Finite Group Databasebeta

← C109×#24451 #42142445

Subgroups — C109×#24451 #42142445

Order 27904.

1580 conjugacy classes of subgroups.

The subgroup lattice has 958 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C109C211yesmaximal, characteristic, complemented
2C2×#469×C109C211yesmaximal, characteristic, complemented
3C2×#449×C109C211yesmaximal, characteristic, complemented
4C2×#449×C109C211yesmaximal, characteristic, complemented
5C2×#417×C109C211yesmaximal, characteristic, complemented
6C109×#2416C211yesmaximal, characteristic, complemented
7C109×#2041C211yesmaximal, characteristic, complemented
8C109×#2034C211yesmaximal, characteristic, complemented
9C109×#2011C211yesmaximal, characteristic, complemented
10C109×#1999C211yesmaximal, characteristic, complemented
11C109×#1880C211yesmaximal, characteristic, complemented
12C109×#1874C211yesmaximal, characteristic, complemented
13C109×#1870C211yesmaximal, characteristic, complemented
14C109×#1865C211yesmaximal, characteristic, complemented
15C109×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C22×#41×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C22×D8×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic
21C22×M16×C109C2211yescharacteristic
22#550×C109—24no—
23#550×C109—24no—
24C2×#127×C109—21no—
25C2×#127×C109C2211yescharacteristic
26C2×#121×C109—21no—
27C2×#121×C109—21no—
28C2×#121×C109—21no—
29C2×#121×C109C2211yescharacteristic
30C2×#121×C109C2211yescharacteristic
31C2×#121×C109C2211yescharacteristic
32C2×#121×C109C2211yescharacteristic
33C2×C4×Q8×C109C2211yescharacteristic
34C2×C4×D4×C109—21no—
35C2×C4×D4×C109C2211yescharacteristic
36C22×C4⋊C4×C109C2211yescharacteristic
37#469×C109—24no—
38#449×C109—24no—
39#449×C109—24no—
40C2×#106×C109C2211yescharacteristic
41#417×C109—24no—
42C2×#103×C109C2211yescharacteristic
43C2×#103×C109C2211yescharacteristic
44C2×#103×C109C2211yescharacteristic
45C2×#102×C109C2211yescharacteristic
46C2×#102×C109C2211yescharacteristic
47C2×#102×C109C2211yescharacteristic
48C2×#102×C109C2211yescharacteristic
49C2×#102×C109C2211yescharacteristic
50C2×#102×C109C2211yescharacteristic
51C2×#102×C109C2211yescharacteristic
52C2×C22⋊C8×C109C2211yescharacteristic
53C2×C22⋊C8×C109C2211yescharacteristic
54C2×C22⋊C8×C109C2211yescharacteristic
55#396×C109—21no—
56#394×C109—21no—
57#390×C109C2211yescharacteristic
58#389×C109C2211yescharacteristic
59#386×C109—21no—
60#380×C109C2211yescharacteristic
61#340×C109C2211yescharacteristic
62#340×C109C2211yescharacteristic
63#336×C109C2211yescharacteristic
64#336×C109C2211yescharacteristic
65C2×#41×C109—22no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—22no—
69C2×#41×C109—22no—
70C2×#41×C109—22no—
71C2×#41×C109—22no—
72C2×#41×C109—41no—
73C2×#41×C109—41no—
74C2×#41×C109—41no—
75C2×#41×C109—41no—
76C2×#41×C109D414yescomplemented
77C22×Q8×C109C2311yescharacteristic
78C22×D4×C109—21no—
79C22×D4×C109—21no—
80C22×D4×C109—21no—
81C22×D4×C109—21no—
82C22×D4×C109—21no—
83C22×D4×C109—21no—
84C22×D4×C109—21no—
85C22×D4×C109—21no—
86C22×D4×C109D411yescharacteristic
87C22×D4×C109C2311yescharacteristic
88C22×D4×C109C2311yescharacteristic
89C22×D4×C109C2311yescharacteristic
90C23×C4×C109—21no—
91C23×C4×C109—21no—
92C23×C4×C109—21no—
93C23×C4×C109C2311yescharacteristic
94C23×C4×C109C2311yescharacteristic
95C2×SD16×C109—22no—
96C2×SD16×C109—22no—
97C2×SD16×C109—22no—
98C2×D8×C109—22no—
99C2×D8×C109—22no—
100C2×D8×C109—22no—
101C2×D8×C109—41no—
102C2×D8×C109—41no—
103C2×D8×C109—41no—
104C2×M16×C109—22no—
105C2×M16×C109—22no—
106C2×M16×C109—41no—
107C22×C8×C109C2311yescharacteristic
108C22×C8×C109C2311yescharacteristic
109C22×C8×C109C2311yescharacteristic
110C22×C8×C109C2311yescharacteristic
111#127×C109—28no—
112#127×C109—22no—
113#127×C109—22no—
114#121×C109—28no—
115#121×C109—28no—
116#121×C109—22no—
117#121×C109—22no—
118#121×C109—22no—
119#121×C109—22no—
120#121×C109—22no—
121#121×C109—22no—
122#121×C109—41no—
123#121×C109—44no—
124#121×C109D414yescomplemented
125C4×Q8×C109—22no—
126C4×Q8×C109—22no—
127C4×D4×C109—28no—
128C4×D4×C109—22no—
129C4×D4×C109—22no—
130C2×C4⋊C4×C109—21no—
131C2×C4⋊C4×C109—22no—
132C2×C4⋊C4×C109—21no—
133C2×C4⋊C4×C109—21no—
134C2×C4⋊C4×C109—41no—
135C2×C4⋊C4×C109D411yescharacteristic
136C2×C4⋊C4×C109C2311yescharacteristic
137C2×C4⋊C4×C109C2311yescharacteristic
138C2×C4⋊C4×C109C2311yescharacteristic
139C2×C4⋊C4×C109C2311yescharacteristic
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×C109D411yescharacteristic
148C2×C22⋊C4×C109D411yescharacteristic
149C2×C42×C109—21no—
150C2×C42×C109C2311yescharacteristic
151#106×C109—22no—
152#103×C109—22no—
153#103×C109—22no—
154#103×C109D414yescomplemented
155#102×C109—22no—
156#102×C109—22no—
157#102×C109—22no—
158#102×C109—22no—
159#102×C109—22no—
160#102×C109—22no—
161#102×C109—41no—
162C22⋊C8×C109—22no—
163C22⋊C8×C109—22no—
164C22⋊C8×C109—41no—
165#95×C109—21no—
166#95×C109—21no—
167C24×C109—21no—
168C24×C109—21no—
169C24×C109—21no—
170C24×C109C2×D411yescharacteristic
171C24×C109C2×D411yescharacteristic
172#41×C109—28no—
173#41×C109—44no—
174#41×C109—44no—
175#41×C109—44no—
176#41×C109—44no—
177#41×C109—44no—
178#41×C109—44no—
179#41×C109—44no—
180C2×Q8×C109—21no—
181C2×Q8×C109—21no—
182C2×Q8×C109—21no—
183C2×Q8×C109C2×D412yes—
184C2×Q8×C109C2×D412yes—
185C2×Q8×C109#4112yes—
186C2×D4×C109—24no—
187C2×D4×C109—24no—
188C2×D4×C109—22no—
189C2×D4×C109—24no—
190C2×D4×C109—24no—
191C2×D4×C109—24no—
192C2×D4×C109—24no—
193C2×D4×C109—22no—
194C2×D4×C109—21no—
195C2×D4×C109—21no—
196C2×D4×C109—21no—
197C2×D4×C109—21no—
198C2×D4×C109—21no—
199C2×D4×C109—21no—
200C2×D4×C109—21no—
201C2×D4×C109—21no—
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—21no—
209C2×D4×C109—21no—
210C2×D4×C109—41no—
211C2×D4×C109—42no—
212C2×D4×C109—42no—
213C2×D4×C109—42no—
214C2×D4×C109—42no—
215C2×D4×C109—42no—
216C2×D4×C109—42no—
217C2×D4×C109—42no—
218C2×D4×C109—42no—
219C2×D4×C109—42no—
220C2×D4×C109—42no—
221C2×D4×C109—42no—
222C2×D4×C109—81no—
223C2×D4×C109—81no—
224C2×D4×C109—81no—
225C2×D4×C109—81no—
226C2×D4×C109—81no—
227C2×D4×C109—81no—
228C2×D4×C109—81no—
229C2×D4×C109C2×D412yes—
230C2×D4×C109C2×D412yes—
231C22×C4×C109—21no—
232C22×C4×C109—21no—
233C22×C4×C109—21no—
234C22×C4×C109—21no—
235C22×C4×C109—21no—
236C22×C4×C109—24no—
237C22×C4×C109—21no—
238C22×C4×C109—21no—
239C22×C4×C109—24no—
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—42no—
249C22×C4×C109—42no—
250C22×C4×C109—42no—
251C22×C4×C109—42no—
252C22×C4×C109—42no—
253C22×C4×C109—42no—
254C22×C4×C109—81no—
255C22×C4×C109C2×D411yescharacteristic
256C22×C4×C109C2×D411yescharacteristic
257C22×C4×C109C2×D411yescharacteristic
258C22×C4×C109C2×D412yes—
259C22×C4×C109C2×D412yes—
260C22×C4×C109C2×D411yescharacteristic
261C22×C4×C109C2411yescharacteristic
262SD16×C109—44no—
263D8×C109—44no—
264D8×C109—44no—
265M16×C109—44no—
266C2×C8×C109—21no—
267C2×C8×C109—21no—
268C2×C8×C109—21no—
269C2×C8×C109—21no—
270C2×C8×C109—21no—
271C2×C8×C109—21no—
272C2×C8×C109—21no—
273C2×C8×C109—21no—
274C2×C8×C109—21no—
275C2×C8×C109—21no—
276C2×C8×C109—21no—
277C2×C8×C109C2×D412yes—
278C4⋊C4×C109—24no—
279C4⋊C4×C109—22no—
280C4⋊C4×C109—21no—
281C4⋊C4×C109—21no—
282C4⋊C4×C109—21no—
283C4⋊C4×C109—21no—
284C4⋊C4×C109—21no—
285C4⋊C4×C109—21no—
286C4⋊C4×C109—42no—
287C4⋊C4×C109—42no—
288C4⋊C4×C109C2×D412yes—
289C4⋊C4×C109C2×D412yes—
290C22⋊C4×C109—24no—
291C22⋊C4×C109—22no—
292C22⋊C4×C109—24no—
293C22⋊C4×C109—22no—
294C22⋊C4×C109—42no—
295C22⋊C4×C109—42no—
296C22⋊C4×C109—42no—
297C22⋊C4×C109—42no—
298C22⋊C4×C109—81no—
299C42×C109—24no—
300C42×C109—21no—
301C42×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—22no—
310C23×C109—22no—
311C23×C109—21no—
312C23×C109—21no—
313C23×C109—21no—
314C23×C109—21no—
315C23×C109—21no—
316C23×C109—21no—
317C23×C109—41no—
318C23×C109—41no—
319C23×C109—41no—
320C23×C109—41no—
321C23×C109—41no—
322C23×C109—41no—
323C23×C109—41no—
324C23×C109—41no—
325C23×C109—41no—
326C23×C109—41no—
327C23×C109—41no—
328C23×C109—41no—
329C23×C109—41no—
330C23×C109—41no—
331C23×C109—41no—
332C23×C109—41no—
333C23×C109—41no—
334C23×C109—41no—
335C23×C109—41no—
336C23×C109#12012yes—
337C23×C109C22×D411yescharacteristic
338Q8×C109—22no—
339Q8×C109—22no—
340Q8×C109—22no—
341Q8×C109#12114yescomplemented
342D4×C109—22no—
343D4×C109—22no—
344D4×C109—22no—
345D4×C109—22no—
346D4×C109—44no—
347D4×C109—48no—
348D4×C109—48no—
349D4×C109—48no—
350D4×C109—41no—
351D4×C109—41no—
352D4×C109—41no—
353D4×C109—41no—
354D4×C109—41no—
355D4×C109—41no—
356D4×C109—41no—
357D4×C109—41no—
358D4×C109—84no—
359D4×C109—84no—
360D4×C109—84no—
361D4×C109—84no—
362D4×C109—84no—
363C2×C4×C109—21no—
364C2×C4×C109—22no—
365C2×C4×C109—21no—
366C2×C4×C109—22no—
367C2×C4×C109—21no—
368C2×C4×C109—22no—
369C2×C4×C109—21no—
370C2×C4×C109—22no—
371C2×C4×C109—22no—
372C2×C4×C109—22no—
373C2×C4×C109—22no—
374C2×C4×C109—21no—
375C2×C4×C109—22no—
376C2×C4×C109—21no—
377C2×C4×C109—21no—
378C2×C4×C109—22no—
379C2×C4×C109—21no—
380C2×C4×C109—21no—
381C2×C4×C109—21no—
382C2×C4×C109—48no—
383C2×C4×C109—48no—
384C2×C4×C109—41no—
385C2×C4×C109—41no—
386C2×C4×C109—41no—
387C2×C4×C109—41no—
388C2×C4×C109—41no—
389C2×C4×C109—41no—
390C2×C4×C109—41no—
391C2×C4×C109—41no—
392C2×C4×C109—41no—
393C2×C4×C109—41no—
394C2×C4×C109—41no—
395C2×C4×C109—41no—
396C2×C4×C109—41no—
397C2×C4×C109—41no—
398C2×C4×C109—84no—
399C2×C4×C109#12012yes—
400C2×C4×C109AGL(1,ℤ/8)12yes—
401C2×C4×C109C22×D411yescharacteristic
402C2×C4×C109C22×D411yescharacteristic
403C2×C4×C109C22×D411yescharacteristic
404C2×C4×C109C2×#4111yescharacteristic
405C2×C4×C109H(5,𝔽2)11yescharacteristic
406C2×C4×C109H(5,𝔽2)11yescharacteristic
407C8×C109—22no—
408C8×C109—41no—
409C8×C109—41no—
410C8×C109—41no—
411C22×C109—22no—
412C22×C109—22no—
413C22×C109—22no—
414C22×C109—41no—
415C22×C109—41no—
416C22×C109—41no—
417C22×C109—41no—
418C22×C109—41no—
419C22×C109—42no—
420C22×C109—42no—
421C22×C109—41no—
422C22×C109—41no—
423C22×C109—42no—
424C22×C109—42no—
425C22×C109—41no—
426C22×C109—42no—
427C22×C109—42no—
428C22×C109—41no—
429C22×C109—41no—
430C22×C109—41no—
431C22×C109—81no—
432C22×C109—81no—
433C22×C109—81no—
434C22×C109—81no—
435C22×C109—81no—
436C22×C109—81no—
437C22×C109—81no—
438C22×C109—81no—
439C22×C109—81no—
440C22×C109—81no—
441C22×C109—81no—
442C22×C109—81no—
443C22×C109—81no—
444C22×C109—81no—
445C22×C109—81no—
446C22×C109C2×#12011yescharacteristic
447C22×C109D4211yescharacteristic
448C22×C109#54611yescharacteristic
449C22×C109C2×AGL(1,ℤ/8)11yescharacteristic
450C22×C109#57511yescharacteristic
451C22×C109#57611yescharacteristic
452C22×C109#57711yescharacteristic
453C4×C109—22no—
454C4×C109—24no—
455C4×C109—22no—
456C4×C109—41no—
457C4×C109—41no—
458C4×C109—42no—
459C4×C109—42no—
460C4×C109—81no—
461C4×C109—81no—
462C4×C109C2×#12111yescharacteristic
463C4×C109#53411yescharacteristic
464C4×C109D4211yescharacteristic
465C4×C109#54611yescharacteristic
466#24451C10911yesmaximal, characteristic, direct product factor, Sylow
467C2×C109—42no—
468C2×C109—81no—
469C2×C109—82no—
470C2×C109—82no—
471C2×C109—161no—
472C2×C109#241011yescharacteristic
473C2×C109#300611yescharacteristic
474C2×C109#301211yescharacteristic
475C2×C109#327111yescharacteristic
476C2×C109#327411yescharacteristic
477C2×C109#330911yescharacteristic
478C2×C109#333211yescharacteristic
479C2×#550C2×C10911yescharacteristic, complemented
480C2×#469C2×C10911yescharacteristic, complemented
481C2×#449C2×C10911yescharacteristic, complemented
482C2×#449C2×C10911yescharacteristic, complemented
483C2×#417C2×C10911yescharacteristic, complemented
484#2416C2×C10911yescharacteristic, complemented
485#2041C2×C10911yescharacteristic, complemented
486#2034C2×C10911yescharacteristic, complemented
487#2011C2×C10911yescharacteristic, complemented
488#1999C2×C10911yescharacteristic, complemented
489#1880C2×C10911yescharacteristic, complemented
490#1874C2×C10911yescharacteristic, complemented
491#1870C2×C10911yescharacteristic, complemented
492#1865C2×C10911yescharacteristic, complemented
493#1788C2×C10911yescharacteristic, complemented
494C109#2445111yescharacteristic, direct product factor, Sylow
495C22×#41C22×C10911yescharacteristic
496C22×#41C22×C10911yescharacteristic
497C22×SD16C22×C10911yescharacteristic
498C22×D8C22×C10911yescharacteristic
499C22×D8C22×C10911yescharacteristic
500C22×M16C22×C10911yescharacteristic
501#550—24no—
502#550—24no—
503C2×#127—21no—
504C2×#127C22×C10911yescharacteristic
505C2×#121—21no—
506C2×#121—21no—
507C2×#121—21no—
508C2×#121C22×C10911yescharacteristic
509C2×#121C22×C10911yescharacteristic
510C2×#121C22×C10911yescharacteristic
511C2×#121C22×C10911yescharacteristic
512C2×C4×Q8C22×C10911yescharacteristic
513C2×C4×D4—21no—
514C2×C4×D4C22×C10911yescharacteristic
515C22×C4⋊C4C22×C10911yescharacteristic
516#469—24no—
517#449—24no—
518#449—24no—
519C2×#106C22×C10911yescharacteristic
520#417—24no—
521C2×#103C22×C10911yescharacteristic
522C2×#103C22×C10911yescharacteristic
523C2×#103C22×C10911yescharacteristic
524C2×#102C22×C10911yescharacteristic
525C2×#102C22×C10911yescharacteristic
526C2×#102C22×C10911yescharacteristic
527C2×#102C22×C10911yescharacteristic
528C2×#102C22×C10911yescharacteristic
529C2×#102C22×C10911yescharacteristic
530C2×#102C22×C10911yescharacteristic
531C2×C22⋊C8C22×C10911yescharacteristic
532C2×C22⋊C8C22×C10911yescharacteristic
533C2×C22⋊C8C22×C10911yescharacteristic
534#396—21no—
535#394—21no—
536#390C22×C10911yescharacteristic
537#389C22×C10911yescharacteristic
538#386—21no—
539#380C22×C10911yescharacteristic
540#340C22×C10911yescharacteristic
541#340C22×C10911yescharacteristic
542#336C22×C10911yescharacteristic
543#336C22×C10911yescharacteristic
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—22no—
550C2×#41—22no—
551C2×#41—41no—
552C2×#41—41no—
553C2×#41—41no—
554C2×#41—41no—
555C2×#41D4×C10914yescomplemented
556C22×Q8C23×C10911yescharacteristic
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—21no—
563C22×D4—21no—
564C22×D4—21no—
565C22×D4D4×C10911yescharacteristic
566C22×D4C23×C10911yescharacteristic
567C22×D4C23×C10911yescharacteristic
568C22×D4C23×C10911yescharacteristic
569C23×C4—21no—
570C23×C4—21no—
571C23×C4—21no—
572C23×C4C23×C10911yescharacteristic
573C23×C4C23×C10911yescharacteristic
574C2×SD16—22no—
575C2×SD16—22no—
576C2×SD16—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C2×D8—41no—
582C2×D8—41no—
583C2×M16—22no—
584C2×M16—22no—
585C2×M16—41no—
586C22×C8C23×C10911yescharacteristic
587C22×C8C23×C10911yescharacteristic
588C22×C8C23×C10911yescharacteristic
589C22×C8C23×C10911yescharacteristic
590#127—28no—
591#127—22no—
592#127—22no—
593#121—28no—
594#121—28no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—22no—
599#121—22no—
600#121—22no—
601#121—41no—
602#121—44no—
603#121D4×C10914yescomplemented
604C4×Q8—22no—
605C4×Q8—22no—
606C4×D4—28no—
607C4×D4—22no—
608C4×D4—22no—
609C2×C4⋊C4—21no—
610C2×C4⋊C4—22no—
611C2×C4⋊C4—21no—
612C2×C4⋊C4—21no—
613C2×C4⋊C4—41no—
614C2×C4⋊C4D4×C10911yescharacteristic
615C2×C4⋊C4C23×C10911yescharacteristic
616C2×C4⋊C4C23×C10911yescharacteristic
617C2×C4⋊C4C23×C10911yescharacteristic
618C2×C4⋊C4C23×C10911yescharacteristic
619C2×C22⋊C4—21no—
620C2×C22⋊C4—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4D4×C10911yescharacteristic
627C2×C22⋊C4D4×C10911yescharacteristic
628C2×C42—21no—
629C2×C42C23×C10911yescharacteristic
630#106—22no—
631#103—22no—
632#103—22no—
633#103D4×C10914yescomplemented
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—22no—
640#102—41no—
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—21no—
648C24—21no—
649C24C2×D4×C10911yescharacteristic
650C24C2×D4×C10911yescharacteristic
651#41—28no—
652#41—44no—
653#41—44no—
654#41—44no—
655#41—44no—
656#41—44no—
657#41—44no—
658#41—44no—
659C2×Q8—21no—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8C2×D4×C10912yes—
663C2×Q8C2×D4×C10912yes—
664C2×Q8#41×C10912yes—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—24no—
669C2×D4—24no—
670C2×D4—24no—
671C2×D4—24no—
672C2×D4—22no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—21no—
679C2×D4—21no—
680C2×D4—21no—
681C2×D4—21no—
682C2×D4—21no—
683C2×D4—21no—
684C2×D4—21no—
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—41no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—42no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—42no—
700C2×D4—42no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4—81no—
705C2×D4—81no—
706C2×D4—81no—
707C2×D4—81no—
708C2×D4C2×D4×C10912yes—
709C2×D4C2×D4×C10912yes—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—21no—
726C22×C4—21no—
727C22×C4—42no—
728C22×C4—42no—
729C22×C4—42no—
730C22×C4—42no—
731C22×C4—42no—
732C22×C4—42no—
733C22×C4—81no—
734C22×C4C2×D4×C10911yescharacteristic
735C22×C4C2×D4×C10911yescharacteristic
736C22×C4C2×D4×C10911yescharacteristic
737C22×C4C2×D4×C10912yes—
738C22×C4C2×D4×C10912yes—
739C22×C4C2×D4×C10911yescharacteristic
740C22×C4C24×C10911yescharacteristic
741SD16—44no—
742D8—44no—
743D8—44no—
744M16—44no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—21no—
751C2×C8—21no—
752C2×C8—21no—
753C2×C8—21no—
754C2×C8—21no—
755C2×C8—21no—
756C2×C8C2×D4×C10912yes—
757C4⋊C4—24no—
758C4⋊C4—22no—
759C4⋊C4—21no—
760C4⋊C4—21no—
761C4⋊C4—21no—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—42no—
766C4⋊C4—42no—
767C4⋊C4C2×D4×C10912yes—
768C4⋊C4C2×D4×C10912yes—
769C22⋊C4—24no—
770C22⋊C4—22no—
771C22⋊C4—24no—
772C22⋊C4—22no—
773C22⋊C4—42no—
774C22⋊C4—42no—
775C22⋊C4—42no—
776C22⋊C4—42no—
777C22⋊C4—81no—
778C42—24no—
779C42—21no—
780C42—21no—
781C23—21no—
782C23—21no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—22no—
789C23—22no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—21no—
795C23—21no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—41no—
805C23—41no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—41no—
815C23#120×C10912yes—
816C23C22×D4×C10911yescharacteristic
817Q8—22no—
818Q8—22no—
819Q8—22no—
820Q8#121×C10914yescomplemented
821D4—22no—
822D4—22no—
823D4—22no—
824D4—22no—
825D4—44no—
826D4—48no—
827D4—48no—
828D4—48no—
829D4—41no—
830D4—41no—
831D4—41no—
832D4—41no—
833D4—41no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—84no—
838D4—84no—
839D4—84no—
840D4—84no—
841D4—84no—
842C2×C4—21no—
843C2×C4—22no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—21no—
854C2×C4—22no—
855C2×C4—21no—
856C2×C4—21no—
857C2×C4—22no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—48no—
862C2×C4—48no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—84no—
878C2×C4#120×C10912yes—
879C2×C4AGL(1,ℤ/8)×C10912yes—
880C2×C4C22×D4×C10911yescharacteristic
881C2×C4C22×D4×C10911yescharacteristic
882C2×C4C22×D4×C10911yescharacteristic
883C2×C4C2×#41×C10911yescharacteristic
884C2×C4H(5,𝔽2)×C10911yescharacteristic
885C2×C4H(5,𝔽2)×C10911yescharacteristic
886C8—22no—
887C8—41no—
888C8—41no—
889C8—41no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—41no—
894C22—41no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—42no—
902C22—42no—
903C22—41no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—42no—
908C22—42no—
909C22—41no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22C2×#120×C10911yescharacteristic
926C22D42×C10911yescharacteristic
927C22#546×C10911yescharacteristic
928C22C2×AGL(1,ℤ/8)×C10911yescharacteristic
929C22#575×C10911yescharacteristic
930C22#576×C10911yescharacteristic
931C22#577×C10911yescharacteristic
932C4—22no—
933C4—22no—
934C4—24no—
935C4—41no—
936C4—42no—
937C4—42no—
938C4—41no—
939C4—81no—
940C4—81no—
941C4C2×#121×C10911yescharacteristic
942C4#534×C10911yescharacteristic
943C4D42×C10911yescharacteristic
944C4#546×C10911yescharacteristic
945C2—42no—
946C2—81no—
947C2—82no—
948C2—82no—
949C2—161no—
950C2C109×#241011yescharacteristic
951C2C109×#300611yescharacteristic
952C2C109×#301211yescharacteristic
953C2C109×#327111yescharacteristic
954C2C109×#327411yescharacteristic
955C2C109×#330911yescharacteristic
956C2C109×#333211yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C2×C4×D4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#550×C109C2semidirect
2. C2×#469×C109C2semidirect
3. C2×#449×C109C2semidirect
4. C2×#449×C109C2semidirect
5. C2×#417×C109C2semidirect
6. C109×#2416C2semidirect
7. C109×#2041C2semidirect
8. C109×#2034C2semidirect
9. C109×#2011C2semidirect
10. C109×#1999C2semidirect
11. C109×#1880C2semidirect
12. C109×#1874C2semidirect
13. C109×#1870C2semidirect
14. C109×#1865C2semidirect
15. C109×#1788C2semidirect
76. C2×#41×C109D4semidirect
124. #121×C109D4semidirect
154. #103×C109D4semidirect
341. Q8×C109#121semidirect
466. #24451C109direct (N × H)
479. C2×#550C2×C109semidirect
480. C2×#469C2×C109semidirect
481. C2×#449C2×C109semidirect
482. C2×#449C2×C109semidirect
483. C2×#417C2×C109semidirect
484. #2416C2×C109semidirect
485. #2041C2×C109semidirect
486. #2034C2×C109semidirect
487. #2011C2×C109semidirect
488. #1999C2×C109semidirect
489. #1880C2×C109semidirect
490. #1874C2×C109semidirect
491. #1870C2×C109semidirect
492. #1865C2×C109semidirect
493. #1788C2×C109semidirect
494. C109#24451direct (N × H)
555. C2×#41D4×C109semidirect
603. #121D4×C109semidirect
633. #103D4×C109semidirect
820. Q8#121×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#550×C1092
C2×#469×C1092
C2×#449×C1092
C2×#417×C1092
C109×#24162
C109×#20412
C109×#20342
C109×#20112
C109×#19992
C109×#18802
C109×#18742
C109×#18702
C109×#18652
C109×#17882
#24451109