Finite Group Databasebeta

← C109×#24396 #42142390

Subgroups — C109×#24396 #42142390

Order 27904.

1444 conjugacy classes of subgroups.

The subgroup lattice has 914 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#536×C109C211yesmaximal, characteristic, complemented
2C2×#468×C109C211yesmaximal, characteristic, complemented
3C2×#465×C109C211yesmaximal, characteristic, complemented
4C2×#448×C109C211yesmaximal, characteristic, complemented
5C2×#408×C109C211yesmaximal, characteristic, complemented
6C109×#2615C211yesmaximal, characteristic
7C109×#2036C211yesmaximal, characteristic, complemented
8C109×#2035C211yesmaximal, characteristic, complemented
9C109×#2000C211yesmaximal, characteristic, complemented
10C109×#2000C211yesmaximal, characteristic, complemented
11C109×#1894C211yesmaximal, characteristic, complemented
12C109×#1892C211yesmaximal, characteristic, complemented
13C109×#1875C211yesmaximal, characteristic, complemented
14C109×#1854C211yesmaximal, characteristic, complemented
15C109×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C23×Q8×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C22×SD16×C109C2211yescharacteristic
20C22×M16×C109C2211yescharacteristic
21C23×C8×C109C2211yescharacteristic
22#536×C109—24no—
23#536×C109—24no—
24C2×C4⋊Q8×C109—21no—
25C2×#124×C109—21no—
26C2×#123×C109—21no—
27C2×#123×C109—21no—
28C2×C22⋊Q8×C109C2211yescharacteristic
29C2×C22⋊Q8×C109C2211yescharacteristic
30C2×C22⋊Q8×C109C2211yescharacteristic
31C2×C22⋊Q8×C109C2211yescharacteristic
32C2×#121×C109C2211yescharacteristic
33C2×#121×C109C2211yescharacteristic
34C2×#121×C109C2211yescharacteristic
35C2×#117×C109C2211yescharacteristic
36#468×C109—24no—
37#465×C109—24no—
38#448×C109—24no—
39C2×#107×C109C2211yescharacteristic
40C2×#106×C109C2211yescharacteristic
41C2×#103×C109C2211yescharacteristic
42C2×#103×C109C2211yescharacteristic
43C2×#103×C109C2211yescharacteristic
44C2×#103×C109C2211yescharacteristic
45C2×#103×C109C2211yescharacteristic
46C2×#103×C109C2211yescharacteristic
47C2×#102×C109C2211yescharacteristic
48C2×#102×C109C2211yescharacteristic
49#408×C109—24no—
50C2×C22⋊C8×C109C2211yescharacteristic
51C2×C22⋊C8×C109C2211yescharacteristic
52C2×C22⋊C8×C109C2211yescharacteristic
53C2×C22⋊C8×C109C2211yescharacteristic
54#393×C109—21no—
55#392×C109—21no—
56#392×C109—21no—
57#392×C109—21no—
58#380×C109C2211yescharacteristic
59#380×C109C2211yescharacteristic
60#380×C109C2211yescharacteristic
61#340×C109C2211yescharacteristic
62#340×C109C2211yescharacteristic
63#340×C109C2211yescharacteristic
64#340×C109C2211yescharacteristic
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—22no—
69C2×#41×C109—41no—
70C2×#41×C109—41no—
71C22×Q8×C109—22no—
72C22×Q8×C109—22no—
73C22×Q8×C109—21no—
74C22×Q8×C109—22no—
75C22×Q8×C109—22no—
76C22×Q8×C109—41no—
77C22×Q8×C109—41no—
78C22×Q8×C109D411yescharacteristic
79C22×Q8×C109C2311yescharacteristic
80C22×Q8×C109C2311yescharacteristic
81C22×D4×C109—21no—
82C22×D4×C109—21no—
83C22×D4×C109—21no—
84C22×D4×C109D411yescharacteristic
85C22×D4×C109D411yescharacteristic
86C22×D4×C109D411yescharacteristic
87C22×D4×C109C2311yescharacteristic
88C23×C4×C109—21no—
89C23×C4×C109C2311yescharacteristic
90C23×C4×C109C2311yescharacteristic
91C23×C4×C109C2311yescharacteristic
92C2×SD16×C109—22no—
93C2×SD16×C109—22no—
94C2×SD16×C109—22no—
95C2×SD16×C109—22no—
96C2×SD16×C109—41no—
97C2×SD16×C109—41no—
98C2×M16×C109—22no—
99C2×M16×C109—22no—
100C2×M16×C109—41no—
101C22×C8×C109—22no—
102C22×C8×C109—22no—
103C22×C8×C109—41no—
104C22×C8×C109C2311yescharacteristic
105C22×C8×C109C2311yescharacteristic
106C22×C8×C109C2311yescharacteristic
107C22×C8×C109C2311yescharacteristic
108C4⋊Q8×C109—28no—
109#124×C109—28no—
110#123×C109—28no—
111#123×C109—28no—
112C22⋊Q8×C109—22no—
113C22⋊Q8×C109—22no—
114C22⋊Q8×C109—22no—
115C22⋊Q8×C109—22no—
116C22⋊Q8×C109—22no—
117C22⋊Q8×C109—22no—
118C22⋊Q8×C109D414yescomplemented
119C22⋊Q8×C109D414yescomplemented
120#121×C109—22no—
121#121×C109—22no—
122#121×C109—22no—
123#121×C109—22no—
124#121×C109—41no—
125#121×C109—41no—
126#117×C109—22no—
127#117×C109—22no—
128C2×C4⋊C4×C109—21no—
129C2×C4⋊C4×C109—21no—
130C2×C4⋊C4×C109—21no—
131C2×C4⋊C4×C109—21no—
132C2×C4⋊C4×C109C2311yescharacteristic
133C2×C4⋊C4×C109C2311yescharacteristic
134C2×C4⋊C4×C109C2311yescharacteristic
135C2×C4⋊C4×C109C2311yescharacteristic
136C2×C4⋊C4×C109C2311yescharacteristic
137C2×C22⋊C4×C109—21no—
138C2×C22⋊C4×C109—21no—
139C2×C22⋊C4×C109—21no—
140C2×C22⋊C4×C109—21no—
141C2×C22⋊C4×C109—21no—
142C2×C22⋊C4×C109—21no—
143C2×C22⋊C4×C109—21no—
144C2×C22⋊C4×C109—21no—
145C2×C22⋊C4×C109—21no—
146C2×C22⋊C4×C109—21no—
147C2×C22⋊C4×C109—21no—
148C2×C42×C109—21no—
149#107×C109—22no—
150#106×C109—22no—
151#103×C109—22no—
152#103×C109—22no—
153#103×C109—22no—
154#103×C109—22no—
155#103×C109—41no—
156#103×C109—41no—
157#102×C109—22no—
158#102×C109—22no—
159C22⋊C8×C109—22no—
160C22⋊C8×C109—22no—
161C22⋊C8×C109—22no—
162C22⋊C8×C109D414yescomplemented
163#95×C109—21no—
164#95×C109—21no—
165#95×C109—21no—
166C24×C109—21no—
167C24×C109C2×D411yescharacteristic
168C24×C109C2×D411yescharacteristic
169C24×C109C2×D411yescharacteristic
170#41×C109—44no—
171#41×C109—44no—
172#41×C109—44no—
173#41×C109—44no—
174C2×Q8×C109—24no—
175C2×Q8×C109—22no—
176C2×Q8×C109—22no—
177C2×Q8×C109—21no—
178C2×Q8×C109—21no—
179C2×Q8×C109—21no—
180C2×Q8×C109—21no—
181C2×Q8×C109—21no—
182C2×Q8×C109—21no—
183C2×Q8×C109—21no—
184C2×Q8×C109—21no—
185C2×Q8×C109—21no—
186C2×Q8×C109—21no—
187C2×Q8×C109—41no—
188C2×Q8×C109—44no—
189C2×Q8×C109—44no—
190C2×Q8×C109—44no—
191C2×Q8×C109—44no—
192C2×Q8×C109—42no—
193C2×Q8×C109—42no—
194C2×Q8×C109C2×D412yes—
195C2×Q8×C109C2×D412yes—
196C2×D4×C109—22no—
197C2×D4×C109—22no—
198C2×D4×C109—22no—
199C2×D4×C109—22no—
200C2×D4×C109—22no—
201C2×D4×C109—22no—
202C2×D4×C109—21no—
203C2×D4×C109—21no—
204C2×D4×C109—21no—
205C2×D4×C109—21no—
206C2×D4×C109—21no—
207C2×D4×C109—21no—
208C2×D4×C109—41no—
209C2×D4×C109—41no—
210C2×D4×C109—41no—
211C2×D4×C109—42no—
212C2×D4×C109—42no—
213C2×D4×C109—42no—
214C2×D4×C109—81no—
215C2×D4×C109—81no—
216C2×D4×C109—81no—
217C2×D4×C109—81no—
218C2×D4×C109—81no—
219C2×D4×C109—81no—
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—24no—
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—42no—
243C22×C4×C109—42no—
244C22×C4×C109C2×D411yescharacteristic
245C22×C4×C109C2×D411yescharacteristic
246C22×C4×C109C2×D412yes—
247C22×C4×C109C2×D412yes—
248C22×C4×C109C2×D411yescharacteristic
249C22×C4×C109C2×D412yes—
250C22×C4×C109#4112yes—
251C22×C4×C109C2411yescharacteristic
252SD16×C109—44no—
253SD16×C109—44no—
254M16×C109—44no—
255C2×C8×C109—21no—
256C2×C8×C109—21no—
257C2×C8×C109—21no—
258C2×C8×C109—21no—
259C2×C8×C109—21no—
260C2×C8×C109—21no—
261C2×C8×C109—21no—
262C2×C8×C109—21no—
263C2×C8×C109—21no—
264C2×C8×C109—21no—
265C2×C8×C109—44no—
266C2×C8×C109C2×D412yes—
267C2×C8×C109C2×D412yes—
268C4⋊C4×C109—24no—
269C4⋊C4×C109—24no—
270C4⋊C4×C109—24no—
271C4⋊C4×C109—24no—
272C4⋊C4×C109—21no—
273C4⋊C4×C109—21no—
274C4⋊C4×C109—21no—
275C4⋊C4×C109—21no—
276C4⋊C4×C109—21no—
277C4⋊C4×C109—21no—
278C4⋊C4×C109—21no—
279C4⋊C4×C109—21no—
280C4⋊C4×C109C2×D412yes—
281C4⋊C4×C109C2×D412yes—
282C22⋊C4×C109—24no—
283C22⋊C4×C109—24no—
284C22⋊C4×C109—24no—
285C22⋊C4×C109—24no—
286C22⋊C4×C109—24no—
287C22⋊C4×C109—42no—
288C22⋊C4×C109—42no—
289C22⋊C4×C109—42no—
290C22⋊C4×C109—81no—
291C22⋊C4×C109—81no—
292C22⋊C4×C109—81no—
293C42×C109—24no—
294C23×C109—21no—
295C23×C109—21no—
296C23×C109—21no—
297C23×C109—21no—
298C23×C109—21no—
299C23×C109—21no—
300C23×C109—21no—
301C23×C109—21no—
302C23×C109—21no—
303C23×C109—21no—
304C23×C109—21no—
305C23×C109—21no—
306C23×C109—21no—
307C23×C109—21no—
308C23×C109—21no—
309C23×C109—21no—
310C23×C109—21no—
311C23×C109—21no—
312C23×C109—21no—
313C23×C109—41no—
314C23×C109—41no—
315C23×C109—41no—
316C23×C109—41no—
317C23×C109—41no—
318C23×C109—41no—
319C23×C109—41no—
320C23×C109#12012yes—
321C23×C109#12112yes—
322C23×C109C22×D411yescharacteristic
323Q8×C109—22no—
324Q8×C109—22no—
325Q8×C109—22no—
326Q8×C109—22no—
327Q8×C109—44no—
328Q8×C109—48no—
329Q8×C109—41no—
330Q8×C109—41no—
331Q8×C109—41no—
332Q8×C109—41no—
333D4×C109—44no—
334D4×C109—44no—
335D4×C109—44no—
336D4×C109—41no—
337D4×C109—41no—
338D4×C109—41no—
339D4×C109—41no—
340D4×C109—84no—
341D4×C109—84no—
342D4×C109—84no—
343C2×C4×C109—21no—
344C2×C4×C109—21no—
345C2×C4×C109—21no—
346C2×C4×C109—21no—
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—22no—
354C2×C4×C109—22no—
355C2×C4×C109—22no—
356C2×C4×C109—22no—
357C2×C4×C109—22no—
358C2×C4×C109—22no—
359C2×C4×C109—21no—
360C2×C4×C109—21no—
361C2×C4×C109—21no—
362C2×C4×C109—48no—
363C2×C4×C109—41no—
364C2×C4×C109—41no—
365C2×C4×C109—41no—
366C2×C4×C109—41no—
367C2×C4×C109—41no—
368C2×C4×C109—41no—
369C2×C4×C109—41no—
370C2×C4×C109—41no—
371C2×C4×C109—41no—
372C2×C4×C109—41no—
373C2×C4×C109—41no—
374C2×C4×C109—41no—
375C2×C4×C109—41no—
376C2×C4×C109—41no—
377C2×C4×C109—41no—
378C2×C4×C109—41no—
379C2×C4×C109—41no—
380C2×C4×C109—41no—
381C2×C4×C109—41no—
382C2×C4×C109—41no—
383C2×C4×C109—41no—
384C2×C4×C109#12012yes—
385C2×C4×C109#12112yes—
386C2×C4×C109C22×D411yescharacteristic
387C2×C4×C109C22×D411yescharacteristic
388C2×C4×C109C22×D411yescharacteristic
389C2×C4×C109C2×#4111yescharacteristic
390C2×C4×C109H(5,𝔽2)11yescharacteristic
391C2×C4×C109H(5,𝔽2)11yescharacteristic
392C8×C109—22no—
393C8×C109—22no—
394C8×C109—41no—
395C8×C109—41no—
396C22×C109—22no—
397C22×C109—22no—
398C22×C109—22no—
399C22×C109—22no—
400C22×C109—22no—
401C22×C109—22no—
402C22×C109—41no—
403C22×C109—41no—
404C22×C109—41no—
405C22×C109—41no—
406C22×C109—41no—
407C22×C109—41no—
408C22×C109—41no—
409C22×C109—41no—
410C22×C109—41no—
411C22×C109—41no—
412C22×C109—41no—
413C22×C109—41no—
414C22×C109—41no—
415C22×C109—41no—
416C22×C109—41no—
417C22×C109—81no—
418C22×C109—81no—
419C22×C109—81no—
420C22×C109—81no—
421C22×C109—81no—
422C22×C109—81no—
423C22×C109—81no—
424C22×C109C2×#12011yescharacteristic
425C22×C109C2×#12111yescharacteristic
426C22×C109#53411yescharacteristic
427C22×C109#57711yescharacteristic
428C22×C109#57711yescharacteristic
429C22×C109#57711yescharacteristic
430C22×C109#57811yescharacteristic
431C4×C109—22no—
432C4×C109—22no—
433C4×C109—41no—
434C4×C109—42no—
435C4×C109—42no—
436C4×C109—42no—
437C4×C109—42no—
438C4×C109—81no—
439C4×C109—81no—
440C4×C109—81no—
441C4×C109D4211yescharacteristic
442C4×C109D4211yescharacteristic
443C4×C109#54611yescharacteristic
444C4×C109#54611yescharacteristic
445#24396C10911yesmaximal, characteristic, direct product factor, Sylow
446C2×C109—42no—
447C2×C109—42no—
448C2×C109—81no—
449C2×C109—161no—
450C2×C109#241011yescharacteristic
451C2×C109#301011yescharacteristic
452C2×C109#301311yescharacteristic
453C2×C109#305711yescharacteristic
454C2×C109#306311yescharacteristic
455C2×C109#320011yescharacteristic
456C2×C109#320111yescharacteristic
457C2×#536C2×C10911yescharacteristic, complemented
458C2×#468C2×C10911yescharacteristic, complemented
459C2×#465C2×C10911yescharacteristic, complemented
460C2×#448C2×C10911yescharacteristic, complemented
461C2×#408C2×C10911yescharacteristic, complemented
462#2615C2×C10911yescharacteristic
463#2036C2×C10911yescharacteristic, complemented
464#2035C2×C10911yescharacteristic, complemented
465#2000C2×C10911yescharacteristic, complemented
466#2000C2×C10911yescharacteristic, complemented
467#1894C2×C10911yescharacteristic, complemented
468#1892C2×C10911yescharacteristic, complemented
469#1875C2×C10911yescharacteristic, complemented
470#1854C2×C10911yescharacteristic, complemented
471#1787C2×C10911yescharacteristic, complemented
472C109#2439611yescharacteristic, direct product factor, Sylow
473C22×#41C22×C10911yescharacteristic
474C23×Q8C22×C10911yescharacteristic
475C22×SD16C22×C10911yescharacteristic
476C22×SD16C22×C10911yescharacteristic
477C22×M16C22×C10911yescharacteristic
478C23×C8C22×C10911yescharacteristic
479#536—24no—
480#536—24no—
481C2×C4⋊Q8—21no—
482C2×#124—21no—
483C2×#123—21no—
484C2×#123—21no—
485C2×C22⋊Q8C22×C10911yescharacteristic
486C2×C22⋊Q8C22×C10911yescharacteristic
487C2×C22⋊Q8C22×C10911yescharacteristic
488C2×C22⋊Q8C22×C10911yescharacteristic
489C2×#121C22×C10911yescharacteristic
490C2×#121C22×C10911yescharacteristic
491C2×#121C22×C10911yescharacteristic
492C2×#117C22×C10911yescharacteristic
493#468—24no—
494#465—24no—
495#448—24no—
496C2×#107C22×C10911yescharacteristic
497C2×#106C22×C10911yescharacteristic
498C2×#103C22×C10911yescharacteristic
499C2×#103C22×C10911yescharacteristic
500C2×#103C22×C10911yescharacteristic
501C2×#103C22×C10911yescharacteristic
502C2×#103C22×C10911yescharacteristic
503C2×#103C22×C10911yescharacteristic
504C2×#102C22×C10911yescharacteristic
505C2×#102C22×C10911yescharacteristic
506#408—24no—
507C2×C22⋊C8C22×C10911yescharacteristic
508C2×C22⋊C8C22×C10911yescharacteristic
509C2×C22⋊C8C22×C10911yescharacteristic
510C2×C22⋊C8C22×C10911yescharacteristic
511#393—21no—
512#392—21no—
513#392—21no—
514#392—21no—
515#380C22×C10911yescharacteristic
516#380C22×C10911yescharacteristic
517#380C22×C10911yescharacteristic
518#340C22×C10911yescharacteristic
519#340C22×C10911yescharacteristic
520#340C22×C10911yescharacteristic
521#340C22×C10911yescharacteristic
522C2×#41—22no—
523C2×#41—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—41no—
527C2×#41—41no—
528C22×Q8—22no—
529C22×Q8—22no—
530C22×Q8—21no—
531C22×Q8—22no—
532C22×Q8—22no—
533C22×Q8—41no—
534C22×Q8—41no—
535C22×Q8D4×C10911yescharacteristic
536C22×Q8C23×C10911yescharacteristic
537C22×Q8C23×C10911yescharacteristic
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—21no—
541C22×D4D4×C10911yescharacteristic
542C22×D4D4×C10911yescharacteristic
543C22×D4D4×C10911yescharacteristic
544C22×D4C23×C10911yescharacteristic
545C23×C4—21no—
546C23×C4C23×C10911yescharacteristic
547C23×C4C23×C10911yescharacteristic
548C23×C4C23×C10911yescharacteristic
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—22no—
552C2×SD16—22no—
553C2×SD16—41no—
554C2×SD16—41no—
555C2×M16—22no—
556C2×M16—22no—
557C2×M16—41no—
558C22×C8—22no—
559C22×C8—22no—
560C22×C8—41no—
561C22×C8C23×C10911yescharacteristic
562C22×C8C23×C10911yescharacteristic
563C22×C8C23×C10911yescharacteristic
564C22×C8C23×C10911yescharacteristic
565C4⋊Q8—28no—
566#124—28no—
567#123—28no—
568#123—28no—
569C22⋊Q8—22no—
570C22⋊Q8—22no—
571C22⋊Q8—22no—
572C22⋊Q8—22no—
573C22⋊Q8—22no—
574C22⋊Q8—22no—
575C22⋊Q8D4×C10914yescomplemented
576C22⋊Q8D4×C10914yescomplemented
577#121—22no—
578#121—22no—
579#121—22no—
580#121—22no—
581#121—41no—
582#121—41no—
583#117—22no—
584#117—22no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4C23×C10911yescharacteristic
590C2×C4⋊C4C23×C10911yescharacteristic
591C2×C4⋊C4C23×C10911yescharacteristic
592C2×C4⋊C4C23×C10911yescharacteristic
593C2×C4⋊C4C23×C10911yescharacteristic
594C2×C22⋊C4—21no—
595C2×C22⋊C4—21no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—21no—
600C2×C22⋊C4—21no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—21no—
604C2×C22⋊C4—21no—
605C2×C42—21no—
606#107—22no—
607#106—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—22no—
612#103—41no—
613#103—41no—
614#102—22no—
615#102—22no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—22no—
619C22⋊C8D4×C10914yescomplemented
620#95—21no—
621#95—21no—
622#95—21no—
623C24—21no—
624C24C2×D4×C10911yescharacteristic
625C24C2×D4×C10911yescharacteristic
626C24C2×D4×C10911yescharacteristic
627#41—44no—
628#41—44no—
629#41—44no—
630#41—44no—
631C2×Q8—24no—
632C2×Q8—22no—
633C2×Q8—22no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—41no—
645C2×Q8—44no—
646C2×Q8—44no—
647C2×Q8—44no—
648C2×Q8—44no—
649C2×Q8—42no—
650C2×Q8—42no—
651C2×Q8C2×D4×C10912yes—
652C2×Q8C2×D4×C10912yes—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—22no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—41no—
666C2×D4—41no—
667C2×D4—41no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4—81no—
675C2×D4—81no—
676C2×D4—81no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—24no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—42no—
700C22×C4—42no—
701C22×C4C2×D4×C10911yescharacteristic
702C22×C4C2×D4×C10911yescharacteristic
703C22×C4C2×D4×C10912yes—
704C22×C4C2×D4×C10912yes—
705C22×C4C2×D4×C10911yescharacteristic
706C22×C4C2×D4×C10912yes—
707C22×C4#41×C10912yes—
708C22×C4C24×C10911yescharacteristic
709SD16—44no—
710SD16—44no—
711M16—44no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—21no—
719C2×C8—21no—
720C2×C8—21no—
721C2×C8—21no—
722C2×C8—44no—
723C2×C8C2×D4×C10912yes—
724C2×C8C2×D4×C10912yes—
725C4⋊C4—24no—
726C4⋊C4—24no—
727C4⋊C4—24no—
728C4⋊C4—24no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4—21no—
737C4⋊C4C2×D4×C10912yes—
738C4⋊C4C2×D4×C10912yes—
739C22⋊C4—24no—
740C22⋊C4—24no—
741C22⋊C4—24no—
742C22⋊C4—24no—
743C22⋊C4—24no—
744C22⋊C4—42no—
745C22⋊C4—42no—
746C22⋊C4—42no—
747C22⋊C4—81no—
748C22⋊C4—81no—
749C22⋊C4—81no—
750C42—24no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—21no—
766C23—21no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23—41no—
776C23—41no—
777C23#120×C10912yes—
778C23#121×C10912yes—
779C23C22×D4×C10911yescharacteristic
780Q8—22no—
781Q8—22no—
782Q8—22no—
783Q8—22no—
784Q8—44no—
785Q8—48no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790D4—44no—
791D4—44no—
792D4—44no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799D4—84no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—22no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—22no—
813C2×C4—22no—
814C2×C4—22no—
815C2×C4—22no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—48no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—41no—
840C2×C4—41no—
841C2×C4#120×C10912yes—
842C2×C4#121×C10912yes—
843C2×C4C22×D4×C10911yescharacteristic
844C2×C4C22×D4×C10911yescharacteristic
845C2×C4C22×D4×C10911yescharacteristic
846C2×C4C2×#41×C10911yescharacteristic
847C2×C4H(5,𝔽2)×C10911yescharacteristic
848C2×C4H(5,𝔽2)×C10911yescharacteristic
849C8—22no—
850C8—22no—
851C8—41no—
852C8—41no—
853C22—22no—
854C22—22no—
855C22—22no—
856C22—22no—
857C22—22no—
858C22—22no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
870C22—41no—
871C22—41no—
872C22—41no—
873C22—41no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22—81no—
878C22—81no—
879C22—81no—
880C22—81no—
881C22C2×#120×C10911yescharacteristic
882C22C2×#121×C10911yescharacteristic
883C22#534×C10911yescharacteristic
884C22#577×C10911yescharacteristic
885C22#577×C10911yescharacteristic
886C22#577×C10911yescharacteristic
887C22#578×C10911yescharacteristic
888C4—22no—
889C4—22no—
890C4—42no—
891C4—42no—
892C4—41no—
893C4—42no—
894C4—42no—
895C4—81no—
896C4—81no—
897C4—81no—
898C4D42×C10911yescharacteristic
899C4D42×C10911yescharacteristic
900C4#546×C10911yescharacteristic
901C4#546×C10911yescharacteristic
902C2—42no—
903C2—42no—
904C2—81no—
905C2—161no—
906C2C109×#241011yescharacteristic
907C2C109×#301011yescharacteristic
908C2C109×#301311yescharacteristic
909C2C109×#305711yescharacteristic
910C2C109×#306311yescharacteristic
911C2C109×#320011yescharacteristic
912C2C109×#320111yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC109×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C22×#41×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#536×C109C2semidirect
2. C2×#468×C109C2semidirect
3. C2×#465×C109C2semidirect
4. C2×#448×C109C2semidirect
5. C2×#408×C109C2semidirect
7. C109×#2036C2semidirect
8. C109×#2035C2semidirect
9. C109×#2000C2semidirect
10. C109×#2000C2semidirect
11. C109×#1894C2semidirect
12. C109×#1892C2semidirect
13. C109×#1875C2semidirect
14. C109×#1854C2semidirect
15. C109×#1787C2semidirect
118. C22⋊Q8×C109D4semidirect
119. C22⋊Q8×C109D4semidirect
162. C22⋊C8×C109D4semidirect
445. #24396C109direct (N × H)
457. C2×#536C2×C109semidirect
458. C2×#468C2×C109semidirect
459. C2×#465C2×C109semidirect
460. C2×#448C2×C109semidirect
461. C2×#408C2×C109semidirect
463. #2036C2×C109semidirect
464. #2035C2×C109semidirect
465. #2000C2×C109semidirect
466. #2000C2×C109semidirect
467. #1894C2×C109semidirect
468. #1892C2×C109semidirect
469. #1875C2×C109semidirect
470. #1854C2×C109semidirect
471. #1787C2×C109semidirect
472. C109#24396direct (N × H)
575. C22⋊Q8D4×C109semidirect
576. C22⋊Q8D4×C109semidirect
619. C22⋊C8D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#536×C1092
C2×#468×C1092
C2×#465×C1092
C2×#448×C1092
C2×#408×C1092
C109×#26152
C109×#20362
C109×#20352
C109×#20002
C109×#18942
C109×#18922
C109×#18752
C109×#18542
C109×#17872
#24396109