Finite Group Databasebeta

← C109×#32163 #42150157

Subgroups — C109×#32163 #42150157

Order 27904.

854 conjugacy classes of subgroups.

The subgroup lattice has 734 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2544C211yesmaximal, characteristic, complemented
2C109×#2512C211yesmaximal, characteristic, complemented
3C109×#2072C211yesmaximal, characteristic, complemented
4C109×#2054C211yesmaximal, characteristic, complemented
5C109×#2042C211yesmaximal, characteristic, complemented
6C109×#2012C211yesmaximal, characteristic, complemented
7C109×#2012C211yesmaximal, characteristic, complemented
8C109×#2011C211yesmaximal, characteristic
9C109×#1983C211yesmaximal, characteristic, complemented
10C109×#1968C211yesmaximal, characteristic, complemented
11C109×#1957C211yesmaximal, characteristic, complemented
12C109×#1926C211yesmaximal, characteristic, complemented
13C109×#1916C211yesmaximal, characteristic, complemented
14C109×#1879C211yesmaximal, characteristic, complemented
15C109×#1864C211yesmaximal, characteristic, complemented
16C22×SD16×C109C2211yescharacteristic
17C22×D8×C109C2211yescharacteristic
18C22×D8×C109C2211yescharacteristic
19C2×#127×C109C2211yescharacteristic
20C2×#126×C109—21no—
21C2×#124×C109C2211yescharacteristic
22C2×#124×C109C2211yescharacteristic
23C2×C4×D4×C109C2211yescharacteristic
24C2×#106×C109C2211yescharacteristic
25C2×C4⋊C8×C109C2211yescharacteristic
26C2×#103×C109C2211yescharacteristic
27C2×#103×C109C2211yescharacteristic
28C2×#103×C109C2211yescharacteristic
29C2×#102×C109C2211yescharacteristic
30C2×#102×C109C2211yescharacteristic
31C2×#102×C109C2211yescharacteristic
32C2×#102×C109C2211yescharacteristic
33C2×#102×C109C2211yescharacteristic
34C2×#102×C109C2211yescharacteristic
35C2×#102×C109C2211yescharacteristic
36C2×C4×C8×C109C2211yescharacteristic
37#397×C109—21no—
38#396×C109—21no—
39#394×C109—21no—
40#394×C109—21no—
41#391×C109C2211yescharacteristic
42#390×C109C2211yescharacteristic
43#390×C109C2211yescharacteristic
44#390×C109C2211yescharacteristic
45#390×C109C2211yescharacteristic
46#389×C109C2211yescharacteristic
47#388×C109—21no—
48#386×C109—21no—
49#386×C109—21no—
50#384×C109C2211yescharacteristic
51C4×C4⋊C4×C109C2211yescharacteristic
52C4×C4⋊C4×C109C2211yescharacteristic
53#340×C109C2211yescharacteristic
54#340×C109C2211yescharacteristic
55#336×C109C2211yescharacteristic
56#336×C109C2211yescharacteristic
57#336×C109C2211yescharacteristic
58#336×C109C2211yescharacteristic
59C22×Q8×C109C2311yescharacteristic
60C22×D4×C109—21no—
61C22×D4×C109—21no—
62C22×D4×C109C2311yescharacteristic
63C22×D4×C109C2311yescharacteristic
64C22×D4×C109C2311yescharacteristic
65C23×C4×C109—21no—
66C2×SD16×C109—22no—
67C2×SD16×C109—41no—
68C2×SD16×C109—41no—
69C2×D8×C109—22no—
70C2×D8×C109—41no—
71C2×D8×C109—41no—
72C2×D8×C109—41no—
73C2×D8×C109—41no—
74C2×D8×C109—41no—
75C22×C8×C109C2311yescharacteristic
76C22×C8×C109C2311yescharacteristic
77C22×C8×C109C2311yescharacteristic
78C22×C8×C109C2311yescharacteristic
79#127×C109—22no—
80#127×C109—41no—
81#126×C109—44no—
82#124×C109—22no—
83#124×C109—41no—
84#124×C109—41no—
85#124×C109—41no—
86C4×D4×C109—41no—
87C4×D4×C109—41no—
88C2×C4⋊C4×C109—21no—
89C2×C4⋊C4×C109—21no—
90C2×C4⋊C4×C109—21no—
91C2×C4⋊C4×C109D411yescharacteristic
92C2×C4⋊C4×C109D411yescharacteristic
93C2×C4⋊C4×C109C2311yescharacteristic
94C2×C4⋊C4×C109C2311yescharacteristic
95C2×C4⋊C4×C109C2311yescharacteristic
96C2×C4⋊C4×C109C2311yescharacteristic
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×C109—21no—
103C2×C22⋊C4×C109—21no—
104C2×C22⋊C4×C109—21no—
105C2×C22⋊C4×C109—21no—
106C2×C22⋊C4×C109—21no—
107C2×C22⋊C4×C109—21no—
108C2×C22⋊C4×C109—21no—
109C2×C22⋊C4×C109—21no—
110C2×C42×C109—21no—
111C2×C42×C109C2311yescharacteristic
112C2×C42×C109C2311yescharacteristic
113C2×C42×C109C2311yescharacteristic
114#106×C109—41no—
115C4⋊C8×C109—41no—
116#103×C109—41no—
117#103×C109—41no—
118#103×C109—41no—
119#102×C109—22no—
120#102×C109—22no—
121#102×C109—41no—
122#102×C109—41no—
123#102×C109—41no—
124#102×C109—41no—
125#102×C109—41no—
126C4×C8×C109—41no—
127#95×C109—21no—
128#95×C109—21no—
129#95×C109—21no—
130#95×C109—21no—
131#95×C109D411yescharacteristic
132#95×C109D411yescharacteristic
133C24×C109—21no—
134C24×C109—21no—
135C24×C109—21no—
136C2×Q8×C109—21no—
137C2×Q8×C109—21no—
138C2×Q8×C109—21no—
139C2×Q8×C109—21no—
140C2×Q8×C109—21no—
141C2×Q8×C109—21no—
142C2×D4×C109—21no—
143C2×D4×C109—21no—
144C2×D4×C109—21no—
145C2×D4×C109—21no—
146C2×D4×C109—21no—
147C2×D4×C109—21no—
148C2×D4×C109—21no—
149C2×D4×C109—21no—
150C2×D4×C109—21no—
151C2×D4×C109—21no—
152C2×D4×C109—21no—
153C2×D4×C109—21no—
154C2×D4×C109—21no—
155C2×D4×C109—21no—
156C2×D4×C109—21no—
157C2×D4×C109—21no—
158C2×D4×C109—21no—
159C2×D4×C109—42no—
160C2×D4×C109—42no—
161C2×D4×C109—42no—
162C2×D4×C109—42no—
163C2×D4×C109—81no—
164C2×D4×C109—81no—
165C2×D4×C109#4112yes—
166C22×C4×C109—21no—
167C22×C4×C109—21no—
168C22×C4×C109—21no—
169C22×C4×C109—21no—
170C22×C4×C109—21no—
171C22×C4×C109—42no—
172C22×C4×C109—81no—
173C22×C4×C109—81no—
174C22×C4×C109C2×D411yescharacteristic
175C22×C4×C109C2×D411yescharacteristic
176C22×C4×C109C2×D411yescharacteristic
177C22×C4×C109C2×D411yescharacteristic
178C22×C4×C109C2×D411yescharacteristic
179C22×C4×C109C2×D411yescharacteristic
180C22×C4×C109C2411yescharacteristic
181SD16×C109—44no—
182D8×C109—44no—
183D8×C109—44no—
184C2×C8×C109—21no—
185C2×C8×C109—21no—
186C2×C8×C109—21no—
187C2×C8×C109—21no—
188C2×C8×C109—21no—
189C2×C8×C109—21no—
190C2×C8×C109—21no—
191C2×C8×C109—21no—
192C2×C8×C109—21no—
193C2×C8×C109—21no—
194C2×C8×C109—21no—
195C2×C8×C109#4112yes—
196C4⋊C4×C109—22no—
197C4⋊C4×C109—22no—
198C4⋊C4×C109—21no—
199C4⋊C4×C109—21no—
200C4⋊C4×C109—21no—
201C4⋊C4×C109—21no—
202C4⋊C4×C109—21no—
203C4⋊C4×C109—21no—
204C4⋊C4×C109—21no—
205C4⋊C4×C109—21no—
206C4⋊C4×C109—42no—
207C4⋊C4×C109—42no—
208C4⋊C4×C109—81no—
209C22⋊C4×C109—42no—
210C22⋊C4×C109—42no—
211C22⋊C4×C109—42no—
212C22⋊C4×C109—42no—
213C22⋊C4×C109—42no—
214C22⋊C4×C109—42no—
215C22⋊C4×C109—42no—
216C22⋊C4×C109—42no—
217C22⋊C4×C109—42no—
218C22⋊C4×C109—81no—
219C22⋊C4×C109—81no—
220C22⋊C4×C109—81no—
221C22⋊C4×C109—81no—
222C42×C109—21no—
223C42×C109—21no—
224C42×C109—21no—
225C42×C109—21no—
226C42×C109—21no—
227C42×C109—21no—
228C42×C109—42no—
229C23×C109—22no—
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×C109—41no—
242C23×C109—41no—
243C23×C109—41no—
244C23×C109—41no—
245C23×C109—41no—
246C23×C109—41no—
247C23×C109—41no—
248C23×C109—41no—
249C23×C109—41no—
250C23×C109C22×D411yescharacteristic
251Q8×C109—41no—
252Q8×C109—41no—
253Q8×C109—41no—
254Q8×C109—41no—
255D4×C109—22no—
256D4×C109—22no—
257D4×C109—41no—
258D4×C109—41no—
259D4×C109—41no—
260D4×C109—41no—
261D4×C109—41no—
262D4×C109—41no—
263D4×C109—41no—
264D4×C109—41no—
265D4×C109—41no—
266D4×C109—41no—
267D4×C109—84no—
268D4×C109—84no—
269C2×C4×C109—21no—
270C2×C4×C109—21no—
271C2×C4×C109—21no—
272C2×C4×C109—21no—
273C2×C4×C109—21no—
274C2×C4×C109—21no—
275C2×C4×C109—21no—
276C2×C4×C109—21no—
277C2×C4×C109—21no—
278C2×C4×C109—21no—
279C2×C4×C109—21no—
280C2×C4×C109—21no—
281C2×C4×C109—21no—
282C2×C4×C109—21no—
283C2×C4×C109—21no—
284C2×C4×C109—21no—
285C2×C4×C109—41no—
286C2×C4×C109—41no—
287C2×C4×C109—41no—
288C2×C4×C109—41no—
289C2×C4×C109—41no—
290C2×C4×C109—41no—
291C2×C4×C109—41no—
292C2×C4×C109—41no—
293C2×C4×C109—41no—
294C2×C4×C109—41no—
295C2×C4×C109—41no—
296C2×C4×C109—41no—
297C2×C4×C109—41no—
298C2×C4×C109—41no—
299C2×C4×C109—41no—
300C2×C4×C109—84no—
301C2×C4×C109#13512yes—
302C2×C4×C109AGL(1,ℤ/8)12yes—
303C2×C4×C109C2×#4111yescharacteristic
304C2×C4×C109C2×#4111yescharacteristic
305C2×C4×C109H(5,𝔽2)11yescharacteristic
306C2×C4×C109H(5,𝔽2)11yescharacteristic
307C2×C4×C109H(5,𝔽2)11yescharacteristic
308C2×C4×C109H(5,𝔽2)11yescharacteristic
309C8×C109—22no—
310C8×C109—41no—
311C8×C109—41no—
312C8×C109—41no—
313C22×C109—42no—
314C22×C109—42no—
315C22×C109—42no—
316C22×C109—81no—
317C22×C109—81no—
318C22×C109—81no—
319C22×C109—81no—
320C22×C109—81no—
321C22×C109—81no—
322C22×C109—81no—
323C22×C109—81no—
324C22×C109—81no—
325C22×C109—81no—
326C22×C109—81no—
327C22×C109—81no—
328C22×C109—81no—
329C22×C109—81no—
330C22×C109—81no—
331C22×C109—81no—
332C22×C109—81no—
333C22×C109—81no—
334C22×C109#53511yescharacteristic
335C22×C109#54611yescharacteristic
336C22×C109#55011yescharacteristic
337C22×C109C2×#13511yescharacteristic
338C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
339C22×C109#57611yescharacteristic
340C22×C109#57711yescharacteristic
341C4×C109—22no—
342C4×C109—22no—
343C4×C109—41no—
344C4×C109—41no—
345C4×C109—41no—
346C4×C109—41no—
347C4×C109—81no—
348C4×C109—81no—
349C4×C109—81no—
350C4×C109—81no—
351C4×C109—81no—
352C4×C109#53811yescharacteristic
353C4×C109#53811yescharacteristic
354C4×C109#55311yescharacteristic
355C4×C109#56011yescharacteristic
356#32163C10911yesmaximal, characteristic, direct product factor, Sylow
357C2×C109—82no—
358C2×C109—161no—
359C2×C109—161no—
360C2×C109#271411yescharacteristic
361C2×C109#320711yescharacteristic
362C2×C109#322411yescharacteristic
363C2×C109#329711yescharacteristic
364C2×C109#330611yescharacteristic
365C2×C109#339411yescharacteristic
366C2×C109#339911yescharacteristic
367#2544C2×C10911yescharacteristic, complemented
368#2512C2×C10911yescharacteristic, complemented
369#2072C2×C10911yescharacteristic, complemented
370#2054C2×C10911yescharacteristic, complemented
371#2042C2×C10911yescharacteristic, complemented
372#2012C2×C10911yescharacteristic, complemented
373#2012C2×C10911yescharacteristic, complemented
374#2011C2×C10911yescharacteristic
375#1983C2×C10911yescharacteristic, complemented
376#1968C2×C10911yescharacteristic, complemented
377#1957C2×C10911yescharacteristic, complemented
378#1926C2×C10911yescharacteristic, complemented
379#1916C2×C10911yescharacteristic, complemented
380#1879C2×C10911yescharacteristic, complemented
381#1864C2×C10911yescharacteristic, complemented
382C109#3216311yescharacteristic, direct product factor, Sylow
383C22×SD16C22×C10911yescharacteristic
384C22×D8C22×C10911yescharacteristic
385C22×D8C22×C10911yescharacteristic
386C2×#127C22×C10911yescharacteristic
387C2×#126—21no—
388C2×#124C22×C10911yescharacteristic
389C2×#124C22×C10911yescharacteristic
390C2×C4×D4C22×C10911yescharacteristic
391C2×#106C22×C10911yescharacteristic
392C2×C4⋊C8C22×C10911yescharacteristic
393C2×#103C22×C10911yescharacteristic
394C2×#103C22×C10911yescharacteristic
395C2×#103C22×C10911yescharacteristic
396C2×#102C22×C10911yescharacteristic
397C2×#102C22×C10911yescharacteristic
398C2×#102C22×C10911yescharacteristic
399C2×#102C22×C10911yescharacteristic
400C2×#102C22×C10911yescharacteristic
401C2×#102C22×C10911yescharacteristic
402C2×#102C22×C10911yescharacteristic
403C2×C4×C8C22×C10911yescharacteristic
404#397—21no—
405#396—21no—
406#394—21no—
407#394—21no—
408#391C22×C10911yescharacteristic
409#390C22×C10911yescharacteristic
410#390C22×C10911yescharacteristic
411#390C22×C10911yescharacteristic
412#390C22×C10911yescharacteristic
413#389C22×C10911yescharacteristic
414#388—21no—
415#386—21no—
416#386—21no—
417#384C22×C10911yescharacteristic
418C4×C4⋊C4C22×C10911yescharacteristic
419C4×C4⋊C4C22×C10911yescharacteristic
420#340C22×C10911yescharacteristic
421#340C22×C10911yescharacteristic
422#336C22×C10911yescharacteristic
423#336C22×C10911yescharacteristic
424#336C22×C10911yescharacteristic
425#336C22×C10911yescharacteristic
426C22×Q8C23×C10911yescharacteristic
427C22×D4—21no—
428C22×D4—21no—
429C22×D4C23×C10911yescharacteristic
430C22×D4C23×C10911yescharacteristic
431C22×D4C23×C10911yescharacteristic
432C23×C4—21no—
433C2×SD16—22no—
434C2×SD16—41no—
435C2×SD16—41no—
436C2×D8—22no—
437C2×D8—41no—
438C2×D8—41no—
439C2×D8—41no—
440C2×D8—41no—
441C2×D8—41no—
442C22×C8C23×C10911yescharacteristic
443C22×C8C23×C10911yescharacteristic
444C22×C8C23×C10911yescharacteristic
445C22×C8C23×C10911yescharacteristic
446#127—22no—
447#127—41no—
448#126—44no—
449#124—22no—
450#124—41no—
451#124—41no—
452#124—41no—
453C4×D4—41no—
454C4×D4—41no—
455C2×C4⋊C4—21no—
456C2×C4⋊C4—21no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4D4×C10911yescharacteristic
459C2×C4⋊C4D4×C10911yescharacteristic
460C2×C4⋊C4C23×C10911yescharacteristic
461C2×C4⋊C4C23×C10911yescharacteristic
462C2×C4⋊C4C23×C10911yescharacteristic
463C2×C4⋊C4C23×C10911yescharacteristic
464C2×C22⋊C4—21no—
465C2×C22⋊C4—21no—
466C2×C22⋊C4—21no—
467C2×C22⋊C4—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C42—21no—
478C2×C42C23×C10911yescharacteristic
479C2×C42C23×C10911yescharacteristic
480C2×C42C23×C10911yescharacteristic
481#106—41no—
482C4⋊C8—41no—
483#103—41no—
484#103—41no—
485#103—41no—
486#102—22no—
487#102—22no—
488#102—41no—
489#102—41no—
490#102—41no—
491#102—41no—
492#102—41no—
493C4×C8—41no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95D4×C10911yescharacteristic
499#95D4×C10911yescharacteristic
500C24—21no—
501C24—21no—
502C24—21no—
503C2×Q8—21no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×D4—21no—
510C2×D4—21no—
511C2×D4—21no—
512C2×D4—21no—
513C2×D4—21no—
514C2×D4—21no—
515C2×D4—21no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—42no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4—42no—
530C2×D4—81no—
531C2×D4—81no—
532C2×D4#41×C10912yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—42no—
539C22×C4—81no—
540C22×C4—81no—
541C22×C4C2×D4×C10911yescharacteristic
542C22×C4C2×D4×C10911yescharacteristic
543C22×C4C2×D4×C10911yescharacteristic
544C22×C4C2×D4×C10911yescharacteristic
545C22×C4C2×D4×C10911yescharacteristic
546C22×C4C2×D4×C10911yescharacteristic
547C22×C4C24×C10911yescharacteristic
548SD16—44no—
549D8—44no—
550D8—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8#41×C10912yes—
563C4⋊C4—22no—
564C4⋊C4—22no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—42no—
574C4⋊C4—42no—
575C4⋊C4—81no—
576C22⋊C4—42no—
577C22⋊C4—42no—
578C22⋊C4—42no—
579C22⋊C4—42no—
580C22⋊C4—42no—
581C22⋊C4—42no—
582C22⋊C4—42no—
583C22⋊C4—42no—
584C22⋊C4—42no—
585C22⋊C4—81no—
586C22⋊C4—81no—
587C22⋊C4—81no—
588C22⋊C4—81no—
589C42—21no—
590C42—21no—
591C42—21no—
592C42—21no—
593C42—21no—
594C42—21no—
595C42—42no—
596C23—22no—
597C23—41no—
598C23—41no—
599C23—41no—
600C23—41no—
601C23—41no—
602C23—41no—
603C23—41no—
604C23—41no—
605C23—41no—
606C23—41no—
607C23—41no—
608C23—41no—
609C23—41no—
610C23—41no—
611C23—41no—
612C23—41no—
613C23—41no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23C22×D4×C10911yescharacteristic
618Q8—41no—
619Q8—41no—
620Q8—41no—
621Q8—41no—
622D4—22no—
623D4—22no—
624D4—41no—
625D4—41no—
626D4—41no—
627D4—41no—
628D4—41no—
629D4—41no—
630D4—41no—
631D4—41no—
632D4—41no—
633D4—41no—
634D4—84no—
635D4—84no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—21no—
639C2×C4—21no—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—84no—
668C2×C4#135×C10912yes—
669C2×C4AGL(1,ℤ/8)×C10912yes—
670C2×C4C2×#41×C10911yescharacteristic
671C2×C4C2×#41×C10911yescharacteristic
672C2×C4H(5,𝔽2)×C10911yescharacteristic
673C2×C4H(5,𝔽2)×C10911yescharacteristic
674C2×C4H(5,𝔽2)×C10911yescharacteristic
675C2×C4H(5,𝔽2)×C10911yescharacteristic
676C8—22no—
677C8—41no—
678C8—41no—
679C8—41no—
680C22—42no—
681C22—42no—
682C22—42no—
683C22—81no—
684C22—81no—
685C22—81no—
686C22—81no—
687C22—81no—
688C22—81no—
689C22—81no—
690C22—81no—
691C22—81no—
692C22—81no—
693C22—81no—
694C22—81no—
695C22—81no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22#535×C10911yescharacteristic
702C22#546×C10911yescharacteristic
703C22#550×C10911yescharacteristic
704C22C2×#135×C10911yescharacteristic
705C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
706C22#576×C10911yescharacteristic
707C22#577×C10911yescharacteristic
708C4—22no—
709C4—22no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—81no—
715C4—81no—
716C4—81no—
717C4—81no—
718C4—81no—
719C4#538×C10911yescharacteristic
720C4#538×C10911yescharacteristic
721C4#553×C10911yescharacteristic
722C4#560×C10911yescharacteristic
723C2—82no—
724C2—161no—
725C2—161no—
726C2C109×#271411yescharacteristic
727C2C109×#320711yescharacteristic
728C2C109×#322411yescharacteristic
729C2C109×#329711yescharacteristic
730C2C109×#330611yescharacteristic
731C2C109×#339411yescharacteristic
732C2C109×#339911yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC109×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C4×C4⋊C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C109×#2544C2semidirect
2. C109×#2512C2semidirect
3. C109×#2072C2semidirect
4. C109×#2054C2semidirect
5. C109×#2042C2semidirect
6. C109×#2012C2semidirect
7. C109×#2012C2semidirect
9. C109×#1983C2semidirect
10. C109×#1968C2semidirect
11. C109×#1957C2semidirect
12. C109×#1926C2semidirect
13. C109×#1916C2semidirect
14. C109×#1879C2semidirect
15. C109×#1864C2semidirect
356. #32163C109direct (N × H)
367. #2544C2×C109semidirect
368. #2512C2×C109semidirect
369. #2072C2×C109semidirect
370. #2054C2×C109semidirect
371. #2042C2×C109semidirect
372. #2012C2×C109semidirect
373. #2012C2×C109semidirect
375. #1983C2×C109semidirect
376. #1968C2×C109semidirect
377. #1957C2×C109semidirect
378. #1926C2×C109semidirect
379. #1916C2×C109semidirect
380. #1879C2×C109semidirect
381. #1864C2×C109semidirect
382. C109#32163direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#25442
C109×#25122
C109×#20722
C109×#20542
C109×#20422
C109×#20122
C109×#20112
C109×#19832
C109×#19682
C109×#19572
C109×#19262
C109×#19162
C109×#18792
C109×#18642
#32163109