Finite Group Databasebeta

← C109×#18249 #42136243

Subgroups — C109×#18249 #42136243

Order 27904.

936 conjugacy classes of subgroups.

The subgroup lattice has 912 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3560C211yesmaximal, characteristic
2C109×#3112C211yesmaximal, characteristic, complemented
3C109×#3108C211yesmaximal, characteristic, complemented
4C109×#2637C211yesmaximal, characteristic, complemented
5C109×#1612C211yesmaximal, characteristic, complemented
6C109×#1610C211yesmaximal, characteristic, complemented
7C109×#1609C211yesmaximal, characteristic, complemented
8C109×#1607C211yesmaximal, characteristic, complemented
9C109×#1606C211yesmaximal, characteristic, complemented
10C109×#1604C211yesmaximal, characteristic, complemented
11C109×#1603C211yesmaximal, characteristic, complemented
12C109×#1601C211yesmaximal, characteristic, complemented
13C109×#1517C211yesmaximal, characteristic, complemented
14C109×#1512C211yesmaximal, characteristic, complemented
15C109×#1473C211yesmaximal, characteristic, complemented
16#563×C109—21no—
17#560×C109—21no—
18#553×C109—21no—
19#553×C109—21no—
20#551×C109—21no—
21#547×C109—21no—
22#546×C109—21no—
23#546×C109—21no—
24#542×C109—21no—
25#539×C109—21no—
26#539×C109C2211yescharacteristic
27#538×C109—21no—
28#538×C109—21no—
29#538×C109C2211yescharacteristic
30#537×C109C2211yescharacteristic
31#534×C109C2211yescharacteristic
32#532×C109C2211yescharacteristic
33#529×C109C2211yescharacteristic
34C2×#126×C109C2211yescharacteristic
35C2×C4×Q8×C109C2211yescharacteristic, complemented
36#483×C109C2211yescharacteristic, complemented
37#480×C109C2211yescharacteristic
38#480×C109C2211yescharacteristic
39#480×C109C2211yescharacteristic, complemented
40#479×C109—21no—
41#477×C109—21no—
42#464×C109—21no—
43#460×C109—21no—
44#451×C109C2211yescharacteristic, complemented
45#448×C109C2211yescharacteristic
46#448×C109C2211yescharacteristic
47#448×C109C2211yescharacteristic, complemented
48#440×C109—21no—
49#440×C109—21no—
50C4×Q16×C109—21no—
51C4×SD16×C109—21no—
52#432×C109C2211yescharacteristic, complemented
53#431×C109C2211yescharacteristic, complemented
54#398×C109—21no—
55#398×C109C2211yescharacteristic, complemented
56#397×C109C2211yescharacteristic
57#396×C109—21no—
58#395×C109C2211yescharacteristic, complemented
59#393×C109C2211yescharacteristic
60#388×C109—21no—
61#387×C109—21no—
62#382×C109C2211yescharacteristic, complemented
63#328×C109C2211yescharacteristic, complemented
64#328×C109C2211yescharacteristic, complemented
65#327×C109C2211yescharacteristic
66#327×C109C2211yescharacteristic
67#327×C109C2211yescharacteristic
68#327×C109C2211yescharacteristic
69#327×C109C2211yescharacteristic, complemented
70#327×C109C2211yescharacteristic, complemented
71#324×C109C2211yescharacteristic, complemented
72#324×C109C2211yescharacteristic, complemented
73#323×C109C2211yescharacteristic
74#323×C109C2211yescharacteristic
75C2×#41×C109—21no—
76C2×#41×C109—21no—
77C22×Q8×C109C2311yescharacteristic
78C22×D4×C109—21no—
79C2×Q16×C109—21no—
80C2×SD16×C109—21no—
81C2×SD16×C109—21no—
82C2×SD16×C109—21no—
83C4⋊Q8×C109—21no—
84C4⋊Q8×C109D411yescharacteristic
85#127×C109D411yescharacteristic
86#126×C109—21no—
87#126×C109—21no—
88#126×C109—21no—
89#126×C109—21no—
90#126×C109—21no—
91#126×C109—21no—
92#126×C109—21no—
93#126×C109—21no—
94#126×C109—21no—
95#125×C109—21no—
96#125×C109—21no—
97#125×C109D411yescharacteristic
98#124×C109—21no—
99#124×C109—21no—
100#124×C109—21no—
101#124×C109—21no—
102#124×C109D411yescharacteristic
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—
115C22⋊Q8×C109—21no—
116C22⋊Q8×C109—21no—
117C22⋊Q8×C109—21no—
118C22⋊Q8×C109—21no—
119C22⋊Q8×C109—21no—
120C22⋊Q8×C109—21no—
121C22⋊Q8×C109—21no—
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×C109C2311yescharacteristic
136#121×C109C2311yescharacteristic
137#121×C109C2311yescharacteristic
138#120×C109—21no—
139#120×C109—21no—
140#120×C109—21no—
141#120×C109—21no—
142#120×C109—21no—
143C4×Q8×C109—21no—
144C4×Q8×C109—21no—
145C4×Q8×C109—21no—
146C4×Q8×C109—21no—
147C4×Q8×C109D411yescharacteristic
148C4×D4×C109—21no—
149C4×D4×C109—21no—
150C4×D4×C109—21no—
151C4×D4×C109—21no—
152C4×D4×C109—21no—
153C4×D4×C109—21no—
154C4×D4×C109—21no—
155C4×D4×C109—21no—
156C4×D4×C109D411yescharacteristic
157C4×D4×C109D411yescharacteristic
158C4×D4×C109D411yescharacteristic
159#117×C109—21no—
160#117×C109—21no—
161C2×C4⋊C4×C109—21no—
162C2×C4⋊C4×C109—21no—
163C2×C4⋊C4×C109—21no—
164C2×C4⋊C4×C109—21no—
165C2×C4⋊C4×C109—21no—
166C2×C4⋊C4×C109D411yescharacteristic
167C2×C4⋊C4×C109D411yescharacteristic
168C2×C4⋊C4×C109C2311yescharacteristic
169C2×C4⋊C4×C109C2311yescharacteristic
170C2×C22⋊C4×C109—21no—
171C2×C22⋊C4×C109—21no—
172C2×C22⋊C4×C109—21no—
173C2×C22⋊C4×C109—21no—
174C2×C22⋊C4×C109D411yescharacteristic
175C2×C22⋊C4×C109D411yescharacteristic
176C2×C22⋊C4×C109C2311yescharacteristic
177C2×C42×C109—21no—
178C2×C42×C109C2311yescharacteristic
179#107×C109—21no—
180#107×C109—21no—
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—
193C22⋊C8×C109C2311yescharacteristic
194C22⋊C8×C109C2311yescharacteristic
195C22⋊C8×C109C2311yescharacteristic
196C22⋊C8×C109C2311yescharacteristic
197#97×C109—21no—
198C4×C8×C109—21no—
199#95×C109—21no—
200#95×C109—21no—
201#95×C109—21no—
202#95×C109—21no—
203#95×C109—21no—
204#95×C109C2311yescharacteristic
205#95×C109C2311yescharacteristic
206C24×C109—21no—
207C24×C109C2×D411yescharacteristic
208#41×C109—81no—
209#41×C109—81no—
210#41×C109—81no—
211#41×C109—81no—
212C2×Q8×C109—21no—
213C2×Q8×C109—21no—
214C2×Q8×C109—21no—
215C2×Q8×C109—21no—
216C2×Q8×C109—42no—
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—81no—
231C2×D4×C109—81no—
232C2×D4×C109C2×D411yescharacteristic
233C2×D4×C109C2×D411yescharacteristic
234C2×D4×C109C2×D411yescharacteristic
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×C109C2×D411yescharacteristic
248C22×C4×C109C2×D411yescharacteristic
249C22×C4×C109C2×D411yescharacteristic
250C22×C4×C109C2×D411yescharacteristic
251C22×C4×C109C2×D411yescharacteristic
252C22×C4×C109C2411yescharacteristic
253Q16×C109—42no—
254SD16×C109—42no—
255SD16×C109—42no—
256SD16×C109—42no—
257C2×C8×C109—21no—
258C2×C8×C109—21no—
259C2×C8×C109—21no—
260C2×C8×C109—21no—
261C4⋊C4×C109—21no—
262C4⋊C4×C109—21no—
263C4⋊C4×C109—21no—
264C4⋊C4×C109—21no—
265C4⋊C4×C109—21no—
266C4⋊C4×C109—21no—
267C4⋊C4×C109—21no—
268C4⋊C4×C109—21no—
269C4⋊C4×C109—21no—
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—42no—
281C4⋊C4×C109—41no—
282C4⋊C4×C109—41no—
283C4⋊C4×C109—81no—
284C4⋊C4×C109—81no—
285C4⋊C4×C109C2×D411yescharacteristic
286C4⋊C4×C109C2×D411yescharacteristic
287C4⋊C4×C109C2×D411yescharacteristic
288C4⋊C4×C109C2×D411yescharacteristic
289C22⋊C4×C109—21no—
290C22⋊C4×C109—21no—
291C22⋊C4×C109—21no—
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—42no—
315C22⋊C4×C109—81no—
316C42×C109—21no—
317C42×C109—21no—
318C42×C109—21no—
319C42×C109—41no—
320C42×C109—41no—
321C42×C109C2×D411yescharacteristic
322C42×C109C2×D411yescharacteristic
323C42×C109C2×D411yescharacteristic
324C42×C109C2×D411yescharacteristic
325C23×C109—21no—
326C23×C109—21no—
327C23×C109—21no—
328C23×C109—21no—
329C23×C109—21no—
330C23×C109—21no—
331C23×C109—41no—
332C23×C109—41no—
333C23×C109—81no—
334C23×C109—81no—
335C23×C109—81no—
336C23×C109C22×D411yescharacteristic
337Q8×C109—22no—
338Q8×C109—22no—
339Q8×C109—41no—
340Q8×C109—41no—
341Q8×C109—41no—
342Q8×C109—81no—
343Q8×C109—81no—
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—41no—
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—
362C2×C4×C109—21no—
363C2×C4×C109—21no—
364C2×C4×C109—22no—
365C2×C4×C109—21no—
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—21no—
375C2×C4×C109—41no—
376C2×C4×C109—41no—
377C2×C4×C109—41no—
378C2×C4×C109—41no—
379C2×C4×C109—41no—
380C2×C4×C109—41no—
381C2×C4×C109—41no—
382C2×C4×C109—41no—
383C2×C4×C109—41no—
384C2×C4×C109—41no—
385C2×C4×C109—41no—
386C2×C4×C109—41no—
387C2×C4×C109—41no—
388C2×C4×C109—41no—
389C2×C4×C109—41no—
390C2×C4×C109—81no—
391C2×C4×C109—81no—
392C2×C4×C109—81no—
393C2×C4×C109—81no—
394C2×C4×C109—81no—
395C2×C4×C109—81no—
396C2×C4×C109—81no—
397C2×C4×C109—81no—
398C2×C4×C109#12011yescharacteristic
399C2×C4×C109#12011yescharacteristic
400C2×C4×C109#12011yescharacteristic
401C2×C4×C109#12011yescharacteristic
402C2×C4×C109C22×D411yescharacteristic
403C2×C4×C109C22×D411yescharacteristic
404C8×C109—41no—
405C8×C109—41no—
406C8×C109—41no—
407C8×C109—41no—
408C22×C109—21no—
409C22×C109—21no—
410C22×C109—41no—
411C22×C109—41no—
412C22×C109—41no—
413C22×C109—41no—
414C22×C109—41no—
415C22×C109—41no—
416C22×C109—41no—
417C22×C109—41no—
418C22×C109—41no—
419C22×C109—41no—
420C22×C109—41no—
421C22×C109—41no—
422C22×C109—81no—
423C22×C109—81no—
424C22×C109—162no—
425C22×C109C2×#12011yescharacteristic
426C22×C109#57611yescharacteristic
427C22×C109#57711yescharacteristic
428C4×C109—21no—
429C4×C109—21no—
430C4×C109—21no—
431C4×C109—21no—
432C4×C109—21no—
433C4×C109—21no—
434C4×C109—41no—
435C4×C109—41no—
436C4×C109—41no—
437C4×C109—41no—
438C4×C109—41no—
439C4×C109—41no—
440C4×C109—42no—
441C4×C109—41no—
442C4×C109—41no—
443C4×C109—81no—
444C4×C109—81no—
445C4×C109—81no—
446#18249C10911yesmaximal, characteristic, direct product factor, Sylow
447C2×C109—21no—
448C2×C109—21no—
449C2×C109—81no—
450C2×C109—81no—
451C2×C109—81no—
452C2×C109—81no—
453C2×C109#301211yescharacteristic
454C2×C109#302211yescharacteristic
455C2×C109#302511yescharacteristic
456#3560C2×C10911yescharacteristic
457#3112C2×C10911yescharacteristic, complemented
458#3108C2×C10911yescharacteristic, complemented
459#2637C2×C10911yescharacteristic, complemented
460#1612C2×C10911yescharacteristic, complemented
461#1610C2×C10911yescharacteristic, complemented
462#1609C2×C10911yescharacteristic, complemented
463#1607C2×C10911yescharacteristic, complemented
464#1606C2×C10911yescharacteristic, complemented
465#1604C2×C10911yescharacteristic, complemented
466#1603C2×C10911yescharacteristic, complemented
467#1601C2×C10911yescharacteristic, complemented
468#1517C2×C10911yescharacteristic, complemented
469#1512C2×C10911yescharacteristic, complemented
470#1473C2×C10911yescharacteristic, complemented
471C109#1824911yescharacteristic, direct product factor, Sylow
472#563—21no—
473#560—21no—
474#553—21no—
475#553—21no—
476#551—21no—
477#547—21no—
478#546—21no—
479#546—21no—
480#542—21no—
481#539—21no—
482#539C22×C10911yescharacteristic
483#538—21no—
484#538—21no—
485#538C22×C10911yescharacteristic
486#537C22×C10911yescharacteristic
487#534C22×C10911yescharacteristic
488#532C22×C10911yescharacteristic
489#529C22×C10911yescharacteristic
490C2×#126C22×C10911yescharacteristic
491C2×C4×Q8C22×C10911yescharacteristic, complemented
492#483C22×C10911yescharacteristic, complemented
493#480C22×C10911yescharacteristic
494#480C22×C10911yescharacteristic
495#480C22×C10911yescharacteristic, complemented
496#479—21no—
497#477—21no—
498#464—21no—
499#460—21no—
500#451C22×C10911yescharacteristic, complemented
501#448C22×C10911yescharacteristic
502#448C22×C10911yescharacteristic
503#448C22×C10911yescharacteristic, complemented
504#440—21no—
505#440—21no—
506C4×Q16—21no—
507C4×SD16—21no—
508#432C22×C10911yescharacteristic, complemented
509#431C22×C10911yescharacteristic, complemented
510#398—21no—
511#398C22×C10911yescharacteristic, complemented
512#397C22×C10911yescharacteristic
513#396—21no—
514#395C22×C10911yescharacteristic, complemented
515#393C22×C10911yescharacteristic
516#388—21no—
517#387—21no—
518#382C22×C10911yescharacteristic, complemented
519#328C22×C10911yescharacteristic, complemented
520#328C22×C10911yescharacteristic, complemented
521#327C22×C10911yescharacteristic
522#327C22×C10911yescharacteristic
523#327C22×C10911yescharacteristic
524#327C22×C10911yescharacteristic
525#327C22×C10911yescharacteristic, complemented
526#327C22×C10911yescharacteristic, complemented
527#324C22×C10911yescharacteristic, complemented
528#324C22×C10911yescharacteristic, complemented
529#323C22×C10911yescharacteristic
530#323C22×C10911yescharacteristic
531C2×#41—21no—
532C2×#41—21no—
533C22×Q8C23×C10911yescharacteristic
534C22×D4—21no—
535C2×Q16—21no—
536C2×SD16—21no—
537C2×SD16—21no—
538C2×SD16—21no—
539C4⋊Q8—21no—
540C4⋊Q8D4×C10911yescharacteristic
541#127D4×C10911yescharacteristic
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#126—21no—
548#126—21no—
549#126—21no—
550#126—21no—
551#125—21no—
552#125—21no—
553#125D4×C10911yescharacteristic
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C10911yescharacteristic
559#123—21no—
560#123—21no—
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—
571C22⋊Q8—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8C23×C10911yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
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#121C23×C10911yescharacteristic
592#121C23×C10911yescharacteristic
593#121C23×C10911yescharacteristic
594#120—21no—
595#120—21no—
596#120—21no—
597#120—21no—
598#120—21no—
599C4×Q8—21no—
600C4×Q8—21no—
601C4×Q8—21no—
602C4×Q8—21no—
603C4×Q8D4×C10911yescharacteristic
604C4×D4—21no—
605C4×D4—21no—
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4D4×C10911yescharacteristic
613C4×D4D4×C10911yescharacteristic
614C4×D4D4×C10911yescharacteristic
615#117—21no—
616#117—21no—
617C2×C4⋊C4—21no—
618C2×C4⋊C4—21no—
619C2×C4⋊C4—21no—
620C2×C4⋊C4—21no—
621C2×C4⋊C4—21no—
622C2×C4⋊C4D4×C10911yescharacteristic
623C2×C4⋊C4D4×C10911yescharacteristic
624C2×C4⋊C4C23×C10911yescharacteristic
625C2×C4⋊C4C23×C10911yescharacteristic
626C2×C22⋊C4—21no—
627C2×C22⋊C4—21no—
628C2×C22⋊C4—21no—
629C2×C22⋊C4—21no—
630C2×C22⋊C4D4×C10911yescharacteristic
631C2×C22⋊C4D4×C10911yescharacteristic
632C2×C22⋊C4C23×C10911yescharacteristic
633C2×C42—21no—
634C2×C42C23×C10911yescharacteristic
635#107—21no—
636#107—21no—
637#107—21no—
638#106—21no—
639C4⋊C8—21no—
640C4⋊C8—21no—
641#103—21no—
642#103—21no—
643#103—21no—
644#103—21no—
645#103—21no—
646#102—21no—
647#102—21no—
648#102—21no—
649C22⋊C8C23×C10911yescharacteristic
650C22⋊C8C23×C10911yescharacteristic
651C22⋊C8C23×C10911yescharacteristic
652C22⋊C8C23×C10911yescharacteristic
653#97—21no—
654C4×C8—21no—
655#95—21no—
656#95—21no—
657#95—21no—
658#95—21no—
659#95—21no—
660#95C23×C10911yescharacteristic
661#95C23×C10911yescharacteristic
662C24—21no—
663C24C2×D4×C10911yescharacteristic
664#41—81no—
665#41—81no—
666#41—81no—
667#41—81no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—42no—
673C2×Q8C2×D4×C10911yescharacteristic
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—81no—
687C2×D4—81no—
688C2×D4C2×D4×C10911yescharacteristic
689C2×D4C2×D4×C10911yescharacteristic
690C2×D4C2×D4×C10911yescharacteristic
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4C2×D4×C10911yescharacteristic
704C22×C4C2×D4×C10911yescharacteristic
705C22×C4C2×D4×C10911yescharacteristic
706C22×C4C2×D4×C10911yescharacteristic
707C22×C4C2×D4×C10911yescharacteristic
708C22×C4C24×C10911yescharacteristic
709Q16—42no—
710SD16—42no—
711SD16—42no—
712SD16—42no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—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⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—42no—
737C4⋊C4—41no—
738C4⋊C4—41no—
739C4⋊C4—81no—
740C4⋊C4—81no—
741C4⋊C4C2×D4×C10911yescharacteristic
742C4⋊C4C2×D4×C10911yescharacteristic
743C4⋊C4C2×D4×C10911yescharacteristic
744C4⋊C4C2×D4×C10911yescharacteristic
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—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—21no—
766C22⋊C4—21no—
767C22⋊C4—21no—
768C22⋊C4—21no—
769C22⋊C4—21no—
770C22⋊C4—42no—
771C22⋊C4—81no—
772C42—21no—
773C42—21no—
774C42—21no—
775C42—41no—
776C42—41no—
777C42C2×D4×C10911yescharacteristic
778C42C2×D4×C10911yescharacteristic
779C42C2×D4×C10911yescharacteristic
780C42C2×D4×C10911yescharacteristic
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—41no—
788C23—41no—
789C23—81no—
790C23—81no—
791C23—81no—
792C23C22×D4×C10911yescharacteristic
793Q8—22no—
794Q8—22no—
795Q8—41no—
796Q8—41no—
797Q8—41no—
798Q8—81no—
799Q8—81no—
800D4—41no—
801D4—41no—
802D4—41no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—81no—
813D4—81no—
814D4—81no—
815D4—81no—
816D4—81no—
817D4—81no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—22no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—21no—
824C2×C4—21no—
825C2×C4—21no—
826C2×C4—21no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—21no—
830C2×C4—21no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4—41no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—81no—
847C2×C4—81no—
848C2×C4—81no—
849C2×C4—81no—
850C2×C4—81no—
851C2×C4—81no—
852C2×C4—81no—
853C2×C4—81no—
854C2×C4#120×C10911yescharacteristic
855C2×C4#120×C10911yescharacteristic
856C2×C4#120×C10911yescharacteristic
857C2×C4#120×C10911yescharacteristic
858C2×C4C22×D4×C10911yescharacteristic
859C2×C4C22×D4×C10911yescharacteristic
860C8—41no—
861C8—41no—
862C8—41no—
863C8—41no—
864C22—21no—
865C22—21no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—41no—
875C22—41no—
876C22—41no—
877C22—41no—
878C22—81no—
879C22—81no—
880C22—162no—
881C22C2×#120×C10911yescharacteristic
882C22#576×C10911yescharacteristic
883C22#577×C10911yescharacteristic
884C4—21no—
885C4—21no—
886C4—21no—
887C4—21no—
888C4—21no—
889C4—21no—
890C4—41no—
891C4—41no—
892C4—41no—
893C4—41no—
894C4—41no—
895C4—41no—
896C4—42no—
897C4—41no—
898C4—41no—
899C4—81no—
900C4—81no—
901C4—81no—
902C2—21no—
903C2—21no—
904C2—81no—
905C2—81no—
906C2—81no—
907C2—81no—
908C2C109×#301211yescharacteristic
909C2C109×#302211yescharacteristic
910C2C109×#302511yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC109×#3560C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C2×C42×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#3112C2semidirect
3. C109×#3108C2semidirect
4. C109×#2637C2semidirect
5. C109×#1612C2semidirect
6. C109×#1610C2semidirect
7. C109×#1609C2semidirect
8. C109×#1607C2semidirect
9. C109×#1606C2semidirect
10. C109×#1604C2semidirect
11. C109×#1603C2semidirect
12. C109×#1601C2semidirect
13. C109×#1517C2semidirect
14. C109×#1512C2semidirect
15. C109×#1473C2semidirect
35. C2×C4×Q8×C109C22semidirect
36. #483×C109C22semidirect
39. #480×C109C22semidirect
44. #451×C109C22semidirect
47. #448×C109C22semidirect
52. #432×C109C22semidirect
53. #431×C109C22semidirect
55. #398×C109C22semidirect
58. #395×C109C22semidirect
62. #382×C109C22semidirect
63. #328×C109C22semidirect
64. #328×C109C22semidirect
69. #327×C109C22semidirect
70. #327×C109C22semidirect
71. #324×C109C22semidirect
72. #324×C109C22semidirect
446. #18249C109direct (N × H)
457. #3112C2×C109semidirect
458. #3108C2×C109semidirect
459. #2637C2×C109semidirect
460. #1612C2×C109semidirect
461. #1610C2×C109semidirect
462. #1609C2×C109semidirect
463. #1607C2×C109semidirect
464. #1606C2×C109semidirect
465. #1604C2×C109semidirect
466. #1603C2×C109semidirect
467. #1601C2×C109semidirect
468. #1517C2×C109semidirect
469. #1512C2×C109semidirect
470. #1473C2×C109semidirect
471. C109#18249direct (N × H)
491. C2×C4×Q8C22×C109semidirect
492. #483C22×C109semidirect
495. #480C22×C109semidirect
500. #451C22×C109semidirect
503. #448C22×C109semidirect
508. #432C22×C109semidirect
509. #431C22×C109semidirect
511. #398C22×C109semidirect
514. #395C22×C109semidirect
518. #382C22×C109semidirect
519. #328C22×C109semidirect
520. #328C22×C109semidirect
525. #327C22×C109semidirect
526. #327C22×C109semidirect
527. #324C22×C109semidirect
528. #324C22×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35602
C109×#31122
C109×#31082
C109×#26372
C109×#16122
C109×#16102
C109×#16092
C109×#16072
C109×#16062
C109×#16042
C109×#16032
C109×#16012
C109×#15172
C109×#15122
C109×#14732
#18249109