Finite Group Databasebeta

← C73×#26359 #32935763

Subgroups — C73×#26359 #32935763

Order 18688.

904 conjugacy classes of subgroups.

The subgroup lattice has 676 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#476×C73C211yesmaximal, characteristic, complemented
2C2×#428×C73C211yesmaximal, characteristic, complemented
3C73×#2440C211yesmaximal, characteristic, complemented
4C73×#2363C211yesmaximal, characteristic
5C73×#2093C211yesmaximal, characteristic, complemented
6C73×#2087C211yesmaximal, characteristic, complemented
7C73×#2067C211yesmaximal, characteristic, complemented
8C73×#2057C211yesmaximal, characteristic, complemented
9C73×#1948C211yesmaximal, characteristic, complemented
10C73×#1919C211yesmaximal, characteristic, complemented
11C73×#1895C211yesmaximal, characteristic
12C73×#1874C211yesmaximal, characteristic
13C73×#1864C211yesmaximal, characteristic, complemented
14C73×#1854C211yesmaximal, characteristic, complemented
15C73×#1851C211yesmaximal, characteristic, complemented
16C22×M16×C73C2211yescharacteristic
17C2×C4⋊Q8×C73C2211yescharacteristic
18C2×C22⋊Q8×C73—21no—
19C2×#121×C73C2211yescharacteristic
20C2×C4×D4×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22C22×C4⋊C4×C73C2211yescharacteristic
23#476×C73—24no—
24#428×C73—24no—
25C2×#107×C73C2211yescharacteristic
26C2×#107×C73C2211yescharacteristic
27C2×#107×C73C2211yescharacteristic
28C2×#106×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×#106×C73C2211yescharacteristic
31C2×C4⋊C8×C73C2211yescharacteristic
32C2×C4⋊C8×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×C22⋊C8×C73C2211yescharacteristic
38#398×C73—21no—
39#395×C73—21no—
40#390×C73—21no—
41#390×C73C2211yescharacteristic
42#389×C73C2211yescharacteristic
43#389×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#388×C73—21no—
46#386×C73—21no—
47#385×C73—21no—
48#384×C73C2211yescharacteristic
49#380×C73C2211yescharacteristic
50C4×C4⋊C4×C73C2211yescharacteristic
51C4×C22⋊C4×C73—21no—
52C4×C22⋊C4×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#340×C73C2211yescharacteristic
58#340×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73—21no—
62C22×D4×C73—21no—
63C22×D4×C73C2311yescharacteristic
64C23×C4×C73—21no—
65C23×C4×C73—21no—
66C23×C4×C73C2311yescharacteristic
67C2×M16×C73—22no—
68C2×M16×C73—22no—
69C2×M16×C73—22no—
70C22×C8×C73C2311yescharacteristic
71C22×C8×C73C2311yescharacteristic
72C22×C8×C73C2311yescharacteristic
73C22×C8×C73C2311yescharacteristic
74C4⋊Q8×C73—22no—
75C4⋊Q8×C73—41no—
76C22⋊Q8×C73—44no—
77#121×C73—22no—
78#121×C73Q814yescomplemented
79C4×D4×C73—22no—
80C4×D4×C73—41no—
81#117×C73—22no—
82#117×C73—41no—
83C2×C4⋊C4×C73—22no—
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—41no—
92C2×C4⋊C4×C73C2311yescharacteristic
93C2×C4⋊C4×C73C2311yescharacteristic
94C2×C4⋊C4×C73C2311yescharacteristic
95C2×C4⋊C4×C73C2311yescharacteristic
96C2×C4⋊C4×C73C2311yescharacteristic
97C2×C4⋊C4×C73C2311yescharacteristic
98C2×C4⋊C4×C73C2311yescharacteristic
99C2×C22⋊C4×C73—21no—
100C2×C22⋊C4×C73—21no—
101C2×C22⋊C4×C73—21no—
102C2×C22⋊C4×C73—21no—
103C2×C22⋊C4×C73—21no—
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73D411yescharacteristic
106C2×C22⋊C4×C73D411yescharacteristic
107C2×C42×C73—21no—
108C2×C42×C73—21no—
109C2×C42×C73C2311yescharacteristic
110C2×C42×C73C2311yescharacteristic
111#107×C73—22no—
112#107×C73—22no—
113#107×C73—41no—
114#106×C73—22no—
115#106×C73—22no—
116#106×C73D414yescomplemented
117C4⋊C8×C73—22no—
118C4⋊C8×C73—22no—
119#102×C73—22no—
120#102×C73—22no—
121#102×C73—22no—
122#102×C73—41no—
123C22⋊C8×C73—22no—
124#95×C73—21no—
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×C73C2×D411yescharacteristic
133C2×Q8×C73—42no—
134C2×Q8×C73—42no—
135C2×Q8×C73—81no—
136C2×D4×C73—24no—
137C2×D4×C73—21no—
138C2×D4×C73—21no—
139C2×D4×C73—21no—
140C2×D4×C73—21no—
141C2×D4×C73—21no—
142C2×D4×C73—81no—
143C2×D4×C73—81no—
144C2×D4×C73C2×Q812yes—
145C22×C4×C73—21no—
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—21no—
153C22×C4×C73—21no—
154C22×C4×C73—21no—
155C22×C4×C73—21no—
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×C73C2×D411yescharacteristic
163C22×C4×C73C2×D411yescharacteristic
164C22×C4×C73C2×D411yescharacteristic
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73C2×Q812yes—
168C22×C4×C73#4112yes—
169C22×C4×C73C2411yescharacteristic
170M16×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×C73#4112yes—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
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—42no—
195C4⋊C4×C73—42no—
196C4⋊C4×C73—42no—
197C4⋊C4×C73—42no—
198C4⋊C4×C73—42no—
199C4⋊C4×C73—81no—
200C4⋊C4×C73—81no—
201C4⋊C4×C73C2×D412yes—
202C4⋊C4×C73C2×D412yes—
203C4⋊C4×C73C2×Q812yes—
204C22⋊C4×C73—24no—
205C22⋊C4×C73—22no—
206C22⋊C4×C73—22no—
207C22⋊C4×C73—42no—
208C22⋊C4×C73—42no—
209C22⋊C4×C73—42no—
210C22⋊C4×C73—42no—
211C22⋊C4×C73—81no—
212C42×C73—21no—
213C42×C73—21no—
214C42×C73—21no—
215C42×C73—21no—
216C42×C73—42no—
217C42×C73—81no—
218C23×C73—21no—
219C23×C73—21no—
220C23×C73—21no—
221C23×C73—21no—
222C23×C73—21no—
223C23×C73—21no—
224C23×C73—22no—
225C23×C73—41no—
226C23×C73—41no—
227C23×C73—41no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73C22⋊Q812yes—
232C23×C73C22×D411yescharacteristic
233Q8×C73—84no—
234D4×C73—22no—
235D4×C73—22no—
236D4×C73—41no—
237D4×C73—41no—
238D4×C73—84no—
239C2×C4×C73—21no—
240C2×C4×C73—21no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—22no—
246C2×C4×C73—22no—
247C2×C4×C73—22no—
248C2×C4×C73—22no—
249C2×C4×C73—22no—
250C2×C4×C73—21no—
251C2×C4×C73—22no—
252C2×C4×C73—22no—
253C2×C4×C73—21no—
254C2×C4×C73—21no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—21no—
258C2×C4×C73—41no—
259C2×C4×C73—41no—
260C2×C4×C73—41no—
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—84no—
277C2×C4×C73—84no—
278C2×C4×C73C22⋊Q812yes—
279C2×C4×C73AGL(1,ℤ/8)12yes—
280C2×C4×C73#13712yes—
281C2×C4×C73C22×D411yescharacteristic
282C2×C4×C73C22×Q811yescharacteristic
283C2×C4×C73C2×#4111yescharacteristic
284C2×C4×C73C2×#4111yescharacteristic
285C2×C4×C73H(5,𝔽2)11yescharacteristic
286C2×C4×C732−1+411yescharacteristic
287C8×C73—22no—
288C8×C73—22no—
289C8×C73—41no—
290C8×C73—41no—
291C22×C73—22no—
292C22×C73—22no—
293C22×C73—22no—
294C22×C73—41no—
295C22×C73—41no—
296C22×C73—41no—
297C22×C73—41no—
298C22×C73—42no—
299C22×C73—42no—
300C22×C73—42no—
301C22×C73—81no—
302C22×C73—81no—
303C22×C73—81no—
304C22×C73—81no—
305C22×C73C2×C22⋊Q811yescharacteristic
306C22×C73D4211yescharacteristic
307C22×C73#54711yescharacteristic
308C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
309C22×C73C2×#13711yescharacteristic
310C22×C73#57611yescharacteristic
311C22×C73#57711yescharacteristic
312C4×C73—22no—
313C4×C73—22no—
314C4×C73—22no—
315C4×C73—42no—
316C4×C73—41no—
317C4×C73—42no—
318C4×C73—41no—
319C4×C73—42no—
320C4×C73—81no—
321C4×C73—81no—
322C4×C73—81no—
323C4×C73—81no—
324C4×C73#52511yescharacteristic
325C4×C73#53911yescharacteristic
326C4×C73D4×Q811yescharacteristic
327C4×C73#55411yescharacteristic
328#26359C7311yesmaximal, characteristic, direct product factor, Sylow
329C2×C73—42no—
330C2×C73—82no—
331C2×C73#244911yescharacteristic
332C2×C73#307911yescharacteristic
333C2×C73#308111yescharacteristic
334C2×C73#326611yescharacteristic
335C2×C73#327411yescharacteristic
336C2×C73#334511yescharacteristic
337C2×C73#335711yescharacteristic
338C2×#476C2×C7311yescharacteristic, complemented
339C2×#428C2×C7311yescharacteristic, complemented
340#2440C2×C7311yescharacteristic, complemented
341#2363C2×C7311yescharacteristic
342#2093C2×C7311yescharacteristic, complemented
343#2087C2×C7311yescharacteristic, complemented
344#2067C2×C7311yescharacteristic, complemented
345#2057C2×C7311yescharacteristic, complemented
346#1948C2×C7311yescharacteristic, complemented
347#1919C2×C7311yescharacteristic, complemented
348#1895C2×C7311yescharacteristic
349#1874C2×C7311yescharacteristic
350#1864C2×C7311yescharacteristic, complemented
351#1854C2×C7311yescharacteristic, complemented
352#1851C2×C7311yescharacteristic, complemented
353C73#2635911yescharacteristic, direct product factor, Sylow
354C22×M16C22×C7311yescharacteristic
355C2×C4⋊Q8C22×C7311yescharacteristic
356C2×C22⋊Q8—21no—
357C2×#121C22×C7311yescharacteristic
358C2×C4×D4C22×C7311yescharacteristic
359C2×#117C22×C7311yescharacteristic
360C22×C4⋊C4C22×C7311yescharacteristic
361#476—24no—
362#428—24no—
363C2×#107C22×C7311yescharacteristic
364C2×#107C22×C7311yescharacteristic
365C2×#107C22×C7311yescharacteristic
366C2×#106C22×C7311yescharacteristic
367C2×#106C22×C7311yescharacteristic
368C2×#106C22×C7311yescharacteristic
369C2×C4⋊C8C22×C7311yescharacteristic
370C2×C4⋊C8C22×C7311yescharacteristic
371C2×#102C22×C7311yescharacteristic
372C2×#102C22×C7311yescharacteristic
373C2×#102C22×C7311yescharacteristic
374C2×#102C22×C7311yescharacteristic
375C2×C22⋊C8C22×C7311yescharacteristic
376#398—21no—
377#395—21no—
378#390—21no—
379#390C22×C7311yescharacteristic
380#389C22×C7311yescharacteristic
381#389C22×C7311yescharacteristic
382#389C22×C7311yescharacteristic
383#388—21no—
384#386—21no—
385#385—21no—
386#384C22×C7311yescharacteristic
387#380C22×C7311yescharacteristic
388C4×C4⋊C4C22×C7311yescharacteristic
389C4×C22⋊C4—21no—
390C4×C22⋊C4C22×C7311yescharacteristic
391#340C22×C7311yescharacteristic
392#340C22×C7311yescharacteristic
393#340C22×C7311yescharacteristic
394#340C22×C7311yescharacteristic
395#340C22×C7311yescharacteristic
396#340C22×C7311yescharacteristic
397#336C22×C7311yescharacteristic
398#336C22×C7311yescharacteristic
399C22×Q8—21no—
400C22×D4—21no—
401C22×D4C23×C7311yescharacteristic
402C23×C4—21no—
403C23×C4—21no—
404C23×C4C23×C7311yescharacteristic
405C2×M16—22no—
406C2×M16—22no—
407C2×M16—22no—
408C22×C8C23×C7311yescharacteristic
409C22×C8C23×C7311yescharacteristic
410C22×C8C23×C7311yescharacteristic
411C22×C8C23×C7311yescharacteristic
412C4⋊Q8—22no—
413C4⋊Q8—41no—
414C22⋊Q8—44no—
415#121—22no—
416#121Q8×C7314yescomplemented
417C4×D4—22no—
418C4×D4—41no—
419#117—22no—
420#117—41no—
421C2×C4⋊C4—22no—
422C2×C4⋊C4—21no—
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—41no—
430C2×C4⋊C4C23×C7311yescharacteristic
431C2×C4⋊C4C23×C7311yescharacteristic
432C2×C4⋊C4C23×C7311yescharacteristic
433C2×C4⋊C4C23×C7311yescharacteristic
434C2×C4⋊C4C23×C7311yescharacteristic
435C2×C4⋊C4C23×C7311yescharacteristic
436C2×C4⋊C4C23×C7311yescharacteristic
437C2×C22⋊C4—21no—
438C2×C22⋊C4—21no—
439C2×C22⋊C4—21no—
440C2×C22⋊C4—21no—
441C2×C22⋊C4—21no—
442C2×C22⋊C4—21no—
443C2×C22⋊C4D4×C7311yescharacteristic
444C2×C22⋊C4D4×C7311yescharacteristic
445C2×C42—21no—
446C2×C42—21no—
447C2×C42C23×C7311yescharacteristic
448C2×C42C23×C7311yescharacteristic
449#107—22no—
450#107—22no—
451#107—41no—
452#106—22no—
453#106—22no—
454#106D4×C7314yescomplemented
455C4⋊C8—22no—
456C4⋊C8—22no—
457#102—22no—
458#102—22no—
459#102—22no—
460#102—41no—
461C22⋊C8—22no—
462#95—21no—
463#95—21no—
464#95—21no—
465#95—21no—
466#95—21no—
467#95D4×C7311yescharacteristic
468#95D4×C7311yescharacteristic
469C24—21no—
470C24C2×D4×C7311yescharacteristic
471C2×Q8—42no—
472C2×Q8—42no—
473C2×Q8—81no—
474C2×D4—24no—
475C2×D4—21no—
476C2×D4—21no—
477C2×D4—21no—
478C2×D4—21no—
479C2×D4—21no—
480C2×D4—81no—
481C2×D4—81no—
482C2×D4C2×Q8×C7312yes—
483C22×C4—21no—
484C22×C4—21no—
485C22×C4—21no—
486C22×C4—21no—
487C22×C4—21no—
488C22×C4—21no—
489C22×C4—21no—
490C22×C4—21no—
491C22×C4—21no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—42no—
495C22×C4—42no—
496C22×C4—42no—
497C22×C4—42no—
498C22×C4—81no—
499C22×C4—81no—
500C22×C4C2×D4×C7311yescharacteristic
501C22×C4C2×D4×C7311yescharacteristic
502C22×C4C2×D4×C7311yescharacteristic
503C22×C4C2×D4×C7311yescharacteristic
504C22×C4C2×D4×C7311yescharacteristic
505C22×C4C2×Q8×C7312yes—
506C22×C4#41×C7312yes—
507C22×C4C24×C7311yescharacteristic
508M16—28no—
509C2×C8—21no—
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×C8C2×D4×C7312yes—
520C2×C8#41×C7312yes—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
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—42no—
533C4⋊C4—42no—
534C4⋊C4—42no—
535C4⋊C4—42no—
536C4⋊C4—42no—
537C4⋊C4—81no—
538C4⋊C4—81no—
539C4⋊C4C2×D4×C7312yes—
540C4⋊C4C2×D4×C7312yes—
541C4⋊C4C2×Q8×C7312yes—
542C22⋊C4—24no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—42no—
546C22⋊C4—42no—
547C22⋊C4—42no—
548C22⋊C4—42no—
549C22⋊C4—81no—
550C42—21no—
551C42—21no—
552C42—21no—
553C42—21no—
554C42—42no—
555C42—81no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—21no—
560C23—21no—
561C23—21no—
562C23—22no—
563C23—41no—
564C23—41no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23C22⋊Q8×C7312yes—
570C23C22×D4×C7311yescharacteristic
571Q8—84no—
572D4—22no—
573D4—22no—
574D4—41no—
575D4—41no—
576D4—84no—
577C2×C4—21no—
578C2×C4—21no—
579C2×C4—21no—
580C2×C4—21no—
581C2×C4—21no—
582C2×C4—21no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—22no—
587C2×C4—22no—
588C2×C4—21no—
589C2×C4—22no—
590C2×C4—22no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—21no—
595C2×C4—21no—
596C2×C4—41no—
597C2×C4—41no—
598C2×C4—41no—
599C2×C4—41no—
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—84no—
615C2×C4—84no—
616C2×C4C22⋊Q8×C7312yes—
617C2×C4AGL(1,ℤ/8)×C7312yes—
618C2×C4#137×C7312yes—
619C2×C4C22×D4×C7311yescharacteristic
620C2×C4C22×Q8×C7311yescharacteristic
621C2×C4C2×#41×C7311yescharacteristic
622C2×C4C2×#41×C7311yescharacteristic
623C2×C4H(5,𝔽2)×C7311yescharacteristic
624C2×C42−1+4×C7311yescharacteristic
625C8—22no—
626C8—22no—
627C8—41no—
628C8—41no—
629C22—22no—
630C22—22no—
631C22—22no—
632C22—41no—
633C22—41no—
634C22—41no—
635C22—41no—
636C22—42no—
637C22—42no—
638C22—42no—
639C22—81no—
640C22—81no—
641C22—81no—
642C22—81no—
643C22C2×C22⋊Q8×C7311yescharacteristic
644C22D42×C7311yescharacteristic
645C22#547×C7311yescharacteristic
646C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
647C22C2×#137×C7311yescharacteristic
648C22#576×C7311yescharacteristic
649C22#577×C7311yescharacteristic
650C4—22no—
651C4—22no—
652C4—22no—
653C4—42no—
654C4—41no—
655C4—42no—
656C4—42no—
657C4—41no—
658C4—81no—
659C4—81no—
660C4—81no—
661C4—81no—
662C4#525×C7311yescharacteristic
663C4#539×C7311yescharacteristic
664C4D4×Q8×C7311yescharacteristic
665C4#554×C7311yescharacteristic
666C2—42no—
667C2—82no—
668C2C73×#244911yescharacteristic
669C2C73×#307911yescharacteristic
670C2C73×#308111yescharacteristic
671C2C73×#326611yescharacteristic
672C2C73×#327411yescharacteristic
673C2C73×#334511yescharacteristic
674C2C73×#335711yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#121×C73C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C22⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#476×C73C2semidirect
2. C2×#428×C73C2semidirect
3. C73×#2440C2semidirect
5. C73×#2093C2semidirect
6. C73×#2087C2semidirect
7. C73×#2067C2semidirect
8. C73×#2057C2semidirect
9. C73×#1948C2semidirect
10. C73×#1919C2semidirect
13. C73×#1864C2semidirect
14. C73×#1854C2semidirect
15. C73×#1851C2semidirect
78. #121×C73Q8semidirect
116. #106×C73D4semidirect
328. #26359C73direct (N × H)
338. C2×#476C2×C73semidirect
339. C2×#428C2×C73semidirect
340. #2440C2×C73semidirect
342. #2093C2×C73semidirect
343. #2087C2×C73semidirect
344. #2067C2×C73semidirect
345. #2057C2×C73semidirect
346. #1948C2×C73semidirect
347. #1919C2×C73semidirect
350. #1864C2×C73semidirect
351. #1854C2×C73semidirect
352. #1851C2×C73semidirect
353. C73#26359direct (N × H)
416. #121Q8×C73semidirect
454. #106D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#476×C732
C2×#428×C732
C73×#24402
C73×#23632
C73×#20932
C73×#20872
C73×#20672
C73×#20572
C73×#19482
C73×#19192
C73×#18952
C73×#18742
C73×#18642
C73×#18542
C73×#18512
#2635973