Finite Group Databasebeta

← C109×#11165 #42129159

Subgroups — C109×#11165 #42129159

Order 27904.

850 conjugacy classes of subgroups.

The subgroup lattice has 602 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#421×C109C211yesmaximal, characteristic
2C22×#104×C109C211yesmaximal, characteristic
3C2×#413×C109C211yesmaximal, characteristic
4C2×#344×C109C211yesmaximal, characteristic, complemented
5C109×#1738C211yesmaximal, characteristic, complemented
6C2×#339×C109C211yesmaximal, characteristic, complemented
7C109×#1728C211yesmaximal, characteristic, complemented
8C22×#41×C109C2211yescharacteristic
9C22×M16×C109C2211yescharacteristic
10C22×M16×C109C2211yescharacteristic
11C22×M16×C109C2211yescharacteristic
12C22×M16×C109C2211yescharacteristic
13C2×#117×C109C2211yescharacteristic
14C22×C42×C109C2211yescharacteristic
15#421×C109—22no—
16#421×C109—22no—
17C2×#104×C109—22no—
18C2×#104×C109—22no—
19C2×#104×C109—22no—
20C2×#104×C109—22no—
21#413×C109—22no—
22#413×C109—22no—
23C2×#101×C109C412yescomplemented
24C2×#100×C109C412yescomplemented
25#344×C109—22no—
26#341×C109—22no—
27#339×C109—22no—
28#336×C109—22no—
29C2×#41×C109—21no—
30C2×#41×C109—21no—
31C2×#41×C109—21no—
32C2×#41×C109—21no—
33C2×#41×C109—21no—
34C2×#41×C109—21no—
35C2×#41×C109—21no—
36C2×#41×C109—21no—
37C2×#41×C109—21no—
38C2×#41×C109—21no—
39C2×#41×C109D412yes—
40C2×#41×C109D412yes—
41C22×Q8×C109C2×C411yescharacteristic
42C22×D4×C109—21no—
43C22×D4×C109C2×C411yescharacteristic
44C23×C4×C109—21no—
45C23×C4×C109—21no—
46C23×C4×C109C2311yescharacteristic
47C2×M16×C109—21no—
48C2×M16×C109—21no—
49C2×M16×C109—21no—
50C2×M16×C109—21no—
51C2×M16×C109—21no—
52C2×M16×C109—21no—
53C2×M16×C109—21no—
54C2×M16×C109—21no—
55C2×M16×C109—21no—
56C2×M16×C109—21no—
57C2×M16×C109—21no—
58C2×M16×C109—21no—
59C2×M16×C109—21no—
60C2×M16×C109—21no—
61C2×M16×C109—21no—
62C2×M16×C109—21no—
63C2×M16×C109—21no—
64C2×M16×C109—21no—
65C2×M16×C109—21no—
66C2×M16×C109—21no—
67C2×M16×C109C2×C412yes—
68C2×M16×C109C2×C412yes—
69C2×M16×C109D412yes—
70C2×M16×C109D412yes—
71C22×C8×C109—21no—
72C22×C8×C109—21no—
73C22×C8×C109—21no—
74C22×C8×C109—21no—
75#117×C109—21no—
76#117×C109—21no—
77#117×C109—21no—
78#117×C109D412yes—
79C2×C4⋊C4×C109—21no—
80C2×C22⋊C4×C109—21no—
81C2×C42×C109—21no—
82C2×C42×C109—21no—
83C2×C42×C109—21no—
84C2×C42×C109—21no—
85C2×C42×C109—21no—
86C2×C42×C109—21no—
87C2×C42×C109D412yes—
88#104×C109—28no—
89#104×C109—28no—
90#101×C109—24no—
91#100×C109—24no—
92C24×C109—21no—
93C24×C109#4111yescharacteristic
94#41×C109—22no—
95#41×C109—22no—
96#41×C109—22no—
97#41×C109—22no—
98#41×C109—22no—
99#41×C109—22no—
100#41×C109—22no—
101#41×C109—22no—
102#41×C109—41no—
103#41×C109—41no—
104#41×C109—41no—
105#41×C109—41no—
106#41×C109—41no—
107#41×C109—41no—
108#41×C109—41no—
109#41×C109—41no—
110C2×Q8×C109—21no—
111C2×Q8×C109—21no—
112C2×Q8×C109—21no—
113C2×Q8×C109—21no—
114C2×Q8×C109—21no—
115C2×Q8×C109C22⋊C412yes—
116C2×D4×C109—22no—
117C2×D4×C109—22no—
118C2×D4×C109—21no—
119C2×D4×C109—21no—
120C2×D4×C109—21no—
121C2×D4×C109—21no—
122C2×D4×C109—21no—
123C2×D4×C109—41no—
124C2×D4×C109—41no—
125C2×D4×C109—41no—
126C2×D4×C109—41no—
127C2×D4×C109C22⋊C412yes—
128C22×C4×C109—21no—
129C22×C4×C109—22no—
130C22×C4×C109—22no—
131C22×C4×C109—22no—
132C22×C4×C109—44no—
133C22×C4×C109—41no—
134C22×C4×C109—41no—
135C22×C4×C109—41no—
136C22×C4×C109—41no—
137C22×C4×C109—41no—
138C22×C4×C109—41no—
139C22×C4×C109—41no—
140C22×C4×C109C22×C411yescharacteristic
141C22×C4×C109C2×D411yescharacteristic
142C22×C4×C109C2×D411yescharacteristic
143C22×C4×C109C2×D411yescharacteristic
144C22×C4×C109C2×D411yescharacteristic
145C22×C4×C109C2×D411yescharacteristic
146C22×C4×C109C2×D411yescharacteristic
147C22×C4×C109#4111yescharacteristic
148C22×C4×C109#4111yescharacteristic
149C22×C4×C109#4111yescharacteristic
150C22×C4×C109#4111yescharacteristic
151C22×C4×C109#4111yescharacteristic
152C22×C4×C109#4111yescharacteristic
153C22×C4×C109#4111yescharacteristic
154M16×C109—22no—
155M16×C109—22no—
156M16×C109—22no—
157M16×C109—22no—
158M16×C109—22no—
159M16×C109—22no—
160M16×C109—22no—
161M16×C109—22no—
162M16×C109—41no—
163M16×C109—41no—
164M16×C109—41no—
165M16×C109—41no—
166M16×C109—41no—
167M16×C109—41no—
168M16×C109—41no—
169M16×C109—41no—
170C2×C8×C109—22no—
171C2×C8×C109—22no—
172C2×C8×C109—22no—
173C2×C8×C109—22no—
174C2×C8×C109—41no—
175C2×C8×C109—41no—
176C2×C8×C109—41no—
177C2×C8×C109—41no—
178C2×C8×C109—41no—
179C2×C8×C109—41no—
180C2×C8×C109—41no—
181C2×C8×C109—41no—
182C4⋊C4×C109—22no—
183C4⋊C4×C109—41no—
184C22⋊C4×C109—22no—
185C22⋊C4×C109—41no—
186C42×C109—22no—
187C42×C109—22no—
188C42×C109—22no—
189C42×C109—41no—
190C42×C109—41no—
191C42×C109—41no—
192C23×C109—22no—
193C23×C109—42no—
194C23×C109—41no—
195C23×C109—41no—
196C23×C109—82no—
197C23×C109#11711yescharacteristic
198C23×C109#12111yescharacteristic
199C23×C109#12311yescharacteristic
200C23×C109#12311yescharacteristic
201C23×C109#12311yescharacteristic
202C23×C109#12411yescharacteristic
203C23×C109#12611yescharacteristic
204Q8×C109—22no—
205Q8×C109—22no—
206Q8×C109—41no—
207Q8×C109—41no—
208D4×C109—22no—
209D4×C109—22no—
210D4×C109—42no—
211D4×C109—42no—
212D4×C109—42no—
213D4×C109—42no—
214D4×C109—41no—
215D4×C109—41no—
216C2×C4×C109—24no—
217C2×C4×C109—22no—
218C2×C4×C109—42no—
219C2×C4×C109—44no—
220C2×C4×C109—44no—
221C2×C4×C109—41no—
222C2×C4×C109—41no—
223C2×C4×C109—42no—
224C2×C4×C109—42no—
225C2×C4×C109—42no—
226C2×C4×C109—42no—
227C2×C4×C109—42no—
228C2×C4×C109—42no—
229C2×C4×C109—82no—
230C2×C4×C109C2×C22⋊C411yescharacteristic
231C2×C4×C109#11711yescharacteristic
232C2×C4×C109C4×D411yescharacteristic
233C2×C4×C109C4×D411yescharacteristic
234C2×C4×C109C4×D411yescharacteristic
235C2×C4×C109C4×D411yescharacteristic
236C2×C4×C109#12011yescharacteristic
237C2×C4×C109#12011yescharacteristic
238C2×C4×C109#12111yescharacteristic
239C2×C4×C109#12111yescharacteristic
240C2×C4×C109#12111yescharacteristic
241C2×C4×C109#12111yescharacteristic
242C2×C4×C109#12111yescharacteristic
243C2×C4×C109#12111yescharacteristic
244C2×C4×C109#12111yescharacteristic
245C2×C4×C109#12311yescharacteristic
246C2×C4×C109#12311yescharacteristic
247C2×C4×C109#12311yescharacteristic
248C2×C4×C109#12311yescharacteristic
249C2×C4×C109#12311yescharacteristic
250C2×C4×C109#12311yescharacteristic
251C2×C4×C109#12311yescharacteristic
252C2×C4×C109#12411yescharacteristic
253C2×C4×C109#12411yescharacteristic
254C2×C4×C109#12411yescharacteristic
255C2×C4×C109#12611yescharacteristic
256C2×C4×C109#12611yescharacteristic
257C2×C4×C109#12611yescharacteristic
258C8×C109—42no—
259C8×C109—42no—
260C8×C109—42no—
261C8×C109—42no—
262C22×C109—22no—
263C22×C109—22no—
264C22×C109—22no—
265C22×C109—41no—
266C22×C109—41no—
267C22×C109—41no—
268C22×C109—41no—
269C22×C109—42no—
270C22×C109—82no—
271C22×C109—82no—
272C22×C109—82no—
273C22×C109#38111yescharacteristic
274C22×C109#38811yescharacteristic
275C22×C109#38811yescharacteristic
276C22×C109#39411yescharacteristic
277C22×C109#39411yescharacteristic
278C22×C109#39711yescharacteristic
279C22×C109#39711yescharacteristic
280C4×C109—44no—
281C4×C109—42no—
282C4×C109—82no—
283C4×C109#38611yescharacteristic
284C4×C109#38611yescharacteristic
285C4×C109#38811yescharacteristic
286C4×C109#38811yescharacteristic
287C4×C109#39411yescharacteristic
288C4×C109#39411yescharacteristic
289C4×C109#39711yescharacteristic
290C4×C109#39711yescharacteristic
291#11165C10911yesmaximal, characteristic, direct product factor, Sylow
292C2×C109—21no—
293C2×C109—21no—
294C2×C109—21no—
295C2×C109—21no—
296C2×C109—21no—
297C2×C109—21no—
298C2×C109—82no—
299C2×C109#144011yescharacteristic
300C2×C109#193212yes—
301C2×#421C2×C10911yescharacteristic
302C22×#104C2×C10911yescharacteristic
303C2×#413C2×C10911yescharacteristic
304C2×#344C2×C10911yescharacteristic, complemented
305#1738C2×C10911yescharacteristic, complemented
306C2×#339C2×C10911yescharacteristic, complemented
307#1728C2×C10911yescharacteristic, complemented
308C109#1116511yescharacteristic, direct product factor, Sylow
309C22×#41C22×C10911yescharacteristic
310C22×M16C22×C10911yescharacteristic
311C22×M16C22×C10911yescharacteristic
312C22×M16C22×C10911yescharacteristic
313C22×M16C22×C10911yescharacteristic
314C2×#117C22×C10911yescharacteristic
315C22×C42C22×C10911yescharacteristic
316#421—22no—
317#421—22no—
318C2×#104—22no—
319C2×#104—22no—
320C2×#104—22no—
321C2×#104—22no—
322#413—22no—
323#413—22no—
324C2×#101C4×C10912yescomplemented
325C2×#100C4×C10912yescomplemented
326#344—22no—
327#341—22no—
328#339—22no—
329#336—22no—
330C2×#41—21no—
331C2×#41—21no—
332C2×#41—21no—
333C2×#41—21no—
334C2×#41—21no—
335C2×#41—21no—
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41D4×C10912yes—
341C2×#41D4×C10912yes—
342C22×Q8C2×C4×C10911yescharacteristic
343C22×D4—21no—
344C22×D4C2×C4×C10911yescharacteristic
345C23×C4—21no—
346C23×C4—21no—
347C23×C4C23×C10911yescharacteristic
348C2×M16—21no—
349C2×M16—21no—
350C2×M16—21no—
351C2×M16—21no—
352C2×M16—21no—
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16C2×C4×C10912yes—
369C2×M16C2×C4×C10912yes—
370C2×M16D4×C10912yes—
371C2×M16D4×C10912yes—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376#117—21no—
377#117—21no—
378#117—21no—
379#117D4×C10912yes—
380C2×C4⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C42—21no—
383C2×C42—21no—
384C2×C42—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42—21no—
388C2×C42D4×C10912yes—
389#104—28no—
390#104—28no—
391#101—24no—
392#100—24no—
393C24—21no—
394C24#41×C10911yescharacteristic
395#41—22no—
396#41—22no—
397#41—22no—
398#41—22no—
399#41—22no—
400#41—22no—
401#41—22no—
402#41—22no—
403#41—41no—
404#41—41no—
405#41—41no—
406#41—41no—
407#41—41no—
408#41—41no—
409#41—41no—
410#41—41no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—21no—
414C2×Q8—21no—
415C2×Q8—21no—
416C2×Q8C22⋊C4×C10912yes—
417C2×D4—22no—
418C2×D4—22no—
419C2×D4—21no—
420C2×D4—21no—
421C2×D4—21no—
422C2×D4—21no—
423C2×D4—21no—
424C2×D4—41no—
425C2×D4—41no—
426C2×D4—41no—
427C2×D4—41no—
428C2×D4C22⋊C4×C10912yes—
429C22×C4—21no—
430C22×C4—22no—
431C22×C4—22no—
432C22×C4—22no—
433C22×C4—44no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4—41no—
440C22×C4—41no—
441C22×C4C22×C4×C10911yescharacteristic
442C22×C4C2×D4×C10911yescharacteristic
443C22×C4C2×D4×C10911yescharacteristic
444C22×C4C2×D4×C10911yescharacteristic
445C22×C4C2×D4×C10911yescharacteristic
446C22×C4C2×D4×C10911yescharacteristic
447C22×C4C2×D4×C10911yescharacteristic
448C22×C4#41×C10911yescharacteristic
449C22×C4#41×C10911yescharacteristic
450C22×C4#41×C10911yescharacteristic
451C22×C4#41×C10911yescharacteristic
452C22×C4#41×C10911yescharacteristic
453C22×C4#41×C10911yescharacteristic
454C22×C4#41×C10911yescharacteristic
455M16—22no—
456M16—22no—
457M16—22no—
458M16—22no—
459M16—22no—
460M16—22no—
461M16—22no—
462M16—22no—
463M16—41no—
464M16—41no—
465M16—41no—
466M16—41no—
467M16—41no—
468M16—41no—
469M16—41no—
470M16—41no—
471C2×C8—22no—
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—41no—
476C2×C8—41no—
477C2×C8—41no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C4⋊C4—22no—
484C4⋊C4—41no—
485C22⋊C4—22no—
486C22⋊C4—41no—
487C42—22no—
488C42—22no—
489C42—22no—
490C42—41no—
491C42—41no—
492C42—41no—
493C23—22no—
494C23—42no—
495C23—41no—
496C23—41no—
497C23—82no—
498C23#117×C10911yescharacteristic
499C23#121×C10911yescharacteristic
500C23#123×C10911yescharacteristic
501C23#123×C10911yescharacteristic
502C23#123×C10911yescharacteristic
503C23#124×C10911yescharacteristic
504C23#126×C10911yescharacteristic
505Q8—22no—
506Q8—22no—
507Q8—41no—
508Q8—41no—
509D4—22no—
510D4—22no—
511D4—42no—
512D4—42no—
513D4—42no—
514D4—42no—
515D4—41no—
516D4—41no—
517C2×C4—24no—
518C2×C4—22no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—44no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—82no—
531C2×C4C2×C22⋊C4×C10911yescharacteristic
532C2×C4#117×C10911yescharacteristic
533C2×C4C4×D4×C10911yescharacteristic
534C2×C4C4×D4×C10911yescharacteristic
535C2×C4C4×D4×C10911yescharacteristic
536C2×C4C4×D4×C10911yescharacteristic
537C2×C4#120×C10911yescharacteristic
538C2×C4#120×C10911yescharacteristic
539C2×C4#121×C10911yescharacteristic
540C2×C4#121×C10911yescharacteristic
541C2×C4#121×C10911yescharacteristic
542C2×C4#121×C10911yescharacteristic
543C2×C4#121×C10911yescharacteristic
544C2×C4#121×C10911yescharacteristic
545C2×C4#121×C10911yescharacteristic
546C2×C4#123×C10911yescharacteristic
547C2×C4#123×C10911yescharacteristic
548C2×C4#123×C10911yescharacteristic
549C2×C4#123×C10911yescharacteristic
550C2×C4#123×C10911yescharacteristic
551C2×C4#123×C10911yescharacteristic
552C2×C4#123×C10911yescharacteristic
553C2×C4#124×C10911yescharacteristic
554C2×C4#124×C10911yescharacteristic
555C2×C4#124×C10911yescharacteristic
556C2×C4#126×C10911yescharacteristic
557C2×C4#126×C10911yescharacteristic
558C2×C4#126×C10911yescharacteristic
559C8—42no—
560C8—42no—
561C8—42no—
562C8—42no—
563C22—22no—
564C22—22no—
565C22—22no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—42no—
571C22—82no—
572C22—82no—
573C22—82no—
574C22#381×C10911yescharacteristic
575C22#388×C10911yescharacteristic
576C22#388×C10911yescharacteristic
577C22#394×C10911yescharacteristic
578C22#394×C10911yescharacteristic
579C22#397×C10911yescharacteristic
580C22#397×C10911yescharacteristic
581C4—44no—
582C4—42no—
583C4—82no—
584C4#386×C10911yescharacteristic
585C4#386×C10911yescharacteristic
586C4#388×C10911yescharacteristic
587C4#388×C10911yescharacteristic
588C4#394×C10911yescharacteristic
589C4#394×C10911yescharacteristic
590C4#397×C10911yescharacteristic
591C4#397×C10911yescharacteristic
592C2—21no—
593C2—21no—
594C2—21no—
595C2—21no—
596C2—21no—
597C2—21no—
598C2—82no—
599C2C109×#144011yescharacteristic
600C2C109×#193212yes—
subgroupG/H
centerC2×C4×C109#121
commutatorC22×C4C22×C4×C109
Frattini, cosocleC23×C4C23×C109
socleC22×C109#388
prime radicalC22×#41×C109C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C4×C109 ◁ C23×C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
4. C2×#344×C109C2semidirect
5. C109×#1738C2semidirect
6. C2×#339×C109C2semidirect
7. C109×#1728C2semidirect
23. C2×#101×C109C4semidirect
24. C2×#100×C109C4semidirect
291. #11165C109direct (N × H)
304. C2×#344C2×C109semidirect
305. #1738C2×C109semidirect
306. C2×#339C2×C109semidirect
307. #1728C2×C109semidirect
308. C109#11165direct (N × H)
324. C2×#101C4×C109semidirect
325. C2×#100C4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#421×C1092
C22×#104×C1092
C2×#413×C1092
C2×#344×C1092
C109×#17382
C2×#339×C1092
C109×#17282
#11165109