Finite Group Databasebeta

← C109×#24435 #42142429

Subgroups — C109×#24435 #42142429

Order 27904.

1550 conjugacy classes of subgroups.

The subgroup lattice has 950 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#550×C109C211yesmaximal, characteristic, complemented
2C2×#466×C109C211yesmaximal, characteristic, complemented
3C2×#449×C109C211yesmaximal, characteristic, complemented
4C2×#449×C109C211yesmaximal, characteristic, complemented
5C2×#416×C109C211yesmaximal, characteristic, complemented
6C109×#2414C211yesmaximal, characteristic, complemented
7C109×#2041C211yesmaximal, characteristic, complemented
8C109×#2033C211yesmaximal, characteristic, complemented
9C109×#2011C211yesmaximal, characteristic, complemented
10C109×#1999C211yesmaximal, characteristic, complemented
11C109×#1880C211yesmaximal, characteristic, complemented
12C109×#1875C211yesmaximal, characteristic, complemented
13C109×#1869C211yesmaximal, characteristic, complemented
14C109×#1863C211yesmaximal, characteristic, complemented
15C109×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C22×#41×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C22×D8×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic
21C23×C8×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×C109C2211yescharacteristic
29C2×#121×C109C2211yescharacteristic
30C2×#121×C109C2211yescharacteristic
31C2×#121×C109C2211yescharacteristic
32C2×C4×Q8×C109C2211yescharacteristic
33C2×C4×D4×C109—21no—
34C2×C4×D4×C109C2211yescharacteristic
35C2×#117×C109C2211yescharacteristic
36#466×C109—24no—
37#449×C109—24no—
38#449×C109—24no—
39C2×#107×C109C2211yescharacteristic
40#416×C109—24no—
41C2×#103×C109C2211yescharacteristic
42C2×#103×C109C2211yescharacteristic
43C2×#103×C109C2211yescharacteristic
44C2×#102×C109C2211yescharacteristic
45C2×#102×C109C2211yescharacteristic
46C2×#102×C109C2211yescharacteristic
47C2×#102×C109C2211yescharacteristic
48C2×#102×C109C2211yescharacteristic
49C2×#102×C109C2211yescharacteristic
50C2×#102×C109C2211yescharacteristic
51C2×C22⋊C8×C109C2211yescharacteristic
52C2×C22⋊C8×C109C2211yescharacteristic
53C2×C22⋊C8×C109C2211yescharacteristic
54#394×C109—21no—
55#392×C109—21no—
56#390×C109—21no—
57#390×C109C2211yescharacteristic
58#389×C109C2211yescharacteristic
59#388×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×C109C2311yescharacteristic
93C23×C4×C109C2311yescharacteristic
94C2×SD16×C109—22no—
95C2×SD16×C109—22no—
96C2×SD16×C109—22no—
97C2×D8×C109—22no—
98C2×D8×C109—22no—
99C2×D8×C109—22no—
100C2×D8×C109—41no—
101C2×D8×C109—41no—
102C2×D8×C109—41no—
103C22×C8×C109—22no—
104C22×C8×C109—22no—
105C22×C8×C109—41no—
106C22×C8×C109C2311yescharacteristic
107C22×C8×C109C2311yescharacteristic
108C22×C8×C109C2311yescharacteristic
109C22×C8×C109C2311yescharacteristic
110#127×C109—28no—
111#127×C109—22no—
112#127×C109—22no—
113#121×C109—28no—
114#121×C109—28no—
115#121×C109—22no—
116#121×C109—22no—
117#121×C109—22no—
118#121×C109—22no—
119#121×C109—22no—
120#121×C109—22no—
121#121×C109—41no—
122#121×C109D414yescomplemented
123C4×Q8×C109—22no—
124C4×Q8×C109—22no—
125C4×D4×C109—28no—
126C4×D4×C109—22no—
127C4×D4×C109—22no—
128#117×C109—22no—
129#117×C109—41no—
130C2×C4⋊C4×C109—21no—
131C2×C4⋊C4×C109—21no—
132C2×C4⋊C4×C109D411yescharacteristic
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×C109D411yescharacteristic
146C2×C22⋊C4×C109D411yescharacteristic
147C2×C42×C109—21no—
148C2×C42×C109—21no—
149C2×C42×C109C2311yescharacteristic
150#107×C109—22no—
151#103×C109—22no—
152#103×C109—22no—
153#103×C109D414yescomplemented
154#102×C109—22no—
155#102×C109—22no—
156#102×C109—22no—
157#102×C109—22no—
158#102×C109—22no—
159#102×C109—22no—
160#102×C109—41no—
161C22⋊C8×C109—22no—
162C22⋊C8×C109—22no—
163C22⋊C8×C109—41no—
164#95×C109—21no—
165#95×C109—21no—
166C24×C109—21no—
167C24×C109—21no—
168C24×C109—21no—
169C24×C109C2×D411yescharacteristic
170C24×C109C2×D411yescharacteristic
171#41×C109—28no—
172#41×C109—44no—
173#41×C109—44no—
174#41×C109—44no—
175#41×C109—44no—
176#41×C109—44no—
177#41×C109—44no—
178#41×C109—44no—
179C2×Q8×C109—21no—
180C2×Q8×C109—21no—
181C2×Q8×C109—21no—
182C2×Q8×C109C2×D412yes—
183C2×Q8×C109C2×D412yes—
184C2×Q8×C109#4112yes—
185C2×D4×C109—24no—
186C2×D4×C109—24no—
187C2×D4×C109—22no—
188C2×D4×C109—24no—
189C2×D4×C109—24no—
190C2×D4×C109—24no—
191C2×D4×C109—24no—
192C2×D4×C109—22no—
193C2×D4×C109—21no—
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—41no—
210C2×D4×C109—42no—
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—81no—
220C2×D4×C109—81no—
221C2×D4×C109—81no—
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×C109C2×D412yes—
229C2×D4×C109C2×D412yes—
230C22×C4×C109—21no—
231C22×C4×C109—21no—
232C22×C4×C109—21no—
233C22×C4×C109—21no—
234C22×C4×C109—21no—
235C22×C4×C109—24no—
236C22×C4×C109—21no—
237C22×C4×C109—21no—
238C22×C4×C109—24no—
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—42no—
248C22×C4×C109—42no—
249C22×C4×C109—42no—
250C22×C4×C109—42no—
251C22×C4×C109C2×D411yescharacteristic
252C22×C4×C109C2×D411yescharacteristic
253C22×C4×C109C2×D411yescharacteristic
254C22×C4×C109C2×D412yes—
255C22×C4×C109C2×D412yes—
256C22×C4×C109C2×D411yescharacteristic
257C22×C4×C109C2411yescharacteristic
258SD16×C109—44no—
259D8×C109—44no—
260D8×C109—44no—
261C2×C8×C109—21no—
262C2×C8×C109—21no—
263C2×C8×C109—21no—
264C2×C8×C109—21no—
265C2×C8×C109—21no—
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—44no—
273C2×C8×C109C2×D412yes—
274C4⋊C4×C109—24no—
275C4⋊C4×C109—22no—
276C4⋊C4×C109—21no—
277C4⋊C4×C109—21no—
278C4⋊C4×C109—21no—
279C4⋊C4×C109—21no—
280C4⋊C4×C109—21no—
281C4⋊C4×C109—21no—
282C4⋊C4×C109—81no—
283C4⋊C4×C109C2×D412yes—
284C4⋊C4×C109C2×D412yes—
285C22⋊C4×C109—24no—
286C22⋊C4×C109—22no—
287C22⋊C4×C109—24no—
288C22⋊C4×C109—22no—
289C22⋊C4×C109—42no—
290C22⋊C4×C109—42no—
291C22⋊C4×C109—42no—
292C22⋊C4×C109—42no—
293C22⋊C4×C109—81no—
294C22⋊C4×C109—81no—
295C42×C109—24no—
296C42×C109—21no—
297C42×C109—21no—
298C42×C109—42no—
299C23×C109—21no—
300C23×C109—21no—
301C23×C109—21no—
302C23×C109—21no—
303C23×C109—21no—
304C23×C109—21no—
305C23×C109—21no—
306C23×C109—22no—
307C23×C109—22no—
308C23×C109—21no—
309C23×C109—21no—
310C23×C109—21no—
311C23×C109—21no—
312C23×C109—21no—
313C23×C109—21no—
314C23×C109—41no—
315C23×C109—41no—
316C23×C109—41no—
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#12012yes—
334C23×C109C22×D411yescharacteristic
335Q8×C109—22no—
336Q8×C109—22no—
337Q8×C109—22no—
338Q8×C109#12114yes—
339D4×C109—22no—
340D4×C109—22no—
341D4×C109—22no—
342D4×C109—22no—
343D4×C109—44no—
344D4×C109—48no—
345D4×C109—48no—
346D4×C109—48no—
347D4×C109—41no—
348D4×C109—41no—
349D4×C109—41no—
350D4×C109—41no—
351D4×C109—41no—
352D4×C109—41no—
353D4×C109—41no—
354D4×C109—41no—
355D4×C109—84no—
356D4×C109—84no—
357D4×C109—84no—
358D4×C109—84no—
359D4×C109—84no—
360C2×C4×C109—21no—
361C2×C4×C109—22no—
362C2×C4×C109—21no—
363C2×C4×C109—22no—
364C2×C4×C109—21no—
365C2×C4×C109—22no—
366C2×C4×C109—21no—
367C2×C4×C109—22no—
368C2×C4×C109—22no—
369C2×C4×C109—22no—
370C2×C4×C109—22no—
371C2×C4×C109—21no—
372C2×C4×C109—22no—
373C2×C4×C109—21no—
374C2×C4×C109—22no—
375C2×C4×C109—21no—
376C2×C4×C109—21no—
377C2×C4×C109—21no—
378C2×C4×C109—21no—
379C2×C4×C109—48no—
380C2×C4×C109—48no—
381C2×C4×C109—41no—
382C2×C4×C109—41no—
383C2×C4×C109—41no—
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#12012yes—
396C2×C4×C109#13512yes—
397C2×C4×C109C22×D411yescharacteristic
398C2×C4×C109C22×D411yescharacteristic
399C2×C4×C109C22×D411yescharacteristic
400C2×C4×C109C2×#4111yescharacteristic
401C2×C4×C109H(5,𝔽2)11yescharacteristic
402C2×C4×C109H(5,𝔽2)11yescharacteristic
403C8×C109—22no—
404C8×C109—41no—
405C8×C109—41no—
406C8×C109—41no—
407C22×C109—22no—
408C22×C109—22no—
409C22×C109—22no—
410C22×C109—41no—
411C22×C109—41no—
412C22×C109—41no—
413C22×C109—41no—
414C22×C109—42no—
415C22×C109—42no—
416C22×C109—41no—
417C22×C109—41no—
418C22×C109—42no—
419C22×C109—42no—
420C22×C109—41no—
421C22×C109—42no—
422C22×C109—42no—
423C22×C109—41no—
424C22×C109—41no—
425C22×C109—41no—
426C22×C109—41no—
427C22×C109—81no—
428C22×C109—81no—
429C22×C109—81no—
430C22×C109—81no—
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×C109C2×#12011yescharacteristic
443C22×C109D4211yescharacteristic
444C22×C109#54611yescharacteristic
445C22×C109C2×#13511yescharacteristic
446C22×C109#57511yescharacteristic
447C22×C109#57611yescharacteristic
448C22×C109#57611yescharacteristic
449C4×C109—22no—
450C4×C109—24no—
451C4×C109—22no—
452C4×C109—41no—
453C4×C109—41no—
454C4×C109—42no—
455C4×C109—42no—
456C4×C109—81no—
457C4×C109—81no—
458C4×C109C2×#12111yescharacteristic
459C4×C109#53411yescharacteristic
460C4×C109D4211yescharacteristic
461C4×C109#54611yescharacteristic
462#24435C10911yesmaximal, characteristic, direct product factor, Sylow
463C2×C109—42no—
464C2×C109—81no—
465C2×C109—82no—
466C2×C109—82no—
467C2×C109—161no—
468C2×C109#241011yescharacteristic
469C2×C109#300211yescharacteristic
470C2×C109#300811yescharacteristic
471C2×C109#326811yescharacteristic
472C2×C109#328711yescharacteristic
473C2×C109#330511yescharacteristic
474C2×C109#330911yescharacteristic
475C2×#550C2×C10911yescharacteristic, complemented
476C2×#466C2×C10911yescharacteristic, complemented
477C2×#449C2×C10911yescharacteristic, complemented
478C2×#449C2×C10911yescharacteristic, complemented
479C2×#416C2×C10911yescharacteristic, complemented
480#2414C2×C10911yescharacteristic, complemented
481#2041C2×C10911yescharacteristic, complemented
482#2033C2×C10911yescharacteristic, complemented
483#2011C2×C10911yescharacteristic, complemented
484#1999C2×C10911yescharacteristic, complemented
485#1880C2×C10911yescharacteristic, complemented
486#1875C2×C10911yescharacteristic, complemented
487#1869C2×C10911yescharacteristic, complemented
488#1863C2×C10911yescharacteristic, complemented
489#1788C2×C10911yescharacteristic, complemented
490C109#2443511yescharacteristic, direct product factor, Sylow
491C22×#41C22×C10911yescharacteristic
492C22×#41C22×C10911yescharacteristic
493C22×SD16C22×C10911yescharacteristic
494C22×D8C22×C10911yescharacteristic
495C22×D8C22×C10911yescharacteristic
496C23×C8C22×C10911yescharacteristic
497#550—24no—
498#550—24no—
499C2×#127—21no—
500C2×#127C22×C10911yescharacteristic
501C2×#121—21no—
502C2×#121—21no—
503C2×#121C22×C10911yescharacteristic
504C2×#121C22×C10911yescharacteristic
505C2×#121C22×C10911yescharacteristic
506C2×#121C22×C10911yescharacteristic
507C2×C4×Q8C22×C10911yescharacteristic
508C2×C4×D4—21no—
509C2×C4×D4C22×C10911yescharacteristic
510C2×#117C22×C10911yescharacteristic
511#466—24no—
512#449—24no—
513#449—24no—
514C2×#107C22×C10911yescharacteristic
515#416—24no—
516C2×#103C22×C10911yescharacteristic
517C2×#103C22×C10911yescharacteristic
518C2×#103C22×C10911yescharacteristic
519C2×#102C22×C10911yescharacteristic
520C2×#102C22×C10911yescharacteristic
521C2×#102C22×C10911yescharacteristic
522C2×#102C22×C10911yescharacteristic
523C2×#102C22×C10911yescharacteristic
524C2×#102C22×C10911yescharacteristic
525C2×#102C22×C10911yescharacteristic
526C2×C22⋊C8C22×C10911yescharacteristic
527C2×C22⋊C8C22×C10911yescharacteristic
528C2×C22⋊C8C22×C10911yescharacteristic
529#394—21no—
530#392—21no—
531#390—21no—
532#390C22×C10911yescharacteristic
533#389C22×C10911yescharacteristic
534#388—21no—
535#380C22×C10911yescharacteristic
536#340C22×C10911yescharacteristic
537#340C22×C10911yescharacteristic
538#336C22×C10911yescharacteristic
539#336C22×C10911yescharacteristic
540C2×#41—22no—
541C2×#41—22no—
542C2×#41—22no—
543C2×#41—22no—
544C2×#41—22no—
545C2×#41—22no—
546C2×#41—22no—
547C2×#41—41no—
548C2×#41—41no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41D4×C10914yescomplemented
552C22×Q8C23×C10911yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—21no—
556C22×D4—21no—
557C22×D4—21no—
558C22×D4—21no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4D4×C10911yescharacteristic
562C22×D4C23×C10911yescharacteristic
563C22×D4C23×C10911yescharacteristic
564C22×D4C23×C10911yescharacteristic
565C23×C4—21no—
566C23×C4—21no—
567C23×C4C23×C10911yescharacteristic
568C23×C4C23×C10911yescharacteristic
569C2×SD16—22no—
570C2×SD16—22no—
571C2×SD16—22no—
572C2×D8—22no—
573C2×D8—22no—
574C2×D8—22no—
575C2×D8—41no—
576C2×D8—41no—
577C2×D8—41no—
578C22×C8—22no—
579C22×C8—22no—
580C22×C8—41no—
581C22×C8C23×C10911yescharacteristic
582C22×C8C23×C10911yescharacteristic
583C22×C8C23×C10911yescharacteristic
584C22×C8C23×C10911yescharacteristic
585#127—28no—
586#127—22no—
587#127—22no—
588#121—28no—
589#121—28no—
590#121—22no—
591#121—22no—
592#121—22no—
593#121—22no—
594#121—22no—
595#121—22no—
596#121—41no—
597#121D4×C10914yescomplemented
598C4×Q8—22no—
599C4×Q8—22no—
600C4×D4—28no—
601C4×D4—22no—
602C4×D4—22no—
603#117—22no—
604#117—41no—
605C2×C4⋊C4—21no—
606C2×C4⋊C4—21no—
607C2×C4⋊C4D4×C10911yescharacteristic
608C2×C4⋊C4C23×C10911yescharacteristic
609C2×C4⋊C4C23×C10911yescharacteristic
610C2×C4⋊C4C23×C10911yescharacteristic
611C2×C4⋊C4C23×C10911yescharacteristic
612C2×C22⋊C4—21no—
613C2×C22⋊C4—21no—
614C2×C22⋊C4—21no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
619C2×C22⋊C4—21no—
620C2×C22⋊C4D4×C10911yescharacteristic
621C2×C22⋊C4D4×C10911yescharacteristic
622C2×C42—21no—
623C2×C42—21no—
624C2×C42C23×C10911yescharacteristic
625#107—22no—
626#103—22no—
627#103—22no—
628#103D4×C10914yescomplemented
629#102—22no—
630#102—22no—
631#102—22no—
632#102—22no—
633#102—22no—
634#102—22no—
635#102—41no—
636C22⋊C8—22no—
637C22⋊C8—22no—
638C22⋊C8—41no—
639#95—21no—
640#95—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24C2×D4×C10911yescharacteristic
645C24C2×D4×C10911yescharacteristic
646#41—28no—
647#41—44no—
648#41—44no—
649#41—44no—
650#41—44no—
651#41—44no—
652#41—44no—
653#41—44no—
654C2×Q8—21no—
655C2×Q8—21no—
656C2×Q8—21no—
657C2×Q8C2×D4×C10912yes—
658C2×Q8C2×D4×C10912yes—
659C2×Q8#41×C10912yes—
660C2×D4—24no—
661C2×D4—24no—
662C2×D4—22no—
663C2×D4—24no—
664C2×D4—24no—
665C2×D4—24no—
666C2×D4—24no—
667C2×D4—22no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
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—41no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—42no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—42no—
692C2×D4—42no—
693C2×D4—42no—
694C2×D4—81no—
695C2×D4—81no—
696C2×D4—81no—
697C2×D4—81no—
698C2×D4—81no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4C2×D4×C10912yes—
704C2×D4C2×D4×C10912yes—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—24no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—24no—
714C22×C4—21no—
715C22×C4—21no—
716C22×C4—21no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—42no—
723C22×C4—42no—
724C22×C4—42no—
725C22×C4—42no—
726C22×C4C2×D4×C10911yescharacteristic
727C22×C4C2×D4×C10911yescharacteristic
728C22×C4C2×D4×C10911yescharacteristic
729C22×C4C2×D4×C10912yes—
730C22×C4C2×D4×C10912yes—
731C22×C4C2×D4×C10911yescharacteristic
732C22×C4C24×C10911yescharacteristic
733SD16—44no—
734D8—44no—
735D8—44no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—44no—
748C2×C8C2×D4×C10912yes—
749C4⋊C4—24no—
750C4⋊C4—22no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—81no—
758C4⋊C4C2×D4×C10912yes—
759C4⋊C4C2×D4×C10912yes—
760C22⋊C4—24no—
761C22⋊C4—22no—
762C22⋊C4—24no—
763C22⋊C4—22no—
764C22⋊C4—42no—
765C22⋊C4—42no—
766C22⋊C4—42no—
767C22⋊C4—42no—
768C22⋊C4—81no—
769C22⋊C4—81no—
770C42—24no—
771C42—21no—
772C42—21no—
773C42—42no—
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—21no—
780C23—21no—
781C23—22no—
782C23—22no—
783C23—21no—
784C23—21no—
785C23—21no—
786C23—21no—
787C23—21no—
788C23—21no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
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#120×C10912yes—
809C23C22×D4×C10911yescharacteristic
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8#121×C10914yes—
814D4—22no—
815D4—22no—
816D4—22no—
817D4—22no—
818D4—44no—
819D4—48no—
820D4—48no—
821D4—48no—
822D4—41no—
823D4—41no—
824D4—41no—
825D4—41no—
826D4—41no—
827D4—41no—
828D4—41no—
829D4—41no—
830D4—84no—
831D4—84no—
832D4—84no—
833D4—84no—
834D4—84no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—22no—
841C2×C4—21no—
842C2×C4—22no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—22no—
846C2×C4—21no—
847C2×C4—22no—
848C2×C4—21no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—21no—
853C2×C4—21no—
854C2×C4—48no—
855C2×C4—48no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—41no—
862C2×C4—41no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4#120×C10912yes—
871C2×C4#135×C10912yes—
872C2×C4C22×D4×C10911yescharacteristic
873C2×C4C22×D4×C10911yescharacteristic
874C2×C4C22×D4×C10911yescharacteristic
875C2×C4C2×#41×C10911yescharacteristic
876C2×C4H(5,𝔽2)×C10911yescharacteristic
877C2×C4H(5,𝔽2)×C10911yescharacteristic
878C8—22no—
879C8—41no—
880C8—41no—
881C8—41no—
882C22—22no—
883C22—22no—
884C22—22no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—41no—
889C22—41no—
890C22—42no—
891C22—42no—
892C22—41no—
893C22—42no—
894C22—42no—
895C22—41no—
896C22—41no—
897C22—41no—
898C22—41no—
899C22—42no—
900C22—42no—
901C22—41no—
902C22—81no—
903C22—81no—
904C22—81no—
905C22—81no—
906C22—81no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—81no—
911C22—81no—
912C22—81no—
913C22—81no—
914C22—81no—
915C22—81no—
916C22—81no—
917C22C2×#120×C10911yescharacteristic
918C22D42×C10911yescharacteristic
919C22#546×C10911yescharacteristic
920C22C2×#135×C10911yescharacteristic
921C22#575×C10911yescharacteristic
922C22#576×C10911yescharacteristic
923C22#576×C10911yescharacteristic
924C4—22no—
925C4—22no—
926C4—24no—
927C4—41no—
928C4—42no—
929C4—42no—
930C4—41no—
931C4—81no—
932C4—81no—
933C4C2×#121×C10911yescharacteristic
934C4#534×C10911yescharacteristic
935C4D42×C10911yescharacteristic
936C4#546×C10911yescharacteristic
937C2—42no—
938C2—81no—
939C2—82no—
940C2—82no—
941C2—161no—
942C2C109×#241011yescharacteristic
943C2C109×#300211yescharacteristic
944C2C109×#300811yescharacteristic
945C2C109×#326811yescharacteristic
946C2C109×#328711yescharacteristic
947C2C109×#330511yescharacteristic
948C2C109×#330911yescharacteristic
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×#466×C109C2semidirect
3. C2×#449×C109C2semidirect
4. C2×#449×C109C2semidirect
5. C2×#416×C109C2semidirect
6. C109×#2414C2semidirect
7. C109×#2041C2semidirect
8. C109×#2033C2semidirect
9. C109×#2011C2semidirect
10. C109×#1999C2semidirect
11. C109×#1880C2semidirect
12. C109×#1875C2semidirect
13. C109×#1869C2semidirect
14. C109×#1863C2semidirect
15. C109×#1788C2semidirect
76. C2×#41×C109D4semidirect
122. #121×C109D4semidirect
153. #103×C109D4semidirect
462. #24435C109direct (N × H)
475. C2×#550C2×C109semidirect
476. C2×#466C2×C109semidirect
477. C2×#449C2×C109semidirect
478. C2×#449C2×C109semidirect
479. C2×#416C2×C109semidirect
480. #2414C2×C109semidirect
481. #2041C2×C109semidirect
482. #2033C2×C109semidirect
483. #2011C2×C109semidirect
484. #1999C2×C109semidirect
485. #1880C2×C109semidirect
486. #1875C2×C109semidirect
487. #1869C2×C109semidirect
488. #1863C2×C109semidirect
489. #1788C2×C109semidirect
490. C109#24435direct (N × H)
551. C2×#41D4×C109semidirect
597. #121D4×C109semidirect
628. #103D4×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×#466×C1092
C2×#449×C1092
C2×#416×C1092
C109×#24142
C109×#20412
C109×#20332
C109×#20112
C109×#19992
C109×#18802
C109×#18752
C109×#18692
C109×#18632
C109×#17882
#24435109