Finite Group Databasebeta

← C109×#14095 #42132089

Subgroups — C109×#14095 #42132089

Order 27904.

2158 conjugacy classes of subgroups.

The subgroup lattice has 1176 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#123×C109C211yesmaximal, characteristic
2C2×#390×C109C211yesmaximal, characteristic
3C2×#387×C109C211yesmaximal, characteristic, complemented
4C2×C4×C4⋊C4×C109C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊C4×C109C211yesmaximal, characteristic, complemented
6C109×#1441C211yesmaximal, characteristic, complemented
7C109×#1439C211yesmaximal, characteristic, complemented
8C109×#1439C211yesmaximal, characteristic, complemented
9C109×#1438C211yesmaximal, characteristic
10C109×#1437C211yesmaximal, characteristic, complemented
11C109×#1437C211yesmaximal, characteristic, complemented
12C109×#1437C211yesmaximal, characteristic, complemented
13C109×#1437C211yesmaximal, characteristic, complemented
14C109×#1436C211yesmaximal, characteristic, complemented
15C109×C22⋊#95C211yesmaximal, characteristic, complemented
16C23×D4×C109C2211yescharacteristic
17C24×C4×C109C2211yescharacteristic
18C2×#123×C109—24no—
19C2×#123×C109—24no—
20C2×#123×C109C418yescomplemented
21C22×C4⋊C4×C109C2211yescharacteristic
22C22×C4⋊C4×C109C2211yescharacteristic
23C22×C4⋊C4×C109C2211yescharacteristic
24C22×C4⋊C4×C109C2211yescharacteristic
25C22×C22⋊C4×C109C2211yescharacteristic
26C22×C22⋊C4×C109C2211yescharacteristic
27C22×C22⋊C4×C109C2211yescharacteristic
28C22×C22⋊C4×C109C2211yescharacteristic
29C22×C22⋊C4×C109C2211yescharacteristic
30C22×C22⋊C4×C109C2211yescharacteristic
31C22×C22⋊C4×C109C2211yescharacteristic
32C22×C22⋊C4×C109C2211yescharacteristic
33C22×C22⋊C4×C109C2211yescharacteristic
34C22×C22⋊C4×C109C2211yescharacteristic
35C22×C22⋊C4×C109C2211yescharacteristic
36C22×C42×C109C2211yescharacteristic
37C22×C42×C109C2211yescharacteristic
38C22×C42×C109C2211yescharacteristic
39C22×C42×C109C2211yescharacteristic
40#390×C109—24no—
41#387×C109—24no—
42C4×C4⋊C4×C109—24no—
43C4×C22⋊C4×C109—24no—
44C2×#95×C109C2211yescharacteristic
45C2×#95×C109C2211yescharacteristic
46C2×#95×C109C2211yescharacteristic
47C2×#95×C109C2211yescharacteristic
48C2×#95×C109C2211yescharacteristic
49C2×#95×C109C2211yescharacteristic
50C2×#95×C109C2211yescharacteristic
51C2×#95×C109C2211yescharacteristic
52C2×#95×C109C2211yescharacteristic
53C2×#95×C109C2211yescharacteristic
54C2×#95×C109C2211yescharacteristic
55C2×#95×C109C2211yescharacteristic
56C2×#95×C109C2211yescharacteristic
57C2×#95×C109C2211yescharacteristic
58C25×C109C2311yescharacteristic
59C25×C109C2311yescharacteristic
60C22×D4×C109—22no—
61C22×D4×C109—22no—
62C22×D4×C109—22no—
63C22×D4×C109—22no—
64C22×D4×C109—41no—
65C22×D4×C109—41no—
66C22×D4×C109C2×C414yes—
67C23×C4×C109—22no—
68C23×C4×C109—22no—
69C23×C4×C109—22no—
70C23×C4×C109—22no—
71C23×C4×C109—41no—
72C23×C4×C109—41no—
73C23×C4×C109C2×C414yes—
74C23×C4×C109C2311yescharacteristic
75C23×C4×C109C2311yescharacteristic
76C23×C4×C109C2311yescharacteristic
77C23×C4×C109C2311yescharacteristic
78C23×C4×C109C2311yescharacteristic
79C23×C4×C109C2311yescharacteristic
80C23×C4×C109C2311yescharacteristic
81C23×C4×C109C2311yescharacteristic
82C23×C4×C109C2311yescharacteristic
83C23×C4×C109C2311yescharacteristic
84C23×C4×C109C2311yescharacteristic
85C23×C4×C109C2311yescharacteristic
86C23×C4×C109C2311yescharacteristic
87#123×C109—232no—
88C2×C4⋊C4×C109—22no—
89C2×C4⋊C4×C109—22no—
90C2×C4⋊C4×C109—22no—
91C2×C4⋊C4×C109—22no—
92C2×C4⋊C4×C109—22no—
93C2×C4⋊C4×C109—22no—
94C2×C4⋊C4×C109—22no—
95C2×C4⋊C4×C109—41no—
96C2×C4⋊C4×C109C2×C414yes—
97C2×C4⋊C4×C109C2×C414yes—
98C2×C4⋊C4×C109D414yes—
99C2×C4⋊C4×C109D414yes—
100C2×C22⋊C4×C109—22no—
101C2×C22⋊C4×C109—22no—
102C2×C22⋊C4×C109—22no—
103C2×C22⋊C4×C109—22no—
104C2×C22⋊C4×C109—22no—
105C2×C22⋊C4×C109—22no—
106C2×C22⋊C4×C109—22no—
107C2×C22⋊C4×C109—22no—
108C2×C22⋊C4×C109—22no—
109C2×C22⋊C4×C109—22no—
110C2×C22⋊C4×C109—22no—
111C2×C22⋊C4×C109—22no—
112C2×C22⋊C4×C109—22no—
113C2×C22⋊C4×C109—22no—
114C2×C22⋊C4×C109—22no—
115C2×C22⋊C4×C109—22no—
116C2×C22⋊C4×C109—22no—
117C2×C22⋊C4×C109—22no—
118C2×C22⋊C4×C109—22no—
119C2×C22⋊C4×C109—22no—
120C2×C22⋊C4×C109—22no—
121C2×C22⋊C4×C109—22no—
122C2×C22⋊C4×C109—22no—
123C2×C22⋊C4×C109—41no—
124C2×C22⋊C4×C109—41no—
125C2×C22⋊C4×C109—41no—
126C2×C22⋊C4×C109—41no—
127C2×C22⋊C4×C109—41no—
128C2×C22⋊C4×C109—41no—
129C2×C22⋊C4×C109C2×C414yes—
130C2×C22⋊C4×C109C2×C414yes—
131C2×C22⋊C4×C109C2×C414yes—
132C2×C22⋊C4×C109D414yes—
133C2×C42×C109—22no—
134C2×C42×C109—22no—
135C2×C42×C109—22no—
136C2×C42×C109—22no—
137C2×C42×C109—22no—
138C2×C42×C109—22no—
139C2×C42×C109—22no—
140C2×C42×C109—22no—
141C2×C42×C109—22no—
142C2×C42×C109—41no—
143C2×C42×C109—41no—
144C2×C42×C109—41no—
145#95×C109—22no—
146#95×C109—22no—
147#95×C109—22no—
148#95×C109—22no—
149#95×C109—22no—
150#95×C109—22no—
151#95×C109—22no—
152#95×C109—22no—
153#95×C109—22no—
154#95×C109—22no—
155#95×C109—41no—
156#95×C109—41no—
157#95×C109—41no—
158#95×C109—41no—
159C24×C109—21no—
160C24×C109—21no—
161C24×C109—21no—
162C24×C109—21no—
163C24×C109—21no—
164C24×C109—21no—
165C24×C109—21no—
166C24×C109—21no—
167C24×C109—21no—
168C24×C109—21no—
169C24×C109—21no—
170C24×C109—21no—
171C24×C109—21no—
172C24×C109—21no—
173C24×C109—21no—
174C24×C109—21no—
175C24×C109—21no—
176C24×C109—21no—
177C24×C109—21no—
178C24×C109—21no—
179C24×C109—21no—
180C24×C109—21no—
181C24×C109—21no—
182C24×C109—21no—
183C24×C109—21no—
184C24×C109—21no—
185C24×C109C22×C412yes—
186C24×C109C22×C412yes—
187C24×C109C2×D412yes—
188C24×C109#4112yes—
189C24×C109C2411yescharacteristic
190C2×D4×C109—28no—
191C2×D4×C109—28no—
192C2×D4×C109—44no—
193C2×D4×C109—44no—
194C2×D4×C109—44no—
195C2×D4×C109—44no—
196C2×D4×C109—44no—
197C22×C4×C109—21no—
198C22×C4×C109—21no—
199C22×C4×C109—21no—
200C22×C4×C109—21no—
201C22×C4×C109—21no—
202C22×C4×C109—21no—
203C22×C4×C109—21no—
204C22×C4×C109—21no—
205C22×C4×C109—21no—
206C22×C4×C109—21no—
207C22×C4×C109—21no—
208C22×C4×C109—21no—
209C22×C4×C109—21no—
210C22×C4×C109—21no—
211C22×C4×C109—21no—
212C22×C4×C109—21no—
213C22×C4×C109—28no—
214C22×C4×C109—21no—
215C22×C4×C109—21no—
216C22×C4×C109—21no—
217C22×C4×C109—21no—
218C22×C4×C109—21no—
219C22×C4×C109—21no—
220C22×C4×C109—21no—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—21no—
224C22×C4×C109—21no—
225C22×C4×C109—21no—
226C22×C4×C109—21no—
227C22×C4×C109—21no—
228C22×C4×C109—21no—
229C22×C4×C109—21no—
230C22×C4×C109—21no—
231C22×C4×C109—21no—
232C22×C4×C109—21no—
233C22×C4×C109—21no—
234C22×C4×C109—21no—
235C22×C4×C109—21no—
236C22×C4×C109—21no—
237C22×C4×C109—21no—
238C22×C4×C109—21no—
239C22×C4×C109—21no—
240C22×C4×C109—21no—
241C22×C4×C109—21no—
242C22×C4×C109—21no—
243C22×C4×C109—21no—
244C22×C4×C109—21no—
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—21no—
254C22×C4×C109—21no—
255C22×C4×C109—21no—
256C22×C4×C109—28no—
257C22×C4×C109—21no—
258C22×C4×C109—21no—
259C22×C4×C109—21no—
260C22×C4×C109—21no—
261C22×C4×C109—21no—
262C22×C4×C109—21no—
263C22×C4×C109—21no—
264C22×C4×C109—21no—
265C22×C4×C109—21no—
266C22×C4×C109—21no—
267C22×C4×C109—21no—
268C22×C4×C109—21no—
269C22×C4×C109—21no—
270C22×C4×C109—21no—
271C22×C4×C109—44no—
272C22×C4×C109—44no—
273C22×C4×C109—44no—
274C22×C4×C109—44no—
275C22×C4×C109—44no—
276C22×C4×C109C22×C412yes—
277C22×C4×C109C22×C412yes—
278C22×C4×C109C22×C412yes—
279C22×C4×C109C22×C412yes—
280C22×C4×C109C22×C412yes—
281C22×C4×C109C2×D412yes—
282C22×C4×C109C2×D412yes—
283C22×C4×C109C2×D412yes—
284C22×C4×C109C2×D412yes—
285C22×C4×C109C2×D412yes—
286C22×C4×C109C2×D412yes—
287C22×C4×C109C2×D412yes—
288C22×C4×C109C2×D412yes—
289C22×C4×C109#4112yes—
290C22×C4×C109#4112yes—
291C22×C4×C109#4112yes—
292C22×C4×C109#4112yes—
293C22×C4×C109#4112yes—
294C22×C4×C109#4112yes—
295C4⋊C4×C109—28no—
296C4⋊C4×C109—28no—
297C4⋊C4×C109—44no—
298C4⋊C4×C109C22⋊C4116yescomplemented
299C22⋊C4×C109—28no—
300C22⋊C4×C109—28no—
301C22⋊C4×C109—28no—
302C22⋊C4×C109—28no—
303C22⋊C4×C109—28no—
304C22⋊C4×C109—44no—
305C22⋊C4×C109—44no—
306C22⋊C4×C109—44no—
307C22⋊C4×C109—44no—
308C22⋊C4×C109—44no—
309C22⋊C4×C109—44no—
310C42×C109—28no—
311C42×C109—44no—
312C42×C109—44no—
313C42×C109—44no—
314C23×C109—22no—
315C23×C109—22no—
316C23×C109—22no—
317C23×C109—22no—
318C23×C109—22no—
319C23×C109—22no—
320C23×C109—22no—
321C23×C109—22no—
322C23×C109—22no—
323C23×C109—22no—
324C23×C109—22no—
325C23×C109—22no—
326C23×C109—22no—
327C23×C109—22no—
328C23×C109—22no—
329C23×C109—22no—
330C23×C109—22no—
331C23×C109—22no—
332C23×C109—22no—
333C23×C109—22no—
334C23×C109—22no—
335C23×C109—22no—
336C23×C109—22no—
337C23×C109—22no—
338C23×C109—22no—
339C23×C109—41no—
340C23×C109—41no—
341C23×C109—41no—
342C23×C109—41no—
343C23×C109—41no—
344C23×C109—41no—
345C23×C109—41no—
346C23×C109—41no—
347C23×C109—41no—
348C23×C109—41no—
349C23×C109—41no—
350C23×C109—41no—
351C23×C109—41no—
352C23×C109—41no—
353C23×C109—41no—
354C23×C109—41no—
355C23×C109—41no—
356C23×C109—41no—
357C23×C109—41no—
358C23×C109—41no—
359C23×C109—41no—
360C23×C109—41no—
361C23×C109—41no—
362C23×C109—41no—
363C23×C109—41no—
364C23×C109—41no—
365C23×C109—41no—
366C23×C109—41no—
367C23×C109—41no—
368C23×C109—41no—
369C23×C109—41no—
370C23×C109—41no—
371C23×C109—41no—
372C23×C109—41no—
373C23×C109—41no—
374C23×C109—41no—
375C23×C109—41no—
376C23×C109—41no—
377C23×C109—41no—
378C23×C109—41no—
379C23×C109—41no—
380C23×C109—41no—
381C23×C109—41no—
382C23×C109—41no—
383C23×C109C4×D414yes—
384C23×C109C23×C411yescharacteristic
385C23×C109C22×D411yescharacteristic
386C23×C109C22×D411yescharacteristic
387C23×C109C22×D411yescharacteristic
388C23×C109C2×#4111yescharacteristic
389C23×C109C2×#4111yescharacteristic
390C23×C109C2×#4111yescharacteristic
391C23×C109C2×#4111yescharacteristic
392C23×C109C2×#4111yescharacteristic
393C23×C109C2×#4111yescharacteristic
394C23×C109C2×#4111yescharacteristic
395C23×C109H(5,𝔽2)11yescharacteristic
396C23×C109H(5,𝔽2)11yescharacteristic
397C23×C109H(5,𝔽2)11yescharacteristic
398C23×C1092−1+411yescharacteristic
399D4×C109—416no—
400C2×C4×C109—22no—
401C2×C4×C109—22no—
402C2×C4×C109—22no—
403C2×C4×C109—22no—
404C2×C4×C109—22no—
405C2×C4×C109—22no—
406C2×C4×C109—22no—
407C2×C4×C109—22no—
408C2×C4×C109—22no—
409C2×C4×C109—22no—
410C2×C4×C109—22no—
411C2×C4×C109—22no—
412C2×C4×C109—22no—
413C2×C4×C109—22no—
414C2×C4×C109—22no—
415C2×C4×C109—22no—
416C2×C4×C109—22no—
417C2×C4×C109—22no—
418C2×C4×C109—22no—
419C2×C4×C109—22no—
420C2×C4×C109—22no—
421C2×C4×C109—22no—
422C2×C4×C109—22no—
423C2×C4×C109—22no—
424C2×C4×C109—22no—
425C2×C4×C109—22no—
426C2×C4×C109—22no—
427C2×C4×C109—22no—
428C2×C4×C109—22no—
429C2×C4×C109—22no—
430C2×C4×C109—22no—
431C2×C4×C109—22no—
432C2×C4×C109—22no—
433C2×C4×C109—22no—
434C2×C4×C109—22no—
435C2×C4×C109—22no—
436C2×C4×C109—22no—
437C2×C4×C109—22no—
438C2×C4×C109—22no—
439C2×C4×C109—22no—
440C2×C4×C109—22no—
441C2×C4×C109—22no—
442C2×C4×C109—22no—
443C2×C4×C109—22no—
444C2×C4×C109—22no—
445C2×C4×C109—416no—
446C2×C4×C109—41no—
447C2×C4×C109—41no—
448C2×C4×C109—41no—
449C2×C4×C109—41no—
450C2×C4×C109—41no—
451C2×C4×C109—41no—
452C2×C4×C109—41no—
453C2×C4×C109—41no—
454C2×C4×C109—41no—
455C2×C4×C109—41no—
456C2×C4×C109—41no—
457C2×C4×C109—41no—
458C2×C4×C109—41no—
459C2×C4×C109—41no—
460C2×C4×C109—41no—
461C2×C4×C109—41no—
462C2×C4×C109—41no—
463C2×C4×C109—41no—
464C2×C4×C109—41no—
465C2×C4×C109—41no—
466C2×C4×C109—41no—
467C2×C4×C109—41no—
468C2×C4×C109—41no—
469C2×C4×C109—41no—
470C2×C4×C109—41no—
471C2×C4×C109—41no—
472C2×C4×C109—41no—
473C2×C4×C109—41no—
474C2×C4×C109—41no—
475C2×C4×C109—41no—
476C2×C4×C109—41no—
477C2×C4×C109—41no—
478C2×C4×C109—41no—
479C2×C4×C109—41no—
480C2×C4×C109—41no—
481C2×C4×C109—41no—
482C2×C4×C109—41no—
483C2×C4×C109—41no—
484C2×C4×C109—41no—
485C2×C4×C109—41no—
486C2×C4×C109—41no—
487C2×C4×C109—41no—
488C2×C4×C109C2×C22⋊C414yes—
489C2×C4×C109C2×C22⋊C414yes—
490C2×C4×C109C2×C22⋊C414yes—
491C2×C4×C109#12314yescomplemented
492C22×C109—24no—
493C22×C109—24no—
494C22×C109—24no—
495C22×C109—42no—
496C22×C109—42no—
497C22×C109—42no—
498C22×C109—42no—
499C22×C109—42no—
500C22×C109—42no—
501C22×C109—42no—
502C22×C109—42no—
503C22×C109—42no—
504C22×C109—42no—
505C22×C109—42no—
506C22×C109—42no—
507C22×C109—42no—
508C22×C109—42no—
509C22×C109—42no—
510C22×C109—42no—
511C22×C109—42no—
512C22×C109—42no—
513C22×C109—42no—
514C22×C109—81no—
515C22×C109—81no—
516C22×C109—81no—
517C22×C109—81no—
518C22×C109—81no—
519C22×C109—81no—
520C22×C109—81no—
521C22×C109—81no—
522C22×C109C22×C22⋊C411yescharacteristic
523C22×C109C2×C4×D411yescharacteristic
524C22×C109C4×#4111yescharacteristic
525C22×C109C4×#4111yescharacteristic
526C22×C109C4×#4111yescharacteristic
527C22×C109#51811yescharacteristic
528C22×C109#52011yescharacteristic
529C22×C109C2×#12311yescharacteristic
530C22×C109#52511yescharacteristic
531C22×C109#52511yescharacteristic
532C22×C109#52511yescharacteristic
533C22×C109#52911yescharacteristic
534C22×C109#52911yescharacteristic
535C22×C109#53211yescharacteristic
536C22×C109#53211yescharacteristic
537C22×C109#53811yescharacteristic
538C22×C109#53911yescharacteristic
539C22×C109#54011yescharacteristic
540C22×C109#54211yescharacteristic
541C22×C109D4211yescharacteristic
542C22×C109D4211yescharacteristic
543C22×C109#54611yescharacteristic
544C22×C109#54611yescharacteristic
545C22×C109#54611yescharacteristic
546C22×C109#54711yescharacteristic
547C22×C109#54811yescharacteristic
548C22×C109#54811yescharacteristic
549C22×C109#55011yescharacteristic
550C22×C109#55011yescharacteristic
551C22×C109#55111yescharacteristic
552C22×C109#55111yescharacteristic
553C22×C109#55211yescharacteristic
554C22×C109#55311yescharacteristic
555C22×C109#55311yescharacteristic
556C22×C109#55911yescharacteristic
557C4×C109—24no—
558C4×C109—24no—
559C4×C109—24no—
560C4×C109—24no—
561C4×C109—42no—
562C4×C109—42no—
563C4×C109—42no—
564C4×C109—42no—
565C4×C109—42no—
566C4×C109—42no—
567C4×C109—42no—
568C4×C109—81no—
569C4×C109—81no—
570#14095C10911yesmaximal, characteristic, direct product factor, Sylow
571C2×C109—44no—
572C2×C109—82no—
573C2×C109#229711yescharacteristic
574C2×C109C4×#12311yescharacteristic
575C2×C109#233511yescharacteristic
576C2×C109D4×C22⋊C411yescharacteristic
577C2×C109#234111yescharacteristic
578C2×C109#235911yescharacteristic
579C2×C109#237411yescharacteristic
580C2×C109#244311yescharacteristic
581C2×C109#244511yescharacteristic
582C2×C109#245611yescharacteristic
583C2×C109#245811yescharacteristic
584C2×C109#246111yescharacteristic
585C2×C109#247111yescharacteristic
586C2×C109#255411yescharacteristic
587C2×C109#255811yescharacteristic
588C22×#123C2×C10911yescharacteristic
589C2×#390C2×C10911yescharacteristic
590C2×#387C2×C10911yescharacteristic, complemented
591C2×C4×C4⋊C4C2×C10911yescharacteristic, complemented
592C2×C4×C22⋊C4C2×C10911yescharacteristic, complemented
593#1441C2×C10911yescharacteristic, complemented
594#1439C2×C10911yescharacteristic, complemented
595#1439C2×C10911yescharacteristic, complemented
596#1438C2×C10911yescharacteristic
597#1437C2×C10911yescharacteristic, complemented
598#1437C2×C10911yescharacteristic, complemented
599#1437C2×C10911yescharacteristic, complemented
600#1437C2×C10911yescharacteristic, complemented
601#1436C2×C10911yescharacteristic, complemented
602C22⋊#95C2×C10911yescharacteristic, complemented
603C109#1409511yescharacteristic, direct product factor, Sylow
604C23×D4C22×C10911yescharacteristic
605C24×C4C22×C10911yescharacteristic
606C2×#123—24no—
607C2×#123—24no—
608C2×#123C4×C10918yescomplemented
609C22×C4⋊C4C22×C10911yescharacteristic
610C22×C4⋊C4C22×C10911yescharacteristic
611C22×C4⋊C4C22×C10911yescharacteristic
612C22×C4⋊C4C22×C10911yescharacteristic
613C22×C22⋊C4C22×C10911yescharacteristic
614C22×C22⋊C4C22×C10911yescharacteristic
615C22×C22⋊C4C22×C10911yescharacteristic
616C22×C22⋊C4C22×C10911yescharacteristic
617C22×C22⋊C4C22×C10911yescharacteristic
618C22×C22⋊C4C22×C10911yescharacteristic
619C22×C22⋊C4C22×C10911yescharacteristic
620C22×C22⋊C4C22×C10911yescharacteristic
621C22×C22⋊C4C22×C10911yescharacteristic
622C22×C22⋊C4C22×C10911yescharacteristic
623C22×C22⋊C4C22×C10911yescharacteristic
624C22×C42C22×C10911yescharacteristic
625C22×C42C22×C10911yescharacteristic
626C22×C42C22×C10911yescharacteristic
627C22×C42C22×C10911yescharacteristic
628#390—24no—
629#387—24no—
630C4×C4⋊C4—24no—
631C4×C22⋊C4—24no—
632C2×#95C22×C10911yescharacteristic
633C2×#95C22×C10911yescharacteristic
634C2×#95C22×C10911yescharacteristic
635C2×#95C22×C10911yescharacteristic
636C2×#95C22×C10911yescharacteristic
637C2×#95C22×C10911yescharacteristic
638C2×#95C22×C10911yescharacteristic
639C2×#95C22×C10911yescharacteristic
640C2×#95C22×C10911yescharacteristic
641C2×#95C22×C10911yescharacteristic
642C2×#95C22×C10911yescharacteristic
643C2×#95C22×C10911yescharacteristic
644C2×#95C22×C10911yescharacteristic
645C2×#95C22×C10911yescharacteristic
646C25C23×C10911yescharacteristic
647C25C23×C10911yescharacteristic
648C22×D4—22no—
649C22×D4—22no—
650C22×D4—22no—
651C22×D4—22no—
652C22×D4—41no—
653C22×D4—41no—
654C22×D4C2×C4×C10914yes—
655C23×C4—22no—
656C23×C4—22no—
657C23×C4—22no—
658C23×C4—22no—
659C23×C4—41no—
660C23×C4—41no—
661C23×C4C2×C4×C10914yes—
662C23×C4C23×C10911yescharacteristic
663C23×C4C23×C10911yescharacteristic
664C23×C4C23×C10911yescharacteristic
665C23×C4C23×C10911yescharacteristic
666C23×C4C23×C10911yescharacteristic
667C23×C4C23×C10911yescharacteristic
668C23×C4C23×C10911yescharacteristic
669C23×C4C23×C10911yescharacteristic
670C23×C4C23×C10911yescharacteristic
671C23×C4C23×C10911yescharacteristic
672C23×C4C23×C10911yescharacteristic
673C23×C4C23×C10911yescharacteristic
674C23×C4C23×C10911yescharacteristic
675#123—232no—
676C2×C4⋊C4—22no—
677C2×C4⋊C4—22no—
678C2×C4⋊C4—22no—
679C2×C4⋊C4—22no—
680C2×C4⋊C4—22no—
681C2×C4⋊C4—22no—
682C2×C4⋊C4—22no—
683C2×C4⋊C4—41no—
684C2×C4⋊C4C2×C4×C10914yes—
685C2×C4⋊C4C2×C4×C10914yes—
686C2×C4⋊C4D4×C10914yes—
687C2×C4⋊C4D4×C10914yes—
688C2×C22⋊C4—22no—
689C2×C22⋊C4—22no—
690C2×C22⋊C4—22no—
691C2×C22⋊C4—22no—
692C2×C22⋊C4—22no—
693C2×C22⋊C4—22no—
694C2×C22⋊C4—22no—
695C2×C22⋊C4—22no—
696C2×C22⋊C4—22no—
697C2×C22⋊C4—22no—
698C2×C22⋊C4—22no—
699C2×C22⋊C4—22no—
700C2×C22⋊C4—22no—
701C2×C22⋊C4—22no—
702C2×C22⋊C4—22no—
703C2×C22⋊C4—22no—
704C2×C22⋊C4—22no—
705C2×C22⋊C4—22no—
706C2×C22⋊C4—22no—
707C2×C22⋊C4—22no—
708C2×C22⋊C4—22no—
709C2×C22⋊C4—22no—
710C2×C22⋊C4—22no—
711C2×C22⋊C4—41no—
712C2×C22⋊C4—41no—
713C2×C22⋊C4—41no—
714C2×C22⋊C4—41no—
715C2×C22⋊C4—41no—
716C2×C22⋊C4—41no—
717C2×C22⋊C4C2×C4×C10914yes—
718C2×C22⋊C4C2×C4×C10914yes—
719C2×C22⋊C4C2×C4×C10914yes—
720C2×C22⋊C4D4×C10914yes—
721C2×C42—22no—
722C2×C42—22no—
723C2×C42—22no—
724C2×C42—22no—
725C2×C42—22no—
726C2×C42—22no—
727C2×C42—22no—
728C2×C42—22no—
729C2×C42—22no—
730C2×C42—41no—
731C2×C42—41no—
732C2×C42—41no—
733#95—22no—
734#95—22no—
735#95—22no—
736#95—22no—
737#95—22no—
738#95—22no—
739#95—22no—
740#95—22no—
741#95—22no—
742#95—22no—
743#95—41no—
744#95—41no—
745#95—41no—
746#95—41no—
747C24—21no—
748C24—21no—
749C24—21no—
750C24—21no—
751C24—21no—
752C24—21no—
753C24—21no—
754C24—21no—
755C24—21no—
756C24—21no—
757C24—21no—
758C24—21no—
759C24—21no—
760C24—21no—
761C24—21no—
762C24—21no—
763C24—21no—
764C24—21no—
765C24—21no—
766C24—21no—
767C24—21no—
768C24—21no—
769C24—21no—
770C24—21no—
771C24—21no—
772C24—21no—
773C24C22×C4×C10912yes—
774C24C22×C4×C10912yes—
775C24C2×D4×C10912yes—
776C24#41×C10912yes—
777C24C24×C10911yescharacteristic
778C2×D4—28no—
779C2×D4—28no—
780C2×D4—44no—
781C2×D4—44no—
782C2×D4—44no—
783C2×D4—44no—
784C2×D4—44no—
785C22×C4—21no—
786C22×C4—21no—
787C22×C4—21no—
788C22×C4—21no—
789C22×C4—21no—
790C22×C4—21no—
791C22×C4—21no—
792C22×C4—21no—
793C22×C4—21no—
794C22×C4—21no—
795C22×C4—21no—
796C22×C4—21no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—21no—
800C22×C4—21no—
801C22×C4—28no—
802C22×C4—21no—
803C22×C4—21no—
804C22×C4—21no—
805C22×C4—21no—
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—21no—
812C22×C4—21no—
813C22×C4—21no—
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—21no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—21no—
829C22×C4—21no—
830C22×C4—21no—
831C22×C4—21no—
832C22×C4—21no—
833C22×C4—21no—
834C22×C4—21no—
835C22×C4—21no—
836C22×C4—21no—
837C22×C4—21no—
838C22×C4—21no—
839C22×C4—21no—
840C22×C4—21no—
841C22×C4—21no—
842C22×C4—21no—
843C22×C4—21no—
844C22×C4—28no—
845C22×C4—21no—
846C22×C4—21no—
847C22×C4—21no—
848C22×C4—21no—
849C22×C4—21no—
850C22×C4—21no—
851C22×C4—21no—
852C22×C4—21no—
853C22×C4—21no—
854C22×C4—21no—
855C22×C4—21no—
856C22×C4—21no—
857C22×C4—21no—
858C22×C4—21no—
859C22×C4—44no—
860C22×C4—44no—
861C22×C4—44no—
862C22×C4—44no—
863C22×C4—44no—
864C22×C4C22×C4×C10912yes—
865C22×C4C22×C4×C10912yes—
866C22×C4C22×C4×C10912yes—
867C22×C4C22×C4×C10912yes—
868C22×C4C22×C4×C10912yes—
869C22×C4C2×D4×C10912yes—
870C22×C4C2×D4×C10912yes—
871C22×C4C2×D4×C10912yes—
872C22×C4C2×D4×C10912yes—
873C22×C4C2×D4×C10912yes—
874C22×C4C2×D4×C10912yes—
875C22×C4C2×D4×C10912yes—
876C22×C4C2×D4×C10912yes—
877C22×C4#41×C10912yes—
878C22×C4#41×C10912yes—
879C22×C4#41×C10912yes—
880C22×C4#41×C10912yes—
881C22×C4#41×C10912yes—
882C22×C4#41×C10912yes—
883C4⋊C4—28no—
884C4⋊C4—28no—
885C4⋊C4—44no—
886C4⋊C4C22⋊C4×C109116yescomplemented
887C22⋊C4—28no—
888C22⋊C4—28no—
889C22⋊C4—28no—
890C22⋊C4—28no—
891C22⋊C4—28no—
892C22⋊C4—44no—
893C22⋊C4—44no—
894C22⋊C4—44no—
895C22⋊C4—44no—
896C22⋊C4—44no—
897C22⋊C4—44no—
898C42—28no—
899C42—44no—
900C42—44no—
901C42—44no—
902C23—22no—
903C23—22no—
904C23—22no—
905C23—22no—
906C23—22no—
907C23—22no—
908C23—22no—
909C23—22no—
910C23—22no—
911C23—22no—
912C23—22no—
913C23—22no—
914C23—22no—
915C23—22no—
916C23—22no—
917C23—22no—
918C23—22no—
919C23—22no—
920C23—22no—
921C23—22no—
922C23—22no—
923C23—22no—
924C23—22no—
925C23—22no—
926C23—22no—
927C23—41no—
928C23—41no—
929C23—41no—
930C23—41no—
931C23—41no—
932C23—41no—
933C23—41no—
934C23—41no—
935C23—41no—
936C23—41no—
937C23—41no—
938C23—41no—
939C23—41no—
940C23—41no—
941C23—41no—
942C23—41no—
943C23—41no—
944C23—41no—
945C23—41no—
946C23—41no—
947C23—41no—
948C23—41no—
949C23—41no—
950C23—41no—
951C23—41no—
952C23—41no—
953C23—41no—
954C23—41no—
955C23—41no—
956C23—41no—
957C23—41no—
958C23—41no—
959C23—41no—
960C23—41no—
961C23—41no—
962C23—41no—
963C23—41no—
964C23—41no—
965C23—41no—
966C23—41no—
967C23—41no—
968C23—41no—
969C23—41no—
970C23—41no—
971C23C4×D4×C10914yes—
972C23C23×C4×C10911yescharacteristic
973C23C22×D4×C10911yescharacteristic
974C23C22×D4×C10911yescharacteristic
975C23C22×D4×C10911yescharacteristic
976C23C2×#41×C10911yescharacteristic
977C23C2×#41×C10911yescharacteristic
978C23C2×#41×C10911yescharacteristic
979C23C2×#41×C10911yescharacteristic
980C23C2×#41×C10911yescharacteristic
981C23C2×#41×C10911yescharacteristic
982C23C2×#41×C10911yescharacteristic
983C23H(5,𝔽2)×C10911yescharacteristic
984C23H(5,𝔽2)×C10911yescharacteristic
985C23H(5,𝔽2)×C10911yescharacteristic
986C232−1+4×C10911yescharacteristic
987D4—416no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—22no—
991C2×C4—22no—
992C2×C4—22no—
993C2×C4—22no—
994C2×C4—22no—
995C2×C4—22no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—22no—
999C2×C4—22no—
1000C2×C4—22no—
1001C2×C4—22no—
1002C2×C4—22no—
1003C2×C4—22no—
1004C2×C4—22no—
1005C2×C4—22no—
1006C2×C4—22no—
1007C2×C4—22no—
1008C2×C4—22no—
1009C2×C4—22no—
1010C2×C4—22no—
1011C2×C4—22no—
1012C2×C4—22no—
1013C2×C4—22no—
1014C2×C4—22no—
1015C2×C4—22no—
1016C2×C4—22no—
1017C2×C4—22no—
1018C2×C4—22no—
1019C2×C4—22no—
1020C2×C4—22no—
1021C2×C4—22no—
1022C2×C4—22no—
1023C2×C4—22no—
1024C2×C4—22no—
1025C2×C4—22no—
1026C2×C4—22no—
1027C2×C4—22no—
1028C2×C4—22no—
1029C2×C4—22no—
1030C2×C4—22no—
1031C2×C4—22no—
1032C2×C4—22no—
1033C2×C4—416no—
1034C2×C4—41no—
1035C2×C4—41no—
1036C2×C4—41no—
1037C2×C4—41no—
1038C2×C4—41no—
1039C2×C4—41no—
1040C2×C4—41no—
1041C2×C4—41no—
1042C2×C4—41no—
1043C2×C4—41no—
1044C2×C4—41no—
1045C2×C4—41no—
1046C2×C4—41no—
1047C2×C4—41no—
1048C2×C4—41no—
1049C2×C4—41no—
1050C2×C4—41no—
1051C2×C4—41no—
1052C2×C4—41no—
1053C2×C4—41no—
1054C2×C4—41no—
1055C2×C4—41no—
1056C2×C4—41no—
1057C2×C4—41no—
1058C2×C4—41no—
1059C2×C4—41no—
1060C2×C4—41no—
1061C2×C4—41no—
1062C2×C4—41no—
1063C2×C4—41no—
1064C2×C4—41no—
1065C2×C4—41no—
1066C2×C4—41no—
1067C2×C4—41no—
1068C2×C4—41no—
1069C2×C4—41no—
1070C2×C4—41no—
1071C2×C4—41no—
1072C2×C4—41no—
1073C2×C4—41no—
1074C2×C4—41no—
1075C2×C4—41no—
1076C2×C4C2×C22⋊C4×C10914yes—
1077C2×C4C2×C22⋊C4×C10914yes—
1078C2×C4C2×C22⋊C4×C10914yes—
1079C2×C4#123×C10914yescomplemented
1080C22—24no—
1081C22—24no—
1082C22—24no—
1083C22—42no—
1084C22—42no—
1085C22—42no—
1086C22—42no—
1087C22—42no—
1088C22—42no—
1089C22—42no—
1090C22—42no—
1091C22—42no—
1092C22—42no—
1093C22—42no—
1094C22—42no—
1095C22—42no—
1096C22—42no—
1097C22—42no—
1098C22—42no—
1099C22—42no—
1100C22—42no—
1101C22—42no—
1102C22—81no—
1103C22—81no—
1104C22—81no—
1105C22—81no—
1106C22—81no—
1107C22—81no—
1108C22—81no—
1109C22—81no—
1110C22C22×C22⋊C4×C10911yescharacteristic
1111C22C2×C4×D4×C10911yescharacteristic
1112C22C4×#41×C10911yescharacteristic
1113C22C4×#41×C10911yescharacteristic
1114C22C4×#41×C10911yescharacteristic
1115C22#518×C10911yescharacteristic
1116C22#520×C10911yescharacteristic
1117C22C2×#123×C10911yescharacteristic
1118C22#525×C10911yescharacteristic
1119C22#525×C10911yescharacteristic
1120C22#525×C10911yescharacteristic
1121C22#529×C10911yescharacteristic
1122C22#529×C10911yescharacteristic
1123C22#532×C10911yescharacteristic
1124C22#532×C10911yescharacteristic
1125C22#538×C10911yescharacteristic
1126C22#539×C10911yescharacteristic
1127C22#540×C10911yescharacteristic
1128C22#542×C10911yescharacteristic
1129C22D42×C10911yescharacteristic
1130C22D42×C10911yescharacteristic
1131C22#546×C10911yescharacteristic
1132C22#546×C10911yescharacteristic
1133C22#546×C10911yescharacteristic
1134C22#547×C10911yescharacteristic
1135C22#548×C10911yescharacteristic
1136C22#548×C10911yescharacteristic
1137C22#550×C10911yescharacteristic
1138C22#550×C10911yescharacteristic
1139C22#551×C10911yescharacteristic
1140C22#551×C10911yescharacteristic
1141C22#552×C10911yescharacteristic
1142C22#553×C10911yescharacteristic
1143C22#553×C10911yescharacteristic
1144C22#559×C10911yescharacteristic
1145C4—24no—
1146C4—24no—
1147C4—24no—
1148C4—24no—
1149C4—42no—
1150C4—42no—
1151C4—42no—
1152C4—42no—
1153C4—42no—
1154C4—42no—
1155C4—42no—
1156C4—81no—
1157C4—81no—
1158C2—44no—
1159C2—82no—
1160C2C109×#229711yescharacteristic
1161C2C4×#123×C10911yescharacteristic
1162C2C109×#233511yescharacteristic
1163C2D4×C22⋊C4×C10911yescharacteristic
1164C2C109×#234111yescharacteristic
1165C2C109×#235911yescharacteristic
1166C2C109×#237411yescharacteristic
1167C2C109×#244311yescharacteristic
1168C2C109×#244511yescharacteristic
1169C2C109×#245611yescharacteristic
1170C2C109×#245811yescharacteristic
1171C2C109×#246111yescharacteristic
1172C2C109×#247111yescharacteristic
1173C2C109×#255411yescharacteristic
1174C2C109×#255811yescharacteristic
subgroupG/H
center, socleC24×C109C24
commutatorC23C23×C4×C109
Frattini, cosocleC24C24×C109
prime radicalC23×D4×C109C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
3. C2×#387×C109C2semidirect
4. C2×C4×C4⋊C4×C109C2semidirect
5. C2×C4×C22⋊C4×C109C2semidirect
6. C109×#1441C2semidirect
7. C109×#1439C2semidirect
8. C109×#1439C2semidirect
10. C109×#1437C2semidirect
11. C109×#1437C2semidirect
12. C109×#1437C2semidirect
13. C109×#1437C2semidirect
14. C109×#1436C2semidirect
15. C109×C22⋊#95C2semidirect
20. C2×#123×C109C4semidirect
298. C4⋊C4×C109C22⋊C4semidirect
491. C2×C4×C109#123semidirect
570. #14095C109direct (N × H)
590. C2×#387C2×C109semidirect
591. C2×C4×C4⋊C4C2×C109semidirect
592. C2×C4×C22⋊C4C2×C109semidirect
593. #1441C2×C109semidirect
594. #1439C2×C109semidirect
595. #1439C2×C109semidirect
597. #1437C2×C109semidirect
598. #1437C2×C109semidirect
599. #1437C2×C109semidirect
600. #1437C2×C109semidirect
601. #1436C2×C109semidirect
602. C22⋊#95C2×C109semidirect
603. C109#14095direct (N × H)
608. C2×#123C4×C109semidirect
886. C4⋊C4C22⋊C4×C109semidirect
1079. C2×C4#123×C109semidirect

Maximal subgroups

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

subgroupindex
C22×#123×C1092
C2×#390×C1092
C2×#387×C1092
C2×C4×C4⋊C4×C1092
C2×C4×C22⋊C4×C1092
C109×#14412
C109×#14392
C109×#14382
C109×#14372
C109×#14362
C109×C22⋊#952
#14095109