Finite Group Databasebeta

← C109×#24901 #42142895

Subgroups — C109×#24901 #42142895

Order 27904.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#450×C109C211yesmaximal, characteristic
2C2×C4×SD16×C109C211yesmaximal, characteristic, complemented
3C109×#2423C211yesmaximal, characteristic, complemented
4D4×C22⋊C4×C109C211yesmaximal, characteristic
5C109×#2094C211yesmaximal, characteristic, complemented
6C109×#2077C211yesmaximal, characteristic, complemented
7C109×#2055C211yesmaximal, characteristic, complemented
8C109×#2035C211yesmaximal, characteristic, complemented
9C109×#1934C211yesmaximal, characteristic, complemented
10C109×#1923C211yesmaximal, characteristic, complemented
11C109×#1880C211yesmaximal, characteristic, complemented
12C109×#1877C211yesmaximal, characteristic, complemented
13C109×#1864C211yesmaximal, characteristic, complemented
14C109×#1802C211yesmaximal, characteristic, complemented
15C109×#1786C211yesmaximal, characteristic
16C23×D4×C109C2211yescharacteristic
17C22×SD16×C109C2211yescharacteristic
18C22×SD16×C109C2211yescharacteristic
19C2×C22⋊Q8×C109C2211yescharacteristic
20C2×C4×Q8×C109C2211yescharacteristic, complemented
21C2×C4×D4×C109C2211yescharacteristic
22C2×C4×D4×C109C2211yescharacteristic
23C22×C22⋊C4×C109—21no—
24#450×C109—24no—
25C4×SD16×C109—24no—
26C2×#106×C109C2211yescharacteristic, complemented
27C2×#106×C109C2211yescharacteristic, complemented
28C2×C4⋊C8×C109C2211yescharacteristic, complemented
29C2×#103×C109C2211yescharacteristic, complemented
30C2×#103×C109C2211yescharacteristic, complemented
31C2×#102×C109C2211yescharacteristic
32C2×#102×C109C2211yescharacteristic
33C2×#102×C109C2211yescharacteristic
34C2×#102×C109C2211yescharacteristic
35C2×#102×C109C2211yescharacteristic
36C2×#102×C109C2211yescharacteristic
37C2×C22⋊C8×C109C2211yescharacteristic
38C2×C22⋊C8×C109C2211yescharacteristic
39C2×C4×C8×C109C2211yescharacteristic, complemented
40#399×C109—21no—
41#398×C109—21no—
42#391×C109C2211yescharacteristic, complemented
43#390×C109C2211yescharacteristic
44#390×C109C2211yescharacteristic
45#389×C109C2211yescharacteristic, complemented
46#388×C109—21no—
47#387×C109—21no—
48#386×C109—21no—
49#386×C109—21no—
50#384×C109C2211yescharacteristic, complemented
51#380×C109C2211yescharacteristic
52#380×C109C2211yescharacteristic
53#379×C109—21no—
54C4×C22⋊C4×C109C2211yescharacteristic
55#340×C109C2211yescharacteristic, complemented
56#340×C109C2211yescharacteristic, complemented
57#340×C109C2211yescharacteristic, complemented
58#340×C109C2211yescharacteristic, complemented
59#336×C109C2211yescharacteristic, complemented
60#336×C109C2211yescharacteristic, complemented
61C25×C109—21no—
62C22×Q8×C109C2311yescharacteristic
63C22×D4×C109—22no—
64C22×D4×C109—22no—
65C22×D4×C109—22no—
66C22×D4×C109—22no—
67C22×D4×C109—21no—
68C22×D4×C109—41no—
69C22×D4×C109—41no—
70C22×D4×C109C2311yescharacteristic
71C22×D4×C109C2311yescharacteristic
72C23×C4×C109—21no—
73C23×C4×C109—21no—
74C23×C4×C109C2311yescharacteristic
75C2×SD16×C109—22no—
76C2×SD16×C109—22no—
77C2×SD16×C109—22no—
78C2×SD16×C109—22no—
79C2×SD16×C109—41no—
80C2×SD16×C109D414yes—
81C22×C8×C109C2311yescharacteristic
82C22×C8×C109C2311yescharacteristic
83C22×C8×C109C2311yescharacteristic
84C22×C8×C109C2311yescharacteristic
85C22⋊Q8×C109—22no—
86C22⋊Q8×C109—41no—
87C4×Q8×C109—22no—
88C4×Q8×C109—41no—
89C4×D4×C109—22no—
90C4×D4×C109—22no—
91C4×D4×C109—41no—
92C4×D4×C109—41no—
93C2×C4⋊C4×C109—21no—
94C2×C4⋊C4×C109—21no—
95C2×C4⋊C4×C109—21no—
96C2×C4⋊C4×C109—21no—
97C2×C4⋊C4×C109—21no—
98C2×C4⋊C4×C109C2311yescharacteristic
99C2×C4⋊C4×C109C2311yescharacteristic
100C2×C4⋊C4×C109C2311yescharacteristic
101C2×C4⋊C4×C109C2311yescharacteristic
102C2×C4⋊C4×C109C2311yescharacteristic
103C2×C22⋊C4×C109—21no—
104C2×C22⋊C4×C109—21no—
105C2×C22⋊C4×C109—21no—
106C2×C22⋊C4×C109—21no—
107C2×C22⋊C4×C109—21no—
108C2×C22⋊C4×C109—21no—
109C2×C22⋊C4×C109—21no—
110C2×C22⋊C4×C109—21no—
111C2×C22⋊C4×C109—21no—
112C2×C22⋊C4×C109—44no—
113C2×C22⋊C4×C109D411yescharacteristic
114C2×C22⋊C4×C109D411yescharacteristic
115C2×C42×C109—21no—
116C2×C42×C109C2311yescharacteristic
117C2×C42×C109C2311yescharacteristic
118#106×C109—22no—
119#106×C109—41no—
120C4⋊C8×C109—41no—
121#103×C109—22no—
122#103×C109—41no—
123#102×C109—22no—
124#102×C109—22no—
125#102×C109—22no—
126#102×C109—22no—
127#102×C109—22no—
128#102×C109—41no—
129C22⋊C8×C109—22no—
130C22⋊C8×C109—41no—
131C4×C8×C109—22no—
132#95×C109—21no—
133#95×C109—21no—
134#95×C109—21no—
135#95×C109—21no—
136#95×C109—21no—
137#95×C109D411yescharacteristic
138#95×C109D411yescharacteristic
139C24×C109—21no—
140C24×C109—24no—
141C24×C109—21no—
142C24×C109—42no—
143C24×C109—42no—
144C24×C109—42no—
145C24×C109—42no—
146C24×C109—81no—
147C24×C109—81no—
148C24×C109C2×D411yescharacteristic
149C2×Q8×C109—21no—
150C2×Q8×C109—21no—
151C2×Q8×C109—21no—
152C2×Q8×C109—21no—
153C2×Q8×C109—21no—
154C2×Q8×C109C2×D412yes—
155C2×D4×C109—24no—
156C2×D4×C109—21no—
157C2×D4×C109—21no—
158C2×D4×C109—21no—
159C2×D4×C109—21no—
160C2×D4×C109—21no—
161C2×D4×C109—21no—
162C2×D4×C109—21no—
163C2×D4×C109—21no—
164C2×D4×C109—42no—
165C2×D4×C109—42no—
166C2×D4×C109—44no—
167C2×D4×C109—44no—
168C2×D4×C109—44no—
169C2×D4×C109—44no—
170C2×D4×C109C2×D412yes—
171C2×D4×C109#4112yes—
172C2×D4×C109#4112yes—
173C2×D4×C109#4112yes—
174C22×C4×C109—21no—
175C22×C4×C109—21no—
176C22×C4×C109—21no—
177C22×C4×C109—21no—
178C22×C4×C109—21no—
179C22×C4×C109—21no—
180C22×C4×C109—21no—
181C22×C4×C109—21no—
182C22×C4×C109—21no—
183C22×C4×C109—21no—
184C22×C4×C109—21no—
185C22×C4×C109—21no—
186C22×C4×C109—42no—
187C22×C4×C109—42no—
188C22×C4×C109—42no—
189C22×C4×C109—42no—
190C22×C4×C109—81no—
191C22×C4×C109—81no—
192C22×C4×C109C2×D411yescharacteristic
193C22×C4×C109C2×D411yescharacteristic
194C22×C4×C109C2×D411yescharacteristic
195C22×C4×C109C2×D411yescharacteristic
196C22×C4×C109C2×D411yescharacteristic
197C22×C4×C109C2411yescharacteristic
198SD16×C109—28no—
199SD16×C109—44no—
200C2×C8×C109—21no—
201C2×C8×C109—21no—
202C2×C8×C109—21no—
203C2×C8×C109—21no—
204C2×C8×C109—21no—
205C2×C8×C109—21no—
206C2×C8×C109—21no—
207C2×C8×C109—21no—
208C2×C8×C109—21no—
209C2×C8×C109—21no—
210C2×C8×C109—21no—
211C2×C8×C109C2×D412yes—
212C4⋊C4×C109—21no—
213C4⋊C4×C109—21no—
214C4⋊C4×C109—21no—
215C4⋊C4×C109—21no—
216C4⋊C4×C109—21no—
217C4⋊C4×C109—21no—
218C4⋊C4×C109—21no—
219C4⋊C4×C109—21no—
220C4⋊C4×C109—21no—
221C4⋊C4×C109—21no—
222C4⋊C4×C109—42no—
223C4⋊C4×C109—42no—
224C4⋊C4×C109—42no—
225C4⋊C4×C109—81no—
226C4⋊C4×C109—81no—
227C22⋊C4×C109—41no—
228C22⋊C4×C109—42no—
229C22⋊C4×C109—42no—
230C22⋊C4×C109—42no—
231C22⋊C4×C109—42no—
232C22⋊C4×C109—42no—
233C22⋊C4×C109—42no—
234C22⋊C4×C109—81no—
235C22⋊C4×C109—81no—
236C22⋊C4×C109—81no—
237C22⋊C4×C109SD1614yescomplemented
238C42×C109—21no—
239C42×C109—21no—
240C42×C109—21no—
241C42×C109—21no—
242C42×C109—42no—
243C23×C109—21no—
244C23×C109—22no—
245C23×C109—21no—
246C23×C109—22no—
247C23×C109—22no—
248C23×C109—21no—
249C23×C109—21no—
250C23×C109—21no—
251C23×C109—21no—
252C23×C109—22no—
253C23×C109—48no—
254C23×C109—48no—
255C23×C109—41no—
256C23×C109—41no—
257C23×C109—41no—
258C23×C109—41no—
259C23×C109—41no—
260C23×C109—41no—
261C23×C109—41no—
262C23×C109—41no—
263C23×C109—41no—
264C23×C109—41no—
265C23×C109—84no—
266C23×C109—84no—
267C23×C109—84no—
268C23×C109—84no—
269C23×C109—84no—
270C23×C109C2×SD1612yes—
271C23×C109C22×D411yescharacteristic
272Q8×C109—22no—
273Q8×C109—22no—
274Q8×C109—41no—
275Q8×C109—41no—
276D4×C109—22no—
277D4×C109—22no—
278D4×C109—22no—
279D4×C109—22no—
280D4×C109—22no—
281D4×C109—48no—
282D4×C109—41no—
283D4×C109—41no—
284D4×C109#12314yes—
285C2×C4×C109—21no—
286C2×C4×C109—21no—
287C2×C4×C109—21no—
288C2×C4×C109—21no—
289C2×C4×C109—21no—
290C2×C4×C109—21no—
291C2×C4×C109—22no—
292C2×C4×C109—21no—
293C2×C4×C109—21no—
294C2×C4×C109—21no—
295C2×C4×C109—21no—
296C2×C4×C109—21no—
297C2×C4×C109—21no—
298C2×C4×C109—21no—
299C2×C4×C109—41no—
300C2×C4×C109—41no—
301C2×C4×C109—41no—
302C2×C4×C109—41no—
303C2×C4×C109—41no—
304C2×C4×C109—41no—
305C2×C4×C109—41no—
306C2×C4×C109—41no—
307C2×C4×C109—41no—
308C2×C4×C109—41no—
309C2×C4×C109—41no—
310C2×C4×C109—41no—
311C2×C4×C109—41no—
312C2×C4×C109—41no—
313C2×C4×C109—41no—
314C2×C4×C109—41no—
315C2×C4×C109—41no—
316C2×C4×C109—41no—
317C2×C4×C109—41no—
318C2×C4×C109—41no—
319C2×C4×C109—41no—
320C2×C4×C109—84no—
321C2×C4×C109—84no—
322C2×C4×C109C2×SD1612yes—
323C2×C4×C109C2×SD1612yes—
324C2×C4×C109C22×D411yescharacteristic
325C2×C4×C109C2×#4111yescharacteristic
326C2×C4×C109C2×#4111yescharacteristic
327C2×C4×C109C2×#4111yescharacteristic
328C2×C4×C109H(5,𝔽2)11yescharacteristic
329C2×C4×C109H(5,𝔽2)11yescharacteristic
330C8×C109—22no—
331C8×C109—41no—
332C8×C109—41no—
333C8×C109—41no—
334C22×C109—22no—
335C22×C109—24no—
336C22×C109—22no—
337C22×C109—22no—
338C22×C109—42no—
339C22×C109—41no—
340C22×C109—42no—
341C22×C109—41no—
342C22×C109—41no—
343C22×C109—42no—
344C22×C109—42no—
345C22×C109—42no—
346C22×C109—41no—
347C22×C109—42no—
348C22×C109—42no—
349C22×C109—42no—
350C22×C109—42no—
351C22×C109—816no—
352C22×C109—81no—
353C22×C109—81no—
354C22×C109—81no—
355C22×C109—81no—
356C22×C109#52511yescharacteristic
357C22×C109D4211yescharacteristic
358C22×C109#54611yescharacteristic
359C22×C109C22×SD1611yescharacteristic
360C22×C109#57511yescharacteristic
361C22×C109#57611yescharacteristic
362C22×C109#57711yescharacteristic
363C4×C109—22no—
364C4×C109—22no—
365C4×C109—41no—
366C4×C109—42no—
367C4×C109—41no—
368C4×C109—41no—
369C4×C109—81no—
370C4×C109—81no—
371C4×C109—81no—
372C4×C109—81no—
373C4×C109—81no—
374C4×C109C2×#12311yescharacteristic
375C4×C109#53811yescharacteristic
376C4×C109#54611yescharacteristic
377C4×C109#55111yescharacteristic
378#24901C10911yesmaximal, characteristic, direct product factor, Sylow
379C2×C109—42no—
380C2×C109—44no—
381C2×C109—82no—
382C2×C109#241811yescharacteristic
383C2×C109#310111yescharacteristic
384C2×C109#311811yescharacteristic
385C2×C109#326811yescharacteristic
386C2×C109D4×SD1611yescharacteristic
387C2×C109#329511yescharacteristic
388C2×C109#332311yescharacteristic
389C2×#450C2×C10911yescharacteristic
390C2×C4×SD16C2×C10911yescharacteristic, complemented
391#2423C2×C10911yescharacteristic, complemented
392D4×C22⋊C4C2×C10911yescharacteristic
393#2094C2×C10911yescharacteristic, complemented
394#2077C2×C10911yescharacteristic, complemented
395#2055C2×C10911yescharacteristic, complemented
396#2035C2×C10911yescharacteristic, complemented
397#1934C2×C10911yescharacteristic, complemented
398#1923C2×C10911yescharacteristic, complemented
399#1880C2×C10911yescharacteristic, complemented
400#1877C2×C10911yescharacteristic, complemented
401#1864C2×C10911yescharacteristic, complemented
402#1802C2×C10911yescharacteristic, complemented
403#1786C2×C10911yescharacteristic
404C109#2490111yescharacteristic, direct product factor, Sylow
405C23×D4C22×C10911yescharacteristic
406C22×SD16C22×C10911yescharacteristic
407C22×SD16C22×C10911yescharacteristic
408C2×C22⋊Q8C22×C10911yescharacteristic
409C2×C4×Q8C22×C10911yescharacteristic, complemented
410C2×C4×D4C22×C10911yescharacteristic
411C2×C4×D4C22×C10911yescharacteristic
412C22×C22⋊C4—21no—
413#450—24no—
414C4×SD16—24no—
415C2×#106C22×C10911yescharacteristic, complemented
416C2×#106C22×C10911yescharacteristic, complemented
417C2×C4⋊C8C22×C10911yescharacteristic, complemented
418C2×#103C22×C10911yescharacteristic, complemented
419C2×#103C22×C10911yescharacteristic, complemented
420C2×#102C22×C10911yescharacteristic
421C2×#102C22×C10911yescharacteristic
422C2×#102C22×C10911yescharacteristic
423C2×#102C22×C10911yescharacteristic
424C2×#102C22×C10911yescharacteristic
425C2×#102C22×C10911yescharacteristic
426C2×C22⋊C8C22×C10911yescharacteristic
427C2×C22⋊C8C22×C10911yescharacteristic
428C2×C4×C8C22×C10911yescharacteristic, complemented
429#399—21no—
430#398—21no—
431#391C22×C10911yescharacteristic, complemented
432#390C22×C10911yescharacteristic
433#390C22×C10911yescharacteristic
434#389C22×C10911yescharacteristic, complemented
435#388—21no—
436#387—21no—
437#386—21no—
438#386—21no—
439#384C22×C10911yescharacteristic, complemented
440#380C22×C10911yescharacteristic
441#380C22×C10911yescharacteristic
442#379—21no—
443C4×C22⋊C4C22×C10911yescharacteristic
444#340C22×C10911yescharacteristic, complemented
445#340C22×C10911yescharacteristic, complemented
446#340C22×C10911yescharacteristic, complemented
447#340C22×C10911yescharacteristic, complemented
448#336C22×C10911yescharacteristic, complemented
449#336C22×C10911yescharacteristic, complemented
450C25—21no—
451C22×Q8C23×C10911yescharacteristic
452C22×D4—22no—
453C22×D4—22no—
454C22×D4—22no—
455C22×D4—22no—
456C22×D4—21no—
457C22×D4—41no—
458C22×D4—41no—
459C22×D4C23×C10911yescharacteristic
460C22×D4C23×C10911yescharacteristic
461C23×C4—21no—
462C23×C4—21no—
463C23×C4C23×C10911yescharacteristic
464C2×SD16—22no—
465C2×SD16—22no—
466C2×SD16—22no—
467C2×SD16—22no—
468C2×SD16—41no—
469C2×SD16D4×C10914yes—
470C22×C8C23×C10911yescharacteristic
471C22×C8C23×C10911yescharacteristic
472C22×C8C23×C10911yescharacteristic
473C22×C8C23×C10911yescharacteristic
474C22⋊Q8—22no—
475C22⋊Q8—41no—
476C4×Q8—22no—
477C4×Q8—41no—
478C4×D4—22no—
479C4×D4—22no—
480C4×D4—41no—
481C4×D4—41no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—21no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—21no—
487C2×C4⋊C4C23×C10911yescharacteristic
488C2×C4⋊C4C23×C10911yescharacteristic
489C2×C4⋊C4C23×C10911yescharacteristic
490C2×C4⋊C4C23×C10911yescharacteristic
491C2×C4⋊C4C23×C10911yescharacteristic
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—44no—
502C2×C22⋊C4D4×C10911yescharacteristic
503C2×C22⋊C4D4×C10911yescharacteristic
504C2×C42—21no—
505C2×C42C23×C10911yescharacteristic
506C2×C42C23×C10911yescharacteristic
507#106—22no—
508#106—41no—
509C4⋊C8—41no—
510#103—22no—
511#103—41no—
512#102—22no—
513#102—22no—
514#102—22no—
515#102—22no—
516#102—22no—
517#102—41no—
518C22⋊C8—22no—
519C22⋊C8—41no—
520C4×C8—22no—
521#95—21no—
522#95—21no—
523#95—21no—
524#95—21no—
525#95—21no—
526#95D4×C10911yescharacteristic
527#95D4×C10911yescharacteristic
528C24—21no—
529C24—24no—
530C24—21no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—42no—
535C24—81no—
536C24—81no—
537C24C2×D4×C10911yescharacteristic
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8C2×D4×C10912yes—
544C2×D4—24no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—42no—
554C2×D4—42no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4C2×D4×C10912yes—
560C2×D4#41×C10912yes—
561C2×D4#41×C10912yes—
562C2×D4#41×C10912yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—42no—
576C22×C4—42no—
577C22×C4—42no—
578C22×C4—42no—
579C22×C4—81no—
580C22×C4—81no—
581C22×C4C2×D4×C10911yescharacteristic
582C22×C4C2×D4×C10911yescharacteristic
583C22×C4C2×D4×C10911yescharacteristic
584C22×C4C2×D4×C10911yescharacteristic
585C22×C4C2×D4×C10911yescharacteristic
586C22×C4C24×C10911yescharacteristic
587SD16—28no—
588SD16—44no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8C2×D4×C10912yes—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—42no—
612C4⋊C4—42no—
613C4⋊C4—42no—
614C4⋊C4—81no—
615C4⋊C4—81no—
616C22⋊C4—41no—
617C22⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4SD16×C10914yescomplemented
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—42no—
632C23—21no—
633C23—22no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23C2×SD16×C10912yes—
660C23C22×D4×C10911yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#123×C10914yes—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—22no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—84no—
710C2×C4—84no—
711C2×C4C2×SD16×C10912yes—
712C2×C4C2×SD16×C10912yes—
713C2×C4C22×D4×C10911yescharacteristic
714C2×C4C2×#41×C10911yescharacteristic
715C2×C4C2×#41×C10911yescharacteristic
716C2×C4C2×#41×C10911yescharacteristic
717C2×C4H(5,𝔽2)×C10911yescharacteristic
718C2×C4H(5,𝔽2)×C10911yescharacteristic
719C8—22no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—24no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—42no—
731C22—41no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#525×C10911yescharacteristic
746C22D42×C10911yescharacteristic
747C22#546×C10911yescharacteristic
748C22C22×SD16×C10911yescharacteristic
749C22#575×C10911yescharacteristic
750C22#576×C10911yescharacteristic
751C22#577×C10911yescharacteristic
752C4—22no—
753C4—22no—
754C4—41no—
755C4—41no—
756C4—41no—
757C4—42no—
758C4—81no—
759C4—81no—
760C4—81no—
761C4—81no—
762C4—81no—
763C4C2×#123×C10911yescharacteristic
764C4#538×C10911yescharacteristic
765C4#546×C10911yescharacteristic
766C4#551×C10911yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2C109×#241811yescharacteristic
771C2C109×#310111yescharacteristic
772C2C109×#311811yescharacteristic
773C2C109×#326811yescharacteristic
774C2D4×SD16×C10911yescharacteristic
775C2C109×#329511yescharacteristic
776C2C109×#332311yescharacteristic
subgroupG/H
center, socleC23×C109C22×D4
commutator, Frattini, cosocleC22×C4C24×C109
prime radicalC23×D4×C109C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C109 ◁ C4×C22⋊C4×C109 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×C4×SD16×C109C2semidirect
3. C109×#2423C2semidirect
5. C109×#2094C2semidirect
6. C109×#2077C2semidirect
7. C109×#2055C2semidirect
8. C109×#2035C2semidirect
9. C109×#1934C2semidirect
10. C109×#1923C2semidirect
11. C109×#1880C2semidirect
12. C109×#1877C2semidirect
13. C109×#1864C2semidirect
14. C109×#1802C2semidirect
20. C2×C4×Q8×C109C22semidirect
26. C2×#106×C109C22semidirect
27. C2×#106×C109C22semidirect
28. C2×C4⋊C8×C109C22semidirect
29. C2×#103×C109C22semidirect
30. C2×#103×C109C22semidirect
39. C2×C4×C8×C109C22semidirect
42. #391×C109C22semidirect
45. #389×C109C22semidirect
50. #384×C109C22semidirect
55. #340×C109C22semidirect
56. #340×C109C22semidirect
57. #340×C109C22semidirect
58. #340×C109C22semidirect
59. #336×C109C22semidirect
60. #336×C109C22semidirect
237. C22⋊C4×C109SD16semidirect
378. #24901C109direct (N × H)
390. C2×C4×SD16C2×C109semidirect
391. #2423C2×C109semidirect
393. #2094C2×C109semidirect
394. #2077C2×C109semidirect
395. #2055C2×C109semidirect
396. #2035C2×C109semidirect
397. #1934C2×C109semidirect
398. #1923C2×C109semidirect
399. #1880C2×C109semidirect
400. #1877C2×C109semidirect
401. #1864C2×C109semidirect
402. #1802C2×C109semidirect
404. C109#24901direct (N × H)
409. C2×C4×Q8C22×C109semidirect
415. C2×#106C22×C109semidirect
416. C2×#106C22×C109semidirect
417. C2×C4⋊C8C22×C109semidirect
418. C2×#103C22×C109semidirect
419. C2×#103C22×C109semidirect
428. C2×C4×C8C22×C109semidirect
431. #391C22×C109semidirect
434. #389C22×C109semidirect
439. #384C22×C109semidirect
444. #340C22×C109semidirect
445. #340C22×C109semidirect
446. #340C22×C109semidirect
447. #340C22×C109semidirect
448. #336C22×C109semidirect
449. #336C22×C109semidirect
626. C22⋊C4SD16×C109semidirect

Maximal subgroups

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

subgroupindex
C2×#450×C1092
C2×C4×SD16×C1092
C109×#24232
D4×C22⋊C4×C1092
C109×#20942
C109×#20772
C109×#20552
C109×#20352
C109×#19342
C109×#19232
C109×#18802
C109×#18772
C109×#18642
C109×#18022
C109×#17862
#24901109