Finite Group Databasebeta

← C109×#18609 #42136603

Subgroups — C109×#18609 #42136603

Order 27904.

874 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#3518C211yesmaximal, characteristic
2C109×#3252C211yesmaximal, characteristic, complemented
3C109×#3185C211yesmaximal, characteristic, complemented
4C109×#3076C211yesmaximal, characteristic, complemented
5C109×#1652C211yesmaximal, characteristic, complemented
6C109×#1651C211yesmaximal, characteristic, complemented
7C109×#1646C211yesmaximal, characteristic, complemented
8C109×#1645C211yesmaximal, characteristic, complemented
9C109×#1638C211yesmaximal, characteristic, complemented
10C109×#1637C211yesmaximal, characteristic, complemented
11C109×#1634C211yesmaximal, characteristic, complemented
12C109×#1633C211yesmaximal, characteristic, complemented
13C109×#1550C211yesmaximal, characteristic, complemented
14C109×#1489C211yesmaximal, characteristic, complemented
15C109×#1483C211yesmaximal, characteristic, complemented
16Q82×C109C2211yescharacteristic
17#556×C109—21no—
18#556×C109—22no—
19#556×C109—21no—
20#556×C109C2211yescharacteristic
21#555×C109—21no—
22#555×C109C2211yescharacteristic
23D4×Q8×C109C2211yescharacteristic
24#548×C109—21no—
25#542×C109—22no—
26#542×C109—21no—
27#533×C109—21no—
28#533×C109C2211yescharacteristic
29#533×C109C2211yescharacteristic
30#529×C109—21no—
31#529×C109C2211yescharacteristic
32#519×C109—21no—
33C4×#41×C109C2211yescharacteristic
34#498×C109C2211yescharacteristic
35#494×C109C2211yescharacteristic
36#487×C109C2211yescharacteristic
37#487×C109C2211yescharacteristic
38#479×C109—21no—
39#479×C109—21no—
40#478×C109—21no—
41#477×C109C2211yescharacteristic
42#477×C109C2211yescharacteristic
43#476×C109C2211yescharacteristic
44#476×C109C2211yescharacteristic
45#475×C109C2211yescharacteristic
46#474×C109C2211yescharacteristic
47#470×C109—21no—
48#470×C109—22no—
49#468×C109—21no—
50#464×C109—21no—
51#462×C109C2211yescharacteristic
52#461×C109C2211yescharacteristic
53#441×C109—22no—
54#427×C109—21no—
55#423×C109C2211yescharacteristic
56C2×C4⋊C8×C109C2211yescharacteristic
57#416×C109—21no—
58C4×M16×C109C2211yescharacteristic
59#333×C109C2211yescharacteristic
60#333×C109C2211yescharacteristic
61#332×C109C2211yescharacteristic
62#332×C109C2211yescharacteristic
63Q8⋊C8×C109C2211yescharacteristic
64Q8⋊C8×C109C2211yescharacteristic
65Q8⋊C8×C109C2211yescharacteristic
66Q8⋊C8×C109C2211yescharacteristic
67D4⋊C8×C109C2211yescharacteristic
68D4⋊C8×C109C2211yescharacteristic
69D4⋊C8×C109C2211yescharacteristic
70D4⋊C8×C109C2211yescharacteristic
71C2×#41×C109D411yescharacteristic
72C22×Q8×C109—21no—
73C2×Q16×C109—22no—
74C2×Q16×C109—21no—
75C2×SD16×C109—21no—
76C2×M16×C109—21no—
77C2×M16×C109—21no—
78C22×C8×C109—21no—
79C4⋊Q8×C109—22no—
80C4⋊Q8×C109—21no—
81C4⋊Q8×C109—21no—
82C4⋊Q8×C109—21no—
83C4⋊Q8×C109C2311yescharacteristic
84C4⋊Q8×C109C2311yescharacteristic
85C4⋊Q8×C109C2311yescharacteristic
86C4⋊Q8×C109C2311yescharacteristic
87#126×C109—22no—
88#126×C109—22no—
89#126×C109—22no—
90#126×C109—22no—
91#126×C109—21no—
92#125×C109—21no—
93#125×C109—21no—
94#125×C109D411yescharacteristic
95#124×C109—22no—
96#124×C109—22no—
97#124×C109—22no—
98#124×C109—22no—
99#124×C109—21no—
100#124×C109D411yescharacteristic
101#123×C109—22no—
102#123×C109—21no—
103C22⋊Q8×C109—22no—
104C22⋊Q8×C109—22no—
105C22⋊Q8×C109—21no—
106C22⋊Q8×C109—21no—
107C22⋊Q8×C109—21no—
108C22⋊Q8×C109—22no—
109C22⋊Q8×C109—21no—
110C22⋊Q8×C109—21no—
111C22⋊Q8×C109D411yescharacteristic
112C22⋊Q8×C109D412yes—
113#121×C109—22no—
114#121×C109—21no—
115#121×C109—21no—
116#121×C109D411yescharacteristic
117C4×Q8×C109—22no—
118C4×Q8×C109—22no—
119C4×Q8×C109—22no—
120C4×Q8×C109—21no—
121C4×Q8×C109—21no—
122C4×Q8×C109—21no—
123C4×Q8×C109—21no—
124C4×Q8×C109—21no—
125C4×Q8×C109—21no—
126C4×Q8×C109D411yescharacteristic
127C4×Q8×C109D412yes—
128C4×Q8×C109C2311yescharacteristic
129C4×Q8×C109C2311yescharacteristic
130C4×D4×C109—22no—
131C4×D4×C109—21no—
132C4×D4×C109—21no—
133C4×D4×C109—21no—
134C4×D4×C109—21no—
135C4×D4×C109D411yescharacteristic
136C4×D4×C109C2311yescharacteristic
137C4×D4×C109C2311yescharacteristic
138#117×C109—22no—
139#117×C109—22no—
140#117×C109—21no—
141#117×C109—21no—
142#117×C109—21no—
143#117×C109—21no—
144#117×C109—21no—
145#117×C109—21no—
146#117×C109—21no—
147#117×C109D411yescharacteristic
148C2×C42×C109—21no—
149C2×C42×C109C2311yescharacteristic
150#107×C109—21no—
151#107×C109—21no—
152#107×C109—21no—
153#106×C109—22no—
154#106×C109—21no—
155#106×C109—21no—
156#106×C109—21no—
157C4⋊C8×C109—21no—
158C4⋊C8×C109—21no—
159C4⋊C8×C109C2311yescharacteristic
160C4⋊C8×C109C2311yescharacteristic
161C4⋊C8×C109C2311yescharacteristic
162C4⋊C8×C109C2311yescharacteristic
163#103×C109—21no—
164#103×C109—21no—
165#103×C109—22no—
166#103×C109—21no—
167#103×C109—22no—
168#103×C109—21no—
169#103×C109—21no—
170#102×C109—21no—
171#102×C109—21no—
172#102×C109—21no—
173#97×C109—21no—
174C4×C8×C109C2311yescharacteristic
175C4×C8×C109C2311yescharacteristic
176#41×C109—22no—
177#41×C109—41no—
178C2×Q8×C109—22no—
179C2×Q8×C109—22no—
180C2×Q8×C109—21no—
181C2×Q8×C109—21no—
182C2×Q8×C109—21no—
183C2×Q8×C109—42no—
184C2×Q8×C109—42no—
185C2×Q8×C109C2×D411yescharacteristic
186C2×Q8×C109C2×D411yescharacteristic
187C2×Q8×C109C2×D412yes—
188C2×D4×C109—21no—
189C2×D4×C109—22no—
190C2×D4×C109—21no—
191C2×D4×C109C2×D411yescharacteristic
192C2×D4×C109C2×D411yescharacteristic
193C22×C4×C109—22no—
194C22×C4×C109—21no—
195C22×C4×C109—21no—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109C2×D411yescharacteristic
199C22×C4×C109C2×D411yescharacteristic
200C22×C4×C109C2×D411yescharacteristic
201Q16×C109—44no—
202Q16×C109—81no—
203SD16×C109—81no—
204M16×C109—42no—
205M16×C109—81no—
206C2×C8×C109—21no—
207C2×C8×C109—21no—
208C2×C8×C109—21no—
209C2×C8×C109—21no—
210C2×C8×C109—21no—
211C2×C8×C109—21no—
212C2×C8×C109—42no—
213C4⋊C4×C109—22no—
214C4⋊C4×C109—22no—
215C4⋊C4×C109—22no—
216C4⋊C4×C109—22no—
217C4⋊C4×C109—21no—
218C4⋊C4×C109—21no—
219C4⋊C4×C109—22no—
220C4⋊C4×C109—21no—
221C4⋊C4×C109—21no—
222C4⋊C4×C109—22no—
223C4⋊C4×C109—21no—
224C4⋊C4×C109—21no—
225C4⋊C4×C109—21no—
226C4⋊C4×C109—21no—
227C4⋊C4×C109—21no—
228C4⋊C4×C109—21no—
229C4⋊C4×C109—21no—
230C4⋊C4×C109—21no—
231C4⋊C4×C109—21no—
232C4⋊C4×C109—41no—
233C4⋊C4×C109—41no—
234C4⋊C4×C109C2×D411yescharacteristic
235C4⋊C4×C109C2×D412yes—
236C4⋊C4×C109C2×D411yescharacteristic
237C4⋊C4×C109C2×D411yescharacteristic
238C4⋊C4×C109C2×D411yescharacteristic
239C22⋊C4×C109—22no—
240C22⋊C4×C109—22no—
241C22⋊C4×C109—22no—
242C22⋊C4×C109—22no—
243C22⋊C4×C109—22no—
244C22⋊C4×C109—22no—
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—41no—
254C42×C109—22no—
255C42×C109—22no—
256C42×C109—22no—
257C42×C109—21no—
258C42×C109—21no—
259C42×C109—22no—
260C42×C109—21no—
261C42×C109—21no—
262C42×C109—41no—
263C42×C109C2×D411yescharacteristic
264C42×C109C2×D411yescharacteristic
265C42×C109C2×D411yescharacteristic
266C42×C109C2411yescharacteristic
267C23×C109—21no—
268C23×C109—21no—
269C23×C109#12011yescharacteristic
270Q8×C109—21no—
271Q8×C109—21no—
272Q8×C109—21no—
273Q8×C109—42no—
274Q8×C109—44no—
275Q8×C109—42no—
276Q8×C109—41no—
277Q8×C109—41no—
278Q8×C109—41no—
279Q8×C109—41no—
280Q8×C109—82no—
281Q8×C109#13712yes—
282D4×C109—21no—
283D4×C109—21no—
284D4×C109—21no—
285D4×C109—21no—
286D4×C109—42no—
287D4×C109—81no—
288D4×C109—82no—
289C2×C4×C109—21no—
290C2×C4×C109—21no—
291C2×C4×C109—21no—
292C2×C4×C109—21no—
293C2×C4×C109—21no—
294C2×C4×C109—21no—
295C2×C4×C109—21no—
296C2×C4×C109—22no—
297C2×C4×C109—21no—
298C2×C4×C109—21no—
299C2×C4×C109—22no—
300C2×C4×C109—21no—
301C2×C4×C109—41no—
302C2×C4×C109—42no—
303C2×C4×C109—44no—
304C2×C4×C109—41no—
305C2×C4×C109—41no—
306C2×C4×C109—41no—
307C2×C4×C109—41no—
308C2×C4×C109—41no—
309C2×C4×C109—41no—
310C2×C4×C109—81no—
311C2×C4×C109#12011yescharacteristic
312C2×C4×C109#12011yescharacteristic
313C2×C4×C109#12011yescharacteristic
314C2×C4×C109C22×D411yescharacteristic
315C2×C4×C109C22×D411yescharacteristic
316C2×C4×C109C22×D411yescharacteristic
317C8×C109—22no—
318C8×C109—41no—
319C8×C109—41no—
320C8×C109—41no—
321C8×C109—41no—
322C8×C109—41no—
323C22×C109—21no—
324C22×C109—21no—
325C22×C109—21no—
326C22×C109—41no—
327C22×C109—41no—
328C22×C109—41no—
329C22×C109—41no—
330C22×C109—41no—
331C22×C109—41no—
332C22×C109C2×#12011yescharacteristic
333C4×C109—21no—
334C4×C109—22no—
335C4×C109—21no—
336C4×C109—21no—
337C4×C109—21no—
338C4×C109—42no—
339C4×C109—41no—
340C4×C109—41no—
341C4×C109—41no—
342C4×C109—41no—
343C4×C109—42no—
344C4×C109—41no—
345C4×C109—81no—
346C4×C109—81no—
347C4×C109C2×#13711yescharacteristic
348C4×C109#57511yescharacteristic
349C4×C109#57711yescharacteristic
350C4×C109#57811yescharacteristic
351#18609C10911yesmaximal, characteristic, direct product factor, Sylow
352C2×C109—41no—
353C2×C109—81no—
354C2×C109—81no—
355C2×C109#300711yescharacteristic
356C2×C109#301311yescharacteristic
357C2×C109#301811yescharacteristic
358#3518C2×C10911yescharacteristic
359#3252C2×C10911yescharacteristic, complemented
360#3185C2×C10911yescharacteristic, complemented
361#3076C2×C10911yescharacteristic, complemented
362#1652C2×C10911yescharacteristic, complemented
363#1651C2×C10911yescharacteristic, complemented
364#1646C2×C10911yescharacteristic, complemented
365#1645C2×C10911yescharacteristic, complemented
366#1638C2×C10911yescharacteristic, complemented
367#1637C2×C10911yescharacteristic, complemented
368#1634C2×C10911yescharacteristic, complemented
369#1633C2×C10911yescharacteristic, complemented
370#1550C2×C10911yescharacteristic, complemented
371#1489C2×C10911yescharacteristic, complemented
372#1483C2×C10911yescharacteristic, complemented
373C109#1860911yescharacteristic, direct product factor, Sylow
374Q82C22×C10911yescharacteristic
375#556—21no—
376#556—22no—
377#556—21no—
378#556C22×C10911yescharacteristic
379#555—21no—
380#555C22×C10911yescharacteristic
381D4×Q8C22×C10911yescharacteristic
382#548—21no—
383#542—22no—
384#542—21no—
385#533—21no—
386#533C22×C10911yescharacteristic
387#533C22×C10911yescharacteristic
388#529—21no—
389#529C22×C10911yescharacteristic
390#519—21no—
391C4×#41C22×C10911yescharacteristic
392#498C22×C10911yescharacteristic
393#494C22×C10911yescharacteristic
394#487C22×C10911yescharacteristic
395#487C22×C10911yescharacteristic
396#479—21no—
397#479—21no—
398#478—21no—
399#477C22×C10911yescharacteristic
400#477C22×C10911yescharacteristic
401#476C22×C10911yescharacteristic
402#476C22×C10911yescharacteristic
403#475C22×C10911yescharacteristic
404#474C22×C10911yescharacteristic
405#470—22no—
406#470—21no—
407#468—21no—
408#464—21no—
409#462C22×C10911yescharacteristic
410#461C22×C10911yescharacteristic
411#441—22no—
412#427—21no—
413#423C22×C10911yescharacteristic
414C2×C4⋊C8C22×C10911yescharacteristic
415#416—21no—
416C4×M16C22×C10911yescharacteristic
417#333C22×C10911yescharacteristic
418#333C22×C10911yescharacteristic
419#332C22×C10911yescharacteristic
420#332C22×C10911yescharacteristic
421Q8⋊C8C22×C10911yescharacteristic
422Q8⋊C8C22×C10911yescharacteristic
423Q8⋊C8C22×C10911yescharacteristic
424Q8⋊C8C22×C10911yescharacteristic
425D4⋊C8C22×C10911yescharacteristic
426D4⋊C8C22×C10911yescharacteristic
427D4⋊C8C22×C10911yescharacteristic
428D4⋊C8C22×C10911yescharacteristic
429C2×#41D4×C10911yescharacteristic
430C22×Q8—21no—
431C2×Q16—22no—
432C2×Q16—21no—
433C2×SD16—21no—
434C2×M16—21no—
435C2×M16—21no—
436C22×C8—21no—
437C4⋊Q8—22no—
438C4⋊Q8—21no—
439C4⋊Q8—21no—
440C4⋊Q8—21no—
441C4⋊Q8C23×C10911yescharacteristic
442C4⋊Q8C23×C10911yescharacteristic
443C4⋊Q8C23×C10911yescharacteristic
444C4⋊Q8C23×C10911yescharacteristic
445#126—22no—
446#126—22no—
447#126—22no—
448#126—22no—
449#126—21no—
450#125—21no—
451#125—21no—
452#125D4×C10911yescharacteristic
453#124—22no—
454#124—22no—
455#124—22no—
456#124—22no—
457#124—21no—
458#124D4×C10911yescharacteristic
459#123—22no—
460#123—21no—
461C22⋊Q8—22no—
462C22⋊Q8—22no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8—21no—
466C22⋊Q8—22no—
467C22⋊Q8—21no—
468C22⋊Q8—21no—
469C22⋊Q8D4×C10911yescharacteristic
470C22⋊Q8D4×C10912yes—
471#121—22no—
472#121—21no—
473#121—21no—
474#121D4×C10911yescharacteristic
475C4×Q8—22no—
476C4×Q8—22no—
477C4×Q8—22no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×Q8—21no—
482C4×Q8—21no—
483C4×Q8—21no—
484C4×Q8D4×C10911yescharacteristic
485C4×Q8D4×C10912yes—
486C4×Q8C23×C10911yescharacteristic
487C4×Q8C23×C10911yescharacteristic
488C4×D4—22no—
489C4×D4—21no—
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4D4×C10911yescharacteristic
494C4×D4C23×C10911yescharacteristic
495C4×D4C23×C10911yescharacteristic
496#117—22no—
497#117—22no—
498#117—21no—
499#117—21no—
500#117—21no—
501#117—21no—
502#117—21no—
503#117—21no—
504#117—21no—
505#117D4×C10911yescharacteristic
506C2×C42—21no—
507C2×C42C23×C10911yescharacteristic
508#107—21no—
509#107—21no—
510#107—21no—
511#106—21no—
512#106—21no—
513#106—22no—
514#106—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8C23×C10911yescharacteristic
518C4⋊C8C23×C10911yescharacteristic
519C4⋊C8C23×C10911yescharacteristic
520C4⋊C8C23×C10911yescharacteristic
521#103—21no—
522#103—21no—
523#103—22no—
524#103—21no—
525#103—22no—
526#103—21no—
527#103—21no—
528#102—21no—
529#102—21no—
530#102—21no—
531#97—21no—
532C4×C8C23×C10911yescharacteristic
533C4×C8C23×C10911yescharacteristic
534#41—22no—
535#41—41no—
536C2×Q8—22no—
537C2×Q8—22no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—42no—
542C2×Q8—42no—
543C2×Q8C2×D4×C10911yescharacteristic
544C2×Q8C2×D4×C10911yescharacteristic
545C2×Q8C2×D4×C10912yes—
546C2×D4—21no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4C2×D4×C10911yescharacteristic
550C2×D4C2×D4×C10911yescharacteristic
551C22×C4—22no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4C2×D4×C10911yescharacteristic
557C22×C4C2×D4×C10911yescharacteristic
558C22×C4C2×D4×C10911yescharacteristic
559Q16—44no—
560Q16—81no—
561SD16—81no—
562M16—42no—
563M16—81no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—21no—
567C2×C8—21no—
568C2×C8—21no—
569C2×C8—21no—
570C2×C8—42no—
571C4⋊C4—22no—
572C4⋊C4—22no—
573C4⋊C4—22no—
574C4⋊C4—22no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—22no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—41no—
591C4⋊C4—41no—
592C4⋊C4C2×D4×C10911yescharacteristic
593C4⋊C4C2×D4×C10912yes—
594C4⋊C4C2×D4×C10911yescharacteristic
595C4⋊C4C2×D4×C10911yescharacteristic
596C4⋊C4C2×D4×C10911yescharacteristic
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—22no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—21no—
610C22⋊C4—21no—
611C22⋊C4—41no—
612C42—22no—
613C42—22no—
614C42—22no—
615C42—21no—
616C42—21no—
617C42—22no—
618C42—21no—
619C42—21no—
620C42—41no—
621C42C2×D4×C10911yescharacteristic
622C42C2×D4×C10911yescharacteristic
623C42C2×D4×C10911yescharacteristic
624C42C24×C10911yescharacteristic
625C23—21no—
626C23—21no—
627C23#120×C10911yescharacteristic
628Q8—21no—
629Q8—21no—
630Q8—21no—
631Q8—42no—
632Q8—44no—
633Q8—42no—
634Q8—41no—
635Q8—41no—
636Q8—41no—
637Q8—41no—
638Q8—82no—
639Q8#137×C10912yes—
640D4—21no—
641D4—21no—
642D4—21no—
643D4—21no—
644D4—42no—
645D4—81no—
646D4—82no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—22no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—21no—
659C2×C4—41no—
660C2×C4—42no—
661C2×C4—44no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—81no—
669C2×C4#120×C10911yescharacteristic
670C2×C4#120×C10911yescharacteristic
671C2×C4#120×C10911yescharacteristic
672C2×C4C22×D4×C10911yescharacteristic
673C2×C4C22×D4×C10911yescharacteristic
674C2×C4C22×D4×C10911yescharacteristic
675C8—22no—
676C8—41no—
677C8—41no—
678C8—41no—
679C8—41no—
680C8—41no—
681C22—21no—
682C22—21no—
683C22—21no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22C2×#120×C10911yescharacteristic
691C4—21no—
692C4—22no—
693C4—21no—
694C4—21no—
695C4—21no—
696C4—42no—
697C4—41no—
698C4—41no—
699C4—41no—
700C4—41no—
701C4—42no—
702C4—41no—
703C4—81no—
704C4—81no—
705C4C2×#137×C10911yescharacteristic
706C4#575×C10911yescharacteristic
707C4#577×C10911yescharacteristic
708C4#578×C10911yescharacteristic
709C2—41no—
710C2—81no—
711C2—81no—
712C2C109×#300711yescharacteristic
713C2C109×#301311yescharacteristic
714C2C109×#301811yescharacteristic
subgroupG/H
center, socleC22×C109C2×#120
commutator, Frattini, cosocleC42C24×C109
prime radicalC109×#3518C2
LCSG ▷ C42 ▷ 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×#3252C2semidirect
3. C109×#3185C2semidirect
4. C109×#3076C2semidirect
5. C109×#1652C2semidirect
6. C109×#1651C2semidirect
7. C109×#1646C2semidirect
8. C109×#1645C2semidirect
9. C109×#1638C2semidirect
10. C109×#1637C2semidirect
11. C109×#1634C2semidirect
12. C109×#1633C2semidirect
13. C109×#1550C2semidirect
14. C109×#1489C2semidirect
15. C109×#1483C2semidirect
351. #18609C109direct (N × H)
359. #3252C2×C109semidirect
360. #3185C2×C109semidirect
361. #3076C2×C109semidirect
362. #1652C2×C109semidirect
363. #1651C2×C109semidirect
364. #1646C2×C109semidirect
365. #1645C2×C109semidirect
366. #1638C2×C109semidirect
367. #1637C2×C109semidirect
368. #1634C2×C109semidirect
369. #1633C2×C109semidirect
370. #1550C2×C109semidirect
371. #1489C2×C109semidirect
372. #1483C2×C109semidirect
373. C109#18609direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#35182
C109×#32522
C109×#31852
C109×#30762
C109×#16522
C109×#16512
C109×#16462
C109×#16452
C109×#16382
C109×#16372
C109×#16342
C109×#16332
C109×#15502
C109×#14892
C109×#14832
#18609109