Finite Group Databasebeta

← C109×#18283 #42136277

Subgroups — C109×#18283 #42136277

Order 27904.

886 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3564C211yesmaximal, characteristic
2C109×#3117C211yesmaximal, characteristic, complemented
3C109×#3104C211yesmaximal, characteristic, complemented
4C109×#2604C211yesmaximal, characteristic, complemented
5C109×#1618C211yesmaximal, characteristic
6C109×#1617C211yesmaximal, characteristic, complemented
7C109×#1615C211yesmaximal, characteristic, complemented
8C109×#1614C211yesmaximal, characteristic, complemented
9C109×#1606C211yesmaximal, characteristic
10C109×#1605C211yesmaximal, characteristic, complemented
11C109×#1603C211yesmaximal, characteristic, complemented
12C109×#1602C211yesmaximal, characteristic, complemented
13C109×#1506C211yesmaximal, characteristic, complemented
14C109×#1500C211yesmaximal, characteristic, complemented
15C109×#1473C211yesmaximal, characteristic, complemented
16#563×C109—21no—
17#563×C109—21no—
18#556×C109—21no—
19#554×C109—21no—
20#552×C109—21no—
21#552×C109—21no—
22#551×C109—21no—
23#551×C109—21no—
24#544×C109C2211yescharacteristic
25#543×C109C2211yescharacteristic
26#542×C109—21no—
27#541×C109—21no—
28#541×C109—21no—
29#539×C109—21no—
30#539×C109C2211yescharacteristic
31#538×C109C2211yescharacteristic
32#533×C109C2211yescharacteristic
33#529×C109C2211yescharacteristic
34C2×#126×C109C2211yescharacteristic
35C2×C4×Q8×C109C2211yescharacteristic
36#484×C109C2211yescharacteristic
37#484×C109C2211yescharacteristic
38#484×C109C2211yescharacteristic
39#481×C109C2211yescharacteristic
40#479×C109—21no—
41#477×C109—21no—
42#464×C109—21no—
43#462×C109—21no—
44#451×C109C2211yescharacteristic
45#451×C109C2211yescharacteristic
46#451×C109C2211yescharacteristic
47#448×C109C2211yescharacteristic
48#441×C109—21no—
49#440×C109—21no—
50C4×Q16×C109—21no—
51C4×Q16×C109—21no—
52#432×C109C2211yescharacteristic
53#431×C109C2211yescharacteristic
54#400×C109C2211yescharacteristic
55#399×C109C2211yescharacteristic
56#395×C109C2211yescharacteristic
57#393×C109C2211yescharacteristic
58#389×C109—21no—
59#388×C109—21no—
60#388×C109—21no—
61#387×C109—21no—
62#376×C109C2211yescharacteristic
63#328×C109C2211yescharacteristic
64#328×C109C2211yescharacteristic
65#328×C109C2211yescharacteristic
66#328×C109C2211yescharacteristic
67#328×C109C2211yescharacteristic
68#328×C109C2211yescharacteristic
69#327×C109C2211yescharacteristic
70#327×C109C2211yescharacteristic
71#324×C109C2211yescharacteristic
72#324×C109C2211yescharacteristic
73#323×C109C2211yescharacteristic
74#323×C109C2211yescharacteristic
75C22×Q8×C109C2311yescharacteristic
76C2×Q16×C109—21no—
77C2×Q16×C109—21no—
78C2×Q16×C109—21no—
79C2×SD16×C109—21no—
80C4⋊Q8×C109—21no—
81C4⋊Q8×C109—21no—
82C4⋊Q8×C109—21no—
83C4⋊Q8×C109D411yescharacteristic
84C4⋊Q8×C109D411yescharacteristic
85#126×C109—21no—
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#126×C109—21no—
96#126×C109—21no—
97#126×C109—21no—
98#125×C109—21no—
99#125×C109—21no—
100#125×C109—21no—
101#125×C109—21no—
102#125×C109—21no—
103#125×C109—21no—
104#125×C109—21no—
105#125×C109—21no—
106#125×C109—21no—
107#125×C109D411yescharacteristic
108#124×C109—21no—
109#124×C109—21no—
110#124×C109—21no—
111#124×C109D411yescharacteristic
112#123×C109—21no—
113#123×C109—21no—
114#123×C109—21no—
115#123×C109—21no—
116#123×C109—21no—
117#123×C109—21no—
118#123×C109—21no—
119#123×C109—21no—
120C22⋊Q8×C109—21no—
121C22⋊Q8×C109—21no—
122C22⋊Q8×C109—21no—
123C22⋊Q8×C109—21no—
124C22⋊Q8×C109—21no—
125C22⋊Q8×C109—21no—
126C22⋊Q8×C109—21no—
127C22⋊Q8×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×C109C2311yescharacteristic
135C22⋊Q8×C109C2311yescharacteristic
136C22⋊Q8×C109C2311yescharacteristic
137#121×C109—21no—
138#121×C109C2311yescharacteristic
139#120×C109—21no—
140C4×Q8×C109—21no—
141C4×Q8×C109—21no—
142C4×Q8×C109—21no—
143C4×Q8×C109—21no—
144C4×Q8×C109—21no—
145C4×Q8×C109—21no—
146C4×Q8×C109—21no—
147C4×Q8×C109D411yescharacteristic
148C4×Q8×C109D411yescharacteristic
149C4×Q8×C109D411yescharacteristic
150C4×D4×C109—21no—
151C4×D4×C109—21no—
152C4×D4×C109—21no—
153C4×D4×C109—21no—
154C4×D4×C109—21no—
155C4×D4×C109D411yescharacteristic
156#117×C109—21no—
157#117×C109—21no—
158#117×C109—21no—
159#117×C109—21no—
160#117×C109—21no—
161#117×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×C109D411yescharacteristic
174C2×C22⋊C4×C109D411yescharacteristic
175C2×C22⋊C4×C109C2311yescharacteristic
176C2×C42×C109—21no—
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#103×C109—21no—
191#103×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×C109C2×D411yescharacteristic
207C2×Q8×C109—21no—
208C2×Q8×C109—21no—
209C2×Q8×C109—21no—
210C2×Q8×C109—21no—
211C2×Q8×C109—21no—
212C2×Q8×C109—42no—
213C2×Q8×C109C2×D411yescharacteristic
214C2×Q8×C109C2×D411yescharacteristic
215C2×Q8×C109C2×D411yescharacteristic
216C2×D4×C109—21no—
217C2×D4×C109—21no—
218C2×D4×C109—21no—
219C2×D4×C109C2×D411yescharacteristic
220C22×C4×C109—21no—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—21no—
224C22×C4×C109—21no—
225C22×C4×C109—21no—
226C22×C4×C109—21no—
227C22×C4×C109—21no—
228C22×C4×C109—21no—
229C22×C4×C109C2×D411yescharacteristic
230C22×C4×C109C2×D411yescharacteristic
231C22×C4×C109C2×D411yescharacteristic
232C22×C4×C109C2×D411yescharacteristic
233C22×C4×C109C2×D411yescharacteristic
234C22×C4×C109C2411yescharacteristic
235Q16×C109—42no—
236Q16×C109—42no—
237Q16×C109—42no—
238SD16×C109—42no—
239C2×C8×C109—21no—
240C2×C8×C109—21no—
241C2×C8×C109—21no—
242C2×C8×C109—21no—
243C4⋊C4×C109—21no—
244C4⋊C4×C109—21no—
245C4⋊C4×C109—21no—
246C4⋊C4×C109—21no—
247C4⋊C4×C109—21no—
248C4⋊C4×C109—21no—
249C4⋊C4×C109—21no—
250C4⋊C4×C109—21no—
251C4⋊C4×C109—21no—
252C4⋊C4×C109—21no—
253C4⋊C4×C109—21no—
254C4⋊C4×C109—21no—
255C4⋊C4×C109—21no—
256C4⋊C4×C109—21no—
257C4⋊C4×C109—21no—
258C4⋊C4×C109—21no—
259C4⋊C4×C109—21no—
260C4⋊C4×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—42no—
275C4⋊C4×C109—42no—
276C4⋊C4×C109—41no—
277C4⋊C4×C109—41no—
278C4⋊C4×C109C2×D411yescharacteristic
279C4⋊C4×C109C2×D411yescharacteristic
280C4⋊C4×C109C2×D411yescharacteristic
281C4⋊C4×C109C2×D411yescharacteristic
282C22⋊C4×C109—21no—
283C22⋊C4×C109—21no—
284C22⋊C4×C109—21no—
285C22⋊C4×C109—21no—
286C22⋊C4×C109—21no—
287C22⋊C4×C109—21no—
288C22⋊C4×C109—21no—
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—42no—
304C22⋊C4×C109—42no—
305C42×C109—21no—
306C42×C109—21no—
307C42×C109—21no—
308C42×C109—21no—
309C42×C109—21no—
310C42×C109—21no—
311C42×C109—21no—
312C42×C109—42no—
313C42×C109—41no—
314C42×C109—41no—
315C42×C109C2×D411yescharacteristic
316C42×C109C2×D411yescharacteristic
317C42×C109C2×D411yescharacteristic
318C42×C109C2×D411yescharacteristic
319C23×C109—21no—
320C23×C109—21no—
321C23×C109—21no—
322C23×C109—21no—
323C23×C109—41no—
324C23×C109—41no—
325C23×C109C22×D411yescharacteristic
326Q8×C109—22no—
327Q8×C109—22no—
328Q8×C109—41no—
329Q8×C109—41no—
330Q8×C109—41no—
331Q8×C109—41no—
332Q8×C109—41no—
333Q8×C109—81no—
334Q8×C109—81no—
335Q8×C109—81no—
336D4×C109—41no—
337D4×C109—41no—
338D4×C109—41no—
339D4×C109—81no—
340D4×C109—81no—
341C2×C4×C109—21no—
342C2×C4×C109—21no—
343C2×C4×C109—22no—
344C2×C4×C109—22no—
345C2×C4×C109—21no—
346C2×C4×C109—21no—
347C2×C4×C109—21no—
348C2×C4×C109—21no—
349C2×C4×C109—21no—
350C2×C4×C109—21no—
351C2×C4×C109—21no—
352C2×C4×C109—21no—
353C2×C4×C109—21no—
354C2×C4×C109—21no—
355C2×C4×C109—21no—
356C2×C4×C109—21no—
357C2×C4×C109—41no—
358C2×C4×C109—41no—
359C2×C4×C109—41no—
360C2×C4×C109—41no—
361C2×C4×C109—41no—
362C2×C4×C109—41no—
363C2×C4×C109—41no—
364C2×C4×C109—41no—
365C2×C4×C109—41no—
366C2×C4×C109—41no—
367C2×C4×C109—41no—
368C2×C4×C109—41no—
369C2×C4×C109—41no—
370C2×C4×C109—41no—
371C2×C4×C109—81no—
372C2×C4×C109—81no—
373C2×C4×C109—81no—
374C2×C4×C109—81no—
375C2×C4×C109—81no—
376C2×C4×C109#12011yescharacteristic
377C2×C4×C109#12011yescharacteristic
378C2×C4×C109#12011yescharacteristic
379C2×C4×C109#12011yescharacteristic
380C2×C4×C109C22×D411yescharacteristic
381C2×C4×C109C22×D411yescharacteristic
382C8×C109—41no—
383C8×C109—41no—
384C8×C109—41no—
385C8×C109—41no—
386C22×C109—21no—
387C22×C109—21no—
388C22×C109—41no—
389C22×C109—41no—
390C22×C109—41no—
391C22×C109—41no—
392C22×C109—41no—
393C22×C109—41no—
394C22×C109—81no—
395C22×C109—81no—
396C22×C109C2×#12011yescharacteristic
397C22×C109#57811yescharacteristic
398C22×C109#57811yescharacteristic
399C4×C109—21no—
400C4×C109—21no—
401C4×C109—21no—
402C4×C109—21no—
403C4×C109—21no—
404C4×C109—21no—
405C4×C109—42no—
406C4×C109—41no—
407C4×C109—41no—
408C4×C109—41no—
409C4×C109—41no—
410C4×C109—41no—
411C4×C109—41no—
412C4×C109—42no—
413C4×C109—41no—
414C4×C109—41no—
415C4×C109—41no—
416C4×C109—41no—
417C4×C109—81no—
418C4×C109—81no—
419#18283C10911yesmaximal, characteristic, direct product factor, Sylow
420C2×C109—21no—
421C2×C109—21no—
422C2×C109—81no—
423C2×C109—81no—
424C2×C109#301111yescharacteristic
425C2×C109#301811yescharacteristic
426C2×C109#302511yescharacteristic
427#3564C2×C10911yescharacteristic
428#3117C2×C10911yescharacteristic, complemented
429#3104C2×C10911yescharacteristic, complemented
430#2604C2×C10911yescharacteristic, complemented
431#1618C2×C10911yescharacteristic
432#1617C2×C10911yescharacteristic, complemented
433#1615C2×C10911yescharacteristic, complemented
434#1614C2×C10911yescharacteristic, complemented
435#1606C2×C10911yescharacteristic
436#1605C2×C10911yescharacteristic, complemented
437#1603C2×C10911yescharacteristic, complemented
438#1602C2×C10911yescharacteristic, complemented
439#1506C2×C10911yescharacteristic, complemented
440#1500C2×C10911yescharacteristic, complemented
441#1473C2×C10911yescharacteristic, complemented
442C109#1828311yescharacteristic, direct product factor, Sylow
443#563—21no—
444#563—21no—
445#556—21no—
446#554—21no—
447#552—21no—
448#552—21no—
449#551—21no—
450#551—21no—
451#544C22×C10911yescharacteristic
452#543C22×C10911yescharacteristic
453#542—21no—
454#541—21no—
455#541—21no—
456#539—21no—
457#539C22×C10911yescharacteristic
458#538C22×C10911yescharacteristic
459#533C22×C10911yescharacteristic
460#529C22×C10911yescharacteristic
461C2×#126C22×C10911yescharacteristic
462C2×C4×Q8C22×C10911yescharacteristic
463#484C22×C10911yescharacteristic
464#484C22×C10911yescharacteristic
465#484C22×C10911yescharacteristic
466#481C22×C10911yescharacteristic
467#479—21no—
468#477—21no—
469#464—21no—
470#462—21no—
471#451C22×C10911yescharacteristic
472#451C22×C10911yescharacteristic
473#451C22×C10911yescharacteristic
474#448C22×C10911yescharacteristic
475#441—21no—
476#440—21no—
477C4×Q16—21no—
478C4×Q16—21no—
479#432C22×C10911yescharacteristic
480#431C22×C10911yescharacteristic
481#400C22×C10911yescharacteristic
482#399C22×C10911yescharacteristic
483#395C22×C10911yescharacteristic
484#393C22×C10911yescharacteristic
485#389—21no—
486#388—21no—
487#388—21no—
488#387—21no—
489#376C22×C10911yescharacteristic
490#328C22×C10911yescharacteristic
491#328C22×C10911yescharacteristic
492#328C22×C10911yescharacteristic
493#328C22×C10911yescharacteristic
494#328C22×C10911yescharacteristic
495#328C22×C10911yescharacteristic
496#327C22×C10911yescharacteristic
497#327C22×C10911yescharacteristic
498#324C22×C10911yescharacteristic
499#324C22×C10911yescharacteristic
500#323C22×C10911yescharacteristic
501#323C22×C10911yescharacteristic
502C22×Q8C23×C10911yescharacteristic
503C2×Q16—21no—
504C2×Q16—21no—
505C2×Q16—21no—
506C2×SD16—21no—
507C4⋊Q8—21no—
508C4⋊Q8—21no—
509C4⋊Q8—21no—
510C4⋊Q8D4×C10911yescharacteristic
511C4⋊Q8D4×C10911yescharacteristic
512#126—21no—
513#126—21no—
514#126—21no—
515#126—21no—
516#126—21no—
517#126—21no—
518#126—21no—
519#126—21no—
520#126—21no—
521#126—21no—
522#126—21no—
523#126—21no—
524#126—21no—
525#125—21no—
526#125—21no—
527#125—21no—
528#125—21no—
529#125—21no—
530#125—21no—
531#125—21no—
532#125—21no—
533#125—21no—
534#125D4×C10911yescharacteristic
535#124—21no—
536#124—21no—
537#124—21no—
538#124D4×C10911yescharacteristic
539#123—21no—
540#123—21no—
541#123—21no—
542#123—21no—
543#123—21no—
544#123—21no—
545#123—21no—
546#123—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8—21no—
554C22⋊Q8—21no—
555C22⋊Q8—21no—
556C22⋊Q8—21no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8C23×C10911yescharacteristic
562C22⋊Q8C23×C10911yescharacteristic
563C22⋊Q8C23×C10911yescharacteristic
564#121—21no—
565#121C23×C10911yescharacteristic
566#120—21no—
567C4×Q8—21no—
568C4×Q8—21no—
569C4×Q8—21no—
570C4×Q8—21no—
571C4×Q8—21no—
572C4×Q8—21no—
573C4×Q8—21no—
574C4×Q8D4×C10911yescharacteristic
575C4×Q8D4×C10911yescharacteristic
576C4×Q8D4×C10911yescharacteristic
577C4×D4—21no—
578C4×D4—21no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4D4×C10911yescharacteristic
583#117—21no—
584#117—21no—
585#117—21no—
586#117—21no—
587#117—21no—
588#117—21no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—21no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4D4×C10911yescharacteristic
594C2×C4⋊C4D4×C10911yescharacteristic
595C2×C4⋊C4C23×C10911yescharacteristic
596C2×C4⋊C4C23×C10911yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4D4×C10911yescharacteristic
601C2×C22⋊C4D4×C10911yescharacteristic
602C2×C22⋊C4C23×C10911yescharacteristic
603C2×C42—21no—
604C2×C42—21no—
605C2×C42C23×C10911yescharacteristic
606#107—21no—
607#107—21no—
608#107—21no—
609#106—21no—
610C4⋊C8—21no—
611C4⋊C8—21no—
612#103—21no—
613#103—21no—
614#103—21no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#102—21no—
620C22⋊C8C23×C10911yescharacteristic
621C22⋊C8C23×C10911yescharacteristic
622C22⋊C8C23×C10911yescharacteristic
623C22⋊C8C23×C10911yescharacteristic
624#97—21no—
625C4×C8—21no—
626#95—21no—
627#95—21no—
628#95—21no—
629#95—21no—
630#95—21no—
631#95C23×C10911yescharacteristic
632#95C23×C10911yescharacteristic
633C24C2×D4×C10911yescharacteristic
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—42no—
640C2×Q8C2×D4×C10911yescharacteristic
641C2×Q8C2×D4×C10911yescharacteristic
642C2×Q8C2×D4×C10911yescharacteristic
643C2×D4—21no—
644C2×D4—21no—
645C2×D4—21no—
646C2×D4C2×D4×C10911yescharacteristic
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×C4C2×D4×C10911yescharacteristic
657C22×C4C2×D4×C10911yescharacteristic
658C22×C4C2×D4×C10911yescharacteristic
659C22×C4C2×D4×C10911yescharacteristic
660C22×C4C2×D4×C10911yescharacteristic
661C22×C4C24×C10911yescharacteristic
662Q16—42no—
663Q16—42no—
664Q16—42no—
665SD16—42no—
666C2×C8—21no—
667C2×C8—21no—
668C2×C8—21no—
669C2×C8—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4—21no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—21no—
697C4⋊C4—21no—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—42no—
702C4⋊C4—42no—
703C4⋊C4—41no—
704C4⋊C4—41no—
705C4⋊C4C2×D4×C10911yescharacteristic
706C4⋊C4C2×D4×C10911yescharacteristic
707C4⋊C4C2×D4×C10911yescharacteristic
708C4⋊C4C2×D4×C10911yescharacteristic
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—21no—
720C22⋊C4—21no—
721C22⋊C4—21no—
722C22⋊C4—21no—
723C22⋊C4—21no—
724C22⋊C4—21no—
725C22⋊C4—21no—
726C22⋊C4—21no—
727C22⋊C4—21no—
728C22⋊C4—21no—
729C22⋊C4—21no—
730C22⋊C4—42no—
731C22⋊C4—42no—
732C42—21no—
733C42—21no—
734C42—21no—
735C42—21no—
736C42—21no—
737C42—21no—
738C42—21no—
739C42—42no—
740C42—41no—
741C42—41no—
742C42C2×D4×C10911yescharacteristic
743C42C2×D4×C10911yescharacteristic
744C42C2×D4×C10911yescharacteristic
745C42C2×D4×C10911yescharacteristic
746C23—21no—
747C23—21no—
748C23—21no—
749C23—21no—
750C23—41no—
751C23—41no—
752C23C22×D4×C10911yescharacteristic
753Q8—22no—
754Q8—22no—
755Q8—41no—
756Q8—41no—
757Q8—41no—
758Q8—41no—
759Q8—41no—
760Q8—81no—
761Q8—81no—
762Q8—81no—
763D4—41no—
764D4—41no—
765D4—41no—
766D4—81no—
767D4—81no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—41no—
798C2×C4—81no—
799C2×C4—81no—
800C2×C4—81no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4#120×C10911yescharacteristic
804C2×C4#120×C10911yescharacteristic
805C2×C4#120×C10911yescharacteristic
806C2×C4#120×C10911yescharacteristic
807C2×C4C22×D4×C10911yescharacteristic
808C2×C4C22×D4×C10911yescharacteristic
809C8—41no—
810C8—41no—
811C8—41no—
812C8—41no—
813C22—21no—
814C22—21no—
815C22—41no—
816C22—41no—
817C22—41no—
818C22—41no—
819C22—41no—
820C22—41no—
821C22—81no—
822C22—81no—
823C22C2×#120×C10911yescharacteristic
824C22#578×C10911yescharacteristic
825C22#578×C10911yescharacteristic
826C4—21no—
827C4—21no—
828C4—21no—
829C4—21no—
830C4—21no—
831C4—21no—
832C4—42no—
833C4—41no—
834C4—41no—
835C4—41no—
836C4—41no—
837C4—41no—
838C4—41no—
839C4—42no—
840C4—41no—
841C4—41no—
842C4—41no—
843C4—41no—
844C4—81no—
845C4—81no—
846C2—21no—
847C2—21no—
848C2—81no—
849C2—81no—
850C2C109×#301111yescharacteristic
851C2C109×#301811yescharacteristic
852C2C109×#302511yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
prime radical#538×C109C22
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×#3117C2semidirect
3. C109×#3104C2semidirect
4. C109×#2604C2semidirect
6. C109×#1617C2semidirect
7. C109×#1615C2semidirect
8. C109×#1614C2semidirect
10. C109×#1605C2semidirect
11. C109×#1603C2semidirect
12. C109×#1602C2semidirect
13. C109×#1506C2semidirect
14. C109×#1500C2semidirect
15. C109×#1473C2semidirect
419. #18283C109direct (N × H)
428. #3117C2×C109semidirect
429. #3104C2×C109semidirect
430. #2604C2×C109semidirect
432. #1617C2×C109semidirect
433. #1615C2×C109semidirect
434. #1614C2×C109semidirect
436. #1605C2×C109semidirect
437. #1603C2×C109semidirect
438. #1602C2×C109semidirect
439. #1506C2×C109semidirect
440. #1500C2×C109semidirect
441. #1473C2×C109semidirect
442. C109#18283direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#35642
C109×#31172
C109×#31042
C109×#26042
C109×#16182
C109×#16172
C109×#16152
C109×#16142
C109×#16062
C109×#16052
C109×#16032
C109×#16022
C109×#15062
C109×#15002
C109×#14732
#18283109