Finite Group Databasebeta

← C109×#32353 #42150347

Subgroups — C109×#32353 #42150347

Order 27904.

662 conjugacy classes of subgroups.

The subgroup lattice has 586 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2563C211yesmaximal, characteristic
2C109×#2508C211yesmaximal, characteristic, complemented
3C109×#2101C211yesmaximal, characteristic, complemented
4C109×#2092C211yesmaximal, characteristic
5C109×#2085C211yesmaximal, characteristic, complemented
6C109×#2067C211yesmaximal, characteristic
7C109×#2058C211yesmaximal, characteristic, complemented
8C109×#2057C211yesmaximal, characteristic, complemented
9C109×#1949C211yesmaximal, characteristic, complemented
10C109×#1934C211yesmaximal, characteristic
11C109×#1926C211yesmaximal, characteristic
12C109×#1916C211yesmaximal, characteristic, complemented
13C109×#1864C211yesmaximal, characteristic
14C109×#1862C211yesmaximal, characteristic
15C109×#1846C211yesmaximal, characteristic, complemented
16C2×C4⋊Q8×C109C2211yescharacteristic
17C2×C4×D4×C109C2211yescharacteristic
18C2×#107×C109C2211yescharacteristic
19C2×#107×C109C2211yescharacteristic
20C2×#107×C109C2211yescharacteristic
21C2×#106×C109C2211yescharacteristic
22C2×#106×C109C2211yescharacteristic
23C2×#106×C109C2211yescharacteristic
24C2×C4⋊C8×C109C2211yescharacteristic
25C2×#102×C109C2211yescharacteristic
26C2×#102×C109C2211yescharacteristic
27C2×#102×C109C2211yescharacteristic
28C2×#102×C109C2211yescharacteristic
29C2×C4×C8×C109C2211yescharacteristic
30#400×C109—21no—
31#398×C109—21no—
32#393×C109—21no—
33#393×C109—21no—
34#390×C109C2211yescharacteristic
35#390×C109C2211yescharacteristic
36#389×C109C2211yescharacteristic
37#389×C109C2211yescharacteristic
38#389×C109C2211yescharacteristic
39#389×C109C2211yescharacteristic
40#387×C109—21no—
41#382×C109—21no—
42#382×C109C2211yescharacteristic
43#382×C109C2211yescharacteristic
44#382×C109C2211yescharacteristic
45#380×C109—21no—
46#380×C109—21no—
47C4×C4⋊C4×C109C2211yescharacteristic
48C4×C4⋊C4×C109C2211yescharacteristic
49#340×C109C2211yescharacteristic
50#340×C109C2211yescharacteristic
51#340×C109C2211yescharacteristic
52#340×C109C2211yescharacteristic
53#340×C109C2211yescharacteristic
54#340×C109C2211yescharacteristic
55#336×C109C2211yescharacteristic
56#336×C109C2211yescharacteristic
57#336×C109C2211yescharacteristic
58#336×C109C2211yescharacteristic
59C22×Q8×C109—21no—
60C22×D4×C109C2311yescharacteristic
61C23×C4×C109—21no—
62C22×C8×C109C2311yescharacteristic
63C22×C8×C109C2311yescharacteristic
64C22×C8×C109C2311yescharacteristic
65C22×C8×C109C2311yescharacteristic
66C4⋊Q8×C109—41no—
67C4⋊Q8×C109—41no—
68C4×D4×C109—41no—
69C4×D4×C109—41no—
70C2×C4⋊C4×C109—21no—
71C2×C4⋊C4×C109—21no—
72C2×C4⋊C4×C109—21no—
73C2×C4⋊C4×C109—21no—
74C2×C4⋊C4×C109—21no—
75C2×C4⋊C4×C109D411yescharacteristic
76C2×C4⋊C4×C109D411yescharacteristic
77C2×C4⋊C4×C109C2311yescharacteristic
78C2×C4⋊C4×C109C2311yescharacteristic
79C2×C4⋊C4×C109C2311yescharacteristic
80C2×C4⋊C4×C109C2311yescharacteristic
81C2×C4⋊C4×C109C2311yescharacteristic
82C2×C4⋊C4×C109C2311yescharacteristic
83C2×C4⋊C4×C109C2311yescharacteristic
84C2×C22⋊C4×C109—21no—
85C2×C22⋊C4×C109—21no—
86C2×C22⋊C4×C109—21no—
87C2×C22⋊C4×C109—21no—
88C2×C22⋊C4×C109—21no—
89C2×C42×C109—21no—
90C2×C42×C109C2311yescharacteristic
91C2×C42×C109C2311yescharacteristic
92C2×C42×C109C2311yescharacteristic
93#107×C109—41no—
94#107×C109—41no—
95#107×C109—41no—
96#106×C109—41no—
97#106×C109—41no—
98#106×C109—41no—
99C4⋊C8×C109—22no—
100#102×C109—22no—
101#102×C109—41no—
102#102×C109—41no—
103#102×C109Q814yescomplemented
104C4×C8×C109—22no—
105#95×C109—21no—
106#95×C109—21no—
107#95×C109—21no—
108#95×C109—21no—
109#95×C109—21no—
110#95×C109—21no—
111#95×C109—21no—
112#95×C109—21no—
113#95×C109—21no—
114#95×C109—21no—
115#95×C109—21no—
116#95×C109D411yescharacteristic
117#95×C109D411yescharacteristic
118C24×C109—21no—
119C2×Q8×C109—42no—
120C2×Q8×C109—81no—
121C2×Q8×C109—81no—
122C2×D4×C109—21no—
123C2×D4×C109—21no—
124C2×D4×C109—21no—
125C2×D4×C109—21no—
126C2×D4×C109—21no—
127C2×D4×C109C2×Q812yes—
128C22×C4×C109—21no—
129C22×C4×C109—21no—
130C22×C4×C109—21no—
131C22×C4×C109—21no—
132C22×C4×C109—21no—
133C22×C4×C109—21no—
134C22×C4×C109—21no—
135C22×C4×C109—42no—
136C22×C4×C109—42no—
137C22×C4×C109—42no—
138C22×C4×C109C2×D411yescharacteristic
139C22×C4×C109C2×D411yescharacteristic
140C22×C4×C109C2×D411yescharacteristic
141C22×C4×C109C2×D411yescharacteristic
142C22×C4×C109C2×D411yescharacteristic
143C22×C4×C109C2×D411yescharacteristic
144C22×C4×C109C2411yescharacteristic
145C2×C8×C109—21no—
146C2×C8×C109—21no—
147C2×C8×C109—21no—
148C2×C8×C109—21no—
149C2×C8×C109—21no—
150C2×C8×C109—21no—
151C2×C8×C109—21no—
152C2×C8×C109—21no—
153C2×C8×C109—21no—
154C2×C8×C109—21no—
155C2×C8×C109C2×Q812yes—
156C2×C8×C109#4112yes—
157C4⋊C4×C109—22no—
158C4⋊C4×C109—21no—
159C4⋊C4×C109—21no—
160C4⋊C4×C109—21no—
161C4⋊C4×C109—21no—
162C4⋊C4×C109—21no—
163C4⋊C4×C109—21no—
164C4⋊C4×C109—21no—
165C4⋊C4×C109—21no—
166C4⋊C4×C109—21no—
167C4⋊C4×C109—21no—
168C4⋊C4×C109—21no—
169C4⋊C4×C109—21no—
170C4⋊C4×C109—21no—
171C4⋊C4×C109—41no—
172C4⋊C4×C109—42no—
173C4⋊C4×C109—42no—
174C4⋊C4×C109—81no—
175C4⋊C4×C109—81no—
176C4⋊C4×C109—81no—
177C4⋊C4×C109C2×Q812yes—
178C22⋊C4×C109—42no—
179C22⋊C4×C109—81no—
180C22⋊C4×C109—81no—
181C22⋊C4×C109—81no—
182C22⋊C4×C109—81no—
183C42×C109—21no—
184C42×C109—21no—
185C42×C109—21no—
186C42×C109—21no—
187C42×C109—21no—
188C42×C109—21no—
189C42×C109—42no—
190C23×C109—22no—
191C23×C109—41no—
192C23×C109—41no—
193C23×C109—41no—
194C23×C109—41no—
195C23×C109—41no—
196C23×C109—41no—
197C23×C109C22×D411yescharacteristic
198Q8×C109—84no—
199D4×C109—22no—
200D4×C109—22no—
201D4×C109—41no—
202D4×C109—41no—
203C2×C4×C109—21no—
204C2×C4×C109—21no—
205C2×C4×C109—21no—
206C2×C4×C109—21no—
207C2×C4×C109—21no—
208C2×C4×C109—21no—
209C2×C4×C109—21no—
210C2×C4×C109—22no—
211C2×C4×C109—21no—
212C2×C4×C109—21no—
213C2×C4×C109—21no—
214C2×C4×C109—21no—
215C2×C4×C109—21no—
216C2×C4×C109—21no—
217C2×C4×C109—21no—
218C2×C4×C109—21no—
219C2×C4×C109—21no—
220C2×C4×C109—21no—
221C2×C4×C109—41no—
222C2×C4×C109—41no—
223C2×C4×C109—41no—
224C2×C4×C109—41no—
225C2×C4×C109—41no—
226C2×C4×C109—41no—
227C2×C4×C109—41no—
228C2×C4×C109—41no—
229C2×C4×C109—41no—
230C2×C4×C109—41no—
231C2×C4×C109—41no—
232C2×C4×C109—41no—
233C2×C4×C109—41no—
234C2×C4×C109—41no—
235C2×C4×C109—41no—
236C2×C4×C109—41no—
237C2×C4×C109—41no—
238C2×C4×C109—41no—
239C2×C4×C109—41no—
240C2×C4×C109—41no—
241C2×C4×C109—84no—
242C2×C4×C109#13512yes—
243C2×C4×C109C22×Q811yescharacteristic
244C2×C4×C109C2×#4111yescharacteristic
245C2×C4×C109H(5,𝔽2)11yescharacteristic
246C2×C4×C109H(5,𝔽2)11yescharacteristic
247C2×C4×C1092−1+411yescharacteristic
248C2×C4×C1092−1+411yescharacteristic
249C8×C109—22no—
250C8×C109—22no—
251C8×C109—41no—
252C8×C109—41no—
253C22×C109—42no—
254C22×C109—42no—
255C22×C109—42no—
256C22×C109—81no—
257C22×C109—81no—
258C22×C109—81no—
259C22×C109—81no—
260C22×C109#53511yescharacteristic
261C22×C109#54711yescharacteristic
262C22×C109D4×Q811yescharacteristic
263C22×C109C2×#13511yescharacteristic
264C22×C109#57511yescharacteristic
265C22×C109#57611yescharacteristic
266C22×C109#57711yescharacteristic
267C4×C109—22no—
268C4×C109—41no—
269C4×C109—41no—
270C4×C109—41no—
271C4×C109—41no—
272C4×C109—42no—
273C4×C109—41no—
274C4×C109—81no—
275C4×C109—81no—
276C4×C109—81no—
277C4×C109—81no—
278C4×C109—81no—
279C4×C109—81no—
280C4×C109#53911yescharacteristic
281C4×C109#54411yescharacteristic
282C4×C109#55411yescharacteristic
283C4×C109#56311yescharacteristic
284#32353C10911yesmaximal, characteristic, direct product factor, Sylow
285C2×C109—82no—
286C2×C109#272011yescharacteristic
287C2×C109#321111yescharacteristic
288C2×C109#322411yescharacteristic
289C2×C109#334111yescharacteristic
290C2×C109#334811yescharacteristic
291C2×C109#338111yescharacteristic
292C2×C109#338911yescharacteristic
293#2563C2×C10911yescharacteristic
294#2508C2×C10911yescharacteristic, complemented
295#2101C2×C10911yescharacteristic, complemented
296#2092C2×C10911yescharacteristic
297#2085C2×C10911yescharacteristic, complemented
298#2067C2×C10911yescharacteristic
299#2058C2×C10911yescharacteristic, complemented
300#2057C2×C10911yescharacteristic, complemented
301#1949C2×C10911yescharacteristic, complemented
302#1934C2×C10911yescharacteristic
303#1926C2×C10911yescharacteristic
304#1916C2×C10911yescharacteristic, complemented
305#1864C2×C10911yescharacteristic
306#1862C2×C10911yescharacteristic
307#1846C2×C10911yescharacteristic, complemented
308C109#3235311yescharacteristic, direct product factor, Sylow
309C2×C4⋊Q8C22×C10911yescharacteristic
310C2×C4×D4C22×C10911yescharacteristic
311C2×#107C22×C10911yescharacteristic
312C2×#107C22×C10911yescharacteristic
313C2×#107C22×C10911yescharacteristic
314C2×#106C22×C10911yescharacteristic
315C2×#106C22×C10911yescharacteristic
316C2×#106C22×C10911yescharacteristic
317C2×C4⋊C8C22×C10911yescharacteristic
318C2×#102C22×C10911yescharacteristic
319C2×#102C22×C10911yescharacteristic
320C2×#102C22×C10911yescharacteristic
321C2×#102C22×C10911yescharacteristic
322C2×C4×C8C22×C10911yescharacteristic
323#400—21no—
324#398—21no—
325#393—21no—
326#393—21no—
327#390C22×C10911yescharacteristic
328#390C22×C10911yescharacteristic
329#389C22×C10911yescharacteristic
330#389C22×C10911yescharacteristic
331#389C22×C10911yescharacteristic
332#389C22×C10911yescharacteristic
333#387—21no—
334#382—21no—
335#382C22×C10911yescharacteristic
336#382C22×C10911yescharacteristic
337#382C22×C10911yescharacteristic
338#380—21no—
339#380—21no—
340C4×C4⋊C4C22×C10911yescharacteristic
341C4×C4⋊C4C22×C10911yescharacteristic
342#340C22×C10911yescharacteristic
343#340C22×C10911yescharacteristic
344#340C22×C10911yescharacteristic
345#340C22×C10911yescharacteristic
346#340C22×C10911yescharacteristic
347#340C22×C10911yescharacteristic
348#336C22×C10911yescharacteristic
349#336C22×C10911yescharacteristic
350#336C22×C10911yescharacteristic
351#336C22×C10911yescharacteristic
352C22×Q8—21no—
353C22×D4C23×C10911yescharacteristic
354C23×C4—21no—
355C22×C8C23×C10911yescharacteristic
356C22×C8C23×C10911yescharacteristic
357C22×C8C23×C10911yescharacteristic
358C22×C8C23×C10911yescharacteristic
359C4⋊Q8—41no—
360C4⋊Q8—41no—
361C4×D4—41no—
362C4×D4—41no—
363C2×C4⋊C4—21no—
364C2×C4⋊C4—21no—
365C2×C4⋊C4—21no—
366C2×C4⋊C4—21no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4D4×C10911yescharacteristic
369C2×C4⋊C4D4×C10911yescharacteristic
370C2×C4⋊C4C23×C10911yescharacteristic
371C2×C4⋊C4C23×C10911yescharacteristic
372C2×C4⋊C4C23×C10911yescharacteristic
373C2×C4⋊C4C23×C10911yescharacteristic
374C2×C4⋊C4C23×C10911yescharacteristic
375C2×C4⋊C4C23×C10911yescharacteristic
376C2×C4⋊C4C23×C10911yescharacteristic
377C2×C22⋊C4—21no—
378C2×C22⋊C4—21no—
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C42—21no—
383C2×C42C23×C10911yescharacteristic
384C2×C42C23×C10911yescharacteristic
385C2×C42C23×C10911yescharacteristic
386#107—41no—
387#107—41no—
388#107—41no—
389#106—41no—
390#106—41no—
391#106—41no—
392C4⋊C8—22no—
393#102—22no—
394#102—41no—
395#102—41no—
396#102Q8×C10914yescomplemented
397C4×C8—22no—
398#95—21no—
399#95—21no—
400#95—21no—
401#95—21no—
402#95—21no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95D4×C10911yescharacteristic
410#95D4×C10911yescharacteristic
411C24—21no—
412C2×Q8—42no—
413C2×Q8—81no—
414C2×Q8—81no—
415C2×D4—21no—
416C2×D4—21no—
417C2×D4—21no—
418C2×D4—21no—
419C2×D4—21no—
420C2×D4C2×Q8×C10912yes—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—42no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4C2×D4×C10911yescharacteristic
432C22×C4C2×D4×C10911yescharacteristic
433C22×C4C2×D4×C10911yescharacteristic
434C22×C4C2×D4×C10911yescharacteristic
435C22×C4C2×D4×C10911yescharacteristic
436C22×C4C2×D4×C10911yescharacteristic
437C22×C4C24×C10911yescharacteristic
438C2×C8—21no—
439C2×C8—21no—
440C2×C8—21no—
441C2×C8—21no—
442C2×C8—21no—
443C2×C8—21no—
444C2×C8—21no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8C2×Q8×C10912yes—
449C2×C8#41×C10912yes—
450C4⋊C4—22no—
451C4⋊C4—21no—
452C4⋊C4—21no—
453C4⋊C4—21no—
454C4⋊C4—21no—
455C4⋊C4—21no—
456C4⋊C4—21no—
457C4⋊C4—21no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—41no—
465C4⋊C4—42no—
466C4⋊C4—42no—
467C4⋊C4—81no—
468C4⋊C4—81no—
469C4⋊C4—81no—
470C4⋊C4C2×Q8×C10912yes—
471C22⋊C4—42no—
472C22⋊C4—81no—
473C22⋊C4—81no—
474C22⋊C4—81no—
475C22⋊C4—81no—
476C42—21no—
477C42—21no—
478C42—21no—
479C42—21no—
480C42—21no—
481C42—21no—
482C42—42no—
483C23—22no—
484C23—41no—
485C23—41no—
486C23—41no—
487C23—41no—
488C23—41no—
489C23—41no—
490C23C22×D4×C10911yescharacteristic
491Q8—84no—
492D4—22no—
493D4—22no—
494D4—41no—
495D4—41no—
496C2×C4—21no—
497C2×C4—21no—
498C2×C4—21no—
499C2×C4—21no—
500C2×C4—21no—
501C2×C4—21no—
502C2×C4—21no—
503C2×C4—22no—
504C2×C4—21no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—21no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—41no—
515C2×C4—41no—
516C2×C4—41no—
517C2×C4—41no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—84no—
535C2×C4#135×C10912yes—
536C2×C4C22×Q8×C10911yescharacteristic
537C2×C4C2×#41×C10911yescharacteristic
538C2×C4H(5,𝔽2)×C10911yescharacteristic
539C2×C4H(5,𝔽2)×C10911yescharacteristic
540C2×C42−1+4×C10911yescharacteristic
541C2×C42−1+4×C10911yescharacteristic
542C8—22no—
543C8—22no—
544C8—41no—
545C8—41no—
546C22—42no—
547C22—42no—
548C22—42no—
549C22—81no—
550C22—81no—
551C22—81no—
552C22—81no—
553C22#535×C10911yescharacteristic
554C22#547×C10911yescharacteristic
555C22D4×Q8×C10911yescharacteristic
556C22C2×#135×C10911yescharacteristic
557C22#575×C10911yescharacteristic
558C22#576×C10911yescharacteristic
559C22#577×C10911yescharacteristic
560C4—22no—
561C4—41no—
562C4—41no—
563C4—41no—
564C4—41no—
565C4—41no—
566C4—42no—
567C4—81no—
568C4—81no—
569C4—81no—
570C4—81no—
571C4—81no—
572C4—81no—
573C4#539×C10911yescharacteristic
574C4#544×C10911yescharacteristic
575C4#554×C10911yescharacteristic
576C4#563×C10911yescharacteristic
577C2—82no—
578C2C109×#272011yescharacteristic
579C2C109×#321111yescharacteristic
580C2C109×#322411yescharacteristic
581C2C109×#334111yescharacteristic
582C2C109×#334811yescharacteristic
583C2C109×#338111yescharacteristic
584C2C109×#338911yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC22×D4×C109C23
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
2. C109×#2508C2semidirect
3. C109×#2101C2semidirect
5. C109×#2085C2semidirect
7. C109×#2058C2semidirect
8. C109×#2057C2semidirect
9. C109×#1949C2semidirect
12. C109×#1916C2semidirect
15. C109×#1846C2semidirect
103. #102×C109Q8semidirect
284. #32353C109direct (N × H)
294. #2508C2×C109semidirect
295. #2101C2×C109semidirect
297. #2085C2×C109semidirect
299. #2058C2×C109semidirect
300. #2057C2×C109semidirect
301. #1949C2×C109semidirect
304. #1916C2×C109semidirect
307. #1846C2×C109semidirect
308. C109#32353direct (N × H)
396. #102Q8×C109semidirect

Maximal subgroups

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

subgroupindex
C109×#25632
C109×#25082
C109×#21012
C109×#20922
C109×#20852
C109×#20672
C109×#20582
C109×#20572
C109×#19492
C109×#19342
C109×#19262
C109×#19162
C109×#18642
C109×#18622
C109×#18462
#32353109