Finite Group Databasebeta

← C109×#18262 #42136256

Subgroups — C109×#18262 #42136256

Order 27904.

1012 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3534C211yesmaximal, characteristic
2C109×#3094C211yesmaximal, characteristic, complemented
3C109×#3091C211yesmaximal, characteristic, complemented
4C109×#2498C211yesmaximal, characteristic, complemented
5C109×#1618C211yesmaximal, characteristic, complemented
6C109×#1616C211yesmaximal, characteristic, complemented
7C109×#1615C211yesmaximal, characteristic, complemented
8C109×#1613C211yesmaximal, characteristic, complemented
9C109×#1612C211yesmaximal, characteristic, complemented
10C109×#1610C211yesmaximal, characteristic, complemented
11C109×#1609C211yesmaximal, characteristic, complemented
12C109×#1607C211yesmaximal, characteristic, complemented
13C109×#1504C211yesmaximal, characteristic, complemented
14C2×#327×C109C211yesmaximal, characteristic, complemented
15C109×#1468C211yesmaximal, characteristic, complemented
16#562×C109—21no—
17#560×C109—21no—
18#553×C109—21no—
19#551×C109—21no—
20#546×C109—21no—
21#546×C109—21no—
22#546×C109—21no—
23D42×C109—21no—
24#540×C109—21no—
25#539×C109—21no—
26#539×C109C2211yescharacteristic
27#538×C109—21no—
28#538×C109C2211yescharacteristic
29#537×C109C2211yescharacteristic
30#534×C109—21no—
31#534×C109C2211yescharacteristic
32#525×C109C2211yescharacteristic
33C2×#123×C109C2211yescharacteristic
34C2×#121×C109C2211yescharacteristic
35C2×#117×C109C2211yescharacteristic, complemented
36#485×C109—21no—
37#484×C109C2211yescharacteristic, complemented
38#483×C109C2211yescharacteristic, complemented
39#482×C109—21no—
40#482×C109—21no—
41#482×C109—21no—
42#481×C109C2211yescharacteristic
43#481×C109C2211yescharacteristic, complemented
44#481×C109C2211yescharacteristic, complemented
45#480×C109C2211yescharacteristic
46#480×C109C2211yescharacteristic, complemented
47#480×C109C2211yescharacteristic, complemented
48#428×C109—21no—
49#427×C109—21no—
50#418×C109—21no—
51#416×C109—21no—
52#407×C109C2211yescharacteristic, complemented
53C2×C22⋊C8×C109C2211yescharacteristic, complemented
54#400×C109C2211yescharacteristic, complemented
55#399×C109C2211yescharacteristic, complemented
56#398×C109C2211yescharacteristic, complemented
57#397×C109C2211yescharacteristic, complemented
58#388×C109—21no—
59#387×C109—21no—
60#386×C109—21no—
61#380×C109—21no—
62C2×#95×C109C2211yescharacteristic, complemented
63#328×C109C2211yescharacteristic, complemented
64#328×C109C2211yescharacteristic, complemented
65#327×C109C2211yescharacteristic
66#327×C109C2211yescharacteristic
67#327×C109C2211yescharacteristic, complemented
68#327×C109C2211yescharacteristic, complemented
69#327×C109C2211yescharacteristic, complemented
70#327×C109C2211yescharacteristic, complemented
71#324×C109C2211yescharacteristic, complemented
72#324×C109C2211yescharacteristic, complemented
73#323×C109C2211yescharacteristic, complemented
74#323×C109C2211yescharacteristic, complemented
75C2×#41×C109—21no—
76C2×#41×C109D411yescharacteristic
77C22×D4×C109—21no—
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109D411yescharacteristic
81C22×D4×C109D411yescharacteristic
82C23×C4×C109—21no—
83C23×C4×C109C2311yescharacteristic
84C2×M16×C109—21no—
85C22×C8×C109—21no—
86#127×C109—21no—
87#126×C109—21no—
88#126×C109—21no—
89#126×C109—21no—
90#126×C109—21no—
91#125×C109—21no—
92#125×C109—21no—
93#124×C109—21no—
94#124×C109—21no—
95#124×C109—21no—
96#123×C109—21no—
97#123×C109—21no—
98#123×C109—21no—
99#123×C109—21no—
100#123×C109—21no—
101#123×C109—21no—
102#123×C109—21no—
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—
110C22⋊Q8×C109—21no—
111C22⋊Q8×C109—21no—
112C22⋊Q8×C109—21no—
113C22⋊Q8×C109—21no—
114C22⋊Q8×C109—21no—
115C22⋊Q8×C109D411yescharacteristic
116C22⋊Q8×C109C2311yescharacteristic
117#121×C109—21no—
118#121×C109—21no—
119#121×C109—21no—
120#121×C109—21no—
121#121×C109—21no—
122#121×C109—21no—
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×C109D411yescharacteristic
133#121×C109D411yescharacteristic
134#121×C109D411yescharacteristic
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—
143#120×C109—21no—
144#120×C109—21no—
145#120×C109—21no—
146C4×D4×C109—21no—
147C4×D4×C109—21no—
148C4×D4×C109—21no—
149C4×D4×C109—21no—
150C4×D4×C109—21no—
151C4×D4×C109—21no—
152C4×D4×C109—21no—
153C4×D4×C109—21no—
154#117×C109—21no—
155#117×C109—21no—
156#117×C109—21no—
157#117×C109—21no—
158#117×C109—21no—
159#117×C109D411yescharacteristic
160C2×C4⋊C4×C109—21no—
161C2×C4⋊C4×C109—21no—
162C2×C4⋊C4×C109D411yescharacteristic
163C2×C4⋊C4×C109D411yescharacteristic
164C2×C4⋊C4×C109C2311yescharacteristic
165C2×C4⋊C4×C109C2311yescharacteristic
166C2×C4⋊C4×C109C2311yescharacteristic
167C2×C22⋊C4×C109—21no—
168C2×C22⋊C4×C109—21no—
169C2×C22⋊C4×C109—21no—
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—
177#107×C109—21no—
178#107×C109—21no—
179#107×C109—21no—
180#107×C109—21no—
181#106×C109—21no—
182#106×C109—21no—
183#106×C109—21no—
184#106×C109—21no—
185#103×C109—21no—
186#103×C109—21no—
187#102×C109—21no—
188#102×C109—21no—
189#102×C109—21no—
190#102×C109—21no—
191#102×C109—21no—
192#102×C109—21no—
193C22⋊C8×C109—21no—
194C22⋊C8×C109—21no—
195C22⋊C8×C109C2311yescharacteristic
196C22⋊C8×C109C2311yescharacteristic
197C22⋊C8×C109C2311yescharacteristic
198C22⋊C8×C109C2311yescharacteristic
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×C109—21no—
208C24×C109C2×D411yescharacteristic
209C24×C109C2×D411yescharacteristic
210#41×C109—42no—
211#41×C109—81no—
212#41×C109—81no—
213C2×Q8×C109—21no—
214C2×Q8×C109C2×D411yescharacteristic
215C2×D4×C109—21no—
216C2×D4×C109—21no—
217C2×D4×C109—21no—
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—42no—
233C2×D4×C109—42no—
234C2×D4×C109—81no—
235C2×D4×C109—81no—
236C2×D4×C109—81no—
237C2×D4×C109—81no—
238C2×D4×C109—82no—
239C2×D4×C109C2×D411yescharacteristic
240C2×D4×C109C2×D411yescharacteristic
241C2×D4×C109C2×D411yescharacteristic
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—21no—
250C22×C4×C109—21no—
251C22×C4×C109—21no—
252C22×C4×C109—21no—
253C22×C4×C109—42no—
254C22×C4×C109—42no—
255C22×C4×C109—42no—
256C22×C4×C109—81no—
257C22×C4×C109C2×D411yescharacteristic
258C22×C4×C109C2×D411yescharacteristic
259C22×C4×C109C2×D411yescharacteristic
260C22×C4×C109C2×D411yescharacteristic
261C22×C4×C109C2×D411yescharacteristic
262C22×C4×C109C2×D411yescharacteristic
263C22×C4×C109C2×D411yescharacteristic
264C22×C4×C109C2×D411yescharacteristic
265C22×C4×C109C2411yescharacteristic
266M16×C109—42no—
267C2×C8×C109—21no—
268C2×C8×C109—21no—
269C2×C8×C109—21no—
270C2×C8×C109—21no—
271C2×C8×C109—42no—
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×C109—21no—
289C4⋊C4×C109—42no—
290C4⋊C4×C109—81no—
291C4⋊C4×C109C2×D411yescharacteristic
292C4⋊C4×C109C2×D411yescharacteristic
293C4⋊C4×C109C2×D411yescharacteristic
294C4⋊C4×C109C2×D411yescharacteristic
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—21no—
317C22⋊C4×C109—21no—
318C22⋊C4×C109—21no—
319C22⋊C4×C109—21no—
320C22⋊C4×C109—42no—
321C22⋊C4×C109—41no—
322C22⋊C4×C109—41no—
323C22⋊C4×C109—81no—
324C42×C109—21no—
325C42×C109—21no—
326C42×C109—21no—
327C42×C109—41no—
328C42×C109—41no—
329C23×C109—21no—
330C23×C109—21no—
331C23×C109—22no—
332C23×C109—21no—
333C23×C109—21no—
334C23×C109—21no—
335C23×C109—21no—
336C23×C109—21no—
337C23×C109—21no—
338C23×C109—41no—
339C23×C109—41no—
340C23×C109—41no—
341C23×C109—42no—
342C23×C109—81no—
343C23×C109—81no—
344C23×C109—81no—
345C23×C109—81no—
346C23×C109—81no—
347C23×C109#12011yescharacteristic
348C23×C109#12011yescharacteristic
349C23×C109C22×D411yescharacteristic
350Q8×C109—41no—
351Q8×C109—81no—
352D4×C109—41no—
353D4×C109—41no—
354D4×C109—41no—
355D4×C109—41no—
356D4×C109—41no—
357D4×C109—41no—
358D4×C109—41no—
359D4×C109—41no—
360D4×C109—41no—
361D4×C109—42no—
362D4×C109—42no—
363D4×C109—81no—
364D4×C109—81no—
365D4×C109—81no—
366D4×C109—81no—
367D4×C109—81no—
368D4×C109—81no—
369D4×C109—81no—
370D4×C109—81no—
371D4×C109—81no—
372D4×C109—81no—
373D4×C109—81no—
374D4×C109—81no—
375C2×C4×C109—22no—
376C2×C4×C109—22no—
377C2×C4×C109—22no—
378C2×C4×C109—21no—
379C2×C4×C109—21no—
380C2×C4×C109—21no—
381C2×C4×C109—21no—
382C2×C4×C109—21no—
383C2×C4×C109—21no—
384C2×C4×C109—21no—
385C2×C4×C109—21no—
386C2×C4×C109—21no—
387C2×C4×C109—21no—
388C2×C4×C109—41no—
389C2×C4×C109—41no—
390C2×C4×C109—41no—
391C2×C4×C109—41no—
392C2×C4×C109—41no—
393C2×C4×C109—41no—
394C2×C4×C109—41no—
395C2×C4×C109—41no—
396C2×C4×C109—41no—
397C2×C4×C109—41no—
398C2×C4×C109—41no—
399C2×C4×C109—41no—
400C2×C4×C109—41no—
401C2×C4×C109—41no—
402C2×C4×C109—41no—
403C2×C4×C109—41no—
404C2×C4×C109—41no—
405C2×C4×C109—81no—
406C2×C4×C109—81no—
407C2×C4×C109—81no—
408C2×C4×C109—81no—
409C2×C4×C109—81no—
410C2×C4×C109—81no—
411C2×C4×C109—81no—
412C2×C4×C109—84no—
413C2×C4×C109#12011yescharacteristic
414C2×C4×C109#12011yescharacteristic
415C2×C4×C109C22×D411yescharacteristic
416C2×C4×C109C22×D411yescharacteristic
417C8×C109—41no—
418C8×C109—41no—
419C8×C109—41no—
420C8×C109—41no—
421C22×C109—21no—
422C22×C109—21no—
423C22×C109—21no—
424C22×C109—21no—
425C22×C109—21no—
426C22×C109—21no—
427C22×C109—21no—
428C22×C109—42no—
429C22×C109—42no—
430C22×C109—41no—
431C22×C109—41no—
432C22×C109—41no—
433C22×C109—41no—
434C22×C109—41no—
435C22×C109—41no—
436C22×C109—41no—
437C22×C109—41no—
438C22×C109—41no—
439C22×C109—41no—
440C22×C109—41no—
441C22×C109—41no—
442C22×C109—81no—
443C22×C109—81no—
444C22×C109—162no—
445C22×C109—162no—
446C22×C109#45812yes—
447C22×C109C2×#12011yescharacteristic
448C22×C109#57611yescharacteristic
449C22×C109#57711yescharacteristic
450C4×C109—21no—
451C4×C109—21no—
452C4×C109—21no—
453C4×C109—21no—
454C4×C109—42no—
455C4×C109—41no—
456C4×C109—41no—
457C4×C109—41no—
458C4×C109—41no—
459C4×C109—41no—
460C4×C109—41no—
461C4×C109—41no—
462C4×C109—41no—
463C4×C109—81no—
464C4×C109—81no—
465C4×C109—81no—
466#18262C10911yesmaximal, characteristic, direct product factor, Sylow
467C2×C109—21no—
468C2×C109—21no—
469C2×C109—22no—
470C2×C109—41no—
471C2×C109—81no—
472C2×C109—81no—
473C2×C109—81no—
474C2×C109—81no—
475C2×C109#301211yescharacteristic
476C2×C109#301811yescharacteristic
477C2×C109C2×#45811yescharacteristic
478#3534C2×C10911yescharacteristic
479#3094C2×C10911yescharacteristic, complemented
480#3091C2×C10911yescharacteristic, complemented
481#2498C2×C10911yescharacteristic, complemented
482#1618C2×C10911yescharacteristic, complemented
483#1616C2×C10911yescharacteristic, complemented
484#1615C2×C10911yescharacteristic, complemented
485#1613C2×C10911yescharacteristic, complemented
486#1612C2×C10911yescharacteristic, complemented
487#1610C2×C10911yescharacteristic, complemented
488#1609C2×C10911yescharacteristic, complemented
489#1607C2×C10911yescharacteristic, complemented
490#1504C2×C10911yescharacteristic, complemented
491C2×#327C2×C10911yescharacteristic, complemented
492#1468C2×C10911yescharacteristic, complemented
493C109#1826211yescharacteristic, direct product factor, Sylow
494#562—21no—
495#560—21no—
496#553—21no—
497#551—21no—
498#546—21no—
499#546—21no—
500#546—21no—
501D42—21no—
502#540—21no—
503#539—21no—
504#539C22×C10911yescharacteristic
505#538—21no—
506#538C22×C10911yescharacteristic
507#537C22×C10911yescharacteristic
508#534—21no—
509#534C22×C10911yescharacteristic
510#525C22×C10911yescharacteristic
511C2×#123C22×C10911yescharacteristic
512C2×#121C22×C10911yescharacteristic
513C2×#117C22×C10911yescharacteristic, complemented
514#485—21no—
515#484C22×C10911yescharacteristic, complemented
516#483C22×C10911yescharacteristic, complemented
517#482—21no—
518#482—21no—
519#482—21no—
520#481C22×C10911yescharacteristic
521#481C22×C10911yescharacteristic, complemented
522#481C22×C10911yescharacteristic, complemented
523#480C22×C10911yescharacteristic
524#480C22×C10911yescharacteristic, complemented
525#480C22×C10911yescharacteristic, complemented
526#428—21no—
527#427—21no—
528#418—21no—
529#416—21no—
530#407C22×C10911yescharacteristic, complemented
531C2×C22⋊C8C22×C10911yescharacteristic, complemented
532#400C22×C10911yescharacteristic, complemented
533#399C22×C10911yescharacteristic, complemented
534#398C22×C10911yescharacteristic, complemented
535#397C22×C10911yescharacteristic, complemented
536#388—21no—
537#387—21no—
538#386—21no—
539#380—21no—
540C2×#95C22×C10911yescharacteristic, complemented
541#328C22×C10911yescharacteristic, complemented
542#328C22×C10911yescharacteristic, complemented
543#327C22×C10911yescharacteristic
544#327C22×C10911yescharacteristic
545#327C22×C10911yescharacteristic, complemented
546#327C22×C10911yescharacteristic, complemented
547#327C22×C10911yescharacteristic, complemented
548#327C22×C10911yescharacteristic, complemented
549#324C22×C10911yescharacteristic, complemented
550#324C22×C10911yescharacteristic, complemented
551#323C22×C10911yescharacteristic, complemented
552#323C22×C10911yescharacteristic, complemented
553C2×#41—21no—
554C2×#41D4×C10911yescharacteristic
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4D4×C10911yescharacteristic
559C22×D4D4×C10911yescharacteristic
560C23×C4—21no—
561C23×C4C23×C10911yescharacteristic
562C2×M16—21no—
563C22×C8—21no—
564#127—21no—
565#126—21no—
566#126—21no—
567#126—21no—
568#126—21no—
569#125—21no—
570#125—21no—
571#124—21no—
572#124—21no—
573#124—21no—
574#123—21no—
575#123—21no—
576#123—21no—
577#123—21no—
578#123—21no—
579#123—21no—
580#123—21no—
581#123—21no—
582#123—21no—
583#123—21no—
584#123—21no—
585#123—21no—
586#123—21no—
587#123—21no—
588C22⋊Q8—21no—
589C22⋊Q8—21no—
590C22⋊Q8—21no—
591C22⋊Q8—21no—
592C22⋊Q8—21no—
593C22⋊Q8D4×C10911yescharacteristic
594C22⋊Q8C23×C10911yescharacteristic
595#121—21no—
596#121—21no—
597#121—21no—
598#121—21no—
599#121—21no—
600#121—21no—
601#121—21no—
602#121—21no—
603#121—21no—
604#121—21no—
605#121—21no—
606#121—21no—
607#121—21no—
608#121—21no—
609#121—21no—
610#121D4×C10911yescharacteristic
611#121D4×C10911yescharacteristic
612#121D4×C10911yescharacteristic
613#121C23×C10911yescharacteristic
614#121C23×C10911yescharacteristic
615#121C23×C10911yescharacteristic
616#120—21no—
617#120—21no—
618#120—21no—
619#120—21no—
620#120—21no—
621#120—21no—
622#120—21no—
623#120—21no—
624C4×D4—21no—
625C4×D4—21no—
626C4×D4—21no—
627C4×D4—21no—
628C4×D4—21no—
629C4×D4—21no—
630C4×D4—21no—
631C4×D4—21no—
632#117—21no—
633#117—21no—
634#117—21no—
635#117—21no—
636#117—21no—
637#117D4×C10911yescharacteristic
638C2×C4⋊C4—21no—
639C2×C4⋊C4—21no—
640C2×C4⋊C4D4×C10911yescharacteristic
641C2×C4⋊C4D4×C10911yescharacteristic
642C2×C4⋊C4C23×C10911yescharacteristic
643C2×C4⋊C4C23×C10911yescharacteristic
644C2×C4⋊C4C23×C10911yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—21no—
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—21no—
650C2×C22⋊C4—21no—
651C2×C22⋊C4D4×C10911yescharacteristic
652C2×C22⋊C4D4×C10911yescharacteristic
653C2×C22⋊C4C23×C10911yescharacteristic
654C2×C42—21no—
655#107—21no—
656#107—21no—
657#107—21no—
658#107—21no—
659#106—21no—
660#106—21no—
661#106—21no—
662#106—21no—
663#103—21no—
664#103—21no—
665#102—21no—
666#102—21no—
667#102—21no—
668#102—21no—
669#102—21no—
670#102—21no—
671C22⋊C8—21no—
672C22⋊C8—21no—
673C22⋊C8C23×C10911yescharacteristic
674C22⋊C8C23×C10911yescharacteristic
675C22⋊C8C23×C10911yescharacteristic
676C22⋊C8C23×C10911yescharacteristic
677#95—21no—
678#95—21no—
679#95—21no—
680#95—21no—
681#95—21no—
682#95C23×C10911yescharacteristic
683#95C23×C10911yescharacteristic
684C24—21no—
685C24—21no—
686C24C2×D4×C10911yescharacteristic
687C24C2×D4×C10911yescharacteristic
688#41—42no—
689#41—81no—
690#41—81no—
691C2×Q8—21no—
692C2×Q8C2×D4×C10911yescharacteristic
693C2×D4—21no—
694C2×D4—21no—
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—21no—
699C2×D4—21no—
700C2×D4—21no—
701C2×D4—21no—
702C2×D4—21no—
703C2×D4—21no—
704C2×D4—21no—
705C2×D4—21no—
706C2×D4—21no—
707C2×D4—21no—
708C2×D4—21no—
709C2×D4—21no—
710C2×D4—42no—
711C2×D4—42no—
712C2×D4—81no—
713C2×D4—81no—
714C2×D4—81no—
715C2×D4—81no—
716C2×D4—82no—
717C2×D4C2×D4×C10911yescharacteristic
718C2×D4C2×D4×C10911yescharacteristic
719C2×D4C2×D4×C10911yescharacteristic
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—21no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—42no—
734C22×C4—81no—
735C22×C4C2×D4×C10911yescharacteristic
736C22×C4C2×D4×C10911yescharacteristic
737C22×C4C2×D4×C10911yescharacteristic
738C22×C4C2×D4×C10911yescharacteristic
739C22×C4C2×D4×C10911yescharacteristic
740C22×C4C2×D4×C10911yescharacteristic
741C22×C4C2×D4×C10911yescharacteristic
742C22×C4C2×D4×C10911yescharacteristic
743C22×C4C24×C10911yescharacteristic
744M16—42no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—21no—
766C4⋊C4—21no—
767C4⋊C4—42no—
768C4⋊C4—81no—
769C4⋊C4C2×D4×C10911yescharacteristic
770C4⋊C4C2×D4×C10911yescharacteristic
771C4⋊C4C2×D4×C10911yescharacteristic
772C4⋊C4C2×D4×C10911yescharacteristic
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—21no—
778C22⋊C4—21no—
779C22⋊C4—21no—
780C22⋊C4—21no—
781C22⋊C4—21no—
782C22⋊C4—21no—
783C22⋊C4—21no—
784C22⋊C4—21no—
785C22⋊C4—21no—
786C22⋊C4—21no—
787C22⋊C4—21no—
788C22⋊C4—21no—
789C22⋊C4—21no—
790C22⋊C4—21no—
791C22⋊C4—21no—
792C22⋊C4—21no—
793C22⋊C4—21no—
794C22⋊C4—21no—
795C22⋊C4—21no—
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—42no—
799C22⋊C4—41no—
800C22⋊C4—41no—
801C22⋊C4—81no—
802C42—21no—
803C42—21no—
804C42—21no—
805C42—41no—
806C42—41no—
807C23—21no—
808C23—21no—
809C23—22no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—21no—
814C23—21no—
815C23—21no—
816C23—41no—
817C23—41no—
818C23—41no—
819C23—42no—
820C23—81no—
821C23—81no—
822C23—81no—
823C23—81no—
824C23—81no—
825C23#120×C10911yescharacteristic
826C23#120×C10911yescharacteristic
827C23C22×D4×C10911yescharacteristic
828Q8—41no—
829Q8—81no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—42no—
840D4—42no—
841D4—81no—
842D4—81no—
843D4—81no—
844D4—81no—
845D4—81no—
846D4—81no—
847D4—81no—
848D4—81no—
849D4—81no—
850D4—81no—
851D4—81no—
852D4—81no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
862C2×C4—21no—
863C2×C4—21no—
864C2×C4—21no—
865C2×C4—21no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—41no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—81no—
884C2×C4—81no—
885C2×C4—81no—
886C2×C4—81no—
887C2×C4—81no—
888C2×C4—81no—
889C2×C4—81no—
890C2×C4—84no—
891C2×C4#120×C10911yescharacteristic
892C2×C4#120×C10911yescharacteristic
893C2×C4C22×D4×C10911yescharacteristic
894C2×C4C22×D4×C10911yescharacteristic
895C8—41no—
896C8—41no—
897C8—41no—
898C8—41no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—21no—
905C22—21no—
906C22—42no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—41no—
911C22—41no—
912C22—41no—
913C22—41no—
914C22—41no—
915C22—41no—
916C22—41no—
917C22—41no—
918C22—41no—
919C22—41no—
920C22—81no—
921C22—81no—
922C22—162no—
923C22—162no—
924C22#458×C10912yes—
925C22C2×#120×C10911yescharacteristic
926C22#576×C10911yescharacteristic
927C22#577×C10911yescharacteristic
928C4—21no—
929C4—21no—
930C4—21no—
931C4—21no—
932C4—42no—
933C4—41no—
934C4—41no—
935C4—41no—
936C4—41no—
937C4—41no—
938C4—41no—
939C4—41no—
940C4—41no—
941C4—81no—
942C4—81no—
943C4—81no—
944C2—21no—
945C2—21no—
946C2—22no—
947C2—41no—
948C2—81no—
949C2—81no—
950C2—81no—
951C2—81no—
952C2C109×#301211yescharacteristic
953C2C109×#301811yescharacteristic
954C2C2×#458×C10911yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC109×#3534C2
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C109×#3094C2semidirect
3. C109×#3091C2semidirect
4. C109×#2498C2semidirect
5. C109×#1618C2semidirect
6. C109×#1616C2semidirect
7. C109×#1615C2semidirect
8. C109×#1613C2semidirect
9. C109×#1612C2semidirect
10. C109×#1610C2semidirect
11. C109×#1609C2semidirect
12. C109×#1607C2semidirect
13. C109×#1504C2semidirect
14. C2×#327×C109C2semidirect
15. C109×#1468C2semidirect
35. C2×#117×C109C22semidirect
37. #484×C109C22semidirect
38. #483×C109C22semidirect
43. #481×C109C22semidirect
44. #481×C109C22semidirect
46. #480×C109C22semidirect
47. #480×C109C22semidirect
52. #407×C109C22semidirect
53. C2×C22⋊C8×C109C22semidirect
54. #400×C109C22semidirect
55. #399×C109C22semidirect
56. #398×C109C22semidirect
57. #397×C109C22semidirect
62. C2×#95×C109C22semidirect
63. #328×C109C22semidirect
64. #328×C109C22semidirect
67. #327×C109C22semidirect
68. #327×C109C22semidirect
69. #327×C109C22semidirect
70. #327×C109C22semidirect
71. #324×C109C22semidirect
72. #324×C109C22semidirect
73. #323×C109C22semidirect
74. #323×C109C22semidirect
466. #18262C109direct (N × H)
479. #3094C2×C109semidirect
480. #3091C2×C109semidirect
481. #2498C2×C109semidirect
482. #1618C2×C109semidirect
483. #1616C2×C109semidirect
484. #1615C2×C109semidirect
485. #1613C2×C109semidirect
486. #1612C2×C109semidirect
487. #1610C2×C109semidirect
488. #1609C2×C109semidirect
489. #1607C2×C109semidirect
490. #1504C2×C109semidirect
491. C2×#327C2×C109semidirect
492. #1468C2×C109semidirect
493. C109#18262direct (N × H)
513. C2×#117C22×C109semidirect
515. #484C22×C109semidirect
516. #483C22×C109semidirect
521. #481C22×C109semidirect
522. #481C22×C109semidirect
524. #480C22×C109semidirect
525. #480C22×C109semidirect
530. #407C22×C109semidirect
531. C2×C22⋊C8C22×C109semidirect
532. #400C22×C109semidirect
533. #399C22×C109semidirect
534. #398C22×C109semidirect
535. #397C22×C109semidirect
540. C2×#95C22×C109semidirect
541. #328C22×C109semidirect
542. #328C22×C109semidirect
545. #327C22×C109semidirect
546. #327C22×C109semidirect
547. #327C22×C109semidirect
548. #327C22×C109semidirect
549. #324C22×C109semidirect
550. #324C22×C109semidirect
551. #323C22×C109semidirect
552. #323C22×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#35342
C109×#30942
C109×#30912
C109×#24982
C109×#16182
C109×#16162
C109×#16152
C109×#16132
C109×#16122
C109×#16102
C109×#16092
C109×#16072
C109×#15042
C2×#327×C1092
C109×#14682
#18262109