Finite Group Databasebeta

← C109×#24428 #42142422

Subgroups — C109×#24428 #42142422

Order 27904.

1632 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#546×C109C211yesmaximal, characteristic, complemented
2C2×#466×C109C211yesmaximal, characteristic, complemented
3C2×#449×C109C211yesmaximal, characteristic, complemented
4C2×#447×C109C211yesmaximal, characteristic, complemented
5C2×#416×C109C211yesmaximal, characteristic, complemented
6C109×#2414C211yesmaximal, characteristic, complemented
7C109×#2042C211yesmaximal, characteristic, complemented
8C109×#2036C211yesmaximal, characteristic, complemented
9C109×#2012C211yesmaximal, characteristic, complemented
10C109×#2000C211yesmaximal, characteristic, complemented
11C109×#1879C211yesmaximal, characteristic, complemented
12C109×#1875C211yesmaximal, characteristic, complemented
13C109×#1869C211yesmaximal, characteristic, complemented
14C109×#1862C211yesmaximal, characteristic, complemented
15C109×#1786C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C23×D4×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic, complemented
19C22×D8×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic
21C23×C8×C109C2211yescharacteristic, complemented
22#546×C109—24no—
23#546×C109—24no—
24C2×#124×C109C2211yescharacteristic
25C2×#123×C109—21no—
26C2×C22⋊Q8×C109C2211yescharacteristic
27C2×#121×C109—21no—
28C2×#121×C109C2211yescharacteristic
29C2×#121×C109C2211yescharacteristic
30C2×#121×C109C2211yescharacteristic, complemented
31C2×#120×C109—21no—
32C2×C4×D4×C109C2211yescharacteristic
33C2×C4×D4×C109C2211yescharacteristic
34C2×#117×C109C2211yescharacteristic, complemented
35C22×C22⋊C4×C109—21no—
36#466×C109—24no—
37#449×C109—24no—
38#447×C109—24no—
39C2×#107×C109C2211yescharacteristic, complemented
40#416×C109—24no—
41C2×#103×C109C2211yescharacteristic, complemented
42C2×#103×C109C2211yescharacteristic, complemented
43C2×#103×C109C2211yescharacteristic, complemented
44C2×#102×C109C2211yescharacteristic
45C2×#102×C109C2211yescharacteristic
46C2×#102×C109C2211yescharacteristic
47C2×#102×C109C2211yescharacteristic
48C2×#102×C109C2211yescharacteristic
49C2×#102×C109C2211yescharacteristic
50C2×#102×C109C2211yescharacteristic, complemented
51C2×C22⋊C8×C109C2211yescharacteristic
52C2×C22⋊C8×C109C2211yescharacteristic
53C2×C22⋊C8×C109C2211yescharacteristic, complemented
54#394×C109—21no—
55#392×C109—21no—
56#390×C109—21no—
57#390×C109C2211yescharacteristic, complemented
58#389×C109C2211yescharacteristic, complemented
59#388×C109—21no—
60#380×C109C2211yescharacteristic
61#340×C109C2211yescharacteristic, complemented
62#340×C109C2211yescharacteristic, complemented
63#336×C109C2211yescharacteristic, complemented
64#336×C109C2211yescharacteristic, complemented
65C25×C109—21no—
66C2×#41×C109—22no—
67C2×#41×C109—22no—
68C2×#41×C109—22no—
69C2×#41×C109—41no—
70C2×#41×C109—41no—
71C2×#41×C109D414yescomplemented
72C22×Q8×C109C2311yescharacteristic
73C22×D4×C109—21no—
74C22×D4×C109—21no—
75C22×D4×C109—22no—
76C22×D4×C109—22no—
77C22×D4×C109—22no—
78C22×D4×C109—22no—
79C22×D4×C109—21no—
80C22×D4×C109—21no—
81C22×D4×C109—21no—
82C22×D4×C109—41no—
83C22×D4×C109—41no—
84C22×D4×C109D411yescharacteristic
85C22×D4×C109C2311yescharacteristic
86C22×D4×C109C2311yescharacteristic
87C22×D4×C109C2311yescharacteristic
88C23×C4×C109—21no—
89C23×C4×C109—21no—
90C23×C4×C109C2311yescharacteristic
91C23×C4×C109C2311yescharacteristic
92C2×SD16×C109—22no—
93C2×SD16×C109—41no—
94C2×SD16×C109—41no—
95C2×D8×C109—22no—
96C2×D8×C109—22no—
97C2×D8×C109—22no—
98C2×D8×C109—22no—
99C2×D8×C109—22no—
100C2×D8×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
108#124×C109—22no—
109#124×C109—22no—
110#123×C109—28no—
111C22⋊Q8×C109—22no—
112C22⋊Q8×C109—22no—
113#121×C109—28no—
114#121×C109—22no—
115#121×C109—22no—
116#121×C109—22no—
117#121×C109—22no—
118#121×C109—41no—
119#121×C109D414yescomplemented
120#120×C109—28no—
121C4×D4×C109—22no—
122C4×D4×C109—22no—
123C4×D4×C109—22no—
124C4×D4×C109—22no—
125#117×C109—22no—
126#117×C109—41no—
127C2×C4⋊C4×C109—21no—
128C2×C4⋊C4×C109—21no—
129C2×C4⋊C4×C109D411yescharacteristic
130C2×C4⋊C4×C109C2311yescharacteristic
131C2×C4⋊C4×C109C2311yescharacteristic
132C2×C4⋊C4×C109C2311yescharacteristic
133C2×C4⋊C4×C109C2311yescharacteristic
134C2×C22⋊C4×C109—28no—
135C2×C22⋊C4×C109—21no—
136C2×C22⋊C4×C109—21no—
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×C109D411yescharacteristic
147C2×C22⋊C4×C109D411yescharacteristic
148C2×C42×C109—21no—
149C2×C42×C109C2311yescharacteristic
150#107×C109—22no—
151#103×C109—22no—
152#103×C109—22no—
153#103×C109—22no—
154#102×C109—22no—
155#102×C109—22no—
156#102×C109—22no—
157#102×C109—22no—
158#102×C109—22no—
159#102×C109—41no—
160#102×C109D414yescomplemented
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—24no—
168C24×C109—21no—
169C24×C109—21no—
170C24×C109—42no—
171C24×C109—42no—
172C24×C109—42no—
173C24×C109—42no—
174C24×C109—81no—
175C24×C109—81no—
176C24×C109C2×D411yescharacteristic
177C24×C109C2×D411yescharacteristic
178#41×C109—28no—
179#41×C109—44no—
180#41×C109—44no—
181#41×C109—44no—
182C2×Q8×C109—21no—
183C2×Q8×C109—21no—
184C2×Q8×C109—21no—
185C2×Q8×C109—21no—
186C2×Q8×C109—21no—
187C2×Q8×C109C2×D412yes—
188C2×D4×C109—24no—
189C2×D4×C109—22no—
190C2×D4×C109—24no—
191C2×D4×C109—22no—
192C2×D4×C109—24no—
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—41no—
208C2×D4×C109—42no—
209C2×D4×C109—42no—
210C2×D4×C109—42no—
211C2×D4×C109—44no—
212C2×D4×C109—44no—
213C2×D4×C109—44no—
214C2×D4×C109—42no—
215C2×D4×C109—42no—
216C2×D4×C109—44no—
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×C109C2×D412yes—
225C2×D4×C109C2×D412yes—
226C2×D4×C109C2×D412yes—
227C2×D4×C109#4112yes—
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—24no—
236C22×C4×C109—24no—
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—42no—
246C22×C4×C109—42no—
247C22×C4×C109—81no—
248C22×C4×C109—81no—
249C22×C4×C109C2×D411yescharacteristic
250C22×C4×C109C2×D411yescharacteristic
251C22×C4×C109C2×D411yescharacteristic
252C22×C4×C109C2×D411yescharacteristic
253C22×C4×C109C2×D412yes—
254C22×C4×C109C2×D412yes—
255C22×C4×C109C2411yescharacteristic
256SD16×C109—44no—
257D8×C109—44no—
258D8×C109—44no—
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—21no—
266C2×C8×C109—21no—
267C2×C8×C109—21no—
268C2×C8×C109—21no—
269C2×C8×C109—21no—
270C2×C8×C109—44no—
271C2×C8×C109C2×D412yes—
272C4⋊C4×C109—24no—
273C4⋊C4×C109—22no—
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×C109—81no—
281C4⋊C4×C109C2×D412yes—
282C4⋊C4×C109C2×D412yes—
283C22⋊C4×C109—24no—
284C22⋊C4×C109—24no—
285C22⋊C4×C109—24no—
286C22⋊C4×C109—24no—
287C22⋊C4×C109—22no—
288C22⋊C4×C109—22no—
289C22⋊C4×C109—24no—
290C22⋊C4×C109—42no—
291C22⋊C4×C109—42no—
292C22⋊C4×C109—42no—
293C22⋊C4×C109—42no—
294C22⋊C4×C109—81no—
295C22⋊C4×C109—81no—
296C42×C109—21no—
297C42×C109—21no—
298C42×C109—42no—
299C23×C109—21no—
300C23×C109—22no—
301C23×C109—21no—
302C23×C109—21no—
303C23×C109—22no—
304C23×C109—21no—
305C23×C109—21no—
306C23×C109—22no—
307C23×C109—21no—
308C23×C109—21no—
309C23×C109—21no—
310C23×C109—21no—
311C23×C109—21no—
312C23×C109—21no—
313C23×C109—21no—
314C23×C109—22no—
315C23×C109—48no—
316C23×C109—48no—
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—84no—
335C23×C109—84no—
336C23×C109—84no—
337C23×C109—84no—
338C23×C109—84no—
339C23×C109#12012yes—
340C23×C109#13512yes—
341C23×C109C22×D411yescharacteristic
342Q8×C109—22no—
343Q8×C109—22no—
344Q8×C109—41no—
345Q8×C109—41no—
346D4×C109—22no—
347D4×C109—22no—
348D4×C109—22no—
349D4×C109—22no—
350D4×C109—22no—
351D4×C109—44no—
352D4×C109—48no—
353D4×C109—48no—
354D4×C109—41no—
355D4×C109—41no—
356D4×C109—41no—
357D4×C109—41no—
358D4×C109—41no—
359D4×C109—41no—
360D4×C109—84no—
361D4×C109—84no—
362D4×C109—84no—
363D4×C109#12114yes—
364C2×C4×C109—21no—
365C2×C4×C109—21no—
366C2×C4×C109—22no—
367C2×C4×C109—22no—
368C2×C4×C109—22no—
369C2×C4×C109—22no—
370C2×C4×C109—21no—
371C2×C4×C109—21no—
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—21no—
379C2×C4×C109—21no—
380C2×C4×C109—21no—
381C2×C4×C109—21no—
382C2×C4×C109—48no—
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—41no—
396C2×C4×C109—41no—
397C2×C4×C109—41no—
398C2×C4×C109—41no—
399C2×C4×C109—84no—
400C2×C4×C109#12012yes—
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—24no—
413C22×C109—22no—
414C22×C109—22no—
415C22×C109—22no—
416C22×C109—22no—
417C22×C109—22no—
418C22×C109—41no—
419C22×C109—42no—
420C22×C109—42no—
421C22×C109—41no—
422C22×C109—41no—
423C22×C109—41no—
424C22×C109—42no—
425C22×C109—41no—
426C22×C109—42no—
427C22×C109—41no—
428C22×C109—42no—
429C22×C109—41no—
430C22×C109—41no—
431C22×C109—42no—
432C22×C109—42no—
433C22×C109—42no—
434C22×C109—42no—
435C22×C109—816no—
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×C109—81no—
447C22×C109C2×#12011yescharacteristic
448C22×C109D4211yescharacteristic
449C22×C109#54611yescharacteristic
450C22×C109C2×#13511yescharacteristic
451C22×C109#57511yescharacteristic
452C22×C109#57611yescharacteristic
453C22×C109#57611yescharacteristic
454C4×C109—22no—
455C4×C109—41no—
456C4×C109—42no—
457C4×C109—41no—
458C4×C109—41no—
459C4×C109—42no—
460C4×C109—42no—
461C4×C109—81no—
462C4×C109—81no—
463C4×C109C2×#12111yescharacteristic
464C4×C109#53411yescharacteristic
465C4×C109D4211yescharacteristic
466C4×C109#54611yescharacteristic
467#24428C10911yesmaximal, characteristic, direct product factor, Sylow
468C2×C109—42no—
469C2×C109—42no—
470C2×C109—44no—
471C2×C109—82no—
472C2×C109—161no—
473C2×C109#241011yescharacteristic
474C2×C109#300211yescharacteristic
475C2×C109#300811yescharacteristic
476C2×C109#326811yescharacteristic
477C2×C109#328011yescharacteristic
478C2×C109#329711yescharacteristic
479C2×C109#331911yescharacteristic
480C2×#546C2×C10911yescharacteristic, complemented
481C2×#466C2×C10911yescharacteristic, complemented
482C2×#449C2×C10911yescharacteristic, complemented
483C2×#447C2×C10911yescharacteristic, complemented
484C2×#416C2×C10911yescharacteristic, complemented
485#2414C2×C10911yescharacteristic, complemented
486#2042C2×C10911yescharacteristic, complemented
487#2036C2×C10911yescharacteristic, complemented
488#2012C2×C10911yescharacteristic, complemented
489#2000C2×C10911yescharacteristic, complemented
490#1879C2×C10911yescharacteristic, complemented
491#1875C2×C10911yescharacteristic, complemented
492#1869C2×C10911yescharacteristic, complemented
493#1862C2×C10911yescharacteristic, complemented
494#1786C2×C10911yescharacteristic, complemented
495C109#2442811yescharacteristic, direct product factor, Sylow
496C22×#41C22×C10911yescharacteristic
497C23×D4C22×C10911yescharacteristic
498C22×SD16C22×C10911yescharacteristic, complemented
499C22×D8C22×C10911yescharacteristic
500C22×D8C22×C10911yescharacteristic
501C23×C8C22×C10911yescharacteristic, complemented
502#546—24no—
503#546—24no—
504C2×#124C22×C10911yescharacteristic
505C2×#123—21no—
506C2×C22⋊Q8C22×C10911yescharacteristic
507C2×#121—21no—
508C2×#121C22×C10911yescharacteristic
509C2×#121C22×C10911yescharacteristic
510C2×#121C22×C10911yescharacteristic, complemented
511C2×#120—21no—
512C2×C4×D4C22×C10911yescharacteristic
513C2×C4×D4C22×C10911yescharacteristic
514C2×#117C22×C10911yescharacteristic, complemented
515C22×C22⋊C4—21no—
516#466—24no—
517#449—24no—
518#447—24no—
519C2×#107C22×C10911yescharacteristic, complemented
520#416—24no—
521C2×#103C22×C10911yescharacteristic, complemented
522C2×#103C22×C10911yescharacteristic, complemented
523C2×#103C22×C10911yescharacteristic, complemented
524C2×#102C22×C10911yescharacteristic
525C2×#102C22×C10911yescharacteristic
526C2×#102C22×C10911yescharacteristic
527C2×#102C22×C10911yescharacteristic
528C2×#102C22×C10911yescharacteristic
529C2×#102C22×C10911yescharacteristic
530C2×#102C22×C10911yescharacteristic, complemented
531C2×C22⋊C8C22×C10911yescharacteristic
532C2×C22⋊C8C22×C10911yescharacteristic
533C2×C22⋊C8C22×C10911yescharacteristic, complemented
534#394—21no—
535#392—21no—
536#390—21no—
537#390C22×C10911yescharacteristic, complemented
538#389C22×C10911yescharacteristic, complemented
539#388—21no—
540#380C22×C10911yescharacteristic
541#340C22×C10911yescharacteristic, complemented
542#340C22×C10911yescharacteristic, complemented
543#336C22×C10911yescharacteristic, complemented
544#336C22×C10911yescharacteristic, complemented
545C25—21no—
546C2×#41—22no—
547C2×#41—22no—
548C2×#41—22no—
549C2×#41—41no—
550C2×#41—41no—
551C2×#41D4×C10914yescomplemented
552C22×Q8C23×C10911yescharacteristic
553C22×D4—21no—
554C22×D4—21no—
555C22×D4—22no—
556C22×D4—22no—
557C22×D4—22no—
558C22×D4—22no—
559C22×D4—21no—
560C22×D4—21no—
561C22×D4—21no—
562C22×D4—41no—
563C22×D4—41no—
564C22×D4D4×C10911yescharacteristic
565C22×D4C23×C10911yescharacteristic
566C22×D4C23×C10911yescharacteristic
567C22×D4C23×C10911yescharacteristic
568C23×C4—21no—
569C23×C4—21no—
570C23×C4C23×C10911yescharacteristic
571C23×C4C23×C10911yescharacteristic
572C2×SD16—22no—
573C2×SD16—41no—
574C2×SD16—41no—
575C2×D8—22no—
576C2×D8—22no—
577C2×D8—22no—
578C2×D8—22no—
579C2×D8—22no—
580C2×D8—41no—
581C22×C8—22no—
582C22×C8—22no—
583C22×C8—41no—
584C22×C8C23×C10911yescharacteristic
585C22×C8C23×C10911yescharacteristic
586C22×C8C23×C10911yescharacteristic
587C22×C8C23×C10911yescharacteristic
588#124—22no—
589#124—22no—
590#123—28no—
591C22⋊Q8—22no—
592C22⋊Q8—22no—
593#121—28no—
594#121—22no—
595#121—22no—
596#121—22no—
597#121—22no—
598#121—41no—
599#121D4×C10914yescomplemented
600#120—28no—
601C4×D4—22no—
602C4×D4—22no—
603C4×D4—22no—
604C4×D4—22no—
605#117—22no—
606#117—41no—
607C2×C4⋊C4—21no—
608C2×C4⋊C4—21no—
609C2×C4⋊C4D4×C10911yescharacteristic
610C2×C4⋊C4C23×C10911yescharacteristic
611C2×C4⋊C4C23×C10911yescharacteristic
612C2×C4⋊C4C23×C10911yescharacteristic
613C2×C4⋊C4C23×C10911yescharacteristic
614C2×C22⋊C4—28no—
615C2×C22⋊C4—21no—
616C2×C22⋊C4—21no—
617C2×C22⋊C4—21no—
618C2×C22⋊C4—21no—
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#107—22no—
631#103—22no—
632#103—22no—
633#103—22no—
634#102—22no—
635#102—22no—
636#102—22no—
637#102—22no—
638#102—22no—
639#102—41no—
640#102D4×C10914yescomplemented
641C22⋊C8—22no—
642C22⋊C8—22no—
643C22⋊C8—41no—
644#95—21no—
645#95—21no—
646C24—21no—
647C24—24no—
648C24—21no—
649C24—21no—
650C24—42no—
651C24—42no—
652C24—42no—
653C24—42no—
654C24—81no—
655C24—81no—
656C24C2×D4×C10911yescharacteristic
657C24C2×D4×C10911yescharacteristic
658#41—28no—
659#41—44no—
660#41—44no—
661#41—44no—
662C2×Q8—21no—
663C2×Q8—21no—
664C2×Q8—21no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8C2×D4×C10912yes—
668C2×D4—24no—
669C2×D4—22no—
670C2×D4—24no—
671C2×D4—22no—
672C2×D4—24no—
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—41no—
688C2×D4—42no—
689C2×D4—42no—
690C2×D4—42no—
691C2×D4—44no—
692C2×D4—44no—
693C2×D4—44no—
694C2×D4—42no—
695C2×D4—42no—
696C2×D4—44no—
697C2×D4—42no—
698C2×D4—42no—
699C2×D4—81no—
700C2×D4—81no—
701C2×D4—81no—
702C2×D4—81no—
703C2×D4—81no—
704C2×D4C2×D4×C10912yes—
705C2×D4C2×D4×C10912yes—
706C2×D4C2×D4×C10912yes—
707C2×D4#41×C10912yes—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—21no—
715C22×C4—24no—
716C22×C4—24no—
717C22×C4—21no—
718C22×C4—21no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—21no—
722C22×C4—21no—
723C22×C4—21no—
724C22×C4—21no—
725C22×C4—42no—
726C22×C4—42no—
727C22×C4—81no—
728C22×C4—81no—
729C22×C4C2×D4×C10911yescharacteristic
730C22×C4C2×D4×C10911yescharacteristic
731C22×C4C2×D4×C10911yescharacteristic
732C22×C4C2×D4×C10911yescharacteristic
733C22×C4C2×D4×C10912yes—
734C22×C4C2×D4×C10912yes—
735C22×C4C24×C10911yescharacteristic
736SD16—44no—
737D8—44no—
738D8—44no—
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—21no—
748C2×C8—21no—
749C2×C8—21no—
750C2×C8—44no—
751C2×C8C2×D4×C10912yes—
752C4⋊C4—24no—
753C4⋊C4—22no—
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—21no—
757C4⋊C4—21no—
758C4⋊C4—21no—
759C4⋊C4—21no—
760C4⋊C4—81no—
761C4⋊C4C2×D4×C10912yes—
762C4⋊C4C2×D4×C10912yes—
763C22⋊C4—24no—
764C22⋊C4—24no—
765C22⋊C4—24no—
766C22⋊C4—24no—
767C22⋊C4—22no—
768C22⋊C4—22no—
769C22⋊C4—24no—
770C22⋊C4—42no—
771C22⋊C4—42no—
772C22⋊C4—42no—
773C22⋊C4—42no—
774C22⋊C4—81no—
775C22⋊C4—81no—
776C42—21no—
777C42—21no—
778C42—42no—
779C23—21no—
780C23—22no—
781C23—21no—
782C23—21no—
783C23—22no—
784C23—21no—
785C23—21no—
786C23—22no—
787C23—21no—
788C23—21no—
789C23—21no—
790C23—21no—
791C23—21no—
792C23—21no—
793C23—21no—
794C23—22no—
795C23—48no—
796C23—48no—
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—84no—
815C23—84no—
816C23—84no—
817C23—84no—
818C23—84no—
819C23#120×C10912yes—
820C23#135×C10912yes—
821C23C22×D4×C10911yescharacteristic
822Q8—22no—
823Q8—22no—
824Q8—41no—
825Q8—41no—
826D4—22no—
827D4—22no—
828D4—22no—
829D4—22no—
830D4—22no—
831D4—44no—
832D4—48no—
833D4—48no—
834D4—41no—
835D4—41no—
836D4—41no—
837D4—41no—
838D4—41no—
839D4—41no—
840D4—84no—
841D4—84no—
842D4—84no—
843D4#121×C10914yes—
844C2×C4—21no—
845C2×C4—21no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—21no—
851C2×C4—21no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—21no—
855C2×C4—22no—
856C2×C4—21no—
857C2×C4—21no—
858C2×C4—21no—
859C2×C4—21no—
860C2×C4—21no—
861C2×C4—21no—
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—41no—
878C2×C4—41no—
879C2×C4—84no—
880C2×C4#120×C10912yes—
881C2×C4C22×D4×C10911yescharacteristic
882C2×C4C22×D4×C10911yescharacteristic
883C2×C4C22×D4×C10911yescharacteristic
884C2×C4C2×#41×C10911yescharacteristic
885C2×C4H(5,𝔽2)×C10911yescharacteristic
886C2×C4H(5,𝔽2)×C10911yescharacteristic
887C8—22no—
888C8—41no—
889C8—41no—
890C8—41no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—22no—
897C22—24no—
898C22—42no—
899C22—42no—
900C22—41no—
901C22—41no—
902C22—41no—
903C22—42no—
904C22—41no—
905C22—42no—
906C22—41no—
907C22—42no—
908C22—41no—
909C22—41no—
910C22—42no—
911C22—41no—
912C22—42no—
913C22—42no—
914C22—42no—
915C22—816no—
916C22—81no—
917C22—81no—
918C22—81no—
919C22—81no—
920C22—81no—
921C22—81no—
922C22—81no—
923C22—81no—
924C22—81no—
925C22—81no—
926C22—81no—
927C22C2×#120×C10911yescharacteristic
928C22D42×C10911yescharacteristic
929C22#546×C10911yescharacteristic
930C22C2×#135×C10911yescharacteristic
931C22#575×C10911yescharacteristic
932C22#576×C10911yescharacteristic
933C22#576×C10911yescharacteristic
934C4—22no—
935C4—41no—
936C4—41no—
937C4—42no—
938C4—42no—
939C4—41no—
940C4—42no—
941C4—81no—
942C4—81no—
943C4C2×#121×C10911yescharacteristic
944C4#534×C10911yescharacteristic
945C4D42×C10911yescharacteristic
946C4#546×C10911yescharacteristic
947C2—42no—
948C2—42no—
949C2—44no—
950C2—82no—
951C2—161no—
952C2C109×#241011yescharacteristic
953C2C109×#300211yescharacteristic
954C2C109×#300811yescharacteristic
955C2C109×#326811yescharacteristic
956C2C109×#328011yescharacteristic
957C2C109×#329711yescharacteristic
958C2C109×#331911yescharacteristic
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×#546×C109C2semidirect
2. C2×#466×C109C2semidirect
3. C2×#449×C109C2semidirect
4. C2×#447×C109C2semidirect
5. C2×#416×C109C2semidirect
6. C109×#2414C2semidirect
7. C109×#2042C2semidirect
8. C109×#2036C2semidirect
9. C109×#2012C2semidirect
10. C109×#2000C2semidirect
11. C109×#1879C2semidirect
12. C109×#1875C2semidirect
13. C109×#1869C2semidirect
14. C109×#1862C2semidirect
15. C109×#1786C2semidirect
18. C22×SD16×C109C22semidirect
21. C23×C8×C109C22semidirect
30. C2×#121×C109C22semidirect
34. C2×#117×C109C22semidirect
39. C2×#107×C109C22semidirect
41. C2×#103×C109C22semidirect
42. C2×#103×C109C22semidirect
43. C2×#103×C109C22semidirect
50. C2×#102×C109C22semidirect
53. C2×C22⋊C8×C109C22semidirect
57. #390×C109C22semidirect
58. #389×C109C22semidirect
61. #340×C109C22semidirect
62. #340×C109C22semidirect
63. #336×C109C22semidirect
64. #336×C109C22semidirect
71. C2×#41×C109D4semidirect
119. #121×C109D4semidirect
160. #102×C109D4semidirect
467. #24428C109direct (N × H)
480. C2×#546C2×C109semidirect
481. C2×#466C2×C109semidirect
482. C2×#449C2×C109semidirect
483. C2×#447C2×C109semidirect
484. C2×#416C2×C109semidirect
485. #2414C2×C109semidirect
486. #2042C2×C109semidirect
487. #2036C2×C109semidirect
488. #2012C2×C109semidirect
489. #2000C2×C109semidirect
490. #1879C2×C109semidirect
491. #1875C2×C109semidirect
492. #1869C2×C109semidirect
493. #1862C2×C109semidirect
494. #1786C2×C109semidirect
495. C109#24428direct (N × H)
498. C22×SD16C22×C109semidirect
501. C23×C8C22×C109semidirect
510. C2×#121C22×C109semidirect
514. C2×#117C22×C109semidirect
519. C2×#107C22×C109semidirect
521. C2×#103C22×C109semidirect
522. C2×#103C22×C109semidirect
523. C2×#103C22×C109semidirect
530. C2×#102C22×C109semidirect
533. C2×C22⋊C8C22×C109semidirect
537. #390C22×C109semidirect
538. #389C22×C109semidirect
541. #340C22×C109semidirect
542. #340C22×C109semidirect
543. #336C22×C109semidirect
544. #336C22×C109semidirect
551. C2×#41D4×C109semidirect
599. #121D4×C109semidirect
640. #102D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#546×C1092
C2×#466×C1092
C2×#449×C1092
C2×#447×C1092
C2×#416×C1092
C109×#24142
C109×#20422
C109×#20362
C109×#20122
C109×#20002
C109×#18792
C109×#18752
C109×#18692
C109×#18622
C109×#17862
#24428109