Finite Group Databasebeta

← C109×#29068 #42147062

Subgroups — C109×#29068 #42147062

Order 27904.

870 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2496C211yesmaximal, characteristic, complemented
2C109×#2428C211yesmaximal, characteristic
3C109×#2099C211yesmaximal, characteristic, complemented
4C109×#2041C211yesmaximal, characteristic, complemented
5C109×#2034C211yesmaximal, characteristic, complemented
6C109×#2034C211yesmaximal, characteristic, complemented
7C109×#1957C211yesmaximal, characteristic, complemented
8C109×#1941C211yesmaximal, characteristic, complemented
9C109×#1936C211yesmaximal, characteristic, complemented
10C109×#1926C211yesmaximal, characteristic, complemented
11C109×#1895C211yesmaximal, characteristic, complemented
12C109×#1895C211yesmaximal, characteristic, complemented
13C109×#1864C211yesmaximal, characteristic, complemented
14C109×#1762C211yesmaximal, characteristic, complemented
15C109×#1753C211yesmaximal, characteristic, complemented
16C22×M16×C109C2211yescharacteristic
17C2×#127×C109C2211yescharacteristic
18C2×#126×C109—21no—
19C2×#121×C109—21no—
20C2×#121×C109C2211yescharacteristic
21C2×#121×C109C2211yescharacteristic
22C2×C4×D4×C109C2211yescharacteristic
23C2×#106×C109C2211yescharacteristic
24C2×#106×C109C2211yescharacteristic
25C2×#102×C109C2211yescharacteristic
26C2×#102×C109C2211yescharacteristic
27C2×#102×C109C2211yescharacteristic
28C2×#102×C109C2211yescharacteristic
29C2×#102×C109C2211yescharacteristic
30C2×#102×C109C2211yescharacteristic
31C2×#102×C109C2211yescharacteristic
32C2×#102×C109C2211yescharacteristic
33C2×C22⋊C8×C109C2211yescharacteristic
34C2×#97×C109C2211yescharacteristic
35C2×C4×C8×C109C2211yescharacteristic
36#400×C109—21no—
37#397×C109—21no—
38#394×C109—21no—
39#392×C109—21no—
40#390×C109C2211yescharacteristic
41#389×C109C2211yescharacteristic
42#389×C109C2211yescharacteristic
43#389×C109C2211yescharacteristic
44#387×C109—21no—
45#386×C109—21no—
46#384×C109C2211yescharacteristic
47#380×C109C2211yescharacteristic
48#380×C109C2211yescharacteristic
49C4×C4⋊C4×C109C2211yescharacteristic
50C4×C22⋊C4×C109C2211yescharacteristic
51#340×C109C2211yescharacteristic
52#340×C109C2211yescharacteristic
53#340×C109C2211yescharacteristic
54#340×C109C2211yescharacteristic
55#340×C109C2211yescharacteristic
56#340×C109C2211yescharacteristic
57#336×C109C2211yescharacteristic
58#336×C109C2211yescharacteristic
59C22×D4×C109—21no—
60C22×D4×C109—21no—
61C22×D4×C109—21no—
62C22×D4×C109—21no—
63C22×D4×C109C2311yescharacteristic
64C22×D4×C109C2311yescharacteristic
65C23×C4×C109—21no—
66C23×C4×C109C2311yescharacteristic
67C2×M16×C109—22no—
68C2×M16×C109—41no—
69C2×M16×C109—41no—
70C22×C8×C109C2311yescharacteristic
71C22×C8×C109C2311yescharacteristic
72C22×C8×C109C2311yescharacteristic
73C22×C8×C109C2311yescharacteristic
74#127×C109—22no—
75#127×C109—41no—
76#126×C109—44no—
77#121×C109—22no—
78#121×C109—22no—
79#121×C109—44no—
80#121×C109—41no—
81#121×C109—41no—
82C4×D4×C109—22no—
83C4×D4×C109—41no—
84C2×C4⋊C4×C109—21no—
85C2×C4⋊C4×C109—21no—
86C2×C4⋊C4×C109—21no—
87C2×C4⋊C4×C109—21no—
88C2×C4⋊C4×C109—21no—
89C2×C4⋊C4×C109C2311yescharacteristic
90C2×C4⋊C4×C109C2311yescharacteristic
91C2×C4⋊C4×C109C2311yescharacteristic
92C2×C4⋊C4×C109C2311yescharacteristic
93C2×C4⋊C4×C109C2311yescharacteristic
94C2×C4⋊C4×C109C2311yescharacteristic
95C2×C22⋊C4×C109—21no—
96C2×C22⋊C4×C109—21no—
97C2×C22⋊C4×C109—21no—
98C2×C22⋊C4×C109—21no—
99C2×C22⋊C4×C109—21no—
100C2×C22⋊C4×C109—21no—
101C2×C22⋊C4×C109—21no—
102C2×C22⋊C4×C109D411yescharacteristic
103C2×C22⋊C4×C109D411yescharacteristic
104C2×C42×C109—21no—
105C2×C42×C109C2311yescharacteristic
106C2×C42×C109C2311yescharacteristic
107#106×C109—22no—
108#106×C109—41no—
109#102×C109—22no—
110#102×C109—22no—
111#102×C109—22no—
112#102×C109—22no—
113#102×C109—22no—
114#102×C109—41no—
115#102×C109—41no—
116#102×C109—41no—
117C22⋊C8×C109—22no—
118#97×C109—41no—
119C4×C8×C109—41no—
120#95×C109—21no—
121#95×C109—21no—
122#95×C109—21no—
123#95×C109—21no—
124#95×C109—21no—
125#95×C109—21no—
126#95×C109D411yescharacteristic
127#95×C109D411yescharacteristic
128C24×C109—21no—
129C24×C109—21no—
130C24×C109C2×D411yescharacteristic
131C2×D4×C109—21no—
132C2×D4×C109—21no—
133C2×D4×C109—21no—
134C2×D4×C109—21no—
135C2×D4×C109—21no—
136C2×D4×C109—21no—
137C2×D4×C109—21no—
138C2×D4×C109—21no—
139C2×D4×C109—21no—
140C2×D4×C109—21no—
141C2×D4×C109—21no—
142C2×D4×C109—42no—
143C2×D4×C109—42no—
144C2×D4×C109—42no—
145C2×D4×C109—42no—
146C2×D4×C109—42no—
147C2×D4×C109—42no—
148C2×D4×C109—42no—
149C2×D4×C109—42no—
150C2×D4×C109—81no—
151C2×D4×C109—81no—
152C2×D4×C109—81no—
153C2×D4×C109—81no—
154C2×D4×C109#4112yes—
155C22×C4×C109—21no—
156C22×C4×C109—21no—
157C22×C4×C109—21no—
158C22×C4×C109—21no—
159C22×C4×C109—21no—
160C22×C4×C109—21no—
161C22×C4×C109—21no—
162C22×C4×C109—21no—
163C22×C4×C109—21no—
164C22×C4×C109—21no—
165C22×C4×C109—21no—
166C22×C4×C109—21no—
167C22×C4×C109—42no—
168C22×C4×C109—42no—
169C22×C4×C109—81no—
170C22×C4×C109C2×D411yescharacteristic
171C22×C4×C109C2×D411yescharacteristic
172C22×C4×C109C2×D411yescharacteristic
173C22×C4×C109C2×D411yescharacteristic
174C22×C4×C109C2×D411yescharacteristic
175C22×C4×C109C2411yescharacteristic
176M16×C109—44no—
177C2×C8×C109—21no—
178C2×C8×C109—21no—
179C2×C8×C109—21no—
180C2×C8×C109—21no—
181C2×C8×C109—21no—
182C2×C8×C109—21no—
183C2×C8×C109—21no—
184C2×C8×C109—21no—
185C2×C8×C109—21no—
186C2×C8×C109—21no—
187C2×C8×C109#4112yes—
188C2×C8×C109#4112yes—
189C4⋊C4×C109—21no—
190C4⋊C4×C109—21no—
191C4⋊C4×C109—21no—
192C4⋊C4×C109—21no—
193C4⋊C4×C109—21no—
194C4⋊C4×C109—21no—
195C4⋊C4×C109—21no—
196C4⋊C4×C109—21no—
197C4⋊C4×C109—21no—
198C4⋊C4×C109—21no—
199C4⋊C4×C109—21no—
200C4⋊C4×C109—42no—
201C4⋊C4×C109—42no—
202C4⋊C4×C109—42no—
203C4⋊C4×C109—42no—
204C4⋊C4×C109—42no—
205C4⋊C4×C109#4112yes—
206C22⋊C4×C109—22no—
207C22⋊C4×C109—22no—
208C22⋊C4×C109—42no—
209C22⋊C4×C109—42no—
210C22⋊C4×C109—42no—
211C22⋊C4×C109—42no—
212C22⋊C4×C109—42no—
213C22⋊C4×C109—42no—
214C22⋊C4×C109—81no—
215C42×C109—21no—
216C42×C109—21no—
217C42×C109—21no—
218C42×C109—21no—
219C42×C109—42no—
220C23×C109—21no—
221C23×C109—22no—
222C23×C109—21no—
223C23×C109—21no—
224C23×C109—21no—
225C23×C109—21no—
226C23×C109—21no—
227C23×C109—21no—
228C23×C109—41no—
229C23×C109—41no—
230C23×C109—41no—
231C23×C109—41no—
232C23×C109—41no—
233C23×C109—41no—
234C23×C109—41no—
235C23×C109—41no—
236C23×C109—41no—
237C23×C109—41no—
238C23×C109—41no—
239C23×C109—41no—
240C23×C109—41no—
241C23×C109C22×D411yescharacteristic
242D4×C109—22no—
243D4×C109—22no—
244D4×C109—41no—
245D4×C109—41no—
246D4×C109—41no—
247D4×C109—41no—
248D4×C109—41no—
249D4×C109—41no—
250D4×C109—84no—
251D4×C109—84no—
252D4×C109—84no—
253D4×C109—84no—
254C2×C4×C109—21no—
255C2×C4×C109—21no—
256C2×C4×C109—21no—
257C2×C4×C109—21no—
258C2×C4×C109—21no—
259C2×C4×C109—21no—
260C2×C4×C109—21no—
261C2×C4×C109—22no—
262C2×C4×C109—21no—
263C2×C4×C109—21no—
264C2×C4×C109—21no—
265C2×C4×C109—21no—
266C2×C4×C109—21no—
267C2×C4×C109—21no—
268C2×C4×C109—41no—
269C2×C4×C109—41no—
270C2×C4×C109—41no—
271C2×C4×C109—41no—
272C2×C4×C109—41no—
273C2×C4×C109—41no—
274C2×C4×C109—41no—
275C2×C4×C109—41no—
276C2×C4×C109—41no—
277C2×C4×C109—41no—
278C2×C4×C109—41no—
279C2×C4×C109—41no—
280C2×C4×C109—41no—
281C2×C4×C109—41no—
282C2×C4×C109—41no—
283C2×C4×C109—41no—
284C2×C4×C109—41no—
285C2×C4×C109—41no—
286C2×C4×C109—41no—
287C2×C4×C109—41no—
288C2×C4×C109—41no—
289C2×C4×C109—84no—
290C2×C4×C109AGL(1,ℤ/8)12yes—
291C2×C4×C109AGL(1,ℤ/8)12yes—
292C2×C4×C109C2×#4111yescharacteristic
293C2×C4×C109C2×#4111yescharacteristic
294C2×C4×C109C2×#4111yescharacteristic
295C2×C4×C109C2×#4111yescharacteristic
296C2×C4×C109H(5,𝔽2)11yescharacteristic
297C2×C4×C109H(5,𝔽2)11yescharacteristic
298C8×C109—22no—
299C8×C109—22no—
300C8×C109—41no—
301C8×C109—41no—
302C22×C109—41no—
303C22×C109—41no—
304C22×C109—41no—
305C22×C109—42no—
306C22×C109—41no—
307C22×C109—41no—
308C22×C109—42no—
309C22×C109—41no—
310C22×C109—41no—
311C22×C109—42no—
312C22×C109—81no—
313C22×C109—81no—
314C22×C109—81no—
315C22×C109—81no—
316C22×C109—81no—
317C22×C109—81no—
318C22×C109—81no—
319C22×C109—81no—
320C22×C109—81no—
321C22×C109—81no—
322C22×C109—81no—
323C22×C109#53211yescharacteristic
324C22×C109#54611yescharacteristic
325C22×C109#54611yescharacteristic
326C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
327C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
328C22×C109#57711yescharacteristic
329C22×C109#57711yescharacteristic
330C4×C109—22no—
331C4×C109—22no—
332C4×C109—41no—
333C4×C109—41no—
334C4×C109—42no—
335C4×C109—41no—
336C4×C109—81no—
337C4×C109—81no—
338C4×C109—81no—
339C4×C109—81no—
340C4×C109—81no—
341C4×C109#52911yescharacteristic
342C4×C109#53811yescharacteristic
343C4×C109#55311yescharacteristic
344C4×C109#55311yescharacteristic
345#29068C10911yesmaximal, characteristic, direct product factor, Sylow
346C2×C109—81no—
347C2×C109—82no—
348C2×C109—161no—
349C2×C109#255911yescharacteristic
350C2×C109#317411yescharacteristic
351C2×C109#318411yescharacteristic
352C2×C109#330611yescharacteristic
353C2×C109#331011yescharacteristic
354C2×C109#332411yescharacteristic
355C2×C109#333211yescharacteristic
356#2496C2×C10911yescharacteristic, complemented
357#2428C2×C10911yescharacteristic
358#2099C2×C10911yescharacteristic, complemented
359#2041C2×C10911yescharacteristic, complemented
360#2034C2×C10911yescharacteristic, complemented
361#2034C2×C10911yescharacteristic, complemented
362#1957C2×C10911yescharacteristic, complemented
363#1941C2×C10911yescharacteristic, complemented
364#1936C2×C10911yescharacteristic, complemented
365#1926C2×C10911yescharacteristic, complemented
366#1895C2×C10911yescharacteristic, complemented
367#1895C2×C10911yescharacteristic, complemented
368#1864C2×C10911yescharacteristic, complemented
369#1762C2×C10911yescharacteristic, complemented
370#1753C2×C10911yescharacteristic, complemented
371C109#2906811yescharacteristic, direct product factor, Sylow
372C22×M16C22×C10911yescharacteristic
373C2×#127C22×C10911yescharacteristic
374C2×#126—21no—
375C2×#121—21no—
376C2×#121C22×C10911yescharacteristic
377C2×#121C22×C10911yescharacteristic
378C2×C4×D4C22×C10911yescharacteristic
379C2×#106C22×C10911yescharacteristic
380C2×#106C22×C10911yescharacteristic
381C2×#102C22×C10911yescharacteristic
382C2×#102C22×C10911yescharacteristic
383C2×#102C22×C10911yescharacteristic
384C2×#102C22×C10911yescharacteristic
385C2×#102C22×C10911yescharacteristic
386C2×#102C22×C10911yescharacteristic
387C2×#102C22×C10911yescharacteristic
388C2×#102C22×C10911yescharacteristic
389C2×C22⋊C8C22×C10911yescharacteristic
390C2×#97C22×C10911yescharacteristic
391C2×C4×C8C22×C10911yescharacteristic
392#400—21no—
393#397—21no—
394#394—21no—
395#392—21no—
396#390C22×C10911yescharacteristic
397#389C22×C10911yescharacteristic
398#389C22×C10911yescharacteristic
399#389C22×C10911yescharacteristic
400#387—21no—
401#386—21no—
402#384C22×C10911yescharacteristic
403#380C22×C10911yescharacteristic
404#380C22×C10911yescharacteristic
405C4×C4⋊C4C22×C10911yescharacteristic
406C4×C22⋊C4C22×C10911yescharacteristic
407#340C22×C10911yescharacteristic
408#340C22×C10911yescharacteristic
409#340C22×C10911yescharacteristic
410#340C22×C10911yescharacteristic
411#340C22×C10911yescharacteristic
412#340C22×C10911yescharacteristic
413#336C22×C10911yescharacteristic
414#336C22×C10911yescharacteristic
415C22×D4—21no—
416C22×D4—21no—
417C22×D4—21no—
418C22×D4—21no—
419C22×D4C23×C10911yescharacteristic
420C22×D4C23×C10911yescharacteristic
421C23×C4—21no—
422C23×C4C23×C10911yescharacteristic
423C2×M16—22no—
424C2×M16—41no—
425C2×M16—41no—
426C22×C8C23×C10911yescharacteristic
427C22×C8C23×C10911yescharacteristic
428C22×C8C23×C10911yescharacteristic
429C22×C8C23×C10911yescharacteristic
430#127—22no—
431#127—41no—
432#126—44no—
433#121—22no—
434#121—22no—
435#121—44no—
436#121—41no—
437#121—41no—
438C4×D4—22no—
439C4×D4—41no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—21no—
442C2×C4⋊C4—21no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4C23×C10911yescharacteristic
446C2×C4⋊C4C23×C10911yescharacteristic
447C2×C4⋊C4C23×C10911yescharacteristic
448C2×C4⋊C4C23×C10911yescharacteristic
449C2×C4⋊C4C23×C10911yescharacteristic
450C2×C4⋊C4C23×C10911yescharacteristic
451C2×C22⋊C4—21no—
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4—21no—
458C2×C22⋊C4D4×C10911yescharacteristic
459C2×C22⋊C4D4×C10911yescharacteristic
460C2×C42—21no—
461C2×C42C23×C10911yescharacteristic
462C2×C42C23×C10911yescharacteristic
463#106—22no—
464#106—41no—
465#102—22no—
466#102—22no—
467#102—22no—
468#102—22no—
469#102—22no—
470#102—41no—
471#102—41no—
472#102—41no—
473C22⋊C8—22no—
474#97—41no—
475C4×C8—41no—
476#95—21no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95D4×C10911yescharacteristic
483#95D4×C10911yescharacteristic
484C24—21no—
485C24—21no—
486C24C2×D4×C10911yescharacteristic
487C2×D4—21no—
488C2×D4—21no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—21no—
492C2×D4—21no—
493C2×D4—21no—
494C2×D4—21no—
495C2×D4—21no—
496C2×D4—21no—
497C2×D4—21no—
498C2×D4—42no—
499C2×D4—42no—
500C2×D4—42no—
501C2×D4—42no—
502C2×D4—42no—
503C2×D4—42no—
504C2×D4—42no—
505C2×D4—42no—
506C2×D4—81no—
507C2×D4—81no—
508C2×D4—81no—
509C2×D4—81no—
510C2×D4#41×C10912yes—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—21no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—42no—
524C22×C4—42no—
525C22×C4—81no—
526C22×C4C2×D4×C10911yescharacteristic
527C22×C4C2×D4×C10911yescharacteristic
528C22×C4C2×D4×C10911yescharacteristic
529C22×C4C2×D4×C10911yescharacteristic
530C22×C4C2×D4×C10911yescharacteristic
531C22×C4C24×C10911yescharacteristic
532M16—44no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8#41×C10912yes—
544C2×C8#41×C10912yes—
545C4⋊C4—21no—
546C4⋊C4—21no—
547C4⋊C4—21no—
548C4⋊C4—21no—
549C4⋊C4—21no—
550C4⋊C4—21no—
551C4⋊C4—21no—
552C4⋊C4—21no—
553C4⋊C4—21no—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—42no—
557C4⋊C4—42no—
558C4⋊C4—42no—
559C4⋊C4—42no—
560C4⋊C4—42no—
561C4⋊C4#41×C10912yes—
562C22⋊C4—22no—
563C22⋊C4—22no—
564C22⋊C4—42no—
565C22⋊C4—42no—
566C22⋊C4—42no—
567C22⋊C4—42no—
568C22⋊C4—42no—
569C22⋊C4—42no—
570C22⋊C4—81no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—42no—
576C23—21no—
577C23—22no—
578C23—21no—
579C23—21no—
580C23—21no—
581C23—21no—
582C23—21no—
583C23—21no—
584C23—41no—
585C23—41no—
586C23—41no—
587C23—41no—
588C23—41no—
589C23—41no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23—41no—
595C23—41no—
596C23—41no—
597C23C22×D4×C10911yescharacteristic
598D4—22no—
599D4—22no—
600D4—41no—
601D4—41no—
602D4—41no—
603D4—41no—
604D4—41no—
605D4—41no—
606D4—84no—
607D4—84no—
608D4—84no—
609D4—84no—
610C2×C4—21no—
611C2×C4—21no—
612C2×C4—21no—
613C2×C4—21no—
614C2×C4—21no—
615C2×C4—21no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—41no—
625C2×C4—41no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—84no—
646C2×C4AGL(1,ℤ/8)×C10912yes—
647C2×C4AGL(1,ℤ/8)×C10912yes—
648C2×C4C2×#41×C10911yescharacteristic
649C2×C4C2×#41×C10911yescharacteristic
650C2×C4C2×#41×C10911yescharacteristic
651C2×C4C2×#41×C10911yescharacteristic
652C2×C4H(5,𝔽2)×C10911yescharacteristic
653C2×C4H(5,𝔽2)×C10911yescharacteristic
654C8—22no—
655C8—22no—
656C8—41no—
657C8—41no—
658C22—42no—
659C22—41no—
660C22—41no—
661C22—42no—
662C22—41no—
663C22—41no—
664C22—42no—
665C22—41no—
666C22—41no—
667C22—41no—
668C22—81no—
669C22—81no—
670C22—81no—
671C22—81no—
672C22—81no—
673C22—81no—
674C22—81no—
675C22—81no—
676C22—81no—
677C22—81no—
678C22—81no—
679C22#532×C10911yescharacteristic
680C22#546×C10911yescharacteristic
681C22#546×C10911yescharacteristic
682C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
683C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
684C22#577×C10911yescharacteristic
685C22#577×C10911yescharacteristic
686C4—22no—
687C4—22no—
688C4—41no—
689C4—42no—
690C4—41no—
691C4—41no—
692C4—81no—
693C4—81no—
694C4—81no—
695C4—81no—
696C4—81no—
697C4#529×C10911yescharacteristic
698C4#538×C10911yescharacteristic
699C4#553×C10911yescharacteristic
700C4#553×C10911yescharacteristic
701C2—81no—
702C2—82no—
703C2—161no—
704C2C109×#255911yescharacteristic
705C2C109×#317411yescharacteristic
706C2C109×#318411yescharacteristic
707C2C109×#330611yescharacteristic
708C2C109×#331011yescharacteristic
709C2C109×#332411yescharacteristic
710C2C109×#333211yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC109×#2428C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C4×C22⋊C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#2496C2semidirect
3. C109×#2099C2semidirect
4. C109×#2041C2semidirect
5. C109×#2034C2semidirect
6. C109×#2034C2semidirect
7. C109×#1957C2semidirect
8. C109×#1941C2semidirect
9. C109×#1936C2semidirect
10. C109×#1926C2semidirect
11. C109×#1895C2semidirect
12. C109×#1895C2semidirect
13. C109×#1864C2semidirect
14. C109×#1762C2semidirect
15. C109×#1753C2semidirect
345. #29068C109direct (N × H)
356. #2496C2×C109semidirect
358. #2099C2×C109semidirect
359. #2041C2×C109semidirect
360. #2034C2×C109semidirect
361. #2034C2×C109semidirect
362. #1957C2×C109semidirect
363. #1941C2×C109semidirect
364. #1936C2×C109semidirect
365. #1926C2×C109semidirect
366. #1895C2×C109semidirect
367. #1895C2×C109semidirect
368. #1864C2×C109semidirect
369. #1762C2×C109semidirect
370. #1753C2×C109semidirect
371. C109#29068direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#24962
C109×#24282
C109×#20992
C109×#20412
C109×#20342
C109×#19572
C109×#19412
C109×#19362
C109×#19262
C109×#18952
C109×#18642
C109×#17622
C109×#17532
#29068109