Finite Group Databasebeta

← C73×#26382 #32935786

Subgroups — C73×#26382 #32935786

Order 18688.

932 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#478×C73C211yesmaximal, characteristic, complemented
2C2×C4×D8×C73C211yesmaximal, characteristic
3C73×#2454C211yesmaximal, characteristic, complemented
4D4×C4⋊C4×C73C211yesmaximal, characteristic, complemented
5C73×#2094C211yesmaximal, characteristic, complemented
6C73×#2083C211yesmaximal, characteristic, complemented
7C73×#2065C211yesmaximal, characteristic, complemented
8C73×#2059C211yesmaximal, characteristic, complemented
9C73×#1941C211yesmaximal, characteristic, complemented
10C73×#1916C211yesmaximal, characteristic, complemented
11C73×#1879C211yesmaximal, characteristic
12C73×#1879C211yesmaximal, characteristic
13C73×#1864C211yesmaximal, characteristic, complemented
14C73×#1864C211yesmaximal, characteristic, complemented
15C73×#1862C211yesmaximal, characteristic, complemented
16C22×D8×C73C2211yescharacteristic
17C2×#125×C73C2211yescharacteristic
18C2×C4×D4×C73C2211yescharacteristic
19C2×C4×D4×C73C2211yescharacteristic
20C2×C4×D4×C73C2211yescharacteristic
21C2×C4×D4×C73C2211yescharacteristic
22C22×C4⋊C4×C73—21no—
23#478×C73—24no—
24C4×D8×C73—24no—
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#106×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×#102×C73C2211yescharacteristic
32C2×#102×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×C4×C8×C73C2211yescharacteristic
38#399×C73—21no—
39#396×C73—21no—
40#390×C73C2211yescharacteristic
41#390×C73C2211yescharacteristic
42#389×C73C2211yescharacteristic
43#389×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#389×C73C2211yescharacteristic
46#385×C73—21no—
47#385×C73—21no—
48#385×C73—21no—
49#384×C73C2211yescharacteristic
50#380×C73—21no—
51#380×C73—21no—
52C4×C4⋊C4×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×D4×C73C2311yescharacteristic
62C22×D4×C73C2311yescharacteristic
63C23×C4×C73—21no—
64C23×C4×C73—21no—
65C23×C4×C73—21no—
66C23×C4×C73—21no—
67C2×D8×C73—22no—
68C2×D8×C73—22no—
69C2×D8×C73Q814yes—
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74#125×C73—22no—
75#125×C73—41no—
76C4×D4×C73—22no—
77C4×D4×C73—22no—
78C4×D4×C73—22no—
79C4×D4×C73—22no—
80C4×D4×C73—22no—
81C4×D4×C73—41no—
82C4×D4×C73—41no—
83C4×D4×C73—41no—
84C2×C4⋊C4×C73—21no—
85C2×C4⋊C4×C73—21no—
86C2×C4⋊C4×C73—21no—
87C2×C4⋊C4×C73—21no—
88C2×C4⋊C4×C73—21no—
89C2×C4⋊C4×C73—21no—
90C2×C4⋊C4×C73—21no—
91C2×C4⋊C4×C73—21no—
92C2×C4⋊C4×C73—44no—
93C2×C4⋊C4×C73D411yescharacteristic
94C2×C4⋊C4×C73D411yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C4⋊C4×C73C2311yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C42×C73C2311yescharacteristic
110C2×C42×C73C2311yescharacteristic
111C2×C42×C73C2311yescharacteristic
112#107×C73—22no—
113#107×C73—22no—
114#106×C73—22no—
115#106×C73—22no—
116#106×C73—41no—
117C4⋊C8×C73—22no—
118#102×C73—22no—
119#102×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—41no—
123#102×C73D414yes—
124C4×C8×C73—22no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—21no—
128#95×C73—21no—
129#95×C73D411yescharacteristic
130#95×C73D411yescharacteristic
131C24×C73—21no—
132C24×C73—21no—
133C2×D4×C73—21no—
134C2×D4×C73—21no—
135C2×D4×C73—21no—
136C2×D4×C73—21no—
137C2×D4×C73—21no—
138C2×D4×C73—21no—
139C2×D4×C73—21no—
140C2×D4×C73—21no—
141C2×D4×C73C2×D412yes—
142C2×D4×C73C2×Q812yes—
143C2×D4×C73C2×Q812yes—
144C2×D4×C73#4112yes—
145C22×C4×C73—24no—
146C22×C4×C73—21no—
147C22×C4×C73—21no—
148C22×C4×C73—21no—
149C22×C4×C73—21no—
150C22×C4×C73—21no—
151C22×C4×C73—21no—
152C22×C4×C73—42no—
153C22×C4×C73—42no—
154C22×C4×C73—42no—
155C22×C4×C73—42no—
156C22×C4×C73—42no—
157C22×C4×C73—42no—
158C22×C4×C73—42no—
159C22×C4×C73—42no—
160C22×C4×C73—81no—
161C22×C4×C73—81no—
162C22×C4×C73—81no—
163C22×C4×C73C2×D411yescharacteristic
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2411yescharacteristic
170D8×C73—28no—
171C2×C8×C73—21no—
172C2×C8×C73—21no—
173C2×C8×C73—21no—
174C2×C8×C73—21no—
175C2×C8×C73—21no—
176C2×C8×C73—21no—
177C2×C8×C73—21no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73C2×D412yes—
182C2×C8×C73C2×Q812yes—
183C4⋊C4×C73—22no—
184C4⋊C4×C73—22no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—42no—
196C4⋊C4×C73—42no—
197C4⋊C4×C73—42no—
198C4⋊C4×C73—42no—
199C4⋊C4×C73—42no—
200C4⋊C4×C73—81no—
201C4⋊C4×C73—81no—
202C4⋊C4×C73—81no—
203C4⋊C4×C73C2×D412yes—
204C4⋊C4×C73#4112yes—
205C22⋊C4×C73—24no—
206C22⋊C4×C73—42no—
207C22⋊C4×C73—42no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—81no—
211C22⋊C4×C73—81no—
212C22⋊C4×C73—81no—
213C42×C73—21no—
214C42×C73—21no—
215C42×C73—21no—
216C42×C73—21no—
217C42×C73—21no—
218C42×C73—21no—
219C23×C73—22no—
220C23×C73—22no—
221C23×C73—22no—
222C23×C73—22no—
223C23×C73—41no—
224C23×C73—41no—
225C23×C73—41no—
226C23×C73—41no—
227C23×C73—41no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—41no—
233C23×C73C22×D411yescharacteristic
234D4×C73—22no—
235D4×C73—22no—
236D4×C73—22no—
237D4×C73—22no—
238D4×C73—22no—
239D4×C73—41no—
240D4×C73—41no—
241D4×C73C22⋊Q814yes—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—22no—
248C2×C4×C73—21no—
249C2×C4×C73—21no—
250C2×C4×C73—21no—
251C2×C4×C73—22no—
252C2×C4×C73—21no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—21no—
259C2×C4×C73—21no—
260C2×C4×C73—48no—
261C2×C4×C73—41no—
262C2×C4×C73—41no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—41no—
267C2×C4×C73—41no—
268C2×C4×C73—41no—
269C2×C4×C73—41no—
270C2×C4×C73—41no—
271C2×C4×C73—41no—
272C2×C4×C73—41no—
273C2×C4×C73—41no—
274C2×C4×C73—41no—
275C2×C4×C73—41no—
276C2×C4×C73—41no—
277C2×C4×C73—84no—
278C2×C4×C73—84no—
279C2×C4×C73—84no—
280C2×C4×C73#13512yes—
281C2×C4×C73AGL(1,ℤ/8)12yes—
282C2×C4×C73C22×D411yescharacteristic
283C2×C4×C73C22×Q811yescharacteristic
284C2×C4×C73C2×#4111yescharacteristic
285C2×C4×C73C2×#4111yescharacteristic
286C2×C4×C73H(5,𝔽2)11yescharacteristic
287C2×C4×C732−1+411yescharacteristic
288C8×C73—22no—
289C8×C73—22no—
290C8×C73—41no—
291C8×C73—41no—
292C22×C73—24no—
293C22×C73—42no—
294C22×C73—42no—
295C22×C73—42no—
296C22×C73—42no—
297C22×C73—42no—
298C22×C73—42no—
299C22×C73—42no—
300C22×C73—42no—
301C22×C73—42no—
302C22×C73—81no—
303C22×C73—81no—
304C22×C73—81no—
305C22×C73—81no—
306C22×C73#52511yescharacteristic
307C22×C73D4211yescharacteristic
308C22×C73D4×Q811yescharacteristic
309C22×C73C2×#13511yescharacteristic
310C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
311C22×C73#57611yescharacteristic
312C22×C73#57711yescharacteristic
313C4×C73—22no—
314C4×C73—22no—
315C4×C73—42no—
316C4×C73—41no—
317C4×C73—41no—
318C4×C73—42no—
319C4×C73—41no—
320C4×C73—41no—
321C4×C73—81no—
322C4×C73—81no—
323C4×C73—81no—
324C4×C73—81no—
325C4×C73C2×C22⋊Q811yescharacteristic
326C4×C73#53911yescharacteristic
327C4×C73#54711yescharacteristic
328C4×C73#55411yescharacteristic
329#26382C7311yesmaximal, characteristic, direct product factor, Sylow
330C2×C73—44no—
331C2×C73—82no—
332C2×C73#244911yescharacteristic
333C2×C73#310511yescharacteristic
334C2×C73#311911yescharacteristic
335C2×C73#326411yescharacteristic
336C2×C73#328411yescharacteristic
337C2×C73#338011yescharacteristic
338C2×C73#338411yescharacteristic
339C2×#478C2×C7311yescharacteristic, complemented
340C2×C4×D8C2×C7311yescharacteristic
341#2454C2×C7311yescharacteristic, complemented
342D4×C4⋊C4C2×C7311yescharacteristic, complemented
343#2094C2×C7311yescharacteristic, complemented
344#2083C2×C7311yescharacteristic, complemented
345#2065C2×C7311yescharacteristic, complemented
346#2059C2×C7311yescharacteristic, complemented
347#1941C2×C7311yescharacteristic, complemented
348#1916C2×C7311yescharacteristic, complemented
349#1879C2×C7311yescharacteristic
350#1879C2×C7311yescharacteristic
351#1864C2×C7311yescharacteristic, complemented
352#1864C2×C7311yescharacteristic, complemented
353#1862C2×C7311yescharacteristic, complemented
354C73#2638211yescharacteristic, direct product factor, Sylow
355C22×D8C22×C7311yescharacteristic
356C2×#125C22×C7311yescharacteristic
357C2×C4×D4C22×C7311yescharacteristic
358C2×C4×D4C22×C7311yescharacteristic
359C2×C4×D4C22×C7311yescharacteristic
360C2×C4×D4C22×C7311yescharacteristic
361C22×C4⋊C4—21no—
362#478—24no—
363C4×D8—24no—
364C2×#107C22×C7311yescharacteristic
365C2×#107C22×C7311yescharacteristic
366C2×#106C22×C7311yescharacteristic
367C2×#106C22×C7311yescharacteristic
368C2×#106C22×C7311yescharacteristic
369C2×C4⋊C8C22×C7311yescharacteristic
370C2×#102C22×C7311yescharacteristic
371C2×#102C22×C7311yescharacteristic
372C2×#102C22×C7311yescharacteristic
373C2×#102C22×C7311yescharacteristic
374C2×#102C22×C7311yescharacteristic
375C2×#102C22×C7311yescharacteristic
376C2×C4×C8C22×C7311yescharacteristic
377#399—21no—
378#396—21no—
379#390C22×C7311yescharacteristic
380#390C22×C7311yescharacteristic
381#389C22×C7311yescharacteristic
382#389C22×C7311yescharacteristic
383#389C22×C7311yescharacteristic
384#389C22×C7311yescharacteristic
385#385—21no—
386#385—21no—
387#385—21no—
388#384C22×C7311yescharacteristic
389#380—21no—
390#380—21no—
391C4×C4⋊C4C22×C7311yescharacteristic
392#340C22×C7311yescharacteristic
393#340C22×C7311yescharacteristic
394#340C22×C7311yescharacteristic
395#340C22×C7311yescharacteristic
396#336C22×C7311yescharacteristic
397#336C22×C7311yescharacteristic
398#336C22×C7311yescharacteristic
399#336C22×C7311yescharacteristic
400C22×D4C23×C7311yescharacteristic
401C22×D4C23×C7311yescharacteristic
402C23×C4—21no—
403C23×C4—21no—
404C23×C4—21no—
405C23×C4—21no—
406C2×D8—22no—
407C2×D8—22no—
408C2×D8Q8×C7314yes—
409C22×C8C23×C7311yescharacteristic
410C22×C8C23×C7311yescharacteristic
411C22×C8C23×C7311yescharacteristic
412C22×C8C23×C7311yescharacteristic
413#125—22no—
414#125—41no—
415C4×D4—22no—
416C4×D4—22no—
417C4×D4—22no—
418C4×D4—22no—
419C4×D4—22no—
420C4×D4—41no—
421C4×D4—41no—
422C4×D4—41no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—21no—
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—21no—
430C2×C4⋊C4—21no—
431C2×C4⋊C4—44no—
432C2×C4⋊C4D4×C7311yescharacteristic
433C2×C4⋊C4D4×C7311yescharacteristic
434C2×C4⋊C4C23×C7311yescharacteristic
435C2×C4⋊C4C23×C7311yescharacteristic
436C2×C4⋊C4C23×C7311yescharacteristic
437C2×C4⋊C4C23×C7311yescharacteristic
438C2×C4⋊C4C23×C7311yescharacteristic
439C2×C4⋊C4C23×C7311yescharacteristic
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4—21no—
444C2×C22⋊C4—21no—
445C2×C22⋊C4—21no—
446C2×C22⋊C4—21no—
447C2×C22⋊C4—21no—
448C2×C42C23×C7311yescharacteristic
449C2×C42C23×C7311yescharacteristic
450C2×C42C23×C7311yescharacteristic
451#107—22no—
452#107—22no—
453#106—22no—
454#106—22no—
455#106—41no—
456C4⋊C8—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#102—22no—
461#102—41no—
462#102D4×C7314yes—
463C4×C8—22no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95—21no—
468#95D4×C7311yescharacteristic
469#95D4×C7311yescharacteristic
470C24—21no—
471C24—21no—
472C2×D4—21no—
473C2×D4—21no—
474C2×D4—21no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4C2×D4×C7312yes—
481C2×D4C2×Q8×C7312yes—
482C2×D4C2×Q8×C7312yes—
483C2×D4#41×C7312yes—
484C22×C4—24no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—42no—
492C22×C4—42no—
493C22×C4—42no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—42no—
499C22×C4—81no—
500C22×C4—81no—
501C22×C4—81no—
502C22×C4C2×D4×C7311yescharacteristic
503C22×C4C2×D4×C7311yescharacteristic
504C22×C4C2×D4×C7311yescharacteristic
505C22×C4C2×D4×C7311yescharacteristic
506C22×C4C2×D4×C7311yescharacteristic
507C22×C4C2×D4×C7311yescharacteristic
508C22×C4C24×C7311yescharacteristic
509D8—28no—
510C2×C8—21no—
511C2×C8—21no—
512C2×C8—21no—
513C2×C8—21no—
514C2×C8—21no—
515C2×C8—21no—
516C2×C8—21no—
517C2×C8—21no—
518C2×C8—21no—
519C2×C8—21no—
520C2×C8C2×D4×C7312yes—
521C2×C8C2×Q8×C7312yes—
522C4⋊C4—22no—
523C4⋊C4—22no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—21no—
529C4⋊C4—21no—
530C4⋊C4—21no—
531C4⋊C4—21no—
532C4⋊C4—21no—
533C4⋊C4—21no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—42no—
538C4⋊C4—42no—
539C4⋊C4—81no—
540C4⋊C4—81no—
541C4⋊C4—81no—
542C4⋊C4C2×D4×C7312yes—
543C4⋊C4#41×C7312yes—
544C22⋊C4—24no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C22⋊C4—81no—
551C22⋊C4—81no—
552C42—21no—
553C42—21no—
554C42—21no—
555C42—21no—
556C42—21no—
557C42—21no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—22no—
562C23—41no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—41no—
570C23—41no—
571C23—41no—
572C23C22×D4×C7311yescharacteristic
573D4—22no—
574D4—22no—
575D4—22no—
576D4—22no—
577D4—22no—
578D4—41no—
579D4—41no—
580D4C22⋊Q8×C7314yes—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—21no—
584C2×C4—21no—
585C2×C4—21no—
586C2×C4—22no—
587C2×C4—21no—
588C2×C4—21no—
589C2×C4—21no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—48no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—41no—
610C2×C4—41no—
611C2×C4—41no—
612C2×C4—41no—
613C2×C4—41no—
614C2×C4—41no—
615C2×C4—41no—
616C2×C4—84no—
617C2×C4—84no—
618C2×C4—84no—
619C2×C4#135×C7312yes—
620C2×C4AGL(1,ℤ/8)×C7312yes—
621C2×C4C22×D4×C7311yescharacteristic
622C2×C4C22×Q8×C7311yescharacteristic
623C2×C4C2×#41×C7311yescharacteristic
624C2×C4C2×#41×C7311yescharacteristic
625C2×C4H(5,𝔽2)×C7311yescharacteristic
626C2×C42−1+4×C7311yescharacteristic
627C8—22no—
628C8—22no—
629C8—41no—
630C8—41no—
631C22—24no—
632C22—42no—
633C22—42no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—42no—
640C22—42no—
641C22—81no—
642C22—81no—
643C22—81no—
644C22—81no—
645C22#525×C7311yescharacteristic
646C22D42×C7311yescharacteristic
647C22D4×Q8×C7311yescharacteristic
648C22C2×#135×C7311yescharacteristic
649C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
650C22#576×C7311yescharacteristic
651C22#577×C7311yescharacteristic
652C4—22no—
653C4—22no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—41no—
658C4—42no—
659C4—41no—
660C4—81no—
661C4—81no—
662C4—81no—
663C4—81no—
664C4C2×C22⋊Q8×C7311yescharacteristic
665C4#539×C7311yescharacteristic
666C4#547×C7311yescharacteristic
667C4#554×C7311yescharacteristic
668C2—44no—
669C2—82no—
670C2C73×#244911yescharacteristic
671C2C73×#310511yescharacteristic
672C2C73×#311911yescharacteristic
673C2C73×#326411yescharacteristic
674C2C73×#328411yescharacteristic
675C2C73×#338011yescharacteristic
676C2C73×#338411yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D8×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C4⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#478×C73C2semidirect
3. C73×#2454C2semidirect
4. D4×C4⋊C4×C73C2semidirect
5. C73×#2094C2semidirect
6. C73×#2083C2semidirect
7. C73×#2065C2semidirect
8. C73×#2059C2semidirect
9. C73×#1941C2semidirect
10. C73×#1916C2semidirect
13. C73×#1864C2semidirect
14. C73×#1864C2semidirect
15. C73×#1862C2semidirect
329. #26382C73direct (N × H)
339. C2×#478C2×C73semidirect
341. #2454C2×C73semidirect
342. D4×C4⋊C4C2×C73semidirect
343. #2094C2×C73semidirect
344. #2083C2×C73semidirect
345. #2065C2×C73semidirect
346. #2059C2×C73semidirect
347. #1941C2×C73semidirect
348. #1916C2×C73semidirect
351. #1864C2×C73semidirect
352. #1864C2×C73semidirect
353. #1862C2×C73semidirect
354. C73#26382direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#478×C732
C2×C4×D8×C732
C73×#24542
D4×C4⋊C4×C732
C73×#20942
C73×#20832
C73×#20652
C73×#20592
C73×#19412
C73×#19162
C73×#18792
C73×#18642
C73×#18622
#2638273