Finite Group Databasebeta

← C109×#32415 #42150409

Subgroups — C109×#32415 #42150409

Order 27904.

616 conjugacy classes of subgroups.

The subgroup lattice has 566 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C109×#2497C211yesmaximal, characteristic
2C109×#2494C211yesmaximal, characteristic
3C109×#2088C211yesmaximal, characteristic, complemented
4C109×#2086C211yesmaximal, characteristic, complemented
5C109×#2085C211yesmaximal, characteristic, complemented
6C109×#2084C211yesmaximal, characteristic, complemented
7C109×#2077C211yesmaximal, characteristic
8C109×#2076C211yesmaximal, characteristic
9C109×#1949C211yesmaximal, characteristic, complemented
10C109×#1947C211yesmaximal, characteristic, complemented
11C109×#1919C211yesmaximal, characteristic, complemented
12C109×#1918C211yesmaximal, characteristic, complemented
13C109×#1850C211yesmaximal, characteristic
14C109×#1808C211yesmaximal, characteristic
15C109×#1807C211yesmaximal, characteristic
16C23×C8×C109C2211yescharacteristic
17C2×#107×C109C2211yescharacteristic
18C2×#107×C109C2211yescharacteristic
19C2×#107×C109C2211yescharacteristic
20C2×#106×C109C2211yescharacteristic
21C2×#106×C109C2211yescharacteristic
22C2×#106×C109C2211yescharacteristic
23C2×C4⋊C8×C109C2211yescharacteristic
24C2×C4⋊C8×C109C2211yescharacteristic
25C2×C22⋊C8×C109C2211yescharacteristic
26#401×C109—21no—
27#400×C109—21no—
28#397×C109—21no—
29#396×C109—21no—
30#389×C109C2211yescharacteristic
31#389×C109C2211yescharacteristic
32#389×C109C2211yescharacteristic
33#389×C109C2211yescharacteristic
34#388×C109—21no—
35#388×C109—21no—
36#387×C109—21no—
37#387×C109—21no—
38#384×C109C2211yescharacteristic
39#382×C109C2211yescharacteristic
40#380×C109C2211yescharacteristic
41#380×C109C2211yescharacteristic
42#380×C109C2211yescharacteristic
43#380×C109C2211yescharacteristic
44C4×C4⋊C4×C109C2211yescharacteristic
45C4×C4⋊C4×C109C2211yescharacteristic
46C4×C22⋊C4×C109C2211yescharacteristic
47#340×C109C2211yescharacteristic
48#340×C109C2211yescharacteristic
49#340×C109C2211yescharacteristic
50#340×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
59C23×C4×C109C2311yescharacteristic
60C22×C8×C109—22no—
61C22×C8×C109—22no—
62C22×C8×C109—41no—
63C22×C8×C109C2311yescharacteristic
64C22×C8×C109C2311yescharacteristic
65C22×C8×C109C2311yescharacteristic
66C22×C8×C109C2311yescharacteristic
67C2×C4⋊C4×C109—21no—
68C2×C4⋊C4×C109—21no—
69C2×C4⋊C4×C109—21no—
70C2×C4⋊C4×C109—21no—
71C2×C4⋊C4×C109—21no—
72C2×C4⋊C4×C109—21no—
73C2×C4⋊C4×C109C2311yescharacteristic
74C2×C4⋊C4×C109C2311yescharacteristic
75C2×C4⋊C4×C109C2311yescharacteristic
76C2×C4⋊C4×C109C2311yescharacteristic
77C2×C4⋊C4×C109C2311yescharacteristic
78C2×C4⋊C4×C109C2311yescharacteristic
79C2×C4⋊C4×C109C2311yescharacteristic
80C2×C4⋊C4×C109C2311yescharacteristic
81C2×C22⋊C4×C109—21no—
82C2×C22⋊C4×C109—21no—
83C2×C22⋊C4×C109—21no—
84C2×C22⋊C4×C109—21no—
85C2×C22⋊C4×C109D411yescharacteristic
86C2×C22⋊C4×C109D411yescharacteristic
87C2×C42×C109—21no—
88C2×C42×C109—21no—
89C2×C42×C109C2311yescharacteristic
90C2×C42×C109C2311yescharacteristic
91#107×C109—22no—
92#107×C109—41no—
93#107×C109—41no—
94#106×C109—22no—
95#106×C109—41no—
96#106×C109—41no—
97C4⋊C8×C109—22no—
98C4⋊C8×C109—22no—
99C22⋊C8×C109—41no—
100#95×C109—21no—
101#95×C109—21no—
102#95×C109—21no—
103#95×C109—21no—
104#95×C109—21no—
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×C109D411yescharacteristic
113#95×C109D411yescharacteristic
114C24×C109C2×D411yescharacteristic
115C22×C4×C109—21no—
116C22×C4×C109—21no—
117C22×C4×C109—21no—
118C22×C4×C109—21no—
119C22×C4×C109—21no—
120C22×C4×C109—21no—
121C22×C4×C109—21no—
122C22×C4×C109—21no—
123C22×C4×C109—21no—
124C22×C4×C109—21no—
125C22×C4×C109—21no—
126C22×C4×C109—21no—
127C22×C4×C109—21no—
128C22×C4×C109—21no—
129C22×C4×C109C2×D411yescharacteristic
130C22×C4×C109C2×D411yescharacteristic
131C22×C4×C109C2×D411yescharacteristic
132C22×C4×C109C2×D411yescharacteristic
133C22×C4×C109C2×D411yescharacteristic
134C22×C4×C109C2411yescharacteristic
135C2×C8×C109—21no—
136C2×C8×C109—21no—
137C2×C8×C109—21no—
138C2×C8×C109—21no—
139C2×C8×C109—21no—
140C2×C8×C109—21no—
141C2×C8×C109—21no—
142C2×C8×C109—21no—
143C2×C8×C109—21no—
144C2×C8×C109—21no—
145C2×C8×C109—44no—
146C2×C8×C109#4112yes—
147C2×C8×C109#4112yes—
148C4⋊C4×C109—21no—
149C4⋊C4×C109—21no—
150C4⋊C4×C109—21no—
151C4⋊C4×C109—21no—
152C4⋊C4×C109—21no—
153C4⋊C4×C109—21no—
154C4⋊C4×C109—21no—
155C4⋊C4×C109—21no—
156C4⋊C4×C109—21no—
157C4⋊C4×C109—21no—
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—42no—
165C4⋊C4×C109—42no—
166C4⋊C4×C109—81no—
167C4⋊C4×C109—81no—
168C4⋊C4×C109—81no—
169C4⋊C4×C109—81no—
170C22⋊C4×C109—22no—
171C22⋊C4×C109—22no—
172C22⋊C4×C109—42no—
173C22⋊C4×C109—81no—
174C22⋊C4×C109—81no—
175C22⋊C4×C109—81no—
176C42×C109—21no—
177C42×C109—21no—
178C42×C109—21no—
179C42×C109—21no—
180C42×C109—81no—
181C42×C109—81no—
182C23×C109—21no—
183C23×C109—21no—
184C23×C109—21no—
185C23×C109—21no—
186C23×C109—21no—
187C23×C109—21no—
188C23×C109#13712yes—
189C23×C109C22×D411yescharacteristic
190C2×C4×C109—21no—
191C2×C4×C109—21no—
192C2×C4×C109—21no—
193C2×C4×C109—21no—
194C2×C4×C109—21no—
195C2×C4×C109—21no—
196C2×C4×C109—21no—
197C2×C4×C109—21no—
198C2×C4×C109—21no—
199C2×C4×C109—21no—
200C2×C4×C109—21no—
201C2×C4×C109—21no—
202C2×C4×C109—21no—
203C2×C4×C109—21no—
204C2×C4×C109—41no—
205C2×C4×C109—41no—
206C2×C4×C109—41no—
207C2×C4×C109—41no—
208C2×C4×C109—41no—
209C2×C4×C109—41no—
210C2×C4×C109—41no—
211C2×C4×C109—41no—
212C2×C4×C109—41no—
213C2×C4×C109—41no—
214C2×C4×C109—41no—
215C2×C4×C109—41no—
216C2×C4×C109—41no—
217C2×C4×C109—41no—
218C2×C4×C109—41no—
219C2×C4×C109—41no—
220C2×C4×C109—41no—
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#13512yes—
233C2×C4×C109C2×#4111yescharacteristic
234C2×C4×C109C2×#4111yescharacteristic
235C2×C4×C109H(5,𝔽2)11yescharacteristic
236C2×C4×C1092−1+411yescharacteristic
237C2×C4×C1092−1+411yescharacteristic
238C2×C4×C1092−1+411yescharacteristic
239C8×C109—22no—
240C8×C109—22no—
241C8×C109—41no—
242C8×C109—41no—
243C22×C109—22no—
244C22×C109—22no—
245C22×C109—22no—
246C22×C109—41no—
247C22×C109—41no—
248C22×C109—41no—
249C22×C109—41no—
250C22×C109#53711yescharacteristic
251C22×C109#54711yescharacteristic
252C22×C109#54711yescharacteristic
253C22×C109C2×#13511yescharacteristic
254C22×C109C2×#13711yescharacteristic
255C22×C109#57611yescharacteristic
256C22×C109#57711yescharacteristic
257C4×C109—22no—
258C4×C109—41no—
259C4×C109—41no—
260C4×C109—41no—
261C4×C109—41no—
262C4×C109—81no—
263C4×C109—81no—
264C4×C109—81no—
265C4×C109—81no—
266C4×C109—81no—
267C4×C109—81no—
268C4×C109—81no—
269C4×C109—81no—
270C4×C109#54111yescharacteristic
271C4×C109#54111yescharacteristic
272C4×C109#55111yescharacteristic
273C4×C109#56311yescharacteristic
274#32415C10911yesmaximal, characteristic, direct product factor, Sylow
275C2×C109—42no—
276C2×C109#272211yescharacteristic
277C2×C109#324811yescharacteristic
278C2×C109#325711yescharacteristic
279C2×C109#333911yescharacteristic
280C2×C109#334011yescharacteristic
281C2×C109#334411yescharacteristic
282C2×C109#334611yescharacteristic
283#2497C2×C10911yescharacteristic
284#2494C2×C10911yescharacteristic
285#2088C2×C10911yescharacteristic, complemented
286#2086C2×C10911yescharacteristic, complemented
287#2085C2×C10911yescharacteristic, complemented
288#2084C2×C10911yescharacteristic, complemented
289#2077C2×C10911yescharacteristic
290#2076C2×C10911yescharacteristic
291#1949C2×C10911yescharacteristic, complemented
292#1947C2×C10911yescharacteristic, complemented
293#1919C2×C10911yescharacteristic, complemented
294#1918C2×C10911yescharacteristic, complemented
295#1850C2×C10911yescharacteristic
296#1808C2×C10911yescharacteristic
297#1807C2×C10911yescharacteristic
298C109#3241511yescharacteristic, direct product factor, Sylow
299C23×C8C22×C10911yescharacteristic
300C2×#107C22×C10911yescharacteristic
301C2×#107C22×C10911yescharacteristic
302C2×#107C22×C10911yescharacteristic
303C2×#106C22×C10911yescharacteristic
304C2×#106C22×C10911yescharacteristic
305C2×#106C22×C10911yescharacteristic
306C2×C4⋊C8C22×C10911yescharacteristic
307C2×C4⋊C8C22×C10911yescharacteristic
308C2×C22⋊C8C22×C10911yescharacteristic
309#401—21no—
310#400—21no—
311#397—21no—
312#396—21no—
313#389C22×C10911yescharacteristic
314#389C22×C10911yescharacteristic
315#389C22×C10911yescharacteristic
316#389C22×C10911yescharacteristic
317#388—21no—
318#388—21no—
319#387—21no—
320#387—21no—
321#384C22×C10911yescharacteristic
322#382C22×C10911yescharacteristic
323#380C22×C10911yescharacteristic
324#380C22×C10911yescharacteristic
325#380C22×C10911yescharacteristic
326#380C22×C10911yescharacteristic
327C4×C4⋊C4C22×C10911yescharacteristic
328C4×C4⋊C4C22×C10911yescharacteristic
329C4×C22⋊C4C22×C10911yescharacteristic
330#340C22×C10911yescharacteristic
331#340C22×C10911yescharacteristic
332#340C22×C10911yescharacteristic
333#340C22×C10911yescharacteristic
334#340C22×C10911yescharacteristic
335#340C22×C10911yescharacteristic
336#340C22×C10911yescharacteristic
337#340C22×C10911yescharacteristic
338#340C22×C10911yescharacteristic
339#340C22×C10911yescharacteristic
340#336C22×C10911yescharacteristic
341#336C22×C10911yescharacteristic
342C23×C4C23×C10911yescharacteristic
343C22×C8—22no—
344C22×C8—22no—
345C22×C8—41no—
346C22×C8C23×C10911yescharacteristic
347C22×C8C23×C10911yescharacteristic
348C22×C8C23×C10911yescharacteristic
349C22×C8C23×C10911yescharacteristic
350C2×C4⋊C4—21no—
351C2×C4⋊C4—21no—
352C2×C4⋊C4—21no—
353C2×C4⋊C4—21no—
354C2×C4⋊C4—21no—
355C2×C4⋊C4—21no—
356C2×C4⋊C4C23×C10911yescharacteristic
357C2×C4⋊C4C23×C10911yescharacteristic
358C2×C4⋊C4C23×C10911yescharacteristic
359C2×C4⋊C4C23×C10911yescharacteristic
360C2×C4⋊C4C23×C10911yescharacteristic
361C2×C4⋊C4C23×C10911yescharacteristic
362C2×C4⋊C4C23×C10911yescharacteristic
363C2×C4⋊C4C23×C10911yescharacteristic
364C2×C22⋊C4—21no—
365C2×C22⋊C4—21no—
366C2×C22⋊C4—21no—
367C2×C22⋊C4—21no—
368C2×C22⋊C4D4×C10911yescharacteristic
369C2×C22⋊C4D4×C10911yescharacteristic
370C2×C42—21no—
371C2×C42—21no—
372C2×C42C23×C10911yescharacteristic
373C2×C42C23×C10911yescharacteristic
374#107—22no—
375#107—41no—
376#107—41no—
377#106—22no—
378#106—41no—
379#106—41no—
380C4⋊C8—22no—
381C4⋊C8—22no—
382C22⋊C8—41no—
383#95—21no—
384#95—21no—
385#95—21no—
386#95—21no—
387#95—21no—
388#95—21no—
389#95—21no—
390#95—21no—
391#95—21no—
392#95—21no—
393#95—21no—
394#95—21no—
395#95D4×C10911yescharacteristic
396#95D4×C10911yescharacteristic
397C24C2×D4×C10911yescharacteristic
398C22×C4—21no—
399C22×C4—21no—
400C22×C4—21no—
401C22×C4—21no—
402C22×C4—21no—
403C22×C4—21no—
404C22×C4—21no—
405C22×C4—21no—
406C22×C4—21no—
407C22×C4—21no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—21no—
411C22×C4—21no—
412C22×C4C2×D4×C10911yescharacteristic
413C22×C4C2×D4×C10911yescharacteristic
414C22×C4C2×D4×C10911yescharacteristic
415C22×C4C2×D4×C10911yescharacteristic
416C22×C4C2×D4×C10911yescharacteristic
417C22×C4C24×C10911yescharacteristic
418C2×C8—21no—
419C2×C8—21no—
420C2×C8—21no—
421C2×C8—21no—
422C2×C8—21no—
423C2×C8—21no—
424C2×C8—21no—
425C2×C8—21no—
426C2×C8—21no—
427C2×C8—21no—
428C2×C8—44no—
429C2×C8#41×C10912yes—
430C2×C8#41×C10912yes—
431C4⋊C4—21no—
432C4⋊C4—21no—
433C4⋊C4—21no—
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—21no—
437C4⋊C4—21no—
438C4⋊C4—21no—
439C4⋊C4—21no—
440C4⋊C4—21no—
441C4⋊C4—21no—
442C4⋊C4—21no—
443C4⋊C4—21no—
444C4⋊C4—21no—
445C4⋊C4—21no—
446C4⋊C4—21no—
447C4⋊C4—42no—
448C4⋊C4—42no—
449C4⋊C4—81no—
450C4⋊C4—81no—
451C4⋊C4—81no—
452C4⋊C4—81no—
453C22⋊C4—22no—
454C22⋊C4—22no—
455C22⋊C4—42no—
456C22⋊C4—81no—
457C22⋊C4—81no—
458C22⋊C4—81no—
459C42—21no—
460C42—21no—
461C42—21no—
462C42—21no—
463C42—81no—
464C42—81no—
465C23—21no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23#137×C10912yes—
472C23C22×D4×C10911yescharacteristic
473C2×C4—21no—
474C2×C4—21no—
475C2×C4—21no—
476C2×C4—21no—
477C2×C4—21no—
478C2×C4—21no—
479C2×C4—21no—
480C2×C4—21no—
481C2×C4—21no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—21no—
485C2×C4—21no—
486C2×C4—21no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—41no—
491C2×C4—41no—
492C2×C4—41no—
493C2×C4—41no—
494C2×C4—41no—
495C2×C4—41no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—41no—
499C2×C4—41no—
500C2×C4—41no—
501C2×C4—41no—
502C2×C4—41no—
503C2×C4—41no—
504C2×C4—41no—
505C2×C4—41no—
506C2×C4—41no—
507C2×C4—41no—
508C2×C4—41no—
509C2×C4—41no—
510C2×C4—41no—
511C2×C4—41no—
512C2×C4—41no—
513C2×C4—41no—
514C2×C4—41no—
515C2×C4#135×C10912yes—
516C2×C4C2×#41×C10911yescharacteristic
517C2×C4C2×#41×C10911yescharacteristic
518C2×C4H(5,𝔽2)×C10911yescharacteristic
519C2×C42−1+4×C10911yescharacteristic
520C2×C42−1+4×C10911yescharacteristic
521C2×C42−1+4×C10911yescharacteristic
522C8—22no—
523C8—22no—
524C8—41no—
525C8—41no—
526C22—22no—
527C22—22no—
528C22—22no—
529C22—41no—
530C22—41no—
531C22—41no—
532C22—41no—
533C22#537×C10911yescharacteristic
534C22#547×C10911yescharacteristic
535C22#547×C10911yescharacteristic
536C22C2×#135×C10911yescharacteristic
537C22C2×#137×C10911yescharacteristic
538C22#576×C10911yescharacteristic
539C22#577×C10911yescharacteristic
540C4—22no—
541C4—41no—
542C4—41no—
543C4—41no—
544C4—41no—
545C4—81no—
546C4—81no—
547C4—81no—
548C4—81no—
549C4—81no—
550C4—81no—
551C4—81no—
552C4—81no—
553C4#541×C10911yescharacteristic
554C4#541×C10911yescharacteristic
555C4#551×C10911yescharacteristic
556C4#563×C10911yescharacteristic
557C2—42no—
558C2C109×#272211yescharacteristic
559C2C109×#324811yescharacteristic
560C2C109×#325711yescharacteristic
561C2C109×#333911yescharacteristic
562C2C109×#334011yescharacteristic
563C2C109×#334411yescharacteristic
564C2C109×#334611yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC24×C109C2×D4
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
3. C109×#2088C2semidirect
4. C109×#2086C2semidirect
5. C109×#2085C2semidirect
6. C109×#2084C2semidirect
9. C109×#1949C2semidirect
10. C109×#1947C2semidirect
11. C109×#1919C2semidirect
12. C109×#1918C2semidirect
274. #32415C109direct (N × H)
285. #2088C2×C109semidirect
286. #2086C2×C109semidirect
287. #2085C2×C109semidirect
288. #2084C2×C109semidirect
291. #1949C2×C109semidirect
292. #1947C2×C109semidirect
293. #1919C2×C109semidirect
294. #1918C2×C109semidirect
298. C109#32415direct (N × H)

Maximal subgroups

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

subgroupindex
C109×#24972
C109×#24942
C109×#20882
C109×#20862
C109×#20852
C109×#20842
C109×#20772
C109×#20762
C109×#19492
C109×#19472
C109×#19192
C109×#19182
C109×#18502
C109×#18082
C109×#18072
#32415109