Finite Group Databasebeta

← C109×#24438 #42142432

Subgroups — C109×#24438 #42142432

Order 27904.

1498 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×#547×C109C211yesmaximal, characteristic, complemented
2C2×#465×C109C211yesmaximal, characteristic, complemented
3C2×#449×C109C211yesmaximal, characteristic, complemented
4C2×#449×C109C211yesmaximal, characteristic, complemented
5C2×#416×C109C211yesmaximal, characteristic, complemented
6C109×#2414C211yesmaximal, characteristic, complemented
7C109×#2043C211yesmaximal, characteristic, complemented
8C109×#2035C211yesmaximal, characteristic, complemented
9C109×#2013C211yesmaximal, characteristic, complemented
10C109×#2000C211yesmaximal, characteristic, complemented
11C109×#1879C211yesmaximal, characteristic, complemented
12C109×#1873C211yesmaximal, characteristic, complemented
13C109×#1869C211yesmaximal, characteristic, complemented
14C109×#1864C211yesmaximal, characteristic, complemented
15C109×#1788C211yesmaximal, characteristic, complemented
16C22×#41×C109C2211yescharacteristic
17C22×#41×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C22×SD16×C109C2211yescharacteristic
20C22×D8×C109C2211yescharacteristic
21C23×C8×C109C2211yescharacteristic
22#547×C109—24no—
23#547×C109—24no—
24C2×C4⋊Q8×C109C2211yescharacteristic
25C2×#123×C109—21no—
26C2×#123×C109—21no—
27C2×C22⋊Q8×C109C2211yescharacteristic
28C2×C22⋊Q8×C109C2211yescharacteristic
29C2×#121×C109—21no—
30C2×#121×C109C2211yescharacteristic
31C2×#121×C109C2211yescharacteristic
32C2×C4×D4×C109C2211yescharacteristic
33C2×C4×D4×C109C2211yescharacteristic
34C2×#117×C109C2211yescharacteristic
35C22×C4⋊C4×C109—21no—
36#465×C109—24no—
37#449×C109—24no—
38#449×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—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×Q8×C109C2311yescharacteristic
79C22×D4×C109—21no—
80C22×D4×C109—21no—
81C22×D4×C109—21no—
82C22×D4×C109—21no—
83C22×D4×C109D411yescharacteristic
84C22×D4×C109C2311yescharacteristic
85C22×D4×C109C2311yescharacteristic
86C23×C4×C109—21no—
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—41no—
95C2×SD16×C109—41no—
96C2×SD16×C109—41no—
97C2×D8×C109—22no—
98C2×D8×C109—22no—
99C2×D8×C109—22no—
100C22×C8×C109—22no—
101C22×C8×C109—22no—
102C22×C8×C109—41no—
103C22×C8×C109C2311yescharacteristic
104C22×C8×C109C2311yescharacteristic
105C22×C8×C109C2311yescharacteristic
106C22×C8×C109C2311yescharacteristic
107C4⋊Q8×C109—22no—
108C4⋊Q8×C109—22no—
109#123×C109—28no—
110#123×C109—28no—
111C22⋊Q8×C109—22no—
112C22⋊Q8×C109—22no—
113C22⋊Q8×C109—22no—
114C22⋊Q8×C109D414yescomplemented
115#121×C109—28no—
116#121×C109—22no—
117#121×C109—22no—
118#121×C109—22no—
119#121×C109—41no—
120C4×D4×C109—22no—
121C4×D4×C109—22no—
122C4×D4×C109—22no—
123C4×D4×C109—22no—
124#117×C109—22no—
125#117×C109—41no—
126C2×C4⋊C4×C109—28no—
127C2×C4⋊C4×C109—21no—
128C2×C4⋊C4×C109—21no—
129C2×C4⋊C4×C109—21no—
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×C109—21no—
146C2×C22⋊C4×C109D411yescharacteristic
147C2×C22⋊C4×C109D411yescharacteristic
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—22no—
156#103×C109—41no—
157#102×C109—22no—
158#102×C109—22no—
159#102×C109—22no—
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—21no—
168C24×C109C2×D411yescharacteristic
169C24×C109C2×D411yescharacteristic
170#41×C109—28no—
171#41×C109—44no—
172#41×C109—44no—
173#41×C109—44no—
174#41×C109—44no—
175#41×C109—44no—
176#41×C109—44no—
177#41×C109—44no—
178C2×Q8×C109—21no—
179C2×Q8×C109—21no—
180C2×Q8×C109—21no—
181C2×Q8×C109—21no—
182C2×Q8×C109—21no—
183C2×Q8×C109—21no—
184C2×Q8×C109—21no—
185C2×Q8×C109—21no—
186C2×Q8×C109—21no—
187C2×Q8×C109—21no—
188C2×Q8×C109C2×D412yes—
189C2×Q8×C109C2×D412yes—
190C2×D4×C109—24no—
191C2×D4×C109—22no—
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—41no—
204C2×D4×C109—42no—
205C2×D4×C109—42no—
206C2×D4×C109—42no—
207C2×D4×C109—42no—
208C2×D4×C109—42no—
209C2×D4×C109—42no—
210C2×D4×C109—42no—
211C2×D4×C109—81no—
212C2×D4×C109—81no—
213C2×D4×C109—81no—
214C2×D4×C109C2×D412yes—
215C2×D4×C109C2×D412yes—
216C2×D4×C109#4112yes—
217C22×C4×C109—21no—
218C22×C4×C109—21no—
219C22×C4×C109—21no—
220C22×C4×C109—21no—
221C22×C4×C109—24no—
222C22×C4×C109—24no—
223C22×C4×C109—21no—
224C22×C4×C109—21no—
225C22×C4×C109—21no—
226C22×C4×C109—21no—
227C22×C4×C109—24no—
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—21no—
236C22×C4×C109—42no—
237C22×C4×C109—42no—
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×D412yes—
246C22×C4×C109C2×D412yes—
247C22×C4×C109C2×D411yescharacteristic
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—24no—
268C4⋊C4×C109—22no—
269C4⋊C4×C109—24no—
270C4⋊C4×C109—21no—
271C4⋊C4×C109—21no—
272C4⋊C4×C109—21no—
273C4⋊C4×C109—21no—
274C4⋊C4×C109—21no—
275C4⋊C4×C109—21no—
276C4⋊C4×C109—81no—
277C4⋊C4×C109C2×D412yes—
278C4⋊C4×C109C2×D412yes—
279C22⋊C4×C109—24no—
280C22⋊C4×C109—24no—
281C22⋊C4×C109—24no—
282C22⋊C4×C109—22no—
283C22⋊C4×C109—22no—
284C22⋊C4×C109—42no—
285C22⋊C4×C109—42no—
286C22⋊C4×C109—42no—
287C22⋊C4×C109—42no—
288C22⋊C4×C109—81no—
289C22⋊C4×C109—81no—
290C42×C109—21no—
291C42×C109—21no—
292C42×C109—42no—
293C23×C109—22no—
294C23×C109—21no—
295C23×C109—22no—
296C23×C109—21no—
297C23×C109—22no—
298C23×C109—21no—
299C23×C109—21no—
300C23×C109—21no—
301C23×C109—21no—
302C23×C109—21no—
303C23×C109—21no—
304C23×C109—21no—
305C23×C109—21no—
306C23×C109—21no—
307C23×C109—21no—
308C23×C109—21no—
309C23×C109—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—41no—
320C23×C109#12012yes—
321C23×C109C22×D411yescharacteristic
322Q8×C109—22no—
323Q8×C109—22no—
324Q8×C109—22no—
325Q8×C109—22no—
326Q8×C109—41no—
327Q8×C109—41no—
328Q8×C109—41no—
329Q8×C109—41no—
330D4×C109—22no—
331D4×C109—22no—
332D4×C109—22no—
333D4×C109—44no—
334D4×C109—48no—
335D4×C109—48no—
336D4×C109—41no—
337D4×C109—41no—
338D4×C109—41no—
339D4×C109—41no—
340D4×C109—84no—
341D4×C109—84no—
342D4×C109#12114yes—
343C2×C4×C109—21no—
344C2×C4×C109—21no—
345C2×C4×C109—21no—
346C2×C4×C109—21no—
347C2×C4×C109—22no—
348C2×C4×C109—22no—
349C2×C4×C109—22no—
350C2×C4×C109—22no—
351C2×C4×C109—21no—
352C2×C4×C109—22no—
353C2×C4×C109—21no—
354C2×C4×C109—22no—
355C2×C4×C109—22no—
356C2×C4×C109—22no—
357C2×C4×C109—21no—
358C2×C4×C109—21no—
359C2×C4×C109—21no—
360C2×C4×C109—21no—
361C2×C4×C109—48no—
362C2×C4×C109—48no—
363C2×C4×C109—48no—
364C2×C4×C109—41no—
365C2×C4×C109—41no—
366C2×C4×C109—41no—
367C2×C4×C109—41no—
368C2×C4×C109—41no—
369C2×C4×C109—41no—
370C2×C4×C109—41no—
371C2×C4×C109—41no—
372C2×C4×C109—41no—
373C2×C4×C109—41no—
374C2×C4×C109—41no—
375C2×C4×C109—41no—
376C2×C4×C109—41no—
377C2×C4×C109—41no—
378C2×C4×C109—41no—
379C2×C4×C109—41no—
380C2×C4×C109—41no—
381C2×C4×C109—41no—
382C2×C4×C109#12012yes—
383C2×C4×C109#13512yes—
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—24no—
396C22×C109—22no—
397C22×C109—22no—
398C22×C109—42no—
399C22×C109—42no—
400C22×C109—41no—
401C22×C109—42no—
402C22×C109—41no—
403C22×C109—42no—
404C22×C109—41no—
405C22×C109—42no—
406C22×C109—41no—
407C22×C109—42no—
408C22×C109—41no—
409C22×C109—41no—
410C22×C109—41no—
411C22×C109—41no—
412C22×C109—41no—
413C22×C109—41no—
414C22×C109—41no—
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—22no—
431C4×C109—41no—
432C4×C109—42no—
433C4×C109—42no—
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#24438C10911yesmaximal, characteristic, direct product factor, Sylow
444C2×C109—42no—
445C2×C109—44no—
446C2×C109—81no—
447C2×C109—161no—
448C2×C109#241011yescharacteristic
449C2×C109#300211yescharacteristic
450C2×C109#301011yescharacteristic
451C2×C109#326711yescharacteristic
452C2×C109#328411yescharacteristic
453C2×C109#330311yescharacteristic
454C2×C109#330711yescharacteristic
455C2×#547C2×C10911yescharacteristic, complemented
456C2×#465C2×C10911yescharacteristic, complemented
457C2×#449C2×C10911yescharacteristic, complemented
458C2×#449C2×C10911yescharacteristic, complemented
459C2×#416C2×C10911yescharacteristic, complemented
460#2414C2×C10911yescharacteristic, complemented
461#2043C2×C10911yescharacteristic, complemented
462#2035C2×C10911yescharacteristic, complemented
463#2013C2×C10911yescharacteristic, complemented
464#2000C2×C10911yescharacteristic, complemented
465#1879C2×C10911yescharacteristic, complemented
466#1873C2×C10911yescharacteristic, complemented
467#1869C2×C10911yescharacteristic, complemented
468#1864C2×C10911yescharacteristic, complemented
469#1788C2×C10911yescharacteristic, complemented
470C109#2443811yescharacteristic, direct product factor, Sylow
471C22×#41C22×C10911yescharacteristic
472C22×#41C22×C10911yescharacteristic
473C22×SD16C22×C10911yescharacteristic
474C22×SD16C22×C10911yescharacteristic
475C22×D8C22×C10911yescharacteristic
476C23×C8C22×C10911yescharacteristic
477#547—24no—
478#547—24no—
479C2×C4⋊Q8C22×C10911yescharacteristic
480C2×#123—21no—
481C2×#123—21no—
482C2×C22⋊Q8C22×C10911yescharacteristic
483C2×C22⋊Q8C22×C10911yescharacteristic
484C2×#121—21no—
485C2×#121C22×C10911yescharacteristic
486C2×#121C22×C10911yescharacteristic
487C2×C4×D4C22×C10911yescharacteristic
488C2×C4×D4C22×C10911yescharacteristic
489C2×#117C22×C10911yescharacteristic
490C22×C4⋊C4—21no—
491#465—24no—
492#449—24no—
493#449—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—22no—
524C2×#41—22no—
525C2×#41—22no—
526C2×#41—22no—
527C2×#41—41no—
528C2×#41—41no—
529C2×#41—41no—
530C2×#41—41no—
531C2×#41D4×C10914yescomplemented
532C22×Q8C23×C10911yescharacteristic
533C22×Q8C23×C10911yescharacteristic
534C22×D4—21no—
535C22×D4—21no—
536C22×D4—21no—
537C22×D4—21no—
538C22×D4D4×C10911yescharacteristic
539C22×D4C23×C10911yescharacteristic
540C22×D4C23×C10911yescharacteristic
541C23×C4—21no—
542C23×C4—21no—
543C23×C4—21no—
544C23×C4C23×C10911yescharacteristic
545C23×C4C23×C10911yescharacteristic
546C2×SD16—22no—
547C2×SD16—22no—
548C2×SD16—22no—
549C2×SD16—41no—
550C2×SD16—41no—
551C2×SD16—41no—
552C2×D8—22no—
553C2×D8—22no—
554C2×D8—22no—
555C22×C8—22no—
556C22×C8—22no—
557C22×C8—41no—
558C22×C8C23×C10911yescharacteristic
559C22×C8C23×C10911yescharacteristic
560C22×C8C23×C10911yescharacteristic
561C22×C8C23×C10911yescharacteristic
562C4⋊Q8—22no—
563C4⋊Q8—22no—
564#123—28no—
565#123—28no—
566C22⋊Q8—22no—
567C22⋊Q8—22no—
568C22⋊Q8—22no—
569C22⋊Q8D4×C10914yescomplemented
570#121—28no—
571#121—22no—
572#121—22no—
573#121—22no—
574#121—41no—
575C4×D4—22no—
576C4×D4—22no—
577C4×D4—22no—
578C4×D4—22no—
579#117—22no—
580#117—41no—
581C2×C4⋊C4—28no—
582C2×C4⋊C4—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4D4×C10911yescharacteristic
588C2×C4⋊C4C23×C10911yescharacteristic
589C2×C4⋊C4C23×C10911yescharacteristic
590C2×C4⋊C4C23×C10911yescharacteristic
591C2×C4⋊C4C23×C10911yescharacteristic
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⋊C4—21no—
601C2×C22⋊C4D4×C10911yescharacteristic
602C2×C22⋊C4D4×C10911yescharacteristic
603C2×C42—21no—
604C2×C42C23×C10911yescharacteristic
605#106—22no—
606#103—22no—
607#103—22no—
608#103—22no—
609#103—22no—
610#103—22no—
611#103—41no—
612#102—22no—
613#102—22no—
614#102—22no—
615#102D4×C10914yescomplemented
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—
629#41—44no—
630#41—44no—
631#41—44no—
632#41—44no—
633C2×Q8—21no—
634C2×Q8—21no—
635C2×Q8—21no—
636C2×Q8—21no—
637C2×Q8—21no—
638C2×Q8—21no—
639C2×Q8—21no—
640C2×Q8—21no—
641C2×Q8—21no—
642C2×Q8—21no—
643C2×Q8C2×D4×C10912yes—
644C2×Q8C2×D4×C10912yes—
645C2×D4—24no—
646C2×D4—22no—
647C2×D4—24no—
648C2×D4—22no—
649C2×D4—21no—
650C2×D4—21no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—21no—
654C2×D4—21no—
655C2×D4—21no—
656C2×D4—21no—
657C2×D4—21no—
658C2×D4—41no—
659C2×D4—42no—
660C2×D4—42no—
661C2×D4—42no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—42no—
666C2×D4—81no—
667C2×D4—81no—
668C2×D4—81no—
669C2×D4C2×D4×C10912yes—
670C2×D4C2×D4×C10912yes—
671C2×D4#41×C10912yes—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—21no—
676C22×C4—24no—
677C22×C4—24no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—24no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—42no—
692C22×C4—42no—
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×C10912yes—
701C22×C4C2×D4×C10912yes—
702C22×C4C2×D4×C10911yescharacteristic
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—24no—
723C4⋊C4—22no—
724C4⋊C4—24no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—81no—
732C4⋊C4C2×D4×C10912yes—
733C4⋊C4C2×D4×C10912yes—
734C22⋊C4—24no—
735C22⋊C4—24no—
736C22⋊C4—24no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—42no—
740C22⋊C4—42no—
741C22⋊C4—42no—
742C22⋊C4—42no—
743C22⋊C4—81no—
744C22⋊C4—81no—
745C42—21no—
746C42—21no—
747C42—42no—
748C23—22no—
749C23—21no—
750C23—22no—
751C23—21no—
752C23—22no—
753C23—21no—
754C23—21no—
755C23—21no—
756C23—21no—
757C23—21no—
758C23—21no—
759C23—21no—
760C23—21no—
761C23—21no—
762C23—21no—
763C23—21no—
764C23—41no—
765C23—41no—
766C23—41no—
767C23—41no—
768C23—41no—
769C23—41no—
770C23—41no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—41no—
775C23#120×C10912yes—
776C23C22×D4×C10911yescharacteristic
777Q8—22no—
778Q8—22no—
779Q8—22no—
780Q8—22no—
781Q8—41no—
782Q8—41no—
783Q8—41no—
784Q8—41no—
785D4—22no—
786D4—22no—
787D4—22no—
788D4—44no—
789D4—48no—
790D4—48no—
791D4—41no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—84no—
796D4—84no—
797D4#121×C10914yes—
798C2×C4—21no—
799C2×C4—21no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—22no—
805C2×C4—22no—
806C2×C4—21no—
807C2×C4—22no—
808C2×C4—21no—
809C2×C4—22no—
810C2×C4—22no—
811C2×C4—22no—
812C2×C4—21no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—48no—
817C2×C4—48no—
818C2×C4—48no—
819C2×C4—41no—
820C2×C4—41no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—41no—
825C2×C4—41no—
826C2×C4—41no—
827C2×C4—41no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4#120×C10912yes—
838C2×C4#135×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—24no—
853C22—42no—
854C22—42no—
855C22—41no—
856C22—42no—
857C22—41no—
858C22—42no—
859C22—41no—
860C22—42no—
861C22—41no—
862C22—42no—
863C22—41no—
864C22—41no—
865C22—41no—
866C22—41no—
867C22—41no—
868C22—41no—
869C22—41no—
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—22no—
886C4—42no—
887C4—41no—
888C4—42no—
889C4—41no—
890C4—42no—
891C4—42no—
892C4—81no—
893C4—81no—
894C4C2×#121×C10911yescharacteristic
895C4#534×C10911yescharacteristic
896C4D42×C10911yescharacteristic
897C4#546×C10911yescharacteristic
898C2—42no—
899C2—44no—
900C2—81no—
901C2—161no—
902C2C109×#241011yescharacteristic
903C2C109×#300211yescharacteristic
904C2C109×#301011yescharacteristic
905C2C109×#326711yescharacteristic
906C2C109×#328411yescharacteristic
907C2C109×#330311yescharacteristic
908C2C109×#330711yescharacteristic
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×#547×C109C2semidirect
2. C2×#465×C109C2semidirect
3. C2×#449×C109C2semidirect
4. C2×#449×C109C2semidirect
5. C2×#416×C109C2semidirect
6. C109×#2414C2semidirect
7. C109×#2043C2semidirect
8. C109×#2035C2semidirect
9. C109×#2013C2semidirect
10. C109×#2000C2semidirect
11. C109×#1879C2semidirect
12. C109×#1873C2semidirect
13. C109×#1869C2semidirect
14. C109×#1864C2semidirect
15. C109×#1788C2semidirect
76. C2×#41×C109D4semidirect
114. C22⋊Q8×C109D4semidirect
160. #102×C109D4semidirect
443. #24438C109direct (N × H)
455. C2×#547C2×C109semidirect
456. C2×#465C2×C109semidirect
457. C2×#449C2×C109semidirect
458. C2×#449C2×C109semidirect
459. C2×#416C2×C109semidirect
460. #2414C2×C109semidirect
461. #2043C2×C109semidirect
462. #2035C2×C109semidirect
463. #2013C2×C109semidirect
464. #2000C2×C109semidirect
465. #1879C2×C109semidirect
466. #1873C2×C109semidirect
467. #1869C2×C109semidirect
468. #1864C2×C109semidirect
469. #1788C2×C109semidirect
470. C109#24438direct (N × H)
531. C2×#41D4×C109semidirect
569. C22⋊Q8D4×C109semidirect
615. #102D4×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#547×C1092
C2×#465×C1092
C2×#449×C1092
C2×#416×C1092
C109×#24142
C109×#20432
C109×#20352
C109×#20132
C109×#20002
C109×#18792
C109×#18732
C109×#18692
C109×#18642
C109×#17882
#24438109