Finite Group Databasebeta

← C109×#24425 #42142419

Subgroups — C109×#24425 #42142419

Order 27904.

1492 conjugacy classes of subgroups.

The subgroup lattice has 910 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#548×C109C211yesmaximal, characteristic, complemented
2C2×#465×C109C211yesmaximal, characteristic, complemented
3C2×#449×C109C211yesmaximal, characteristic, complemented
4C2×#448×C109C211yesmaximal, characteristic, complemented
5C2×#416×C109C211yesmaximal, characteristic, complemented
6C109×#2414C211yesmaximal, characteristic, complemented
7C109×#2042C211yesmaximal, characteristic, complemented
8C109×#2034C211yesmaximal, characteristic, complemented
9C109×#2012C211yesmaximal, characteristic, complemented
10C109×#1999C211yesmaximal, characteristic, complemented
11C109×#1880C211yesmaximal, characteristic, complemented
12C109×#1873C211yesmaximal, characteristic, complemented
13C109×#1869C211yesmaximal, characteristic, complemented
14C109×#1865C211yesmaximal, characteristic, complemented
15C109×#1787C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C23×Q8×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C22×SD16×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic
21C23×C8×C109C2211yescharacteristic
22#548×C109—24no—
23#548×C109—24no—
24C2×#124×C109—21no—
25C2×#124×C109C2211yescharacteristic
26C2×C22⋊Q8×C109—21no—
27C2×C22⋊Q8×C109C2211yescharacteristic
28C2×#121×C109—21no—
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#465×C109—24no—
37#449×C109—24no—
38#448×C109—24no—
39C2×#106×C109C2211yescharacteristic
40#416×C109—24no—
41C2×#103×C109C2211yescharacteristic
42C2×#103×C109C2211yescharacteristic
43C2×#103×C109C2211yescharacteristic
44C2×#103×C109C2211yescharacteristic
45C2×#103×C109C2211yescharacteristic
46C2×#103×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—41no—
69C2×#41×C109—41no—
70C2×#41×C109D414yescomplemented
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×C109C2311yescharacteristic
79C22×Q8×C109C2311yescharacteristic
80C22×D4×C109—21no—
81C22×D4×C109—21no—
82C22×D4×C109—21no—
83C22×D4×C109—21no—
84C22×D4×C109D411yescharacteristic
85C22×D4×C109C2311yescharacteristic
86C22×D4×C109C2311yescharacteristic
87C23×C4×C109—21no—
88C23×C4×C109—21no—
89C23×C4×C109C2311yescharacteristic
90C23×C4×C109C2311yescharacteristic
91C2×SD16×C109—22no—
92C2×SD16×C109—22no—
93C2×SD16×C109—22no—
94C2×SD16×C109—22no—
95C2×SD16×C109—22no—
96C2×SD16×C109—41no—
97C2×D8×C109—22no—
98C2×D8×C109—41no—
99C2×D8×C109—41no—
100C22×C8×C109—22no—
101C22×C8×C109—22no—
102C22×C8×C109—41no—
103C22×C8×C109C2311yescharacteristic
104C22×C8×C109C2311yescharacteristic
105C22×C8×C109C2311yescharacteristic
106C22×C8×C109C2311yescharacteristic
107#124×C109—28no—
108#124×C109—22no—
109#124×C109—22no—
110C22⋊Q8×C109—28no—
111C22⋊Q8×C109—22no—
112C22⋊Q8×C109D414yescomplemented
113#121×C109—28no—
114#121×C109—22no—
115#121×C109—22no—
116#121×C109—22no—
117#121×C109—22no—
118#121×C109—22no—
119#121×C109—41no—
120C4×Q8×C109—22no—
121C4×Q8×C109—22no—
122C4×D4×C109—28no—
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×C109—21no—
130C2×C4⋊C4×C109D411yescharacteristic
131C2×C4⋊C4×C109C2311yescharacteristic
132C2×C4⋊C4×C109C2311yescharacteristic
133C2×C4⋊C4×C109C2311yescharacteristic
134C2×C4⋊C4×C109C2311yescharacteristic
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×C109D411yescharacteristic
146C2×C22⋊C4×C109D411yescharacteristic
147C2×C42×C109—21no—
148C2×C42×C109—21no—
149C2×C42×C109C2311yescharacteristic
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×C109D414yescomplemented
157#102×C109—22no—
158#102×C109—22no—
159#102×C109—22no—
160#102×C109—22no—
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×C109C2×D411yescharacteristic
169C24×C109C2×D411yescharacteristic
170#41×C109—28no—
171#41×C109—44no—
172#41×C109—44no—
173#41×C109—44no—
174C2×Q8×C109—24no—
175C2×Q8×C109—21no—
176C2×Q8×C109—21no—
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—42no—
184C2×Q8×C109—42no—
185C2×Q8×C109—44no—
186C2×Q8×C109—44no—
187C2×Q8×C109—44no—
188C2×Q8×C109—44no—
189C2×Q8×C109C2×D412yes—
190C2×Q8×C109C2×D412yes—
191C2×Q8×C109C2×D412yes—
192C2×Q8×C109#4112yes—
193C2×D4×C109—24no—
194C2×D4×C109—22no—
195C2×D4×C109—24no—
196C2×D4×C109—22no—
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—41no—
209C2×D4×C109—42no—
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—81no—
217C2×D4×C109—81no—
218C2×D4×C109—81no—
219C2×D4×C109C2×D412yes—
220C22×C4×C109—21no—
221C22×C4×C109—21no—
222C22×C4×C109—21no—
223C22×C4×C109—21no—
224C22×C4×C109—21no—
225C22×C4×C109—24no—
226C22×C4×C109—21no—
227C22×C4×C109—21no—
228C22×C4×C109—21no—
229C22×C4×C109—24no—
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—42no—
239C22×C4×C109—42no—
240C22×C4×C109—42no—
241C22×C4×C109—42no—
242C22×C4×C109C2×D411yescharacteristic
243C22×C4×C109C2×D411yescharacteristic
244C22×C4×C109C2×D411yescharacteristic
245C22×C4×C109C2×D411yescharacteristic
246C22×C4×C109C2×D412yes—
247C22×C4×C109C2×D412yes—
248C22×C4×C109C2411yescharacteristic
249SD16×C109—44no—
250SD16×C109—44no—
251D8×C109—44no—
252C2×C8×C109—21no—
253C2×C8×C109—21no—
254C2×C8×C109—21no—
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—44no—
264C2×C8×C109C2×D412yes—
265C4⋊C4×C109—24no—
266C4⋊C4×C109—24no—
267C4⋊C4×C109—22no—
268C4⋊C4×C109—21no—
269C4⋊C4×C109—21no—
270C4⋊C4×C109—21no—
271C4⋊C4×C109—21no—
272C4⋊C4×C109—21no—
273C4⋊C4×C109—21no—
274C4⋊C4×C109—81no—
275C4⋊C4×C109C2×D412yes—
276C4⋊C4×C109C2×D412yes—
277C22⋊C4×C109—24no—
278C22⋊C4×C109—24no—
279C22⋊C4×C109—24no—
280C22⋊C4×C109—24no—
281C22⋊C4×C109—22no—
282C22⋊C4×C109—22no—
283C22⋊C4×C109—42no—
284C22⋊C4×C109—42no—
285C22⋊C4×C109—42no—
286C22⋊C4×C109—42no—
287C22⋊C4×C109—81no—
288C22⋊C4×C109—81no—
289C42×C109—24no—
290C42×C109—21no—
291C42×C109—21no—
292C42×C109—42no—
293C23×C109—21no—
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—22no—
306C23×C109—41no—
307C23×C109—41no—
308C23×C109—41no—
309C23×C109—41no—
310C23×C109—41no—
311C23×C109—41no—
312C23×C109—41no—
313C23×C109—41no—
314C23×C109—41no—
315C23×C109—41no—
316C23×C109—41no—
317C23×C109—41no—
318C23×C109—41no—
319C23×C109#12012yes—
320C23×C109#13512yes—
321C23×C109C22×D411yescharacteristic
322Q8×C109—22no—
323Q8×C109—22no—
324Q8×C109—22no—
325Q8×C109—22no—
326Q8×C109—22no—
327Q8×C109—48no—
328Q8×C109—41no—
329Q8×C109—41no—
330Q8×C109#12114yes—
331D4×C109—22no—
332D4×C109—22no—
333D4×C109—48no—
334D4×C109—44no—
335D4×C109—48no—
336D4×C109—41no—
337D4×C109—41no—
338D4×C109—41no—
339D4×C109—41no—
340D4×C109—41no—
341D4×C109—41no—
342D4×C109—84no—
343D4×C109—84no—
344C2×C4×C109—22no—
345C2×C4×C109—21no—
346C2×C4×C109—22no—
347C2×C4×C109—21no—
348C2×C4×C109—22no—
349C2×C4×C109—22no—
350C2×C4×C109—22no—
351C2×C4×C109—22no—
352C2×C4×C109—22no—
353C2×C4×C109—21no—
354C2×C4×C109—21no—
355C2×C4×C109—22no—
356C2×C4×C109—22no—
357C2×C4×C109—21no—
358C2×C4×C109—22no—
359C2×C4×C109—21no—
360C2×C4×C109—21no—
361C2×C4×C109—21no—
362C2×C4×C109—21no—
363C2×C4×C109—21no—
364C2×C4×C109—21no—
365C2×C4×C109—48no—
366C2×C4×C109—48no—
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#12012yes—
384C2×C4×C109C22×D411yescharacteristic
385C2×C4×C109C22×D411yescharacteristic
386C2×C4×C109C22×D411yescharacteristic
387C2×C4×C109C2×#4111yescharacteristic
388C2×C4×C109H(5,𝔽2)11yescharacteristic
389C2×C4×C109H(5,𝔽2)11yescharacteristic
390C8×C109—22no—
391C8×C109—41no—
392C8×C109—41no—
393C8×C109—41no—
394C22×C109—22no—
395C22×C109—22no—
396C22×C109—22no—
397C22×C109—22no—
398C22×C109—22no—
399C22×C109—22no—
400C22×C109—41no—
401C22×C109—41no—
402C22×C109—41no—
403C22×C109—41no—
404C22×C109—41no—
405C22×C109—41no—
406C22×C109—41no—
407C22×C109—41no—
408C22×C109—42no—
409C22×C109—42no—
410C22×C109—42no—
411C22×C109—81no—
412C22×C109—81no—
413C22×C109—81no—
414C22×C109—81no—
415C22×C109—81no—
416C22×C109—81no—
417C22×C109—81no—
418C22×C109—81no—
419C22×C109—81no—
420C22×C109—81no—
421C22×C109—81no—
422C22×C109C2×#12011yescharacteristic
423C22×C109D4211yescharacteristic
424C22×C109#54611yescharacteristic
425C22×C109C2×#13511yescharacteristic
426C22×C109#57511yescharacteristic
427C22×C109#57711yescharacteristic
428C22×C109#57711yescharacteristic
429C4×C109—22no—
430C4×C109—24no—
431C4×C109—41no—
432C4×C109—42no—
433C4×C109—41no—
434C4×C109—42no—
435C4×C109—41no—
436C4×C109—42no—
437C4×C109—81no—
438C4×C109—81no—
439C4×C109C2×#12111yescharacteristic
440C4×C109#53411yescharacteristic
441C4×C109D4211yescharacteristic
442C4×C109#54611yescharacteristic
443#24425C10911yesmaximal, characteristic, direct product factor, Sylow
444C2×C109—42no—
445C2×C109—42no—
446C2×C109—82no—
447C2×C109—161no—
448C2×C109#241011yescharacteristic
449C2×C109#300211yescharacteristic
450C2×C109#301011yescharacteristic
451C2×C109#327111yescharacteristic
452C2×C109#328211yescharacteristic
453C2×C109#330111yescharacteristic
454C2×C109#332111yescharacteristic
455C2×#548C2×C10911yescharacteristic, complemented
456C2×#465C2×C10911yescharacteristic, complemented
457C2×#449C2×C10911yescharacteristic, complemented
458C2×#448C2×C10911yescharacteristic, complemented
459C2×#416C2×C10911yescharacteristic, complemented
460#2414C2×C10911yescharacteristic, complemented
461#2042C2×C10911yescharacteristic, complemented
462#2034C2×C10911yescharacteristic, complemented
463#2012C2×C10911yescharacteristic, complemented
464#1999C2×C10911yescharacteristic, complemented
465#1880C2×C10911yescharacteristic, complemented
466#1873C2×C10911yescharacteristic, complemented
467#1869C2×C10911yescharacteristic, complemented
468#1865C2×C10911yescharacteristic, complemented
469#1787C2×C10911yescharacteristic, complemented
470C109#2442511yescharacteristic, direct product factor, Sylow
471C22×#41C22×C10911yescharacteristic
472C23×Q8C22×C10911yescharacteristic
473C22×SD16C22×C10911yescharacteristic
474C22×SD16C22×C10911yescharacteristic
475C22×D8C22×C10911yescharacteristic
476C23×C8C22×C10911yescharacteristic
477#548—24no—
478#548—24no—
479C2×#124—21no—
480C2×#124C22×C10911yescharacteristic
481C2×C22⋊Q8—21no—
482C2×C22⋊Q8C22×C10911yescharacteristic
483C2×#121—21no—
484C2×#121C22×C10911yescharacteristic
485C2×#121C22×C10911yescharacteristic
486C2×#121C22×C10911yescharacteristic
487C2×C4×Q8C22×C10911yescharacteristic
488C2×C4×D4—21no—
489C2×C4×D4C22×C10911yescharacteristic
490C2×#117C22×C10911yescharacteristic
491#465—24no—
492#449—24no—
493#448—24no—
494C2×#106C22×C10911yescharacteristic
495#416—24no—
496C2×#103C22×C10911yescharacteristic
497C2×#103C22×C10911yescharacteristic
498C2×#103C22×C10911yescharacteristic
499C2×#103C22×C10911yescharacteristic
500C2×#103C22×C10911yescharacteristic
501C2×#103C22×C10911yescharacteristic
502C2×#102C22×C10911yescharacteristic
503C2×#102C22×C10911yescharacteristic
504C2×#102C22×C10911yescharacteristic
505C2×#102C22×C10911yescharacteristic
506C2×C22⋊C8C22×C10911yescharacteristic
507C2×C22⋊C8C22×C10911yescharacteristic
508C2×C22⋊C8C22×C10911yescharacteristic
509#394—21no—
510#392—21no—
511#390—21no—
512#390C22×C10911yescharacteristic
513#389C22×C10911yescharacteristic
514#388—21no—
515#380C22×C10911yescharacteristic
516#340C22×C10911yescharacteristic
517#340C22×C10911yescharacteristic
518#336C22×C10911yescharacteristic
519#336C22×C10911yescharacteristic
520C2×#41—22no—
521C2×#41—22no—
522C2×#41—22no—
523C2×#41—41no—
524C2×#41—41no—
525C2×#41D4×C10914yescomplemented
526C22×Q8—22no—
527C22×Q8—22no—
528C22×Q8—21no—
529C22×Q8—22no—
530C22×Q8—22no—
531C22×Q8—41no—
532C22×Q8—41no—
533C22×Q8C23×C10911yescharacteristic
534C22×Q8C23×C10911yescharacteristic
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4—21no—
539C22×D4D4×C10911yescharacteristic
540C22×D4C23×C10911yescharacteristic
541C22×D4C23×C10911yescharacteristic
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C23×C10911yescharacteristic
545C23×C4C23×C10911yescharacteristic
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—22no—
550C2×SD16—22no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—41no—
554C2×D8—41no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8C23×C10911yescharacteristic
559C22×C8C23×C10911yescharacteristic
560C22×C8C23×C10911yescharacteristic
561C22×C8C23×C10911yescharacteristic
562#124—28no—
563#124—22no—
564#124—22no—
565C22⋊Q8—28no—
566C22⋊Q8—22no—
567C22⋊Q8D4×C10914yescomplemented
568#121—28no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575C4×Q8—22no—
576C4×Q8—22no—
577C4×D4—28no—
578C4×D4—22no—
579C4×D4—22no—
580#117—22no—
581#117—41no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4D4×C10911yescharacteristic
586C2×C4⋊C4C23×C10911yescharacteristic
587C2×C4⋊C4C23×C10911yescharacteristic
588C2×C4⋊C4C23×C10911yescharacteristic
589C2×C4⋊C4C23×C10911yescharacteristic
590C2×C22⋊C4—21no—
591C2×C22⋊C4—21no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
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⋊C4D4×C10911yescharacteristic
601C2×C22⋊C4D4×C10911yescharacteristic
602C2×C42—21no—
603C2×C42—21no—
604C2×C42C23×C10911yescharacteristic
605#106—22no—
606#103—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—41no—
611#103D4×C10914yescomplemented
612#102—22no—
613#102—22no—
614#102—22no—
615#102—22no—
616C22⋊C8—22no—
617C22⋊C8—22no—
618C22⋊C8—41no—
619#95—21no—
620#95—21no—
621C24—21no—
622C24—21no—
623C24C2×D4×C10911yescharacteristic
624C24C2×D4×C10911yescharacteristic
625#41—28no—
626#41—44no—
627#41—44no—
628#41—44no—
629C2×Q8—24no—
630C2×Q8—21no—
631C2×Q8—21no—
632C2×Q8—21no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—42no—
639C2×Q8—42no—
640C2×Q8—44no—
641C2×Q8—44no—
642C2×Q8—44no—
643C2×Q8—44no—
644C2×Q8C2×D4×C10912yes—
645C2×Q8C2×D4×C10912yes—
646C2×Q8C2×D4×C10912yes—
647C2×Q8#41×C10912yes—
648C2×D4—24no—
649C2×D4—22no—
650C2×D4—24no—
651C2×D4—22no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—21no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—41no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—42no—
668C2×D4—42no—
669C2×D4—42no—
670C2×D4—42no—
671C2×D4—81no—
672C2×D4—81no—
673C2×D4—81no—
674C2×D4C2×D4×C10912yes—
675C22×C4—21no—
676C22×C4—21no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—24no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—24no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—42no—
694C22×C4—42no—
695C22×C4—42no—
696C22×C4—42no—
697C22×C4C2×D4×C10911yescharacteristic
698C22×C4C2×D4×C10911yescharacteristic
699C22×C4C2×D4×C10911yescharacteristic
700C22×C4C2×D4×C10911yescharacteristic
701C22×C4C2×D4×C10912yes—
702C22×C4C2×D4×C10912yes—
703C22×C4C24×C10911yescharacteristic
704SD16—44no—
705SD16—44no—
706D8—44no—
707C2×C8—21no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C2×C8—21no—
715C2×C8—21no—
716C2×C8—21no—
717C2×C8—21no—
718C2×C8—44no—
719C2×C8C2×D4×C10912yes—
720C4⋊C4—24no—
721C4⋊C4—24no—
722C4⋊C4—22no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—81no—
730C4⋊C4C2×D4×C10912yes—
731C4⋊C4C2×D4×C10912yes—
732C22⋊C4—24no—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—42no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—81no—
743C22⋊C4—81no—
744C42—24no—
745C42—21no—
746C42—21no—
747C42—42no—
748C23—21no—
749C23—21no—
750C23—21no—
751C23—21no—
752C23—21no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—22no—
761C23—41no—
762C23—41no—
763C23—41no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23#120×C10912yes—
775C23#135×C10912yes—
776C23C22×D4×C10911yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—22no—
782Q8—48no—
783Q8—41no—
784Q8—41no—
785Q8#121×C10914yes—
786D4—22no—
787D4—22no—
788D4—48no—
789D4—44no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—84no—
798D4—84no—
799C2×C4—22no—
800C2×C4—21no—
801C2×C4—22no—
802C2×C4—21no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—22no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—21no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—22no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—48no—
821C2×C4—48no—
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#120×C10912yes—
839C2×C4C22×D4×C10911yescharacteristic
840C2×C4C22×D4×C10911yescharacteristic
841C2×C4C22×D4×C10911yescharacteristic
842C2×C4C2×#41×C10911yescharacteristic
843C2×C4H(5,𝔽2)×C10911yescharacteristic
844C2×C4H(5,𝔽2)×C10911yescharacteristic
845C8—22no—
846C8—41no—
847C8—41no—
848C8—41no—
849C22—22no—
850C22—22no—
851C22—22no—
852C22—22no—
853C22—22no—
854C22—22no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—42no—
864C22—42no—
865C22—42no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—81no—
870C22—81no—
871C22—81no—
872C22—81no—
873C22—81no—
874C22—81no—
875C22—81no—
876C22—81no—
877C22C2×#120×C10911yescharacteristic
878C22D42×C10911yescharacteristic
879C22#546×C10911yescharacteristic
880C22C2×#135×C10911yescharacteristic
881C22#575×C10911yescharacteristic
882C22#577×C10911yescharacteristic
883C22#577×C10911yescharacteristic
884C4—22no—
885C4—24no—
886C4—41no—
887C4—42no—
888C4—41no—
889C4—42no—
890C4—41no—
891C4—42no—
892C4—81no—
893C4—81no—
894C4C2×#121×C10911yescharacteristic
895C4#534×C10911yescharacteristic
896C4D42×C10911yescharacteristic
897C4#546×C10911yescharacteristic
898C2—42no—
899C2—42no—
900C2—82no—
901C2—161no—
902C2C109×#241011yescharacteristic
903C2C109×#300211yescharacteristic
904C2C109×#301011yescharacteristic
905C2C109×#327111yescharacteristic
906C2C109×#328211yescharacteristic
907C2C109×#330111yescharacteristic
908C2C109×#332111yescharacteristic
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×#548×C109C2semidirect
2. C2×#465×C109C2semidirect
3. C2×#449×C109C2semidirect
4. C2×#448×C109C2semidirect
5. C2×#416×C109C2semidirect
6. C109×#2414C2semidirect
7. C109×#2042C2semidirect
8. C109×#2034C2semidirect
9. C109×#2012C2semidirect
10. C109×#1999C2semidirect
11. C109×#1880C2semidirect
12. C109×#1873C2semidirect
13. C109×#1869C2semidirect
14. C109×#1865C2semidirect
15. C109×#1787C2semidirect
70. C2×#41×C109D4semidirect
112. C22⋊Q8×C109D4semidirect
156. #103×C109D4semidirect
443. #24425C109direct (N × H)
455. C2×#548C2×C109semidirect
456. C2×#465C2×C109semidirect
457. C2×#449C2×C109semidirect
458. C2×#448C2×C109semidirect
459. C2×#416C2×C109semidirect
460. #2414C2×C109semidirect
461. #2042C2×C109semidirect
462. #2034C2×C109semidirect
463. #2012C2×C109semidirect
464. #1999C2×C109semidirect
465. #1880C2×C109semidirect
466. #1873C2×C109semidirect
467. #1869C2×C109semidirect
468. #1865C2×C109semidirect
469. #1787C2×C109semidirect
470. C109#24425direct (N × H)
525. C2×#41D4×C109semidirect
567. C22⋊Q8D4×C109semidirect
611. #103D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#548×C1092
C2×#465×C1092
C2×#449×C1092
C2×#448×C1092
C2×#416×C1092
C109×#24142
C109×#20422
C109×#20342
C109×#20122
C109×#19992
C109×#18802
C109×#18732
C109×#18692
C109×#18652
C109×#17872
#24425109