Finite Group Databasebeta

← C109×#13873 #42131867

Subgroups — C109×#13873 #42131867

Order 27904.

3526 conjugacy classes of subgroups.

The subgroup lattice has 938 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C23×C22⋊C4×C109C211yesmaximal, characteristic
2C2×#388×C109C212yesmaximal, complemented
3C2×#380×C109C211yesmaximal, characteristic, complemented
4C2×#379×C109C211yesmaximal, characteristic
5C2×#379×C109C211yesmaximal, characteristic
6C2×C4×C22⋊C4×C109C211yesmaximal, characteristic, complemented
7C109×#1440C212yesmaximal, complemented
8C109×#1439C212yesmaximal, complemented
9C109×#1437C212yesmaximal, complemented
10C109×C22⋊#95C211yesmaximal, characteristic, complemented
11C109×C22⋊#95C211yesmaximal, characteristic, complemented
12C26×C109C2211yescharacteristic
13C24×C4×C109C2211yescharacteristic
14C24×C4×C109C2211yescharacteristic
15C22×C4⋊C4×C109C2212yescomplemented
16C22×C22⋊C4×C109—28no—
17C22×C22⋊C4×C109C418yescomplemented
18C22×C22⋊C4×C109C2211yescharacteristic
19C22×C22⋊C4×C109C2211yescharacteristic
20C22×C22⋊C4×C109C2212yes—
21C22×C22⋊C4×C109C2212yes—
22C22×C22⋊C4×C109C2212yes—
23C22×C22⋊C4×C109C2212yes—
24C22×C22⋊C4×C109C2211yescharacteristic
25C22×C22⋊C4×C109C2211yescharacteristic
26C22×C22⋊C4×C109C2211yescharacteristic
27C22×C22⋊C4×C109C2211yescharacteristic
28C22×C22⋊C4×C109C2211yescharacteristic
29C22×C22⋊C4×C109C2211yescharacteristic
30C22×C42×C109C2212yescomplemented
31#388×C109—28no—
32#380×C109—24no—
33#379×C109—24no—
34#379×C109—24no—
35C4×C22⋊C4×C109—24no—
36C2×#95×C109C2212yescomplemented
37C2×#95×C109C2212yescomplemented
38C2×#95×C109C2212yescomplemented
39C2×#95×C109C2212yescomplemented
40C2×#95×C109C2212yescomplemented
41C2×#95×C109C2212yescomplemented
42C25×C109—24no—
43C25×C109—24no—
44C25×C109—22no—
45C25×C109—22no—
46C25×C109—22no—
47C25×C109—22no—
48C25×C109—22no—
49C25×C109—22no—
50C25×C109—42no—
51C25×C109—42no—
52C25×C109C2×C414yes—
53C25×C109C2311yescharacteristic
54C25×C109C2311yescharacteristic
55C25×C109C2311yescharacteristic
56C23×C4×C109—22no—
57C23×C4×C109—22no—
58C23×C4×C109—22no—
59C23×C4×C109—22no—
60C23×C4×C109—24no—
61C23×C4×C109—24no—
62C23×C4×C109—42no—
63C23×C4×C109—42no—
64C23×C4×C109C2×C414yes—
65C23×C4×C109C2×C414yes—
66C23×C4×C109C2312yes—
67C23×C4×C109C2312yes—
68C23×C4×C109C2311yescharacteristic
69C23×C4×C109C2311yescharacteristic
70C23×C4×C109C2312yes—
71C23×C4×C109C2312yes—
72C23×C4×C109C2311yescharacteristic
73C23×C4×C109C2311yescharacteristic
74C2×C4⋊C4×C109—24no—
75C2×C4⋊C4×C109—24no—
76C2×C4⋊C4×C109—42no—
77C2×C22⋊C4×C109—24no—
78C2×C22⋊C4×C109—22no—
79C2×C22⋊C4×C109—22no—
80C2×C22⋊C4×C109—22no—
81C2×C22⋊C4×C109—22no—
82C2×C22⋊C4×C109—24no—
83C2×C22⋊C4×C109—24no—
84C2×C22⋊C4×C109—232no—
85C2×C22⋊C4×C109—22no—
86C2×C22⋊C4×C109—22no—
87C2×C22⋊C4×C109—22no—
88C2×C22⋊C4×C109—24no—
89C2×C22⋊C4×C109—24no—
90C2×C22⋊C4×C109—24no—
91C2×C22⋊C4×C109—24no—
92C2×C22⋊C4×C109—22no—
93C2×C22⋊C4×C109—22no—
94C2×C22⋊C4×C109—22no—
95C2×C22⋊C4×C109—24no—
96C2×C22⋊C4×C109—24no—
97C2×C22⋊C4×C109—24no—
98C2×C22⋊C4×C109—24no—
99C2×C22⋊C4×C109—42no—
100C2×C22⋊C4×C109—42no—
101C2×C22⋊C4×C109—42no—
102C2×C22⋊C4×C109—42no—
103C2×C22⋊C4×C109C2×C414yes—
104C2×C22⋊C4×C109C2×C414yes—
105C2×C22⋊C4×C109C2×C414yes—
106C2×C22⋊C4×C109C2×C414yes—
107C2×C22⋊C4×C109D414yes—
108C2×C22⋊C4×C109D414yes—
109C2×C22⋊C4×C109D418yes—
110C2×C42×C109—24no—
111C2×C42×C109—24no—
112C2×C42×C109—42no—
113#95×C109—24no—
114#95×C109—24no—
115#95×C109—24no—
116#95×C109—24no—
117#95×C109—42no—
118#95×C109—42no—
119C24×C109—22no—
120C24×C109—22no—
121C24×C109—22no—
122C24×C109—22no—
123C24×C109—216no—
124C24×C109—216no—
125C24×C109—28no—
126C24×C109—28no—
127C24×C109—28no—
128C24×C109—22no—
129C24×C109—21no—
130C24×C109—21no—
131C24×C109—21no—
132C24×C109—21no—
133C24×C109—21no—
134C24×C109—21no—
135C24×C109—22no—
136C24×C109—21no—
137C24×C109—21no—
138C24×C109—21no—
139C24×C109—21no—
140C24×C109—21no—
141C24×C109—21no—
142C24×C109—22no—
143C24×C109—22no—
144C24×C109—22no—
145C24×C109—22no—
146C24×C109—28no—
147C24×C109—28no—
148C24×C109—44no—
149C24×C109—44no—
150C24×C109—48no—
151C24×C109—48no—
152C24×C109—48no—
153C24×C109—48no—
154C24×C109—48no—
155C24×C109—48no—
156C24×C109—48no—
157C24×C109—48no—
158C24×C109—48no—
159C24×C109—48no—
160C24×C109—44no—
161C24×C109—44no—
162C24×C109—44no—
163C24×C109—44no—
164C24×C109C22×C412yes—
165C24×C109C22×C412yes—
166C24×C109C22×C412yes—
167C24×C109C2×D414yes—
168C24×C109C2×D412yes—
169C24×C109C2×D412yes—
170C24×C109#4114yes—
171C24×C109#4112yes—
172C24×C109#4112yes—
173C24×C109#4112yes—
174C24×C109#4112yes—
175C24×C109C2411yescharacteristic
176C22×C4×C109—21no—
177C22×C4×C109—21no—
178C22×C4×C109—21no—
179C22×C4×C109—21no—
180C22×C4×C109—22no—
181C22×C4×C109—22no—
182C22×C4×C109—28no—
183C22×C4×C109—28no—
184C22×C4×C109—21no—
185C22×C4×C109—21no—
186C22×C4×C109—22no—
187C22×C4×C109—22no—
188C22×C4×C109—22no—
189C22×C4×C109—22no—
190C22×C4×C109—22no—
191C22×C4×C109—22no—
192C22×C4×C109—22no—
193C22×C4×C109—22no—
194C22×C4×C109—22no—
195C22×C4×C109—22no—
196C22×C4×C109—21no—
197C22×C4×C109—21no—
198C22×C4×C109—22no—
199C22×C4×C109—22no—
200C22×C4×C109—22no—
201C22×C4×C109—22no—
202C22×C4×C109—22no—
203C22×C4×C109—22no—
204C22×C4×C109—28no—
205C22×C4×C109—28no—
206C22×C4×C109—22no—
207C22×C4×C109—22no—
208C22×C4×C109—22no—
209C22×C4×C109—22no—
210C22×C4×C109—22no—
211C22×C4×C109—22no—
212C22×C4×C109—22no—
213C22×C4×C109—22no—
214C22×C4×C109—22no—
215C22×C4×C109—22no—
216C22×C4×C109—22no—
217C22×C4×C109—22no—
218C22×C4×C109—22no—
219C22×C4×C109—22no—
220C22×C4×C109—44no—
221C22×C4×C109—44no—
222C22×C4×C109—48no—
223C22×C4×C109—48no—
224C22×C4×C109—48no—
225C22×C4×C109—48no—
226C22×C4×C109C22×C412yes—
227C22×C4×C109C22×C412yes—
228C22×C4×C109C22×C412yes—
229C22×C4×C109C22×C412yes—
230C22×C4×C109C2×D414yes—
231C22×C4×C109C2×D414yes—
232C22×C4×C109C2×D414yes—
233C22×C4×C109C2×D414yes—
234C4⋊C4×C109—48no—
235C22⋊C4×C109—28no—
236C22⋊C4×C109—28no—
237C22⋊C4×C109—28no—
238C22⋊C4×C109—28no—
239C22⋊C4×C109—28no—
240C22⋊C4×C109—48no—
241C22⋊C4×C109—48no—
242C22⋊C4×C109—48no—
243C22⋊C4×C109—48no—
244C22⋊C4×C109—44no—
245C22⋊C4×C109—44no—
246C22⋊C4×C109C22⋊C4116yescomplemented
247C42×C109—48no—
248C23×C109—22no—
249C23×C109—22no—
250C23×C109—22no—
251C23×C109—22no—
252C23×C109—24no—
253C23×C109—24no—
254C23×C109—24no—
255C23×C109—24no—
256C23×C109—24no—
257C23×C109—24no—
258C23×C109—24no—
259C23×C109—24no—
260C23×C109—24no—
261C23×C109—24no—
262C23×C109—24no—
263C23×C109—24no—
264C23×C109—232no—
265C23×C109—22no—
266C23×C109—22no—
267C23×C109—22no—
268C23×C109—22no—
269C23×C109—22no—
270C23×C109—22no—
271C23×C109—22no—
272C23×C109—22no—
273C23×C109—22no—
274C23×C109—22no—
275C23×C109—22no—
276C23×C109—22no—
277C23×C109—24no—
278C23×C109—24no—
279C23×C109—24no—
280C23×C109—24no—
281C23×C109—24no—
282C23×C109—24no—
283C23×C109—24no—
284C23×C109—24no—
285C23×C109—24no—
286C23×C109—24no—
287C23×C109—24no—
288C23×C109—24no—
289C23×C109—416no—
290C23×C109—416no—
291C23×C109—416no—
292C23×C109—416no—
293C23×C109—416no—
294C23×C109—432no—
295C23×C109—432no—
296C23×C109—432no—
297C23×C109—432no—
298C23×C109—41no—
299C23×C109—41no—
300C23×C109—41no—
301C23×C109—41no—
302C23×C109—41no—
303C23×C109—41no—
304C23×C109—41no—
305C23×C109—41no—
306C23×C109—42no—
307C23×C109—42no—
308C23×C109—42no—
309C23×C109—42no—
310C23×C109—42no—
311C23×C109—42no—
312C23×C109—42no—
313C23×C109—42no—
314C23×C109—42no—
315C23×C109—42no—
316C23×C109—42no—
317C23×C109—42no—
318C23×C109—416no—
319C23×C109C2×C22⋊C414yes—
320C23×C109#11714yes—
321C23×C109#11714yes—
322C23×C109C4×D414yes—
323C23×C109C4×D414yes—
324C23×C109#12114yes—
325C23×C109#12314yes—
326C23×C109#12414yes—
327C23×C109#12614yes—
328C23×C109C23×C411yescharacteristic
329C23×C109C22×D412yes—
330C23×C109C22×D411yescharacteristic
331C23×C109C22×D411yescharacteristic
332C23×C109C2×#4111yescharacteristic
333C23×C109C2×#4111yescharacteristic
334C23×C109C2×#4112yes—
335C23×C109C2×#4111yescharacteristic
336C23×C109C2×#4111yescharacteristic
337C23×C109H(5,𝔽2)12yes—
338C23×C109H(5,𝔽2)12yes—
339C2×C4×C109—22no—
340C2×C4×C109—22no—
341C2×C4×C109—22no—
342C2×C4×C109—22no—
343C2×C4×C109—24no—
344C2×C4×C109—24no—
345C2×C4×C109—24no—
346C2×C4×C109—24no—
347C2×C4×C109—22no—
348C2×C4×C109—22no—
349C2×C4×C109—22no—
350C2×C4×C109—22no—
351C2×C4×C109—22no—
352C2×C4×C109—22no—
353C2×C4×C109—24no—
354C2×C4×C109—24no—
355C2×C4×C109—24no—
356C2×C4×C109—24no—
357C2×C4×C109—24no—
358C2×C4×C109—24no—
359C2×C4×C109—416no—
360C2×C4×C109—416no—
361C2×C4×C109—42no—
362C2×C4×C109—42no—
363C2×C4×C109—42no—
364C2×C4×C109—42no—
365C2×C4×C109—42no—
366C2×C4×C109—42no—
367C2×C4×C109—42no—
368C2×C4×C109—42no—
369C2×C4×C109—42no—
370C2×C4×C109—42no—
371C2×C4×C109—42no—
372C2×C4×C109—42no—
373C2×C4×C109—42no—
374C2×C4×C109—42no—
375C2×C4×C109—42no—
376C2×C4×C109—42no—
377C2×C4×C109—42no—
378C2×C4×C109—42no—
379C2×C4×C109—42no—
380C2×C4×C109—42no—
381C2×C4×C109—42no—
382C2×C4×C109—42no—
383C2×C4×C109—42no—
384C2×C4×C109—42no—
385C2×C4×C109—42no—
386C2×C4×C109—42no—
387C2×C4×C109C2×C22⋊C414yes—
388C2×C4×C109C2×C22⋊C414yes—
389C22×C109—24no—
390C22×C109—24no—
391C22×C109—24no—
392C22×C109—24no—
393C22×C109—24no—
394C22×C109—28no—
395C22×C109—28no—
396C22×C109—28no—
397C22×C109—28no—
398C22×C109—24no—
399C22×C109—24no—
400C22×C109—24no—
401C22×C109—24no—
402C22×C109—24no—
403C22×C109—24no—
404C22×C109—24no—
405C22×C109—464no—
406C22×C109—42no—
407C22×C109—42no—
408C22×C109—42no—
409C22×C109—42no—
410C22×C109—42no—
411C22×C109—42no—
412C22×C109—44no—
413C22×C109—44no—
414C22×C109—44no—
415C22×C109—44no—
416C22×C109—44no—
417C22×C109—44no—
418C22×C109—44no—
419C22×C109—44no—
420C22×C109—42no—
421C22×C109—42no—
422C22×C109#38818yescomplemented
423C22×C109C22×C22⋊C411yescharacteristic
424C22×C109C2×#11711yescharacteristic
425C22×C109C2×#11711yescharacteristic
426C22×C109C2×C4×D411yescharacteristic
427C22×C109C2×C4×D411yescharacteristic
428C22×C109#51811yescharacteristic
429C22×C109#51811yescharacteristic
430C22×C109C2×#12111yescharacteristic
431C22×C109C2×#12311yescharacteristic
432C22×C109#52512yes—
433C22×C109#52512yes—
434C22×C109C2×#12411yescharacteristic
435C22×C109C2×#12611yescharacteristic
436C22×C109#53812yes—
437C22×C109#53812yes—
438C22×C109D4212yes—
439C22×C109D4212yes—
440C22×C109#54612yes—
441C22×C109#54612yes—
442C22×C109#54612yes—
443C22×C109#54612yes—
444C22×C109#55112yes—
445C22×C109#55112yes—
446C4×C109—24no—
447C4×C109—24no—
448C4×C109—42no—
449C4×C109—42no—
450C4×C109—44no—
451C4×C109—44no—
452C4×C109—82no—
453C4×C109—82no—
454#13873C10911yesmaximal, characteristic, direct product factor, Sylow
455C2×C109—28no—
456C2×C109—44no—
457C2×C109—44no—
458C2×C109#228011yescharacteristic
459C2×C109C2×#38811yescharacteristic
460C2×C109#231211yescharacteristic
461C2×C109D4×C22⋊C411yescharacteristic
462C2×C109D4×C22⋊C411yescharacteristic
463C2×C109#234211yescharacteristic
464C2×C109#234211yescharacteristic
465C2×C109#241812yes—
466C2×C109#242412yes—
467C2×C109#247212yes—
468C2×C109#248012yes—
469C23×C22⋊C4C2×C10911yescharacteristic
470C2×#388C2×C10912yescomplemented
471C2×#380C2×C10911yescharacteristic, complemented
472C2×#379C2×C10911yescharacteristic
473C2×#379C2×C10911yescharacteristic
474C2×C4×C22⋊C4C2×C10911yescharacteristic, complemented
475#1440C2×C10912yescomplemented
476#1439C2×C10912yescomplemented
477#1437C2×C10912yescomplemented
478C22⋊#95C2×C10911yescharacteristic, complemented
479C22⋊#95C2×C10911yescharacteristic, complemented
480C109#1387311yescharacteristic, direct product factor, Sylow
481C26C22×C10911yescharacteristic
482C24×C4C22×C10911yescharacteristic
483C24×C4C22×C10911yescharacteristic
484C22×C4⋊C4C22×C10912yescomplemented
485C22×C22⋊C4—28no—
486C22×C22⋊C4C4×C10918yescomplemented
487C22×C22⋊C4C22×C10911yescharacteristic
488C22×C22⋊C4C22×C10911yescharacteristic
489C22×C22⋊C4C22×C10912yes—
490C22×C22⋊C4C22×C10912yes—
491C22×C22⋊C4C22×C10912yes—
492C22×C22⋊C4C22×C10912yes—
493C22×C22⋊C4C22×C10911yescharacteristic
494C22×C22⋊C4C22×C10911yescharacteristic
495C22×C22⋊C4C22×C10911yescharacteristic
496C22×C22⋊C4C22×C10911yescharacteristic
497C22×C22⋊C4C22×C10911yescharacteristic
498C22×C22⋊C4C22×C10911yescharacteristic
499C22×C42C22×C10912yescomplemented
500#388—28no—
501#380—24no—
502#379—24no—
503#379—24no—
504C4×C22⋊C4—24no—
505C2×#95C22×C10912yescomplemented
506C2×#95C22×C10912yescomplemented
507C2×#95C22×C10912yescomplemented
508C2×#95C22×C10912yescomplemented
509C2×#95C22×C10912yescomplemented
510C2×#95C22×C10912yescomplemented
511C25—24no—
512C25—24no—
513C25—22no—
514C25—22no—
515C25—22no—
516C25—22no—
517C25—22no—
518C25—22no—
519C25—42no—
520C25—42no—
521C25C2×C4×C10914yes—
522C25C23×C10911yescharacteristic
523C25C23×C10911yescharacteristic
524C25C23×C10911yescharacteristic
525C23×C4—22no—
526C23×C4—22no—
527C23×C4—22no—
528C23×C4—22no—
529C23×C4—24no—
530C23×C4—24no—
531C23×C4—42no—
532C23×C4—42no—
533C23×C4C2×C4×C10914yes—
534C23×C4C2×C4×C10914yes—
535C23×C4C23×C10912yes—
536C23×C4C23×C10912yes—
537C23×C4C23×C10911yescharacteristic
538C23×C4C23×C10911yescharacteristic
539C23×C4C23×C10912yes—
540C23×C4C23×C10912yes—
541C23×C4C23×C10911yescharacteristic
542C23×C4C23×C10911yescharacteristic
543C2×C4⋊C4—24no—
544C2×C4⋊C4—24no—
545C2×C4⋊C4—42no—
546C2×C22⋊C4—24no—
547C2×C22⋊C4—22no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—24no—
553C2×C22⋊C4—232no—
554C2×C22⋊C4—22no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—24no—
558C2×C22⋊C4—24no—
559C2×C22⋊C4—24no—
560C2×C22⋊C4—24no—
561C2×C22⋊C4—22no—
562C2×C22⋊C4—22no—
563C2×C22⋊C4—22no—
564C2×C22⋊C4—24no—
565C2×C22⋊C4—24no—
566C2×C22⋊C4—24no—
567C2×C22⋊C4—24no—
568C2×C22⋊C4—42no—
569C2×C22⋊C4—42no—
570C2×C22⋊C4—42no—
571C2×C22⋊C4—42no—
572C2×C22⋊C4C2×C4×C10914yes—
573C2×C22⋊C4C2×C4×C10914yes—
574C2×C22⋊C4C2×C4×C10914yes—
575C2×C22⋊C4C2×C4×C10914yes—
576C2×C22⋊C4D4×C10914yes—
577C2×C22⋊C4D4×C10914yes—
578C2×C22⋊C4D4×C10918yes—
579C2×C42—24no—
580C2×C42—24no—
581C2×C42—42no—
582#95—24no—
583#95—24no—
584#95—24no—
585#95—24no—
586#95—42no—
587#95—42no—
588C24—22no—
589C24—22no—
590C24—22no—
591C24—22no—
592C24—216no—
593C24—216no—
594C24—28no—
595C24—28no—
596C24—28no—
597C24—22no—
598C24—21no—
599C24—21no—
600C24—21no—
601C24—21no—
602C24—21no—
603C24—21no—
604C24—22no—
605C24—21no—
606C24—21no—
607C24—21no—
608C24—21no—
609C24—21no—
610C24—21no—
611C24—22no—
612C24—22no—
613C24—22no—
614C24—22no—
615C24—28no—
616C24—28no—
617C24—44no—
618C24—44no—
619C24—48no—
620C24—48no—
621C24—48no—
622C24—48no—
623C24—48no—
624C24—48no—
625C24—48no—
626C24—48no—
627C24—48no—
628C24—48no—
629C24—44no—
630C24—44no—
631C24—44no—
632C24—44no—
633C24C22×C4×C10912yes—
634C24C22×C4×C10912yes—
635C24C22×C4×C10912yes—
636C24C2×D4×C10914yes—
637C24C2×D4×C10912yes—
638C24C2×D4×C10912yes—
639C24#41×C10914yes—
640C24#41×C10912yes—
641C24#41×C10912yes—
642C24#41×C10912yes—
643C24#41×C10912yes—
644C24C24×C10911yescharacteristic
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—22no—
650C22×C4—22no—
651C22×C4—28no—
652C22×C4—28no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—22no—
656C22×C4—22no—
657C22×C4—22no—
658C22×C4—22no—
659C22×C4—22no—
660C22×C4—22no—
661C22×C4—22no—
662C22×C4—22no—
663C22×C4—22no—
664C22×C4—22no—
665C22×C4—21no—
666C22×C4—21no—
667C22×C4—22no—
668C22×C4—22no—
669C22×C4—22no—
670C22×C4—22no—
671C22×C4—22no—
672C22×C4—22no—
673C22×C4—28no—
674C22×C4—28no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—22no—
678C22×C4—22no—
679C22×C4—22no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—22no—
683C22×C4—22no—
684C22×C4—22no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—44no—
690C22×C4—44no—
691C22×C4—48no—
692C22×C4—48no—
693C22×C4—48no—
694C22×C4—48no—
695C22×C4C22×C4×C10912yes—
696C22×C4C22×C4×C10912yes—
697C22×C4C22×C4×C10912yes—
698C22×C4C22×C4×C10912yes—
699C22×C4C2×D4×C10914yes—
700C22×C4C2×D4×C10914yes—
701C22×C4C2×D4×C10914yes—
702C22×C4C2×D4×C10914yes—
703C4⋊C4—48no—
704C22⋊C4—28no—
705C22⋊C4—28no—
706C22⋊C4—28no—
707C22⋊C4—28no—
708C22⋊C4—28no—
709C22⋊C4—48no—
710C22⋊C4—48no—
711C22⋊C4—48no—
712C22⋊C4—48no—
713C22⋊C4—44no—
714C22⋊C4—44no—
715C22⋊C4C22⋊C4×C109116yescomplemented
716C42—48no—
717C23—22no—
718C23—22no—
719C23—22no—
720C23—22no—
721C23—24no—
722C23—24no—
723C23—24no—
724C23—24no—
725C23—24no—
726C23—24no—
727C23—24no—
728C23—24no—
729C23—24no—
730C23—24no—
731C23—24no—
732C23—24no—
733C23—232no—
734C23—22no—
735C23—22no—
736C23—22no—
737C23—22no—
738C23—22no—
739C23—22no—
740C23—22no—
741C23—22no—
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—24no—
747C23—24no—
748C23—24no—
749C23—24no—
750C23—24no—
751C23—24no—
752C23—24no—
753C23—24no—
754C23—24no—
755C23—24no—
756C23—24no—
757C23—24no—
758C23—416no—
759C23—416no—
760C23—416no—
761C23—416no—
762C23—432no—
763C23—432no—
764C23—416no—
765C23—432no—
766C23—432no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—42no—
776C23—42no—
777C23—42no—
778C23—42no—
779C23—42no—
780C23—42no—
781C23—42no—
782C23—42no—
783C23—42no—
784C23—42no—
785C23—42no—
786C23—42no—
787C23—416no—
788C23C2×C22⋊C4×C10914yes—
789C23#117×C10914yes—
790C23#117×C10914yes—
791C23C4×D4×C10914yes—
792C23C4×D4×C10914yes—
793C23#121×C10914yes—
794C23#123×C10914yes—
795C23#124×C10914yes—
796C23#126×C10914yes—
797C23C23×C4×C10911yescharacteristic
798C23C22×D4×C10912yes—
799C23C22×D4×C10911yescharacteristic
800C23C22×D4×C10911yescharacteristic
801C23C2×#41×C10911yescharacteristic
802C23C2×#41×C10911yescharacteristic
803C23C2×#41×C10912yes—
804C23C2×#41×C10911yescharacteristic
805C23C2×#41×C10911yescharacteristic
806C23H(5,𝔽2)×C10912yes—
807C23H(5,𝔽2)×C10912yes—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—24no—
813C2×C4—24no—
814C2×C4—24no—
815C2×C4—24no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—24no—
823C2×C4—24no—
824C2×C4—24no—
825C2×C4—24no—
826C2×C4—24no—
827C2×C4—24no—
828C2×C4—416no—
829C2×C4—416no—
830C2×C4—42no—
831C2×C4—42no—
832C2×C4—42no—
833C2×C4—42no—
834C2×C4—42no—
835C2×C4—42no—
836C2×C4—42no—
837C2×C4—42no—
838C2×C4—42no—
839C2×C4—42no—
840C2×C4—42no—
841C2×C4—42no—
842C2×C4—42no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—42no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—42no—
856C2×C4C2×C22⋊C4×C10914yes—
857C2×C4C2×C22⋊C4×C10914yes—
858C22—28no—
859C22—28no—
860C22—24no—
861C22—24no—
862C22—24no—
863C22—24no—
864C22—24no—
865C22—24no—
866C22—28no—
867C22—28no—
868C22—24no—
869C22—24no—
870C22—24no—
871C22—24no—
872C22—24no—
873C22—24no—
874C22—464no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—44no—
879C22—42no—
880C22—42no—
881C22—42no—
882C22—42no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—44no—
888C22—44no—
889C22—44no—
890C22—44no—
891C22#388×C10918yescomplemented
892C22C22×C22⋊C4×C10911yescharacteristic
893C22C2×#117×C10911yescharacteristic
894C22C2×#117×C10911yescharacteristic
895C22C2×C4×D4×C10911yescharacteristic
896C22C2×C4×D4×C10911yescharacteristic
897C22#518×C10911yescharacteristic
898C22#518×C10911yescharacteristic
899C22C2×#121×C10911yescharacteristic
900C22C2×#123×C10911yescharacteristic
901C22#525×C10912yes—
902C22#525×C10912yes—
903C22C2×#124×C10911yescharacteristic
904C22C2×#126×C10911yescharacteristic
905C22#538×C10912yes—
906C22#538×C10912yes—
907C22D42×C10912yes—
908C22D42×C10912yes—
909C22#546×C10912yes—
910C22#546×C10912yes—
911C22#546×C10912yes—
912C22#546×C10912yes—
913C22#551×C10912yes—
914C22#551×C10912yes—
915C4—24no—
916C4—24no—
917C4—42no—
918C4—42no—
919C4—44no—
920C4—44no—
921C4—82no—
922C4—82no—
923C2—28no—
924C2—44no—
925C2—44no—
926C2C109×#228011yescharacteristic
927C2C2×#388×C10911yescharacteristic
928C2C109×#231211yescharacteristic
929C2D4×C22⋊C4×C10911yescharacteristic
930C2D4×C22⋊C4×C10911yescharacteristic
931C2C109×#234211yescharacteristic
932C2C109×#234211yescharacteristic
933C2C109×#241812yes—
934C2C109×#242412yes—
935C2C109×#247212yes—
936C2C109×#248012yes—
subgroupG/H
center, socleC24×C109C24
commutatorC23C23×C4×C109
Frattini, cosocleC24C24×C109
prime radicalC26×C109C22
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C24×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#388×C109C2semidirect
3. C2×#380×C109C2semidirect
6. C2×C4×C22⋊C4×C109C2semidirect
7. C109×#1440C2semidirect
8. C109×#1439C2semidirect
9. C109×#1437C2semidirect
10. C109×C22⋊#95C2semidirect
11. C109×C22⋊#95C2semidirect
15. C22×C4⋊C4×C109C22semidirect
17. C22×C22⋊C4×C109C4semidirect
30. C22×C42×C109C22semidirect
36. C2×#95×C109C22semidirect
37. C2×#95×C109C22semidirect
38. C2×#95×C109C22semidirect
39. C2×#95×C109C22semidirect
40. C2×#95×C109C22semidirect
41. C2×#95×C109C22semidirect
246. C22⋊C4×C109C22⋊C4semidirect
422. C22×C109#388semidirect
454. #13873C109direct (N × H)
470. C2×#388C2×C109semidirect
471. C2×#380C2×C109semidirect
474. C2×C4×C22⋊C4C2×C109semidirect
475. #1440C2×C109semidirect
476. #1439C2×C109semidirect
477. #1437C2×C109semidirect
478. C22⋊#95C2×C109semidirect
479. C22⋊#95C2×C109semidirect
480. C109#13873direct (N × H)
484. C22×C4⋊C4C22×C109semidirect
486. C22×C22⋊C4C4×C109semidirect
499. C22×C42C22×C109semidirect
505. C2×#95C22×C109semidirect
506. C2×#95C22×C109semidirect
507. C2×#95C22×C109semidirect
508. C2×#95C22×C109semidirect
509. C2×#95C22×C109semidirect
510. C2×#95C22×C109semidirect
715. C22⋊C4C22⋊C4×C109semidirect
891. C22#388×C109semidirect

Maximal subgroups

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

subgroupindex
C23×C22⋊C4×C1092
C2×#388×C1092
C2×#380×C1092
C2×#379×C1092
C2×C4×C22⋊C4×C1092
C109×#14402
C109×#14392
C109×#14372
C109×C22⋊#952
#13873109