—
254SD16×C109—42no—
255SD16×C109—81no—
256SD16×C109—81no—
257SD16×C109—81no—
258SD16×C109—81no—
259D8×C109—42no—
260D8×C109—81no—
261D8×C109—81no—
262D8×C109—81no—
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—42no—
270C4⋊C4×C109—21no—
271C4⋊C4×C109—21no—
272C4⋊C4×C109—21no—
273C4⋊C4×C109—21no—
274C4⋊C4×C109—21no—
275C4⋊C4×C109—21no—
276C4⋊C4×C109—21no—
277C4⋊C4×C109—21no—
278C4⋊C4×C109—21no—
279C4⋊C4×C109—21no—
280C4⋊C4×C109—21no—
281C4⋊C4×C109—21no—
282C4⋊C4×C109—21no—
283C4⋊C4×C109—21no—
284C4⋊C4×C109—21no—
285C4⋊C4×C109—21no—
286C4⋊C4×C109—21no—
287C4⋊C4×C109—21no—
288C4⋊C4×C109C2×D411yescharacteristic
289C4⋊C4×C109C2×D411yescharacteristic
290C4⋊C4×C109C2×D411yescharacteristic
291C4⋊C4×C109C2×D411yescharacteristic
292C22⋊C4×C109—21no—
293C22⋊C4×C109—21no—
294C22⋊C4×C109—21no—
295C22⋊C4×C109—21no—
296C22⋊C4×C109—21no—
297C22⋊C4×C109—21no—
298C22⋊C4×C109—21no—
299C22⋊C4×C109—21no—
300C22⋊C4×C109—21no—
301C22⋊C4×C109—21no—
302C22⋊C4×C109—21no—
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—41no—
317C22⋊C4×C109—41no—
318C42×C109—21no—
319C42×C109—21no—
320C42×C109—21no—
321C42×C109—21no—
322C42×C109C2×D411yescharacteristic
323C42×C109C2×D411yescharacteristic
324C42×C109C2×D411yescharacteristic
325C42×C109C2411yescharacteristic
326C23×C109—21no—
327C23×C109—21no—
328C23×C109—21no—
329C23×C109—21no—
330C23×C109—41no—
331C23×C109—81no—
332C23×C109—81no—
333C23×C109—81no—
334C23×C109#12011yescharacteristic
335Q8×C109—41no—
336Q8×C109—41no—
337Q8×C109—41no—
338Q8×C109—41no—
339Q8×C109—41no—
340Q8×C109—41no—
341Q8×C109—81no—
342D4×C109—41no—
343D4×C109—41no—
344D4×C109—41no—
345D4×C109—41no—
346D4×C109—41no—
347D4×C109—41no—
348D4×C109—41no—
349D4×C109—41no—
350D4×C109—41no—
351D4×C109—41no—
352D4×C109—81no—
353D4×C109—81no—
354D4×C109—81no—
355D4×C109—81no—
356D4×C109—81no—
357D4×C109—81no—
358D4×C109—81no—
359D4×C109—81no—
360D4×C109—81no—
361D4×C109—81no—
362D4×C109—81no—
363D4×C109—81no—
364D4×C109—81no—
365D4×C109—82no—
366C2×C4×C109—21no—
367C2×C4×C109—21no—
368C2×C4×C109—21no—
369C2×C4×C109—21no—
370C2×C4×C109—21no—
371C2×C4×C109—21no—
372C2×C4×C109—21no—
373C2×C4×C109—21no—
374C2×C4×C109—41no—
375C2×C4×C109—41no—
376C2×C4×C109—41no—
377C2×C4×C109—42no—
378C2×C4×C109—42no—
379C2×C4×C109—42no—
380C2×C4×C109—42no—
381C2×C4×C109—41no—
382C2×C4×C109—82no—
383C2×C4×C109—81no—
384C2×C4×C109—81no—
385C2×C4×C109—81no—
386C2×C4×C109—81no—
387C2×C4×C109—81no—
388C2×C4×C109#12011yescharacteristic
389C2×C4×C109#12011yescharacteristic
390C2×C4×C109#12011yescharacteristic
391C2×C4×C109C22×D411yescharacteristic
392C2×C4×C109C22×D411yescharacteristic
393C2×C4×C109C22×D411yescharacteristic
394C8×C109—22no—
395C8×C109—41no—
396C8×C109—41no—
397C8×C109—41no—
398C8×C109—41no—
399C8×C109—41no—
400C22×C109—21no—
401C22×C109—21no—
402C22×C109—21no—
403C22×C109—41no—
404C22×C109—41no—
405C22×C109—41no—
406C22×C109—41no—
407C22×C109—41no—
408C22×C109—41no—
409C22×C109—41no—
410C22×C109—41no—
411C22×C109—41no—
412C22×C109—41no—
413C22×C109—41no—
414C22×C109—41no—
415C22×C109—84no—
416C22×C109—81no—
417C22×C109—81no—
418C22×C109—81no—
419C22×C109C2×#12011yescharacteristic
420C4×C109—21no—
421C4×C109—21no—
422C4×C109—21no—
423C4×C109—21no—
424C4×C109—21no—
425C4×C109—21no—
426C4×C109—41no—
427C4×C109—41no—
428C4×C109—41no—
429C4×C109—41no—
430C4×C109—41no—
431C4×C109—41no—
432C4×C109—41no—
433C4×C109—41no—
434C4×C109—81no—
435#19010C10911yesmaximal, characteristic, direct product factor, Sylow
436C2×C109—41no—
437C2×C109—81no—
438C2×C109—81no—
439C2×C109—81no—
440C2×C109—81no—
441C2×C109—161no—
442C2×C109#301811yescharacteristic
443C2×C109#301911yescharacteristic
444C2×C109#302111yescharacteristic
445#3529C2×C10911yescharacteristic, complemented
446#3219C2×C10911yescharacteristic, complemented
447#3214C2×C10911yescharacteristic, complemented
448#3180C2×C10911yescharacteristic, complemented
449#1664C2×C10911yescharacteristic, complemented
450#1662C2×C10911yescharacteristic, complemented
451#1661C2×C10911yescharacteristic, complemented
452#1659C2×C10911yescharacteristic, complemented
453#1657C2×C10911yescharacteristic, complemented
454#1656C2×C10911yescharacteristic, complemented
455#1656C2×C10911yescharacteristic, complemented
456#1655C2×C10911yescharacteristic, complemented
457#1535C2×C10911yescharacteristic, complemented
458#1532C2×C10911yescharacteristic, complemented
459#1530C2×C10911yescharacteristic, complemented
460C109#1901011yescharacteristic, direct product factor, Sylow
461#563—21no—
462#563C22×C10911yescharacteristic
463#562—21no—
464#562—21no—
465#562C22×C10911yescharacteristic
466#562C22×C10911yescharacteristic
467H(3,𝔽4)C22×C10911yescharacteristic
468#560—21no—
469#560—21no—
470#560—21no—
471#532—21no—
472#532C22×C10911yescharacteristic
473#532C22×C10911yescharacteristic, complemented
474#529—21no—
475#529—21no—
476#529C22×C10911yescharacteristic
477#529C22×C10911yescharacteristic
478#525—21no—
479#525—21no—
480#525—21no—
481#501C22×C10911yescharacteristic, complemented
482#497C22×C10911yescharacteristic
483#496C22×C10911yescharacteristic
484#496C22×C10911yescharacteristic
485#496C22×C10911yescharacteristic
486#496C22×C10911yescharacteristic, complemented
487#491C22×C10911yescharacteristic, complemented
488#490C22×C10911yescharacteristic, complemented
489#490C22×C10911yescharacteristic, complemented
490#489C22×C10911yescharacteristic
491#489C22×C10911yescharacteristic
492#489C22×C10911yescharacteristic, complemented
493#466—21no—
494#465—21no—
495#464—21no—
496#463—21no—
497#461—21no—
498#459—21no—
499#452—21no—
500#449—21no—
501#449—21no—
502#449—21no—
503#442—21no—
504#440—21no—
505#432C22×C10911yescharacteristic, complemented
506#432C22×C10911yescharacteristic, complemented
507C2×#97C22×C10911yescharacteristic, complemented
508#330C22×C10911yescharacteristic, complemented
509#330C22×C10911yescharacteristic, complemented
510#330C22×C10911yescharacteristic, complemented
511#330C22×C10911yescharacteristic, complemented
512#329C22×C10911yescharacteristic
513#329C22×C10911yescharacteristic
514#329C22×C10911yescharacteristic
515#329C22×C10911yescharacteristic
516#329C22×C10911yescharacteristic
517#329C22×C10911yescharacteristic
518#329C22×C10911yescharacteristic, complemented
519#329C22×C10911yescharacteristic, complemented
520C2×#41—21no—
521C2×#41—21no—
522C2×#41D4×C10911yescharacteristic
523C2×#41D4×C10911yescharacteristic
524C23×C4—21no—
525C2×Q16—21no—
526C2×SD16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×D8—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C22×C8—21no—
536C4⋊Q8—21no—
537C4⋊Q8D4×C10911yescharacteristic
538C4⋊Q8C23×C10911yescharacteristic
539#127—21no—
540#127D4×C10911yescharacteristic
541#127C23×C10911yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#125—21no—
549#125—21no—
550#125C23×C10911yescharacteristic
551#125C23×C10911yescharacteristic
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124C23×C10911yescharacteristic
558#124C23×C10911yescharacteristic
559#124C23×C10911yescharacteristic
560#124C23×C10911yescharacteristic
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8D4×C10911yescharacteristic
582C22⋊Q8D4×C10911yescharacteristic
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121D4×C10911yescharacteristic
600#121D4×C10911yescharacteristic
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607C4×Q8D4×C10911yescharacteristic
608C4×Q8D4×C10911yescharacteristic
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617C4×D4—21no—
618C4×D4—21no—
619C4×D4D4×C10911yescharacteristic
620C4×D4D4×C10911yescharacteristic
621#117—21no—
622#117—21no—
623#117—21no—
624C2×C42—21no—
625C2×C42C23×C10911yescharacteristic
626#107—21no—
627#106—21no—
628C4⋊C8—21no—
629C4⋊C8—21no—
630#103—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#102—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642C22⋊C8—21no—
643C22⋊C8—21no—
644#97—21no—
645#97C23×C10911yescharacteristic
646#97C23×C10911yescharacteristic
647#97C23×C10911yescharacteristic
648#97C23×C10911yescharacteristic
649#97C23×C10911yescharacteristic
650#97C23×C10911yescharacteristic
651C24—21no—
652#41—81no—
653#41—81no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8C2×D4×C10911yescharacteristic
660C2×Q8C2×D4×C10911yescharacteristic
661C2×Q8C2×D4×C10911yescharacteristic
662C2×Q8C2×D4×C10911yescharacteristic
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—41no—
680C2×D4C2×D4×C10911yescharacteristic
681C2×D4C2×D4×C10911yescharacteristic
682C2×D4C2×D4×C10911yescharacteristic
683C2×D4C2×D4×C10911yescharacteristic
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4—82no—
695C22×C4C2×D4×C10911yescharacteristic
696C22×C4C2×D4×C10911yescharacteristic
697C22×C4C2×D4×C10911yescharacteristic
698Q16—81no—
699SD16—42no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703SD16—81no—
704D8—42no—
705D8—81no—
706D8—81no—
707D8—81no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—42no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4C2×D4×C10911yescharacteristic
734C4⋊C4C2×D4×C10911yescharacteristic
735C4⋊C4C2×D4×C10911yescharacteristic
736C4⋊C4C2×D4×C10911yescharacteristic
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C42—21no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42C2×D4×C10911yescharacteristic
768C42C2×D4×C10911yescharacteristic
769C42C2×D4×C10911yescharacteristic
770C42C24×C10911yescharacteristic
771C23—21no—
772C23—21no—
773C23—21no—
774C23—21no—
775C23—41no—
776C23—81no—
777C23—81no—
778C23—81no—
779C23#120×C10911yescharacteristic
780Q8—41no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785Q8—41no—
786Q8—81no—
787D4—41no—
788D4—41no—
789D4—41no—
790D4—41no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—81no—
798D4—81no—
799D4—81no—
800D4—81no—
801D4—81no—
802D4—81no—
803D4—81no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—82no—
811C2×C4—21no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—42no—
823C2×C4—42no—
824C2×C4—42no—
825C2×C4—42no—
826C2×C4—41no—
827C2×C4—82no—
828C2×C4—81no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4#120×C10911yescharacteristic
834C2×C4#120×C10911yescharacteristic
835C2×C4#120×C10911yescharacteristic
836C2×C4C22×D4×C10911yescharacteristic
837C2×C4C22×D4×C10911yescharacteristic
838C2×C4C22×D4×C10911yescharacteristic
839C8—22no—
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C22—21no—
846C22—21no—
847C22—21no—
848C22—41no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—84no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22C2×#120×C10911yescharacteristic
865C4—21no—
866C4—21no—
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—41no—
872C4—41no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—81no—
880C2—41no—
881C2—81no—
882C2—81no—
883C2—81no—
884C2—81no—
885C2—161no—
886C2C109×#301811yescharacteristic
887C2C109×#301911yescharacteristic
888C2C109×#302111yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC42C24×C109
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#3529C2semidirect
2. C109×#3219C2semidirect
3. C109×#3214C2semidirect
4. C109×#3180C2semidirect
5. C109×#1664C2semidirect
6. C109×#1662C2semidirect
7. C109×#1661C2semidirect
8. C109×#1659C2semidirect
9. C109×#1657C2semidirect
10. C109×#1656C2semidirect
11. C109×#1656C2semidirect
12. C109×#1655C2semidirect
13. C109×#1535C2semidirect
14. C109×#1532C2semidirect
15. C109×#1530C2semidirect
28. #532×C109C22semidirect
36. #501×C109C22semidirect
41. #496×C109C22semidirect
42. #491×C109C22semidirect
43. #490×C109C22semidirect
44. #490×C109C22semidirect
47. #489×C109C22semidirect
60. #432×C109C22semidirect
61. #432×C109C22semidirect
62. C2×#97×C109C22semidirect
63. #330×C109C22semidirect
64. #330×C109C22semidirect
65. #330×C109C22semidirect
66. #330×C109C22semidirect
73. #329×C109C22semidirect
74. #329×C109C22semidirect
435. #19010C109direct (N × H)
445. #3529C2×C109semidirect
446. #3219C2×C109semidirect
447. #3214C2×C109semidirect
448. #3180C2×C109semidirect
449. #1664C2×C109semidirect
450. #1662C2×C109semidirect
451. #1661C2×C109semidirect
452. #1659C2×C109semidirect
453. #1657C2×C109semidirect
454. #1656C2×C109semidirect
455. #1656C2×C109semidirect
456. #1655C2×C109semidirect
457. #1535C2×C109semidirect
458. #1532C2×C109semidirect
459. #1530C2×C109semidirect
460. C109#19010direct (N × H)
473. #532C22×C109semidirect
481. #501C22×C109semidirect
486. #496C22×C109semidirect
487. #491C22×C109semidirect
488. #490C22×C109semidirect
489. #490C22×C109semidirect
492. #489C22×C109semidirect
505. #432C22×C109semidirect
506. #432C22×C109semidirect
507. C2×#97C22×C109semidirect
508. #330C22×C109semidirect
509. #330C22×C109semidirect
510. #330C22×C109semidirect
511. #330C22×C109semidirect
518. #329C22×C109semidirect
519. #329C22×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35292
C109×#32192
C109×#32142
C109×#31802
C109×#16642
C109×#16622
C109×#16612
C109×#16592
C109×#16572
C109×#16562
C109×#16552
C109×#15352
C109×#15322
C109×#15302
#19010109