Finite Group Databasebeta

← C109×#12753 #42130747

Subgroups — C109×#12753 #42130747

Order 27904.

936 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
1C109×#3532C211yesmaximal, characteristic
2C109×#2127C211yesmaximal, characteristic, complemented
3C109×#2121C211yesmaximal, characteristic, complemented
4C2×AΣL(1,𝔽16)×C109C211yesmaximal, characteristic, complemented
5C109×#1913C211yesmaximal, characteristic, complemented
6C109×#1911C211yesmaximal, characteristic, complemented
7C109×#1889C211yesmaximal, characteristic, complemented
8H(3,𝔽4)×C109C411yescharacteristic, complemented
9#560×C109—21no—
10#560×C109C411yescharacteristic, complemented
11#551×C109—21no—
12#551×C109C411yescharacteristic, complemented
13#546×C109—21no—
14#546×C109—21no—
15#546×C109—21no—
16D42×C109—21no—
17D42×C109C411yescharacteristic, complemented
18#538×C109—21no—
19#538×C109—21no—
20#538×C109—21no—
21#535×C109—21no—
22#535×C109C2211yescharacteristic
23#534×C109—21no—
24#534×C109C2211yescharacteristic
25C2×#120×C109—21no—
26C2×#120×C109C2211yescharacteristic
27#518×C109C2211yescharacteristic, complemented
28#421×C109—21no—
29C2×#100×C109C2211yescharacteristic, complemented
30C2×#99×C109—21no—
31C2×#99×C109C2211yescharacteristic, complemented
32C2×#99×C109C2211yescharacteristic, complemented
33#379×C109—21no—
34#354×C109—21no—
35#353×C109—21no—
36#352×C109—21no—
37AΣL(1,𝔽16)×C109—21no—
38AΣL(1,𝔽16)×C109—21no—
39AΣL(1,𝔽16)×C109—21no—
40#342×C109—21no—
41#342×C109—21no—
42H(3,ℤ/4)×C109—21no—
43C25×C109D411yescharacteristic
44C2×#41×C109—21no—
45C2×#41×C109D411yescharacteristic
46C22×D4×C109—21no—
47C22×D4×C109—21no—
48C22×D4×C109—21no—
49C22×D4×C109—21no—
50C22×D4×C109—21no—
51C22×D4×C109D411yescharacteristic
52C22×D4×C109C2311yescharacteristic
53C2×M16×C109—21no—
54#127×C109—21no—
55#127×C109C2×C411yescharacteristic
56#127×C109D411yescharacteristic
57#126×C109—21no—
58#126×C109—21no—
59#126×C109—21no—
60#126×C109—21no—
61#124×C109—21no—
62#124×C109—21no—
63#124×C109—21no—
64#124×C109—21no—
65#124×C109—21no—
66#124×C109C2×C411yescharacteristic
67#124×C109D411yescharacteristic
68#123×C109—21no—
69#123×C109—21no—
70#123×C109—21no—
71#123×C109—21no—
72#123×C109—21no—
73#123×C109—21no—
74#123×C109—21no—
75#123×C109—21no—
76#123×C109C2×C411yescharacteristic
77#123×C109D411yescharacteristic
78C22⋊Q8×C109—21no—
79C22⋊Q8×C109—21no—
80C22⋊Q8×C109—21no—
81#121×C109—21no—
82#121×C109—21no—
83#121×C109—21no—
84#121×C109—21no—
85#121×C109—21no—
86#121×C109—21no—
87#121×C109—21no—
88#121×C109—21no—
89#121×C109—21no—
90#121×C109—21no—
91#121×C109—21no—
92#121×C109—21no—
93#121×C109—21no—
94#121×C109—21no—
95#121×C109—21no—
96#120×C109—21no—
97#120×C109—21no—
98#120×C109—21no—
99#120×C109—21no—
100#120×C109—21no—
101#120×C109—21no—
102#120×C109—21no—
103#120×C109—21no—
104#120×C109—21no—
105#120×C109—21no—
106#120×C109—21no—
107#120×C109—21no—
108#120×C109—21no—
109#120×C109—21no—
110#120×C109C2×C411yescharacteristic
111#120×C109C2×C411yescharacteristic
112#120×C109C2×C411yescharacteristic
113#120×C109D411yescharacteristic
114#120×C109D411yescharacteristic
115#120×C109D411yescharacteristic
116C4×D4×C109—21no—
117C4×D4×C109—21no—
118C4×D4×C109—21no—
119C4×D4×C109—21no—
120C4×D4×C109—21no—
121C4×D4×C109—21no—
122C4×D4×C109—42no—
123#117×C109—21no—
124#117×C109—21no—
125#117×C109D411yescharacteristic
126C2×C22⋊C4×C109—21no—
127C2×C22⋊C4×C109—21no—
128C2×C22⋊C4×C109—21no—
129C2×C22⋊C4×C109—21no—
130C2×C22⋊C4×C109—21no—
131C2×C22⋊C4×C109—21no—
132C2×C22⋊C4×C109—21no—
133C2×C22⋊C4×C109—21no—
134C2×C22⋊C4×C109—21no—
135C2×C22⋊C4×C109—42no—
136C2×C22⋊C4×C109D411yescharacteristic
137C2×C22⋊C4×C109D411yescharacteristic
138#104×C109—42no—
139#100×C109—21no—
140#100×C109—21no—
141#99×C109—21no—
142#99×C109—21no—
143#99×C109—21no—
144#99×C109—21no—
145#99×C109—42no—
146C24×C109—21no—
147C24×C109—21no—
148C24×C109—21no—
149C24×C109—41no—
150C24×C109—41no—
151C24×C109—82no—
152C24×C109C22⋊C411yescharacteristic
153C24×C109C22⋊C411yescharacteristic
154C24×C109C22⋊C411yescharacteristic, complemented
155C24×C109C2×D411yescharacteristic
156C24×C109C2×D411yescharacteristic
157#41×C109—41no—
158#41×C109—41no—
159#41×C109—82no—
160C2×Q8×C109—21no—
161C2×Q8×C109C22⋊C411yescharacteristic, complemented
162C2×D4×C109—21no—
163C2×D4×C109—21no—
164C2×D4×C109—21no—
165C2×D4×C109—21no—
166C2×D4×C109—21no—
167C2×D4×C109—21no—
168C2×D4×C109—21no—
169C2×D4×C109—21no—
170C2×D4×C109—21no—
171C2×D4×C109—21no—
172C2×D4×C109—21no—
173C2×D4×C109—21no—
174C2×D4×C109—21no—
175C2×D4×C109—21no—
176C2×D4×C109—21no—
177C2×D4×C109—21no—
178C2×D4×C109—21no—
179C2×D4×C109—21no—
180C2×D4×C109—21no—
181C2×D4×C109—21no—
182C2×D4×C109—41no—
183C2×D4×C109—41no—
184C2×D4×C109—41no—
185C2×D4×C109—41no—
186C2×D4×C109—82no—
187C2×D4×C109—82no—
188C2×D4×C109—82no—
189C2×D4×C109—82no—
190C2×D4×C109—81no—
191C2×D4×C109—81no—
192C2×D4×C109C22⋊C411yescharacteristic, complemented
193C2×D4×C109C22×C411yescharacteristic
194C2×D4×C109C2×D411yescharacteristic
195C2×D4×C109C2×D411yescharacteristic
196C2×D4×C109C2×D411yescharacteristic
197C22×C4×C109—21no—
198C22×C4×C109—21no—
199C22×C4×C109—21no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—22no—
206C22×C4×C109—41no—
207C22×C4×C109—41no—
208C22×C4×C109—41no—
209C22×C4×C109C22⋊C411yescharacteristic, complemented
210C22×C4×C109C2×D411yescharacteristic
211M16×C109—41no—
212M16×C109—41no—
213C2×C8×C109—41no—
214C4⋊C4×C109—21no—
215C4⋊C4×C109—21no—
216C4⋊C4×C109—21no—
217C4⋊C4×C109—21no—
218C4⋊C4×C109—21no—
219C4⋊C4×C109—21no—
220C4⋊C4×C109—21no—
221C4⋊C4×C109—21no—
222C4⋊C4×C109—21no—
223C4⋊C4×C109—41no—
224C22⋊C4×C109—21no—
225C22⋊C4×C109—21no—
226C22⋊C4×C109—21no—
227C22⋊C4×C109—21no—
228C22⋊C4×C109—21no—
229C22⋊C4×C109—21no—
230C22⋊C4×C109—21no—
231C22⋊C4×C109—21no—
232C22⋊C4×C109—21no—
233C22⋊C4×C109—21no—
234C22⋊C4×C109—21no—
235C22⋊C4×C109—21no—
236C22⋊C4×C109—21no—
237C22⋊C4×C109—21no—
238C22⋊C4×C109—21no—
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—21no—
249C22⋊C4×C109—22no—
250C22⋊C4×C109—41no—
251C22⋊C4×C109—41no—
252C22⋊C4×C109—41no—
253C22⋊C4×C109—41no—
254C22⋊C4×C109—41no—
255C22⋊C4×C109—41no—
256C22⋊C4×C109—84no—
257C22⋊C4×C109C22⋊C411yescharacteristic
258C22⋊C4×C109C22⋊C411yescharacteristic
259C22⋊C4×C109C22⋊C411yescharacteristic, complemented
260C22⋊C4×C109C22⋊C411yescharacteristic, complemented
261C42×C109—21no—
262C42×C109—21no—
263C42×C109—22no—
264C42×C109C22⋊C411yescharacteristic, complemented
265C42×C109C22⋊C411yescharacteristic, complemented
266C23×C109—21no—
267C23×C109—21no—
268C23×C109—21no—
269C23×C109—21no—
270C23×C109—21no—
271C23×C109—21no—
272C23×C109—21no—
273C23×C109—21no—
274C23×C109—42no—
275C23×C109—41no—
276C23×C109—41no—
277C23×C109—42no—
278C23×C109—42no—
279C23×C109—42no—
280C23×C109—41no—
281C23×C109—44no—
282C23×C109—41no—
283C23×C109—41no—
284C23×C109—81no—
285C23×C109—81no—
286C23×C109—81no—
287C23×C109—81no—
288C23×C109—81no—
289C23×C109—81no—
290C23×C109—81no—
291C23×C109—81no—
292C23×C109—81no—
293C23×C109—82no—
294C23×C109—82no—
295C23×C109—82no—
296C23×C109C2×C22⋊C411yescharacteristic
297C23×C109C2×C22⋊C411yescharacteristic
298C23×C109#12011yescharacteristic
299C23×C109#12011yescharacteristic
300C23×C109#12011yescharacteristic
301Q8×C109—41no—
302Q8×C109—81no—
303D4×C109—41no—
304D4×C109—41no—
305D4×C109—41no—
306D4×C109—41no—
307D4×C109—41no—
308D4×C109—42no—
309D4×C109—42no—
310D4×C109—42no—
311D4×C109—42no—
312D4×C109—41no—
313D4×C109—41no—
314D4×C109—41no—
315D4×C109—41no—
316D4×C109—81no—
317D4×C109—81no—
318D4×C109—81no—
319D4×C109—81no—
320D4×C109—81no—
321D4×C109—81no—
322D4×C109—81no—
323D4×C109—81no—
324D4×C109—81no—
325D4×C109—81no—
326D4×C109—81no—
327D4×C109—81no—
328D4×C109—81no—
329D4×C109—81no—
330C2×C4×C109—21no—
331C2×C4×C109—21no—
332C2×C4×C109—21no—
333C2×C4×C109—21no—
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—42no—
341C2×C4×C109—41no—
342C2×C4×C109—42no—
343C2×C4×C109—81no—
344C2×C4×C109—81no—
345C2×C4×C109—81no—
346C2×C4×C109—81no—
347C2×C4×C109—81no—
348C2×C4×C109—81no—
349C2×C4×C109—81no—
350C2×C4×C109—82no—
351C2×C4×C109—81no—
352C2×C4×C109—81no—
353C2×C4×C109—82no—
354C2×C4×C109—161no—
355C2×C4×C109—161no—
356C2×C4×C109C2×C22⋊C411yescharacteristic
357C2×C4×C109#12011yescharacteristic
358C8×C109—81no—
359C22×C109—22no—
360C22×C109—21no—
361C22×C109—21no—
362C22×C109—21no—
363C22×C109—21no—
364C22×C109—41no—
365C22×C109—41no—
366C22×C109—41no—
367C22×C109—41no—
368C22×C109—41no—
369C22×C109—42no—
370C22×C109—41no—
371C22×C109—41no—
372C22×C109—41no—
373C22×C109—41no—
374C22×C109—41no—
375C22×C109—41no—
376C22×C109—41no—
377C22×C109—42no—
378C22×C109—41no—
379C22×C109—42no—
380C22×C109—41no—
381C22×C109—41no—
382C22×C109—41no—
383C22×C109—81no—
384C22×C109—81no—
385C22×C109—81no—
386C22×C109—82no—
387C22×C109—82no—
388C22×C109—81no—
389C22×C109—84no—
390C22×C109—81no—
391C22×C109—161no—
392C22×C109—162no—
393C22×C109#37911yescharacteristic
394C22×C109B(4,𝔽2)11yescharacteristic
395C22×C109#45811yescharacteristic
396C4×C109—21no—
397C4×C109—21no—
398C4×C109—41no—
399C4×C109—41no—
400C4×C109—41no—
401C4×C109—41no—
402C4×C109—41no—
403C4×C109—41no—
404C4×C109—41no—
405C4×C109—41no—
406C4×C109—82no—
407C4×C109—161no—
408C4×C109—161no—
409#12753C10911yesmaximal, characteristic, direct product factor, Sylow
410C2×C109—21no—
411C2×C109—21no—
412C2×C109—21no—
413C2×C109—41no—
414C2×C109—41no—
415C2×C109—41no—
416C2×C109—42no—
417C2×C109—41no—
418C2×C109—81no—
419C2×C109—81no—
420C2×C109—81no—
421C2×C109#179011yescharacteristic
422#3532C2×C10911yescharacteristic
423#2127C2×C10911yescharacteristic, complemented
424#2121C2×C10911yescharacteristic, complemented
425C2×AΣL(1,𝔽16)C2×C10911yescharacteristic, complemented
426#1913C2×C10911yescharacteristic, complemented
427#1911C2×C10911yescharacteristic, complemented
428#1889C2×C10911yescharacteristic, complemented
429C109#1275311yescharacteristic, direct product factor, Sylow
430H(3,𝔽4)C4×C10911yescharacteristic, complemented
431#560—21no—
432#560C4×C10911yescharacteristic, complemented
433#551—21no—
434#551C4×C10911yescharacteristic, complemented
435#546—21no—
436#546—21no—
437#546—21no—
438D42—21no—
439D42C4×C10911yescharacteristic, complemented
440#538—21no—
441#538—21no—
442#538—21no—
443#535—21no—
444#535C22×C10911yescharacteristic
445#534—21no—
446#534C22×C10911yescharacteristic
447C2×#120—21no—
448C2×#120C22×C10911yescharacteristic
449#518C22×C10911yescharacteristic, complemented
450#421—21no—
451C2×#100C22×C10911yescharacteristic, complemented
452C2×#99—21no—
453C2×#99C22×C10911yescharacteristic, complemented
454C2×#99C22×C10911yescharacteristic, complemented
455#379—21no—
456#354—21no—
457#353—21no—
458#352—21no—
459AΣL(1,𝔽16)—21no—
460AΣL(1,𝔽16)—21no—
461AΣL(1,𝔽16)—21no—
462#342—21no—
463#342—21no—
464H(3,ℤ/4)—21no—
465C25D4×C10911yescharacteristic
466C2×#41—21no—
467C2×#41D4×C10911yescharacteristic
468C22×D4—21no—
469C22×D4—21no—
470C22×D4—21no—
471C22×D4—21no—
472C22×D4—21no—
473C22×D4D4×C10911yescharacteristic
474C22×D4C23×C10911yescharacteristic
475C2×M16—21no—
476#127—21no—
477#127C2×C4×C10911yescharacteristic
478#127D4×C10911yescharacteristic
479#126—21no—
480#126—21no—
481#126—21no—
482#126—21no—
483#124—21no—
484#124—21no—
485#124—21no—
486#124—21no—
487#124—21no—
488#124C2×C4×C10911yescharacteristic
489#124D4×C10911yescharacteristic
490#123—21no—
491#123—21no—
492#123—21no—
493#123—21no—
494#123—21no—
495#123—21no—
496#123—21no—
497#123—21no—
498#123C2×C4×C10911yescharacteristic
499#123D4×C10911yescharacteristic
500C22⋊Q8—21no—
501C22⋊Q8—21no—
502C22⋊Q8—21no—
503#121—21no—
504#121—21no—
505#121—21no—
506#121—21no—
507#121—21no—
508#121—21no—
509#121—21no—
510#121—21no—
511#121—21no—
512#121—21no—
513#121—21no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#120—21no—
519#120—21no—
520#120—21no—
521#120—21no—
522#120—21no—
523#120—21no—
524#120—21no—
525#120—21no—
526#120—21no—
527#120—21no—
528#120—21no—
529#120—21no—
530#120—21no—
531#120—21no—
532#120C2×C4×C10911yescharacteristic
533#120C2×C4×C10911yescharacteristic
534#120C2×C4×C10911yescharacteristic
535#120D4×C10911yescharacteristic
536#120D4×C10911yescharacteristic
537#120D4×C10911yescharacteristic
538C4×D4—21no—
539C4×D4—21no—
540C4×D4—21no—
541C4×D4—21no—
542C4×D4—21no—
543C4×D4—21no—
544C4×D4—42no—
545#117—21no—
546#117—21no—
547#117D4×C10911yescharacteristic
548C2×C22⋊C4—21no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—42no—
558C2×C22⋊C4D4×C10911yescharacteristic
559C2×C22⋊C4D4×C10911yescharacteristic
560#104—42no—
561#100—21no—
562#100—21no—
563#99—21no—
564#99—21no—
565#99—21no—
566#99—21no—
567#99—42no—
568C24—21no—
569C24—21no—
570C24—21no—
571C24—41no—
572C24—41no—
573C24—82no—
574C24C22⋊C4×C10911yescharacteristic
575C24C22⋊C4×C10911yescharacteristic
576C24C22⋊C4×C10911yescharacteristic, complemented
577C24C2×D4×C10911yescharacteristic
578C24C2×D4×C10911yescharacteristic
579#41—41no—
580#41—41no—
581#41—82no—
582C2×Q8—21no—
583C2×Q8C22⋊C4×C10911yescharacteristic, complemented
584C2×D4—21no—
585C2×D4—21no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—21no—
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—21no—
603C2×D4—21no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—41no—
607C2×D4—41no—
608C2×D4—82no—
609C2×D4—82no—
610C2×D4—82no—
611C2×D4—82no—
612C2×D4—81no—
613C2×D4—81no—
614C2×D4C22⋊C4×C10911yescharacteristic, complemented
615C2×D4C22×C4×C10911yescharacteristic
616C2×D4C2×D4×C10911yescharacteristic
617C2×D4C2×D4×C10911yescharacteristic
618C2×D4C2×D4×C10911yescharacteristic
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—21no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—22no—
628C22×C4—41no—
629C22×C4—41no—
630C22×C4—41no—
631C22×C4C22⋊C4×C10911yescharacteristic, complemented
632C22×C4C2×D4×C10911yescharacteristic
633M16—41no—
634M16—41no—
635C2×C8—41no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—21no—
640C4⋊C4—21no—
641C4⋊C4—21no—
642C4⋊C4—21no—
643C4⋊C4—21no—
644C4⋊C4—21no—
645C4⋊C4—41no—
646C22⋊C4—21no—
647C22⋊C4—21no—
648C22⋊C4—21no—
649C22⋊C4—21no—
650C22⋊C4—21no—
651C22⋊C4—21no—
652C22⋊C4—21no—
653C22⋊C4—21no—
654C22⋊C4—21no—
655C22⋊C4—21no—
656C22⋊C4—21no—
657C22⋊C4—21no—
658C22⋊C4—21no—
659C22⋊C4—21no—
660C22⋊C4—21no—
661C22⋊C4—21no—
662C22⋊C4—21no—
663C22⋊C4—21no—
664C22⋊C4—21no—
665C22⋊C4—21no—
666C22⋊C4—21no—
667C22⋊C4—21no—
668C22⋊C4—21no—
669C22⋊C4—21no—
670C22⋊C4—21no—
671C22⋊C4—22no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C22⋊C4—41no—
676C22⋊C4—41no—
677C22⋊C4—41no—
678C22⋊C4—84no—
679C22⋊C4C22⋊C4×C10911yescharacteristic
680C22⋊C4C22⋊C4×C10911yescharacteristic
681C22⋊C4C22⋊C4×C10911yescharacteristic, complemented
682C22⋊C4C22⋊C4×C10911yescharacteristic, complemented
683C42—21no—
684C42—21no—
685C42—22no—
686C42C22⋊C4×C10911yescharacteristic, complemented
687C42C22⋊C4×C10911yescharacteristic, complemented
688C23—21no—
689C23—21no—
690C23—21no—
691C23—21no—
692C23—21no—
693C23—21no—
694C23—21no—
695C23—21no—
696C23—42no—
697C23—41no—
698C23—41no—
699C23—42no—
700C23—42no—
701C23—42no—
702C23—41no—
703C23—44no—
704C23—41no—
705C23—41no—
706C23—81no—
707C23—81no—
708C23—81no—
709C23—81no—
710C23—81no—
711C23—81no—
712C23—81no—
713C23—81no—
714C23—81no—
715C23—82no—
716C23—82no—
717C23—82no—
718C23C2×C22⋊C4×C10911yescharacteristic
719C23C2×C22⋊C4×C10911yescharacteristic
720C23#120×C10911yescharacteristic
721C23#120×C10911yescharacteristic
722C23#120×C10911yescharacteristic
723Q8—41no—
724Q8—81no—
725D4—41no—
726D4—41no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—42no—
731D4—42no—
732D4—42no—
733D4—42no—
734D4—41no—
735D4—41no—
736D4—41no—
737D4—41no—
738D4—81no—
739D4—81no—
740D4—81no—
741D4—81no—
742D4—81no—
743D4—81no—
744D4—81no—
745D4—81no—
746D4—81no—
747D4—81no—
748D4—81no—
749D4—81no—
750D4—81no—
751D4—81no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—42no—
763C2×C4—41no—
764C2×C4—42no—
765C2×C4—81no—
766C2×C4—81no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—81no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—82no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—82no—
776C2×C4—161no—
777C2×C4—161no—
778C2×C4C2×C22⋊C4×C10911yescharacteristic
779C2×C4#120×C10911yescharacteristic
780C8—81no—
781C22—22no—
782C22—21no—
783C22—21no—
784C22—21no—
785C22—21no—
786C22—41no—
787C22—41no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—42no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—41no—
799C22—42no—
800C22—41no—
801C22—42no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—81no—
806C22—81no—
807C22—81no—
808C22—82no—
809C22—82no—
810C22—81no—
811C22—84no—
812C22—81no—
813C22—161no—
814C22—162no—
815C22#379×C10911yescharacteristic
816C22B(4,𝔽2)×C10911yescharacteristic
817C22#458×C10911yescharacteristic
818C4—21no—
819C4—21no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—41no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—82no—
829C4—161no—
830C4—161no—
831C2—21no—
832C2—21no—
833C2—21no—
834C2—41no—
835C2—41no—
836C2—41no—
837C2—42no—
838C2—41no—
839C2—81no—
840C2—81no—
841C2—81no—
842C2C109×#179011yescharacteristic
subgroupG/H
center, socleC2×C109#1790
commutatorC2×D4C22×C4×C109
Frattini, cosocleC22×D4C23×C109
prime radicalC109×#3532C2
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C109 ◁ C23×C109 ◁ C22×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#2127C2semidirect
3. C109×#2121C2semidirect
4. C2×AΣL(1,𝔽16)×C109C2semidirect
5. C109×#1913C2semidirect
6. C109×#1911C2semidirect
7. C109×#1889C2semidirect
8. H(3,𝔽4)×C109C4semidirect
10. #560×C109C4semidirect
12. #551×C109C4semidirect
17. D42×C109C4semidirect
27. #518×C109C22semidirect
29. C2×#100×C109C22semidirect
31. C2×#99×C109C22semidirect
32. C2×#99×C109C22semidirect
154. C24×C109C22⋊C4semidirect
161. C2×Q8×C109C22⋊C4semidirect
192. C2×D4×C109C22⋊C4semidirect
209. C22×C4×C109C22⋊C4semidirect
259. C22⋊C4×C109C22⋊C4semidirect
260. C22⋊C4×C109C22⋊C4semidirect
264. C42×C109C22⋊C4semidirect
265. C42×C109C22⋊C4semidirect
409. #12753C109direct (N × H)
423. #2127C2×C109semidirect
424. #2121C2×C109semidirect
425. C2×AΣL(1,𝔽16)C2×C109semidirect
426. #1913C2×C109semidirect
427. #1911C2×C109semidirect
428. #1889C2×C109semidirect
429. C109#12753direct (N × H)
430. H(3,𝔽4)C4×C109semidirect
432. #560C4×C109semidirect
434. #551C4×C109semidirect
439. D42C4×C109semidirect
449. #518C22×C109semidirect
451. C2×#100C22×C109semidirect
453. C2×#99C22×C109semidirect
454. C2×#99C22×C109semidirect
576. C24C22⋊C4×C109semidirect
583. C2×Q8C22⋊C4×C109semidirect
614. C2×D4C22⋊C4×C109semidirect
631. C22×C4C22⋊C4×C109semidirect
681. C22⋊C4C22⋊C4×C109semidirect
682. C22⋊C4C22⋊C4×C109semidirect
686. C42C22⋊C4×C109semidirect
687. C42C22⋊C4×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35322
C109×#21272
C109×#21212
C2×AΣL(1,𝔽16)×C1092
C109×#19132
C109×#19112
C109×#18892
#12753109